Open Collections will be undergoing maintenance Monday June 8th, 2020 11:00 – 13:00 PT. No downtime is expected, but site performance may be temporarily impacted.

Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Investigation of orographic rainfall in south coastal mountains of British Columbia Hetherington, Eugene Douglas 1976

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1976_A1 H48.pdf [ 25.92MB ]
Metadata
JSON: 831-1.0093785.json
JSON-LD: 831-1.0093785-ld.json
RDF/XML (Pretty): 831-1.0093785-rdf.xml
RDF/JSON: 831-1.0093785-rdf.json
Turtle: 831-1.0093785-turtle.txt
N-Triples: 831-1.0093785-rdf-ntriples.txt
Original Record: 831-1.0093785-source.json
Full Text
831-1.0093785-fulltext.txt
Citation
831-1.0093785.ris

Full Text

INVESTIGATION OF OROGRAPHIC RAINFALL IN SOUTH COASTAL MOUNTAINS OF BRITISH COLUMBIA by EUGENE DOUGLAS HETHERINGTON B.A.Sc. (Engineering Physics), University of British Columbia, 1962 M.A. (Meteorology), University of Toronto, 1963 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF FORESTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May, 1976 © Eugene Douglas Hetherington, 1976 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e tha t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d tha t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f F o r e s t r y  The U n i v e r s i t y o f B r i t i s h Co lumbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date May 3. 1976 Research Supervisor: Dr. R. P. W i l l i n g t o n ABSTRACT Storm r a i n f a l l i n the south coastal mountains north of Vancouver, B r i t i s h Columbia was investigated with the c e n t r a l goal of e l u c i d a t i n g and quantifying orographic r a i n f a l l production and d i s t r i b u t i o n using a v a i l a b l e meteorological information. Storm s i z e ranged from 10 to 130 mm with a l l but one storm showing an orographic e f f e c t . C o r r e l a t i o n analysis indicated s i g n i f i c a n t r e l a t i o n s h i p s between the amount of orographic r a i n f a l l and the following storm parameters: wind speed component normal to the mountain b a r r i e r , moisture content of the lower atmosphere, freezing l e v e l and a i r mass s t a b i l i t y . Attempts to c l a s s i f y storm types i n r e l a t i o n to orographic r a i n f a l l , using analysis of variance, met with l i m i t e d success. A p h y s i c a l model for estimating r a i n f a l l i n t e n s i t i e s over windward mountain slopes, based on concepts of p r e c i p i t a t i o n physics and wind flow over mountain b a r r i e r s and incorporating the storm parameters noted above, was adapted and tested on 4 stable and 4 unstable storms. Procedures are given for applying t h i s model. For stable storms, the model can give consistent estimates of r a i n f a l l amount and d i s t r i b u t i o n over the mountain slopes. A standard deviation of ±11% for optimum orographic l i f t i n g conditions was found. For unstable storms, model estimates are u n r e l i a b l e due to uncertainty i n estimating i i i i i convective v e r t i c a l wind v e l o c i t i e s . Eigenvector analysis of areal r a i n f a l l patterns reveals one basic pattern inherent i n most storms, with 98% explained var iance. This r a i n f a l l pattern conforms c lose ly to topographic configurat ion. This thesis thus i l l u s t r a t e s the extent and nature of the dominant influence of topography on r a i n f a l l i n the study area and shows the value of ava i lab le weather data i n explaining and estimating orographic r a i n f a l l . TABLE OF CONTENTS Page ABSTRACT i i LIST OF TABLES x LIST OF FIGURES . x i i i LIST OF SYMBOLS AND ABBREVIATIONS x v i ACKNOWLEDGEMENT. . , xx CHAPTER I. INTRODUCTION 1 Study Objectives. . 2 General Review of the L i t e r a t u r e 3 Presentation of Thesis 5 I I . DESCRIPTION OF STUDY AREA AND DATA COLLECTION 6 C h a r a c t e r i s t i c s of Study Area 6 Location 6 Physiography 8 Vegetation 8 Climate 9 C h a r a c t e r i s t i c A i r Mass Types 10 Reasons for Choice of Study Area 11 Av a i l a b l e Meteorological Information 12 P r e c i p i t a t i o n Data 12 Upper A i r Data 13 Synoptic Weather Data 13 Background on P r e c i p i t a t i o n Measurement 13 Point Measurement of P r e c i p i t a t i o n 14 Gauge Protection from Wind E f f e c t s 15 i v V CHAPTER Page S i t e S e l e c t i o n 17 Network Design 19 D e s c r i p t i o n of P r e c i p i t a t i o n Measurement on Research Forest 19 Period of F i e l d Measurements 20 Instrumentation. 21 Network Design . 24 I n i t i a l network . 24 Modi f i e d network 27 S i t e S e l e c t i o n . 1 28 F i e l d Data C o l l e c t i o n Procedures 28 I I I . STORM ANALYSIS IN RELATION TO OROGRAPHIC RAINFALL PRODUCTION 29 I n t r o d u c t i o n 29 D e s c r i p t i o n of Storm Data Base 31 S e l e c t i o n of Storms 31 S e l e c t i o n of Storm Parameters 32 Wind 33 Moisture 33 S t a b i l i t y 33 Nature of Study Storms 35 Comparison w i t h long term p r e c i p i t a t i o n 35 Storm synoptic f e a t u r e s 37 L o c a l Wind P a t t e r n s 39 Sources of V a r i a b i l i t y i n Storm Data 40 Assessment of Orographic R a i n f a l l Production 42 D e f i n i t i o n s of Orographic Influences 42 Oreigenic u p l i f t 43 I n s t a b i l i t y t r i g g e r i n g 44 Reduced evaporation . . 45 Hindered movement of depressions, f r o n t s and winds 45 Excess storm d u r a t i o n 46 v i CHAPTER Page Determining Occurrence of Orographic Processes i n Study Storms 47 Major o r e i g e n i c u p l i f t 47 Minor o r e i g e n i c u p l i f t 47 P o t e n t i a l i n s t a b i l i t y t r i g g e r i n g 48 Convective i n s t a b i l i t y t r i g g e r i n g 48 Evaporation 49 D e r i v a t i o n of Orographic R a i n f a l l I ndices 51 R e l a t i n g Orographic R a i n f a l l Production to Storm C h a r a c t e r i s t i c s 56 C o r r e l a t i o n s Between Storm Parameters and Orographic R a i n f a l l I n d i c e s . . . . . 56 Re s u l t s 57 Storm C l a s s i f i c a t i o n Based on Occurrence of Orographic Processes and Orographic R a i n f a l l Indices 65 Re s u l t s 65 Storm C l a s s i f i c a t i o n Based on A i r f l o w D i r e c t i o n and Orographic R a i n f a l l I ndices 68 Res u l t s 69 Storm C l a s s i f i c a t i o n s Based on Synoptic Categories and Orographic R a i n f a l l Indices 69 Re s u l t s 72 Storm P a i r Comparisons 77 Summary 80 General Comments on Observed Storm R a i n f a l l C h a r a c t e r i s t i c s 82 P r e c i p i t a t i o n P r o f i l e s - Influence of S t a b i l i t y and Wind D i r e c t i o n 83 S p a t i a l V a r i a t i o n of Orographic E f f e c t s 90 Convective R a i n f a l l 92 Duration of Orographic E f f e c t 93 F r o n t a l Influence on P r e c i p i t a t i o n 93 Conclusions 94 v i i CHAPTER Page IV. ESTIMATION OF OROGRAPHIC PRECIPITATION 96 Introduction 96 Orographic Model Theory 99 Model Assumptions 99 Condensation Rate 100 P r e c i p i t a t i o n Rate 102 Wind Flow 106 Horizontal winds 106 V e r t i c a l motions 107 Nodal surface 109 Modelling wind flow I l l P r e c i p i t a t i o n T r a j e c t o r i e s 113 Obtaining Areal P r e c i p i t a t i o n Estimates. . . . . . . . . 115 A p p l i c a t i o n of Orographic Model to Study Area 115 Exploratory Development 116 Results 120 Procedures for Applying the Model 126 Model adaptation 126 Computation of condensation rate 136 Model A p p l i c a t i o n to Test Storms 141 Stable storms 142 Unstable storms 147 Results 152 1. Stable storms 155 2. Unstable storms . . 160 Discussion 162 Suggested design values f or model parameters. . . . 168 Estimating T o t a l Short-Period P r e c i p i t a t i o n 170 A l t e r n a t i v e Approaches to Estimating P r e c i p i t a t i o n over Mountains 175 Recommendations for Further Studies 177 Conclusions 179 v i i i CHAPTER Page V. VARIATIONS IN PRECIPITATION ON THE RESEARCH FOREST 181 Introduction 181 Areal Patterns of P r e c i p i t a t i o n 181 Eigenvector Analysis 182 Results 183 .Discussion 188 Cor r e l a t i o n Analysis 190 Small Scale Va r i a t i o n s i n P r e c i p i t a t i o n 193 Vectopluviometer Measurements 194 Varia t i o n s i n P r e c i p i t a t i o n Near Sites 7 and 9 197 Wind E f f e c t s on P r e c i p i t a t i o n at Spur-17 203 Variations i n P r e c i p i t a t i o n Among Sites 1-6 205 Conclusions 206 VI. CONCLUSIONS ' 208 BIBLIOGRAPHY 212 APPENDICES I. AIR MASS TEMPERATURES 223 I I . DESCRIPTION OF PRECIPITATION STATIONS 224 I I I . DATA SOURCE INFORMATION 227 IV. RAIN GAUGE CATCH RELATIONSHIPS ON SLOPING GROUND. . . . . . . 229 V. VECTOPLUVIOMETER CALCULATIONS . .• 233 VI. STORM DATA 235 VII. DERIVATION OF CONDENSATION EQUATIONS 246 VIII. MYER'S WIND FLOW MODEL 249 IX. DETERMINATION OF RAINDROP FALL VELOCITY 253 X. OBSERVED PRECIPITATION DATA FOR MODEL STORM PERIODS 256 XI. RATE OF CHANGE IN MIXING RATIO WITH ALTITUDE ALONG SELECTED MOIST ADIABATS ON TEPHIGRAM 257 ix APPENDICES Page XII. SELECTED STORM METEOROLOGICAL CHARACTERISTICS . . . . . . . . 258 XIII. SURFACE WIND DATA AT VANCOUVER INTERNATIONAL AIRPORT AND SAND HEADS LIGHT STATION FOR SELECTED STORM PERIODS. 270 XIV. DIAGRAMS OF OROGRAPHIC MODEL FOR TEST STORMS 37 AND 39 271 XV. COMPUTER PROGRAM FOR EIGENVECTOR ANALYSIS 272 XVI. CAN-TYPE RAIN GAUGE DATA FOR TRANSECTS ON SLOPES OF SITE 7 AND SITE 9 RIDGES 296 i LIST OF TABLES TABLE Page 1. MAXIMUM 24-HOUR RAINFALLS (mm) AT VANCOUVER INTERNATIONAL AIRPORT AND RESEARCH FOREST ADMINISTRATION BUILDING 37 2. CORRELATION COEFFICIENTS BETWEEN STORM PARAMETERS AND RELATIVE OROGRAPHIC RAINFALL INDICES 58 3. CORRELATION COEFFICIENTS BETWEEN STORM PARAMETERS AND ABSOLUTE OROGRAPHIC RAINFALL INDICES 59 4. PERCENT EXPLAINED VARIANCES OF RELATIONSHIPS BETWEEN BOTH STORM PARAMETERS AND ABSOLUTE OROGRAPHIC RAINFALL INDICES DR AND STORM CLASSIFICATION CATEGORIES. . . . 66 5. BOYDEN INSTABILITY INDEX VALUES FOR SYNOPTIC STORM TYPE CATEGORIES 74 6. CONVERSION FACTORS (e) EXTRACTED FROM THE LITERATURE 104 7. RESULTS OF EXPLORATORY CALCULATIONS USING STORM 43 DATA TO ASSESS THE INFLUENCE OF MODEL PARAMETERS BH, PN, Y AND CB ON COMPUTED OROGRAPHIC PRECIPITATION FOR THE NORTHSHORE AREA (NV-LC) 121 8. RESULTS OF EXPLORATORY CALCULATIONS USING STORM 43 DATA TO ASSESS THE INFLUENCE OF MODEL PARAMETERS BH, PN, Y AND CB ON COMPUTED OROGRAPHIC PRECIPITATION FOR THE RESEARCH FOREST AREA (AD-SI) 122 9. COMPUTATION OF OROGRAPHIC CONDENSATION FOR STORM 43a - NORTHSHORE 130 10. COMPUTATION OF SOUTHWEST WIND COMPONENTS AND PRECIPITATION TRAJECTORIES FOR STORM 43 - NORTHSHORE 134 11. MODEL STORM TEST PERIODS AND RADIOSONDE ASCENTS 142 12. OBSERVED OROGRAPHIC PRECIPITATION, COMPUTED OROGRAPHIC CONDENSATION AND CONVERSION FACTORS FOR STABLE AND UNSTABLE MODEL STORMS - NORTHSHORE AREA 153 x x i TABLE Page 13. OBSERVED OROGRAPHIC PRECIPITATION, COMPUTED OROGRAPHIC CONDENSATION AND CONVERSION FACTORS FOR STABLE AND UNSTABLE MODEL STORMS - RESEARCH FOREST AREA. 154 14. DIFFERENCES BETWEEN COMPUTED AND OBSERVED OROGRAPHIC PRECIPITATION AS A PERCENTAGE OF OBSERVED VALUES FOR STABLE MODEL STORMS -NORTHSHORE AREA 160 15. DIFFERENCES BETWEEN COMPUTED AND OBSERVED OROGRAPHIC PRECIPITATION AS A PERCENTAGE OF OBSERVED VALUES FOR STABLE MODEL STORMS - RESEARCH FOREST AREA 160 16. ESTIMATION OF CONVERGENCE COMPONENT OF PRECIPITATION FOR STABLE MODEL STORMS 172 17. COMPUTED AND OBSERVED TOTAL PRECIPITATION FOR STABLE MODEL STORMS - NORTHSHORE AREA 172 18. COMPUTED AND OBSERVED TOTAL PRECIPITATION FOR STABLE MODEL STORMS - RESEARCH FOREST AREA 173 19. COMPUTED TOTAL AND OROGRAPHIC PRECIPITATION AS A PERCENTAGE OF OBSERVED PRECIPITATION FOR STABLE MODEL STORMS - NORTHSHORE AREA 174 20. COMPUTED TOTAL AND OROGRAPHIC PRECIPITATION AS A PERCENTAGE OF OBSERVED PRECIPITATION FOR STABLE MODEL STORMS - RESEARCH FOREST AREA 175 21. CUMULATIVE EXPLAINED VARIANCE FOR THE FIRST 8 EIGENVECTORS (EV) FOR DIFFERENT STORM GROUPS 184 22. CORRELATION COEFFICIENTS FOR STORM PRECIPITATION TOTALS AT RESEARCH FOREST SITES 191 23. CORRELATION COEFFICIENTS FOR SHORT-PERIOD (4-6 HOUR) RAINFALL INTENSITIES AT RESEARCH FOREST SITES. 192 24. RAINDROP INCLINATIONS AND STORM BEARINGS AT SITE 8b AND SPUR-17 196 25. CORRELATION COEFFICIENTS BETWEEN DIFFERENCES IN SHORT-PERIOD PRECIPITATION INTENSITY BETWEEN SITES 8-9 AND SITES 7-LL AND SEVERAL WIND SPEED PARAMETERS 199 x i i TABLE Page 26. SUMMARY OF DIFFERENCES IN SHORT-PERIOD PRECIPITATION INTENSITIES BETWEEN SITES 9-8 AND SITES 7-LL 201 27. SUMMARY OF DIFFERENCES IN SHORT-PERIOD PRECIPITATION INTENSITIES FOR SEVERAL SITE PAIRS 206 LIST OF FIGURES Figure Page 1. Map of study area showing l o c a t i o n of e x i s t i n g p r e c i p i t a t i o n stations used i n study 7 2. Rain gauges used i n study 22 3. Map of U n i v e r s i t y of B r i t i s h Columbia Research Forest study area showing l o c a t i o n of r a i n gauge s i t e s . . . . 25 4. Frequency d i s t r i b u t i o n s of maximum storm r a i n f a l l t o t a l s . . 32 5. Comparison of long-term average and study period monthly p r e c i p i t a t i o n at Vancouver International A i r p o r t and Research Forest Administration Building 36 6. Evaporation of r a i n at several water vapour d e f i c i t s 50 7. Frequency d i s t r i b u t i o n s of absolute orographic r a i n f a l l indices 55 8. Absolute orographic r a i n f a l l indices for Research Forest versus VSW(S-85) . . 61 9. Absolute orographic r a i n f a l l indices for Research Forest versus PW(85-70), MR(85) and.freezing l e v e l 63 10. Absolute orographic r a i n f a l l indices DR versus occurrence of orographic process categories 67 11. VSW(S-85) versus occurrence of orographic process categories and a i r f l o w d i r e c t i o n categories 68 12. Surface maps of synoptic storm types 71 13. Synoptic storm type categories versus absolute orographic r a i n f a l l indices DR, PW(85-70), freezing l e v e l , VSW(S-85) and MR(85) 73 14. Wind rose diagrams of WD(S-85) for synoptic storm type categories 76 x i i i x i v F i g u r e Page 15. Synoptic storm type c a t e g o r i e s versus occurrence of orographic process c a t e g o r i e s 77 16. P r e c i p i t a t i o n p r o f i l e s of storm t o t a l r a t i o s f o r s t a b l e storms and unstable storms 84 17. Mean p r e c i p i t a t i o n p r o f i l e s of 6-hour i n t e n s i t y r a t i o s f o r s t a b l e storms w i t h s o u t h e r l y and southwest winds 86 18. Mean p r e c i p i t a t i o n p r o f i l e s of s h o r t - p e r i o d i n t e n s i t i e s f o r 3 p a i r s of unstable storms 88 19. Comparison of r a i n f a l l data between Research Forest and Northshore areas f o r storm 19 and 42 91 20. Diagram of orographic model 100 21. T h e o r e t i c a l r e l a t i o n s h i p of height of the nodal surface, s t a b i l i t y and wind shear I l l 22. Influence of b a r r i e r height, nodal surface height, l i f t i n g d i s t a n c e and cloud base height on computed orographic condensation r a t e f o r the Research Forest area f o r storm 43a (over l e n g t h AD-SI) 124 23. Diagram of orographic model f o r storm 43a - Northshore area 127 24. V e r t i c a l temperature p r o f i l e f o r storm 43a d e p i c t i n g orographic l i f t i n g f o r model c a l c u l a t i o n s . . 131 25. V a r i a t i o n s i n mean (6-hour) observed orographic r a i n f a l l i n t e n s i t i e s during s t a b l e model storms 143 26. P r e c i p i t a t i o n p r o f i l e s of 6-hour i n t e n s i t y r a t i o s f o r s t a b l e model storms 146 27. V e r t i c a l temperature p r o f i l e s f o r unstable model storms 7 and 14 149 28. P r e c i p i t a t i o n p r o f i l e s of s h o r t - p e r i o d i n t e n s i t y r a t i o s f o r unstable storms 150 29. Observed orographic r a i n f a l l versus computed orographic condensation along p r o f i l e t r a n s e c t s f o r s t a b l e model storms 156 XV F i g u r e Page 30. Comparison of observed versus computed orographic condensation and p r e c i p i t a t i o n along p r o f i l e s f o r s t a b l e model storms 158 31. Comparison of observed versus computed orographic condensation and p r e c i p i t a t i o n along p r o f i l e s over t o t a l l i f t i n g d i s t a n c e f o r s t a b l e model storms 159 32. Observed orographic p r e c i p i t a t i o n versus computed orographic condensation f o r s t a b l e and unstable model storms 161 33. Ranges of conversion f a c t o r s "e" f o r s t a b l e and unstable storms 163 34. A r e a l p a t t e r n s of p r e c i p i t a t i o n r a t e s on the Research Forest f o r storm 38 observed values and f i r s t 2 eigenvectors as derived from t o t a l group of study storms 185 35. A r e a l p a t t e r n s of p r e c i p i t a t i o n on the Research Forest f o r observed values and f i r s t eigenvectors as derived f o r unstable-convective (storm 40) and s o u t h e r l y wind (storm 42) storm groups 186 36. P a t t e r n of estimated mean annual p r e c i p i t a t i o n on Research Forest 188 37. Photographs of vectopluviometer s i t e s 8b and Spur-17 195 38. V a r i a t i o n i n t o t a l storm p r e c i p i t a t i o n across s i t e 9 r i d g e f o r storm 43 can-gauge data 199 39. R e l a t i o n s h i p between d i f f e r e n c e s i n s h o r t - p e r i o d r a i n f a l l i n t e n s i t y s i t e 9 - s i t e 8 and windspeed derived from s i t e 8b vectopluviometer data 200 40. R e l a t i o n s h i p between d i f f e r e n c e i n s h o r t - p e r i o d r a i n f a l l i n t e n s i t y s i t e 7 - s t a t i o n LL and windspeed derived from s i t e 8b vectopluviometer data 202 41. Schematic diagram and photograph of Spur-17 s i t e 204 LIST OF SYMBOLS AND ABBREVIATIONS A - area on thermodynamic chart AD - Administration Building r a i n gauge s t a t i o n A.E.S. - Atmospheric Environment Service AN - anemometer BH - b a r r i e r height C - condensation rate CB - height of cloud base CD - . Cleveland Dam r a i n gauge s t a t i o n Cp - s p e c i f i c heat D - v e r t i c a l depth of orographic l i f t d - r a i n drop diameter DI - absolute orographic r a i n f a l l i n t e n s i t y index D l / l - r e l a t i v e orographic r a i n f a l l i n t e n s i t y index DMR(85-70) - d i f f e r e n c e between mixing r a t i o values at 850 and 700 mb DR - absolute storm t o t a l orographic r a i n f a l l index DR/R - r e l a t i v e storm t o t a l orographic r a i n f a l l index DRR - h o r i z o n t a l r a i n d r i f t DRS - ho r i z o n t a l snow d r i f t E - East e - conversion factor or r a t i o precipitation/condensation Ec - evaporative capacity of atmosphere ENE - East North East ESE - East South East EV - eigenvector F - length along ground over which orographic p r e c i p i t a t i o n i s d i s t r i b u t e d FL - freezing l e v e l g - a c c e l e r a t i o n of gra v i t y G.V.S.D.D. - Greater Vancouver Sewerage and Drainage D i s t r i c t HE - Haney East r a i n gauge s t a t i o n I - r a i n f a l l i n t e n s i t y I.A.S.H. - International A s s o c i a t i o n of S c i e n t i f i c Hydrology k - constant L - low synoptic category LC - Lynn Creek r a i n gauge s t a t i o n Lc - lat e n t heat of condensation LL - Loon Lake r a i n gauge s t a t i o n LP - Langley P r a i r i e r a i n gauge s t a t i o n mA - maritime a r c t i c a i r MC - Marc r a i n gauge s t a t i o n mP - maritime polar a i r MR - Maple Ridge r a i n gauge s i t e Mr - rate of conversion of water vapour to p r e c i p i t a t i o n x v i XV1X MR(85) - mixing r a t i o at 850 mb mT - maritime t r o p i c a l a i r Mv - rate of flow of water vapour N - North NE - North East NNE - North North East NNW - North North West NS - Northshore NV - North Vancouver r a i n gauge s t a t i o n NW - North West 0 - , other storm category ODF - occluded front synoptic category OGF - occluding front synoptic category ONW - onshore wind synoptic category p - atmospheric pressure PDT - P a c i f i c Daylight Time PM - P i t t Meadows r a i n gauge s i t e PMO - Port Meteorological O f f i c e r a i n gauge s t a t i o n PN - nodal surface height PP - P i t t Polder r a i n gauge s t a t i o n PST - P a c i f i c Standard Time PW(100-85) - p r e c i p i t a b l e water 1000-850 mb PW(85-70) - p r e c i p i t a b l e water 850-700 mb PW(100-70) - p r e c i p i t a b l e water 1000-700 mb q - s p e c i f i c humidity R - r a i n f a l l amount r - mixing r a t i o r c - simple c o r r e l a t i o n c o e f f i c i e n t RF - Research Forest RG - recording r a i n gauge R - un i v e r s a l gas constant o RH - r e l a t i v e humidity S - South S1-S13 - r a i n gauge s i t e s on Research Forest S(BOY) - Boyden i n s t a b i l i t y index S(CONV) - convective i n s t a b i l i t y index S(POT) - p o t e n t i a l i n s t a b i l i t y index SD - Seymour F a l l s Dam r a i n gauge s t a t i o n SE - South East SG - standard r a i n gauge SH - Sand Heads Light Station SH(100-85) - wind shear 1000-850 mb SH(85-70) - wind shear 850-700 mb SH(100-70) - wind shear 1000-700 mb SM - Surrey Municipal H a l l r a i n gauge s t a t i o n SSE - South South East SSW - South South West ST - storm t o t a l p r e c i p i t a t i o n SW - South West T - a i r temperature x v i i i t time TC - convective i n s t a b i l i t y t r i g g e r i n g process Td dew point temperature TP - p o t e n t i a l i n s t a b i l i t y t r i g g e r i n g process TR trough synoptic category Tw - wet bulb temperature Atw - wet bulb depression U - oreigenic u p l i f t process u - hor i z o n t a l wind component i n x - d i r e c t i o n UBC - Un i v e r s i t y of B r i t i s h Columbia r a i n gauge s t a t i o n U i - major oreigenic u p l i f t UIL Quillayute Radiosonde Station Um minor oreigenic u p l i f t V h o r i z o n t a l wind speed V - h o r i z o n t a l wind component i n y - d i r e c t i o n VAP - Vancouver International Airport VP - vectopluviometer VS(85) south (180°) wind speed component - 850 mb VS(S-85) - mean south (180°) wind speed component - surface to 850 mb VSW(85) southwest (230°) wind speed component - 850 mb VSW(S-85) - mean southwest (230°) wind speed component - surface to 850 mb V T terminal f a l l v e l o c i t y of p r e c i p i t a t i o n p a r t i c l e s VW(85) - west (270°) wind speed component - 850 mb VW(S-85) - mean west (270°) wind speed component - surface to 850 mb W - West WD(85) wind d i r e c t i o n 850 mb WD(700) - wind d i r e c t i o n 700 mb WD(S-85) mean wind d i r e c t i o n - surface to 850 mb WF warm front - warm sector synoptic category W.M.O. - World Meteorological Organization WNW West North West WS - wind speed WS (8b) wind speed s i t e - 8b vectopluviometer WS(85) - wind speed - 850 mb WS(700) - wind speed - 700 mb WS(SH) - wind speed Sand Heads Light Station WS(VAP) - wind speed Vancouver International A i r p o r t WSW - West South West wv West Vancouver r a i n gauge s t a t i o n X - width of section scoured by orographic p r e c i p i t a t i o n Y hor i z o n t a l distance Z - v e r t i c a l height ZT - Port Hardy radiosonde s t a t i o n e wind shear Y slope angle Pd density of a i r P v density of water vapour Pw density of water e i n c l i n a t i o n angle of raindrop t r a j e c t o r i e s from the v e r t i c a l x i x 6 W - wet bulb potent ia l temperature oj - v e r t i c a l v e l o c i t y ojg - storm bearing ACKNOWLEDGEMENTS I wish to acknowledge the support of the l a t e Dr. W. W. J e f f r e y who was l a r g e l y responsible for my entry into the f i e l d of for e s t hydrology. I am indebted to Dr. B. C. Goodell who replaced Dr. J e f f r e y and provided advice and assistance during i n i t i a l phases of the study. Also, the f i e l d program was greatly f a c i l i t a t e d by the co-operation and assistance of committee member Jack Walters and s t a f f at the U.B.C. Research Forest, and by Fred Downes who measured r a i n f a l l f o r me with u n f a i l i n g dedication. I am e s p e c i a l l y g r a t e f u l to Dr. John Hay for generously giving of his time to provide invaluable advice, c r i t i c i s m and assistance with data analyses and preparation of the thesi s , and to Mike Rose for many h e l p f u l discussions during the development of the t h e s i s . I also wish to thank Dr. R. P. Willington, Dr. T. A. Black and S. 0. (Denis) R u s s e l l for serving on my committee. The co-operation of the Atmospheric Environment Service i n providing synoptic weather information and the Greater Vancouver Sewerage and Drainage D i s t r i c t i n providing r a i n f a l l data i s g r a t e f u l l y acknowledged. A very great contribution has been made by my present employer, the Canadian Forestry Service, P a c i f i c Forest Research Centre i n V i c t o r i a , i n providing the time and resources that enabled me to xx complete t h i s t h e s i s . Above a l l , I owe my deepest gratitude to Bonnie, Donna and Scott who have undergone many, many s a c r i f i c e s to make i t a l l possible CHAPTER I INTRODUCTION P r e c i p i t a t i o n measurements i n mountainous t e r r a i n are generally sparse, p a r t i c u l a r l y at higher elevations, and coastal B r i t i s h Columbia i s no exception. What data do exist are mainly from low elevation s t a t i o n s . As a r e s u l t , knowledge of p r e c i p i t a t i o n patterns i s meagre for mountainous areas, p a r t i c u l a r l y for storm durations of about a day or l e s s . As logging, r e c r e a t i o n a l and other land uses expand further into the mountains, data on short duration r a i n f a l l amounts and i n t e n s i t i e s become increasingly important. Such information i s required, for example, for design of adequate road drainage f a c i l i t i e s and hydrologic studies on man-induced changes i n runoff patterns and other impacts on the water resource. The number of high elevation p r e c i p i t a t i o n stations i s u n l i k e l y to increase s u b s t a n t i a l l y because of cost and a c c e s s i b i l i t y problems. There i s thus a requirement for improved knowledge of p r e c i p i t a t i o n v a r i a b i l i t y i n the rugged t e r r a i n of the coastal mountains and for e s t a b l i s h i n g workable r e l a t i o n s h i p s f o r estimating p r e c i p i t a t i o n amounts i n these mountains from observations taken at lower and more accessible s i t e s . The area chosen for the i n v e s t i g a t i o n i s located i n the lower Fraser V a l l e y near Vancouver i n the south coastal mountains of B r i t i s h Columbia. 1 2 S tudy Obj ec t i v e s This thesis study was motivated by the b e l i e f that a v a i l a b l e information on weather systems and atmospheric conditions could be used, with consideration of l o c a l t e r r a i n configuration, to improve estimates of short duration p r e c i p i t a t i o n amounts and d i s t r i b u t i o n over coastal mountainous t e r r a i n . Attention has been focussed on the orographic component of storm r a i n f a l l on windward mountain slopes, or that portion of the r a i n that occurs as a d i r e c t r e s u l t of the influence of mountains on atmospheric processes. The c e n t r a l goal of the thesis has been to elucidate and quantify orographic r a i n f a l l production i n the context of physiographic and atmospheric conditions occurring i n the study area. The s p e c i f i c study objectives were: 1. To measure and c o l l e c t storm r a i n f a l l within a mountainous area with the aim of quantifying r a i n f a l l v a r i a t i o n s and d i s t r i b u t i o n i n r e l a t i o n to s p e c i f i c t e r r a i n features. 2. To analyze i n d i v i d u a l r a i n storms i n d e t a i l to determine those synoptic and atmospheric c h a r a c t e r i s t i c s which are s p e c i f i c a l l y r elated to the production of orographic r a i n f a l l i n the study area. 3. To develop an a n a l y t i c a l model or procedures for evaluating the orographic component of short-period storm r a i n f a l l i n t e n s i t i e s i n the study area based on t e r r a i n configuration and storm meteorologi-c a l c h a r a c t e r i s t i c s . 4. To assess areal patterns and small scale v a r i a t i o n s of r a i n f a l l within the study area i n r e l a t i o n to topography and meteorological v a r i a b l e s . 3 General Review of the Literature The subject of orographic precipitation has been of long-standing interest in many parts of the world, as evidenced by the recent International Symposium on the Distribution of Precipitation in Mountainous Areas held in Geilo, Norway (World Meteorological Organization, 1972). However, studies of rainfall variability in the mountains of western North America have been limited in number, particularly for short duration rainfall intensities. In the western United States, one of the most comprehensive field studies appears to be that reported by Hamilton (1954) in California. Other analyses or studies of mountain precipitation in the Western States include those by Elliott and Shaffer (1962), Linsley (1958), Smith (1962), U.S. Weather Bureau (1961) and Weaver (1962) for California, Cooper (1967) for Idaho, Spreen (1947) for Colorado, Williams and Peck (1958) for Intermountain Region, and U.S. Weather Bureau (1966) and Wilson (1961) for Washington. In western Canada, precipitation studies on the east slopes of the Rocky Mountains in Alberta have been reported on by Ferguson and Storr (1969) and Reinelt (1968). In British Columbia, a few large scale analyses of precipitation over mountainous regions based on existing data and involving consideration of terrain and meteorological factors have been carried out. Walker (1961) derived annual and shorter period precipitation maps for the province based on orographic modelling principles. Danard (1971) computed the variation of annual precipitation in south central and south coastal British Columbia, while estimation of monthly and annual precipitation formed part of a major study of the Okanagan basin (Storr and Ferguson 1972). Also on the 4 coast, N i k l e v a (1968) examined the e f f e c t of topography and a i r mass s t a b i l i t y on p r e c i p i t a t i o n d i f f e r e n c e s between the east and west coasts of Vancouver I s l a n d . F i e l d i n v e s t i g a t i o n s of mountain r a i n f a l l appear to have been mostly confined to the south coast. Two mountains t r a n s e c t s of p r e c i p i t a t i o n gauges have been e s t a b l i s h e d across the Beaufort Range on Vancouver I s l a n d (Ferguson, Hunter and Schaefer, 1974). The p r i n c i p a l aim of the Beaufort p r o j e c t i s s i m i l a r to that of the present study; namely, to develop r e l a t i o n s h i p s based on m e t e o r o l o g i c a l and physio-graphic parameters f o r e s t i m a t i n g p r e c i p i t a t i o n i n mountainous areas. P r e c i p i t a t i o n gauge networks a l s o form part of more general h y d r o l o g i c s t u d i e s of the small Jamieson Creek watershed near the head of the Seymour R i v e r v a l l e y n o r t h of Vancouver (Jones 1974) and the Carnation Creek watershed on the west coast of Vancouver I s l a n d (Narver, 1974). In a study of storm s n o w f a l l on Mount Seymour w i t h i n the present study area near Vancouver, F i t z h a r r i s (1975) a l s o d i d a cursory examination of orographic r a i n f a l l . The Environment and Land Use Committee S e c r e t a r i a t of the p r o v i n c i a l government has r e c e n t l y undertaken measurements of p r e c i p i t a t i o n at higher e l e v a t i o n s i n c o n j u n c t i o n w i t h watershed and other s t u d i e s on Vancouver Islan d and the southern mainland coast. W i t h i n the general study area, p r e c i p i t a t i o n d i s t r i b u t i o n and occurrence based on e x i s t i n g data have a l s o been the subject of a number of r e p o r t s . Wright and Trenholm (1969) d e s c r i b e the annual and seasonal p a t t e r n of p r e c i p i t a t i o n i n the Vancouver area, w h i l e Schaefer and N i k l e v a (1973) have developed a map of annual p r e c i p i t a t i o n over the mountains to the n o r t h of Vancouver. On a shorter t i m e - s c a l e , Sporns 5 (1964) compared short duration rainfall intensities between mountain and lowland stations in the lower Fraser Valley, while Danard (1975) developed regression equations for 24-hour rainfalls in the mountains north of Vancouver. Analyses of major storm rainfalls in the lower Fraser Valley have also been performed by Bruce (1961) and Sporns (1963). In the context of previous or existing studies, this thesis investigation can be considered complementary to the Beaufort Range study (Ferguson, Hunter and Schaefer, 1974) and, in part, an application on a much smaller scale of the approach taken by Walker (1961). Further references to the literature are contained in the following chapters in relation to specific aspects of the present study. Presentation of Thesis The material in this thesis is presented in the order ascribed to specific study objectives. Chapter II provides background informa-tion on study area characteristics, available meteorological data and field measurement and collection of precipitation data. Chapter III discusses the detailed analysis of storm meteorological characteristics in relation to production of orographic rainfall in the study area. Chapter IV describes the adaptation and application of an orographic model for estimating short-period rainfall intensities over windward mountain slopes. Finally, Chapter V examines areal patterns and small-scale variations of precipitation on the University of British Columbia Research Forest. CHAPTER II DESCRIPTION OF STUDY AREA AND DATA COLLECTION This chapter provides background information on the phys i c a l and c l i m a t i c nature of the study area and the c o l l e c t i o n of meteorologi-c a l and p r e c i p i t a t i o n data. Some general comments associated with measurement of p r e c i p i t a t i o n are also included. C h a r a c t e r i s t i c s of Study Area Location The general study area i s located on the southern f r i n g e of the coastal mountains i n the southwest corner of B r i t i s h Columbia (see inset Figure 1). It l i e s within the lower Fraser V a l l e y region which i s screened from the open P a c i f i c Ocean 150 km to the southwest by the mountains of Vancouver Island, with peaks over 2000 metres, and the Olympic Peninsula with t e r r a i n heights up to 2400 metres. One transect of p r e c i p i t a t i o n stations used i n the study i s located across and north of the c i t y of Vancouver, as indicated i n Figure 1, and was selected e n t i r e l y from the e x i s t i n g network. The second i s located 40 km to the east of Vancouver as indicated i n Figure 1, and includes both e x i s t i n g stations plus s p e c i a l l y i n s t a l l e d study gauges. The U n i v e r s i t y of B r i t i s h Columbia Research Forest, which was the s i t e of the f i e l d study, i s situated at the north end of t h i s transect about 6 km north of Haney. 6 7 ELEVATIONS IN FEET SCALE IT500,000 LEGEND 10 0 KILOMETERS I | 10 5 0 5 MILES I . . . . I I UNIVERSITY OF BRITISH COLUMBIA RESEARCH FOREST EXISTING PRECIPITATION STATIONS F i g u r e 1. Map o f stu d y a r e a showing l o c a t i o n o f e x i s t i n g p r e c i p i t a t i o n s t a t i o n s used i n stu d y . 8 Physiography The lower Fraser V a l l e y r e g i o n comprises a r e l a t i v e l y wide band of low e l e v a t i o n f l a t land bordered on the n o r t h by the coast mountain range (Figure 1 ) . The p o r t i o n of these mountains immediately adjacent to the F r a s e r V a l l e y i s d i s s e c t e d by a number of major south-north o r i e n t e d v a l l e y s . Ridgetops average about 1200 metres e l e v a t i o n w i t h s e v e r a l peaks exceeding 1700 metres. D i r e c t l y north of the c i t y of Vancouver, the t e r r a i n i s r e f e r r e d to as the Northshore mountains. The Research Forest (see Figure 3) covers about 50 square k i l o m e t r e s , w i t h about two-thirds of t h i s area being a c c e s s i b l e v i a an extensive road network. W i t h i n the a c c e s s i b l e part of the F o r e s t , e l e v a t i o n s range from near sea l e v e l to over 750 metres. On the west, i t i s bounded by the comparatively wide P i t t R i v e r V a l l e y , and on the east by the Mount Blanshard r i d g e w i t h a peak e l e v a t i o n near 1700 metres. The g l a c i a t e d topography of the Research Forest has a bench-l i k e form. The southern p o r t i o n i s wedge-like i n shape w i t h a mean slope of 10 percent and a general s o u t h e r l y aspect which i s broken up by numerous k n o l l s . The c e n t r a l p o r t i o n contains three p a r a l l e l south-north v a l l e y s separated by r i d g e s w i t h approximately l e v e l tops averaging 550 to 610 metres e l e v a t i o n . The northern p o r t i o n c o n s i s t s of broken, humpy t e r r a i n which terminates a b r u p t l y i n a steep slope descending to P i t t Lake. Vegetation The area of the Research F o r e s t below about 900 metres f a l l s i n t o the Western Hemlock Zone of K r a j i n a ' s (1969) c l a s s i f i c a t i o n . Here the dominant n a t u r a l l y o c c u r r i n g t r e e species i s western hemlock (Tsuga hetevophylla) w i t h o c c a s i o n a l Douglas f i r (Pseudotsuga menziesii) and western red cedar {Thuja plicatd) . In the subalpine Mountain Hemlock Zone above 900 metres, mountain hemlock and a m a b i l i s f i r become the common species. The Research Forest has a f a i r l y long h i s t o r y of f i r e , e xtensive l o g g i n g , and r e f o r e s t a t i o n . As a r e s u l t , the f o r e s t cover i s discontinuous and uneven, c o n s i s t i n g of patches of o l d growth f o r e s t , second growth stands of v a r y i n g ages and h e i g h t s , and d i v e r s e c l e a r i n g s w i t h low ground cover. The presence of rock outcrops and s e v e r a l lakes completes the rough and broken nature of the landscape surface. Climate The c l i m a t e of south c o a s t a l B.C. i s described from v a r i o u s viewpoints by Hare and Hay (1974), Hare and Thomas (1974), Kendrew and Kerr (1955) and Trewartha (1966). An outstanding f e a t u r e of the c l i m a t e of the lower Fraser V a l l e y Region i s the heavy f a l l and winter p r e c i p i t a t i o n contrasted by r e l a t i v e l y dry s p r i n g and summer periods. The winter weather i s dominated by a w e s t e r l y flow w i t h a procession of f r o n t s and depressions. Sporns (1963), f o r example, found that 93% of the most severe annual storms i n the lower Fraser V a l l e y from 1925-1961 occurred from October to February. P r e c i p i t a t i o n becomes l e s s frequent during the March-May period and from June-September c y c l o n i c a c t i v i t y i s g r e a t l y reduced and heavy r a i n storms are r a r e . This annual p a t t e r n of p r e c i p i t a t i o n i s c o n t r o l l e d by the seasonal m i g r a t i o n of the n o r t h P a c i f i c s u b - t r o p i c a l a n t i c y c l o n e . In summer, i t l i e s o f f the coast pushing storm t r a c k s to the n o r t h , but r e t r e a t s southward i n winter p e r m i t t i n g storm t r a c k s to l i k e w i s e advance southward. 10 Mean annual p r e c i p i t a t i o n i n the study area ranges from l e s s than 1000 millimetres over the southwest part of the Fraser V a l l e y to about 5000 millimetres at higher elevations i n the mountains as shown by Schaefer and Nikleva (1973). Based on records for the Loon Lake sta t i o n , average annual p r e c i p i t a t i o n exceeds 2800 millimetres on the Research Forest. During the winter, snowfall i s heavy on the mid-upper slopes of the mountains. Snow also occurs i n the adjacent Fraser Valley, although most p r e c i p i t a t i o n at these lower l e v e l s occurs as r a i n . C h a r a c t e r i s t i c A i r Mass Types The t r a j e c t o r y of a i r reaching the study area determines i t s temperature, humidity and s t a b i l i t y c h a r a c t e r i s t i c s . Three main types of a i r mass are associated with r a i n f a l l i n coastal B r i t i s h Columbia. Maritime T r o p i c a l (mT) a i r , which comes from t r o p i c a l regions to the southwest, i s warm, humid and r e l a t i v e l y stable due to surface cooling as i t moves northward, and gives r i s e to major r a i n storms. It occ a s i o n a l l y reaches B r i t i s h Columbia i n winter i n the warm sector of f r o n t a l waves, but more often at upper l e v e l s a f t e r occlusion of the warm sector over the ocean. In contrast, Maritime A r c t i c (mA) a i r or i g i n a t e s over the A r c t i c land masses of A s i a and North America and sweeps onto the B r i t i s h Columbia coast from the northwest a f t e r a r e l a t i v e l y short t r i p over the northern P a c i f i c . This a i r i s warmed and humidified as i t moves southward and becomes incr e a s i n g l y unstable i n the process, r e s u l t i n g i n showery p r e c i p i t a t i o n . Maritime Polar (mP) a i r has the same o r i g i n as mA a i r but a longer t r a j e c t o r y over the ocean, a r r i v i n g at the coast from a more westerly d i r e c t i o n . Its properties and p r e c i p i t a t i o n c h a r a c t e r i s t i c s are intermediate between those of mA 11 and mT a i r . In winter, mP a i r frequently a r r i v e s on the coast at upper l e v e l s following f r o n t a l occlusion over the ocean. C h a r a c t e r i s t i c temperature p r o f i l e s for the d i f f e r e n t a i r mass types are given i n Appendix I. Reasons for Choice of Study Area The lower Fraser V a l l e y region was selected f or the general study area f o r several reasons: the great influence of l o c a l mountains on p r e c i p i t a t i o n i n the area (Wright and Trenholm, 1969), an expanse of f l a t land adjacent to a mountain b a r r i e r exposed to p r e v a i l i n g winds, proximity to the U n i v e r s i t y , existence of an established p r e c i p i t a t i o n gauge network including stations within the mountainous areas, and a v a i l a b i l i t y of l o c a l surface weather data from the Vancouver International A i r p o r t . The U n i v e r s i t y of B r i t i s h Columbia Research Forest was chosen f o r f i e l d measurements for several reasons: a good road network providing access to higher elevations and an area of rugged t e r r a i n , a v a i l a b i l i t y of personnel to a s s i s t with i n s t a l l a t i o n of gauges and taking readings, the existence of four permanent meteorological stations, and r e s t r i c t e d public access providing r e l a t i v e security of instrumentation. In some respects the deeply indented, non-uniform mountain b a r r i e r i n the study area might not be considered i d e a l f o r developing p r e d i c t i v e models. Uniform ridges normal to p r e v a i l i n g wind d i r e c t i o n s are generally preferred to optimize chances for es t a b l i s h i n g v i a b l e r e l a t i o n s h i p s . However, t h i s feature of the study area was not considered a l i a b i l i t y but rather, as an opportunity to assess the f e a s i b i l i t y of developing workable r e l a t i o n s h i p s f o r a t e r r a i n 12 configuration which might be considered more t y p i c a l than the often desired uniform condition. A v a i l a b l e Meteorological Information  P r e c i p i t a t i o n Data Data were c o l l e c t e d from two transects of established p r e c i p i t a t i o n stations f or the purpose of assessing l a t e r a l east-west v a r i a t i o n s . Their locations are indicated i n Figure 1 and information on c o l l e c t i o n agency, elevation and gauge type given i n Appendix I I . Instrumentation at these stations included standard, non-recording r a i n gauges and/or d i f f e r e n t versions of recording, tipping-bucket r a i n gauges. The operation of the tipping-bucket mechanism i s such that i n t e n s i t y data recorded by t h i s type of gauge should be compared with volume measurements and corrected where necessary. This procedure i s standard p r a c t i c e at Atmospheric Environment Service (A.E.S.) sta t i o n s . Tipping-bucket data from the Greater Vancouver Sewerage and Drainage D i s t r i c t (G.V.S.D.D.) i n s t a l l a t i o n s were obtained without modification of recorded i n t e n s i t i e s . However, the close proximity of A.E.S. standard gauges to G.V.S.D.D. recording gauges at Cleveland and Seymour F a l l s Dams permitted c o r r e c t i v e adjustments to be made i n recorded i n t e n s i t y data at these two s t a t i o n s . This adjustment procedure had not been applied to data from tip p i n g bucket gauges operated s o l e l y by the Uni v e r s i t y of B r i t i s h Columbia Research Forest at the Spur-17 and Loon Lake s i t e s , because standard gauge readings were discontinued. There i s a considerable v a r i a t i o n i n s i t e c h a r a c t e r i s t i c s of these e x i s t i n g p r e c i p i t a t i o n stations ranging from open grassy areas to roof-top l o c a t i o n s (PMO, WV, NV). Exposure and presence of nearby 13 obstacles could r e s u l t i n wind-induced measurement errors at some of these s i t e s . Since i t was not possible to as c e r t a i n the degree of po t e n t i a l error, the data were used as published. Upper A i r Data Upper a i r temperature, humidity and wind data f o r Port Hardy and Quillayute radiosonde stations were c o l l e c t e d i n several forms: punched computer cards, published reports and o r i g i n a l teletype reports. Port Hardy i s located on northern Vancouver Island 350 km northeast of Vancouver, while Quillayute i s situated on the Olympic Peninsula 190 km to the southwest (Figure 1). Synoptic Weather Data The following information on synoptic weather conditions relevant to storm periods selected for analysis was c o l l e c t e d : synoptic surface weather maps and upper a i r charts f o r 850, 700, 500 and 300 mb l e v e l s ; hourly surface weather reports f o r the Vancouver and Abbotsford International A i r p o r t s ; and wind data from the Spur-17 anemometer on the Research Forest. Unfortunately, the timing mechanism of the Spur-17 anemometer recorder was not functioning properly and very l i m i t e d useful data were obtained. Information on data sources i s given i n Appendix I I I . Background on P r e c i p i t a t i o n Measurement In measuring p r e c i p i t a t i o n , two p r i n c i p a l problems must be addressed: namely, the sources of error involved i n measurement at a p a r t i c u l a r point or s i t e and l o c a t i o n of gauge s i t e s , that i s , network 14 design. Some background in f o r m a t i o n on these problems i s presented i n the f o l l o w i n g s e c t i o n s . For both po i n t measurement and network design, a v a r i e t y of scales of topography, storm systems and w i n d - t e r r a i n i n t e r a c t i o n s are i n v o l v e d . P o i n t Measurement of P r e c i p i t a t i o n A primary aim of p r e c i p i t a t i o n measurement i s to o b t a i n a sample that i s accurate and r e p r e s e n t a t i v e of p r e c i p i t a t i o n over the area surrounding the gauge. In t h i s regard, some p a r t i c u l a r c o n s i d e r a t i o n s f o r point measurement of r a i n f a l l i n mountainous t e r r a i n are o u t l i n e d below. More general i n f o r m a t i o n on the subject of p r e c i p i t a t i o n measurement i s contained i n the e x c e l l e n t summary references by Corbett (1967), Kurtyka (1953), Larson (1971), McKay (1964, 1970), R a i n b i r d (1965), Rodda (1967, 1970, 1971), and the World M e t e o r o l o g i c a l O r g a n i z a t i o n (1970, 1974). Wind i s by f a r the most s i g n i f i c a n t f a c t o r a f f e c t i n g the accuracy and representativeness of r a i n f a l l measurements. When p l a c i n g a r a i n gauge i n the f i e l d , c o n s i d e r a t i o n must be given to both the e f f e c t s of wind on the gauge i t s e l f and the e f f e c t s of the gauge s i t e and surrounding area on wind motions. Because of the importance of wind e f f e c t s , these two f a c t o r s are discussed i n more d e t a i l i n the f o l l o w i n g s e c t i o n s . Other p o t e n t i a l sources of e r r o r are comparatively minor and in c l u d e evaporation, splash e f f e c t s , and e r r o r of measurement (gauge accuracy of r e s o l u t i o n , o b s e r v a t i o n a l mistakes). C a r e f u l gauge i n s t a l l a t i o n and measurement procedures can minimize the i n f l u e n c e of these sources of e r r o r . 15 Gauge P r o t e c t i o n from Wind E f f e c t s Larson and Peck (1974) give an e x c e l l e n t review of wind e f f e c t s on gauge catch. In general, a r e s u l t of r a i n gauge exposure to the wind i s u s u a l l y a r e d u c t i o n i n the amount of water c o l l e c t e d . Hence, to o b t a i n accurate measurements, wind speed and turbulence should be minimized i n the v i c i n i t y of the gau,ge. An e f f e c t i v e way to achieve t h i s goal i s to u t i l i z e the n a t u r a l s h e l t e r provided by the f o r e s t e d environment. The most s u i t a b l e s i t e f o r optimum wind p r o t e c t i o n appears to be a small c i r c u l a r c l e a r i n g i n a uniform f o r e s t cover (Corbett 1967, Geiger 1965, Hamilton 1954, Leonard and Reinhart 1962, P e r e i r a , et a l . 1962, Weiss 1963, Wilson 1954). There are v a r i o u s opinions as to the best s i z e f o r such a c l e a r i n g . A commonly accepted c r i t e r i o n i s that the angle from that gauge o r i f i c e to the surrounding t r e e tops should be about 45° or l e s s ( P e r e i r a , et a l . 1962). However, angles v a r y i n g from 20° (Brown and Peck 1962) to 64° (Wilson 1954) have been recommended, the l a t t e r being f o r a c l e a r i n g w i t h diameter equal to the height of surrounding t r e e s . Most r e p o r t s r e f e r to opening dimensions on l e v e l r a t h e r than s l o p i n g ground. Bleasdale (1959b) has questioned the r e p r e s e n t a t i v e s of r a i n -f a l l measurements i n f o r e s t c l e a r i n g s , c l a i m i n g that they cause p e c u l i a r c o n d i t i o n s of a i r turbulence which produce a r a i n f a l l d i s t r i b u t i o n d i f f e r e n t from that over an u n i n t e r r u p t e d canopy. Although p o s s i b l y not i d e a l , such c l e a r i n g s are the best a v a i l a b l e compromise f o r p r o t e c t i n g gauges from wind e f f e c t s . In rugged t e r r a i n , i t would seem d e s i r a b l e to s e l e c t the smallest p o s s i b l e s i z e c l e a r i n g c o n s i s t e n t w i t h r e p r e s e n t a t i v e catch. 