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Solar radiation model and an analysis of synoptic solar radiation regimes in British Columbia Suckling, Philip Wayne 1977

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A SOLAR RADIATION MODEL AND AN ANALYSIS OF SYNOPTIC SOLAR RADIATION REGIKES IN BRITISH COLUMBIA by P H I L I P WAYNE SUCKLING B . S c , McMaster U n i v e r s i t y , 1973 M . S c , McMaster U n i v e r s i t y , 1974 A THESIS SUBMITTED IN THE REQUIREMENTS DOCTOR OF i n DEPARTMENT PARTIAL FULFILLMENT OF FOR THE DEGREE OF PHILOSOPHY the OF GEOGRAPHY We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA J u l y , 197? © P h i l i p Wayne S u c k l i n g , 1977 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Brit ish Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Geography The University of Brit ish Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 ABSTRACT I n t e r e s t i n the s p a t i a l and t e m p o r a l d i s t r i b u t i o n of s o l a r r a d i a t i o n has i n c r e a s e d r e c e n t l y , p r i m a r i l y as a consequence of the c u r r e n t i n t e r e s t i n the p o t e n t i a l u t i l i z a t i o n o f s o l a r energy. S i n c e the e x i s t i n g s o l a r r a d i a t i o n m o n i t o r i n g network i n most areas i s s p a r s e and l a r g e l y i n a d e q u a t e f o r s o l a r energy f e a s i b i l i t y s t u d i e s , n u m e r i c a l m o d e l l i n g of s o l a r r a d i a t i o n i n c l u d i n g i t s d i r e c t and d i f f u s e components must be used t o p r o v i d e s u p p l e m e n t a l d a t a . I n a d d i t i o n t o i n f o r m a t i o n on a c t u a l r a d i a t i v e v a l u e s , i t may be u s e f u l t o a t t a i n knowledge about the t e m p o r a l and s p a t i a l b e h a v i o u r of s o l a r r a d i a t i o n and a s y n o p t i c m e t e o r o l o g i c a l framework p r e s e n t s one p o s s i b l e approach. A c l o u d l e s s sky s o l a r r a d i a t i o n model based on the o r i g i n a l work of Houghton (195^) was t e s t e d f o r t h e t h r e e C a n a d i a n l o c a t i o n s of Goose, N f l d . , Edmonton, A l t a . and P o r t Hardy, B.C. I n o r d e r t o o b t a i n b e t t e r e s t i m a t e s of the d i r e c t and d i f f u s e components of the t o t a l s o l a r r a d i a t i o n , r e v i s e d v a l u e s of the a e r o s o l parameter and f o r w a r d - and b a c k - s c a t t e r i n g f a c t o r s were d e t e r m i n e d . The model was a l s o v e r i f i e d f o r o t h e r l o c a t i o n s i n B r i t i s h C o l u m b i a . The e f f e c t s o f c l o u d were i n c o r p o r a t e d t h r o u g h the use o f a new c l o u d l a y e r - s u n s h i n e (CLS) model w h i c h calculates the d i r e c t and diffuse components of solar r a d i a t i o n separately. When compared to a previously developed cloud layer model, the CLS model provided better d a i l y estimates of the t o t a l solar r a d i a t i o n f o r the f i v e Canadian locations of Goose, Nfld., Edmonton, A l t a . , Vancouver, B.C., Sandspit, B.C. and Summerland, B.C. The potential a p p l i c a b i l i t y of the CLS model to Canada is discussed. In order to study solar r a d i a t i o n from a synoptic viewpoint, synoptic weather types were established f o r B r i t i s h Columbia and the adjacent areas of the P a c i f i c Ocean. An objective c o r r e l a t i o n c l a s s i f i c a t i o n technique was used fo r t h i s purpose. The synoptic types were described and t h e i r frequency, persistency and sequence analysed. Since pr e c i p i t a b l e water i s one of the required input parameters fo r the solar radiation model, these synoptic types were i n i t i a l l y used to help specify the p r e c i p i t a b l e water f i e l d s for the region. The CLS model was applied to the B r i t i s h Columbia area for the year 1972 and the annual and seasonal s o l a r r a d i a t i o n d i s t r i b u t i o n s were discussed. An assessment of the s p a t i a l v a r i a b i l i t y of solar r a d i a t i o n showed that there i s a considerable advantage to numerically modelling so l a r r a d i a t i o n i n order to supplement the e x i s t i n g measurement network. The solar r a d i a t i o n d i s t r i b u t i o n s , based on both i v c a l c u l a t e d and observed data, were r e l a t e d to the s y n o p t i c weather types and the v a r i a n c e of s o l a r r a d i a t i o n between s y n o p t i c types was shown to be g e n e r a l l y g r e a t e r than the w i t h i n type v a r i a n c e . T h i s allowed the est a b l i s h m e n t of s y n o p t i c s o l a r r a d i a t i o n regimes f o r the B r i t i s h Columbia area. However, i t was shown t h a t knowledge of s y n o p t i c weather types n e i t h e r p r e c l u d e s the need f o r measuring s o l a r r a d i a t i o n nor negates the advantage of n u m e r i c a l l y m o d e l l i n g s o l a r r a d i a t i o n . Although some u s e f u l p o t e n t i a l a p p l i c a t i o n s f o r a s y n o p t i c approach to the study of s o l a r r a d i a t i o n were noted, i t r e q u i r e s a d d i t i o n a l study to overcome the problems of seasonal v a r i a b i l i t y , s p a t i a l s c a l e and r e s o l u t i o n i n the s y n o p t i c - s o l a r r a d i a t i o n r e l a t i o n s h i p s . V TABLE OF CONTENTS Page ABSTRACT i i LIST OF TABLES v i i i LIST OF FIGURES x i i LIST OF SYMBOLS xv ACKNOWLEDGEMENTS x x i CHAPTER 1 INTRODUCTION 1 1.1 GENERAL INTRODUCTION 1 1.2 SPECIFIC OBJECTIVES 4 1.3 ARRANGEMENT OF THIS THESIS 4 2 SOLAR RADIATION MODEL FOR CLOUDLESS CONDITIONS 7 2.1 INTRODUCTION 7 2.2 THE HOUGHTON MODEL 8 2.2.1 D e s c r i p t i o n 8 2.2.2 Performance 12 2.3 MODIFIED VERSION 19 2.3-1 D e t e r m i n a t i o n of t h e A e r o s o l P arameter 19 2.3.2 Performance a t Goose 21 2.3.3 C a l c u l a t i o n and Performance a t Edmonton and P o r t Hardy . . . . 24 2.3 .4 Performance f o r Independent D a t a 29 2 .4 MODEL SENSITIVITY TO METEOROLOGICAL INPUT PARAMETERS 31 2.4.1 S e n s i t i v i t y t o P r e s s u r e . . . . 31 2 .4.2 S e n s i t i v i t y t o Albedo 33 2 .4.3 S e n s i t i v i t y t o P r e c i p i t a b l e Water 35 2.5 APPLICATION IN BRITISH COLUMBIA . . . . 3? v i C h a p t e r Page 3 SOLAR RADIATION MODEL FOR CLOUDY CONDITIONS 43 3.1 INTRODUCTION 43 3.2 THE LAYER MODEL 45 3.2.1 D e s c r i p t i o n 45 3.2.2 Performance on D a i l y B a s i s . . . 51 3.3 THE CLOUD LAYER - SUNSHINE (CLS) MODEL 60 3.3.1 G e n e r a l D e s c r i p t i o n 60 3.3.2 D i r e c t S o l a r R a d i a t i o n Component 60 3.3.3 D i f f u s e S o l a r R a d i a t i o n Component 63 3.3.4 Performance on D a i l y B a s i s . . . 67 3.3.5 Performance f o r F i v e - and Ten-Day D a i l y Means 75 3.4 POTENTIAL APPLICATION IN CANADA . . . . 79 4 SYNOPTIC WEATHER TYPES FOR BRITISH COLUMBIA AND THE ADJACENT AREAS OF THE PACIFIC OCEAN 83 4.1 INTRODUCTION 83 4.2 THE OBJECTIVE CORRELATION CLASSIFICATION TECHNIQUE 85 4.3 SYNOPTIC WEATHER TYPES FOR 1963-72 . . 88 4.3.1 P r o c e d u r e 88 4.3 '2 D e s c r i p t i o n and Frequency . . . 88 4.3«3 S e a s o n a l and I n t r a - a n n u a l F requency D i s t r i b u t i o n s . . . . 92 4.3.4^ P e r s i s t e n c y and Sequence A n a l y s i s 92 4.3.5 Subsequent A p p l i c a t i o n 97 5 PRECIPITABLE WATER 101 5.1 COMPUTATION 101 5.1.1 G e n e r a l P r o c e d u r e 101 5.1.2 C a l c u l a t i o n f o r T h r e e - l e v e l G r i d Data 102 5.2 APPLICATION TO BRITISH COLUMBIA AND THE ADJACENT AREAS OF THE PACIFIC OCEAN . . 108 5.2.1 P r o c e d u r e and R e s u l t s 108 5.2.2 S t a t i s t i c a l S i g n i f i c a n c e o f the S y n o p t i c Type - P r e c i p i t a b l e Water R e l a t i o n s h i p s 113 5.2.3 Subsequent A p p l i c a t i o n 117 v i i Chapter Page 6 SOLAR RADIATION IN BRITISH COLUMBIA . . . . 119 6 .1 APPLICATION OF THE SOLAR RADIATION MODEL 119 6 .1.1 S e l e c t i o n and V a l i d a t i o n of Study Year - 1972 119 6 .1 .2 Procedure 126 6 . 1 . 3 Performance of the CLS Model . . 131 6 .2 DISTRIBUTION OF SOLAR RADIATION . . . . 131 6 .2 .1 Annual D i s t r i b u t i o n 131 6 . 2 . 2 Seasonal D i s t r i b u t i o n 13^ 6 . 3 THE ADVANTAGE OF MODELLING SOLAR RADIATION 1 4 3 7 SYNOPTIC SOLAR RADIATION REGIMES IN BRITISH COLUMBIA 151 7.1 INTRODUCTION 151 7.2 SYNOPTIC TYPE - SOLAR RADIATION RELATIONSHIPS 152 7.2.1 Procedure 152 7.2.2 S t a t i s t i c a l S i g n i f i c a n c e of the R e l a t i o n s h i p s 153 7.2 .3 D e s c r i p t i o n of Sy n o p t i c S o l a r R a d i a t i o n Regimes . 156 7 .3 SOLAR RADIATION WITHIN SYNOPTIC TYPES . 158 7 .3 .1 A n a l y s i s of Temporal V a r i a b i l i t y 158 7.3.2 A n a l y s i s of S p a t i a l V a r i a b i l i t y 166 7 . 3 . 3 A n a l y s i s of the N e c e s s i t y f o r Numerical M o d e l l i n g 176 7 . 4 APPLICATION OF SYNOPTIC SOLAR RADIATION REGIMES 1 8 0 7 .4 .1 I n t r o d u c t i o n 1 8 0 7 .4 .2 Example: In t e r a n n u a l S o l a r R a d i a t i o n V a r i a b i l i t y 1 8 0 7 .5 CONCLUSIONS I87 8 CONCLUSIONS 190 REFERENCES 192 APPENDIX 1: FREQUENCY DATA AND MAPS FOR THE SYNOPTIC WEATHER TYPES 202 APPENDIX 2: MAPS OF SYNOPTIC TYPE - PRECIPITABLE WATER DISTRIBUTIONS 237 APPENDIX 3: MAPS OF SYNOPTIC SOLAR RADIATION TRANSMISSION REGIMES FOR THE BRITISH COLUMBIA AREA 2 4 3 v i i i LIST OF TABLES Table Page 2.1 P e r i o d s of A v a i l a b l e Data Record f o r 'Cloudless Days' Study 13 2.2 C l o u d l e s s Days U t i l i z e d f o r Study 15 2.3 Performance of the Unmodified Houghton Model f o r Model Development Days 17 2.4 Performance of the M o d i f i e d Houghton Model f o r Model Development Days a t Goose . . . . 22 2.5 Values of the A e r o s o l Parameter 'k' . . . . 27 2.6 Performance of the M o d i f i e d Houghton Model f o r Model Development Days at Edmonton and P o r t Hardy 28 2.7 Performance of the Unmodified and M o d i f i e d Houghton Models on Independent Data . . . . 30 2.8 Modelled Values of S o l a r R a d i a t i o n (W rn"2) with V a r y i n g S u r f a c e Pressure (a=0.20, u=15 mm) 32 2.9 Modelled Values of S o l a r R a d i a t i o n (W m"2) with V a r y i n g S u r f a c e Albedo (p=100 kPa, u=15 mm) 34 2.10 Modelled Values of S o l a r R a d i a t i o n (W m"2) wit h V a r y i n g P r e c i p i t a b l e Water (a=0.20, p=100 kPa) 36 2.11 P e r i o d s of A v a i l a b l e Data Record f o r B.C. 'Cloudless Days' Study 38 2.12 C l o u d l e s s Days U t i l i z e d f o r B.C. Study . . . 39 2.13 Performance of the Unmodified and M o d i f i e d Houghton Models a t 3 B.C. L o c a t i o n s . . . . 41 3.1 Cloud T r a n s m i s s i v i t i e s f o r S o l a r R a d i a t i o n from V a r i o u s Sources 50 3.2 Values of the C o e f f i c i e n t s Used i n the Haurwitz (19^8) Cloud T r a n s m i s s i o n F u n c t i o n s 52 i x Table ' Page 3.3 Cloud Type Assignments 53 3.4 Performance of the Layer Model f o r Ki E s t i m a t i o n on a D a i l y B a s i s f o r 1968-70 . . 55 3.5 Performance of the CLS Model f o r Ki E s t i m a t i o n on a D a i l y B a s i s f o r 1968-70 . . 68 3.6 Comparison of the Performances of the Layer and CLS Models on a D a i l y B a s i s f o r 1968-70 70 3.7 Performance of the CLS Model f o r S i and Di E s t i m a t i o n at Goose on a D a i l y B a s i s f o r 1968-70 73 3.8 . Comparison of the Performances of the Layer and CLS Models f o r Five-Day D a i l y Means f o r 1968-70 76 3.9 Comparison of the Performances of the Layer and CLS Models f o r Ten-Day D a i l y Means f o r 1968-70 77 3.10 Number of S o l a r R a d i a t i o n S t a t i o n s i n Canada (Measuring and P o t e n t i a l to Model as of Jan. 1, 1976) 80 4.1 The Sy n o p t i c Types and T h e i r Frequencies . . 91 4.2 Frequency of Occurence by Seasons f o r the Synoptic Type Groups 93 4.3 I n t r a - a n n u a l Frequency of Occurence f o r the Synop t i c Type Groups 94 4.4 P e r s i s t e n c y of the Syno p t i c Weather Types . 96 4.5 Antecedent and Subsequent P a t t e r n s f o r Type 3 98 4.6 S y n o p t i c Types A s s o c i a t e d w i t h the U n c l a s s i f i e d Group (U) More Often Than Expected by Chance . 99 •5.1 R e g r e s s i o n of 3-Level Versus 11-Level P r e c i p i t a b l e Water Values f o r the P e r i o d 1961-70 104 X Table Page 5.2 R e g r e s s i o n of 3-Devel Versus 11-Level P r e c i p i t a b l e Water Values f o r January, A p r i l , J u l y and October 1970 . . 109 5.3 R e p r e s e n t a t i v e E l e v a t i o n s and b C o r r e c t i o n F a c t o r s f o r the Land G r i d P o i n t s i n F i g . 4.1 110 5.4 Average P r e c i p i t a b l e Water (mm) f o r Each Synoptic Type at the Three B.C. Radiosonde S t a t i o n s 114 5.5 Synoptic Type - P r e c i p i t a b l e Water D i s t r i b u t i o n A n a l y s i s : F - r a t i o s f o r the 113 G r i d P o i n t s and B.C. Radiosonde S t a t i o n s 116 6,'i S o l a r R a d i a t i o n Data f o r 1972 Compared to the Long-term Average 122 6.2 Comparison of 1972 Synoptic Weather Type Frequencies 125 6.3 Chi-square Test R e s u l t s f o r 1972 S y n o p t i c Type Frequencies 127 6.4 Values of Surface Albedo Assigned f o r Each Month Duri n g 1972 129 6.5 Values of P r e c i p i t a b l e Water (mm) Assigned f o r Each L o c a t i o n f o r Each Sy n o p t i c Type . . 130 6.6 Performance of the CLS Model on a D a i l y B a s i s f o r E s t i m a t i n g Ki i n the B r i t i s h Columbia Area During 1972 132 6.7 Average D a i l y S o l a r R a d i a t i o n T r a n s m i s s i o n {%) by Month During 1972 136 6.8 6'6$8 D i s t a n c e s (km) Between S t a t i o n s Used i n the Study of the S p a t i a l V a r i a b i l i t y of S o l a r R a d i a t i o n • 144 7.1 F - r a t i o s f o r the S y n o p t i c Type - S o l a r R a d i a t i o n D i s t r i b u t i o n A n a l y s i s f o r the B.C. Study Area 155 7.2 Average T Values (%) f o r A l l Days During 1972 and f o r U n c l a s s i f i e d and M i s s i n g S y n o p t i c Groups 157 x i Table Page 7.3 Synoptic S o l a r R a d i a t i o n Regimes f o r the Ocean Highs 159 7.4 S y n o p t i c S o l a r R a d i a t i o n Regimes f o r the Land Highs 160 7.5 S y n o p t i c S o l a r R a d i a t i o n Regimes f o r Ridges l 6 l 7.6 S y n o p t i c S o l a r R a d i a t i o n Regimes f o r Troughs 162 7.7 S y n o p t i c S o l a r R a d i a t i o n Regimes f o r the Ocean Lows 163 7.8 Average and Standard D e v i a t i o n f o r T f o r S e l e c t e d S y n o p t i c Types at S e l e c t e d L o c a t i o n s 165 7.9 Performancesof the CLS 1,1 Model f o r E s t i m a t i n g Ki f o r Syn o p t i c Types 6, 28 and 24 179 7.10 S y n o p t i c Type Frequencies f o r January From I963 to 1972 181 7.11 S y n o p t i c Type Frequencies f o r J u l y From 1963 to 1972 182 x i i LIST OF FIGURES F i g u r e Page 2.1 D e p l e t i o n Processes i n a C l o u d l e s s Atmosphere 9 2.2 D a i l y Performance of the Unmodified Houghton Model f o r C a l c u l a t i n g S o l a r R a d i a t i o n (MJ m~2daj~1) f o r C l o u d l e s s Days 18 2.3 Measured and C a l c u l a t e d D i f f u s e S o l a r 2 -1 R a d i a t i o n (MJ m day ) f o r C l o u d l e s s Days at Goose 23 3.'i* Cloud Layers Used i n the Layer Model ( i r e f e r s to l a y e r number) 46 3.2 Example of the C o r r e c t i o n f o r Cloud Layer Amount f o r Layers Obstructed by* Lower Cloud 4-9 3.3 Performance of the Layer Model f o r E s t i m a t i n g Ki (MJ m" 2day - : L) at Vancouver f o r a 10$ Random Sample of Days During 1968-70 . . . . 56 3.4 E x t r a p o l a t i o n E r r o r s from S o l a r R a d i a t i o n Measurements 59 3.5 Flow Diagram of the Approaches Taken i n the Laye r and CLS Models 6l 3.6 The I n i t i a l Three P a r t s f o r the C a l c u l a t i o n of the D i f f u s e S o l a r R a d i a t i o n Component i n the CLS Model 64 3.7 Root Mean Square E r r o r s (%) on a D a i l y B a s i s f o r the Layer and CLS S o l a r R a d i a t i o n Models During 1968-70 71 3."8 Performance of the CLS 1,1 Model f o r E l l i m l t i n g Ki (MJ m" 2day _ 1) a t Vancouver f o r a iOfo Random Sample of Days During 1968-70 . 72 3.9 Root Mean Square E r r o r s (%) "for Various A veraging P e r i o d s f o r the CLS 2,1 S o l a r R a d i a t i o n Model During 1968-70 78 x i i i F i g u r e Page 3.10 A v a i l a b l e S o l a r R a d i a t i o n Network i n Canada (as of January 1, 1976) 81 4.1 The 113 P o i n t Data G r i d f o r B r i t i s h Columbia and the Adjacent Areas of the P a c i f i c Ocean 89 5-1 R e l a t i o n s h i p s o f R e g r e s s i o n C o e f f i c i e n t b' to S t a t i o n E l e v a t i o n f o r u^ Versus u ^ A n a l y s i s 106 5.2 R e l a t i o n s h i p of R e g r e s s i o n C o e f f i c i e n t b to S t a t i o n E l e v a t i o n f o r u^ Versus u ^ A n a l y s i s 107 5.3 P r e c i p i t a b l e Water D i s t r i b u t i o n Averaged f o r 1963-72 f o r B.C. and the Adjacent Areas of the P a c i f i c Ocean 112 6.1 S o l a r R a d i a t i o n Measuring and M o d e l l i n g S t a t i o n s i n the B r i t i s h Columbia Area . . . 120 6.2 D i f f e r e n c e Between Mean D a i l y S o l a r R a d i a t i o n Values f o r Months i n 1972 Compared to the Long-term Average 123 6.3 Mean D a i l y Values of S o l a r R a d i a t i o n -2 -1 (MJ m day" ) i n B r i t i s h Columbia During 1972 133 6.4 Mean Percentage S o l a r R a d i a t i o n T r a n s m i s s i o n i n B r i t i s h Columbia During 1972 135 6.5 Average D a i l y S o l a r R a d i a t i o n T r a n s m i s s i o n (fo) During 1972 137 6.6 Mean D a i l y Values of S o l a r R a d i a t i o n -2 -1 (MJ m day ) i n B r i t i s h Columbia During January 1972 139 6.7 Mean D a i l y Values of S o l a r R a d i a t i o n -2 -1 (MJ m day ) i n B r i t i s h Columbia During A p r i l 1972 140 6.8 Mean D a i l y Values of S o l a r R a d i a t i o n -2 -1 (MJ m~ day ) i n B r i t i s h Columbia During J u l y 1972 141 x i v F i g u r e Page 6.9 Mean D a i l y Values of S o l a r R a d i a t i o n -2 -1 (MJ m day ) i n B r i t i s h Columbia During October 1972 142 6.10 R e l a t i v e E x t r a p o l a t i o n E r r o r s from S o l a r R a d i a t i o n Measurements 145 6.11 S o l a r R a d i a t i o n S p a t i a l Coverage i n the B r i t i s h Columb i a Area f o r a +15% E r r o r T olerance ' ~ 148 6.12 S o l a r R a d i a t i o n S p a t i a l Coverage i n the B r i t i s h Columbia Area f o r a +25% E r r o r T olerance ~. 149 ' 7.1 Absolute E x t r a p o l a t i o n E r r o r s from S o l a r R a d i a t i o n Measurements f o r S e l e c t e d S y n o p t i c Types 168 7.2 R e l a t i v e E x t r a p o l a t i o n E r r o r s from S o l a r R a d i a t i o n Measurements f o r Ocean High S y n o p t i c Types 170 7.3 R e l a t i v e E x t r a p o l a t i o n E r r o r s from S o l a r R a d i a t i o n Measurements f o r Land High Sy n o p t i c Types 171 7.4 R e l a t i v e E x t r a p o l a t i o n E r r o r s from S o l a r R a d i a t i o n Measurements f o r Ridge Synoptic Types 172 7.5 R e l a t i v e E x t r a p o l a t i o n E r r o r s from S o l a r R a d i a t i o n Measurements f o r Trough Synoptic Types . . 173 7.6 R e l a t i v e E x t r a p o l a t i o n E r r o r s from S o l a r R a d i a t i o n Measurements f o r Ocean Low Syno p t i c Types 174 7.7 R e l a t i v e E x t r a p b ^ l a t d ' o n i C E r r o r s f f e o m S S o l a r R a d i a t i o n Measurements f o r Types With Low S p a t i a l V a r i a b i l i t y 177 7.8 Mean D a i l y T o t a l S o l a r R a d i a t i o n -2 -1 (MJ m day ) f o r January and J u l y During 1963-72 184 , XV LIST OF SYMBOLS Symbol D e s c r i p t i o n [ t y p i c a l u n i t s i n b r a c k e t s ] a Haurwitz c l o u d t r a n s m i s s i o n c o e f f i c i e n t [KJ m~ h~ ] a 1 p r e c i p i t a b l e water i n t e r c e p t term i n equation (5»^) [mm] A weighting f a c t o r f o r cl o u d i n CLS model Ac Altocumulus c l o u d Ac,c Altocumulus C a s t e l l a n u s c l o u d As A l t o s t r a t u s cloud b Haurwitz cloud t r a n s m i s s i o n c o e f f i c i e n t b' p r e c i p i t a b l e water r e g r e s s i o n c o e f f i c i e n t i n equation (5«^) b p r e c i p i t a b l e water r e g r e s s i o n c o e f f i c i e n t through the o r i g i n i n equation (5«5) B wei g h t i n g f a c t o r f o r sunshine i n CLS model Cb Cumulonimbus cl o u d Cc Cirrocumulus c l o u d C i C i r r u s c l o u d Cs , C i r r o s t r a t u s c l o u d Cu Cumulus cloud Cu++ heavy Cumulus cl o u d CLS cloud l a y e r - sunshine - da dust or a e r o s o l a b s o r p t i o n ds dust or a e r o s o l s c a t t e r i n g D d i s t a n c e between s t a t i o n p a i r i n g s [km] Di d i f f u s e s o l a r r a d i a t i o n on a h o r i z o n t a l s u r f a c e BAT m"2, KJ m~ 2h" 1, MJ m " 2 d a y - 1 ] s x v i Symbol D e s c r i p t i o n [ t y p i c a l u n i t s i n b r a c k e t s ] D* d i f f u s e s o l a r r a d i a t i o n on a h o r i z o n t a l s u r f a c e 0 under c l o u d l e s s c o n d i t i o n s [ w m-2 f R J m - 2 h ~ l f M J ^ d a y - 1 ] D i ^ d i f f u s e s o l a r r a d i a t i o n from C i r r i f o r m p a r t o f the s k y [W m~2, K J m" 2h" 1, MJ m " 2 d a y - 1 ] D^ c s d i f f u s e s o l a r r a d i a t i o n from c l o u d l e s s p a r t of the s k y [W m - 2, K J m""2h_1, MJ m " 2 d a y _ 1 ] Di d i f f u s e s o l a r r a d i a t i o n from the c l o u d y p a r t of t h e sky cy [W m~2, K J m" 2h" 1, MJ m " 2 d a y _ 1 ] ^*mr d i f f u s e s o l a r r a d i a t i o n t h a t i s m u l t i p l y r e f l e c t e d [W m - 2, K J m" 2h _ 1, MJ m " 2 d a y - 1 ] D^ c l o u d l e s s s k y m u l t i p l y r e f l e c t e d d i f f u s e s o l a r r a d i a t i o n [W m~2, K J m ^ h - 1 ] MJ m ~ 2 d a y _ 1 ] D^ D^ f o r d u s t - f r e e atmosphere [w m"2, K J m~ 2h~ 1, MJ m ~ 2 d a y _ 1 ] D c l o u d l e s s s k y d i f f u s e s o l a r r a d i a t i o n s c a t t e r e d f r om t h e d i r e c t beam r,„, -2 V T -2,-1 M T -2, -In |_W m , K J m h , MJ m day J D D o f o r d u s t - f r e e atmosphere [w m~2, K J m" 2h _ 1, MJ m~ 2day _ : L] e a c t u a l vapour p r e s s u r e [ k P a ] e s a t u r a t e d vapour p r e s s u r e [ k P a ] E^ e x p e cted s y n o p t i c t y p e f r e q u e n c y F F - r a t i o s t a t i s t i c Fc Cumulus f r a c t u s c l o u d Fs S t r a t u s f r a c t u s c l o u d g a c c e l e r a t i o n due t o g r a v i t y Cm s ~ 2 ] I s o l a r c o n s t a n t [ l353 W m ] k a e r o s o l o r d u s t parameter i n e q u a t i o n (2.12) K a e r o s o l o r d u s t parameter i n e q u a t i o n (2.9) x v i i Symbol D e s c r i p t i o n [ t y p i c a l u n i t s i n b r a c k e t s ] K l t o t a l s o l a r r a d i a t i o n on a h o r i z o n t a l s u r f a c e [W m~2, K J m" 2h _ 1, MJ m " 2 d a y _ 1 ] K l t o t a l s o l a r r a d i a t i o n on a h o r i z o n t a l s u r f a c e under c l o u d l e s s c o n d i t i o n s rT„, -2 V T -2,-1 ,ffX -2, - I n LW m , K J m h , MJ m day J K l K; f o r d u s t - f r e e atmosphere [w m~2, K J m~ 2h~ 1, MJ m ~ 2 d a y - 1 ] m o p t i c a l a i r mass m r e p r e s e n t s - m i s s i n g d a t a group i n s y n o p t i c a n a l y s i s m^ r e l a t i v e o p t i c a l a i r mass MS^ mean squares between s y n o p t i c t y p e s MS w mean squares w i t h i n s y n o p t i c t y p e s n t o t a l c l o u d amount n^^ c i r r i f o r m c l o u d amount n e f f e c t i v e c l o u d amount f o r d i r e c t s o l a r r a d i a t i o n e n^ c l o u d l a y e r amount n | r e p o r t e d c l o u d l a y e r amount u n c o r r e c t e d f o r o b s t r u c t i o n n g sum of c l o u d amount e x c l u d i n g c i r r i f o r m as seen from the s u r f a c e n sum of r e p o r t e d c l o u d amount beneath a g i v e n l a y e r N number of p a i r i n g s Ns N i m b o s t r a t u s c l o u d CK observed s y n o p t i c type f r e q u e n c y p s t a t i o n a t m o s p h e r i c p r e s s u r e [ k P a ] P X g e n e r a l p r o b a b i l i t y of an event P. p r o b a b i l i t y event w i l l o c c u r a f t e r occurence on p r e v i o u s day x v i i i Symbol D e s c r i p t i o n [ t y p i c a l u n i t s i n b r a c k e t s ] r mixing r a t i o [g kg-"'"] r c o r r e l a t i o n c o e f f i c i e n t f o r s t a t i s t i c a l analyses r ^ c o e f f i c i e n t of p e r s i s t e n c e r c o e f f i c i e n t of s o l a r r a d i a t i o n v a r i a b i l i t y ( i n r e l a t i v e terms) r x y product moment l i n e a r c o r r e l a t i o n c o e f f i c i e n t r s R a y l e i g h or molecular s c a t t e r i n g R-g Besson's c o e f f i c i e n t of p e r s i s t e n c e RH r e l a t i v e humidity RMSE r o o t mean square e r r o r s t o t a l b r i g h t sunshine amount f o r the hour SI d i r e c t s o l a r r a d i a t i o n on a h o r i z o n t a l s u r f a c e [W m"2, KJ m" 2h _ 1, MJ m~ 2day~ 1] SI d i r e c t s o l a r r a d i a t i o n on a h o r i z o n t a l s u r f a c e 0 under c l o u d l e s s c o n d i t i o n s r v , -2 V T -2,-1 M T -2, - l - i [_W m , KJ m h , MJ ra day J Si' Sj.refor d u s t - f r e e atmosphere [w m"2, KJ m" 2h _ 1, MJ m~ 2day" 1] SI d i r e c t s o l a r r a d i a t i o n u n c o r r e c t e d f o r c i r r i f o r m a t t e n u a t i o n [ w m - 2 > K J m - 2 h - l f M J m - 2 d a y - l - | Sc Stratocumulus cloud S D standard d e v i a t i o n SD standard d e v i a t i o n SE standard e r r o r S t S t r a t u s c l o u d t s t a t i s t i c f o r T - t e s t t ^ ^ c i r r i f o r m c l o u d t r a n s m i s s i v i t y t . c loud t r a n s m i s s i v i t y x i x Symbol D e s c r i p t i o n [ t y p i c a l u n i t s i n b r a c k e t s ] T s o l a r r a d i a t i o n t r a n s m i s s i o n through the atmosphere u p r e c i p i t a b l e water [mm] u~ p r e c i p i t a b l e water from 3 l e v e l s (85, 70,and 50 kPa) [mm] u ^ p r e c i p i t a b l e water from 11 l e v e l radiosonde ascent [mm] U u n c l a s s i f i e d s y n o p t i c type group wa water vapour a b s o r p t i o n ws water vapour s c a t t e r i n g mean d i f f e r e n c e between p a i r s of p o i n t s Z s o l a r z e n i t h angle a s u r f a c e albedo a c c l o u d base albedo (XQ^ c i r r i f o r m c l o u d base albedo U d a t r a n s m i s s i o n f u n c t i o n a f t e r a e r o s o l or dust a b s o r p t i o n Udab U d a ^ o r d i f f u s e s°lar r a d i a t i o n U d s t r a n s m i s s i o n f u n c t i o n a f t e r a e r o s o l or dust s c a t t e r i n g U d s b U d s f o r d i f f ' 1 1 3 6 s o l a r r a d i a t i o n d d da ds D D da ds atmospheric l a y e r t r a n s m i s s i o n f u n c t i o n w i t h cloud atmospheric l a y e r t r a n s m i s s i o n f u n c t i o n through cloudy p o r t i o n of the sky only ( i n CLS model) U t r a n s m i s s i o n f u n c t i o n a f t e r R a y l e i g h or molecular s c a t t e r i n g U r s b U r s "^ o r d i f f u s e s o l a r r a d i a t i o n XX Symbol D e s c r i p t i o n [ t y p i c a l u n i t s i n b r a c k e t s ] U t r a n s m i s s i o n f u n c t i o n a f t e r water vapour a b s o r p t i o n wa U , U f o r d i f f u s e s o l a r r a d i a t i o n wab wa U t r a n s m i s s i o n f u n c t i o n a f t e r water vapour s c a t t e r i n g ws U , U f o r d i f f u s e s o l a r r a d i a t i o n wsb ws xx i ACKNOWLEDGEMENTS I would l i k e to thank my s u p e r v i s o r , Dr. John E. Hay, f o r h i s a s s i s t a n c e and advice throughout a l l aspects of t h i s study. The comments and suggestions of the members of my examining committee, e s p e c i a l l y those of Dr. Timothy R. Oke and Dr. M i c h a e l Church, are g r a t e f u l l y acknowledged. I a l s o wish to acknowledge the t e c h n i c a l a s s i s t a n c e of some of my graduate student c o l l e a g u e s . Support f o r t h i s p r o j e c t was r e c e i v e d from the Atmospheric Environment S e r v i c e of Canada, the N a t i o n a l Research C o u n c i l of Canada and the Environment and Land Use Committee S e c r e t a r i a t of B r i t i s h Columbia. The author was f i n a n c i a l l y a s s i s t e d by the H.R. MacMi l l a n F a m i l y F e l l o w s h i p from the U n i v e r s i t y of B r i t i s h Columbia. I would a l s o l i k e to thank C h e r y l f o r her enc ouragement. 1 CHAPTER 1 INTRODUCTION 1.1 GENERAL INTRODUCTION Rec e n t l y , i n t e r e s t i n the s p a t i a l and. temporal d i s t r i b u t i o n of s o l a r r a d i a t i o n has i n c r e a s e d d r a m a t i c a l l y p r i m a r i l y as a consequence of the i n c r e a s e d i n t e r e s t i n the p o t e n t i a l u t i l i z a t i o n of s o l a r energy. S o l a r r a d i a t i o n i n f o r m a t i o n i s needed f o r v i r t u a l l y any l o c a t i o n where a s o l a r energy system i s to be b u i l t . The t o t a l s o l a r r a d i a t i o n (Ki) a v a i l a b l e on a h o r i z o n t a l s u r f a c e i s g e n e r a l l y measured with a pyranometer. Although i n some p a r t s of the world there are r e l a t i v e l y dense networks of these sensors (e.g. Japan and western Europe), the o v e r a l l g l o b a l s p a t i a l coverage i s sparse (Lof et a l , 1966; Thekaekara, 1976). Thekaekara (1976) has c a l c u l a t e d t h a t there i s one s o l a r r a d i a t i o n measuring s t a t i o n f o r every 1.5 X 10^ km of l a n d s u r f a c e m the world and he concluded t h a t t h i s i s inadequate f o r s o l a r energy purposes. In Canada, the m e t e o r o l o g i c a l network c o n s i s t e d of only 51 s t a t i o n s measuring Ki as of January 1, 1976 (Atmospheric Environment S e r v i c e , 1976) which r e p r e s e n t s < 2 one s t a t i o n f o r every 2.0 X 10^ km . In B r i t i s h Columbia, only n i n e s t a t i o n s measure Ki c o n s t i t u t i n g a d e n s i t y of 5 2 one l o c a t i o n per 1.0 X 10^ km . 2 This solar r a d i a t i o n monitoring network is inadequate fo r solar energy f e a s i b i l i t y studies. In order to provide supplemental data to this measurement network and a t t a i n a s a t i s f a c t o r y description of the s p a t i a l character of solar radiation, Hay ( 1 9 7 5 ) concluded that numerical modelling of solar r a d i a t i o n u t i l i z i n g r e a d i l y available meteorological data must be employed i n Canada. This i s e s p e c i a l l y evident i n B r i t i s h Columbia where mountainous topography increases the s p a t i a l v a r i a b i l i t y of solar r a d i a t i o n . The t o t a l solar r a d i a t i o n on a horizontal surface can be expressed as: Kl = SI + DI ( 1 . 