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Mountain precipitation analysis for the estimation of flood runoff in coastal British Columbia Loukas, Athanasios 1994

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MOUNTAIN PRECIPITATION ANALYSIS FOR THE ESTIMATION OF FLOODRUNOFF IN COASTAL BRITISH COLUMBIAByATHANASIOS LOUKASDipL Eng., Aristotle University of Thessaloniki, 1988M.A.Sc., University of British Columbia, 1991A THESIS SUBMIYED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF CIVIL ENGINEERINGWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAAugust 1994© ATHANASIOS LOUKAS, 1994In presenting this thesis in partial fulfillment of therequirements for an advanced degree at the University of BritishColumbia, I agree that the Library shall make it freely availablefor reference and study. I further agree that permission forextensive copying of this thesis for scholarly purposes may begranted by the head of my department or by his or herrepresentatives. It is understood that copying or publication ofthis thesis for financial gain shall not be allowed without mywritten permission.(SiDepartment ofThe University of British ColumbiaVancouver, CanadaDate - —‘-I5’-IABSTRACTA study of the precipitation distribution in coastal British Columbia is described and atechnique is proposed for the reliable estimation of the frequency of rainfall generated floodsfrom ungauged watersheds in the region. A multi-disciplinary investigation was undertakenencompassing the areas of hydrometeorology, meteorological modelling and hydrologicalmodelling. Study components included analysis of long- and short-term precipitation in twomedium sized watersheds located in southwestern coastal British Columbia; development of a24-hour design storm for coastal British Columbia; generalization of the results over thecoastal region of British Columbia; examination of the precipitation distribution during floodproducing storms; identification of the applicability of a meteorological model for theestimation of short-term precipitation; and development of a physically-based stochastic-deterministic procedure for the estimation of flood runoff from ungauged watersheds of theregion.Based on an assessment of the atmospheric processes which affect climate, it wasfound that the strong frontal storms which form over the North Pacific Ocean and traveleastward generate the majority of the precipitation during the winter and fall months, whereasconvective rainshowers and weak frontal storms produce the dry summer period precipitation.Examination of the annual, seasonal, and monthly precipitation in the two studywatersheds, the Seymour River and the Capilano River watersheds, showed that the variationof annual and winter and fall precipitation with elevation follows a curvilinear pattern,increasing up to middle position of the watersheds at an elevation of about 400 m and thendecreasing or leveffing off at the upper elevations. The summer precipitation is moreuniformly distributed over the watersheds than the winter precipitation and accounts for about1125% of the total annual precipitation. The Bergeron two-cloud mechanism has been identifiedas the dominant rainfall producing mechanism during the winter and fall months.Analysis of regional data and results of other regional studies indicate that thecurvilinear pattern found in this study is more general and is similar for the whole of coastalBritish Columbia and the coastal Pacific Northwest.Study of the 175 storms in the Seymour River watershed showed that the individualstorm precipitation is distributed in a pattern similar to that of the annual precipitation and thisdistribution pattern is not affected by the type of the event. Furthennore, the analysis showedthat the storm time distribution is not affected by the elevation, type of the storm, its duration,and its depth. Also, analysis of the data from three sparsely located stations of coastal BritishColumbia indicated that the time distribution of the storms does not change significantly overthe region.With regard to the development of techniques for the better estimation of flood runoff,a 24-hour design storm has been developed by using the data from the Seymour Riverwatershed. Analysis of its spatial distribution revealed that this 24-hour design storm isdistributed in a similar patter to that of the annual precipitation. Also, it was found that the24-hour extreme raiiifall of various return periods is a certain percentage of the mean annualprecipitation. Comparison with regional data and results of other regional studies showed thatthe developed design storm can be transposed over the whole coastal region of BritishColumbia. A comparative study and rainfall-runoff simulation for a real watershed showedthat from the widely used synthetic hyetographs, only the Soil Conservation Service Type IAstorm or the 10% time probability distribution curve of this study can accurately generate theflood runoff from watersheds of the region.The above results of the short-term precipitation distribution with elevation and in timewere tested for extreme storms. Five periods of historical large flood producing storms were111analyzed and it was shown that the fmdiiigs of the short-term precipitation analyses are validfor these extreme storms.The BOUNDP meteorological model was used for the estimation of stormprecipitation in the mountainous area which covers the two study watersheds, but the resultsshowed that this particular model is not capable of simulating the precipitation observed in thearea. As a result, the initial intention of coupling the model with a hydrological model for theestimation of the runoff was abandoned.The above results of the analysis of precipitation in coastal British Columbia and thefindings of previous research on the watershed response of coastal mountainous watershedshave been combined and used for the development of a physically-based stochastic-deterministic procedure. The procedure uses the method of derived distributions and MonteCarlo simulation to estimate the flood frequency for ungauged watersheds of the region. Theprocedure has been tested with data from eight coastal British Columbia watersheds andcompared with the results of other widely used regional techniques. This comparison showedthat the method is reliable and efficient, and requires very limited data, which can be foundfrom a topographical map and the Rainfall Frequency Atlas for Canada.ivTABLE OF CONTENTSABSTRACT iiLIST OF TABLES xiLIST OF FIGURES xiiiACKNOWLEDGMENT xxii1. INTRODUCTION 12. STUDY AREA AND DATA SETS 62.1 Regional Climate 62.2 The Study Watersheds 102.2.1 Topography 102.2.2 Interaction of weather systems with the local topography 122.3 Data Sets 133. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTION 243.1 Introduction 243.2 Spatial Distribution of Precipitation 253.2.1 Annual and seasonal precipitation distribution in the SeymourRiver valley 253.2.2 Annual and seasonal precipitation distribution in the CapilanoRiver valley 273.2.3 Monthly precipitation distribution in the two study watershedvalleys 29v3.2.4 Comparison of mountain and valley precipitation 323.3 Temporal Variation of Precipitation 353.3.1 Seymour river watershed 353.3.2 Capilano river watershed 363.4 Spatial Variation of Precipitation 363.4.1 Seymour river watershed 373.4.2 Capilano river watershed 393.5 Comparison with Other Studies and Regional Data 403.6 Meteorological Mechanisms Affecting the Precipitation Distribution 453.7 Summary 474. STORM PRECIPITATION DISTRIBUTION 634.1 Introduction 634.2 Data Sets 644.3 Spatial Distribution of Storms 664.3.1 Storm precipitation 664.3.1.1 Spatial variation 674.3.2 Duration and average storm intensity 694.3.3 Maximum hourly intensity 704.3.4 Relative start time 704.4 Time Distribution of Storms 714.4.1 Research Procedure 724.4.2 Results 744.5 Antecedent Precipitation 784.6 Summary 80vi5. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIA 985.1 Introduction 985.2 Data Sets and Method of Analysis 1005.3 Time Distribution 1025.4 Spatial Distribution 1065.5 Antecedent Rainfall 1115.6 Simulation of Peak Storm Flow at Jamieson Creek Watershed 1135.7 Summary 1176. STUDY OF ifiSTORICAL LARGE STORMS 1336.1 Introduction 1336.2 The July 11-12, 1972 Rainstorm 1346.2.1 Synoptic conditions 1346.2.2 Spatial distribution 1356.2.3 Time distribution 1366.3 The December 13-18, 1979 Rainstorms 1376.3.1 Synoptic conditions 1376.3.2 The December 13-14, 1979 storm 1386.3.2.1 Spatial distribution 1386.3.2.2 Time distribution 1406.3.3 The December 16-18, 1979 storm 1406.3.3.1 Spatial distribution 1406.3.3.2 Time distribution 1416.4 The October 25-31, 1981 Rainstorms 1426.4.1 Synoptic conditions 142vii6.4.2 The October 25-28, 1981sto. 1436.4.2.1 Spatial distribution 1436.4.2.2 Time distribution 1446.4.3 The October 28-3 1, 1981 storm 1456.4.3.1 Spatial distribution 1456.4.3.2 Time distribution 1466.5 The November 8-11, 1990 Rainstorm 1466.5.1 Synoptic conditions 1466.5.2 Spatial distribution 1476.5.3 Time distribution 1496.6 The November 21-24, 1990 Rainstorm 1496.6.1 Synoptic conditions 1496.6.2 Spatial distribution 1496.6.3 Time distribution 1516.7 Summary 1517. APPLICATION 01? A METEOROLOGICAL MODEL 1607.1 Introduction 1607.2 General Description of the BOUNDP Model 1637.2.1 Overview 1637.2.1.1 The wind model 1647.2.1.2 The water flux model 1667.2.1.3 Estimation of precipitation 1687.3 Data Sets 1697.4 Application 171viii7.4.1 Comp1icaons . 1717.4.2 Results 1737.4.2.1 Calibration of the model 1747.4.2.2 Analysis of the regression coefficients 1777.4.2.3 Verification of the model 1797.5 Summary 1818. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDUREFOR THE ESTIMATION OF FLOOD RUNOFF 2028.1 Introduction 2028.2 Procedure 2078.2.1 Rainfall model 2088.2.2 Watershed response model 2128.3 Application and Results 2168.4 Sensitivity Analysis 2208.5 Comparison with Regional Techniques 2258.5.1 Methods 2268.5.1.1 Index flood method 2268.5.1.2 Method of direct regression of quantiles (DRO) 2278.5.1.3 Method of regression for distribution parameters (RDP) 2278.5.1.4 B.C. Environment method 2288.5.1.5 Russell’s Bayesian methodology 2298.5.2 Application 2308.5.3 Results 2388.6 Summary 242ix9. CONCLUSIONS AND RECOMMENDATIONS .2729.1 Conclusions 2729.2 Recommendations 276REFERENCES 279APPENDICES 299A PRECIPITATION AND STREAMFLOW STATIONS USED IN THE STUDY OFLONG-TERM PRECIPITATION 299B RELATIONSHIP BETWEEN EXTREME 24-HOUR RAINFALL AND MEANANNUAL PRECIPITATION 309C CHARACTERISTICS OF THE 44 BASINS USED FOR THE TESTING OF THEMODIFIED SNYDER FORMULA 318xLIST OF TABLES2.1 Mean monthly precipitation for representative coastal British Columbia stations... 82.2 Precipitation stations in the Seymour River watershed 142.3 Precipitation stations in the Capilano River watershed 153.1 Regression coefficients for the monthly precipitation-Seymour River watershed... 303.2 Regression coefficients for the monthly precipitation-Capilano River watershed... 313.3 Comparison of the annual precipitation gradient for the valley and mountain slope333.4 Regression coefficients for the monthly precipitation-Lower Capilano valley,Hollyburn and Grouse mountains 344.1 Characteristics of the coastal British Columbia stations whose data analyzed 775.1 Characteristics of the coastal British Columbia stations used in the analysis of the24-hour extreme rainfall time distribution 1045.2 Ratio of the 24-hour rainfall and mean annual precipitation for various coastalsubregions of British Columbia 1105.3 Probability distribution of antecedent rainfall for the maximum 24-hour storms forvarious number of days 1125.4 Comparison of the simulated peak flows (m3/sec) using various hyetographs withthe observed flows of Jamieson Creek watershed 1167.1 Precipitation stations used in the application of the BOUNDP model 1758.1 The characteristics of the eight watersheds used in the study 2198.2 Sensitivity Index Values (SI, %) for the mean annual 24-hour rainfall (Rm) 2228.3 Sensitivity Index Values (SI, %) for the standard deviation of the 24-hourrainfall (CYR) 2228.4 Sensitivity Index Values (SI, %) for the mean of storage factor(11m) 223xi8.5 Sensitivity Index Values (SI, %) for the coefficient of variation of KF (CV1)... 2238.6 Sensitivity Index Values (SI, %) for the mean of infiltration abstractions parameter(If) 2248.7 Sensitivity Index Values (SI, %) for the coefficient of variation of I (CVJf) 2248.8 Sensitivity Index Values (SI, %) for the form of the parameters 2258.9 Characteristics of coastal British Columbia watersheds used in the study 2328.10 Regional equations of instantaneous peak flow for the method of Direct Regressionof Quantiles 2348.11 Regional equations of daily peak flow for the method of Direct Regression ofQuantiles 2358.12 Comparison of estimated instantaneous peak flow (m3/sec) for various returnperiods using various methods 2408.13 Comparison of estimated daily peak flow (m3/sec) for various return periodsusing various methods with the fitted Extreme Value type I distribution and theobserved flows 241Al Precipitation stations in coastal British Columbia 300A2 Streamfiow gauging stations in coastal British Columbia 307Bi Characteristics of the sixty-one stations used in the analysis of the 24-hour extremerainfall 310Cl Characteristics of the basins used in the independent test of the modified Snyderformula 319xliLIST OF FIGURES2.1 Map showing coastal British Columbia 192.2 Mean monthly temperatures for coastal British Columbia stations 202.3 The location and instrumentation of the study watersheds 212.4 Area-elevation curves for the two study watersheds 222.5 Comparison of the precipitation accumulations with the snow course data 233.1 The distribution of the annual and seasonal precipitation along the topographicprofile of the Seymour River watershed 493.2 The distribution of the annual and seasonal precipitation along the topographicprofile of the Capilano River watershed 503.3 The coefficients of variation of the annual and seasonal precipitation at theSeymour River watershed 513.4 (a) The distribution of the monthly precipitation at selected stations at the SeymourRiver watershed and (b) its coefficients of variation 523.5 The coefficients of variation of the annual and seasonal precipitation at theCapilano River watershed 533.6 (a) The distribution of the monthly precipitation at selected stations at the CapilanoRiver watershed and (b) its coefficients of variation 543.7 Monthly distribution of the correlation coefficient between several stationsin the Seymour River watershed 553.8 Spatial correlation functions of annual, seasonal, and November and Augustprecipitation in the Seymour River watershed 56xlii3.9 Monthly distribution of the correlation coefficient between several stations in theCapilano River watershed 573.10 Spatial correlation functions of annual, seasonal, and November and Augustprecipitation in the Capilano River watershed 583.11 (a) Distribution of the annual and seasonal precipitation with elevation and (b)coefficients of variation for the annual and seasonal precipitation at differentelevations in the North Cascades, Washington State (after data of Rusmussen andTangborn, 1976) 593.12 Distribution of the mean annual runoff with mean basin elevation for northernCascades region (after data of Rasmussen and Tangborn, 1976) 603.13 Distribution of annual precipitation (a) and its coefficients of variation (b) withelevation for the coastal British Columbia stations (269 stations) 613.14 Distribution of the mean annual runoff with mean basin elevation for coastalBritish Columbia stations 624.1 a) Monthly distribution of the average annual precipitation at station S-i andb) Monthly distribution of the 175 storms analyzed 824.2 a) Precipitation ratio to base station (Vancouver Harbour) for various stationsand types of events and b) its coefficient of variation 834.3 Spatial correlation functions for the various types of storms 844.4 (a) Storm continuity at various elevations and types of storms and (b) Coefficientof variation of storm continuity 854.5 (a) Storm duration ratio to base station for various elevations and types of stormsand (b) Coefficient of variation of storm duration ratio 86xiv4.6 (a) Ratio of the average storm intensity to base station for various elevations and typesof storms and (b) its coefficient of variation 874.7 Ratio of the maximum hourly intensity to base station for various elevations andtypes of storms and (b) its coefficients of variation 884.8 Storm relative start time to the base station at different elevations and types ofstorms 894.9 Time distribution probability curves at station 25B 904.10 Comparison of the time distribution probability curves for different stations andelevations in the Seymour River watershed 914.11 Comparison of the time distribution probability curves for different type of eventsat the station 25B in the Seymour River watershed 924.12 The effect of the storm duration on the time probability distribution curves(Station S-i) 934.13 The effect of the storm precipitation on the time probability distribution curves(Station S-i) 944.14 Comparison of the time probability distribution curves for the Seymour Riverwatershed and three coastal British Columbia stations 954.15 Probability of equality or exceedance of antecedent precipitation at station S-i for(a) October to March storms and (b) April to September storms 964.16 Comparison of the probability of equality or exceedance of the antecedentprecipitation for different elevations for (a) winter and (b) summer 975.1 Distribution of the coastal British Columbia stations with (a) years of record and(b) station elevation 1205.2 Monthly distribution of the occurrence of the annual maximum 24-hour storms atVancouver Harbour (53 years) 121xv5.3 Time probability distributions of 24-hour storms for station S-i 1225.4 Comparison of the time probability distributions for various storms a) ten percentcurves, b) fifty percent curves, and c) ninety percent curves 1235.5 Average time probability distributions for the Seymour River watershed 1245.6 Comparison of the average storm time distribution in the Seymour River watershedwith the results of the Melone (1986) analysis for coastal British Columbia 1265.7 Comparison of the average storm time distribution in the Seymour River watershedwith the results of the Hogg (1980) analysis for coastal British Columbia 1275.8 Comparison of the time probability distributions of the Seymour River watershedwith three coastal British Columbia stations, a) ten percent curves, b) fifty percentcurves, and c) ninety percent curves 1285.9 Comparison of synthetic storms with the average time probability distributions ofthe Seymour River watershed 1295.10 Distribution of rainfall with elevation for various return periods in the SeymourRiver watershed 1305.11 Relationship of the 10-year 24-hour rainfall and mean annual precipitation for thesixty-one recording stations in the coastal British Columbia 1315.12 The watershed model flow chart 1325.13 Estimation of the 10-year flood for the Jamieson Creek watershed using syntheticand derived hyetographs 1336.1 Comparison of the time distribution of the July 11-12, 1972 storm with timeprobability distribution curves at (a) station 1OA and (b) station 14A 1536.2 Comparison of the time distribution of the December 12-14, 1979 storm with timeprobability distribution curves at (a) station Vancouver Harbour, (b) station 1OA and(c) station 14A 154xvi6.3 Comparison of the time distribution of the December 16-19, 1979 storm with timeprobability distribution curves at (a) station Vancouver Harbour, (b) station 10A and(c) station 14A 1556.4 Comparison of the time distribution of the October 25-28, 1981 storm with timeprobability distribution curves at (a) station Vancouver Harbour, (b) station 1OA,(c) station 14A and (d) station 25B 1566.5 Comparison of the time distribution of the October 28-3 1, 1981 storm with timeprobability distribution curves at (a) station Vancouver Harbour, (b) station bA,(c) station 14A and (d) station 25B 1576.6 Comparison of the time distribution of the November 8-11, 1990 storm with timeprobability distribution curves at (a) station Vancouver Harbour, (b) station 14A and(c) station 25B 1586.7 Comparison of the time distribution of the November 2 1-24, 1990 storm with timeprobability distribution curves at (a) station Vancouver Harbour, (b) station 1OA and(c) station 14A 1597.1 Three dimensional map of the calculation domain (latitude and longitude in degreesand elevation in meters with vertical scale 1: 17,500) 1827.2 Three dimensional map of the model domain (latitude and longitude in degrees andelevation in meters with vertical scale 1:32,500) 1837.3 Topographical contour map of the calculation domain (latitude and longitude indegrees) 1847.4 Topographical contour map of the model domain (latitude and longitude indegrees) 1857.5 Undisplaced water flux (mm) for November 10, 1990 (12:00 UTC) 1867.6 Undisplaced water flux (mm) for November 11, 1990 (00:00 UTC) 187xvii7.7 Displaced water flux (mm) for November 10, 1990 (12:00 UTC) 1887.8 Displaced water flux (mm) for November 11, 1990 (00:00 UTC) 1897.9 Predicted precipitation (mm) for November 10, 1990 1907.10 Objectively analyzed precipitation (mm) for November 10, 1990 1917.11 Scattergraphs of observed and predicted precipitation for calibration for a) November10, 1990 and b) total storm period between November 8-13, 1990 1927.12 Regression coefficients versus the average domain precipitation a) Al and b) A2 1937.13 Regression coefficients versus the average domain precipitation a) A3 and A4 1947.14 Regression between the average domain precipitation and the coefficient Al 1957.15 Regression between the precipitation difference between U.B.C. and Grousemountain resort and the coefficient A4 1967.16 Undisplaced water flux (mm) for August 29, 1991(12:00 UTC) 1977.17 Undisplaced water flux (mm) for August 30, 1991 (00:00 UTC) 1987.18 Displaced water flux (mm) for August 29, 1991 (12:00 UTC) 1997.19 Displaced water flux (mm) for August 30, 1991 (00:00 UTC) 2007.20 Scattergraphs of observed and predicted precipitation for verification for a) August28, 1991 and b) total storm between August 26-30, 1991 2018.1 Isopleths of the mean annual 24-hour rainfall in coastal British Columbia(After Rainfall Frequency Atlas for Canada, Hogg and Carr, 1985) 2448.2 Isopleths of the standard deviation of the mean annual 24-hour rainfall in coastalBritish Columbia (After Rainfall Frequency Atlas for Canada,Hogg and Carr, 1985) 2458.3 Comparison of the frequency of the observed and simulated hourly peak flowusing the 24-hour, the 12-hour and the 6-hour storms for the CarnationCreek watershed 246xviii8.4 Comparison of the observed and simulated cumulative time probability distributionsfor the coastal British Columbia 2478.5 Scattergraph between computed and observed time lag for 43 North America basins(Data after Watt and Chow, 1985) 2488.6 Flow chart of the Monte Carlo simulation 2498.7 Map showing the location of the eight coastal British Columbia watersheds wherethe proposed procedure has been applied 2508.8 Flood frequency curves for the Capilano River watershed a) hourly flows,b) daily flows and c) flood volume 2518.9 Flood frequency curves for the Carnation Creek watershed a) hourly flows,b) daily flows and c) flood volume 2528.10 Flood frequency curves for the Chapman Creek watershed a) hourly flows,b) daily flows and c) flood volume 2538.11 Flood frequency curves for the Zeballos River watershed a) hourly flows,b) daily flows and c) flood volume 2548.12 Flood frequency curves for the North Allouette River watershed a) hourly flows,b) daily flows and c) flood volume 2558.13 Flood frequency curves for the Oyster River watershed a) hourly flows, b) daily flowsand c) flood volume 2568.14 Flood frequency curves for the Hirsch Creek watershed a) hourly flows, b) daily flowsand c) flood volume 2578.15 Flood frequency curves for the San Juan River watershed a) hourly flows,b) daily flows and c) flood volume 2588.16 Sensitivity of the procedure to the change of mean 24-hour rainfall depth (Rm) fora) hourly flow, b) daily flow and c) flood volume for CarnationxixCreek watershed .2598.17 Sensitivity of the procedure to the change of standard deviation of the 24-hourannual rainfall (a’R) for a) hourly flow, b) daily flow and c) flood volumefor Carnation Creek watershed 2608.18 Sensitivity of the procedure to the change of mean storage factor of fast runoff(KFm) for a) hourly flow, b) daily flow and c) flood volume for CarnationCreek watershed 2618.19 Sensitivity of the procedure to the change of coefficient of variation of storagefactor (CV1<p) for a) hourly flow, b) daily flow and c) flood volume forCarnation Creek watershed 2628.20 Sensitivity of the procedure to the change of mean final infiltration abstractions(I) for a) hourly flow, b) daily flow and c) flood volume for CarnationCreek watershed 2638.21 Sensitivity of the procedure to the change of coefficient of variation of infiltrationabstractions (CVJf) for a) hourly flow, b) daily flow and c) flood volume forCarnation Creek watershed 2648.22 Sensitivity of the procedure to the form of procedure parameters for a) hourly flow,b) daily flow and c) flood volume for CarnationCreek watershed 2658.23 Homogeneity test for peak instantaneous flow for coastal British Columbiastations 2668.24 Homogeneity test for peak daily flow for coastal British Columbiastations 2678.25 Dimensionless frequency curve of instantaneous peak flow for coastal BritishColumbia (Index Flood Method) 268xx8.26 Dimensionless frequency curve of daily peak flow for coastal British Columbia(Index Flood Method) 2698.27 Comparison of the frequency of the observed instantaneous peak flow with thefrequency of the simulated instantaneous peak flow using various methods for theSanta River watershed 2708.28 Comparison of the frequency of the observed daily peak flow with the frequencyof simulated daily peak flow using various methods for the Santa Riverwatershed 271Bi Relationship of the 2-year 24-hour rainfall and mean annual precipitation for thesixty-one recording stations in coastal British Columbia 312B2 Relationship of the 5-year 24-hour rainfall and mean annual precipitation for thesixty-one recording stations in coastal British Columbia 313B3 Relationship of the 10-year 24-hour rainfall and mean annual precipitation for thesixty-one recording stations in coastal British Columbia 314B4 Relationship of the 25-year 24-hour rainfall and mean annual precipitation for thesixty-one recording stations in coastal British Columbia 315B5 Relationship of the 50-year 24-hour rainfall and mean annual precipitation for thesixty-one recording stations in coastal British Columbia 316B6 Relationship of the 100-year 24-hour rainfall and mean annual precipitation for thesixty-one recording stations in coastal British Columbia 317xxiACKNOWLEDGMENTI would like to thank my thesis supervisor Dr. M.C. Quick who, throughout my study,encouraged and advised me, giving me guidance, but also leaving me the freedom of thinkingand deciding. I am also thankful to the supervisory committee members, Dr. W.F Caselton,Dr. S.T. Chieng, Dr. D.L. Golding and Dr. S.O. Russell for their long discussions andvaluable comments on my thesis.I appreciate the assistance received from the Forest Hydrology Group of the Universityof British Columbia, Dr. D.L. Golding and, especially, Mr. Kuochi Rae, who has beenresponsible for collecting and processing the data from the Seymour River and Capilano Riverwatersheds.This thesis was made possible by the financial assistance given to me by the Universityof British Columbia and the Greek Ministry of National Economy which supported methroughout my doctorate studies with a University Graduate Fellowship and a N.A.T.O.Science and Engineering Scholarship, respectively. This research was also funded by agraduate scholarship awarded by the Earl R. Peterson Memorial Fund.Finally I would like to dedicate my thesis to my wife, Kyriaki Maniati-Loukas, whocontributed in many aspects of this study which could not have been conducted without hermoral support, assistance and inspiration, my newly born daughter, Irene-Evdokia, and myparents, George and Irene Loukas, in appreciation for their love, caring and undying supportthroughout these long years at school.xxiiCHAPTER 1INTRODUCTIONReliable prediction of runoff requires knowledge of the distribution of precipitation in bothspace and time. The analysis of precipitation can be done for different time-scales rangingfrom annual, seasonal, monthly time-scales down to daily, hourly and even shorter time-scales. For long-term reservoir operation, water supply and irrigation, the longer time-scalesare adequate. On the other hand, the study of precipitation in short-term scales (daily, hourly,and storm precipitation) is necessary for the simulation of the runoff and especially of floodflow from the watersheds. For the long time-scales, the spatial variability within a singleclimate region is most likely to be associated with those physiographic factors that influencethe meteorological mechanisms that generate precipitation. Over the long term, relationshipsbetween individual gauge totals should be stable as long as the prevailing precipitationgenerating mechanisms remain the same. This should also be true for the seasonal andmonthly scales, although seasonal differences in meteorological patterns could produceseasonally variable spatial relationships.While the effects of spatial variability in precipitation may be stable over the longtime-scales, this may not be generally true over short time periods. The interaction of themeteorological elements with the topography of the area can be greatly different from stormto storm resulting in different spatial distribution patterns. This is evident in areas whereprecipitation is generated by convective rainstorms which usually cover small areas less than30 kni2 and are quite variable in their spatial distribution. However, in areas whereprecipitation is generated by frontal storms, it is expected that the spatial variability of theshort-term precipitation may be as stable as the longer-term precipitation. In this case theprecipitation data should be examined for similarities between the spatial distribution patternsChapter 1. INTRODUCTIONof the long-term and the short-term precipitation, because if such similarities exist, then long-term data can be used for the estimation of the short-term precipitation patterns in other areasof the same climatic region. This is significant mainly because most of the precipitationstations are storage gauges, capable of measuring long- and medium-term precipitation but notthe short-term precipitation.Another important aspect of the precipitation is the temporal variability of the storm.This is particularly critical for the assessment of the short time-scale precipitation since it isused in the development of the storm hydrographs. Many recent studies have shown theimportance of the accurate assessment of the storm precipitation on the resulting hydrograph(Beven and Hornberger, 1982; Bras et al., 1985; Watts and Calver, 1991). It is thereforeimportant to analyze both the spatial and temporal variability of the short-term precipitation inorder to improve the estimation of the storm-producing precipitation.All the above aspects of precipitation become more difficult to study in mountainousregions where it is often unfeasible to install precipitation gauges at upper elevations becausehillslopes are steep, weather is harsh, and lack of roads and transportation make the collectionof precipitation data difficult. Also, the physiographic features and the complex atmosphericprocesses significantly modify the distribution of precipitation and make the reliableestimation of precipitation difficult (Sevruk, 1989). Hence, in the mountainous areas wherelarge variability in the precipitation exists, the gauge network is never adequate to defme thedetailed precipitation distribution. As an example, in coastal British Columbia there are 269precipitation stations, both recording and storage gauges, for an area of about 210,000 km2.The sparse data network makes the application of hydrology very difficult. On the other hand,the mountainous regions are valuable water resource areas because the streamfiows are usedfor the industrialized and populated areas which exist downstream in the regions. The water2Chapter 1. INTRODUCTIONmay be used in various ways, such as for industry, water supply, irrigation, power generation,and recreation.In the last two decades many models have been developed for the estimation and studyof the precipitation. These models have concentrated on modeling the meteorological causesof spatial and temporal variation. This can be done implicitly using stochastic ormathematical representations of dynamic cells of rainfall during storms (Amorocho and Wu,1977; Georgakakos, 1986; Rodriguez-Iturbe and Eagleson, 1987) or explicitly by modelingthe physics of storm development and progression (Browing et al., 1973; Harrold, 1973; Hilland Browing, 1979; Hoskins, 1983). However, in order to make these models applicable inpractice, they need to be tested against real. precipitation data, Thus, there is a need forempirical studies on the spatial and temporal characteristics of precipitation on different timescales (Berndtsson and Niemczynowicz, 1988), and only a few such studies currently exist.This lack of understanding of the precipitation mechanisms on a regional basis, limits theaccuracy of water resources plans and water management.Even if all the above aspects of precipitation are carefully studied