16 As a basic working rule, a clearing diameter approximately equal to the height of the surrounding trees seems reasonable. The clearings should be at least large enough to avoid direct drip from overhead branches into the gauge. They need not necessarily be circular i f protection is adequate in the direction of prevailing winds during rainfall. On steeply sloping ground and in large openings, some wind will penetrate into the clearing. The effects of shrubs and other obstacles within the clearing on wind turbulence must then be considered. In general, the disturbance created by an obstacle is roughly proportional to its size (Serra 1951). To counter any influence of local wind disturbance on gauge catch, a common recommendation is that surrounding objects should not be closer to the gauge than a distance equal to four times their height (Serra 1951, World Meteorological Organization 1970). Most natural objects in forest clearings, such as small trees and stumps, can be cut to ground level or at least to a level below that of the gauge orifice. In natural openings or open forest stands, low understory vegetation can be very dense. In this situation, placing the gauge in the midst of the low vegetation with the orifice just above the vegetation canopy level should provide even better wind protection. The tops of the bushes should break the wind and greatly reduce its velocity over the gauge. Because of access problems, the nature of the ground cover, or study objectives, it may be necessary to install rain gauges in large open or other exposed areas. Measures which can be taken to reduce wind effects on the gauge include the use of shields (Weiss and Wilson 1958), turf walls (Struzer 1965), and pit gauges (Bleasdale 1959a, Rodda 1969, 17 1970) where the gauge o r i f i c e i s at ground l e v e l . Such measures are generally impractical i n forested mountain t e r r a i n where open s i t e s tend to be very rough due to a combination of i r r e g u l a r ground surface, stumps and slash. A more p r a c t i c a l s o l u t i o n i s to place the gauge close to the ground i n a small, sheltered depression to reduce the wind force on the gauge. S i t e S e l e c t i o n The d e s i r a b l e or best l o c a t i o n for a r a i n gauge s i t e w i l l depend on the nature of the topography, p r e v a i l i n g wind and storm patterns, and ultimately, on the purpose for which the data arebeing c o l l e c t e d . The s i t e selected should provide measurements representative of the r a i n f a l l on the surrounding area. The larger the area, the more useful and e f f i c i e n t i s the measurement. To be representative, the slope and o r i e n t a t i o n of the s i t e should correspond to those of the surroundings. More p a r t i c u l a r l y , l o c a t i o n s considered to be anomalous should be avoided unless the objective i s to define the extent to which a s i t e i s non-representative. Some examples of non-representative s i t e s are near or on the crests of exposed ridges or h i l l tops, at the base of a c l i f f or at the leading edge of a f o r e s t . Sites near narrow c o n s t r i c t i o n s i n v a l l e y bottoms should also be avoided since the wind can undergo considerable a c c e l e r a t i o n at these points. Other undesirable locations w i l l become evident for a given area when the purpose of measurement i s known. In mountainous t e r r a i n , r a i n gauge s i t e s w i l l frequently be located on sloping ground. Some inv e s t i g a t o r s have found that the amount of r a i n received on a sloping ground surface i s often d i f f e r e n t 18 from that collected by a conventionally placed rain gauge with horizontal orifice (Fourcade 1942, Hamilton 1954, Serra 1951). To clarify this apparent contradiction, i t is necessary to distinguish between "meteorological" and "hydrological" rainfall (Serra 1951). Meteorological rainfall is the quantity of rain which passes through a given horizontal surface such as the orifice of a rain gauge. This measure of rainfall is a descriptive climatic parameter. Hydrological rainfall can be defined as the vertical depth of water received at a surface whether the surface is horizontal or inclined. It is the actual amount of water reaching the ground. Hydrological rainfall can be measured by stereo-topped (elliptical) or tilted rain gauges with the orifice placed parallel to the slope of the land. However, both types of rainfall are necessarily related and one can be computed from the other if ground slope, aspect, and inclination and direction of raindrop trajectories are known. The relationship between meteorological and hydrological rainfall and the catches of rain gauges with horizontal, stereo and tilted orifices are described in Appendix IV. Information on raindrop trajectories can be obtained using a directional rain gauge ' such as the type described in the section on instrumentation. Sevruk (1972) gives a useful review of the stereo-horizontal orifice controversy and concludes that stereo orifices are better for measurements on steep, open slopes exposed to winds. However in well sheltered sites, the inclination of the rain gauge orifice should not significantly influence the gauge catch as the rain will f a l l more or less vertically because of reduced wind velocities (Leonard and Reinhart 1962). Network Design Much useful background information on p r e c i p i t a t i o n network design i s contained i n the proceedings of the International Symposium on the Design of Hydrological Networks held i n Quebec C i t y i n 1965 (W.M.O. and I.A.S.H. 1965) and the report by Rodda (1969). However, as noted by Rainbird (1965), r e l a t i v e l y few studies with dense r a i n gauge networks have been reported for areas where orographic influences are marked. Notable exceptions i n Western North America are studies reported by Hamilton and Reimann (1958) and Storr and Ferguson (1972). A d d i t i o n a l studies for other areas are described i n the proceedings of the International Symposium on the D i s t r i b u t i o n of P r e c i p i t a t i o n i n Mountainous Areas held i n Geilo, Norway i n 1972, (World Meteorological Organization 1972). The d i r e c t purpose of most r a i n gauge network studies c i t e d i n the l i t e r a t u r e i s either to measure r a i n f a l l depth over an area or to determine the minimum or optimum number of gauges needed to accomplish t h i s goal. The network of the present study d i f f e r s i n p r i n c i p l e from these objectives i n that i t was designed to investigate factors causing v a r i a b i l i t y i n a r e a l r a i n f a l l rather than to measure a r e a l r a i n f a l l per se. Gauges were located i n r e l a t i o n to the nature of s p e c i f i c topographic features rather than to the broader area of the Research Forest. D e s c r i p t i o n of P r e c i p i t a t i o n Measurement  On Research Forest In conjunction with p r e c i p i t a t i o n measurements at established meteorological stations i n the general study area, a f i e l d program was 20 designed to c o l l e c t a d d i t i o n a l data on r a i n f a l l amounts and a r e a l v a r i a t i o n s within the mountainous t e r r a i n of the Research Forest. The objectives of the f i e l d measurements were twofold: f i r s t , to extend the e x i s t i n g south to north transect of p r e c i p i t a t i o n stations further north into the mountains to define major trends i n orographic r a i n f a l l patterns for development of an a n a l y t i c a l orographic model (see Chapter IV). The second goal was not s p e c i f i c a l l y to define a r e a l r a i n f a l l over the Research Forest, but to determine r e l a t i o n s h i p s between r a i n f a l l and topography which would have v a l i d i t y f o r extrapolation to other areas. Rain gauges were located to examine both meso- and small-scale r a i n f a l l patterns. In t h i s context, v a r i a t i o n s i n p r e c i p i t a t i o n due to s i t e c h a r a c t e r i s t i c s were considered to be errors and steps were taken to minimize t h e i r influence on gauge catch as discussed i n the background section on p r e c i p i t a t i o n measurement. The adopted network design was conditioned by cost of r a i n gauges, access, l o c a t i o n of e x i s t i n g gauges, the general south-north o r i e n t a t i o n of t e r r a i n features, and time required to v i s i t and take readings from a l l the gauges. Period of F i e l d Measurements F i e l d work was i n i t i a t e d during the summer of 1970 with the establishment of a network of r a i n gauges on the U.B.C. Research Forest. R a i n f a l l measurements were taken from August 2 to November 25, at which time snow prevented further access to most gauges. In 1971, measure-ments began again on May 10 and concluded on October 25, a f t e r which the network was dismantled. Concurrently, r a i n f a l l data from established meteorological stations i n the surrounding area were also c o l l e c t e d . Instrumentation The principal gauge used in the study was the Universal weigh type recording gauge (pictured in Figure 2a). The model used has a 20.3 centimetre diameter orifice, 305 millimetre rainfall capacity, 8-day spring wound clock and resolution of 0.8 to 1.3 millimetres. A chart rotation period of 48 hours was employed to obtain a good time resolution of about 5 minutes. No difficulty was experienced in deciphering overlapping traces. For ease of changing charts, the gauges were mounted on stumps or platforms so the orifices were approximately 1.5 metres above the ground surface. Each gauge was carefully levelled and calibrated in the field using a special set of weights. To check on gauge accuracy, the water in the bucket was weighed or the volume measured at the time of each reading and records adjusted where significant differences were noted between this check measure and the recorded chart value. Evaporation is not a problem with this gauge, since rainfall is recorded at time of occurrence, as is any evaporation that occurs. Overall, the performance of the Universal recording gauge was highly satisfactory and dependable. The recording gauge network was supplemented with a number of Canadian standard rain gauges (Figure 2b) which have a 9.1 centimetre diameter orifice, a capacity of about 114 millimetres and a resolution of 0.3 millimetres. A disadvantage of this gauge for use in high rain-f a l l areas is its small capacity and thus the requirement to make frequent visits to measure collected rainfall. These gauges overflowed during some of the larger storms or sequences of rainy days. To suppress evaporation, a small amount of light o i l was added to each 22 c. Can-type gauge d. D i r e c t i o n a l gauge (vectopluviometer) F i g u r e 2. Rain gauges used i n study. 23 gauge at the time of each reading. The gauges were i n s t a l l e d so as to avoid the p o s s i b i l i t y of splash e f f e c t s . Two d i r e c t i o n a l r a i n gauges or vectopluviometers were also i n s t a l l e d i n open areas. The model used i s shown i n Figure 2d and i s a modification of a gauge described by Hamilton (1954). E s s e n t i a l l y i t consists of four c o l l e c t o r s with v e r t i c a l openings spaced 90 degrees apart and oriented toward the c a r d i n a l points of the compass. The c o l l e c t o r s were constructed of 20 centimetre diameter furnace pipe to which metal funnels were attached, welded together using metal straps and mounted on cedar posts approximately 1.5 to 1.3 metres above the ground surface. The r a i n water was c a r r i e d v i a f l e x i b l e tubing to sealed, clear 7.6 centimetre diameter, r i g i d a c r y l i c c y l i n d e r s . The cylinders were graduated so water depth could be read d i r e c t l y , had a plug i n the bottom so water could be drained following each reading or storm period and contained an a i r hole at the top. Water depth could be read to a r e s o l u t i o n of 0.3 m i l l i m e t r e s . Occasional leakage problems were encountered because of inadequate sealing of the base plate and drain plug connection on the c y l i n d e r s . Otherwise, the functioning of the gauges was s a t i s f a c t o r y . The c a l c u l a t i o n of raindrop t r a j e c t o r y i n c l i n a t i o n and storm bearing from vectopluviometer data i s presented i n Appendix V. A d d i t i o n a l r a i n f a l l measurements were taken with inexpensive home-made gauges cons i s t i n g of 1.36 l i t r e j u i c e cans coated with verethane i n which a p l a s t i c funnel was placed. The gauges were mounted as shown i n Figure 2c to prevent t i p p i n g . Based on comparative measurements, weekly catches i n the can-type gauges were within 6% of 24 recording gauge values. Network Design I n i t i a l network. The l o c a t i o n s of r a i n gauge s i t e s established on the Research Forest are shown i n Figure 3. The four permanent p r e c i p i t a t i o n stations are i d e n t i f i e d as Administration Building (AD), Marc (MC), Spur-17 (S17), and Loon Lake (LL). In addition, a recording anemometer i s located at the Spur-17 s i t e . In 1970, 10 Universal recording r a i n gauges were i n s t a l l e d at s i t e s 1 to 10. Standard gauges were also located at s i t e s 4, 7, 8 and 10 as a check on recording gauge measurements. Vectopluviometers were i n s t a l l e d at l o c a t i o n s : (1) at the Spur-17 s i t e on an exposed rocky k n o l l ; (2) i n an open, logged c l e a r i n g near s i t e 8. Standard gauges were placed near these vectopluviometers. Standard gauges were also i n s t a l l e d at site-11 and site-MR, located outside of the Research Forest boundaries about 3 kilometres south of the Administration Building (Figure 1). At the time the network was being set up, p r e c i p i t a t i o n measurements were being taken by f i v e recording gauges i n the Lost Lake and M i l i t z a Lake watersheds, located to the northwest and east of Loon Lake r e s p e c t i v e l y . These measurements formed part of a study operated under the sponsorship of the Faculty of A g r i c u l t u r e , U n i v e r s i t y of B r i t i s h Columbia. This study was terminated early i n 1971. Unfortunately, the records from these gauges proved to be sporadic and generally u n r e l i a b l e . The following r a t i o n a l e was used for gauge placement. Sites 1 to 6 were located to define r a i n f a l l d i s t r i b u t i o n with respect to the Figure 3. Map of U n i v e r s i t y of B r i t i s h Columbia Research Forest study area showing l o c a t i o n of r a i n gauge s i t e s . r i d g e separating the n e a r l y l e v e l Marion Lake v a l l e y from the s l o p i n g headwater area of the Blaney Lake v a l l e y . S i t e p a i r s 1-2, 3-4, 5-6 were spaced about one m i l e apart and form part of the general south-north t r a n s e c t , w h i l e the more c l o s e l y spaced groupings 2-3-6 and 1-4-5 provide i n f o r m a t i o n on east-west v a r i a t i o n s and a cross-check on s i t e r e p r e s e n t a t i v e n e s s . Gauges 7, 8 and 10 were placed along the western edge of the Research Forest to assess south-north v a r i a t i o n s . Site-7 i s l o c a t e d on the top of a small h i l l which p r o j e c t s above the r i d g e l i n e . An a d d i t i o n a l o b j e c t i v e was to compare s i t e - 7 and Loon Lake s t a t i o n data to o b t a i n a measure of wind e f f e c t s , i f any, on r a i n f a l l at the h i l l t o p . The s i t e - 7 gauge was l o c a t e d i n a p a r t i c u l a r l y w e l l - s h e l t e r e d c l e a r i n g , so the data should be r e p r e s e n t a t i v e of a c t u a l r a i n f a l l at that spot. S i m i l a r l y , the s i t e - 9 gauge was placed i n a small opening atop the h i l l west of Gwendoline Lake f o r s m a l l - s c a l e comparison w i t h s i t e - 8 measure-ments. The s i t e - 9 h i l l i s the highest r e a d i l y a c c e s s i b l e p o i n t w i t h i n the boundaries of the Research F o r e s t . S i t e s 7, LL, 8 and 9 l i n k up w i t h s i t e s 1-6 to form west-east t r a n s e c t s across the width of the Research F o r e s t . The gauges at the s i t e s described above provide i n f o r m a t i o n on south-north p a t t e r n s of r a i n f a l l along both eastern and western sides of the Research F o r e s t . E x i s t i n g s t a t i o n s at the Spur-17, A d m i n i s t r a t i o n and Marc s i t e s plus the s i t e - 1 1 gauge complete the south-north sampling w i t h i n the Research Forest area i t s e l f . A d d i t i o n a l data c o l l e c t e d o u t s i d e i t s boundaries extend the t r a n s e c t southward out i n t o the lower Fraser V a l l e y . These a d d i t i o n a l s t a t i o n s are i n d i c a t e d i n Figure 1. 27 The vectopluviometers were employed to gather data on raindrop t r a j e c t o r i e s and low l e v e l wind speeds which would a s s i s t i n e x p l a i n i n g observed r a i n f a l l v a r i a t i o n s and wind e f f e c t s or patterns at d i f f e r e n t p o i n t s on the study area. M o d i f i e d network. F o l l o w i n g p r e l i m i n a r y assessment of r e s u l t s from the i n i t i a l network, some gauges were r e l o c a t e d and new ones added during the 1971 season. The s i t e - 4 gauges were l o c a t e d on a l o g i n the centre of a c i r c u l a r bog. On two occasions during the f a l l of 1970, a bear dismantled the recording gauge and knocked over the standard gauge. In 1971, the r e c o r d i n g gauge was placed at the MR s i t e south of the Research Forest, and the s i t e - 4 standard gauge r e l o c a t e d about 30 metres from i t s i n i t i a l spot. Comparative standard gauge measurements were taken f o r a period at both the o l d and new l o c a t i o n s to check f o r consistency of data. The standard gauges at s i t e s 7, 9 and 10 were removed and r e l o c a t e d . One gauge was placed at s i t e - 1 2 to assess Spur-17 measure-ments. A second standard gauge was placed at s i t e - 1 3 at the end of August. Three t r a n s e c t s of can-type gauges were i n s t a l l e d to assess s m a l l - s c a l e r a i n f a l l p atterns a s s o c i a t e d w i t h the h i l l s on which gauges 7 and 9 were l o c a t e d (see F i g u r e 3). Transect I c o n s i s t e d of 4 gauges located i n small openings, i n c l u d i n g one at s i t e - 7 i t s e l f . Transect I I was comprised of 3 gauges, i n c l u d i n g one at s i t e - 8 and one at the open vectopluviometer s i t e . Transect I I I c o n s i s t e d of 5 gauges, of which 4 were l o c a t e d on an open, logged h i l l s i d e and 1 at s i t e - 9 i t s e l f . The 23 absence of t r e e s meant that the 4 gauges on the h i l l s i d e were exposed to wind e f f e c t s , although they were placed i n p o s i t i o n s which were as s h e l t e r e d as p o s s i b l e . In J u l y , the standard gauges at the Spur-17, Marc, and Loon Lake s i t e s were replaced w i t h r e c o r d i n g tipping-bucket r a i n gauges. An a d d i t i o n a l tipping-bucket r a i n gauge was obtained and operated at s i t e - 1 1 from September 15 to October 30, 1971. S i t e S e l e c t i o n S e l e c t i o n of r a i n gauge s i t e s on the Research Forest was r e s t r i c t e d by the uneven f o r e s t cover and a need to l o c a t e gauges near s p e c i f i c p o i n t s . For most s i t e s , e x i s t i n g openings were used, c l e a r i n g dimensions being a l t e r e d where deemed necessary by c u t t i n g down a few t r e e s . For t h i s reason, opening s i z e s and shapes depart from the suggested i d e a l c i r c u l a r c l e a r i n g of one t r e e height diameter. Vegetation w i t h i n the openings was cut to a l e v e l at or below that of the gauge o r i f i c e . The only openings created s p e c i f i c a l l y f o r the study were those at s i t e s 9 and 10. Since l a r g e t r e e s had to be f e l l e d , the s i z e of these openings was kept to a minimum. F i e l d Data C o l l e c t i o n Procedures A l l gauges on the Research Forest were v i s i t e d on a weekly b a s i s to change c h a r t s and measure c o l l e c t e d r a i n f a l l . Depending on weather c o n d i t i o n s , from 6 to 9 hours were required to v i s i t a l l s i t e s . With the a s s i s t a n c e of Research Forest personnel, a d d i t i o n a l readings were taken from non-recording gauges a f t e r s e l e c t e d storm events. CHAPTER I I I STORM ANALYSIS IN RELATION TO OROGRAPHIC RAINFALL PRODUCTION I n t r o d u c t i o n This chapter i s concerned w i t h an examination of the c h a r a c t e r i s t i c s of orographic r a i n f a l l and the mechanisms r e s p o n s i b l e f o r i t s production i n the study area. The s p e c i f i c o b j e c t i v e s are to des c r i b e observed fe a t u r e s of orographic r a i n f a l l , i d e n t i f y the orographic processes i n v o l v e d and evaluate r e l a t i o n s h i p s between me t e o r o l o g i c a l storm c h a r a c t e r i s t i c s and orographic r a i n f a l l . The in f o r m a t i o n derived from t h i s examination provides the b a s i s f o r i n t e r p r e t i n g , e x p l a i n i n g and est i m a t i n g the magnitude and d i s t r i b u t i o n of orographic r a i n f a l l as covered i n Chapters IV and V. One approach to d e l i n e a t i n g mechanisms involved i n orographic r a i n f a l l production i s to r e l a t e the p r e c i p i t a t i o n to synoptic s c a l e features appearing on a synoptic weather map (Barry, 1967, 1970; Hutchinson, 1972; Jorgensen, 1963; Pedgley, 1970; Shaw, 1962; Wil l i a m s and Peck, 1962). The c o m p l e x i t i e s of weather patterns are u s u a l l y summarized by c l a s s i f y i n g synoptic maps i n t o a l i m i t e d number of c a t e g o r i e s . Barry (1967, 1970) has suggested that such c l a s s i f i c a t i o n may be based on any of the f o l l o w i n g f e a t u r e s : (1) a i r masses (e.g. f r o n t a l systems), (2) pressure p a t t e r n , (3) d i r e c t i o n of a i r flow, 29 30 (4) lar g e - s c a l e (mid-tropospheric) steering of synoptic features. However, a wide v a r i a t i o n i n actual weather conditions may occur with any given synoptic type (Barry, 1967; Lund 1963; Peck, 1972). When dynamic processes such as the occurrence or d i s t r i b u t i o n of orographic r a i n f a l l are considered, simple typing of synoptic weather patterns may be inadequate. For t h i s reason, i t i s necessary to examine r e l a t i o n -ships between dynamic processes and i n d i v i d u a l storm parameters i f v a r i a t i o n s within apparently s i m i l a r synoptic types are to be explained or accounted for (Holland and Crozier, 1973; Nord0, 1972; Peck, 1972; Sinik, 1972; Storebd, 1968; Storr and Ferguson, 1972). It i s possible that storm parameters which exhibit a strong r e l a t i o n s h i p with a given process may also tend to be associated with s p e c i f i c synoptic categories (Holland and Crozier, 1973; Nord0, 1972; U.S. Weather Bureau, 1961; Weaver, 1962). If such i s the case, then these synoptic categories w i l l be a useful guide to i d e n t i f y i n g storm s i t u a t i o n s l i k e l y to produce the weather condition of i n t e r e s t . Following a d e s c r i p t i o n of the storm data base, the r e s u l t s of d e t a i l e d storm analyses are presented. Correlations between storm meteorological parameters and indices of orographic r a i n f a l l were sought to determine which parameters are s i g n i f i c a n t l y r e l a t e d to orographic r a i n f a l l production i n the study area. The r e s u l t s of t h i s a n alysis provided the information required for subsequent attempts to c l a s s i f y storms on the basis of storm parameters relevant to orographic r a i n f a l l production. Storms were grouped or c l a s s i f i e d according to the occurrence of orographic processes, low l e v e l a i r f l o w d i r e c t i o n and synoptic type and r e l a t i o n s h i p s between these various categories and 31 storm parameters evaluated. The main objective of c l a s s i f y i n g storms was to f i n d a means of r e a d i l y i d e n t i f y i n g storms which produce orographic r a i n f a l l i n the study area. In p a r t i c u l a r , since higher r a i n f a l l s are generally more important f o r hydrologic purposes, i t would be h e l p f u l i f storms producing s u b s t a n t i a l orographic r a i n f a l l could be i d e n t i f i e d . To i l l u s t r a t e the d i f f i c u l t i e s involved i n c l a s s i f y i n g storms i n r e l a t i o n to orographic r a i n f a l l , two p a i r s of storms with s i m i l a r synoptic weather patterns but d i f f e r i n g orographic r a i n f a l l are compared. F i n a l l y , to give further i n s i g h t into the nature of orographic r a i n f a l l production i n the study area, some general comments and conclusions concerning observed r a i n f a l l c h a r a c t e r i s t i c s are given. Des c r i p t i o n of Storm Data Base Selection of Storms The charts from automatic recording gauges, described i n Chapter I I , were used to i d e n t i f y and select storm periods for further a n a l y s i s . For t h i s study, a storm was defined as a period of r a i n f a l l i n the Research Forest area during which the maximum t o t a l amount was greater than or equal to 0.5 inch (13 mm) and r a i n was continuous or i n t e r v a l s with no r a i n were l i m i t e d to 3 hours or l e s s . Individual storms were thus separated i n time by at l e a s t 3 hours. One exception was the a d d i t i o n of storm 36 which was separated from storm 37 by only 1.5 hours. The synoptic weather maps and the nature of the time pattern of r a i n f a l l indicated a d i s t i n c t change i n conditions causing the two r a i n f a l l events even though the time separation was very small. In most cases, the i n t e r v a l between separate r a i n storm events was much longer than 3 hours so that even s i t u a t i o n s involving a serie s of i n d i v i d u a l showers could be r e a d i l y i d e n t i f i e d as being associated with p a r t i c u l a r synoptic features. On the basis of the ab o v e . c r i t e r i a , a t o t a l of 42 storms were selected f or analyses. On the Northshore, 4 of these storms were not definable because the showery r a i n f a l l mostly bypassed t h i s area for these storms. Figure 4 shows the frequency d i s t r i b u t i o n of maximum storm r a i n f a l l t o t a l s f o r both the Research Forest and Northshore areas. 50 _ 40 RESEARCH FOREST > u z tu o 111 oc u. 30h 20 I0L 0 17 14 NUMBER OF STORMS I I 50 40 30 20 10 0 NORTHSHORE I 0 25 50 75 100 125 150 " 0 25 50 75 100 125 150 STORM RAINFALL TOTAL (mm) Figure 4 . Frequency d i s t r i b u t i o n s of maximum storm r a i n f a l l t o t a l s . S election of Storm Parameters From the l i t e r a t u r e and consideration of orographic r a i n f a l l theory and l o c a l topography, atmospheric and synoptic storm parameters were selected f or assessment of r e l a t i o n s h i p s with the magnitude and occurrence of orographic r a i n f a l l . The atmospheric v a r i a b l e s were taken or computed d i r e c t l y from radiosonde data. For 33 each storm, the s t a t i o n and p a r t i c u l a r ascent deemed most r e p r e s e n t a t i v e of storm c o n d i t i o n s during r a i n f a l l were s e l e c t e d . The derived data are summarized i n Appendix VI. For some storms data from more than one ascent were ex t r a c t e d to portra y d i f f e r i n g c o n d i t i o n s ahead of and behind f r o n t a l systems or during a p a r t i c u l a r l y long period of r a i n f a l l . Wind. 1. Mean wind components f o r the surface - 850 mb l a y e r f o r the f o l l o w i n g d i r e c t i o n s : southeast (230°), west (270°) and south (180°). 2. Wind components f o r the 850 mb l e v e l f o r the f o l l o w i n g d i r e c t i o n s : southwest (230°), west (270°) and south (180°). 3. Wind d i r e c t i o n s at the 850 and 700 mb l e v e l s and the mean f o r the surface - 850 mb l a y e r . 4. Wind speeds at the 850 and 700 mb l e v e l s . 5. V e r t i c a l wind shear f o r the f o l l o w i n g l a y e r s : 1000-850 mb, 850-700 mb, 1000-700 mb. Moisture. 1. P r e c i p i t a b l e water amounts f o r the f o l l o w i n g l a y e r s : 1000-850 mb, 850-700 mb, 1000-700 mb. 2. Mixing r a t i o value at 850 mb. 3. D i f f e r e n c e i n mixing r a t i o values between 700 and 850 mb. 4. Height of f r e e z i n g l e v e l . S t a b i l i t y . 1. Boyden i n s t a b i l i t y index: This index i s supposed to provide a 34 measure of the mean i n s t a b i l i t y i n the l a y e r below 700 mb. I t was developed f o r use i n assessing i n s t a b i l i t y i n the v i c i n i t y of f r o n t s (Boyden, 1963). The formula f o r the index S(BOY) i s : S(BOY) = Z - T - 200 (1) where Z i s the 1000-700 mb thickness i n decametres and T the 700 mb temperature i n degrees C. S(BOY) w i l l have a value of 94 f o r n e u t r a l i n s t a b i l i t y , greater than 94 f o r i n s t a b i l i t y and l e s s than 94 f o r s t a b i l i t y . For comparison w i t h other i n s t a b i l i t y i n d i c e s , values of 94 or l e s s were taken to i n d i c a t e s t a b l e a i r . P o t e n t i a l i n s t a b i l i t y index: This index was s e l e c t e d as an a l t e r n a t i v e i n d i c e of i n s t a b i l i t y i n the 1000-700 mb l a y e r . I t i s derived using a tephigram p l o t of temperature and humidity. An a i r p a r c e l i s l i f t e d from 1000 mb d r y - a d i a b a t i c a l l y to s a t u r a t i o n , then along the saturated adiabat to 700 mb. The index i s the magnitude of the d i f f e r e n c e between the temperature of the p a r c e l at 700 mb and that of the environment. I t i s p o s i t i v e i f the p a r c e l i s c o l d e r than i t s new environment, and negative i f warmer. From an examination of the data, an index value of 1.0 was a r b i t r a r i l y s e l e c t e d as i n d i c a t i n g n e u t r a l s t a b i l i t y . Lower values thus i n d i c a t e i n s t a b i l i t y and higher v a l u e s , s t a b i l i t y . Convective i n s t a b i l i t y index: This index i s a m o d i f i c a t i o n of the Showalter s t a b i l i t y index ( H a l t i n e r and M a r t i n , 1957) which i s g e n e r a l l y used to i n d i c a t e convective i n s t a b i l i t y or the p o s s i b i l i t y of shower development. I t was derived by l i f t i n g an a i r p a r c e l from 850 mb a d i a b a t i c a l l y to 600 mb. The index i s the magnitude of the d i f f e r e n c e i n 600 mb temperatures between the p a r c e l and the 35 environment. Empirical rules adopted for use of t h i s index were the same as f o r the Showalter index. Simply stated, index values greater than 3 in d i c a t e convective s t a b i l i t y , and l e s s than 3, convective i n s t a b i l i t y with showers probable. A number of other storm-related parameters were examined during the storm analyses. Some of t h i s data i s also tabulated i n Appendix VI to further i l l u s t r a t e the nature of i n d i v i d u a l storms. A d d i t i o n a l parameters included are: height of the base of the lowest s i g n i f i c a n t cloud layer, a i r mass type, excess storm duration computed as the dif f e r e n c e between Surrey Municipal H a l l and maximum Research Forest s t a t i o n duration, and maximum storm r a i n f a l l t o t a l s f o r the Research Forest and Northshore areas. Nature of Study Storms General comments on the climate of the study area are given i n Chapter I I . The information presented below i s s p e c i f i c a l l y r e l a t e d to storms observed during the study period. Comparison with long term p r e c i p i t a t i o n . Figure 5 gives a comparison of monthly p r e c i p i t a t i o n during the study period with long term average values for the Vancouver International Airport and Research Forest - Administration Building Stations (Atmospheric Environment Service). From t h i s data the study period included approximately equal periods of below and above average r a i n f a l l . An examination of shorter duration r a i n f a l l i s more revealing of the r e l a t i o n s h i p of storm amounts to longer term p r e c i p i t a t i o n . Table 1 compares maximum 24-hour r a i n -f a l l s for d i f f e r e n t return periods on a monthly and annual basis with 36 VANCOUVER INT V L AIRPORT 350| 300 RESEARCH FOREST - ADMIN. BLD6. long term average study period 0 N 1970 M J J A S 0 N 1971 S O N M J J A S O N 1970 1971 Figure 5. Comparison of long-term average and study period monthly p r e c i p i t a t i o n at Vancouver International A i r p o r t and Research Forest Administration B u i l d i n g . maximum 24-hour t o t a l s observed at the two stations during the study period (Atmospheric Environment Servic e ) . * In general, the pattern i s sim i l a r to that f o r monthly t o t a l s . Observed values were les s than 2-year return period amounts f or 7 of the 10 months on the Research Forest but only f o r 5 months at the Vancouver A i r p o r t . The highest observed d a i l y t o t a l on the Research Forest, 86.1 mm i n October 1971, has a monthly return period between 5 and 10 years, while that at the Vancouver A i r p o r t , 51.8 mm i n November 1971, has a 10-year return period value. On an annual basis, these maximum values are shown to be only of >vUnpub l i s tied data. 37 TABLE 1 MAXIMUM 24-HOUR RAINFALLS (mm) AT VANCOUVER INTERNATIONAL AIRPORT AND RESEARCH FOREST ADMINISTRATION BUILDING Month Vancouver I n t e r n a t i o n a l A i r p o r t Return Period 2-Yr. 5-Yr. 10-Yr. Observed Research Forest Admin. Bldg. Return P e r i o d 2-Yr. 5-Yr. 10-Yr. Observed 1970: Sept. 21.3 32.9 40.8 22.6 40.8 64.6 79.9 36.1 Oct. 28.7 40.8 49.4 17.8 53.0 76.2 91.4 29.7 Nov. 29.9 43.3 51.8 16.5 56.7 82.3 98.8 38.4 1971: May 15.2 21.9 26.2 13.2 27.4 40.8 50.0 13.0 June 16.5 26.2 32.9 25.1 30.5 45.7 55.5 40.6 J u l y 13.4 23.2 30.5 1.8 ' 29.9 49.4 62.2 24.1 Aug. 14.0 23.2 28.7 7.4 25.0 39.0 48.2 12.4 Sept. 21.3 32.9 40.8 31.0 40.8 64.6 79.9 39.4 Oct. 28.7 40.8 49.4 32.5 53.0 76.2 91.4 86.1 Nov. 29.9 43.3 51.8 51.8 56.7 82.3 93.8 77.0 Annual 46.2 57.4 64.5 _ 95.8 125.0 143.8 -average magnitude, being l e s s than the 2-year value f o r the Research Forest and a l i t t l e g r eater than the 2-year value at the Vancouver A i r p o r t . However, as i n d i c a t e d i n a l a t e r s e c t i o n , a maximum 6-hour i n t e n s i t y having a r e t u r n p e r i o d of 8-10 years was recorded on the Research Forest during a major storm. Storm synoptic f e a t u r e s . The storms examined included a wide v a r i e t y of synoptic weather p a t t e r n s , w i t h s e v e r a l storms combining more than one synoptic f e a t u r e r e l e v a n t to r a i n f a l l production. Approximately 50% of the storms were produced by occluded or o c c l u d i n g 38 fronts, depressions and low pressure troughs. A further 20% of these storms involved warm fronts or f r o n t a l waves d i r e c t l y , while 10% had r a i n f a l l occurring only behind cold or occluded fronts. The remaining 20% involved low pressure areas and troughs or upper disturbances with no d i s c e r n i b l e f r o n t a l involvement. The dominant a i r mass type observed was maritime polar, although maritime A r c t i c a i r was frequently present. Maritime T r o p i c a l a i r occurred during 6 storms at higher l e v e l s only. The s i g n i f i c a n t synoptic scale features can be summarized i n r e l a t i o n to the synoptic-scale low l e v e l wind patterns over the study area. 1. E a s t e r l y (1-159°) winds occurred when closed low pressure centres passed d i r e c t l y over or to the south of the study area. A wide d i r e c t i o n a l range was chosen for t h i s category because of the very small number of cases involved. 2. Southerly (160-200°) winds usually occurred when a sharp low pressure trough was situated near the coast to the west of the study area or when a closed low centre was located to the northwest. These pressure patterns were often associated with occluding f r o n t a l systems. If such troughs extend s u f f i c i e n t l y f a r south, a sustained flow of warm, stable, moist, maritime t r o p i c a l a i r can r e s u l t . 3. Southwesterly (201-250°) winds also occurred ahead of troughs and when closed lows were located to the northwest. They were a l s o t produced by a very broad trough over the eastern P a c i f i c , t h i s l a t t e r pressure pattern often being associated with f r o n t a l waves and flows of r e l a t i v e l y warm, moist, maritime t r o p i c a l or maritime polar a i r . 4. Westerly (251-290°) winds generally occurred when a zonal flow was established between a major high pressure centre over the P a c i f i c to 39 the southwest and a major low pressure centre f a r to the north. F r o n t a l waves and maritime p o l a r a i r were common w i t h t h i s flow p a t t e r n . Westerly winds were a l s o produced by a broad low pressure area s i t u a t e d over c e n t r a l B.G. to the n o r t h of the study area, and during the passage of troughs. 5. Northwesterly (291-360°) winds occurred to the west of sharp low pressure troughs or c l o s e d lows which moved eastward over the study area. Such troughs are o f t e n a s s o c i a t e d w i t h f r o n t a l systems. A northwest f l o w can a l s o be e s t a b l i s h e d by the presence of a strong, sharp high pressure r i d g e o f f s h o r e . A i r flow from the northwest tends to be c o o l , unstable and not too moist. L o c a l Wind Patt e r n s In mountainous areas, the t e r r a i n can s t r o n g l y modify lower-l e v e l meso-scale wind flow p a t t e r n s . For the study area, t h i s means that winds over the mountains may d i f f e r i n d i r e c t i o n from that indicated, by s y n o p t i c - s c a l e maps at l e a s t up to 850 mb and probably higher. One e f f e c t w i l l be to channel or d e f l e c t p r e v a i l i n g low l e v e l winds p a r a l l e l to the north-south o r i e n t e d v a l l e y s . For example, the most frequent wind d i r e c t i o n s recorded by the Spur-17 anemometer at 375 metres e l e v a t i o n on the U.B.C. Research Forest are e i t h e r from the SE to SW or from the NE. In the lower Fraser V a l l e y i t s e l f , surface winds during most storm s i t u a t i o n s tend to flow from the east to southeast as i n d i c a t e d by Vancouver A i r p o r t data. This e a s t e r l y flow plus a north to n o r t h - e a s t e r l y outflow from a d j o i n i n g v a l l e y s to the n o r t h (Boughner, et a l . , 1961) occurs i n response to pressure gradients e s t a b l i s h e d by 40 low pressure systems approaching from.the west. These surface winds are generally l i g h t but can be high under exceptionally strong pressure gradients. As recorded at the Vancouver A i r p o r t , westerly winds w i l l occur i n the wake of fast-moving cold fronts but tend to give way to e a s t e r l i e s within a few hours. One r e s u l t of low l e v e l e a s t e r l y outflow i n the Fraser V a l l e y i s the existence of a wedge of a i r extending southward from the mountains and over which p r e v a i l i n g upper winds must r i s e before they reach the mountains. The extent of the low l e v e l wedge can be assessed using wind data from Vancouver International A i r p o r t and Sand Heads Light Station, located 12.5 km to the southwest of the a i r p o r t (Figure 1). F i r s t l y , when Sand Heads winds are south to southeast while Vancouver A i r p o r t ' s winds are from the east, i t seems reasonable to assume that the wedge s t a r t s or ends near the ground between these two stations and increases i n depth towards the mountains to the north. Secondly, when easterly winds are recorded at both Sand Heads and Vancouver A i r p o r t , the low l e v e l outflow wedge can be assumed to extend southward beyond Sand Heads. This s i t u a t i o n generally occurs with a strong southerly flow a l o f t . T h i r d l y , when winds are from the south to southeast at both Sand Heads and Vancouver A i r p o r t , the low l e v e l outflow wedge i s either smaller and situated close to the mountains than Vancouver Airport or i s non-existent. Wind data from these two stations for selected storm periods are given i n Appendix XIII. Sources of V a r i a b i l i t y i n Storm Data In assessing r e l a t i o n s h i p s between observed r a i n f a l l and storm meteorological c h a r a c t e r i s t i c s , p o t e n t i a l v a r i a b i l i t y i n the representativeness of atmospheric data needs to be recognized. A primary consideration i s the representativeness for the study area of radiosonde data from Quillayute and Port Hardy ascents. A i r mass properties w i l l be modified as the a i r moves between these two stations and the study area. Changes w i l l occur due to in t e r a c t i o n s with the intervening land and sea surfaces and from dynamically induced changes with time. Assuming a mean wind speed of 15 m/s, an a i r parcel would take nearly 4 hours to t r a v e l d i r e c t l y from Quillayute to Vancouver and 7 hours from Port Hardy. In addition, data c o l l e c t e d by Brousaides and Morrissey (1971) indi c a t e that radiosonde humidity measurements were i n error because of improper exposure of the sensing element. They present one graph which indicates that measurements by study period sondes were probably about 7% lower below 500 mb than those taken by an improved device. Humidity values also showed a premature drop-off near the tops of clouds r e s u l t i n g from increased solar energy impinging on the sensor due to reduced o p t i c a l cloud thickness above the sonde. Single radiosonde ascents also provide a l i m i t e d sample of storm conditions both i n space and time. Either s t a t i o n may not be properly positioned r e l a t i v e to the synoptic feature producing p r e c i p i t a t i o n . Radiosonde observations are taken every 12 hours. This long time i n t e r v a l may r e s u l t i n c r i t i c a l storm periods being missed. Assessment of comparative r e l a t i o n s h i p s between storm para-meters and orographic r a i n f a l l requires s e l e c t i o n of data from single radiosonde ascents to represent t o t a l storm conditions for most storms. This procedure ignores the v a r i a t i o n s i n atmospheric conditions and r a i n f a l l production that can occur during storm events. Moreover, 42 different processes and synoptic features may combine to produce the total or net orographic effect for some storms but act separately in others. The use of simplified data to represent overall storm conditions can thus introduce a degree of variation or uncertainty which could tend to obscure real relationships. Assessment of Orographic Rainfall Production  Definitions of Orographic Influences A fundamental requirement for rainfall production is rising air. As air rises it cools, resulting in condensation of water vapour and, if atmospheric conditions are appropriate, precipitation. Rainfall can thus be classified according to the mechanisms causing air to rise; namely, convergence, convectional and orographic types (Bonacina, 1945; Douglas and Glasspoole, 1947). Convergence rainfall results from large-scale convergence of air streams in low pressure areas or depressions, low pressure troughs and along fronts. It is a product of the dynamics of atmospheric circulations largely undisturbed by surface topography. Convectional rainfall is due to instability in the atomosphere which results in air rising of its own accord. Orographic rainfall results from the influence of topography as described below. Mountainous terrain may receive increased precipitation as a result of several different physical processes: (1) additional condensation caused by lifting or deflection of moist, stable air aloft, (2) triggering of vertical convection in unstable air, (3) reduced evaporation of rainfall over higher ground, (4) hindering of the move-ment of small depressions, fronts and winds. Orographic rainfall is 43 usually defined i n terms of process (1) as the r a i n due d i r e c t l y to the l i f t i n g of moist a i r over an orographic b a r r i e r such as a mountain range (Huschke, 1959; Fletcher, 1951). Bonacina (1945), however, preferred to include a l l processes and define orographic r a i n as " r a i n caused or i n t e n s i f i e d i n various ways by the presence of high ground." In t h i s report, the term orographic r a i n f a l l i s used i n the more general sense of Bonacina and the basic orographic influences defined as follows: Oreigenic u p l i f t . A i r may be forced upward by d i r e c t l i f t i n g up a mountain slope, by f u n n e l l i n g up a converging v a l l e y , or by moving over a rougher ground surface. If the a i r i s s u f f i c i e n t l y moist, the r e s u l t w i l l be condensation of moisture or cloud droplets and p r e c i p i t a t i o n a d d i t i o n a l to any that may already be present. If the a i r i s stable, two s i t u a t i o n s may occur: 1. A shallow cloud layer may form from which only d r i z z l e i s l i k e l y to r e s u l t as shown by Mason (1962) and Pedgley (1970). 2. The moisture content of e x i s t i n g rain-bearing clouds may be enhanced or a separate cloud layer formed beneath rain-bearing clouds. In either case, the e x i s t i n g r a i n scours or sweeps out a portion of the orographically induced condensation thereby increasing r a i n f a l l i n t e n s i t y (Pedgley, 1967, 1970, 1971; Sawyer, 1952, 1956; StorebS, 1968). Bergeron (1960, 1965) r e f e r s to the cloud with general p r e c i p i t a t i o n as the " r e l e a s e r " or "seeder" part of the cloud system, and the orographically produced cloud condensation as the "spender" or "feeder" part. Both parts must be present to ensure e f f e c t i v e production of orographic r a i n . Pedgley (1970) has calculated that heaviest orographic rains are produced by scouring of cloud by large 44 d r i z z l e and small r a i n drops only (0.5-1.0 mm r a d i u s ) . Smaller d r i z z l e drops are c a r r i e d away h o r i z o n t a l l y before they can grow much; larger raindrops f a l l so quickly they reach cloud base without growing s u b s t a n t i a l l y . Major orographic r a i n f a l l thus occurs as a r e s u l t of increased i n t e n s i t y of r a i n i n dynamically produced r a i n areas. Bergeron (1965) has termed t h i s process "oreigenic" and Decker (1967) suggests that t h i s term be used to designate clouds, p r e c i p i t a t i o n and atmospheric processes which owe t h e i r genesis to the mountains underneath the a i r flow. Furthermore, the percentage of t o t a l storm r a i n f a l l r e s u l t i n g from the orographic l i f t i n g process may properly be defined as the "orographic component," with the remainder being c a l l e d the "non-orographic component" (Fletcher, 1951). In essence, the three terms orographic r a i n f a l l , oreigenic r a i n f a l l and orographic component are synonymous and could be used interchangeably. However, i n t h i s report, the term "oreigenic u p l i f t " i s applied to the d i r e c t l i f t i n g of moist, stable a i r over a mountain b a r r i e r . I n s t a b i l i t y t r i g g e r i n g . The atmosphere i s unstable i f a parcel of a i r displaced from i t s i n i t i a l p o s i t i o n continues to r i s e independently of the a c t i o n t r i g g e r i n g i t s i n i t i a l displacement (Haltiner and Martin 1957). For the purposes of t h i s study, two types of i n s t a b i l i t y are defined on the basis of the h o r i z o n t a l scale of both the process and r e s u l t i n g p r e c i p i t a t i o n : namely, convective and p o t e n t i a l . 1. The i n s t a b i l i t y i s considered to be oonveotive i f i t r e s u l t s i n formation of i n d i v i d u a l cumulus-type clouds and showers up to a few kilometres i n h o r i z o n t a l extent. This type of i n s t a b i l i t y may be 45 triggered by forced orographic u p l i f t of airflow, d i f f e r e n t i a l surface heating of mountain slopes or induced turbulence such as occurs when a i r moves over a rougher ground surface. 2. An en t i r e layer of a i r i s said to be potentially unstable i f i t i s unstable a f t e r l i f t i n g , regardless of i t s i n i t i a l state (Haltiner and Martin, 1957). Orographic l i f t i n g can be the mechanism that t r i g g e r s or releases the inherent i n s t a b i l i t y , which produces l a r g e -scale overturning and mixing of the unstable layer. For t h i s study, the r e s u l t i n g p r e c i p i t a t i o n must also be widespread for the process to be termed p o t e n t i a l i n s t a b i l i t y t r i g g e r i n g . Reduced evaporation. Rain f a l l i n g i n unsaturated a i r beneath a cloud base w i l l be subject to evaporation (Bergeron, 1949). In the extreme, with l i g h t r a i n , high cloud base and r e l a t i v e l y dry a i r , a l l the r a i n leaving the cloud may evaporate before reaching the ground. Rain occurring over elevated mountain slopes w i l l suffer l e s s evaporation than that over lower elevation v a l l e y bottoms or adjacent f l a t land because of the shorter distance of f a l l from the cloud base. Hence, higher r a i n f a l l i n t e n s i t i e s may be experienced over higher ground. The r e l a t i v e e f f e c t on r a i n f a l l d i s t r i b u t i o n can be almost exactly the same as that due to oreigenic l i f t i n g and could be termed an "apparent" oreigenic e f f e c t . Hindered movement of depressions, fronts and winds. The presence of large mountain chains can impede the motion of small depressions and f r o n t a l systems (Bonacina, 1945). One e f f e c t of t h i s process i s to prolong the duration of r a i n f a l l over and near the 46 mountains. Any, a l l or none of the other three orographic influences could be in operation during such a prolonged storm. Mountains may also divert wind flow. Bergeron (1949, 1960) has described a situation in which topography forced air to rise off the coast of Norway. A south-easterly flow of stable air was deflected away from the mountains to meet the direct south-easterly current as a north-easterly flow. The result was an "orographically conditioned convergence" which produced a strong updraft along the coast, extra low-level condensation, and a consequent intensification of rainfall. Topography can also change the direction of movement of convective shower clouds, and thus the distribution of precipitation, by steering lower level winds along valleys or parallel to major ridges. Excess storm duration. Storm rainfall over the mountains can be prolonged over that on adjacent lowlands in cases where atmospheric moisture content is decreasing but orographic lifting at higher elevations is able to maintain precipitation production. Thus excess storm duration which is actually a result of orographic processes is one of the reasons why mountains receive more total rainfall than adjacent low level ground. Another conceivable situation that could result in differences in mountain-valley precipitation rates in the absence of orographic processes is that in which a front and its associated cloud system are aligned parallel to the mountain barrier. Variations in rainfall intensity with distance away from the front, due strictly to storm dynamics, could produce an apparent orographic effect. 47 Determining Occurrence of  Orographic Processes i n Study Storms The f o l l o w i n g c r i t e r i a were used to determine the occurrence of orographic processes during study storms. These c r i t e r i a are based on observed temporal r a i n f a l l p atterns and a i r mass s t a b i l i t y . On the b a s i s of c o r r e l a t i o n a n a l y s i s r e s u l t s described i n a l a t e r s e c t i o n , the Boyden i n s t a b i l i t y index was chosen to assess i n s t a b i l i t y . A l l c r i t e r i a must be met f o r a storm to be assigned to a given category. Major o r e i g e n i c u p l i f t . 1. S t a b l e a i r mass w i t h Boyden i n s t a b i l i t y index l e s s than or equal to 94 w i t h no unstable l a y e r s present. 2. R a i n f a l l continuous over the mountains. 3. Mean r a i n f a l l i n t e n s i t y at the Research Forest s t a t i o n r e g i s t e r i n g the maximum r a i n f a l l r a t e exceeds that a t the Vancouver I n t e r n a t i o n -a l A i r p o r t by 0.7 mm/hr or more (see f o l l o w i n g s e c t i o n on evaporation). 4. T o t a l storm r a i n f a l l at the mountain s t a t i o n w i t h the highest t o t a l exceeded that at the v a l l e y index s t a t i o n by at l e a s t 50%. 5. R a i n f a l l at the mountain s t a t i o n w i t h the highest storm t o t a l exceeded that at the v a l l e y index s t a t i o n f o r at l e a s t 80% of t o t a l storm d u r a t i o n at the mountain s t a t i o n . Minor o r e i g e n i c u p l i f t . 1. Stable a i r mass w i t h Boyden i n s t a b i l i t y index l e s s than or equal to 94 or an a i r mass w i t h a t l e a s t the lowest 150 mb s t a b l e . 2. R a i n f a l l continuous over the mountains. 48 Mean r a i n f a l l i n t e n s i t y at the Research Forest s t a t i o n r e g i s t e r i n g the maximum r a i n f a l l r a t e exceeds that at the Vancouver I n t e r n a t i o n a l A i r p o r t by 0.7 mm/hr or more (see f o l l o w i n g s e c t i o n on evaporation). T o t a l storm r a i n f a l l at the mountain s t a t i o n w i t h the highest t o t a l exceeded that at the v a l l e y index s t a t i o n by l e s s than 50%. R a i n f a l l a t the mountain s t a t i o n w i t h the highest storm t o t a l exceeded that at the v a l l e y index s t a t i o n f o r l e s s than 80% of t o t a l storm d u r a t i o n a t the mountain s t a t i o n . P o t e n t i a l i n s t a b i l i t y t r i g g e r i n g . Unstable a i r mass w i t h Boyden i n s t a b i l i t y index greater than or equal to 94 w i t h unstable l a y e r s present. R a i n f a l l continuous over the mountains. Mean r a i n f a l l i n t e n s i t y at the Research Forest s t a t i o n r e g i s t e r i n g the maximum r a i n f a l l r a t e exceeds that at the Vancouver I n t e r n a t i o n a l A i r p o r t by 0.7 mm/hr or more (see f o l l o w i n g s e c t i o n on evaporation). Convective i n s t a b i l i t y t r i g g e r i n g . Unstable a i r mass w i t h Boyden i n s t a b i l i t y index greater than or equal to 94 -but w i t h an unstable l a y e r at l e a s t 200 mb deep s t a r t i n g at or below 850 mb. R a i n f a l l over the mountains and Fraser V a l l e y d i s c o n t i n u o u s ; that i s , occurs i n bursts of r a i n separated by periods up to 3 hours of no r a i n or d r i z z l e w i t h i n t e n s i t i e s l e s s than or equal to 0.7 mm/hr (see s e c t i o n on evaporation). 3. Total storm rainfall at the Vancouver International Airport or Surrey Municipal Hall station is less than 40% of that at the mountain station with the highest storm total. This-criterion was chosen to distinguish between.situations involving triggering of showers mainly over the mountains versus situations involving more widespread shower occurrence involving other triggering mechanisms. Evaporation. In order to assess whether a difference in rainfall between mountain and Fraser Valley stations was due to a real orographic uplift process or simply to evaporation, some estimate of evaporation rates is necessary. Evaporation of rain drops falling through a layer of unsaturated air is a function of water vapour deficit, rain drop size distribution and f a l l velocity of the drops. Direct computation of evaporation rates is thus a complicated procedure beyond the scope of this thesis. However, Hardy (1963) has derived a graph which gives the rate of evaporation from Marshall-Palmer (1948) rain drop size-distributions as a function of rainfall intensity for several water vapour deficits (Figure 6). By assuming reasonable upper limits for rainfall intensity and water vapour deficit in the study area, this graph can be used to establish an approximate upper limit for evaporation rates between Vancouver International Airport and the Research Forest. If the difference in rainfall intensity between these two areas exceeds this upper limit for evaporation, then a real orographic uplift process can be assumed. Showalter (1971) has proposed the following formula for computing the water vapour deficit, which he calls evaporative 50 E JC \ 0 10 20 30 40 50 60 70 80 90 100 RAIN INTENSITY (mm/ hr) Figure 6. Evaporation of r a i n at several water vapour d e f i c i t s (Hardy, 1963) capacity Ec, of unsaturated a i r Ec = p«At /(7T ) W W (2) where Ec i s i n g/mJ, p the atmospheric pressure i n mb, At =(T-T ) the w w wet-bulb depression i n °C, T the wet-bulb temperature i n °K and T the w ambient air. temperature i n °K. Using t h i s formula, mean water vapour d e f i c i t s were calculated for each storm for the layer between Vancouver A i r p o r t and 580 m a l t i t u d e , taken as a mean elevation for the northern part of the Research Forest, or between cloud base and Vancouver Ai r p o r t when i t was below 580 m. The r e s u l t i n g data are given i n Appendix VI. The maximum computed mean layer value for Ec i s 1.27 g/m3. A maximum r a i n f a l l i n t e n s i t y must also be chosen. For study storms, the maximum observed 6-hour mean r a i n f a l l i n t e n s i t y on the Research Forest was 11 mm/hr. Based on data for the same storm plus 51 intensity-duration-frequency curves f o r P i t t Polder (Atmospheric Environment Service)* adjacent to the centre portion of the Research Forest where t h i s i n t e n s i t y was recorded, t h i s value appears to have a return period of about 8-10 years. This i n t e n s i t y seems to be a reasonable one to adopt since i t i s not only the maximum recorded during the study period but also represents an unusually high r a i n f a l l event. 