1 ) where Si i s the d i r e c t solar radiation, which i s that portion coming to the surface d i r e c t l y from the solar disc,' and DI i s the d i f f u s e solar radiation, which i s the solar r a d i a t i o n scattered by the atmosphere and received at the surface from the sky hemisphere. In Canada, there are currently only four stations which measure the diffuse solar r a d i a t i o n on a routine basis and none measuring the d i r e c t component (Atmospheric Environment Service, 1 9 7 6 ) . Again, an a l t e r n a t i v e to measurements is to obtain values of.these components from"numerical models. For solar energy studies, knowledge of the solar 3 r a d i a t i o n a v a i l a b l e on s l o p i n g s u r f a c e s i s needed s i n c e s o l a r c o l l e c t o r s are seldom h o r i z o n t a l l y p l a c e d ( D u f f i e and Beckman, 1974). In the absence of s o l a r r a d i a t i o n measurements on s l o p e d s u r f a c e s , values must be c a l c u l a t e d and t h i s r e q u i r e s knowledge of the separate d i r e c t and d i f f u s e components of the t o t a l s o l a r r a d i a t i o n on a h o r i z o n t a l s u r f a c e (Kondratyev, 1969; G a r n i e r and Ohmura, 1970; Hay, 1976a). Knowledge of the d i r e c t componentids a l s o needed f o r the study of the o v e r a l l thermal performanc of b u i l d i n g s (Cole, 19?6). In a d d i t i o n to i n f o r m a t i o n on a c t u a l r a d i a t i v e v a l u e s , i t may be advantageous to g a i n knowledge about the temporal and s p a t i a l behaviour of s o l a r r a d i a t i o n f l u x e s . Vowinckel and O r v i g (1969a), Jacobs (1973) and A l t (1975) have taken a s y n o p t i c approach i n s t u d y i n g the energy budgets of Canadian a r c t i c environments. This i n v o l v e d a n a l y s i n g s y n o p t i c - s c a l e m e t e o r o l o g i c a l events and r e l a t i n g them to changes i n the r a d i a t i o n and energy balance terms. These r e s e a r c h e r s concluded t h a t s y n o p t i c -s c a l e events e x e r c i s e d important c o n t r o l over the e n e r g e t i c of the environments under study. S i n c e s o l a r r a d i a t i o n i s an important term i n the energy balance, i t may be u s e f u l to take such a s y n o p t i c approach f o r the study of s o l a r r a d i a t i o n i n order to p r o v i d e a b a s i s f o r the a n a l y s i s of the s p a t i a l and temporal behaviour of s o l a r r a d i a t i o n d i s t r i b u t i o n s . 4 1.2 SPECIFIC OBJECTIVES v The s p e c i f i c o b j e c t i v e s of t h i s t h e s i s are: (1) To t e s t and f u r t h e r develop a t h e o r e t i c a l l y based numerical model f o r the e s t i m a t i o n of d i r e c t , d i f f u s e r and t o t a l s o l a r r a d i a t i o n under c l o u d l e s s c o n d i t i o n s ; (2) To t e s t and f u r t h e r develop a numerical model f o r the e s t i m a t i o n of d i r e c t , d i f f u s e and t o t a l s o l a r r a d i a t i o n under a c t u a l sky c o n d i t i o n s ; (3) To apply the s o l a r r a d i a t i o n models to B r i t i s h Columbia and to assess the r e l a t i v e merits of such a n u m e r i c a l approach; (4) To r e l a t e s o l a r r a d i a t i o n to s y n o p t i c weather types f o r the B r i t i s h Columbia area i n order to e s t a b l i s h s y n o p t i c s o l a r r a d i a t i o n regimes, to assess numerical m o d e l l i n g of s o l a r r a d i a t i o n w i t h i n a s y n o p t i c framework and to assess the p o t e n t i a l a p p l i c a b i l i t y of t h i s s y n o p t i c approach to the study of s o l a r r a d i a t i o n i n B r i t i s h Columbia. 1.3 ARRANGEMENT OF THIS THESIS In chapter 2, a c l o u d l e s s sky s o l a r r a d i a t i o n model based on the o r i g i n a l work of Houghton (195^) i s t e s t e d f o r three Canadian l o c a t i o n s . M o d i f i c a t i o n s n e c e s s a r y to improve estimates of the d i r e c t and d i f f u s e components of the t o t a l s o l a r r a d i a t i o n are determined and the performance of t h i s m o d i f i e d model evaluated. The 5 s e n s i t i v i t y of t h i s c l o u d l e s s sky s o l a r r a d i a t i o n model to i t s m e t e o r o l o g i c a l input parameters of pr e s s u r e , albedo and p r e c i p i t a b l e water i s analysed and the model i s f u r t h e r t e s t e d f o r l o c a t i o n s i n B r i t i s h Columbia. In chapter 3» "the e f f e c t s of cloud are i n c o r p o r a t e d i n t o the model. I n i t i a l l y , a p r e v i o u s l y developed cloud l a y e r model (Nunez et a l , 1971; Davies et a l , 1975) i s d e s c r i b e d and i t s performance assessed. As an e x t e n s i o n of t h i s model, a new cloud l a y e r - sunshine (CLS) model i s developed i n order to c a l c u l a t e the d i r e c t and d i f f u s e components of the t o t a l s o l a r r a d i a t i o n s e p a r a t e l y and to improve the estimates of the t o t a l f l u x . The p o t e n t i a l a p p l i c a b i l i t y of t h i s CLS model to Canada i s d i s c u s s e d . In order to study s o l a r r a d i a t i o n from a s y n o p t i c viewpoint, s y n o p t i c weather types must be e s t a b l i s h e d f o r the r e g i o n under c o n s i d e r a t i o n . In chapter 4, an o b j e c t i v e c o r r e l a t i o n c l a s s i f i c a t i o n technique i s d e s c r i b e d and subsequently a p p l i e d to B r i t i s h Columbia and the adjacent areas o f - t h e P a c i f i c Ocean i n order to e s t a b l i s h s y n o p t i c weather types f o r the r e g i o n . These are describedaand t h e i r frequency, p e r s i s t e n c y and sequence are analysed. Before a p p l y i n g the s o l a r r a d i a t i o n model to B r i t i s h Columbia, p r e c i p i t a b l e water f i e l d s must be e s t a b l i s h e d f o r the area s i n c e p r e c i p i t a b l e water i s one of the input parameters to the c l o u d l e s s sky model. Chapter 5 presents the procedures f o r p r e c i p i t a b l e water 6 c a l c u l a t i o n and, u s i n g the synoptic weather types, p r e c i p i t a b l e water d i s t r i b u t i o n s are e s t a b l i s h e d . In chapter 6, the CLS s o l a r r a d i a t i o n model i s a p p l i e d to the B r i t i s h Columbia area f o r the year 1972. The performance of the model i s f u r t h e r analysed and the annual and seasonal s o l a r r a d i a t i o n d i s t r i b u t i o n s are discussed. The advantage of modelling s o l a r r a d i a t i o n i s a l s o assessed. The r e l a t i o n s h i p of s o l a r r a d i a t i o n to synoptic weather types i s analysed i n chapter 7. Synoptic s o l a r r a d i a t i o n regimes f o r the B r i t i s h Columbia area are e s t a b l i s h e d and described. The n e c e s s i t y f o r measuring and modelling s o l a r r a d i a t i o n i s evaluated i n terms of the synoptic weather types. F i n a l l y , the p o t e n t i a l a p p l i c a b i l i t y of these synoptic s o l a r r a d i a t i o n regimes i s discussed. 7 CHAPTER 2 SOLAR RADIATION MODEL FOR CLOUDLESS CONDITIONS 2 . 1 INTRODUCTION S o l a r r a d i a t i o n under c l o u d l e s s c o n d i t i o n s can be modelled n u m e r i c a l l y u s i n g standard s y n o p t i c weather data. Based on the o r i g i n a l work of Houghton ( 1 9 5 ^ ) > s e v e r a l r e s e a r c h e r s have developed and u t i l i z e d a simple model f o r the e s t i m a t i o n of s o l a r r a d i a t i o n i n c i d e n t on a h o r i z o n t a l s u r f a c e under c l u d l e s s s k i e s (Monteith, 1 9 6 2 ; Idso, 1 9 6 9 , 1 9 7 0 ; Hay, 1 9 7 0 a ; Nunez, 1 9 7 4 ; Davies et a l , . 1 9 7 5 ) * F o r monthly and d a i l y t o t a l s , the model was shown to perform w e l l i n these s t u d i e s . In t h i s chapter, the performance of the Houghton model f o r e s t i m a t i n g s o l a r r a d i a t i o n a t th r e e Canadian l o c a t i o n s on an h o u r l y and d a i l y b a s i s w i l l be examined. M o d i f i c a t i o n s r e q u i r e d to o b t a i n reasonable estimates of the d i r e c t and d i f f u s e components as w e l l as the t o t a l s o l a r r a d i a t i o n w i l l be presented and the s e n s i t i v i t y of the model t o some of the input parameters w i l l be examined. F i n a l l y , the performance of the r e v i s e d model w i l l be t e s t e d on independent data from three a d d i t i o n a l l o c a t i o n s i n B r i t i s h Columbia. 8 2 . 2 THE HOUGHTON MODEL 2 . 2 . 1 D e s c r i p t i o n On c l o u d l e s s days, s o l a r r a d i a t i o n i n c i d e n t upon a h o r i z o n t a l s u r f a c e a t the bottom of the atmosphere ( K i Q ) i s merely the r e s i d u a l of the s o l a r r a d i a t i o n on a s i m i l a r s u r f a c e at the top of the atmosphere a f t e r d e p l e t i o n by atmospheric a b s o r p t i o n and s c a t t e r i n g . These a b s o r p t i o n and s c a t t e r i n g processes (see F i g . 2 . 1 ) i n c l u d e m o l e c u l a r (Rayleigh) s c a t t e r i n g ( r s ) , water vapour a b s o r p t i o n (wa), a e r o s o l or dust a b s o r p t i o n (da), water vapour s c a t t e r i n g (ws) and a e r o s o l or dust s c a t t e r i n g ( d s ) . As shown i n pr e v i o u s s t u d i e s (Idso, 1 9 6 9 ; Hay, 1 9 7 0 a ; Davies et a l , 1975)» "the d i r e c t beam s o l a r r a d i a t i o n under c l o u d l e s s s k i e s ( S l Q ) at the s u r f a c e can be expressed as: Si = I cos Z U U, U V, ii , ( 2 . 1 ) o o wa da ws ds r s ' v ' - 2 where I i s the s o l a r constant ( l 3 5 3 W f e ~ , Thekaekara and Drummond, 1 9 7 1 ) . Z i s the s o l a r z e n i t h angle (and t h e r e f o r e I Q c o s Z i s the e x t r a t e r r e s t r i a l r a d i a t i o n ) and the U terms are t r a n s m i s s i o n f u n c t i o n s a f t e r a b s o r p t i o n by waterovapoursand a e r o s o l or dust, and s c a t t e r i n g by water vapour, a e r o s o l or dust and a i r ittoleculoG 9 F I G . 2.1 D e p l e t i o n Processes i n a C l o u d l e s s Atmosphere solar beam wa •top of atmosphere 10 molecules ( R a y l e i g h s c a t t e r i n g ) r e s p e c t i v e l y . Houghton (195^) assumed t h a t a b s o r p t i o n of the s o l a r beam occurred b e f o r e s c a t t e r i n g and h a l f of the a e r o s o l or dust d e p l e t i o n was due to a b s o r p t i o n . T h i s procedure w i l l be adopted here. The s c a t t e r e d p o r t i o n of the d i r e c t beam r e a c h i n g the s u r f a c e (D ) can be expressed as f o l l o w s , assuming s t h a t h a l f of the s c a t t e r e d s o l a r r a d i a t i o n reaches the s u r f a c e : D = 0.5 I cos Z U U, ( 1 - U U , U ) . (2.2) s y o wa da ws ds r s F o l l o w i n g Hay (1970a), an a d d i t i o n a l term r e p r e s e n t i n g the f i r s t order component of the m u l t i p l y r e f l e c t e d s o l a r r a d i a t i o n (D^) can be added ass D b * a ( S ; o + D s ) Uwab Udab( 1 ~ U w s b U d s b U r s b ^ ^ where a i s the s u r f a c e r e f l e c t i o n c o e f f i c i e n t or albedo and the b s u b s c r i p t s i n the U terms r e p r e s e n t the t r a n s m i s s i o n f u n c t i o n s f o r d i f f u s e r a d i a t i o n where the o p t i c a l a i r mass m = 1.66 (Hay, 1970a). The incoming d i f f u s e r a d i a t i o n under c l o u d l e s s s k i e s ( D * Q ) i s then the sum D * o = D s - r D b , (2.4) 11 and the t o t a l s o l a r r a d i a t i o n i s the sum of the d i r e c t and d i f f u s e components: K i = SI + D* . (2.5) O 0 0 The t r a n s m i s s i o n f u n c t i o n s used i n t h i s study-were : U = 0.972 - 0.08262m + 0.00933m 2 - 0.00095m 3 + O.OOOO^m"*, (2.6) U = 1 - 0.0225mu, (2.7) ws U = 1 - 0.077(mu) 0- 3, (2.8) wa a n d UD = U d a U d s = ^ ( 2 - 9 ) a. where m i s the o p t i c a l a i r mass, u i s p r e c i p i t a b l e water i n mm and K i s an a e r o s o l or dust parameter. The f o r m u l a t i o n s f o r and U w s are from Houghton's o r i g i n a l curves as gi v e n "by Davies et a l ( 1 9 7 5 ) • O p t i c a l a i r mass i s most c o n v e n i e n t l y c a l c u l a t e d f o r h o u r l y p e r i o d s u s i n g the method of Kasten (1966) f o r r e l a t i v e o p t i c a l a i r mass, m^: 12 r m r (Z) = 1 / Q c o s Z + '0.15,(93.885-Z)" 1 , 2 5 3], (2.10) and then c o r r e c t e d f o r s t a t i o n p r e s s u r e , p ( i n fcP-a), as: . m (Z) p m ( z ) = I § I T | 2 5 ' ( 2 - n ) The f o r m u l a t i o n f o r i s that proposed by McDonald (i960) and subsequently used by Idso (1969)1 Hay (1970a) and Davies et a l (1975). "the a e r o s o l or dust term, Houghton (195^) assumed e q u a l i t y between and such t h a t U = n = k m, (2.12) da ds where the a e r o s o l parameter k was g i v e n the value of 0.975 which corresponds to K = 0.95 i n equation (2.9). 2.2.2 Performance H o u r l y m e t e o r o l o g i c a l data a v a i l a b l e from the Atmospheric Environment S e r v i c e of Canada were analysed f o r each of the f o l l o w i n g l o c a t i o n s : Goose, N f l d . , P o r t Hardy, B.C. and Edmonton, A l t a . The a v a i l a b l e p e r i o d of r e c o r d i s i n d i c a t e d i n Table 2.1. These s t a t i o n s were chosen as a consequence of the a v a i l a b i l i t y of h o u r l y 13 TABLE 2 . 1 P e r i o d s of A v a i l a b l e D a t a Record f o r ' C l o u d l e s s Days' Study L a t i t u d e : Goose P o r t Hardy Edmonton 53°19' N 5 0 ° 4 l ' N 5 3 ° 3 V N L o n g i t u d e : 6 0 ° 2 5 ' W 1 2 7 ° 2 2 ' W 113 3 1 ' W P e r i o d of a v a i l a b l e 1964-1975 1968-1972 1960-1971 d a t a r e c o r d : 14 surface and solar r a d i a t i o n data and twice d a i l y upper a i r data and because of a desire f o r locations representative of contrasting atmospheric environments. Days with cloudless skies during the daylight periods were i d e n t i f i e d with allowance f o r up to four hourly, observations of one tenth cloud cover i n a day being accepted as 'cloudless'.' Table 2.2 l i s t s the days u t i l i z e d £o.rh'riiodelr.ocl",l development' and subsequent 'independent test i n g ' i n section 2.3.4. Input parameters to the model were assigned using the following procedures. The values of the e x t r a t e r r e s t r i a l r a d i a t i o n were calculated using the solar climate calculator program of Furnival et a l (1970). For the surface albedo, S e l l e r s (1965) l i s t s values f o r natural surfaces ranging from 0.10 to 0.30 f o r green meadows and dry Savanna while Monteith (1973) gives values ranging from 0.14 to 0.25 f o r natural vegetation. For fresh snow, S e l l e r s (19^5) gives values of a ranging from 0.75 "to 0.95 and Korff and Vonder Haar (1972) obtained values f o r the albedo of snow ranging from 0.74 to 0.89. On the basis of t h i s information, a i n equation (2.3) was assumed to be 0.2 with no snow and 0.8 with snow. The hourly r a d i a t i o n data source also indicated the presence or absence of snow. An average d a i l y value of pressure 15 TABLE 2.2 Cloudless Days U t i l i z e d f o r Study Model Development: Goose Jan. 8 1964 Jan. 19 1964 Mar. 11 1964 Mar. 14 1964 Apr. 20 1964 Jan. 24 1965 Jan. 6 1966 Mar. 18 I966 May 17 1966 Jan. 24 1967 Feb. 3 I967 Apr. 7 1967 Dec. 11 1967 Jan. 31 1968 Mar. 21 I968 Independent T e s t i s Goose Jan. 6 1969 Feb. 24 1969 Feb. 26 1969 Feb. 27 1969 Feb. 17 1971 Feb. 23 1971 Feb. 20 1973 Mar. 2 1973 Jan. 26 1974 Mar. 9 197^ Apr. 28 197^ Feb. 22 1975 Port Hardy Jan. 26 1968 Feb. 9 1968 Feb. 12 1968 Feb. 15 1968 Feb. 27 1968 Mar. 6 1969 Mar. 10 I969 Mar. 11 I969 Oct. 13 I969 Jan. 16 1970 Mar. 1 1970 Mar. 9 1970 July 27 1971 July 29 1971 Oct. 27 1971 Port Hardy May 6 1972 Oct. 12 1972 Oct. 16 1972 Nov. 15 1972 Dec. 3 1972 Edmonton Aug. 9 i960 Nov. 27 I960 Mar. 18 1961 Sept.13 1961 Sept.14 1961 May 21 1963 May 22 1963 Sept.28 I963 Oct. 7 1964 Oct. 8 1964 Feb. 2 I965 Mar. 19 1965 Dec. 13 1965 Jan. 19 1966 May 6 I966 May 8 1966 Aug. 22 1966 Sept.17 1967 Edmonton Feb. 10 I968 May 19 1968 Nov. 7 1968 June 8 I969 Oct. 17 I969 Oct., 30 1970 Nov. 4 1970 Nov. 22 1970 May 12 1971 July 29 1971 16 was a p p l i e d i n equation (2.11). D a i l y p r e c i p i t a b l e water was c a l c u l a t e d by the method of Hay (1970b) (see s e c t i o n 5.1.1) u s i n g the average of the 0000 and 1200 h GMT radiosonde o b s e r v a t i o n s . Modelled values of s o l a r r a d i a t i o n were c a l c u l a t e d f o r h o u r l y p e r i o d s and summed to o b t a i n d a i l y t o t a l s f o r the f i r s t group of days ((Table 2 . 2(a)] f o r each l o c a t i o n . These h o u r l y and d a i l y t o t a l s were compared to measured v a l u e s , as r e p o r t e d i n the Monthly R a d i a t i o n Summary (Atmospheric Environment S e r v i c e , Toronto, Canada). I t should be noted t h a t the measured s o l a r r a d i a t i o n data f o r Edmonton were from Stony P l a i n (a r u r a l s i t e ) and the m e t e r o l o g i c a l o b s e r v a t i o n s were from the I n t e r n a t i o n a l A i r p o r t . These l o c a t i o n s are about 30 km a p a r t . Model -performance i s summarized i n Table 2.3 u s i n g both r e l a t i v e and a b s o l u t e v a l u e s of the r o o t mean square e r r o r and the average b i a s e r r o r . The l a t t e r i s c a l c u l a t e d as the average per cent d i f f e r e n c e between d a i l y measured and modelled v a l u e s . D a i l y performance i s shown i n F i g . 2.2. Since measurement e r r o r s f o r s o l a r r a d i a t i o n are commonly quoted as b e i n g about 5% of the measured f l u x (Davies et a l , 1970; Latimer, 1972), Table 2.3 i n d i c a t e s t h a t the performance of t h i s model f o r d a i l y t o t a l s of KJ i s good. In r e l a t i v e terms, e r r o r s of l e s s than 9% were found. Measured values of the d i f f u s e component of s o l a r 17 TABLE 2.3 Performance of the Unmodified Houghton Model f o r Model Development Days (a) D a i l y T o t a l s : Mean Root Mean Root Mean Average Measured Square E r r o r Square E r r o r fo B i a s L o c a t i o n feT - 2 , - 1 \ / M T - 2 , - 1 \ fT> . \ E r r o r (MJ m day ) (MJ m day ) (Percentage)  Goose Ki o 13.11 0.56 4 . 3 0.0 Goose S i o 10.07 O.76 7.5 b.7 Goose Di o 3.05 0.72 23.6 - 1 3 . 3 Edmonton K l o 17.77 1.45 8.2 - 0 . 9 P o r t Hardy Ki 13.25 0.97 7.3 4.9 (b) Hourly Values: Mean Root Mean ~, Root Mean Measured Square E r r o r Square E r r o r L o c a t i o n fej m'V1) (KJ m'V1) (Percentage) Goose K l 0 1307 7,5.3 5.8 Goose S 1 0 1003 92.9 9.3 Goose DI 0 304 73-^ 24 . 1 Edmonton K l 0 1519 13^.5 8.9 P o r t Hardy K l 0 1271 128 .5 10.1 FIG. 2.2 D a i l y P e r f o r m a n c e o f t h e U n m o d i f i e d H o u g h t o n M o d e l f o r C a l c u l a t i n g S o l a r R a d i a t i o n (MJ m " 2 d a y _ 1 ) f o r C l o u d l e s s Days G O O S E P O R T H A R D Y E D M O N T O N 30H o "S20-3 ; ° I C H 1 A — i — 10 — I — 20 — i — 30 M e a s u r e d K|. o 30 ^20 D 3 J J °10 u 10 20 30 Measured K| O 30 o "S20H 3 "510 H ,4 10 20 — i — 30 Measured K|, o oo 19 r a d i a t i o n were a v a i l a b l e only f o r Goose. The corresponding d i r e c t component i s c a l c u l a t e d as the d i f f e r e n c e between Ki and Di . As shown i n Table 2.3. d a i l y t o t a l s of S* o o o and Di were g e n e r a l l y over- and under-estimated, r e s p e c t i v e l y . In f a c t , Si was over-estimated on a l l but two days and Di under-estimated i n a l l but one case. The r o o t mean square e r r o r v a l u e s f o r these component f l u x e s were g e n e r a l l y l a r g e r than those f o r Ki . Given t h a t measurement e r r o r s f o r d i f f u s e s o l a r r a d i a t i o n are about -7% (Davies et a l , 1970), these r e s u l t s show t h a t the model's performance (RMSE of 23.6% f o r d a i l y t o t a l s ) i s not good when e s t i m a t i n g d i f f u s e s o l a r r a d i a t i o n . The d e v i a t i o n s between c a l c u l a t e d and measured values of Si and Di are l a r g e and t h e r e f o r e m o d i f i c a t i o n s are . o o n e c e s s a r y to improve model estimates of these components. 2.3 MODIFIED VERSION 2.3.1 D e t e r m i n a t i o n of the A e r o s o l Parameter The p a r t i t i o n i n g of s o l a r r a d i a t i o n between i t s d i r e c t and d i f f u s e components can be a f f e c t e d , i n p a r t , by a e r o s o l or dust s c a t t e r i n g and a b s o r p t i o n . Monteith (1962) and Unsworth and Monteith (1972) have shown t h a t a e r o s o l e f f e c t s vary s p a t i a l l y and i t was t h e r e f o r e d e s i r a b l e to o b t a i n v a l u e s of the a e r o s o l parameter k i n e q u a t i o n (2.12) f o r each l o c a l i t y . Assuming U d a = 20 (Houghton, 1954), the value of k was i n i t i a l l y evaluated f o r h o u r l y p e r i o d s at Goose by s o l v i n g f o r U d ( = u d a = u d s ) i n equation (2.1), S i . i U d = ( I cos Z U U U ) • ( 2 " i 3 ) u x o wa ws r s Then, k was evaluated as l/m • k = ( u d ) . - (2.14) The h o u r l y v a l u e s of k were weighted a c c o r d i n g to the i n c i d e n t S i Q when deter m i n i n g d a i l y mean v a l u e s . The average of these d a i l y values f o r the days i n Table 2.2(a) f o r Goose was O.965 with a range of 0.9^7 to 0.977- The c a l c u l a t e d v a l u e s of k are t h e r e f o r e g e n e r a l l y lower than the p r e v i o u s l y assumed value of 0.975- The use of the new value of k n a t u r a l l y leads to a-moreuaecurat^Iestimate of S i on an average while the d i f f u s e s o l a r r a d i a t i o n o 0 was s t i l l under-estimated and had only a s l i g h t l y lower - 2 -1 r o o t mean square e r r o r of 0.66 MJ m~ day" (compared to - 2 -1 the value of 0.72 MJ m day f o r the unmodified model). The unmodified Houghton model assumes t h a t forward- and b a c k - s c a t t e r i n g were equal and thus h a l f of the s c a t t e r e d s o l a r r a d i a t i o n reaches the ground as d i f f u s e s o l a r r a d i a t i o n . While t h i s i s t r u e of molecular 21 s c a t t e r i n g , s c a t t e r i n g by other a e r o s o l p a r t i c l e s i s d i r e c t e d p r e f e r e n t i a l l y forward (Robinson, I963K With k = O.965 f o r Goose, the r a t i o of forward- to b a c k - s c a t t e r i n g was v a r i e d i n order to determine the value which minimized the e r r o r i n the estimate of the d i f f u s e s o l a r r a d i a t i o n . Values of 0.6b forward- and GJ.M-0 b a c k - s c a t t e r i n g i n p l a c e of 0.5 i n equations (2.2) and (2.3). r e s p e c t i v e l y , tended to improve model accuracy. L e t t a u and L e t t a u (1969) have used values of forward- and b a c k - s c a t t e r i n g of 2/3 and l / 3 , which are not d i s s i m i l a r from the r e v i s e d values c o n s i d e r e d here. 2.3.2 Performance at Goose Table 2.4 shows the performance of t h i s m o d i f i e d v e r s i o n of the Houghton model f o r Goose. Compared with the unmodified model (Table 2.3). "the r e v i s e d model shows a s m a l l d e t e r i o r a t i o n i n K t e s t i m a t i o n . However, s u b s t a n t i a l improvement i s seen f o r both S i Q and D l Q . F i g . 2.3 i n d i c a t e s the improved performance of the m o d i f i e d model f o r e s t i m a t i n g d a i l y v a l u e s of c l o u d l e s s sky d i f f u s e s o l a r r a d i a t i o n at Goose. In s e c t i o n 2.3.4, t h i s m o d i f i e d model w i l l be f u r t h e r t e s t e d on independent data f o r Goose. 22 TABLE 2.4 Performance of the M o d i f i e d Houghton Model f o r Model Development Days at Goose ) ' D a i l y T o t a l s : Mean Root Mean Root Mean Average Measured Square E r r o r Square E r r o r $ Bia s (MJ rn^day-1) (MJ m^day" 1) (Percentage) E r r o r Kl 13.11 0.64 4.9 -2.1 o S* Q 10.07 0.51 5.1 -2.1 Di 3.05 0.48 15.7 -2 .9 ) Hourly Values: Mean Measured (KJ m"^" 1) Kl 1307 o S i Q 1003 D*„ 304 Root Mean Root Mean Square E r r o r Square E r r o r (KJ m-V1) (Percentage). 78.2 6.0 68.7 6.8 49.4 16.3 23 FIG. 2.3 - 2 -1 Measured and C a l c u l a t e d D i f f u s e S o l a r R a d i a t i o n (MJ m day" ) f o r C l o u d l e s s Days at Goose 6H 5H O u n m o d i f i e d m o d e l • m o d i f i e d m o d e l O 4^ o a 3 O U 24 1 H o •o o o m r» o 2 3 M e a s u r e d 0\o ~r 4 5 24 2.3• 3 C a l c u l a t i o n and. Performance at Edmonton and  P o r t Hardy In order to apply the m o d i f i e d Houghton model to s t a t i o n s without d i f f u s e s o l a r r a d i a t i o n data, a method f o r determining the a e r o s o l parameter k i n equation (2.12) from Ki r a t h e r than Si must be developed. For a d u s t - f r e e o o r atmosphere ( i n d i c a t e d by a prime i n the f o l l o w i n g e q u a t i o n s ) , S* * = I cos Z U U U , (2.115) 0 0 wa ws r s ' •J' D! = 0 . 6 I cos Z U ( 1 - U U ), ( 2 . 1 6 ) s 0 wa ws r s ' D' = a ( S i * +D') [ 0 . 4 li) . ( 1 - U ,U , ) J . ( 2 . 1 7 ) b o - s u wab wsb r s b -1 T h e r e f o r e , the values of the d u s t - f r e e c l o u d l e s s sky s o l a r r a d i a t i o n i s K i ' = S i ^ + D' + D£. (2.18) A combination of equations ( 2 . 4 ) , ( 2 . 5 ) and (2.18) can be used to d e r i v e a r a t i o X as Ki Si + D + D, y _ o _ o s b / ? 1 q x K* ' ~ S* * + D' + DI' v ^ . i y ; o o s b To f a c i l i t a t e computations, the m u l t i p l y r e f l e c t e d s o l a r 25 r a d i a t i o n was omitted. Therefore, S I + D o s ^ ^ S J 1 + D ' 1 (2.20) o s S u b s t i t u t i n g from equations (2.1), (2.2), (2.15) and (2.l6) i n t o equation (2.20), X . (I 0co S I « wAs Urs Ud + °- 6 lo o o s Z V U d - 0.6I ocos Z %^rA] / ( I o ° O S Z Uwa Uws Ur S + 0 . 6 l o o o S Z U w a - 0 . 6 l o o o S Z W r a > ' ( 2 , 2 d l ) I f Y r e p r e s e n t s the denominator i n equation (2.21), I cos Z U U U - 0.61 cos Z U U U v „ i o wa ws r s q wa ws r s \ ,.2 0.6 I cos Z U + ( °-y m ) U d, (2.22) which i s i n the form of a q u a d r a t i c equation. S o l v i n g t h i s , a p o s i t i v e v alue of U d can be determined and then s u b s t i t u t e d i n t o equation (2.14) t o o b t a i n h o u r l y values of the a e r o s o l parameter k. Mean d a i l y values can then be c a l c u l a t e d by weigh t i n g a c c o r d i n g to i n c i d e n t K ! q . With t h i s method, an average value of k = O.965 f o r the 15 days a t Goose was ag a i n obtained, i n d i c a t i n g t h a t the d e c i s i o n to omit the m u l t i p l y r e f l e c t e d s o l a r r a d i a t i o n i n the c a l c u l a t i o n of k 26' does not g e n e r a l l y i n v a l i d a t e t h i s approach. The same method, with the m u l t i p l e r e f l e c t i o n term omitted, was then used to c a l c u l a t e average values of k f o r P o r t Hardy and Edmonton. Values of 0.95 (with a range i n mean d a i l y values of 0.924 to O.965) and O.96 (range 0.915 to 0.977) were obtained f o r these two l o c a t i o n s , r e s p e c t i v e l y . Davies et a l (1975) used a va l u e of K = 0.88 which, through equations (2.9) and (2.12), r e s u l t s i n a value f o r k of 0.94 f o r the Lake Ontario area. S l i g h t l y . l o w e r v a l u e s i n t h e i r study compared to the s t a t i o n s r e p o r t e d here are c o n s i s t e n t with the g e n e r a l l y h i g h e r l e v e l of atmospheric p o l l u t i o n a s s o c i a t e d w i t h the g r e a t e r c o n c e n t r a t i o n of i n d u s t r i a l a c t i v i t y i n the southern O n t a r i o r e g i o n . Table 2.5 summarizes these v a l u e s of the a e r o s o l parameter. With the a p p r o p r i a t e mean values of k, Kl was c a l c u l a t e d f o r P o r t Hardy and Edmonton. In the absence of d i f f u s e s o l a r r a d i a t i o n data f o r e i t h e r of these s t a t i o n s , the f o r w a r d - s c a t t e r i n g f a c t o r of 0.60 (and hence back-s c a t t e r i n g of 0.40) as d e r i v e d from the Goose data was used. Although absent i n the c a l c u l a t i o n of k, the m u l t i p l e r e f l e c t i o n term was again i n c l u d e d i n the f i n a l c a l c u l a t i o n of t h e . r a d i a t i o n f l u x e s . T h i s m o d i f i e d Houghton model i s t h e r e f o r e comparable to t h a t used i n the c a l c u l a t i o n s f o r Goose. R e s u l t s are shown i n Table 2.6. Whereas the mod i f i e d 27 TABLE 2.5 Values of the A e r o s o l Parameter ' k' L o c a t i o n andSStudy Value of k Globe (Houghton, 195*0 0.975 Southern On t a r i o (Davies et a l , 1975) 0.940 Goose (Present study) O.965 Edmonton (Present study) O.96O P o r t Hardy (Present study) 0.950 28 TABLE 2.6 Performance of the M o d i f i e d Houghton Model f o r Model Development Days at Edmonton and P o r t Hardy (a) D a i l y T o t a l s : L o c a t i o n Mean Root Mean Root Mean Average Measured Square E r r o r Square E r r o r fo Bias _2J - l , . -2, - l v (Percentage) E r r o r  (MJ m day ) (MJ m day ) fca—^ 'KdEQr.to, Edmonton P o r t Hardy 17.77 13.25 1.36 0.57 7.7 4 . 3 •3^ •1.1 (t>) Hourly Values; L o c a t i o n Edmonton P o r t Hardy , Mean Measured -2 -1\ (KJ m ch L) 1519 1271 Root Mean Square E r r o r (KJ m~ 2h" 1) 130.6 97.7 Root Mean Square E r r o r (Percentage) 8.6 7-7 29 model showed s l i g h t . .deterioration f o r K J q e s t i m a t i o n at Goose, comparison of Tables 2.6 and 2 .3 i n d i c a t e s r e d u c t i o n s i n the r o o t mean square e r r o r s , both i n ab s o l u t e and r e l a t i v e terms, which are s l i g h t f o r Edmonton but s u b s t a n t i a l f o r P o r t Hardy. 2.3«^ Performance f o r Independent Data The c l o u d l e s s days l i s t e d i n Table 2 . 2(b) were used to t e s t the m o d i f i e d v e r s i o n of the Houghton model with independent data from each of the three l o c a t i o n s . The values of k giv e n i n Table 2.5 were used f o r the m o d i f i e d model and, f o r comparison, the unmodified model d i s c u s s e d i n s e c t i o n 2.2 was a l s o used to evaluate s o l a r r a d i a t i o n f o r these days. The performances of these two models f o r KJ , SJ and DJ e s t i m a t i o n at Goose and f o r o o o KJ e s t i m a t i o n at both P o r t Hardy and Edmonton are summarized i n Table 2 . 7 . For both d a i l y t o t a l s and h o u r l y values, r o o t mean square e r r o r s f o r the m o d i f i e d model were g e n e r a l l y l e s s , and i n some s i t u a t i o n s a p p r e c i a b l e r e d u c t i o n s i n e r r o r were achieved. T h i s i n d i c a t e s t h a t the above m o d i f i c a t i o n s are advantageous. One ex c e p t i o n was f o r d i f f u s e s o l a r r a d i a t i o n at Goose where a d e t e r i o r a t i o n occurred i n the independent t e s t i n g of the m o d i f i e d model, d e s p i t e s u b s t a n t i a l improvement i n the Performance of the "Wvaod. TABLE 2.7 Performance of the Unmodified and M o d i f i e d Houghton Models on Independent Data (a) D a i l y T o t a l s ; L o c a t i o n Goose Ki Goose S1 c Goose D l ( Edmonton K l c P o r t Hardy K i Mean Measured o RMSE (MJ m" 2day" 1) (MJ m" 2day" 1) 11.88 9.17 2.71 = 15.3^ 12. 11 Unmodified Model M o d i f i e d Model RMSE RMSE Average ( % ) % Bias (MJ m RMSE 2 d a y " 1 ) Average ( % ) % Bias (t>) H o u r l y Values: Mean Measured '-TO o Location-. o Goose Goose Goose Edmonton Kl i S i Di Kl P o r t Hardy Kl (KJ m"2h 1 ) 1195 924 271 1346 1270 0.83 7.0 5.5 0.63 5.3 3.^ 0.97 10.6 9.5 0.59 6 . 4 2.8 0.31 11.4 - 4 . 6 0.37 13.7 7.3 2.06 13.^ 8.6 1.77. 11.5 5.8 0.67 5-3 2.5 0 . 4 1 3.^ - 4 . 2 Unmodified Model M o d i f i e d Model RMSE RMSE RMSE RMSE (KJ m" 2h _ 1) ( t ) (KJ m~2h~ 4 ) ( * ) 99.6 8.3 8 2 . 4 6.9 117.5 12.7 8 2 . 5 8.9 4 1 . 9 15.5 4 6 . 6 17.2 1 8 8 . 7 1 4 . 0 167.4 12 .4 78.3 6.2 60.3 k.7 31 i n i t i a l t e s t i n g of the same model. R e c a l l i n g t h a t measurement c a p a : b i l i t i e s r a r e " f of t e n c o n s i d e r e d -$% f o r K l and -7% f o r DI (Davies et a l , 1970; Latimer, 1972) and t h e r e f o r e -9% f o r Si where the 'measurement' of the d i r e c t component i s simply the d i f f e r e n c e "between Kj and D i , these r e s u l t s show t h a t the e s t i m a t i o n of s o l a r r a d i a t i o n and i t s components under c l o u d l e s s c o n d i t i o n s can "be a t t a i n e d with a i a c a p a b i l i t y comparable to t h a t of a c t u a l measurements. 