and reliablehydrological models are developed and used, the main problem in hydrology is to matchrecent scientific achievements with practical engineering applications. It is necessary todevelop methods that incorporate all the acquired knowledge in such a way that is easy toapply and significantly improves the solution of the problems or satisfy newly raisedobjectives. The aim of this Thesis is to address the above concerns, to study the precipitationdistribution in the mountainous coastal British Columbia and to use the results for thedevelopment of techniques for the reliable estimation of flood frequency for ungaugedwatersheds.An investigation was undertaken encompassing the areas of hydrometeorology,meteorological modeling and hydrologic modeling. This research program examines the3Chapter 1. INTRODUCTIONprecipitation distribution in long-, medium- and short-term time-scales in time and space forthe coastal British Columbia and proposes a new procedure for the estimation of floodfrequency from ungauged watersheds of the region. Specifically, the location and thetopography of the two study watersheds and the coastal British Columbia are presented inChapter 2. The weather systems and the climate of the region are discussed in detail, and theprecipitation data sets used in the study are presented and their accuracy is tested.Examination of the precipitation starts with an analysis of the annual, seasonal, andmonthly accumulations on the two study watersheds in Chapter 3. This analysis examines thespatial distribution of the long- and medium-term precipitation and associates this distributionwith the physiographical features of the area. In addition the temporal and spatial variabilityof the precipitation in these time-scales are studied. The results are compared with regionalprecipitation and runoff data and the transferability of the results to other areas of coastalBritish Columbia and the Pacific Northwest is investigated as well.In Chapter 4, the storm precipitation distribution both in space and time is analyzed inone of the two study watersheds where hourly data are available. The storms are categorizedinto various types of precipitation events according to temperature and then the effects ofelevation, type of events, storm precipitation and duration on the storm spatial and temporaldistribution are investigated. The transferability of the findings to other areas of coastalBritish Columbia is examined. Similarities between the storm spatial distribution and thelonger-term precipitation spatial distribution are identified.In engineering practice the concept of the design storm is frequently used for theestimation of the flood runoff and for mountainous and rural watersheds it is common practiceto use the 24-hour design storm, For this reason the development of the 24-hour storm for thecoastal British Columbia is investigated in Chapter 5. The spatial distribution of the designstorm is studied in one of the two study watersheds and the relationships between the annual4Chapter 1. INTRODUCTIONprecipitation and the 24-hour storm precipitation are identified. The effect of elevation andthe severity of the storm on the time distribution is examined. The results are compared withregional data and the transferability of the results over the coastal British Columbia isinvestigated.The spatial and temporal distribution of seven severe storms in the study area arecompared with the results of the analysis of the storm precipitation, and the similarities anddifferences are discussed in Chapter 6. The study of the synoptic conditions of these severestorms helps in understanding the atmospheric processes of the flood producing storms in thearea.In addition to the statistical analysis of the precipitation data, the precipitationdistribution is studied with the help of a meteorological model in Chapter 7. The main partsof the model are described and discussed. The model is applied to the study area and theresults are compared with the observed data. The model’s ability to generate the observedprecipitation distribution is discussed.The results of the analysis of the short-term precipitation analysis are combined with ahydrologic model in a physically based stochastic-deterministic procedure to generateestimates of the frequency of peak flow runoff in Chapter 8. The procedure is applied tocoastal British Columbia watersheds and the results are compared with the observed flow data.Furthermore, a sensitivity analysis of the method is performed and the results of the methodare compared with the results from other techniques used for the estimation of the frequencyof peak flow from ungauged watersheds.5CHAPTER 2STUDY AREA AND DATA SETSThe objective of this chapter is to provide background information for the study. Firstly, thecharacteristics of the regional climate of coastal British Columbia are discussed, then thetopography of the two study watersheds and the interaction of the local topography with theweather systems are outlined and finally, the data sets used in the analysis are presented.2.1 Regional ClimateCoastal British Columbia (Fig. 2.1) is part of a larger geographical and climatic region, thecoastal Pacific Northwest which extends southward into Washington and Oregon bounded bythe Cascade Mountain Range, and includes southeast Alaska immediately adjacent to northernBritish Columbia. The coastal Pacific Northwest receives most of its precipitation fromthe prevailing temperate cyclonic systems originating over the north Pacific Ocean, similar toclimatic conditions which are repeated in several temperate regions, for example, in southernChile, in New Zealand, and over the mountainous coastal northwestern Europe, especially inNorway (Kendrew and Kerr, 1955).The main climatic features of the coastal region include relatively high annualprecipitation with the wettest months occurring in fall and winter, and a relatively smallannual range of temperature. The Coastal Mountain Range in British Columbia and southeastAlaska, as well as the Cascade Mountains in Washington and Oregon, modify the air flowwhich moves eastward from the Pacific Ocean. As a result, along the west facing slopes ofthe mountain ranges much higher cloud cover and precipitation are observed than the easternslopes of the mountains. Within the coastal region local variations in precipitation andChapter 2. STUDYAREA AND DATA SETStemperature exist because of the interaction of the weather systems with the local topography.For example, the southeastern lowlands of Vancouver Island, the islands of the Georgia Straitand the Fraser River estuary are located in the rain shadow area of Vancouver Island and theOlympic peninsula mountains. This zone is the driest area of the coastal region and also thewarmest with more hours of bright sunshine during the summer months (Phillips, 1990).Mean monthly precipitation data are included in Table 2.1 for representative stationsextending from Vancouver in the south to Prince George in the north. The location of thestations is shown in Figure 2.1. These data ifiustrate the variability along the coast, and yetalso show that the monthly precipitation distribution as a percentage of the total annualprecipitation is similar for the whole region. Also, it is evident that the summer precipitationis only a small percentage of the total annual precipitation, whereas the largest volume ofprecipitation falls during the fall and winter months. Furthermore, comparison of these datashows that the period of high precipitation starts earlier in the northern than in the southernsub-regions of coastal British Columbia. Williams (1948) noted a southward progression inthe occurrence of the maximum annual daily precipitation of about one degree of latitude foreach 4.5 days.7Chapter 2. STUDYAREA AND DATA SETSTable 2.1 Mean monthly precipitation for representative coastal British Columbia stationsVancouver Carnation CDF Courtenay Kithnat Prince RupertMonth Harbour Airportmm % mm % mm % mm % mm %Jan 218 14 377 14 225 15 351 12 228 9Feb 156 10 348 13 167 11 335 11 222 9Mar 153 10 302 11 142 10 211 7 201 8Apr 91 6 155 6 75 5 185 6 190 8May 68 4 91 3 47 3 106 4 140 6Jun 63 4 72 3 48 3 80 3 130 5Jul 43 3 58 2 34 2 70 2 103 4Aug 55 4 76 3 46 3 123 4 158 6Sept 79 5 135 5 64 4 220 7 233 9Oct 159 10 287 10 156 10 473 16 367 15Nov 214 14 412 15 139 16 402 14 268 11Dec 243 16 458 17 260 17 401 14 284 11Annual 1540 2770 1503 2957 2523Temperature data plotted on Figure 2.2 for three representative stations along coastalBritish Columbia show the relatively small annual range at a given station. The mean wintertemperatures along the coast remain at 2 to 4°C above freezing, which is the highesttemperature of any part of Canada (Phillips, 1990) whereas the average summer temperaturerarely increases above 18°C. Also, from Figure 2.2, a similar trend in mean monthlytemperature distribution between stations is evident. Chapman (1952) noted an averagereduction in mean annual temperature along the coast from 24020’ to 60° north latitude ofabout 0.6°C per degree of latitude.The climate of the coastal British Columbia is caused by the weather systems that aredeveloped over the North Pacific Ocean. Four pressure systems are dominant in Western8Chapter 2. STUDYAREA AND DATA SETSCanada: the sub-tropical high pressures of the North Pacific, the low pressures of middlelatitudes located south and east of the Aleutian Islands (Aleutian low), the high pressures overthe Arctic, and the continental high pressures which are located over the Mackenzie valley inwinter.During the winter months the sub-tropical high pressures and the Aleutian lowpressures dominate. The pressure systems induce westerly winds of variable direction andspeed. The air mass, transported by the westerly winds, acquires large amounts of moistureduring its passage over the Pacific Ocean so that when on encountering the rugged terrain ofcoastal British Columbia much precipitation is released. On a smaller scale, during the winterand fall months the Aleutian low pressures and the high inland pressures of the PacificNorthwest combine to produce strong pressure gradients over western Oregon, Washington,and British Columbia, and these pressure gradients induce strong east and southeast winds(Schaefer, 1978). These winds at Vancouver account for 52% of all winds in winter and 44%of the winds year around (Phillips, 1990) and displace the incoming weather systems to thenorth.Although these rain producing low pressure systems are dominant in the whole of thecoastal Pacific Northwest and especially in coastal British Columbia, there are also timeswhen the continental Arctic high pressure systems dominate and cause cold dry air to betransported over the Rocky mountains and, occasionally, over the Coastal Mountainsproducing prolonged spells of very cold, dry weather.In the summer months the weather systems weaken and move to the north, and thepressure gradient in the region is reversed. The warming of the land creates low pressureswhile the lower temperatures over the ocean create a high pressure system. A pressuregradient with a southeasterly direction develops in the area, but it is much weaker than thewinter pressure gradient described above (Schaefer, 1978). Under the influence of this9Chapter 2. STUDYAREA AND DATA SETSpressure gradient dry northwesterly winds prevail over the coastal British Columbia at thistime of the year. During these summer months, occasional precipitation is generated by weakfrontal systems, which are derived from the main low pressure systems which are now muchfurther north. Occasionally strong summer rainstorms develop when local heating causesadditional convective cloud development which can produce more intense bursts of rainfall.2.2 The Study WatershedsThe two study watersheds, the Seymour River and the Capilano River watersheds aremedium-sized mountainous watersheds located in the southwestern side of the CoastalMountains just north of the City of Vancouver (Fig. 2.3). A reservoir is located in theSeymour River watershed and another in the Capilano River watershed, and both, along withthe Coquitlam Lake reservoir, supply water to the greater Vancouver area. All threewatersheds are under the protection and supervision of a municipal organization, the GreaterVancouver Regional District (GVRD).In the next paragraphs, the topography of the study watersheds along with theinteraction of the weather systems with the local physiographic features will be discussed.2.2.1 TopographyThe areas of the Seymour River and Capilano River watersheds are 180 km2 and 195 km2,respectively. The two watersheds lie between three mountains, Hollyburn, Grouse, andSeymour, all located in the North Shore mountains. The elevations of the mountain peaks are:Hollyburn 1324 m, Grouse 1211 m, and Seymour 1450 m. The mountains lie on the northern10Chapter 2. STUDY AREA AND DATA SETSside of Burrard inlet and their slopes are very steep, so that there is a rapid change in elevationin a short distance of about 10-14 km.The elevation of the watersheds ranges from about 100 m at the downstream boundaryto about 1800 m at the highest point of the divide with about 50 percent of the watersheds’area lying above 800 m (Fig. 2.4). Watershed land slopes are generally steep with aconsiderable area of shallow soils and occasional rock outcrops. The basic topographicfeatures of the watersheds have resulted from the valleys being U-shaped by valley glaciation,which also rounded the lower peaks but sharpened the higher ones. The resulting profiles ofthe main valleys are gentle to moderately steep slopes in the valleys and abrupt steep slopes atthe valley sides. At the higher elevations, the slopes become more mild, rounded at the lowerpeaks.In the headwaters of both Seymour and Capilano Rivers the profile tends to change toV-shaped with hillsides having uniform slope. Most of the small, high elevation tributaries ofboth rivers have slopes greater than 40%.The above topographic characteristics are dominant for both Seymour River andCapilano River watersheds. However, there are some differences. The Capilano river at thelower reaches, below the Capilano Lake reservoir, flows through a narrow canyon, while theSeymour river flows through an open U-shaped valley to its mouth at Burrard Inlet. Also, theSeymour River watershed is elongated while the Capilano River watershed is more rounded(Fig. 2.3).The two study watersheds have a general north-south orientation. However, theSeymour River watershed turns to a northwest-southeast orientation after the middle distancebetween its mouth and its headwaters (Fig. 2.3). These variations of the local topography ofthe study watersheds may affect the local climate and will be examined in the analysis ofprecipitation in the two watersheds.11Chapter 2. STUDY AREA AND DATA SETS2.2.2 Interaction of weather systems with the local topographyThe humid Pacific Ocean air masses, discussed in the previous section, meet massive barriersin their path to the East. First the westerly systems meet the Vancouver Island ranges whichrise to average heights of 2000 m. These mountain ranges protect the Vancouver area fromthe direct onslaught of storms moving off the North Pacific ocean. To a lesser extent suchprotection is also offered by the Olympic Mountains of northwest Washington (Harry andWright, 1967).As the storms continue eastward, they impinge upon the mainland Coastal Mountains.The air mass, which has been modified by its passage over the Vancouver Island mountains,still has high humidity and releases large volumes of precipitation when it is forced to riseover the North Shore Mountains or funnel into the deep dissected valleys. For example, thelargest observed annual precipitation in the coastal British Columbia has been measured, in themiddle of the Seymour River watershed where the funneling of the incoming air mass and theorographic lifting produces heavy precipitation.In the wintertime, the North Shore mountains protect the area from outbreaks of coldArctic air. Only the major surges are able to overcome the mountain barrier, and at thesetimes the cold north wind sweeps the area and brings spells of clear cold weather. However,the cold air retreats as a Pacific storm advances, resulting in snowfall which often turns torainfall as the warmer air moves into the area.Much of the precipitation in the two study watersheds falls as rain, although snowoccurs at the high elevations often as a mixture of rain and snow, or wet snow. The studywatersheds are so well protected by the mountains both to the east and west that surface windsare, in general, light, and their direction depends on the local topography.12Chapter 2. STUDYAREA AND DATA SETS2.3 Data SetsVarious precipitation data sets will be used for the analysis of precipitation in coastal BritishColumbia in this study. The main analysis will be based on data from the two studywatersheds, Seymour River and Capilano River watersheds and will be presented in thissection. Other data sets that will be used later in the analysis are presented whenever they areused.The data used in the analysis has been taken from 9 stations in Seymour Riverwatershed and 7 stations in Capilano River watershed for the period 197 1-1990 (Fig. 2.3).The data set from the Vancouver Harbour station is used to assess the zero elevationprecipitation. The precipitation stations are of two types, manual storage gauges andrecording gauges. Some of the stations are maintained by the Atmospheric EnvironmentService (A.E.S.) and others by the Faculty of Forestry at the University of British Columbia(U.B.C.). The upper elevation stations in the two study watersheds have been installed as partof an ongoing research program between the Faculty of Forestry of the University of BritishColumbia and the Greater Vancouver Regional District (GVRD).Tables 2.2 and 2.3 show the characteristics of the stations. The A.E.S. storage gaugesare A.E.S. type B Standard rain gauges whereas the U.B.C. storage gauges are Sacramentotype. The A.E.S. recording gauges are M.S.C. tipping bucket rain gauges and the U.B.C.gauges are Belfort weighing type. There are six recording stations in the Seymour Riverwatershed that record hourly precipitation whereas all the stations in the Capilano Riverwatershed are storage gauges. The stations cover an elevation range of about 850 m in theSeymour River watershed and 610 m in the Capilano River watershed. Such elevationcoverage is difficult to find elsewhere in coastal British Columbia where the precipitationnetwork is very sparse.13Chapter 2. STUDY AREA AND DATA SETSTable 2.2. Precipitation stations in the Seymour River watershedName Elevation (m) Type OrganizationNorth VancouverSecond Narrows 10 Storage A.E.S.Bridge (NV2B)Seymour Falls Dam 247 Storage A.E.S.(SFD)S-.l’’ 260 Recording U.B.C.S-2 275 Storage U.B.C.1OA 293 Recording U.B.C.14A 488 Recording U.B.C.21A 640 Recording U.B.C.25B** 762 Recording U.B.C.28A 853 Recording U.B.C.t0rage gauge before December 1983Installed in summer of 198014Chapter 2. STUDY AREA AND DATA SETSTable 2.3. Precipitation stations in the Capilano River watershedName Elevation (m) Type OrganizationCapilano (CAP) 93 Storage A.E.S.Cleveland Dam 157 Storage A.E.S.(CD)C-i 610 Storage U.B.C.C-2 320 Storage U.B.C.C-3 518 Storage U.B.C.C-4 427 Storage U.B.C.C-5 610 Storage U.B.C.All stations are located in the valleys of the watersheds but, as mentioned above, thestations cover an elevation range of about 610 m in Capilano River watershed and 850 m inthe Seymour River watershed. Also the upper elevation stations are located in the headwatersof the Capilano River and Seymour River where the slopes are very steep ranging around 60-80%. For this reason, it is believed that these upper stations, bA, 14A, 21A, 25B, 28A andC3, C4, C5, can accurately record the mountain precipitation of the headwaters area of thewatershed.The gauges are charged with antifreeze during the winter time so that both rain andsnow accumulations are measured. The stations, installed in the forest, are located in thecenter of a clear-cut circle of a diameter of about twice the height of the adjacent trees whichhas been found to protect the precipitation catch from both wind and rain shadowing effects.15Chapter 2. STUDYAREA AND DATA SETSHowever, to ensure accuracy, the precipitation measurements have been tested.Firstly, the precipitation records of two gauges, one with wmdshiekl and the other withoutwindshield, 12 m apart at 762 m elevation, were compared and no significant difference wasfound (Kuochi Rae, personal communication). Secondly, the precipitation accumulations atvarious stations were compared with data from an adjacent snow course to test the accuracy ofthe snow measurement. The snow course is located at 1190 m elevation in theOrchid Lakesub-watershed of the Seymour River watershed and is operated by the GVRD.Comparison with data from other snow courses in the area indicates thattheaccumulations at the Orchid Lake are higher than any other snow course in thesouthwesterncoastal region (B.C. Environment, 1992). According to observations the first snow in the areausually falls during the first two weeks ofNovember and the accumulation of snow continuesto April.In this comparison, the mean snow waterequivalent accumulations at the Orchid Lakesnow course from January 1 to April 1 for the period 1972 to 1990 are comparedwith theprecipitation accumulations from the upper elevation stitions of Seymour River watershedvalley (Fig. 2.5). This comparison shows thatthe mean snow accumulation at the snowcourse is always lower than the precipitation accumulations at the valley stations.However,for the snowcourse, some precipitation may fall as rain and some snow will melt as theseasonprogresses. Therefore to make a more meaningful comparison the snowmeltfrom thesnowcourse has been modeled. The simplified energy equations for the estimation of thesnowmelt proposed by Quick and Pipes (1989) are used. These equations have beensuccessfully used in the UBC WatershedModel (Quick, 1993) and they require minimal datalike the minimum and maximum daily airtemperature. Air temperature data are not availableat the Orchid Lake snow course so that the temperature data from the Grouse Mountain Resortstation is used. The Grouse Mountain Resort station is located a few kilometers southof the16Chapter 2. STUDY AREA AND DATA SETSOrchid Lake snow course and has similar elevation to the snow course (1105 m). Thesimulated snowmelt is added to the snow water accumulation and shows that the totalaccumulation or precipitation at the Orchid Lake snow course is lower than precipitationaccumulations at the upper elevation stations 25B and 28A in the Seymour River watershedvalley (Fig. 2.5). An underlying assumption in the above modeling procedure is that all theprecipitation during the period from November to April is falling as snow. A study bySchaefer and Nildeva (1973) at the North Shore mountains has shown that the number of thesnow days during the December to March period increases linearly with elevation at about 27days per 300 m. For the elevation of the Orchid Lake snow course site (1190 m) the numberof snow days is estimated as 96. This number is close to the precipitation days for the sameperiod and so, indicates that the above assumption is valid.Except for the above tests, the corrections that should have been applied to themeasurements are calculated by the equations given by Sevruk (1982). The inaccuracies ofthe precipitation measurement can be classified into three categories, inaccurate precipitationcatch because of the wind, evaporation losses and wetting losses. The corrections forinefficient precipitation catch because of the wind have been calculated using the equationsfor the U.S. standard recording gauge. Beaudry and Golding (1985) measured the wind speedin forest openings in Seymour River watershed with a R.M. Young No. 6001 anemometer aspart of a snowmelt study. Beaudry and Golding found that the wind speed was minimum andin only few occasions was above the threshold velocity of 0.7 rn/sec. It is shown that thecorrection of the precipitation for the wind is between 0 and 4% using the above wind speedand temperature data from the Seymour River watershed stations. The evaporation andwetting losses are considerably smaller because of the wet climate of the area year around.Furthermore, the effect of blowing and drifting snow is minimum because of the small windspeed.17Chapter 2. STUDYAREA AND DATA SETSThe above tests and comparison have shown that the precipitation measurements usedin this study are reliable and they can be used without applying corrections.18Chapter 2. STUDYAREA AND DATA SETSFig. 2.1. Map showing coastal British Columbia1*01Prin.e RupertPACIFIC OCEANCOASTAL BRITISH COLUMBIAKittmat Alberta‘IaI?couverCarnation Creek0 100 200km U.S.A.19wChapter 2. STUDYAREA AND DATA SETSVancouver HarbourCourtenayPrince Rupert18 -16 -14-12 -10-8-6-4-2-0-2IIIIII/////\. ‘S\. 5%‘SS‘ ../\5s\ %5.5.5’5’I-FtIt .._•////I I I I IJAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DECMONTHFig. 2.2. Mean monthly temperatures for coastal British Columbia stations20Chapter 2. STUDYAREA AND DATA SETSFig. 2.3. The location and instrumentation of the study watersheds21Chapter 2. STUDYAREA AND DATA SETS180016001400z 1200! 10::6004002000Seymour River WatershedCapilano River Watershed0 20 40 60 80 100PERCENTAGE OF AREA ABOVE INDICATED ELEVATIONFig. 2.4. Area-elevation curves for the two study watersheds22210025B(762m)190028A(853m)——-OrchidLakesnowwaterequivalent (1190m)—-.-——.——1700——•—OrchidLakesnowwaterequivalent+melt(1190m).—.-——---—————..—..——E1500Q————...—..———1300—.——_____.._..___————..—..__C.)————._••_ILl1100————-.—————_.._•—————.——._•———_•——.—uu—-—..—700—500IIIJAN1FEB1MARCH1APRIL1Fig.2.5.Comparisonof theprecipitationaccumulationswiththesnowcourcedataCHAPTER 3ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTION3.1 IntroductionSeveral studies of the mountain precipitation have previously been carried out (e.g. Storr andFerguson, 1972; Schaefer and Nildeva, 1973; Hanson, 1982; Chacon and Fernandez, 1985).These studies examined the distribution and the variation of precipitation in different climaticregions. The results of this type of study can help our understanding of the physical processesof precipitation generation, and can assist in the reliable prediction of precipitationdistribution and runoff.It is often assumed (Melone, 1986; Barry, 1992) that the precipitation distribution inthe mid-latitude mountainous areas increases almost linearly with elevation. It is importantfor the assessment of hydrology of these regions to test this assumption for individualwatersheds and for a whole region. Furthermore, it is important to investigate whether thedistribution of precipitation can be adequately defined in terms of physiographic factorsbecause in these mountainous regions the database is sparse. Comparison will be madebetween valley and mountain precipitation data. This comparison is necessary for the overallassessment of precipitation in the mountainous areas because most of the precipitation stationsin these areas are located in the valleys. The elevation is usually used as the physiographicparameter to describe the precipitation distribution in space whereas other elements oftopography like aspect and slope affect the precipitation distribution. However, in moststudies the elevation is the most important topographic parameter that affects the precipitationdistribution in space.Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTIONIn this Chapter, the study of long-term precipitation distribution on Coastal Mountainsof British Columbia will be presented. The main part of the study will concentrate on the twostudy watersheds, the Seymour River and the Capilano River watersheds. First, the valleydata will be analyzed and then they will be compared with the limited mountain slope data.The relationships of the precipitation with the topographic parameters will be identified.Also, comparison will be made with other data sources, including precipitation and runoffdata from other watersheds of coastal British Columbia and the Pacific Northwest.3.2 Spatial Distribution of Precipitation3.2.1 Annual and seasonal precipitation distribution in the Seymour RivervalleyThe precipitation stations in the Seymour River watershed used in the analysis are all locatedin the valley, but their elevation increases from 0 m to 853 m, as shown in Figure 2.3 andTable 2.2. The analysis showed that the mean annual precipitation increases quite steadilyfrom the zero elevation station of Vancouver Harbour to the Seymour Falls Dam station at247 m and shows an increase from 1600 mm/year to 4100 mm/year (Fig. 3.1). The increasein precipitation becomes smaller beyond this point, and finally, after station S-i, where themaximum of precipitation occurs (4200 mm/year), there is a steep decrease of precipitation to3200 mm/year at 28A station, the highest station (Fig. 3.1).The mean seasonal precipitation from October to March follows a pattern similar tothe mean annual precipitation (Fig. 3.1). In contrast, during the April-September period theprecipitation gradient becomes smaller below S-i and larger above S-i so that theprecipitation is leveling off over the whole watershed. This six-month dry season from April25Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTIONto September accounts for only 25% of the annual total. The wet period from October toMarch accounts for about 75% of the annual precipitation and the precipitation gradients inthe watershed during this wet period are about the same as the annual gradients.The mean annual precipitation over the whole Seymour River watershed has beencorrelated with the physiographic features. The physiographic features used are: the stationelevation, the horizontal distance from the beginning of the topographical slope, an azimuthparameter, and the average slope between stations. The azimuth was taken as the anglebetween the station S-i and the other stations. The azimuth parameter is the cos(azimuth1800). The station S-i was selected because it is located at the position where the watershedorientation changes (Fig. 2.3). Application of stepwise linear regression shows that thedistance and the elevation are the only significant independent parameters but these twoparameters explain only 74% of the variation of the average annual precipitation, but betterresults are achieved if the analysis is split into two parts, for the upper and lower watershed, aswill now be discussed. This subdivision is also suggested by the graphical plot in Figure 3.1.By separating, the Seymour River watershed into lower and upper parts, below andabove the station S-i (Fig. 2.3), the curvilinear distribution of the annual precipitation can bereplaced by two linear relationships. The annual precipitation at both the lower and the upperwatershed have been correlated to the elevation and distance from the beginning of thetopographical slope. Precipitation data from four stations in the lower watershed and sevenstations in the upper watershed have been used. The following equations describe theprecipitation-elevation and precipitation-distance relationships in the watershed:Lower P=1658+9.38EL R2=O.998 See=69 mm n=4 (3.1)Upper P=40i1-l.O4EL R2=0.65l See=208 mm n=7 (3.2)Lower P=1559+1 16.O6DS R2=0.982 See=224 mm n—4 (3.3)Upper P=6663-1l3.18DS R2=0.948 See=80 mm n=7 (3.4)26Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTIONwhere, P is the mean annual precipitation (mm), EL is the elevation of the station (m), DS isthe distance from the beginning of the topographic slope (kin), and See is the standard error ofestimate (mm). The above equations are significant at 5% significance level (a=O.05)For the lower watershed, the coefficients of determination and the standard error ofestimate of the two regression equations (Eqs. 3.1 and 3.3) show that the mean annualprecipitation is strongly related to both elevation and distance from the beginning of thetopographical slope. However, for the upper watershed the relationship between the meanannual precipitation and distance is better than the relationship with the station elevation.The analysis of the precipitation in the Seymour River watershed showed that theannual and seasonal precipitation increases up to the middle position of the watershed andthen decreases at the upper elevations. The large increase of precipitation at the lower part ofthe watershed and the steep decrease at the upper watershed may be associated with thetopography of the watershed. The Seymour River watershed which has a general north-southorientation, turns to a northwest-southeast orientation after its middle (Fig. 2.3). Theincreased convergence of the incoming air at this position may account for the steep positiveand negative gradients at the lower and upper watershed, respectively. However, it isimportant to examine whether similar precipitation distribution is evident in an adjacentwatershed which has a general north-south orientation. For this reason the precipitationdistribution in Capilano River watershed will be examined in the next paragraphs.3.2.2 Annual and seasonal precipitation distribution in the Capilano RivervalleyThe eight precipitation stations used in the analysis represent an elevation range of 610 m(Table 2.3). The average annual precipitation, both the annual and seasonal, increases from an27Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRiBUTIONaverage of 1600 mm at Vancouver Harbour to about 4500 mm at the middle position of thewatershed (station C-i), and then decreases and levels off at a value of 4000 mm (Fig. 3.2),which is similar to the precipitation distribution at the Seymour River watershed. It should bementioned that the station C-i is located in a small tributary of the Capilano River, the SistersCreek. The orientation of the Sisters Creek is southeast, such that it can receive the incomingair mass directly and its large topographic gradient can trigger heavy precipitation.Unfortunately, the data set of this station, C-i, has many missing data and therefore, station C-1 has been excluded from the analysis.The remaining precipitation stations indicate that the precipitation increases up toabout the position of station C-2 and then levels off. This leveling off of the precipitation isoccurring at about the middle distance from the start of the topographic slope.The seasonal October to March precipitation follows the same pattern as the annualprecipitation (Fig. 3.2). On the other hand, the summer seasonal precipitation from April toSeptember is quite uniformly distributed over the watershed, and it is almost unaffected by thetopography (Fig. 3.2).It is therefore seen that the spatial distribution of the mean annual precipitation in theCapilano River watershed is similar to that of the Seymour River watershed. The onlydifference is that the precipitation at the upper watershed levels off while in the SeymourRiver watershed precipitation shows a decrease at the higher elevations. The change of theorientation of the Seymour River watershed after its middle position may account for thisdifference in the spatial distribution of precipitation between the two watersheds.Because of the observed curvilinear distribution of precipitation the distribution of theannual precipitation at the Capilano River watershed is studied by dividing the watershedarbitrarily at station C-2 into an upper and lower section. The mean annual precipitation wasagain correlated to the topographical parameters. Precipitation data from four stations at the28Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTIONlower watershed and five stations in the upper watershed have been used and the followingrelationships have been developed:Lower P=1483+6.76EL R2=O.983 See=l48 mm n=4 (3.5)Upper P=3597+O.41EL R2=O.329 See=90 mm n=4 (3.6)Lower P=1430+106.18DS R2=O.964 See=69 mm n=4 (3.7)Upper P=3832-l.55DS R2=O.009 See=lO9mm n=4 (3.8)where P. EL, DS and See are as previously stated. Equations 3.5 and 3.7 are significant ata=O.05 whereas equation 3.6 is significant at a=O.Ol and equation 3.8 is not significant ata=O.O 1.The statistical parameters, R2 and See, indicate that both relationships for the lowerwatershed are good. On the other hand, the relationships for the upper watershed between theannual precipitation and either the elevation or the distance from the beginning of thetopographical slope indicate that there is almost no functional relationship betweenprecipitation and either topographical parameters, because the mean annual precipitation at theupper Capilano River watershed is approximately constant, as can be seen from Figure 3.2.3.2.3 Monthly precipitation distribution in the two study watershed valleysRegression analyses were used to develop relationships between mean monthly precipitationand either elevation or distance from the beginning of the topographical slope (Tables 3.1 and3.2). These relationships were developed based on the same lower and upper watershed gaugesite stratification used in the mean annual analyses. Again the relationships for the lowerwatersheds are more consistent than those for the upper watersheds. The analyses show thatduring the wet season from October to April, there are steeper gradients for both the lower andupper watersheds. During the summer dry period from April to September, there is onlysmall variation in the precipitation accumulations over the two study watersheds.29Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTIONTable 3.1Regression coefficients for the monthly precipitation(Y=a÷bX;Y=monthly precipitation;X=elevation (m) or distance from the beginning of the slope (km); a and b = coefficients)SEYMOUR RIVER WATERSHEDwith elevationLower watershed (n=4) Upper watershed (n=7)a b R2 See a b R2 SeeJanuary 189 1.124 0.988 22 446 —0.103 0.373 35February 194 1.137 0.995 14 487 -0.128 0.521 32March 164 0.976 0.997 9 443 —0.151 0.836 17April 119 0.583 0.999 2 283 —0.114 0.758 17May 93 0.509 0.985 11 204 -0.007 0.036* 10June 73 0.335 0.995 4 145 -0.028 0.247 13July 56 0.171 0.965 5 92 -0.002 0.024* 4August 53 0.158 0.807 14 78 -0.007 0.038* 9September 81 0.406 0.992 6 179 -0.035 0.291 14October 154 1.102 0.996 13 400 -0.581 0.214 29November 253 1.571 0.996 18 632 —0.171 0.531 42December 242 1.232 0.995 16 607 —0.278 0.785 38with distanceLower watershed (n=4) Upper watershed (n=7)a b R2 See a b R2 SeeJanuary 177 13.933 0.974 32 757 -12. 