3 Using these values of 1.27 g/m for water vapour d e f i c i t and 11 mm/hr for r a i n f a l l i n t e n s i t y , an evaporation rate of about 1.2 mm/hr/km i s obtained from Hardy's graph (Figure 6). For the 580 m layer between Vancouver International A i r p o r t and the Research Forest, the amount of evaporation at t h i s rate would be 0.7 mm/hr. Hence, a diff e r e n c e i n r a i n f a l l i n t e n s i t y between these two areas which equals or exceeds 0.7 mm/hr i s considered to represent a r e a l orographic u p l i f t e f f e c t . For the study storms, most water vapour d e f i c i t s are well below 3 the maximum computed mean layer value of 1.27 g/m and a l l mean r a i n f a l l i n t e n s i t i e s are also below 11 mm/hr. Hardy's graph (Figure 6) indicates that corresponding evaporation rates would have been small and on the order of p o t e n t i a l sources of error i n r a i n f a l l measurement. Hence, for the p r a c t i c a l purposes of t h i s t h e s i s , evaporation i s not given further consideration beyond use of the 0.7 mm/hr value to define occurrence of oreigenic u p l i f t and i n s t a b i l i t y t r i g g e r i n g processes. Derivation of Orographic  R a i n f a l l Indices In order to assess r e l a t i o n s h i p s between r a i n f a l l and other *Unpublished intensity-duration-frequency data. 52 storm c h a r a c t e r i s t i c s , some measure of storm r a i n f a l l i s required. The following indices of orographic r a i n f a l l were derived f o r t h i s purpose: DR - derived for the Research Forest area by subtracting the storm t o t a l f o r Surrey Municipal H a l l from the maximum recorded storm t o t a l at any s i t e on the Research Forest. A s i m i l a r index was derived for the Northshore area by subtracting storm t o t a l s for Vancouver International A i r p o r t from the maximum recorded storm t o t a l s at the Northshore s t a t i o n s . DI - derived i n a manner s i m i l a r to that for storm t o t a l data using mean 4- to 6-hour r a i n f a l l i n t e n s i t i e s for a representative period of each storm. The 6-hour i n t e n s i t i e s were computed where possible, but 4- and 5-hour values were used because of di f f e r e n c e s between Research Forest and Northshore data and to obtain the largest reasonable sample s i z e . This index was computed f o r a t o t a l of 29 storms. DR/R - derived by d i v i d i n g the Research Forest and Northshore DR values by the respective maximum storm t o t a l s and expressing the r e s u l t as a percent. Dl/I - derived by d i v i d i n g the Research Forest and Northshore DI values by the respective maximum 4- to 6-hour i n t e n s i t i e s and expressing the r e s u l t as a percent. The s e l e c t i o n of the above indices was based on a number of considerations. Of primary concern was the concept of estimating r a i n -f a l l over the mountains by adding a computed orographic component to an amount recorded at an accessible s t a t i o n near the mountains (see Chapter IV). I d e a l l y the v a l l e y s t a t i o n should be located along a l i n e normal to the mountain b a r r i e r and passing through the area of i n t e r e s t , and should be free from orographic influence. An a d d i t i o n a l c r i t e r i o n for s e l e c t i o n of the v a l l e y stations was the need for•continuously recorded storm r a i n f a l l i n t e n s i t y data. I t was assumed that s i m i l a r synoptic weather conditions prevailed over both the Research Forest and Northshore during storm periods, and that v a r i a t i o n s i n storm parameters between these two areas were small. In the study area, the normal to the mountains l i e s i n approximately a SW-SSW to NE-NNE d i r e c t i o n . For the Northshore area indices the Vancouver International A i r p o r t s t a t i o n most nearly f u l f i l l s the above c r i t e r i a . The pattern of annual p r e c i p i t a t i o n i n the Vancouver area (Wright and Trenholm 1969) suggests that orographic influences on r a i n f a l l at t h i s s t a t i o n are small or n e g l i g i b l e f o r most storms. The Surrey Municipal H a l l Station, selected for the Research Forest area indices, does not appear to be quite as free from orographic influences. Storm r a i n f a l l t o t a l s are generally higher than at Vancouver A i r p o r t and annual p r e c i p i t a t i o n shows a trend of increasing values toward the east up the Fraser V a l l e y . Part of the increase i n p r e c i p i t a t i o n between Vancouver A i r p o r t and Surrey Municipal H a l l could be due to l o c a l orographic e f f e c t s including production of f r i c t i o n a l v e r t i c a l v e l o c i t i e s by a i r passing from the smooth ocean over the rougher land surface and l i f t i n g over the escarpment to the southwest of Surrey Municipal H a l l . For i n d i v i d u a l storms, areal v a r i a t i o n s i n convergence r a i n f a l l could also account for some of the d i f f e r e n c e . Thus, the orographic influences at t h i s s t a t i o n due to the mountains to the north would appear to be small for most storms. 54 The indices f or the Research Forest and Northshore areas might also represent d i f f e r e n t portions of the orographic component from another aspect. Because the Seymour Dam s t a t i o n on the Northshore i s further north than the northernmost Research Forest Station, i t may r e g i s t e r the maximum storm r a i n f a l l on an area basis more frequently than stations on the Research Forest. The storm t o t a l indices, DR and DR/R, were selected i n order to use the maximum number of storms i n the an a l y s i s . They represent the net e f f e c t of a l l orographic processes that occur during a storm, integr a t i n g the e f f e c t s of any changes i n winds, a i r mass moisture and s t a b i l i t y that happen to occur. The i n t e n s i t y indices, DI and Dl/ I , were selected with the objective of obtaining a more s p e c i f i c measure of the major orographic process occurring i n each storm. These indices are also more d i r e c t l y r e l a t e d to the modelling procedures described i n Chapter IV. The indices DR and DI are absolute differences and could be expected, on the basis of physical reasoning, to be more c l o s e l y related to other storm c h a r a c t e r i s t i c s than the r e l a t i v e indices DR/R and D l / I . However, these l a t t e r two indices were derived on the chance that they might be useful f o r inter-storm comparisons. Computed index values are tabulated i n Appendix VI. To i l l u s t r a t e the v a r i a t i o n i n d i s t r i b u t i o n between Northshore and Research Forest areas, the frequency of occurrence of DR and DI index values for the two areas are presented i n Figure 7. 55 R E S E A R C H F O R E S T NORTHSHORE 30| o 20| UJ ~D UJ I OC u. <S?30 " 20 UJ 2 IO oc (a) Intensity index DI (mm/hr) R E S E A R C H F O R E S T ~60 ..o o;50 >-40 o § 2 0 w ~ cc 10 0 20 40 60 80 100 120 - 6 0 ^ 5 0 >40 S 3 0 h O20H UJ £ >° 0 NORTHSHORE 20 40 60 80 100 120 (b) Storm t o t a l index DR (mm) Figure 7. Frequency d i s t r i b u t i o n s of absolute orographic r a i n f a l l i n d i c e s . 56 Relating Orographic R a i n f a l l Production to  Storm C h a r a c t e r i s t i c s A number of approaches were taken to assess possible r e l a t i o n -ships between orographic r a i n f a l l production, as represented by the orographic r a i n f a l l indices described above, and the various storm c h a r a c t e r i s t i c s . F i r s t , simple c o r r e l a t i o n analyses were c a r r i e d out between the 23 selected storm parameters, described previously, and these in d i c e s . Second, an attempt was made to group or c l a s s i f y storms on the basis of three categories: namely, occurrence of orographic processes, low l e v e l a i r f l o w d i r e c t i o n and synoptic weather types. An analysis of variance procedure was used to test for s i g n i f i c a n t r e l a t i o n s h i p s between orographic r a i n f a l l i n d i c e s , storm parameters shown by the c o r r e l a t i o n analyses to have a s i g n i f i c a n t a s s o c i a t i o n with the r a i n f a l l indices, and each of the above three categories. The Student's t - t e s t was then used to assess the s i g n i f i c a n c e at the 5% l e v e l of diff e r e n c e s between mean storm parameter values for the sub-groups of storms within each of the three main categories. F i n a l l y , two storm pa i r s are compared to further i l l u s t r a t e i n s p e c i f i c cases the va r i a t i o n s that can occur i n orographic r a i n f a l l production f o r storms with s i m i l a r synoptic weather patterns. Correlations Between Storm  Parameters and Orographic  R a i n f a l l Indices Simple c o r r e l a t i o n c o e f f i c i e n t s between the 23 storm parameters and a l l of the derived orographic r a i n f a l l indices were computed. For comparison of Research Forest and Northshore r e s u l t s , only data from the 38 storms a v a i l a b l e f or the Northshore area were used for co r r e l a t i o n s 57 involving the storm t o t a l indices DR and DR/R. To compare storm t o t a l with i n t e n s i t y index (DI and Dl/I) r e s u l t s , analyses were also performed for DR and DR/R using data from the same 29 storms for which orographic r a i n f a l l i n t e n s i t y indices were derived. The general c r i t e r i o n adopted for s e l e c t i n g s i g n i f i c a n t storm parameters was that the i n d i v i d u a l parameter show a s i g n i f i c a n t c o r r e l a t i o n at the 5% l e v e l f or both the Research Forest and Northshore areas for ei t h e r the storm t o t a l or i n t e n s i t y index. S i g n i f i c a n t c o r r e l a t i o n s f o r both indic e s were taken as further supportive evidence of r e a l r e l a t i o n s h i p s . Results. The c o r r e l a t i o n c o e f f i c i e n t s between the indices and storm parameters are l i s t e d i n Tables 2 and 3 f o r the r e l a t i v e and absolute indices, r e s p e c t i v e l y . The numbers i n brackets r e f e r to the number of storms used i n the a n a l y s i s . A comparison of data i n these two tables shows that the absolute indices DR and DI have a higher number of s i g n i f i c a n t c o r r e l a t i o n s with storm parameters than the r e l a t i v e indices DR/R and D l / I . This r e s u l t confirms the expectation that the absolute indices would show a closer r e l a t i o n s h i p than the r e l a t i v e values. Consequently, with the exception of the occasional reference to DR/R and DI/I, only c o r r e l a t i o n s and storm c l a s s i f i c a t i o n s involving DR and DI w i l l be discussed i n the remainder of t h i s chapter. The c o r r e l a t i o n c o e f f i c i e n t s between storm t o t a l and i n t e n s i t y indices f or the Research Forest and Northshore, re s p e c t i v e l y , were 0.76 and 0.64 between DR and DI, and 0.90 and 0.75 between DR/R and DI/I. These c o r r e l a t i o n s are r e l a t i v e l y high, which suggests that one major orographic process probably dominated most i n d i v i d u a l storms and that the periods selected for computation of the i n t e n s i t y indices were 58 TABLE 2 CORRELATION COEFFICIENTS BETWEEN STORM PARAMETERS AND RELATIVE OROGRAPHIC RAINFALL INDICES Storm Research Forest Northshore Parameter DI/I(29) DR/R(29) DR/R(38) DI/K29) DR/R(29) DR/R(38) VSW(S-85) .43* .45* .36* .34 .47* .43* VW(S-85) .42* .35 .15 .14 .13 .07 VS(S-85) -.01 .02 .11 .18 .30 .31* VSW(85) .22 .27 .12 .18 .34 .28 VW(85) .39* .37* .16 .12 .15 .07 VS(85) -.15 -.11 -.03 .02 .18 .19 WD(S-85) •!5 .12 -.03 -.11 -.19 -.22 WD(85) .19 .18 .02 -.08 -.10 -.15 WD(70) .05 .06 -.06 -.14 -.16 -.21 WS(85) .08 .06 -.01 .11 .21 .13 WS(70) -.15 -.16 -.24 - . 1 3 .01 .02 SH(100-85) -.03 -.01 -.13 -.09 .06 -.03 SH(85-70) -.13 -.12 -.16 .06 .02 .00 SH(100-70) -.11 -.12 -.18 -.13 -.06 -.08 MR(85) .34 .33 .29 -.31 .17 .09 DMR(85-70) .50* .51* .39* .45* .34 .18 PW(100-85) .31 .26 .24 .23 .03 -.01 PW(85-70) .09 .15 .12 .21 .11 .00 PW(100-70) .22 .22 .20 .24 .06 .00 FL -.17 -.21 -.19 -.28 -.07 -.05 S(BOY) .57* .59* .33* .57* .41* .23 S(POT) -.42* -.42* -.31* -.34 -.23 -.21 S(CONV) -.44* -.45* -.27 -.42* -.29 -.23 * S i g n i f i c a n t at the 5% l e v e l . 59 TABLE 3 CORRELATION COEFFICIENTS BETWEEN STORM PARAMETERS AND ABSOLUTE OROGRAPHIC RAINFALL INDICES Storm Research Forest Northshore Paramter DI(29) DR(29) DR(38) DI(29) DR(29) DR(38) VSW(S-85) .57* .63* .60* .43* .66* .66* VW(S-85) .40* .33 .23 .17 .20 .24 VS(S-85) .16 .27 .31* .25 .47* .48* VSW(85) .42* .49* .47* .30 .62* . 64* VW(85) .46* .42* .36* .18 .32 .34* VS(85) .01 .11 .15 .13 .37* .39* WD(S-85) .03 .00 -.04 -.14 -.21 -.17 WD(85) .10 .09 .06 -.03 -.11 -.06 WD(70) .05 .16 .15 -.06 .03 .08 WS(85) .29 .26 .28 .26 .37* .49* WS(70) .11 .23 .18 .05 .39* .38* SH(100-85) .21 .23 .26 .04 .36* .43* SH(85-70) -.02 .06 .12 .04 .15 .28 SH(100-70) .11 .17 .22 -.02 .20 .36* MR(85) .58* .45* .36* .40* .21 .18 DMR(85-70) .44* .22 .07 .35 .06 -.09 PW(100-85) .53* .40* .30 .25 .13 .06 PW(85-70) .43* .45* .51* .26 .33 .39* PW(100-70) .51* .45* .44* .27 .24 .23 FL -.46* -.59* -.54* -.32 -.40* -.41* S(BOY) .43* .26 -.10 .39* .12 -.22 S(POT) -.12 .07 .30 -.08 .18 .41* S(CONV) -.31 -.12 .09 -.25 -.02 .17 * S i g n i f i c a n t at the 5% l e v e l . 60 indeed r e p r e s e n t a t i v e f o r the 29 storm sample. A comparison of DR (29) and DR (38) data i n Table 3 i n d i c a t e s that r e s u l t s obtained using the 29 storms are reasonably r e p r e s e n t a t i v e of those derived using the 38 storms. Hence, the r e s u l t s c i t e d i n the remainder of the report f o r the DR index w i l l r e f e r to DR (38) only. Since the c o r r e l a t i o n c o e f f i c i e n t s i n d i c a t e only the degree of r e l a t i o n s h i p between two v a r i a b l e s , a number of graphs showing v a r i a t i o n s i n magnitude between the i n d i c e s and s e l e c t e d parameters are a l s o given i n F i g u r e s 8 and 9 f o r Research Forest data. These diagrams po r t r a y the maximum, minimum and mean index values f o r d i f f e r e n t ranges of parameter values and i n d i c a t e the number of storms used i n each c a l c u l a t i o n . The c o r r e l a t i o n r e s u l t s are discussed below i n r e l a t i o n to wind, moisture and s t a b i l i t y parameters. 1. Wind parameters: The parameter w i t h the strongest o v e r a l l c o r r e l a t i o n was the wind component parameter VSW(S-85), which was the only parameter to be s i g n i f i c a n t f o r both DR and DI i n d i c e s f o r both the Research Forest and Northshore. This f i n d i n g confirms f o r the study area the t h e o r e t i c a l c o n s i d e r a t i o n that the low l e v e l wind component normal to the mountain b a r r i e r i s the c r i t i c a l f a c t o r f o r orographic r a i n f a l l , given a s u f f i c i e n t supply of moisture. The s i m i l a r parameter VSW(85), r e p r e s e n t i n g the southwest wind component at a higher mean l e v e l , was a l s o s i g n i f i c a n t f o r DR (both areas) but only the Research Forest f o r DI, although the c o r r e l a t i o n c o e f f i c i e n t s were lower. The c o r r e l a t i o n between VSW(S-85) and VSW(85) i s 0.91 f o r the 38 storms. Figure 8 i l l u s t r a t e s the trend of i n c r e a s i n g mean index values w i t h i n c r e a s i n g magnitude of 61 DR x UJ o 7 6 - £ 5 > \ < b 5 3 c/j «. o UJ <* NUMBER OF STORMS -_ 5 -- 9 •- --- m 10 --f l- -0-5 5-8 9-13 1^3 VSW(S-85) (m/s) 0-5 5-9 9-13 >I3 Figure 8. Absolute orographic r a i n f a l l i n d i c e s f o r Research Forest versus VSW(S-85). VSW(S-85). One s a l i e n t f e a t u r e of these graphs i s the markedly higher mean orographic r a i n f a l l component f o r wind speeds exceeding 13 m/s. Another acceptable wind parameter was the wind component parameter VS(S-85) which had s i g n i f i c a n t c o r r e l a t i o n s w i t h the DR index only. The c o e f f i c i e n t s were lower than those f o r VSW(S-85). This r e s u l t suggests that the t e r r a i n i s e f f e c t i v e i n forced l i f t i n g of s o u t h e r l y winds f o r at l e a s t some of the storms, probably as a r e s u l t of c h a n n e l l i n g up the north-south o r i e n t e d v a l l e y s . In view of the v a r i e d t e r r a i n aspects or exposures, i t i s s u r p r i s i n g that t h i s parameter d i d not a l s o c o r r e l a t e more h i g h l y w i t h the DI index as w e l l . The s i g n i f i c a n t c o r r e l a t i o n s w i t h VW(85) i n d i c a t e a l o c a l importance of t e r r a i n w i t h a more w e s t e r l y aspect, p a r t i c u l a r l y i n 62 the Research Forest area. The non-significance of the actual wind d i r e c t i o n and wind speed values further underlines the s e l e c t i v e way i n which the t e r r a i n i n t e r a c t s with the wind, r e s u l t i n g i n e f f e c t i v e forced l i f t i n g of the wind component normal to the general o r i e n t a t i o n of the l i f t i n g b a r r i e r , or f u n n e l l i n g winds aligned p a r a l l e l to indented v a l l e y s . This f i n d i n g i s p a r t i c u l a r l y s i g n i f i c a n t i n that the study area mountain b a r r i e r i s f a r from uniform as noted i n Chapter I I . 2. Moisture parameters: The parameter PW(85-70) was s i g n i f i c a n t for DR (both areas) but only the Research Forest for DI. In contrast, the parameter MR(85) was s i g n i f i c a n t f o r DI (both areas) but only DR for the Research Forest. The graphs i n Figures 9a and 9b show generally increasing index values with increasing moisture contents of the a i r , although the trends are not uniform or l i n e a r . These r e s u l t s i l l u s t r a t e that orographic r a i n f a l l production i n the study area i s indeed s i g n i f i c a n t l y r e l a t e d to or dependent on the amount of a v a i l a b l e atmospheric moisture i n the layer of saturated a i r ; that i s , near the cloud base or lower l e v e l of l i f t i n g (350 mb) and within the layer of expected maximum l i f t i n g and condensation (850-700 mb) i n the lower portion of the cloud mass. It i s d i f f i c u l t to explain why these parameters were not s i g n i f i c a n t for both indices f o r the Northshore and also why the parameter DMR(85-70) did not show higher c o r r e l a t i o n s e s p e c i a l l y with the DI index. The freezing l e v e l (FL) was s i g n i f i c a n t f o r DR (both areas) but only the Research Forest f o r DI. The physical reason for the importance of t h i s parameter l i e s i n the dif f e r e n c e i n weight and 63 x LU ? °-X 1 1 7 -6 _ 5 - -4 - 13 -3 12 -2 1 -1 0 0-5 5-7.5 >7.5 (a) PW(85-70) (nun) 0-5 5-7.5 >7.5 x LU Q Z ^ tr t \ Dl NUMBER OF STORMS 0-5 5-6 6-7 >7 0-5 5-6 6-7 >7 (b) MR(85) (g/kg) DR 2 X LU Q Z 90h 80 70J-60 50f-40h 30 20 IOh 0 10 >850 850 799 <725 800 725 ( c ) F r e e z i n g l e v e l (mb) F i g u r e 9. A b s o l u t e o r o g r a p h i c r a i n f a l l i n d i c e s f o r R e s e a r c h F o r e s t v e r s u s PW(85-70), MR(85) and f r e e z i n g l e v e l . 64 f a l l v e l o c i t i e s of snow versus r a i n p a r t i c l e s . Snow flake s are much l i g h t e r than r a i n drops and are thus c a r r i e d a greater h o r i z o n t a l distance for a given h o r i z o n t a l wind speed. Lower freezing l e v e l s mean greater h o r i z o n t a l spreading of the orographic p r e c i p i t a t i o n above the study area and, consequently, reduced orographic r a i n i n t e n s i t i e s within the study area. Higher freezing l e v e l s mean that a greater percentage of induced orographic r a i n w i l l tend to f a l l within the study area. This concept i s discussed further i n Chapter IV. Figure 9c i l l u s t r a t e s these points, showing generally increasing index values with increasing height of the freezing l e v e l . Again, i t i s d i f f i c u l t to explain why the DI index was not s i g n i f i c a n t for the Northshore. 3. S t a b i l i t y parameters: The Boyden i n s t a b i l i t y index S (BOY) was s i g n i f i c a n t for the DI index but not the DR index, while the other two s t a b i l i t y indices were not s i g n i f i c a n t for both areas for either index. The importance of a i r mass s t a b i l i t y for orographic r a i n f a l l production and d i s t r i b u t i o n has been demonstrated by Smith (1962) and E l l i o t t and Shaffer (1962) f or C a l i f o r n i a and further corroborated for the study area as outlined i n Chapter IV. The apparent non-significance of the s t a b i l i t y indices for the storm t o t a l r a i n f a l l index DR could be a t t r i b u t e d to a tendency for a i r mass s t a b i l i t y to change during the course of many storms. The DR index integrates the e f f e c t s of such changes which would tend to mask c o r r e l a t i o n s which do exi s t between orographic r a i n f a l l and s t a b i l i t y that are presumably picked up by the DI index. The mean DI index values were higher for the unstable storms than f o r the 65 stable ones, being 2.7 vs 1.9 mm/hr for the Research Forest and 3.2 vs 2.5 mm/hr for the Northshore. Storm C l a s s i f i c a t i o n Based on  Occurrence of Orographic Processes  and Orographic R a i n f a l l Indices In order to apply the a n a l y t i c a l procedures for estimating orographic r a i n f a l l described i n Chapter IV, i t i s necessary to i d e n t i f y which i f any of the major orographic processes was operating during a given storm; that i s , oreigenic u p l i f t (U), p o t e n t i a l (TP) or convective (TC) i n s t a b i l i t y t r i g g e r i n g . The storms were thus grouped into four categories: namely, those f o r which each of these three major processes was considered to be dominant and a fourth category containing the remaining storms (0). The analysis of variance procedure was then c a r r i e d out for storm groups i n these categories. Results. The percent explained variances of re l a t i o n s h i p s between the orographic process occurrence categories and both storm parameters and absolute orographic r a i n f a l l indices DR are given i n Table 4. The re l a t i o n s h i p s involving the orographic r a i n f a l l indices DR are s i g n i f i c a n t but there are wide v a r i a t i o n s i n index values about the means for each category as shown i n Figure 10. The highest mean index values are d e f i n i t e l y associated with the oreigenic u p l i f t (U) and po t e n t i a l i n s t a b i l i t y t r i g g e r i n g (TP) categories, the differences between the means of these categories and those of the other two being s i g n i f i c a n t at the 5% l e v e l . As expected by d e f i n i t i o n , the r e l a t i o n -ships involving the three i n s t a b i l i t y parameters S(BOY), S(POT) and S(CONV) are also s i g n i f i c a n t . 66 TABLE 4 PERCENT EXPLAINED VARIANCES OF RELATIONSHIPS BETWEEN BOTH STORM PARAMETERS AND ABSOLUTE OROGRAPHIC RAINFALL INDICES DR AND STORM CLASSIFICATION CATEGORIES Storm Parameter Occurrence of Orographic Process A i r f l o w D i r e c t i o n Synoptic Storm Type VSW(S-85) 15 23* 27 VW(S-85) 11 61* 38* VS(S-85) 21* 42* 35* VSW(85) 13 28* 27 VW(85) 7 61* 42* VS(85) 18 48* 44* WD(S-85) 9 62* 40* WD(85) 4 66* 42* WD (70) 2 56* 48* WS (85) 18 12 44* WS(70) 19 25* 48* SH(100-85) 37* 7 25 SH(85-70) 21* 5 6 SH(100-70) 27* 10 26 MR(85) 3 2 17 DMR(85) 23* 1 6 PW(100-85) 4 4 18 PW(85-70) 7 12 30* PW(100-70) 3 8 26 FL 5 5 48* S(BOY) 52* 1 36* S(POT) 52* 4 56* S(CONV) 52* 1 27 DR(RF) 25* 10 38* DR(NS) 32* 18 42* * S i g n i f i c a n t at the 5% l e v e l . 67 RESEARCH FOREST 2 2 X UJ Q _ J < or o OT 90 80 70 60 50 40 30 20 10 0 14 NUMBER OF STORMS U TP TC 0 NORTHSHORE x UJ Q < O 2 or o 110 100 90 80 70 60 50 40 30 20 10 0 14 U TP TC 0 Figure 10. Absolute orographic r a i n f a l l indices DR versus occurrence of orographic process categories. VS(S-85) i s the only other parameter which had a s i g n i f i c a n t r e l a t i o n s h i p with the orographic r a i n f a l l indices that i s also s i g n i f i c a n t l y correlated with the orographic process occurrence categories. Although the r e l a t i o n s h i p involving VSW(S-85) i s not s i g n i f i c a n t , Figure 11a shows that higher mean values of t h i s parameter are associated with the oreigenic u p l i f t (U) and p o t e n t i a l i n s t a b i l i t y t r i g g e r i n g (TP) categories. However, the only s i g n i f i c a n t differences i n means i s between the p o t e n t i a l i n s t a b i l i t y t r i g g e r i n g (TP) and "other" (0) categories. The s i g n i f i c a n t r e l a t i o n s h i p s with the three wind shear parameters SH(100-85), SH(85-70) and SH(100-70), as well as with DMR (85-70), are not too useful since these parameters are not s i g n i f i c a n t l y r e l a t e d to the orographic r a i n f a l l i ndices. 6 8 2 5 2 0 co \ 2 o UJ UJ 0 . co o z I 0 NUMBER OF STORMS fl T P TC 0 S SW W (a) Occurrence of orographic process c a t e g o r i e s (b) A i r f l o w d i r e c t i o n c a t e g o r i e s Figure 11. VSW(S-85) versus occurrence of orographic process c a t e g o r i e s and a i r f l o w d i r e c t i o n c a t e g o r i e s . Storm C l a s s i f i c a t i o n Based on  A i r f l o w D i r e c t i o n and Orographic  R a i n f a l l I ndices Grouping of storms on the b a s i s of wind fl o w patterns has been suggested by Barry (1967, 1970), as noted p r e v i o u s l y , and a p p l i e d i n C a l i f o r n i a , as reported by the U.S. Weather Bureau (1961). In the present study, the f o l l o w i n g a i r f l o w c a t e g o r i e s have been defined using the mean surface to 850 mb wind d i r e c t i o n s WD(S-85) as noted i n the d i s c u s s i o n of storm synoptic f e a t u r e s at the beginning of t h i s chapter: e a s t e r l y (1-159°), so u t h e r l y (160-200°), southwesterly (201-250°), we s t e r l y (251-290°) and northwesterly (291-360°). The a n a l y s i s of var i a n c e procedure was c a r r i e d out f o r storm groups i n these c a t e g o r i e s . 69 Results. From r e s u l t s obtained during the simple c o r r e l a t i o n analyses between orographic r a i n f a l l indices and storm parameters, the parameter WD(S-85) was found to c o r r e l a t e s i g n i f i c a n t l y only with the wind parameters WD(85), VW(S-85), VS(S-85), VW(85), VS(85) and WD(70). The c o r r e l a t i o n c o e f f i c i e n t between WD(S-35) and WD(85) i s 0.98 which indicates that WD(85) could equally well be used to define the a i r f l o w categories. As shown i n Table 4, the grouping of a i r f l o w d i r e c t i o n into categories produces s i g n i f i c a n t r e l a t i o n s h i p s with a l l the wind d i r e c t i o n and speed parameters except WS(85), but does not r e s u l t i n a s i g n i f i c a n t r e l a t i o n s h i p with the orographic r a i n f a l l i n d i c e s . However, the main parameter of i n t e r e s t i s VSW(S-85) which does have a s i g n i f i c a n t r e l a t i o n s h i p with the orographic r a i n f a l l indices as well as with the a i r f l o w categories. Figure l i b shows the v a r i a t i o n s of VSW(S-85) values for each a i r f l o w category. The northwesterly category i s not given because the 2 storms i n t h i s category were not included i n the analysis due to lack of r a i n f a l l data for the Northshore area as explained previously. The mean wind speed component for the south-westerly category i s s i g n i f i c a n t l y d i f f e r e n t from that for the southerly category but not from the westerly category. Storm C l a s s i f i c a t i o n Based on  Synoptic Categories and  Orographic R a i n f a l l Indices One advantage of using synoptic weather patterns to c l a s s i f y storms i s that the categorizing features are displayed i n map form and need not be c a l c u l a t e d . From an evaluation of the selected study storms, s i x synoptic storm-type categories were adopted as defined below. The 70 analysis of variance procedure was then c a r r i e d out for storm groups i n these categories. In addition, a covariance analysis was car r i e d out to determine which storm parameters show a s i g n i f i c a n t r e l a t i o n s h i p with the orographic r a i n f a l l index DR a f t e r the variance explained by the synoptic categories has been accounted f o r . The synoptic storm-type categories are based on synoptic pressure pattern or f r o n t a l features i d e n t i f i e d from surface weather maps. The feature which appeared to be most c l o s e l y r e l a t e d to production of the major amount of storm r a i n f a l l i n the study area was categorized f o r each storm. The diagrams i n Figure 12 i l l u s t r a t e examples of each synoptic category. The following d e f i n i t i o n s were applied: Warm front-warm sector (WF): the f r o n t a l wave passed within 2° l a t i t u d e of the study area. Occluding front (OGF): one for which the surface f r o n t a l wave passed within 2-4° l a t i t u d e to the south of the study area. Occluded front (PDF): one for which the surface wave was situated more than 4° l a t i t u d e to the south of the study area. Low (L): a closed low pressure centre extended i t s influence over the study area. The l o c a t i o n of the low centre with respect to the study area i s dependent on the s i z e of the low. The centre of a large d i f f u s e low may be located several hundred kilometers away while a smaller system might need to pass within about 200 km. Trough (TR): an i d e n t i f i a b l e low pressure trough moved across the study area or remained offshore with i t s centre l i n e between 48-50° l a t i t u d e l y i n g east of 135° longitude. (a) warm front - warm sector (b) occluding front Onshore wind (ONW): a i r streams not d i r e c t l y associated with the other f i v e synoptic types. This category included storms caused by upper-level disturbances not r e f l e c t e d i n the surface pressure pattern. Results. The percent explained variance of r e l a t i o n s h i p s between the synoptic categories and the various storm parameters are given i n Table 4. The orographic r a i n f a l l indices both show s i g n i f i c a n t r e l a t i o n s h i p s . However i n terms of index magnitude, i l l u s t r a t e d i n Figure 13a, only the mean values f o r the warm front-warm sector category (WF) are s i g n i f i c a n t l y d i f f e r e n t from the means of the other categories for both in d i c e s . Three storm parameters which have s i g n i f i c a n t r e l a t i o n s h i p s with the orographic r a i n f a l l indices are also s i g n i f i c a n t l y r e l a t e d to the synoptic categories: namely, PW(85-70), freezing l e v e l and S(BOY). As shown i n Figure 13b, the warm front-warm sector category (WF) r e g i s t e r s the highest values of PW(85-70). In addition, t h i s category i s the only one for which the mean parameter value i s s i g n i f i c a n t l y d i f f e r e n t from the others, i n t h i s case from those of the three non-f r o n t a l categories L, TR and ONW. The warm front-warm sector category (WF) also has the highest mean fr e e z i n g l e v e l , as shown i n Figure 13c, the mean value being the only one that i s s i g n i f i c a n t l y d i f f e r e n t from those of the other categories. The S(BOY) values f o r each storm i n s i x synoptic categories are l i s t e d i n Table 5. The mean value for the trough category (TR) i s s i g n i f i c a n t l y d i f f e r e n t from those for the three f r o n t a l categories WF, OGF and ODF. However, f or t h i s s t a b i l i t y parameter i t i s more important 110 RESEARCH FOREST 2 100 | 2 ~ 9 0 h U l Q 80 -70 -60 50 ? 40 o *- 30 i 2 0 £ I 0 co NUMBER OF STORMS I 10 £ 100 S 90 80 H UJ 70 o z 60 _,• 50 H 40 o ^ 30 I 20 P I O h co NORTHSHORE 73 WF OGF ODF L TR ONW WF OGF ODF L TR (a) Absolute orographic r a i n f a l l indices DR ONW S 5 O N I IO 00 $ 0. (b) WF OGF ODF L TR ONW PW(85-70) WF OGF ODF L TR (c) Freezing l e v e l ONW WF OGF ODF TR ONW WF OGF ODF (e) MR(85) TR ONW (d) VSW(S-85) Figure 13. Synoptic storm type categories versus absolute orographic r a i n f a l l indices DR, PW(85-70), freezing l e v e l , VSW(S-85) and MR(85). to note the meaning of the numbers i n terms of s t a b i l i t y r a t h e r than i n terms of mean val u e s . The data i n Table 5 show the f o l l o w i n g : a l l but one warm front-warm sector (WF) storms were s t a b l e , a l l o c c l u d i n g f r o n t a l (OGF) storms were n e u t r a l or s t a b l e , f i v e of s i x trough category (TR) storms were unstable, low type (L) storms were n e u t r a l or u n s t a b l e , w h i l e onshore wind (ONW) and occluded f r o n t a l (OGF) category storms were of mixed s t a b i l i t y . TABLE 5 BOYDEN INSTABILITY INDEX VALUES FOR SYNOPTIC STORM TYPE CATEGORIES Category WF OGF ODF L TR . i ONW 91 91 91 94 94 92 92 92 91 94 95 92 93 93 91 95 95 94 93 94 94 95 95 95 93 94 94 95 95 95 93 95 96 96 95 95 96 97 Average 92.9 92.8 93 94.6 95.0 94.6 Although the other storm parameters s i g n i f i c a n t l y r e l a t e d to the r a i n f a l l i n d i c e s are not s i g n i f i c a n t o v e r a l l w i t h respect to the synoptic c a t e g o r i e s , there are s i g n i f i c a n t d i f f e r e n c e s between mean parameter values f o r some of these synoptic c a t e g o r i e s For the s i x synoptic c a t e g o r i e s the v a r i a t i o n s i n magnitude of the parameters VSW(S-85) and MR(85) are shown i n Figure 13d and 13e, r e s p e c t i v e l y . For 75 VSW(S-85), the mean value for the warm front-warm sector category (WF), which i s the highest of them a l l , i s s i g n i f i c a n t l y d i f f e r e n t from those of the low (L) and onshore wind (ONW) types while the mean of the occluded category (OGF) i s s i g n i f i c a n t l y d i f f e r e n t only from that of the low category (L). For MR(85), the warm front-warm sector category (WF) again has the highest mean value which i s s i g n i f i c a n t l y d i f f e r e n t only from the trough (TR) and low (L) categories. For WD(S-85), the means for the warm front-warm sector (WF) and onshore wind (ONW) categories are s i g n i f i c a n t l y d i f f e r e n t from those for the low (L) and occluded f r o n t a l (OGF) categories. The wind rose diagrams i n Figure 14 in d i c a t e that mean wind d i r e c t i o n i s southwest for the f i r s t two categories (WF and ONW) and south for the l a t t e r two categories (L and OGF). Figure 15 indicates the r e l a t i o n s h i p between the occurrence of orographic process categories and the synoptic categories. Almost a l l of the major oreigenic u p l i f t (Ui) events were associated with f r o n t a l system categories, whereas convective i n s t a b i l i t y t r i g g e r i n g (TC) was r e s t r i c t e d to the non-frontal categories. P o t e n t i a l i n s t a b i l i t y t r i g g e r i n g (TP) showed l i t t l e preference f o r any of the synoptic categories occurring for a l l except the OGF category. The covariance analysis involving the orographic r a i n f a l l index DR as the dependent v a r i a b l e , synoptic categories and each of the storm parameters revealed that very few of the parameters were s i g n i f i c a n t i n the presence of the synoptic categories. In f a c t , for both the Research Forest and Northshore r a i n f a l l i n d i c e s , only three v a r i a b l e s were s i g n i f i c a n t ; namely, the wind component parameters VSW(S-85), VS(S-85) 76 N 270c 236 205< 295 240* 219 T R r J I 160° 179° 239 ONW Figure 14. Wind rose diagrams of WD(S-85) for synoptic storm type categories. and VSW(85). This r e s u l t would seem to i l l u s t r a t e the overriding importance of the wind component normal to the mountain b a r r i e r or p a r a l l e l to the channelling v a l l e y s f o r production of orographic rain-f a l l i n the study area. 77 co UJ o z LU ce tr o o o LL o ce UJ m Z WF OGF ODF I I ONW LEGEND • M T P I^W^l T C \ SYNOPTIC S T O R M T Y P E CATEGORIES Synoptic storm type c a t e g o r i e s F i g u r e 15. Synoptic storm type c a t e g o r i e s versus occurrence of orographic process c a t e g o r i e s . Storm Pair" Comparisons Storm c h a r a c t e r i s t i c s and orographic r a i n f a l l are compared f o r storms 39 and 44 and storms 3 and 9. Surface synoptic weather maps, v e r t i c a l temperature-dewpoint (humidity) p r o f i l e s and r a i n f a l l graphs f o r these storms are given i n Appendix X I I , w h i l e other storm data are l i s t e d i n Appendix VI. Storms 39 and 44 are two storms w i t h very s i m i l a r f r o n t a l and pressure p a t t e r n s and v e r t i c a l temperature p r o f i l e s . Both storms involved a southwest-westerly flow of moist, s t a b l e , maritime t r o p i c a l / maritime polar a i r . Despite these apparent s i m i l a r i t i e s , storm 44 had l i t t l e or no orographic r a i n f a l l component during the main part of the storm w h i l e storm 39 had a marked d i f f e r e n c e between v a l l e y and mountain r a i n f a l l . The reasons f o r t h i s c o n t r a s t i n orographic r a i n f a l l p r oduction are probably r e l a t e d to s u b t l e d i f f e r e n c e s i n wind f l o w 78 patterns and a i r mass s t a b i l i t y . Storm 44 had an unstable layer between 900 and 850 mb r i g h t beneath the f r o n t a l inversion, but the Boyden s t a b i l i t y index of 91 vs 93 for storm 39 suggests that the net s t a b i l i t y of the a i r was higher during storm 44. If i t can be assumed that the extent of extended l i f t i n g of stable a i r upwind of a b a r r i e r increases with increasing a i r mass s t a b i l i t y , then the r e l a t i v e degree of l i f t i n g between v a l l e y and mountain slope would have been l e s s i n storm 44 because of i t s greater net s t a b i l i t y . In addition, such extended l i f t i n g could have triggered the unstable layer of storm 44 to release p r e c i p i t a t i o n over the Fraser V a l l e y . The moisture content and freezing l e v e l were both higher i n storm 39. These parameters would influence p r e c i p i t a t i o n rate and d i s t r i b u t i o n over the mountains but the differences i n moisture content and height of freezing l e v e l cannot account f o r the apparent lack of an orographic component i n storm 44. One other factor which may have contributed s i g n i f i c a n t l y to the d i f f e r e n c e i n orographic r a i n f a l l i s the low l e v e l e a s t e r l y outflow i n the Fraser V a l l e y . During storm 39, the winds were SSE at Sand Heads and ESE at Vancouver A i r p o r t , which suggests that the sloping low l e v e l out-flow wedge started between these stations near the ground as discussed i n the section on l o c a l winds. In contrast, the surface winds during the major part of storm 44 were from the ENE at both st a t i o n s . This data suggests a strong outflow from the t r i b u t a r y v a l l e y s north of the Fraser V a l l e y and a f a i r l y deep layer of outflow winds. If t h i s were the case, then the r e l a t i v e amount of e f f e c t i v e l i f t i n g of p r e v a i l i n g southwesterly storm winds between Fraser V a l l e y p r e c i p i t a t i o n stations and the mountain slopes would have been greatly reduced. In summary, the most p l a u s i b l e explanation for the apparent lack of an orographic r a i n f a l l component i n storm 44 i s that an unusually deep layer of low l e v e l outflow winds combined with extended l i f t i n g of very stable a i r to greatly reduce or eliminate e f f e c t i v e differences i n orographic l i f t i n g between v a l l e y and mountain s i t e s and stimulate release of p r e c i p i t a t i o n from a shallow unstable layer upwind of, as well as over the b a r r i e r . Storms 3 and 9 are two a d d i t i o n a l stable storms with s i m i l a r f r o n t a l and pressure patterns and v e r t i c a l temperature p r o f i l e s , but a marked di f f e r e n c e i n orographic r a i n f a l l production. Storm 9 had no orographic component while storm 3 had major orographic r a i n f a l l . For these storms, the reason f o r t h i s r e s u l t could be related mainly to differences i n wind flow patterns. The Boyden s t a b i l i t y index for storm 9 (92) i s s l i g h t l y lower than that for storm 3 (93), while the moisture content and freezing l e v e l were both higher during storm 3. These f a c t o r s would not have played a major r o l e i n causing the . di f f e r e n c e s i n orographic r a i n f a l l . However, mean surface - 850 mb winds were westerly (270°) during storm 9 versus a more southwesterly (245°) d i r e c t i o n f or storm 3. Behind the f r o n t a l wave, winds s h i f t e d to a north-westerly d i r e c t i o n i n storm 9 but remained westerly i n storm 3. It i s possible that the winds during storm 9 could have been deflected p a r a l l e l to the mountain flank north of the Fraser V a l l e y r e s u l t i n g i n l i t t l e orographic l i f t within the study area. Another important f a c t o r i s the low l e v e l outflow. The surface winds were SE at both Sand Heads and Vancouver Airport during storm 3, i n d i c a t i n g a r e l a t i v e l y small low l e v e l outflow wedge close to the mountains. In contrast, surface winds were E at Sand Heads and ENE at Vancouver A i r p o r t during storm 9 80 indicating a relatively deep outflow layer over the Fraser Valley and in the tributary valleys to the north. This situation is very similar to that for storm 44 and would have greatly reduced effective orographic lifting during storm 9. It is also possible that variations in convergence rainfall normal to the cold fronts, which were aligned more or less parallel to the mountain barrier, could have contributed to differences in apparent orographic effects between these two storms. However, more information on the cloud systems would be required to adequately assess this possibility. Summary The correlation analyses have shown that a number of storm parameters have significant simple correlations with the absolute orographic rainfall indices DI and DR. The graphs in Figures 8 and 9 show that these correlations represent a trend of increasing mean index values with increasing parameter values. In a l l cases, there is a fairly large range in index values about the mean value. This high scatter in the data is probably due to several factors including the fact that the relationships are multi-variate in nature rather than bi-variate and some of the upper air data might not be representative as discussed in the first part of this chapter. Some variability will also be introduced by the rainfall indices themselves as noted in the section on index derivation. The differences in correlations between the Research Forest and Northshore could be partially due to the differences between the indices already mentioned. However, because of differences in local topography, they could conceivably be due in part to effective 81 d i f f e r e n c e s i n the l i f t i n g a c t i o n of the l o c a l t e r r a i n i n the two areas. The storm c l a s s i f i c a t i o n analyses have i n d i c a t e d t h a t , w i t h the exception of the Boyden i n s t a b i l i t y index, i n d i v i d u a l storm parameters having a s i g n i f i c a n t r e l a t i o n s h i p w i t h orographic r a i n f a l l i n d i c e s are of l i t t l e value i n determining the occurrence of s p e c i f i c orographic processes. Their occurrence must be i n f e r r e d from the b a s i c d e f i n i t i o n s i n terms of s t a b i l i t y when mountain r a i n f a l l data i s not a v a i l a b l e . S i m i l a r l y , the a i r f l o w d i r e c t i o n c a t e g o r i e s showed l i t t l e i d e n t i f i c a t i o n w i t h orographic r a i n f a l l production as defined by the orographic r a i n f a l l i n d i c e s . However, the a n a l y s i s d i d i n d i c a t e an a s s o c i a t i o n of higher VSW(S-85) values w i t h the southwest wind flow category, which has important i m p l i c a t i o n s i n r e l a t i o n to warm f r o n t a l s i t u a t i o n s as noted below. The storm c l a s s i f i c a t i o n a n a l y s i s i n v o l v i n g synoptic c a t e g o r i e s has shown that the warm front-warm sector synoptic storm type stands out above the other c a t e g o r i e s i n r e l a t i o n to possessing storm parameter values s i g n i f i c a n t l y a s s o c i a t e d w i t h the production of major orographic r a i n f a l l i n the study area. The mean parameter values are s i g n i f i c a n t l y higher or d i f f e r e n t than those f o r some or a l l of the other synoptic c a t e g o r i e s f o r DR, PW(85-70), f r e e z i n g l e v e l , VSW(S-85), MR(85) and WD(S-85). Warm front-warm sector storms are mostly s t a b l e , a f a c t o r of importance f o r a n a l y t i c a l model a p p l i c a t i o n . In c o n t r a s t , the onshore wind synoptic type has the lowest mean orographic r a i n f a l l index values but not the lowest values of the other storm parameters. The trough category storms were mainly unstable, as would be expected, possessed the lowest mean values of PW(85-70) and f r e e z i n g l e v e l height, and had 82 r e l a t i v e l y low mean values of MR(85) and the orographic r a i n f a l l i n d i c e s . Otherwise, the v a r i a t i o n s or s i m i l a r i t i e s of r e l a t i o n s h i p s between storm parameters and synoptic categories are such that the r o l e of the remaining synoptic categories i n i d e n t i f y i n g conditions producing r e l a t i v e l y high or low orographic r a i n f a l l i s rather l i m i t e d . Some of the v a r i a t i o n s observed could be due to the s i m p l i f i e d nature of the c l a s s i f i c a t i o n , which i d e n t i f i e s each storm with a s i n g l e synoptic category l a b e l , and to errors i n s e l e c t i n g the dominating r a i n f a l l producing feature. That i s , the synoptic categories are not n e c e s s a r i l y mutually-exclusive f o r a l l storms. However, the s c a t t e r i n the data would seem to be larger than could be accounted for by these sources of error and the general conclusions remain v a l i d . The two storm p a i r comparisons have shown that apparent s i m i l a r i t y of synoptic weather patterns and v e r t i c a l temperature pro-f i l e s does not automatically imply s i m i l a r i t y i n production or occurrence of orographic r a i n f a l l f o r any given area. Individual atmospheric c h a r a c t e r i s t i c s must be c a r e f u l l y examined. For the l o c a l study area, i n p a r t i c u l a r , l i f t i n g of p r e v a i l i n g storm winds upwind of the mountains by low l e v e l outflow i n the Fraser V a l l e y and t r i b u t a r y v a l l e y s appears to be a s i g n i f i c a n t factor i n determining the r e l a t i v e amount of l i f t and, hence, orographic p r e c i p i t a t i o n between upwind Fraser V a l l e y s i t e s and the mountain slopes. General Comments on Observed Storm  R a i n f a l l C h a r a c t e r i s t i c s In a d d i t i o n to the r e s u l t s described thus f a r , a number of i n t e r e s t i n g observations on orographic r a i n f a l l c h a r a c t e r i s t i c s emerged 83 from the analyses. Some general comments and conclusions concerning these observations are given below to provide further i n s i g h t s into the nature of orographic r a i n f a l l production i n the study area. P r e c i p i t a t i o n P r o f i l e s - Influence  of S t a b i l i t y and Wind D i r e c t i o n C o r r e l a t i o n analyses have indicated a s i g n i f i c a n t influence on orographic p r e c i p i t a t i o n i n the study area of a i r mass s t a b i l i t y and both the southwest and south wind speed components. The e f f e c t s of these parameters can be more s p e c i f i c a l l y i l l u s t r a t e d by examining p r e c i p i t a t i o n p r o f i l e s for i n d i v i d u a l storms or groups of storms. Storms involving major oreigenic u p l i f t and p o t e n t i a l i n s t a b i l i t y t r i g g e r i n g have been examined with t h i s objective and the r e s u l t s portrayed i n Figures 16-18. The t e r r a i n p r o f i l e s i n these diagrams represent an average elevation across a s t r i p 3.2 km i n width, oriented SW (230°)-NE (50°) and centred across Cleveland Dam (CD) on the Northshore and s i t e - 3 (S3) on the Research Forest. P r e c i p i t a t i o n data have been normalized for comparison by taking r a t i o s with values from North Vancouver and Administration Building stations for the Northshore and Research Forest, r e s p e c t i v e l y . P r o f i l e s of storm t o t a l r a t i o s f o r stable and unstable storms are given i n Figure 16. The p r o f i l e s of mean annual p r e c i p i t a t i o n , presented for comparison, were developed from data taken from Wright and Trenholm (1969) and the Atmospheric Environment Service.* These curves show a gradual increase i n p r e c i p i t a t i o n over the Fraser V a l l e y with a *Temperature and p r e c i p i t a t i o n 1941-1970, B r i t i s h Columbia, Environment Canada, Downsview, Ontario. steeper r i s e over the mountains. For the Northshore area, a l l three p r o f i l e s are quite s i m i l a r except for the markedly higher r a t i o at Seymour Dam (SD) f o r unstable storms. This feature could be a t t r i b u t e d to the r o l e of higher t e r r a i n near t h i s s t a t i o n i n f o r c i n g release of a d d i t i o n a l i n s t a b i l i t y . In the Research Forest area, the p r o f i l e s are nearly i d e n t i c a l over the mountains but the stable storms have noticeably higher r a t i o s over the Fraser V a l l e y . This r e s u l t could be interpreted i n two ways. F i r s t l y , i t could i n d i c a t e a more frequent extension of the orographic l i f t i n g e f f e c t upwind of the mountains for stable a i r which would r e s u l t i n higher r a t i o s over the Fraser Valley. Or, secondly, i t could ind i c a t e a tendency for orographic t r i g g e r i n g of i n s t a b i l i t y to occur close to the mountains which would r e s u l t i n lower r a t i o s over the Fraser V a l l e y . This d i f f e r e n c e between stable and unstable storms i s not d i s c e r n i b l e f or the Northshore area. The influence of wind d i r e c t i o n has been examined by comparing r a t i o s of mean 6-hour r a i n f a l l i n t e n s i t i e s for storms with surface -850 mb winds from the southwest (206-260°) to those with winds from the south (160-205°) f o r both stable and unstable cases. The contrast i n p r o f i l e s for stable storms i s dramatic as shown i n Figure 17. The southwest curves represent the mean of four storms (3, 38, 39, 43) and the south curves the mean of the remaining s i x oreigenic u p l i f t cases. With southwest winds, the amount of p r e c i p i t a t i o n increases substanti-a l l y over the Fraser V a l l e y and even more steeply over the mountains. This r e s u l t i s probably due to both an extension of the orographic l i f t i n g e f f e c t upwind from the b a r r i e r and the sloping surface of the low l e v e l outflow wedge when i t occurs. In the Northshore Mountains, 86 DISTANCE (KM) (a) Northshore area WINDS SOUTHWEST DISTANCE (K M) (b) R e s e a r c h F o r e s t a r e a Figure 17. Mean p r e c i p i t a t i o n p r o f i l e s of 6-hour i n t e n s i t y r a t i o s f o r stable storms with southerly and southwest winds. 87 the r a i n f a l l i n t e n s i t y north of the b a r r i e r (Grouse Mountain ridge) a c t u a l l y decreased. This was the case for 3 of the 4 storms used to compute the mean p r o f i l e . The true maximum r a i n i n t e n s i t y would have occurred between stations LC and SD f o r these 3 storms and possibly f or the fourth storm as w e l l . In contrast, there was l i t t l e i f any upwind extension of orographic l i f t i n g with southerly winds. As shown i n Figure 17, a s i g n i f i c a n t increase i n p r e c i p i t a t i o n i n t e n s i t y does not occur u n t i l the southern edge of the mountains i s reached and then the rate of increase i s lower than with southwest winds. This r e s u l t i s due to the stable a i r being able to flow around the ends of the ridges and into the deeply indented v a l l e y s of the Capilano, Seymour, P i t t and Alouette Rivers. The more gradual l i f t i n g occurs over the lower t e r r a i n i n the v a l l e y s (including the Research Forest) and as a r e s u l t of convergent f u n n e l l i n g up these v a l l e y s . Thus, with southerly winds the layer of low l e v e l outflow i n the Fraser V a l l e y , when i t existed, did not appear to exert a s i g n i f i c a n t l i f t i n g of p r e v a i l i n g storm winds upwind of the mountains. For unstable storms the s i t u a t i o n i s more complex insofar as uniformity of storm c h a r a c t e r i s t i c s i s concerned. P r o f i l e s of 6-hour p r e c i p i t a t i o n i n t e n s i t y r a t i o s are compared for three pa i r s of storms (Figure 18). Storms 11 and 24 had southerly winds with i n s t a b i l i t y present from a low l e v e l . Storms 14 and 37 had southwesterly winds also with i n s t a b i l i t y present from a low l e v e l . Storms 7 and 19 were stable at lower l e v e l s but had an unstable layer a l o f t i n which the i n s t a b i l i t y was released as a r e s u l t of orographic l i f t i n g . Winds were westerly for storm 7 but southwesterly for storm 19. For storms 7 and 19, the rate of increase i n r a i n f a l l i n t e n s i t y i s r e l a t i v e l y uniform over the ent i r e p r o f i l e f o r both study areas. This r e s u l t i s probably due to a combina-t i o n of a sloping wedge of low l e v e l outflow as indicated by low l e v e l wind data, extended upwind l i f t i n g of the stable a i r and release of i n s t a b i l i t y i n the unstable layer over both the Fraser V a l l e y and mountains. The combined influence of wind d i r e c t i o n and i n s t a b i l i t y i s most c l e a r l y i l l u s t r a t e d i n the Northshore area p r o f i l e s f o r the other two storm pa i r s (Figure 18a) . For storms 14 and 37 with southwest winds, there i s only a gradual increase i n r a i n i n t e n s i t y over the Fraser V a l l e y but a steep increase s t a r t i n g near the edge of the mountains. Wind data i n d i c a t e a small or non-existent low l e v e l outflow wedge during these two storms. For storms 11 and 24 with southerly winds, there i s no change over the Fraser V a l l e y but a s i m i l a r steep increase i n r a i n f a l l rate over the mountains. The low l e v e l outflow wedge was also close to the mountains or lacking f o r these storms. These r e s u l t s suggest that only a r e l a t i v e l y small l i f t was needed to release the i n s t a b i l i t y present and that s u f f i c i e n t l i f t was imparted to the a i r by the mountain slopes even when southerly winds had the opportunity to penetrate into the mountain v a l l e y s . In the Research Forest area, the sharp d i f f e r e n c e i n l i f t i n g e f f e c t near the edge of the mountains i s not so apparent. For storms 14 and 37 with southwest winds, the rate of increase i n r a i n i n t e n s i t y i s gradual over the Fraser V a l l e y with a steeper increase s t a r t i n g near the mountains (between stations LP and MR). This p r o f i l e i s s i m i l a r to that f o r these storms i n the Northshore area. For storms 11 and 24 with southerly winds, r a i n i n t e n s i t i e s over 90 the Fraser V a l l e y are r e l a t i v e l y higher than for storms 14 and 37 but the rate of increase i s greater than i n the Northshore area and also greater than that i n the Research Forest area for stable storms with southerly winds. The reason, for t h i s feature i s not clear but i s probably r e l a t e d to the processes involved i n the release of i n s t a b i l i t y . S p a t i a l V a r i a t i o n of  Orographic E f f e c t s A comparison of r a i n f a l l data from Northshore and Research Forest Stations reveals a c e r t a i n degree of v a r i a b i l i t y i n the magnitude and occurrence of orographic e f f e c t s between these two areas during s i n g l e storm events. Moreover, the extent of observed di f f e r e n c e s varied with the type of e f f e c t . For example, convectively triggered showery r a i n f a l l often exhibited marked dif f e r e n c e s i n magnitude as might be expected. Figure 19a portrays comparative sets of r a i n f a l l hyetograms for storm 19 which involved t r i g g e r i n g of p o t e n t i a l i n s t a b i l i t y . More or l e s s continuous r a i n f e l l on both areas, but the magnitude and timing of c e r t a i n portions of the storm do d i f f e r . In t h i s s i t u a t i o n , the differences i n timing could have been caused, at l e a s t i n part, by v a r i a t i o n s i n storm dynamics rather than s o l e l y by the e f f e c t s of topography. However, the notably higher r a i n f a l l at Seymour F a l l s Dam can probably be a t t r i b u t e d mainly to the greater l i f t i n g e f f e c t of t e r r a i n i n the v i c i n i t y of t h i s s t a t i o n . Figure 19b displays graphs of r a i n f a l l for storm 42 which involved a widespread oreigenic u p l i f t e f f e c t of stable a i r and a southerly flow of wind. In t h i s case, the r a i n f a l l over both areas was reasonably s i m i l a r i n timing although i n t e n s i t i e s were higher at Seymour Dam (SD) than over the Research 91 (a) Storm 19, November 15-16, 1970 Figure 19. Comparison of rainfall data between Research Forest and Northshore areas for storms 19 and 42. 