2.4 MODEL SENSITIVITY TO METEOROLOGICAL INPUT PARAMETERS 2.4.1 S e n s i t i v i t y to Pres s u r e M e t e o r o l o g i c a l i n p u t parameters t o the c l o u d l e s s s o l a r r a d i a t i o n model are s u r f a c e pressure, s u r f a c e albedo and p r e c i p i t a b l e water. E r r o r s may e x i s t i n the assign e d v a l u e s of these and i t i s t h e r e f o r e important to t e s t the s e n s i t i v i t y of the model to changes i n the values of these parameters. For i l l u s t r a t i o n , the s e n s i t i v i t y w i l l be demonstrated by a p p l i c a t i o n to an a r b i t r a r i l y chosen a r t i f i c i a l d ata s e t corresponding to e x t r a t e r r e s t r i a l d ata f o r P o r t Hardy on October 4, 1976. Table 2.8 i l l u s t r a t e s the s e n s i t i v i t y of the m o d i f i e d Houghton model to changes i n s u r f a c e p r e s s u r e . Values of 0.20 f o r the albedo, which i s a p p r o p r i a t e f o r grass ( S e l l e r s , 1965) and .15 mm f o r p r e c i p i t a b l e water 32 TABLE 2.8 2 M o d e l l e d V a l u e s o f S o l a r R a d i a t i o n (W m ) w i t h V a r y i n g S u r f a c e P r e s s u r e (a-=0.20, u=15 mm) (a) KiQ (b) S | Q (c) BlQ Time P r e s s u r e (kPa) fo Change Over: (LAT) 99 100 101 102 103 99-103 100-101 0800 210 210 209 208 207 1.4 0.5 1000 483 481 480 479 478 1.0 0.2 1200 586 585 584 582 581 0.9 0.2 1400 483 481 480 479 478 1.0 0.2 1600 210 210 209 208 207 1 1.4 0.5 0800 138 137 136 135 134 2.9 0.7 1000 380 378 377 375 373 1.9 0.3 1200 476 474 472 470 468 1.7 0.4 1400 380 378 377 375 373 1.9 0.3 1600 138 137 136 135 134 2.9 0.7 0800 73 73 73 73 74 1.4 0.0 1000 103 103 104 104 105 , 1.9 1.0 1200 110 111 112 112 113 2.7 0.9 1400 103 103 104 104 105 1.9 1.0 1600 73 73 73 73 74 1.4 0.0 I 33 which i s a t y p i c a l October value f o r the west coast (Hay, 1970a) were used. For a r a t h e r l a r g e range of pressures from a low of 990kPa to a high of 103")kPa, very l i t t l e change ( l e s s than Zfo) i n the modelled values of K J was o observed f o r any hour of the day. Devi a t i o n s were higher f o r the component f l u x e s s i n c e , as pressure increased, S J q decreased while D : J q increased s l i g h t l y . Changes i n pressure produced changes i n both component f l u x e s but as these tended to compensate each other and the component f l u x e s are of lower i n t e n s i t y , i t was found that the l a r g e s t r e l a t i v e e r r o r s occurred f o r S 1 q and D 1 q and, correspondingly, a weaker s e n s i t i v i t y to pressure change was found f o r the t o t a l f l u x . G e n e r a l l y , the model i s seen to be very i n s e n s i t i v e to pressure changes and, t h e r e f o r e , the use of one value of p f o r the e n t i r e day was considered adequate. 2.4.2 S e n s i t i v i t y to Albedo With pressure held constant at an a r b i t r a r i l y chosen value of lOOfikBa and p r e c i p i t a b l e water again assigned a value of . 1 5 mm, K J q and i t s components were c a l c u l a t e d u s i n g the modified Houghton model w i t h the surface albedo v a r y i n g from 0.10 ( i . e . dark s o i l ) to 0.80 ( i . e . f r e s h snow) f o r the same data set as i n the previous s e c t i o n . R e s u l t s are shown i n Table 2.9. A l l of the change i n K J q c a l c u l a t i o n occurred i n the d i f f u s e component'since a changes a f f e c t the 34 TABLE 2.9 •'• "-2 M o d e l l e d V a l u e s o f S o l a r R a d i a t i o n (jfr: m~ 0 w i t h V a r y i n g S u r f a c e A l b edo (p=100CkEa'!, u='.15 mm) (a) K 1 q (b) D i Q Time Al b e d o fo Change Over: (LAT) 0910 0020 0.30 0. 50 0.80 0.10-0.80 0. 20-0.30 0800 208 210 211 215 220 5-6 0.5 1000 477 481 485 493 506 5.9 0.8 1200 580 585 590 600 614 5.7 0.9 1400 477 481 485 493 506 5.9 0.8 1600 208 210 211 215 220 5.6 0.5 0800 71 73 75 78 83 15.6 2.7 1000 99 103 107 115 127 24.8 3-8 1200 106 111 116 126 140 27.6 4.4 1400 99 103 107 115 127 24.8 3.8 1600 71 73 75 78 83 15.6 2.7 35 m u l t i p l y r e f l e c t e d s o l a r r a d i a t i o n only. A c o n s i d e r a b l e change i n albedo from 0 . 1 0 to 0 . 8 0 produced a change i n Kj. q e s t i m a t i o n of l e s s than 6%. However, t h i s corresponds to changes i n DI e s t i m a t i o n of up to 28%. I t i s improbable t h a t such a l a r g e e r r o r i n albedo would ever occur. A more r e a l i s t i c margin of e r r o r might be - 0 . 1 0 which r e p r e s e n t s the v a r i a b i l i t y i n albedo f o r vegetated s u r f a c e s ( S e l l e r s , 1 9 6 5 ) . From Table 2 . 9 , i t can be seen t h a t a change i n a from 0 . 2 0 to 0 . 3 0 produced l e s s than a 1% change i n the c a l c u l a t e d v a l u e f o r Kl while f o r DI , changes of up to o 0 4.4% occurred. In the absence of a more s o p h i s t i c a t e d method f o r a s s i g n i n g the s u r f a c e albedo, the e r r o r s a s s o c i a t e d w i t h the p r e s e n t approach ( 0 . 8 0 i n presence of snow cover; 0 . 2 0 w i t h no snow present) were accepted .-inu thisQStudyv;f" -2 . 4 . 3 S e n s i t i v i t y to P r e c i p i t a b l e Water The m o d i f i e d Houghton model and the same data s e t were used to study the e f f e c t s of v a r y i n g p r e c i p i t a b l e water from " 5 nim "to : 2 5 mm with the s u r f a c e pressure and albedo h e l d constant a t lOOCkPa and 0 . 2 0 , r e s p e c t i v e l y . R e s u l t s are g i v e n i n Table 2 . 1 0 . As expected, Kl decreased as u i n c r e a s e d . T h i s i s a consequence of a l a r g e decrease i n the d i r e c t component which i s only p a r t i a l l y o f f s e t by a s m a l l i n c r e a s e i n the d i f f u s e s o l a r 36 TABLE 2.10 Modelled Values of S o l a r R a d i a t i o n (Wjum' ,J ) with V a r y i n g P r e c i p i t a b l e Water (oc=0.20, p=1000kPa) Time P r e c i p i t a b l e Water (mm) fo Change Over: (LAT) .10 1$ 20 •2*5 5-25. 10-15 0800 224 216 210 204 200 11.3 2.8 1000 505 491 481 7^3 465 8.2 2.1 1200 611 596 585 575 567 7-5 1.9 1400 505 491 481 7^3 465 8.2 2.1 1600 224 216 210 204 200 11.3 . 2.8 0800 156 146 137 128 121 25.3 6.4 1000 410 393 378 365 353 14.9 3.9 1200 ' 509 490 474 459 446 13.2 3.3 1400 . 410 393 378 365 353 14.9 3-9 1600 156. 146 137 128 121 25.3 . 6.4 0800 67 70 73 76 79 16.4 4.2 1000 95 99 103 108 112 16.4 4.0 1200 102 106 111 116 121 17.0 4.6 1400 95 99 103 108 112 16.4 4.0 1600 67 70 73 76 79 16.4 4.2 37 r a d i a t i o n . F o r a l a r g e change i n u of ,720 mm ( i . e . from 5-;. to 2 5 ; mm), Kl changed "by up to 11.3% ( f o r l a r g e ' o z e n i t h a n g l e s ) . However, f o r a more r e a l i s t i c d i u r n a l + change or e r r o r of - 0 5 ' mm, as i l l u s t r a t e d by a change i n u from 110 to 115 mm, Kl v a r i e d by l e s s than 3% while SI Q and D i Q v a r i e d by up to 6.4% and 4 . 6 % , r e s p e c t i v e l y . S i n c e measurement a c c u r a c i e s f o r t o t a l and d i f f u s e s o l a r r a d i a t i o n are o f t e n quoted as -5% and -7% r e s p e c t i v e l y (Davies et a l , 1970; Latimer, 1972) and d i r e c t s o l a r r a d i a t i o n would t h e r e f o r e have an a s s o c i a t e d 'measurement' e r r o r of about - 9 % , i t can be concluded t h a t the model i s r a t h e r i n s e n s i t i v e to reasonable changes i n the p r e c i p i t a b l e water parameter. T h e r e f o r e , u t i l i z i n g an average value of u c a l c u l a t e d from two radiosonde ascents (0000 and 1200 h GMT) f o r each day was c o nsidered s u f f i c i e n t . 2 . 5 APPLICATION IN BRITISH COLUMBIA The c l o u d l e s s s o l a r r a d i a t i o n model was f u r t h e r t e s t e d f o r t h r e e l o c a t i o n s i n B r i t i s h Columbia: Vancouver, Summerland and S a n d s p i t (see Table 2 . 1 1 ) . C l o u d l e s s days a v a i l a b l e f o r study are l i s t e d i n Table 2 . 1 2 . Since h o u r l y m e t e o r o l o g i c a l o b s e r v a t i o n s are not a v a i l a b l e a t Summerland, the c l o u d l e s s days f o r t h i s s t a t i o n were determined u s i n g the o b s e r v a t i o n s from P e n t i c t o n l o c a t e d about 15 km to the south. The P e n t i c t o n d a t a were a l s o used 38 TABLE 2 .11 P e r i o d s of A v a i l a b l e Data Record f o r B.C. 'Cloudless Days* Study L a t i t u d e : Longitude: P e r i o d of a v a i l a b l e data r e c o r d : Vancouver 4-9 15* N 1 2 3 ° 1 5 ' W Summerland 4-9 3 4 ' N 1 1 9 ° 3 9 * W 1964-1972 1966-1972 S a n d s p i t 53 15* N 1 3 1 ° ^ 9 ' W 1968-1972 39 TABLE 2.12 Cloudless Days U t i l i z e d f o r B.C. Study Vancouver Feb. 24 1964 Aug. 22 1964 July 24 1965 Aug. Ik 1967 Aug. 15 1967 Mar. 9 1969 Mar. 10 1969 Mar. 11 1969 Oct. 12 1969 Feb. 28 1970 Mar. 10 1970 June 5 1970 June 19 1970 Aug. 10 1971 Aug. 11 1971 Sept.22 1971 July 15 1972 Summerland AMpr.4 491966 Aug. 14 1967 Aug. 16 1967 Aug. 25 1967 Sept.15 1967 Sept.16 1967 Feb. 8 1968 Feb. 15 1968 July 26 1969 Aug. 31 1969 July 16 1971 July 17 1971 July 18 1971 July 26 1971 Aug. 10 1971 Aug. 26 1971 Sandspit Feb. 12 1968 Feb. 13 1968 Feb. 14 1968 May 8 1968 May 9 1968 May 13 1968 June 11 1969 June 18 1969 Sept.11 1970 July 30 1971 4-0 to determine the s u r f a c e p r e s s u r e to be used i n the Summerland c a l c u l a t i o n s . P r e c i p i t a b l e water was c a l c u l a t e d u s i n g the P o r t Hardy radiosonde data f o r the c o a s t a l s t a t i o n s of Vancouver and S a n d s p i t and the i n l a n d P r i n c e George radiosonde i n f o r m a t i o n f o r Summerland. P r i n c e George was j the c l o s e s t i n l a n d radiosonde l o c a t i o n to Summerland at t h a t time. Both the unmodified Houghton model d e s c r i b e d i n s e c t i o n 2 . 2 and the m o d i f i e d model d e s c r i b e d i n s e c t i o n 2 . 3 were t e s t e d . For the l a t t e r , the a e r o s o l parameter k was set, at 0 . 9 5 0 , the value determined i n the a n a l y s i s of the P o r t Hardy data. The performances of these two models are shown i n Table 2 . 1 3. Comparison with Tables 2 . 3 , 2A, 2 . 6 and 2 . 7 i n d i c a t e s t h a t these models have a performance here s i m i l a r to t h a t f o r the three o r i g i n a l s t a t i o n s s t u d i e d . C o n s i d e r a b l e improvement i s seen f o r K i Q e s t i m a t i o n u s i n g the m o d i f i e d v e r s i o n compared to the unmodified Houghton model. On a d a i l y b a s i s , the r o o t mean square e r r o r s i n d i c a t e t h a t K 4 Q was c a l c u l a t e d to w i t h i n -6%. The- average percent b i a s a e r r o r s ( i . e . d e v i a t i o n s from measured) i n d i c a t e t h a t a higher value of k may be a p p r o p r i a t e f o r S a n d s p i t while lower val u e s f o r Vancouver and Summerland may be warranted. However, c o n s i d e r i n g a g a i n t h a t s o l a r r a d i a t i o n measurement e r r o r s are about ~5$» t h i s performance w i t h k = 0 . 9 5 0 i s s/imilar^andv „ TABLE 2.13 Performance of the Unmodified and M o d i f i e d Houghton Models at 3 B.C. L o c a t i o n s (a) D a i l y T o t a l s : Mean Unmodified Model M o d i f i e d Model  L o c a t i o n Measured RMSE RMSE Average RMSE RMSE Average (MJ m" 2day" 1) (MJ m^day" 1) ( % ) % Bias (MJ m" 2day" 1) ( % ) % Bi a s Vancouver 20.74 1.85 8.9 7.6 1.14 5-5 2.9 Summerland 21.96 2.09 8.7 1.31 6.0 4 .5 Sandspit 21.22 1.16 5.5 3.6 0.62 2.9 -1.4 Hourly Values: Mean L o c a t i o n Measured (KJ m" 2h - 1) Unmodified RMSE (KJ m" 2h _ 1) Model RMSE ( f ) M o d i f i e d RMSE (KJ m" 2h _ 1) Model RMSE ( $ ) Vancouver 1645 171.7 10.4 122.2 7.4 Summerland I678 192.5 11.5 140.1 8.3 S a n d s p i t 1690 105.0 6.2 68.2 4.0 42 w i l l t h e r e f o r e he used f o r the c a l c u l a t i o n of s o l a r r a d i a t i o n i n B r i t i s h Columbia i n chapter 6. 3^ CHAPTER 3 SOLAR RADIATION MODEL FOR CLOUDY CONDITIONS 3.1 INTRODUCTION Clouds have the most v a r i a b l e and o f t e n the g r e a t e s t a t t e n u a t i n g e f f e c t on the t r a n s m i s s i o n of s o l a r r a d i a t i o n through the atmosphere. In order to c a l c u l a t e Ki at the s u r f a c e with c l o u d present, some r e s e a r c h e r s have d e r i v e d s t a t i s t i c a l r e l a t i o n s h i p s "between the r a t i o of a c t u a l to c l o u d l e s s sky s o l a r r a d i a t i o n and the r a t i o of measured to t o t a l p o s s i b l e number of hours of b r i g h t sunshine (Angstrom, 1924; K i m b a l l , 1927; Bennett, I965, 1967; E x e l l , 1976) or the t o t a l amount of cloud (Kimball, 1928; Neumann, 195^; Mateer, 19&3; Kimura and Stephenson, 1969; Thompson, 1976). These formulae do not c o n s i d e r the i n t e n s i t y of s o l a r r a d i a t i o n r e q u i r e d to r e g i s t e r on a sunshine r e c o r d e r or the e f f e c t s of d i f f e r e n t cloud types and cloud l a y e r s . These models perform reasonably w e l l o n l y f o r monthly mean data while the e m p i r i c a l c o e f f i c i e n t s i n the r e l a t i o n s h i p s v a r y s p a t i a l l y and te m p o r a l l y (Bennett, 1965» 1967; Kimura and Stephenson, 1969; Thompson, 1976) and the degree of c o r r e l a t i o n between s o l a r r a d i a t i o n and these parameters i s o f t e n low (Bennett, 1969)• 44 The e f f e c t s of d i f f e r e n t cloud types have been i n c o r p o r a t e d i n t o the s o l a r r a d i a t i o n t r a n s m i s s i o n s t u d i e s of London (1957). Monteith (1962), Lumb (1964), L e t t a u and Lettau ( i $ 0$9 ) and Hay (1970a). The performance of these models was b e t t e r ; however, only one cloud l a y e r was con s i d e r e d . Thus the e f f e c t s of m u l t i p l e l a y e r s were igno r e d . R e c e n t l y , a clo u d l a y e r model has been de v i s e d (Nunez et a l , 1971; Davies et a l , 1975) which u t i l i z e s m u l t i - l e v e l cloud types and amounts. Again, the c l o u d l e s s sky s o l a r r a d i a t i o n v a l u e i s used as input to the model. T h i s approach allows the assignment of d i f f e r e n t s o l a r r a d i a t i o n t r a n s m i s s i v i t i e s f o r d i f f e r e n t c l o u d types and a l s o takes i n t o c o n s i d e r a t i o n the f a c t t h a t clouds can occur i n s e v e r a l l a y e r s . Compensation i s a l s o made f o r the o b s c u r i n g of cloud by lower l e v e l s . I n d i v i d u a l t r a n s m i s s i o n v a l u e s are c a l c u l a t e d f o r each l a y e r and then combined to give an o v e r a l l bulk t r a n s m i s s i o n . Nunez et a l (1971) showed t h a t t h i s model was s u p e r i o r to the s t a t i s t i c a l r e l a t i o n s h i p s o u t l i n e d above. In t h i s chapter, the cloud l a y e r model, which w i l l be r e f e r r e d to as the 'Layer' model, w i l l be t e s t e d and analysed f o r a number of Canadian l o c a t i o n s . S i n c e the Layer model does not c o n s i d e r the d i r e c t , a n d d i f f u s e components of s o l a r r a d i a t i o n s e p a r a t e l y , a more r e f i n e d 45 model which allows f o r t h i s c a l c u l a t i o n w i l l he d e r i v e d . T h i s l a t t e r model u t i l i z e s the same data as the Layer model, with cloud analysed by l a y e r , but a l s o r e q u i r e s a knowledge of the r e p o r t e d h o u r l y b r i g h t sunshine amounts. The performancesof t h i s cloud l a y e r - sunshine model (which w i l l be r e f e r r e d to as the CLS model) w i l l be analysed arid compared to t h a t of the Layer model. The p o t e n t i a l f o r a p p l i c a t i o n of the CLS model w i l l be d i s c u s s e d by c o n s i d e r i n g the number of Canadian s t a t i o n s which r e p o r t the 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 data. 3.2 THE LAYER MODEL 3.2.1 D e s c r i p t i o n T h i s model c o n s i d e r s l a y e r s of cloud as shown i n F i g . 3«1 with the t r a n s m i s s i v i t y (U^) of each l a y e r i c a l c u l a t e d as: U. = 1 - (1-t.) n., (3.1) where t ^ i s the t r a n s m i s s i v i t y f o r the p a r t i c u l a r cloud type and n^ i s the amount of cloud as a f r a c t i o n i n the l a y e r (Davies et a l , 1975). The t o t a l t r a n s m i s s i v i t y through a l l of the cloud l a y e r s i s the product of the i n d i v i d u a l c l o u d l a y e r t r a n s m i s s i v i t i e s . T h e r e f o r e , the s o l a r r a d i a t i o n at the s u r f a c e i s 46 F I G . 3.1 C l o u d L a y e r s Used i n t h e L a y e r M o d e l ( i r e f e r s t o l a y e r number) i i = 4 ^ ^ ^ i = 3 ^ ^ ^ ^ 7^ Ki = Kl TT U., (3.2) 0 i = l 1 where j i s the number of l a y e r s . Schneider and D i c k i n s o n (1976) have demonstrated the importance of m u l t i p l e r e f l e c t i o n f o r cloudy s i t u a t i o n s n o t i n g t h a t f o r h i g h s u r f a c e albedo s i t u a t i o n s , Kl can be underestimated by over 3°^ i f t h i s term i s n e g l e c t e d . T h e r e f o r e , f o l l o w i n g Davies et a l (1975)> "the e f f e c t s of m u l t i p l e r e f l e c t i o n between the s u r f a c e and cloud base are added such t h a t the complete s o l a r r a d i a t i o n model becomes Kl = Kl' n U. ( 1 + na a ) , (3-3) 0 i = l 1 c where n i s the t o t a l c loud amount, a i s the cloud base c albedo and,a i s the s u r f a c e albedo. S i n c e c l o u d l a y e r amounts are re p o r t e d from s u r f a c e based o b s e r v a t i o n s , a c o r r e c t i o n must be a p p l i e d to upper l a y e r amounts to negate the e f f e c t of obscuringg by the l a y e r s below. The assumption has been made t h a t the f r a c t i o n of the unobstructed sky covered by an upper cloud i s r e p r e s e n t a t i v e of the t o t a l sky covered by t h a t cloud l a y e r (Davies et a l , 1975)• Thus, the c o r r e c t e d amount of cloud i n a l a y e r becomes 48 ni= n[ / ( l - n x ) , (3.4) where n| i s the reported cloud layer amount and n x i s the simple sum of reported cloud amount f o r the layers beneath. In the example shown i n F i g . 3.2 where n*^  = 0.5, n£ = 0.3 and n^ = 0.1, n^ = n"^  = 0.5 while the corrected amount f o r the second layer becomes n 2 = 0.3 / (1-0.5) = 0.6 and for the t h i r d layer, n = 0.1 / (1-0.8) = 0.5. If n reaches 1.0, higher layers are completely obscuredd and must be neglected. Few measurements or estimates of the cloud type t r a n s m i s s i v i t i e s (t^) are available and those reported vary widely-as shown i n Table 3«1« Variations are due to the angle of incidence of the solar beam which affects the o p t i c a l depth of the cloud (this i s proportional to the o p t i c a l a i r mass m), cloud thickness, cloud height and cloud composition. Many of these variables are not routinely measured. The work of Haurwitz (19^ -8) allows f o r a variable transmissivity dependent upon o p t i c a l a i r mass f#Mrc*i i s an advantage over other schemes. He defined * i = ( K T - ) <-»-) e ( " b m ) . (3.5) o where a and b are c o e f f i c i e n t s obtained by Haurwitz by least-squares procedures from his observed data. Haurwitz's 49 F I G . 3 . 2 Example of the C o r r e c t i o n f o r Cloud Layer Amounts f o r Layers Obstructed by Lower Cloud n^ = . 1 n^ = .5 n. • 3 1 .6 .5 .5 TABLE 3.1 Cloud T r a n s m i s s i v i t i e s f o r S o l a r R a d i a t i o n from V a r i o u s Sources T r a n s m i s s i o n ( % ) Cloud Types Fog Ns St Haurwitz (from L i s t , 1966) 1 7 . - 1 9 15-25 24-25 29-35 Houghton (1954) - - - - 25 London (1957) — 17-25 27-41 Vowinckel and Or v i g (1962) P o l a r Oceans -- -- 30-70 A r c t i c Coasts — -- 31-60 Edmonton: -- -- 28-50 Dartmouth: -- -- 20-29 Makarevsky (Kondratyev,1969) Drummond & Hickey (1971) Vonder Haar & Cox (1972)" — - - 35-50 Reynolds et a l (1975) L i o u (1976) - - 3 25-49 Cu Cb As Ac Cs C i  — — 4 1 45-52 65 - 8 4 80-85 — 20 -- 4 8 4 8 78 -- 23 20 44-50 __ 75 -84 40-68 50-72 45-88 - - 65-91 38-67 - _ — 50-78 57 -84 - 77-IOO 31-60 _ _ 31-47 25-60 33-78 — 79-112 38-44 -- -- 28-38 38-44 - - 20-91 _ _ — — -- 10-35 46-73 6 2 - 8 4 45 45 40-80' 40-80 35-50 15-25 -- 25-55 25-55 — 27-46 10-14 3 -- 27-40 27-40 — 10-23 3 1 4 - 2 8 51 values of a and b f o r d i f f e r e n t cloud types are g i v e n i n Tstole 3.2. F o l l o w i n g the works of Nunez et a l (1971), Atwater and Brown (197^) and Davies et a l (1975), the Haurwitz t r a n s m i s s i o n f u n c t i o n s w i l l "be used i n t h i s study. The Atmospheric Environment S e r v i c e of Canada r e p o r t s 16 d i f f e r e n t cloud type c a t e g o r i e s . These must t h e r e f o r e "be reduced to the 8 d i f f e r e n t c a t e g o r i e s used "by Haurwitz. F o l l o w i n g the d e s c r i p t i o n s of the c l o u d types g i v e n i n the Manual of Standard Procedures f o r  S u r f a c e Weather Observing and R e p o r t i n g (Department of T r a n s p o r t , 1970) and the work of Hay (1970a), the cloud types were assigned as shown i n Table 3-3» 3.2.2 Performance on D a i l y B a s i s For the three year p e r i o d 1968-70, s o l a r r a d i a t i o n and h o u r l y m e t e o r o l o g i c a l data, i n c l u d i n g cloud amounts and types i n up to f o u r l a y e r s , were obtained from the Atmospheric Environment S e r v i c e of Canada f o r the f o l l o w i n g s i x l o c a t i o n s : Goose, N f l d . , Edmonton, A l t a . , Summerland, B.C., Vancouver, B.C., S a n d s p i t , B.C. and P o r t Hardy, B.C. Values f o r the e x t r a t e r r e s t r i a l r a d i a t i o n were a g a i n c a l c u l a t e d u s i n g the s o l a r c l i m a t e c a l c u l a t o r program of F u r n i v a l et a l (1970). The c l o u d l e s s sky s o l a r r a d i a t i o n ( K J Q) h o u r l y values were c a l c u l a t e d u s i n g the m o d i f i e d v e r s i o n of the Houghton model as d e s c r i b e d i n 52 TABLE 3-2 Values of the Coe f f i c i e n t s Used i n the Haurwitz (19^8) -2 -1 Cloud Transmission Functions ('a'ahas units of KJ m h ) Cloud Type: Fog Ns St Sc As Ac Cs C i •a' 645.3 ^69.3 997.2 1453.9 1634.1 2199.8 3649.5 3 ^ . 2 'b' 0.028 -.167 0.159 0.104 O.O63 0.112 0.148 0.079 \ 53 TABLE 3.3 Cloud. Type Assignments A d d i t i o n a l Types Assigned Haurwitz Cloud Type to Same Category Fog O b s t r u c t i o n Ns Cb S t Fs Sc Cu Fc C u — As Ac Ac,c 54 s e c t i o n 2.3 with the a e r o s o l parameter f o r P o r t Hardy being a p p l i e d to a l l B.C. l o c a t i o n s . Radiosonde ascents were used to c a l c u l a t e p r e c i p i t a b l e water f o r Goose, Edmonton, P o r t Hardy and P r i n c e George, B.C. with the P o r t Hardy data a l s o a p p l i e d to Vancouver and S a n d s p i t . The P r i n c e George r e s u l t s were used f o r Summerland. As was the case i n cha p t e r 2, the s u r f a c e albedo was assumed to be 0.2 f o r no snow cover and 0.8 w i t h snow pr e s e n t . The cloud base albedo i n equation (3»3) was assumed to be 0.6 f o l l o w i n g London (1957), Davies et a l (1975) and Hay (1976a). . F o r Summerland, P e n t i c t o n m e t e o r o l o g i c a l data were used. Values of s o l a r r a d i a t i o n were c a l c u l a t e d f o r h o u r l y p e r i o d s and summed to o b t a i n d a i l y t o t a l s and subsequently compared to the measured v a l u e s . The performances of the model on a d a i l y b a s i s are summarized i n Table 3«4 u s i n g both r e l a t i v e and ab s o l u t e values of the r o o t mean square e r r o r and the average b i a s e r r o r . The l a t t e r i s i n d i c a t e d by the r a t i o of average measured to average modelled s o l a r r a d i a t i o n . F i g . 3.3 i l l u s t r a t e s the performance of t h i s model at Vancouver f o r a 10% sample of the days generated u s i n g random number procedures. The r o o t mean square e r r o r s f o r a l l s t a t i o n s ranged from -12.2% to -22.9% with an average of 18.5% f o r the s i x l o c a t i o n s . In absolute terms, the range was -1.48 to -2.26 MJ m~ 2day _ 1 with an average of -2.02 MJ m" 2day~ 1. 55 TABLE 3.4 Performance of the Layer Model f o r Kl E s t i m a t i o n on a D a i l y B a s i s f o r 1968-70 Mean Mean . Measured L o c a t i o n # days Measured Modelled RMSE RMSE /Modelled ( / M J m^day" 1 ) ( Goose 1065 10.31 10.05 2. 04 19.8 1. 026 Edmonton 1035 12.11 12.72 2. 24 18.5 0. 952 Summerland 885 12.06 12.10 1. 48 12.2 0. 997 Vancouver 1070 11.91 11.53 1. 90 16.0 1. 033 S a n d s p i t 1089 9.83 8.85 2. 25 22.9 1. 110 P o r t Hardy 1085 10.42 9.44 2. 26 21.7 1. 104 56 F I G . Performance of the Layer Model at Vancouver f o r a 10% Random 3-3 f o r E s t i m a t i n g K| (MJ m~ 2day _ 1) Sample of Days Dur i n g 1968-70 30-1 254 20H 1 15 U O u 10 5 H • / / • •• • /% —r— 10 15 20 M e a s u r e d —r— 25 30 57 These r e s u l t s compare wi t h a value of approximately -1.55 M3i m~ 2day - 1 (12.0%) obtained by Davies et a l (1975) f o r Grimsby, On t a r i o based on only 114 days d u r i n g the p e r i o d J u l y to November 19&9• ^he b i a s e r r o r s show t h a t , on the average, model o v e r - e s t i m a t i o n occurred at Edmonton and to a Hesser extent at Summerland while u n d e r - e s t i m a t i o n o c c u r r e d a t the other l o c a t i o n s . Average u n d e r - e s t i m a t i o n was more than 10% at both Sandspit and P o r t Hardy and c o n t r i b u t e d to the l a r g e r r o o t mean square e r r o r s at these l o c a t i o n s . Davies et a l (1975) found b i a s e r r o r s r a n g i n g up to 5% f o r f i v e southern Ontario l o c a t i o n s d u r i n g J u l y 1972 to June 1973 with both over- and u n d e r - e s t i m a t i o n occurringcon an average. The b i a s e r r o r s i n the p r e s e n t study may have been due to a s p a t i a l v a r i a t i o n i n the cloud t r a n s m i s s i v i t i e s . Hay (1970a) has mapped the monthly mean bulk c l o u d r e f l e c t i v i t y and a b s o r p t i v i t y f o r Canada and h i s r e s u l t s i n d i c a t e t h a t at l e a s t on ... average, the s p a t i a l v a r i a t i o n i s not l a r g e and i n any case the e f f e c t i s i n the opposite d i r e c t i o n to t h a t i m p l i e d i n the c u r r e n t study. The average model e s t i m a t i o n e r r o r of about + -2 -1 . . . -2. MJ m day can be compared to s o l a r r a d i a t i o n estimates e x t r a p o l a t e d from measuring s t a t i o n s to other l o c a t i o n s . S u c k l i n g and Hay (1976) have shown t h a t e x t r a p o l a t i o n s of measured s o l a r r a d i a t i o n over d i s t a n c e s of 250 km produce 58 average expected e r r o r s of 3>5 MJ m day" with any d i s t a n c e g r e a t e r than 50 km producing average expected -2 -1 e r r o r s g r e a t e r than 2 MJ m day (see F i g . 3-^). The r e s u l t s of a s i m i l a r study u s i n g o n l y summer data "by W i l s o n and P e t z o l d (1972) are a l s o shown i n F i g . 3-^. T h e i r data i n d i c a t e even l a r g e r e r r o r s a s s o c i a t e d with s o l a r r a d i a t i o n e x t r a p o l a t i o n s . Given the d e n s i t y of s t a t i o n s measuring s o l a r r a d i a t i o n i n Canada (see s e c t i o n 3'^). i t would appear t h a t u s i n g a model such as the Layer model i s indeed a b e t t e r approach than e x t r a p o l a t i n g from the a v a i l a b l e r e c o r d i n g s t a t i o n s . Although the Layer model performs reasonably w e l l , i t does not c o n s i d e r the d i r e c t and d i f f u s e components of s o l a r r a d i a t i o n s e p a r a t e l y . I t a l s o i m p l i c i t l y assumes t h a t f o r a g i v e n hour, the p o r t i o n of t h a t hour d u r i n g which s o l a r r a d i a t i o n i s r e c e i v e d i s g i v e n by ( l - n ) where n i s the f r a c t i o n a l t o t a l c l o u d amount. T h i s i m p l i e s a uniform d i s t r i b u t i o n of clouds over the sky hemisphere. In order to c a l c u l a t e the component f l u x e s s e p a r a t e l y and to improve on t h i s i m p l i c i t assumption i n the Layer model, a r e f i n e d model was developed and w i l l be d e s c r i b e d i n the f o l l o w i n g s e c t i o n s . F I G . 3.4 E x t r a p o l a t i o n E r r o r s f r o m S o l a r R a d i a t i o n Measurements 5 H -*• i >v o cs 3 Z O < > 4 4 3 ^ 2 H Q oi < Q Z 1 < i — / i / / / / / 7 / . . S u c k l i n g & Hay ( 1 9 7 6 ) - W i l s o n & P e t z o l d ( 1 9 7 2 ) vo 0 +• 0 T T 200 400 600 800 DISTANCE BETWEEN STATIONS Ckm) — I — -1000 1200 6o 3.3 THE CLOUD LAYER - SUNSHINE (CLS) MODEL 3.3*1- General D e s c r i p t i o n The CLS model uses the same input data as the Layer model except f o r the a d d i t i o n a l requirement of h o u r l y recorded b r i g h t sunshine amounts. F i g . 3.5 i l l u s t r a t e s i n a f l o w diagram the d i f f e r e n t approaches taken by the Layer and CLS models. Whereas the Layer model c a l c u l a t e s a bulk t r a n s m i s s i o n f o r Kl f o r the e n t i r e h o r i z o n t a l extent of the atmosphere based on the product of i n d i v i d u a l l a y e r t r a n s m i s s i v i t i e s (see F i g . 3'l)» the CLS model c o n s i d e r s the d i r e c t and d i f f u s e components s e p a r a t e l y . In t h i s model, the p o r t i o n of the hour d u r i n g which d i r e c t s o l a r r a d i a t i o n i s r e c e i v e d i s c a l c u l a t e d u s i n g both h o u r l y t o t a l c loud amount and recorded sunshine v a l u e s . The d i f f u s e component i s i n i t i a l l y broken i n t o t h r e e p a r t s : the p o r t i o n from the c l o u d l e s s sky, the p o r t i o n from the sky covered by c i r r i f o r m clouds o n l y and the p o r t i o n from the remaining clouded sky. T r a n s m i s s i o n through the l a t t e r i s c a l c u l a t e d u s i n g a l a y e r e d r o u t i n e s i m i l a r to t h a t i n the Layer model. In both models, m u l t i p l e r e f l e c t i o n i s added l a s t l y and t h i s comprises a f o u r t h p a r t of the d i f f u s e s o l a r r a d i a t i o n component i n the CLS model. 3.3.2 D i r e c t S o l a r R a d i a t i o n Component In order to c a l c u l a t e the p o r t i o n of the hour 61 FIG. 3.5 Flow Diagram of the Approaches Taken i n the Layer and. CLS Models Layer Model CLS Model K i For each of f o u r l a y e r s , c a l c u l a t e t o t a l t r a n s -m i s s i o n and combine f o r o v e r a l l t r a n s m i s s i o n . Add m u l t i p l e r e f l e c t i o n . Ki C a l c u l a t e d i r e c t t r a n s m i s s i o n . > f f V S i D i D i Di cs cy t \ r v D i f f u s e I D i ; K i „ C a l c u l a t e m three p a r t s as i n F i g . 