885 0.774 21February 180 14. 198 0.995 13 838 —14.692 0.923 13March 153 12. 143 0.992 16 748 —13.449 0.894 14April 113 7.213 0.983 13 503 —9.807 0.754 17May 88 6.259 0.956 19 255 —1.942 0.367 8June 70 4.148 0.979 9 243 —3.961 0.671 8July 55 2.083 0.921 9 113 —0.783 0.381 3August 52 1.851 0.711 17 97 —0.795 0.069* 9September 77 4.973 0.955 15 270 -3.843 0.476 12October 143 13.571 0.969 14 613 -8.573 0.615 21November 236 19.467 0.981 38 1091 —19.286 0.908 19December 228 15.379 0.995 15 1162 —24.598 0.818 35N.B. All equations are significant at a=0.05 except for the ones noted* Not significant at a=0.0130Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTIONTable 3.2Regression coefficients for the monthly precipitation(Y=a-i-bX;Y=monthly precipitation (mm);X=elevation (m) or distance from the beginning of the slope (1cm); a and b = coefficients)CAPILANO RIVER WATERSHEDwith elevationLower watershed (n=4) Upper watershed (n=4)a b R2 See a b R2 SeeJanuary 169 0.705 0.999 4 364 0.099 0.699 10February 163 0.912 0.964 29 461 0.019 0.237 5March 131 0.808 0.942 33 392 0.069 0.232 19April 113 0.365 0.988 7 218 0.051 0.744 5May 85 0.349 0.992 5 178 0.068 0.416 12June 77 0.127 0.791 11 98 0.041 0.988 1July 58 0.118 0.958 4 87 0.031 0.483 5August 53 0.096 0.938 4 78 0.018 0.509 3September 77 0.271 0.991 4 144 0.056 0.896 3October 143 0.705 0.997 6 353 0.062 0.642 7November 212 1.038 0.961 35 575 —0.023 0.046* 16December 215 0.998 0.965 31 549 0.009 0.031* 8with distanceLower watershed (n=4) Upper watershed (n=4)a b R2 See a b R2 SeeJanuary 162 11.134 0.991 11 391 0.736 0.078* 17February 156 14.333 0.947 35 466 0.179 0.041* 6March 125 12.639 0.917 40 431 -0.246 0.006* 22April 110 5.723 0.967 11 227 0.561 0.177 8May 83 5.431 0.958 12 209 0.261 0.012* 16June 76 1.984 0.768 11 98 0.708 0.606 4July 57 1.884 0.967 4 94 0.253 0.071* 6August 53 1.502 0.911 5 75 0.431 0.562 3September 75 4.199 0.953 10 147 0.851 0.408 7October 137 11.096 0.981 16 371 0.412 0.058* 11November 203 16.325 0.945 41 605 -1.514 0.411 12December 207 15.711 0.951 37 569 —0.594 0.281 6N.B. AU equations are significant at a=0.05 except for the ones noted*Not significant at a=0.0131Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTION3.2.4 Comparison of mountain and valley precipitationThe distribution of precipitation over both the mountain slopes and the valleys is important forthe assessment of the total hydrology of the mountainous regions. Mountain precipitationmeasurements are very limited and in this study the assessment of the mountain precipitationhas been made using the data from Hollyburn Ridge at 930 m and Grouse Mountain Resort at1128 m elevation for the period 1971-1990. These measurements will be compared with thedata from the Capilano River watershed which has been used to assess the valley precipitationgradients.The precipitation gradient for the mountain slopes and the valley region will becompared in two different ways, firstly, as a function of elevation, and secondly, as a functionof distance from the start of the mountain region. The valley only reaches a high elevation ata considerable distance from the start of the mountains, and the precipitation gradients forsimilar elevations for the valley and mountain regions are quite different, as indicated in Table3.3. However, the valley precipitation gradients at the same distance from the start of themountain region are similar to the gradient at the immediately adjacent, but much highermountain slope. Therefore, it appears that the valley convergence produces the same increasein precipitation as the orographic lifting caused by the mountain slopes.32Chapter 3. ANNUAL AND SEASONAL PRECIPITATIONDISTRIBUTIONTable 3.3. Comparison of the annual precipitation gradient for the valley and mountain slopeGradient with elevation Gradient with distance(mmIlOO m) (mmlkm)Hollybum Mountain 140 124Grouse Mountain 129 134Lower Seymour Valley 910 117Lower Capilano Valley 680 125The mean annual precipitation for stations in the lower Capilano watershed and at thetwo mountain stations has been correlated with the distance from the start of the slope and thepercentage of barrier height, respectively, where the percentage of the barrier height for themountain stations is the ratio of the station elevation to the mountain top elevation. For thevalley stations, the elevation is assumed to be the elevation of the immediately adjacentmountain slope. The following equations describe these relationships:P=1537 + 109.20D5 R2=0.890 See=283 mm n=7 (3.9)P=1692+1595.77BH R2=0.974 See=ll2mm n=7 (3.10)where P, DS, See are as previously stated and BH is the percentage of barrier height. Theabove equations are significant at a=0.05.The above relationships should not be extrapolated for the area beyond the Hollyburnand Grouse mountains because there are no data for the mountain slopes at this region. Itwould be very interesting and important to study the precipitation distribution at the mountain33Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTIONslopes beyond the first mountain peaks and to compare it with the known valley precipitationdistribution.Similar relationships have been developed for the monthly precipitation of the lowerCapilano valley and the adjacent mountain slopes (Table 3.4). The results showed that thepercentage of barrier height is a better overall predictor of the monthly precipitation for bothvalleys and the adjacent mountain slopes.Table 3.4Regression coefficients for the monthly precipitation (Y=at-bX; Y=monthly precipitation (mm);X=distance from the beginning of the slope (1cm) or percentage of barrier height;a and b = coefficients)Lower Capilano valley-Hollyburn and Grouse mountainswith distance with % of barrier heighta b R2 See a b R2 SeeJanuary 161 11.048 0.953 18 204 92.872 0.521 38February 149 14.069 0.837 46 218 79.374 0.299* 52March 124 12.576 0.911 29 170 104.571 0.844 19April 108 5.689 0.961 8 129 50.386 0.776 12May 95 5.781 0.682 29 90 121.672 0.971 9June 90 2.387 0.222* 33 70 100.073 0.996 3July 68 2.161 0.306* 24 57 70.196 0.828 14August 64 1.807 0.225* 25 49 73.299 0.943 8September 87 4.528 0.606 27 79 104.552 0.987 5October 150 11.433 0.884 31 165 172.108 0.902 24ovember 206 16.367 0.939 31 258 159.486 0.856 28December 200 15.501 0.931 31 266 108.91 0.742 28N.B. All equations are significant at a=0.05 except for the ones noted* Significant at a=0.0134Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTION3.3 Temporal Variation of PrecipitationThe temporal variation of the annual, seasonal and monthly precipitation at the two studywatersheds has been studied using the coefficient of variation CV where CV = SDIX, SDbeing the standard deviation, and X the average annual or monthly precipitation.3.3.1 Seymour river watershedThe analysis showed that the variation of annual precipitation is least where the amount ofprecipitation is greatest and this occurs at the mid-position of the Seymour watershed.Conversely, the variability of the annual precipitation was greatest at both the lower andhigher parts of the watershed where precipitation amounts are less (Fig. 3.3).A similar pattern has been observed for the seasonal October to March precipitation,but no definable pattern is distinguishable for the summer precipitation (Fig. 3.3). However,the overall variation of precipitation for both seasons is small, having coefficient of variationof 15-20%. This is characteristic of a humid climate.Examination of the average monthly precipitation showed that the precipitationdecreases from January to July and August and then increases, having its maximum inNovember (Fig. 3.4a). On the other hand, the precipitation variation follows an oppositepattern being largest when the precipitation is least and vice versa (Fig. 3.4b). The variationfor all stations is smallest in March and largest in August or July.35Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTION3.3.2 Capilano river watershedThe analysis of the precipitation variation in the Capilano watershed showed an annual andseasonal pattern similar to the precipitation variation in the Seymour watershed. The smallestvariation of the annual and wet period precipitation is observed at the mid-position of thewatershed where the largest precipitation occurs, which is consistent with the more persistentcloud cover at this position resulting in more uniform precipitation. During the dry period,the smallest variation is observed at a higher elevation (Fig. 3.5). In general, the values ofcoefficient of variation range between 13-27 % with the largest values being observed at thelower and higher elevations.The average monthly precipitation in the Capilano watershed shows almost exactly thesame distribution pattern as in the Seymour watershed, decreasing from January to June,leveling off in July and August and increasing after September having the maximum inNovember (Fig. 3.6a). The coefficient of variation of the monthly precipitation follows anopposite pattern to that of the monthly precipitation. The smallest variation is observed inMarch or April and the largest in July or August. The general trend of variation is to decreasefrom January to April or March, to increase then till August and to decrease after September(Fig. 3.6b).3.4 Spatial Variation of PrecipitationTo study the spatial variability of precipitation the Pearson’s correlation coefficient (r)is used:36Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTIONxxj—_______r= N (3.11)_{[x2 ()2][2 ()2]}where N is the number of pairs of values of stations i and j, and x is the annual, seasonal ormonthly precipitation. The correlation coefficient gives the statistical association between theprecipitation series at two stations. It will be assumed that the correlation coefficient is only afunction of distance (Bras and Rodriguez-Iturbe, 1985). The correlation may be expressed as:r(d)=r(O) exp(-d/d0 (3.12)where d is the distance between stations i and j, d0 is the correlation radius (it is the distanceat which the correlation reduces by a factor of e) and r(O) is the value of the correlationfunction at a short distance (theoretically equal to 1, but because of random errors in themeasurements it is less that 1). For the two study watersheds all the stations in the watershedare used to obtain the correlation functions.3.4.1 Seymour River watershedThe monthly distributions of the correlation coefficients for seven stations in the SeymourRiver watershed are shown in Figure 3.7. The mean values of the correlation coefficient arelarge for the monthly, annual and seasonal totals during the period October-March, so that theprecipitation at different stations is, in general, well correlated. The only exception is thecorrelation coefficients between the records of station 28A, the highest station, and VancouverHarbour, the lowest station, for March and April (Fig. 3.7). The localized rain showers duringthat period of the year may account for this weak correlation.37Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTIONThe correlation functions for the annual, seasonal, and the wettest and driest monthsare shown in Figure 3.8. The highest correlation has been observed for the Novemberprecipitation (the wettest month) with r values larger than 0.88 for distances smaller than 32km. The annual totals and the precipitation during the wet period October-March followabout the same pattern. On the other hand, the correlation coefficient decreases for theAugust precipitation (the driest month) and for the seasonal totals during the April-Septemberperiod, having values smaller than 0.65 for distances smaller than 32 km.The reason for these high values of r is that during the wet period October-March, thestrong frontal systems cover the whole watershed with precipitation. During the dry period,from April to September, the source of precipitation is convective rain showers and weakfrontal systems, which are a little more variable across the watershed, so that the coefficient ofcorrelation is smaller than the values of r during the wet period.The expressions of the correlation functions for the Seymour watershed andcorrespond to the curves of Figure 3.8 are:Annual total: r(d)=0.964exp(-0.005d) (3.13)Seasonal total (Oct.-Mar.): r(d)=0.974exp(-0.005d) (3.14)November total: r(d)=O.95Oexp(-0.003d) (3.15)Seasonal total (Apr.-Sep.): r(d)=0.93lexp(-0.013d) (3.16)August total: r(d)=0.96Oexp(-0.01 3d) (3.17)It is therefore seen that the precipitation is highly correlated for distances shorter than32 km.38Chapter 3. ANNUAL AND SEASONAL PRECIPiTATION DISTRIBUTION3.4.2 Capilano River watershedFigure 3.9 shows the monthly distributions of the correlation coefficients for the sevenstations of Capilano River watershed. The values of the correlation coefficient are high and inmost cases larger than 0.70. The highest correlation is observed during the wettest month,November.The correlation functions for the annual, seasonal totals, and for the wettest and driestmonths are presented in Figure 3.10. The highest correlation is again observed during thewettest month, November. In November r takes values larger than 0.88 for distances smallerthan 32 1cm. The correlation coefficient takes values larger than 0.83 and 0.79 for distancessmaller than 32 km for the seasonal precipitation October-March and the annual totals,respectively. During the summer the correlation coefficients are larger than 0.74 for distancesless than 32 km. For the driest month, August, the correlation coefficient is larger than anyother month for distances smaller than 15 km. This can be explained because the precipitationis generated by convective rain showers, which result in higher correlation of precipitation forsmaller distances.The expressions for the correlation functions developed for the Capilano watershedand correspond to the curves of Figure 3.10 are:Annual total: r(d)=0.94Oexp(-0.006d) (3.18)Seasonal total (Oct.-Mar.): r(d)=0.93lexp(-0.004d) (3.19)November total: r(d)=0.9l8exp(-0.002d) (3.20)Seasonal total (Apr.-Mar.): r(d)=0.973exp(-0.009d) (3.21)August total: r(d)=0.95Oexp(-0.006d) (3.22)39Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTIONThe correlation analysis for both study watersheds showed that the correlationcoefficient is usually large ranging from 0.80 for the wet period of October to March to 0.6for the dry period of April to September, for distances less than 32 km.3.5 Comparison with Other Studies and Regional DataThe transferability of the results of this study has been examined by comparing the resultswith other studies in the greater region of the coastal Pacific Northwest. It is very importantto examine whether the leveling off of the precipitation at high elevations is a general resultfor the coastal Pacific Northwest, especially because some of the literature assumes that theprecipitation in the mid-latitude areas increases almost linearly with elevation up to the topelevation (Barry, 1992). At least two studies have investigated the distribution ofprecipitation in the mountains of the Pacific Northwest region. In the first of these studies,Schermerhorn (1967) related the annual precipitation in the Northern Washington State tolarge scale topographic and latitude factors. When Schermerhorn plotted the mean annualprecipitation against the station elevation, he found that the annual precipitation follows acurvilinear pattern increasing up to about 400-500 m elevation, and then decreasing at theupper elevations.The second study, by Rasmussen and Tangborn (1976), analyzed the annual andseasonal precipitation of 38 stations on the west slopes of the North Cascades region ofWashington, an area of about 20,000 km2. They found that the annual precipitation increaseswith station elevation up to an elevation of 400-500 m, and then levels off at the upperelevations (Fig. 3.1 la) but they concluded that this leveling was due to inaccurate data. Asimilar distribution was also observed for the winter precipitation, whereas, during summer,the precipitation was more uniformly distributed with elevation (Fig. 3.1 la).40Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTIONIn the same study, Rasmussen and Tangborn (1976) examined the coefficient ofvariation and showed that the summer precipitation is more variable than the annual and thewinter precipitation, which have values of about 10-20 % (Fig. 3.1 ib), but no discerniblechange in coefficient of variation with elevation was observed.In both these earlier studies, Rasmussen and Tangborn as well as Schermerhornconcluded that precipitation increases with elevation even though their data can be shown tobe more consistent with the leveling off of precipitation, as found in the present study. Theystated that the precipitation pattern observed was the result of inefficient precipitation gaugesand inadequate location.An indirect way for the examination of the precipitation distribution is by studying therunoff distribution with elevation over the whole region, The runoff is the result ofprecipitation, evapotranspiration, and change of basin storage. Studies in San Joaquin Riverbasin in California (Longacre and Blaney, 1962), northeastern U.S.A. (Dingman, 1981) andthe Alps (Barry, 1992) have shown that the evapotranspiration decreases rapidly withelevation. Longacre and Blaney (1962) measured the mean annual evaporation from reservoirwater surfaces at various elevations in San Joaquin River basin. They found that the meanannual evaporation decreases linearly for the first 1200 m of elevation from 1800 mm to 1150mm. Above the 1200 m there is a decrease to about 914 mm at 2400 m and above thiselevation there is only a slight change with elevation. This change of evaporation withelevation is indicative of the pattern of evaporation decrease with elevation although theevapotranspiration values can be significantly lower because of soil water limitations. Inanother study, Dingman (1981) found that the mean annual evapotranspiration in NewHampshire and Vermont decreases linearly with elevation from 580 mm at sea level to 500mm at 600 m, Similar results have been reported by Barry (1992) for the Alps but for higher41Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTIONelevations. It has been found that the mean annual evapotranspiration in the Alps decreases ata rate of 20 mmIlOO m elevation from the sea level to 4000 m.There are no available studies of evapotranspiration change with elevation in coastalBritish Columbia. The various measurements in this region have shown that the mean annualevapotranspiration in forested mountainous watersheds varies between 450 mm to 710 mm(Schaefer and Nildeva, 1973). It is reasonable to assume a linear decrease ofevapotranspiration with elevation, as the previous studies have shown. In addition, runoff ismuch larger than evapotranspiration so that the final estimates of precipitation are not overlysensitive to the change of evapotranspiration with elevation.The basin storage change is small when glaciers are not present, the accumulation ofsnow at high elevations melts during spring and summer, and there are no man-madereservoirs in the basin. Hence, if the runoff from a number of basins from the hydrologicallyhomogeneous region of the coastal Pacific Northwest shows a definite distribution patternwith mean basin elevation, then its distribution can be used as a qualitative indication of theprecipitation distribution with elevation over the region.In the study of Rasmussen and Tangborn (1976), the mean annual runoff from 36basins located in the western and eastern side of North Cascades was analyzed. From thesedata, eight basins located in the eastern rain shadow side of the Cascade Mountains wereexcluded. Figure 3.12 shows the distribution of the mean annual runoff of the remaining 28basins as a function of their mean basin elevation. The mean annual runoff shows a similarpattern to that of the annual precipitation, except for one station. The mean annual runoffincreases with the mean elevation of the basin up to about 800 m, and then decreases at theupper elevations.The one basin that exhibited a high runoff value at a high elevation was found to have53.3% of its area covered by glaciers (South Fork Cascade River in Fig. 3.12). The effects of42Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTIONglaciers on the basin runoff are well documented for the coastal Pacific Northwest (Fountainand Tangborn, 1985; Moore, 1992). Recent studies in the greater area of the PacificNorthwest have shown that the glaciers in the area are shrinking. For example, Pelto (1989)noted that the area of South Cascade Glacier in Washington State, decreased from 3.1 km2 in1955 to 2.8 km2 in 1989, and Moore (1992) reported that the area of the Sentinel Glacier inBritish Columbia decreased from 1.85 km2 in 1966 to 1.75 km2 in 1989. Hence, the highlyglacierized basins will show large runoff from this extra glacier melt.Although these streamfiow runoff studies generally confirm the precipitation analysesof this study, further confirmation can be obtained by examining precipitation data from otherstations in coastal British Columbia. To carry out this examination, data from 269precipitation stations located on the west slopes of the Coastal Mountains were analyzed.Precipitation data published by Environment Canada (1981) were used. The precipitationstations used in the analysis are shown in Table Al in Appendix A. Figure 3.13a shows thedistribution of the mean annual precipitation and its variation with the station elevation. Thearea of the coastal British Columbia is about 211,000 km2. and the interaction of the weathersystems with the topographical features causes this large variation. Although it is not possibleto distinguish a defmable pattern of precipitation distribution because of the large variation ofprecipitation for the same elevation, it is possible to observe certain trends. For example, it isevident that the mean annual precipitation does not continue to increase with elevation, andmay even decrease at the higher elevations.The above study on basin mean annual runoff in the north Cascade region has beenextended by using data within coastal British Columbia. The purpose is to check theprecipitation distribution with elevation observed at the coastal region of British Columbia,by analyzing the mean annual runoff from basins within the region. Streamfiow data43Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRJB UTIONpublished by Environment Canada (1989) were used. Basins meeting the following criteriawere considered for the analysis:• the drainage area must lie in the west side of the Coastal Mountains,• there must not be any storage impoundment,• there must be more than nine years of record, and• the glacierizeci percentage of the basin should be smaller than 1% of the total basin area.Forty-seven basins meeting these criteria were selected for analysis. The streamfiow stationsused in the analysis are shown in Table A2 in Appendix A.The mean annual runoff of each of the forty-seven basins was plotted against the meanbasin elevation in Figure 3.14. The mean elevation of the basins was determined from1:50,000 topographical maps. Although the variability is high, it is evident that the runoffincreases with the mean basin elevation up to 400 m and then decreases at higher elevations,except for one basin (Fig. 3.14). This basin is the Zeballos River basin located in the west ofVancouver Island, and it exhibits one of the largest runoff responses in coastal BritishColumbia. Unfortunately, there are no precipitation data in the intermediate area to test thereliability of these runoff measurements.The results of the Rasmussen and Tangborn (1976), and Schermerhorn (1967) studies,and the analyses presented above for coastal British Columbia precipitation and runoff werebased on stations that are far apart and are not located in the same watershed. However, theycover large areas and give a good indication of the regional distribution of precipitation withelevation. All their results are comparable with the more detailed results found in this studyfor the Seymour River and Capilano River watersheds. The valley elevation where themaximum precipitation occurs, is about 400 m in the Capilano watershed, whereas in the44Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTIONSeymour watershed it is less because of the topography of the area, and these valleyelevations correspond to neighboring mountain slope elevations of 1200 to 1300 m. Beyondthese points of maximum precipitation, the precipitation either levels off or decreases.Furthermore, the uniformity of the summer precipitation distribution and the low values of thetemporal variation of the winter and the annual precipitation observed in this study also havebeen revealed in the regional data.Analysis of the coefficient of variation of the precipitation data from the 269 stationsin coastal British Columbia showed that the variation of precipitation decreases at an elevationrange of about 400-700 m and that the maximum variation is observed at the low or high-levelstation (Fig. 3.13b). These results support the findings of the analysis of the temporalvariation of precipitation in the two study watersheds.3.6. Meteorological Mechanisms Affecting the Precipitation DistributionExamination of the precipitation distribution in the Seymour River and Capilano Riverwatersheds revealed a distinct pattern of precipitation distribution which seems to repeat in thecoastal region of the Pacific Northwest. The precipitation does not continue to increase withelevation but increases up to an elevation and then either decreases or levels off. Theprocesses involved in the rapid production of hydrometeors in low-level orographically liftedair have been addressed by Bergeron’s suggestion of a two-cloud system (Bergeron, 1960;Browning et al, 1974, 1975). According to the Bergeron’s mechanism an upper “seeder” cloudis assumed to precipitate with no influence from the terrain. This cloud is associated with theascent in the regional synoptic-scale disturbance. Its mid-troposphere position and itstemperature cause the formation of ice crystals. The precipitation from the regional “seeder”cloud is partly evaporated on its way to the earth’s surface. This decreases the precipitation45Chapter 3. ANNUAL AND SEASONAL PRECIPITATIONDISTRIBUTIONrate at the surface but moistens the low-level air. When this low-level air is orographicaflylifted or funneled in valleys, it reaches saturation quickly and a dense low-level cloud or fog isformed. This low-level cloud is called the “feeder” cloud, and is positioned at the low andmiddle elevations of the mountainous area and it is controlled by the orography. The fallinghydrometeors collect cloud droplets, from this “feeder” cloud, and grow in size. Furthermore,the number of the falling droplets or ice crystals increases at the position of the low-level“feeder” cloud so that its position defines the position of the maximum precipitation.The “seeder-feeder” mechanism is an idealization. In reality, the two clouds may becombined into one and the upper “seeder” cloud may be affected by the terrain (Smith, 1989).It is believed that the Bergeron’s two-cloud mechanism is responsible for the steepprecipitation gradients at the lower study watersheds. Furthermore, Barry and Chorley (1987)noted that the elevation of the maximum precipitation is close to the mean cloud base. Forthe nearby Mount Seymour, Fitzharris (1975) estimated the layer of the mean cloud base atabout 500 m or even lower. However, the elevation of this layer changes from storm to storm,and depends on the topography and the air mass characteristics. This mid-elevation positionof the lower “feeder” cloud generates the steep precipitation gradients observed in the twostudy watersheds and indicated in the regional precipitation and runoff data.Above the mid-position of the watersheds, the precipitation is generated mainly by theupper “seeder” cloud, which is either not influenced or influenced only to a small degree bythe topography. As a result, the precipitation over the upper watershed becomes moreuniform and levels off. This is the distribution that is observed in the Capilano Riverwatershed. However, the precipitation in the valley of the Seymour River watersheddecreases after its middle position. The change of Seymour valley orientation at this middleposition may be responsible for the abrupt decrease of the precipitation at the upper elevations46Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTIONand the steeper gradients at the lower Seymour River watershed than the lower Capilanovalley.The “seeder-feeder” mechanism is likely to produce the precipitation in the study areaduring frontal storms. This type of precipitation occurs in winter and fall and accounts forabout 75% of the annual precipitation.In the summer, the precipitation becomes more uniform over the two watersheds.During this period, the strength of the weather systems decline and the precipitation in thearea is produced either by convective rain showers or weak frontal systems. Under theseconditions the air is able to intrude further in the watershed resulting in more uniformprecipitation over the watersheds.3.7 SummaryThis study has shown that long-term precipitation distribution in the two study watershedsdoes increase linearly with elevation up to a certain position or elevation and then beyond thisposition the precipitation levels off or even decreases. This position seems to be around themiddle of the watersheds where the valley elevation is about 400 m and the neighboringmountain elevation is about 1000 m. The Bergeron two cloud “seeder-feeder” system isassumed to be the mechanism that generates most of the precipitation in the area during thewinter and fall months. During the summer the precipitation gradients in the study watershedsbecome smaller and more uniform precipitation is observed over the area.Another important finding of this study is that the precipitation for both the lowervalleys and the adjacent mountain slopes is similar. Correlation of the annual precipitationwith the topographical features showed that the barrier height controls the precipitation47Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTIONgeneration for both the valley and the mountain slopes, and so can better explain the variationof the precipitation.The temporal variation of the annual and seasonal October to March precipitation is,usually, small with the smallest variation being observed at the mid-watershed. Thevariability of the precipitation increases at the upper and lower elevations. The orographiclifting and the valley convergence are most efficient at the middle position of the watersheds,resulting in high cloud cover and precipitation. The lower part of the watersheds is slightlyaway from the effects of the orography and so it receives more variable precipitation.The monthly precipitation decreases in summer and takes its maximum value inNovember. The temporal variation of monthly precipitation follows the opposite pattern. Thelargest variation is observed during the summer months for all elevations.Application of the spatial correlation to the study watersheds showed that the spatialvariation is generally small, even for the dry summer period and in all cases the correlationcoefficient was larger than 0.65 for distances smaller than 32 km.The results of this study, and especially the spatial distribution of the precipitation withelevation, have been compared with the results of two previous studies of precipitation in thecoastal Pacific Northwest as well as with the findings of the precipitation and runoff analysesfor coastal British Columbia. This comparison suggests that the precipitation distributionobserved in the two study watersheds is more general and can possibly be used for the greatercoastal area of the Pacific Northwest when data are not available. However, the findings ofthis study might not be applicable to other areas and should be compared with observed datato detect any similarities or differences.48Fig.3.1.Thedistributionoftheannualandseasonalprecipitationalongthetopographicprofileof theSeymourRiverwatershed.ANNUAL——-OCT-MARAPR-SEPcciVALLEYPROFILEMOUNTAINPROFiLE•STATIONSI IS45004000z 3000525002000z15000 1000-J w500 0F‘C——I48121620DISTANCE(km)242832z 0 I— a C) Ui 0 ft 0 z 0 -J UiANNUALOCT-MARAPR-SEPVALLEYPROFILEMOUNTAINPROFILESTA11ONSIIIIIIII500045004000350030002500200015001000 500 0SIIII//,I/II/\—II/——I///,//—102030DISTANCE(km)Fig.3.2.ThedistributionoftheannualandseasonalprecipitationalongthetopographicprofileoftheCapilanoRiverwatershed.40Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTION28- - -- ANNUAL27—— OCT-MAR26 APR-SEP25241--23< 22> ./u 21 /O/-. ‘ji20- /19 —.,o18- —..LU ——O 17- \..o ‘S16II5- ————I14o‘ 4 ‘ 8 ‘ 12 ‘ 16 ‘ 20 ‘ 24 28 32DISTANCE (km)Fig. 3.3. The coefficients of variation of the annual and seasonal precipitationat the Seymour River watershed.51z00Izw()UULii0C)200 -100090Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTION- - -- Vancouver Harbour—— s-i14A28A700600500z400 -300 -—•(a)/ .