92 Forest (SI). This d i f f e r e n c e i s probably a t t r i b u t a b l e to the southerly a i r f l o w experiencing a greater degree of convergent l i f t i n g near s t a t i o n SD due to funnelling up the Seymour Val l e y than that experienced over the Research Forest near the mouth of the P i t t Lake V a l l e y . Convective R a i n f a l l The occurrence of an orographic r a i n f a l l component during almost a l l observed storms has already been mentioned. It i s p a r t i c u l a r l y i n t e r e s t i n g to note that the mountains experienced more r a i n even during widespread dynamically produced showery conditions. In t h i s s i t u a t i o n , i t i s possible that the elevated topography ensured or increased release of i n s t a b i l i t y to produce more showers over the mountains. The configuration of the mountain block north of Vancouver i s such that west to northwesterly winds w i l l be topographically l i f t e d along Howe Sound to the west of the Research Forest. Once shower clouds are produced, they can t r a v e l downwind to ;give r a i n f a l l over the Research Forest. Those storms with a westerly flow of unstable a i r u s u a l l y seem to produce showers over the mountains but not always over the Fraser V a l l e y . The r a i n f a l l at mountain r a i n gauge s i t e s could also be biased due to topographic steering of winds and thus shower clouds over these s i t e s . A greater reduction i n r a i n i n t e n s i t y from evaporation below cloud bases would occur over the low elevation Fraser V a l l e y f l a t l a n d s than over the mountains. F i n a l l y , one could speculate that some orographic i n t e n s i f i c a t i o n of convective r a i n could occur, although the information to e i t h e r prove or disprove t h i s hypothesis i s lacking, at l e a s t for the present study. 93 Duration of Orographic E f f e c t The duration of occurrence of an orographic e f f e c t varied considerably for i n d i v i d u a l storms, ranging from near zero to nearly 100 percent of t o t a l storm duration. One reason for t h i s r e s u l t could have been the v a r i a t i o n i n type of orographic process during the storm period experienced by many of the storms. Other v a r i a t i o n s might have involved embedded hig h - l e v e l convective c e l l s feeding lower l e v e l clouds or l o c a l differences i n orographic cloud depth or evaporation e f f e c t s . F rontal Influence on P r e c i p i t a t i o n During several but not a l l storms in v o l v i n g warm, occluding or occluded f r o n t a l systems, r a i n f a l l i n t e n s i t i e s did not change appreciably following passage of the fr o n t s . R a i n f a l l i n t e n s i t i e s remained high behind these f r o n t a l types during 13 of 19 cases over the mountains but only 4 of 19 over the Fraser V a l l e y . This observation r a i s e s the question of f r o n t a l influence on p r e c i p i t a t i o n r e l a t i v e to the r o l e played by topography. For major C a l i f o r n i a storms, Weaver (1962) has concluded that "fronts play a minor r o l e i n p r e c i p i t a t i o n i n comparison with other convergence producing synoptic features." Tschirhart (1960) has suggested that mountain b a r r i e r s deform the shape of warm f r o n t a l surfaces and thereby modify the timing and production of p r e c i p i t a t i o n . However, for low sloping warm f r o n t a l surfaces the f r o n t a l surface could also conceivably become e f f e c t i v e l y replaced by the high elevation mountains as i t moves onto the coast. Indeed, the i d e n t i t y of surface warm fronts on synoptic weather maps i s often obscured over mountainous areas. Occluded fronts could also i n t e r a c t with topography i f the 94 occlusion is low enough. These points further il l u s t r a t e the limitations of frontal synoptic types as discriminatory indicators of orographic r a i n f a l l and indicate possible confounding of frontal and orographic influences on r a i n f a l l . Three further points concerning the occurrence of precipitation relative to fronts were evident. F i r s t l y , for the storms examined, the percentage of storm r a i n f a l l occurring ahead of or behind frontal systems varied from near zero to near 100 percent. When rain f e l l both ahead of and behind occluded or occluding fronts, there was a tendency for much higher absolute r a i n f a l l amounts to occur after frontal passage than i f rain f e l l only behind the front. Finally, during the study period, very l i t t l e r a i n f a l l occurred along or could be attributed directly to cold fronts, most of the associated precipitation coming as showers in the onshore flow of unstable air behind the cold fronts. Conclusions The analyses described in this chapter indicate that several individual storm parameters do exhibit significant correlations with orographic r a i n f a l l and that these specific parameters do have a logical physical explanation for their linkage with the orographic r a i n f a l l component. The analyses have also shown that grouping or classifying storms in relation to orographic r a i n f a l l or parameters highly associated with i t s production is a d i f f i c u l t task to accomplish. While some relationships involving the storm classification categories were s t a t i s t i c a l l y significant, a wide range or variation in orographic r a i n f a l l index or storm parameter values was evident. These latter two findings can be attributed to limitations in the data and to complexities i n storm processes, topographic configuration and wind-terra in in te rac t ions . They also suggest that s imi la r orographic r a i n f a l l can be produced by various combinations of ind iv idua l storm parameters or parameter values which can occur for a var ie ty of synoptic weather condit ions. Thus, re l iance must u l t imate ly be placed on detai led examination of i nd iv idua l storm atmospheric charac te r i s t i cs to adequately assess the p robab i l i ty of occurrence of substant ial orogra-phic r a i n f a l l or of a given orographic process, as also i l l u s t r a t e d by the storm pair comparisons. CHAPTER IV ESTIMATION OF OROGRAPHIC PRECIPITATION Introduction This chapter i s concerned with the in v e s t i g a t i o n of a n a l y t i c a l procedures f o r estimating short-period orographic p r e c i p i t a t i o n over mountainous t e r r a i n . Estimation of mountain area p r e c i p i t a t i o n has commonly been done for mean annual p r e c i p i t a t i o n using s t a t i s t i c a l regressions based s o l e l y on physiographic parameters such as t e r r a i n slope, o r i e n t a t i o n , elevation, degree of exposure and distance from moisture source, e.g. Solomon, et a l . 1963. Danard (1971, 1975) incorporated atmospheric parameters i n an orographic p r e c i p i t a t i o n index which he used i n conjunction with topographic features to develop regression equations f o r annual p r e c i p i t a t i o n i n south c e n t r a l and south coastal B r i t i s h Columbia. He also applied t h i s regression approach to 24-hour r a i n f a l l s i n the mountains north of Vancouver (Danard, 1975). Platzman (1948) has also shown that s t a t i s t i c a l regressions can be suc c e s s f u l l y applied to short-period p r e c i p i t a t i o n i f relevant meteoro-l o g i c a l parameters are taken into account. In a study of p r e c i p i t a t i o n over the Willamette watershed i n Oregon, he developed a r e l a t i o n s h i p between 6-hour r a i n f a l l t o t a l s , mean 6-hour wind v e l o c i t i e s and surface dewpoint temperatures. An a l t e r n a t i v e method of transposing short-period r a i n f a l l data i n mountainous areas, demonstrated for extreme 96 97 r a i n f a l l events i n the Vancouver, B.C.' area by Sporns (1964), i s to use r a t i o s of mountain to low e l e v a t i o n v a l l e y r a i n f a l l . R e l a t i o n s h i p s based on s t a t i s t i c a l r e g ressions are g e n e r a l l y only r e l i a b l e f o r the s p e c i f i c area i n which they are developed. For more general a p p l i c a b i l i t y or e x t r a p o l a t i o n of f i n d i n g s to other areas, n o n - s t a t i s t i c a l models based on p h y s i c a l theory are more appropriate. Short-period i n d i v i d u a l storm or p a r t i a l - s t o r m orographic r a i n f a l l can be r e a l i s t i c a l l y evaluated from p h y s i c a l models which consider a p p r o p r i a t e m e t e o r o l o g i c a l and topographic parameters and terrain-atmospheric i n t e r a c t i o n s . The b a s i c approach i n v o l v e s use. of a m e t e o r o l o g i c a l formula which gives the r a t e of condensation from moist a i r forced to r i s e over a mountain b a r r i e r , i n conjunction w i t h a model or estimate of the orographic i n f l u e n c e on wind flow or v e r t i c a l a i r motions. The c r i t i c a l f a c t o r i s the wind model. Using very simple assumptions, Pedgley (1967, 1970) and Sawyer (1952) derived condensation r a t e s of the same magnitude as observed mountain p r e c i p i t a t i o n . M e t e o r o l o g i c a l p r e c i p i t a t i o n f o r e c a s t i n g procedures a l s o apply condensation formulae and account f o r orographic e f f e c t s by using estimates of o r o g r a p h i c a l l y - i n d u c e d v e r t i c a l v e l o c i t i e s (Harley, 1963, 1965). More elaborate wind flow models which can be adapted to l o c a l t e r r a i n c o n f i g u r a t i o n s have been devised. Much of the r e l e v a n t work on orographic wind fl o w model development and a p p l i c a t i o n to p r e c i p i t a t i o n e s t i m a t i o n appears to have been done i n the western United States (Myers, 1959, 1962; Knox, 1960; U.S. Weather Bureau, 1961, 1966; E l l i o t t and Hovind, 1964; E l l i o t t and E l l i o t t , 1968; F r a s e r , et a l . 1973). Sarker (1966, 1967) developed h i s own model i n I n d i a which he 98 compared w i t h that described by the U.S. Weather Bureau (1961). More l o c a l l y , Walker (1961) used c l a s s i c a l mountain a i r flow theory to model wind flow and p r e c i p i t a t i o n d i s t r i b u t i o n over the mountains of B r i t i s h Columbia. Most wind flow models deal w i t h s t a b l e a i r flow. However, the analyses of Chapter I I I and the work of Smith (1962) and E l l i o t t and Shaffer (1962) i n d i c a t e the high s i g n i f i c a n c e of a i r mass s t a b i l i t y to orographic r a i n f a l l production and thus, by i n f e r e n c e , to i t s computa-t i o n . From a study of p r e c i p i t a t i o n over Vancouver I s l a n d , N i k l e v a (1968) a l s o concluded that c o n s i d e r a t i o n of s t a b i l i t y w i l l be necessary i n developing procedures f o r orographic p r e c i p i t a t i o n f o r e c a s t i n g . Two r e p o r t s of orographic p r e c i p i t a t i o n models which appear to have taken i n s t a b i l i t y i n t o account are those by E l l i o t t and Hovind (1964) and E l l i o t t and E l l i o t t (1969). This chapter describes the adaptation and t e s t i n g of p h y s i c a l modelling procedures of the type mentioned above f o r e s t i m a t i n g s h o r t -period (6-hour) storm r a i n f a l l i n t e n s i t i e s over the mountain slopes north of the Fraser V a l l e y . This model combines concepts of p r e c i p i t a t i o n physics and wind fl o w over mountain b a r r i e r s . The b a s i c theory of the orographic model i s f i r s t d escribed. Then the a p p l i c a t i o n of the model to i n d i v i d u a l storms i n the study area i s discussed, i n c l u d i n g a d e t a i l e d o u t l i n e of computational procedures and an assessment of a p p l i c a b i l i t y to both s t a b l e and unstable storm c o n d i t i o n s . 99 Orographic Model Theory The theory and background i n f o r m a t i o n on the orographic model have been ex t r a c t e d from a number of references as i n d i c a t e d i n the f o l l o w i n g s e c t i o n s . B a s i c a l l y , the model accounts f o r l i f t i n g of a i r up a mountain slope, computation of the r e s u l t i n g condensation and d i s t r i b u t i o n on the ground v i a p r e c i p i t a t i o n t r a j e c t o r i e s . A s i m p l i f i e d diagram of the model i s shown i n Figure 20 f o r reference during the ensuing d i s c u s s i o n of model c h a r a c t e r i s t i c s . Model Assumptions 1. Two-dimensional a i r flow i n a v e r t i c a l plane normal to a uniform mountain b a r r i e r of i n f i n i t e extent i s assumed. The flow may represent an average over a few k i l o m e t r e s or tens of k i l o m e t r e s i n the transverse d i r e c t i o n (W.M.O. 1973). 2. Steady-state, laminar flow of s t a b l e a i r i s assumed, w i t h the wind moving smoothly i n n e a r l y p a r a l l e l streamlines w i t h no t u r b u l e n t motion. 3. At some height above the mountain slope, c a l l e d the nodal surface, the wind fl o w becomes h o r i z o n t a l and the induced orographic updraft decreases to zero. 4. There i s no convergence or divergence of the a i r w i t h i n the defined boundaries of the model. In essence, conservation of mass i s r e a l i z e d except f o r p r e c i p i t a t e d water vapour, which amounts to a few percent at most and may be neglected i n t h i s context (U.S. Weather Bureau, 1961; W.M.O., 1973). 5. The processes i n v o l v e d are a d i a b a t i c , except f o r the changes of s t a t e of water. 100 NODAL SURFACE INFLOW \ V A V V \ V V AIR STREAMLINE OUTFLOW BARRIER HEIGHT Figure 20. Diagram of orographic model. 6. P r e c i p i t a t i o n enhancement, or the orographic r a i n f a l l component, i s proportional to the rate of induced condensation. 7. In t h i s t h e s i s , the a i r between cloud base and nodal surface i s assumed to be saturated. This assumption i s not e s s e n t i a l for a p p l i c a t i o n of the model. Condensation Rate The rate of orographic p r e c i p i t a t i o n i s r e l a t e d to the rate of condensation produced by the l i f t i n g of moist a i r over the mountain 101 b a r r i e r . Condensation rates can be computed by a number of d i f f e r e n t formulae as summarized by Harley (1963). Three basic approaches have been used i n orographic modelling a p p l i c a t i o n s . One method involves computing the dif f e r e n c e i n hor i z o n t a l moisture f l u x between inflow and outflow sections of the model. The basic r e l a t i o n s h i p for condensation i n a layer bounded by two streamlines, the inflow v e r t i c a l and outflow t r a j e c t o r y (Figure 20) i s : C, = 0.0367 V i A p. (r. 7 ) h l l - o (3) Y where C, i s the condensation rate i n mm/hr, V. the mean inflow wind h l speed i n m/s, A p_^  the pressure d i f f e r e n c e i n mb between the top and bottom of the layer at inflow, r . and r mean inflow and outflow mixing 1 o r a t i o s i n g/kg, and Y the ho r i z o n t a l distance over which the p r e c i p i t a t i o n i s d i s t r i b u t e d ( E l l i o t t and Hovind, 1964; Fletcher, 1951; Myers, 1962; U.S. Weather Bureau, 1961). The de r i v a t i o n of t h i s equation i s given i n Appendix VII. An a l t e r n a t i v e approach involves computing the rate of condensation i n a v e r t i c a l column of unit cross section (Knox, 1960; Sarker, 1966; Walker, 1961). For a saturated layer of a i r the equation i s : C z = .036w d ( r i - r 2 ) (4) where C^ i s the condensation rate i n mm/hr, to the mean v e r t i c a l v e l o c i t y for the layer i n cm/sec, the mean density of dry a i r for the layer i n d 3 kg/m , r ^ and r ^ the mixing r a t i o s i n gm/kg at the bottom and top of the layer, r e s p e c t i v e l y . The de r i v a t i o n of t h i s equation i s also given i n i n Appendix VII. Sarker (1966) modified t h i s equation (4) by adding a 102 term to account f o r convergence or divergence of a i r i n the column or l a y e r . A t h i r d method f o r e v a l u a t i n g the condensation r a t e , employed by Bergeron (1960) and Wilson (1961), i s that developed by Fulks (1935). He derived an equation which gives the r a t e of condensation f o r a saturated l a y e r of a i r of u n i t t h i c k n e s s (100 m) having a u n i t r a t e of v e r t i c a l r i s e (1 m/s), and assuming a d i a b a t i c l i f t i n g . Knowing the temperature, t h i c k n e s s and v e r t i c a l v e l o c i t y of a l a y e r , the r a t e of condensation can be obtained using a Table, d e r i v e d from the Fulks equation, which i s included i n the Smithsonian M e t e o r o l o g i c a l Tables ( L i s t , 1966). P r e c i p i t a t i o n Rate In many s t u d i e s , p a r t i c u l a r l y those i n v o l v i n g computation of maximum probable p r e c i p i t a t i o n , the r a t e of orographic p r e c i p i t a t i o n i s assumed equal to the r a t e of condensation (Knox, 1960; Myers, 1962; Sarker, 1966, 1967; U.S. Weather Bureau 1961; Walker, 1961). However, i t i s u n l i k e l y that the p r e c i p i t a t i o n process i s 100 percent e f f i c i e n t as pointed out by E l l i o t t and Shaffer (1962). The p r e c i p i t a t i o n r a t e (I) can be derived from the condensation r a t e (C) by the r e l a t i o n : I = eC (5) where e i s the f r a c t i o n of condensate removed as p r e c i p i t a t i o n . Information concerning t h i s conversion f a c t o r i s sparse. Some authors have speculated that the conversion may be n e a r l y complete f o r e x t r a o r d i n a r y storms w i t h very deep cloud l a y e r s and heavy p r e c i p i t a t i o n ( E l l i o t t and Hovind, 1964; Ludlam, 1956). However, f o r most storms the 103 conversion f a c t o r i s l i k e l y l e s s than 1.0. Table 6 summarizes conversion f a c t o r s reported i n the l i t e r a t u r e i n r e l a t i o n to b a r r i e r height and a i r mass s t a b i l i t y . The d e r i v a t i o n of conversion f a c t o r s greater than 1.0 i s probably due to one of two major f a c t o r s : namely, the use of t o t a l observed p r e c i p i t a t i o n (Know, 1960; Myers, 1962) r a t h e r than the orographic component, which the model computes, and a p p l i c a t i o n of the model to unstable s i t u a t i o n s . High conversion f a c t o r s f o r unstable cases do not n e c e s s a r i l y i n d i c a t e a greater e f f i c i e n c y . Rather, added convective o v e r t u r n i n g of unstable a i r would tend to produce greater orographic p r e c i p i t a t i o n r a t e s which may not be taken i n t o account by the model ( E l l i o t t and Hovind, 1964). The values reported by Marwitz (1974) and D i r k s (1972), and probably that by Newton (1962), can be considered r e p r e s e n t a t i v e of a c t u a l conversion e f f i c i e n c i e s s i n c e they were deduced s o l e l y from a c t u a l moisture and wind measurements i n the clouds. Values of "e" based on ground measurements of p r e c i p i t a t i o n and model c a l c u l a t i o n s should probably be considered model c o e f f i c i e n t s s i n c e they are subject to a number of e r r o r s and sources of v a r i a t i o n which are described i n l a t e r s e c t i o n s . From t h e i r r e s u l t s , E l l i o t t and Hovind (1964) have concluded that the higher b a r r i e r was probably more e f f i c i e n t i n removing the water i t condenses. Both Myers (1962) and the U.S. Weather Bureau (1961) noted an a s s o c i a t i o n of high "e" values w i t h heavy r a i n and low "e" values w i t h l i g h t r a i n cases. In Table 6, the ranges of "e" values shown f o r i n d i v i d u a l sources represent the f o l l o w i n g : Myers (1962) compared successive 6-hour storm i n t e r v a l p r e c i p i t a t i o n to the model estimate f o r a near 104 TABLE 6 CONVERSION FACTORS (e) EXTRACTED FROM THE LITERATURE Source B a r r i e r Height (m) Stabl e S t a b i l i t y Near Neu t r a l Unstable Mixture E l l i o t t and Shaffer (1962) 1220 2100 0.35 0.67 E l l i o t t and Hovind (1964) 1220 0.17 2100 0.26 0.26 0.27 E l l i o t t and E l l i o t t (1973) 0.50 Knox (1960) 1700 0.96 a Myers (1962) 2400 0.35-1.2, .64* U.S. Weather Bureau (1961) 1200-2400 0-3, 0.99 U.S. Weather Bureau (1966) 1660 1660 0.36-1.1 1.0-10.8 W.M.O. (1973) 2450 0.79 (0.33-1.1) D i r k s (1972) 0.40r 0.65 b Marwitz (1974) 1650 0.62 b Braham (1952) 0.19 C Newton (1962) 0.50° used t o t a l observed p r e c i p i t a t i o n versus orographic component deduced from a i r c r a f t measurements valu e f o r thunderstorm 0.35 bar i n d i c a t e s mean of s e v e r a l values 105 n e u t r a l storm (0.35-1.18) and a l s o compared computed to observed p r e c i p i t a t i o n f o r 23 winter storms to o b t a i n the range 0.14-2.20 w i t h a mean of 0.62; a t o t a l of 111 cases were stud i e d by the U.S. Weather Bureau (1961) to o b t a i n the range 0-3 w i t h a mean of 0.99; the U.S. Weather Bureau (1966) derived conversion f a c t o r s from 0.36-1.06 and 1.0-10.8 f o r successive 6-hour i n t e r v a l s during two storms over the Cascade mountains i n Washington; the W.M.O. (1973) report gives a s i n g l e storm mean of 0.79 w i t h i n d i v i d u a l values along the slope t r a n s e c t (length Y i n F i g u r e 20) v a r y i n g from 0.33 to 1.1; E l l i o t t and E l l i o t t (1973) note, from t h e i r experience i n applying an orographic model s i m i l a r to that o u t l i n e d i n t h i s chapter, that a conversion f a c t o r of 0.50 i s c h a r a c t e r i s t i c of broad mountain areas. A c t u a l orographic r a i n f a l l i n t e n s i t i e s over the mountains are estimated from recorded r a i n f a l l data by s u b t r a c t i n g r a i n f a l l measured at an upwind s t a t i o n considered to be f r e e from or subject to minimal orographic e f f e c t s . This procedure introduces some b i a s because of d i f f e r e n c e s i n e l e v a t i o n and a r e a l v a r i a t i o n s i n f a c t o r s which i n f l u e n c e convergence p r e c i p i t a t i o n such as a i r mass s t a b i l i t y and degree of s a t u r a t i o n . The reduced cloud depth through which r a i n f a l l s over higher ground may be p a r t i a l l y o f f s e t by raindrop evaporation beneath the cloud base over lower ground. To account f o r p o t e n t i a l r e d u c t i o n i n convergence r a i n f a l l over the mountains, the U.S. Weather Bureau (1961) a p p l i e d a r e d u c t i o n f a c t o r to upwind convergence r a i n f a l l values based on vthe r a t i o of depths of p r e c i p i t a b l e water over high and low ground. However, E l l i o t t and Shaffer (1962) found t h i s r e d u c t i o n to be n e g l i g i b l e f o r the 1220 metre high Santa Ynez range i n C a l i f o r n i a . 106 Wind Flow Mountains influence synoptic and meso-scale c h a r a c t e r i s t i c s i n a number of important ways. One of the most extensively studied e f f e c t s has been the creation of l e e waves and eddies. Stringer (1972) gives an excellent review of mountain wave phenomena. However, since production of orographic r a i n f a l l i s mainly re l a t e d to flow on the windward side of mountain slopes, a t t e n t i o n i s here r e s t r i c t e d to windward e f f e c t s . In addition, Fraser et a l . (1973) point out that for broad mountains, such as those i n the present study area, the t e r r a i n i s not conducive to the formation of large amplitude lee waves. Horizontal winds. A i r approaching a mountain b a r r i e r w i l l either flow over i t , around the ends or through low passes. The path i t takes w i l l depend on the dimensions and shape of the b a r r i e r , the wind speed and d i r e c t i o n , and the s t a b i l i t y of the a i r . A i r which i s unstable or of near neutral s t a b i l i t y w i l l encounter l i t t l e resistance to flowing over a mountain ridge. However, ascent i s i n h i b i t e d f o r stable a i r , the resistance to l i f t i n g increasing with increasing s t a b i l i t y (Buettner, et a l . 1964; Pedgley, 1967; Weaver, 1962). Stable a i r thus has a greater tendency to flow around a mountain, or be deflected p a r a l l e l to a ridge rather than pass over i t . For stable a i r , the windward flow over mountain ridges w i l l tend to be laminar. For unstable a i r , release of i n s t a b i l i t y w i l l r e s u l t i n turbulent, v e r t i c a l convection and mixing over and beyond the windward slope. The r e s u l t i n g outflow over the ridge c r e s t w i l l tend to be uniform with no shear for unstable a i r , whereas i n stable cases the v e r t i c a l wind shear 107 of the inflow w i l l be c a r r i e d to the outflow section ( E l l i o t t and Hovind, 1964). In either case, the h o r i z o n t a l wind w i l l speed up i n passing over the ridge. Atmospheric s t a b i l i t y also has an influence on a i r flow upwind of the mountain b a r r i e r . Stable a i r begins r i s i n g some distance upwind of a b a r r i e r , whereas unstable a i r tends to r i s e more abruptly s t a r t i n g near the base of the mountain slope (Smith, 1962). If the a i r i s s u f f i c i e n t l y stable, low l e v e l flow may be blocked e n t i r e l y , forming a stagnant zone upwind of the b a r r i e r ridge that e f f e c t i v e l y changes i t s shape and reduces the b a r r i e r height (Fraser et a l . , 1973; N i c h o l l s , 1973). The upper l e v e l flow w i l l s t i l l undergo some deformation, but diagrams presented by Fraser et a l . (1973) suggest that the degree of l i f t i n g w i l l be decreased. E l l i o t t and Shaffer (1962) have shown that when the low l e v e l wind flow i s i n a d i r e c t i o n normal to the mountain ridge or within a span of about 45° centered on the normal, maximum orographic l i f t i n g w i l l occur. Otherwise, the a i r w i l l tend to turn i n a d i r e c t i o n more p a r a l l e l to the b a r r i e r , p a r t i c u l a r l y i f winds are l i g h t or the a i r i s stable. However, as long as there i s a wind component normal to the mountain slope some orographic l i f t i n g can be expected. Yordanov and Godev (1973) have even shown that v e r t i c a l motions are induced when wind flows p a r a l l e l to an obstacle, although the l i f t i n t h i s case would l i k e l y be quite small and r e s t r i c t e d to the immediate v i c i n i t y of the obstacle or slope i t s e l f . V e r t i c a l motions. As stable a i r flows over a mountain b a r r i e r , the amount of l i f t decreases upward from the ground. It i s equal to the height of the r i d g e only at the s u r f a c e , decreasing to zero at the nodal surface where flow e s s e n t i a l l y l e v e l s o f f . The o r o g r a p h i c a l l y - i n d u c e d v e r t i c a l v e l o c i t y (^Q) near the ground can be computed from the equation co = V.VZ (6) o where V i s the h o r i z o n t a l wind v e l o c i t y and VZ represents the mean ground slope (Danard, 1971; Knox, 1960). The exact nature of the f a l l -o f f w i t h height of t e r r a i n - i n d u c e d v e r t i c a l v e l o c i t y i n the atmosphere i s unknown. The simplest approach i s to assume a l i n e a r decrease to zero at the nodal surface ( E l l i o t t and S h a f f e r , 1962). Berkofsky (1964) and Estoque (1957) i n d i c a t e that v e r t i c a l v e l o c i t y p r o f i l e s are more l i k e l y to have a p a r a b o l i c form which can be approximated by a r e l a t i o n s h i p of the form " = % l P l k ( 7 ) where p and p are atmospheric pressures at the surface and at any s s p e c i f i c l e v e l , r e s p e c t i v e l y , and k i s a constant w i t h values between 2 and 4. Knox (1960) assumed that v e r t i c a l v e l o c i t i e s decrease by a f a c t o r of 2 every 1000 m as given by Z-Zs a) = a) ( % ) 1 0 ^ 3 " (8) o where Z g and Z are the height of the ground and any s p e c i f i c l e v e l , r e s p e c t i v e l y . Equations (7) and (8) do not decrease to zero u n t i l the top of the atmosphere ra t h e r than at a lower nodal surface. Orographi-c a l l y induced v e r t i c a l v e l o c i t i e s can a l s o be derived from the h o r i z o n -t a l f l o w models of Myers (1962) and F r a s e r , et a l . (1973) described below, or by a p p l y i n g mountain a i r f l o w theory (Walker, 1961). The magnitude of orographic v e r t i c a l motions are on the order of 1 to 2 m/s 109 i n comparison with v e l o c i t i e s of 10 to 20 cm/s for convergence or f r o n t a l l i f t i n g (Ludlam, 1956). V e r t i c a l updrafts associated with unstable a i r d i f f e r i n v e r t i c a l p r o f i l e and magnitude from those induced i n stable a i r . Vul'fson (1961) has concluded that average v e l o c i t i e s of ascending motions i n developing convective clouds increase with increasing height p r a c t i c a l l y throughout the whole depth of the cloud. Weak convective updrafts are about 1 to 2 m/s while those occurring with strong convective a c t i v i t y may a t t a i n 6 m/s (Ludlam, 1956). Nodal surface. The v e r t i c a l extent of orographic l i f t i n g e f f e c t s has been the subject of widespread i n t e r p r e t a t i o n . One approach has been to assume that most induced condensation occurs below a l e v e l at which atmospheric moisture content becomes n e g l i g i b l e . Several authors selected 500 mb (about 5500 m) for t h i s l e v e l (Harley, 1965; Sawyer, 1952; Wilson, 1961), while Pedgley (1970) proposed 3000 m. Sawyer (1956) suggested that l i f t i n g e f f e c t s might be r e s t r i c t e d to as low as 1500 m for stable a i r or extend over 6100 m for a i r of near neutral s t a b i l i t y . For computation of maximum probable p r e c i p i t a t i o n , a nodal surface at or near the tropopause (about 300 mb or 9100 m) i s usually assumed (Knox, 1960; U.S. Weather Bureau, 1961, 1966). In contrast, Bergeron (1960) chose an upper l e v e l of only 1.4 km, marked by a f r o n t a l inversion, for a s p e c i a l case of orographically-induced u p l i f t along the coast of Norway. In modelling a i r f l o w on the windward side of a mountain ridge, Myers (1962) provided a quantitative method of defining the height of 110 the nodal surface. His analysis indicated the presence of more than one nodal surface, each surface bounding layers of ascending and descending a i r , r e s p e c t i v e l y . In addition, Myers states that the nodal surface w i l l be close to, but below the tropopause for a i r of neutral s t a b i l i t y and at lower elevations f o r more stable a i r . In a p r a c t i c a l a p p l i c a t i o n of Myers approach, E l l i o t t and E l l i o t t (1969) experienced computational d i f f i c u l t i e s i n determining the nodal surface value. E l l i o t t and Shaffer (1962) have taken a basic equation employed by Myers (1962) and derived an equation which indicates that the nodal surface i s twice the b a r r i e r height f o r . a i r of neutral s t a b i l i t y . Under stable conditions the nodal surface would be below t h i s l e v e l , and under unstable conditions, above i t . This f i n d i n g indicates a lower nodal surface than that predicted by Myers (1962) noted above, and would appear to r e s u l t from the assumptions made by E l l i o t t and Shaffer i n de r i v i n g t h i s equation. E l l i o t t and Shaffer (1962) also derive an expression for determining the height of the nodal surface which includes a s t a b i l i t y term. Figure 21 shows curves of height of nodal surface against the s t a b i l i t y index AT for contrasting conditions of no wind shear (B = 0) 3 and high wind shear (g = 5 x 10 m/sec/100 mb) i n the inflow wind pro-f i l e . These curves indicate an abrupt r i s e i n nodal surface height as i n s t a b i l i t y (negative AT) i s achieved. In the case of c o n d i t i o n a l l y or convectively unstable a i r whose i n s t a b i l i t y i s released over a b a r r i e r , E l l i o t t and Hovind (1964) suggest that the nodal surface coincides with the top of the p o s i t i v e area on a thermodynamic diagram (tephigram) (see Haltiner and Martin, 1957, p. 63) rather than n e c e s s a r i l y the tropopause as indicated i n Figure 21. I l l STABILITY INDEX (°C) F i g u r e 21. T h e o r e t i c a l r e l a t i o n s h i p of height of the nodal surface, s t a b i l i t y and wind shear ( E l l i o t t and S h a f f e r , 1962). Mo d e l l i n g wind flow. T h e o r e t i c a l models f o r computing the p a t t e r n of a i r f l o w on windward mountain slopes f o r a p p l i c a t i o n to p r e c i p i t a t i o n s t u d i e s have been developed by F r a s e r , et a l . (1973), Knox (1960), Myers (1959, 1962) and Sarker (1966, 1967). The method elaborated by Myers has received the most widespread a t t e n t i o n and t e s t i n g ( E l l i o t t and E l l i o t t , 1969; E l l i o t t and Hovind, 1964; U.S. Weather Bureau, 1961). Walker (1961) used a modified v e r s i o n of l i n e a r i z e d a i r f l o w theory i n h i s study. The more recent a i r f l o w model of F r a s e r , et a l . was developed i n c o n j u n c t i o n w i t h f i e l d s t udies of winter orographic clouds and s n o w f a l l over the Cascade Mountains of Washington State. A l l models take the same b a s i c approach. Since wind observations above mountain ridges are g e n e r a l l y l a c k i n g , the outflow 112 wind p r o f i l e s are derived from known or assumed inflow p r o f i l e s of wind, temperature and humidity by applying basic physical laws which govern atmospheric behaviour. Myers developed a complex energy-balanced flow model i n which the f i e l d s of pressure, temperature and wind are adjusted for mutual consistency through use of the B e r n o u l l i and hydrostatic equations, as well as a p p l i c a t i o n of c o n t i n u i t y of mass and adiabatic laws. Once the outflow v e l o c i t y and pressure on one streamline are s p e c i f i e d , the p o s i t i o n and wind speed for a l l remaining streamlines can be derived. The r e s u l t i s a family of solutions f o r the outflow wind p r o f i l e . By analogy with hydraulics, Myers invoked the p r i n c i p l e of minimum energy to choose the s o l u t i o n representing the flow that nature would select (the true flow). This procedure could be applied to a number of v e r t i c a l s spaced at consecutive points along the mountain slope. However, Myers (1962) has demonstrated that a one-step operation to derive the outflow p r o f i l e d i r e c t l y at the ridge crest i s adequate. The development of Myers' method i s presented i n Appendix VIII. In a subsequent analysis, Myers and Lott (1963) modified the basic two-dimensional model f o r a p p l i c a t i o n to three-dimensional wind flow c a l c u l a t i o n s . Fraser, et a l . (1973) develop more complex mathematical expressions for computing streamline p o s i t i o n s and outflow wind speeds for stable flow, using a v o r t i c i t y equation, adiabatic and thermodynamic laws, c o n t i n u i t y of mass and the B e r n o u l l i equation. They also consider the e f f e c t s of blocking of low l e v e l a i r flow upwind of the mountains on flow over the b a r r i e r . 113 The method of modelling a i r f l o w adopted by the U.S. Weather Bureau (1961) i s s i m i l a r to that of Myers w i t h the exception that the pressure l e v e l of the nodal surface i s p r e - s e l e c t e d . A number of out-flow wind p r o f i l e s are computed u n t i l one i s found that r e f l e c t s the d e s i r e d nodal surface pressure. A much simpler approach i s to s e l e c t the nodal surface pressure and simply space the outflow streamlines i n d i r e c t p r o p o r t i o n to the spacing at i n f l o w (World M e t e o r o l o g i c a l O r g a n i z a t i o n , 1973). The equation f o r c o n t i n u i t y of mass w i l l then provide the outflow wind speeds. A comparison of p r e c i p i t a t i o n amounts computed by t h i s s i m p l i f i e d procedure w i t h p r e d i c t i o n s of the more s o p h i s t i c a t e d model of Myers y i e l d e d n e a r l y i d e n t i c a l r e s u l t s f o r both approaches (World M e t e o r o l o g i c a l O r g a n i z a t i o n , 1973). In view of t h i s f i n d i n g , the d i f f i c u l t i e s encountered by E l l i o t t and E l l i o t t (1969) mentioned above, the complex c o n f i g u r a t i o n s (e.g. non-ideal) of most n a t u r a l t e r r a i n , and the l i m i t e d amount of upper a i r data a v a i l a b l e , the use of the s i m p l i f i e d approach f o r p r a c t i c a l e s t i m a t i o n of orographic p r e c i p i t a t i o n appears to be more than j u s t i f i e d . P r e c i p i t a t i o n T r a j e c t o r i e s The t r a j e c t o r i e s of p r e c i p i t a t i o n p a r t i c l e s are determined by (1) v e r t i c a l f a l l due to g r a v i t y , (2) h o r i z o n t a l d r i f t caused by the h o r i z o n t a l wind component, and (3) v e r t i c a l r i s e r e s u l t i n g from the upward component of wind flowing over the orographic b a r r i e r . Most models assume an instantaneous change from snow to r a i n at the f r e e z i n g l e v e l as shown i n F i g u r e 20 although the U.S. Weather Bureau (1961) d i d introduce a 50 mb wet snow l e v e l above the f r e e z i n g l e v e l . F a l l 114 v e l o c i t i e s of p r e c i p i t a t i o n p a r t i c l e s are estimated as o u t l i n e d below. The h o r i z o n t a l d r i f t (Y ) of a p r e c i p i t a t i o n p a r t i c l e i n f a l l i n g from n top to bottom of a given atmospheric l a y e r bounded by two streamlines i s : YH " (9) T where Y i s i n metres, V i s the mean h o r i z o n t a l wind speed i n the l a y e r H i n m/s, AZ the th i c k n e s s of the l a y e r i n metres and V the r a t e of f a l l i n m/s. Since VAZ i s constant between any two streamlines (conservation of mass), d r i f t s computed at i n f l o w may be a p p l i e d anywhere between the same two streamlines (W.M.O., 1973). The e f f e c t of the upward component of the wind i s a u t o m a t i c a l l y taken i n t o account by the slope of the streamlines (W.M.O., 1973). The f a l l v e l o c i t i e s of r a i n drops can be estimated using observed or assumed r a i n f a l l i n t e n s i t i e s and e s t a b l i s h e d r e l a t i o n s h i p s between i n t e n s i t i e s , drop s i z e s and t e r m i n a l v e l o c i t i e s of f a l l . R e l a t i o n s h i p s between r a i n f a l l i n t e n s i t y and median drop s i z e developed independently by Laws and Parsons (1943), A t l a s and Plank (1953), and Rogers, et a l . (1967) were p l o t t e d on l o g - l o g graph paper f o r comparison. The r e s u l t i n g curves were more or l e s s p a r a l l e l and c l o s e l y spaced. Since the r e s u l t s of Laws and Parsons have been widely accepted, t h e i r data were used i n the present study and are presented i n Appendix XI. The conclusions of Gunn and Kinzer (1949) concerning r a i n drop s i z e s and t e r m i n a l v e l o c i t i e s have a l s o had wide acceptance (Dingle and Lee, 1972; Foote and Du T o i t , 1969; Wischmeier and Smith, 1958; Wobus, 1971) . A graph of t e r m i n a l f a l l v e l o c i t y versus r a i n drop diameter i s 115 included i n Appendix IX. The f a l l v e l o c i t i e s of snowflakes must be estimated from studies reported i n the l i t e r a t u r e . Langleben (1954) reports f a l l v e l o c i t i e s near 1 m/s for three case studies where the v e l o c i t i e s remained reasonably constant with height. He also presents data which indicates v e l o c i t i e s ranging from 0.5 to about 1.5 m/s. Using radar measurements, Douglas, et a l . (1957) concluded that snowflake terminal v e l o c i t i e s ranged from 0.3 to 1.8 m/s. Obtaining Areal P r e c i p i t a t i o n  Estimates By d e f i n i t i o n , the orographic model i s two-dimensional, providing estimates of p r e c i p i t a t i o n along a narrow s t r i p which may i n r e a l i t y represent an average over a width of a few kilometres as already noted. P r e c i p i t a t i o n over an area such as a watershed may be estimated by applying the model to a series of p a r a l l e l s t r i p s across the area. Knox (1960) adopted t h i s approach, using three s t r i p s 25 km i n width and 210-260 km long to derive estimates of maximum probable p r e c i p i t a t i o n over the Feather River watershed i n C a l i f o r n i a , while the U.S. Weather Bureau (1966) tested the orographic model i n Washington and Oregon using s t r i p s 23 km i n width and 110-160 km i n length. A p p l i c a t i o n of Orographic Model  to Study Area The orographic model has been adapted to the study area and tested against observed p r e c i p i t a t i o n i n both the Northshore and Research Forest areas. From the analyses described i n Chapter III and i n consideration of model assumptions and a v a i l a b i l i t y of observed 116 p r e c i p i t a t i o n data, the four s t a b l e storms w i t h o r e i g e n i c u p l i f t and southwest winds ( i . e . storms 3, 38, 39 and 43) were considered the most s u i t a b l e f o r t e s t i n g of the model. C a l c u l a t i o n s were a l s o done f o r four storms w i t h southwest winds and i n v o l v i n g p o t e n t i a l i n s t a b i l i t y t r i g g e r i n g ( i . e . storms 7, 14, 19, 37) to assess model a p p l i c a b i l i t y to unstable s i t u a t i o n s . In adapting the model, e x p l o r a t o r y computations were c a r r i e d out using storm 43 data to assess s u i t a b i l i t y of model parameter values and evaluate the r e l a t i v e i n f l u e n c e of v a r i a t i o n s i n these parameters. Storm 43 i s a l s o used to i l l u s t r a t e procedures to f o l l o w i n a p p l y i n g the model. The r e s u l t s of analyses are given f o l l o w i n g a d i s c u s s i o n of methods employed i n model development. Ex p l o r a t o r y Development A p p l i c a t i o n of the orographic model in v o l v e d s e v e r a l steps. The f i r s t step was to determine the p h y s i c a l dimensions of the model: namely, the b a r r i e r height (BH), d i s t a n c e over which l i f t i n g occurs (Y) and height of the nodal surface (PN) as shown i n F i g u r e 20. Next, the f o l l o w i n g model features were e s t a b l i s h e d : f r e e z i n g l e v e l , p r e c i p i t a -t i o n t r a j e c t o r i e s and height of cloud base. F i n a l l y , model c a l c u l a t i o n s of orographic condensation were c a r r i e d out and the r e s u l t s compared against observed p r e c i p i t a t i o n v a l u e s . The f o l l o w i n g paragraphs d e s c r i b e how each of the model parameters were d e r i v e d . The b a r r i e r height would normally be determined by s e l e c t i n g a t r a n s e c t normal to the b a r r i e r and averaging e l e v a t i o n s across a given width of s t r i p . As i n d i c a t e d i n the s e c t i o n on p r e c i p i t a t i o n p r o f i l e s i n Chapter I I I , a 3.2 km wide s t r i p o r i e n t e d SW (230°)-NE (50°) was 117 used, the transect o r i e n t a t i o n being chosen on the basis of c o r r e l a t i o n a nalysis r e s u l t s . The t e r r a i n i n the study area does not present the i n f i n i t e uniform b a r r i e r normal to storm winds assumed by model theory. However, i n the northshore area, the mountain slope chosen for the study does have a southwest aspect several kilometers i n width. In the Research Forest area, the lower slopes of the Research Forest have a south-westerly aspect but the dominant Mount Blanshard ridge has a more westerly aspect. This v a r i a t i o n i n t e r r a i n makes t h i s area l e s s i d e a l than the Northshore area for model a p p l i c a t i o n , i n that the major b a r r i e r i s not normal to the southwest wind component indicated by c o r r e l a t i o n a n a l y s i s to be the most s i g n i f i c a n t f or orographic r a i n f a l l production on the Research Forest. Given the complexity of t e r r a i n , the c o r r e l a t i o n r e s u l t s were considered to be the best indic a t o r of net orographic influence and the southwest-northeast transect o r i e n t a t i o n was adopted for model c a l c u l a t i o n s for the Research Forest area. Because of the slope to the southern-most portions of the b a r r i e r ridges, b a r r i e r crest elevations of 915, 1070 and 1220 metres were selected from an examination of topographic maps for exploratory assessment of the influence of t e r r a i n height on computed p r e c i p i t a t i o n . Conceptually, the l i f t i n g distance should be c l o s e l y related to the h o r i z o n t a l distance between the s t a r t of r i s e i n t e r r a i n elevation and the top of the b a r r i e r . For stable a i r , there i s a tendency for induced l i f t i n g to be extended upwind of the b a r r i e r as has already been noted. Moreover, i n the study area, low-level outflow winds i n the Fraser V a l l e y can create a " l i f t i n g surface" which extends south of the mountains as discussed i n Chapter I I I . Consequently, the e f f e c t i v e l i f t i n g distance tends to be greater than that indicated by t e r r a i n 118 c o n f i g u r a t i o n alone. P r e c i p i t a t i o n measurements i n the Fraser V a l l e y south of the mountains are u s e f u l i n i n d i c a t i n g the upwind extent of orographic l i f t i n g as shown i n the p r e c i p i t a t i o n p r o f i l e s of Figures 16 to 18 i n Chapter I I I . From an examination of p r e c i p i t a t i o n data, h o r i z o n t a l l i f t i n g d i s t a n c e values of 17.5, 23.8 and 35 km were chosen fo r e x p l o r a t o r y c a l c u l a t i o n s . The p r e c i p i t a t i o n p r o f i l e s suggest a greater r a t e of l i f t over the mountains than over the Fraser V a l l e y . For t h i s e x p l o r a t o r y phase of model development, a uniform s i n g l e - s t a g e l i f t was assumed. A two-stage d i f f e r e n c e i n l i f t i n g r a t e was taken i n t o account i n subsequent a p p l i c a t i o n s of the model described i n a l a t e r s e c t i o n . In a d d i t i o n , the height of the low l e v e l o utflow l a y e r at the i n i t i a l p oint of l i f t was taken to be 305 metres, versus ground l e v e l , to account f o r surface f r i c t i o n e f f e c t s on winds near the surface. C a l c u l a t i o n s by E l l i o t t and Shaffer (1962) suggest a nodal surface height at l e s s than twice the b a r r i e r height f o r s t a b l e a i r . Based on the curves i n F i g u r e 21 f o r the Santa Ynez mountains, which have a c r e s t height of about 1200 metres, a nodal surface at 1.7 times the b a r r i e r height was s e l e c t e d f o r i n i t i a l c a l c u l a t i o n s . Subsequently, a nodal surface l e v e l based on a r a t i o of 2.5 was used, which represents a 50% increase i n depth between the ground and the nodal surface f o r a b a r r i e r height of 1200 metres. In a d d i t i o n , computations were undertaken f o r a nodal surface at 655 mb f o r a l l three s e l e c t e d b a r r i e r heights and at 600 mb f o r a b a r r i e r height of 1070 metres. On the b a s i s of comparisons of computed condensation w i t h observed p r e c i p i t a t i o n , computations i n v o l v i n g higher nodal surface l e v e l s d i d not appear to be necessary. 119 Once the physical dimensions of the model are established, a d d i t i o n a l model features required include freezing l e v e l , p r e c i p i t a t i o n t r a j e c t o r i e s , and cloud base height. For exploratory c a l c u l a t i o n s for storm 43, the freezing l e v e l was assumed to be horizontal at the height indicated by the selected storm 43 radiosonde ascent. For stable a i r i n which orographic l i f t i n g extends above the environmental freezing l e v e l , t h i s l e v e l w i l l tend to lower downwind. This lowering of the freezing l e v e l i s taken into account i n subsequent a p p l i c a t i o n s of the model described l a t e r . In addition, p r e c i p i t a t i o n t r a j e c t o r y computations were s i m p l i f i e d by using a mean ho r i z o n t a l wind speed for the e n t i r e r a i n and snow layers separately rather than c a l c u l a t i n g p r e c i p i t a t i o n p a r t i c l e movement between streamlines on a layer by layer basis. From the l i t e r a t u r e , discussed previously, a f a l l v e l o c i t y for snow of 1 m/s was selected, while a value of 5.4 m/s was chosen for r a i n using storm 43 i n t e n s i t y data and the graphs in,Appendix IX. These f a l l v e l o c i t i e s were used i n computing t r a j e c t o r i e s , and instant conversion from snow to r a i n at the f r e e z i n g l e v e l was assumed. T r a j e c t o r i e s were extended d i r e c t l y to ground l e v e l below the lowest streamline. Cloud base heights above ground can be estimated for the study area from surface weather reports at Vancouver and Abbotsford a i r p o r t s . Cloud base heights at 968, 916 and 885 mb were selected to assess the influence of t h i s parameter on model r e s u l t s . Actual cloud base heights varied over t h i s range during storm 43. The procedures followed i n actual model computation of p r e c i p i t a t i o n are outlined i n a l a t e r section. The objective at t h i s point i s to examine the magnitude of computed p r e c i p i t a t i o n i n r e l a t i o n 120 to observed data as a r e s u l t of varying basic model parameter values. To derive observed p r e c i p i t a t i o n averages, p r e c i p i t a t i o n s t a t i o n locations were projected normally onto a l i n e oriented southwest (230°) to northeast (50°) with minor adjustments to preserve spacing unduly modified by t h i s l a t e r a l p r o jection. Averages along the transects were derived by weighting according to distances between st a t i o n s . For the exploratory evaluation, comparisons have been made between computed and observed orographic p r e c i p i t a t i o n over the mountains between North Vancouver (NV) and Lynn Creek (LC) stations on the Northshore, and the Administration Building (AD) and s i t e - 1 (SI) on the Research Forest. Observed p r e c i p i t a t i o n data f o r storm 43 are given i n Appendix X. The observed mean 6-hour orographic r a i n f a l l i n t e n s i t i e s used to t e s t the model for storm 43 (43a) are 3.91 mm/hour between stations NV and LC and 2.86 mm/hour between s i t e s AD and SI. Observed orographic r a i n f a l l was computed as described on page 105 with no adjustment of the convergence component over the mountains. Meteorological c h a r a c t e r i s t i c s of storm 43 are outlined i n the next section. Results. The r e s u l t s of exploratory c a l c u l a t i o n s are given i n Table 7 for the Northshore and Table 3 for the Research Forest. These data show that computed condensation rates exceed observed p r e c i p i t a t i o n rates for a number of combinations of model parameter values and, l i k e -wise, that s i m i l a r condensation rates or conversion factors (e) can r e s u l t from d i f f e r e n t parameter value combinations. For nodal surface heights 1.7 times b a r r i e r heights (BH = 915 m, PN = 825 mb; BH = 1070 m, PN = 800 mb; BH = 1220 m, PN = 770 mb), computed condensation i s le s s than observed p r e c i p i t a t i o n f o r a l l Northshore cases and several 121 TABLE 7 RESULTS OF EXPLORATORY CALCULATIONS USING STORM 43 DATA TO ASSESS THE INFLUENCE OF MODEL PARAMETERS BH, PN, Y AND CB ON COMPUTED OROGRAPHIC PRECIPITATION FOR THE NORTHSHORE AREA (NV-LC) Y = 17.5 km Y = 23.8 km Y = 35 km BH PN CB C e C e C e (m) (mb) (mb) (mm/hr) (mm/hr) (mm/hr) 915 825 835 916 968 1.22 2.02 2.05 3.20 1.94 1.91 0.94 1.53 1.54 4.16 2.56 2.54 0.70 1.11 1.15 5.59 3.52 3.40 740 885 916 968 2.48 3.41 3.61 1.58 1.15 1.08 1.79 2.51 2.53 2.18 1.56 1.55 1.55 1.96 1.96 2.52 1.99 1.99 655 885 916 968 4.34 5.13 5.20 0.90 0.76 0.75 3.83 4.34 4.41 1.02 0.90 0.89 2.61 3.05 3.15 1.50 1.28 1.24 1070 800 885 916 968 2.00 2.94 2.98 1.96 1.33 1.31 1.63 2.23 2.26 2.40 1.75 1.73 1.31 1.55 1.60 2.98 2.52 2.44 700 885 916 968 4.32 5.08 5.12 0.91 0.77 0.76 3.33 3.86 3.86 1.17 1.01 1.01 2.50 2.93 2.93 1.56 1.33 1.33 655 885 916 968 5.58 6.19 6.33 0.70 0.63 0.61 4.15 4.61 4.70 0.94 0.85 0.83 3.01 3.35 3.35 1.30 1.17 1.17 600 885 916 968 5.70 6.47 6.57 0.69 0.60 0.59 4.54 4.97 5.15 0.86 0.79 0.76 3.66 3.92 4.11 1.07 1.00 0.95 1220 770 885 916 963 2.98 3.45 3.49 1.31 1.13 1.12 2.41 2.53 2.62 ,62 .55 .49 1.73 1.83 1.85 2.26 2.14 2.11 655 885 916 968 6.76 7.19 7.23 0.58 0.54 0.53 5.46 5.71 5.80 0.72 0.68 0.67 3.62 3.90 3.97 1.08 1.00 0.98 TABLE 8 RESULTS OF EXPLORATORY CALCULATIONS USING STORM 4-3 DATA TO ASSESS THE INFLUENCE OF MODEL PARAMETERS BH, PN, Y AND CB ON COMPUTED OROGRAPHIC PRECIPITATION FOR THE RESEARCH FOREST AREA (AD-SI) Y = 17.5 km Y = 23.8 km Y = 35 km BH PN CB C e C e C e (m) (mb) (mb) (mm/hr) (mm/hr) (mm/hr) 915 825 885 916 968 740 885 916 968 655 885 916 968 1070 800 885 916 963 700 885 916 968 655 885 916 968 600 885 916 968 1220 770 885 916 968 655 885 916 968 600 968 1.36 2.10 1.12 2.03 1.41 1.79 2.43 1.18 1.96 3.11 0.92 2.32 3.96 0.72 3.07 4.44 0.64 3.28 4.67 0.61 . 