3.6 C i Add m u l t i p l e r e f l e c t i o n D i mr Ki 62 d u r i n g which d i r e c t s o l a r r a d i a t i o n i s r e c e i v e d , an e f f e c t i v e c l o u d amount ( n g ) i s c a l c u l a t e d as A n + B (1-s) n = s — , (3.6) A + B where n i s the sum of the c l o u d amounts as seen from the s u r f a c e but e x c l u d i n g c i r r i f o r m , s i s the t o t a l b r i g h t sunshine amountsas a f r a c t i o n of the hour and A and B are w e i g h t i n g f a c t o r s f o r the c l o u d and sunshine measurements. Thisnprocedure assumes t h a t s u f f i c i e n t d i r e c t s o l a r r a d i a t i o n passes through c i r r i f o r m clouds to r e g i s t e r on the sunshine r e c o r d s . The d i r e c t component of s o l a r r a d i a t i o n u n c o r r e c t e d f o r cirriform*''attenuation ( S i ) i s then c a l c u l a t e d as Si = ( 1 - n ) S i . (3.7) x e o The p o r t i o n of d i r e c t s o l a r r a d i a t i o n through c i r r i f o r m c loud does undergo some a t t e n u a t i o n , and as a r e s u l t the d i r e c t s o l a r r a d i a t i o n becomes S i = [ ( l - n e ) - n C i ( l - t C i ) ] S i Q , (3.8) where nn . i s the amount of c i r r i f ormmcloud as seen from:?. tJie s u r f a c e ( i . e . n C i = n - n ) and t C i i s the t r a n s m i s s i v i t y 63 of the c i r r i f o r m cloud (as taken from the Haurwitz t r a n s -m i s s i o n f u n c t i o n s ) . In the case of the d i r e c t component, i t i s a p p r o p r i a t e to use the amount of c i r r i f o r m v i s i b l e to a ground-based observer. 3'3'3 D i f f u s e S o l a r R a d i a t i o n Component The d i f f u s e component of s o l a r r a d i a t i o n i s i n i t i a l l y c a l c u l a t e d i n -three p a r t s as i l l u s t r a t e d i n F i g . 3.6. F o r the c l o u d l e s s p o r t i o n of the sky, the d i f f u s e s o l a r r a d i a t i o n (Di ) i s g i v e n by c s m c s = ( 1 _ n ) m o - ( 3 , 9 ) F o r the p o r t i o n of the sky covered by c i r r i f o r m c l o u d (as seen from the s u r f a c e ) , the d i f f u s e s o l a r r a d i a t i o n ( D l C i ) i s g i v e n by D 1ci = "cAi m o ' ( 3 - 1 0 where ± n • i s agai n the Haurwitz c i r r i f o r m t r a n s m i s s i v i t y . In equations (3-9) and (3.10), o n l y D I q i s used s i n c e the i n c i d e n t d i r e c t s o l a r r a d i a t i o n (Si ) f o r these p o r t i o n s o of the sky was c o n s i d e r e d i n the c a l c u l a t i o n of SI i n s e c t i o n 3'3«2. For the 'cloudy p o r t i o n * ( e x c l u d i n g c i r r i f o r m 64 FIG. 3.6 The I n i t i a l Three Parts f o r the C a l c u l a t i o n of the D i f f u s e S o l a r R a d i a t i o n Component i n the CLS Model 65 as seen from the s u r f a c e ) of the sky, the d i f f u s e s o l a r r a d i a t i o n (Dl ). i s c a l c u l a t e d by a l a y e r e d procedure cy j s i m i l a r to t h a t f o r the Layer model. I n i t i a l l y , c l o u d l a y e r amounts are c a l c u l a t e d u s i n g equation ( 3 . 4 ) . I f c i r r i f o r m clouds are present, then the amount f o r such l a y e r s t h a t i s i n the 'cloudy p o r t i o n ' of the sky ( r e g i o n 2 i n F i g . 3 -6) i s then c a l c u l a t e d as n i ( C i ) = n i " n C i ( 3 - H ) where ^ ( r j j j i s "the 'cloudy p o r t i o n * l a y e r amount f o r a c i r r i f o r m l a y e r and n^ i s the t o t a l amount i n the c i r r i f o r m l a y e r c a l c u l a t e d from equation ( 3 . 4 ) . The Haurwitz t r a n s m i s s i v i t i e s ( t ^ ) from equation ( 3 - 5 ) are used f o r the v a r i o u s cloud types to c a l c u l a t e i n d i v i d u a l l a y e r t r a n s m i s s i v i t i e s f o r onl y the 'cloudy p o r t i o n ' of the sky (U(r) where U! = 1 - ( 1-t.) ^ i . ( 3 . 1 2 ) s The d i f f u s e s o l a r r a d i a t i o n through the 'cloudy p o r t i o n ' i s then g i v e n by 3 DI = n K I f i ' U!, ( 3 . 1 3 ) cy s o i 66 where j i s the number of l a y e r s . Whereas the c a l c u l a t i o n s of Dl and Dl,-,. used Dl , DI u t i l i z e s Kl s i n c e both cs O i o cy o d i r e c t and d i f f u s e s o l a r r a d i a t i o n are i n c i d e n t upon the top of these clouds and t r a n s m i t t e d only as d i f f u s e s o l a r r a d i a t i o n . M u l t i p l e r e f l e c t i o n i s then added as a f o u r t h p a r t of the d i f f u s e s o l a r r a d i a t i o n (Di ) as * mr Di = (Si + Di +Dln. + Dl ) a (a n +an.nn.), (3.14) mr cs C i cy c s C i C i w where a i s the s u r f a c e albedo and a and an. are the c 0 1 n o n - c i r r i f o r m and c i r r i f o r m c loud base albedoes, r e s p e c t i v e l y . The c l o u d base albedo i s s p l i t i n t o two p a r t s s i n c e the c i r r i f o r m albedo d i f f e r s c o n s i d e r a b l y from t h a t of other clouds (London, >1957; Canover, 1965; L i o u , 1976). In t h i s study, a was a g a i n assumed to be 0.2 f o r no snow cover and 0.8 when snow was pre s e n t . F o l l o w i n g Davies et a l (1975) and Hay (1976a), a was assigne d the constant c value of 0.6 s i n c e the albedoes of n o n - c i r r i f o r m clouds are a l l moderately high. London (1957) had n o n - c i r r i f o r m c l o u d albedoes r a n g i n g from 0.5 to 0.7 although other s t u d i e s have shown c o n s i d e r a b l e v a r i a t i o n (Canover, 1965; Drummond and Hickey, 1971; Reynolds et a l , 1975; L i o u , 1976). A value of 0.2 was assigned f o r (London, 1957; Drummond and Hickey, 1971) which i s c o n s i d e r a b l y lower than t h a t f o r other clouds, 67 f o r other c l o u d s . The d i f f u s e component of s o l a r r a d i a t i o n i s t h e r e f o r e g i v e n by Dl = Di + Din. + Di + DI . (3-15) cs C i cy mr F i n a l l y , the t o t a l s o l a r r a d i a t i o n i s giv e n by the sum of the d i r e c t and d i f f u s e components. Thus, Kl = [ [ ( l - n e ) - n c i ( l - t c i ) ] S i o + [ ( l - n ) - h a C i t c i ] D i Q + n s K l Q T f ^ J Q 1 + a ( a c n s ' + a c i n C i ) ] . (3.16) 3.3.4 Performance on D a i l y B a s i s For the same three year p e r i o d (1968-70) and f i v e of the s i x s t a t i o n s used i n the Layer model a n a l y s i s i n s e c t i o n 3«2.2 (Port Hardy l a c k e d sunshine data d u r i n g t h i s p e r i o d ) , the performance of the CLS model was analysed. Three v e r s i o n s of the model were t e s t e d with the weig h t i n g c o e f f i c i e n t s i n equation (3«6) being g i v e n values of ( i ) A = B = 1; ( i i ) A = 2 and B = 1; and ( i i i ) A = 1 and B = 2. The r e s u l t s on a d a i l y b a s i s are g i v e n i n Table 3«5-Of the three v e r s i o n s , the f i r s t two (which w i l l be r e f e r r e d to as the CLS 1,1 and CLS 2,1 models) performed much b e t t e r than the t h i r d ( r e f e r r e d to as the CLS 1,2 model). These 68 TABLE 3.5 Performance of the CLS Model f o r Ki E s t i m a t i o n on a D a i l y B a s i s f o r 1968-70 Mean Mean Measured L o c a t i o n A B # days Measured Modelled RMSE RMSE /Modelled ( MJ m" 2day" 1 ) ( % ) Goose 1 1 IO65 10.31 10.63' 1.78 17.2 O.970 2 1 1065 10.31 10.40 1.64 15.9 0.992 1 2 1065 10.31 10.88 2.06 20.0 0.948 Edmonton 1 1 1035 12.11 13.23 2.32 19.2 0.915 2 1 1035 12.11 12.93 2.02 16.7 0.937 1 2 1035 12.1-1 13.54 2.74 22.7 0.895 Summerland 1 1 885 12.06 12.38 1.38 11.5 0.975 2 1 885 12.06 12.22 1.25 10.4 0.987 1 2 885 12.06 12.54 I.63 13.5 0.962 Vancouver .1 1 1070 11.91 11.87 1.27 10.6 1.003 2 1 1070 11.91 11.69 1.36 11.4 1.019 1 2 1070 11.91 12.05 1.33 11.2 0.988 S a n d s p i t 1 1 1089 9.83 9.25 1.45 14.7 1.062 2 1 1089 9.83 9.08 1.64 16.6 1.082 1 2 1089 9.83 9.43 l . 4 o 14.2 1.043 69 had average r o o t mean square e r r o r values of lk,6% and lk.2% r e s p e c t i v e l y compared to l6tjfo f o r the CLS 1,2 v e r s i o n when r e s u l t s f o r a l l f i v e s t a t i o n s are averaged. These r e s u l t s can he compared to those f o r the Layer model g i v e n i n Table 3.k. T h i s comparison i s summarized i n Table 3-6 and shown i n F i g . 3«7« The CLS 2,1 model- estimated s o l a r r a d i a t i o n b e t t e r than the Layer model at each of the f i v e l o c a t i o n s and by 3>7f° on average (root mean square e r r o r of lk.2% compared to 17-9%)' For the west coast s t a t i o n s of Vancouver and Sandspit, the CLS 1,1 and CLS 1,2 models showed even more improvement. The s l i g h t l y improved performance of the CLS 1,1 model compared to the Layer model f o r e s t i m a t i n g Kl at Vancouver i s shown by examining F i g s . 3-8 and 3-3 where 10% samples of days generated u s i n g random number procedures are i l l u s t r a t e d f o r each model. As was the case f o r the Layer model, average b i a s e r r o r s s t i l l e x i s t f o r the CLS model with average over-e s t i m a t i o n at Goose, Edmonton and Summerland ( f o r the CLS 1,1 and CLS 2,1 models) and u n d e r - e s t i m a t i o n at Vancouver and S a n d s p i t . . . . .\ For Goose, the performance of the CLS model f o r e s t i m a t i n g the separate d i r e c t and d i f f u s e components of s o l a r r a d i a t i o n can be analysed s i n c e d i f f u s e s o l a r r a d i a t i o n i s measured at t h i s s t a t i o n . Table 3-7 summarizes 70 TABLE 3.6 Comparison of the Performances of the Layer and CLS Models on a Daily Basis f o r 1968-70 Root Mean Square •Errors (*-) Location Models Layer CLS 1,1 CLS 2,1 CLS 1,; Goose 19.8 17.2 15-9 20.0 Edmonton 18.5 19.2 16.7 22.7 Summerland 12.2 11.5 10.4 13.5 Vancouver 16.0 10.6 11.4 11.2 Sandspit 22.9 14.7 16.6 14.2 Average 17.9 14.6 14.2 I6.3 71 FIG. 3.7 Root Mean Square Errors- {%) on a D a i l y B a s i s or the L a y e r and CLS S o l a r R a d i a t i o n Models D u r i n g 1968-70 2 J o • o o • 0 Layer D V CLS 1,2 0 n CLS 1,1 V • CLS 2,1 is* o o O o c o E "O -a c _o £ £ to > o ( J c o > c o to LLl O < LU > < 72 V F I G . 3.8 P e r f o r m a n c e o f t h e CLS 1,1 M o d e l f o r E s t i m a t i n g K\ (MJ m 2 d a y " a t V a n c o u v e r f o r a 10% Random Sample o f Days D u r i n g 1 9 6 8 - 7 0 3(H 25H 2o^  3 5 I OH 5H •A • 4 > "20" — 1 — 30 10 15 M e a s u r e d 25 73 TABLE 3 . 7 Performance of the CLS Model f o r Si and DI E s t i m a t i o n at Goose on a D a i l y B a s i s f o r 1 9 6 8 - 7 0 # Mean Mean Measured A B Days Measured Modelled RMSE RMSE /Modelled ( --MJ - 2 . -1 m day ____) <*) K l 1 1 938 1 0 . 8 8 1 1 . 2 0 1 . 8 2 1 6 . 7 0 . 9 7 2 Si 1 1 938 4 . 9 9 5 . 6 2 1 . 5 5 3 1 . 1 0 . 8 8 9 DI 1 1 938 5 - 8 9 5 . 5 9 1 . 7 9 3 0 . 4 1 . 0 5 5 K l 2 1 938 1 0 . 8 8 1 0 . 9 6 I . 6 7 1 5 - 3 0 . 9 9 3 ' Si 2 1 938 4 . 9 9 5.40 1 . 4 3 2 8 . 7 0 . 9 2 5 DI 2 1 938 5 - 8 9 5 . 5 6 1 . 7 9 3 0 . 4 1 . 0 5 9 Kl 1 2 938 1 0 . 8 8 11.46 2 . 1 1 • 1 9 . 4 0 . 949 S i 1 2 938 4 . 9 9 5.84 1.82 3 6 . 5 0 . 8 | 5 Di 1 2 938 5 - 8 9 5 . 6 2 1 . 7 8 . 3 0 . 3 1 . 0 4 7 7^ these r e s u l t s . Although the r e l a t i v e r o o t mean square e r r o r s f o r S i and Bit ( 2 8 . 7 $ and 3 0 . 4 $ r e s p e c t i v e l y ) are much hi g h e r than f o r Kl (15.3%) f o r the CLS 2 , 1 model v e r s i o n , the ab s o l u t e e r r o r s are i n a s i m i l a r range (1.4-3 and I . 7 9 MJ m~ 2day _ 1 compared to I . 6 7 MJ m" 2day~ 1). The average b i a s e r r o r s , i n d i c a t e d by the r a t i o of average measured to average c a l c u l a t e d f l u x , show t h a t the d i r e c t and d i f f u s e components are, on the average, over- and under-estimated, r e s p e c t i v e l y . O v e r a l l , both the CLS 1,1 and CLS 2 , 1 models performed w i t h s i m i l a r c a p a b i l i t y . However, r e g i o n a l p r e f e r e n c e s are evident and w i l l be f u r t h e r d i s c u s s e d i n chapter 6 where the cloud l a y e r - sunshine model i s a p p l i e d to B r i t i s h Columbia. G e n e r a l l y , i t appears t h a t the d a i l y performances of the CLS 1,1 and CLS 2 , 1 models were s l i g h t l y b e t t e r than t h a t of the Layer model. As was the case f o r the Layer model, the CLS model produces -2 -1 r o o t mean square e r r o r s of l e s s than 2 MJ m day E x t r a p o l a t i o n s of s o l a r r a d i a t i o n values f o r d i s t a n c e s g r e a t e r than 50 km from s t a t i o n s where Kl i s measured — 2 — 1 produce e r r o r s l a r g e r than 2 MJ m~ day" (see F i g . 3 - 4 ) . T h e r e f o r e , there i s a d i s t i n c t advantage to u s i n g n u m e r i c a l models f o r s o l a r r a d i a t i o n e s t i m a t i o n i n areas where measured val u e s are not a v a i l a b l e . 75 3.3-5 Performance f o r F i v e - and Ten-Day D a i l y Means The c e n t r a l l i m i t theorem would suggest t h a t the c a l c u l a t i o n of s o l a r r a d i a t i o n f l u x e s over longer p e r i o d s should produce b e t t e r agreement between the estimated and measured val u e s (e.g. Davies et a l , 1975). The r e s u l t s of the Layer model and the CLS 1,1 and CLS 2,1 models were analysed f o r f i v e - d a y and ten-day d a i l y means (see Tables 3.8 and 3«9» r e s p e c t i v e l y ) . Compared to the d a i l y Ki performances (Table 3«6), i"t i s apparent t h a t , i n a l l cases, improvement r e s u l t e d when values were averaged over l o n g e r a v e r a g i n g p e r i o d s . T h i s i s f u r t h e r i l l u s t r a t e d i n F i g . 3.9 where the r e s u l t s f o r the CLS 2,1 model are p l o t t e d with the a d d i t i o n of three-day d a i l y means. A l l s t a t i o n s experienced a s i m i l a r drop i n RMSE of about s i x percentage p o i n t s (except Goose where RMSE dropped nine percentage p o i n t s ) between 1 day and 10 day averaging p e r i o d s . From Tables 3-6, 3'8 and 3«9» i t can a l s o be seen t h a t the advantage of u s i n g the CLS model over the Layer model di m i n i s h e s as the averaging p e r i o d i s lengthened. Compared to the CLS 2,1 model, the Layer model becomes s u p e r i o r f o r Edmonton f o r f i v e - d a y d a i l y means and f o r both Summerland and Edmonton f o r ten-day d a i l y means. F o r s e v e r a l of the l o c a t i o n s , both models are approaching or w i t h i n -5% of measured val u e s when modelled values are averaged over t e n days. 76 TABLE 3.8 Comparison of the PerformancesooftitheLLayeraandCCiLSModeiLs f o r Five-Day D a i l y Means f o r 1968-70 Root Mean Square E r r o r s (% ) L o c a t i o n Model: Layer CLS 1,1 CLS 2,1 Goose 10.3 10.3 8.4 Edmonton 10.5 14.7 11.6 i Summerland 6.7 7.7 6.3 Vancouver 9.4 5-7 6.3 Sandspit 15.6 9.2 11.3 Average 10.5 9.5 8.8 77 TABLE 3.9 Comparison of the Performances of the Layer and CLS Models f o r Ten-Day D a i l y Means f o r 1968-70 Root Mean Square E r r o r s (% ) L o c M c a t i o n Model: Layer CLS 1,1 CLS 2,1 Goose 7.8 8.4 6.3 Edmonton 8.7 14.1 10.8 Summerland 4.9 7.0 * 5.5 Vancouver 7.5 4.4 5-0 S a n d s p i t 14.2 8.3 10.4 Average 8.6 8.4 7.6 78 F I G . 3 . 9 R o o t M e a n S q u a r e E r r o r s {%) f o r V a r i o u s A v e r a g i n g P e r i o d s f o r t h e C L S 2 , 1 S o l a r R a d i a t i o n M o d e l D u r i n g 1 9 6 8 - 7 0 16 4 £1 4 UJ12-cu o r> cr t o c l O o to o o 8 64 A • •A • A T 5 - r — 10 A v e r a g i n g P e r i o d C d a y s D • G o o s e O E d m o n t o n A S u m m e r l a n d A V a n c o u v e r • S a n d s p i t A v e r a g e 79 3 . 4 POTENTIAL APPLICATION IN CANADA As o f J a n u a r y 1, 1 9 7 6 , t h e r e were 51 s t a t i o n s m e a s u r i n g t o t a l s o l a r r a d i a t i o n (Kj. ) i n C a n a d a ( A t m o s p h e r i c E n v i r o n m e n t S e r v i c e , 1 9 7 6 ) . The CLS model c a n s u p p l e m e n t t h i s s o l a r r a d i a t i o n n e t w o r k "by c a l c u l a t i n g Kl f o r l o c a t i o n s where h o u r l y m e t e o r o l o g i c a l ( i n c l u d i n g c l o u d ) and s u n s h i n e d a t a a r e a v a i l a b l e . V a l u e s o f p r e c i p i t a b l e w a t e r w o u l d have t o be a s s i g n e d u s i n g n e a r b y r a d i o s o n d e s t a t i o n s o r , i n most c a s e s , by some o t h e r method s u c h as u s i n g s t a t i s t i c a l r e l a t i o n s h i p s b etween u and s u r f a c e v a p o u r p r e s s u r e ( e . g . M o n t e i t h , 1961; I d s o , 1 9 6 9 ; Hay, 1 9 7 0 b ) . The s t a t i o n s w i t h measured o r a p o t e n t i a l t o model, s o l a r r a d i a t i o n d a t a i n v a r i o u s r e g i o n s o f C a n a d a were d e t e r m i n e d f r o m t h e c l i m a t o l o g i c a l d a t a i n v e n t o r y c a t a l o g u e s ( A t m o s p h e r i c E n v i r o n m e n t S e r v i c e , 1 9 7 6 ) . T h e s e a r e summarized i n T a b l e 3 . 1 0 and F i g . 3 . 1 0 . A t o t a l o f 134 l o c a t i o n s ( 5 1 measured and 8 3 m o d e l l e d ) e x i s t w h i c h i s 2 . 6 t i m e s t h e t o t a l f o r m e a s u r i n g s t a t i o n s a l o n e . T h i s r e p r e s e n t s a 4 2 d e n s i t y o f one s t a t i o n p e r 7.4 X 10 km . The i n c r e a s e i s s m a l l i n t h e n o r t h e r n t e r r i t o r i e s and, e x c l u d i n g t h i s a r e a , an i n c r e a s e i n t h e number o f l o c a t i o n s o f 3 - 2 t i m e s i s a v a i l a b l e i n s o u t h e r n C a n a d a w i t h a d e n s i t y o f one p e r 4 2 5 . 1 X 10 km . F o r B r i t i s h C o l u m b i a , a s t a t i o n d e n s i t y o f 4 2 one p e r 4 . 1 X 10 km r e s u l t s when m o d e l l e d d a t a a r e u s e d t o s u p p l e m e n t t h e s o l a r r a d i a t i o n measurement n e t w o r k . H i s t o r i c a l l y , s o l a r r a d i a t i o n has b e e n measured 80 TABLE 3.10 Number of S o l a r R a d i a t i o n S t a t i o n s i n Canada (Measuring and P o t e n t i a l to Model as of Jan. 1, 1976) VurrNumber Number F r a c t i o n a l Region Measuring can Model T o t a l Increase E a s t coast p r o v i n c e s 7 17 • 24 3.4 Quebec 6 11 17 2.8 O n t a r i o 6 13 19 3.2 P r a i r i e p r o v i n c e s 8 23 31 3-9 B r i t i s h Columbia 9 14 23 2.6 The North 15' 5 20 1.3 Canada ( e x c l . North) 36 78 114 3.2 C anada 51 83 134 2.6 81 FIG. 3.10 A v a i l a b l e S o l a r R a d i a t i o n Network i n Canada (as o f J a n u a r y 1, 1976) 500 km • m e a s u r e d o m o d e l l e d 82 f o r a r e l a t i v e l y s h o r t p e r i o d of time when compared to the much l o n g e r cloud and sunshine records (Atmospheric Environment S e r v i c e , 1972a). Usi n g the CLS model, the t o t a l s o l a r r a d i a t i o n r e c o r d f o r many l o c a t i o n s can be extended back i n time by a p p r e c i a b l e amounts, thus g i v i n g a means of o b t a i n i n g a more r e l i a b l e i n d i c a t o r of average v a l u e s , v a r i a b i l i t y and tre n d s . There are o n l y f o u r s t a t i o n s i n Canada (Goose, Toronto, Montreal and Resolute, NWT) t h a t measure d i f f u s e s o l a r r a d i a t i o n on a r o u t i n e b a s i s (Atmospheric Environment S e r v i c e , 1976). Since the CLS model c a l c u l a t e s the d i r e c t and d i f f u s e components s e p a r a t e l y , t h i s model has gr e a t p o t e n t i a l f o r i n c r e a s i n g our s p a t i a l knowledge of these component f l u x e s . Thus, i t can be concluded t h a t the CLS model has a c o n s i d e r a b l e p o t e n t i a l f o r expanding the s p a t i a l and temporal knowledge of s o l a r r a d i a t i o n and i t s component f l u x e s i n Canada. 83 CHAPTER 4 SYNOPTIC WEATHER TYPES FOR BRITISH COLUMBIA AND THE ADJACENT AREAS OF THE PACIFIC OCEAN 4.1 INTRODUCTION . The c l a s s i f i c a t i o n of s y n o p t i c weather maps pr o v i d e s a convenient means of summarizing the c o m p l e x i t i e s of the day-to-day weather p a t t e r n s and combining the i n d i v i d u a l days i n t o a l i m i t e d number of c a t e g o r i e s or types f o r purposes of r e l a t i n g p a r t i c u l a r atmospheric or c l i m a t o l o g i c a l c h a r a c t e r i s t i c s to the s y n o p t i c s c a l e events. Examples of a p p r o p r i a t e c h a r a c t e r i s t i c s are p r e c i p i t a b l e water and s o l a r r a d i a t i o n r e c e i p t at the s u r f a c e . I d e a l l y , the t y p i n g scheme i s designed such t h a t , f o r the g i v e n atmospheric c h a r a c t e r i s t i c , the d i f f e r e n c e s between weather maps of one type are s m a l l compared to the d i f f e r e n c e s between maps of d i f f e r e n t types. Once e s t a b l i s h e d , the s y n o p t i c weather types form a u s e f u l t o o l e n a b l i n g one to g e n e r a l i z e -and c a t e g o r i z e c l i m a t o l o g i c a l f e a t u r e s f o r the area.under c o n s i d e r a t i o n . In the prese n t study, s y n o p t i c weather types w i l l be E e l a t e d l i n i t i a l l y to p r e c i p i t a b l e water f i e l d s i n order to o b t a i n values of u over l a r g e areas f o r input i n t o the c l o u d l e s s sky s o l a r r a d i a t i o n model. A l s o , s o l a r r a d i a t i o n 84 d i s t r i b u t i o n p a t t e r n s over B r i t i s h C o l u m b i a w i l l be r e l a t e d t o the s y n o p t i c t y p e s i n o r d e r t o e s t a b l i s h and d e s c r i b e s y n o p t i c s o l a r r a d i a t i o n regimes f o r t h e r e g i o n . B e f o r e t h i s can be done, s y n o p t i c weather t y p e s must be e s t a b l i s h e d f o r the a r e a . Over the y e a r s , s y n o p t i c weather p a t t e r n c l a s s i f i -c a t i o n approaches have f o l l o w e d two main methods: those" w h i c h c o n s i d e r the ' k i n e m a t i c ' or moving p a t t e r n and t h o s e w h i c h c o n s i d e r the ' s t a t i c * o r s t a t i o n a r y p a t t e r n ( B a r r y and P e r r y , 1 9 7 3 ) ' The k i n e m a t i c approach c o n s i d e r s parameters such as a i r f l o w d i r e c t i o n a t t h e s u r f a c e or a t upper l e v e l s (e.g. Lamb, 1950; B a r r y , I960; Thompson, 1973; Knowles and Jehn, 1975). l a r g e - s c a l e ' s t e e r i n g * f e a t u r e s (e.g. Baur, 1951) or the t r a c k s o f d e p r e s s i o n s (e.g. Thomas, I960; R e i t a n , 1974). The s t a t i c approach c o n s i d e r s the p a t t e r n o f the o v e r a l l p r e s s u r e f i e l d e i t h e r s u b j e c t i v e l y by v i s u a l map e x a m i n a t i o n (e.g. P u t n i n s , 1966; Maunder, 1 9 6 8 ; B a r r y , 1974) o r o b j e c t i v e l y u s i n g m a t h e m a t i c a l f u n c t i o n s (e.g. Friedman, 1955; Hare e t a l , 1957) or c o r r e l a t i o n t e c h n i q u e s (e.g. Lund, 1963). The c h o i c e o f t e c h n i q u e depends upon computingacapaci.ty, -data a v a i l a b i l i t y and t h e u l t i m a t e a p p l i c a t i o n . I n t h i s s t u d y , t h e t y p i n g scheme w i l l be used as a t o o l i n a n a l y s i n g the p a t t e r n and d i s t r i b u t i o n of- p r e c i p i t a b l e water and s o l a r r a d i a t i o n . Whereas the f o r e c a s t i n g o f m e t e o r o l o g i c a l events s uch as p r e c i p i t a t i o n may w a r r a n t a ' k i n e m a t i c * t e c h n i q u e , 85 a ' s t a t i c ' p a t t e r n of the a c t u a l p r e s s u r e f i e l d may be more a p p r o p r i a t e f o r the presen t p r e c i p i t a b l e water and s o l a r r a d i a t i o n anaLyS:es». S i n c e the aim of t h i s study i s to use s y n o p t i c t y p i n g as a t o o l r a t h e r than to develop s y n o p t i c c l i m a t o l o g i c a l c l a s s i f i c a t i o n techniques, the o b j e c t i v e c o r r e l a t i o n technique of Lund (1963) w a s employed i n s t e a d o f a new p a t t e r n r e c o g n i t i o n technique such as t h a t of Bauer (1975) or LeDrew ( 1 9 7 6 ) . Lund's technique has been a p p l i e d i n rec e n t s t u d i e s by Hartrafitftselt a l (1970) f o r areas i n the U n i t e d S t a t e s , Kociuba (1974) f o r A l b e r t a and Paegle and K i e r u l f f (1974) f o r the western U n i t e d S t a t e s . 4 . 2 THE OBJECTIVE CORRELATION CLASSIFICATION TECHNIQUE The o b j e c t i v e c o r r e l a t i o n c l a s s i f i c a t i o n technique f o r c l a s s i f y i n g weather maps takes p o i n t values of pressure or the h e i g h t of a constant p r e s s u r e s u r f a c e and determines the degree of s i m i l a r i t y between any two data s e t s r e p r e s e n t i n g the s y n o p t i c weather maps. F o r t h i s assessment, the product moment'-, l i n e a r c o r r e l a t i o n c o e f f i c i e n t i s g e n e r a l l y used (Lund, I963). T h i s can be d e f i n e d as: n 2 (x.-x) (y.-y) _ -1 -L -1-86 where and y^ are the values of pressure or he i g h t at corr e s p o n d i n g g r i d p o i n t s or s t a t i o n s on' each map, x and y are the corres p o n d i n g mean valu e s on each map and n i s the t o t a l number of g r i d p o i n t s or s t a t i o n s b e i ng c o n s i d e r e d . Maps c o r r e l a t e d h i g h l y are con s i d e r e d to form a 'type'. F o l l o w i n g Lund (1963), the technique r e q u i r e s t h a t the c o r r e l a t i o n between each p a i r of maps be determined and then the map wit h the most c o r r e l a t i o n c o e f f i c i e n t s above a c e r t a i n chosen t h r e s h o l d value i s s e l e c t e d to re p r e s e n t Type 1. A l l maps i n the sample with a c o r r e l a t i o n c o e f f i c i e n t with Type 1 above the t h r e s h o l d value are then a b s t r a c t e d . The remaining map wit h the h i g h e s t number of c o r r e l a t i o n c o e f f i c i e n t s above the t h r e s h o l d i s then chosen to r e p r e s e n t Type 2, and so on u n t i l s u f f i c i e n t types are found or u n t i l i n s u f f i c i e n t maps are contained w i t h i n the next chosen type. In the f i n a l assignment, a g i v e n map i s r e a l l o c a t e d to the type w i t h which i t has the h i g h e s t c o r r e l a t i o n . T h i s c o r r e l a t i o n technique y i e l d s a c o r r e l a t i o n c o e f f i c i e n t v a r y i n g from -1.00 to +1.00 between any two maps. Maps c o r r e l a t e at +1.00 w i t h themselves and a t -1.00 i f the two maps have i d e n t i c a l i s o b a r i c c o n f i g u r a t i o n s but w i t h the low and hig h p r e s s u r e areas interchanged. S c h o l e f i e l d (1973) demonstrated some of the main c h a r a c t e r i s t i c s of t h i s technique t h a t l i m i t i t s a b i l i t y 87 to d i s t i n g u i s h some s y n o p t i c s i t u a t i o n s . These c h a r a c t e r i s t i c s are: maps with i d e n t i c a l i s o b a r i c c o n f i g u r a t i o n s , d i r e c t i o n s of f l o w and h o r i z o n t a l p r e s s u r e g r a d i e n t s but d i f f e r i n g c e n t r a l p r e s s u r e s (e.g. i d e n t i c a l lows except f o r c e n t r a l p r e s s u r e s such as 975kPa and lOOOkEa) c o r r e l a t e with r v = 1.00; and, maps t h a t have i d e n t i c a l i s o b a r i c xy c o n f i g u r a t i o n s but d i f f e r e n t h o r i z o n t a l p r e s s u r e g r a d i e n t s c o r r e l a t e very h i g h . T h i s l a t t e r c h a r a c t e r i s t i c , a l s o demonstrated by Bauer (1975)• i n d i c a t e s t h a t the technique i s somewhat l i m i t e d i n i t s a b i l i t y to d i s t i n g u i s h systems of d i f f e r e n t i n t e n s i t y i n the same l o c a t i o n . The c h o i c e of a t h r e s h o l d value f o r the c o r r e l a t i o n c o e f f i c i e n t i s somewhat s u b j e c t i v e and i n v o l v e s c o n s i d e r a t i o n of the s i z e of the study area, the type of data being c o r r e l a t e d , the purpose of the c l a s s i f i c a t i o n and the d e s i r e d degree o f s i m i l a r i t y between maps of one type ( H a r t r a n f t et a l , 1970). S a b i n (1974) showed t h a t 0.8 was the optimal t h r e s h o l d value f o r the work being c a r r i e d out by the Un i t e d S t a t e s A i r Fo r c e i n a map t y p i n g p r o j e c t f o r the c o n t i n e n t a l U n i t e d S t a t e s . The s i z e of the areas b e i n g used i n t h e i r s t u d i e s was much s m a l l e r than t h a t i n the pres e n t study. Lund (19^3) used a t h r e s h o l d value o f 0.7 f o r a l a r g e g e o g r a p h i c a l area i n the n o r t h e a s t e r n U n i t e d S t a t e s . T h i s value was adopted f o r the present study s i n c e p r e l i m i n a r y work showed t h a t a value of 0.8 produced 88 an unacceptably l a r g e number of types and u n c l a s s i f i e d days. 4.3 SYNOPTIC WEATHER TYPES FOR 1963-72 4.3.1 Procedure Data f o r a 113 p o i n t g r i d c o v e r i n g B r i t i s h Columbia and the adjacent areas of the P a c i f i c Ocean (see F i g . 4.1) were e x t r a c t e d from the North American r e c t a n g u l a r g r i d of m e t e o r o l o g i c a l data a v a i l a b l e from the Canadian M e t e o r o l o g i c a l Centre. T h i s g r i d i s drawn on a p o l a r s t e r e o g r a p h i c p r o j e c t i o n with a g r i d p o i n t s p a c i n g a v e r a g i n g 381 km. Values of the lOO^kt'a h e i g h t s f o r 0000 h GMT f o r each day i n the t e n year p e r i o d 1963-72 were analysed. Due to computer l i m i t a t i o n s , data were analysed one year at a time with 25 types chosen per year. The r e s u l t i n g 250 type p a t t e r n s were i n t u r n analysed as a group u s i n g the same procedures as f o r the annual analyses and from t h i s the f i n a l types were determined. To q u a l i f y as a f i n a l type, a minimum of 37 days (or about Vfo of the t o t a l 3653 days) had to be a l l o c a t e d to th a t type. 4.3.2 D e s c r i p t i o n and Frequency For the ten year p e r i o d , 28 types i n f i v e b a s i c groups were i d e n t i f i e d . These groups were s u b j e c t i v e l y named from the dominant, map f e a t u r e s . There were a l s o 89 F I G . 4.1 The 113 P o i n t D a t a G r i d f o r B r i t i s h C o l u m b i a and t h e A d j a c e n t A r e a s o f t h e P a c i f i c Ocean 90 u n c l a s s i f i e d and m i s s i n g data groups r e p r e s e n t i n g 2 3 . 8 % and 2.5% of the t o t a l number of days, r e s p e c t i v e l y . Table 4 . 1 l i s t s the types and t h e i r f r e q u e n c i e s d u r i n g the te n year p e r i o d . Maps and summary data f o r these s y n o p t i c weather types are g i v e n i n Appendix 1. From Table 4 . 1 , 'Highs' r e p r e s e n t e d 4 3 . 6 % of a l l days while 'Lows' c o n s t i t u t e d o n l y 3 0 . 1 % . Maunder ( 1 9 6 8 ) , u s i n g a s u b j e c t i v e c l a s s i f i c a t i o n technique i n a two year study ( 1964-65) f o r an area centred over Vancouver I s l a n d , found t h a t 38% of the maps were Highs and 54% were Lows. The d i s c r e p a n c y between the two s t u d i e s may be due, i n p a r t , to the much l a r g e r area and low g r i d p o i n t d e n s i t y used i n the p r e s e n t a n a l y s i s . T h i s may r e s u l t i n a f a i l u r e to r e c o g n i s e s m a l l lows near Vancouver I s l a n d e s p e c i a l l y i n summer. Bauer (1975) has noted t h a t f o r l a r g e g r i d areas, the Lund technique w i l l o f t e n overlook s m a l l l o c a l l y s i g n i f i c a n t f e a t u r e s . Another p o s s i b l e source of d i s c r e p a n c y i s the f a c t t h a t the s u b j e c t i v e technique used by Maunder ' f o r c e s ' many maps i n t o a type which would otherwise remain u n c l a s s i f i e d i n a more o b j e c t i v e c l a s s i f i c a -t i o n . Only 8% o f Maunder*s maps were miscellaneous or u n c l a s s i f i e d . The dominant 'Ocean Highs' and 'Ocean Lows* found i n the p r e s e n t a n a l y s i s were a l s o e vident i n Maunder's study. 91 TABLE 4 . 1 The S y n o p t i c Types and T h e i r Frequencies % of Group Type # Map Date Frequency. - T o t a l Ocean Highs _ Land Highs Kid*^e'sia^aa Troughs u*:-" ? Ocean Lows 2 J u l y 5 1 9 6 4 318 8 . 