%./ N.////I//IIII I I I I I IJAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC- - -- Vancouver Harbour—— s-i14A28A8070605040/(b)30 -20 I I I I I IJAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DECMONTHSFig. 3.4. (a) The distribution of the monthly precipitation at selected stationsat the Seymour River watershed and (b) Its coefficients of variation.52Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRiBUTION28 —27 - - -- ANNUALS... S..—— OCT-MAR25Z 24 APR-SEP023/22 “,. /S... • /21 ‘S. /S...2O /- S / /19 .18 S..’ /LI.. /b17 S..’.\ /0o16 “15 - “ I 714 - — — _,—__II13 I I I0 10 20 30 40DISTANCE (km)Fig. 3.5. The coefficients of variation of the annual and seasonal precipitationat the Capilano River watershed.53Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTION700600500z400300° 2001000 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC100JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DECMONTHSFig. 3.6. (a) The distribution of the monthly precipitation at selected stationsat the Capilano River watershed and (b) its coefficients of variation.- - -- Vancouver Harbour (a)—— Cleveland DamC-4C-5———%..,/////// ,.—I I I I I I I I I I- - -- Vancouver Harbour—— Cleveland DamC-40-5z0I9080706050403020(b)54Chapter 3. ANNUAL AND SEASONAL PRECIPITATIONDISTRIBUTIONI—zwC)LIUw00zI—.—— s**— -. — — —._c——-— — -/‘-V’10.90.80.70.60.50.40.30.20.1010.90.80.70.60.50.40.30.20.10I0.90.80.70.60.50.40.30.20.10- - -- S-I - Seymour Falls Dam—— S-I-bAS-I-28AJAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC— -—-- N_._._—-•1/// - - - - 28A-I 4A\ /‘ — — 28A-S228A - Seymour Falls DamJAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DECMONTHSFig. 3.7. Monthly distribution of the correlation coefficient betweenseveral stations in the Seymour River watershed.551—09 0.8--—:-----..—:-----..—.-————-—.—•—•07—.—.—•I-.-——z——Lu——--•=-c0.6it Lu o o0.5ANNUAL0.4SEASONALOCT-MAR0.3——-SEASONALAPR-SEPoNOVEMBER0.2-AUGUST0.1-0—IIIIIIIIII048121620242832DISTANCE(km)Fig.3.8.Spatialcorrelationfunctionsof annual,seasonal,andNovemberandAugustprecipitationintheSeymourRiverwatershed.10.90.80.70.60.50.40.30.20.10I0.90.80.70.60.50.40.30.20.1010.90.80.70.60.50.40.30.20.10Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTION- - -- Vancouver Harbour - 0-2—— Vancouver Harbour - C-3Vancouver Harbour - 0-5JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DECIzw0UUw0C)z0IIIS_S‘V’L..—. St S—5% 5 F—55 SF‘,- - -- 0-2 - Capilario—— 0-2-0-3C-2-C-5JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC.-.—.—.--.— —_-.S.— — —S_F %51055% I,- - -- 0-5 - Cleveland Dam——C-5-C-40-50-3JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DECMONTHSFig. 3.9. Monthly distribution of the correlation coefficient betweenseveral stations in the Capilano River watershed.57.1______-..—--.—.—..-:::: 0.7- 0.6-Ui0o o0.5-0.4-ANNUALw-SEASONALOCT-MAR0.3——-SEASONALAPR-SEP0-..-..-NOVEMBER0.2-AUGUST0.1-0IIIIIIIIIIIII048121620242832DISTANCE(km)Fig.3.10.Spatialcorrelationfunctionsofannual,seasonal,andNovemberandAugustprecipitationintheCapilanoRiverwatershed.Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTIONz0U0IzUi0UUUi00STATION ELEVATION (m)Fig.3.1 1 a) Distribution of the annual and seasonal precipitation with elevationand (b) coefficients of variation for the annual and seasonal precipitationat different elevations in the North Cascades, Washington State.(after data of Rasmussen and Tangbom, 1976)z00.0Ui040003500ANNUAL (a)t WINTER30000 SUMMER+2500a a •+• a + a2000 .1+ a+1500 a + + +1000 a50000 e0 II+0 20040060050403020100800 1000 1200 1400 1600 180000 0a+0000ANNUALWINTERSUMMER(b)90000+a00a+aIa0 200 400 600 800 1000 1200 1400 1600 1800595000—SouthForkCascadeRiver4000-U—3000EUL1•.LL 0UUzU2000-1000-U0IIIIIII0200400600800100012001400160018002000MEANBASINELEVATION(m)Fig.3.12.Distributionofthemeanannual runoffwithmeanbasinelevationfor northernCascadesregion(afterdataofRasmussenandTangbom, 1976)Chapter 3. ANNUAL AND SEASONAL PRECIPITATION DISTRIBUTION500045004000350030002500200015001000500032302826Z 2402220> 180Uw 140o 121086STATION ELEVATION (m)Fig. 3.13. Distribution of annual precipitation (a) and its coefficient of variation (b)with elevation for coastal British Columbia stations (269 stations).0 200 400 600 800 1000 12000 200 400 600 800 1000 1200615000—•ZeballosRiver450040003500•3000E0LL u25001oIII2000I•I.•II1500•II1000 500•0020040060080010001200MEANBASINELEVA11ON(m)Fig.3.14.DistributionofthemeanannualrunoffwithmeanbasinelevationforcoastalBritishColumbiastations.CHAPTER 4STORM PRECIPITATION DISTRIBUTION4.1 IntroductionThe precipitation distribution and variability in longer time-scales namely, annual, seasonaland monthly scales is adequate for long-term reservoir operation, water supply and irrigation.On the other hand, the knowledge of precipitation in short time-scales like daily, hourly andduring a storm is necessary for the simulation of runoff and especially for flood flows. Theimportance of adequately defining the spatial and temporal distribution of storm precipitationfor modeling streamfiow and evaluating the runoff response of a watershed has been wellrecognized among hydrologists (Beven and Hornberger, 1982; Bras et al, 1985; Watts andCalver, 1991). The need for better estimation, description and modeling of precipitation hasled hydrologists to identify the spatial and time variation of precipitation and quantify thisvariation in many different climates (Sharon, 1980; Bemdtsson and Niemcynowitz, 1986;Hughes and Wright, 1988; Corradini and Melone, 1989; Wheater et al, 1991). Theimportance of the precipitation distribution becomes critical for the mountainous watershedswhere the weather systems interact with the topography resulting in highly non-uniformprecipitation over the area. Hence, it is necessary to study the precipitation in detail, in orderto understand its distribution and, consequently, be able to predict the river flows withimproved accuracy.The objective of this chapter is to present the results of the study of spatial and timedistribution of storm precipitation in the Seymour River watershed, to compare the results63Chapter 4. STORM PRECIPITATION DISTRIBUTIONwith data from other coastal British Columbia stations and finally, to identify similaritiesbetween the distribution of the storm precipitation and the annual and seasonal precipitation.4.2 Data SetsThe data for the analysis have been taken from six recording stations in the Seymourwatershed for the period December 1983 to December 1990. The data from the stations S-i,1OA, 14A, 21A, 25B and 28A have been used (Table 2.2 and Fig. 2.3). The data set from theVancouver Harbour station is used to assess the zero elevation precipitation. The stations areunder the jurisdiction of two organizations, the Atmospheric Environment Service (A.E.S.)and the Faculty of Forestry of the University British Columbia (U.B.C.).Data in hourly time increments have been used. The stations 21A and 28A (Table2.2) are equipped with charts that can be read with an accuracy of three hours. The other fourstations the precipitation can be read in hourly increments. Therefore, the stations 21A and28A will not be used in the analysis of intensity and duration but they will be used in the studyof the storm precipitation distribution.A storm is defined as the precipitation period separated from the preceding andsucceeding rainfall by 6 or more hours at all stations. All storms used had mean watershedprecipitation exceeding 20 mm, and the average storm intensity was larger than 1 mm/h.Within the data period 175 network storms having total duration from 10 hours to 7 daysqualified for the study.Attention is paid so that the seasonal distribution of the storms analyzed follows themonthly precipitation distribution. Figure 4.1 compares the monthly distribution of theaverage annual precipitation distribution at station S-l with the monthly distribution of the175 storms analyzed.64Chapter 4. STORM PRECIPITATION DISTRIBUTIONThe storms have been classified as rainfall events, mixed ram and snow events andsnowfall events according to whether the temperature at 762 m elevation (station 25B) wasabove 2°C, between 00 and 2°C or below 0°C, respectively. The transitional air temperaturefrom snow to rain has been examined by Rohrer (1989). Rohrer determined that thistemperature is around 2°C. This same transitional temperature is used in the U.B.C.watershed model (Quick, 1993) for the classification of the precipitation into snow and rain.The rainfall events have also been separated into summer and winter storms toexamine if the distribution is different for the winter frontal and the summer convective rains.Forty-three events (25% of the 175 events) were classified as rainfall storms of the October-March period, fifty-three events (30% of the 175 events) as April to September rain storms,forty-four (25% of the 175 events) as snowfalls, and thirty five events (20% of the 175events) as mixed snow and rain events.The division of the events on the above categories has been made using air temperaturedata from the Vancouver Harbour and the 25B stations. The majority of the events had aduration larger than 24 hours so that the mean daily temperature was assumed to give theaverage temperature during the storms. For the periods of missing temperature data at station25B, the Vancouver Harbour data and an average temperature lapse rate of 0.90C per 100 melevation was used to estimate the mean daily temperature at the higher elevation stations inthe Seymour River watershed. This lapse rate was found from the temperature data at thestations Vancouver Harbour and 25B. It should be noted that during a particular storm it maysnow at the upper elevations, while raining at the middle and lower elevations. Hence, thesame storm can produce three types of precipitation, rainfall, snowfall, and mixed rain andsnow, over the elevation range of the study watershed.65Chapter 4. STORM PRECIPITATION DISTRIBUTION4.3 Spatial Distribution of StormsThe spatial distribution of the storms in the Seymour River watershed is investigated byexamining the ratio of the value of certain storm features at each of the stations compared withthe base station, Vancouver Harbour. The storm features analyzed are: the storm depth, thestorm duration, the average storm intensity, the maximum hourly intensity and the relativestart time of the storm. The spatial distribution of each of these storm features will beexamined.4.3.1 Storm precipitationBased on the precipitation measured at the base station, the ratio of precipitation for all typesof events increases to about 3.5 at 260 m (station S-i), and then decreases abruptly to about2.8 at 293 m (station bA). This large decrease coincides with the turn of the Seymour Rivervalley to the northwest. For rainfall events during the winter period (October to March) theratio seems to stabilize at a value of about 2.7 at the upper watershed (Fig. 4.2a). The April toSeptember rain events show a leveling of the ratio up to an elevation of about 600 m and thenthe ratio increases to a maximum of 3.2 at 853 m (station 28A) (Fig. 4.2a). For the mixedevents there is a constant decrease of the ratio to about 2.55 at 853 m (Fig. 4.2a). Thesnowfall events show a decrease in the ratio to about 2.3 at 600 m elevation, and then the ratioincreases to 2.8 at 853 m (Fig. 4.2a).The variation of the precipitation ratio increases up to the station S-i (293 m), andthen either levels off or increases. For the winter rainfall events the variation decreases afterstation S-i, but then levels off before increasing at the upper station. For the summer rainfallsthe variation increases slowly for all elevations. The snow events and the mixed events show66Chapter 4. STORM PRECIPITATION DISTRIBUTIONsimilar variation, except for the snow events in which the variation increases at the top stationat 853 m. Most of the variation at the upper watershed is high, between 30-60 % (Fig. 4.2b).The above results indicate that the precipitation always increases with elevation up tothe middle watershed, and then decreases and levels off at the upper elevations. This isevident for the winter rainfall storms and the mixed rain-snow events. However, theprecipitation during the snow events and the summer rainfalls increases, on average, at the topstation 28A at 853 m. A possible explanation is that at low temperatures the air is becomingmore stable and after the subsidence that occurs immediately after the middle watershed, thesnowfall increases again as the air is forced to lift over the steep headwater slopes of thewatershed. Somewhat unexpectedly, there is a similar increase for summer rain events in theupper watershed, when convective instability may occur as the warm air is forced to rise overthe steep slopes, generating larger precipitation and larger intensities at the upper watershedduring the summer months (Barry, 1992). Data from more stations are required tosubstantiate this precipitation increase at the upper elevations during the snow and summerrain events, so that no definite conclusions can be made at present.The above results also show that the storm precipitation has a similar distributionpattern to the distribution of the long-term precipitation, although the increase of stormprecipitation with elevation is larger than the annual and seasonal precipitation increase. Thestorms analyzed in this study are the larger storms, which must therefore have a steeperprecipitation gradient than the smaller storms.4.3.1.1 Spatial variationTo study the spatial variability of the storm precipitation the correlation coefficient (r) is usedas it has been used in Chapter 3 for the annual precipitation. It is again assumed that the67Chapter 4. STORM PRECIPITATION DISTRiBUTIONcorrelation coefficient is only function of distance. The underlying assumption of the spatialcorrelation is that the precipitation field is homogeneous and isotropic.The spatial correlation functions developed in this way using the data sets for the 175storms from the seven stations are:Rainfall October-March r(d) = 0.942exp(-0.005d) (4.1)Rainfall April-September r(d) = 0.924exp(-0.008d) (4.2)Snow r(d) = 0.925exp(-0.003d) (4.3)Mixed Rain and Snow r(d) = 0,999exp(-0.OlOd) (4.4)Figure 4.3 shows the above correlation functions. All the types of storms have correlationcoefficients larger than 0.75 for distances smaller than 32 km. Furthermore, the snow and thewinter rainfall events have similar correlation functions and their values are always larger thanthe correlations for the April-September events.These results show that during the snow and winter rainfall events the precipitation isthe least variable in space and more consistent relationships exist between the stormaccumulations of the various stations. The precipitation during the winter months is generatedby strong frontal systems, and these systems cover large areas, producing more uniformprecipitation over the medium-sized watershed.On the other hand, the largest spatial variability is observed during the summer storms.The precipitation during this period of the year is produced by weak frontal systems andconvective rains. Even though these types of precipitation systems cover the wholewatershed, they produce more variable precipitation than the winter storms, but even so theoverall spatial variability of precipitation can still be considered small.68Chapter 4. STORM PRECIPITATION DISTRiBUTION4.3.2 Duration and average storm intensityThe total duration of the storm is assessed as the time when precipitation is first recorded atany station and the time that it ceases at all stations. At each individual station, the duration isthe time period in which non-zero precipitation was recorded.The ratio of storm duration at each station divided by the total duration gives anindication of the continuity of precipitation. The average duration of storm at zero elevation(Vancouver Harbour) is only 45 % of the total duration, whereas it is about 75 % at the midand upper watershed. No significant differences have been observed for the different type ofevents (Fig. 4.4a). The variation of the storm continuity is larger (30 %-50 %) at the zeroelevation and smaller (20 %) at the mid-position. The summer rainfalls and the snow eventsshow the largest variation in storm continuity at the low elevations whereas for the mixedevents the variation in storm continuity is larger at the upper watershed than at mid-elevation(Fig. 4.4b).The relative storm duration at each station to that of the base station VancouverHarbour has also been studied. The analysis shows that the duration is about twice at the mid-position and at the upper watershed (Fig. 4.5a). Small differences are observed among thedifferent type of events. The variation of these results is larger at the upper watershed forsnow events and summer rainfalls, and at the mid-position for the winter storms and the mixedevents (Fig. 4.4b).Comparing these results with the previous results of the storm precipitation, one cansee that large precipitation at the upper watershed is mainly due to larger duration. A secondreason for the large precipitation at the mid-position of the watershed is the larger averagestorm intensities. Examination of the average storm intensity (storm depth over duration)indicates that the average storm intensity at the mid-position is, on average, about 90 % larger69Chapter 4. STORM PRECIPITATION DISTRIBUTIONthan the average storm intensity at zero elevation (Fig. 4.6a). At the upper watershed theaverage storm rate decreases except for the summer events for which the intensity increases.The convective nature of the precipitation during this period may account for this increase.The variation of the average storm intensity is larger at the mid-position for the winterrainfalls and mixed events, and at the upper watershed for the summer rains and the snowevents (Fig. 4.6b).The above results show that the larger precipitation at the mid-position is due to thelarger storm duration and the larger average storm intensities. However, the average intensitydecreases at the upper watershed, and then levels off.4.3.3 Maximum hourly intensityThe maximum hourly intensity increases from the base station to the mid-position of thewatershed by about 100%, and then either decreases for higher elevation (mixed events),decreases and levels off (winter rainfails) or decreases and then increases at the upperelevation (snow events and summer rainfall) (Fig. 4.7a). The largest variation of themaximum hourly intensity is observed at the upper elevation for all type of events except forthe mixed events for which the largest variation is observed at the mid-position. The snowevents and the summer rainfalls show the largest variation of the maximum hourly intensity(Fig. 4.7b).4.3.4 Relative start timeExamination of the start time of the storms showed that the storms started most of the time atthe mid-position of the watershed and later at the upper and lower watershed (Fig. 4.8). The70Chapter 4. STORM PRECIPITATIONDISTRIBUTIONlarge convergence of the incoming air mass, due to the valley funneling and the orographiclifting increases the condensation so that the storms start first in the middle and upperwatershed.4.4 Time Distribution of StormsThe time distribution of rainfall within a storm is an important characteristic of theprecipitation. There are very few studies that have dealt with the determination of the timedistribution of storms. One classical study is that of Huff (1967) who analyzed 261 stormsfrom a rain gage network covering a 1,037 km2 area in Illinois. From these data, Huffdeveloped a method of characterizing temporal distributions of storm precipitation.Recognizing the variability of hyetographs, Huff expressed temporal distributions ofprecipitation as isopleths of probabilities of dimensionless accumulated storm depths anddurations. He also categorized the storms by the quartile of the storm having the maximumprecipitation. These curves are known as “Huff curves” and have been used for designhyetographs inputs to hydrologic models (Terstriep and Stall, 1974; U.S.D.A., 1980; Bontaand Rao, 1992; Muzilc, 1993). Bonta and Rao (1989) regionalized the Huff curves anddeveloped dimensionless hyetographs for Ohio, Illinois and Texas, and studied the similaritiesand differences between these curves. They found that the Huff curves may be usedthroughout the Midwestern U.S.A. In an earlier paper, Bonta and Rao (1987) concluded thatthe sampling interval of precipitation data and the method identifying storms have only minoreffects on the development of the Huff curves. On the other hand they found that the seasonof year exerts a significant effect on the Huff curves.Coastal British Columbia and the greater region of the coastal Pacific Northwest havea totally different climate from that of the Midwestern U.S.A and therefore probably have71Chapter 4. STORM PRECIPITATIONDISTRIBUTIONdifferent precipitation time distribution curves. In this part of the thesis the 175 stormscollected for seven years (1983-1990) in the Seymour River watershed will be used for theanalysis and development of the time distribution of storms and the examination of the factorsaffecting the storm hyetographs.4.4.1 Research ProcedureThe procedure used by Huff (1967) is adopted for this study. The hyetographs of the 175storms of variable duration will be used to determine the dimensionless hyetographs. Thesedimensionless hyetographs will then be used to express the temporal distribution of storms asprobability distributions (Fig. 4.9). The 10% distribution means that 10% of the storms havea time distribution above this curve. In many cases a median time distribution will be mostuseful, but in others an extreme type of storm distribution (10% or 90%), may be usedbecause such a distribution might maximize the runoff.The only difference between the present study and Huffs work is that the empiricalprobability curves will not be classified by the quartile of the storm having the heaviestprecipitation. Huffs data from Illinois consisted of about 67% thunderstorm rainfall, so that itwas crucial for Huff to categorize the storms by quartile of maximum precipitation, becausethe large intensities during the periods of heavy precipitation have a major effect on thegeneration of the flood runoff. In coastal British Columbia most of the precipitation, as hasbeen discussed in Chapter 2, is produced, even during the summer, by frontal systems. Thisfrontal precipitation is characterized by the small to medium intensities and the long durationresulting in more uniform precipitation pattern, and therefore the classification of the stormsby quartile of heaviest precipitation is rendered unnecessary.72Chapter 4. STORM PRECIPITATION DISTRJB UTIONThe developed curves were compared both visually and statistically. The statisticaltest is by applying the Kolmogorov-Smyrnov (KS) two-sample test (Haan, 1978). Thisprocedure tests for significant differences between two independent cumulative frequencydistributions.The analysis of the storm precipitation has been performed for the five stations usedand for the four types of events. The objective is to evaluate, first, the effect of the elevationand then to identify any changes in the time distribution of the storms with elevation. The50%, 10% and 90% time probability curves for all the stations in the study watershed will becompared.Secondly, the effect of the event type on the time distribution of the storms will beexamined comparing curves at the station 25B at 762 m elevation. These curves have beendeveloped for each type of event, according to their earlier classification into October-Marchrainfall, April-September rainfall, snowfall, and mixed events of rain and snow. Again thetime probability distribution curves 50%, 10% and 90% will be compared.The third test will be to examine the effect of storm duration and storm precipitationdepth on the storm time distribution. This test is critical for the identification of anysignificant changes of the hyetographs with storm duration and precipitation depth and it willbe performed at station S-i.Finally, data collected at three other coastal British Columbia stations have beenanalyzed and their time probability distribution curves have been developed. These resultswill be compared with the data from the Seymour River watershed. Large differencesbetween the various sets of curves would indicate that the developed curves for the SeymourRiver watershed cannot be regionalized over large areas, but on the other hand, similaritybetween the curves developed for the Seymour River watershed and the curves for the other73Chapter 4. STORM PRECIPITATIONDISTRIBUTIONthree coastal British Columbia stations would indicate that they could be used for hydrologicdesign in the whole region of the coastal British Columbia.4.4.2 ResultsThe time distribution of the analyzed 175 storms was determined for all stations in the studywatershed. Figure 4.10 shows the comparison of the 10%, 50%, and 90% curves for all thefive stations. Visual examination of these curves shows that there is no large differencebetween the developed curves except for the 90% curve for the Vancouver Harbour (Fig.4.10). This curve deviates from the rest of the curves. However, the KS test showed nosignificant differences between any of the curves from any station at the 5% level. Hence, theelevation and the topography exert a large effect on the storm precipitation and duration butonly affect the storm time distribution to a very small degree.After classifying the storms into the different type of events, the time distributionprobability curves were determined for each station. Very few storms at the lower elevationswere either snowfalls or mixed events. For example, all the events in Vancouver Harbourwere categorized as rainfall events whereas only seven events were snow storms and fourwere mixed snow and rain events at station S-i at 260 m elevation. On the other hand, atstation 25B at 762 m elevation forty-four storms were classified as snow storms, 35 events asmixed rain and snow events and the remaining events were rain storms. For this reason theeffect of the different type of events on the storm time distribution is examined by using thedeveloped curves at station 25B (Fig. 4.11). Visual comparison of the 10%, 50%, and 90%curves for the various types of events indicates very small differences among the curves forthe various types of the events. Furthermore, the KS test showed no significant differencesbetween any of the curves of the four types of the events at the 5% level, so that the effect of74Chapter 4. STORM PRECIPITATION DISTRIBUTIONthe type of the events is minimal on the time distribution of the storms. This probablyhappens because similar storms during the winter produce the various types of the events.Moreover, it should be mentioned that it is the largest storms and the storms that cover thewhole watershed that have been analyzed and this criterion might have excluded the rareconvective storms that occur only at the upper watershed. Hence, the larger summerrainstorms have a similar time distribution to that of the winter storms. This is also evidentfrom the comparison of the time distribution of the winter and summer rainstorms at allstations.It is important to examine whether the time distribution of storms is affected by thestorm depth and duration. For this reason, the storms at station S-i are categorized intogroups of storms having duration smaller than 24 hours (65 storms), between 24 hours and 48hours (65 storms), and larger than 48 hours (45 storms). Examination of the 10%, 50%, and90% curves shows that the storm duration affects the time distribution of the storms only to avery small degree (Fig. 4.12). Application of the KS test, also, shows that this variation is notstatistically significant at the 5% level.In a similar way the storms are classified according to the total storm precipitation intogroups of storms having storm precipitation smaller than 50.8 mm (78 storms), between 50.8mm and 101.6 mm (52 storms), and larger than 101.6 mm (45 storms). Visual examination ofthe median and the more extreme time distribution probability curves indicates that the stormtime distribution is not affected by the total storm precipitation (Fig. 4.13). Furthermore, theKS test showed no significant differences between the various time probability distributioncurves of any duration and storm precipitation group at the 5% level.The above results suggest that one set of time probability distribution curves, derivedfrom all 175 storms at all seven stations, can be used. In the next paragraphs this average timedistribution probability curves will be used.75Chapter 4. STORM PRECIPITATION DISTRIBUTIONIt is important that the storm time probability curves developed in this study should becompared with the time distribution of storms from other areas in the same climatic region.For this reason data from three stations located in different areas of coastal British Columbiawere used to develop time distribution probability curves. Similarities between the developedcurves for the Seymour River watershed and the curves for the other three stations would thenindicate that the Seymour River watershed curves could be used for hydrologic design in areasof the greater climatic region. The stations used for this analysis are the Carnation Creek CDFstation, the Courtenay Puntledge BCHP station, and the Kitimat station. These stations areA.E.S. stations and are located at different areas of