3.90 5.83 0.49 4.73 6.39 0.45 4.94 1.99 1.44 1.94 3.16 0.91 2.78 3.38 0.85 2.81 4.88 0.59 3.89 6.14 0.47 4.87 6.47 0.44 4.89 5.76 0.50 5.01 7.14 0.40 5.83 7.53 0.38 5.93 6.41 0.45 5.64 7.99 0.36 6.59 7.99 0.36 6.59 3.91 0.73 3.42 5.26 0.54 4.15 5.29 0.54 4.23 7.35 0.39 6.11 8.85 0.32 6.81 9.16 0.31 6.94 10.28 0.28 8.08 2.55 0.79 3.62 1.60 1.36 2.10 1.46 1.36 2.10 1.23 1.62 1.77 0.93 2.28 1.25 0.87 2.35 1.22 0.73 2.85 1.00 0.60 3.32 0.86 0.58 3.38 0.85 1.47 1.79 1.60 1.03 1.91 1.50 1.02 2.39 1.20 0.74 3.05 0.94 0.59 3.50 0.82 0.58 3.50 0.82 0.57 3.34 0.86 0.49 3.90 0.73 0.48 3.98 0.72 0.51 4.30 0.67 0.43 4.83 0.59 0.43 4.83 0.59 0.84 2.21 1.29 0.69 2.50 1.14 0.68 2.55 1.12 0.47 4.73 0.60 0.42 4.96 0.58 0.41 5.07 0.56 0.35 5.38 0.49 123 Research Forest cases. These r e s u l t s suggest that the assumptions used by E l l i o t t and Shaffer (1962) i n developing the curves i n Figure 21 are not n e c e s s a r i l y applicable to the present study area. Tables 7 and 8 also show that conversion factors for the Research Forest are lower than those f o r the Northshore for the same BH, PN, Y and CB values, but are si m i l a r i n magnitude for the same BH, PN, and CB values but with Y = 17.5 km for the Northshore and 35 km for the Research Forest. Although explanations could be made for t h i s r e s u l t , too much weight could not be put on them because of the s i m p l i f i c a t i o n s employed i n these preliminary c a l c u l a t i o n s and t h e i r intended use simply as in d i c a t o r s of probable magnitudes of model parameters. The data i n Table 8 have been used to plot a number of curves i l l u s t r a t i n g the r e l a t i v e influence on computed condensation rates of each of the basic model parameters. Figure 22a shows a l i n e a r increase i n condensation rate with increasing b a r r i e r height. Figure 22b shows a s l i g h t l y c u r v i l i n e a r and sub s t a n t i a l increase i n condensation rate with increasing height of the nodal surface up to 655 mb. The rate of increase between 655 and 600 mb drops noticeably for a b a r r i e r height of 1070 metres but only s l i g h t l y f o r a b a r r i e r of 1220 m. The main reason for t h i s decrease above 655 mb for storm 43 i s that induced condensation at higher l e v e l s does not contribute to orographic p r e c i p i t a t i o n on the windward slope because of a r e l a t i v e l y low freezing l e v e l , which influences p r e c i p i t a t i o n t r a j e c t o r i e s , and the r e l a t i v e l y short distance over which l i f t i n g occurs. In r e a l i t y , i t i s also possible that the top of the cloud layer and hence moisture a v a i l a b i l i t y , could be low enough to l i m i t the height to which induced condensation could take place. 124 15 20 25 30 35 980 960 -940 920 900 8 8 0 LIFTING DISTANCE (KM) CLOUD BASE (mb) (c) (d) gure 22. Influence of b a r r i e r height, nodal surface height, l i f t i n g distance and cloud base height on computed orographic condensation rate for the Research Forest area for storm 43a (over length AD-SI). 125 Figure 22c shows a steeper decrease in computed condensation rate with increasing l i f t i n g distance for shorter distances between 17.5 and 23.8 km than between 23.8 and 35 km. Figure 22d illustrates the change in computed condensation due to varying the cloud base height. The rate of change is similar for a l l three barrier heights, with the relative change being greatest for the lowest barrier. In summary, these exploratory calculations have indicated the degree of change in computed condensation rates to be expected by vary-ing the basic model parameter values. They have also shown that the range of parameter values examined is sufficient to account for observed rates of precipitation for storm 43. In specific situations, the barrier height w i l l be fixed by the terrain i t s e l f . Cloud base height can be estimated from direct observations, i f available. Other-wise, the air can be assumed to be saturated from i n i t i a l level of l i f t i n g . As shown in Figure 22d for storm 43, this assumption would result in a negligible difference in computed condensation over the mountain slope for a cloud base at or below 916 mb, but would result in an increase of about 15% i f the cloud base.were at 885 mb. The cloud base height could affect the relative distribution of orographic precipitation along the line of l i f t . A comparison of conversion factors in both Tables 7 and 3, particularly for a barrier height of 1070 metres as determined from selected terrain profiles, indicates that a nodal surface level about 655 to 600 mb would be suitable for model application in the study area. On the basis of these exploratory calculations, the l i f t i n g distance for the Research Forest area should possibly be greater than 126 f o r the Northshore area. Further i n f o r m a t i o n on the s e l e c t i o n of Y values i s given i n the next s e c t i o n , as i n c o r p o r a t i o n of a two-stage l i f t i n t o the model and c o n s i d e r a t i o n of l o c a l t e r r a i n c o n f i g u r a t i o n modify the r e l a t i v e condensation r a t e s between these two areas obtained by assuming a simple one-stage uniform l i f t . Procedures f o r Applying the Model The procedures o u t l i n e d below f o r applying the model are s i m i l a r to those o u t l i n e d i n the W.M.O. (1973) manual but w i t h some m o d i f i c a t i o n s . Data f o r storm 43a t e s t period 0600-1200 PDT October 25, 1971 i n the Northshore area and radiosonde ascent 1200 Z October 25 at Port Hardy are used f o r t h i s example (Table 11). M e t e o r o l o g i c a l c h a r a c t e r i s t i c s of storm 43 are given i n Appendices VI and X I I . This storm was s e l e c t e d to i n d i c a t e methods of handling some a t y p i c a l f e a t u r e s such as an anomalous change i n f r e e z i n g l e v e l w i t h l i f t i n g and a r e l a t i v e l y high cloud base. The f o l l o w i n g d e s c r i p t i o n assumes that the reader i s f a m i l i a r w i t h the ba s i s f o r choosing v a r i o u s model parameter values as described i n the previous s e c t i o n on ex p l o r a t o r y development and the f o l l o w i n g s e c t i o n s on a p p l i c a t i o n to t e s t storms. The procedures are presented at t h i s p o i n t because an understanding of how the model works w i l l be h e l p f u l i n i n t e r p r e t i n g the r e s u l t s that f o l l o w . The model c o n s i s t s e s s e n t i a l l y of two p a r t s ; namely, c o n s t r u c t i o n of a s c a l e diagram on s u i t a b l e graph paper (Figure 23) and computation of o r o g r a p h i c a l l y induced condensation. Model adaptation. The f i r s t stage of model a p p l i c a t i o n i n v o l v e s determining the p h y s i c a l dimensions of the model and preparing 127 D I S T A N C E (KM) Figure 23. Diagram of orographic model for storm 43a - Northshore area 128 a s c a l e diagram as shown i n F i g u r e 23. Following s e l e c t i o n of a tran s e c t normal to the mountain b a r r i e r , the ground p r o f i l e i s determined. Average e l e v a t i o n s across a s t r i p 3.2 km i n width were used as already noted. V e r t i c a l height measurements are converted to pressure u n i t s (mb), using pressure-height data from the radiosonde r e p o r t , h o r i z o n t a l d i s t a n c e s are measured i n k i l o m e t r e s and the ground p r o f i l e drawn on the diagram. The s e l e c t i o n of h o r i z o n t a l l i f t i n g d i s t a n c e (Y) i s discussed i n the next s e c t i o n s on a p p l i c a t i o n of the model to t e s t storms. In t h i s example, a t o t a l d i s t a n c e of 22.5 km was chosen. In the W.M.O. (1973) r e p o r t , the ground p r o f i l e i s d i v i d e d i n t o segments based on s i g n i f i c a n t breaks i n t e r r a i n slope and the ground i t s e l f serves as the lower boundary f o r l i f t i n g of a i r flow. For t h i s example, the lower streamline or l i f t i n g surface has been determined f o l l o w i n g c o n s i d e r a t i o n of low l e v e l outflow and extended l i f t i n g of s t a b l e a i r i n the v a l l e y upwind of the mountain slope. The l i f t i n g d i s t a n c e has been d i v i d e d i n t o two segments as shown i n Figure 23. The p h y s i c a l o u t l i n e of the model diagram i s completed by drawing i n the nodal surface i n t h i s case at 650 mb, and c o n s t r u c t i n g v e r t i c a l s between the lower streamline and nodal surface at the i n f l o w and outflow ( b a r r i e r c r e s t ) p o i n t s and at s e l e c t e d break p o i n t s i n between. The streamlines at i n f l o w can be spaced at any d e s i r e d i n t e r v a l . The W.M.O. (1973) chose i n t e r v a l s of 25 mb up to the 800 mb l e v e l and 50 mb above. In t h i s study, the depth between lower and upper boundaries has been d i v i d e d i n t o 10 l a y e r s of equal thickness f o r computational convenience. A d d i t i o n a l sub-layers must al s o be 129 considered at cloud base l e v e l and upper l e v e l s of inflow as described i n the section on computation of condensation. Streamlines at outflow and intermediate v e r t i c a l s are spaced i n the same proportion as at inflow. The pressure l e v e l s for streamline spacing are l i s t e d i n columns 1 to 3 i n Table 9 as an a i d to construction of the diagram and computation of induced condensation. The streamlines are drawn as shown i n Figure 23. In a d d i t i o n to streamlines bounding the layers, stream-l i n e s representing the mid-point of each layer are also drawn i n as shown i n Figure 23, the pressure values for mid-layer streamlines being l i s t e d i n columns 4 to 6 i n Table 9. The layers are numbered on the diagram for convenience. The height of cloud base was estimated to be 920 mb from surface weather reports at nearby Vancouver and Abbotsford a i r p o r t s . Where such information i s not a v a i l a b l e , i t i s recommended that the cloud base be assumed to be at ground l e v e l . The cloud base l e v e l i s drawn on the diagram as shown i n Figure 23. In t h i s study, a l l a i r above cloud base i s assumed to be saturated. In the W.M.O. (1973) report, p r o v i s i o n i s made f o r unsaturated a i r above cloud base. To determine the height of the freezing l e v e l , the v e r t i c a l temperature p r o f i l e i s plotted on a tephigram* chart as shown i n Figure 24. The freezing l e v e l at inflow i s indicated by the i n t e r s e c -t i o n of t h i s environmental temperature curve with the 0°C isotherm on the tephigram. As a i r i s l i f t e d over the mountain b a r r i e r , the freezing *A tephigram i s a thermo-dynamic chart which depicts r e l a t i v e v a r i a t i o n s i n atmospheric pressure, temperature, mixing r a t i o (humidity), plus dry and moist adiabatic lapse rates. Copies of tephigrams were obtained from the Atmospheric Environment Service. TABLE 9 COMPUTATION OF OROGRAPHIC CONDENSATION FOR STORM 43a - NORTHSHORE p — P — — P „ r P „ r r i - r r i - r „ AP — r 1 * „1 P i 1 Po P i 1 Po r i NV nv LC LC NV LC V CNV C L C L a y e r (mb) (mb) (mb) (mb) (mb) (mb) (g/kg) (mb) (g/kg) (mb) (g/kg) (g/kg) (g/kg) (mb) (m/s) 996 967 882 1 979 951 879 5.23 a - - 882 4.70 - 0.53 34.6 5.2 - 3.500 2a 961 935 859 5.48 a 912 5.37 - - 0.11 - 6.0 b 5.2 0.126 2 944 920 847 5.87 3 899 5.58 862 5.06 0.29 0.81 34.6 8.3 3.056 8.537 927 904 836 3 892 872 812 910 888 824 6.26 873 5.67 340 5.14 0.59 1.12 34.6 13.2 9.889 18.773 4 858 840 789 875 856 301 5.94 843 5.51 820 5.06 0.43 0.38 34.6 17.6 9.610 19.667 5 823 809 766 840 824 778 5.65 823 5.37 799 4.97 0.28 0.68 34.6 21.0 7.467 18.133 6 738 777 743 806 793 754 5.41 794 5.21 778 4.95 0.20 0.46 34.6 23.9 6.070 13.960 7 754 745 720 771 761 731 5.18 763 5.05 757 4.95 0.13 0.23 34.6 23.5 3.379 6.863 8 737 729 708 5.32 732 5.23 730 5.19 0.09 0.13 34.6 22.6 2.583 3.731 9a 719 713 696 5.08 716 5.03 716 5.03 0.05 0.05 9 685 682 673 702 693 685 4.87 — — — — — — — 10 650 650 650 667 666 662 4.47 — — — — — — — 9b 699 0.05 10.0? 22.5 0.413 -9c 692 0.05 1 3 . 5 b 22.4 - 0.555 T o t a l 43.093 93.719 *C = 0.0367 V A p ( r i - r ^ ) a C l o u d base p r e s s u r e 920 mb used t o d e t e r m i n e r . C (0-LC) = 93.719/23.5 = 3 . 9 9 mm/hr. b A d j u s t e d Ap = 1/2 a c t u a l . C (NV-LC) = (93.719-43.093)/5.8 = 8.73 mm/hr. 131 Figure 24. V e r t i c a l temperature p r o f i l e for storm 43a depicting orographic l i f t i n g for model c a l c u l a t i o n s . 132 l e v e l w i l l tend to lower i n stable a i r . As the a i r moves along any given streamline, i t s pressure, temperature and mixing r a t i o of any point on the streamline may be determined from the tephigram. The inflow pressure values of streamlines are marked on the inflow temperature p r o f i l e on the tephigram. For points located below the cloud base l e v e l (non-saturated a i r ) , the a i r i s assumed to cool with l i f t i n g at the dry adiabatic lapse rate and i s thus moved along a dry adiabat l i n e , or p a r a l l e l to one, on the tephigram u n t i l cloud base l e v e l (condensation l e v e l ) i s reached. This procedure i s shown for the mid-layer streamlines of layers 1 and 2 i n Figure 24. In saturated a i r above cloud base, a i r cools at a moist adiabatic lapse rate. The a i r i s thus moved along or p a r a l l e l to a curved moist adiabat l i n e on the tephigram to the pressure l e v e l of the streamline at the outflow v e r t i c a l . For those streamlines which i n t e r s e c t the 0°C temperature l i n e between inflow and outflow, the pressure at the freezing point i s determined from the tephigram (Figure 24) and plotted on the respective streamlines i n the model diagram (Figure 23). The f r e e z i n g l i n e i s then drawn by j o i n i n g these points as shown i n Figure 23. Because of the presence of a f r o n t a l inversion i n storm 43, orographic l i f t i n g has resulted i n an anomalous drop i n the f r e e z i n g l e v e l at the i n v e r s i o n as shown i n Figure 23. This anomaly creates problems for constructing p r e c i p i t a t i o n t r a j e c t o r i e s . The s o l u t i o n adopted i n t h i s case was to draw the freezing l e v e l between points above and below the inversion on a l i n e p a r a l l e l to r a i n drop t r a j e c t o r i e s i n that layer, so as to approximately balance the t r i a n g u l a r areas on 133 eit h e r side of t h i s l i n e which are cut o f f by t h i s procedure. The method of constructing t r a j e c t o r i e s downwind of the inversion i s described below. P r e c i p i t a t i o n i s assumed to f a l l as snow above the freezing l e v e l and as r a i n below. The average f a l l v e l o c i t y of p r e c i p i t a t i o n p a r t i c l e s (V^) has been taken as 5.8 m/s for r a i n and 1.0 m/s for snow. The computation of p r e c i p i t a t i o n t r a j e c t o r i e s i s i l l u s t r a t e d i n Table 10. The f i r s t step i s to compute mean inflow wind components normal to the b a r r i e r (V) for each la y e r . In the W.M.O. (1973) report, wind speeds are computed for upper and lower streamlines for each layer and an average of the two values taken to obtain the mean speed for the layer. Comparative c a l c u l a t i o n s indicated l i t t l e d i f f e r e n c e i n wind speeds using t h i s approach versus values obtained using the mid-layer stream-l i n e pressure alone. Thus, to s i m p l i f y computations, mean layer inflow wind speed components were determined using mid-layer pressures only as shown i n columns 4 to 8 i n Table 10, where u i s the angle between the normal to the mountain and the wind d i r e c t i o n . The heights of the streamlines bounding each layer are l i s t e d i n Table 10 i n m i l l i b a r s (column 1) and metres (column 3), from which the depths of each layer at inflow (AZ) i n metres are determined and l i s t e d i n column 9. The ho r i z o n t a l d r i f t of p r e c i p i t a t i o n p a r t i c l e s within any given layer i s calculated using the equation VAZ/V^. The d r i f t s computed at inflow may be used anywhere between the same two streamlines (see theory secti o n ) . The h o r i z o n t a l r a i n d r i f t (DRR) and h o r i z o n t a l snowdrift (DRS) between streamlines i n each layer are l i s t e d i n columns 10 and 12 of Table 10. P r e c i p i t a t i o n t r a j e c t o r i e s are constructed from the lowest TABLE 10 COMPUTATION OF SOUTHWEST WIND COMPONENTS AND PRECIPITATION TRAJECTORIES FOR STORM 43 - NORTHSHORE • ZDRR P i P i Inflow Wind V DRR ZDRR DRS m Layer (mb) (mb) Z i (deg) (m/s) (deg) COS y (m/s) AZ (m) (km) (km) ( f e m ) 966 53 17.1 1 979 207 175 9.0 55 0.574 5.2 308 276 0.28 -2a 961 361 175 9.0 55 0.574 5.2 16.32 2 927 944 515 669 185 11.8 45 0.707 8.3 308 441 0.72 16.38 3 892 910 823 977 201 15.1 29 0.875 13.2 308 701 1.42 15.68 4 858 875 1130 1285 216 18.1 14 0.970 17.6 308 935 2.35 5.42 14.75 5 823 840 1452 1622 230 21.0 0 1.000 21.0 337 1220 3.57 7.08 13.53 6 788 806 1791 1967 244 24.6 14 0.970 23.9 345 1422 5.00 8.25 12.10 7 754 771 2141 2323 250 25.0 20 0.940 23.5 356 1442 6.44 8.37 10.66 8 737 2507 256 25.2 26 0.899 22.6 381 1485 7.92 8.61 9a 719 2704 259 25.9 29 0.875 22.7 • 9.18 9 635 702 2895 3111 260 26.0 30 0.866 22.5 407 1579 9.50 9.16 10 650 667 3333 3548 263 26.0 33 0.839 21.8 437 1643 11.14 9.53 l b 973 257 175 9.0 55 0.574 5.2 9b 699 2930 260 26.0 30 0.866 22.5 9c 692 3018 261 26.0 31 0.857 22.3 Co 135 streamline up. The trajectories in the lowest layer (1) have been extended at the same rate directly from the lower streamline to the selected point on the ground as shown in Figure 23 and the starting point on the lower trajectory determined accordingly. Column 11 in Table 10 gives accumulated horizontal rain drifts from any point on the lower boundary streamline. Once a starting point is selected, these values can be used to plot the precipitation trajectory up to the freezing level. Column 13 in Table 10 shows the accumulated horizontal drift distances for rain from the inflow vertical for each streamline for the trajectory passing through station NV. Above the freezing level, the data in column 12 in Table 10 are used to plot snow trajectories. These values are not accumulated because of the varying height at which trajectories intersect the freezing level. Where the freezing level lies between the bounding streamlines of a layer, the rain trajectory in that layer below the freezing line is assumed to follow the mean trajectory for the entire layer. Similarly, the snow trajectory in that layer above the freezing line is assumed to follow the mean trajectory for the entire layer which passes through the point at which the rain trajectory intersects the freezing level. The slope of the snow traj ectory in this layer can be determined with sufficient accuracy by estimating the starting point on the lower streamline (below the freezing level) marking the appropriate horizontal drift distance on the upper streamline, and then drawing the snow trajectory parallel to a line joining these two points but through the end point of the rain trajectory at the freezing level. In the W.M.O. (1973) report, an additional streamline is drawn through the end of the 136 r a i n t r a j e c t o r y and the snow-drift between the freezing l e v e l and top streamline computed separately. This procedure would have to be followed for each p r e c i p i t a t i o n t r a j e c t o r y which crosses the freezing l e v e l . The procedure used i n t h i s study, as outlined above, i s simpler, less time-consuming and w i l l cause no s i g n i f i c a n t change i n computed condensation. Comparative c a l c u l a t i o n s using study data gave differences of l e s s than one percent. For t r a j e c t o r i e s which are influenced by the drop i n freezing l e v e l at the f r o n t a l inversion a s l i g h t l y d i f f e r e n t procedure has been followed. Rain and snow t r a j e c t o r i e s upwind of and including the modified freezing l e v e l at the inversion are constructed as outlined above. T r a j e c t o r i e s between the top of the inversion (see Figure 23) and the point downwind where a normal snow t r a j e c t o r y would i n t e r s e c t the f r e e z i n g l e v e l are assumed to have a d r i f t intermediate between that adopted for snow and r a i n . Very simply, as shown for the t r a j e c -tory through s t a t i o n LC i n Figure 23, a l i n e i s drawn between the point of i n t e r s e c t i o n of the r a i n t r a j e c t o r y with the freezing l e v e l and the point at the top of the inversion to represent the t r a j e c t o r y between those two l e v e l s . . As a consequence, a common snow-trajectory i s assumed above the inversion point for t r a j e c t o r i e s which f a l l within the influence of the inversion. This s i t u a t i o n i s an anomaly which should not be encountered too often but i s presented to i l l u s t r a t e one method of dealing with i t . Computation of condensation rate. Table 9 gives the computation of orographic condensation rate under the two p r e c i p i t a t i o n t r a j e c t o r i e s passing through stations NV and LC. The h o r i z o n t a l 137 condensation equation (3), repeated below, i s used to c a l c u l a t e the condensation rate: C = 0.0367 ViAPi ( r i - r o ) (mm/hr) ^ ± Q ^ The c a l c u l a t i o n s for layer 1 can be used to i l l u s t r a t e the procedure and also show how to deal with layers i n t e r s e c t i n g the cloud base. The f i r s t step i s to determine the saturated mixing r a t i o value at the inflow v e r t i c a l f o r the mid-layer streamline. If t h i s streamline s t a r t s below cloud base, as i s the case for layer 1, then the value at cloud base pressure (920 mb) i s used. The mixing r a t i o value i s read o f f the tephigram chart to be about 5.23 g/kg for layer 1 and l i s t e d i n column 7 of Table 9. The next step i s to determine the pressure at which the mid-layer streamline i n t e r s e c t s each p r e c i p i t a t i o n t r a j e c t o r y . For the NV t r a j e c t o r y t h i s i n t e r s e c t i o n occurs at 924 mb, below the cloud base and thus i n non-saturated a i r , while for the LC t r a j e c t o r y i t occurs at 882 mb which i s noted i n column 10 of Table 9. As seen i n Figure 23, only a small t r i a n g l e of saturated a i r above cloud base l i e s upwind of the NV t r a j e c t o r y i n layer 1. For p r a c t i c a l purposes t h i s p a r t i c u l a r amount of condensation could be ignored as i t represents a very small f r a c t i o n (0.3%) of the t o t a l condensation. However, to c a l c u l a t e t h i s condensation, the mixing r a t i o s along the upper streamline of layer 1 (2a) are required. In addition, the streamline passing through the i n t e r s e c t i o n of the NV t r a j e c t o r y with the cloud base i s drawn on the model diagram (lb i n 138 Figure 23). Table 9 shows the inflow value at cloud base of 5.48 g/kg in column 7 for streamline 2a and its intersection with the NV trajectory pressure of 912 mb in column 8. The mixing ratios corresponding to the two intersection pressures are then determined and listed in column 9 for the upper streamline crossing of the NV trajectory (5.37 g/kg) and column 11 for the mid-layer streamline crossing of the LC trajectory (4.70 g/kg). These subsequent mixing ratios may be determined in two ways. Firstly, they may be read directly off the tephigram but this procedure is time-consuming and subject to accumulated errors. To help avoid this d i f f i -culty, the rates of change of mixing ratio values with altitude have been extracted from a tephigram for a number of moist adiabats and tabulated in Appendix XI. Use of this extracted data greatly facilitates calculations, provides more consistent results and reduces chances for error. The desired mixing ratio is obtained by multiplying the pressure difference between inflow (or cloud base) and trajectory on a given streamline by the mean rate of decrease in mixing ratio in that depth (obtained by interpolation from the table in Appendix XI), and subtracting the result from the inflow mixing ratio value. For example, the pressure difference between inflow (cloud base) and the LC trajec-tory along the mid-layer streamline is 920-882 = 38 mb. The moist adiabat for this streamline lies about mid-way between the 6 and 8°C adiabats and mostly between the 4 and 5 g/kg mixing ratio lines as shown in Figure 24. From the table in Appendix XI, the rate of change in mixing ratio between 920 and 882 mb is about 0.014 g/kg. Multiplying the pressure change (38 mb) by this value and subtracting the result 139 from the i n f l o w mixing r a t i o 5.23 g/kg gives the mixing r a t i o of 4.70 g/kg l i s t e d i n column 11 of Table 9. The next step i s to determine the d i f f e r e n c e s i n mixing r a t i o s between i n f l o w and t r a j e c t o r y by s u b t r a c t i n g the t r a j e c t o r y values i n columns 9 and 11 from the i n f l o w values i n column 7 of Table 9, and l i s t i n g the r e s u l t s i n columns 12 and 13. For the LC t r a j e c t o r y , s u b t r a c t i n g 4.70 from 5.23 kg gives 0.53 g/kg (column 13). I f the only need were to determine the average condensation over the e n t i r e l i f t i n g d i s t a n c e between i n f l o w and t r a j e c t o r y , or between two s p e c i f i c t r a j e c t o r i e s , then the step of a c t u a l l y determining t o t a l mixing r a t i o values could be el i m i n a t e d and only the d i f f e r e n c e computed. However, when both condensation values are d e s i r e d or more than two t r a j e c t o r i e s are i n v o l v e d , computations are s i m p l i f i e d by c a l c u l a t i n g the t o t a l mixing r a t i o s f o r each t r a j e c t o r y and then determining d i f f e r e n c e s f o r any combination r e q u i r e d . The depth of the l a y e r at i n f l o w , 34.6 mb, i s l i s t e d i n column 14 and the mean wind speed c a l c u l a t e d i n Table 10, 5.2 m/s, i s l i s t e d i n column 15 of Table 9. In column 14, the pressure d i f f e r e n c e of 6.0 mb l i s t e d f o r streamline 2a i s one-half of the d i f f e r e n c e of 12.0 mb at the i n f l o w v e r t i c a l between the streamline (2a) at the top of l a y e r 1 and streamline l b which passes through the poi n t of i n t e r s e c t i o n of the NV t r a j e c t o r y w i t h the cloud base (Figure 23). This adjusted pressure d i f f e r e n c e i s used as a device to s i m p l i f y computations. To d e r i v e the condensation represented by the small t r i a n g l e , the mean d i f f e r e n c e i n mixing r a t i o f o r the l a y e r bounded by these two streamlines i s r e q u i r e d . Because the mixing r a t i o d i f f e r e n c e at the lower streamline i s zero, the 140 mean f o r the l a y e r can be obtained by m u l t i p l y i n g the mixing r a t i o f o r the streamline by 1/2 or simply by m u l t i p l y i n g any component of the condensation equation (10) by 1/2. In a d d i t i o n , the mean wind speed f o r t h i s l a y e r i s c a l c u l a t e d from wind speeds determined f o r the bounding streamlines i n Table, 10. Using data from columns 12 to 15, values of C"*" = 0.0367 VApAr are computed and l i s t e d i n columns 16 and 17 of Table 9. For the LC t r a j e c t o r y , a value of C"*" = 3.500 mm/hr/km i s obtained. As shown i n Figure 23, the NV and LC t r a j e c t o r i e s do not extend up to the nodal surface but i n t e r s e c t the i n f l o w v e r t i c a l w i t h i n l a y e r 9 at pressures of 699 and 692 mb, r e s p e c t i v e l y . These pressures are l i s t e d i n column 1 of Table 9 as 9b and 9c. The condensation i n the t r i a n g l e s bounded by the i n f l o w v e r t i c a l , s treamline 9a and t r a j e c t o r i e s o i s computed i n the same manner as f o r the sm a l l t r i a n g l e at cloud base. The pressures and mixing r a t i o s at t r a j e c t o r y i n t e r s e c t i o n s and i n f l o w along s t r e a m l i n e 9a are determined and l i s t e d i n Table 9. Mean wind speeds f o r the t r i a n g u l a r areas are computed from data i n Table 10 and l i s t e d i n column 15 and one-half the pressure d i f f e r e n c e s at i n f l o w are l i s t e d i n column 14. A f t e r values of C^ " are computed f o r a l l l a y e r s f o r a l l t r a j e c t o r i e s , values f o r each t r a j e c t o r y are summed as shown i n Table 9. These values are 43.093 mm/hr/km f o r the NV t r a j e c t o r y and 93.719 f o r the LC t r a j e c t o r y . To o b t a i n the average condensation over the e n t i r e d i s t a n c e between i n f l o w and t r a j e c t o r y , these values are simply d i v i d e d by the appropriate h o r i z o n t a l d i s t a n c e as shown at the bottom of Table 9 f o r the LC t r a j e c t o r y , the computed condensation being 141 3.99 mm/hr. S i m i l a r l y , to o b t a i n the average condensation between two t r a j e c t o r i e s , the d i f f e r e n c e i n values between the two t r a j e c t o r i e s i s c a l c u l a t e d and d i v i d e d by the d i s t a n c e between the t r a j e c t o r i e s as shown a l s o at the bottom of Table 9. The r e s u l t i n g condensation between the NV and LC t r a j e c t o r i e s i s thus 8.73 mm/hr. To o b t a i n an estimate of orographic p r e c i p i t a t i o n , the computed condensation value must be m u l t i p l i e d by a conversion f a c t o r as discussed p r e v i o u s l y and i l l u s t r a t e d i n the s e c t i o n on r e s u l t s of model a p p l i c a t i o n to t e s t storms. Model A p p l i c a t i o n to Test Storms The orographic model has been t e s t e d using four s t a b l e storms i n v o l v i n g o r e i g e n i c u p l i f t and four unstable storms i n v o l v i n g p o t e n t i a l i n s t a b i l i t y t r i g g e r i n g as already mentioned. The storm t e s t periods and corresponding radiosonde ascents used are l i s t e d i n Table 11. These t e s t periods were chosen on the b a s i s of being r e p r e s e n t a t i v e of the period of maximum orographic r a i n f a l l and a l s o of r e l a t i n g a p p r o p r i a t e l y to the timing of radiosonde ascents. For most storms, 6-hour periods were used, t h i s being the most common i n t e r v a l employed i n other s t u d i e s (U.S. Weather Bureau 1961, 1966; W.M.O., 1973). Figure 25 i l l u s t r a t e s the v a r i a t i o n s i n r a i n f a l l i n t e n s i t i e s during the four s t a b l e t e s t storms. For unstable storm 19 i n both study areas and unstable storm 7 on the Northshore, the orographic e f f e c t was i n o p e r a t i o n f o r a sho r t e r time and periods of 4 and 5 hours, r e s p e c t i v e l y , were chosen. Observed t o t a l p r e c i p i t a t i o n at study s t a t i o n s f o r the t e s t periods are given i n Appendix X I I . Orographic r a i n f a l l values were derived as discussed on pages 105 and 120. 142 TABLE 11 MODEL STORM TEST PERIODS AND RADIOSONDE ASCENTS Storm Study No. Area Test Period Radiosonde Ascent 3 NS, RF 1400- -2000 PDT Sept, . 5, 1970 UIL 0000Z Sept. 6, 1970 38 NS, RF 1500- -2100 PDT Oct. 3, 1971 UIL ooooz Oct. 4, 1971 39 NS, RF 1800- -2400 PDT Oct. 12, 1971 UIL ooooz Oct. 13, 1971 43a NS, RF 0600--1200 PDT Oct. 25, 1971 ZT 1200Z Oct. 25, 1971 43b NS, RF 1200- -1800 PDT Oct. 25, 1971 UIL ooooz Oct. 26, 1971 7 NS 0300--0800 PDT Sept . 22, 1970 UIL 1200Z Sept. 22, 1970 RF 0300--0900 PDT Sept . 22, 1970 UIL 1200Z Sept. 22, 1970 14 NS 0900--1500 PDT Oct. 23, 1970 UIL ooooz Oct. 24, 1970 RF 1100- -1700 PDT Oct. 23, 1970 UIL ooooz Oct. 24, 1970 19 NS, RF 1500- -1900 PST Nov. 15, 1970 UIL ooooz Nov. 15, 1970 37 NS 1700- -2300 PDT Sept . 27, 1971 UIL ooooz Sept. 28, 1971 RF 1800- -2400 PDT Sept . 27, 1971 UIL ooooz Sept. 28, 1971 In the f o l l o w i n g s e c t i o n s , establishment of the p h y s i c a l dimensions o f the model i s discussed s e p a r a t e l y f o r s t a b l e and unstable storms and procedures o u t l i n e d f o r choosing b a s i c model parameter values. General storm data are l i s t e d i n Appendix VI w h i l e f u r t h e r m e t e o r o l o g i c a l c h a r a c t e r i s t i c s of each model t e s t storm are given i n Appendix X I I , i n c l u d i n g surface weather map, v e r t i c a l temperature-dew-point (humidity) p r o f i l e s , mass curves and hyetograms of r a i n f a l l . S t a b l e storms. The m e t e o r o l o g i c a l f e a t u r e s of the fou r s t a b l e t e s t storms are g e n e r a l l y s i m i l a r : namely, they are a l l c h a r a c t e r i z e d by a southwesterly flow of warm, moist and s t a b l e or apparently s t a b l e a i r , warm f r o n t a l synoptic p a t t e r n s , r e l a t i v e l y high f r e e z i n g l e v e l s and a major orographic r a i n f a l l component r e s u l t i n g from o r e i g e n i c u p l i f t . 143 oc X \ I 5 t 4 UJ Z I oc n d 38 39 43 ri_d "08 24 17 24 ' 12 24 07 12 24 18 24 12 21 SEPT. 5 OCT. 2-4 OCT. 12 OCT. 24~25 (a) Northshore ' 08 24 17 24 12 2 4 07 12 24 18 24 12 21 SEPT. 5 OCT. 2 -4 OCT. 12 OCT. 24-25 (b) Research Forest Figure 25. Var i a t i o n s i n mean (6-hour) observed orographic r a i n f a l l i n t e n s i t i e s during stable model storms. 144 However, v a r i a t i o n s i n pressure patterns and inherent degree of s t a b i l i t y can r e s u l t i n v a r i a t i o n s i n the form of the low l e v e l outflow wedge and i n the degree of extended orographic l i f t i n g upwind of the mountains. The shapes of p r e c i p i t a t i o n p r o f i l e s shown i n Figure 26 i l l u s t r a t e the r e s u l t i n g r e l a t i v e v a r i a t i o n s i n r a i n f a l l upwind of the b a r r i e r f o r these four storms ( r e f e r a l s o to d i s c u s s i o n on p r e c i p i t a t i o n p r o f i l e s i n Chapter I I I ) . Low l e v e l e a s t e r l y outflow i n the Fraser V a l l e y helps extend the l i f t i n g of p r e v a i l i n g storm winds to the south of the mountains as discussed i n Chapter I I I . Because the v e r t i c a l extent of these e a s t e r l i e s was not known, i t had to be a r b i t r a r i l y defined. For the purposes of the orographic model, the e f f e c t i v e top of the shear zone between the low l e v e l e a s t e r l i e s and p r e v a i l i n g upper l e v e l winds was assumed to s t a r t at a nominal 50 metres above ground over the Fraser V a l l e y and r i s e l i n e a r l y to i n t e r s e c t the mountain slopes at a height of 460 metres. For the Northshore area, the s t a r t of t h i s " l i f t i n g s u r f a c e " was determined on the b a s i s of surface wind data at Vancouver I n t e r n a t i o n a l A i r p o r t and Sand Heads L i g h t S t a t i o n given i n Appendix X I I I . During storms 3 and 43a, winds were from the southeast at both s t a t i o n s and the s t a r t i n g point was set at 3 km northeast of Vancouver A i r p o r t . During storms 38 and 39, winds were e a s t e r l y at the A i r p o r t but s o u t h e a s t e r l y at Sand Heads so the s t a r t i n g p o i n t was set at 3 km SW of Vancouver A i r p o r t . For the Research Forest area, the height of the low l e v e l outflow wedge above Surrey M u n i c i p a l H a l l was set at the same height as e s t a b l i s h e d over Vancouver A i r p o r t f o r each storm, w i t h the surface a l s o r i s i n g to l i n e a r l y to i n t e r s e c t the mountain slope at a 145 height of 460 metres. Model diagrams presented i n Appendix XIV i l l u s t r a t e these forms f o r the low l e v e l outflow wedge. In a d d i t i o n to low l e v e l outflow, the nodal surface height had to be e s t a b l i s h e d . The a c t u a l height of the nodal surface w i l l probably vary from storm to storm. To make the model g e n e r a l l y a p p l i c a b l e , a nodal surface pressure of 650 mb was s e l e c t e d on the b a s i s of e x p l o r a t o r y c a l c u l a t i o n s f o r use i n a l l s t a b l e storm computations. During the l a s t part of storm 43, r a i n f a l l i n t e n s i t i e s were much higher than during the f i r s t part of the storm. I t would appear that there was a change i n s t a b i l i t y of the a i r , which was not detected or i n d i c a t e d by radiosonde data, and that r e l e a s e of the i n s t a b i l i t y i n t e n s i f i e d the p r e c i p i t a t i o n . This part of the storm has been l a b e l l e d 43b and considered to be an unstable storm as described i n the next s e c t i o n . The p r e c i p i t a t i o n p r o f i l e s i n Figure 26 show a steeper r a t e of increase over the mountains than over the Fraser V a l l e y f o r a l l four storms i n the Research Forest area and f o r storms 38 and 39 i n the Northshore area. On t h i s b a s i s , a two-step l i f t i n g p r o f i l e was adopted. For the Northshore area, the s t a r t i n g point of p r e c i p i t a t i o n i n c r e a s e v a r i e s between the A i r p o r t (VAP) and UBC s t a t i o n s . For the model, e f f e c t i v e orographic l i f t i n g was assumed to s t a r t at an average p o s i t i o n 3 km northeast of Vancouver A i r p o r t f o r a l l four storms as shown i n F i g u r e 23. For the f i r s t stage of l i f t i n g over the Fraser V a l l e y , the assumed surface of the low l e v e l outflow wedge serves as the lower boundary or streamline. The second stage of l i f t i n g was assumed to 147 s t a r t at the point of r i s e i n t e r r a i n of the Northshore mountains, that i s at 16.7 km northeast of Vancouver A i r p o r t , and continue l i n e a r l y to the b a r r i e r crest at 26.5 km from the Airport (Appendix XIV). This d i r e c t l i f t over the mountain slope, as opposed to l i f t i n g p a r a l l e l to t e r r a i n configuration, was chosen i n part to account for extended upwind l i f t i n g of stable a i r and i n part because the short distance of l i f t i n g and l i m i t e d amount of observed data did not appear to warrant a more complex model configuration. The t o t a l h o r i z o n t a l l i f t i n g distance for the Northshore area was thus set at 23.5 km. For the Research Forest area, the s t a r t i n g point of p r e c i p i t a t i o n increase appears to be near or a l i t t l e northeast of Surrey Municipal H a l l (Figure 26 p r o f i l e s ) . For the model, e f f e c t i v e orographic l i f t i n g was assumed to s t a r t at an average p o s i t i o n 4 km northeast of Surrey Municipal H a l l (Appendix XIV). The f i r s t stage of l i f t i n g i s along the assumed low l e v e l outflow wedge surface. The second stage of l i f t i n g was also assumed to s t a r t at the point of s i g n i f i c a n t r i s e i n t e r r a i n of the mountains or 21 km northeast of Surrey Municipal H a l l , and continue l i n e a r l y to the b a r r i e r c r est at 35 km from t h i s s t a t i o n . The t o t a l h o r i z o n t a l l i f t i n g distance for the Research Forest area was thus set at 31 km. This distance i s longer than that chosen f o r the Northshore area, a r e s u l t that i s consistent with the i n d i c a t i o n s of the exploratory c a l c u l a t i o n s (page 125). Unstable storms. The synoptic patterns of the four unstable storms are more diverse than those for the stable cases, each belonging to a d i f f e r e n t synoptic category (see Appendix VI). The wind flow was 148 southwesterly f o r storms 19 and 37 but more w e s t e r l y f o r storms 7 and 14, the a i r was c o o l f o r a l l unstable storms as exe m p l i f i e d by r e l a t i v e l y low f r e e z i n g l e v e l s , and p o t e n t i a l i n s t a b i l i t y t r i g g e r i n g r e s u l t e d i n a major orographic r a i n f a l l component. D i f f e r e n c e s i n the nature of the i n s t a b i l i t y d i c t a t e d d i f f e r e n c e s i n approach to d e f i n i n g model c o n f i g u r a t i o n as o u t l i n e d below. During storm 37, the winds s h i f t e d and the orographic e f f e c t decreased as the c o l d low moved south-ward along the coast. The t e s t p e r i o d was s e l e c t e d from the i n i t i a l part of the storm when a major orographic component was present. For storms 7 and 19, a deep unstable l a y e r was present above a deep s t a b l e l a y e r near the ground as i l l u s t r a t e d by the v e r t i c a l temperature p r o f i l e f o r storm 7 i n Figure 27a. Orographic l i f t i n g of the s t a b l e a i r at lower l e v e l s caused r e l e a s e of the i n s t a b i l i t y at upper l e v e l s . The p r e c i p i t a t i o n p r o f i l e s f o r storms 7 and 19 i n d i c a t e extended l i f t i n g upwind of the mountains as shown i n F i g u r e 28. Hence, these storms were t r e a t e d as s t a b l e cases f o r s e l e c t i o n of l i f t i n g d i s t a n c e s , and the same di s t a n c e s and procedures used f o r the s t a b l e storms were used. For both storms 7 and 19, surface winds were e a s t e r l y at Vancouver A i r p o r t and s o u t h e r l y at Sand Heads L i g h t S t a t i o n so the s t a r t of the low l e v e l outflow wedge was set at 3 km southwest of the A i r p o r t . The nodal surface l e v e l was e s t a b l i s h e d as being at the top of the unstable l a y e r defined by the i n t e r s e c t i o n of the moist adiabat along which l i f t i n g takes place i n t h i s l a y e r w i t h the environmental temperature curve. The assumption i s made that r e l e a s e of i n s t a b i l i t y over the mountain b a r r i e r r e s u l t s i n thorough mixing of the a i r such that a moist a d i a b a t i c lapse r a t e i s achieved i n the unstable l a y e r . 149 September 22, 1970 - 1200Z (UIL) October 24, 1970 - 0000Z (UIL) (a) Storm 7 (b) Storm 14 Figure 27. V e r t i c a l temperature p r o f i l e s for unstable model storms 7 and 14. RATIO 6-HOUR INTENSITIES STATION / SITE I O O o RATIO 6-HOUR INTENSITIES STATION / SEYMOUR DAM ELEVATION ( M ) 151 This procedure set the nodal surface at 580 mb f o r storm 7 and 700 mb f o r storm 19. The s t a b l e and unstable l a y e r s were assumed to be i n the same p r o p o r t i o n above the outflow c r e s t as at i n f l o w . The atmosphere was then d i v i d e d i n t o l a y e r s and model computations c a r r i e d out i n the same manner as f o r s t a b l e storms. In r e a l i t y , t u r b u l e n t mixing of a i r i n the unstable l a y e r would modify the h o r i z o n t a l wind s t r u c t u r e and produce v e r t i c a l a i r motions which could exceed those r e s u l t i n g from laminar f l o w of s t a b l e a i r over the b a r r i e r . As there appeared to be no r e a l i s t i c o b j e c t i v e method of determining the magnitude of convective v e r t i c a l v e l o c i t i e s f o r i n d i v i d u a l storms, laminar flow was a p p l i e d to t e s t the r e s u l t s obtained using t h i s assumption. Storm 43b would seem to be s i m i l a r i n nature to storms 7 and 19, i n that r e l e a s e of upper l e v e l i n s t a b i l i t y probably took p l a c e . For storms 14 and 37, a deep unstable l a y e r was present from a low l e v e l as i l l u s t r a t e d f o r storm 14 i n Figure 27b. Assuming an absence of low l e v e l e a s t e r l y outflow i n the Fraser V a l l e y , orographic l i f t i n g e f f e c t s would not be expected to extend very f a r upwind f o r unstable a i r of t h i s nature i n that unstable a i r can more e a s i l y f l o w over b a r r i e r s than s t a b l e a i r . P o t e n t i a l i n s t a b i l i t y should be r e l e a s e d by d i r e c t l i f t i n g over the mountain slope. For both storms 14 and 37, Vancouver A i r p o r t and Sand Heads winds were south to s o u t h e a s t e r l y i n d i c a t i n g that low l e v e l e a s t e r l y outflow was of r e l a t i v e l y small extent or p o s s i b l y non-existent. For storm 37, the p r e c i p i t a t i o n p r o f i l e s of Figure 28 show that e f f e c t i v e l i f t i n g was i n i t i a t e d near the base of the mountains f o r both study areas. For storm 14, the p r e c i p i t a t i o n increase s t a r t e d f u r t h e r upwind i n both areas. This d i f f e r e n c e i n response could 152 be related to differences i n low l e v e l outflow or to differences i n the degree and character of atmospheric i n s t a b i l i t y . For consistency and i n consideration of basic concepts and model a p p l i c a t i o n to areas not influenced by low l e v e l outflow, a single-stage l i f t s t a r t i n g near but a l i t t l e upwind of the mountains and r i s i n g l i n e a r l y to the b a r r i e r crest was assumed. For the Northshore area, e f f e c t i v e orographic l i f t i n g was taken to s t a r t 2.8 km southwest of the s t a r t i n r i s e i n t e r r a i n (at s t a t i o n PMO to f a c i l i t a t e computations) at a nominal height of 150 metres (Appendix XIV). For the Research Forest area, the star t of orographic l i f t i n g was taken 3 km southwest of the point of s i g n i f i c a n t r i s e i n t e r r a i n also at a height of 150 metres (Appendix XIV). This procedure gave a l i f t i n g distance of 12.6 km for the North-shore and 17 km for the Research Forest. The nodal surface was taken as being at the top of the unstable layer, as defined for storms 7 and 19, which i s 715 mb for storm 14 and 625 mb for storm 37. As for storms 7 and 19, model computations were c a r r i e d out using the assumption of laminar flow. Results. The r e s u l t s of model c a l c u l a t i o n s f o r both stable and unstable storms are summarized i n Tables 12 and 13 i n which computed orographic condensation and conversion factors ( r a t i o of observed precipitation/computed condensation) are presented for i n t e r v a l s along the p r o f i l e as well as for the t o t a l l i f t i n g distances. For the North-shore, data for WV-CD and NV-LC, as well as 0-CD and 0-LC, are presented separately because these two pa i r s of stations are a c t u a l l y along l i n e s which are p a r a l l e l but about 4 km apart and thus have a 153 TABLE 12 OBSERVED OROGRAPHIC PRECIPITATION, COMPUTED OROGRAPHIC CONDENSATION AND CONVERSION FACTORS FOR STABLE AND UNSTABLE MODEL STORMS - NORTHSHORE AREA Storm No. O-UBC UBC-PMO PMO-NV WV-CD mm/hr NV-LC CD-LC O-CD O-LC Stable storms: 3 Observed 0.19 1.15 2.98 4.35 4.97 5.45 2.09 2.46 Computed 0.93 2.98 4.10 7.02 9.89 10.23 3.44 4.60 e 0.20 0.39 0.73 0.62 0.50 0.53 0.61 0.53 38 Observed 0.04 0.42 1.56 3.07 4.29 5.59 1.14 1.65 Computed 0.86 1.17 2.43 4.72 9.83 10.46 2.22 3.62 e 0.05 0.36 0.64 0.65 0.44 0.53 0.51 0.46 39 Observed 0.09 0.50 1.42 2.63 3.90 4.72 1.09 1.53 Computed 0.80 1.64 3.09 5.61 8.49 8.86 2.54 3.62 e 0.11 0.30 0.46 0.47 0.46 0.53 0.43 0.42 43a Observed 0.41 1.51 2.60 3.52 3.91 4.44 2.01 2.24 Computed 0.60 2.18 3.70 6.51 8.73 8.58 3.05 3.99 e 0.68 0.69 0.70 0.54 0.45 0.52 0.66 0.56 Unstable storms: 7 Observed 0.0 0.23 1.43 2.90 3.21 3.79 1.09 1.27 Computed 0.75 2.41 5.07 8.09 12.40 13.36 3.75 5.39 e 0.0 0.10 0.28 0.36 0.26 0.28 0.29 0.24 14 Observed _ _ 1.50 1.59 1.84 1.91 1.57 1.65 Computed - - 1.85 2.30 2.24 2.21 1.94* 2.03: e - • - 0.81 0.69 0.82 0.86 0.81 0.81 19 Observed 0.25 0.98 1.62 1.56 2.09 2.01 1.08 1.32 Comput ed 0.18 1.32 2.79 4.38 8.74 9.87 2.07 3.39 e 1.39 0.74 0.58 0.36 0.24 0.20 0.52 0.39 37 Observed _ _ 0.32 0.47 1.24 1.39 0.28 0.74 Computed - - 3.62 4.60 4.48 4.35 3.86* 4.02: e - - 0.09 0.10 0.28 0.32 0.07 0.18 43b Observed 0.79 3.07 4.53 4.61 4.90 5.43 3.23 3.59 Computed 1.22 2.37 3.78 5.38 7.48 8.02 3.00 3.86 e 0.65 1.30 1.20 0.86 0.66 0.68 1.08 0.93 *Zero point at station PM0. 154 TABLE 13 OBSERVED OROGRAPHIC PRECIPITATION, COMPUTED OROGRAPHIC CONDENSATION AND CONVERSION FACTORS FOR STABLE AND RESEARCH FOREST UNSTABLE AREA MODEL STORMS -Storm No. O-MR MR-AD AD-S3 AD-SI mm/hr S3-S1 O-Sl Stable storms: 3 Observed Computed e 0.55 1.63 0.34 1.67 3.93 0.42 3.32 8.12 0.41 3.76 8.14 0.46 4.78 8.19 0.58 1.37 3.29 0.42 38 Observed Computed e 0.74 1.02 0.73 1.85 2.84 0.65 2.92 7.90 0.37 3.21 8.53 0.38 3.90 9.98 0.39 1.41 3.80 0.50 39 Observed Computed e 0.96 1.02 0.94 2.29 3.15 0.73 3.27 6.67 0.49 3.54 6.76 0.52 4.18 6.95 0.60 1.68 2.50 0.67 43a Observed Computed e 0.83 1.55 0.54 2.54 3.64 0.70 2.96 7.22 0.41 2.86 6.90 0.41 2.59 6.18 0.42 1.50 2.95 0.51 Unstable storms: 7 Observed Computed e 1.23 2.57 0.48 2.49 5.75 0.43 2.97 11.47 0.26 3.11 11.52 0.27 3.43 11.66 0.29 1.81 4.86 0.37 14 Observed Comput ed e 0.66 0.89* 0.74 1.51 1.76 0.86 1.93 2.15 0.90 2.07 2.16 0.96 2.41 2.19 1.10 1.54 1.72* 0.90 19 Observed Computed e 1.56 1.12 1.39 3.97 2.55 1.56 4.67 8.07 0.58 4.62 8.76 0.53 4.50 10.34 0.44 2.55 2.86 0.89 37 Observed Computed e 0.10 2.12* 0.05 0.55 3.67 0.15 1.18 4.09 0.29 1.41 4.23 0.33 1.94 4.58 0.42 0.78 3.53* 0.22 43b Observed Computed e 0.60 1.38 0.43 2.42 3.20 0.76 4.81 6.81 0.71 5.23 6.53 0.80 6.20 5.89 1.05 1.81 2.66 0.68 155 s l i g h t l y d i f f e r e n t r e l a t i o n to the b a r r i e r . These data show a v a r i a t i o n i n derived conversion f a c t o r values along the p r o f i l e , a fin d i n g s i m i l a r to that reported for other studies (U.S. Weather Bureau 1966; W.M.O. 1973). The widest f l u c t u a t i o n s i n conversion f a c t o r s tend to occur i n the upwind section over the Fraser V a l l e y , with values for mountain slope segments being more c o n s i s t e n t l y s i m i l a r f o r any given storm. For both the Northshore and Research Forest areas, the o v e r a l l ranges of conversion f a c t o r s are very s i m i l a r , although comparative values do d i f f e r f o r i n d i v i d u a l storms. These f a c t o r s are discussed below i n r e l a t i o n to stable and unstable storm types. 1. Stable storms: The orographic model assumes stable, laminar a i r flow and thus i s most v a l i d l y a p p l i c a b l e to storms with a stable atmosphere. As shown i n Table 12, the conversion factors vary along the l i f t i n g distance for each storm. However, the r e l a t i o n s h i p between computed orographic condensation and observed orographic p r e c i p i t a t i o n along the transect i s highly s i g n i f i c a n t as shown i n Figure 29. The co r r e l a t i o n c o e f f i c i e n t (r ) i s 0.96 for the Northshore and 0.90 for c the Research Forest. These graphs were derived using data for each of the four storms for the following transect segments: UBC-PMO, PMO-NV, NV-LC, WV-CD and CD-LC for the Northshore area; 0-MR, MR-AD, AD-S3 and S3-S1 for the Research Forest area. The slopes of the regression l i n e s i n Figure 29 represent mean conversion factor values for a l l data. The value of 0.49 f o r the Northshore was used to derive computed p r e c i p i t a t i o n from (b) Research Forest area Figure 29. Observed orographic r a i n f a l l versus computed orographic condensation along p r o f i l e transects for stable model storms. 157 computed condensation values along the p r o f i l e transects i n both study areas i n order to assess the r e l i a b i l i t y of using a sing l e conversion factor f o r a l l points along the transect. The Northshore conversion factor was chosen for two reasons. F i r s t l y , the b a r r i e r i s normal to the s i g n i f i c a n t southwest wind component, versus a more complex t e r r a i n configuration i n the Research Forest area, and was considered to provide better conditions f o r optimum orographic l i f t i n g . Secondly, for a p p l i c a t i o n of r e s u l t s to hydrologic studies, such as culvert design, i t i s preferable to overestimate rather than underestimate p r e c i p i t a t i o n . Figure 30 gives the comparative observed and computed orographic p r e c i p i t a t i o n plus computed condensation along the p r o f i l e transects for stable model storms, while Figure 31 gives the same information f o r t o t a l l i f t i n g distances. The graphs i n Figures 30 and 31 show a f a i r l y close correspondence between computed and observed p r e c i p i t a t i o n d i s t r i b u t i o n along the p r o f i l e and as an average over the t o t a l l i f t i n g distance. Of p a r t i c u l a r i n t e r e s t i s the graph f o r storm 43a for the Research Forest (Figure 30d) which shows that the model has predicted the observed decrease i n p r e c i p i t a t i o n between segments AD-S3 and S3-S1. This apparent anomaly i n the actual p r e c i p i t a t i o n pattern, that i s a maximum i n t e n s i t y w ell upwind of the b a r r i e r crest, resulted when a r e l a t i v e l y low freezing l e v e l combined with a warm f r o n t a l inversion i n such a way that orographic l i f t i n g was able to modify p r e c i p i t a t i o n t r a j e c t o r i e s so as to change the usual trend of increasing i n t e n s i t i e s up to or near the b a r r i e r crest 158 NORTHSHORE RESEARCH FOREST 2 -8 §6 I-t 4 a. o 2 LU E o COMPUTED CONDENSATION COMPUTED PRECIPITATION • i OBSERVED PRECIPITATION • i^ n l i O-UBC I UBC- PMO-PMO NV ill WV-CD NV-LC CD-LC (a) S t o r m 3a O-MR MR-AD AD-S3 AD-SI S3-SI 2 ~ 8 § 6 \-t 4 § 2 L U £ 0 LH. O-UBC UBC-PMO PMO-NV nU WV-CD NV-LC CD-LC (b) S t o r m 38a O-MR MR-AD AD-S3 AD-SI S3-SI O-UBC UBC- PMO- WV-CD NV-LC CD-LC PMO NV ( c ) S to rm 39 O-MR MR-AD AD-S3 AD-SI S3-SI UBC-PMO O-MR MR-AD AD-S3 AD-SI S3-SI (d) S t o r m 43a F i g u r e 3 0 . C o m p a r i s o n o f o b s e r v e d v e r s u s computed o r o g r a p h i c c o n d e n s a t i o n and p r e c i p i t a t i o n a l o n g p r o f i l e s f o r s t a b l e mode l s t o r m s . 159 tr x \ z 2 5 4 I 3 t- , £ 2r o. o I LU tr o_ o • COMPUTED CONDENSATION ^ COMPUTED PRECIPITATION • OBSERVED PRECIPITATION 38 i i 39 43 i l l j 1 ill 5 4 3 2 -38 39 43 1 iill ill O-CD O-LC O-CD O-LC O-CD O-LC O-CD O-LC O-SI O-SI O-SI O-SI NORTHSHORE RESEARCH FOREST Figure 31. Comparison of observed versus computed orographic condensation and p r e c i p i t a t i o n over t o t a l l i f t i n g distance for stable model storms. observed i n other study storms. These r e s u l t s support the general v a l i d i t y of the model. Tables 14 and 15 i l l u s t r a t e the r e l a t i v e d ifferences between computed and observed orographic p r e c i p i t a t i o n r e s u l t i n g from use of the mean conversion f a c t o r value of 0.49. These tables show higher r e l a t i v e v a r i a t i o n s at upwind s i t e s over the Fraser Va l l e y than over the mountain slopes. For the three slope segments i n the Northshore area, where model r e s u l t s are most applicable, WV-CD, NV-LC, and CD-LC, 9 of 12 computed values are within ±9% of observed, the maximum deviation i s 25% while the standard deviation was computed to be ±11%. For the three slope segments i n the Research Forest area, MR-AD, AD-S3 and S3-S1, the v a r i a t i o n s are higher with a maximum deviation of 33% and a standard d e v i a t i o n of ±24%. These higher deviations r e s u l t from using the conversion factor derived from Northshore data. 160 TABLE 14 DIFFERENCES BETWEEN COMPUTED AND OBSERVED OROGRAPHIC PRECIPITATION AS A PERCENTAGE OF OBSERVED VALUES FOR STABLE MODEL STORMS - NORTHSHORE AREA Storm O-UBC UBC-PMO PMO-NV WV-CD NV-LC CD-LC O-CD O-LC No. % 3 158 27 -32 -21 -2 -8 -19 -9 38 950 36 -24 -25 12 -8 _4 7 39 333 60 6 5 7 -8 14 16 43a -29 -29 -30 -9 9 -5 -26 -13 TABLE 15 DIFFERENCES BETWEEN COMPUTED AND OBSERVED OROGRAPHIC PRECIPITATION AS A PERCENTAGE OF OBSERVED VALUES FOR STABLE MODEL STORMS -RESEARCH FOREST AREA Storm O-MR MR-AD AD-S3 AD-SI S3-S1 O-Sl No. % 3 45 16 20 6 -16 13 38 -48 -25 32 30 25 3 39 -48 -33 0 -6 -19 -27 43a -8 -30 20 18 17 -3 2. Unstable storms: The orographic model has been applied to the four unstable storms to get an indication of how useful the orographic model might be for this type of storm despite violation of the basis assumption of stability. The results for unstable storms have been summarized in Tables 12 and 13. In addition, the data are compared graphically with data for stable storms. In Figure 32, computed condensation is plotted against observed orographic precipitation for representative 161 0 1 2 3 4 5 OBSERVED PRECIPITATION (MM/HR) (a) Northshore (NV-LC) tr. i \ 2 2 8 < i 4 o o Q U J 2 t-a. o 0 -I 1 1 • — STABLE STORM A -UNSTABLE STORM A — STORM 4 3 B 0 I 2 3 4 OBSERVED PRECIPITATION (MM/HR) (b) Northshore (O-LC) 2 3 4 5 OBSERVED PRECIPITATION (MM/HR) (c) Research Forest (AD-SI) or i \ 5 28 2 6 t -< z U J § 4 o o o U J 2 ZD 0 . s. o o 0 i - r A J I 0 1 2 3 4 OBSERVED PRECIPITATION (MM/HR) (d) Research Forest (O-SI) Figure 32, Observed orographic p r e c i p i t a t i o n versus computed orographic condensation f o r stable and unstable model storms. 