7 ~ " 5 / June 6 196-3 111 3 . 0 19 June 12 1966 105 2 . 9 22 Jan. 15 1 9 6 3 9 4 2 . 6 25 J u l y 13 1966 90 2 . 5 13 May 14 1 9 6 4 5 5 1 . 5 18 J u l y 10 1 9 6 5 4 9 1 . 3 A l l Ocean Highs ' 822 2 2 . 5 6 Sept. 1 1 1970 6 5 1 . 8 20 Jan. 4 1 9 7 0 48 1 . 3 28 May 5 1 9 7 2 37 1 . 0 A l l Land Highs . 150 4 . 1 1 Mar. 3 1 9 6 4 2 6 0 7 . 1 2 4 Apr. 27 1 9 6 5 119 3 . 3 16 Apr. 25 1 9 6 3 108 3 . 0 12 Nov. 15 1 9 6 4 95 2 . 6 17 J u l y 2 3 1968 40 l . l A l l R'id;ges.ic ! & 9 S 6 2 2 1 7 . 0 10 Apr. 7 1 9 7 0 73 2 . 0 11 Jan. 30 1 9 6 6 5 9 1 . 6 7 Mar. 17 1 9 6 3 5 4 1 . 5 A l l Troughs.: ighffl 186 5 . 1 4 Nov. 19 1 9 6 9 288 7 . 9 3 Oct. 11 1 9 6 7 146 4 . 0 26 Oct. 3 ;1968 104 2 . 8 15 Oct. 25 1 9 6 3 102 2 . 8 • 8 J u l y 27 1 9 6 5 58 1 . 6 9 Jan. 4 1 9 6 5 5 2 1 . 4 14 Nov. 27 1970 4 3 1 . 2 2 3 Dec. 21 1 9 6 4 4 3 1 . 2 21 Dec. 2 9 1970 4o 1 . 1 27 Dec. 10 1 9 6 8 37 1 . 0 A l l Ocean Lows 9 1 3 2 5 . 0 92 4.3-3 Seasonal and In t r a - a n n u a l Frequency D i s t r i b u t i o n s Table 4.2 i n d i c a t e s t h a t there was a marked se a s o n a l v a r i a t i o n i n the occurence of the v a r i o u s s y n o p t i c weather types. Ocean Highs were dominant i n summer (June to August) with these p a t t e r n s c o n s t i t u t i n g 46.3$ of a l l summer days whereas Lows were q u i t e i n f r e q u e n t . Maunder (1968) found t h a t Lows comprised 38$ of summer days again i n d i c a t i n g t h a t the technique used here may have missed s m a l l summer Lows. In winter, Ocean Lows accounted f o r 43.6$ of a l l days while a l l c a t e g o r i e s of Highs were much l e s s f r e q u e n t . T h i s i s i n c l o s e r agreement w i t h Maunder*s f i n d i n g s where h i s 'Gulf of A l a s k a Lows' accounted f o r 39•8$ of wint e r days. Table 4,5 Table teg shows t h a t the frequency of occurence f o r the v a r i o u s types f l u c t u a t e d s l i g h t l y between ye a r s . . The year 1964 had the h i g h e s t frequency of Highs as w e l l as the lowest frequency of Lows. The opposite was the case f o r the year 1969. 4.3.4 P e r s i s t e n c y and Sequence A n a l y s i s S c h o l e f i e l d (1972) noted t h a t one of the most important aspects of weather p a t t e r n c l a s s i f i c a t i o n i s the a n a l y s i s of the .pe r s i s t e n c y of the determined types. Knowledge of t h i s i s important i n order to implement the t y p i n g scheme f o r f o r e c a s t use or f o r c l i m a t o l o g i c a l a p p l i c a t i o n s . Besson (1924) d e f i n e d a c o e f f i c i e n t of TABLE 4.2 Frequency of Occurence by Seasons for the Synoptic Type Groups Groun # Types Winter Spring Summer Autumn A l l Year • (Dec -Feb) (Mar-May) (Jun-Aug) (Sept-Nov) Frea $ Freq Freq Freq JL. Freq f Ocean Highs 7 97 10.7 186 20.2 426 46.3 113 12.4 822 22.5 Land Highs 3 45 5.0 55 6.0 25 2.7 25 2.7 150 4.1 Ridges idp;e 3 5 112 12.4 162 17.7 I69 18.4 179 19.7 622 17.0 A l l Highs 15 254 28.1 403 43.8 620 67.4 317 34.8 1594 43.6 T,:p©u!ghsu^:- 3 74 8.2 • 52 5.7 22 2.4 38 4.2 186 5-1 Ocean Lows; 10 394 43.6 200 21.7 34 3.7 285 31.3 913 25.0 A l l Lows 13 468 51.8 252 27.4 56 6.1 323 35.5 1099 30.1 U n c l a s s i f i e d 2 181 20.0 265 28.8 244 26.5 270 29.7 960 26.3 & Missing T A B L E 4.3 I n t r a - a n n u a l F r e q u e n t j y a j T O c c u r e n c e f o r t h e S y n o p t i c T y p e G r o u p s G r o u p 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 Avera,£ O c e a n H i g h s 113 107 84 82 92 50 63 81 86 64 82 . 2 L a n d ' H i g h s 10 8 12 16 11 26 19 17 9 22 15.0 R ' i d g e s i d - r a s 44 73 64 67 59 66 58 71 57 63 62.2 A l l H i g h s 167 188 160 165 162 142 l4o 169 152 149 159.4 T r o u g h s u^;-; 16 18 18 18 16 12 19 25 21 23 18 .6 O c e a n L o w s 99 73 95 90 84 109 110 91 89 73 91.3 A l l L o w s 115 91 113 108 100 121 129 116 110 96 109.9 U n c l a s s i f i e d 75 83 92 90 93 99 77 75 86 100 87.0 Missing M i s s i n g 8 4 0 2 10 4 19 5 17 21 9.0. 95 r p e r s i s t e n c e (R-n) where ( 4 . 2 ) P i s the g e n e r a l p r o b a b i l i t y of an event ( i . e . the r a t i o of t o t a l occurences or days to t o t a l p o s s i b l e or t o t a l number of days) and P^ i s the p r o b a b i l i t y t h a t the event w i l l occur a f t e r an occurence on the pre v i o u s day. Brooks and C a r r u t h e r s (1953) d e r i v e d a c o e f f i c i e n t comparable to a c o r r e l a t i o n c o e f f i c i e n t ( i . e . no p e r s i s t e n c e equals zero and complete p e r s i s t e n c e equals one) from Besson's p e r s i s t e n c e c o e f f i c i e n t such t h a t 1 P (R B + D 2 which r e w r i t t e n i n terms of P and P^ i s 1 - P. 2 r p = 1 - ( 1 - P > ' Values of r were c a l c u l a t e d f o r each of the s y n o p t i c weather types i n the presen t study and are g i v e n i n Table 4 . 4 . P e r s i s t e n c e c l a s s e s were a r b i t r a r i l y d e f i n e d as f o l l o w s : V 0 . 6 0 P e r s i s t e n t r p 00150 - 0 . 5 9 Moderately P e r s i s t e n t Jr r p r P r P 0 . 4 0 - 0 . 4 9 Intermediate 0 . 3 0 - 0 . 3 9 Moderately T r a n s i e n t < 0 . 3 0 T r a n s i e n t ( 4 . 3 ) ( 4 . 4 ) 96 TABLE 4 . 4 P e r s i s t e n c y of the Sy n o p t i c Weather Types Group Type # Ocean Highs J L P e r s i s t e n c e C l a s s Land Highs ~ R i d g e l i c ^ = -Tiroughs't'.&h.s Ocean Lows U n c l a s s i f i e d M i s s i n g 2 . 0 8 7 . 4 6 5 . 6 6 P e r s i s t e n t 5 . 0 3 0 . 2 2 5 .36 Mod. T r a n s i e n t 19 . 0 2 9 ,190 . 3 0 Mod. T r a n s i e n t 22 . 0 2 6 .351 .56 Mod. P e r s i s t e n t 25 . 0 2 5 . 2 0 0 . 3 3 Mod. T r a n s i e n t 13 . 0 1 5 . 4 0 0 . 6 3 P e r s i s t e n t 18 . 0 1 3 .286 .48 Intermediate 6 .018 . 2 9 2 .48 Intermediate 20 . 0 1 3 .417 . 6 5 P e r s i s t e n t 28 .0.10 .270 .46 Intermediate 1 . 0 7 1 . 3 6 5 . 5 3 Mod. P e r s i s t e n t 24 . 0 3 3 .210 . 3 3 Mod. T r a n s i e n t 16 - . 0 3 0 .167 .26 T r a n s i e n t 12 . 0 2 6 . 2 5 3 .41 Intermediate 17 .011 . 2 2 5 . 3 9 Mod. T r a n s i e n t 10 . 0 2 0 .137 . 2 3 T r a n s i e n t 11 .016 . 3 3 9 .55 Mod. P e r s i s t e n t 7 . 0 1 5 .130 . 2 2 T r a n s i e n t 4 . 0 7 9 .472 . 6 7 P e r s i s t e n t 3 . 0 4 0 . 1 6 4 . 2 4 T r a n s i e n t 26 . 0 2 8 . 144 . 2 2 T r a n s i e n t 15 . 0 2 8 .216 . 3 5 Mod. T r a n s i e n t 8 .016 .155 . 2 6 T r a n s i e n t 9 .014 • 385 .61 P e r s i s t e n t 14 . 0 1 2 . 3 4 9 .57 Mod. P e r s i s t e n t 23 . 0 1 2 .326 . 5 4 Mod. P e r s i s t e n t 21 .011 . 0 5 0 . 0 8 T r a n s i e n t 27 . 0 1 0 . 1 8 9 • 33 Mod. T r a n s i e n t . 2 3 8 . 4 6 3 . 5 0 Mod. P e r s i s t e n t . 0 2 5 . 133 . 2 1 T r a n s i e n t 97 G e n e r a l l y , p e r s i s t e n t and t r a n s i e n t t y p e s "both o c c u r i n a l l groups. The more f r e q u e n t t y p e s (Types 2, 4 and l ) tended t o he p e r s i s t e n t but Type 3» "the f o u r t h most common, was t r a n s i e n t . T h i s concept of t r a n s i e n t type l e a d s t o an a n a l y s i s o f the sequence of t y p e s . F o r example, a l t h o u g h Type 3 was t r a n s i e n t , i t was f o l l o w e d and p r e c e d e d ^ by t y p e s w i t h i n i t s own group (Ocean Lows) much more o f t e n t h a n e x p e c t e d from i t s g e n e r a l f r e q u e n c y o f occurence (see Table 4 .5) . T h i s c h a r a c t e r i s t i c of b e i n g a s s o c i a t e d w i t h t y p e s from w i t h i n t h e i r own group was common t o most t y p e s . Types which are f o l l o w e d by and preceeded by the u n c l a s s i f i e d group (U) more o f t e n t h a n expected by chance can be s a i d t o be a s s o c i a t e d w i t h p o o r l y d e f i n e d weather p a t t e r n sequences. Such t y p e s are summarized i n T a b l e 4 .6. A l l t h r e e Land Highs a r e i n c l u d e d ( a l t h o u g h Type 20 o n l y f o r the 'precededo, by' a n a l y s i s ) and a l l were among the l e a s t f r e q u e n t t y p e s . I n f a c t , the 14 most f r e q u e n t t y p e s were a l l a s s o c i a t e d w i t h the u n c l a s s i f i e d c a t e g o r y l e s s o f t e n t h a n expected by chance i n d i c a t i n g t h a t the b e t t e r d e v e l o p e d weather sequences are a l s o the more f r e q u e n t ones. 4.3.5 Subsequent A p p l i c a t i o n Once e s t a b l i s h e d , the s y n o p t i c weather types can be used t o d e s c r i b e s p a t i a l p a t t e r n s of p r e c i p i t a b l e w a t e r 9 8 i TABLE 4 . 5 Antecedent and Subsequent P a t t e r n s f o r Type 3 Number of Occurences — Ocean Highs Land Highs R'id'gesii'i^es Troughs;.-: M"! S Ocean Lows Expected Preceeded or Followed by 33 6 25 7 36 Ocean Lows (excl.Type 3) 30 U n c l a s s i f i e d / M i s s i n g 39 A c t u a l Followed M 14 0 11 8 8 2 5 8 31 A c t u a l Preceed J2Z 13 0 17 15 82 58 19 99 TABLE 4 . 6 S y n o p t i c Types A s s o c i a t e d with the U n c l a s s i f i e d Group (U) More Often Than Expected "by Chance Type Frequency Followed "by U Preceeded by U expect a c t u a l expect a c t u a l 6 (Land High) 65 15 22 15 22 20 (Land High) 48 ( 11 6 ) 11 18 28 (Land High) 37 9 12 9 12 8 (Ocean Low) 58 14 23 14 24 14 (Ocean Low) 43 10 16 10 16 18 (Ocean High) 49 12 25 ( 12 9 I 100 and s o l a r r a d i a t i o n w i t h i n the r e g i o n . In chapter 5> the d i s t r i b u t i o n of p r e c i p i t a b l e water with r e s p e c t to s y n o p t i c type w i l l be analysed. Subsequently, values of p r e c i p i t a b l e water w i l l be assigned f o r v a r i o u s l o c a t i o n s by knowing the s y n o p t i c type f o r the day. T h i s p r e c i p i t a b l e water i n f o r m a t i o n w i l l be used i n chapter 6 as input to the s o l a r r a d i a t i o n model f o r t o t a l s o l a r r a d i a t i o n c a l c u l a t i o n s i n B r i t i s h Columbia. The s o l a r r a d i a t i o n d i s t r i b u t i o n s e s t a b l i s h e d i n chapter 6 w i l l then be r e l a t e d to the s y n o p t i c weather types i n chapter ? 7 i n order to e s t a b l i s h s y n o p t i c s o l a r r a d i a t i o n regimes f o r B r i t i s h Columbia. 101 CHAPTER 5 PRECIPITABLE WATER 5 . 1 COMPUTATION 5 . 1 . 1 General Procedure One of the m e t e o r o l o g i c a l parameters t h a t must be s p e c i f i e d as input to the c l o u d l e s s sky s o l a r r a d i a t i o n model i s p r e c i p i t a b l e water (u). P r e c i p i t a b l e water i s d e f i n e d as the mass of water vapour contained i n a v e r t i c a l column of a i r , of u n i t c r o s s - s e c t i o n , between any two l e v e l s (Mcintosh and Thorn, 1 9 7 2 ) . F o r a g i v e n l a y e r , u ( i n mm) i s g i v e n by: P-i u = H * o p r p 2 g S r dp, ( 5 . D where p^ and p 2 are the two pressure l e v e l s (kPa) being _ p c o n s i d e r e d , g i s a c c e l e r a t i o n due to g r a v i t y (m s ) and -1 r i s the average mixing r a t i o f o r the l a y e r (g kg ). In terms of r e l a t i v e humidity (RH), Hay (1970b) g i v e s 6 2 1 . 9 s_ s RH 1+ RH 2 ( p r p 2 ) u p r p 2 98 -Pj+Pg" . 2 . where e g i s s a t u r a t i o n vapour pressure (kPa) at the wet bulb 102 temperature and RH i s g i v e n as a decimal f r a c t i o n . F o r the e n t i r e v e r t i c a l extent of the atmosphere, n u = 2 u , (5.3) i = l p i p i + l where n i s the t o t a l number of l a y e r s being c o n s i d e r e d i n the atmospheric column. T h i s method can be used to c a l c u l a t e p r e c i p i t a b l e water where upper a i r radiosonde data are a v a i l a b l e and was the method employed f o r c a l c u l a t i n g u i n the s t u d i e s i n chapters 2 and J>. In the absence of radiosonde data, the value of p r e c i p i t a b l e water must be obtained by u s i n g an a l t e r n a t e method. Often, r e l a t i o n s h i p s between u and the a c t u a l s u r f a c e vapour p r e s s u r e (e) or dew p o i n t have been used (Monteith, 1961; Smith, 1966; Hay, 1970b; Atwater and B a l l , 1976). However, these e m p i r i c a l r e l a t i o n s h i p s have c o e f f i c i e n t s which are s p a t i a l l y v a r i a b l e (Hay, 1970b). In the p r e s e n t study, upper a i r im^Qrmationawas'bavailableeat three l e v e l s (85>!> 700 and 50<fikBaj) f o r the r e c t a n g u l a r g r i d used i n the s y n o p t i c t y p i n g a n a l y s i s (see F i g . 4.1). T h e r e f o r e , a method was sought by which u c o u l d be obtained f o r the B r i t i s h Columbia r e g i o n u s i n g t h i s upper a i r i n f o r m a t i o n . 5.1.2 C a l c u l a t i o n f o r T h r e e - l e v e l G r i d Data The a v a i l a b l e three l e v e l g r i d data i n c l u d e d temperature and dew p o i n t d e p r e s s i o n twice d a i l y (0000 and 103 1200 h GMT). These three l e v e l s (85? 70.1;) and 5 0 W a ) s u p p l i e d two l a y e r s from which to c a l c u l a t e p r e c i p i t a b l e water. S i n c e p r e c i p i t a b l e water i s concentrated i n the lowest l a y e r s , a c a l c u l a t i o n based on atmospheric l e v e l s b e g i n n i n g at 850kPa w i l l underestimate the a c t u a l value of u. Therefore, a r e l a t i o n s h i p was sought between precipitabibe water c a l c u l a t e d from a complete eleven l e v e l radiosonde ascent ( u ^ ) and from the three l e v e l s of 85.?, 700 and 500kPa ( u ^ ) . For the radiosonde s t a t i o n s of Goose, N f l d . , R e s o l u t e , NWT, Edmonton, A l t a . , P o r t Hardy, B.C., P r i n c e George, B.C. and F o r t Nelson, B.C., u^ and u ^ were c a l c u l a t e d u s i n g twice d a i l y values f o r the t e n year, p e r i o d 1961-70. Regressions of u^ versus u ^ were performed where u l l = a ' + " b ' u 3 » ( 5 . 4 ) and, f o r c i n g the r e g r e s s i o n through the o r i g i n , u l l = b o u 3 ' ( 5 - 5 ) where a', b* and b Q are r e g r e s s i o n c o e f f i c i e n t s . R e s u l t s f o r the 6 l o c a t i o n s are g i v e n i n Table 5-l« S i n c e these s t a t i o n s are at d i f f e r e n t e l e v a t i o n s , d e v i a t i o n s i n the v a l u e s of the r e g r e s s i o n c o e f f i c i e n t s can be expected s i n c e h i g h e r s t a t i o n s would have r e l a t i v e l y l e s s of t h e i r t o t a l 104 TABLE 5.1 R e g r e s s i o n of 3-Level Versus 11-Level P r e c i p i t a b l e Water Values f o r the P e r i o d 1961-70 L o c a t i o n # Days a' SE of a* V r SE b 0 SE 0 Goose 7215 1.0 .04 1.74 • 97 1.8 I.85 1.9 R e s o l u t e 7006 0.6 .02 1.77 .97 1.0 1.89 1.0 Edmonton 7262 0.4 .03 1.39 .98 1.3 1.43 1.3 P o r t Hardy- 7190 3.8 .05 1.62 .94 2.1 2.03 2.7 P r i n c e George 7263 0.5 .03 1.40 .98 1.1 1.46 1.2 F o r t Nelson 7240 0.2 .03 1.61 .98 1.3 I.63 1.3 N.B. r i s the c o r r e l a t i o n c o e f f i c i e n t f o r equation (5-4). S E i s the standard e r r o r (mm) f o r equation (5«4). S E q i s the standard e r r o r (mm) f o r equation (5-5)• u n i t s f o r a' and S E of a' are mm. 105 p r e c i p i t a b l e water contained i n the layer beneath 85 kPa. P l o t t i n g b' (Fig. 5.1) and b Q (Fig. 5.2) versus s t a t i o n elevation showed a systematic rel a t i o n s h i p between these parameters. A value of b' or b Q = 1 can be expected f o r elevations that correspond to the 850kPa l e v e l . Titus (1967) has shown that the average a l t i t u d e of the 85r'kRa l e v e l f o r the ten year period 1951-60 was 1460 m over Vancouver Island (seasonal range from 1410 m to 1510 m) and 1420 m over Fort Nelson (seasonal range from 1350 m to 14-70 m) which gives an approximate average value of 144-0 m f o r B r i t i s h Columbia. Therefore, a regression slope value of 1.0 f o r an elevation of 1440 m has also been plotted i n Figs. 5«1 and 5-2. E s p e c i a l l y f o r the b Q versus elevation relationship (Fig. 5.2), a strong l i n e a r relationship i s evident with an upward deviation i n the l i n e f o r the west coast s t a t i o n of Port Hardy. Since the intercept term (a') i n equation (5. i s not conveniently related to elevation and since the standard errors f o r the regression through the o r i g i n are only s l i g h t l y larger than the normal regression (see Table 5»l)» the use of the c o e f f i c i e n t b was chosen f o r land areas. In order to extend the r e l a t i o n s h i p to ocean locations, data f o r Ocean Station *P' (Latitude 50°N, Longitude l45°W) were analysed. Since the f u l l record for I96I-70 was not available at our i n s t i t u t i o n , data f o r the 4 months of January, A p r i l , July and October 1970 106 FIG. 5-1 ' R e l a t i o n s h i p o f R e g r e s s i o n C o e f f i c i e n t V t o S t a t i o n E l e v a t i o n f o r V e r s u s u ^ A n a l y s i s 2.01 1.6 - | # p ° r t H a r d y # F o r t N e l s o n 1 . 4 J 1.2 10 08H 06 ©Resolute • O . o o s e ©Prince G e o r g e " ' E d m o n t o n • 85 kPa "r~~~i 1 — i 1 — i 1 1 1 1 — T 1 1 — i — i — 500 1000 1500 E l e v a t i o n C m ) 107 FIG. 5-2 R e l a t i o n s h i p of R e g r e s s i o n C o e f f i c i e n t b to S t a t i o n E l e v a t i o n f o r Versus u ^ A n a l y s i s 2.0-f 1.8 H 1.6J 1 4 H o 12 10H 0 8 H >Port H a r d y • R e s o l u t e • " G o o s e 06-f 0 • F o r t N e l s o n • P r i n c e G e o r g e • E d m o n t o n • 85 kPa - i 1 1 1 1 1 1 1 1 — i 1 r 500 1000 1500 E l e v a t i o n ( m . ) 108 (Department of Transport, 1970b) were analysed f o r the 3 B.C. radiosonde s t a t i o n s and Ocean S t a t i o n *P' (see Table 5 - 2 ). R e s u l t s f o r the 3 B.C. s t a t i o n s were s i m i l a r to those f o r the t e n year p e r i o d i n Table 5»1 i n d i c a t i n g t h a t the s e l e c t e d 4 month data s e t was r e p r e s e n t a t i v e . For Ocean S t a t i o n *P*, the r e g r e s s i o n through the o r i g i n had a v e r y l a r g e standard e r r o r compared to the other r e s u l t s . T h e r e f o r e , the use of b' = 2 . 1 with an a d d i t i o n of a' = 7 . 4 4 mm i n equation (5*4) was adopted f o r the c a l c u l a t i o n of p r e c i p i t a b l e water over the ocean. 5 . 2 APPLICATION TO BRITISH COLUMBIA AND THE ADJACENT AREAS OF THE PACIFIC OCEAN 3 . 2 . 1 Procedure and R e s u l t s To apply the above procedure to the s y n o p t i c study area i n F i g . 4 . 1 , a r e p r e s e n t a t i v e e l e v a t i o n f o r each g r i d p o i n t was needed. These e l e v a t i o n s were c a l c u l a t e d from topographic maps (Bartholomew, 1957) as the a r e a l mean e l e v a t i o n w i t h i n an a r b i t r a r i l y chosen r a d i u s of 5 ° km around each g r i d p o i n t . F o r land s t a t i o n s , the values of b Q were then determined from F i g . 5 . 2 . Table 5 - 3 l i s t s the r e p r e s e n t a t i v e e l e v a t i o n s and values of b Q used f o r each l a n d g r i d p o i n t as numbered i n F i g . 4 . 1 . P r e c i p i t a b l e water was then c a l c u l a t e d u s i n g equation ( 5 - 5 ) . Over the ocean, u was c a l c u l a t e d from equation ( 5 . 4 ) w i t h a' = 7 •4'.-mm and b' = 2 . 1 . 109 TABLE 5.2 R e g r e s s i o n of 3-Level Versus 11-Level P r e c i p i t a b l e Water Values f o r January, A p r i l , J u l y and October 1970 L o c a t i o n # Days a' SE of a' b* r SE b b o SE 0 Ocean S t a t i o n 'P 246 7.4 • 19 2.08 .94 2.3 3.26 6.1 P o r t Hardy 244 3.8 .25 1.58 .95 2.0 2.01 2.8 P r i n c e George 244 0.4 .17 1.39 .97 1.2 1.44 1.2 F o r t Nelson 243 0.1 .16 1.58 .98 1.2 1.59 1.2 N.B. r i s the c o r r e l a t i o n c o e f f i c i e n t f o r equation (5*4). SE i s the standard e r r o r (mm) f o r equation (5.4). SE i s the 0 standard e r r o r (mm) f o r equation (5.5). u n i t s f o r a' and SE of a ' are mm. 110 TABLE 5.3 R e p r e s e n t a t i v e E l e v a t i o n s and b Q C o r r e c t i o n F a c t o r s f o r the Land G r i d P o i n t s i n F i g . 4.1 P o i n t E l e v a t i o n (m) p_ 1 163 1.76 2 1536 0.95 3 1636 0.89 5 535 1.54 6 1728 0.83 7 1430 1.01 8 2188 O.56 12 1242 1.11 13 862 1.34 14 1430 1.01 15 1256 1. 10 21 165 1.76 22 1454 0.99 23 1292 1.08 24 680 1.45 30 286 I.69 31 1270 1.10 32 1020 ' 1.24 33 644 1.47 40 1088 1.20 4l 680 1.45 42 604 1.50 43 320 1.67 49 91 1.85 50 ^ 1260 - 1. 10 51 744 1.41 P o i n t E l e v a t i o n (m) o 52 165 I.76 53 320 I.67 54 320 I.67 61 903 1.32 62 1338 1.06 63 636 1.48 64 178 I.76 65 91 1.85 72 2740 0.24 73 1256 1.10 74 274 1.70 75 274 1.70 76 68 1.88 83 884 1.32 84 398 1.62 85 531 1.54 91 119 1.80 92 241 1.72 93 450 1.59 94 499 1.56 95 • 90 1.85 101 90 1.85 102 13 2.03 103 463 1.58 104 18 2.03 I l l D a i l y v a l u e s of u were c a l c u l a t e d as the average of the 1200 GMT (0400 PST) and 0000 GMT (next day) (1600 PST) values f o r a l l days i n the t e n year p e r i o d ( 1 9 6 3 - 7 2 ) of the s y n o p t i c study. The o v e r a l l average p r e c i p i t a b l e water d i s t r i b u t i o n f o r the t e n year p e r i o d i s shown i n F i g . 5 « 3 ' G e n e r a l l y , u values were h i g h over the ocean and low over l a n d with e s p e c i a l l y low v a l u e s i n the mountainous r e g i o n s . Values tended to decrease northward. These i n f l u e n c e s of topography and l a t i t u d e were a l s o observed by Hay (1971) i n a study of the d i s t r i b u t i o n of p r e c i p i t a b l e water over Canada. Maps of the average p r e c i p i t a b l e water f o r the s y n o p t i c types were evaluated and s e l e c t e d examples are g i v e n i n Appendix 2 . In a l l cases, the g e n e r a l p a t t e r n observed f o r the o v e r a l l average i n F i g . 5 ' 3 was preserved w i t h u b e i n g h i g h over the ocean and lower over l a n d and d e c r e a s i n g poleward. A 'Lund-type* c o r r e l a t i o n a n a l y s i s (see s e c t i o n 4 . 2 ) was performed to compare these v a r i o u s p a t t e r n s w i t h each other. C o r r e l a t i o n c o e f f i c i e n t values were a l l g r e a t e r than 0 . 8 5 i n d i c a t i n g t h a t the ' p a t t e r n s ' of u f o r each s y n o p t i c weather type are a l l s i m i l a r . However, as i n d i c a t e d i n s e c t i o n 4 . 2 i n the p r e v i o u s chapter, t h i s c o r r e l a t i o n technique does not c o n s i d e r the r e l a t i v e magnitudes. 112 F I G . 5-3 P r e c i p i t a b l e Water D i s t r i b u t i o n A v e r a g e d f o r 1963-72 f o r B.C. and t h e A d j a c e n t A r e a s o f t h e P a c i f i c Ocean (u i n mm) 113 5.2.2 S t a t i s t i c a l S i g n i f i c a n c e of the S y n o p t i c Type - P r e c i p i t a b l e Water R e l a t i o n s h i p s In the p r e v i o u s s e c t i o n , i t was shown t h a t the ' p a t t e r n s ' of p r e c i p i t a b l e water were s i m i l a r between s y n o p t i c types. However, magnitude was not c o n s i d e r e d i n the 'Lund-type* c o r r e l a t i o n comparison. Radiosonde c a l c u l a t e d p r e c i p i t a b l e water values f o r the 3 B.C. radiosonde s t a t i o n s show t h a t the mean values of u can vary c o n s i d e r a b l y between s y n o p t i c types (Table 5-4). At P o r t Hardy, f o r example, values of u ranged from an average of 0.91 cm f o r Type 20, a Land High c e n t r e d over n o r t h e r n A l a s k a predominantly i n winter, to an average of 1.93 cm f o r Type 13, a summer Ocean High. A n a l y s i s of v a r i a n c e was performed on the s y n o p t i c type - p r e c i p i t a b l e water d i s t r i b u t i o n s to determine whether the s y n o p t i c types were a c t u a l l y d i s c r i m i n a t i n g p r e c i p i t a b l e water d i s t r i b u t i o n s , T h i s a n a l y s i s was performed i n two stages: f i r s t l y , w i t h r e s p e c t to time and, secondly, with r e s p e c t to space. With r e s p e c t to time, the w i t h i n s y n o p t i c type v a r i a n c e and between s y n o p t i c type v a r i a n c e were analysed f o r each g r i d p o i n t s e p a r a t e l y . F o l l o w i n g B l a l o c k (i960), an F - r a t i o was c a l c u l a t e d f o r each of the 113 g r i d p o i n t s p l u s the 3 B.C. radiosonde s t a t i o n s where MS. F = — , (5.6) 114 TABLE 5.4 Average P r e c i p i t a b l e Water (mm) f o r Each Sy n o p t i c Type at the Three B.C. Radiosonde S t a t i o n s S y n o p t i c P r e c i p i t a b l e Water (mm)  Group Type P o r t Hardy P r i n c e George F o r t Nelson Ocean Highs 2 18.6 14.5 14.8 5 16.0 13.3 13.7 19 16.2 11.6 11.4 22 13.1 8.0 7.0 25 16.1 13.4 14.5 13 19.3 15.6 16.6 18 \ 17.7 14.8 15.7 Land Highs 6 14.2 9.4 10.2 20 9.1 5.2 4.5 28 12.5 9.1 99/.14 Ridges 1 15.2 10.5 9.4 24 18.6 13.4 12.4 16 15.7 12.4 12.8 12 16.1 10.4 10.5 17 16.4 13.5 13.5 Troughs 10 13-9 9.5 8.0 11 13.2 8.1 6.4 7 13.1 9.0 8.1 Ocean Lows 4 15.2 9.1 6.8 3 16.6 10.7 9.0 26 17.6 11.8 10.5 15 16.3 10.2 8.3 ' 8 12.3 7.9 6.6 9 9.3 5.0 2.4 14 10.2 6.1 4.0 23 10.7 5.4 3.7 21 13.5 8.7 6.6 27 13.4 8.1 5.0 U n c l a s s i f i e d 15. 1 10.6 10.1 M i s s i n g 14.8 10.8 9.1 A l l Days 15.4 10.8 10.0 115 where MS w and MS^ are the mean squares of p r e c i p i t a b l e water w i t h i n types and between types r e s p e c t i v e l y . R e s u l t s are g i v e n i n Table 5«5» From Panofsky and B r i e r (1958), an F - r a t i o g r e a t e r than 1.4-7 ( f o r the a p p r o p r i a t e degrees of freedom a t the 5f° confidence l e v e l ) and 1.71 (at the lfo c o n f i d e n c e l e v e l ) i n d i c a t e s t h a t , w i t h r e s p e c t to p r e c i p i t a b l e water, the s y n o p t i c weather types e x h i b i t g r e a t e r v a r i a n c e between than w i t h i n types. In a l l cases, the value of F i s l a r g e r than these c r i t i c a l v a l u e s i n d i c a t i n g t h a t the s y n o p t i c types do indeed d i s c r i m i n a t e p r e c i p i t a b l e water d i s t r i b u t i o n s , over time. To determine which s y n o p t i c types had ' d i f f e r e n t ' and ' s i m i l a r * p r e c i p i t a b l e water d i s t r i b u t i o n s when s p a t i a l l y compared to other s y n o p t i c types, a T - t e s t 'by matched p a i r s ' was performed. T h i s method i n v o l v e d a n a l y s i n g each s y n o p t i c type a g a i n s t each other type s e p a r a t e l y , thus d e r i v i n g 29 v a l u e s of the s t a t i s t i c t f o r each s y n o p t i c type (N.B. There were 28 types p l u s u n c l a s s i f i e d and m i s s i n g data groups f o r a t o t a l of 3° ' t y p e s ' ) . F o l l o w i n g B l a l o c k (I960), t = — r 2 — I . (5.7) ^ - S D / ( N - l ) 2 where X^ i s the mean d i f f e r e n c e between each p a i r of p o i n t s on the two maps, i s the standard d e v i a t i o n between p a i r i n g s and N i s the number of p a i r i n g s (113 i n t h i s a n a l y s i s ) . 116 TABLE 5.5 Synoptic Type - Precipitable.Water D i s t r i b u t i o n Analysis: F-ratios f o r the 113 Grid Points and B.C. Radiosonde Stations Location F-r a t i o Location Port Hardy 13.7 37 Pr. George 22.7 38 Ft. Nelson 36.5 39 1 7.6 40 2 11.8 41 3 14.6 42 4 3.8 43 5 3.4 44 6 7.3 45 7 10.2 46 8 13.7 47 9 4.4 48 10 4.2 49 11 4.1 50 12 4.9 51 13 6.2 52 14 8.8 53 15 14.6 54 16 6.1 55 17 6.8 56 18 6.9 57 19 6.4 58 20 5.4 59 21 5.4 60 22 9-3 61 23 15.8 62 24 23.8 63 25 7.8 64 ' 26 9.6 65 27 10.7 66 28 9.9 67 29 7.-7 68 3© 1,7.4 69 31 12.4 70 32 19.7 71 33 24.5 72 34 9.2 73 35 U . 5 74 36 . 13.1 75 F - r a t i o Location F-rat] 13.3 76 20.6 11.2 77 19.9 11.3 78 22.6 15.0 79 . 23.5 21.1 80 22.1 25.0 81 18.7 26.6 82 18.8 11. 1 83 21.7 13.7 84 25.7 13.8 85 25.1 13.7 86 22.8 13.8 87 19.6 13. 1 88 24.1 17. 1 89 24.9 21.0 90 21.2 27.6 91 20.2 26.4 92 20.2 27.5 93 21.3 14.6 94 25.4 16.2 95 22.7 12.8 96 17.7 11.9 97 21.6 14.8 1 - 98 21.5 17.8 99 16.3 18.3 100 18.9 23.7 101 19.1 26.8 102 19.9 26.7 103 20.4 23.4 104 17.9 18.1 105 16.8 19.3 106 19-7 16.4 107 19.5 15.7 108 16.6 16.5 109 14.6 20.4 110 17.6 22.0 111 17.0 26.6 112 16.8 26.5 113 15.2 23.8 117 T h i s procedure y i e l d s a symmetrical m a t r i x of t values f o r the s y n o p t i c types. Values of t below 2.62 (Panofsky and B r i e r , 1958) at the 1% confidence l e v e l ( f o r the degrees of freedom i n t h i s study) i n d i c a t e d t h a t the two types under c o n s i d e r a t i o n had the 'same' s p a t i a l p r e c i p i t a b l e water d i s t r i b u t i o n s . Of the 435 combinations of s y n o p t i c type comparisons (30 'types* X 29 t values f o r each / 2 s i n c e i t s a symmetrical m a t r i x ) , only 54 or 12.4% had the 'same' p r e c i p i t a b l e water d i s t r i b u t i o n s at the 1% confidence l e v e l . Of these, most were between types w i t h i n the same s y n o p t i c group ( i . e . Ocean Highs, Land Highs, e t c . ) . The above r e s u l t s i n d i c a t e t h a t although the g e n e r a l ' p a t t e r n s ' of p r e c i p i t a b l e water are c o n s i s t e n t over B r i t i s h Columbia and the adjacent areas of the P a c i f i c Ocean,, the s y n o p t i c weather types can d i s c r i m i n a t e p r e c i p i t a b l e water d i s t r i b u t i o n s q u i t e w e l l when magnitude i s a l s o c o n s i d e r e d . 5.2.3 • Subsequent A p p l i c a t i o n In the p r e v i o u s s e c t i o n , i t was shown t h a t the s y n o p t i c types do d i s c r i m i n a t e p r e c i p i t a b l e water f i e l d s . T h e r e f o r e , the s y n o p t i c type - p r e c i p i t a b l e water d i s t r i b u t i o n maps can be used to s p e c i f y u f o r a g i v e n day of known s y n o p t i c type f o r any l o c a t i o n on the map. S p e c i f i c a t i o n of u i s accomplished by i n t e r p o l a t i o n between i s o l i n e s on maps such as those shown i n Appendix 2. 118 T h i s procedure w i l l be employed i n the next chapter to o b t a i n values of u f o r use i n the s o l a r r a d i a t i o n model a p p l i e d to B r i t i s h Columbia. 119 CHAPTER 6 SOLAR RADIATION IN BRITISH COLUMBIA 6.1 APPLICATION OF THE SOLAR RADIATION MODEL 6.1.1 S e l e c t i o n and V a l i d a t i o n of Study Year - 1972 In order to expand the s o l a r r a d i a t i o n information f o r B r i t i s h Columbia, the CLS model was a p p l i e d . One year was chosen f o r study to l i m i t the amount of computation. S i n c e subsequent a n a l y s i s of s y n o p t i c type - s o l a r r a d i a t i o n r e l a t i o n s h i p s was to be undertaken, a year from the p e r i o d of the s y n o p t i c study i n chapter k was needed. Being the most re c e n t of these y e a r s , 1972 had the l a r g e s t p o t e n t i a l number of s o l a r r a d i a t i o n s t a t i o n s f o r the r e g i o n and hence was chosen f o r study. F i g . 6.1 shows the l o c a t i o n of the ten s t a t i o n s t h a t measured Kj. i n the area d u r i n g 1972 and an a d d i t i o n a l 13 l o c a t i o n s which had measurements of h o u r l y c l o u d data and b r i g h t sunshine a l l o w i n g supplementataon:. ;:'of^theosolar r a d i a t i o n network by use of the CLS model. Thus, a t o t a l of 23 s t a t i o n s with Kj i n f o r m a t i o n was a v a i l a b l e . Of the t e n measuring s t a t i o n s , f i v e a l s o measured the a p p r o p r i a t e c l o u d and sunshine parameters which enabled f u r t h e r independent t e s t i n g of the CLS model. For Summerland, the m e t e o r o l o g i c a l o b s e r v a t i o n s of c l o u d were obtained from P e n t i c t o n . 