the coastal British Columbia (Fig. 2.1).Because of the different microclimates of the areas of the three stations, different criteria wereused for the selection of the storms analyzed (Table 4.1). The number of years of record isdifferent for these stations and so is the number of the events used for the analysis. However,it is believed that these data depict the storm distribution pattern over coastal BritishColumbia.76Table4.1.CharacteristicsofthecoastalBritishColumbiastationswhosedataanalyzedMinimumSamplingInterstormMaximumUsualDurationPenodNumberDepth(mm)Interval(his)Interval(his)Duration(his)Range(his)of RecordofStormCarnationCreekCDF351611920-401975-19861700CourtenayPuntledgeBCHP20168012-301964-1991334Kltimat30168620401979-1991128Chapter 4. STORM PRECIPITATION DISTRIBUTIONThe time distribution probability curves developed from the data from the threestations and the average curves developed for the Seymour River watershed are compared inFigure 4.14. The comparison shows that the time probability distribution curves of the threeBritish Columbia stations are similar. Furthermore, these curves are similar to the averageSeymour curves shape. Especially, the 90% curves have a similar shape and show very smalldeviation. There is larger deviation between the 10% and the 90% curves but the KS testshowed that this variation is not significant at the 5% level.The above results indicate that the average curves for the Seymour River watershedcould probably be used for the distribution of design storm throughout the coastal BritishColumbia. However, the differences that do exist from one area to another need to beevaluated by using these curves in watershed models. If these differences in the timedistribution probability curves do not significantly affect the simulation of the watershedresponse, then it is reasonable to use the time probability distribution curves developed in thisstudy for the hydrologic design in the whole region.4.5. Antecedent PrecipitationThe antecedent precipitation is a traditional hydrologic index of the soil moisture conditions ina watershed. The soil moisture storage is of particular interest to the hydrologist especiallywhen dealing with mountainous and rural watersheds. The impervious area in both of thesewatersheds is small and the response of the watershed to the precipitation input is controlledby the soil moisture storage. For this reason, the data from the Seymour River watershed havebeen analyzed to obtain the probability estimates of the magnitude of rainfall for periods of 1,2, 3, and 5 days before the occurrence of the storm. The analysis has been done separately forthe October-to-March (winter) storms and the April-to-September (summer) storms.78Chapter 4. STORM PRECIPITATION DISTRIBUTIONFigure 4.15 shows the probability curves of the antecedent precipitation of severaldays at station S-i. According to the analysis the antecedent precipitation is high at station 5-1 especially during the winter months. During the summer period the antecedent precipitationprobability curves of several days become more uniform and the antecedent precipitationsignificantly decreases compared to the winter period. For example, there is 50% probabilitythat the 1-day antecedent precipitation will be larger than 10 mm during the months fromOctober to March, whereas there is only 15% probability that the one-day antecedentprecipitation will be larger than 10 mm during the months from April to September.The antecedent precipitation probability curves at three sites in the study watershed isalso compared (Fig. 4.16). It has been assumed that the station Vancouver Harbour, S-i, and25B represent the lower, middle, and the upper watershed, respectively. This analysis showedthat the antecedent precipitation during the October-to-March period follows a spatial patternsimilar to that of the storm precipitation presented earlier in this Chapter. The antecedentprecipitation increases up to middle watershed (station S-i), and then decreases at the upperwatershed (station 25B). However, the antecedent probability curves converge for the lowprobability levels and similar conditions exist over the middle and upper watershed (Fig.4.16a).The examination of the antecedent precipitation probability curves during the April toSeptember period showed that the soil moisture conditions are more uniform for the wholewatershed and for all the probability levels (Fig. 4. l6b).Even though the antecedent conditions could vary over the whole region of coastalBritish Columbia, the results of this section could be used as a first approximation in absenceof measured data.79Chapter 4. STORM PRECIPITATION DISTRIBUTION4.6 SummaryThe above results show that the topography of the Seymour River watershed plays a verysignificant role in the distribution of precipitation. The largest precipitation is observed at themid-position of the watershed. At this position the valley orientation changes to a northwest-southeast direction. The increased convergence of the incoming air mass produces largeprecipitation, about 200% larger than the zero elevation precipitation. This increase, onaverage, is due to the larger average storm intensities combined with the larger duration.After this middle position the precipitation becomes more uniform at the upper watershed andthe significance of the average storm intensities diminishes so that the larger duration isresponsible for the large precipitation amounts.The precipitation in the coastal British Columbia is generated mainly by strong frontalsystems coming from a southwest direction. This frontal precipitation is characterized by thesmall to moderate intensities and long duration. As a result, the median time distribution ofall types of storms is found to be linear. The time distribution of storms is not affected by theelevation, the type of the event, the storm depth and duration. Analysis of the precipitationrecords of three stations in coastal British Columbia showed that the time probabilitydistribution curves found for the Seymour River watershed may be used in other areas of theregion.The antecedent precipitation of several days has been examined. The results showedthat the antecedent precipitation is relatively high for the whole watershed. However, itincreases with elevation especially in the winter period and for low probability levels. Insummer the antecedent precipitation is affected less by the elevation and drier conditionsprevail.80Chapter 4. STORM PRECIPITATION DISTRIBUTIONThe results of this study should be tested over the same climatic region in order togeneralize them and test the transferability of the findings. Such work has already been donefor the time distribution but not for the spatial distribution of the precipitation. In coastalBritish Columbia there are 96 recording gauges across an area of about 210,000 km2. Thesparcity of the data precludes the examination of the distribution of precipitation in spacewithin a hydrologic unit such as a watershed, and for a short-time scale, such as a stormperiod. This study indicates that the storm precipitation has a similar distribution pattern tothat of the annual and seasonal precipitation. In Chapter 3 it has been shown that the annualand seasonal precipitation distribution across the coastal British Columbia is similar to thatfound in the Seymour River watershed, increasing with elevation up to 400-800 m and theneither leveling off or decreasing at the upper elevations. In light of the findings presented inthis Chapter, it can be assumed that the storm precipitation follows a similar pattern to that ofthe annual precipitation. This distribution can be used as a first approximation in the absenceof measurements in the greater climatic region of coastal British Columbia.81Chapter 4. STORM PRECIPITATION DISTRIBUTION17z015140C)12D 1110DzUI 7I—U0I— 4zUIC)UIC-01716151413121110z 9UID 80UIU-543210Fig. 4.1 a) Monthly distribution of the average annual precipitation at station S-Iand (b) Monthly distribution of the 175 storms analyzed.(a)JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DECJAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DECMONTHS82Chapter 4. STORM PRECIPITATION DISTRIBUTION3.8zo 3.63.4Ia-3.20wa.. 2.8z02.42.2w91.81.6Q1.4I1.2I0.90.8zQ0.7O.60.50.400.3U0.20.10Fig. 4.2 a) Precipitation ratio to base station (Vancouver Harbour) for variousstations and types of events and (b) its coefficient of variation.0 200 400 600 8000 200 400 600 800ELEVATION (m)83DISTANCE(km)10.90.80.70.60.5It00___RAINOCTMM.INSEP-APRSNOWMIXEDRNN.SNOW0.10048121620242832Fig.4.3.SpatialcorrelationfunctiOnSforthevarioUStypesofstorms.Chapter 4. STORM PRECIPITATION DISTRIBUTION1z0z0U0LUC)UULU0C-)0.90.80.70.60.50.40.30.20.1010.90.80.70.60.50.40.30.2 -0.100 200 400 600 800(b)RAINFALL OCT-MARRAINFALLAPR-SEPSNOWMbCURE RAIN-SNOW.—. S..S. SS.. *I I I I I I0 200 400 600 800ELEVATION (m)Fig. 4.4. (a) Storm continuity at various elevations and types of storms(b) Coefficient of variation of storm continuity.85Chapter 4. STORM PRECIPITATION DISTRIBUTION2.22.12o 1.91 1.8z 1.71.61.51.41.31.21.1110.9zO 0.8> 0.6U0 05Ui 0.400.3Ui8 0.20.10ELEVATION (m)Fig. 4.5. (a) Storm duration ratio to base station for various elevationsand types of storms (b) Coefficient of variation of storm duration ratio.0 200 400 600 8000 200 400 600 80086Chapter 4. STORM PRECIPITATION DISTRIBUTION2.121.91.81.7Q 1.6I—1.51.41.31.21.1I0.80.7zQ 0.60.5o 04Ui0.3LLUUio 0.2C.)0.10ELEVATION (m)Fig. 4.6. (a) Ratio of the average storm intensity to base station for variouselevations and types of storms and (b) its coefficient of variation.0 200 400 600 80087Chapter 4. STORM PRECIPITATION DISTRiBUTION21.91.81.7o 1.61.51.41.31.21.11.71.61.51.4zo 1.31.21.1LI0I- 0.8zw 0.70.6U-0.5o 0.40.30.20.10Fig. 4.7. a) Ratio of the maximum hourly intensity to base station for variouselevations and types of storms and (b) its coefficient of variation.882.10 200 400 600 8000 200 400 600 800ELEVATION (m)0—1-2-3-5-6800:I... 0 w I—00-40200400600ELEVATION(m)Fig.4.8.Stormrelativestarttimetothebasestationatdifferentelevationsandtypeof storm.06CUMULATIVEPERCENTOFSTORMPRECIPITATION-cz.aoo00000000,,0C,0•.m.-UDC) m0.-I0 ,<,1C)“_I00 CD0) —o0r000CD0NOLLfliiisiaNOLLV1IJI31dIAIIOISA?1dV1f3z 0 I 0 C) Lii 0100 90 80 70 60 50 40 30 20 10 0100CUMULATIVEPERCENTOFSTORMDURATIONFig.4.10.Comparisonofthetimedistributionprobabilitycurvesfordifferent stationsandelevationsintheSeymourRiverwatershed020406080z 0 I. a 0 w a: a a: P U) U 0 I. z w 0 a: Ui a Ui100 90 80 70 60 50 40 30 20 10 020406080100CUMULATIVEPERCENTOFSTORMDURATiONFig.4.11.Comparisonof thetimedistributionprobabilitycurvesfordifferenttypeofeventsatthestation25BintheSeymour Riverwatershed.01009O8Ow 7060U) 5oI. 4Ow a >iii3020C)10 0100CUMULATIVEPERCENTOFSTORMDURATIONFig.4.12.Theeffectofthestormdurationonthetimeprobabilitydistributioncurves(StationS-i)020406080z 0 I— a C) Lii 0100 90 80 70 60 50 40 30 20 10 0100CUMULATIVEPERCENTOFSTORMDURATIONFig.4.13.Theeffectofthestormprecipitationonthetimeprobabilitydistributioncurves(StationS-i)020406080100Z900 8070Ui 0 600 -500 I— z Ui 40U’Ui 030Ui20010 0020406080100COMULATIVEPERCENTOFSTORMDURATiONFig.4.14.Comparisonof thetimeprobabilitydistributioncurvesfor SeymourRiverwatershedandthreeCoastalBritishColumbiastations.w0zw—“ \SOS %_ —0 I I0 20 40 60 80 100 120 140 160 180 200ANTECEDENT PRECIPITATION (mm)Fig. 4.15. Probability of equality or exceedance of antecedent precipitationat station S-i for (a) October to March storms and (b) April to September stormsChapter 4. STORM PRECIPITATION DISTRIBUTION10.90.80.70.60.50.40.30.20.1010.90.80.70.60.50.40.30.20.1(b)1-DAY2-DAY3-DAY5-DAY96Chapter 4. STORM PRECIPITATIONDISTRJBUTIONwC)zwUiC.)0-JDaUiLL.0-J0UiC)zUi1—0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.10(a)3-DAY VANCOUVER HARBOUR3-DAYS-I3-DAY25B\‘ \. \\ \.. “\ \ S\ •\ 5S*\ \ ‘S\ \ 5’N,•\ \. ‘S\ %. ‘S.5’. S5’-‘S..I I I I I I ._0 20 40 60 80 100 120 140 160 180 2000.90.80.70.60.50.40.30.20.10 0 20 40 60 80 100 120 140 160 180 200ANTECEDENT PRECIPITATION (mm)Fig. 4.16. Comparison of the probability of equality or exceedence of the antecedentprecipitation for different elevations for (a) winter and (b) summer.97CHAPTER 524-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIA5.1 IntroductionThe estimation of peak flows is necessary for the design of hydrotechnical structures. Ifstreamfiow data are available, a conventional flood frequency technique is applied.Unfortunately there are many streams for which measurements are not available and in thesecases many different approaches can be used as will be presented in Chapter 8 of the thesis.One of these methods is the event-based simulation of individual large events, in which adesign storm can be derived and used as input to a watershed model for the estimation of thestorm runoff hydrograph, which provides estimates of the volume of runoff and the peak flow.The design storm considerations include the return period, the total storm depth, the stormduration, the storm temporal distribution, the storm spatial characteristics, the time responseof the watershed and the antecedent soil moisture state of the watershed.The return period of the storm is selected on the basis of minimizing the cost orassuring a certain level of protection of the hydraulic structure, and consequently of thecommunity. In Canada, the level of protection is determined by the Provinces and depends onthe type of structures (Watt et al., 1989). The total precipitation depth at a point is a functionof the return period and the storm duration, which is linked to the time of concentration of thewatershed. The variation of the rainfall intensity during the storm is an important factor indetermining the timing and the magnitude of the peak flows. In addition, the spatial coverageof the storm influences the runoff generation and is especially important for larger basins.In earlier studies in Canada the focus was on the derivation of the design storm forChapter 5. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIAurban watersheds, usually 1-hour to 12-hour storm (Hogg, 1980; Hogg, 1982; Marsalek andWatt, 1984; Watt et aL, 1986). This study is concentrated on the derivation and study of the24-hour design storm for coastal British Columbia mountainous and rural watersheds.This choice of the 24-hour storm duration has been based on many factors. Firstly, theprecipitation in the coastal British Columbia is generated mainly by long duration frontalstorms as it has been discussed in Chapter 2. Most of these storms have a duration of about aday as it has been shown from the regional data analyzed in Chapter 4. Secondly, theresponse of small and medium mountainous watersheds is in the order of several hours so thata long duration storm is required for the generation of peak flows. One might think that ashort duration storm may be more adequate for the estimation of peak flow from small steepwatersheds of the region. Extensive research in the Jamieson Creek watershed, a small steepwatershed which will be used later in the analysis, showed that for rain storms the time lagvaried between 5.5 hours to 15 hours with an average of about 8.5 hours (Cheng, 1976). Forthe most intense and severe storms the time lag decreases down to 2-2.5 hours (Loukas, 1991).These results show that a design storm of longer duration from that of the time lag, like a 6-hour, 12-hour or 24-hour storm could be adequate for the simulation of the peak flow.However, simulation of the peak flows from coastal British Columbia watersheds showed thatthe 24-hour storm is more suitable, especially for the larger return period floods, as will beshown in Chapter 8 of the thesis (Fig. 8.3). Furthermore, the choice of the 24-hour stormduration is a pragmatic one. Of the 269 precipitation stations located in the coastal BritishColumbia, an area of about 210,000 km2. 173 are storage gauges which are used to measurethe daily precipitation. These stations have longer records than the recording stations (Fig.5.1), which implies more reliable frequency analysis, since the use of the 24-hour designstorm can expand the usable data both in space and time resulting in better estimation of floodrunoff from ungauged watersheds.99ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIASince the storm duration of 24 hours is accepted to be adequate for small and mediummountainous and rural watersheds, the time distribution of the storm and its variation in spaceare the most important parameters of the design storm.The objective of this Chapter is to present the results of the development of a 24-hourdesign storm using data from the Seymour River watershed. Important parts of this study willbe, firstly, to examine whether the temporal distribution changes with elevation, secondly, toidentify the spatial distribution of the precipitation, thirdly, to compare the developed stormwith other synthetic storms used in the hydrologic design, and finally to investigate thepossibility of transferring the results in other areas of coastal British Columbia. It should benoted that the scarcity of both precipitation and streamfiow data in this mountainous regionrestricts the application of conventional flood frequency analysis and therefore the use of thedesign storm concept along with rainfall-runoff simulation is one of the methods used in thepractical application of hydrology. Also, the study of the 24-hour design storm is differentfrom the analysis of the storm precipitation presented in Chapter 4, since in this Chapter onlythe extreme rainfall events with duration of 24 hours will be analyzed.5.2 Data Sets and Method of AnalysisData from five precipitation recording gauges in the Seymour River watershed will beanalyzed. The data sets from the stations Vancouver Harbour, S-l, bA, l4A and 25B areused. The characteristics of the stations have been shown in Table 2.2 and their location hasbeen presented in Figure 2.3 of Chapter 2. The stations cover an elevation range of about 760m. The Vancouver Harbour station is the sea-level station and the 25B station is the secondhighest station of the Seymour watershed located at 762 m elevation (Table 2.2).The maximum 24-hour rainfall usually occurs in the period from October to January100ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIA(Fig. 5.2) when precipitation is generated by strong frontal systems coming from the NorthPacific Ocean. As has been mentioned in Chapter 4, the precipitation during these systems ischaracterized by long duration and small to moderate intensities.The selection criteria of the storms have been chosen to identify the 2 or 3 largerstorms per year for each station. Hourly rain data were used for the analysis of the storms. The24-hour storms selected for the analysis have rainfall depths larger than 55 mm for VancouverHarbour and larger than 90 mm at the other stations. Under these criteria, 21 storms for theperiod 1976-1990 for the Vancouver Harbour station, 23 storms for the period 1984-1990 forthe station s-i, 32 storms for the station 1OA for the period 1976-1990, 28 storms for 14A forthe period 1980-1990, and 16 storms for the station 25B for the period 1980-1990 wereselected.Analysis of the data for the study of the time distribution is achieved by a method verysimilar to the one presented by Huff (1967) and used for the analysis of the stormprecipitation in Chapter 4. To compare different storms, rainfall for each event was expressedas the cumulative percentage of the total twenty-four-hour rainfall for twenty-four equal timeincrements through the storm. The resulting values were then used to calculate the timeprobability distributions which provide quantitative measures of both interstorm variabifityand the general characteristics of the time sequence of the rainfall. For the few storms whichlasted less than 24 hours, the residual time increments were entered as zero rainfall tocomplete the fixed 24-hour duration event.The developed time probability curves will be compared both visually and statistically.The statistical test is the Kolmogorov-Smirnov (KS). two sample test (Haan, 1977), whichtests for significant differences between two independent cumulative frequency distributions.The spatial distribution of the maximum 24-hour storms will be analyzed in the studywatershed, and then the application of this distribution to other areas of the coastal British101Chapter 5. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIAColumbia region will be investigated in the next paragraphs.5.3 Time DistributionApplying the above mentioned method of analysis, time probability distributions weredeveloped for each of the five stations, and an example is shown in Figure 5.3 for station S-i.The percentages are defined such that, for example, for the thirty percent time distributioncurve, thirty percent of the storms will have a time distribution above the curve. The timeprobability distributions of ten, thirty, fifty, seventy, and ninety percent are shown in Figure5.3.It is important to know how the time distribution of the storm varies at differentelevations. A detailed data base is difficult to find in coastal British Columbia. However forthe Seymour River watershed data are available at five stations for an elevation range of about760 m. The fifty, ten and ninety percent time probability distributions for different elevationsare compared in Figure 5.4. From this figure it is observed that the storm time distributionwith elevation does not vary significantly and even the extreme time probability curves of tenand ninety percent have similar patterns. The largest deviation of the results is observed forthe 90% curves. However, application of the KS test shows no significant differences at the5% level between the curves from the stations at various elevations. Because of the smalldifferences of the storm time distribution with elevation, average time probability distributionshave been developed using the 120 storm distributions from all stations in the study watershed(Fig. 5.5).It is important to examine whether the 24-hour storm time distribution for theSeymour River watershed can be transferred to other areas of coastal British Columbia.Similarities between the developed time probability curves for the Seymour River watershed102ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIAand the curves developed in other studies for the same region or by using regional data wouldthen indicate that the Seymour River watershed curves could be used for hydrologic design inother areas of the same climatic region. For this reason the time probability distributioncurves developed for the Seymour River watershed wifi be compared firstly with the stormtime distributions from other studies in the region and then with the time probability curvesusing other coastal British Columbia data.Melone (1986) analyzed the time distribution of the largest 24-hour storm of recordobserved at each of 58 recording stations across coastal British Columbia, and developed thetime probability distributions of the 24-hour storm for the 58 stations. In Figure 5.6 theresults of Melone’s work are compared with the average time probability distributions for theSeymour River watershed. It is evident from this comparison that the results of this studycover the time distribution of the extreme 24-hour storms in coastal British Columbia stations.Only the ten percent curves deviate, and a possible explanation for this deviation may be thatMelone analyzed only the largest 24-hour storm for each of the 58 stations whereas in thepresent study a large number of storms have been analyzed for each station in the studywatershed. However, the general pattern of the rain distribution, at least during the mostextreme storms, is similar to the pattern observed in the study watershed. In addition, thestatistical KS test showed that there are no significant differences between any of the curves atthe 5% level.The results of this study were also compared to the results that Hogg (1980) reported.Hogg analyzed 119 12-hour events from coastal British Columbia stations. Hogg suggested(Hogg, personal communication) that the time distribution of the 24-hour design storm shouldbe similar to the 12-hour storm. Figure 5.7 shows the comparison of Hogg’s results with theresults of this study. It is evident from this figure that the 24-hour design storm developed inthis study has a similar time distribution to the 12-hour design storm developed by Hogg for103ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIAthe British Columbia coast. Also, the statistical KS test showed that there are no significantdifferences between any of the curves at 5% level.The findings of this study are also compared with the time distribution of the extreme24-hour storms from other areas of the same climatic region. Data sets from three stationslocated in different areas of coastal British Columbia were used to develop time probabilitydistribution curves. The stations used for this analysis are the Carnation Creek CDF station,the Courtenay Puntledge BCHP station, and the Kitimat station (Fig. 2.1) which has been usedin Chapter 4 for the comparison of the storm precipitation time distribution. Because of thedifferent microclimates of the areas of the three stations, different criteria were used for theselection of the 24-hour extreme storms analyzed (Table 5.1). The number of years of recordis different for these stations and so is the number of the events used for the analysis.Table 5.1. Characteristics of the coastal British Columbia station used in the analysis of the24-hour extreme rainfall time distribution.Greatest Mean Annual Minimum Period of NumberStation Name 24-hour 24-hour Storm Depth Record ofRainfall Depth (mm) (mm) Storms(mm)Carnation Creek CDF 230 96.9 70 1975-1986 50CourtenayPuntledge 124 69.9 55 1964-1991 50Kitimat 123 92.7 55 1979-1991 31104ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIAThe time distribution probability curves developed from the data from the threestations and the average curves developed for the Seymour River watershed are compared inFigure 5.8. The comparison shows that the curves of the three British Columbia stations aresimilar. Furthermore, these curves are similar to the average Seymour curve shapes. Thevariability that exists between the time probability curves may be explained by the differencesbetween the microclimates of each site. However, the KS test showed no significantdifferences between these curves at the 5% level. The above three comparisons suggest thatthe results of the study can be transferred to other regions of coastal British Columbia withoutloss of accuracy.The results of this present work have been compared with some other design stormsused by engineers in every day practice. Four such design storms were considered: the SoilConservation Service Type I and Soil Conservation Service Type IA storms (U.S.D.A.,1986), the Hershfield storm (Hershfield, 1962) and the storms that can be developed usingIntensity-Duration-Frequency (IDF) curves, the so-called Alternating Block Method (Chow etal., 1988). The first two design storms were developed by the U.S. Department of AgricultureSoil Conservation Service (SCS). The SCS developed five 24-hour duration storms, and thestorms called Type I and Type IA were developed for use on the coastal side of the SierraNevada and Cascade mountains of Oregon, Washington and Northern California, and thecoastal regions of Alaska. These hyetographs were derived from information presented byHershfield (1961), by Miller, Frederick, and Tracey (1973) and from additional storm data.These two storms, SCS Type I and IA, are extensively used in coastal British Columbia sincethe province is located within the greater climatic region for which the storms are designed.The Hershfield storm (Hershfield, 1962) was developed by analyzing data from 50widely separated stations with different rainfall regimes across the U.S.A. and an averagecurve was prepared for all storm durations.105ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIAThe Alternating Block Method is a popular technique among practicing engineers.This method is a simple way of developing a design hyetograph from Intensity-Duration-Frequency curves. One design hyetograph can be developed for each return period and eachstorm duration.These various design storms are compared in Figure 5.9 and the comparison indicatesa significantly different rainfall pattern than the observed values. The Alternating BlockMethod synthetic hyetograph represents a totally different time distribution pattern from theobserved. The curve SCS Type IA shows better agreement with the 10% curve developed inthis study. It is evident from the above comparison that most of the synthetic hyetographsrepresent storms with intense periods of rain. On the other hand, the observed pattern is moreuniform and does not contain intense bursts of rain.It is important, however, to identify whether the variations observed between thesynthetic hyetographs and the derived time distributions significantly affect the simulation ofthe runoff. This analysis will be presented at the end of the Chapter after the presentation ofthe spatial distribution of the extreme 24-hour storms and the analysis of the antecedentrainfall.5.4 Spatial DistributionAs indicated from the results of the analysis of mean annual precipitation in Chapter 3, themain spatial variation of the precipitation is variation with elevation for medium to smallmountainous watersheds. In this part of the Chapter the spatial distribution of the designstorm with elevation will be examined.In the Seymour River watershed the 24-hour maximum storm data have been analyzedand the Extreme Value I (Gumbel) probability distribution has been fitted to the data. The106ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIAresults (Fig. 5.10) show that, for all the return periods, the rainfall increases up to the middleposition of the watershed (station S-i, at 260 m), and then abruptly decreases (station bA, at293 m), before a further slight increase and leveling off at the upper elevations (Fig. 5.10).This particular rain distribution is similar to the distribution of the mean annual precipitationand mean storm precipitation in the study watershed. Both the mean annual precipitation andthe extreme 24-hour storms increase by an average factor of about 2.5 between the VancouverHarbour and S-l stations and then decrease to a factor of 1.7 at station bOA and then increaseand level off to a factor of 2.0 at station 25B. The reason for the abrupt decrease of the rainafter the S-b station is the topography of the area. At the position of station S-i the SeymourRiver valley turns to the northwest and the resulting increased convergence of the incomingair mass generates large precipitation at this middle position. Unfortunately, there are notenough recording stations in the area in order to compare the observed rainfall distribution inthe study watershed with the precipitation distribution in adjacent watersheds. However, theanalysis of the long term annual, seasonal, and monthly precipitation accumulations from thenearby Capilano watershed, presented in Chapter 3, showed that the precipitation distributionin Capilano watershed is similar to that of the Seymour watershed except for the largedecrease after the middle of the watershed. Hence, it seems that the rainfall in the study areaincreases for the first topographical rise and then either levels off or even decreases. Thegenerality of this conclusion for the coastal British Columbia will be examined in the nextparagraphs.Three aspects will be examined. Firstly, it is important to examine the spatialdistribution of rainfall over the watershed during the extreme events. The results shown inFigure 5.11 are based on all the extreme events and they have not necessarily occurred at thesame time throughout the watershed. However, the analysis of the storm precipitation in thestudy watershed have shown that the rainfall during a single storm also has a similar107ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIAdistribution. Furthermore, a study of the spatial and temporal disthbution of extremehistorical storms will be presented in Chapter 6 and it will be shown that during an individualstorm the precipitation is distributed with a similar pattern to that of the storm and meanannual precipitation found in Chapters 3 and 4. It is also very important to note that the stormrainfall increases and decreases, on average, at a similar rate as the mean annual precipitation.Secondly, it is important to evaluate whether the spatial distribution of the extremeprecipitation observed in the Seymour River watershed is transferable to the coastal BritishColumbia region. Unfortunately, there are not enough recording precipitation stations in theregion to analyze the spatial distribution of the short term precipitation. However, there aremore storage gauges which could give a good indication of the spatial distribution of thelonger term precipitation. The analysis presented in Chapter 3 has shown that the meanannual precipitation in the coastal Pacific Northwest increases up to an elevation of 400-800m, and then either levels off or even decreases at higher elevations. Hence, the long-termprecipitation in the greater region has a spatial distribution pattern with elevation similar to theone observed in the Seymour River watershed except that there is not such a large decrease ofthe rainfall after the middle position of the watershed. This leads to the third question ofwhether the extreme 24-hour storm rainfall is a certain percentage of the mean annualprecipitation. If this is true then the mean annual precipitation could be