162 p r o f i l e segments i n both study areas. These graphs i l l u s t r a t e dramatically the wide v a r i a t i o n s or scatter obtained for unstable storms i n contrast with the close c l u s t e r i n g of stable storm points. Except f o r the Research Forest 0-S1 data (Figure 32d), storm 43b also tends to be set well apart from both the stable and other unstable storm groupings. The marked differences between stable and unstable r e s u l t s are further i l l u s t r a t e d i n Figure 33 which indicates the ranges of conversion factors obtained for these two storm types. In a l l cases, the o v e r a l l range f o r the unstable storms greatly exceeds that for the stable storms. Storm 43b has noticeably higher conversion factor values than the other unstable storms for 5 of the 8 distances i n the Northshore area, but f i t s within the unstable storm range i n the Research Forest area. The graphs i n Figure 33 further h i g h l i g h t the r e l a t i v e l y conservative range of conversion f a c t o r values over the mountain slope segments and t o t a l l i f t i n g distances for the four stable storms. Discussion. A comparison of derived conversion factors with those reported i n the l i t e r a t u r e (see Table 6) shows that the r e s u l t s are consistent with those found i n other studies. For stable storms i n the study area, the t o t a l range i n conversion factor values for mountain segments and t o t a l l i f t i n g distances i s 0.42-0.66 for the Northshore and 0.37-0.67 for the Research Forest. These values are higher than those reported by E l l i o t t and Hovind (1964) for stable a i r and lower than the slope average found by the W.M.O. (1973) but within the range noted for d i s t r i b u t i o n along the same slope i n t h i s l a t t e r report. These ranges I 163 1.6 -= 1.4 JO "or 1.21— o o 1.0 < LL 0.8 !o.6H or ;o.4 |o.2 I s -u -o -STABLE UNSTABLE STORM 43 B O I • S U S U S U S U S U S U s u s u 0-UBC UBC-PMO PMO-NV WV-CD NV-LC CO-LC O-CD O-LC (a) Northshore 1.6-> 1.4 -or 1.2-o o 1.0-< u. 0.8 -z § 0 . 6 -or £ 0 . 4 - . § 0 . 2 -0 — I S - STABLE U - UNSTABLE O - STORM 4 3 B s u s u s u s u s u s u 0-MR MR-AD AD —S3 AD-SI S3-SI O-SI (b) Research Forest Figure 33. Ranges of conversion factors "e" for stable and unstable storms. 164 i n conversion f a c t o r s also l i e within the range of reported values for near neutral storms, f a l l i n g between average values for low (2100 m) b a r r i e r s indicated by E l l i o t t and Shaffer (1962), within the range reported by Myers (1962) and below the value found by Knox (1960). In addition, the conversion f a c t o r s noted above also conform f a i r l y c l o s e l y to most of the data reported for storms of unknown s t a b i l i t y or involving a mixture of stable and unstable storms. Remarkably, the mean conversion factor of 0.49 for the Northshore i s nearly i d e n t i c a l to the value of 0.50 suggested by E l l i o t t and E l l i o t t (1973) as being representative for broad mountain areas. For unstable storms i n the study area, the t o t a l range i n conversion factor values for mountain slope segments and t o t a l l i f t i n g distances i s 0.07-1.08 f o r the North-shore and 0.22-1.10 for the Research Forest. These values encompass those reported i n the l i t e r a t u r e for unstable storms and also f i t within the range reported for storms for which s t a b i l i t y i s not s p e c i f i c a l l y i d e n t i f i e d as well as for near neutral storms (Table 6). This comparison indicates that the approach taken i n adapting the orographic model to the study area i s reasonable and the parameter values chosen r e a l i s t i c . The model i s thus shown to be a p p l i c a b l e to the short l i f t i n g distances involved i n t h i s study, 13-30 km, i n comparison with the much greater distances of 65-160 km reported for many of the other studies (Knox, 1960; U.S. Weather Bureau 1961, 1966; W.M.O.' 1973). Furthermore, the r e l a t i v e l y good reproduction of the p r e c i p i t a t i o n d i s t r i b u t i o n along the p r o f i l e s f o r stable storms obtained by assuming a mean conversion factor would also seem to support the v a l i d i t y of using a 2-stage l i f t for the study area. The closeness of 165 the conversion factor values and low standard deviation for estimated stable storm p r e c i p i t a t i o n over the mountains i s p a r t i c u l a r l y encouraging i n the l i g h t of possible sources of v a r i a t i o n . For example, natural v a r i a t i o n s i n actual conversion e f f i c i e n c i e s can be expected because of v a r i a t i o n s i n storm c h a r a c t e r i s t i c s , including atmospheric temperature and humidity, depth of cloud, height of cloud base, degree of s t a b i l i t y of the a i r , convergence p r e c i p i t a t i o n and evaporation of f a l l i n g p r e c i p i t a t i o n beneath the cloud base or between cloud lay e r s . Estimates of observed orographic r a i n f a l l could be i n error due to po t e n t i a l a r e a l v a r i a t i o n s i n the convergence component between Fraser V a l l e y and mountain s i t e s (U.S. Weather Bureau, 1961). In addition, some v a r i a b i l i t y i n r e s u l t s w i l l be introduced by errors i n measurement of observed p r e c i p i t a t i o n and as a consequence of the s i m p l i f i e d nature of the model, including the use of fi x e d values f o r nodal surface height and p r e c i p i t a t i o n f a l l v e l o c i t i e s and the instant conversion of snow to r a i n at the fr e e z i n g l e v e l . Another important source of v a r i a t i o n would be the use of non-representative radiosonde data, p a r t i c u l a r l y wind data. Because of the distance between the radiosonde stations and the study area, and the intervening influence of topography on lower l e v e l winds, there are bound to be differences i n flow patterns or d i r e c t i o n s at lea s t below b a r r i e r crest heights. Apart from considerations of low l e v e l outflow i n the Fraser Valley, such differences have been ignored and radiosonde wind data used without modification i n the model. However, despite these s i m p l i f i c a t i o n s and p o t e n t i a l sources of v a r i a t i o n , the model has produced f a i r l y consistent r e s u l t s over the mountain slopes for stable storms. 166 In contrast to the conservative range of stable storm conversion f a c t o r s f o r mountain slope segments, a wider v a r i a b i l i t y i n observed-computed r a t i o s and diffe r e n c e s over the Fraser V a l l e y has been noted. This r e s u l t i s not s u r p r i s i n g . In the mountains, the topography helps define the l i f t i n g surface f a i r l y w e l l . Over the Fraser Valley, d e f i n i t i o n of the l i f t i n g surface has been more a r b i t r a r y and e f f e c t i v e l i f t i n g probably v a r i e s more from storm to storm depending on degree of a i r mass s t a b i l i t y and nature of low l e v e l outflow. V a r i a b i l i t y i n re s u l t s would be introduced according to dif f e r e n c e s i n actual versus assumed height and extent of l i f t i n g over the Fraser Valley, as we l l as by differences i n atmospheric c h a r a c t e r i s t i c s between v a l l e y and mountain areas. For example, E l l i o t t and E l l i o t t (1973) suggest that cloud layers which are separated upwind of the mountains might become merged with orographic l i f t i n g over the mountains. A v a r i a t i o n i n conversion factors between the Northshore and Research Forest areas has been noted f o r i n d i v i d u a l storms, with the mean value being lower for the Research Forest. Stable storm conversion factors for AD-SI and 0-S1 tend to be cl o s e r i n magnitude to those f o r NV-LC and O-LC, res p e c t i v e l y , than f o r WV-CD and O-CD. An important cause of these differences could be differences i n l o c a l terrain-wind i n t e r a c t i o n s . The WV-CD statio n s are aligned closer to the highest part of the l i f t i n g ridge for southwest winds than the NV-LC stations which are located nearer to the end of the ridge. Consequently, orographic l i f t i n g d i r e c t l y over NV-LC, and thus the rate of orographic p r e c i p i t a t i o n , could be a l i t t l e l e s s than over WV-CD as the a i r has more of an opportunity to flow around the end of the ridge at that point. 167 In the Research Forest area, two terrain factors could potentially reduce orographic lifting, and hence orographic precipitation, in the vicinity of the chosen-transect. First, the south-north oriented ridge could.tend to deflect southwest winds more parallel to the ridge. Second, the ridge crest is sloping upward from south to north and its effective mean lifting height could be lower than that indicated by simply averaging crest elevation across the 3.2 km strip. A real reduction in orographic lifting over the Research Forest and NV-LC transects, not taken into account by the model, would in part help explain why conversion factors obtained using station CD data tend to be higher than those for the other two sites for stable storms. Another possibility is that the derived precipitation at Surrey Municipal Hall is not entirely free from orographic effects as discussed in Chapter III. An overestimation of the convergence component would result in an under-estimation of the orographic component and hence, of the conversion factors for the Research Forest area. A relatively high variability in unstable storm conversion factors for both study areas has been noted. This result could be attributed to many causes. The problem of spatial variability in release of instability has already been discussed in Chapter III in relation to storm 19. For the storms examined, the vertical depth of cloud and continuity of saturated air could have been more variable than among the stable storms. Model calculations for unstable storms are probably even more critically dependent on proper timing of radiosonde observations than for stable storms because of the need to adequately assess the depth of unstable layers. Weaver (1962) found that even 168 radiosonde ascents at 6-hour i n t e r v a l s were seldom adequate to p r o p e r l y evaluate the r o l e of i n s t a b i l i t y near f r o n t s or other areas of marked convergence. This problem can be c r i t i c a l as suggested by r e s u l t s f o r storm 43b. An e q u a l l y important i f not o v e r - r i d i n g source of v a r i a b i l i t y i s the l a c k of i n f o r m a t i o n on convective v e r t i c a l motions i n unstable a i r f o r study storms. The use of s t a b l e , laminar f l o w f o r unstable storm c a l c u l a t i o n s d i d produce conversion f a c t o r values which f a l l w i t h i n the range reported i n the l i t e r a t u r e , but the r e s u l t s are so v a r i a b l e that t h i s approach must be considered u n r e l i a b l e . Suggested design values f o r model parameters. In summary, the orographic model i n v e s t i g a t e d i n t h i s t h e s i s would appear to be most s u i t a b l e f o r estimating p r e c i p i t a t i o n during major storms w i t h s t a b l e a i r where there i s a higher p r o b a b i l i t y of a saturated atmosphere to great heights and c o n s i s t e n t e f f i c i e n c y i n converting o r o g r a p h i c a l l y -induced condensation to p r e c i p i t a t i o n . Indeed, one of the major a p p l i c a t i o n s of t h i s model has been i t s use i n estimating maximum probable p r e c i p i t a t i o n (Knox, 1960; U.S. Weather Bureau 1961, 1966). The model has only been t e s t e d against four s t a b l e storms which occurred i n September and October. I t r e q u i r e s f u r t h e r t e s t i n g against major storms which occur during a l l months of the year to confirm model parameter values adopted during t h i s study. However, these parameter values can serve as u s e f u l guides i n the i n t e r i m , at l e a s t f o r the mountains north of the Fraser V a l l e y and the adjacent mainland coast i n the l e e of Vancouver I s l a n d . For s t a b l e storms i n these mainland areas, the f o l l o w i n g 169 interim design values and considerations are recommended. The t e r r a i n w i l l determine the b a r r i e r height. Wind components normal to the l i f t i n g b a r r i e r should be used. The c o r r e l a t i o n between the southwest wind component and orographic r a i n f a l l on the Research Forest could be a t y p i c a l and use of a d i r e c t i o n other than normal to a b a r r i e r would have to be indicated by a si m i l a r c o r r e l a t i o n study. The presence of low l e v e l outflow i n the Fraser V a l l e y confounds the d i r e c t e f f e c t of topographic l i f t i n g i n t h i s area. Hence, i t was necessary to set the l i f t i n g distance accordingly. E x i s t i n g r a i n f a l l and wind data could be used likewise to e s t a b l i s h l i f t i n g distances i n other parts of the lower Fraser V a l l e y . In other areas where no low l e v e l outflow i s suspected, i t w i l l s t i l l be necessary to make some allowance f o r upwind extension of l i f t i n g i n stable a i r . Data f o r the Northshore area suggest that t h i s e f f e c t might extend from 3 to 17 km upwind of the mountain slope. In comparison, the U.S. Weather Bureau (1961) adopted a value of 8 km to account for t h i s factor i n i t s c a l c u l a t i o n s of p r e c i p i t a t i o n along the C a l i f o r n i a coast. This value seems to be a reasonable compromise and i t i s recommended that l i f t i n g be i n i t i a t e d 8 km upwind of the f i r s t s i g n i f i c a n t r i s e i n t e r r a i n i n s i m i l a r areas where there i s no a d d i t i o n a l information to in d i c a t e otherwise. A nodal surface at 650 mb i n conjunction with a conversion factor of about 0.50 should be applic a b l e for b a r r i e r s up to about 1220 metres i n height. This nodal surface pressure could be acceptable for higher b a r r i e r s but a d i f f e r e n t conversion factor might be necessary. Average f a l l i n g rates f o r p r e c i p i t a t i o n p a r t i c l e s can be set at 5.8 m/s for r a i n and 1.0 m/s f o r snow. In comparison, values of 6.0 and 1.5 m/s have been used i n 170 s t u d i e s of maximum probable p r e c i p i t a t i o n (U.S. Weather Bureau 1961; W.M.O. 1973). For p r a c t i c a l purposes, use of these higher values would not a p p r e c i a b l y change computed p r e c i p i t a t i o n and t h e i r use should not be necessary unless the o b j e c t i v e i s the same, that i s to estimate maximum probable p r e c i p i t a t i o n . Cloud base heights can be estimated i f s u i t a b l e surface weather r e p o r t s are a v a i l a b l e , otherwise the cloud base may be assumed to be at ground l e v e l . As already noted, the design model parameter values suggested above apply to the protected southern mainland c o a s t a l mountains. The a i r reaching these mountains w i l l have had some moisture removed during passage over the mountains of the Olympic Peninsula and Vancouver I s l a n d . For the west coast of Vancouver I s l a n d and exposed areas of the mainland coast, i t i s l i k e l y t hat a higher conversion f a c t o r would be r e q u i r e d , assuming higher atmospheric moisture content r e s u l t s i n higher a c t u a l p r e c i p i t a t i o n and assuming other model parameter values remain unchanged. Estimating T o t a l Short-period  P r e c i p i t a t i o n T o t a l s h o r t - p e r i o d (6-hour) p r e c i p i t a t i o n i s the sum of the orographic and convergence components. As described i n the s e c t i o n on model procedures, the convergence components i n the study areas were taken as the t o t a l observed p r e c i p i t a t i o n at Vancouver I n t e r n a t i o n a l A i r p o r t and Surrey M u n i c i p a l H a l l f o r the Northshore and Research Forest areas, r e s p e c t i v e l y . Hence, f o r the study areas, t o t a l estimated p r e c i p i t a t i o n can be obtained by a d d i t i o n of computed orographic and observed convergence values ( p a r t i a l computed). However, i n other areas, 171 the s t a t i o n f o r which observed data i s a v a i l a b l e might be located close to the mountain slope and thus be under the influence of orographic e f f e c t s . The problem i n t h i s case would be to estimate the convergence component of t o t a l p r e c i p i t a t i o n measured at such a s t a t i o n . One s o l u t i o n would be to use the model to estimate orographic p r e c i p i t a t i o n between two c l o s e l y spaced p r e c i p i t a t i o n t r a j e c t o r i e s centred on the observing s t a t i o n . The d i f f e r e n c e between the s t a t i o n t o t a l and the derived orographic value could be used as an estimate of the convergence component. This approach has been followed f o r stable model storms using s t a t i o n WV for the Northshore and s i t e MR f o r the Research Forest as observation points. Exploratory c a l c u l a t i o n s indicated that the most use f u l r e s u l t s were obtained using p r e c i p i t a t i o n t r a j e c t o r i e s spaced 2 km apart, one terminating at the s t a t i o n i t s e l f and one terminating 2 km downwind. The use of t r a j e c t o r i e s centred on the stations gave orographic values that were f a r too low. A conversion factor of 0.49 was used i n computing orographic p r e c i p i t a t i o n from the condensation values. Computation of the convergence component i s i l l u s t r a t e d i n Table 16 which also gives the observed values. The observed, p a r t i a l computed (computed orographic + observed convergence) and t o t a l computed (computed orographic + estimated convergence) values of t o t a l p r e c i p i t a t i o n are l i s t e d i n Tables 17 and 13. To f a c i l i t a t e comparisons, the r a t i o s of p a r t i a l and t o t a l computed to t o t a l observed p r e c i p i t a t i o n plus the r a t i o of computed to observed orographic components are presented as percentages i n Tables 19 and 20. The a d d i t i o n of observed convergence to computed orographic values reduces the v a r i a t i o n between computed and observed 172 TABLE 16 ESTIMATION OF CONVERGENCE COMPONENT OF PRECIPITATION FOR STABLE MODEL STORMS Northshore Research Forest Storm C Obs. Est. Obs. C Obs. Est. Obs. No. (WV+2) .49C WV Conv. VAP (MR+2) .49C MR Conv. SM mm/hr 3 4.79 2.35 4.39 2.04 0.71 3.13 1.53 2.29 0.76 1.19 38 2.08 1.02 1.32 0.30 0.13 1.43 0.70 2.11 1.41 0.64 39 3.26 1.60 2.03 0.43 0.46 2.08 1.02 3.00 1.93 1.09 43 3.37 1.65 3.61 1.96 0.64 2.96 1.45 2.92 1.47 1.27 TABLE 17 COMPUTED AND OBSERVED TOTAL PRECIPITATION FOR STABLE MODEL STORMS - NORTHSHORE AREA Storm No. O-UBC UBC-PMO PMO-NV mm WV-/hr -CD NV-LC CD--LC 0--CD 0--LC 3 Observed 0.90 1.86 3.69 5 .06 5. 68 6 .16 2 .80 3 .17 P a r t i a l com. 3 1.17 2.17 2.72 4 .15 5. 56 5 .72 2 .40 2 .96 Tot a l com.b 3.21 3.50 4.05 5 .48 6. 89 7 .05 3 .73 4 .29 38 Observed 0.17 0.55 1.69 3 .20 4. 42 5 .72 1 .27 1 .73 P a r t i a l com. 0.55 0.68 1.32 2 .44 4. 95 5 .26 1 .22 1 .90 Total com. 0.72 0.87 1.49 2 .61 5. 12 5 .43 1 .39 2 .07 39 Observed 0.55 0.96 1.88 3 .09 4. 36 5 .18 1 .55 1 .99 P a r t i a l com. 0.98 1.26 1.97 3 .21 4. 62 4 .80 1 .70 2 .23 Tot a l com. 0.95 1.23 1.94 3 .18 4. 59 4 .77 1 .67 2 .20 43a Observed 1.05 2.15 3,24 4 .16 4. 55 5 .08 2 .65 2 .88 P a r t i a l com. 1.39 1.71 2.45 3 .83 4. 92 4 .34 2 .13 2 .60 Tot a l com. 2.25 3.03 3.77 5 .15 6. 24 6 .16 3 .45 3 .92 aComputed orographic 4- observed convergence (VAP) ^Computed orographic + estimated convergence (WV+2) 173 TABLE 13 COMPUTED AND OBSERVED TOTAL PRECIPITATION FOR STABLE MODEL STORMS - RESEARCH FOREST AREA Storm O-MR MR-AD AD-S3 AD-SI S3-S1 O-SI No. mm /hr 3 Observed 1.74 2.86 4.51 4.95 5.97 2.56 P a r t i a l computed 1.99 3.12 5.17 5.18 5.20 2.80 T o t a l computed^ 1.56 2.69 4.74 4.75 4.77 2.37 38 Observed 1.38 2.49 3.56 3.85 4.54 2.05 P a r t i a l computed 1.14 2.03 4.51 4.82 5.53 2.01 T o t a l computed 1.91 2.80 5.28 5.59 6.30 2.78 39 Observed 2.05 3.38 4.36 4.63 5.27 2.77 P a r t i a l computed 1.59 2.63 4.36 4.40 4.49 2.32 T o t a l computed 2.48 3.52 5.25 5.29 5.38 3.21 43a Observed 2.10 3.81 4.23 4.13 3.86 2.77 P a r t i a l computed 2.03 3.05 4.81 4.65 4.30 2.72 T o t a l computed 2.23 3.25 5.01 4.85 4.50 2.92 Estimated orographic + observed convergence (SM) Estimated orographic + estimated convergence (MR+2) ( t o t a l ) p r e c i p i t a t i o n i n comparison w i t h the v a r i a t i o n which occurs when the orographic components alone are compared. However, the use of estimated convergence values changes the r e l a t i v e degree of v a r i a t i o n . The r e s u l t i s that d i f f e r e n c e s between computed and observed t o t a l p r e c i p i t a t i o n are both increased and decreased i n r e l a t i o n to d i f f e r -ences r e s u l t i n g from the use of observed convergence values. There i s no apparent p a t t e r n i n these changes e i t h e r i n r e l a t i o n to d i f f e r e n t storms or to i n t e r v a l s along the p r e c i p i t a t i o n p r o f i l e s f o r i n d i v i d u a l storms. For mountain slope segments, the range of d i f f e r e n c e s f o r the Northshore area remains s i m i l a r w i t h a maximum d e v i a t i o n of 28% and a s l i g h t l y higher standard d e v i a t i o n of +15%. For the Research Forest 174 TABLE 19 COMPUTED TOTAL AND OROGRAPHIC PRECIPITATION AS A PERCENTAGE OF OBSERVED PRECIPITATION FOR STABLE MODEL STORMS - NORTHSHORE AREA Storm No. O-UBC UBC-PMO PMO-NV % WV-CD NV-LC CD-LC O-CD O-LC 9. 3 Orographic 258 127 68 79 98 92 81 91 P a r t i a l com. b 130 117 74 82 98 93 86 93 T o t a l com. c 357 188 110 108 121 114 133 135 38 Orographic 1050 136 76 75 112 92 96 107 P a r t i a l com. 324 124 78 76 112 92 96 107 T o t a l com. 424 158 88 82 116 95 109 116 39 Orographic 433 160 106 105 107 92 114 116 P a r t i a l com. 178 131 105 104 106 93 110 112 T o t a l com. 173 128 103 . 103 105 92 108 110 43a Orographic 71 71 70 91 109 95 74 87 P a r t i a l com. 132 80 76 92 108 95 80 90 T o t a l com. 214 141 116 124 137 121 130 136 Computed orographic/observed orographic " P a r t i a l computed/total observed °Total computed/total observed area, the range i s higher w i t h a maximum d e v i a t i o n of 48%, but the standard d e v i a t i o n i s a l i t t l e lower at ±20%. One consequence of the need to estimate the convergence component i s the increased u n c e r t a i n t y i n estimated p r e c i p i t a t i o n . In some cases the estimates may a c t u a l l y be improved w h i l e i n others the d i f f e r e n c e s between computed and a c t u a l p r e c i p i t a t i o n may be increased. 175 TABLE 20 COMPUTED TOTAL AND OROGRAPHIC PRECIPITATION AS A PERCENTAGE OF OBSERVED PRECIPITATION FOR STABLE MODEL STORMS - RESEARCH FOREST AREA Storm O-MR MR-AD AD-S3 AD-SI S3-S1 0-Sl No. % 3 , . a Orographic ^ 145 116 120 106 84 118 P a r t i a l computed 114 109 115 105 87 109 T o t a l computed 0 90 94 105 96 80 93 38 Orographic 52 75 132 130 125 97 P a r t i a l computed 83 82 127 125 122 98 T o t a l computed 138 112 148 145 139 136 39 Orographic 52 67 100 94 81 73 P a r t i a l computed 76 78 100 95 85 84 T o t a l computed 121 104 120 114 102 116 43a Observed 92 70 120 118 117 97 P a r t i a l computed 97 80 114 113 111 98 T o t a l computed 106 85 118 117 117 105 Computed orographic/observed orographic P a r t i a l computed/total observed C T o t a l computed/total observed A l t e r n a t i v e Approaches to Est i m a t i n g P r e c i p i t a t i o n over Mountains Ferguson (1972) has noted the three main approaches that can be taken to est i m a t i n g p r e c i p i t a t i o n over mountainous areas: namely, (1) p h y s i c a l models of the type i n v e s t i g a t e d i n t h i s t h e s i s , (2) s t a t i s -t i c a l r e g r e s s i o n equations r e l a t i n g p r e c i p i t a t i o n to physiographic v a r i a b l e s , and (3) a combined p h y s i c a l - s t a t i s t i c a l model. The s t a t i s t i c a l approach i n v o l v i n g o n ly physiographic parameters i s s t r i c t l y v a l i d only f o r the area i n which the r e g r e s s i o n equation i s developed. The combined p h y s i c a l - s t a t i s t i c a l approach has two expressions. One 176 method i n v o l v e s the use of m e t e r o l o g i c a l v a r i a b l e s to develop r e g r e s s i o n equations (Platzman 1948) o r d e r i v a t i o n of an (orographic) p r e c i p i t a t i o n parameter or index based on p h y s i c a l p r i n c i p l e s which i n t u r n i s used to develop r e g r e s s i o n equations (Danard 1971, 1975). Regression Equations developed i n t h i s way are s t i l l o n l y v a l i d f o r the area i n which they are developed. The second method i n v o l v e s the use of s t a t i s t i c a l l y derived r e l a t i o n s h i p s to estimate the values of parameters i n a p h y s i c a l model or equation ( E l l i o t t and Shaffer 1962). This approach would have more general a p p l i c a b i l i t y . Another approach would be to attempt to s i m p l i f y the orographic model i n order to reduce computation time. E l l i o t t and Shaffer (1962) took t h i s approach to one extreme and developed the f o l l o w i n g r e l a t i o n -s h ip: I = ek(u) DX ( n ) where I i s orographic p r e c i p i t a t i o n r a t e , e i s the f r a c t i o n of condensate removed as p r e c i p i t a t i o n , k represents r a t e of condensation per u n i t of l i f t , to i s the mean v e r t i c a l v e l o c i t y over the depth of l i f t , D i s the mean depth of l i f t between ground and nodal surface, X i s the average width of s e c t i o n scoured by p r e c i p i t a t i o n and F i s the length* along the ground over which the p r e c i p i t a t i o n i s d i s t r i b u t e d . They derived co from the expression co = % V VZ (12) where V\ i s the i n f l o w h o r i z o n t a l wind speed at ground l e v e l and VZ the t e r r a i n slope, and assumed a saturated atmosphere w i t h pseudo-adiabatic (moist) lapse r a t e . Walker (1961) used Fulks Table ( L i s t , 1966) to 177 derive condensation rates and s i m p l i f i e d t r a j e c t o r y analyses by assuming v e r t i c a l f a l l o u t and applying an adjustment f a c t o r . Similar s i m p l i f i c a t i o n s were tested during exploratory c a l c u l a t i o n s using storm 43 data, including use of mean inflow wind speed and mean mixing r a t i o d i f f e r e n c e i n equation (3) and s i m p l i f i e d p r e c i p i t a t i o n t r a j e c t o r i e s . These s i m p l i f i c a t i o n s merely added another source of v a r i a t i o n or error and were not p a r t i c u l a r l y time-saving. Hence, further a p p l i c a t i o n of t h i s approach was abandoned. Moreover, the use of a computer would e s s e n t i a l l y eliminate the need for such a l t e r a t i o n s of the basic model procedures. Recommendations for Further Studies The model has been tested on a small number of storms which occurred during the f a l l months and found r e l i a b l e for stable cases only. Further t e s t i n g i s required on major storms with stable a i r which occur during a l l seasons. Testing should be done i n the same area to take advantage of the experience gained i n t h i s study and the a v a i l a b i l i t y of p r e c i p i t a t i o n data. However, the model needs testing i n other coastal areas wherever s u f f i c i e n t data are a v a i l a b l e . Information i s needed on conversion f a c t o r s for higher b a r r i e r s and the a p p l i c a -b i l i t y of the model to areas downwind of the i n i t i a l l i f t i n g b a r r i e r . To support the use of p r e c i p i t a t i o n models of the type investigated i n t h i s study, more quantitative information on l o c a l low l e v e l wind flow patterns and terrain-wind i n t e r a c t i o n s , and how to make appropriate adjustments to radiosonde wind data would be extremely valuable. S p e c i f i c information on wind flow on upwind mountain slopes under 178 d i f f e r e n t degrees of a i r mass s t a b i l i t y would a l s o be h e l p f u l . The l a c k of s p e c i f i c low l e v e l wind flow p a t t e r n s f o r storm s i t u a t i o n s was c i t e d as one of the main problems i n assessi n g orographic i n f l u e n c e s on p r e c i p i t a t i o n i n the Beaufort Range study (Ferguson, Hunter and Schaefer, 1974). Studies of wind p r o f i l e s and r e l a t i o n s h i p s of the type c a r r i e d out by the U.S. Weather Bureau (1961) and Weaver (1962) i n C a l i f o r n i a would a l s o be very u s e f u l i n B r i t i s h Columbia. To f a c i l i t a t e computations, a computer program of the model should be developed or obtained, i f p o s s i b l e , from other agencies or i n d i v i d u a l s who have already done so ( E l l i o t t and E l l i o t t , 1973; U.S. Weather Bureau, 1966). With the help of a computer, an o p t i m i z a t i o n technique such as EVOP could be used to o b t a i n the most s u i t a b l e combinations of model parameter values (McNeil and R u s s e l l , 1972). In a d d i t i o n to f u r t h e r examination of the s i m p l i f i e d f l o w model used i n t h i s t h e s i s , c o n s i d e r a t i o n should be given to t e s t i n g the more complex wind flow models of Myers (1962) (Appendix V I I I ) and Fraser, et a l . (1973) which r e q u i r e the use of a computer f o r p r a c t i c a l a p p l i c a t i o n . The present model has been t e s t e d against mean 6-hour r a i n f a l l i n t e n s i t i e s . Further work could be done to t e s t the model against e i t h e r shorter or longer period data or, conversely, to r e l a t e maximum 6-hour storm i n t e n s i t i e s to values f o r s h o r t e r o r longer periods (U.S. Weather Bureau, 1966). In t h i s way, model r e s u l t s would have a p o t e n t i a l l y wide a p p l i c a b i l i t y . F i n a l l y , ways should be sought to improve estimates of the convergence component of p r e c i p i t a t i o n f o r s i t u a t i o n s where t h i s determination i s necessary. 179 Conclusions The orographic model has been adapted and tested on four stable and four unstable storms i n an area where the t e r r a i n departs from the t h e o r e t i c a l l y i d e a l c onfiguration and i s separated by distance and intervening mountains from the sources of upper a i r data. In addition, d i r e c t orographic e f f e c t s are confounded by a d d i t i o n a l l i f t i n g imparted to p r e v a i l i n g storm winds by low l e v e l outflow i n the v a l l e y upwind of the mountains. Despite these apparent l i m i t a t i o n s , these t e s t s i n d i c a t e that the model can c o n s i s t e n t l y provide reasonable estimates of the magnitude and d i s t r i b u t i o n of orographic p r e c i p i t a t i o n over the mountain slope upwind of the b a r r i e r crest for major storms with stable a i r which occur during the f a l l months of September and October. Moreover, the range of conversion factors for p r e c i p i t a t i o n over the mountain slopes and over the t o t a l l i f t i n g distances found i n t h i s study for stable storms i s conservative and consistent with values reported i n the l i t e r a t u r e f o r studies i n other areas. These two factors i n d i c a t e that the adaptation of the model and s e l e c t i o n of model parameter values have been r e a l i s t i c . Differences i n conversion factors between the Northshore and Research Forest areas were found for i n d i v i d u a l storms. However, the o v e r a l l ranges i n conversion factor values for p r e c i p i t a t i o n over the mountain slopes were s u f f i c i e n t l y s i m i l a r and conservative to support the v a l i d i t y of the model and the approach taken i n adapting i t to these two s p e c i f i c areas. For the unstable storms, the conversion factors obtained were within the range reported i n the l i t e r a t u r e but the r e s u l t s were s u f f i c i e n t l y v a r i a b l e that the approach taken must be considered 180 u n r e l i a b l e . The chief problems with unstable storms are the lack of information on convective v e r t i c a l motions for s p e c i f i c storms, p o t e n t i a l l y inadequate timing of radiosonde ascents and s p a t i a l v a r i a b i l i t y i n the release of i n s t a b i l i t y . The most promising use of the model i s for estimating p r e c i p i t a t i o n on windward mountain slopes during stable storms with major p r e c i p i t a t i o n . On the basis of r e s u l t s f o r the l i m i t e d number of stable test storms examined, the r e l i a b i l i t y of the model for t h i s a p p l i c a t i o n would appear to be f a i r l y high. For conditions of optimum orographic l i f t i n g of storm winds, model estimates with a r e l a t i v e l y low standard deviation of ±11% and a maximum deviation of 25% were obtained. While t h i s study has shown the p o t e n t i a l value of the model for a p p l i c a t i o n i n the coastal mountains of southwestern B r i t i s h Columbia, a d d i t i o n a l t e s t i n g and development i s d e f i n i t e l y required and recommendations f o r further studies have been made. In the interim, design values of model parameters and other considerations for applying the model on windward slopes i n the mountains north of the Fraser Va l l e y and on the coa s t a l mainland i n the lee of Vancouver Island have been suggested. CHAPTER V VARIATIONS IN PRECIPITATION ON THE RESEARCH FOREST Introduction The p r e c i p i t a t i o n data c o l l e c t e d on the Research Forest i t s e l f have been examined with the objective of i d e n t i f y i n g a r e a l patterns and assessing small scale v a r i a t i o n s i n r e l a t i o n to t e r r a i n features and meteorological v a r i a b l e s . A r e a l p r e c i p i t a t i o n patterns have been studied using eigenvector a n a l y s i s , while the s p a t i a l r e l a t i o n s h i p s between st a t i o n p a i r s have been examined using c o r r e l a t i o n a n a l y s i s . Small scale v a r i a t i o n s i n p r e c i p i t a t i o n at a number of s i t e s within the Research Forest have also been examined, including the r e s u l t s of vectopluviometer measurements, v a r i a t i o n s near s i t e s 7 and 9 which are situated on ridgetops, wind e f f e c t s on p r e c i p i t a t i o n at the Spur-17 s i t e , and v a r i a t i o n s among s i t e s 1-6. Areal Patterns of P r e c i p i t a t i o n The a p p l i c a t i o n of the orographic model discussed i n the previous chapter has shown that the general d i s t r i b u t i o n of p r e c i p i t a -t i o n i n the Research Forest area can be explained by f i r s t - o r d e r l i f t i n g e f f e c t s of l o c a l t e r r a i n . This r e s u l t suggests that the general pattern of p r e c i p i t a t i o n on the Research Forest should be strongly r e l a t e d to t e r r a i n features. Eigenvector analysis has been used to i d e n t i f y 181 182 p r i n c i p a l patterns of storm p r e c i p i t a t i o n to help assess to what extent p r e c i p i t a t i o n i s r e l a t e d to topography within the Research Forest. In addition, c o r r e l a t i o n s between p r e c i p i t a t i o n data for storm p a i r s have been derived to determine the nature of r e l a t i o n s h i p s among measurement s i t e s . This information serves as another measure of the degree of influence of t e r r a i n on p r e c i p i t a t i o n patterns. Eigenvector Analysis Eigenvectors are orthogonal functions which can be used to describe or represent patterns or arrays of data. They have an advantage over other types of orthogonal functions i n that they are derived from the data i t s e l f and account for a higher proportion of t o t a l variance than other orthogonal representations (Stidd, 1967; Kutzbach, 1967; Probert-Jones, 1973). Eigenvectors have been used to examine a v a r i e t y of meteorological data, with p a r t i c u l a r a p p l i c a t i o n to p r e c i p i t a t i o n patterns reported by Stidd (1967), Kutzbach (1967) and Dyer (1975). As noted above, eigenvector analysis was used to i d e n t i f y basic patterns of a r e a l p r e c i p i t a t i o n on the Research Forest. An a d d i t i o n a l objective was to determine i f s p e c i f i c patterns thus i d e n t i f i e d could be r e l a t e d to meteorological parameters, p a r t i c u l a r l y winds or a i r mass s t a b i l i t y , and topography. A computer program was developed using several IBM subroutines and based on the approach outlined by Stidd (1967), to apply the eigenvector technique. A copy of t h i s program plus an example of i t s a p p l i c a t i o n i s given i n Appendix XV. Computations were c a r r i e d out using both t o t a l storm 183 precipitation and mean short period, mostly 6-hour, rainfall intensities for intervals representative of each storm on the Research Forest. Analyses were done for a l l possible storms (a maximum of 40 due to computer storage limitations - storm number 35 only was omitted), sub-samples of storms to include site-4 and station-LL data, 13 stable storms, 9 storms involving potential instability triggering, 8 storms involving convective instability triggering, 17 storms with southerly winds (160°-205°) and 23 storms with southwest-westerly winds (206-315°). For comparison with individual storm data, total precipitation values measured during the study period were used in conjunction with data from Research Forest stations MC, AD and LL to estimate mean annual precipitation at each site. Results. The results of the eigenvector analysis are summarized in Table 21 which gives the cumulative explained variances for the first 8 eigenvectors, and Figures 34 to 36 which show pertinent precipitation patterns. The outstanding feature of these results is the fact that the first eigenvector accounts for almost a l l of the variance, with the total variance being explained by the first 4 to 6 eigenvectors in most cases. Moreover, the explained variance for short period intensities is only slightly less than that for storm totals (Table 21). Others have also found that the first few eigenvectors contain most of the variance (Stidd, 1967; Kutzbach, 1967). Even for convective storms where a high degree of variability in areal precipitation might be expected, the first eigenvector accounts for over 96% of the total variance (Table 21). 184 TABLE 21 CUMULATIVE EXPLAINED VARIANCE FOR THE FIRST 8 EIGENVECTORS (EV) FOR DIFFERENT STORM GROUPS Storm Group EV1 EV2 EV3 EV4 EV5 EV6 EV7 EV8 Al l storms (40) . ST 0.991 0.996 0.998 0.999 0.999 1.000 1.000 1.000 I 0.980 0.989 0.993 0.996 0.998 0.999 0.999 1.000 Stable storms (13) ST 0.991 0.997 0.998 0.999 1.000 1.000 1.000 1.000 I 0.980 0.992 0.996 0.998 0.999 1.000 1.000 1.000 Unstable -TP storms (9) ST 0.997 0.998 0.999 1.000 1.000 1.000 1.000 1.000 I 0.990 0.996 0.998 0.999 1.000 1.000 1.000 1.000 j Unstable - TC storms (8) ST 0.975 0.990 0.994 0.997 0.999 1.000 1.000 1.000 I 0.964 0.982 0.994 0.998 1.000 1.000 1.000 1.000 Storms with  southerly  winds (17) ST 0.992 0.997 0.998 0.999 0.999 1.000 1.000 1.000 I 0.986 0.993 0.996 0.998 0.999 0.999 1.000 1.000 Storms with  s'outhwest- westerly winds  (23) ST 0.992 0.997 0.999 0.999 1.000 1.000 1.000 1.000 I 0.978 0.989 0.994 0.998 0.999 0.999 1.000 1.000 ST - storm total precipitation data I - short-period precipitation intensity data (-c) eigenvector 2 1 8 5 (d) topography (m) Figure 34. Areal patterns of p r e c i p i t a t i o n rates on the Research Forest f or storm 38 observed values and f i r s t 2 eigenvectors as derived from t o t a l group of study storms. 186 observed Eigenvector I (a) Storm 4 0 (total storm precipitation - mm ) observed Eigenvector I (b) Storm 42 ( 6 - h o u r precipitat ion intensity - m m / h r ) Figure 35. Area l patterns of p r ec ip i t a t i on on the Research Forest for observed values and f i r s t eigenvectors as derived for unstable-convective (storm 40) and southerly wind (storm 42) storm groups. 187 For a l l storm groups and f o r both storm t o t a l s and short period i n t e n s i t i e s , the f i r s t eigenvector produced a s i n g l e p a t t e r n w h i l e each of the second and t h i r d eigenvectors produced two pa t t e r n s . The two patterns i n each case are i d e n t i c a l but w i t h the signs ( p o s i t i v e or negative) of eigenvector p r e c i p i t a t i o n values reversed. The patterns f o r eigenvector 1 are n e a r l y i d e n t i c a l f o r storm groups i n v o l v i n g a l l storms, s t a b l e and unstable (TP) storms and storms w i t h southwest-westerly winds. In a l l cases, eigenvector 1 patterns were e s s e n t i a l l y the same f o r both storm t o t a l s and s h o r t - p e r i o d i n t e n s i t i e s . For eigenvectors 2 and 3, the patterns v a r i e d among the d i f f e r e n t storm groups, but no s i g n i f i c a n c e can be attached to the d i f f e r e n c e s because of the n e g l i g i b l e v a r i a n c e explained by these two eigenvectors. Figure 34 i l l u s t r a t e s f o r storm 38 the patte r n s of a r e a l s h o r t - p e r i o d p r e c i p i t a t i o n i n t e n s i t i e s d erived from the f i r s t two eigenvectors f o r the " a l l storm" group plus a map of topographic contours f o r comparison. The a l t e r n a t e p a t t e r n f o r eigenvector 2 would have the same i s o h y e t a l l i n e c o n f i g u r a t i o n but p o s i t i v e and negative signs would be reversed. For the unstable (TC) storm group, the a r e a l p a t t e r n i s a l i t t l e d i f f e r e n t f o r eigenvector 1 from that represented by storm 38, as portrayed i n Figure 35a f o r storm 40 storm t o t a l p r e c i p i t a t i o n . In a d d i t i o n , the eigenvector 1 p a t t e r n f o r storms w i t h s o u t h e r l y winds a i s o d i f f e r e d a l i t t l e from those of the other storm groups as shown i n Fi g u r e 35b f o r storm 42 i n t e n s i t y data. The p a t t e r n f o r estimated mean annual p r e c i p i t a t i o n i s given i n F i g u r e 36. 188 Figure 36. Pattern of estimated mean annual p r e c i p i t a t i o n (mm) on Research Forest. Discussion. A comparison of p r e c i p i t a t i o n isohyets for eigenvector 1 i n Figure 34b with the topographic contours i n Figure 34d i n d i c a t e s a strong a s s o c i a t i o n between the p r e c i p i t a t i o n pattern and topographic configuration. P r e c i p i t a t i o n gradient i s highest over the southern portion of the Research Forest, as i s t e r r a i n slope, and lowest over the northern portion where the t e r r a i n l e v e l s out. The influence of the major ridge to the east (not shown on the diagram of Figure 34d) i s indicated by the north-south alignment of the isohyets over the northern part of the Research Forest. The fact that the eigenvector analysis indicates e s s e n t i a l l y one basic 189 p a t t e r n i n a l l storms and that t h i s p a t t e r n conforms f a i r l y c l o s e l y to topographic contours i s c l e a r evidence of the dominating i n f l u e n c e of t e r r a i n on the d i s t r i b u t i o n of r a i n f a l l on the Research F o r e s t . The p a t t e r n of mean annual p r e c i p i t a t i o n shown i n Figure 35 i s a l s o very s i m i l a r to the eigenvector p a t t e r n i n Figure 34b and the topographic p a t t e r n i n Figure 34d, thus lending f u r t h e r support to t h i s c o n c l u s i o n . The eigenvector analyses f o r c o n v e c t i v e l y unstable and souther-l y wind storm groups i n d i c a t e that c o n s i s t e n t v a r i a t i o n s i n the b a s i c p r e c i p i t a t i o n p a t t e r n on the Research Forest do occur f o r these types of storms as shown i n Figure 35. The eigenvector 1 p a t t e r n v a r i a t i o n f o r c o n v e c t i v e l y unstable storms (Figure 35a) i s to be expected s i n c e observed r a i n f a l l was produced by a s e r i e s of i n d i v i d u a l shower clouds r a t h e r than by a widespread cloud system. I t i s more s u r p r i s i n g to note the s i m i l a r i t y of the b a s i c p a t t e r n w i t h that f o r a l l storms than to note the d i f f e r e n c e . For storms w i t h s o u t h e r l y winds, the p r i n c i p a l d i f f e r e n c e i n the eigenvector 1 p a t t e r n i s the c o n f i g u r a t i o n of isohyets over the e a s t - c e n t r a l p o r t i o n of the Research Forest (Figure 35b). In t h i s area, the isohyets are a l i g n e d north-south versus east-west f o r the " a l l - s t o r m " p a t t e r n (Figure 35b). One p o s s i b l e explanation i s that s o u t h e r l y winds flow p a r a l l e l to the main Mount Blanshard r i d g e and the small r i d g e on the east s i d e of the Research Forest and are subject to a l a t e r a l (westerly) extended l i f t i n g f o r only a short d i s t a n c e from these r i d g e s (Yordanov and Godev 1973). Winds f l o w i n g northward up the Blaney Creek V a l l e y i n the centre of the Research Forest would be l i f t e d more gr a d u a l l y than over the small r i d g e s on e i t h e r s i d e . This a c t i o n would r e s u l t i n a reduced orographic e f f e c t i n t h i s area as suggested by the 190 2.4 mm/hr isohyet for the eigenvector i n Figure 35b. The s i m i l a r i t y of isohyetal patterns over most of the r e s t of the Research Forest shows that net l i f t i n g e f f e c t s of t e r r a i n i n the other parts of the Research Forest are s i m i l a r f o r both southerly and southwesterly winds, and that they adhere f a i r l y c l o s e l y to the shape of the t e r r a i n as noted above. In summary, there thus appears to be a general a s s o c i a t i o n between p r e c i p i t a t i o n patterns, southwest-westerly winds, southerly winds and convective i n s t a b i l i t y . Because of the persistency of the eigenvector 1 patterns and the n e g l i g i b l e value of the remaining eigenvectors for explaining p r e c i p i t a t i o n d i s t r i b u t i o n there was no point i n seeking further r e l a t i o n s h i p s between r a i n f a l l areal patterns and other meteorological parameters or storm c h a r a c t e r i s t i c s . C o r r e l a t i o n Analysis Paired c o r r e l a t i o n analyses were performed for Research Forest s i t e s using t o t a l storm p r e c i p i t a t i o n and short-period r a i n f a l l i n t e n s i t i e s for a l l storms, the r e s u l t s of which are tabulated i n Tables 22 and 23. A l l c o r r e l a t i o n c o e f f i c i e n t s were s i g n i f i c a n t at the 5% l e v e l . The c o r r e l a t i o n c o e f f i c i e n t s are p a r t i c u l a r l y high for storm t o t a l data, exceeding 0.8 for a l l s i t e p a i r s and 0.9 for most. The lowest c o r r e l a t i o n s are those between s i t e - 9 and s i t e s 1-6 and between st a t i o n AD and s i t e s 1, 4 and 5. For the short-period i n t e n s i t y data, the c o r r e l a t i o n c o e f f i c i e n t s are lower but s t i l l r e l a t i v e l y high, exceeding 0.7 for a l l s i t e p a i r s except PP-9, LL-PP, LL-10 and LL-AD. The lowest c o r r e l a t i o n s are those between s i t e 10 and a l l other s i t e s , s t a t i o n AD and s i t e s 1, 4, 5, 8-10, LL, s t a t i o n PP and s i t e s 2, 8-10, LL, TABLE 22 CORRELATION COEFFICIENTS FOR STORM PRECIPITATION TOTALS AT RESEARCH FOREST SITES AD SI S2 S3 S4* S5 S6 S7 S8 S9 SIO LL PP AD 1.0 0.89 0.94 0.92 0.85 0.88 0.92 0.95 0.93 0.92 0.94 0.97 0.96 SI 1.0 0.98 0.99 0.99 0.99 0.98 0.94 0.94 0.83 0.92 0.99 0.93 S2 1.0 0.99 0.97 0.98 0.99 0.97 0.96 0.89 0.94 0.97 0.95 S3 1.0 0.99 0.99 0.99 0.97 0.95 0.87 0.93 0.99 0.95 S4* 1.0 0.99 0.99 0.92 0.90 0.81 0.89 0.99 0.92 S5 1.0 0.99 0.95 0.94 0.83 0.92 0.99 0.92 S6 1.0 0.97 0.96 0.88 0.93 0.99 0.95 S7 1.0 0.98 0.94 0.95 0.99 0.98 S8 1.0 0.96 0.97 0.98 0.97 S9 1.0 0.93 0.98 0.92 SIO 1.0 0.97 0.95 LL 1.0 0.97 PP 1.0 *Based on data for 1970 storms only. TABLE 23 CORRELATION COEFFICIENTS FOR SHORT-PERIOD (4-6 HOUR) RAINFALL INTENSITIES AT RESEARCH FOREST SITES AD SI S2 S3 S4* S5 S6 S7 S8 S9 S10 LL+ PP AD 1.0 0.83 0.86 0.86 0.80 0.81 0.88 0.88 0.77 0.71 0.73 0.62 0.88 SI 1.0 0.93 0.96 0.95 0.97 0.95 0.92 0.88 0.78 0.74 0.86 0.85 S2 1.0 0.96 0.89 0.90 0.95 0.88 0.85 0.80 0.71 0.72 0.77 S3 1.0 0.95 0.96 0.99 0.93 0.90 0.81 0.70 0.88 0.83 S4* 1.0 0.99 0.93 0.92 0.90 0.80 0.70 - 0.84 S5 1.0 0.96 0.94 0.91 0.81 0.72 0.92 0.85 S6 1.0 0.94 0.90 0.81 0.70 0.93 0.85 S7 1.0 0.94 0.88 0.76 0.96 0.88 S8 1.0 0.95 0.78 0.90 0.77 S9 1.0 0.79 0.75 0.66 S10 1.0 0.48 0.74 LL+ 1.0 0.65 PP 1.0 *Based on data for 1970 storms only. +Based on data for 1971 storms only. 193 and site 9 and sites AD, 1-6, 10. The fact that correlations for storm totals are higher than those for the intensity data is probably due to an averaging out of short-period anomalies as a result of variations in wind direction and speed, air mass stability, and low level terrain-wind interactions during the course of a storm. Variations in storm duration at individual sites could also be a contributing factor. The high correlation coefficient values are further evidence of the persistency of areal patterns or relative relationships in precipitation between gauge sites indicated by the eigenvector analysis. These strong correlations are particularly significant in view of the variety of storm types and conditions which produced the precipitation on which the analyses are based. Thus, in conjunction with the eigenvector results, the correlation analysis gives another indication of the dominant role played by topography in determining the distribution of precipitation on the Research Forest. Correlation data can also help establish the representatives of site measurements as discussed in a later section in relation, particu-larly, to sites 7 and 9. Small Scale Variations in Precipitation Small scale variations in precipitation are those due principally to low level or second-order wind-terrain interactions, assuming representative gauge measurements. An assessment is given of small scale variations in precipitation near or at sites 7, 9, and Spur-17 and of variations along the ridge on the east side of the Research Forest. Precipitation data will indicate the magnitude of such 194 variations, while low level wind data are also required for development of predictive relationships. As noted in Chapter II, anticipated wind measurements from the Spur-17 meteorological site are not reliable because of improper functioning of the anemometer recorder. However, some information on low level wind speeds was derived from vecto-pluviometer data as described below. Vectopluviometer Measurements The principles of vectopluviometer measurements are summarized in Appendix V. Vectopluviometers were placed at site 8b adjacent to site 8 and at the Spur-17 meterological site (Figure 1). Figure 37 presents photographs of the vectopluviometers at sites 8b and Spur-17. Figure 37a illustrates the large clearing of site 8b, while Figure 37b shows the exposure to the southeast of the Spur-17 site. Measurements from these gauges were taken for periods varying from one day to one week and are directly applicable to a total of 23 individual storm periods. Vectopluviometer data provide information on the mean inclination of raindrop trajectories (6) from the vertical and mean direction or bearing of storm winds (to) during the measurement period. If rainfall intensity data are also available, mean low level horizontal wind speeds (V ) can be derived from the equation VH = VT t a n 9 ( 1 2 ) where V is the terminal velocity of raindrops estimated from the graphs in Appendix IX. The ranges and means (arithmetic average) of raindrop inclinations and storm bearings at sites 8b and Spur-17, derived from (a) View towards the SW across s i t e 8b Figure 37. Photographs of vectopluviometer s i t e s 8b and Spur-17. 