120 FIG.. 6.1 S o l a r R a d i a t i o n M e a s u r i n g and M o d e l l i n g S t a t i o n s i n t h e B r i t i s h C o l u m b i a A r e a • m e a s u r e d • m e a s u r e d & mode l led • mode l led 121 The r e p r e s e n t a t i v e n e s s of the year 1972 was analysed i n i t i a l l y with r e s p e c t to s o l a r r a d i a t i o n measurements f o r S a n d s p i t , Summerland, Vancouver and Beaverlodge, A l t a . and f o r Annette, A l a s k a (55°02' N; 131°3V W) i n the A l a s k a n panhandle n o r t h of P r i n c e Rupert. Data f o r t h i s l a s t s t a t i o n were e x t r a c t e d from the C l i m a t o l o g i c a l Data N a t i o n a l Summary (U.S. Department of Commerce, 1972) hut were a v a i l a b l e only f o r January to August. Long-term averages f o r Annette were determined from e a r l i e r volumes of t h i s p u b l i c a t i o n . The average d a i l y values f o r 1972 and f o r the long-term are shown f o r a l l f i v e l o c a t i o n s i n Table 6.1. In a l l cases, the 1972 s o l a r r a d i a t i o n v a l u e s were w i t h i n 5% of the long-term average. F i g . 6.2 i l l u s t r a t e s the percentage d i f f e r e n c e between mean d a i l y v a l u e s of KJ by month f o r 1972 compared to the long-term monthly averages. Trends f o r the v a r i o u s s t a t i o n s were s i m i l a r (e.g. above average i n January, August, October and December with below average values i n February, March, June and November). Therefore, with r e s p e c t to s o l a r r a d i a t i o n r e c e i p t , 1972 was not an anomalous year on the average although some i n d i v i d u a l months e x h i b i t e d c o n s i s t e n t above or below average c o n d i t i o n s . With r e s p e c t to s y n o p t i c weather types, the r e p r e s e n t a t i v e n e s s of the year 1972 was a l s o analysed., The frequency of the v a r i o u s s y n o p t i c types and comparison w i t h t h e i r average f r e q u e n c i e s over the ten year 1963-72 122 TABLE 6.1 S o l a r R a d i a t i o n Data f o r 1972 Compared to the Long-term Average # Years Long-term 1972 % L o c a t i o n Record D a i l y Average D a i l y Average D i f f e r e n c e (MJ m~ 2day _ 1) (MJ m" 2day _ 1) San d s p i t , B.C. 4 9.95 10.23 +2.8 Summerland, B.C. 10 12.86 12.99 +1.0 Vancouver, B.C. 13 11.95 11.93 -0.2 Beaverlodge, A l t a . 11 11.90 11.86 -0.3 Annette, A l a s k a 15 12.90 12.30 -4.7 (Jan.-Aug. only) 123 F I G . 6.2 J D i f f e r e n c e Between Mean D a i l y S o l a r R a d i a t i o n Values f o r Months i n 1972 Compared to the Long-term Average u c <0 C u. 30 i 20 10 £-104 -20 H -30 • J A • S a n d s p i t • S u m m e r l a n d A V a n c o u v e r r B e a v e r l o d g e v A n n e t t e A • v A • • V A • V A ~A -T M A M T T "T" A O N D J J M o n t h 1972 124 p e r i o d are g i v e n i n Table 6.2. Summarizing,' there were " more u n c l a s s i f i e d and m i s s i n g days, Land Highs and Troughs than average w i t h s l i g h t l y more Ridges. The l a r g e r groups of Ocean Highs and Ocean Lows occu r r e d l e s s o f t e n d u r i n g 1972 than t h e i r t e n year averages. Some of the i n d i v i d u a l types had l a r g e d i f f e r e n c e s between t h e i r 1972 and t e n year average f r e q u e n c i e s such as low f r e q u e n c i e s f o r Type 14 (0.23 of average), Type 22 (O.32 of average), Type 26 (0.^8 of average) and the h i g h f r e q u e n c i e s f o r Type 28 (1.62 of average), Type 23 (l.<S§ of average) and Type 6 (1.54 of average). In absolute terms, Type 2 had the l a r g e s t d e v i a t i o n from average o c c u r r i n g o n l y 21 times compared to a t e n year average of 31«8. However, d e s p i t e these i n d i v i d u a l f e a t u r e s , the i n t r a - a n n u a l a n a l y s i s i n Table 4.3 showed t h a t , except f o r a l a r g e number of u n c l a s s i f i e d and m i s s i n g days, 1972 was not the most anomalous year. A. Chi-square a n a l y s i s was performed to determine s t a t i s t i c a l l y whether 1972 was an anomalous year s y n o p t i c a l l y . From Panofsky and B r i e r (1958), „ m (O.-E.) 2 • i = l i where 0^  i s the observed type frequency, E^ i s the expected or t e n year average type frequency and m i s the t o t a l number 2 of types. Included i n Table 6.2 are the values of (0—E^) /E^ 125 TABLE 6.2 Comparison of 1972 Synopti 1972 Group Type Frequency Ocean Highs 2 21 5 10 19 8 22 3 25 12 13 4 18 6 Total 64 Land Highs 6 10 20 6 28 6 Total 22 Ridges 1 23 24 17 16 8 12 10 17 5 Total 63 Troughs 10 8 11 7 7 8 Total 23 Ocean Lows 4 23 3 11 26 5 15 6 8 7 9 6 14 1 23 7 21 3 27 4 Total 73 U n c l a s s i f i e d 100 Missing 21 : Weather Type Frequencies (O.-E^ 2 Average 1972/Average gr Frequency Frequency i 31.8 0.66 3.668 11.1 0.90 0.109 10.5 0.76 0.595 9.4 0.32 4.357 9.0 1.33 1.000 5.5 0.73 0.490 4.9 1.22 0.247 82.2 0.78 6.5 1.54 1.885 4.8 1.25 0.300 3.7 1.62 1.430 15.0 1.47 26.0 0.88 0.346 11.9 1.43 2.186 10.8 0.74 0.726 9-5 1.05 0.026 4.0 1.25 0.250 62.2 1.01 7.3 1.10 0.067 5.9 1.19 0.205 5.4 1.48 1.252 18.6 1.24 28.8 0.80 1.168 14.6 , 0.75 0.888 10.4 0.48 2.803 10.2 0.59 1.729 5.8 1.21 0.248 5-2 1.15 0.123 4.3 0.23 2.533 4.3 I.63 1.695 4.0 0.75 0.250 3.7 1.08 0.024 91.3 0.80 87.0 1.15 1.943 9.0 2.33 16.000 126 f o r each type. Summary r e s u l t s of t h i s t e s t are g i v e n i n Table 6.3* S i n c e the number of m i s s i n g days i s not a d i r e c t f u n c t i o n of s y n o p t i c s i t u a t i o n s , Chi-square f o r the 28 types p l u s u n c l a s s i f i e d group i s of most r e l e v a n c e . T h i s value (32.5^3) i s below the c r i t i c a l value (see T a b l e 6.3) at each of the 1%, 5% and 10% confidence l e v e l s . T h e r e f o r e , 1972 was not an anomalous year w i t h r e s p e c t to s y n o p t i c type f r e q u e n c i e s . 6.1.2 Procedure In order to c a l c u l a t e s o l a r r a d i a t i o n , i t i s n e c e s s a r y to determine a value f o r the a e r o s o l parameter k f o r use i n the c a l c u l a t i o n of the c l o u d l e s s sky s o l a r r a d i a t i o n v a l u e s . .Following the r e s u l t s of s e c t i o n 2.5, the value of k = 0.950 determined i n the a n a l y s i s of P o r t Hardy data was used f o r the e n t i r e study area. In the absence of a method f o r a s s i g n i n g d a i l y v a l u e s f o r the s u r f a c e albedo, a was a s s i g n e d by c o n s i d e r i n g the p r e c i p i t a t i o n data contained i n the monthly m e t e o r o l o g i c a l r e c o r d s (Atmospheric Environment S e r v i c e , 1972b) f o r each s t a t i o n supplemented w i t h snow cover data where a v a i l a b l e (Atmospheric Environment S e r v i c e , 1972c, 1973). S e l l e r s (1965) g i v e s values of a = 0.2 f o r n a t u r a l v e g e t a t i o n and a = 0.8 f o r f r e s h snow with a d e c r e a s i n g as the snow ages. F o l l o w i n g t h i s , values of a were assigned f o r the e n t i r e month -for each s t a t i o n a c c o r d i n g t o : 127 TABLE 6.3 Chi-square Test R e s u l t s f o r 1972 S y n o p t i c Type Frequencies Types Chi-square Degrees of Freedom 1 to 28 30.600 27 1 to 28 + U n c l a s s i f i e d 32.543 28 1 to 28 + U + M i s s i n g 48.543 29 L i m i t i n g Chi-square Degrees of Freedom Confidence L e v e l 10 % 5 % 1 % 2$ 35.56 38.88 45.67 30 40.26 43.77 50.89 128 a = 0 . 8 f o r continuous snow cover with s u b s t a n t i a l f r e s h snow d u r i n g the month, a = 0 . 7 f o r continuous snow cover, a = 0 . 4 f o r t r a n s i t i o n a l months with some snow, a = 0 . 2 f o r no snow cover d u r i n g almost a l l of the month. The assigned values of a f o r the 13 m o d e l l i n g s t a t i o n s p l u s the 5 measuring s t a t i o n s where the model was to be f u r t h e r t e s t e d are g i v e n i n Table 6 . 4 . I t i s a l s o necessary to have d a i l y values of p r e c i p i t a b l e water f o r input to the c l o u d l e s s sky s o l a r r a d i a t i o n model. These were assigned by u t i l i z i n g the s p a t i a l r e l a t i o n s h i p s between s y n o p t i c weather types and p r e c i p i t a b l e water d i s t r i b u t i o n s found over the t e n year p e r i o d (see chapter 5 ) . From the s y n o p t i c type - p r e c i p i t a b l e water d i s t r i b u t i o n s , v a l u e s of u were determined f o r each of the l o c a t i o n s f o r each s y n o p t i c type. These are g i v e n i n Table 6 . 5 * Given the s y n o p t i c type f o r the day, v a l u e s of u were then obtained from t h i s t a b l e . The c l o u d l e s s sky model, together with the input data d e s c r i b e d above, p r o v i d e d v a l u e s of K j Q and i t s d i r e c t and d i f f u s e components f o r each day d u r i n g 1972 f o r each l o c a t i o n . The CLS model, with h o u r l y m e t e o r o l o g i c a l o b s e r v a t i o n s of c l o u d and b r i g h t sunshine, was then used to o b t a i n v a l u e s of K J i n i t i a l l y f o r the f i v e s t a t i o n s where the model was f u r t h e r t e s t e d and then subsequently f o r the other 13 l o c a t i o n s . 1 2 9 TABLE 6 . 4 Val'ues of S u r f a c e Albedo Assigned for, Each Month Dur i n g 1 9 7 2 L o c a t i o n Jan Feb Mar Apr May Jun J u l Aug Sep Oct Nov Dec A b b o t s f o r d . 7 . 4 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 4 C a s t l e g a r . 8 . 8 . 7 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 4 . 7 Cranbrook . 8 . 8 . 7 . 4 . 2 2 2 . 2 . 2 . 2 . 2 . 2 . 7 F o r t S t John . 8 . 8 . 7 . 4 . 2 . 2 . 2 . 2 . 4 . 4 . 7 . 7 Kamioops . 8 . 8 . 4 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 4 L y t t o n . 8 . 8 . 4 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 4 P o r t Hardy . 7 . 4 . 4 . 4 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 4 P r i n c e George . 8 . 8 . 7 . 4 . 2 . 2 . 2 . 2 . 2 . 2 . 4 • 7 P r i n c e Rupert . 7 . 4 . 4 . 4 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 4 S a n d s p i t . 7 . 7 . 4 . 4 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 Smithers . 8 . 8 . 7 . 4 . 2 . 2 . 2 . 2 . 2 . 4 . 4 . 7 Summerland . 8 . 7 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 4 T o f i n o . 4 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 Vancouver . 4 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 4 V i c t o r i a I.A. . 4 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 4 Wats onnlakeke . 8 . 8 . 8 . 8 . 4 . 2 . 2 . 2 . 2 . 4 . 7 . 8 Whitehorse . 8 . 8 . 7 . 7 . 4 . . 2 . 2 . 2 . 4 . 4 . • 7 . 8 W i l l i a m s Lake . 8 . 8 . 7 . 2 . 2 . 2 . 2 . 2 . 2 . 4 . 4 . 7 1 3 0 TABLE 6 . 5 -Values of P r e c i p i t a b l e Water (mm) Assigned f o r Each L o c a t i o n f o r Each Sy n o p t i c Type 0 <c CD rf T3 H CD I-H-u CD •p fl u rf rf CQ O cd 0 O CQ >> W) u -p CQ rf CD H CQ <+-{ W) 0 Pt U CD •H U H > •H O S CQ 0 u O A O ft ft CD 0 U fl rf -p H & -P O 0 rf CD CQ CD fl 0 O 0 CD •H CD 0 -P fl 00 H •p T=S -p £ •H 0 -P CQ -P H ft CQ rf -p fl •H fl O -P •H H > 3 ni •P rf >> -P u u rf e Pi O rf •H rf , f l •H EH < O O PH PH PH PH oa oa oa EH > > % & 2 1 2 9 9 1 2 9 1 0 1 9 11 1 3 1 5 1 1 9 1 7 1 3 14 9 8 1 0 5 1 1 8 8 1 2 9 10 16 11 1 2 1 3 1 1 9 9 1 1 5 1 2 1 2 9 8 1 0 1 9 1 2 8 8 10 8 1 0 16 9 1 1 1 3 9 8 1 5 1 3 14 8 7 9 2 2 8 5 5 6 6 6 1 3 6 9 1 1 7 6 1 2 9 1 0 5 4 6 2 5 11 8 8 1 2 9 10 16 10 1 2 14 1 0 9 1 5 1 2 1 2 1 0 9 1 0 1 3 1 2 9 9 14 1 0 1 1 1 9 1 2 14 1 6 1 2 1 0 1 7 1 3 14 1 1 10 1 1 18 1 3 9 9 1 2 1 0 1 1 18 l l 11 1 3 1 1 1 0 1 7 14 14 9 8 11 6 9 7 7 8 7 7 14 7 8 1 0 7 7 1 3 3 1 0 1 1 6 5 7 2 0 7 4 4 5 9 4 4 6 4 4 9 7 8 3 2 4 2 8 8 5 5 6 5 6 1 2 5 7 9 5 5 1 0 8 8 5 4 5 1 1 0 7 7 8 8 8 1 5 8 1 1 1 3 8 8 14 11 1 1 .6 5 8 24 1 2 8 8 1 1 9 10 1 9 10 14 17 1 0 9 17 1 3 14 9 8 10 1 6 1 1 8 8 10 8 9 1 6 9 1 0 1 2 9 8 1 5 1 2 1 3 8 7 9 1 2 9 7 7 9 7 7 1 6 8 11 14 8 7 1 4 10 11 7 6 8 1 7 10 9 9 1 1 9 9 16 1 0 1 0 1 2 10 9 1 5 1 1 1 2 8 7 1 0 1 0 9 7 7 8 7 7 14 8 1 0 1 2 8 7 1 3 1 0 1 1 6 5 8 1 1 9 6 6 7 6 7 1 3 7 9 1 1 7 6 1 2 1 0 11 5 4 7 7 1 0 6 6 7 7 7 8 1 3 7 7 9 7 7 1 3 1 1 1 2 5 4 7 4 11 6 6 7 7 9 1 5 7 1 0 1 3 8 8 1 5 1 2 1 3 5 4 7 3 1 2 8 8 9 8 1 0 1 7 9 1 1 14 9 8 16 1 3 14 7 6 9 2 6 1 0 6 6 8 7 8 18 8 1 3 1 6 9 7 16 11 1 2 7 6 8 1 5 1 2 7 7 8 8 1 0 16 8 1 0 1 3 8 8 1 5 1 3 14 6 5 8 8 1 0 6 6 7 7 8 1 2 7 8 10 7 7 1 2 1 2 1 2 5 4 7 9 9 5 5 3 5 7 9 4 5 7 4 6 1 0 10 1 1 2 2 5 14 1 0 6 6 4 5 7 1 0 5 6 8 5 6 1 2 1 2 1 2 3 3 5 2 3 9 5 5 3 5 7 1 1 4 6 8 4 5 1 1 11 11 3 2 5 2 1 11 7 7 7 7 8 1 3 7 9 11 7 7 1 3 1 2 1 3 5 4 7 2 7 11 6 6 5 6 8 1 3 6 1 0 1 2 7 6 1 3 1 2 1 3 4 3 7 U 1 0 7 7 8 7 8 1 5 8 1 0 1 2 8 7 14 1 1 1 2 6 5 8 m 1 0 7 7 8 7 8 1 5 8 1 0 1 2 8 7 14 11 1 2 6 5 8 131 6.1.3 Performance of the CLS Model An assessment of the performances of the CLS 1,1 and CLS 2,1 models i n B r i t i s h Columbia d u r i n g 1972 i s g i v e n i n Table 6.6. S o l a r r a d i a t i o n i s g e n e r a l l y estimated -2 -1 with a r o o t mean square e r r o r of l e s s than 2 MJ m day or 20$ (except the CLS 2,1 model at Whitehorse). These r e s u l t s are c o n s i s t e n t with the p r e v i o u s a n a l y s i s g i v e n i n Table 3«5« From Table 6.6, i t can be seen t h a t the CLS 1,1 model was b e t t e r than the CLS 2,1 model f o r a l l l o c a t i o n s except Summerland where the CLS 1,1 model was only s l i g h t l y i n f e r i o r . Thus, the CLS 1,1 model was chosen f o r a p p l i c a t i o n i n the B r i t i s h Columbia area. The model was used to c a l c u l a t e K l at these f i v e s t a t i o n s f o r days when measurements were m i s s i n g and to c a l c u l a t e Kl f o r the 13 a d d i t i o n a l l o c a t i o n s i n the study area having the r e q u i r e d m e t e o r o l o g i c a l and b r i g h t sunshine data. 6.2 DISTRIBUTION OF SOLAR RADIATION 6.2.1 Annual D i s t r i b u t i o n For the 23 s t a t i o n s shown i n F i g . 6.1, s o l a r r a d i a t i o n f o r 1972 was analysed. The mean d a i l y values of Kl on an annual b a s i s are shown i n F i g . 6.3. Values -2 -1 ranged from near 10 MJ m day m the f a r n o r t h and a l o n g -2 the n o r t h e r n coast of B r i t i s h Columbia to near lk MJ m day i n the southern i n t e r i o r r e g i o n s of the p r o v i n c e . G e n e r a l l y , v a l u e s were lower i n the n o r t h compared to 132 TABLE 6.6 Performance of the CLS Model on a Daily Basis for Estimating K i i n the B r i t i s h Columbia Area During 1972 Mean Mean Measured Location A B # days Measured Modelled RMSE RMSE /Modelled ( :-MJ m" 2day" 1 ) ( % ) Port Hardy 1 1 358 10.71 9.91 1.57 14.6 1.080 2 1 358 10.71 9.69 1.77 16.5 1.106 Sandspit 1 1 348 10.04 9.38 1.38 13.7 1.071 2 1 348 10.04 9.15 1.60 15.9 1.098 Summerland 1 1 339 13.23 13.61 I.63 12.3 0.972 2 1 339 13.23 13.43 1.51 11.4 0.985 Vancouver 1 1 358 12.07 11.75 1.43 11.8 1.028 2 1 358 12.07 11.59 1.46 12.1 1.041 Whitehorse 1 1 307 9.40 • 9.89 1.72 18.3 0.951 2 1 307 9.40 9.64 2.16 23.0 0.975 133 PIG. 6.3 -2 -1 Mean D a i l y Values of S o l a r R a d i a t i o n (MJ m day i n B r i t i s h Columbia During 1972 .10.3 .10.3 .107 .12.2 11.3 .121 .11.9 .132 .129 k,o •* 1 3 4 the south and lower on the coast than i n the i n t e r i o r . To p a r t i a l l y compensate f o r the lower average e x t r a t e r r e s t r i a l r a d i a t i o n i n the n o r t h , F i g . 6 . 4 p r e s e n t s t h i s data i n the form of mean percentage s o l a r r a d i a t i o n t r a n s m i s s i o n ( T ) . The lowest hulk t r a n s m i s s i v i t i e s were found along the coas t ( 4 l % to 44%) while the values i n the f a r n o r t h were only s l i g h t l y h i g h e r being between 45% and 4 7 % . The h i g h e s t ' T valu e s were found i n the southern i n t e r i o r r a n g i n g up to 5 4 % . 6 . 2 . 2 Seasonal D i s t r i b u t i o n The average d a i l y atmospheric t r a n s m i s s i v i t i e s are g i v e n by month f o r each of the 2 3 s t a t i o n s i n Table 6 . 7 V In order to summarize t h i s data, f i v e subregions were i d e n t i f i e d (The North, C e n t r a l I n t e r i o r , Southern I n t e r i o r , North Coast, South Coast) and the monthly t r a n s m i s s i v i t i e s averaged w i t h i n these subregions. The r e s u l t i n g s easonal trends are shown i n F i g . 6 . 5 « G e n e r a l l y , the average s o l a r r a d i a t i o n t r a n s m i s s i o n was lowest i n wint e r and h i g h e s t i n s p r i n g or summer f o r a l l r e g i o n s . Except f o r The North, a l l r e g i o n s experienced a secondary minimum i n June. The two c o a s t a l subregions were g e n e r a l l y i n phase e x p e r i e n c i n g the lowest t r a n s m i s s i v i t i e s except i n autumn when The North was lowest. In summer ( J u l y and August), the South Coast subregion experienced much h i g h e r T values thus d e v i a t i n g from i t s p a r a l l e l behaviour to t h a t of the 135 FIG. 6.4 Mean P e r c e n t a g e S o l a r R a d i a t i o n T r a n s m i s s i o n i n B r i t i s h C o l u m b i a D u r i n g 1972 TABLE 6.7 Average D a i l y S o l a r R a d i a t i o n Subregion L o c a t i o n Jan Feb j Vlar The North F o r t Nelson 39 44 48 Watson Lake 37 44 52 Whitehorse 40 50 57 C e n t r a l I n t e r i o r Beaverlodge 49 49 55 F o r t St John 43 46 55 P r i n c e George 43 46 52 Smithers 39 42 52 Will iams Lake 44 53 6i Southern I n t e r i o r C a s t l e g a r 37 42 43 Cranbrook 48 55 62 Kamioops 40 50 48 L y t t o n 40 49 49 Mt Kobau 50 56 48 Summerland 41 44 46 North Coast Cape S t James 38 34 36 P o r t Hardy 32 30 35 P r i n c e Rupert 37 37 34 Sandspit 35 37 42 South Coast Abbotsford 33 ' 34 33 Nanaimo 32 33 34 T o f i n o 28 29 30 Vancouver 30 36 35 V i c t o r i a I.A. 31 35 35 i s s i o n (%) by Month Dur i n g 1972 Apr May Jun J u l Aug Sep Oct Nov Dec Year 54 59 51 55 55 43 42 36 35 47 60 60 53 52 49 38 •42 26 28 45 60 56 54 51 48 43 38 ,35 32 47 59 62 50 53 57 41 47 42 45 51 63 67 56 56 59 46 51 35 36 51 52 64 52 58 59 44 46 27 34 48 50 6 l 50 55 53 41 46 24 37 46 51 63 54 63 63 48 56 36 41 53 49 55 47 6 l 67 50 51 30 33 47 6 l 58 54 63 69 51 50 39 41 54 50 59 49 65 64 52 53 30 32 49 52 62 51 65 65 51 53 35 34 51 57 58 46 62 67 58 58 35 43 53 51 54 47 62 65 54 53 31 35 49 44 53 44 53 54 54 46 37 40 44 37 53 45 52 53 45 48 32 34 41 44 52 40 49 53 43 46 25 27 41 45 51 41 46 41 47 43 30 38 41 40 49 42 60 62 46 48 31 30 42 43 53 43 61 62 48 50 31 26 43 41 51 45 55 56 51 50 32 31 42 44 52 46 61 62 50 50 31 28 44 43 53 46 63 65 46 49 33 27 44 137 FIG. 6.5 A v e r a g e D a i l y S o l a r R a d i a t i o n T r a n s m i s s i o n ( % ) D u r i n g 197-2 The North A A Central Interior A A Southern Interior O O North Coast • • South Coast 65 60 -1 55H 50-1 c o 45 I AO Q_ O a) 35 > < 30 25-» / A--/-, A / / / / I: 4 i i ••' i ' I A - / - A ' / • / M \ o \ &/ V i i \ \ii p-li \ *; .1 il 8 I I \ \ •  \ \ \ I 1 \ \ '. \ \ \ \ \ \ A- A I •. 1 -a 1 \ • • » / O.l; VA' \ i P ..' \\\ * \ \ \ » P i \\\\ I I A m--4 w / P-C-> i i M - r A M J J M o n t h S O N o 1972 138 North Coast. The three i n l a n d subregions had s i m i l a r t r a n s m i s s i v i t i e s f o r the f i r s t h a l f of the year a f t e r which values f o r The North were c o n s i d e r a b l y lower. Seasonal v a r i a t i o n s i n the absolute magnitude of s o l a r r a d i a t i o n r e c e i v e d at the s u r f a c e are i l l u s t r a t e d i n F i g s . 6.6 through 6.9 where mean d a i l y values of K i f o r each of the 23 s t a t i o n s are presented f o r the months of January, A p r i l , J u l y and October d u r i n g 1972. In January — 2 -1 ( F i g . 6.6), v a l u e s ranged from 1.3 MJ m day" a t Whitehorse - 2 - 1 to 5«0 MJ m day at Mt. Kobau with the g e n e r a l f e a t u r e s of the annual d i s t r i b u t i o n b e i n g maintained ( i . e . lower val u e s i n the n o r t h compared to the south and lower v a l u e s on the coast than i n l a n d ) . During A p r i l ( F i g . 6.7)» Ki i n The North was v e r y high b e i n g exceeded by only some of the more s o u t h e r l y i n t e r i o r s t a t i o n s and none of the c o a s t a l l o c a t i o n s . Values on the South Coast were s i m i l a r to those on the North Coast. Q u a n t i t i e s of Ki were i n the range of 13 to 19 MJ m" 2day _ 1. By J u l y ( F i g . 6.8), the, values i n The North were a g a i n among the lowest. S o l a r r a d i a t i o n r e c e i p t was much h i g h e r on the South Coast compared to the North Coast d u r i n g t h i s month ( r e f l e c t i n g the h i g h e r t r a n s m i s s i v i t i e s shown i n F i g . 6.5) and was s i m i l a r to . -2 t h a t found i n the Southern I n t e r i o r approaching 25 MJ m day In October ( F i g . 6.9), the mean annual p a t t e r n was again r e - e s t a b l i s h e d w i t h lower values i n the n o r t h e r n and c o a s t a l areas compared to the Southern I n t e r i o r . 139 FIG'. 6.6 - 2 Mean D a i l y V a l u e s o f S o l a r R a d i a t i o n (MJ m day i n B r i t i s h C o l u m b i a D u r i n g J a n u a r y 1972 .1.3 140 FIG. 6.7 Mean D a i l y Values of S o l a r R a d i a t i o n (MJ m~ 2day - 1) i n B r i t i s h Columbia During A p r i l 1972 141 F I G . 6.8 -2 -1 Mean D a i l y V a l u e s of S o l a r R a d i a t i o n (MJ m day ) i n B r i t i s h C o l u m b i a D u r i n g J u l y 1972 .19.4 .200 .21.4 .21.7 21.4 .226 .207 .24.7 142 F I G . 6.9 - 2 - 1 Mean D a i l y V a l u e s o f S o l a r R a d i a t i o n (MJ m day ) i n B r i t i s h C o l u m b i a D u r i n g O c t o b e r 1972 143 6.3 THE ADVANTAGE OF MODELLING SOLAR RADIATION The advantage of u s i n g numerical models to add^d'ata to the e x i s t i n g s o l a r r a d i a t i o n network i n B r i t i s h Columbia can he assessed by s t u d y i n g the s p a t i a l v a r i a b i l i t y of s o l a r r a d i a t i o n . T h i s , i n tu r n , can be analysed by c o n s i d e r i n g the standard d e v i a t i o n of s o l a r r a d i a t i o n between p a i r i n g s of measurement s t a t i o n s (Wilson and P e t z o l d , 1972; S u c k l i n g and Hay, 1976). The r e s u l t s of these two s t u d i e s have a l r e a d y been presented i n F i g . J>.k where the standard d e v i a t i o n was expressed i n ab s o l u t e terms as a f u n c t i o n of d i s t a n c e between s t a t i o n p a i r i n g s . In r e l a t i v e terms, a c o e f f i c i e n t of v a r i a b i l i t y , r , can be d e f i n e d ass r = § 5 = X 100%, (6.2) v ( K i 1 + K i 2 ) / 2 where SD i s the standard d e v i a t i o n i n the d a i l y d i f f e r e n c e s of s o l a r r a d i a t i o n between the two s t a t i o n s and Ki ^  and K i g are the mean d a i l y values of s o l a r r a d i a t i o n f o r each s t a t i o n . The s t a t i o n s and the s e p a r a t i o n d i s t a n c e s used by S u c k l i n g and Hay (1976) are g i v e n i n Table 6.8 but now with the a d d i t i o n of Mt. Kobau. C o e f f i c i e n t s of s o l a r r a d i a t i o n v a r i a b i l i t y were c a l c u l a t e d f o r each of the 36 s t a t i o n p a i r i n g s and these values are p l o t t e d a g a i n s t s e p a r a t i o n d i s t a n c e s i n F i g . 6.10. To make g e n e r a l i z e d use of these r e s u l t s i t i s necessary to assume t h a t the r e l a t i o n s h i p 144 TABLE 6.8 D i s t a n c e s (km) Between S t a t i o n s Used i n the Study of the S p a t i a l V a r i a b i l i t y of S o l a r R a d i a t i o n ra CD fi cti I'D >> Ti nd p • U CD o5 •H -P ni o > H ft CO K e M ra •H o CD Ti CD • P cd o fi ft M e nJ o oS ni w O > CD 0$ O £ rQ H O o u -P W CD £ > O ni fi -P CD Ti s m w S a n d s p i t - 155 410 720 750 940 950 830 1180 Cape S t . James - 280 590 625 840 850 850 ll60 P o r t Hardy - 305 350 575 585 7^ 0 980 Nanaimo - 55 315 315 750 850 Vancouver - 265 265 725 800 Summerland - 60 640 600 Mt. Kobau - - 700 640 Beaverlodge - 410 Edmonton 145 F i g . 6.10 R e l a t i v e E x t r a p o l a t i o n E r r o r s f r o m S o l a r R a d i a t i o n Measurements 50-1 § 40 ^_ Q_ O O > c. 0 30 20 H 8 10 u 0^ T T 200 400 600 800 1000 D i s t a n c e B e t w e e n S t a t i o n s ( k m ) 1200 146 "between s o l a r r a d i a t i o n v a r i a t i o n and d i s t a n c e "between s t a t i o n s i s independent of l o c a t i o n (homogeneous) and of d i r e c t i o n ( i s o t r o p i c ) . Then r e l a t i v e e r r o r s f o r s o l a r r a d i a t i o n extrapoihationncan "be obtained from F i g . 6.10. For example, e x t r a p o l a t i o n s of s o l a r r a d i a t i o n measurements over d i s t a n c e s of 50 km would produce average e r r o r s i n s o l a r r a d i a t i o n estimates of -15$ while e x t r a p o l a t i o n s over d i s t a n c e s of 180 km would produce average e r r o r s of *25$. In a study of the s p a t i a l v a r i a b i l i t y of s o l a r r a d i a t i o n i n Labrador, W i l s o n and P e t z o l d (1976) found t h a t the corresponding d i s t a n c e f o r -15$ e x t r a p o l a t i o n e r r o r s was 75 km. The s h o r t e r d i s t a n c e i n the presen t study may be due to the l e s s uniform topography i n B r i t i s h Columbia. F i g . 6.1 showed the s t a t i o n s i n the B r i t i s h Columbia area d u r i n g 1972 which measured K l or had the p o t e n t i a l to estimate Kl u s i n g the CLS model. As of January 1, 1976, P r i n c e George had been added to the K l measurement network and Kelowna, P e n t i c t o n and Terra c e were added to those having the a p p r o p r i a t e data f o r a p p l i c a t i o n of the CLS model (Atmospheric Environment S e r v i c e , 1976). The need f o r u s i n g n u m e r i c a l m o d e l l i n g to supplement the e x i s t i n g Kj. measurement network can be s t u d i e d by c o n s i d e r i n g the e x t r a p o l a t i o n e r r o r a n a l y s i s g i v e n i n the previous paragraph. In chapter 3 and s e c t i o n 6.1.3, i t was found t h a t the CLS model can gi v e estimates of s o l a r r a d i a t i o n a c c u r a t e to about -15$ when compared to measurements. Therefore, f o r a -15f° e r r o r 14-7 t o l e r a n c e , no e x t r a p o l a t i o n from the m o d e l l i n g s t a t i o n s i s p e r m i s s i b l e . F o r the s o l a r r a d i a t i o n measuring s t a t i o n s , a -15$ e r r o r t o l e r a n c e allows e x t r a p o l a t i o n s of s o l a r r a d i a t i o n up to 50 km from the s t a t i o n . From t h i s , F i g . 6.11 shows the s p a t i a l coverage a t t a i n e d i n the B r i t i s h Columbia area i f an e r r o r t o l e r a n c e of -15$ i s accepted f o r s o l a r r a d i a t i o n v a l u e s . T h i s map shows t h a t a l l p o t e n t i a l m o d e l l i n g s t a t i o n s are u s e f u l f o r extending the s o l a r r a d i a t i o n network to p o i n t l o c a t i o n s except f o r P e n t i c t o n and Kelowna. These l a t t e r two l o c a t i o n s are both w i t h i n 50 km of the Summerland measuring s i t e and, hence, w i t h i n the -15$ e r r o r e x t r a p o l a t i o n c a p a b i l i t i e s of the Summerland data i f the e a r l i e r assumptions of homogeneity and isotropyj^v are v a l i d . The o v e r a l l s p a t i a l coverage of B r i t i s h Columbia H -i s , however, s t i l l q u i t e l i m i t e d a t t h i s -15$ e r r o r l e v e l . I f an e r r o r of -25$ f o r d a i l y values of Kl i s t o l e r a b l e , then the s p a t i a l coverage i s c o n s i d e r a b l y g r e a t e r as i n d i c a t e d i n F i g . 6.12. F o r the measurement s i t e s , e x t r a p o l a t i o n s up'to a 180 km r a d i u s are p e r m i s s i b l e . F o r the m o d e l l i n g s t a t i o n s , a -25$ e r r o r i s a s s o c i a t e d with a + "t -20$ e x t r a p o l a t i o n e r r o r ( i . e . -20$ s p a t i a l e x t r a p o l a t i o n and -15$ m o d e l l i n g e r r o r ' y i e l d a -25$ o v e r a l l r o o t mean square e r r o r ) . From F i g . 6.10, t h i s corresponds to an e x t r a p o l a t i o n r a d i u s of 100 km around these s t a t i o n s . I t should be noted t h a t only seven of the m o d e l l i n g s t a t i o n s (Watson Lake, F o r t S t . John, Te r r a c e , Smithers, W i l l i a m s Lake, 148 FIG. 6 . 1 1 S o l a r R a d i a t i o n S p a t i a l Coverage i n the B r i t i s h Columbia Area f o r a - 1 5 % E r r o r T o l e r a n c e O model l ing s tat ions 149 150 Cranbrook and to a l e s s e r extent Kamloops)Cmakeraocontribution to the e x t e n s i o n of s p a t i a l coverage at t h i s -25% e r r o r l e v e l . T h i s a n a l y s i s , however, has ignored the s p e c i f i c e f f e c t s of l o c a l topography s i n c e s o l a r r a d i a t i o n e x t r a p o l a t i o n s have been a p p l i e d e q u a l l y i n a l l d i r e c t i o n s . F o r t h i s reason, the r e s u l t s must be viewed w i t h c a u t i o n s i n c e some of the oibfter m o d e l l i n g s t a t i o n s may be u s e f u l due to topographic i n f l u e n c e s on the s o l a r r a d i a t i o n regimes. T h i s a n a l y s i s shows t h a t t h e r e i s a c o n s i d e r a b l e advantage and need f o r numerical m o d e l l i n g i n order to expand the s p a t i a l coverage of s o l a r r a d i a t i o n i n B r i t i s h Columbia. The inadequacy of the present measurement network i n Canada and the r e s u l t i n g n e c e s s i t y to n u m e r i c a l l y model s o l a r r a d i a t i o n p o s t u l a t e d by Hay (1975) i s s u b s t a n t i a t e d by these r e s u l t s . T h i s assessment of the need f o r the numerical m o d e l l i n g of s o l a r r a d i a t i o n w i l l be d i s c u s s e d i n terms of s y n o p t i c weather types i n the next chapter. 151 CHAPTER 7 SYNOPTIC SOLAR RADIATION REGIMES IN BRITISH COLUMBIA 7.1 INTRODUCTION • Some r e c e n t s t u d i e s have attempted to use a s y n o p t i c approach i n the study of r a d i a t i o n and energy budgets (Vowinckel and Orvig, 1969a, 1969b, 1971, 1973; Jacobs, 1973; A l t , 1975). Vowinckel and O r v i g used s y n o p t i c data to c a l c u l a t e complete r a d i a t i v e and energy budgets (Vowinckel and Or v i g , 1969a) with a subsequent e x t e n s i o n to a number of c i r c u l a t i o n types (e.g. Vowinckel and Orvig, 1969b) i n order to d i s c u s s the i n f l u e n c e of p a r t i c u l a r s y n o p t i c events on the c l i m a t e and ge n e r a l c i r c u l a t i o n . T h i s approach or t o o l was used i n t h e i r analyses of energy budgets i n p o l a r r e g i o n s (Vowinckel and O r v i g , 1971, 1973). Jacobs (1973) s t u d i e d the s p e c i f i c r e l a t i o n s h i p s of s y n o p t i c a c t i v i t y to snow and i c e accumulation and a b l a t i o n on B a f f i n I s l a n d . A main premise of h i s study was t h a t the r e l a t i v e f r e q u e n c i e s of i n d i v i d u a l kinds of s y n o p t i c events determine the i n t e r a n n u a l v a r i a t i o n s i n c l i m a t i c c o n d i t i o n s . He found t h a t these, i n tu r n , tended to a f f e c t accumulation and a b l a t i o n r a t e s . In a s i m i l a r study, A l t (1975) analysed the i n t e r a c t i o n of s y n o p t i c 152 s c a l e i n f l u e n c e s on the energy and mass balances of Meighen Ice Cap i n the Northwest T e r r i t o r i e s . The l i m i t e d number of s y n o p t i c types c o n s i d e r e d i n her study showed l i t t l e d i s c r i m i n a t i o n between s o l a r r a d i a t i o n amounts but s u b s t a n t i a l i n f l u e n c e upon the mass balance of the i c e cap was found. In a l l of these s t u d i e s , s y n o p t i c data were used as a t o o l to analyse the e n e r g e t i c behaviour f o r a p a r t i c u l a r area. In the present study, the s y n o p t i c types d e s c r i b e d i n chapter 4 w i l l be r e l a t e d to s p a t i a l p a t t e r n s of s o l a r r a d i a t i o n i n order to e s t a b l i s h s y n o p t i c s o l a r r a d i a t i o n regimes f o r B r i t i s h Columbia. Subsequently, these s y n o p t i c type - s o l a r r a d i a t i o n r e l a t i o n s h i p s w i l l be s t a t i s t i c a l l y analysed and d e s c r i b e d . The s p a t i a l v a r i a b i l i t y of s o l a r r a d i a t i o n and the n e c e s s i t y f o r n u m e r i c a l m o d e l l i n g to supplement the s o l a r r a d i a t i o n measurement network w i l l be d i s c u s s e d i n terms of the s y n o p t i c types. Examples of the p o t e n t i a l a p p l i c a t i o n of these s y n o p t i c s o l a r r a d i a t i o n regimes w i l l be presented i n order to assess the u s e f u l n e s s of a s y n o p t i c approach to the study of s o l a r r a d i a t i o n and recommendations f o r f u r t h e r study w i l l be g i v e n . 