used as an index ofstorm rainfall. The above hypothesis is probably reasonable because most of the annualprecipitation is caused by the same type of low pressure systems and most of this rainfalloccurs in the fall and winter. This hypothesis will be examined in the next paragraphs.The analyzed extreme 24-hour rainfall data for return periods of 2-, 5-, 10-, 25-, 50-,and 100-year return period and mean annual precipitation were obtained from EnvironmentCanada, Atmospheric Environment Service for sixty-one recording stations across coastalBritish Columbia. Thirty-five stations are located in the southwest mainland coast, thirteen on108ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIAthe east of Vancouver Island and the Gulf Islands, six on the west of Vancouver Island, andseven are located on the north mainland coast and Queen Charlotte Islands. The sixty-onestations used in the study are listed in Table Bi in Appendix B.The extreme 24-hour rainfall for the sixty-one British Columbia stations has beenplotted against the station mean annual precipitation and regression analysis has also beenperformed between the extreme 24-hour storm rainfall of the various return periods and themean annual precipitation. The results of this analysis are shown in Appendix B. Figure 5.11presents the results for the 10-year 24-hour rainfall and indicates that this storm is, on average,5.7% of the mean annual precipitation.However, analyses of this type are biased towards southwestern coastal BritishColumbia since most of the recording stations are located in that region. For this reasonseparate analyses have been carried out for the southwest mainland coast, for east VancouverIsland, west Vancouver Island, and the north coast of British Columbia. The results aresummarized in Table 5.2 which lists the mean and the range in percentage of the extreme24-hour precipitation against the mean annual precipitation. There is a significant overlappingbetween the ranges for the various return periods and sub-regions but it can be observed thatthe average value increases as the return period increases. Also from this Table can be seenthat the ratio of the extreme 24-hour rainfall and the mean annual precipitation has itsmaximum value for the east coast of Vancouver Island, the dryer of the four sub-regions andalso, the variation of the ratio is the largest in this sub-region.109ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIATable 5.2. Ratio of the 24-hour rainfall and mean annual precipitation for various coastalsub-regions of British Columbia.Return Southwest East Coast of West Coast of North B.C. CoastPeriod Mainland B.C. Vancouver Vancouver Island(years) Coast (%) Island (%) (%) (%)2 4.1 (3.0-5.3) 5.1 (3.3-7.3) 4.2 (3.3-4.8) 3.8 (3.2-4.3)5 5.1 (3.6-6.5) 6.6 (3.9-10.3) 5.2 (4.3-6.2) 4.9 (4.0-6.1)10 5.8 (4.0-7.5) 7.7 (4.4-12.3) 5.9 (5.0-7.2) 5.7 (4.5-7.4)25 6.7 (4.5-8.6) 8.9 (5.0-14.9) 6.8 (5.8-8.4) 6.6 (5.1-8.9)50 7.4 (4.9-9.8) 9.9 (5.4-16.7) 7.5 (6.4-9.3) 7.3 (5.6-8.9)100 8.0 (5.3-10.9) 10.8 (5.8-18.6) 8.1 (7.0-10.2) 7.9 (6.0-11.2)Mean AnnualPrecipitation 1968 (982-3600) 1122 (619-1656) 2824 (1870-3943) 2050 (1137-3 155)(mm)The above analysis indicates that an estimate of extreme 24-hour rainfall estimate can be madebased on mean annual precipitation at a location. Therefore, it is reasonable to suppose thatthe distribution of long term precipitation with elevation is an index for the distribution ofstorm rainfall. This conclusion is supported by the results found for the Seymour Riverwatershed, as previously discussed. This means that the largest storm rainfall does not increaselinearly with elevation, but increases at the low and middle elevation, and then levels off at thetop elevations.110ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIA5.5 Antecedent RainfallThe antecedent rainfall for periods of several days before the design storm is important to thehydrologist, particularly if the problem involves rural or mountainous basins as opposed tohighly impervious urban watersheds. The antecedent rainfall characterizes the soil moistureconditions in the watershed prior to the occurrence of the storm and therefore, controls theresponse of the watershed.Table 5.3 shows the estimates obtained for the antecedent rainfall at three stations inthe Seymour River watershed for five probability levels and for 1- to 5- day periods. It isassumed that the three stations represent the lower, middle and upper watershed (stationsVancouver Harbour, S-l, and 25B, respectively).These results show that the antecedent rainfall increases with elevation. Furthermore,there is a fifty percent probability that the 1-day antecedent rainfall at the middle and upperwatershed will be about 20 mm. This is critical for the generation of the runoff from the steephillslopes of the watershed and shows that there is a high probability that the soil moisturelevels will be high, especially throughout the winter period.The antecedent rainfall statistics may vary considerably in the same climatic region butthe results of this study give a good first approximation.111ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIATable 5.3. Probability distribution of antecedent rainfall (mm) for the maximum 24-hourstorms for various numbers of days.Probability(%) 1-day 2-days 3-days 5-daysVancouver Harbour10 62.0 81.4 93.4 135.330 22.2 43.2 52.4 77.250 7.9 22.9 30.1 44.170 2.8 12.2 17.0 25.290 1.0 6.5 9.7 14.4s-i10 82.2 129.6 158.0 244.430 38.4 66.7 83.2 129.350 17.9 34.3 43.8 68.470 8.4 17.7 23.1 36.290 3.9 9.1 12.2 19.125B10 87.0 154.6 262.9 565.530 43.9 85.8 133.0 242.350 22.1 47.6 67.3 104.070 11.1 26.4 34.0 44.790 5.6 14.7 17.2 19.2112ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIA5.6 Simulation of Peak Stream Flow at Jamieson Creek WatershedThe observed time distributions and the synthetic hyetographs presented earlier have beenused as input to a simple watershed model for the calculation of streamfiow runoff. Thestreamfiow data have been taken from the Jamieson Creek watershed. Jamieson Creek is asmall tributary of the Seymour River, and is located in the headwaters of the river system. Thebasin has an area of 2.99 km2, and its elevation ranges from 305 to 1310 m above mean sealevel so that there is a good variation in elevation. Jamieson Creek is characterized by steephillslopes having an average gradient of 48%.Because of the small area of the Jamieson Creek watershed, rainfall data from onestation were considered adequate. The station 25B is located in the middle of the watershed,so that it is assumed to represent the average rainfall over the watershed, and its data havebeen used to estimate the 24-hour rainfall depth. This assumption was confirmed in an earlier,more detailed study (Loukas and Quick, 1993b) in which five stations within the JamiesonCreek watershed were used.The 24-hour rainfall for various return periods has been distributed in time accordingto the observed and synthetic hydrographs and the resulting storms have been used as input toan event based watershed model. The watershed model was developed in a previous studyand it was shown to give good simulation of the watershed response (Loukas, 1991).The watershed model is an event model which uses a linear reservoir routing techniqueand simulates the fast runoff with a series of cascading reservoirs and the slow runoff with onelarge reservoir (Fig. 5.12). The whole process is infiltration controlled using a powerrelationship as:F=If+a.t_b (5.1)113Chapter 5. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIAwhere Ps is the rainfall infiltrated and diverted to slow runoff (mm/h), Ij is the finalinfiltration abstractions (mm/h), and a and b are constants. The remaining rainfall Pf from thetotal rainfall P is diverted to the stream as fast runoff.In the previous study this model was kept deliberately simple for a first analysis withthe intention of adding more complexity to handle soil moisture, but the model was found toperform well, so that no additional complexity was added to it.An assumption that underlies the application of rainfall-runoff simulation for theestimation of the extreme flows is that the return period of the peak flow is the same as thereturn period of the 24-hour rainfall depth. This assumption is common in the application ofdesign storms for practical purposes, but it has been challenged (Dickinson et al., 1992). Theabove assumption should hold if the watershed is small and the only causative factor of floodsis the extreme rainfalls which occur at certain periods of the year. The annual floods in thewatersheds of coastal British Columbia can be generated by rainfall, rain on snow, and snowmelt events (Melone, 1985). In the case of Jamieson Creek watershed, rainfall and rain onsnow are the dominant flood producing mechanisms. The annual rain generated floods wereidentified and separately analyzed from the rain on snow floods.Generally, there are a number of combinations of watershed conditions, extremestorms of various return periods and time distributions that can produce a flood of a givenreturn period. For example, a 10-year rain storm over dry soil can produce peak flowsignificantly less than a 10-year flood because of the larger abstractions to the soil storage.However, for this study area, analysis of the time of the occurrence of the largest annual24-hour rainfall showed that there is about 75% probability that the maximum 24-hour stormwill occur in the period from October to January (Fig. 5.2), and during this time period thesoil in the study area is wet. More specifically, as already discussed in the previous section,analysis of the antecedent rainfall prior to the extreme events showed that there is fifty percent114ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIAchance that the 1-day antecedent rainfall at the upper Seymour River watershed will be largerthan 20 mm. Hence, it has been assumed that the soil is saturated at the beginning of theextreme storm and the abstractions to the soil moisture storage have been set to zero.Using the above assumptions, tests have been made to compare the observed raingenerated peak flows with the simulated flows using the various synthetic and derivedhyetographs. These analyses have been used to generate the 2-, 5-, 10-, 25-, 50-, and 100-yearfloods from the Jamieson Creek watershed. Table 5.4 shows the comparison of the simulatedpeak flows using the various hyetographs with the observed rain generated peak flows for theJamieson Creek watershed. These results indicate that the 10% time probability distributioncurve derived earlier in this Chapter gives results that are close to the observed peak flows.The agreement is better for small return periods. It should be noted that the “observed” 25, 50,and 100-year floods are extrapolations of the observed flows of 16 years using the fittedExtreme Value I (Gumbel) probability distribution. Hence, it is reasonable to expect highervariation between the simulated and the “observed” peak flows for the larger return periods.Of the various well known rainfall design storms, only the SCS Type IA curve gavereasonably good results. The other synthetic storms produce larger peak flows than theobserved flows for all the return periods. The Alternate Block Method hyetograph producesthe highest peaks because of the inherent assumption of the method that all the intensities fordurations from 1 to 24 hours will occur in the design storm. Furthermore, the arrangement ofthe intensities in symmetrical fashion around the middle of the storm duration is anotherreason for the over-maximization of the storm and consequently the peak flow. The SCSType I and the Hershfield hyetographs produce higher estimates of the peak flow by about20% and 10%, respectively (Table 5.4).115ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIATable 5.4. Comparison of the simulated peak flows (m3/sec) using various hyetographs withthe observed flows of Jamieson Creek watershed.Return Period (years)Hyetographused 2 5 10 25 50 10010% curve 7.01 9.10 10.48 12.25 13.52 14.8150% curve 5.10 6.62 7.63 8.90 9.84 10.7890% curve 6.10 7.90 9.12 10.64 11.7 12.81ABM 11.49 14.49 16.69 19.83 21.83 23.79Hershfield 8.11 10.53 12.12 14.14 15.64 17.13SCS Type I 8.73 11.33 13.05 15.22 16.84 18.44SCS Type IA 7.21 9.35 10.77 12.57 13.90 15.23Observed 6.20 8.85 10.60 12.82 14.47 16.10From the derived time distributions only the 10% curve, derived in this study, gives peak flowestimates close to the observed flows. The 50% and the 90% curves produce the lower peakflows of all the hyetographs tested.In addition to the peak flow itself, two other important considerations for theapplication of the design storm are the shape of the resulting hydrograph and the timing of thepeak flow. Figure 5.13 compares the observed and the simulated 10-year flood hydrographsfor the various hyetographs. The SCS Type IA storm and the derived 10% storm gave similarhydrographs to the observed hydrograph. The hydrograph of the 10% storm has higher flowsat the beginning of the event and it peaks later than the SCS Type IA hydrograph. However,116ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIAthe hydrograph volumes are similar. The other synthetic hyetographs produce hydrographsdifferent in shape from the observed hydrograph. The hydrograph generated by theAlternating Block Method curve significantly overestimates the peak flow and has a moresymmetrical shape than the other hydrographs. The SCS Type I and Hershfield storms bothgave similar hydrographs but the Hershfield storm produced a more delayed peak flow.Finally, the derived curves of 50% and 90% produce the most delayed and flat hydrographs(Fig. 5.13).The above results show that the design storm derived in this study, using the 10% timeprobability distribution curve, gave the best results. For the other design storms only the SCSType IA storm should be used for the estimation of peak flows from mountainous watershedsin the study area, and gives reasonable results provided that attention is paid to theassumptions discussed at the beginning of this section.5.7 SummaryThe distribution of the extreme 24-hour storms in space and time has been analyzed using therainfall data from the Seymour River watershed. The choice of the 24-hour storm durationwas based on meteorological, hydrological and pragmatic reasons. Firstly, the extreme stormsare strong winter frontal storms which usually have a duration of about a day. Secondly, theresponse of rural and mountainous watersheds in the study area is in the order of several hoursso that a long duration storm should be used as a design storm. Finally, the use of the 24-hourdesign storm expands the usable data both in space and time since there are more and longerdaily records from storage precipitation gauges and only a few recording gauges in coastalBritish Columbia.The analysis showed that the time distribution of the 24-hour storms does not change117ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIAsignificantly over the elevation range of the data in the Seymour River watershed andtherefore, average time probability distributions have been developed. The transferability ofthe derived storm time distributions was tested against the results of other studies whichanalyzed rainfall data from coastal British Columbia and actual data from three coastal BritishColumbia stations. This comparison showed that the 24-hour storm time distributions of thisstudy appear to be transferable to other areas of coastal region of British Columbia.Examination of other synthetic storms revealed that most of these storms have a timedistribution which is characterized by bursts of intense rain which do not appear to beobserved in the Seymour River watershed data or in other data from recording rain gauges inthe region. Application of the derived and synthetic storms to a real watershed showed thatthe 10% time probability curve and the SCS Type IA curve gave good estimation of the peakflow. Furthermore, the shape and the time to peak of the hydrograph is similar for these twostorms. These results justify the application of either the storm hyetograph derived in thisstudy using the 10% curve, or the SCS Type IA hyetograph, for the estimation of peak flow incoastal British Columbia.Study of the extreme 24-hour storm rainfall in the Seymour River watershed indicatesthat the storm rainfall increases up to the middle position of the basin, and then decreases, andlevels off at the top elevations. It is very important to note that the extreme 24-hour rainfall ishighly correlated with mean annual precipitation. Analysis of the extreme 24-hour rainfall forthe four sub-regions of the coastal British Columbia showed that the 24-hour storm depth is acertain percentage of the mean annual precipitation and agrees with earlier findings by Melone(1986). Therefore, the mean annual precipitation can be used as an index for the 24-hourstorm depth. The results presented in Chapter 3 have shown that the mean annualprecipitation in coastal British Columbia increases up to 400-800 m in elevation, and thenlevels off or even decreases at the upper elevations. Also, the study of the storm precipitation118ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIApresented in Chapter 4 and the analysis of extreme historical storms that will be presented inthe next Chapter indicate that the storm distribution across a watershed follows a similarcurvilinear pattern, increasing at the lower elevations and then leveling off or even decreasingat elevations above 800 m. Similar results for the annual and seasonal precipitation have beenfound for the northern Cascade region in Washington State which indicates that the results ofthis study may be transferable to the greater region of the Pacific Northwest.The above conclusions together with the results of the analysis of the storm timedistribution are significant for the estimation of the peak flows from the coastal watersheds.Furthermore, the result of this study indicates that the extreme 24-hour rainfall can beestimated as a certain percentage of the mean annual precipitation. Of the 269 precipitationstations in coastal British Columbia, 96 are recording gauges, and from these stations only 61have records long enough to assure a reliable frequency analysis. Therefore, this studyindicates that, until more extensive and long-term recording rain gage data are available, theannual data are a valuable guide for design flood estimation.119ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIA0z00U0UICDzUIC.)UI00z0Cl)U0UICDzUIC)UI010090807060504030201001009080706050403020100YEARS OF RECORD0 200 400 600 800 1000 1200STATION ELEVATION (m)Fig. 5.1. Distribution of the coastal British Columbia stations witha) years of record, and b) station elevation.12026 24 ‘12 20 18 16() z LU 0 LUI’0LL10 6 4 2-0JANFEBMARAPRMAYJUNJULAUGSEPOCTNOVDECMONTHFig.5.2.Monthlydistributionoftheoccurenceoftheannualmaximum24-hourstormsatVancouverHarbour(53years).ZTCUMULATIVEPERCENTAGEOFSTORMPRECIPITATION-rs3C.010)•%J0)CD000000000091:13CD30•0•0.00CCl)00)VI914fl7O3HSI1I197VISVO31OIkVIOJSNDIScIII1OH-frZçJdvy3ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIA10090807060504030z200Io9O8070Cl) 6050LuCD30zLu0LuQ 0Lu>I-. 1009080o 706050403020100Fig.5.4. Comparison of the time probability distributions for various stationsa) ten percent curves, b)fifty percent curves, and c) ninety percent curvesTIME (h)123-nCDC;’CDp.j7fCUMULATIVEPERCENTAGEOFSTORMPRECIPITATION-‘rzc..n-Co0000000000-Im0C0)0VIffWfl7O3HSIJJJ7VISVO3fOd1VIOISNDISIIflOH-frZçJ?th2l(3100z 0901-8000Ui 70a: 605040—a: 30200tO 0TIME(hours)Fig.5.6Comparisonof theaveragestormtimedistributionintheSeymourRiverwatershedwiththeresuftsoftheMelone(1986)analysisforcoastalBritishColumbia.04812162024z100 90 80 70 60 50 40 30 20 10 0TIME(hours)Fig.5.7ComparisonoftheaveragestormtimedistributionsintheSeymourRiverwatershedwiththeresultsoftheHogg(1980)analysisforcoastalBritishColumbia.04812162024ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIA1009080706050403020z0IC.)90080600U-o 40w3020UiC-)crUi0Ui> 1009080D706050403020100Fig. 5.8. Comparison of the time probability distributions of the Seymour Riverwatershed and three coastal British Columbia stations, a) ten percent curves,b) fifty percent curves, and c) ninety percent curves.TIME (hours)127100z Q90I-80o0w7060LI.o w50w40000W 30w20010 0TIME(hours)Fig.5.9Compansonof syntheticstormswiththeaveragetimeprobabilitydistributionsintheSeymourRiverwatershed.04812162024340320300280260240E220-J 200Z180160140120100 80 60ELEVA11ON(m)Fig.5.10. Distributionof rainfall withelevationforextreme24-hour stormsof variousreturnperiodsintheSeymourRiverwatershed.0200400600800R24=0.057a260240220200p180-J-J140120;100 80 60 40 20a.fl2=0.815SEE=19.4mma I•UU.a•.U_a•.—a a..U.••10-YEAR24-HOURRAINFAIi____REGRESSIONUNEIIIIIIIIII60010001400180022002600300034003800MEANANNUALPRECIPITA11ON(mm)Fig.5.11.Relationshipofthe10-year24-hourrainfallandmeanannualprecipitationforthesixty-onerecordingstationsincoastalBritishColumbia.ChapterS. 24-HOUR DESIGN STORM FOR COASTAL BRITISH COLUMBIARAINFALLPt‘sfFig. 5.12. The watershed model flow chart.4INFILTRATIONCONTROLLEDP= P-Pft S*JKF,1j KFJ KSFAST RUNOFF SLOW RUNOFFWATERSHED OUTFLOW13118 17 16 15 14 13 12 11 10 9 8 7TIME(hours)Fig.5.13Comparisonofthe10-year observedfloodhydrographwithsimulatedhydrographsusingsyntheticandderivedhyetographs,for theJamiesonCreekwatershed.0204060CHAPTER 6STUDY OF HISTORICAL LARGE STORMS6.1 IntroductionIn Chapters 4 and 5 the spatial and temporal distribution of the storm precipitation and the 24-hour maximum rainfall was analyzed. The storms analyzed were the largest for the record ofthe stations in the Seymour River watershed. However, it is important to examine historicallarge storms that have caused flooding in the greater area of Vancouver and the lower Fraservalley. In this Chapter the synoptic meteorological conditions of these severe storms will bepresented, their spatial and time distribution will be examined with the available data from thegreater Vancouver area and Seymour River watershed, and finally they will be compared withthe results of the study of storm precipitation in Chapter 4 and the analysis of the 24-hourrainfall presented in Chapter 5.Five storm periods that have caused severe flooding will be presented. Summaries ofthe synoptic conditions of these storms are available from Atmospheric Environment Servicestorm studies. The storms that will be presented occurred in winter, fall and summer so thattheir analysis will give an overall description of the meteorological conditions of floodproducing mechanisms.[‘33Chapter 6. STUDY OF HISTORICAL LARGE STORMS6.2 The July 11-12, 1972 Rainstorm6.2.1 Synoptic conditionsThe first storm occurred in July. July is one of the driest months of the year for the studyarea. But on July 11-12, 1972 the area was deluged by a rainfall unprecedented for thatmonth. This storm was frontal and occurred under a strong southwesterly flow of warm moistair, not common for the dry season of April to September, and it had many characteristics ofthe winter storms.On July 11 at approximately 10 a.m. Pacific Standard Time the leading frontal waveapproached Vancouver bringing continuous rainfall. Twenty four hours later the cold front ofthe second wave passed over the area. Its passage through the lower Fraser Valley abruptlycut off the continuous rainfall, although a few post-frontal showers where observed, especiallyin the northeast Lower Fraser Valley. Radiosonde soundings from Quillayute, Washingtonhelp to explain the development of the strong moist southwesterly upper- air flow over thecoast (Schaefer, 1973). On July 11, 1972, an air mass with wet bulb potential temperature of12- 14°C extended up to 500 mb and the layer between 600 and 750 mb was very dry. Above500 mb the air was near saturation at a wet bulb potential temperature of 18-19°C and warmadvection was underway at all levels. By the morning of July 12 the entire air column hadwarmed by 4-5°C except for the layer just above the cooler surface water. The wet bulbpotential temperature ranged from 14°C at surface, to 17°C at 600 mb and 19-20°C at 500mb. At 500 mb strong west-southwest winds of 60 knots were recorded (Schaefer, 1973).Twelve hours later the winds had increased to 70 knots, the frontal system had passed over theFraser valley and cold winds swept the area lowering the mean daily temperature by 2°C.134Chapter 6. STUDY OF HISTORICAL LARGE STORMS6.2.2 Spatial distributionSchaefer (1973) compared data from 78 A.E.S. stations. He found that the total stormprecipitation increased from 60-77 mm at low elevations to about 150 to 180 mm at themountains. Schaefer’s data for the high elevations were based only on measurements on theNorth Shore mountain slope stations. Such a station, the Hollyburn Ridge at 910 m recordedan all time record of 167.4 mm. Schaeffer presented no data for the valleys of the NorthShore which extended further into the mountain range. Examination of the Seymour valleydata shows that the total storm depth was 128.4 for station lOA, 142.2 mm for station 14A,143.3 mm for station 21A and 173.5 mm for station 28A. These data compared to 148.8 mmat Seymour Falls Dam and 89.7 mm at Vancouver Harbour give a ratio to base precipitation ofabout 1.6 for the upper and mid-watershed except for the station 28A for which the ratio is1.93. These values are well below the values found in Chapter 4 which are in the order of 2.8-3.0.The 24-hour precipitation was not larger than the annual 24-hour maximum for mostof the stations in the area. However, the Hollyburn Ridge station, which received the greateststorm accumulation reported by all stations in the area, showed a new record for the dailyprecipitation of 167 mm. For the upper Seymour watershed the 24-hour precipitation had areturn period less than 2 years.However, the picture changes when these accumulations are compared with the Julyrecords. The daily accumulation of 73.7 mm in Vancouver Harbour is the largest for 53 yearsof record. For Seymour Falls Dam the 103.1 mm is the third largest daily rainfall in 63 years.So, in general this storm was not extreme by annual standards, but by July standards wasexceptional.135Chapter 6. STUDY OF HISTORICAL LARGE STORMSThe duration of the continuous storm increased from 25 hours at low lands to 30-3 1hours on the mountain tops (Schaefer, 1973). For the Seymour watershed stations theduration ranged from 46 hours at 1OA and 21A to about 60 hours at 28A. Comparing thesevalues with the 29 hours of storm duration at Vancouver Harbour shows a duration ratio ofabout 1.55 for 1OA and 21A and 2.07 for 28A. Schaeffer (1973) pointed out that the meanprecipitation rate increased with elevation from 2.5 mm/h at low elevations to 8 mm/h at themountain tops. However, from the above results we can see that the average precipitationintensity for the upper Seymour remained relatively constant at about 3 mm/h, as much as thelow elevation value.As the Schaefer study (1973) showed, the large precipitation on the mountain slopeswas primarily due to greater intensities. However, the results of this study suggest that in theSeymour valley which extends further into the mountainous range, the larger precipitation wastotally due to larger duration. As Schaefer (1973) pointed out, the moist but stable air massforced to rise over the mountain slopes released its moisture at much higher rate than at lowelevations. However, the valley convergence was not as efficient as the orographic lifting.But the storm duration was more prolonged at the upper Seymour River watershed and theincreased roughness of the mountain range is probably the reason for this.6.2.3 Time distributionFigure 6.1 compares the time distribution of the storm with the time probability distributioncurves found in Chapter 4. The time distribution of the storm in station lOA is well belowthe 50 % probability curve whereas the distribution for l4A is below the 50 % curve for the40 % of the storm duration and then it rises over this curve. These results show that the stormintensity remains relatively constant for most of the duration for 1OA whereas the higher136Chapter 6. STUDY OF HISTORICAL LARGE STORMSintensities occur at the beginning of storm at 14A. However, both curves can beapproximated by a line.6.3 The December 13-18, 1979 Rainstorms6.3.1 Synoptic conditionsDuring most of December 1979 much of British Columbia was affected by a mild moistsouthwesterly flow of air both at the surface and aloft. Throughout the early days ofDecember 1979 usual amounts of precipitation had fallen over the southern coast. OnDecember 13, 1979 the wet southwesterly moisture condition was intensified by the pressureof an almost stationary frontal system which stayed over the lower Fraser valley and southernVancouver Island. A series of minor depressions and waves which moved constantlynortheastward along the front delayed the passage of the front over the area. As a result,southern coastal British Columbia received large amounts of continuous rain, very mildtemperatures and strong winds. The rain was intensified as the waves approached the coast(Chilton, 1980). Inspection of the December 13 tephigraph from Quillayute, Washingtonreveals a stable profile with a warm and moist air mass aloft. The wet bulb potentialtemperature was 12°C at 500 mb, and the persisting surface dew points reached 10°C for thedays of December 13 and 14 (Schaefer, 1980). This situation described the first storm period.The heavy rain during this period resulted in mudslides and local flooding causing widespreadinconvenience.After the heavy rain of December 14, the front and the associated southwesterly flowof moist air were moved to the south. In part this was in response to the strong continentalArctic high pressures centered over the interior of British Columbia. The mean daily137Chapter 6. STUDY OF HISTORICAL LARGE STORMStemperature at Vancouver Harbour dropped from 6.5°C to 2.6°C on December 15, 1979.Radiosonde sounding revealed mid-level drying and surface cooling (Schaefer, 1980). Thesouthwesterly flow during this time affected southern Washington and Oregon states.However, on December 16 and 17 the southwesterly flow again moved north andstarted affecting the southwestern Coastal British Columbia. The tephigraph of December 16showed a very stable and moist profile with wet bulb potential temperatures reached 16°C forthe 600 mb level and above. During this period, the persisting dew points reached 11°C. OnDecember 18 the profile became drier aloft and less stable producing showers that followedthe passage of the frontal system over the area.The synoptic conditions that produced these two storms do not occur every winter onthe south coast at least not to the extent of the December 1979 events (Chilton, 1980).However, the resulting storms were very similar to most of the winter storms which occur inthe area.The two distinctive storm periods of December 13-14 and December 16-18 will beanalyzed separately. Even though these two storms were generated by the same system theirdistribution was different.6.3.2 The December 13-14, 1979 storm6.3.2.1 Spatial distributionSchaefer (1980) compiled data from 18 stations in the greater Vancouver area and VancouverIsland. For the first storm larger precipitation fell over Vancouver Island than in theVancouver area. In the Seymour River watershed the precipitation gradient was lower thanthe average gradient reported in Chapter 4. The storm precipitation increased from 112.3 mm138Chapter 6. STUDY OF HISTORICAL LARGE STORMSat Vancouver Harbour to 196.2 mm at Seymour Falls Dam and then decreased to 152.9 mm at1OA and leveled off at 173.2 mm at 14A. These values represent a ratio of 1.75 at SeymourFalls Dam, 1.36 at 1OA and 1.54 at 14A. The maximum 24-hour rainfall fallen at VancouverHarbour (80.5 mm) during the storm had a return period of about 4 years. The return periodsdecreased at the mountains. The 121.4 mm in 24 hours at 1OA had 2.5 years return periodwhereas the 123.2 mm at 14A was only a 2-year storm. Examination of the data from otherstations in the area showed that this pattern of the decrease of return periods with elevationwas more general over the southwestern British Columbia (Schaefer, 1980). However,because of the wet period preceding the storm and the heavy 24-hour rainfalls exceeding 120mm, the chance for landslides had increased. Actually, many landslides were reported duringthe two-day period between December 13 and 14.Examination of the duration of the storm showed that the storm had about the sameduration at the lower elevations as in the mountainous area, being 41 hours at VancouverHarbour and only 46 hours at 14A. As a result the larger rainfall at the upper Seymourwatershed was the result of higher intensities. The average rainfall intensity increased from2.73 mm/h at Vancouver Harbour to about 3.75 mm/h at lOA and l4A. These valuesrepresent an increase equal to 37%. The same increase has also been observed for the stormprecipitation.The maximum hourly intensity increased by 70% between the lower and upperwatershed. Checking the start time of the storm reveals that the storm started 3 hours earlierat the upper watershed. This resulted from the increased roughness of the mountains and theorographic lifting which promote the condensation of the hydrometeors.139Chapter 6. STUDY OF HISTORICAL LARGE STORMS6.3.2.2 Time distributionFigure 6.2 compares the time distribution of the December 13-14 storm with the curvesdeveloped from the analysis of the 175 storms presented in Chapter 4. It seems that thedistribution of the storm in time changes as the elevation changes (Fig. 6.2). At VancouverHarbour