196 vectopluviometer data, are l i s t e d i n Table 24. For raindrop i n c l i n a t i o n , the ranges are s i m i l a r at both s i t e s but the mean at Spur-17 i s much lower than at s i t e 8b. One possible reason i s a reduction i n gauge catches at Spur-17 which i s situated i n a very exposed spot on the end of a ridge as shown i n Figure 37b. Wind e f f e c t s on p r e c i p i t a t i o n at Spur-17 are discussed further i n a l a t e r section. TABLE 24 RAINDROP INCLINATIONS AND STORM BEARINGS AT SITE 8b AND Spur-17 Raindrop i n c l i n a t i o n (deg) S i t e 8b Spur-17 Storm bearing (deg) Site 8b Spur-17 Mean 34.9 19.6 116 120 Range 3.9-50.0 5.4-45.9 62-130 18-212 Mean storm wind d i r e c t i o n s are from the SSE at both s i t e s but the range at s i t e 8b i s much smaller. It would appear that the slope of the small ridge on which s i t e 8b i s located exerts a more constraining e f f e c t on l o c a l wind flow than the more open t e r r a i n at,Spur-17. The i n t e r e s t i n g feature of these r e s u l t s i s the i n d i c a t i o n that near ground l e v e l winds on the Research Forest tend to flow, on the average, from an east-southeasterly d i r e c t i o n . This flow pattern, conditioned by pressure gradients, surface f r i c t i o n and t e r r a i n o r i e n t a t i o n , i s s i m i l a r to that observed at the Vancouver International A i r p o r t . Jackson and A l r i d g e (1972) concluded that the main value of vectopluviometers i s to ind i c a t e whether i n c l i n a t i o n of r a i n f a l l i s l i k e l y to be a problem i n measuring r a i n f a l l . They found that vecto-pluviometers exposed to the general windflow over a watershed were 197 u n r e l i a b l e f o r p r e d i c t i n g the catch of i n d i v i d u a l t i l t e d gauges as a r e s u l t of m o d i f i c a t i o n of r a i n f a l l d i r e c t i o n by topography w i t h i n the watershed. In the present study, gauges were located i n f o r e s t c l e a r i n g s or on f l a t s i t e s so that vectopluviometer data were not required to c o r r e c t r a i n gauge measurements f o r slope e f f e c t s . The main value of the vectopluviometers has been to provide an estimate of low l e v e l wind speeds and d i r e c t i o n s w i t h i n the study area. The d i f f i c u l t y of f i n d i n g s u i t a b l e s i t e s i n rugged areas, such as the Research F o r e s t , which are open and exposed to p r e v a i l i n g winds places a l i m i t on the number and, hence, usefulness of vectopluviometers. V a r i a t i o n s i n P r e c i p i t a t i o n  Near S i t e s 7 and 9 S i t e s 7 and 9 were lo c a t e d on the top of k n o l l s or small r i d g e s adjacent to s i t e s LL and 8, r e s p e c t i v e l y , to assess the i n f l u e n c e of winds on p r e c i p i t a t i o n over these two s m a l l s c a l e t e r r a i n f e a t u r e s . C o r r e l a t i o n analyses were c a r r i e d out between d i f f e r e n c e s i n short period p r e c i p i t a t i o n i n t e n s i t i e s between the s t a t i o n s of each p a i r and a number of wind speed parameters. Transects of can-type gauges were a l s o e s t a b l i s h e d on the slopes of these two r i d g e s to assess l o c a l p r e c i p i t a t i o n v a r i a t i o n s w i t h e l e v a t i o n (see Chapter I I and F i g u r e 3). The can-gauge data f o r a l l s i t e s are given i n Appendix XVI f o r r e f e r e n c e . Eigenvector analyses of storm p r e c i p i t a t i o n patterns c l e a r l y show s i t e - 9 to be an anomaly (Figures 34 and 35). In a d d i t i o n , the r e s u l t s of p a i r e d - c o r r e l a t i o n analyses given i n Tables 22 and 23 show that s i t e - 9 has r e l a t i v e l y low c o r r e l a t i o n s w i t h most other s i t e s , f o r both 198 storm t o t a l and short period p r e c i p i t a t i o n data, suggesting the p o s s i b i l i t y r a i n f a l l measurements may not be representative of p r e c i p i t a t i o n on the s i t e 9 ridge for at l e a s t some of the storms. As noted i n Chapter I I , the opening s i z e at s i t e 9 was kept to a minimum. The opening was le s s than one tree-height diameter and could conceivably have been the cause of non-representative measurements. An eigenvector analysis of can-gauge data revealed that the f i r s t eigenvector explains 99.8% of the variance. Figure 38 gives the eigenvector 1 pattern plus observed values for storm 43, t h i s data representing the maximum changes with elevation measured by the can-gauges. This graph shows a decrease i n p r e c i p i t a t i o n with elevation up both slopes of the ridge. The decrease i s 27% for an elevation change of 370 metres on the southwest slope and 29% for a d i f f e r e n c e of 210 metres on the northeast slope. The c o r r e l a t i o n r e s u l t s i n Table 25 show a r e l a t i v e l y high c o r r e l a t i o n of i n t e n s i t y d ifferences with wind speeds derived from s i t e 8b vectopluviometer data (WS-8b) but low c o r r e l a t i o n s with the other wind parameters. Figure 39 gives the graph of s i t e 9 -s i t e 8 i n t e n s i t y d i f f e r e n c e s versus s i t e 8b wind speeds. Although the l e a s t squares l i n e a r regression l i n e i n Figure 39 appears to be an inadequate model for describing the r e l a t i o n s h i p between these two v a r i a b l e s , attempts to derive a model to f i t the data points more c l o s e l y were unsuccessful. However, the r e l a t i o n s h i p i s s u r p r i s i n g l y good considering that the wind speeds are i n d i r e c t estimates of mean values over t o t a l storm periods and that s i t e 9 p r e c i p i t a t i o n data appear to have been subject to s i t e e r r o r s . Because of the wide scatter of data points, the r e l a t i o n s h i p has l i m i t e d value for p r e d i c t i o n 199 Figure 38. V a r i a t i o n i n t o t a l storm p r e c i p i t a t i o n across s i t e 9 ridge for storm 43 for can-gauge data. TABLE 25 CORRELATION COEFFICIENTS BETWEEN DIFFERENCES IN SHORT-PERIOD PRECIPITATION INTENSITY BETWEEN SITES 8-9 AND SITES 7-LL AND SEVERAL WIND SPEED PARAMETERS vsw VS VSW VS ws WS WS WS (S-85) (S-85) (85) (85) (85) (VAP) (SH) (8b) S i t e 9 - Sit e 3 -0.28 0.05 -0.20 0.16 -0.17 -0.18 -0.35 -0.57 Si t e 7 - Sit e LL 0.18 0.22 0.19 0.29 0.28 0.06 -0.18 -0.75 200 Figure 39. Relationship between di f f e r e n c e i n short-period r a i n f a l l i n t e n s i t y s i t e 9-site 8 and windspeed derived from s i t e 8b vectopluviometer data. purposes. The mean, standard deviation and range of s i t e 9-site 8 i n t e n s i t y d i f f e r e n c e s are also l i s t e d i n Table 26 to i l l u s t r a t e the nature of observed v a r i a t i o n . The elevation d i f f e r e n c e between s i t e s 8 and 9 i s 220 metres. Eigenvector analyses of storm p r e c i p i t a t i o n patterns show a r e l a t i v e l y steep gradient between s i t e s 7 and LL (Figures 34 and 35) in d i c a t i n g a l o c a l l y induced v a r i a t i o n i n p r e c i p i t a t i o n between these two s i t e s . The data i n Tables 22 and 23 show r e l a t i v e l y high c o r r e l a t i o n s between s i t e 7 and most other s i t e s i n contrast to s i t e 9 201 TABLE 26 SUMMARY OF DIFFERENCES IN SHORT-PERIOD PRECIPITATION INTENSITIES BETWEEN.SITES 9-8 AND SITES 7-LL Mean Standard D e v i a t i o n Minimum mm/hr Maximum S i t e 9-Site 8 -0.27 0.41 -1.74 0.68 S i t e 7 - S i t e LL -0.46 0.30 -1.28 -0.13 v a l u e s . This r e s u l t suggests that gauge catch at s i t e 7 was probably r e p r e s e n t a t i v e of p r e c i p i t a t i o n f a l l i n g on that k n o l l top. Can-gauge p r e c i p i t a t i o n data show a maximum d i f f e r e n c e between the base and top of the eastern slope of the s i t e - 7 K n o l l (7C1-7C4) of l e s s than 9% and a mean d i f f e r e n c e of only 3%. Moreover, p r e c i p i t a t i o n increased w i t h e l e v a t i o n between s i t e s 7C1 and 7C4 f o r 8 of 11 measurement periods i n contrast to the general decrease up the s i t e - 9 r i d g e slopes. However, f o r s h o r t - p e r i o d r a i n f a l l i n t e n s i t i e s , s i t e - L L values exceeded those at s i t e - 7 i n a l l cases f o r which comparative data were a v a i l a b l e . The same trend a l s o holds f o r estimated mean annual p r e c i p i t a t i o n (Figure 36) based on t o t a l s measured at these s i t e s during the study p e r i o d . These r e s u l t s suggest that s i t e LL r e c e i v e s an e x t r a amount of p r e c i p i t a t i o n , p o s s i b l y as a r e s u l t of s p i l l - o v e r due to wind a c c e l e r a t i o n over the s i t e - 7 k n o l l , the small h i l l immediately to the south and through the small draw between these two h i l l s (see Figure 3). A r e a l p r e c i p i t a t i o n p atterns shown i n Figures 34, 35 and 36 a l s o show s i t e - L L p r e c i p i t a t i o n as being perhaps higher than f i r s t - o r d e r or l a r g e s c a l e orographic l i f t i n g might otherwise i n d i c a t e . C o r r e l a t i o n analyses of s i t e 7-LL sh o r t - p e r i o d p r e c i p i t a t i o n i n t e n s i t y d i f f e r e n c e s w i t h wind speed parameters gave r e s u l t s s i m i l a r to those f o r s i t e - 9 data as shown i n Table 26. The graph i n Figure 40 shows the r e l a t i o n s h i p between s i t e 7-LL i n t e n s i t y d i f f e r e n c e s and s i t e 8b wind speeds. The slope of the r e g r e s s i o n l i n e i s only s l i g h t l y l e s s than that f o r s i t e 9 data shown i n Fi g u r e 39. Table 26 a l s o gives a summary of s h o r t - p e r i o d r a i n f a l l i n t e n s i t y d i f f e r e n c e s between s i t e s 7 and LL. The e l e v a t i o n d i f f e r e n c e between s i t e s 7 and LL i s 180 metres. The v a r i a t i o n s between can-gauge and s i t e s 7-LL data show that c a u t i o n must be exercised i n e x t r a p o l a t i n g these r e s u l t s to other s i t u a t i o n s because of the h i g h l y dependent r e l a t i o n s h i p s between wind d i r e c t i o n s and t e r r a i n c o n f i g u r a t i o n . F i g u r e 40. R e l a t i o n s h i p between d i f f e r e n c e i n sh o r t - p e r i o d r a i n f a l l i n t e n s i t y s i t e 7 - s t a t i o n LL and windspeed derived from s i t e 8b vectopluviometer data. 203 Wind E f f e c t s on P r e c i p i t a t i o n at Spur-17 The Spur-17 meteorological s t a t i o n i s situated i n the open on the leading edge of a r e l a t i v e l y narrow north-south oriented ridge at an elevation of 370 metres (Figure 3). Because of the exposed l o c a t i o n , p r e c i p i t a t i o n measurements at t h i s s i t e may be expected to suff e r from wind e f f e c t s on two accounts. F i r s t l y , the s i t e i t s e l f might receive l e s s actual p r e c i p i t a t i o n than adjacent t e r r a i n at lower elevations due to a c c e l e r a t i o n of wind over the end of the ridge. Secondly, a r a i n gauge placed at t h i s spot would tend to undercatch due to a c c e l e r a t i o n of wind over the gauge i t s e l f . In order to evaluate the magnitude of t h i s combination of wind e f f e c t s , a d d i t i o n a l standard gauges were placed i n a more sheltered spot about 18 metres north of the Spur-17 meteorological compound and at an adjacent lower elevation (290) metres l o c a t i o n ( s i t e 12). Figure 41 gives a schematic diagram of the Spur-17 s i t e plus a photograph showing the view to the south across the s i t e , the anemometer tower i n the compound being v i s i b l e above the screen of trees. The r a i n gauges were mostly read on a weekly basis and 15 measurement periods are a v a i l a b l e for comparisons. The more sheltered gauge at the Spur-17 s i t e caught an average of 8% more r a i n f a l l than the exposed gauge and also caught more r a i n i n a l l cases. In contrast, measurements for the lower elevation site-12.gauge averaged only 1% l e s s than those of the sheltered Spur-17 gauge, and were within ±4% i n a l l cases except for two periods involving convective shower r a i n f a l l . 204 Legend: SG - standard r a i n gauge VP - vectopluviometer AN - anemometer Scale: 1 cm = 6 metres (a) Schematic diagram of Spur-17 s i t e . (b) View to the south across the Spur-17 s i t e . Figure 41. Schematic diagram and photograph of Spur-17 s i t 205 Variations i n P r e c i p i t a t i o n  Among Sites 1-6 Gauges 1 to 6 were placed across the small ridge on the east side of the Research Forest with the objective of assessing the small scale or second-order influence of the ridge and Marion Lake V a l l e y on p r e c i p i t a t i o n d i s t r i b u t i o n . The orographic model a p p l i c a t i o n discussed i n Chapter IV has shown that d i f f e r e n c e s i n p r e c i p i t a t i o n between s i t e s 3 and 1 can be explained by f i r s t - o r d e r or large scale orographic l i f t i n g e f f e c t s for southwest-westerly winds. Furthermore, the eigen-vector analysis of a l l 38 storms has shown the existence of a basic pattern of p r e c i p i t a t i o n d i s t r i b u t i o n approximately normal to the o r i e n t a t i o n of t h i s ridge (Figure 34b). This r e s u l t indicates that f i r s t - o r d e r l i f t i n g of storm winds by the Mount Blanshard ridge to the east tends to mask any small-scale influence of the smaller ridge or v a l l e y for many or most storms. However, the eigenvector 1 pattern for storms with southerly winds (Figure 35b) suggests a l o c a l l i f t i n g influence of t h i s small ridge, as discussed previously. The north-south eigenvector 1 isohyetal pattern over the small ridge for convectively unstable storms (Figure 35a) i s probably i n d i c a t i v e of topographic steering of shower clouds by the Mount Blanshard ridge rather than of any small scale e f f e c t of the smaller ridge. Thus, the v a r i a t i o n s between measurements at s i t e s 1-6 appear to be explainable i n terms of f i r s t - o r d e r orographic influences for the most part. Table 27 summarizes the mean, standard deviation, minimum and maximum values of differences between pai r s of s i t e s across and along the small ridge ( s i t e s 1-6). Mean di f f e r e n c e s across the ridge are very 206 TABLE 27 SUMMARY OF DIFFERENCES IN SHORT-PERIOD PRECIPITATION INTENSITIES FOR SEVERAL SITE PAIRS Site pair Mean Standard Deviation mm/hr Minimum Maximum 3-2 0.02 0.28 -0.78 0.55 3-6 0.08 0.17 -0.31 0.38 4-5 0.03 0.26 -0.45 0.76 4-1 -0.20 0.44 -0.92 0.81 1-5 0.14 0.30 -0.46 0.84 6-2 0.07 0.24 -0.55 2.11 5-6 0.12 0.43 -0.56 1.46 4-3 0.20 0.42 -0.45 1.10 1-2 0.14 0.54 -1.44 1.71 small and are smaller than those along the ridge except where site 1 is involved. In general, the range in difference values along the ridge is a l i t t l e higher than across i t , while the ranges for most of these site pairs are similar to those for site pairs 8-9 or 7-LL shown in Table 26. In summary, these data really do not clearly indicate what, if any, the small scale effects of the sites 1-6 ridge and valley might be. Conclusions The analyses discussed in this chapter have shown that f i r s t -order orographic lifting or deflection of storm winds is a dominant factor controlling the distribution of precipitation on the Research Forest. For major storms involving continuous rainfall, the precipita-tion patterns conform fairly closely to the general terrain configuration. Small scale variations due to local low level wind-207 t e r r a in interact ions appear to be small i n r e l a t i o n to f i r s t -o rde r orographic effects. . The larger anomaly at the site-9 r idge was due at least i n part to site-induced measurement er rors . Corre la t ion analyses have shown that knowledge of low l e v e l wind speeds close to or wi th in the area of concern are essent ia l for assessing smaller scale wind effects on p rec ip i t a t i on d i s t r i b u t i o n . I t has also been shown that vectopluviometers can provide useful ind i rec t estimates of l o c a l wind speeds i f sui table s i tes can be found. CHAPTER VI CONCLUSIONS Orographic r a i n f a l l has been investigated with the objective of u t i l i z i n g a v a i l a b l e synoptic weather information to elucidate and quan-t i f y i t s production and d i s t r i b u t i o n i n the south coastal mountains of B r i t i s h Columbia. The study area chosen offered a range of mountain slopes exposed to p r e v a i l i n g storm winds and an expanse of lowlands upwind which permitted maximum opportunity for major orographic influence on atmospheric processes to occur and be i d e n t i f i e d . C o r r e l a t i o n analyses have demonstrated that i t i s possible to determine s i g n i f i c a n t r e l a t i o n s h i p s between orographic r a i n f a l l amount and i n d i v i d u a l storm parameters. Furthermore, the a s s o c i a t i o n between the r a i n f a l l and storm parameters have l o g i c a l , p hysical explanations. Attempts to c l a s s i f y or group storms into general types, using an analysis of variance procedure, with the objective of being able to r a p i d l y i d e n t i f y synoptic s i t u a t i o n s associated with occurrence of s p e c i f i c orographic processes or magnitude of orographic r a i n f a l l met with l i m i t e d success. Only one synoptic pattern provided a reasonably good l i n k between major orographic r a i n f a l l and atmospheric c h a r a c t e r i s -t i c s s i g n i f i c a n t l y related to i t s production. Hence, the i n d i v i d u a l features of each storm need to be examined to assess the p r o b a b i l i t y of occurrence of given orographic e f f e c t s or substantial orographic r a i n f a l l production. 208 209 Procedures for estimating the amount and d i s t r i b u t i o n of p r e c i p i t a t i o n on windward mountain slopes r e s u l t i n g from f i r s t - o r d e r orographic influence on atmospheric processes have been applied with a reasonable degree of success to c e r t a i n storm s i t u a t i o n s . An orographic model which u t i l i z e s upper a i r wind, temperature and humidity data i n conjunction with t e r r a i n configuration was adapted to two l o c a t i o n s i n the study area and tested on 4. stable and 4 unstable storms. The storm parameters found to be s i g n i f i c a n t l y r e l a t e d to orographic r a i n f a l l by c o r r e l a t i o n analyses are also incorporated into t h i s model. B a s i c a l l y , the model provides estimates of orographic condensation which must be converted into p r e c i p i t a t i o n values and added to an observed value upwind of the mountain slope. For stable storms, the model produced r e s u l t s which gave conversion f a c t o r s that compare favourably with those reported i n the l i t e r a t u r e . Moreover, model estimates of p r e c i p i t a t i o n amount and d i s t r i b u t i o n over the mountain slopes were co n s i s t e n t l y s i m i l a r to observed r a i n f a l l . For optimum orographic l i f t i n g conditions, r a i n f a l l estimates had a standard deviation of only ±11% with a maximum deviation of 25%. If the s t a t i o n providing observed p r e c i p i t a t i o n upwind of the mountains i s not free from orographic influence, the model can be used to estimate the proportion due to orographic e f f e c t s . This approach was tested for stable storms and resulted i n a s l i g h t increase i n the uncertainty of model estimates. For the study area, low l e v e l outflow of a i r i n the v a l l e y upwind of the mountain slope appears to exert an influence on l i f t i n g of storm winds upwind of the mountains. This factor had to be incorporated into the model. 210 For unstable storms, the model produced estimates of condensation that exceeded observed r a i n f a l l and conversion factors that are s i m i l a r i n range to those reported i n the l i t e r a t u r e . However, the r e s u l t s were highly v a r i a b l e and thus u n r e l i a b l e , one of the main reasons being a lack of knowledge of convective v e r t i c a l a i r motions for study storms. Procedures for using the model have been outlined and design values for model parameters suggested for a p p l i c a t i o n of the model to windward slopes north of the Fraser V a l l e y and on the mainland coast i n the lee of Vancouver Island. Because of the small sample of storms examined, further t e s t i n g of the model i s required both for the study area and p a r t i c u l a r l y for other areas on the coast for a l l seasons of the year. The model i s most useful for a p p l i c a t i o n to major storms with stable a i r . Examination of areal storm t o t a l and short-period p r e c i p i t a t i o n patterns using eigenvector a n a l y s i s revealed one basic pattern inherent i n most storms which explained 98% of variance i n a r e a l d i s t r i b u t i o n s and which was shown to conform f a i r l y c l o s e l y to topographic configuration. Paired c o r r e l a t i o n analysis of p r e c i p i t a t i o n data lent further support to t h i s conclusion. Small scale v a r i a t i o n s i n p r e c i p i t a t i o n caused by l o c a l terrain-wind i n t e r a c t i o n s were found to be generally minor i n r e l a t i o n to larger scale orographically conditioned p r e c i p i t a t i o n d i s t r i b u t i o n . In summary, t h i s thesis has shown that a v a i l a b l e synoptic weather information can be used s u c c e s s f u l l y to explain observed orographic influences on p r e c i p i t a t i o n i n the study area and to provide, i n conjunction with an appropriate model, reasonable estimates of p r ec ip i t a t i on amount and d i s t r i b u t i o n on windward mountain slopes. Furthermore, the various analyses have demonstrated that topography exerts a dominant influence on r a i n f a l l production and d i s t r i b u t i o n i n the study area, and shown the nature and extent of th i s influence. BIBLIOGRAPHY A t l a s , D. and V. G. Plank. 1953. Drop s i z e h i s t o r y during a shower. J . Meteor., V o l . 10, 291-295. , Atmospheric Environment S e r v i c e . Temperature and p r e c i p i t a t i o n 1941-1970, B r i t i s h Columbia. Department of the Environment, Downsview, Ontario. Barry, R. G. 1976. The prospect f o r synoptic c l i m a t o l o g y : a case study. In.Liverpool Essays i n Geography (Ed., S t e e l , R. W. and R. Lawton), Longmans, London, 85-106. . 1974. Further C l i m a t o l o g i c a l Studies of B a f f i n I s l a n d Northwest T e r r i t o r i e s . Tech. B u l l . No. 65, Inland Waters D i r e c t o r a t e , Water Resources Branch, Environment Canada. Bergeron, T. 1949. The problem of. a r t i f i c i a l c o n t r o l of r a i n f a l l on the globe: The c o a s t a l orographic maxima of p r e c i p i t a t i o n i n autumn and wi n t e r . T e l l u s , V o l . 1, No. 3, 15-32. . 1960. Problems and methods of r a i n f a l l i n v e s t i g a t i o n . In Physics of p r e c i p i t a t i o n , Geophysical Monograph Number 5, Amer. Geophys. Union, 5-30. . 1965. On the l o w - l e v e l r e d i s t r i b u t i o n of atmospheric water caused by orography. Proc. I n t . Conf. on Cloud P h y s i c s , Tokyo and Sapporo, 96-100. Berkofsky, L. 1964. The f a l l - o f f w i t h height of t e r r a i n - i n d u c e d v e r t i c a l motions. J . Appl. Meteor., V o l . 3, 410-414. Bleasdale, A. 1959a. The measurement of r a i n f a l l . Weather, V o l . 14, 12-18. . 1959b. Water and woodlands: I n v e s t i g a t i o n s i n the United Kingdom i n t o the water r e l a t i o n s h i p s of woodlands and the problem of measuring r a i n f a l l over woods. I.A.S.H. Symp. of Hannoversch-Munden, V o l . 1, Water and Woodlands, 87-91. Bonacina, L. C. W. 1945. Orographic r a i n f a l l and i t s place i n the hydrology of the globe. Q. J . Roy. Met. S o c , V o l . 71, 41-55. 212 213 Boughner, C. C , M. K. Thomas and B. S. V. Cudbird. 1961. A survey of t e r m i n a l weather c o n d i t i o n s at P i t t Meadows, B.C. Canada, Dept. of Transport, M e t e o r o l o g i c a l Branch, CIR-3443, TEC-346. Boyden, C. J . 1963. A simple i n s t a b i l i t y index f o r use as a synoptic parameter. Met. Mag. London, V o l . 92, 198-210. Braham, R. R., J r . 1952. The water and energy budgets of the thunder-storm and t h e i r r e l a t i o n to thunderstorm development. J . Meteor., V o l . 9, 227-242. Brousaides, F. J . and J . F. Morrissey. 1971. Improved humidity measurements w i t h a redesigned radiosonde humidity duct. B u l l . Amer. Met. S o c , V o l . 52, No. 9, 870-875. Brown, M. J . and E. L. Peck. 1962. R e l i a b i l i t y of p r e c i p i t a t i o n measurements as r e l a t e d to exposure. J . Appl. Meteor., V o l . 1, 203-207. Bruce, J . P. 1961. Frequency of heavy r a i n f a l l s i n the lower Fraser V a l l e y . Canada, Dept. of Transport, M e t e o r o l o g i c a l Branch, CIR-3468, TEC-354. Buettner, K. J . K., G. Maykut, J . Turner and J . Zimmerman. 1964. Orographic deformation of wind flow. Dept. of the Army P r o j e c t No. 1A0-11001-B-021-01, Dept. of Atmos. S c i . , Univ. of Washington, S e a t t l e . Cooper, C. F. 1967. R a i n f a l l i n t e n s i t y and e l e v a t i o n i n southwestern Idaho. Water Resour. Res., V o l . 3, No. 1, 131-137. Corbett, E. S. 1967. Measurement and e s t i m a t i o n of p r e c i p i t a t i o n on experimental watersheds. I n t . Symp. on For. Hydrology, Pergamon Press, London, 107-127. Danard, M. 1971. A simple method of computing the v a r i a t i o n of annual p r e c i p i t a t i o n over mountainous t e r r a i n . Boundary-Layer Meteorology, V o l . 2, 188-206. . 1975. A model f o r the v a r i a t i o n of p r e c i p i t a t i o n over the Greater Vancouver Water D i s t r i c t catchment bas i n s . Report No. 15 prepared f o r Water I n v e s t i g a t i o n s Branch, Water Resources S e r v i c e , Province of B r i t i s h Columbia. Decker, F. W. 1967. Comments on the a d j e c t i v e s " o r e i g e n i c " and orographic. Mon. Wea. Rev., V o l . 95, No. 10, 699. D i n g l e , A. N. and Y. Lee. 1972. Terminal f a l l s p e e d s of r a i n d r o p s . J . Appl. Meteor., V o l . 11, 877-879. 214 D i r k s , R. A. 1972. The n a t u r a l e f f i c i e n c y of orographic p r e c i p i t a t i o n . Third Nat. Conf. Weather M o d i f i c a t i o n , Rapid C i t y , S.D., Amer. Meteor. Soc. Douglas, C. K. M. and J . Glasspoole. 1947. M e t e o r o l o g i c a l c o n d i t i o n s i n heavy orographic r a i n f a l l . Q. J . Roy. Met. S o c , V o l . 73, 11-42. Douglas, R. H., K. L. S. Gunn and J . S. M a r s h a l l . 1957. P a t t e r n i n the v e r t i c a l of snow generation. J . Meteor., V o l . 14, No. 2, 95-114. Dyer, T. G. J . 1975. The assignment of r a i n f a l l s t a t i o n s i n t o homogeneous groups: an a p p l i c a t i o n of p r i n c i p a l component a n a l y s i s . J . Appl. Meteor., V o l . 14, No. 6, 1005-1012. E l l i o t t , R. D. and R. W. E l l i o t t . 1969. Guide to orographic cloud seeding area of e f f e c t model. North American Weather Consultants, Goleta, C a l i f . E l l i o t t , R. D. and E. L. Hovind. 1964. The water balance of orographic clouds. J . Appl. Meteor., V o l . 3, 235-239. E l l i o t t , R. D. and R. W. Shaffer. 1962. The development of q u a n t i t a -t i v e r e l a t i o n s h i p s between orographic p r e c i p i t a t i o n and air-mass parameters f o r use i n f o r e c a s t i n g and cloud seeding e v a l u a t i o n . J . Appl. Meteor. V o l . 1, 218-228. Estoque, M. 1957. A g r a p h i c a l l y i n t e g r a b l e p r e d i c t i o n model i n c o r p o r a t i n g orographic i n f l u e n c e s . J . Meteor., V o l . 14, 293-296. Ferguson, H. L. 1972. P r e c i p i t a t i o n network design f o r l a r g e mountainous areas. Proc. D i s t r i b u t i o n of P r e c i p i t a t i o n i n Mountainous Areas, G e i l o Symposium, Norway, V o l . I , 85-105. Ferguson, H. L., H. I. Hunter and D. G. Schaefer. 1974. The IHD Mountain t r a n s e c t s p r o j e c t . Part I , design and p r e l i m i n a r y r e s u l t s . Atmospheric Environment S e r v i c e , Dept. of Environment CMRR3/74. Ferguson, H. L. and D. S t o r r . 1969. Some current s t u d i e s of l o c a l p r e c i p i t a t i o n v a r i a b i l i t y over Western Canada. Proc. Symp. on Water Balance i n North America, Banff, A l b e r t a . Amer. Water Resour. Assoc., 80-100. F i t z h a r r i s , B. B. 1975. Snow accumulation and d e p o s i t i o n on a west coast m i d - l a t i t u d e mountain. Ph.D. Thesis, Dept. of Geography, U n i v e r s i t y of B r i t i s h Columbia, Vancouver. F l e t c h e r , R. D. 1951. Hydrometeorology i n the United States. In Compendium of Meteorology, Amer. Meteor. S o c , Boston, Mass., 1033-1047. 215 Foote, G. B. and P. S. Du T o i t . 1969. Terminal v e l o c i t y of raindrops a l o f t . J . Appl. Meteor., V o l . 8, 249-253. Fourcade, H. G. 1942. Some notes on the e f f e c t s of the incidence of r a i n on the d i s t r i b u t i o n of r a i n f a l l over the surface of u n l e v e l ground. Roy. Soc. South A f r i c a Trans., V o l . 29, 236-254. Frase r , A. B., R. C. Easter and P. V. Hobbs. 1973. A t h e o r e t i c a l study of the flow of a i r and f a l l o u t of s o l i d p r e c i p i t a t i o n over mountainous t e r r a i n : Part I. A i r f l o w model. J . Atmos. S c i . , V o l . 30, 801-812. F u l k s , J . R. 1935. Rate of p r e c i p i t a t i o n from a d i a b a t i c a l l y ascending a i r . Mon. Wea. Rev., V o l . 63, No. 10, 291-294. Geiger, R. 1965. The c l i m a t e near the ground. Second e d i t i o n , Cambridge Harvard Press. Gunn, R. and G. D. K i n z e r . 1949. The t e r m i n a l v e l o c i t y of f a l l f o r water d r o p l e t s i n stagnant a i r . J . Meteor., V o l . 6, 243-248. H a l t i n e r , G. J . and F. L. M a r t i n . 1957. Dynamical and p h y s i c a l meteorology. McGraw-Hill Book Co. Inc., N.Y. Hamilton, E. L. 1954. R a i n f a l l sampling on rugged t e r r a i n . U.S. Dept. of A g r i c u l t u r e Tech. B u l l . 1096. Hamilton, E. L. and L. F. Reimann. 1958. S i m p l i f i e d method of sampling r a i n f a l l on the San Dimas Experimental F o r e s t . Tech. Paper No. 26. C a l i f o r n i a Forest and Range Experiment S t a t i o n , Forest S e r v i c e , U.S. Dept. of A g r i c u l t u r e , 8 p. Hardy, K. R. 1963. The development of r a i n d r o p - s i z e d i s t r i b u t i o n s and i m p l i c a t i o n s r e l a t e d to the physics of p r e c i p i t a t i o n . J . Atmos. S c i . , V o l . 20, 299-312. Hare, F. K. and J . E. Hay. 1974. Climate of Canada. In c l i m a t e s of North America, Ed. Bryson, R. A. and F. K. Hare, E l s e v i e r S c i e n t i f i c Publ. Co., Amsterdam. Hare, F. K. and M. K. Thomas. 1974. Climate Canada. Wiley P u b l i s h e r s of Canada L t d . , Toronto. Harley, W. S. 1963. Q u a n t i t a t i v e p r e c i p i t a t i o n f o r e c a s t i n g . Can. Dept. of Transport, M e t e o r o l o g i c a l Branch CIR-3805, TEC-456. . 1965. An o p e r a t i o n a l method f o r q u a n t i t a t i v e p r e c i p i t a t i o n f o r e c a s t i n g . J . Appl. Meteor., V o l . 4, No. 3, 305-319. Hendrick, R. L. and G. H. Comer. 1970. Space v a r i a t i o n s of p r e c i p i t a -t i o n and i m p l i c a t i o n s f o r r a i n gauge network design. J . of Hydrology, V o l . 10, No. 2, 151-163. 216 H e r s h f i e l d , D. M. 1965. On the spacing of rainguages. Symp. on Design of H y d r o l o g i c a l Networks, Quebec. Publ. No. 67 of I.A.S.H., 72-81. Holland, J . D. and C. L. C r o z i e r . 1973. Further e v a l u a t i o n of the e f f e c t s of cloud seeding i n the p r e c i p i t a t i o n physics p r o j e c t . Can. Meteor. Memoirs No. 29, Atmospheric Environment S e r v i c e . Horton, R. E. 1919. The measurement of r a i n f a l l and snow. New England Water Works Assoc. Jour., V o l . 33, 14-65. Huschke, R. E. 1959. Glossary of meteorology. Amer. Meteor. S o c , Boston, Mass. Hutchinson, P. 1972. The use of modified time s e r i e s a n a l y s i s technique f o r the determination of a r e a l p r e c i p i t a t i o n a c c u r a c i e s . Proc. I n t . Symp. on the D i s t r i b u t i o n of P r e c i p i t a t i o n i n Mountainous Areas, V o l . I I , G e i l o , Norway, W.M.O. Pub. No. 326, 448-465. Jackson, R. J . and R. A l d r i d g e . 1972. R a i n f a l l measurements at T a i t a Experimental S t a t i o n , New Zealand: Part 2 - T i l t e d raingauges and vectopluviometers. New Zealand J . of Hydrology, V o l . I I , No. 1, 15-37. Jones, R. D. 0. 1974. Op t i m i z a t i o n of the r a i n gauge network on the Jamieson Creek watershed. B.S.F. Thesis, Faculty, of F o r e s t r y , U n i v e r s i t y of B r i t i s h Columbia, Vancouver. Jorgensen, D. L. 1963. A computer de r i v e d synoptic c l i m a t o l o g y of p r e c i p i t a t i o n from winter storms. J . Appl. Meteor., V o l . 2, No. 2, 226-234. Kendrew, W. G. and D. Kerr. 1955. The c l i m a t e of B r i t i s h Columbia and the Yukon T e r r i t o r y . Queen's P r i n t e r , Ottawa, Canada. Knox, J . B. 1960. Procedures f o r e s t i m a t i n g maximum p o s s i b l e p r e c i p i t a t i o n . B u l l . 88, C a l i f o r n i a State Dept. of Water Resources. K r a j i n a , V. J . 1969. Ecology of western t r e e s i n B r i t i s h Columbia. Ecology of western North America. V o l . 2, No. 1. Kurtyka, J . C. 1953. P r e c i p i t a t i o n measurements study. State of I l l i n o i s , State Water Survey D i v i s i o n , Urbana, I l l i n o i s . Kutzbach, J . E. 1967. E m p i r i c a l eigenvectors of s e a - l e v e l pressure, surface temperature and p r e c i p i t a t i o n complexes over North America. J . Appl. Meteor., V o l . 6, No. 10, 791-802. Langleben, M. P. 1954. The t e r m i n a l v e l o c i t y of snowflakes. Q. J . Roy. Meteor: S o c , V o l . 80, No. 344, 174-181. 217 Larson, L. W. 1971. P r e c i p i t a t i o n and i t s measurement a s t a t e of the a r t . Water Resources S e r i e s No. 24, Water Resources Research I n s t i t u t e , U n i v e r s i t y of Wyoming, Laramie, Wyoming. 74 p. Larson, L. W. and E. L. Peck. 1974. Accuracy of p r e c i p i t a t i o n measurement f o r h y d r o l o g i c modelling. Water Resour. Res., V o l . 10, No. 4, 857-863. Laws, J . 0. and D. A. Parsons. 1943. The r e l a t i o n of r a i n d r o p - s i z e to i n t e n s i t y . Trans. Amer. Geophys. Union, V o l . 24, 452-459. Leonard, R. E. and K. G. Reinhart. 1962. Some observations on p r e c i p i t a t i o n measurement on f o r e s t e d experimental watersheds. U.S. Forest S e r v i c e , Northeastern Forest Experimental S t a t i o n Research Note NE-6. L i n s l e y , R. K. 1968. C o r r e l a t i o n of r a i n f a l l i n t e n s i t y and topography i n northern C a l i f o r n i a . Trans. Amer. Geophys. Union, V o l . 39, No. 1, 15-18. L i s t , R. J . 1966. Smithsonian M e t e o r o l o g i c a l Tables, 6th r e v i s e d ed., Smithsonian I n s t i t u t i o n , Washington, D.C. Ludlam, F. H. 1956. The s t r u c t u r e of r a i n clouds. Weather, V o l . I I , 187-196. Lund, I. A. 1963. Map-pattern c l a s s i f i c a t i o n by s t a t i s t i c a l methods. J . A p p l. Meteor., V o l . 2, No. 1, 56-65. M a r s h a l l , J . S. and W. McK. Palmer. 1948. The d i s t r i b u t i o n of raindrops w i t h s i z e . J . Meteor., V o l . 5, 165-166. Marwitz, J . D. 1974. An a i r f l o w case study over the San Juan Mountains of Colorado. J . Appl. Meteor., V o l . 13, No. 4, 450-458. Mason, B. I . 1962. Clouds, r a i n and r a i n making. Cambridge,Univ. Press. McKay, G. A. 1964. M e t e o r o l o g i c a l measurements f o r watershed research. Proc. Hydrology Symp. No. 4 on Research Watersheds, Guelph, Ontario. _. 1970. P r e c i p i t a t i o n . S e c t i o n I I , Handbook on the 1 P r i n c i p l e s of Hydrology, Can. Nat. Committee f o r the I.H.D., Ottawa. McNeil, R. Y. and S. 0. R u s s e l l . 1972. The use of EV0P as a h y d r o l o g i c t o o l . Proc. Second I n t e r n a t i o n a l Symposium i n Hydrology, "Decisions w i t h inadequate h y d r o l o g i c data," held i n Fort C o l l i n s , Colorado. 218 Myers, V. A. 1959. Factors i n C a l i f o r n i a orographic r a i n . Paper presented at 177th N a t i o n a l Meeting of the American M e t e o r o l o g i c a l S o c i e t y , San Diego, C a l i f . 28 pp. . 1962. A i r f l o w on the windward side of a la r g e r i d g e . J . Geophy. Res., V o l . 67, No. 11, 4267-4291. Narver, D. W. 1974. Carnation Creek Experimental Watershed P r o j e c t Annual Report f o r 1973. Canada, Dept. of Environment, F i s h e r i e s and Marine S e r v i c e , P a c i f i c B i o l o g i c a l S t a t i o n , Nanaimo, B.C. Newton, C. W. 1962. Dynamics of severe convective storms. Report No. 9, N a t i o n a l Severe Storms P r o j e c t , U.S. Weather Bureau, Kansas C i t y , Mo., 44 pp. N i c h o l l s , J . M. 1973. The a i r f l o w over mountains - Research 1958-1972. Tech. Note No. 127, WMO No. 355, World M e t e o r o l o g i c a l O r g a n ization, Geneva. N i k l e v a , S. 1968. The e f f e c t of i n s t a b i l i t y on orographic p r e c i p i t a -t i o n over Vancouver I s l a n d . Can. Dept. of Transport, Met. Branch, TEC 698. Nord0, J . 1972. Orographic p r e c i p i t a t i o n i n mountainous areas. Proc. I n t . Symp. on the D i s t r i b u t i o n of P r e c i p i t a t i o n i n Mountainous Areas, V o l . I , G e i l o , Norway, W.M.O. Pub. No. 326, 31-56. Peck, E. L. 1972. R e l a t i o n of orographic winter p r e c i p i t a t i o n p a t t e r n s to m e t e o r o l o g i c a l parameters. Proc. I n t . Symp. on the D i s t r i b u t i o n of P r e c i p i t a t i o n i n Mountainous Areas, V o l . I I , G e i l o , Norway, W.M.O. Pub. No. 326, 234-241. Pedgley, D. E. 1967. Why so much r a i n ? Weather, V o l . 22, No. 12, 478-482. . 1970. Heavy r a i n f a l l s over Snowdonia. Weather, V o l . 25, No. 8, 340-350. . 1971. Some weather patte r n s i n Snowdonia. Weather, V o l . 26, No. 10, 412-444. Penner, C. M. 1955. A th r e e - f r o n t model f o r synoptic analyses. Q. J . Roy. Met. S o c , V o l . 81, 89-91. P e r e i r a , H. C , J . S. G. McCulloch, M. Dagg, P. H. Hosegood and M. A. C. P r a t t . 1962. Assessment of the r a i n components of the h y d r o l o g i c a l c y c l e . East A f r i c a n A g r i c u l t u r a l and F o r e s t r y J o u r n a l , S p e c i a l Issue, 8-15. Pers, R. 1932. R e l a t i o n s entre l e s donnees pluviometriques et l e s p r e c i p i t a t i o n s t o t a l e s r e c u e i l l i e s par un ba s s i n . La Meteorologie, V o l . 8, 101. 219 Platzman, G.. W. 1948. Computation of maximum r a i n f a l l i n the Willamette Basin. Trans. Amer. Geophys. Union, V o l . 29, No. 4, 467-472. Probert-Jones, J . R. 1973. Orthogonal p a t t e r n (eigenvector) a n a l y s i s of random and p a r t l y random f i e l d s . Proc. T h i r d Conference on P r o b a b i l i t y and S t a t i s t i c s i n Atmospheric Science held i n Boulder, Colorado. American M e t e o r o l o g i c a l S o c i e t y , p. 187-192. R a i n b i r d , A. F. 1965. P r e c i p i t a t i o n - b a s i c p r i n c i p l e s of network design. ,Symp. on Design of H y d r o l o g i c a l Networks, Quebec, Publ. No. 67 of I.A.S.H., 19-30. R e i n e l t , E. R. 1968. The e f f e c t of topography on the p r e c i p i t a t i o n regime of Watertori N a t i o n a l Park. The A l b e r t a n Geographer, V o l . 4, 19-30. Rodda, J . C. 1967. The r a i n f a l l measurement problem. I.A.S.H. Gen. Assembly of Bern, 215-231. . 1969. H y d r o l o g i c a l network design - needs, problems and approaches. Reports on WMO/IHD P r o j e c t s , No. 12, World M e t e o r o l o g i c a l O r g a n i z a t i o n , Geneva, 57 pp. . 1970. On the questions of r a i n f a l l measurement and repre s e n t a t i v e n e s s . I.A.S.H. Symp. on World Water Balance, Univ. of Reading, England, V o l . 1, 173-186. . 1971. The p r e c i p i t a t i o n measurement paradox - the instrument accuracy problem. Reports on WMO/IHD P r o j e c t s , No. 16, World M e t e o r o l o g i c a l O r g a n i z a t i o n , Geneva, 42 pp. Rogers, J . S., L. C. Johnson, D. M. A. Jones and B. A. Jones, J r . 1967. Sources of e r r o r i n c a l c u l a t i n g the k i n e t i c energy of r a i n f a l l . J . S o i l and Water Conservation, 140-142. Sarker, R. P. 1966. A dynamical model of orographic r a i n f a l l . Mon. Wea. Rev., V o l . 94, No. 9, 555-572. . 1967. Some m o d i f i c a t i o n s i n a dynamical model of orographic r a i n f a l l . Mon. Wea. Rev., V o l . 95, No. 10, 673-684. Sawyer, J . S. 1952. A study of the r a i n f a l l of two synoptic s i t u a t i o n s . Q. J . Roy. Met S o c , V o l . 78, 321-346. . 1956. The p h y s i c a l and dynamical problems of orographic r a i n f a l l . Weather, I I : 375-381. Schaefer, D. G. and S. N. N i k l e v a . 1973. Mean p r e c i p i t a t i o n and snow-f a l l maps f o r a mountainous area of p o t e n t i a l urban development. Proc. of the Western Snow Conference, 80-39. 220 Serra, L. 1951. I n t e r p r e t a t i o n des mesures pluviometriques, l o i s de l a p l u v i o s i t e . I.A.S.H. Gen. Assembly of B r u x e l l e s , 9-25. Sevruk, B. 1972. P r e c i p i t a t i o n measurements by means of storage gauges w i t h stereo and h o r i z o n t a l o r i f i c e s i n the Baye de Montreux Watershed. Proc. I n t . Symp. on the D i s t r i b u t i o n of P r e c i p i t a t i o n i n Mountains Areas, G e i l o , Norway, W.M.O. Pub. 326, 86-95. Shaw, E. M. 1962. An a n a l y s i s of the o r i g i n s of p r e c i p i t a t i o n i n Northern England. Q. J . Roy. Met. S o c , V o l . 88, 539-547. Showalter, A. K. 1971. Evaporative c a p a c i t y of unsaturated a i r . Water Resour. Res., V o l . 7, No. 3, 688-691. S i n i k , N. 1972. A p o s s i b i l i t y of a i r f l o w - p r e c i p i t a t i o n regime i n v e s t i g a t i o n s . Proc. I n t . Symp. on the D i s t r i b u t i o n of P r e c i p i t a t i o n i n Mountainous Areas, V o l . I I , G e i l o , Norway, W.M.O. Pub. No. 326, 128-139. Smith, T. B. 1962. P h y s i c a l s t u d i e s of the Santa Barbara cloud seeding p r o j e c t . J . Appl. Meteor., V o l . 1, 208-217. Solomon, S. I . , J . P. D e n o u v i l l i e z , E. J . Chart, J . A. Woolley, and C. Cadou. 1968. The use of a square g r i d system f o r computer es t i m a t i o n of p r e c i p i t a t i o n , temperature and r u n o f f . Water Resour. Res., V o l . 4, No. 5, 919-925. Sporns, U. 1963. Frequency and s e v e r i t y of storms i n the lower Fraser V a l l e y , B.C. Canada, Dept. of Transport, M e t e o r o l o g i c a l Branch, CIR-3848, TEC-469. . 1964. On the t r a n s p o s i t i o n of s h o r t - d u r a t i o n r a i n f a l l i n t e n s i t y data i n mountainous reg i o n s . Canada, Dept. of Transport, M e t e o r o l o g i c a l Branch, CIR-4032, TEC-519. Spreen, Wm. C. 1947. A determination of the e f f e c t of topography upon p r e c i p i t a t i o n . Trans. Amer. Geophys. Union, V o l . 28, 285-290. Storebo, P. B. 1968. P r e c i p i t a t i o n formation i n a mountainous coast r e g i o n . T e l l u s , V o l . 20, No. 2, 239-249. S t o r r , D. and H. L. Ferguson. 1972. The d i s t r i b u t i o n of p r e c i p i t a t i o n i n some mountainous Canadian watersheds. Proc. I n t . Symp. on the D i s t r i b u t i o n of P r e c i p i t a t i o n i n Mountainous Areas, V o l . I I , G e i l o , Norway, W.M.O. Pub. No. 326, 243-263. S t i d d , C. K. 1967. The use of eigenvectors f o r c l i m a t i c estimates. J . Appl. Meteor. V o l . 6, No. 4, 255-264. S t r i n g e r , E. T. 1972. Foundations of Climatology. W. H. Freeman and Co., San F r a n c i s c o . 221 Str u z e r , L. R. 1965. P r i n c i p a l shortcomings of methods of measuring atmospheric p r e c i p i t a t i o n and means of improving them. Soviet Hydrology: Selected Papers, Amer. Geophys. Union, No. 1, 21-35. Trewartha, G. T. 1966. The earth's problem c l i m a t e s . The U n i v e r s i t y of Wisconsin Press, Methuen & Co. L t d . , London. T s c h i r h a r t , G. I960. Notes sur l a v a r i a t i o n temporelle des p r e c i p i t a t i o n s . I.A.S.H. Gen. Assembly of H e l s i n k i , Publ. No. 53, 238-249. U.S. Weather Bureau. 1961. Interim r e p o r t - probable maximum p r e c i p i t a t i o n i n C a l i f o r n i a . Hydrometeorological Report No. 36, Washington, D.C. _. 1966. Probable maximum p r e c i p i t a t i o n , Northwest States. Hydrometeorological Report No. 43, Washington, D.C. V u l ' f s o n , N. I. 1961. Convective motions i n a f r e e atmosphere. Translated from Russian, (U.S. Dept. of Commerce and the N a t i o n a l Science Foundation, Washington, D.C). I s r a e l Program f o r S c i e n t i f i c T r a n s l a t i o n s , Jerusalem, 1964. Walker, E. F. 1961. A synoptic c l i m a t o l o g y f o r p a r t s of the Western C o r d i l l e r a . M c G i l l U n i v e r s i t y A r c t i c Meteorology Group, Contract AF19(604)3865, S c i e n t i f i c Report No. 8, P u b l i c a t i o n i n Meteorology No. 35. Weaver, R. L. 1962. Meteorology of h y d r o l o g i c a l l y c r i t i c a l storms i n C a l i f o r n i a . Hydrometeorological Report No. 37, U.S. Weather Bureau, Washington, D.C. Weiss, L. L. 1963. Securing more n e a r l y t r u e p r e c i p i t a t i o n measure-ments. Jour. H y d r a u l i c s D i v i s i o n , Amer. Soc. C i v i l Engr., 11-18. Weiss, L. L. and W. T. Wilson. 1958. P r e c i p i t a t i o n gauge s h i e l d s . I.A.S.H. Gen. Assembly of Toronto, V o l . 1, 462-484. W i l l i a m s , P. and E. L. Peck. 1962. T e r r a i n i n f l u e n c e s .on p r e c i p i t a t i o n i n the Intermountain West as r e l a t e d to syno p t i c s i t u a t i o n s . J . Appl. Meteor., V o l . 1, No. 3, 343-347. Wilson, J . W. 1961. A model f o r p r e d i c t i n g p r e c i p i t a t i o n amounts i n S e a t t l e and Western Washington. Dept. of Meteor, and Climat., Univ. of Washington, S e a t t l e . Contract No. AF(604)-5192, P r o j e c t No. 8641, Task No. 86414, Tec. Rept. No. 2, 40 p. Wilson, W. T. 1954. A n a l y s i s of w i n t e r p r e c i p i t a t i o n observations i n co-operative snow i n v e s t i g a t i o n s . Mon. Wea. Rev., V o l . 82, 183-195. 222 Wischmeier, W. H. and D. D. Smith. 1958. R a i n f a l l energy and i t s r e l a t i o n s h i p to s o i l l o s s . Trans. Amer. Geophys. Union, V o l . 39, No. 2, 285-291. Wobus, H. B. 1971. C a l c u l a t i o n of the t e r m i n a l v e l o c i t y of water drops. J . Appl. Meteor., V o l . 10, 751-754. World M e t e o r o l o g i c a l O r g a n i z a t i o n and I n t e r n a t i o n a l A s s o c i a t i o n of S c i e n t i f i c Hydrology. 1965. Proc. Symp. on Design of H y d r o l o g i c a l Networks, Quebec, Pub. No. 67 of I.A.S.H. World M e t e o r o l o g i c a l O r g a n i z a t i o n . 1970. Guide to hydrometeorological p r a c t i c e s . W.M.O. - No. 168, TP 82. . 1972. Proc. I n t . Symp. on the D i s t r i b u t i o n of P r e c i p i t a t i o n i n Mountainous Areas, G e i l o , Norway, W.M.O. Pub. 326. . 1973. Manual f o r e s t i m a t i o n of probable maximum p r e c i p i t a -t i o n . Operational Hydrology. Report No. 1, W.M.O. No. 332, Geneva. ,_. 1974. Annotated b i b l i o g r a p h y on p r e c i p i t a t i o n measurement instruments. Rep. 17, W.M.O.-343, 278 pp. Wright, J . B. and C. H. Trenholm. 1969. Greater Vancouver p r e c i p i t a t i o n . Can. Dept. of Transport, Met. Branch, TEC-722. Yordanov, D. and N. Godev. 1973. P a r a m e t r i z a t i o n of o r o g r a p h i c a l e f f e c t s i n the p l a n e t a r y boundary l a y e r . Boundary-layer Meteorology, V o l . 5, 309-320. APPENDIX I AIR MASS TEMPERATURES* Pressure l e v e l mTw mPs Temperatures (°C) mPw mA cold mA 1000 mb 15-25 16 12 9 3 850 mb 14 9 5 0 -7 700 mb 4 0 -3 -10 -17 500 mb -11 -17 -21 -29 -36 400 mb -23 -30 -34 -42 -50 300 mb -42 -47 -52 -51 -200 mb -62 - - - -Tropopause 200 mb 240 mb 275 mb 350 mb 400 mb e 15-18 12-16 10-13 5-10 0-4 w mTw - maritime tropical-winter mPs - maritime polar-summer mPw - maritime polar-winter mA - maritime a r c t i c *Data taken from notes - Univ e r s i t y of Toronto course on synoptic meteorology (1962); s i m i l a r values are also given by Penner (1955). 223 APPENDIX II DESCRIPTION OF PRECIPITATION STATIONS The following tables present information on stations f o r which p r e c i p i t a t i o n data were c o l l e c t e d and used during the course of the study. The following abbreviations are employed. A.E.S. - Atmospheric Environment Service G.V.S.D.D. - Greater Vancouver Sewerage and Drainage D i s t r i c t R.F. - Research Forest SG - Standard, non-recording r a i n gauge RG - Recording r a i n gauge VP - Vectopluviometer 224 225 Ex i s t i n g P r e c i p i t a t i o n Stations Station Name Agency Elevation (meters) Gauge SG Type RG PP - P i t t Polder A.E.S. 1.5 * HE - Haney East A.E.S. 30 * LP - Langley P r a i r i e A.E.S. 87 * SM - Surrey Municipal H a l l A.E.S. 76 VAP - Vancouver I n t ' l A i r p o r t A.E.S. 5 * UBC-University of B.C. A.E.S. 87 PMO - Vancouver PMO A.E.S. 60 * •k WV - West Vancouver C i t y H a l l G.V.S.D.D. 60 A NV - North Vancouver Cit y H a l l G.V.S.D.D. 170 CD - Cleveland Dam G.V.S.D.D. 155 * Cleveland Dam A.E.S. 155 LC - N. Vancouver Lynn Creek A.E.S. 190 •k SD - Seymour F a l l s Dam G.V.S.D.D. 200 Seymour F a l l s Dam A.E.S. 200 * 226 Research Forest and Study S t a t i o n s E l e v a t i o n Gauge Type S t a t i o n Name Agency (Meters) SG RG VP 1 - S i t e 1 305 A 2 - S i t e 2 305 A 3 - S i t e 3 585 A 4 - S i t e 4 595 A A 5 - S i t e 5 460 A 6 - S i t e 6 410 A 7 - S i t e 7 545 * 8 - S i t e 8 555 9 - S i t e 9 775 * 10 - S i t e 10 545 11 - S i t e 11 395 A A 12 - S i t e 12 305 A 13 - S i t e 13 530 A 8b - S i t e 8b 500 A A AD - A d m i n i s t r a t i o n B u i l d i n g A •E.S.-R.F. 145 A A MC - Marc R .F. 185 S17 - Spur 17 R .F. 375 A A A LN - Loon Lake R .F. 365 A MR - Maple Ridge 34 A A PM - P i t t Meadows A i r p o r t 3 A APPENDIX I I I DATA SOURCE INFORMATION 1. S c i e n t i f i c Support Unit, Atmospheric Environment Service, 739 West Hastings Street, Vancouver, B.C. - copies of weather maps obtained from micro-film - p r e c i p i t a t i o n i n t e n s i t y and frequency data 2. Weather O f f i c e , Atmospheric Environment Service, 416 Cowley Crescent, Vancouver International A i r p o r t South, Richmond, B.C. - synoptic weather maps - hourly surface weather data for Vancouver and Abbotsford A i r p o r t s : temperatures, cloud cover, wind speed and d i r e c t i o n and atmospheric pressure - plotted tephigrams showing upper a i r temperature and humidity data - teletype reports of Port Hardy and Quillayute radiosonde ascent data; t h i s information i s normally only kept f o r a short period and then disposed of 3. Regional Climate Data Centre, Atmospheric Environment Service, 302 Denison Road, V i c t o r i a , B.C. - montly p r e c i p i t a t i o n records f o r recording and non-recording gauges 4. Atmospheric Environment Service, 4905 D u f f e r i n Street, Downsview, Ontario. - punched cards of radiosonde data for Port Hardy - publishes Monthly B u l l e t i n of Canadian Upper A i r Data 227 228 5. National Climatic Center, Federal Building, A s h e v i l l e , North Carolina, 28801 U.S.A. - punched cards of radiosonde data for Quillayute, Washington 6. Greater Vancouver Sewerage and Drainage D i s t r i c t , 2294 West 10th Avenue, Vancouver, B.C. - p r e c i p i t a t i o n records from agency gauges 7. U.B.C. Research Forest, c/o Faculty of Forestry, U n i v e r s i t y of B.C., Vancouver, B.C. - p r e c i p i t a t i o n records f o r gauges operated by the Research Forest APPENDIX IV RAIN GAUGE CATCH RELATIONSHIPS ON SLOPING GROUND S e r r a (1951) has p r e s e n t e d a comprehensive d i s c u s s i o n o f t h e r e l a t i o n s h i p s between c a t c h e s o f r a i n gauges w i t h h o r i z o n t a l , s t e r e o and t i l t e d o r i f i c e s and t h e a n g l e of i n c l i n a t i o n o f r a i n f a l l , ground s l o p e and t h e d i f f e r e n c e i n a n g l e between s l o p e a s p e c t and s t o r m wind d i r e c t i o n . Most o f t h e f o l l o w i n g m a t e r i a l i s based on S e r r a ' s p r e s e n t a t i o n w h i c h i s r e a l l y a resume o f e a r l i e r work by H o r t o n (1919), P e r s (1932) and F o u r c a d e ( 1 9 4 2 ) . H a m i l t o n (1954) p r o v i d e s an e x c e l l e n t example of a p r a c t i c a l a p p l i c a t i o n of t h e s e c o n c e p t s t o p r e c i p i t a t i o n measurement s t u d i e s i n t h e San Dimas E x p e r i m e n t a l F o r e s t i n C a l i f o r n i a . The number o f r a i n d r o p s r e a c h i n g t h e ground p e r u n i t a r e a "S" of a h o r i z o n t a l s u r f a c e i s t h e same whether t h e d r o p t r a j e c t o r i e s a r e v e r t i c a l o r i n c l i n e d as shown i n F i g u r e I V - 1 , assuming c o n s t a n t wind speed and d i r e c t i o n . However, f o r s l o p i n g s u r f a c e s t h e s i t u a t i o n i s d i f f e r e n t as d e p i c t e d i n F i g u r e IV-2,. I n t h e s e d i a g r a m s , a i s t h e s l o p e a n g l e w i t h t h e h o r i z o n t a l , 0 t h e i n c l i n a t i o n o f r a i n d r o p t r a j e c t o r i e s f r o m t h e v e r t i c a l , and t h e l e n g t h OA' o r OA^', r e p r e s e n t s t h e s u r f a c e a r e a c o r r e s p o n d i n g t o i t s h o r i z o n t a l p r o j e c t i o n OA or OA^ w h i c h i s e q u a l t o "S". 229 Figure IV-3. Rain gauge o r i f i c e positions on sloping ground. 231 If the r a i n f a l l s v e r t i c a l l y , OA' or OA^' receives the same number of drops as OA or OA^. Although these drops are more spread out on the ground, the t o t a l p r e c i p i t a t i o n i s the same. On the other hand, i f the r a i n f a l l s o bliquely, the ground surface OA' w i l l receive the same number of drops as the extended h o r i z o n t a l projection OA", and OA^' the same as the co n s t r i c t e d h o r i z o n t a l p r o j e c t i o n OA^". A windward slope thus receives more r a i n than a h o r i z o n t a l l y projected surface and a leeward slope l e s s , since OA" > OA and OA^" < OA^. A gauge with a hor i z o n t a l aperture of unit area S w i l l catch a meteorological r a i n f a l l of depth h. To obtain the t o t a l volume of water H received by the ground surface with h o r i z o n t a l l y projected area S, the depth h must be m u l t i p l i e d by both S and the r a t i o OA" = R. OA Simple geometric c a l c u l a t i o n s give R = OA" = 1 ± tan a tan 9 OA where the + sign corresponds to windward slopes the the - sign to l e e -ward slopes. Hence H = h S (1 ± tan a tan 6). g The r e l a t i o n s h i p s between catches by gauges with ho r i z o n t a l o r i f i c e s (Figure IV-3a) and t i l t e d c i r c u l a r o r i f i c e s (Figure IV-3b) both with u n i t c r o s s - s e c t i o n a l area a, and Stereo or e l l i p t i c a l o r i f i c e s with h o r i z o n t a l p r o j e c t i o n a (Figure IV-3c) can now be demonstrated. If gauge type "a" catches a r a i n f a l l of depth h, that of type "b" w i l l catch h, = h cos a (1 ± tan a tan 6) b and the t h i r d of type "c" w i l l catch h = h (1 ± tan a tan 6). 