7.2 SYNOPTIC TYPE - SOLAR RADIATION RELATIONSHIPS 7.2.1 Procedure , The average s o l a r r a d i a t i o n t r a n s m i s s i o n s f o r 1 5 3 each of the s y n o p t i c types were determined f o r the 23 l o c a t i o n s i n F i g . 6.1 f o r the year 1972 and f o r s e l e c t e d Kl measuring s t a t i o n s over l o n g e r p e r i o d s . R e s u l t s of the s o l a r r a d i a t i o n t r a n s m i s s i o n d i s t r i b u t i o n s a c c o r d i n g to s y n o p t i c types w i l l be gi v e n i n s e c t i o n 7«2.3« In order to determine whether the s y n o p t i c types are a c t u a l l y d i s c r i m i n a t i n g between s o l a r r a d i a t i o n t r a n s m i s s i o n d i s t r i b u t i o n s , an a n a l y s i s of v a r i a n c e i s performed on the s y n o p t i c type - s o l a r r a d i a t i o n d i s t r i b u t i o n s i n a manner s i m i l a r to t h a t used i n the s y n o p t i c type -p r e c i p i t a b l e water a n a l y s i s i n s e c t i o n 5«2.2. As was the case f o r the p r e c i p i t a b l e water d i s c u s s i o n , t h i s a n a l y s i s i s performed i n two stages: f i r s t l y , w ith r e s p e c t to time and, secondly, with r e s p e c t to space. 7.2.2 S t a t i s t i c a l S i g n i f i c a n c e of the R e l a t i o n s h i p s With r e s p e c t to time, the wiibhin and between s y n o p t i c type v a r i a n c e s were analysed f o r each l o c a t i o n s e p a r a t e l y with F - r a t i o s b e i n g obtained u s i n g the procedure d e s c r i b e d i n section* 5'2.2. F o r Vancouver, Summerland, and Beaverlodge, F - r a t i o s . were c a l c u l a t e d f o r the ten year p e r i o d 1963-72 while the f i v e year p e r i o d 1968-72 was used f o r P o r t Hardy, Cape S t . James, San d s p i t , and the a d d i t i o n a l s t a t i o n of Edmonton, A l t a . F o r the remaining 17 s t a t i o n s i n the B.C. s o l a r r a d i a t i o n study area, F - r a t i o s were 154 c a l c u l a t e d f o r 1972 only. The r e s u l t s are given i n Table 7«1« F - r a t i o s were c o n s i s t e n t l y above the c r i t i c a l v a l u e s (obtained from Panofsky and B r i e r , 1958) at both the Yfo and 5$ confidence l e v e l s f o r a l l s t a t i o n s except Edmonton. T h i s indiida-ttes t h a t the s y n o p t i c types e x h i b i t g r e a t e r s o l a r r a d i a t i o n v a r i a n c e between types than w i t h i n types except f o r Edmonton, Edmonton i s j u s t o u t s i d e of the s y n o p t i c study area and, t h e r e f o r e , one would.not expect the s y n o p t i c t y p i n g to show a h i g h degree of d i s c r i m i n a t i o n between s o l a r r a d i a t i o n v a l u e s at t h i s s t a t i o n . Moreover, the l o c a l i t i e s with the lowest but s i g n i f i c a n t F - r a t i o s (Cranbrook, Beaverlodge and Whitehorse) are a l l l o c a t e d near the edge of the s y n o p t i c study area. F o r 1972, a T - t e s t 'by matched p a i r s ' was performed to determine which s y n o p t i c types had ' d i f f e r e n t ' and ' s i m i l a r ' s o l a r r a d i a t i o n d i s t r i b u t i o n s when s p a t i a l l y compared to other s y n o p t i c types. As was the case f o r the s y n o p t i c type - p r e c i p i t a b l e water a n a l y s i s i n s e c t i o n 5'2.2, t h i s method i n v o l v e d comparing each s y n o p t i c type with each other type, s e p a r a t e l y , d e r i v i n g 29 values of the s t a t i s t i c t f o r each s y n o p t i c type. F o r the a p p r o p r i a t e degrees of freedom, val u e s of t below 2.81 at the 1$ confidence l e v e l and 2.07 at the 5% confidence l e v e l (Panofsky and B r i e r , 1958) i n d i c a t e d t h a t the two types had the 'same' s o l a r r a d i a t i o n .1 155 TABLE 7.1 F - r a t i o s f o r the S y n o p t i c Type - S o l a r R a d i a t i o n D i s t r i b u t i o n A n a l y s i s f o r the B.C. Study Area L o c a t i o n 1963-72: Vancouver Summerland Beaverlodge 5% c r i t i c a l F-value 1.46 1.46 1.46 lf0 c r i t i c a l C a l c u l a t e d 1968-72: P o r t Hardy 1.46 Cape S t . James 1.46 S a n d s p i t 1.46 Edmonton 1.46 1972: A b b o t s f o r d 1.49 C a s t l e g a r 1.49 Cranbrook 1.49 F o r t Nelson 1.49 F o r t S t . John 1.49 Kamloops 1.49 L y t t o n 1.49 Mt. Kobau 1.49 Nanaimo 1.49 P r i n c e George 1.49 P r i n c e Rupert 1.49 Smithers 1.49 T o f i n o 1.49 V i c t o r i a I.A. 1.49 Watson Lake 1.49 Whitehorse 1.49 W W i l l i a m s Lake 1.49 F-value F - r a t i o 1.69 13.5 1.69 8.8 1.69 1.87 I.69 7.9 1.69 .7.9 1.69 6.5 1.69 1.42 1.74 3-5' 1.74 3.5 1.74 1.84 1.74 2.1 1.74 3.1 1.74 3.9 1.74 3.0 1.74 2.1 1.74 4.7 1.74 3-7 1.74 3-7 1.74 3.0 1.74 4.6 1.74 4.4 1.74 2.5 1.74 1.93 1.74 2.5 156 d i s t r i b u t i o n s . Of the 435 combinations of s y n o p t i c type comparisons, 131 or 30.1% had the 'same* s o l a r r a d i a t i o n p a t t e r n s at the 1% confidence l e v e l while 98 or 22.5$ had the 'same* d i s t r i b u t i o n s at the 5$ confidence l e v e l . G e n e r a l l y , p a i r i n g s with the 'same' p a t t e r n s e o n s i s j e d s of types from w i t h i n the same s y n o p t i c group. Fo r the m a j o r i t y of cases, s p a t i a l d i f f e r e n c e s i n the s o l a r r a d i a t i o n t r a n s m i s s i o n p a t t e r n s were found between s y n o p t i c types. Thus, the above r e s u l t s i n d i c a t e t h a t the s y n o p t i c weather types do g e n e r a l l y d i s c r i m i n a t e between s o l a r r a d i a t i o n t r a n s m i s s i o n d i s t r i b u t i o n s . 7.2.3 D e s c r i p t i o n of S y n o p t i c S o l a r R a d i a t i o n Regimes The average s o l a r r a d i a t i o n t r a n s m i s s i o n (T) f o r each of the 23 l o c a t i o n s was c a l c u l a t e d a c c o r d i n g to s y n o p t i c type f o r 1972. Table 7.2 l i s t s these average t r a n s m i s s i v i t i e s f o r a l l days (as shown e a r l i e r i n F i g . 6.4) and the average T values f o r the u n c l a s s i f i e d and m i s s i n g s y n o p t i c groups. F o r most s t a t i o n s , T was above the annual average f o r the u n c l a s s i f i e d days and c o n s i s t e n t l y below f o r the m i s s i n g data group. Values of T f o r each s y n o p t i c type are g i v e n i n a s e r i e s of maps i n Appendix 3> These maps are of the same format as F i g . 6.4 where the o v e r a l l average 157 TABLE 7-2 Average T Values (% ) f o r A l l Days During 1972 and f o r U n c l a s s i f i e d and M i s s i n g S y n o p t i c Groups Region L o c a t i o n A l l Days U m The Norths F o r t Nelson 47 49 45 Watson Lake 45 49 42 Whitehorse 47 46 44 C e n t r a l I n t e r i o r : Beaverlodge 51 51 46 F o r t S t . John 51 52 45 P r i n c e George 48 50 41 Smithers 46 48 39 W i l l i a m s Lake 53 53 45 Southern I n t e r i o r : C a s t l e g a r 47 50 39 Cranbrook 54 56 50 Kamioops 49 50 39 L y t t o n 51 52 44 Mt. Kobau 53 56 48 Summerland 49 51 39 North Coast: Cape S t . James 44 50 37 P o r t Hardy 41 46 34 P r i n c e Rupert 41 45 38 S a n d s p i t 41 47 36 South Coast: Ab b o t s f o r d 42 46 37 Nanaimo 43 47 T o f i n o 42 45 36 Vancouver 44 48 34 V i c t o r i a I.A. 44 47 36 158 t r a n s m i s s i v i t i e s were shown. Summary d e s c r i p t i o n s of the major f e a t u r e s of these s y n o p t i c s o l a r r a d i a t i o n regimes are g i v e n f o r each of the f i v e s y n o p t i c groups i n Tables 7.3 "to 7.7- In s e c t i o n 7.4, the p o t e n t i a l a p p l i c a t i o n of t h i s i n f o r m a t i o n w i l l be dascussediiaMianngxampilje^ •„ 7 studiedr.-7.3 SOLAR RADIATION WITHIN SYNOPTIC TYPES 7•• 3• 1 A n a l y s i s of Temporal V a r i a b i l i t y Before c o n s i d e r i n g the p o t e n t i a l a p p l i c a t i o n of the s y n o p t i c s o l a r r a d i a t i o n regimes d e s c r i b e d i n the p r e v i o u s s e c t i o n , the temporal and s p a t i a l v a r i a b i l i t y of s o l a r r a d i a t i o n w i t h i n s y n o p t i c types w i l l be analysed. With r e s p e c t to temporal v a r i a b i l i t y , i f a s y n o p t i c type e x h i b i t s l i t t l e v a r i a t i o n i n s o l a r r a d i a t i o n t r a n s m i s s i o n f o r d i f f e r e n t days at a g i v e n l o c a t i o n , then i t would be p o s s i b l e to estimate KJ by simply knowing the s y n o p t i c type. T h i s would e l i m i n a t e the need f o r e i t h e r measuring or m o d e l l i n g s o l a r r a d i a t i o n f o r the l o c a t i o n . As an example of the v a r i a b i l i t y of s o l a r r a d i a t i o n w i t h i n a s y n o p t i c type f o r a g i v e n l o c a t i o n , Table?7,r.'8 p r e s e n t s the average T and i t s standard d e v i a t i o n f o r the most fre q u e n t s y n o p t i c type i n each s y n o p t i c group f o r the f o l l o w i n g a r b i t r a r i l y s e l e c t e d s i t e s : Whitehorse, P r i n c e George, Sandspit, Vancouver, Summerland and Cranbrook. TABLE 7.3 S y n o p t i c S o l a r R a d i a t i o n Regimes f o r the Ocean Highs R a d i a t i o n S y n o p t i c Transmission Type Map Map General D i s c u s s i o n 2 Fig.A.1.1 Fig.A.3.1 A l a r g e High i n the c e n t r a l North P a c i f i c w i t h weak gra d i e n t s b r i n g s only moderately c l e a r c o n d i t i o n s to B.C. with highest T values i n the i n t e r i o r r e g i o n s while some c o a s t a l cloud i s present and reduces T valu e s i n those areas. Values of T are s i m i l a r everywhere to the o v e r a l l averages g i v e n i n Table 1.2. 5 Fig.A.1.2 Fig.A . 3 .2 A s t r o n g High c l o s e r to the coast than i n Type 2 a s s o c i a t e d with c l e a r c o n d i t i o n s i n a l l areas. Most T values are w e l l above the annual averages while n o r t h e r n areas have lower T values than those i n the south due to f u r t h e r d i s t a n c e s ^ from the centre of the High as w e l l as l a t i t u d i n a l e f f e c t s . vo 19 Fig.A.1.3 Fig.A.3*3 T h i s High extends fiurlther i n l a n d with s t r o n g e r c l e a r i n g i n f l u e n c e s i n the south. Lower T values a l o n g the coast r e f l e c t the presence of a weak Low i n the G u l f of A l a s k a . 22 Fig.A. 1.4 Fig.A.3.4 T h i s winter High l i e s j u s t o f f the coast and bringshhjrgh T values e s p e c i a l l y to p a r t s of the coast. C l e a r i n g e f f e c t s are not f e l t i n the Yukon. 25 Fig.A.1.5 Fig.A . 3 . 5 An extensive and s t r o n g High dominates B.C. b r i n g i n g c l e a r c o n d i t i o n s with w e l l above average T values to a l l areas. 13 Fig.A.1.6 Fig.A .3 .6 A s t r o n g High out i n the P a c i f i c produces c l e a r c o n d i t i o n s r e f l e c t e d i n hig h T valu e s on the coast and i n the i n t e r i o r . A n o r t h e r n Low bri n g s c l o u d to Yukon areas with r e s u l t i n g lower T v a l u e s . A low i n A l b e r t a does the same f o r Cranbrook. 18 Fig.A . 1 . 7 Fig.A . 3 . 7 An extensive High r e s u l t s i n hig h T values i n most r e g i o n s . Exceptions i n c l u d e The North i n f l u e n c e d by a -small Yukon Low and some c o a s t a l s t a t i o n s (Port Hardy, Vancouver) p o s s i b l y due to f o g . TABLE 7.4 S y n o p t i c S o l a r R a d i a t i o n Regimes f o r the Land Highs R a d i a t i o n S y n o p t i c T r a n s m i s s i o n Type Map Map General D i s c u s s i o n n 6 Fig.A.1.8 Fig.A . 3 . 9 A High centred over the A l a s k a n panhandle has a s t r o n g c l e a r i n g e f f e c t on c o a s t a l s t a t i o n s where w e l l above average T values occur. Moderate (40s to low 50s) t r a n s m i s s i v i t i e s which are near average occur at i n t e r i o r and n o r t h e r n s t a t i o n s . O v e r a l l , T v a l u e s are r e l a t i v e l y uniform i n d i c a t i n g the g e n e r a l dominance of t h i s High. 20 Fig.A . 1 . 9 Fig.A . 3 . 9 A s t r o n g High f a r to the n o r t h o f A l a s k a has a minimal e f f e c t i n b r i n g i n g c l e a r c o n d i t i o n s to B r i t i s h Columbia r e s u l t i n g i n near average T v a l u e s at most s t a t i o n s w i t h h i g h e s t values i n the i n t e r i o r r e g i o n s . ^ 28 Fig.A .1.10 Fig.A .3.10 A l a r g e High centred i n the Northwest T e r r i t o r i e s b r i n g s 0 very c l e a r c o n d i t i o n s to B.C. e s p e c i a l l y f o r i n t e r i o r and the South Coast r e g i o n s . Some of the h i g h e s t o v e r a l l t r a n s m i s s i v i t i e s occur-with t h i s High. TABLE 7.5 S y n o p t i c S o l a r R a d i a t i o n Regimes f o r Ridges R a d i a t i o n S y n o p t i c T r a n s m i s s i o n Type Map Map General D i s c u s s i o n 1 Fig.A .1.11 Fig.A .3.11 T h i s Ridge has a centre w e l l to the south w i t h l i t t l e c l e a r i n g i n f l u e n c e i n B.C. A Low to the west of A l a s k a i s a s s o c i a t e d with "below average T valu e s on the coast. 24- Fig.A .1.12 Fig.A .3.12 A Ridge o r i e n t e d east-west across southern B.C. b r i n g s l e s s cloudy c o n d i t i o n s and high T valu e s to southern areas e s p e c i a l l y i n l a n d . A Low p r e s s u r e area i n A l a s k a accounts f o r lower T values i n n o r t h e r n areas e s p e c i a l l y on the North Coast. 16 Fig.A .1.13 Fig.A .3.13 This Ridge runs n o r t h - s o u t h o f f s h o r e b r i n g i n g c l e a r e r c o n d i t i o n s and hence h i g h e r t r a n s m i s s i v i t i e s e s p e c i a l l y to n o r t h e r n and C e n t r a l I n t e r i o r r e g i o n s . A s m a l l Low i n A l b e r t a and southern B r i t i s h Columbia p a r t i a l l y o f f s e t s the c l e a r i n g i n f l u e n c e of the Ridge i n southern areas. • 12 F i g . A . l . l 4 Fig.A.3.14 I n t e r i o r and the South Coast r e g i o n s have h i g h T values' due to ..the i n f l u e n c e of t h i s Ridge which runs across southern and c e n t r a l B.C. The e f f e c t of a s t r o n g Low west of A l a s k a i s p a r t i a l l y f e l t on the North Coast and i n the North where lower T values occur. 17 Fig.A .1.15 Fig.A .3.15 A l o n g narrow Ridge along the whole coa s t dominates r the e n t i r e map b r i n g i n g h i g h abo.ve\average T values to most l o c a t i o n s . ON TABLE 7.6 S y n o p t i c S o l a r R a d i a t i o n Regimes f o r Troughs Raddiationn S y n o p t i c T r a n s m i s s i o n Type Map Map General D i s c u s s i o n 10 F i g . A . l . l 6 Fig.A.3.16 A trough running i n a west-east d i r e c t i o n from the G u l f of A l a s k a to a Low i n the p r a i r i e s b r i n g s low T values to c o a s t a l areas while moderately h i g h t r a n s m i s s i v i t i e s are maintained i n l a n d . 11 Fig.A.1.17 Fig.A .3.17 This Trough runs from southern A l a s k a along the e n t i r e coast b r i n g i n g cloudy c o n d i t i o n s and low T values e s p e c i a l l y f o r most i n t e r i o r s t a t i o n s s i n c e f r o n t s a s s o c i a t e d with t h i s trough would be over the i n l a n d areas• 7 Fig.A.1.18 Fig.A .3.18 This Trough extends from west of A l a s k a along the coast. The a s s o c i a t e d cloudy i n f l u e n c e i s f e l t o n l y on the c o a s t a l areas of B.C. where moderately low T v a l u e s occur. The i n t e r i o r r e g i o n s are i n f l u e n c e d by the c l e a r i n g e f f e c t s of a High to the n o r t h e a s t . ON TABLE 7.7 Sy n o p t i c S o l a r R a d i a t i o n Regimes f o r the Ocean Lows R a d i a t i o n S y n o p t i c T r a n s m i s s i o n Type Map Map General D i s c u s s i o n 4 Fig.A .1.19 Fig.A.3.19 An extensive Low i n the c e n t r a l North P a c i f i c "brings r e l a t i v e l y cloudy c o n d i t i o n s to a l l areas with e s p e c i a l l y low T valu e s on the co a s t . 3 Fig.A .1.20 Fig.A .3«20 C l o s e r to the coast, t h i s Low i n f l u e n c e s the coast "bringing even lower T v a l u e s . A l l other areas experience T valu e s "below the annual average. 26 Fig.A .1.21 Fig.A .3.21 A Low i n the G u l f of A l a s k a a f f e c t s the e n t i r e coast w i t h cloud and hence low t r a n s m i s s i v i t i e s . A High i n A l b e r t a o f f s e t s the cloud e f f e c t s of t h i s Low f o r p a r t s of the i n t e r i o r r e g i o n s . 15 Fig.A.1.22 Fig.A .3.22 R e l a t i v e l y cloudy c o n d i t i o n s with low T values occur i n The North and along the coast due to the presence of t h i s Low along the Alaskan panhandle. Higher near average t r a n s m i s s i v i t i e s e x i s t f u r t h e r i n l a n d away from the i n f l u e n c e of t h i s Low. 8 Fig.A .1.23 Fig.A.3.23 T h i s Low i s s i t u a t e d o f f the coast and the a s s o c i a t e d cloud r e s u l t s i n low T values on the coast only. High t r a n s m i s s i v i t i e s occur i n The North and i n t e r i o r " r e g i o n s . 9 Fig,A.1.24 Fig.A .3.24 A Low j u s t o f f Vancouver I s l a n d has a s t r o n g c l o u d i n g e f f e c t f o r the South Coast and P o r t Hardy with a s s o c i a t e d low t r a n s m i s s i v i t i e s . Values ofT are hi g h e r i n l a n d and i n The North p o s s i b l y due to the c l e a r i n g e f f e c t s of a High i n the Northwest T e r r i t o r i e s . ON continued . . . TABLE 7.7 cont. R a d i a t i o n S y n o p t i c T r a n s m i s s i o n Type Map Map General D i s c u s s i o n 14 Fig.A .1.25 Fig.A .3.25 Only 1 day of t h i s type occurred d u r i n g 1972. Although the Low f o r t h i s type i s near the coast, h i g h T values e x i s t e d i n southern areas (except at T o f i n o ) f o r t h i s 1 day while low values of T were found i n The North d e s p i t e the e x i s t e n c e of a High i n the Yukon. No e x p l a n a t i o n i s r e a d i l y a v a i l a b l e f o r t h i s anaomaly. 23 Fig.A.1.26 Fig.A .3.26 T h i s Low o f f Vancouver I s l a n d i n f l u e n c e s the c o a s t a l areas b r i n g i n g cloudy and low T c o n d i t i o n s to these r e g i o n s , T r a n s m i s s i v i t i e s i n the Southern I n t e r i o r are a l s o below average. In The North, a High i n the Yukon ON b r i n g s high T values to these s t a t i o n s . 21 Fig.A .1.27 Fig.A.3.27 An extensive Low along the e n t i r e c o a s t dominates the e n t i r e area b r i n g i n g cloudy c o n d i t i o n s and hence very low t r a n s m i s s i v i t i e s to a l l s t a t i o n s . 27 Fig.A.1.28 Fig.A .3.28 A s t r o n g Low west of the Queen C h a r l o t t e I s l a n d s b r i n g s , cloudy and hence low T c o n d i t i o n s to the c o a s t e s p e c i a l l y f o r n o r t h e r n c o a s t a l s t a t i o n s . Some Southern I n t e r i o r s t a t i o n s are p a r t i a l l y i n f l u e n c e d by the lower T c o n d i t i o n s a s s o c i a t e d with t h i s Low. The c l e a r i n g e f f e c t s of a High i n the Northwest T e r r i t o r i e s are f e l t a t n o r t h e r n and e a s t e r n l o c a t i o n s . 165 TABLE 7.8 Average and Standard D e v i a t i o n f o r T f o r S e l e c t e d S y n o p t i c Types at S e l e c t e d L o c a t i o n s Type 2 Type 6 Type 1 Type 10 Type 4 A l l Days (a) Whitehorse Average T (%) 53 52 64 41 47 Standard D e v i a t i o n 15 14 18 16 17 17 (b) P r i n c e George Standard Average T (%) D e v i a t i o n 50 IB 46 20 46 17 49 14 32 15 48 19 Type 2 Type 6 Type 1 Type 10 Type 4 A l l Days (c) S a n d s p i t Average T {%) 45 55 39 39 29 41 Standard D e v i a t i o n IE 13 19 18 15 18 (d) Vancouver Average T (%) 44 52 39 40 26 44 Standard D e v i a t i o n 17 13 20 18 20 22 Type 2 Type 6 Type 1 Type 10 Type 4 A l l Days (e) Summerland Average T (%) 50 47 44 51 30 49 Standard D e v i a t i o n — I S 18 20 15 14 20 ( f ) Cranbrook Average T (fd) 55 50 51 60 48 54 Standard D e v i a t i o n 18 17 22 18 17 19 166 D e s p i t e the f a c t t h a t between type temporal v a r i a b i l i t y was g e n e r a l l y found to be g r e a t e r than w i t h i n type v a r i a b i l i t y i n s e c t i o n 7.2.2, the standard d e v i a t i o n s i n d i c a t e d i i n Table 7.8 are i n f a c t r a t h e r l a r g e . F o r example, at Vancouver, the average T f o r Type 2 i s 44% with a standard + d e v i a t i o n of -17 percentage p o i n t s s u g g e s t i n g t h a t the range of t r a n s m i s s i o n s f o r this- type was from 27% to 6l% f o r one standard d e v i a t i o n . F o r a t y p i c a l J u l y day with e x t r a t e r r e s t r i a l -2 -1 r a d i a t i o n of 40 MJ m day , t h i s r e p r e s e n t s a range f o r K i i n ab s o l u t e terms from 10.8 to 24.4 MJ m" 2day - 1-. T h i s i s an unacceptably l a r g e range and, t h e r e f o r e , t h i s a n a l y s i s i n d i c a t e s t h a t knowledge of the s y n o p t i c type f o r a day cannot r e p l a c e the need f o r measured and n u m e r i c a l l y modelled s o l a r r a d i a t i o n v a l u e s . 7.3.2 A n a l y s i s of S p a t i a l V a r i a b i l i t y I f the s p a t i a l v a r i a t i o n of s o l a r r a d i a t i o n w i t h i n some s y n o p t i c types i s low, then the presen t s o l a r r a d i a t i o n measurement network may be s u f f i c i e n t s i n c e K i c o u l d be e x t r a p o l a t e d from these s t a t i o n s thus n e g a t i n g the need f o r n u m e r i c a l l y m o d e l l i n g s o l a r r a d i a t i o n under such s y n o p t i c s i t u a t i o n s . The s p a t i a l v a r i a b i l i t y of s o l a r r a d i a t i o n was analysed i n s e c t i o n 6.3 by u s i n g equation (6.2) to c a l c u l a t e a c o e f f i c i e n t of v a r i a b i l i t y f o r p a i r s of s t a t i o n s i n the B r i t i s h Columbia a r e a and comparing these to the d i s t a n c e 167 between s t a t i o n p a i r i n g s (see F i g . 6.10). In ab s o l u t e terms, a s i m i l a r a n a l y s i s has been performed f o r t h i s area by S u c k l i n g and Hay (1976) (see Fig.3 .k) where the standard d e v i a t i o n s of s o l a r r a d i a t i o n between p a i r i n g s of measuring s t a t i o n s were c a l c u l a t e d . The annual r e l a t i o n s h i p i s not n e c e s s a r i l y r e p r e s e n t a t i v e of the e n t i r e year. F o r Labrador, W i l s o n and P e t z o l d (1976) found d i f f e r e n c e s f o r the summer and wint e r r e l a t i o n s h i p s . As an e x t e n s i o n to t h i s study, standard d e v i a t i o n s of measured s o l a r r a d i a t i o n between s t a t i o n p a i r i n g s were c a l c u l a t e d f o r each separate s y n o p t i c type f o r the f i v e y ear p e r i o d 1968-72 u s i n g the same s t a t i o n s i n the B r i t i s h Columbia area used i n s e c t i o n 6.3. R e s u l t s f o r the most common type i n each of the f i v e s y n o p t i c groups are p l o t t e d i n F i g . 7.1 along w i t h the o v e r a l l average curve from F i g . 3«4. A wide s c a t t e r about the average curve i s evide n t ; however, i n d i v i d u a l types e x h i b i t some r e g u l a r i t y w i t h the Ocean High (Type 2) c o n s i s t e n t l y above the l i n e and the Ocean Low (Type 4) c o n s i s t e n t l y below the l i n e . The lower e r r o r s f o r Type 4 are l a r g e l y due to the f a c t t h a t the average s o l a r r a d i a t i o n r e c e i v e d f o r t h i s t . t y p e i i s i t s e l f r e l a t i v e l y low (see Table 7-7)• Th e r e f o r e , i n an attempt to remove the e f f e c t s of t h i s o v e r a l l v a r i a t i o n i n s o l a r r a d i a t i o n i n p u t , i t was decided to assess the s p a t i a l v a r i a b i l i t y of s o l a r r a d i a t i o n i n terms of the c o e f f i c i e n t of v a r i a b i l i t y , r^.. 1 6 8 •FIG. 7.1 A b s o l u t e E x t r a p o l a t i o n E r r o r s from S o l a r R a d i a t i o n Measurements f o r S e l e c t e d S y n o p t i c Types 8 74 64 0 * C N c 4 o > CU Q o c O 34 uo 2 O o • l y r j e : O 6 • 1 • 10 • 4 O • • • / o • A • • o o A o o • o ft. o • • • • • • ^ All Days l I I I I I 200 400 600 800 1000 1200 D i s t a n c e ( k m ) 169 F o r each of the f i v e s y n o p t i c groups, the three most f r e q u e n t types were s e l e c t e d f o r study. P l o t s of r y versus d i s t a n c e between s t a t i o n p a i r i n g s (D) are g i v e n i n F i g s . ?.2 to 7«6. In each case, the average curve f o r a l l days shown i n F i g . 6.10 has "been p l o t t e d . C o n s i d e r a b l e s c a t t e r about the average curve i s e v i d e n t f o r a l l s y n o p t i c groups. W i t h i n groups, some s y n o p t i c types e x h i b i t a l e s s pronounced i n c r e a s e i n r y with d i s t a n c e ( i . e . Type 5 of the Ocean Highs, Types 6 and 28 of the Land Highs and Type 16 of the R i d g e s ) . Although i n F i g . 7.1 Ocean Low Type 4 showed the l e a s t pronounced absolute i n c r e a s e i n e r r o r with d i s t a n c e , much l a r g e r r e l a t i v e e r r o r s are evident i n F i g . 7'6. T h i s was a l s o the case f o r the other Ocean Lows. These p l o t s have been drawn without c o n s i d e r a t i o n of the d i r e c t i o n between s t a t i o n s . J u l i a n and Thiebaux (1975) found c o n s i d e r a b l e a n i s t r o p y i n the study of s i m i l a r c o r r e l a t i o n f i e l d s f o r 50 'kPa g e o p o t e n t i a l h e i g h t and 50.rkBa temperature when data were s t r a t i f i e d a c c o r d i n g to zonal or m e r i d i o n a l o r i e n t a t i o n . Some of the r e l a t i o n s h i p s i n F i g s . 7>2 to 7-6 show s i m i l a r a n i s o t r o p y . F o r example, p a i r i n g s running SW-NE across the study area ( i . e . those e x c l u d i n g the North Coast s i t e s of S a n d s p i t , Cape S t . James and P o r t Hardy) have been c i r c l e d f o r Type 19 i n F i g . 7«2, Type 24 i n F i g . 7.4 and Type 26 i n F i g . 7.6. In a l l three of these cases, i t i s evident t h a t there were two d i s t i n c t d i s t r i b u t i o n regimes f o r s o l a r r a d i a t i o n . E x c l u d i n g the 170 F I G . 7 . 2 Relative Extrapolation Errors from Solar Radiation Measurements fo r Ocean High Synoptic Types 60-Type: • 5 T® 19 50 All Days 40-1 30 20 ® ® ® ® . ® ® ® * s ® ® ® T 10-® 0 - r 200 400 600 D Ckm) 800 1000 1200 1 7 1 FIG. 7.3 R e l a t i v e E x t r a p o l a t i o n E r r o r s from S o l a r R a d i a t i o n Measurements f o r Land High S y n o p t i c Types 60 40-20-1 10 HJ • T y p e : • 6 T ® 20 • 28 ® 50-i ® ® 0 + TT ' T \ i T • • ^ • ® « ® ® T ® A l l D a y s 9 • ® 30 H U : •! * «... I T T I I I | I I 200 400 600 800 1000 1200 D C k m ) 172 FIG. 7.4 R e l a t i v e E x t r a p o l a t i o n E r r o r s from S o l a r R a d i a t i o n Measurements f o r Ridge Sy n o p t i c Types Type: • 1 • ®24 T • 16 • T T • A l l Days • • . * ® ® ® • • T ® 1 I I ™ M M M T I I 200 400 600 800 1000 1200 D Ckm) 173 FIG. 7.5 R e l a t i v e E x t r a p o l a t i o n E r r o r s from S o l a r R a d i a t i o n Measurements f o r Trough Sy n o p t i c Types 6CH 50-1 40 30 20 A 10 Type: • 10 • 11 • 7 T T • T • T • \ • . • A l l Days • • I I I I 200 400 600 800 1000 1200 D (km) 1 7 4 FIG. 7 . 6 R e l a t i v e E x t r a p o l a t i o n E r r o r s from S o l a r R a d i a t i o n Measurements f o r Ocean Low Sy n o p t i c Types 8(H 70 60 H 50-1 40 30-1 20-1 104 0-J Type: • 4 • 3 • ®26 ® I T T • ® ® ® ® ® • ® • • ® ® ® ® ® ® All Days 200 400 600 800 1000 1260 D ( k m ) 175 North Coast l o c a t i o n s , p a i r i n g s were g e n e r a l l y below the average curve while p a i r i n g s i n v o l v i n g Sandspit, Cape S t . James and P o r t Hardy ( i n c l u d i n g combinations among these s t a t i o n s ) were above the average curve. T h i s i n d i c a t e s t h a t (probably due to the presence of low pressure areas to the northwest of the Queen C h a r l o t t e I s l a n d s ) there was more s p a t i a l v a r i a b i l i t y i n the s o l a r r a d i a t i o n d i s t r i b u t i o n i n the n o r t h e r n c o a s t a l area f o r these types while more s p a t i a l l y uniform c o n t r o l s e x i s t e d to the south and east. A n i s o t r o p y y i s a l s o evident f o r Type 20 i n F i g . 7.3 where p a i r i n g s i n v o l v i n g Beaverlodge and Edmonton have been c i r c l e d . F o r g i v e n d i s t a n c e s , much h i g h e r values of occurred f o r these p a i r i n g s ( i n c l u d i n g the Edmonton -Beaverlodge combination) compared to a l l others i n d i c a t i n g t h a t there were q u i t e d i f f e r e n t d i s t r i b u t i o n s of s o l a r r a d i a t i o n on e i t h e r s i d e of the Rocky Mountains. F o r the Land Highs ( F i g . 7 « 3 ) i t h i s d i r e c t i o n a l b i a s i s best developed i n Type 20. In a l l of the above examples, i t i s p o s s i b l e to i d e n t i f y two d i s t i n c t regimes which c o n t r i b u t e to the l a r g e r s c a t t e r f o r Types 19, 2k, 26 and 20. Among the Troughs ( F i g . 7.5)1 Type 7 had a much l a r g e r s c a t t e r than the other two types. However, no s y s t e m a t i c a n i s t r o p y c o u l d be i d e n t i f i e d f o r t h i s type. T h i s a n a l y s i s shows t h a t the s p a t i a l v a r i a b i l i t y f o r some s y n o p t i c types ( i . e . Types 5» 6> 28 and 16) i s l e s s 176 than t h a t i n d i c a t e d i n F i g . 6.10 while f o r others the l a r g e r v a r i a b i l i t y r e s u l t s from a d i r e c t i o n a l i n f l u e n c e i n the r e l a t i o n s h i p . F o r these l a t t e r cases, r e l a t i v e e x t r a p o l a t i o n e r r o r can be assumed s m a l l e r i f s p e c i f i c r e g i o n s are excluded ( i . e . e x c l u s i o n of the North Coast f o r Types 19, 24 and 26 and A l b e r t a f o r Type 20). F i g . 7.7 g i v e s the r e l e v a n t curves f o r these types t h a t e x h i b i t l e s s e r s p a t i a l v a r i a b i l i t y than t h a t f o r the o v e r a l l s i t u a t i o n . For these types, the present s o l a r r a d i a t i o n o b s e r v a t i o n a l network may be s u f f i c i e n t thereby e l i m i n a t i n g the need f o r n u m e r i c a l l y m o d e l l i n g the s o l a r r a d i a t i o n at a d d i t i o n a l s i t e s . T h i s h y p othesis w i l l be analysed i n the next s e c t i o n . 