the largest intensities occurred at the beginning of the storm while the heaviestintensities in the Seymour River watershed occurred at the end of the storm (Fig. 6.2).6.3.3 The December 16-18, 1979 storm6.3.3.1 Spatial distributionThe second storm of the December 13-18, 1979 period was more severe for the lower Fraservalley than for Vancouver Island. This is the result of the passage of the front to the northeastand its intensification, as the radiosonde soundings have shown (Schaefer, 1980). This secondstorm precipitated larger amounts on the mountains and valleys than at the low lands. Thetotal storm depth at Vancouver Harbour was 155.8 mm while 347.4 mm fell at Seymour FallsDam, 249.7 mm at 1OA and 243.1 mm at 14A. These values represent an increase of about220% at Seymour Falls Dam and about 60% for the upper watershed over the precipitationaccumulation at the Vancouver Harbour station.However the intensification of the rain was greater at the lower elevations. The 24-hour maximum rainfall of 121.1 mm at Vancouver Harbour had a return period of 60 years.The return periods decreased to about 3 years at Seymour Falls Dam (151.8 mm), 4 years at1OA (139.7 mm) and 2 years at 14A (124.5 mm). The 24-hour rainfall accumulations, as theabove data show, increased by 25% at the middle of the Seymour valley and leveled off at the140Chapter 6. STUDY OF HISTORICAL LARGE STORMSupper watershed.Similar variation of the return periods has also been observed in the greater area ofVancouver. For example, the daily precipitation of 87.5 mm at the Vancouver InternationalAirport had a return period of 70 years while the 136 mm fallen at Coquitlam Lake stationwere only a 3-year 24-hour storm accumulation.Examination of the storm duration reveals that the storm lasted 56 hours at VancouverHarbour and 67 hours at 1OA and 14A. These values represent an increase of 20% in durationbetween the upper and the lower watershed. This means that the larger precipitation at theupper watershed was not only due to the longer storm duration but also due to greater stormintensities. Comparison of the average storm intensities showed that the Vancouver Harbourvalue of 2.78 mm/h increased by about 30% at the upper watershed. However, the maximumhourly intensity remains relatively constant. In light of these results one can say that, at leastfor the upper Seymour River watershed, the larger accumulations were due to both longerduration and higher storm intensities.Examination of the time that the storm started shows that the storm started first at theupper and mid-watershed, namely about 5 hours earlier at 1OA and 2 hours earlier at 14A thanat Vancouver Harbour.6.3.3.2 Time distributionFigure 6.3 shows the time distribution of storm for the stations Vancouver Harbour, 1OA and14A. The storm has different distribution at Vancouver Harbour than it has at the upperwatershed. At Vancouver Harbour the highest intensities occurred in the mid-duration of thestorm whereas for the two other stations there is intensification of the storm just before its halfduration, followed by a lull.141Chapter 6. STUDY OF HISTORICAL LARGE STORMS6.4 The October 25-31, 1981 Rainstorms6.4.1 Synoptic conditionsThe weather of October 1981 over the southwestern British Columbia was dominated by threelarge scale circulation patterns (Schaefer, 1982). These included a low pressure trough(October 1-9), a high pressure ridge (October 10-24), and a southwesterly flow (October 25-31). Frontal storms generated in the North Pacific Ocean and transported by the westerliesimpinge on the southwestern coast of British Columbia on October 25. For the first days ofthe period of October 25-31, the weather systems were similar to the winter systems thatproduce large precipitation in the area. The wet weather during October 25-27 wasaccompanied by freezing levels well above 2000 m and at about 1500 m on October 28.However, by that time satellite images showed that tropical moisture generated in the vicinityof Hawaii was swept into the southwesterly flow, ahead of an advancing frontal zone (Horita,1981). From Quillayute tephigrams, it appears that this injection of tropical moisture in thesystem created a large scale instability (Horita, 1981). This warm moist air associated withthe final heavy rainstorm during October 30-31 brought freezing levels up to 3000 m onOctober 31.Two storms can be identified for the period October 25-31, 1981. The first is thestorm of October 25 to 28 and the second started on October 28 and lasted until November 1.These two storms were associated with two disastrous events. During the first storm, alandslide occurred just before midnight of October 27 in the small M Creek watershed whichflows from the steep mountain slopes into Howe sound (Fig. 2.3). The mixture of mud, treetrunks, water and boulders burst down on the highway, washing out the bridge and killing fivepeople in a car that was on the bridge. Two more cars drove over the edge of the 15 meter142Chapter 6. STUDY OF HISTORICAL LARGE STORMSdrop where the bridge used to be. Also, a small house built near the beach was washed out tosea by the debris torrent while another house was battered by the debris.The second storm was very severe for the area of North and West Vancouver. Theheavy rains on October 30 and 31 resulted in flooding of Seymour River, Lynn Creek andMosquito Creek in the North Shore mountains. The floods claimed the life of a man sweptaway by the floodwaters of Mosquito Creek. The roaring waters of the rivers and creeks ofthe area burst and overtopped their banks flooding residential areas causing millions of dollarsin damage. The muddy flood waters of Seymour River eroded the footings of two bridgesjeopardizing the stability of the structures. Finally, a mudslide into Capilano Lake reservoircreated turbitity problems in the drinking water.The spatial and temporal distribution of the two storms will be examined separately inthe next paragraphs.6.4.2 The October 25-28, 1981 storm6.4.2.1 Spatial distributionThe first storm of the period October 25-28 was very severe in the Vancouver area. Thestorm was intensified by the convergence of the valleys but not by the orographic lifting, asthe data show. For example the Hollyburn Ridge station (910 m) on the southern slopes ofHollyburn mountain received only 83.8 mm while the Seymour Falls Dam station in thenearby Seymour River valley, received 158.9 mm in the same period. In the Seymour Riverwatershed the storm exhibited very large increases. The Vancouver Harbour stormprecipitation was only 37.6 mm whereas the rainfall increased to 158.9 mm at Seymour FallsDam, 223 mm at 1OA, 223 at l4A and 203.5 at 25B. These values show that the storm143Chapter 6. STUDY OF HISTORICAL LARGE STORMSrainfall increased by about 4 times between the lower and mid-watershed and then increasedand fmally leveled off in the upper watershed at a ratio of about 5.5.The storm was not as large or as severe as the storm depth ratios might indicate. The24-hour rainfall at Vancouver Harbour had a return period of less than 2 years. But theseverity increased to 3.5 years at lOA (134 mm), to 4 years at 14A (149.8) and 2.5 years at25B (142.2 mm). Station 25B is located 15 km east of M Creek watershed and the 24-hourrainfall accumulation was 142 mm. O’Loughlin (1972) showed that when the 24-hour rainfallexceeds the 120 mm the steep slopes of the area are prone to landslides, and therefore thisstorm rainfall accumulation is capable of producing landslides in the already wet steephillslopes.The storm lasted only 75% longer at the upper watershed. As a result, the large rainfallat the top of the watershed was due to large average storm intensities, which increased byabout 200% at the upper Seymour River watershed.The storm started about 6 hours earlier at the upper Seymour River watershed than atVancouver Harbour.6.4.2.2 Time distributionFigure 6.4 shows the time distribution of the storm for four stations. It seems that the timedistribution of the storm did not change with elevation. High intensities occurred for allelevations at the middle of the storm duration and then for the rest of the storm the stormintensities were moderate.144Chapter 6. STUDY OF HISTORICAL LARGE STORMS6.4.3 The October 28-31, 1981 storm6.4.3.1 Spatial distributionThe second storm of the period October 25-31, 1981 was more severe than the first storm.The injection of tropical highly unstable moist air in the frontal system is the causative reasonfor the severity of the storm. For this storm of October 28-31, as for the October 25-28 storm,the valley convergence was much more efficient than the orographic lifting. Hollyburn Ridgereceived only 212 mm while Seymour Falls Dam received 486 mm. In the upper SeymourRiver watershed the storm precipitation dropped to 213.4 mm at bA, 243.9 mm at 14A and278.6 mm at 25B. These precipitation accumulations represent a ratio to the VancouverHarbour precipitation of 4.54 for Seymour Falls Dam, 2.0 for bA, 2.3 for 14A and 2.6 for25B. Also, it is significant that the precipitation accumulation at Hollyburn Ridge station issimilar to the accumulations observed at the Seymour valley stations located further inwardsin the mountainous area.The severity of the storm increased with elevation in the Seymour River watershed.The return period of the 78.5 mm in 24 hours at Vancouver Harbour had a return period of 3.5years while the return period increased to 9 years at Seymour Falls Dam (205.5 mm), 10 yearsat 14A (183.9 mm) and 15 years at 25B (210.9). The return periods of the 24-hour storm inthe valleys on the North Shore mountains were larger than on the mountain slopes. Forcomparison the return period at Hollyburn Ridge was only 4.3 years (136.4 mm) while atLynn Creek it was 10 years (136 mm).These extreme storms were dependent on both the higher intensities and the prolongedduration. The duration increased by 50% in the mountains whereas the average storm rate andthe maximum hourly intensity increased by 70%. Furthermore, the storm started, on average,145Chapter 6. STUDY OF HISTORICAL LARGE STORMS5 hours earlier in the upper Seymour watershed than at the Vancouver Harbour station.6.4.3.2 Time distributionFigure 6.5 shows that the storm has similar time distribution pattern at all elevations. Thelarger intensities were observed at the middle of the storm at about October 29.6.5 The November 8-11, 1990 Rainstorm6.5.1 Synoptic conditionsNovember is the wettest month of the year for the southwestern British Columbia. On theevening of November 8, 1990 a strong warm front associated with a large Pacific low pressuresystem moved into southwestern British Columbia. Satellite images revealed that this warmunstable air mass was generated in the North Pacific close to Hawaii. Highly moist tropicalair was injected in the system. The storm was named “ Pineapple Express” by the U.S.National Weather Service forecasters.The storm moved slowly as a number of waves and troughs progressed eastward,causing heavy precipitation. The heavy precipitation started in the early morning hours ofNovember 9th and lasted until the evening of November 10th in the lowland areas andcontinued until the evening of November 11th in the mountainous areas. The storm coverageextended from northern coastal British Columbia to northern Washington State.Severe widespread flooding was reported in all the coastal region, but the hardest hitareas were the eastern Lower Mainland and the Whatcom County in Washington State. Thestrong southwesterly flow of air was associated with high freezing levels and so the flooding146Chapter 6. STUDY OF HISTORICAL LARGE STORMSwas aggravated by the melting of the accumulated snow. In Chilliwack and Sumas Prairielarge areas were evacuated when the Chilliwack River rose 2 to 2.5 m, overtopping its banksand flooding large areas. The flooding was estimated to have a return period of 200 years.Poor highway conditions were blamed in the deaths of two people and injuries to four others.The estimated damage approached 10 million dollars. Furthermore, clogging of the drainagesystems resulted in flooding of basements and streets in Vancouver. The heavy precipitationresulted in numerous mudslides and rockslides which disrupted traffic on the major highways.In Washington State the damage was comparable to that of the Chilliwack - Sumas areas.6.5.2 Spatial DistributionThe precipitation amounts varied greatly across the south coast of British Columbia. Thesouthwestern and central Vancouver Island reported amounts of 150 to 200 mm but areas inthe Northern Vancouver Island received even larger amounts. In the greater Vancouver areathe rain amounts varied around 100 mm, whereas they increased in the north and east lowerFraser Valley due to orographic lifting and valley convergence. For example, in Squamish,north of Vancouver the rainfall accumulation was 310 mm while in the eastern lower Fraservalley the precipitation amounts rose quickly from over 150 mm at Abbotsford to 200 mm atChilliwack and to 337 mm at Hope.In the Seymour River watershed the same pattern was observed. The precipitationincreased from 108 mm at Vancouver Harbour to 460 mm at Seymour Falls Dam and thenleveled off at 339.6 and 354.3 mm at stations 14A and 25B, respectively. These values showthat the precipitation increased by more than 4 times between the lower and upper watershedand then decreased and leveled off at a ratio of about 3.2.The severity of the storm increased in the same pattern as the storm depths. The return147Chapter 6. STUDY OF HISTORICAL LARGE STORMSperiod of the 24-hour rainfall increased from about 1 year at Vancouver to 9 years atAbbotsford (79.6 mm), 10 years at Chilliwack (99.4 mm) and to more than 100 years at Hope(173.1 mm).In the Seymour River watershed the severity of the storm increased up to the middleposition and then declined. The return period of the 24-hour rainfall at Vancouver Harbourwas 1.2 years (55 mm) and increased to 33 years at Seymour Falls Dam (300 mm) and thendecreased to 10-years and 5-years at 14A (173.3 mm) and 25B (170.2 mm), respectively. The300 mm reported in Seymour Falls Dam is the second largest 24-hour event of record, and thelargest value reported during this storm for the whole southwestern British Columbia. Theresult of the very large precipitation accumulations were that many landslides, mudslides androckslides occurred in the mountainous area east of Hope.Examination of the storm duration showed that the storm lasted about 57 hours inVancouver Harbour and about 80 hours at the upper Seymour River watershed. These valuesindicated a ratio of storm duration of about 1.40 between the low level areas and the upperstudy watershed.The above results reveal that the larger storm precipitation at upper and mid-watershedwas mainly due to the larger storm intensities, which increased from 1.89 mm/h at VancouverHarbour to 4.26 mmlh and 4.51 mm/h at 14A and 25B, respectively. These values show anincrease of about 2.3 times between the upper and the lower watershed. Furthermore, thesame has been observed for the maximum hourly intensity which increased from 3.8 mm/h atVancouver Harbour to about 12.0 mm/h at the upper watershed, representing an increase ofmore than 300%.The storm started, on average, about 24 hours earlier at the middle and upperwatershed than at Vancouver Harbour. These results along with the findings for the stormduration show that the orographic lifting and the valley convergence triggered the intense148Chapter 6. STUDY OF HISTORICAL LARGE STORMSstorm earlier and the mountain roughness delayed the passage of the storm by about 24 hours.6.5.3 Time distributionThe time distribution at the Vancouver Harbour was uniform and followed the 50% timeprobability curve (Fig. 6.6a). At the upper watershed the high intensities were observed afterthe middle of the storm. This pattern remained consistent for the two upper elevation stations14A and 25B (Fig. 6.6b and c).6.6 The November 21-24, 1990 Rainstorm6.6.1 Synoptic conditionsFor the second time in November 1990 a strong frontal storm impinged on southwesternBritish Columbia bringing heavy rain. This system, like the previous one, had been injectedwith moist subtropical air during its passage over the North Pacific. However, this system didnot stay over the area as long as the November 8-11, 1990 system. It moved from asouthwesterly direction to the northeast. Heavy rain did fall but was not as continuous or asheavy as the previous storm. Flooding was reported in greater Vancouver and Victoria but theworst flooding occurred in Washington State, north and west of Seattle.6.6.2 Spatial distributionThis storm was not as severe as the previous November 8-11, 1990 storm. The storm wasintensified over the mountain slopes and the valleys as compared to low level areas. The total149Chapter 6. STUDY OF HISTORICAL LARGE STORMSstorm depth increased from about 60 mm in Vancouver to 101.3 mm at Abbotsford, 132.1 mmat Chilliwack and 247.8 mm at Hope. The rain shadow effect was not as strong with thissystem so that the heavy precipitation extended further east of the Coast Mountains. Largeamounts of precipitation in the Victoria area caused flooding (94.8 mm in Victoria Airport).In the Seymour River watershed, large increases in the valley had occurred. The totalstorm depth at Vancouver Harbour was 57.4 mm but increased to 439.5 mm at Seymour FallsDam. At the upper watershed the storm precipitation amount decreased and leveled off at 240mm. These values represent an increase of about 700% at Seymour Falls Dam and 300% atthe upper watershed over the precipitation at Vancouver Harbour.The intensification of the rain followed a similar pattern to that of the rain distribution.The 24-hour maximum rain at Vancouver Harbour (27.4 mm) had a return period smaller thana year, but increased at Seymour Falls Dam (228.3 mm) to 10.5 years and 4 years at 1OA(139.4 mm) and 8 years at 14A (178.1 mm). The same distribution of the return periods hasbeen observed for the greater area. For example the return period of the daily rainfall atVancouver Airport, Abbotsford and Chilliwack was less than one year while it was 15 years atHope.The storm duration increased from 37 hours at Vancouver Harbour to 61 and 71 hoursat 1OA and 14A, respectively. The above results of duration and precipitation indicate that thehigher intensities at the upper watershed are mainly responsible for the increase ofprecipitation at the higher elevations as compared to the middle and low elevationsExamination of the average storm intensity revealed that the storm intensity increased by130% between the lower and upper watershed (from 1.55 mm/h to about 3.5 mm/h). Also,the maximum hourly intensity increased by about 170% between the lower and upperwatershed.The storm started about 20 hours earlier at the upper Seymour River watershed than at150Chapter 6. STUDY OF HISTORICAL LARGE STORMSVancouver Harbour.6.6.3 Time distributionThe storm had different time distribution at Vancouver Harbour station from that at the upperstudy watershed. At the Vancouver Harbour station the storm was not continuous and twodifferent storm periods can be distinguished (Fig. 6.7a). This resulted in two steep parts ofthe curve in the beginning and the end and a flat area at the middle of the storm duration. Atthe upper watershed the time distribution is similar at 1OA and 14A stations. The largerincrease after the middle duration represents the heavy rainfall on November 23, 1990. Onecan observe that this part of the time distribution curve is reasonably linear (Fig. 6.7b, c).6.7 SummaryExamination of five storms showed that the main flood-producing mechanism in the area isthe frontal systems that developed over the North Pacific Ocean and moved eastward untilthey impinge on the coastal British Columbia. The warm, wet flow of air is occasionallyintensified with the injection of humid tropical air, and, as a result, very large precipitationaccumulations are generated in the study area.These frontal systems are capable of producing more than one storm as themeteorological conditions change and the systems move away north or south and then againmove over the study area. These systems occur mainly during the winter and fall months andrarely during summer. The importance of this for the hydrology of the region is that the soilmoisture storage is mostly filled during the wet winter and fall months and combined with theheavy precipitation results in large floods and slope instability.151Chapter 6. STUDY OF HISTORICAL LARGE STORMSFrom the examination of the limited data in the Seymour River watershed, it isevident that, in general, the severe storms have a spatial distribution similar to the distributionfound in the analysis of the 175 storms in Chapter 4 and the results of the 24-hour maximumrainfall in Chapter 5. Furthermore, the increased roughness and the orographic lifting and thevalley convergence cause the severe storms to start earlier at the upper Seymour Riverwatershed than at the low-level Vancouver area. Also, for the same reasons the duration ofthe storms is significantly increased in the mountainous area. As a result, the largeraccumulations at the upper study watershed are due to the high intensities and the longdurations. The time distribution of the storms analyzed varied for the same station from stormto storm but it was within the range of the results presented in Chapter 4.The comparison of the severe storms with the findings of the analysis of the stormprecipitation in the Seymour River watershed shows that, in general, the severe storms havesimilar spatial and temporal distribution characteristics to the less severe storms analyzed inChapter 4 of the thesis. This is significant because it confirms that the previous results can beused for the estimation of extreme storms that produce flooding and other related problems inthe area. Furthermore, similar storm studies by Atmospheric Environment Service (Schaefer,1979a; Schaefer, 1979b) indicate that flood producing storms in other areas of coastal BritishColumbia have similar characteristics as those observed in the greater Vancouver area. This isnot surprising since the same large-scale atmospheric circulation produces storms that impingein the north or south coast of British Columbia depending of the regional circulation patterns.152z0aC.)w0LL0wC-)w0wCUMULATIVE PERCENT OF STORM DURATIONFig. 6.1 Comparison of the time distribution of the July 11 -12, 1979 storm withtime probability distribution curves at (a) station I OA and (b) station I 4A153Chapter 6. STUDY OF HISTORICAL LARGE STORMS100..— (a)—‘....... ,I.:‘, ..,0 / /•.-/, .. , ,,60.•. / ,// 50%0 / i/ / ---- 10%n. ‘I / /.//#0 / // —-— 90%I .•• /Afl / ,./• / 30%-T... f ,/ /, ... I / / —— 70%I, .•• / // /•‘v. ... f / /‘..•• / ,. / —..—.. JULY 11-12, 1972g:/,/ /v ,.../ / /I/I ,•• /10 /‘/... / /4’ .0 —I F..• .—‘ I I I I I I I I0 20 40 60 80 1001009080706050403020100 0 20 40 60 80 100Chapter 6. STUDY OF HISTORICAL LARGE STORMSz000waU0I—zUi0UiaLU50%10%90%30%70%DECEMBER 12-14,19791009080706050403020100 0 20 40 60 80 100CUMULA11VE PERCENT OF STORM DURA11ONFig. 6.2 Comparison of the time distribution of the December 12-14, 1979 stormwith time probability distribution curves at (a) station Vancouver Harbour(b) station 1OA and (c) station 14A154Chapter 6. STUDY OF HISTORICAL LARGE STORMSz000wCCl)U0Izw0UiCUi50%10%90%30%70%DECEMBER 16-19,1979100 •90 /4-/// a80 / ...:‘///..70 -6050...... /// /“ Is .../ /‘,uI.. F •5.• /,V ‘.:•/ ,20 /•Z’ ,:‘‘100 —0 20 40 60 80 10010090807060504030201000 20 40 60 80 100CUMULATIVE PERCENT OF STORM PRECIPITATIONFig. 6.3 Comparison of the time distribution of the December 16-19, 1979 stormwith time probability distribution curves at (a) station Vancouver Harbour(b) station I OA and (C) station 1 4A155Chapter 6. STUDY OF HISTORICAL LARGE STORMS50%30%——•70%OCTOBER 25-28 1981CUMULATIVE PERCENT OF STORM DURATIONFig. 6.4. Comparison of the time distribution of the October 25-28, 1981 stormwith time distribution probability curves at (a) station Vancouver Harbour(b) station 1 OA, (C) station 1 4A and (d) station 25B1106806040200-100 -80604020z0pciwaCIzUiC.)UiaUi( I 20 40 60 80 100U 0 20 40 60 80 100156chapter 6. STUDY OF HISTORICAL LARGE STORMS1806040200 20 40 60 80 10050%30%—70%OCTOBER2e-31,1981CUMULA]1VE PERCENT OF STORM DURA11ONFig. 6.5. Comparison of the time distribution of the October 28-31, 1981 stormwith time distribution probability curves at (a) station Vancouver Harbour(b) station 1 OA, (C) station 1 4A arid (d) station 25BI VU806040200 0 20 40 60 80 100100157Chapter 6. STUDY OF HISTORICAL LARGE STORMSz000w0Cl)LI0Izw0waUi10090807060504030201001009080706050403020100— 50%10%90%30%—— 70%NOVEMBER8-12,1990Fig. 6.6 Comparison of the time distribution of the November 8-11, 1990 stormwith time probability distribution curves at (a) Vancouver Harbour(b) station 1 4A and (C) station 25B0 20 40 60 80 100CUMULATIVE PERCENT OF STORM DURATION158Chapter 6. STUDY OF HISTORICAL LARGE STORMSz0I.0C-)LU0—50%10%90%30%—— 70%NOVEMBER 21-241990Fig. 6.7 Comparison of the time distribution of the November 21-24, 1990 stormwith time probability distribution curves at (a) Vancouver Harbour(b) station 1 OA and (C) station 1 4A1590 20 40 60 80 100CUMULATIVE PERCENT OF STORM DURATIONCHAPTER 7APPLICATION OF A METEOROLOGICAL MODEL7.1 IntroductionIn the previous Chapters, the study of precipitation was carried out by statistical analysis ofthe existent database. The findings of this analysis are then generalized over the coastalregion of British Columbia and relationships between the short-term and the long-termprecipitation were identified to extend the application of the results over the region. Anotherway to estimate precipitation is by using meteorological models. Several theoreticalmeteorological models have been proposed which can evaluate the short-term precipitationconsidering the appropriate meteorological and topographic parameters and terrain-atmospheric interactions. The basic approach uses a wind model to calculate the horizontaland vertical air motions induced by the mountain terrain. This wind model is then used todrive the rain model which estimates the condensation from the moist air mass as it passesover the mountain regions.The wind field can be regarded as the combined effect of three major factors: synoptic-scale forcing, topographic blocking or channeling, and thermal effects. The synoptic-scalepressure field itself can be greatly modified by the dynamic and thermodynamic effects oflarge-scale topography. Relatively simple models suitable for the diagnosis or forecasting ofthe wind field have been used and can be grouped into three types according to the approachadopted: mass conservation models, models using one-layer vertically integrated primitiveequations of motion and models using one-level primitive equations. Mass conservationmodels (Dickerson, 1978; Ross et al., 1988) assume a well-mixed, constant density layerbeneath a low-level inversion where mass is conserved. The second simplified model(bOChapter 7. APPLICATION OFA METEOROLOGICAL MODELapproach uses the equations of motion, vertically integrated for a well-mixed boundary layer(Lavoie, 1974; Overland et aL, 1979). In these models mass is conserved in the mixed layerbut not the layers above. The third type of model uses the primitive equations for one levelwithout a continuity equation. For example, Danard (1977) proposed a model which requiresthe geostrophic wind at the surface and at 850 mb, the lower tropospheric lapse rate andsurface air temperature. It integrates to a steady state the tendency equations at the surfaceonly for wind, pressure and potential temperature. Mass and Dempsey (1985) extend thatapproach to calculate surface wind and temperature using equations for horizontal momentumand temperature tendency in sigma coordinates. The wind field is determined by the verticaltemperature structure. Thermally-induced circulations due to diabatic forcing can also beincluded. The model has been applied at southwestern coastal British Columbia, westernWashington and north-western Oregon.The above types of wind models require a modest amount of initial data andcomputing resources and are useful for analysis and forecasting of wind for engineeringpurposes. However, the current trend is to embed mesoscale models capable of resolvingregional detail in general circulation models (Giorgi and Bates, 1989; Giorgi, 1990). Thistype of approach will be useful for climate assessments and scenarios of changed forcings.The estimated wind field is used as input to a precipitation model for the estimation ofprecipitation field over complex terrain. Modeling of orographic precipitation has followedtwo broad lines of approach. Some analytical studies (Elliot and Shaffer, 1962; Danard,1971; Rhea, 1978) have used a combination of the Bernoulli equation, the continuity equationand hydrostatic flow for mountains of arbitrary shape. Other analyses (Walker, 1961; Wilson,1978) have been based on the perturbation method and idealized barriers. In this approach themotion in a (x, z) plane can be expressed as a perturbation superimposed on a steady basiccurrent of velocity.161Chapter 7. APPUCATION OF A METEOROLOGICAL MODELThe essential components of any type of orographic precipitation models includemeasures of the adiabatic ascent or descent, condensation or evaporation, and precipitation ofthe condensate. The treatment of water substance in the above models is quite variable. Insome models, all of the condensed moisture is precipitated, others use various precipitationefficiency factors (Marwitz, 1974). In some models (Young, 1974 and Nickerson et al., 1978)cloud microphysics is also incorporated.Both the wind models and the precipitation models can be set up in three dimensionsbut in most cases a vertical cross section can reasonably represent the storm’s flow pattern intoa project basin. This reduction to two dimensions simplifies the calculations and reveals therelevant factors in storm precipitation (Wiesner, 1970). Furthermore, the meteorologicalmodels can simulate the physical processes over the full-atmosphere or just in the boundary-layer of the atmosphere which extends a few kilometers over the terrain. Even thoughprecipitation is generated several kilometers above the earth’s surface, the horizontal variationsof precipitation should be correlated to horizontal variations of the physical processes in theAtmospheric Boundary Layer (ABL). These models are flexible, and more simple andsuitable for engineering design than the full-atmosphere models. In addition to the simplicityanother advantage of boundary-layer models compared to full-atmosphere models is that theformer appear to be relatively free of truncation errors associated with using the sigmacoordinates in steep terrain (Danard and Jorgensen, 1992). Hence boundary-layer modelscan, hypothetically, be used with very small grid sizes in a mountainous terrain.This Chapter presents the results of the application of a boundary-layer meteorologicalmodel in the study area north of Vancouver. The model is the BOUNDP model and it istested in an area which has a highly variable topography. Furthermore, an additional test ofthe model is the small grid size. The model will be used to simulate historic storms, and thento predict the precipitation over the area for particular storms. The purpose of this testing of162Chapter Z APPLICATION OF A METEOROLOGICAL MODELthe model is to evaluate its performance and to identify whether it is suitable for theforecasting of runoff from mountainous watersheds of the region if it is combined with ahydrological model or whether it can be used for the estimation of the Probable MaximumPrecipitation and consequently, the Probable Maximum Flood.Firstly, a brief description of the model will be given. Then, the input data necessaryfor the application of the model will be discussed. The results of the application of the modelwill be presented in the next section. Finally, the concluding remarks will be stated.7.2 General Description of the BOUNDP Model7.2.1 OverviewThe meteorological model BOUNDP was designed by Danard and Jorgensen (1992). Themodel was used in this study because it was readily available with advice and help from Dr.Danard and it has been used in hydrological applications by the British Columbia HydropowerAuthority. The test of the model is the first independent test of the model against observeddata.The model consists of two main parts, the calculation of surface winds and thecomputation of the vertical flux of water at the top of the Atmospheric Boundary Layer(ABL). These two parts will be briefly described in the next paragraphs.163Chapter 7. APPLICATION OF A METEOROLOGICAL MODEL7.2.1.1 The wind modelThe wind model is adapted from the models designed for British Columbia Ministry ofForests (Danard and Galbraith, 1991) and the U.S. National Weather Service (Danard andGalbraith, 1989) and has been presented in detail in two papers (Danard, 1988 and Danard,1989). The wind model calculates the geostrophic wind Vg which is the air movementresulting when the pressure force and the Coriolis force are in balance. The geostrophic windis the result of the pressure gradient and the rotation of the earth assuming no friction and notopography.From the geostrophic wind Vg the model calculates the large-scale velocity u* usingthe expression:u*=C8V (7.1)whereg[in( A] + B2is the geostrophic momentum transfer coefficient (square root of the conventional dragcoefficient), k is the von Karman’s constant (0.35), h is the height of the atmosphericboundary layer (ABL), z0 is the roughness length, and A and B are universal generalizedsimilarity functions.The height of the Atmospheric Boundary Layer is calculated from the formulaproposed by Brown (1981):164Chapter 7. APPLICATION OFA METEOROLOGICAL MODELh=cbj (7.2)where f is the Coriolis parameter and eb is a dimensionless factor less than 0.3 for stableconditions (L>0) and greater than 0.3 for unstable conditions (L<0).The universal generalized similarity functions, A and B, are calculated using themethod of Danard (1988).The component wind which is necessary for the calculation of the vertical water flux isthe balanced surface wind . is the unaccelerated wind for which the large-scale pressuregradient, the Coriolis and the frictional forces are in balance. The balanced surface windspeed is estimated by:=ç[1fl[]+f2[]] (7.3)where uK is the large-scale wind velocity, z0 is the roughness length over water L is theMonin-Obukhov length, Za is the anemometer height andf2(za/L) is a stability correction termand k is the von Karman’s constant (k=0.35).The first law of thermodynamics is applied to the surface in the form:L=_v.vo+Kv2(e_o)+Q_c(e_e) (7.4)where 9 is the surface potential temperature, Kt is the horizontal thermal diffusivity, 8 is theinitial surface potential temperature, Q is the diabatic heating rate, C is a nudging coefficient,165Chapter Z APPLICATION OF A METEOROLOGICAL MODELand 8ç is the large-scale potential temperature. The diabatic heating rate, Q, can be foundassuming that the surface pressure tendency is hydrostatic.Then, the equation of motion is integrated in the form:(7.5)where 9 is the surface wind at any level in ABL, Z is the terrain elevation, R is the gasconstant, T is the surface air temperature, g is the acceleration of gravity, p5 is the surfacepressure, f is the Coriolis parameter, k is the von Karmans constant, P is the frictional forcepet unit mass in the surface layer and it is assumed = Cf . 