232 The ground surface with h o r i z o n t a l p r o j e c t i o n S w i l l thus receive a volume of r a i n f a l l H as follows: g In the f i r s t case as already discussed, t h i s w i l l be H = h S (1 ± tan a tan 0 ) . g In the second case, t h i s w i l l be h^ m u l t i p l i e d by the r a t i o of the p a r a l l e l r e ceiving areas of the o r i f i c e and the ground H = h, S/cos a = h S (1 ± tan a tan 9 ) . g b — In the t h i r d case, t h i s w i l l be h^ m u l t i p l i e d by the r a t i o of the p a r a l l e l r e c e i v i n g areas of the o r i f i c e and the ground H = h S/cos a = h S (1 ± tan a tan 9 ) . g c T~7 , 1/cos a In each case, the amount received by the ground i s the same, as i t must be, which suggests that what could be considered errors i n measurement are i n fact only errors i n i n t e r p r e t a t i o n of measurement, assuming n e g l i g i b l e differences i n wind e f f e c t s on catches by gauges with d i f f e r i n g o r i f i c e configurations. Since r a i n does not always f a l l from a d i r e c t i o n normal to a given slope, the d i r e c t i o n from which i t does f a l l must also be taken into account. If u = Y -co i s the angle between the d i r e c t i o n co from s s which the r a i n i s f a l l i n g and slope aspect y, the c o r r e c t i o n factor K by which the meteorological catch (horizontal o r i f i c e ) must be m u l t i p l i e d to obtain the hydrological r a i n f a l l becomes K = 1 ± tan a tan 9 cos y where a and 9 vary between 0 and II/2 and y between 0 and II. APPENDIX V VECTOPLUVIOMETER CALCULATIONS A d i r e c t i o n a l r a i n gauge or vectopluviometer of the type described i n Chapter II i s used i n conjunction with a conventional r a i n gauge to obtain a measure of the angles 6 and a required i n the re l a t i o n s h i p s presented i n Appendix IV. The d i r e c t i o n a l gauge catches the horizontal components of r a i n f a l l while a nearby v e r t i c a l gauge c o l l e c t s the v e r t i c a l component. The mean angle of i n c l i n a t i o n and d i r e c t i o n of r a i n f a l l during a given storm or measurement period can be evaluated from the t o t a l catches of the four ho r i z o n t a l and one v e r t i c a l c o l l e c t o r s as follows (Fourcade, 1942; Hamilton, 1954): h = catch of v e r t i c a l r a i n gauge N s = catches of v e r t i c a l apertures of vectopluviometer E W 9 = angle of i n c l i n a t i o n of r a i n from the v e r t i c a l OJ = d i r e c t i o n of storm s N-S = h n = hor i z o n t a l components of r a i n f a l l E-W = h e To f i n d the mean storm d i r e c t i o n : tan 0 = h tan 0 = h then tan OJ = h n _n e _e s _e h h h n 233 234 or subst i tu t ing tan co = tan 9 s e tan 6 n To f ind the mean i n c l i n a t i o n of the r a i n : tan 6 = h and since h = tan 9 n __n n h cos to h s then tan 6 = tan 9 or tan 9 = tan 9 n e cos to s in to s s Using data obtained from the vectopluviometer, the catch of v e r t i c a l r a i n gauges with hor izonta l o r i f i c e s could be adjusted to give the actual r a i n f a l l received on the sloping ground surface. APPENDIX VI STORM DATA Legend f o r column headings 1. Radiosonde ascent time i s given for Greenwich Mean Time 00 Z = 0000 GMT 12 Z = 1200 GMT 2. Syn. Cat. - Synoptic category 3. AF Cat. - Airflow category 4. Occur Cat. - Occurrence of orographic process category 5. Excess duration - i s the d i f f e r e n c e i n storm duration between Surrey Municipal H a l l and the Research Forest Station with longest duration. 6. Other headings and symbols are defined i n the l i s t of symbols preceding the main text. 235 Table A - l 236 Storm data Storm 'Storm Radiosonde Ascent Syn AF Occur vsw VW VS No. Period Stn. Time Day Cat Cat Cat (S-85) (S-85) (S-85) 1970 (Z) (m/s) (m/s) (m/s) 2 Sept. 2-3 UIL 00 Sept. 3 OGF SW Ui 9.2 2.1 11.8 ZT 00 Sept. 3 6.1 1.4 7.9 3 Sept. 5-6 UIL 12 WF W Ui 7.2 7.7 2.1 UIL 00 Sept. 6 11.6 10.0 5.1 4 Sept. 16-17 UIL 12 Sept. 17 ODF SW 0 11.8 5.5 11.8 5 Sept. 18 UIL 12 Sept. 18 T SW 0 10.0 7.1 7.1 6 Sept. 19 UIL 12 Sept. 19 T SW 0 4.9 3.2 3.8 7 Sept. 21-22 UIL 12 Sept. 22 WF w T p 16.5 18.7 3.3 8 Oct. 4 ZT 12 Oct. 4 ONW w TC 4.2 6.0 0.0 9 Oct. 8-9 ZT 00 Oct. 9 WF w none 6.1 8.0 0.0 10 Oct. 10-11 ZT 12 Oct. 11 ONW w Um 6.9 7.9 .1.4 11 Oct. 17-18 UIL 12 Oct. 18 ONW S Tp 13.4 2.5 17.8 12 Oct. 19-20 UIL 00 Oct. 20 ODF s Um 4.0 0.0 7.9 UIL 12 Oct. 20 2.0 5.2 0.0 13 Oct. 22-23 UIL 00 Oct. 23 ODF SW Ui 7.5 0.0 20.7 14 Oct. 23 UIL 00 Oct. 24 T w TP 9.9 8.7 5.0 15 Nov. 5-6 UIL 00 Nov. 6 L E 0 0.0 o . o - 2.6 16 Nov. 7-8 UIL 00 Nov. 8 ODF s 0 5.0 0.0 9.9 UIL 12 Nov. 8 13.4 7.6 11.7 17 Nov. 8-9 UIL 00 Nov. 9 T SW TC 10.0 7.1 7.1 18 Nov. 10-11 UIL 00 Nov. 11 ODF s Ui 12.5 0.0 24.6 UIL 12 Nov. 11 13.2 0.0 22.9 19 Nov. 15-16 UIL 00 Nov. 16 ODF SW TP 23.5 12.5 21.7 21 Nov. 24 UIL 12 Nov. 24 - ONW w 0 9.2 12.0 0.0 1971 22 May 18-19 ZT 00 May 19 ONW w 0 5.1 10.9 0.0 23 May 29-30 UIL 12 May 29 T NW TP 2.7 6.9 0.0 24 June 6-7 UIL 00 June 7 L s T p 3.0 0.0 5.9 25 June 13 UIL 00 June 14 L s TC 6.9 2.7 7.5 26 June 22-23 UIL 00 June 23 T s TC 5.2 0.0 9.0 27 June 24 UIL 12 June 24 ODF s Ui 6.3 0.0 14.5 UIL 00 June 25 12.9 0.0 20.0 28 June 25 UIL 12 June 25 T SW TO 11.0 8.4 7.1 29 July 10-11 UIL 00 July 11 L s TC 5.7 0.7 7.9 30 Aug. 21 UIL 00 Aug. 22 ONW s 0 6.3 3.0 6.3 31 Sept. 1-2 UIL 00 Sept. 2 OGF E 0 0.0 0.0 0.0 UIL 12 Sept. 2 4.2 9.1 0.0 32 Sept. 4-5 UIL 00 Sept. 5 OGF s U i 6.4 0.0 10.0 UIL 12 Sept. 5 3.5 3.9 0.7 •33 Sept. 8 UIL 00 Sept. 9 ONW SW 0 4.0 3.1 2.6 34 Sept. 10 UIL 00 Sept. 11 ONW s 0 9.9 1.2 13.9 .Continued 237 Table A-l Storm data Storm Storm Radiosonde Ascent Syn AF Occur VSW VW VS No. Period Stn. Time Day Cat Cat Cat (S-85) (S-85) (S-85) 1971 (Z) (m/s) (m/s) (m/s) 35 Sept. 26 UIL 00 Sept . 27 L E TC 0.0 0.0 0.0 36 Sept. 27 UIL 12 Sept . 27 T W TP 2.9 2.6 1.5 37 Sept. 27-29 UIL 12 Sept . 28 L SW TP 7.5 4.0 6.9 UIL 00 Sept . 29 5.6 3.0 5.2 ZT 12 Sept . 28 1.5 2.0 0.0 38 Oct. 2-4 UIL 00 Oct. 4 WF SW Ui 16.9 9.0 15.6 ZT 12 Oct. 3 7.7 1.7 9.9 39 Oct. 12-13 UIL 00 Oct. 13 WF SW Ui 8.9 7.8 4.5 ZT 12 Oct. 12 6.4 0.0 10.0 40 Oct. 14 UIL 12 Oct. 14 T NW TC 2.5 5.4 0.0 41 Oct. 18-19 UIL 00 Oct. 19 OGF s Um 5.1 0.0 11.6 42 Oct. 21-22 UIL 00 Oct. 22 OGF s Ui 8.9 0.0 20.3 UIL 12 Oct. 22 12.7 1.6 17.9 ZT 00 Oct. 22 0.0 0.0 16.9 43 Oct. 24-25 UIL 12 Oct. 25 WF SW Ui 14.5 6.8 14.5 ZT 00 Oct. 25 13.4 5.3 14.6 UIL 00 Oct. 26 10.3 10.3 3.8 44 Nov. 2-3 ZT 00 Nov. 3 WF SW Um 4.8 0.0 13.2 UIL 12 Nov. 3 11.8 7.7 9.2 UIL 00 Nov. 4 11.8 3.4 12.6 238 Table A-2 Storm data Storm vsw VW VS WD WD WS WD WS SH SH No. (85) (85) (85) (S-85) (85) (85) (70) (70) (100-85) (85-70) (m/s) (m/s) (m/s) (deg) (deg) (m/s) (deg) (m/s) (m/s/km) (m/s/kin 2 13.6 6.3 13.6 190 205 15 235 17 7.8 5.7 14.5 8.6 12.3 190 215 15 215 19 9.6 5.7 3 9.8 11.9 1.0 255 265 12 300 23 8.2 14.8 12.3 14.9 1.3 245 265 15 265 23 10.3 5.0 4 17.6 8.9 16.8 205 208 19 210 22 8.8 1.4 5 12.9 8.7 9.7 225 222 13 224 12 5.9 0.3 6 4.9 3.2 3.8 220 220 5 230 6 0.0 0.0 7 17.3 19.7 3.5 260 260 20 264 28 12.5 5.0 8 7.4 8.9 0.8 275 265 9 265 16 6.7 5.1 9 9.2 12.0 0.0 270 270 12 285 24 9.0 7.7 10 6.4 9.9 0.0 260 280 10 275 16 8.2 3.2 11 14.1 4.7 16.3 188 196 17 209 17 8.2 2.6 12 8.5 1.0 11.9 170 185 12 195 20 6.9 11.8 8.0 6.9 0.0 300 278 7 165 9 4.5 9.1 13 13.5 0.0 26.6 160 170 27 208 27 15.1 11.7 14 10.4 11.8 2.1 240 260 12 255 12 9.1 5.9 15 0.0 0.0 0.0 130 90 1 110 5 3.8 6.5 16 5.7 0.0 9.9 170 175 10 185 10 3.0 1.3 14.3 8.0 12.7 213 212 15 214 19 6.8 2.6 17 11.8 10.4 6.0 225 240 12 245 16 6.8 3.9 18 17.4 0.0 27.0 170 180 27 195 17 15.1 7.8 20.8 8.2 22.6 175 200 24 200 16 16.5 5.2 19 29.6 19.3 23.0 210 220 30 225 22 16.3 3.8 21 11.5 15.0 0.0 270 270 15 265 25 10.5 4.5 22 8.6 14.5 0.0 295 285 15 285 17 5.3 1.3 23 1.4 6.1 0.0 300 310 8 210 5 3.8 1.3 24 4.0 0.0 7.9 170 170 8 170 20 15.0 12.8 25 8.7 3.4 9.4 200 200 10 210 10 3.8 0.6 26 4.5 0.0 8.9 175 170 9 190 16 3.0 5.1 27 9.0 0.0 17.7 165 170 18 210 22 9.0 7.8 19.9 4.5 25.6 180 190 26 195 28 15.7 1.9 28 13.0 10.0 8.4 230 230 13 240 14 6.0 2.0 29 5.7 0.7 7.9 185 185 8 185 8 1.5 0.6 30 8.2 3.8 8.2 205 205 9 195 27 3.7 11.5 31 0.0 0.0 0.0 90 90 4 130 3 1.5 1.9 5.0 9.4 0.0 295 290 10 290 10 5.6 1.3 32 6.4 0.0 10.0 180 180 10 205 20 5.9 7.0 6.0 4.6 3.9 260 260 4 180 10 6.0 8.3 33 10.0 7.7 6.4 230 230 10 230 14 8.8 1.9 34 12.1 4.8 13,2 185 200 14 215 26 8.9 3.8 .Continued 239 Table A-2 Jtorm VSW VW VS WD WD WS WD WS SH SH No. (85) (85) (85) (S-85) (85) (85) (70) (70) (100-85) (85-7C (m/s) (m/s) (m/s) (deg) (deg) (m/s) (deg) (m/s) (m/s/km) (m/s/1 35 0.0 0.0 0.0 90 90 1 90 1 - -36 3.8 3.8 1.4 240 250 4 270 6 1.5 2.6 37 11.6 6.9 9.8 210 215 12 235 10 9.8 3.9 7.9 6.1 5.1 210 220 8 225 8 3.7 0.6 1.9 2.9 0.0 270 280 3 255 5 1.9 1.6 38 19.0 14.6 12.2 210 230 19 245 24 11.0 5.0 15.6 6.2 16.9 190 200 18 210 21 12.6 2.9 39 13.2 13.2 4.8 240 250 14 260 22 8.9 5.7 15.6 6.2 16.9 180 200 18 245 29 13.8 13.4 40 3.1 7.8 0.0 295 300 9 285 8 8.3 2.0 41 6.5 0.0 12.9 165 170 13 205 20 8.3 7.8 42 12.6 0.0 21.9 165 175 22 205 26 9.8 8.4 23.8 7.5 28.0 185 195 29 205 24 17.3 4.5 11.4 0.0 24.5 140 165 27 190 40 17.4 12.3 43 15.5 9.2 13.1 205 215 16 265 22 9.0 10.9 20.0 14.4 13.9 200 226 20 260 26 11.6 9.0 11.3 11.3 4.1 250 250 12. 265 22 5.9 7.0 44 12.6 0.0 5.0 160 175 22 240 26 14.5 16.9 18.0 13.8 11.6 220 230 18 260 31 9.4 10.9 21.6 21.6 7.9 255 250 23 235 32 15.0 7.0 240 Table A-3 Storm data Storm SH MR DMR PW PW PW No. (100-70) (85) (85-70) (100-85) (85-70) (100-70) FL S(BOY) S (POT) (m/s/km) (g/kg) (mb) 2 5.1 7.60 0.87 11.81 10.44 22.25 650 91 10.2 7.0 6.94 1.53 11.84 6.41 18.24 700 93 3.6 3 8.9 5.99 1.29 10.87 10.24 21.11 630 89 11.0 7.9 8.20 2.20 13.49 10.52 24.01 630 93 4.8 4 6.1 8.20 2.90 13.06 9.32 22.38 710 94 4.3 5 2.7 5.78 2.20 11.23 6.05 17.28 785 95 -1.1 6 0.0 4.93 1.86 9.42 5.94 15.36 830 95 0.0 7 8.4 8.09 2.71 13.64 10.16 23.80 700 95 3.3 3 5.5 6.25 1.92 10.46 8.41 18.87 700 95 1.8 9 8.3 5.95 0.92 11.63 8.03 19.66 720 92 6.3 10 5.5 4.55 1.02 9.40 3.84 13.24 850 92 2.9 11 4.1 6.12 2.19 11.05 7.59 18.64 780 95 0.7 12 5.9 6.43 2.19 10.31 7.54 17.85 760 94 3.0 4.2 4.42 1.25 8.15 5.84 13.99 850 93 1.3 13 8.7 4.52 0.44 7.95 6.55 14.50 850 91 6.3 14 7.4 4.42 1.77 8.33 5.08 13.41 860 95 -0.8 15 1.8 4.52 1.63 8.33 5.51 13.84 850 94 1.1 16 1.7 5.42 2.35 9.25 5.41 14.66 815 95 0.4 4.5 5.04 1.72 9.58 3.23 12.81 825 94 0.5 17 5.2 4.69 1.96 7.44 4.83 12.27 840 95 -0.3 18 4.5 5.08 0.91 8.84 6.76 15.60 815 91 6.5 4.9 5.66 1.94 9.47 7.11 16.58 790 94 3.0 19 5.5 6.85 2.61 11.71 8.33 20.04 750 95 1.4 21 4.5 3.93 1.63 9.37 6.38 14.75 885 96 -0.7 22 2.8 4.23 1.30 8.94 4.95 13.89 870 94 2.2 23 1.8 4.52 0.94 8.79 4.55 13.34 850 94 2.1 24 13.8 6.38 2.82 10.92 7.06 17.98 790 95 -0.3 25 1.7 4.52 1.63 9.07 5.38 14.45 850 95 0.6 26 3.8 6.85 2.35 12.19 7.72 19.91 760 94 1.5 27 7.0 4.52 0.53 6.38 5.16 11.54 850 91 7.5 8.0 5.61 1.50 9.55 6.48 16.03 785 93 3.6 28 3.5 4.66 2.16 8.26 5.03 13.29 845 96 -1.6 29 0.7 5.38 1.74 10.26 5.64 16.90 800 94 0.9 30 7.9 6.75 1.26 9.88 4.29 14.17 700 92 1.9 31 0.7 7.44 2.22 12.67 9.12 21.79 710 86 0.1 2.4 6.12 1.82 10.90 4.83 15.73 780 93 1.0 32 5.4 7.66 2.44 12.60 7.77 20.37 710 95 1.3 3.4 6.12 1.35 10.92 7.98 18.90 740 92 3.3 33 3.8 8.09 3.85 13.89 7.80 21.69 730 97 0.0 34 4.1 6.21 2.89 11.40 4.57 15.97 790 96 -2.0 .Continued 241 Table A-3 Storm data Storm SH MR DMR PW PW PW No. (100-70) (85) (85-70) (100-85) (85-70) (100-70) FL S(BOY) S(POT) (m/s/km) (g/kg) (mb) 35 _ 5.54 2.01 7.92 4.64 12.56 800 95 0.8 36 2.1 5.23 1.86 9.35 5.38 14.73 800 95 0.2 37 3.5 4.72 1.83 8.86 5.84 14.70 820 95 0.0 1.9 5.65 2.22 5.05 5.05 10.10 810 95 -0.3 1.4 3.99 1.64 7.44 4.65 12.09 880 95 0.5 38 7.5 6.85 2.35 13.44 10.13 23.57 655 93 4.0 7.2 8.54 2.45 12.73 8.20 20.93 760 94 3.9 39 7.1 7.55 1.64 11.84 6.54 18.37 680 93 5.7 11.9 6.12 0.82 11.40 8.15 19.55 720 91 6.8 43 3.5 4.23 1.73 8.89 5.10 13.99 865 95 -0.3 41 8.1 4.49 1.65 7.98 5.33 13.31 850 94 1.5 42 7.7 4.52 0.47 8.13 6.50 14.63 850 93 6.2 6.6 5.01 1.59 6.68 6.02 12.70 820 94 5.7 14.6 5.46 1.93 9.04 6.25 15.29 800 91 3.7 43 7.6 5.70 0.85 8.86 6.17 15.05 740 93 7.6 9.5 5.42 1.80 9.27 7.59 16.86 730 92 6.2 6.5 6.29 0.80 10.51 7.04 17.55 700 92 4.3 44 10.9 4.11 0.41 7.34 5.92 13.26 910 90 8.7 9.5 4.52 0.53 9.42 7.62 17.04 770 91 8.3 10.3 6.21 0.72 10.34 7.29 17.63 700 91 7.5 242 Table A-4 Storm data Storm Cloud E c DR DR DR/R DR/R DI No,. S(CONV) Air Mass Base (RF) (NS) (RF) (NS) (RF) 2 6.6 mTw/mPs 2.0 3 11.8 mTw/ mPs 5.6 4 0.7 mPs 5 0.0 mPw 6 2.7 mA 7 1.0 mPs 8 5.0 mPs/mPw 9 6.6 mPs/mPw 10 5.8 mPs/mPw 11 1.6 mPw 12 1.0 mPw 3.2 13 10.0 mPs/mA 14 0.6 mA 15 4.0 mPw/mA 16 -0.2 mA 1.1 17 1.5 mA 18 9.0 mPw 0.7 19 1.0 mPw 21 0.5 mA 22 4.0 mPw/mA 23 3.0 mA 24 0.0 mPs /mPw 25 2.3 mA 26 4.2 mPs/mPw 27 13.0 mPs/mPw 5.8 mPw/mA 28 0.2 mA 29 3.7 mPw/mA 30 3.5 mTw/mPs 31 1.7 mPs 3.2 32 5.1 mTw/mPs 6.5 33 -0.4 mPs 34 -1.7 mPs :mb) (m) (g/m3) (mm) 995 150 0.15 31.5 990 150 980 300 0.32 68.1 970 370 925 750 0.25 25.4 920 800 0.58 5.8 900 960 0.25 12.4 980 305 0.20 38.4 875 1160 0.54 15.0 960 250 0.08 0.3 980 300 0.15 9.9 935 600 0.40 29.2 850 1360 0.27 15.7 900 900 940 500 0.23 9.1 935 540 0.43 30.0 950 490 0.15 21.1 915 850 0.38 8.1 910 850 890 1070 0.67 18.0 920 790 0.35 18.8 930 670 900 915 0.43 48.8 920 670 0.43 3.0 885 1160 0.28 3.0 895 1070 1.27 16.8 890 1070 0.33 17.3 930 760 0.50 12.2 910 910 0.15 13.0 890 1070 0.89 8.4 920 760 850 1400 0.58 18.5 870 1310 0.40 35.1 925 760 0.95 9.1 910 760 0.40 14.0 850 1370 875 1220 0.32 27.7 935 670 940 650 0.30 6.4 900 910 0.53 11.2 (mm) (%) (%) (mm; 34.5 57 64 3.0 62.2 85 87 5.1 38.4 46 63 1.5 34.8 55 96 -4.3 60 59 -46.5 74 82 4.1 8.1 79 78 0.8 1.0 1 8 0.0 3.6 68 67 0.8 37.1 85 95 2.8 62.0 41 78 0.5 32.3 31 65 1.3 47.0 85 95 3.0 23.4 66 71 2.3 31.2 31 73 1.3 22.9 79 79 1.3 30.5 37 65 0.8 73.2 94 90 6.1 8.6 17 64 -5.1 20 28 0.8 - 96 - -14.5 51 52 2.5 6.4 69 68 -5.1 81 71 -51.1 18 67 0.8 42.2 92 99 1.8 20.8 92 92 -33.3 43 82 -11.7 52 42 1.3 16.3 69 54 2.8 5.3 41 38 — 15.0 75 87 -.Continued 243 Table A-4 Storm data Storm Cloud E DR DR DR/R DR/R DI No. S(CONV) A i r Mass Base (RF) (NS) (RF) (NS) (RF) (mb) (m) (g/m3) (mm) 35 1.3 mA 850 1440 1.26 19.3 36 1.4 mA 905 910 1.00 17.8 37 1.7 mA 975 305 0.28 40.4 i 0.4 975 305 1.8 975 305 38 4.5 mTw/mPs 915 920 0.54 83.8 3.2 915 920 39 4.6 mTw/mPs 940 730 0.50 45.7 6.4 940 730 40 0.1 mA 950 610 0.26 19.1 41 6.9 mPs/mA 910 850 0.43 8.9 42 8.0 mPw/mA 845 1370 0.30 34.8 9.3 860 1370 2.5 920 760 43 5.7 mPs/mPw 920 760 0.40 88.6 7.2 920 760 7.2 970 305 44 10.1 mPs/mPw 975 300 0.21 15.7 8.0 980 300 5.8 895 1070 54.4 20.1 100 78 56 82 99 32 67 97.5 71 67.8 17 (%) 54 83 91 57 72 75 56 (mm) 2.8 4.3 5.6 0.8 1.8 3.0 0.0 244 Table A-5 Storm data Storm DI DI/I DI/I Max. storm rain Excess No. (NS) (RF) (NS) (RF) (NS) Duration (mm) (%) (%) (mm) (mm) (hr) 2 2.0 50 40 55.4 54.4 2.0 3 5.8 80 88 80.5 71.5 7.5 4 2.0 40 44 55.2 61.0 0.0 5 - - - 10.7 36.3 1.2 6 - - - 20.8 7.4 0.0 7 4.8 84 73 51.9 57.0 3.6 8 1.0 40 67 19.1 10.4 1.0 9 0.0 0 0 17.0 13.0 0.0 10 0.0 60 0 14.5 5.3 5.4 11 5.1 73 94 34.3 38.9 7.8 12 3.3 14 59 38.4 79.9 1.8 13 2.0 33 50 29.5 49.3 0.0 14 4.3 86 89 35.3 49.6 1.2 15 2.3 75 82 32.0 33.0 1.0 16 4.1 31 59 25.9 42.6 0.0 17 1.3 71 50 22.9 29.0 5.2 18 1.8 30 58 50.4 47.0 6.0 19 3.8 92 65 52.2 81.0 8.3 21 - - - 17.8 13.5 1.3 22 0.0 33 0 15.5 18.3 0.0 23 - - - 17.5 - 22.0 24 1.3 53 36 34.1 27.9 1.5 25 - - - 17.8 9.4 7.1 26 - - - 16.0 7.1 0.0 27 3.0 23 48 46.3 76.2 0.8 28 3.3 100 100 20.1 42.6 15.7 29 - - - 38.1 22.6 1.6 33 - - - 21.4 40.6 0.0 31 2.0 63 53 28.7 27.9 5.3 32 1.8 80 47 39.8 30.2 5.8 33 _ _ _ 15.5 14.0 0 34 - - - 15.0 17.3 0 .Continued 245 Table A-5 Storm data Storm DI DI/I DI/I Max. storm rain Excess No. (NS) (RF) (NS) (RF) (NS) Duration (mm) (%) (%) (mm) (mm) (hr) 35 — — — 19.3 — 4.6 36 - - - 24.2 - 1.7 37 3."3 20 44 72.0 100.0 6.3 38 4.1 84 96 111.8 129.0 7.7 39 6.4 85 93 55.8 60.8 0.6 40 _ _ _ 19.3 _ 4.1 41 2.0 23 47 27.2 35.3 3.3 42 3.3 64 50 52.4 74.0 2.0 43 4.8 69 95 125.5 130.0 3.2 44 0.0 0 0 90.7 121.7 4.5 APPENDIX VII DERIVATION OF CONDENSATION EQUATIONS 1. Horizontal moisture transport Figure VII-1 Consider mass transport of moisture through the volume bounded by two streamlines and two v e r t i c a l planes as shown i n Figure VII-1. The storage equation for water vapour i s : M = (Mv. - Mv ) (1) r 1 o where -M i s the rate of conversion of water vapour to p r e c i p i t a t i o n i n g/s, Mv^ the rate of inflow of water vapour, and MV q the rate of outflow of water vapour. This equation can be expanded to: CTT Y A x p = [ V i p v . ( A x A Z . ) - V p v ( A x A Z ) ] H w x l o o o (2) 246 247 where C i s the condensation rate i n cm/sec, p the density of water H w 3 i n g/cm , V i and Vo the mean inflow and outflow v e l o c i t i e s i n cm/sec, . 3 and pv. and pv the inflow and outflow density of water vapour i n g/cm . x o v P. (3) Using the expression for mixing r a t i o r: r = 3d and the hydrostatic equation AZ = - ^ - (4) P d g 3 where p, i s the density of a i r i n g/cm and g the a c c e l e r a t i o n of d 2 gravity i n cm/sec , equation (2) becomes: CH Y pw = [ V i < r i p d ) ( ^ i } - V ° ( r ° P d ) ( ^ o ) ] (5) P d g P d g By considering the co n t i n u i t y equation V.Ap. = V Ap (6) x x o o equation (5) can be reduced to: C = ViApi ( r i - r o ) cm/sec (7) pwg Y  or C„ = .0367 ViAp. ( r i - r o ) mm/sec (8) rl X 2. V e r t i c a l moisture transport Let AZ be the thickness of a column of a i r of un i t cross 3 section, p the density of water i n gm/cm , p and p, 0, the density of w d i dz 3 3 dry a i r i n gm/cm , p and p ^ the density of water vapour i n gm/cm and co^  and M the v e r t i c a l v e l o c i t i e s i n cm/sec at the bottom and top of the laye r . Assuming conservation of mass, the rate of condensation (C ) i s 248 given by: C p = [pv to - pv io.] (9) V W J .1 z z Using the equation for the mixing r a t i o : r = p . P d equation (9) becomes: Cv Pw = [ p d l r l " Pd2 r2 W 2 ] ^ ( 1 0 ) If to and p, are mean values for the layer, equation 10 can be expressed d as: C = .036 wp.Cr. - r_) mm/hr (11) v a 1 2 3 where w i s i n cm/sec, p, i n kg/m and r.. , r„ i n g/kg. d 1 , z APPENDIX V I I I MYERS WIND FLOW MODEL The f o l l o w i n g model f o r wind f l o w over a mountain b a r r i e r was developed by Myers (1959, 1962) and f i r s t a p p l i e d by the U.S. Weather Bureau (1961). The four b a s i c laws which govern f l o w that i s two-dimensional, laminar, a d i a b a t i c and, except near the ground, f r i c t i o n -l e s s are: 1. C o n t i n u i t y of mass where i n t e g r a t i o n i s v e r t i c a l l y between any two streamlines, S and / Vdp = constant (1) 2. B e r n o u l l i ' s equation f o r motion along a streamline (2) 3. Hy d r o s t a t i c equation dp = -p dgdZ (3) 4. A d i a b a t i c laws (a) Unsaturated a i r .286 (4) 249 250 (b) Saturated a i r m .286 T , v T p L (q -q„) ^ = (/) + " / 2 (5) T l P l C p These adiabatic laws may be solved g r a p h i c a l l y on a tephigram of other thermodynamic chart. In addition to the basic laws, Myers derived the energy equation (V. 2 - V 2 ) - 1 (V 2 - V 2) = 2RA (6) k„ 4 3 z— 2 1 3 k x where A i s defined by: A = - / Td (lnp) (7) and i s approximated by: A = | [ ( T 1 + T 3) l n (P 1/P 3) + (T 3 + T 4) l n (p 3/p 4) - ( T 1 + T 2) In (P 1/P 2) " (T 2 + T 4) In ( p 2 / p 4 ) ] (8) and and k^ are c o e f f i c i e n t s of f r i c t i o n . The p h y s i c a l s i g n i f i c a n c e of A i s " i l l u s t r a t e d i n Figure VIII-2 where i t i s shown to be the area enclosed by the four curves on a thermo-dynamic chart, which represents an energy change. By equal area transformation, the Area A' derived from the Canadian tephigram i s equal to R times the area on a T-lnP thermodynamic chart, of A' = RA. Myers also derived the following equation by integrating the B e r n o u l l i (2) and hydrostatic (3) equations, taking f r i c t i o n into account and assuming T ^ = ^12h • V l 2 l n ( P 2 / P 2 h } + I ( V 2 2 " V l 2 ) / k l - ° ( 9 ) where p 2 ^ i s the hydrostatic b a r r i e r pressure and i s the mean 251 temperature derived using the temperature corresponding to p^^. The equation of continuity can be integrated to give: (v 1 + v 3) ( ? 1 - P 3 ) = (v 2 + v 4) (p 2 - p 4) (10) The streamlines of a i r flow over a mountain slope are shown i n Figures VIII-1 and 1. If the wind, temperature and humidity p r o f i l e s for the inflow v e r t i c a l are known and the wind speed and pressure on one streamline at the outflow v e r t i c a l are assumed, then the wind speeds and positi o n s of a l l other streamlines on the outflow v e r t i c a l are completely s p e c i f i e d by the governing laws. The outflow v e r t i c a l wind flow above a ridge crest i s obtained by the following steps: 1. A tentative surface wind speed, V^, i s assigned at the ridge c r e s t . 2. The ridge crest surface pressure, p^j i s computed from equation (9) and the adiabatic laws or thermodynamic chart. The corresponding temperature T^ i s then obtained from the adiabatic laws or thermo-dynamic chart. 3. The outflow pressure, temperature and wind speed, p^, T^ and V^, on the second streamline are determined from the inflow v a r i a b l e s and surface (ground streamline) v a r i a b l e s by simultaneous so l u t i o n of the energy equation (6), the continuity equation (10) and the appropriate adiabatic law. The v a r i a b l e A i n equation (6) i s obtained from equation (8) or a thermodynamic chart by estimating p.. A sol u t i o n for p, i s obtained and checked with the estimated 4 4 value. Successive approximations w i l l y i e l d simultaneous solutions of equations (6) and (10). 4. The outflow v a r i a b l e s on the next streamline proceeding upward are determined by r e p e t i t i o n of step 3, using the values from the streamline j u s t computed. 5. This procedure i s continued layer by layer upward to the f i r s t nodal surface where p^ = P^-6. The computation i s repeated for a succession of d i f f e r e n t tentative ground outflow speeds V^. 7. The computed outflow wind speed p r o f i l e i s selected which has the 2 2 smallest value of (V^ - ) at the f i r s t nodal surface. This p r o f i l e contains the minimum increase i n k i n e t i c energy over the inflow k i n e t i c energy which, according to Myers, i s the outflow nature would tend to s e l e c t . Figure VI'II-1. Streamlines Figure VIII-2. Temperatures on thermodynamic chart. APPENDIX IX DETERMINATION OF RAIN DROP FALL VELOCITY From observed or assumed r a i n f a l l i n t e n s i t y , the median drop diameter i s f i r s t determined from the graph of Figure IX-1. This drop diameter value i s then entered on the graph of Figure IX-2 to obtain the corresponding terminal f a l l v e l o c i t y . Figure IX-1 was drawn using the r e l a t i o n s h i p reported by Laws and Parsons (1949) (which has been converted from English to metric u n i t s ) . Figure IX-2 was drawn from tabulated data given by Gunn and Kinzer (1949) and also presented by L i s t (1966). 253 TERMINAL FALL VELOCITY (M/S) Figure IX-2. Terminal f a l l v e l o c i t y f o r water drops i n stagnant a i r versus drop diameter (Gunn and K i n z e r , 1949; L i s t 1966). APPENDIX X OBSERVED PRECIPITATION FOR MODEL STORM PERIODS Research Forest Storm SM MR AD S3 SI No. Storm t e s t period mm/hr 3 1400-2000 PDT Sept . 5, 1970 1. 19 2. 29 3 .43 5 .59 6. 35 7 0300-0900 PDT Sept . 22, 1970 1. 22 3. 68 3 .73 4 .65 4. 65 14 1100-1700 PDT Oct. 23, 1970 0. 46 1. 78 2 .16 2 .62 3. 12 19 1500-1900 PST Nov. 15, 1970 0. 71 3. 82 5 .54 5 .21 5. 21 37 1800-2400 PDT Sept . 27, 1971 0. 94 1. 14 1 .83 2 .41 3. 53 38 1500-2100 PDT Oct. 3, 1971 0. 64 2. 11 2 .87 4 .24 4. 83 39 1800-2400 PDT Oct. 12, 1971 1. 09 3. 00 3 .76 4 .95 5. 59 43a 0600-1200 PDT Oct. 25, 1971 1. 27 2. 92 4 .70 3 .76 3. 96 43b 1200-1800 PDT Oct. 25, 1971 2. 79 3. 98 6 .43 8 .76 9. 22 Northshore Storm VAP UBC PMO WV NV CD LC SD No. Storm t e s t period mm/hr 3 1400-2000 PDT Sept . 5, 1970 0.71 1. 09 2.62 4 .39 4.75 5.72 6.60 3.76 7 0300-0800 PDT Sept . 22, 1970 1.57 1. 47 2.03 3 .81 3.96 5.13 5.59 5.18 14 0900-1500 PDT Oct. 23, 1970 0.51 1. 14 2.03 2 .08 1.98 2.11 2.72 4.70 19 1500-1900 PST Nov. 15, 1970 1.91 2. 41 3.37 3 .43 3.68 3.51 4.32 5.84 37 1700-2300 PDT Sept . 27, 1971 2.29 1. 32 2.03 1 .57 2.67 2.97 3.86 5.79 38 1500-2100 PDT Oct. 3, 1971 0.13 0. 20 0.89 1 .32 2.49 5.08 6.35 4.06 39 1800-2400 PDT Oct. 12, 1971 0.46 0. 64 1.27 2 .03 2.49 4.14 6.22 6.86 43a 0600-1200 PDT Oct. 25, 1971 0.64 1. 45 2.84 3 .61 3.63 4.70 5.46 5.13 43b 1200-1800 PDT Oct. 25, 1971 2.62 4. 19 7.19 6 .27 7.11 8.18 7.92 5.33 APPENDIX XI RATE OF CHANGE IN MIXING RATIO (r) WITH ALTITUDE ALONG SELECTED MOIST ADIABATS ON TEPHIGRAM Temperature of moist adiabat at 1000 mb (°C) r 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 (g/kg) (rate of decrease i n r - g/kg/mb) 18 16 .022 14 .021 .023 12 .020 .020 .022 .024 10 .017 .019 .020 .022 .024 9 o .016 .017 .019 .020 .022 .024 O -7 .016 .017 .018 .019 .021 .023 .026 7 .014 .016 .017 .018 .019 .021 .024 .026 6 .014 .014 .016 .017 .018 .019 .021 .024 .026 5 .012 .012 .013 .014 .015 .016 .017 .019 .020 .022 .025 4 .011 .011 .012 .013 .014 .015 .017 .018 .020 3 .010 .011 .011 .013 .013 .014 .015 .016 2.5 .010 .010 .011 .013 .013 .013 .014 2.0 .009 .009 .010 .011 .011 .013 .014 1.5 .007 .008 .008 .009 .009 .010 1.0 .006 .006 .007 .007 .008 0.8 257 APPENDIX XII MODEL STORM METEOROLOGICAL CHARACTERISTICS 258 Figure XII-1. Data for storm 3, September 5-6, 1970. MASS CURVES OF RAINFALL RAINFALL INTENSITY Figure XII-2. Data for storm 7, September 21-22, 1970. 261 TEMPERATURE - DEWPOINT PROFILES OOOOZ - OCTOBER 9, 1970 ( Z T ) MASS CURVES OF RAINFALL RAINFALL INTENSITY Figure XII-3. Data for storm 9, October 8-9, 1970. SURFACE WEATHER MAP 0000 Z - OCTOBER 24,1970 TEMPERATURE-DEWPOI NT PROFILES OOOOZ - OCTOBER 24,1970 (UIL) Figure XII-4. Data for storm 14, October 23, 1970. Figure XII-5. Data for storm 19, November 15-16, 1970. 2 SEPT 27 03 06 09 12 15 18 21 SEPTEMBER 28 RAIN INTENSITY 03 06 SEPT. 29 Figure XII-6. Data for storm 37, September 27-29, 1971, 19 22 OCT. 2 Ol 0 4 07 10 13 16 19 22 O C T O B E R 3 01 0 4 07 OCT. 4 '////////////////////// T E M P E R A T U R E - D E W P O I N T P R O F I L E S OOOOZ - OCTOBER 4 , 1971 (UIL) M A S S C U R V E S O F RAINFALL E •E >-H CO L L l < or |0I 0 4 07 10 13 16 19 22 OCTOBER 3 01 0 4 0 7 OCT. 4 RAIN INTENSITY Figure XII-7. Data for storm 38, October 2-4, 1971. 266 SURFACE WEATHER MAP OOOOZ- OCTOBER 13, 1971 10 ^ 5 so' Ao / / / / / / / / / / / / / / / //,,///, TEMPERATURE-DEWPOI NT PROFILES OOOOZ - OCTOBER 13, 1971 (UIL) or 50 40 30 3 20 o 10 o < - SI --/ AD ~ J / ' / / -/ - J? SM i i • 16 18 20 22 OCTOBER 12 02 13 MASS CURVES OF RAINFALL 16 18 20 22 OCTOBER 12 RAINFALL INTENSITY 13 Figure XII-8. Data for storm 39, October 12-13, 1971. MASS CURVES OF RAINFALL RAINFALL INTENSITY Figure XII-9. Data for storm 43, October 24-25, 1971. 268 TEMPERATURE — DEWPOINT PROFILES OOOOZ - OCTOBER 26,1971 (UIL) Figure XII-10. Data for storm 43b, October 25, 1971. APPENDIX X I I I SURFACE WIND DATA AT VANCOUVER INTERNATIONAL AIRPORT AND SAND HEADS LIGHT STATION FOR SELECTED STORM PERIODS Vancouver A i r p o r t Sand Heads L i g h t Stn. Storm No. Storm t e s t period D i r e c t i o n Speed (m/s) D i r e c t i o n Speed (m/s) 2 2200-0400 PDT Sept. 2-3, 1970 E 4 ESE 9 3 1400-2000 PDT Sept. 5, 1970 SE 6 SE 12 7 0300-0900 PDT Sept. 22, 1970 E 2 S 11 9 2100-0500 PDT Oct. 8-9, 1970 ENE 4 E 7 11 0500-1100 PDT Oct. 18, 1970 SE 6 SE 10 14 0900-1700 PDT Oct. 23, 1970 SE 5 SSE 10 18 0200-0800 PST Nov. 11, 1970 E 5 E 9 19 1500-1900 PST Nov. 15, 1970 E 7 SE 14 24 2000-0100 PDT June 6-7, 1971 S 1 S 3 27 1200-1800 PDT June 24, 1971 E 8 E 10 37 1700-2400 PDT Sept. 27, 1971 SSE 3 S 6 38 1500-2100 PDT Oct. 3, 1971 ESE 4 SE 7 39 1800-2400 PDT Oct. 12, 1971 ESE 5 SSE 12 42 0300-0900 PDT Oct. 22, 1971 E 7 E 10 43a 0600-1200 PDT Oct. 25, 1971 SSE 9 SE 15 43b 1200-1800 PDT Oct. 25, 1971 SSE 10 SE 15 44 0300-1500 PST Nov. 3, 1971 ENE 5 ENE 7 1500-2000 PST Nov. 3, 1971 ESE 4 ESE 7 APPENDIX XIV Stable Storm 39 271 APPENDIX XV COMPUTER PROGRAM FOR EIGENVECTOR ANALYSIS This program derives eigenvectors and eigenvalues f o r an array of data and produces as output the input data, matrices of eigenvectors and m u l t i p l i e r s , eigenvalues, sum of eigenvalues, cumulative explained variance and reconstituted data matrix. In addition, the program can also produce ar e a l or histogram pl o t s of input data or reconstituted data corresponding to any given eigenvector or combination of eigenvectors. A l i s t i n g of the program with sample output i s given i n the following pages. The program was developed for a PDP-11 computer but i s i n FORTRAN language and should be useable on most larger computers with l i t t l e modification. The input to the program i s of the following form: Card 1: Columns 1-80: Program t i t l e to be printed atop each page. Card 2: Columns 4-5 : Number of events (storms) (II) -(maximum of 40) 9-10: Number of stations (12) -(maximum of 12) 15: Type of plo t required - 0 = a e r i a l p l o t , 1 = histogram. Cards 3 to X: (X = II + 2) Columns 1-60: Data - each of the II event (storm) cards contains 12 s t a t i o n data values ( p r e c i p i t a t i o n ) . Format is(12F5.2). 272 273 Cards XI: Columns 3-5: Index of eigenvector required 99 = program s e l e c t s most s i g n i f i c a n t eigenvectors 100 = program uses a l l eigenvectors to reproduce input data matrix Y = performs analysis for eigenvector Y where 1<Y<I1 (This card may be repeated f o r any number of i n d i v i d u a l eigenvectors). The program has been set up f o r a s p e c i f i c a p p l i c a t i o n but can be adjusted f o r any other a p p l i c a t i o n by modifying the appropriate FORMAT statements. In p a r t i c u l a r , the procedures for de r i v i n g the FORMAT statements for the histogram and a r e a l plots are described below. The loc a t i o n s of data points on the histogram are established using FORMAT statement 660. The r e l a t i v e locations of the stations are determined to the nearest tenth of an inch to f i t within the width of a computer sheet, beginning at,zero. (In the hori z o n t a l d i r e c t i o n , the computer typewriter moves i n increments of 0.1 inch). For example, by using a s c a l i n g factor 1 km = 0.16 inch, 0, 12.3, 21.1, 25.4, ... km become 0.0, 2.0, 3.4, 4.1, ...inches. These distances i n inches are mu l t i p l i e d by 10 and 12 added to each to obtain the required number of hor i z o n t a l tab movements, e.g. 12, 32, 46, 53... These tab numbers are inserted into FORMAT statement 660, e.g. 660 FORMAT ('b', F4.1, T12, A l , T32, A l , T46, A l , T53_, A l , . . . ) . The v e r t i c a l scale on the histogram i s set using statement 12 (l i n e 142) and statements in v o l v i n g ROW ( l i n e s 167 and 169). For the attached example, a maximum p o s i t i v e value of 87.0, increments of 3.0, and negative values to -48.0 are obtained as follows: f i r s t set ROW =90.0 ( l i n e 167) and ROW = ROW-3.0 ( l i n e 169); i n statement 12 (l i n e 142) the f i r s t number 30.5 r e f e r s to the number of p o s i t i v e 274 increments (30) w i t h 0.5 added to account f o r rounding o f f , w h i l e the second number i n the denominator (3) i s determined using the maximum sc a l e value (87) f o r CQ(I,J) to o b t a i n a value f o r ICQ(I,J) = 1. The p o s i t i o n s of s t a t i o n s and data p o i n t s on the a r e a l p l o t are es t a b l i s h e d using FORMAT statement 662. The r e l a t i v e l o c a t i o n s of s t a t i o n s are f i r s t e s t a b l i s h e d so as to f i t onto a computer sheet. The computer t y p e w r i t e r moves i n increments of 0.1 inch i n the h o r i z o n t a l d i r e c t i o n , as i n d i c a t e d above, w h i l e the s h i f t i n the v e r t i c a l d i r e c t i o n i s c l o s e to 0.17 i n c h . Using these va l u e s , the appropriate number of h o r i z o n t a l tab movements and v e r t i c a l l i n e s h i f t s f o r each s t a t i o n l o c a t i o n are determined and i n s e r t e d i n t o FORMAT statement 662. The data (e.g. p r e c i p i t a t i o n values) are centred on the l i n e below the s t a t i o n marker. £ V l VECTOR OF CUMULATIVE EXPLAINED VARIATION, C F VECTOR E RESTRUCTURED TO SYMMETRIC MATRIX, SUBROUTINE EIG C LATER DESTROYS F AND STORES EIGENVALUES IN ITS DIAGONA C JK VECTOR OF INDICES OF DIAGONAL ELEMENTS OF 0 , C SS DIAGONAL ELEMENTS OF EIGENVALUE MATRIX. C RQ TRANSPOSE OF R ,  C CC MATRIX OF MULTIPLIERS, C CQ RECONSTITUTED DATA MATRIX, C R EIGENVECTORS IN VECTOR FORM,  C ~B INPUT DATA MATRIX, C D PRODUCT OF B AND ITS TRANSPOSE, C E D I N VECTOR FORM,  C TITLE HEADING TO BE PRINTED ATOP EACH PAGE, C HISTGM MATRIX FOR STORAGE OF POINTS FOR HISTOGRAM, C ICQ MATRIX OF LOCATIONS OF POINTS FOR HISTOGRAM,  C 1001 LOGICAL* 1 HISTGM(46,12) , IBLANK,IPLUS 1002 DIMENSION VE C40) , F (1600) , JK (40) ,85(40)  1003 DIMENSION RQ(40 ,40 ) ,CC(40 ,12 ) ,CQ(40 ,12 ) ,R (1600 ) 1004 DIMENSION B (40 ,12 ) ,D(40 ,40 ) , ,E(i600) 1005 DIMENSION ICQ(40 ,12 ) ,T ITLE(20 ) 1006 EQUIVALENCE (D,E,RG) 1007 DATA IBLANK/ ' ' / )006 DATA I P L U S / e + g / C C ISW IS A SWITCH WHICH, WHEN SET TO 1 , ENABLES THE PROGRAM TO C OUTPUT INTERMEDIATE RESULTS TO FACILITATE DEBUGGING, WHEN TEST] C PROGRAM, SET ISW TO 1 , OTHERWISE SET TO 0 , C 1009 ISWa0  C ISW=1 C C READ AND WRITE THE HEADING TO BE PRINTED ATOP EACH PAGE.  C 1010 759 R E A D ( 5 , 7 6 0 ) ( T I T L E ( I ) , 1 * 1 , 2 0 ) 1011 760 FORMAT(20A4)  1012 WRITE ( 6 , 7 6 1 ) ( T I T L E ( I ) , 1 = 1,20) 1013 761 F Q R M A T ( * l % 8 ( / ) , « * , 2 0 A 4 / ) C  C READ DIMENSIONS FOR ARRAYSS C l i t NUMBER OF ROWS (STORMS) IN INPUT MATRIX, C 12: NUMBER OF COLUMNS (STATIONS) IN INPUT MATRIX.  C C READ VARIABLE TO INDICATE WHICH PLOT IS TO BE PRODUCED! C IPLOT » 08 AERIAL PRECIPITATION PATTERN.  C IPLOT • 1! HISTOGRAM, C 5010 READ(5,998) I I , 12 , IPLOT  5015 998 FORMAT £315) C C IDIMEN IS A VARIABLE WHICH MUST BE SET TO THE MAXIMUM ALLOWABLE C VALUE OF II , C 3016 IQIMENS40  C C READ AND WRITE THE DATA MATRIX B , C FORTRAN IV 006-01 SOURCE L I S T I N G PAGE 002 2 7 6 0017 WRITE ( 6 , 1 0 2 ) 0016 102 FORMAT ( e 0INPUT DATA?*/' « , H ( , B » ) / ) 0019 00 801 1=1,11 0020 R E A D C S , 9 9 i ) ( B ( I , J ) , J * l , I 2 ) 0021 991 FORMAT(12F5 12?  0022 801 WRITE(6,802)CB ( I,J),J«1,I2) 0023 802 FORMAT (* ' , 1 2 F 1 1 , 3 ) C C "READ INDEX OF1 EIGENVECTOR REQUIRED* C « 99 ? ALLOWS PROGRAM TO SELECT MOST SIGNIFICANT EIGENVECTO C «100 ? ALL EIGENVECTORS USED TO RECONSTITUTE EXACT INPUT DAT C MATRIX C 0024 1 REAPC5,99fe.ENDs99999)NKQ 0021 I F ( N K Q f E Q 7 t r W T i T T S 9 " 0027 996 FORMAT 115) C C FORM D , THE PRODUCT OF MATRIX B AND ITS TRANSPOSE, C 0028 DQ 10 1*1,11  0029 DO 10 J * 1 , I 1 0030 D C I , J ) B 0 , 0031 D O 10 K s j , 1 2  0032 10 D C I , J ) « D C I , J ) * B l _ f K ) * B C J , K ) 0033 IF CISWjEO,0)60 TO 806 0035 00 807 i n , I I  0036 807 WRITEC6,808)CDCI,J)»J=1,I1) 0037 808 FORMAT (' D ",16F8,3) 0038 806 CONTINUE  C C CALL ROUTINE WHICH RESTRUCTURES VECTOR E TO SYMMETRIC MATRIX C ( I N VECTOR FORM),  C 0039 NaIDIMEN 0040 I F ( I S W , E Q . n WRITE lb, 809) C C E ( I • ( J - 1 ) » I D I M E N ) , I s 1 , 1 1 ) , J g 1,11) 0042 809 FORMAT C' E *,16F8.3) 0043 CALL MSTRCE,F,N,0,1) 0044 I 4 ? U » C I l + l ) / 2  0045 IF(ISW»EQa)WRTTrC6,810) CF ( I ) , I * 1,14) 0047 810 FORMAT C' F f f 1 6 F 6 , 3 ) C C CALL ROUTINE WHICH COMPUTES EIGENVALUES AND EIGENVECTORS OF REA C SYMMETRIC MATRIX F ( I N VECTOR FORM) AND STORES THEM IN VECTOR C 0048 N s l l 0049 MV B0 0050 CALL EIG£N(F,RiN,MV)  00S1 I F C I S W . E Q * 1 ) W R I T E ( 6 , 8 1 0 ) C F C I ) , 1 * 1 , 1 4 ) 0053 I F ( I S W . E 0 « l ) W R I T E C 6 , 8 1 l ) ( C R C I + C 4 - l ) * N ) , 1*1, H ) # J H . I i ) 0055 8 U FORMAT ( g R g , 1 6 F 6 , 3 )  C C FORM RQ , THE TRANSPOSE OF R , AND PRINT THE EIGENVECTORS, C ; _ _ _ 0056 I FCNKQ fGE,99)WRITEC8,812) 0058 812 FORMATC e0EIGENVECTORS:'/« ' , 1 3 C ' * ' ) / ) 0059 DO 721 1 8 1 , 1 1  0060 I M = C I - 1 ) * N ORTRAN I V 0 0 6 - 0 1 SOURCE L I S T I N G P A G E 003 277 1061 DO 781 J=1,I1 1062 721 ROCIr J)=RCIM+J) •063 I F C N K Q j L T , 9 9 ) 6 0 TO 767 1065 DO 813 1=1,11 1066 813 WRITE (6,765)1, ( R Q C I iJ),J=1.I1) )067 C C 7 6 2 F O R M A T ( * 0 S I 2 , 2 X , 2 0 F 6 I 3 /' * , 4 X , 2 0 F 6 , 3 ) FORM AND P R I N T M A T R I X OF M U L T I P L I E R S CC BY M U L T I P L Y I N G RQ 9068 C c W R I T E ( 6 , 8 l 5 ) 5069 J 0 7 0 5071 8 1 5 7 6 7 F O R M A T C ' 0 M U L T I P L I E R S ? F , 1 2 ( * = ' ) / ) DO 1 1 1=1 , 1 1 DO 1 1 J = i , I 2 3072 3073 3074 11 C C C I , J ) = 0 , 0 DO 11 Km,11 C C t I , J ) s C C C I , J ) + R Q C I , K ) * B C K , J ) 3075 3077 3078 8 1 6 I F ( N K Q , L T , 9 9 ) GO TO S 7 9 DO 8 1 6 1 * 1 , 1 1 W R I T E ( 6 , 8 0 2 ) C C C ( I , J ) , J ? 1 , I 2 ) c c c FORM VECTOR OF E I G E N V A L U E S WHICH ARE STORED I N DI A G O N A L E N T R I E S F ( I N VECTOR F O R M ) , 3079 9080 c DO 38 1 = 4 , 1 1 S S ( I ) = F ( I * ( I + i ) / 2 ) 3081 3082 c 38 J K t D a l C O N T I N U E c R E A R R A N G E E I G E N V A L U E S I N ORDER OF I N C R E A S I N G M A G N I T U D E , 3 0 8 3 u W R I T E ( 6 , 8 1 8 ) 3 0 6 4 3 0 8 5 6 1 8 F O R M A T ( ' O E I G E N V A L U E S & C O R R E S P O N D I N G E I G E N V E C T O R NUMBERS?*/' «,< ! '= * ) / ) DO 3 9 K = 1 , I 1 3 0 8 6 3087 3 0 8 9 DQ 3 9 H 2 , I 1 I F ( S S ( I ) , G T , S S C I M ) ) GO TO 3 9 S S S = S S ( I ) 8 0 9 0 8 0 9 1 3 0 9 2 J J K = J K ( I ) S S C I ) * 5 S ( I M ) J K C I ) a J K ( I M ) 8 0 9 3 3 0 9 4 3 0 9 5 3 9 S S C I * 1 ) = S S S J K ( I * 1 ) = J J K C O N T I N U E 3 0 9 6 3 0 9 7 c 8 1 9 W R I T E ( 6 , 8 1 9 ) C S S ( I ) , J K ( I ) , 1 = 1 , 1 1 ) F O R M A T ( 1 0 C F 9 . 3 , « ( ' , 1 2 , * ) * ) ) c p SUM THE E I G E N V A L U E S AND STORE THE TOTAL I N Q , 0 0 9 8 Q = 0,0 0 0 9 9 0 1 0 0 0 1 0 1 41 DO 4 1 1=1,11 Q=Q+SS ( I ) C O N T I N U E 0 1 0 2 0 1 0 3 c 6 2 1 W R I T E ( 6 , 8 2 1 ) Q F O R M A T ( F 0SUM OF THE E I G E N V A L U E S ; ' / ' ' , 2 3 C * = * ) / / « % F 1 1 , 3 ) c O B T A I N SV ( T H E SUM OF THE E I G E N V A L U E S ) AND VE ( T H E C U M U L A T I "ORTRAN IV SOURCE LISTING PAGE 004 278 C EXPLAINED VARIATION), C S104 SV90-.0 3105 I l P l - H t l 3106 PQ 441 1*1,11  3107 K=I1P1*I 3108 SV=SS(K)+SV 3109 441 VE(!Q*SV/Q C C CHECK SIGNIFICANCE OF EIGENVECTORS, C i i i  3110 I l M l s I l - 1 3111 DQ 104 K?1,X1M1 Z> 11 a CVARSVECK*!) + .03  0113 IF CVe CK),GT,CVAR) GO TO 442 0115 104 CONTINUE C , , C SET INSIGNIFICANT VECTOR COMPONENTS TO 0 , C 0116 442 KgK-1 0117 IF(NKQ,GT,99) GO TO 591 0119 DO 443 I f j j K 0120 DO 443 4*1,11  0121 RG(JK(X),J)=0,0 0122 443 CONTINUE C C PRINT THE CUMULATIVE EXPLAINED VARIATION, C 0123 591 WRITE(6,577) (VE(K) , K s l , I l ) 0124 577 FORMATC*0CUMULATIVE EXPLAINED VARIATION!*/' * , 3 0 ( * = ' ) / / ( f *,20F 1)) 0125 GO TO 590 C C SET ALL EIGENVECTOR COMPONENTS TO 0 EXCEPT FOR THE SPECIFIED C EIGENVECTOR. PRINT THE INDEX OF THIS EIGENVECTOR,  C 0126 579 DO 578 I«1,I1 0127 DO 578 J ? l , 11 0TTS IFCJ.EQTflKQ) 60 TO 57B :  0130 R O ( J , I ) s 0 , 0 0131 576 CONTINUE  0132 WRITE(6,761)(TITLE(I),I*1,20) 0133 WRITE(6,995)NKQ 0134 995 FORMAT ( #0EIGENVECTOR NUMBER ! f / e * , l 9 ( y 3 ' ) / / ' M U )  0135 590 CONTINUE C C RECONSTITUTE AND PRINT THE INPUT DATA MATRIX.  C 0136 DO 12 1*1,11 0137 IMM*(I*1)*N  0138 DO 12 J=1,I2 0139 C Q ( I , J ) s 0 , 0 0140 DO 12 K = 1»11 0141 CQ(I,J) 9 CQ(I,J) + RQ(K,I)*CC(K»J) 0142 12 ICOCI,J)«IFIX(30,5*CQ(I,J)/3,0) 0143 WRITE(fe,989) 0144 989 FORMAT( e0RECONSTITUTED DATA MATRIX!*/* #,26(«s*)/) FORTRAN IV 006-01 SOURCE LISTING PAGE 005 279 0145 0146 C C C 950 DO 950 1=1,11 WRITE(6,802)CCQ(I,J),J=1,I2) PLOT AERIAL PATTERN IF REQUESTED. 0147 0149 0150 IF(IPLOT ?EQ f1)60 TO 667 DO 661 1=1,11 WRITE(6,761)(TITLE(J),J=l,20) 0151 0152 764 WRITE(6,764)I,NKO FORMAT(* STORM NUMBER ?,13,T21,*EIGENVECTOR NUMBER 8 LT21,21('**)) ,13/' M 5 C -0153 c 661 WRITE(6,662) (CQ(I,J),J = 1,12) C • CHANGE THIS FORMAT STATEMENT IF STATION LOCATIONS DIFFER, , 0154 C 662 MfMllllft HMMtHMIIllttftMHIUM | 1 Ml 1 M H M II M f M f • FORMAT(*0ST27,»+*/T25,F5,2,14(/),T12,«+*/T9,,F5,2/T7,F5,2,5 t ,T41,< + V T 2 6 , ' - r +',T39,F5.2/T24,F5.2,T30,F5,2) 0155 C C GO TO 1 PLOT HISTOGRAM IF REQUESTED, 0156 0157 C 667 DO 665 1=1,11 DO 663 JJ=1,I2 0158 0159 0160 DO 663 I I - l , 4 6 H I S T G M d l , JJ)=IBLANK IF(II.EQ,ICQ(I,JJ))HISTGM(II,JJ)»IPLUS 0162 0163 0164 663 CONTINUE WRITE(6,761)(TITLE(J),J=1,20) WRITE(6,764)I,NKQ 0165 0166 0167 669 WRITE(6,669) FORMAT(*0 e) ROW=90,0 0168 0169 0170 664 DO 664 11=1,46 ROW=ROW-3,0 WRITE(6,660)ROW,(HISTGM(II,JJ),JJ=1,12) c c c • • « CHANGE THIS FORMAT STATEMENT IF STATION LOCATIONS ,•,,»,»•»•«•«»«»•»»•»•§•»• IHIIMIIIMIMMI »•»»••» DIFFER $ , ••«»••••* 0171 0172 0173 660 665 FORMAT C * *,F5,1,T12,A1,T32,A1,T46,A1,T53,A1,T58,A1 CONTINUE GO TO 1 ,T61,A1) 0174 0175 99999 STOP END F O R T R A N I V 0 0 6 * 0 1 S O U R C E L I S T I N G P A G E 0 0 1 2 8 0 C 0 M « i | i t i ! i f t l l M l l t * > l f | i | < l l l t l l l < * > I I I M * > l < « l l l * l l M M I I t M t l l > c C S U B R O U T I N E M S T R C  C P U R P O S E C C H A N G E S T O R A G E M O D E O F A M A T R I X C ^ C U S A G E C C A L L M S T R C A , R , N , M S A , M S R ) C  C D E S C R I P T I O N O F P A R A M E T E R S C A - N A M E O F I N P U T M A T R I X C R - N A M E O F O U T P U T M A T R I X C N * N U M B E R O F R O W S A N D C O L U M N S I N A A N D R C M S A - O N E D I G I T N U M B E R F O R S T O R A G E M O D E O F M A T R I X A C 0 » G E N E R A L  C 1 - S Y M M E T R I C C 2 * D I A G O N A L C M S R » S A M E A S M S A E X C E P T F O R M A T R I X R C R E M A R K S C M A T R I X R C A N N O T B E I N T H E S A M E L O C A T I O N A S M A T R I X A  C M A T R I X A M U S T B E A S Q U A R E M A T R I X C C S U B R O U T I N E S A N D F U N C T I O N S U B P R O G R A M S R E Q U I R E D C L O C C C M E T H O D  C M A T R I X A I S R E S T R U C T U R E D T O F O R M M A T R I X R . C M S A M S R C 0 0 M A T R I X A I S M O V E D T O M A T R I X R _ _ _ _ _ n ^ _ _ _ _ _ _ f _ ^ :  C A R E U S E D T O F O R M A S Y M M E T R I C M A T R I X C 0 g T H E D I A G O N A L E L E M E N T S O F A G E N E R A L M A T R I X A R E U S E D  C T O F O R M A D I A G O N A L M A T R I X C I 0 A S Y M M E T R I C M A T R I X I S E X P A N D E D T O F O R M A G E N E R A L C M A T R I X rxnTAJRTX ^ A ~ T S ~ M O V E D T O M A T R I X ~ R C I 2 T H E D I A G O N A L E L E M E N T S O F A S Y M M E T R I C M A T R I X ARE C U S E D T O F O R M A D I A G O N A L M A T R I X  C 2 0 A D I A G O N A L M A T R I X I S E X P A N D E D B Y I N S E R T I N G M I S S I N G C Z E R O E L E M E N T S T O F O R M A G E N E R A L M A T R I X C g 1 A D I A G O N A L M A T R I X I S E X P A N D E D B Y I N S E R T I N G M I S S I N G  C Z E ^ O ^ E T I I M T N T S T O F O R M A S Y M M E T R I C ~ 1 I A T R T X C 2 2 M A T R I X A I S M O V E D T O M A T R I X R C C 0 0 0 1 S U B R O U T I N E M S T R C A , R , N , M S A , M S R ) c 0 0 0 3 DQ 8 0 I « l , N  0 0 0 4 DO 2 0 J s l , N C J _ I F J ? J S _ G E N E R A L , F O R M E L E M E N T _ _ _ _ _ _ _ _ _ _ c ~ ' ' ~ FORTRAN IV D06-01 SOURCE LISTING PAGE 002 281 0005 C C i» IF(MSR) 5 ,10 ,5 IF IN LOWER TRIANGLE OF SYMMETRIC OR DIAGONAL R, BYPASS 0006 t 5 I F ( I * J ) 10,10,20 0007 C c 10 CALL L O C U , J , IR ,N ,N ,MSR) IF IN UPPER AND OFF DIAGONAL OF DIAGONAL R, BYPASS 0008 c c IFCIR) 20 ,20 ,15 c c OTHERWISE, FORM RCI ,J ) 0009 15 RCIR)=0.0 0010 c c CALL L O C C I , J , I A , N , N , M S A ) IF THERE IS NO A C I , J ) , LEAVE R ( I , J ) AT 0,0 0011 0012 c 18 IFt IA) 20 ,20 ,18 R(IR)=A(IA) 0013 0014 0015 20 CONTINUE RETURN END F O R T R A N IV 006*01 S O U R C E L I S T I N G P A G E 001 282 C c c c c S U B R O U T I N E L O C c c c P U R P O S E C O M P U T E A V E C T O R S U B S C R I P T FOR AN E L E M E N T I N A M A T R I X OF S P E C I F I E D S T O R A G E MODE c c c U S A G E C A L L L O C ( I , J , I R , N . M . M S . c c c D E S C R I P T I O N OF P A R A M E T E R S I - ROW NUMBER OF E L E M E N T c c c J - C O L U M N NUMBER OF E L E M E N T IR * R E S U L T A N T V E C T O R S U B S C R I P T N * NUMBER OF ROWS IN M A T R I X c c c M m NUMBER OF C O L U M N S IN M A T R I X MS * O N E D I G I T NUMBER FOR S T O R A G E MODE OF M A T R I X 0 - G E N E R A L c c c 1 * S Y M M E T R I C 2 - D I A G O N A L c c c R E M A R K S N O N E c c c S U B R O U T I N E S AND F U N C T I O N S U B P R O G R A M S R E Q U I R E D NONE c c c METHOD MS»0 S U B S C R I P T I S C O M P U T E D FOR A M A T R I X WITH N*M E L E M E N T S I N S T O R A G E ( G E N E R A L M A T R I X . c c c MS«1 S U B S C R I P T I S C O M P U T E D FOR A M A T R I X WITH N * ( N * l ) / 2 IN S T O R A G E ( U P P E R T R I A N G L E OF S Y M M E T R I C M A T R I X ) , I F E L E M E N T I S I N LOWER T R I A N G U L A R P O R T I O N . S U B S C R I P T I S c c c C O R R E S P O N D I N G E L E M E N T IN U P P E R T R I A N G L E , M$*2 S U B S C R I P T I S C O M P U T E D FOR A M A T R I X WITH N E L E M E N T S IN S T O R A G E ( D I A G O N A L E L E M E N T S OF D I A G O N A L M A T R I X ) . c c c _ _ _ _ _ _ _ _ ^ ^ D I A G O N A L tAND T H E R E F O R E NOT IN S T O R A G E ) , IR I S S E T TO Z E R O , c c 0001 S U B R O U T I N E L O C ( I , J , I R , N , M , M S ) 0002 0003 c I X » I J X « J 0004 0005 0006 10 I F ( M S * 1 ) 10 ,20,30 I R X ? N * ( J X * 1 ) + I X GO TO 36 0007 0008 0009 20 22 I F ( I X - J X ) 22 ,24 ,24 I R X P I X T ( J X * J X * J X ) / 2 GQ TO 36 0010 0011 0012 24 30 I R X = J X + C l X * I X * I X ) / 2 GO TO 36 IRXB0 0013 I F £ I X * J X ) 36 ,32 ,36 FORTRAN IV D06*01 SOURCE LISTING PAGE 002 283 0014 0015 0016 0017 32 IRXslX 36 IR« IRX RETURN END FORTRAN IV 006-01 SOURCE LISTING PAGE 001 284 C C C C SUBROUTINE EIGEN C c c c PURPOSE COMPUTE EIGENVALUES AND EIGENVECTORS OF A REAL SYMMETRIC MATRIX c c c USAGE CALL EIGEN (A» R,N,MV) c c c DESCRIPTION OF PARAMETERS A - ORIGINAL MATRIX (SYMMETRIC), DESTROYED IN COMPUTATION. c c c RESULTANT EIGENVALUES ARE DEVELOPED IN DIAGONAL OF MATRIX A IN DESCENDING ORDER8 R - RESULTANT MATRIX OF EIGENVECTORS (STORED COLUMNWISE, c c c IN SAME SEQUENCE AS EIGENVALUES) N - ORDER OF MATRICES A AND R MV - INPUT CODE c c c 0 COMPUTE EIGENVALUES AND EIGENVECTORS 1 COMPUTE EIGENVALUES ONLY (R NEED NOT BE DIMENSIONED BUT MUST STILL APPEAR IN CALLING c SEQUENCE) _ c REMARKS c c c ORIGINAL MATRIX A MUST BE REAL SYMMETRIC (STORAGE MUQE = U MATRIX A CANNOT BE IN THE SAME LOCATION AS MATRIX R c c c SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED NONE c c c METHOD DIAGQNALIZATION METHOD ORIGINATED BY JACOEI AND ADAPTED BY VON NEUMANN FOR LARGE COMPUTERS AS FOUND IN 'MATHEMATICAi c c c METHODS FOR DIGITAL COMPUTERS', EDITED BY A. RALSTON AND H . S , WILF, JOHN WILEY AND SONS, NEW YORK, 1962, CHAPTER 7 0001 c c SUBROUTINE EIGEN(A,R,N,MV) 000? c c DIMENSION A(1 ) ,R(1 ) c c c IF A DOUBLE PRECISION VERSION'OF THIS ROUTINE IS DESIRED, THE C IN COLUMN 1 SHOULD BE REMOVED FROM THE DOUBLE PRECISION c STATEMENT WHICH FOLLOWS, u c DOUBLE PRECISION A,R,ANORM,ANRMX,THR,X,Y,SINX,SINX2,CQSX, c c c 1CQSX2,SINCS,RANGE THE C MUST ALSO BE REMOVED FROM DOUBLE PRECISION STATEMENTS c c c APPEARING IN OTHER ROUTINES USED IN CONJUNCTION WITH THIS ROUTINE, c THE DOUBLE PRECISION VERSION OF THIS SUBROUTINE MUST ALSO F O R T R A N I V 0 0 6 * 0 1 S O U R C E L I S T I N G P A G E 002 285 C C O N T A I N D O U B L E P R E C I S I O N F O R T R A N F U N C T I O N S « S Q R T I N S T A T E M E N T S C 4 0 , 6 8 , 7 5 , A N D 7 8 M U S T B E C H A N G E D T O D S Q R T , A B S I N S T A T E M E N T C 6 2 M U S T B E C H A N G E D T O D A B S , T H E C O N S T A N T I N S T A T E M E N T 5 S H O U L D C B E C H A N G E D T O i f 0 D * 1 2 , C C C C G E N E R A T E I D E N T I T Y M A T R I X 0 0 0 3 0 0 0 4 C 5 R A N G E ? ! , 0 E * 6 I F ( M V * 1 ) 1 0 , 2 5 , 1 0 0 0 0 5 0 0 0 6 0 0 0 7 1 0 I Q = » N D O 2 0 J = i , N I Q = I Q T N 0 0 0 8 0 0 0 9 0 0 1 0 D O 2 0 1 = 1 , N I J = I Q t I R ( I J ) = 0 , 0 0 0 1 1 0 0 1 2 0 0 1 3 1 5 2 0 I F ( I * J ) 2 0 , 1 5 , 2 0 R ( I J ) = 1 , 0 C O N T I N U E C C C C O M P U T E I N I T I A L A N D F I N A L N O R M S ( A N Q R M A N D A N Q R M X ) 0 0 1 4 0 0 1 5 0 0 1 6 2 5 A N Q R M = 0 , 0 D O 3 5 1 = 1 , N D O 3 5 J = I , N 0 0 1 7 0 0 1 8 0 0 1 9 3 0 I F C I w J ) 3 0 , 3 5 , 3 0 I A = I + ( J * J * J ) / 2 A N Q R M = A N Q R M + A ( I A ) * A ( I A ) 0 0 2 0 0 0 2 1 0 0 2 2 3 5 4 0 C O N T I N U E I F ( A N Q R M ) 1 6 5 , 1 6 5 , 4 0 A N 0 R M = 1 . 4 1 4 * S Q R T ( A N Q R M ) 0 0 2 3 p A N R M X = A N Q R M * R A N G E / F L Q A T ( N ) L c I N I T I A L I Z E I N D I C A T O R S A N D C O M P U T E T H R E S H O L D , T H R 0 0 2 4 0 0 2 5 c I N D = 0 T H R = A N Q R M 0 0 2 6 0 0 2 7 0 0 2 8 4 5 5 0 5 5 T H R = T H R / F L O A T ( N ) L = i M = L T 1 c C C C O M P U T E S I N A N D C O S 0 0 2 9 0 0 3 0 0 0 3 1 6 0 M Q * ( M * M * M ) / 2 L Q = ( L * L - U ) / 2 L M = L + M Q 0 0 3 2 0 0 3 3 0 0 3 4 6 2 6 5 I F C A B S ( A ( L M ) ) - T H R ) 1 3 0 , 6 5 , 6 5 I N D = t L L ' L t L Q 0 0 3 5 0 0 3 6 0 0 3 7 6 6 M M = M t M Q X = 0 , 5 * ( A ( L L ) - A ( M M ) ) Y = - A ( L M ) / S Q R T ( A ( L M ) * A ( L M ) + X * X ) 0 0 3 8 0 0 3 9 0 0 4 0 7 0 7 5 I F C X ) 7 0 , 7 5 , 7 5 S I N X = Y / S Q R T C 2 » 0 * ( 1 , 0 + C S Q R T ( i „ 0 * Y * Y ) ) ) ) 0 0 4 1 S I N X 2 = S I N X * S I N X F O R T R A N I V 0 0 6 - 0 1 S O U R C E L I S T I N G P A G E 0 0 3 286 0 0 4 2 0 0 4 3 0 0 4 4 7 8 C C C O S X s S Q R T C 1 • 0 " S I N X 2 ) C 0 S X 2 ? C 0 S X * C 0 S X S I N C S S S I N X * C Q S X R O T A T E L A N D M C O L U M N S 0 0 4 5 0 0 4 6 C I L Q » N * ( L * 1 ) I M Q ? N * ( M * n 0 0 4 7 0 0 4 8 0 0 4 9 ~ " W ~ 1 2 5 1 * 1 , N I Q = ( I * I * I ) / 2 I P ( I » L ) 8 0 , 1 1 5 , 8 0 0 0 5 0 0 0 5 1 0 0 5 2 8 0 8 5 I F C 1 - M ) 8 5 , 1 1 5 , 9 0 I M S I t M Q G O T O 9 5 0 0 5 3 0 0 5 4 0 0 5 5 9 0 9 5 1 0 0 I M = M + I Q I F C I - L ) 1 0 0 , 1 0 5 , 1 0 5 I L = I + L Q 0 0 5 6 0 0 5 7 0 0 5 8 1 0 5 1 1 0 G O T O 1 1 0 I L « L + I Q X _ A C I L ) * C 0 3 X " A ( I M ) * S I N X 0 0 5 9 0 0 6 0 0 0 6 1 1 1 5 A C I M ) s A C I L ) * S I N X + A C I M ) * C Q S X A ( I L ) = X I F C M V * i ) 1 2 0 , 1 2 5 , 1 2 0 0 0 6 2 0 0 6 3 0 0 6 4 1 2 0 I L R » I L Q + I I M R " I M Q * I X a R ( l L R ) * C O S X - R C I M R ) * S I N X 0 0 6 5 0 0 6 6 0 0 6 7 1 2 5 R C I M R ) s R ( I L R ) * S l N X * R ( l M R ) * C O S X R C I L R ) » X C O N T I N U E 0 0 6 8 0 0 6 9 0 0 7 0 X s 2 „ 0 * A ( L M ) * S I N C S Y f A ( L L ) * C 0 S X 2 t A ( M M ) * S l N X 2 » X X s A C L L ) * S I N X 2 + A ( M M ) * C Q S X 2 + X 0 0 7 1 0 0 7 2 0 0 7 3 A ( L M ) * ( A C L L ) - A ( M M ) ) * S I N C S + A C L M ) * ( C 0 S X 2 * S I N X 2 ) A ( L L ) ? Y A ( M M ) « X C C T E S T S F O R C O M P L E T I O N C T E S T F O R M * L A S T C O L U M N 0 0 7 4 c 1 3 0 I F C M « N ) 1 3 5 , 1 4 0 , 1 3 5 0 0 7 5 0 0 7 6 1 3 5 C M B M T I G O T O 6 0 C f* T E S T F O R L = S E C O N D F R O M L A S T C O L U M N 0 0 7 7 G 1 4 0 I F ( L » ( N * 1 ) ) 1 4 5 , 1 5 0 , 1 4 5 0 0 7 8 0 0 7 9 0 0 8 0 1 4 5 1 5 0 L = L + 1 G O T O 5 5 I F ( I N D ^ l ) 1 6 0 , 1 5 5 , 1 6 0 0 0 8 1 0 0 8 2 1 5 5 C I N D * 0 G O T O 5 0 C C O M P A R E T H R E S H O L D W I T H F I N A L N O R M c 0 0 8 3 1 6 0 I F ( T H R - A N R M X ) 1 6 5 , 1 6 5 , 4 5 C FORTRAN IV 006*01 SOURCE LISTING PAGE 004 287 C SORT EIGENVALUES AND EIGENVECTORS C 0084 165 IQ = -N 0085 DO 165 1=1,N 0086 IQ=IQ+N 0087 L L = I * C I * I « I ) / 2 0088 JO=N*(1-2) 0089 DO 185 J * I , N 0090 JQ=JQ+N 0091 MM=J+(J*J*J) /2 0092 IF (A(LL)*A(MM)) 170, 185, 185 0093 170 X=A(LL) 0094 A(LL)=A(MM) 0095 A(MM)=X 0096 IF (MV- l ) 175,185,175 0097 175 DO 180 K = 1, N 0098 ILR=IO+K 0099 IMR=JQ+K 0100 X=R(ILR) 0101 R(ILR)=R(IMR) 0102 180 R(IMR)=X 0103 185 CONTINUE 0104 RETURN 0105 END AREAL STORM RAINFALL PATTERN - RESEARCH FOREST INPUT DATA? 8 X S S S S S S 8 S S 12,400 16,800 27.400 4,600 13,000 9,100 36,100 9.900 66,800 13,700 80,500 14,500 22.600 17,300 24,900 31,500 37,300 37,600 29,700 38,400 36,600 42,400 36,600 40.400 EIGENVECTORS? 3 3 3 8 3 3 3 3 8 3 3 3 3 1 0.699 0,165 0,428 0,549 2 -0 ,690 0,096 0,209 0,686 3 «0.103-0,654 0 ,713*0 ,229 4 -0 ,158 0,732 0 ,514-0 ,419 MULTIPLIERS? : : : : : : : : : : : : 36,387 41,762 51,944 18,235 18,876 12,985 4,621 -6 ,436 0,381 60,649 8,614 2,207 89,275 •9 ,393 0,372 96.485 * 16,761 -0 ,893 -0 ,178 0.122 -0 .633 0,706 EIGENVALUES ft CORRESPONDING EIGENVECTOR NUMBERS? : : : : s : : : : : : : : : : : : : : e : : : : : : : : : : s : : : : : : : : : s 0,177 -0 .253 1 .041 ( 4) 68,728( 3) 1371 ,826C 2)26724,039( 1) SUM OF THE EIGENVALUES ? 3 S S S S 3 8 S S S S 3 3 3 8 3 3 S S 3 B S S 28165.635 CUMULATIVE EXPLAINED VARIATION! 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5.3 1.000 1,000 0,998 0,949 RECONSTITUTED DATA MATRIX? 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 S 3 3 3 3 3 3 3 3 12,400 16,800 27,400 4,600 13,000 9,100 36,100 9,900 68,800 13,700 80,500 14.500 22,600 17*300 24,900 31,500 37,300 37,600 29,700 38,400 36,600 42,400 36.600 40.400 289 AREAL STORM RAINFALL PATTERN - RESEARCH FOREST STORM NUMBER 1 EIGENVECTOR NUMBER100  +__ + 16.80 • + 68.80 80.50 38.10 290 AREAL STORM RAINFALL PATTERN * RESEARCH FOREST EIGENVECTOR NUMBER: 1 RECONSTITUTED DATA MATRIX?  : : : : : : : : : : : : : : : : 3 : : : s : : : : : 2S,427 294,63 36.598 42.381 62.385 67.484 S.999 6,885 8,563 9,998 14,717 15.906 15,574 17,875 22,233 25,959 38,211 41,297 19.974 22^924 28,513 33.291 49.004 52,962 291 AREAL STORM RAINFALL PATTERN - RESEARCH FOREST STORM NUMBER i EIGENVECTOR NUMBER I + 25,43 t 2 9 , i 8 36,30 + + 42 9 38 62,39 67,422 232, i RAINFALL TRANSECT - SURREY MUNICIPAL HALL-RESEARCH FOREST TNPirrTlATAS 57,200 29,200 49,800 80,500 79.000 8,100 6,900 10,900 14,500 13,200 38,400 31,800 34,300 36,600 35.300 50,300 $07610 40,400 40,400 38,100 EIGENVECTORS:  "1 0,745 0,133 0,423 0,499 2 1.0.644,0,074 0,374 0,664  3 -0 ,176 0,812 0 ,447*0 ,332 0 f 0 0 6 * 0 , 5 6 4 0 ,694*0 ,448 MULTIPLIERS?  : : : : : : : : : : : : 85.009 56,368 73.197 97,508 94.522 10,312 19,520 6,764 -12 .405 -13 ,356 - 3 , 0 3 5 1,197 1.995 0,531 -0 ,077 -0 .094 0.177 -0 .130 -0 .380 0.472 EIGENVALUES & CORRESPONDING EIGENVECTOR NUMBERS? ::::3:3:::::::::::::::::::::::::::::::::: 0 ^ 2 4 ( 4 ) T 4 7 9 r r r 3 ) 8 l £ y 7 3 W r ~ 2 T 3 4 2 0 3 , 8 9 l C n SUM OF THE EIGENVALUES?  ::::::E:::::::::::::::: 35084.613 CUMULATIVE EXPLAINED VARIATION? S535SSSSSSSSSS8CS58S88SSSS35S5 1,000 1,000 1,000 0,975 RECONSTITUTED DATA MATRIX? 57,200 29,200 49,800 80,500 79,000 8,100 6,900 10,900 14,500 13,200 38.400 31,800 34,300 36,600 35,300 50,300 40,600 40,400 40,400 38.100 293 RAINFALL TRANSECT - SURREY MUNICIPAL HALL-RESEARCH FOREST STORM NUMBER 1 EIGENVECTOR NUMBER100 87,0 84,0 81.0 78,0 75,0 72,0 69,0 66,0 63,0 60,0 57.0 + 54,0 51.0 • 48,0 45,0 42,0 39,0 36,0 33,0 30,0 + 27,0 24,0 21,0 18,0 15,0 12.0 9.0 6,0 3.0 0.0 - 3 . 0 »6»0 • 9,0 • 12,0 • 15,0 • 18.0 • 21,0 • 24,0 • 27,0 - 3 0 , 0 • 33,0 • 36,0 • 3 9 , 0 • 42,0 • 4 5 , 0 • 48,0 294 RAINFALL TRANSECT - SURREY MUNICIPAL HALL-RESEARCH FOREST EIGENVECTOR NUMBERS S S S S S S B S S S S S S B B S 8 S S 1 RECONSTITUTED DATA MATRIX;  I : : : : : : : : : : : : : : : : : ; : : : ; : : : 6 3 . 3 0 3 41*975 5 4 . 5 0 7 7 2 « 6 U 7 0 . 3 8 7 1 1 . 8 7 6 7 , 4 7 7 9 , 7 0 9 1 2 , 9 3 4 1 2 , 5 3 8 3 5 , 9 7 0 2 3 , 8 5 1 3 0 , 9 7 2 4 1 , 2 5 9 3 9 , 9 9 6 4 2 , 4 0 6 2 8 , 1 1 9 3 6 , 5 1 3 4 8 . 6 4 1 4 7 . 1 5 1 295 RAINFALL TRANSECT - SURREY MUNICIPAL HALL-RESEARCH FOREST STORM NUMBER 1 EIGENVECTOR NUMBER 1 87,0 64,0 81.0 78,0 75,0 72.0 t l l 69,0 66,0 63,0 • 60,0 57,0 54,0 + 51,0 48,0 45.0 42,0 39.0 36.0 * 33,0 30,0 27.0 j 24,0 i 21,0 18,0 15,0 12,0 9.0 6.0 3,0 0.0 - 3 , 0 - 6 , 0 - 9 . 0 - 1 2 . 0 - 1 5 , 0 - 1 8 . 3 - 2 1 . 0 - 2 4 , 0 - 2 7 . 0 -30,0" - 3 3 , 0 - 36 .0 - 39 .0 - 4 2 , 0 - 4 5 . 0 • 48,0 APPENDIX XVI CAN-TYPE GAUGE DATA FOR TRANSECTS ON SLOPES OF SITE-7 AND SITE-9 RIDGES CO 1 rH m rH 1 CO rH CN 1 CO 21-28 i OO CO CN o i-H 1 CO . 10-15 . 22-28 i 00 CN 11-16 16-23 23-26 rH >s rH 00 < 60 < Aug. Sept. 4 J ft cu oo mm 4-1 ft V OO + J ft cu oo Sept Oct. 4-1 O o 4-1 O o 4-1 O o 7C1 _ 35.05 14. 02 20. 80 42.76 44.87 14.02 77.35 114. 27 53.28 94. 64 111. 47 7C2 28.74 36.69 14. 02 21. 03 42.76 44.40 13.55 76.41 108. 19 51.18 94. 64 110. 99 7C3 29.21 36.45 11. 68 21. 97 37.16 38.32 12.62 68.47 90. 20 43.70 81. 79 93. 94 7C4 - 36.45 15. 19 21. 97 43.00 43.93 14.72 76.88 110. 30 53.98 96. 51 115. 67 8C1 32.95 39.26 22. 20 19. 63 44.87 44.87 16.82 76.18 138. 10 68.70 108. 66 144. 84 8C2 - - 16. 82 42.30 41.13 15.66 71.27 118. 94 48.14 102. 35 128. 06 8C3 - - 19. 63 19. 40 43.23 49.54 18.46 81.32 130. 16 60.29 110. 53 128. 06 9C1 31.55 42.53 24. 30 20. 10 49.31 51.64 18.46 95.11 139. 04 68.47 109. 60 145. 82 9C2 29.21 40.66 22. 43 17. 76 50.01 51.18 17.53 97.44 136. 94 70.34 115. 44 144. 88 9C3 28.28 40.43 21. 26 19. 63 47.67 52.34 17.29 87.63 129. 46 61.69 104. 92 123. 85 9C4 29.21 41.60 22. 43 16. 82 48.61 51.18 17.76 92.54 133. 43 62.86 105. 39 124. 55 9C5 - 41.36 23. 13 15. 19 43.46 51.88 14.02 83.66 105. 86 52.11 94. 87 104. 22 vo 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0093785/manifest

Comment

Related Items