7.3.3 A n a l y s i s of the N e c e s s i t y f o r Numerical M o d e l l i n g In s e c t i o n 6.3, i t was concluded t h a t there was indeed a need and advantage to model s o l a r r a d i a t i o n f f o r the a v a i l a b l e s t a t i o n s i n B r i t i s h Columbia. In view of the d i s c u s s i o n i n the p r e v i o u s s e c t i o n , t h i s assessment w i l l be r e - e v a l u a t e d f o r the s y n o p t i c types which e x h i b i t e d low s p a t i a l v a r i a b i l i t y ( i . e . Types 5, 6, 28, 16, 19, 24, 26 and 20). In chapter 3 and s e c t i o n 6.1.3, i t was shown th a t the CLS model has the a b i l i t y to c a l c u l a t e Kl w i t h an accuracy of approximately -15$ on a d a i l y b a s i s . I t was a l s o concluded i n chapter 3 t h a t the model was more u s e f u l 1 7 7 FIG. 7 . 7 R e l a t i v e E x t r a p o l a t i o n E r r o r s f r o m S o l a r R a d i a t i o n M easurements f o r T y p e s W i t h Low S p a t i a l V a r i a b i l i t y I l I I I 1 200 400 600 800 1000 1200 D ( k m ) 178 t h a n e x t r a p o l a t i o n s o f m e asured s o l a r r a d i a t i o n "beyond a b o u t 50 km. From F i g . 7 . 7 , i t c a n be s e e n t h a t s y n o p t i c t y p e s w i t h l o w e r s p a t i a l v a r i a b i l i t y have c o n s i d e r a b l y l o w e r r y v a l u e s f o r l a r g e d i s t a n c e s e p a r a t i o n s compared t o t h e o v e r a l l l a v e r a g e c u r v e ; however, l i t t l e r e d u c t i o n i s a t t a i n e d f o r s h o r t e r d i s t a n c e s . R e l a t i v e e r r o r s f r o m e x t r a p o l a t i o n s d r o p b e l o w - 15$ f o r o n l y a few o f t h e t y p e s ( T y p e s 6 , 2 8 , 24) f o r d i s t a n c e s b e y o n d 50 km. S i n c e e x t r a p o l a t i o n e r r o r s a r e c o n s i d e r e d f o r s p e c i f i c s y n o p t i c t y p e s , t h e n t h e m o d e l l i n g e r r o r s s h o u l d a l s o be c o n s i d e r e d b y s y n o p t i c t y p e . F o r T y p e s 6 , 28 and 2 4 , t h e p e r f o r m a n c e v o f t h e C L S 1,1 model i s summarized i n T a b l e 7»9« F o r t h e s e 3 s y n o p t i c t y p e s , t h e r o o t mean s q u a r e e r r o r s f o r e s t i m a t i n g K l d u r i n g 1972 f o r B . C . s t a t i o n s were g e n e r a l l y l o w e r t h a n - 1 5 $ , a v e r a g i n g 1 0 . 8 $ , 7$ and 1 2 . 3 $ f o r T y p e s 6 , 28 and 24, r e s p e c t i v e l y . I n f a c t , f o r t h e s e 3 s y n o p t i c t y p e s , t h e m o d e l l i n g e r r o r s a r e c o n s i s t e n t l y l e s s t h a n t h e e x t r a p o -l a t i o n e r r o r s f o r a l l d i s t a n c e s g r e a t e r t h a n 50 km. T h e r e f o r e , d e s p i t e t h e f a c t t h a t s o l a r r a d i a t i o n e x t r a p o l a -t i o n e r r o r s f o r t h e s e 3 s y n o p t i c t y p e s d r o p p e d b e l o w -15$ f o r e x t r a p o l a t i o n d i s t a n c e s o f g r e a t e r t h a n 50 km, i t i s s t i l l more a d v a n t a g e o u s t o m odel s o l a r r a d i a t i o n f o r any l o c a t i o n g r e a t e r t h a n 5 ° km f r o m an e x i s t i n g m e a s u r i n g s t a t i o n i f t h e 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 d a t a a r e a v a i l a b l e . Thus, i t c a n be c o n c l u d e d t h a t e v e n f o r s y n o p t i c t y p e s w i t h l o w s o l a r r a d i a t i o n s p a t i a l v a r i a b i l i t y , i t i s 179 TABLE 7.9 Performance of the CLS 1,1 Model f o r Estimating K i f o r Synoptic Types 6, 28 and 24 A l l Type 6 Type 28 Type 24 Days Port Hardy: RMSE (MJ m" 2day~ 0.99 2.41 1.73 1.57 RMSE (* ) 10.7 10.4 13.0 14.6 Vancouver: RMSE (MJ m" 2, -day 1.44 1.05 1.62 1.43 RMSE (* ) 15.5 4.0 8.6 11.8 Sandspit: RMSE (MJ m~ day h 0.66 1.78 2.26 1.38 RMSE (* ) 7.3 11.1 19.6 13.7 Summerland: RMSE (MJ m" 2^  -day 0.78 0.72 1.56 I.63 RMSE (* ) 9.5 2.6 8.0 12.3 Average: RMSE (MJ m" day 0.97 1.49 1.79 1.50 RMSE 10.8 7.0 12.3 13.1 180 s t i l l advantageous to n u m e r i c a l l y model s o l a r r a d i a t i o n i n order to supplement the e x i s t i n g s o l a r r a d i a t i o n m o n i t o r i n g network. 7 . 4 APPLICATION OF SYNOPTIC SOLAR RADIATION REGIMES 7 . 4 . 1 I n t r o d u c t i o n P o t e n t i a l a p p l i c a t i o n s of i n f o r m a t i o n on s y n o p t i c s o l a r r a d i a t i o n regimes i n c l u d e analyses of i n t e r a n n u a l s o l a r r a d i a t i o n v a r i a b i l i t y , past s o l a r r a d i a t i o n d i s t r i b u t i o n s and anomalies and the p e r s i s t e n c e of low energy s o l a r r a d i a t i o n regimes f o r s o l a r energy f e a s i b i l i t y s t u d i e s . One of these, i n t e r a n n u a l s o l a r r a d i a t i o n v a r i a b i l i t y , w i l l be presented and analysed as an example of the u s e f u l n e s s and problems encountered by a s y n o p t i c approach to the study of s o l a r r a d i a t i o n c l i m a t o l o g y . 7 . 4 . 2 Example: Int e r a n n u a l S o l a r R a d i a t i o n V a r i a b i l i t y In order to assess the i n t e r a n n u a l v a r i a b i l i t y of s o l a r r a d i a t i o n i n terms of s y n o p t i c weather types, the f r e q u e n c i e s of s y n o p t i c types and the mean value s of s o l a r r a d i a t i o n must be summarized. For the months of January and J u l y f o r the t e n years from 1 9 ^ 3 to 1 9 7 2 , s y n o p t i c type f r e q u e n c i e s are summarized i n Tables 7 - 1 0 and 7 - H » r e s p e c t i v e l y . Mean d a i l y s o l a r r a d i a t i o n values were c a l c u l a t e d f o r the same p e r i o d f o r t h r e e s o l a r r a d i a t i o n measuring s t a t i o n s : Vancouver, Summerland and Beaverlodge. 181 TABLE 7.10 S y n o p t i c Type Frequencies f o r January From 19&3 to 1972 S y n o p t i c Group Ocean Highs Land Highs Ridges Troughs Ocean Lows U n c l a s s i f i e d M i s s i n g Fype 64 65 66 62 68 62 20 21 22 2 2 1 2 1 5 1 19 4 3 1 22 16 4 2 3 1 1 3 25 13 1 18 6 2 1 1 20 2 1 2 6 1 2 28 1 1 1 1 6 2 4 1 24 1 16 1 12 1 1 1 17 1 10 2 1 2 •1 1 2 11 7 2 3 7 1 1 1 4 5 12 12 5 2 1 6 9 3 1 1 2 1 1 2 26 3 2 1 1 1 15 2 1 1 2 1 3 8 1 l 1 1 1 9 1 5 2 2 5 3 1 14 1 4 2 23 1 1 3 2 1 2 21 1 1 1 27 1 2 1 u 3 2 4 1 5 13 6 4 8 15 m 2 2 1 4 1 3 182 TABLE 7.11 S y n o p t i c Type Frequencies f o r J u l y From 19&3 ^° 1972 S y n o p t i c Group Ocean Highs Land Highs Ridges Troughs Ocean Lows 4 3 26 15 8 9 14 23 21 27 •ype 61 64 65 66 6Z 68 62 ZO Zl 2 17 12 9 11 •9 4 15 5 2 1 5 2 3 3 2 1 6 3 5 3 19 2 1 1 1 l 2 22 25 2 3 5 2 3 3 3 13 2 1 14 2 1 18 3 3 3 1 1 1 2 6 1 20 28 1 1 1 1 6 l 1 24 1 2 2 4 1 16 1 1 1 3 4 1 12 1 3 1 17 1 4 3 1 10 1 2 11 7 2 1 1 1 U n c l a s s i f i e d U 3 7 7 3 7 8 f 5 12 14 M i s s i n g m l 1 1 1 2 1 1 8 3 These val u e s are p l o t t e d i n F i g . 7 . 8 . F o r January, some of the major i n t e r a n n u a l v a r i a t i o n s can he e x p l a i n e d i n terms of the s y n o p t i c type f r e q u e n c i e s . January I 9 6 3 experienced r e l a t i v e l y high mean valu e s of Kj. at "both Vancouver and Summerland. From Table 7.10, Type 2 2 occurred 1 6 times d u r i n g t h i s January. T h i s i s more o f t e n than f o r any of the subsequent- years. Type 2 2 i s an Ocean High w i t h high s o l a r r a d i a t i o n t r a n s m i s s i v i t i e s e s p e c i a l l y on the c o a s t (see Table 7 - 3 and F i g . A . 3 - 4 ) . S i n c e Summerland g e n e r a l l y has higher T v a l u e s f o r Ocean Lows (see Table 7 » 7 ) and u n c l a s s i f i e d days (see Table 7 . 2 ) than Vancouver, the mean d a i l y Kj. f o r the month i s h i g h e r at Summerland. Beaverlodge, on the otherhand, i s much f u r t h e r i n l a n d and away from the c l e a r i n g i n f l u e n c e of Type 2 2 ' s High and, t h e r e f o r e , does not have an anomolously h i g h s o l a r r a d i a t i o n r e c e i p t d u r i n g t h i s January. January I 9 6 9 r e c e i v e d h i g h average Ki amounts at a l l t h ree l o c a t i o n s . From Table 7-10, t h i s i n i t i a l l y seems unusual s i n c e Ocean Lows dominated t h i s month. However, f i v e of these days were a Type 9 p a t t e r n which i s a r e l a t i v e l y s m a l l low o f f Vancouver I s l a n d . T h i s type i s not a s s o c i a t e d w i t h e x c e s s i v e cloud c o n d i t i o n s i n l a n d (see Table 7 . 7 ) . Another f o u r days were Type 14- p a t t e r n s which i s another r e l a t i v e l y s m a l l c o a s t a l low (see F i g . A . 1 . 2 5 ) although the s o l a r r a d i a t i o n c h a r a c t e r i s t i c s f o r 184 F I G . 7.8 Mean D a i l y T o t a l S o l a r R a d i a t i o n (MJ m 2 d a y - 1 ) f o r J a n u a r y and J u l y D u r i n g 1 9 6 3 - 7 2 ( a ) J a n u a r y : 4.5-i 4.OH • Summerland - • Vancouver -A Beaverlodge 3.54 c o £3.0H" 2-54 20. 63 64 65 66^  6*7 68 69 70 71 72~ ( b ) J u l y : 25-24-23-^ 22-2 *1 20 H 19 4 18 ^3 64 65 66 &7 68 69 70 71 72~ 185 t h i s type were i n c o n c l u s i v e (see Table 7 . 7 )• The e f f e c t s of these Lows would be f e l t p r i m a r i l y a t Vancouver thus e x p l a i n i n g the lower Kj r e c e i p t at t h i s s t a t i o n compared to Summerland and Beaverlodge. A r e l a t i v e l y l a r g e number of u n c l a s s i f i e d and m i s s i n g days (10) unfortuna<telyy h i n d e r s f u r t h e r e x p l a n a t i o n of the s o l a r r a d i a t i o n values f o r t h i s January. F o r I965 and 1971, F i g . 7 . 8(a) shows th a t January was a month wit h r e l a t i v e l y low Kl r e c e i p t at a l l t h r e e s t a t i o n s . D u r i n g both of these years, Type 4 was the most f r e q u e n t s y n o p t i c type. T r a n s m i s s i o n v a l u e s are r e l a t i v e l y low f o r a l l s t a t i o n s f o r t h i s type e s p e c i a l l y a l o n g the coast (see Table 7 -7)• T h i s type was a l s o f r e q u e n t d u r i n g 1966 c r e a t i n g low Kj values f o r t h i s month. However, Type 7 i a Trough with low t r a n s m i s s i v i t i e s r e s t r i c t e d to the coast and h i g h e r values i n l a n d , occurred 7 times p o s s i b l y a c c o u n t i n g f o r the much higher s o l a r r a d i a t i o n r e c e i p t at Summerland compared to Vancouver. 1 The much lower Kl r e c e i p t at Beaverlodge compared to Summerland may have been due to e f f e c t s beyond the s y n o p t i c study area. F o r J u l y |[Fig. 7 . 8 ( b ) ] , Beaverlodge g e n e r a l l y r e c e i v e d l e s s Kj than the other two l o c a t i o n s . T h i s may have been due to a g r e a t e r d i s t a n c e from the c l e a r i n g e f f e c t s of the Ocean Highs which, as i n d i c a t e d i n Table 7 . 1 1 , dominated d u r i n g t h i s month. 186 Although the absolute f l u c t u a t i o n s of mean s o l a r r a d i a t i o n between J u l y s were l a r g e (up to 4.7 -2 -1 MJ m day ) f o r Vancouver), these r e p r e s e n t i n t e r a n n u a l changes of 21% at most, whereas, f o r Januarys, a b s o l u t e -2 -1 f l u c t u a t i o n s of up to 1.5 MJ m day ( f o r Summerland) r e p r e s e n t i n g r e l a t i v e f l u c t u a t i o n s of 46% were experienced. C o n s i d e r i n g t h i s , i t may be expected t h a t the observed f l u c t u a t i o n s d u r i n g J u l y s would be more d i f f i c u l t t o e x p l a i n i n terms of s y n o p t i c types. F o r example, r e l a t i v e l y h i g h v a l u e s of mean K i occurred d u r i n g J u l y 1965 at Vancouver and Summerland with somewhat low values d u r i n g J u l y 1966. Yet, f o r both years, s i m i l a r Ocean High f r e q u e n c i e s o c c u r r e d . A l s o , as mentioned i n chapter 4, s m a l l e r - s c a l e f e a t u r e s o c c u r r i n g i n the summer are not r e c o g n i s e d by the present s y n o p t i c t y p i n g a n a l y s i s due to the l a r g e (38I km) g r i d p o i n t s p a c i n g and the l a r g e area under study. T h i s was e v i d e n t by the d i s c r e p a n c y between the number of summer Lows found i n the p r e s e n t study compared to t h a t observed by Maunder (I968). T h e r e f o r e , s m a l l - s c a l e Lows which may be present d u r i n g a p a r t i c u l a r J u l y would not be d e t e c t e d by the present s y n o p t i c a n a l y s i s and these may, f o r example, account f o r the changes i n s o l a r r a d i a t i o n between J u l y 1965 and J u l y 1966. While there i s a l a c k of success i n e x p l a i n i n g i n t e r a n n u a l v a r i a b i l i t y f o r J u l y , the r e s u l t s f o r January 187 are encouraging. It may "be argued that the r e l a t i v e interannual solar r a d i a t i o n fluctuations during Januarys were much larger and, hence, the success i n explaining these fluctuations i n terms of synoptic solar r a d i a t i o n regimes i s a s i g n i f i c a n t contribution. Also, i t may be concluded that, i n January, large-scale synoptic controls are the dominant fac t o r while, i n July, smaller-scale features are often more important, but these are unfortunately beyond the resolution of the present synoptic typing analysis. 7.5 CONCLUSIONS It has been shown that the v a r i a t i o n of solar r a d i a t i o n transmissions i s generally greater between synoptic types than within types. This has allowed synoptic solar r a d i a t i o n regimes to be defined and these have been described i n section 7.2.3' However, analysis of the temporal and s p a t i a l v a r i a b i l i t y of solar r a d i a t i o n within synoptic types has shown that knowledge of synoptic solar r a d i a t i o n regimes does not preclude the need fo r measuring solar r a d i a t i o n nor negate the advantage of numerically modelling solar r a d i a t i o n i n order to supplement the e x i s t i n g solar r a d i a t i o n monitoring network i n the B r i t i s h Columbia area. Extrapolation errors are so large, even f o r a given synoptic type, that there i s a need f o r the solar r a d i a t i o n measuring stations to be augmented by modelled values 188 f o r other l o c a t i o n s wherever p o s s i b l e . Therefore, as was the c o n c l u s i o n i n s e c t i o n 6.3> there i s indeed an advantage to modelling s o l a r r a d i a t i o n i n order to supplement t h i s data network. This assessment has been made on the b a s i s of one s p e c i f i c synoptic t y p i n g scheme. A d d i t i o n a l study i s warranted i n which a more appropriate synoptic c l a s s i f i c a t i o n may evolve. For example, the r e s u l t s may vary f o r analyses based on d i f f e r e n t g r i d p o i n t spacing, a r e a l s c a l e or l o c a t i o n . In an example of the p o t e n t i a l a p p l i c a b i l i t y of synoptic s o l a r r a d i a t i o n regimes, a n a l y s i s of the i n t e r a n n u a l v a r i a b i l i t y of s o l a r r a d i a t i o n showed th a t a d d i t i o n a l study i s necessary. This c o n c l u s i o n i s based on the f a c t t h a t , although synoptic i n f o r m a t i o n proved to be u s e f u l f o r a n a l y s i n g the i n t e r a n n u a l v a r i a b i l i t y of Ki f o r January, the i n t e r a n n u a l v a r i a b i l i t y f o r J u l y was not w e l l explained i n terms of synoptic weather types. This was p o s s i b l y due to the i n a b i l i t y of the synoptic t y p i n g scheme to r e s o l v e s m a l l e r - s c a l e features which occur i n summer. Therefore, a d d i t i o n a l study of these r e l a t i o n s h i p s i s warranted i n order to determine the e f f e c t i v e n e s s of t h i s synoptic approach to the study of s o l a r r a d i a t i o n . Although some of the r e s u l t s i n d i c a t e t h a t there may be some u s e f u l p o t e n t i a l a p p l i c a t i o n s of synoptic - s o l a r r a d i a t i o n r e l a t i o n s h i p s , more rigorous analyses of the seasonal 1 8 9 v a r i a b i l i t y of solar r a d i a t i o n transmissions within synoptic types and the effects of s p a t i a l scale and r e s o l u t i o n are needed. 1 9 0 CHAPTER 8 CONCLUSIONS The main c o n c l u s i o n s e v o l v i n g from t h i s t h e s i s are summarized as f o l l o w s : ( 1 ) A t h e o r e t i c a l l y based model f o r the e s t i m a t i o n of s o l a r r a d i a t i o n under c l o u d l e s s c o n d i t i o n s has been shown to perform w e l l on a d a i l y b a s i s f o r s e v e r a l l o c a t i o n s i n Canada. In order to o b t a i n b e t t e r estimates of the d i r e c t and d i f f u s e components of s o l a r r a d i a t i o n , m o d i f i c a t i o n s were n e c e s s a r y which i n c l u d e d values f o r the a e r o s o l parameter k somewhat lower than i n the o r i g i n a l model and forward- and b a c k - s c a t t e r i n g f a c t o r s of 0 . 6 and 0 . 4 i n s t e a d of 0 . 5 f o r each. (2) A new cl o u d l a y e r - sunshine (CLS) model has been shown to perform b e t t e r on a d a i l y b a s i s at a number of Canadian l o c a t i o n s than a p r e v i o u s l y developed c l o u d l a y e r model. T h i s CLS model has the added advantage of c a l c u l a t i n g the d i r e c t and d i f f u s e s o l a r r a d i a t i o n components s e p a r a t e l y . E stimates of the t o t a l f l u x can g e n e r a l l y be c a l c u l a t e d to w i t h i n -15% of the measured v a l u e s . 191 (3) An assessment of the s p a t i a l v a r i a b i l i t y of s o l a r ' r a d i a t i o n i n the B r i t i s h Columbia area showed t h a t there i s a c o n s i d e r a b l e advantage to n u m e r i c a l l y m o d e l l i n g s o l a r r a d i a t i o n g i v e n the sparse o b s e r v a t i o n a l network. A n a l y s i s of the a v a i l a b l e s o l a r r a d i a t i o n and m e t e o r o l o g i c a l d a t a i n Canada shows t h a t , by u s i n g the CLS model, the number of l o c a t i o n s with s o l a r r a d i a t i o n i n f o r m a t i o n can be almost t r i p l e d . (4) S y n o p t i c s o l a r r a d i a t i o n regimes were e s t a b l i s h e d f o r the B r i t i s h Columbia area and the v a r i a n c e of s o l a r r a d i a t i o n between s y n o p t i c types was shown to be g e n e r a l l y g r e a t e r than the w i t h i n type v a r i a n c e . However, i t was shown t h a t knowledge of s y n o p t i c weather types does not p r e c l u d e the need f o r measuring s o l a r r a d i a t i o n nor negate the advantage of n u m e r i c a l l y m o d e l l i n g s o l a r r a d i a t i o n i n o r d e r to supplement the e x i s t i n g m o n i t o r i n g network i n the B r i t i s h Columbia area. 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Orv i g , 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 , 143-166. Wilson, R.G. and D.E. P e t z o l d (1972): D a i l y s o l a r r a d i a t i o n d i f f e r e n c e s between s t a t i o n s i n southern Canada: A p r e l i m i n a r y a n a l y s i s . C l i m a t o l o g i c a l B u l l e t i n , M c G i l l U n i v e r s i t y , Montreal, 11, 15-22. Wilson, R.G. and D.E. P e t z o l d (1976): A s o l a r r a d i a t i o n network e v a l u a t i o n f o r the C h u r c h i l l R i v e r b a s i n . Papers i n C l i m a t o l o g y - The Cam A l l e n  Memorial Volume, McMaster U n i v e r s i t y , ed. J.A. Davies, Hamilton, 84-109. 202 APPENDIX 1• FREQUENCY DATA AND MAPS FOR THE SYNOPTIC WEATHER TYPES The s y n o p t i c weather types are presented i n t h i s appendix a c c o r d i n g to s y n o p t i c group. F o r each group, a t a b l e i s i n i t i a l l y g i v e n c o n t a i n i n g frequency data summarized by month and by year f o r each type w i t h i n the group. T h i s t a b l e i s f o l l o w e d by maps of the 1000'kBa h e i g h t s ( i n decametres) f o r each type w i t h i n ' t h e s y n o p t i c group. The f o l l o w i n g index i n d i c a t e s the page on which each s y n o p t i c group begins: Group Types Paf.'ja Page Ocean Highs 2, 5, 19, 22, 25, 13, 18 203 Land Highs 6, 20, 28 ' 211 Ridges i . ^ e s 1, 24, l6, 12, 17 215 .Troughsughn 10, 11, 7 221 Ocean Lows 4, 3, 26, 15, 8, 9, 14, 23, 225 21, 27 U n c l a s s i f i e d / M i s s i n g (Table only) 236 203 TABLE A.1.1 Frequency Data f o r Ocean Highs Type _2 12 22 n 18 January 6 1 11 30 • 0 1 0 February 5 1 4 16 0 0 0 March 9 3 3 13 5 0 0 A p r i l 33 5 13 1 11 1 8 May 27 22 14 4 3 8 3 June 55 30 20 7 9 1 3 J u l y 80 30 8 0 22 20 15 August 58 10 7 0 23 17 11 September 15 5 4 2 9 3 7 October 22 1 14 5 4 2 0 November 6 2 3 7 0 1 1 December 2 1 4 9 4 1 1 1963 47 9 9 20 9 14 5 1964 52 16 15 10 5 7 2 1965 28 15 3 11 14 4 9 1966 37 11 11 8 9 1 5 1967 23 10 16 14 9 16 : 4 1968 17 3 14 5 3 3 5 1969 36 8 4 5 4 1 5 1970 29 17 10 5 14 4 2 1971 28 12 15 13 11 1 6 1972 21 10 8 3 12 4 6 T o t a l 318 111 105 94 90 55 49 204 FIG. A . l . l Ocean High: S y n o p t i c Type 2 ( J u l y 5, 1964) (lOOOkB'a Heights i n Decametres) -75 . H 1 4 0 C 2 0 5 FIG. A . 1 . 2 Ocean High: S y n o p t i c Type 5 (June 6 , 1 9 6 3 ) (lOOOkPi'a Heights i n Decamatres) 2 0 6 F I G . A . 1 . 3 Ocean H i g h : S y n o p t i c Type 1 9 (June 1 2 , 1 9 6 6 ) (lOOOkBa H e i g h t s . i n D e c a m e t r e s ) 207 F I G . A.1.4 Ocean High: S y n o p t i c Type 22 (January 15, 1963) ( l 0 0 0 k B & Heights i n Decametres) 208 FIG. A.1.5 Ocean High: S y n o p t i c Type 25 ( J u l y 13, 1966) (100:.kPa Heights i n Decametres) 130° 209 FIG. A.1.6 Ocean High: Synoptic Type 13 (May 14, 1964) (100 kPa Heights i n Decametres) H -5 25 10 5 f l60o 210 F I G . A.1.7 Ocean H i g h : S y n o p t i c Type 18 ( J u l y 10, 1965) (lOOOk-BSo H e i g h t s i n D e c a m e t r e s ) 2 1 1 TABLE A . 1 . 2 Frequency Data f o r Land Highs Type _6 20 28 J anuary 4 14 2 February 0 5 3 March 5 8 3 A p r i l 7 4 3 May 6 2 17 June '9 1 2 J u l y 1 0 2 August 9 0 1 September 15 0 2 October 3 2 1 November 0 2 0 December 6 10 1 1963 5 3 2 1964 3 2 3 1965 8 2 2 1966 6 8 2 1967 9 0 2 1968 6 11 9 1969 7 4 8 1970 7 9 1 1971 4 3 2 1972 10 6 6 T o t a l 65 48 37 212 F I G . A.1.8 Land High: Synoptic Type 6 (September 11, 1970) (lOOOkEa Heights i n Decametres) 10 15 \2° 140c 2 1 3 F I G . A . 1 . 9 Land High: S y n o p t i c Type 2 0 (January 4 , 1 9 7 0 ) (lOO'.kPa Heights i n Decametres) 10 45. '40. 35-30 10 25 214 F I G . A.1.10 Land High: S y n o p t i c Type 28 (May 5, 1972) (100'0kR& Heights i n Decametres) H/10 10 215 TABLE A.1.3 Frequency Data f o r Range's id{tes Type _1 24 116 12 11 January 13 1 2 3 1 February 36 1 3 11 1 March 21 0 5 9 2 A p r i l 24 12 16 4 1 May 31 10 15 3 9 June 18 8 12 2 8 J u l y 9 9 11 5 8 August 19 25 16 11 8 September 30 18 16 9 2 October 16 25 4 21 0 November 19 6 3 10 0 December 24 4 5 7 0 1963 21 9 10 3 1 1964 31 12 14 15 1 1965 26 11 16 6 5' 1966 24 13 l l 16 3 1967 23 6 10 15 5 1968 31 13 8 6 8 1969 36 4 8 6 4 1970 21 19 14 12 5 1971 24 15 9 6 3 1972 23 17 8 10 5 T o t a l 260 119 108 95 40 216 FIG. A.1.11 Ridge: S y n o p t i c Type 1 (March 3, 1964) (lOOOkl'a Heights i n Decametres) -10 -5 J V \i-1( -—10 -•—"^15 20 H 2 1 7 F I G . A . 1 . 1 2 Ridge: S y n o p t i c Type 24 ( A p r i l 2 7 , - 1 9 6 5 ) (lOOOkla Heights i n Decametres) 218 FIG.AA.1.13 Ridge: S y n o p t i c Type 16 ( A p r i l 25, 19°3) (lOOOkEa Heights i n Decametres) 2 1 9 FIG. A.1.14 R i d g e ; S y n o p t i c Type 1 2 (November 1 5 . 1 9 6 4 ) (lOOOkBa H e i g h t s i n D e c a m e t r e s ) 2 2 0 FIG. A.1.15 Ridge: S y n o p t i c Type 17 ( J u l y 2 3 , 1 9 6 8 ) (lOOOkBk Heights i n Decametres) 221 TABLE A.1.4 Frequency Data f o r Troughsughs January February March A p r i l May June J u l y August September October November December Type 10 I i _Z 8 11 3 17 20 2 10 9 5 9 0 12 5 1 1 8 0 0 3 0 5 1 0 5 4 4 4 3 2 3 3 6 9 2 6 5 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 5 4 7 8 2 8 8 1 9 4 10 4 9 3 4 3 2 7 5 11 3 8 17 0 15 2 4 8 7 8 T o t a l 73 59 54 222 FIG. A.1.16 Trough:' Synoptic Type 10 ( A p r i l 7, 1970) (lOOOkRa Heights i n Decametres) 10-.-5 ( — - \ 1 5 ~~~ „10 " — " 2 0 ^ H 223 FIG. A.1.17 Trough: S y n o p t i c Type 11 (January 30, 1966) (lOOOkEa Heights i n Decametres) 224 F I G . A.1.18 Trough: Synoptic Type 7 (March 17, 1963) (lOOOkEa Heights i n Decametres) 225 TABLE A.1.5 Frequency Data f o r Ocean Lows _4. H 2 26 i i January 51 8 8 9 February 54 13 - 7 9 March 27 15 5 8 A p r i l 9 14 10 8 May 12 10 3 4 June 1 5 2 2 J u l y 0 3 1 0 August 2 2 1 5 September 10 12 22 9 October 29 25 15 24 November 34 20 19 10 December 59 19 11 14 1963 47 15 7 8 1964 16 13 6 16 1965 26 16 14 8 1966 . 36 12 7 6 1967 18 17 10 7 1968 36 11 17 18 1969 36 13 19 7 1970 32 17 8 12 1971 18 21 11 14 1972 23 11 5 6 T o t a l 288 146 104 102 Type _8 _2 14 21 21 22 5 19 7 10 3 4 1 8 0 8 7 6" .2 5 4 3 7 9 LO 5 5 2 3 1 6 0 1 1 0 1 4 1 0 0 0 0 1 0 2 0 0 0 1 0 0 0 1 0 1 2 0 0 4 2 3 0 2 2 5 0 5 4 10 6 3 7 9 8 12 11 7 7 6 3 3 5 4 1 5 4 3 8n. 2 0 4 9 10 3 3 2 9 6 2 4 1 7 8 4 8 2 5 5 6 3 1 8 0 9 7 8 5 2 8 5 2 6 5 2 5 2 4 3 5 2 9 2 7 6 1 7 3 4 58 52 43 43 40 37 226 FIG. A.1.19 Ocean Low: S y n o p t i c Type 4 (November 19i 1969) (lOOOkRS) Heights i n Decametres) 227 FIG. A.1.20 Ocean Low: S y n o p t i c Type 3 (October 11, 1967) (lOOOkl'a Heights i n Decametres) 130° 228 F I G . A.1.21 Ocean Low: S y n o p t i c Type 26 (October 3, 1968) (lOOOkPa Heights i n Decametres) 229 F I G . A.1.22 Ocean Low: S y n o p t i c Type 15 ( O c t o b e r 25, 1963) (lOOOkRa H e i g h t s i n D e c a m e t r e s ) \ -15 -10 \ •5 \ N 230 FIG. A.1.23 Ocean Low: S y n o p t i c Type 8 ( J u l y 27, 1965) (lOOOkiRa H e i g h t s i n D e c a m e t r e s ) 231 FIG. A.1.24 Ocean Low: S y n o p t i c Type 9 (January 4, 1965) (lOOOkEa Heights i n Decametres) 2 3 2 FIG. A . 1 . 2 5 Ocean Low: Synoptic Type 14 (November 2 7 , 1970) (lOOOkEa Heights i n Decametres) 20 25 Hv H 30 233 F I G . A.1.26 Ocean Low: S y n o p t i c Type 23 (December 21, 1964) (lOOOkEa Heights i n Decametres) 2 3 4 FIG. A . 1 . 2 7 Ocean Low: S y n o p t i c Type 2 1 (December 2 9 , 1 9 7 0 ) (lOOOkla Heights i n Decametres) 2 3 5 FIG. A.1.28 Ocean Low: S y n o p t i c Type 2 7 (December 10, 1968) (lOOOkEa Heights i n Decametres) 236 TABLE A.1.6 Frequency Data f o r U n c l a s s i f i e d and M i s s i n g Days U n c l a s s i f i e d M i s s i n g January 63 12 F ebruary 40 5 March 96 9 A p r i l 61 8 May 87 4 June 91 1 J u l y 68 7 August 71 6 September 82 7 October 65 12 November 91 13 December 55 6 1963 75 8 1964 83 4 1965 92 0 1966 90 2 1967 93 10 1968 99 4 1969 77 19 1970 75 5 1971 86 17 1972 100 21 T o t a l 870 90 237 APPENDIX 2 MAPS OF SYNOPTIC TYPE - PRECIPITABLE WATER DISTRIBUTIONS P r e c i p i t a b l e water d i s t r i b u t i o n maps are presented i n t h i s appendix f o r the most common s y n o p t i c weather type i n each s y n o p t i c group. Values g i v e n are i n m i l l i m e t r e s . The f o l l o w i n g i s an index of the contents of t h i s appendix: Type Page Ocean High Type 2 238 Land High Type 6 239 Ridge' Type 240 Tirouih'Type'ip 241 Ocean Low Type 4 242 2 3 8 F I G . A . 2 . 1 D i s t r i b u t i o n of P r e c i p i t a b l e Water (mm) f o r Ocean High S y n o p t i c Type 2 !30° 239 F I G . A.2.2 D i s t r i b u t i o n of P r e c i p i t a b l e Water (mm) f o r Land High S y n o p t i c Type 6 240 F I G . A . 2 . 3 D i s t r i b u t i o n of P r e c i p i t a b l e Water (mm) f o r Ridge Sy n o p t i c Type 1 241 F I G . A . 2 . 4 D i s t r i b u t i o n of P r e c i p i t a b l e Water (mm) f o r Trough S y n o p t i c Type 10 2 4 2 i FIG. A . 2 . 5 D i s t r i b u t i o n of P r e c i p i t a b l e Water (mm) f o r Ocean Low S y n o p t i c Type 4 243 APPENDIX 3 MAPS OF SYNOPTIC SOLAR RADIATION TRANSMISSION REGIMES FOR THE BRITISH COLUMBIA AREA This appendix presents maps of the values of s o l a r r a d i a t i o n t r a n s m i s s i o n (T) expressed as a percentage at each of the 23 study s i t e s i n the B r i t i s h Columbia area f o r each of the 28 s y n o p t i c weather types. The order of p r e s e n t a t i o n i s the same as t h a t i n Appendix 1. The f o l l o w i n g index i n d i c a t e s the page on which each s y n o p t i c group begins: Group Types Page Ocean Highs 2, 5, 1'9, 22, 25, 13. 18 244 Land Highs 6, 20, 28 251 Ridges 1, 24, 16, 12, 17 254 Troughs 10, 11, 7 259 Ocean Lows 4, 3. 26, 15, 8, 9, 14, 23, 21, 27 262 244 F I G . A.3.1 Synoptic S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Ocean High: Synoptic Type 2 2 4 5 FIG. A . 3 . 2 -S y n o p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Ocean High: Synoptic Type 5 246 F I G . A . 3 . 3 S y n o p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r OceanLHigR: Synoptic Type 19 24-7 FIG. A.3.4 S y n o p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Ocean High: S y n o p t i c Type 22 248 F I G . A . 3 . 5 S y n o p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Ocean High: S y n o p t i c Type 2 5 249 FIG. A.3.6 Synoptic Solar Radiation Transmission Regime for Ocean High: Synoptic Type 1 3 250 F I G . A . 3 . 7 S y n o p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Ocean High: S y n o p t i c Type 18 251 2 5 2 FIG'. A. 3. 9 S y n o p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Land High: S y n o p t i c Type 2 0 2 5 3 FIG. A . 3 . 1 0 Synoptic. S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Land High: Synoptic Type 28 2 5 4 F I G . A . 3 . 1 1 S y n o p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Ridge: S y n o p t i c Type 1 2 5 5 FIG; A.3 .12 Synoptic S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Ridge: Synoptic Type 24 256 F I G . A.3.13 Synoptic Solar Radiation Transmission Regime for Ridge: Synoptic Type 16 2 5 7 FIG. A.3 .14 Syno p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Ridge: S y n o p t i c Type 12 258 FIG'. A. 3.15 Synoptic Solar Radiation Transmission Regime fo r Ridge: Synoptic Type 17-259 F I G ' . A . 3 . 1 6 Synoptic Solar Radiation Transmission Regime f o r Trough: Synoptic Type 10 260 F I G . A.3.17 S y n o p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Trough: Sy n o p t i c Type 11 2 6 1 F I G . A.3.18 . S y n o p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r T r o u g h : S y n o p t i c Type 7 2 6 2 F I G . A . 3 . 1 9 Synoptic Solar Radiation Transmission Regime for Ocean Low: Synoptic Type 4 263 FIG. A.3 . 2 0 S y n o p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Ocean Low: S y n o p t i c Type 3 2 6 4 F I G . A . 3 . 2 1 . S y n o p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Ocean Low: Syn o p t i c Type 2 6 2 6 5 FIG. A . 3 . 2 2 S y n o p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Ocean Low: Syn o p t i c Type 15 2 6 6 F I G . A . 3 . 2 3 S y n o p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Ocean Low: S y n o p t i c Type 8 2 6 7 FIG. A.3.24 S y n o p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Ocean Low: S y n o p t i c Type 9 2 6 8 FIG. A.3.25 S y n o p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Ocean Low: Syn o p t i c Type 14-2 6 9 F I G ' . A . 3 . 2 6 Synoptic S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Ocean Low: Syn o p t i c Type 2 3 270 , F I G . A.3.27 S y n o p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n Regime f o r Ocean Low: Synoptic Type 21 271 FIG. A.3.28 S y n o p t i c S o l a r R a d i a t i o n T r a n s m i s s i o n R e g i m e f o r Ocean Low: S y n o p t i c Type 27 

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