92, Km is the momentumhorizontal diffusivity, C is a nudging coefficient, and is the balanced wind the speed ofwhich is given in Equation 7.3.The estimated wind field around and over the mountains is estimated solvingEquations 7.4 and 7.5 and then, this wind is used as input to the water flux model whichapproximates the condensation processes in the ABL. The water flux model will be brieflypresented in the next paragraphs.7.2.1.2 The water flux modelThe basic predictor is the vertical flux of the water at the top of the Atmospheric BoundaryLayer (ABL). The vertical flux can be written as:W=Wb+E (7.6)166Chapter 7. APPLICATION OF A METEOROLOGICAL MODELwhere = (r + r )pv is the non-turbulent flux of water (or undisplaced flux), r is the watervapour mixing ratio, rj is the mixing ratio of condensed water (having a value of 5x104), p isthe air density, VP is the vertical velocity relative to an isobaric surface and E is theevaporation from the earth’s surface. Wb is usually larger than E.It can be proven (Danard and Jorgensen, 1992) that the vertical velocity can be writtenas:(7.7)with:gp dtV0 = -—aHYHVPSgpVpVdogp Hwhere g is the acceleration of gravity, p is the air density, p is the surface pressure, 0’H is thevalue of the sigma coordinate a = -, at the top of the ABL (aH 0.9), and V is the wind atthe top of the ABL.The term V of the above equation represents the effect of the surface pressuretendency and it is usually small. The term V0 is the effect of the orography (upslope, anddownslope motion) and it is positive as air is moving from high pressure (low elevation) tolow pressure (high elevation). Finally, the term V represents the effect of convergence due tofriction or orography.When the atmospheric water vapour is displaced vertically upwards, it takes some timefor it to condense and to grow to precipitation size and begin falling. Precipitation dropletsare carried with the winds as they fall. Furthermore, the precipitation is initially in the form167Chapter 7. APPLICATION OF A METEOROLOGICAL MODELof ice at the top layers of ABL even for summer storms. The ice particles can be transportedover a very large distance by the wind. The vertical water flux estimated by the Equations 7.6and 7.7 is the undisplaced water generated at each grid ignoring the movement of the dropletsdue to horizontal wind. In order to account for the horizontal movement of the precipitationdroplets, a routine for the estimation of the downwind displacement of the water flux has beenincorporated in the model (displaced water flux).7.2.2.3 Estimation of precipitationOnce the values of the displaced vertical water flux W are calculated, they are then fitted tothe observed precipitation P at a number of stations, through regression. Various relationshipscould be used. The first is:P=A1+2W (7.8)where A1 and A2 are regression coefficients. The coefficient A1 represents the precipitationthat occurs over a horizontal smooth surface with no topography.Another relationship is:P=4+A2w+3 (7.9)which has been shown to account for the effects of W on duration as well as on the intensity(Danard, 1971).Another alternative relationship is:168Chapter 7. APPLICATION OFA METEOROLOGICAL MODELP=A+A2W+3+4Z (7.10)where Z is the terrain elevation. This equation also accounts for the small topographicvariations. The efficiency of the above equations will be tested in the application of themodel.The meteorological input data are available every 6 hours from the CanadaMeteorologic Centre. However, the model averages the vertical water flux over a 24-hourperiod for each of the four 6-hour time steps. The average 24-hour vertical water flux is usedin Equations 7.8, 7.9, and 7.10.Finally, the model uses an objective analysis procedure in order to minimize thediscrepancies between the estimated and observed precipitation (Danard and Jorgensen, 1992).The result is called objectively analyzed precipitation and it should be similar to the observedprecipitation.7.3 Data SetsThe meteorological model BOUNDP has been applied to the North Shore mountain areawhich covers the two study watersheds, the Seymour River and Capilano River watersheds.The data sets required by the model for its application will be presented in the nextparagraphs.Two types of data are required by the model: a) data that are necessary to initialize themodel run and b) data that are used throughout the running of the model. The initial datarequirements include: i) terrain elevation (mean elevation of each grid cell), ii) waterpercentage of each grid cell, iii) water temperature, iv) ice percentage of each grid cell.Topographical data have been digitized for the whole Province of British Columbia by the169Chapter 7. APPLICATION OF A METEOROLOGICAL MODELBritish Columbia Department of Environment, Land and Parks. The terrain elevations aresupplied for a grid 30”x30”, and then are averaged for the model grid cells. The waterfraction is digitized from topographical maps of 1:50,000 scale. The water temperature is notnecessary input data and is calculated by the model. The ice-fraction is considered to be zerofor the storms simulated in this study.Data used throughout the running of the model are: i) height and temperature at 700,800, and 1000 mb, pressure levels and ii) boundary-layer relative humidity. The heights andtemperatures at 700, 850, and 1000 mb were retrieved from the Canada Meteorological Centre(CMC) for a grid of l°xl°. These data are the output of the CMC finite element model. Thismodel accepts radiosonde measurements usually every 24 hours from a very sparse radiosondenetwork across Canada. The model then interpolates and forecasts the meteorologicalelements every 6 hours for the next 24 hours for a grid of 1°xl°. When a new set ofmeasurements are available the model updates the forecasts of these data. The 24:00 UTC(Universal Coordinated Time) data for each day are the updated data and the 06:00 UTC,12:00 UTC, and 18:00 UTC data are the forecast data. These data are available for 5 days aweek, from Monday to Friday. For the weekends, only the forecast output of the CMC finiteelement model is used.The meteorological data of l°xl° needs to be interpolated, once more, to theBOUNDP model grid. In this study, the interpolation is achieved by using B-splines (IMSL,1989). Fourth order polynomials are used for both latitude and longitude for the interpolation.The meteorological data, retrieved from CMC, contained no information about relativehumidity. To compute the relative humidity, the Equation 7.11 is used (Linsley et a!, 1982):RH=lOO(h1201T+Td’1 (7.11)1l2+0.9T )170Chapter 7. APPLICATION OF A METEOROLOGICAL MODELwhere T is the air temperature, and Td is the dew point temperature.The mean daily temperature of the Vancouver Harbour A.E.S. station is used as the airtemperature. The dew point temperature cannot be smaller than the minimum temperature forhumid air. Quick (1987) has used the minimum daily temperature as the dew-pointtemperature for the calculation of smowmelt with success. This assumption has been adoptedin the present study.The Equation 7.11 approximates the relative humidity to within 0.6% in the range of -25°C to 45°C (Linsley et al, 1982). Furthermore, the value used in the simulation is thesurface value whereas the average relative humidity of ABL is required. However, it isassumed that Equation 7.11 gives an average value over the domain since upsiope areas havelarger relative humidity than downslope areas. Moreover, testing of the model with variousvalues of relative humidity showed that the model is insensitive to the humidity and itsvariations.7.4. Application7.4.1 ComplicationsThe precipitation was initially simulated for an area covering a latitude range from 49° 15’ to49° 35’ and a longitude range from 123° 18’ to 122° 48’. The calculation domain consisted of20x20 grids each having dimensions l’xl’ or l.2x1.8 km. approximately. The modelcalculates the water flux in the grids located at the edge of the calculation domain, using thevalues of water flux from grids outside the calculation domain. Hence, five grid widthsaround the calculation domain have been added increasing it to the model domain, whichcovered an area from 49° 10’ to 49° 40’ latitude and from 123° 10’ to 122° 50’ longitude.171Chapter 7. APPLICATION OF A METEOROLOGICAL MODELThe model for this very fine grid mesh gave very large values of vertical water flux.The water flux was in the range of 10,000-100,000 mm/day. The water flux should be in therange of hundreds of mm/day. In view of these unreasonable results, the number of the bordergrids was increased from five to fifteen grids increasing the distance of the border around thecalculation domain from 9 km to 27 km in the longitudinal direction and from 6 to 18 km inthe latitudinal direction. This was done because the model interpolates outside the modeldomain resulting in very large vertical fluxes. However, application of the model to theincreased model domain gave similar results. No further attempt was made to increase theborder grid size because the model then would have become inefficient, having a modeldomain about twice the calculation domain.The small grid size gives a much better description of the topography of the area butresults in very steep slopes. It is believed that these steep slopes resulted in numericalinstability and consequently, in unreasonable results. The elevation from one grid to the nextcould be increased by more than 1000 m. This large elevational increase is, for the model,like an infinite increase in elevation between grids. In this case, the model produces verylarge values of the water flux.The next step was to increase the grid size. Increasing the grid size results insmoothing of the topography, giving smaller slopes. The grid size was increased to 2’x3’,which is 3.6x3.6 1cm, approximately. The precipitation was then simulated for an areacovering a latitude range from 49° 15’ to 49° 35’ and a longitude range from 123° 18’ to 122°48’. The new calculation domain consisted of lOxlO grids. Six grids around the calculationdomain have been added, increasing it to the model domain, which covers an area from 49003’ to 49° 47’ latitude and from 123° 36’ to 122° 30’ longitude.The application of the model to the new model domain gave more reasonable waterflux values. The above problems in the application of the BOUNDP model prove that the172Chapter 7. APPUCATION OF A METEOROLOGICAL MODELmodel is affected by the grid size and consequently, the steepness or smoothness of the modeldomain is a very important factor. Small grid size results in numerical instabilities givingunreasonable results.Figures 7.1 and 7.2 are the three dimensional topographical maps of the calculationand model domain for the grid size (2’x3’) used in the modeling, respectively. Thetopographical contour maps are shown in figures 7.3 and 7.4.The results that will be discussed in the next paragraphs are the results obtained fromthe application of the model to the domain of 2’x3’ grid size which gave the acceptable results.7.4.2 ResultsThe meteorological data necessary for the application of the model where readily available forthe years 1990-1992. Seven large historical storms from this period were selected for theapplication of the model BOUNDP. The storms used are: August 29-30, 1990, October 24-27, 1990, November 8-13, 1990, November 21-24, 1990, April 3-4, 1991, August 26-30,1991, November 16-18, 1991. The daily accumulations at 33 stations in the area (Table 7.1)during these storms where used to compare the computed to the observed precipitation. Thefirst four storms were used to estimate the regression coefficients of the Equations 7.8, 7.9,7.10 (Calibration). The next three storms were used for the application of the model in fullprognostic mode, using the analyzed regression coefficients of the historic storms(Verification).Care is needed when comparing the modeled and observed precipitation because themeteorological input data and the modeled precipitation are referred to Universal CoordinatedTime (UTC) whereas the observed precipitation is referred to Pacific Standard Time (PST).Observed climate day for class 1 A.E.S. station begins at 08:00 PST (16:00 UTC) and ends at173Chapter 7. APPLICATION OF A METEOROLOGICAL MODEL08:00 PST (16:00 UTC) of the next morning. To compute the vertical flux for A.E.S.stations, the model is run with input data for 12:00 UTC of the day and 00:00 UTC of the nextday. The resulted displaced vertical water fluxes were averaged to produce climate dayvalues.7.4.2.1 Calibration of the modelAlthough four storms were used for the calibration of the model, only the results for thesimulation of the November 10, 1990 will be shown. These results are the best resultsachieved throughout the calibration procedure. The storm impinged on the area on November8-13, 1990 causing severe floods in the Greater Vancouver Area as has been discussed inChapter 6. The largest daily precipitation was observed on November 10, 1990 at theSeymour Falls Dam station. The 300 mm recorded is the second largest daily accumulation in64 years of record.Figures 7.5 and 7.6 show the undisplaced vertical water flux for November 10 (12:00UTC) and November 11(00:00 UTC), respectively. The undisplaced vertical water flux forthese two days has a similar pattern but larger values of water flux are observed for November11(00:00 UTC). Figures 7.7 and 7.8 show the downwind displaced water flux for November10 (12:00 UTC) and November 11(00:00 UTC). The distribution patterns of the downwinddisplaced water flux for these two days are totally different and the values of the fluxincrease considerably on November 11 (00:00 UTC). Around that time the heaviestprecipitation was recorded.174Chapter 7. APPLICATION OF A METEOROLOGICAL MODELTable 7.1. Precipitation stations used in the application of the BOUNDP modelStation Name ID number* Latitude Longitude Elevation(m)BURNABY CAPITOL HILL 1101146 49 17’ 122 59’ 183BURNABY METROTOWN 11OA1ND 4913’ 123 00’ 125BURNABY MTN TERMINAL 1101155 49 16’ 122 56’ 137BURNABY SIMON FR. UNIV. 1101158 49 17’ 122 55’ 366IOCO REFINERY 1103660 49 18’ 122 53’ 53COQUITLAM COMO LAKE AV. 1101889 49 16’ 122 52’ 160PORT MOODY GLENAYRE 1106CL2 49 17’ 122 53’ 130VANCOUVER HARBOUR 1108446 49 18’ 123 07’ 0VANCOUVER KITSILANO 1108453 49 16’ 123 10’ 12VANCOUVER UBC 1108487 49 15’ 123 15’ 87N.VANC.DOLLARTON 11ONFNF 4919’ 122 57’ 52N.VANC.ORANDBOUL. 110EF57 4919’ 12303’ 111N.VANC.GROUSE MTN RES. 1105658 49 23’ 123 05’ 1128N.VANC.HIGHLANDS 11OEFNN 4921’ 12307’ 130N.VANC.CLEVELAND DAM 110EF56 4922’ 123 06’ 157N.VANC.LONSDALE 1105665 49 19’ 123 04’ 308N.VANC.REDONDA DR. 1 10N6F5 49 22’ 123 05’ 229N.VANC.WHARVES 1105669 49 19’ 123 07’ 6N.VANC.2NDNARROWS 1105666 4918’ 12301’ 4N.VANC.SONORA DR. 11ON6FF 4922’ 123 06’ 183N.VANC.SEYMOUR HATCH. 110N666 49 26’ 122 58’ 210N.VANC.SEYMOUR FALLS 1107200 49 26’ 122 58’ 244W.VANC.CYPRESS PARK 1108828 49 21’ 123 15’ 155W.VANC.MILLSTREAM 1108840 49 22’ 123 08’ 381LIONS BAY 1104634 49 28’ 123 14’ 137S-i UBC 49 28’ 122 57’ 2401OA UBC 49 32’ 123 00’ 29314A UBC 4932’ 12301’ 48821A UBC 49 32’ 123 01’ 64025B UBC 4933’ 12302’ 71628A UBC 4933’ 12303’ 853C—i UBC 49 26’ 123 11’ 610C-2 UBC 49 27’ 123 06’ 320*Qfficjal A.E.S. Station Number175Chapter 7. APPLICATION OF A METEOROLOGICAL MODELThe downwind displaced vertical water flux is used for the estimation of precipitation.The daily observations of 33 stations in the greater study area were used for the fitting ofEquations 7.8, 7.9, 7.10. Table 7.1 shows the stations used and their topographical andgeographical characteristics.Each one of the Equations 7.8, 7.9, 7.10 were used for all four historic storms. Theresults showed that Equation 7.10 gives a better explanation of the variation of precipitation inspace, so that it was decided only to use this equation for the verification of the model.Figure 7.9 shows the model estimated precipitation using Equation 7.10 for November10, 1990. Figure 7.10 shows the objectively analyzed precipitation for the same day. Figure7.1 la is the scatter graph of the observed and calculated precipitation for November 10, 1990.Figure 7.1 lb is the scattergraph of the total observed and calculated precipitation for the stormNovember 8-13, 1990.It is clear, from Figure 7.11, that the model underestimates the high precipitation andoverestimates the smaller precipitation which is observed at the lower elevations. The highvalues of precipitation for November 10, 1990 were observed in Seymour valley, whereincreased convergence generates large amounts of precipitation. The model precipitation forthis particular position is underestimated by more than 100%. Correlation analysis betweenthe estimated and observed precipitation for November 10, 1990 showed that the correlationcoefficient is 0.807. However, the regression line is flat and its slope and intercept isstatistically significantly different from the line of perfect agreement (1:1 line) at 5% level(Fig. 7.lla). The results improved when the total storm precipitation of November 8-13,1990 is considered (Fig. 7.1 ib). The correlation coefficient between the observed and theestimated precipitation increased to 0.905, but still the slope and the intercept of the regressionline is significantly different from the line of perfect agreement at 5% level. The176Chapter 7. APPLICATION OF A METEOROLOGICAL MODELimprovement is the result of the overestimation of precipitation by the model during the lowerprecipitation days.The application of the model to the historic storms shows that the best possibleprediction is achieved for the larger storms and the storms that result in considerableaccumulations in the lowlands. These storms were deep frontal storms and cause severeflooding in the greater Vancouver area. On the other hand, the model gave very poor resultsfor the smaller storms. The correlation coefficients between the simulated and the observedprecipitation are very low, being between 0.10-0.20.Another general observation is the underestimation of the large precipitation in themiddle Seymour and Capilano valleys, which reaches 100%, and the overestimation of thelower precipitation at the low elevations. This large precipitation results from the increasedconvergence of the incoming air. The topography of the area is so variable that the grid sizesmoothed out the critical topographical features, and so eliminated the causative factors of theincreased precipitation.As a result of the underprediction of the precipitation in the middle valleys, the modeldoes not depict the precipitation distribution pattern found from the analysis of the observedstorm precipitation in the Seymour River watershed. That analysis, in Chapter 4 showed thatthe precipitation always increases up to the mid-position of the valley and then eitherdecreases or levels off.7.4.2.2 Analysis of the regression coefficientsThe coefficients found from the application of the model for the four historic storms wereanalyzed in order to fmd appropriate values for the use of the model in the prognostic mode.177Chapter 7. APPLICATION OF A METEOROLOGICAL MODELThe coefficients A1,A2,A3, and A4 of Equation 7.10 are plotted against the averageprecipitation over the area. Figure 7.12 shows the variation of A1 and A2 with the averageprecipitation. The values of A1 increase linearly, except for three values which are lower thanexpected. Coefficient A2 ranges about a constant value.The next figure (Fig. 7.13) shows that, except for three cases, the value of A3 rangesaround zero for all the values of the average precipitation. The values of coefficient A4increase with the average precipitation over the study area but they do not show a consistentlinear relationship. The coefficient A4 was then plotted against the precipitation differencebetween the Grouse mountain resort station and the U.B.C. station and this caused therelationship to become linear. This might be expected, since A4 is the multiplicator ofelevation in Equation 7.10 and, thus, indicates the effect of the orography on the precipitation.From the above relationships, it is clear that the regression coefficients can bepredicted knowing or estimating the average precipitation over the greater area and theprecipitation difference between the mountains and the lowlands. The values of coefficientA1 were correlated against the average precipitation except for the three outlier values. Theresultant equation is,4=O.98OI (7.12)with R2=0.867 (Fig. 7.14). If the average precipitation av is available from some othersource such as satellite or radar data, the value of the A1 coefficient can be estimated fromEquation 7.12.An average value ofA2=O.293 is used for coefficient A2. The coefficient A3 is putequal to zero. Danard (1971) showed that the quadratic term W2 of Equation 7.10 accountsfor the effect of W on the duration as well as on the intensity. In the study area strong frontal178Chapter 7. APPLICATION OF A METEOROLOGICAL MODELsystems generate the large storms. These storms cover large areas having small to moderateintensity and large duration. The areal variation of the intensity and the duration is not aslarge as it is in convective storms. This probably explains the average value of zero of thecoefficient A3.The values of A4 were correlated with the precipitation difference between Grousemountain resort station and U.B.C. station. The resultant equation is:A4°6962Grouse—UBC (7.13)withR2=0.870 (Fig. 7.15).7.4.2.3 Verification of the modelThe storms of April 3-4, 1991, August 26-30, 1991, and November 16-18, 1991 were used forthe application of the model in prognostic mode. The results of the best simulation, that ofAugust 26-30, 1991 storm will be presented in the next paragraphs.Figures 7.16 and 7.17 show the undisplaced flux of August 29, 1991 (12:00 UTC) andAugust 30, 1991 (00:00 UTC). It seems that the general pattern is the same in both figures.Figures 7.18 and 7.19 show the downwind displaced vertical water flux for both the abovedates. The pattern is different in these two figures. With the use of the predicted values of theregression coefficients, the precipitation is predicted and compared to the observed values.Figures 7.20a and 7.20b show the scatter graphs between predicted and observed precipitationfor August 29, 1991 and for the storm period August 26-30, 1991. Correlation analysisbetween the observed and simulated precipitation showed that the correlation coefficient forAugust 29, 1991 is 0.589. Furthermore, the regression line between the observed and179Chapter 7. APPUCATION OF A METEOROLOGICAL MODELmodeled precipitation is flat and significantly different from the line of perfect agreement atthe 5% level. The model overpredicts the lower precipitation and underpredicts the highprecipitation that occurred in the mountain valleys by about 50% (Fig. 7.20a).The results improve when the total storm precipitation from August 26 to August 30,1991 is considered. The correlation coefficient between the predicted and observedprecipitation takes a value of 0.690. The improved correlation for the total storm period is theresult of the overprediction of precipitation during the low precipitation days andunderprediction of the high precipitation days. Hence, the total storm precipitation is betterestimated by the model. However, again the regression line is significantly different from theline of perfect agreement at the 5% level (Fig. 7.20b).From the results of the application of the model for the prognosis of storms, it is clearthat the results compare better to the observed precipitation amounts for the high precipitationdays than for the low precipitation days. The correlation coefficients between the observedand simulated precipitation for the high precipitation days are, on average, about 0.600. Thesimulation of the low precipitation days gave poor results with r values around 0.100.However, the regression line even for the high precipitation days was statistically differentfrom the line of perfect agreement. The regression line was usually flat which shows that themodel severely underpredicts the high precipitation accumulations in the valleys andoverpredicts the low precipitation in the lowlands. Hence, the model fails to reproduce thegeneral spatial distribution pattern of precipitation over the greater area that has been observedand described in Chapter 4.Application of another meteorological model, similar to the BOUNDP model, by Rhea(1978) in the Rocky Mountains of Colorado showed that the model gives the best results forridges and high plateaux, but overestimates amounts in narrow mountain valleys andunderestimates for broad intermontane basins. These findings show that this type of model180Chapter 7. APPLICATION OF A METEOROLOGICAL MODELdoes not at present describe the complex meteorological conditions which are needed toaccurately simulate the mountainous precipitation.7.5 SummaryThe application of the model BOUNDP in the study area showed that the model is verysensitive to the grid size of the calculation domain. Small grid size causes numericalinstability because of the steepness of the terrain. The numerical instability was eliminatedwhen the grid size was increased from l.2x1.8 km to 3.6x3.6 km. This increased grid sizesmoothed out the critical features of the topography which are responsible for the generationof the precipitation in the valleys. As a result the model underpredicts the high precipitationwhich occurs in the mountain valleys. This large accumulation of precipitation is the result ofthe funneling of the incoming air mass and the resultant increased convergence. Furthermorethe model overpredicts the low precipitation in the lowlands so that it fails to reproduce theareal precipitation distribution over the area.The model overpredicts also the precipitation during the low precipitation days andunderpredicts the precipitation during significant accumulations. When the total stormprecipitation over a number of days is considered the overprediction of the low precipitationand the underprediction of the high precipitation are partially compensated.The real test of the model for hydrologic applications will be to use the model inconjunction with a hydrologic watershed model for the simulation of the runoff from themountainous areas. However, the very large underprediction of high precipitation, by even100%, and the misrepresentation of the areal precipitation pattern negate this testing. Theunderprediction of the large storms reduces the reliability of the model for flood modeling.181Chapter Z APPUCATION OF A METEOROLOGICAL MODEL\ / \ \ \2.\\\ )-N<Fig. 7.1. Three dimensional map of the calculation domain (latitude andlongitude in degrees and elevation in meters with vertical scale 1:17,500)182Chapter 7. APPUCATION OF A METEOROLOGICAL MODELNf7.NFig. 7.2. Three dimensional map of the model domain (latitude and longitudein degrees and elevation in meters with vertical scale 1:32,500)183Chapter 7. APPLICATION OF A METEOROLOGICAL MODEL122.63 122.68 122.93 122.98 123.83 123.08 123.13 123.18 123.23 123.28‘‘ \J- 49.5349.53‘I49.50 ) / 49.50L49.4749.4349.43- 49.4049.4049.37 ) 49.371%49.33 - / 49.3349.30 49.3049.27 I I I I 49.27122.83 122.88 122.93 122.98 123.03 123.08 123.13 123.16 123.23 123.28Fig. 7.3. Topographical contour map of the calculation domain (latitude andlongitude in degrees)184Chapter Z APPUCATION OF A METEOROLOGICAL MODEL122.53122.63122.73122.63122.93123.03123.13123.23 123.33123.43123.53r/J’C49.7749.7049.6349.5649.6349.5649.4949.4249.4249.4949.3549.35—49.28 49.2849.2149.21 -49. 1449.1449.07 I I I I I I I I I I I I I I I I122.53 122.63122.73122.83122.93123.03123.13123.23123.33123.43123.53Fig. 7.4. Topographical contour map of the model domain (latitude andlongitude In degrees)185Chapter 7. APPUCATION OF A METEOROLOGICAL MODEL122.83 122.88 122.93 122.9849.57‘ —I--—49.53 -49.50 -49.47 -N‘%,49.43 -49.40 -49.37 )49.33 -49.30-49.27122.83 122.88 122.93 122.98 123.0349.27123.08 123.13 123.18 123.23 123.28Fig. 7.5. Undisplaced water flux (mm) for November 10, 1990 (12:00 UTC)123.03 123.08 123.13 123.18 123.23 123.28‘4 pE4933- 49.30186Chapter?. APPUCATION OFA METEOROLOGICAL MODEL122.83 122.88 122.93 122.98 123.03 123.08 123.13 123.18 123.23 123.2849.47 49.4749.43 \\ \ 49.4349.30- 49.3049.27 I I 49.27122.83 122.89 122.93 122.98 123.03 123.08 123.13 123.18 123.23 123.28FIg. 7.6. Undisplaced water flux (mm) for November 11, 1990 (00:00 UTC)187Chapter 7. APPUCATION OF it METEOROLOGICAL MODEL122.82 122.87 122.92 122.97 123.02 123.07 123.13 123.18 123.23 123.28I I I I I I 49.57::: J // I I.4943 494349.40 - 49.4049.27 I I I 49.27122.82 122.87 122.92 122.97 123.02 123.07 123.13 123.18 123.23 123.28Fig. 7.7. Displaced water flux (mm) for November 10, 1990 (12:00 LJTC)188Chapter Z APPLICATION OF A METEOROLOGICAL MODEL122.83 122.68 122.93 122.98 123.03 123.08 123.13 123.18 123.23 123.2849.57 49.57I I I I49.5349.53I 49.5049.50 -49 43 49 4349.4749.47 -49.4049.3749.3749.4049.3049.3349.3349.3049.27 49.27122.63 122.88 122.93 122.98 123.03 123.08 123.13 123.18 123.23 123.28Fig. 7.8. Displaced water flux (mm) for November 11, 1990 (00:00 UTC)189Chapter 7. APPLICATION OF A METEOROLOGICAL MODEL122.88 122.93 122.98 123.03 123.08 123.13‘I49.53 -49.50 -49.47 -49.43-49.40 -49.37 -49.331Ø—49.30 -49.27 I I I122.83 122.88 122.93 122.98 123.03 123.08 123.13 123.18Fig. 7.9. Predicted precipitation (mm) for November 10, 1990122.8349.57123.18 123.23 123.2849.5749.5349.5049.4749.4349.4049.3749.3349.3049.27123.23 123.28190Chapter 7. APPUCATION OF A METEOROLOGICAL MODEL122.83 122.88 122.93 122.96 123.03 123.08 123.13 123.18 123.23 123.2849.57 49.57a;I’ I49.63 - 49.6349.60 49.5049.47 - 49.4749.43 - 49.4349.40- / - 49.4049.37 -- 49.3749.33 - 49.33I II 7/49.3049.30 -49.27122.83 122.68 122.93 122.96 123.03 123.08 123.13 123.18 123.23 123.28Fig. 7.10. Objectively analyzed precipitation (mm) for November 10, 1990191z000wIz0IC-)w0ww01:1 line— — —— Regression linea)r = 0.807I-p--I.IIIChapter 7. APPUCATION OF A METEOROLOGICAL MODEL320280240200160120804007006005004003002000I I I I I I I I I I I I I40 80 120 160 200 240 280 320100100 300 500 700OBSERVED PRECIPITATION (mm)Fig. 7.11. Scattergraphs of observed and predicted precipitation for calibrationfor a) November 10, 1990 and b) total storm period between November 8-13, 1990192Chapter 7. APPLICATION OFA METEOROLOGICAL MODEL8070 -60 -50 -40 -30 -20 -AVERAGE PRECIPITATION (mm)Fig. 7.12. Regression coefficients versus the average domain precipitationa) Al and b) A2a).10 -...I—zLUC)L1L1LU00IzLU0LLLU00.I I I I I I I I I06543210—1-2-3-4-5.a0 20 40 60 80 100• b)U.. UU. I.U U—I I I I I I0 20 40 60 80 100193Chapter 7. APPUCATION OF A METEOROLOGICAL MODEL0.3a).—0.25 -0.2 -0.15 -Z 01 -wC)0.05 -w0C-)-0.05-0.1-0.1510090802403020100 0 20 40 60 80 100AVERAGE PRECIPITATION (mm)Fig. 7.13. Regression coefficients versus the average domain precipitationa) A3 and b) A4— I—— —...——I I I0 20 40 60 80 100- b)--...-B-..B— I I I1940 01 I— z Ui C.) U U Ui 0 060 50 40 30 20 100cM0204060AVERAGEPRECIPITATION(mm)Fig.7.14.RegressionbetweentheaveragedomainprecipitationandthecoefficientAl100 90 80 70.600I— znw“40w0030020 10 0-10-1010305070PRECIPITATIONDIFFERENCEBETWEENU.B.C.ANDGROUSEMTNRESORTA.E.S.STATIONSFig.7.15.RegressionbetweentheprecipitationdifferencebetweenU.B.C.andGrousemountainresortandthecoefficientA4Chapter 7. APPUCATION OFA METEOROLOGICAL MODEL122.83 122.88 122.93 122.98 123.03 123.08 123.13 123.18 123.23 123.28\ :::::4943 —-320494349.40 - - 49.40—- 270—_-____-——--—____049.33 -______________-49.33:::I122.83 122.88 122.93 122.98 123.03 123.08 123.13 123.18 123.23 123.28Fig. 7.16. Undisplacecl water flux (mm) for August 29, 1991 (12:00 UTC)197Chapter 7. APPLICATION OFA METEOROLOGICAL MODEL122.83 122.88 122.93 122.98 123.83 123.08 123.13 123.18 123.23 123.2849.57 49.5749.5349.53Ez:::::://149.50-26e 49.4749.4049.5049.43 49.4349.4049.37 49.3749.3349.3349.3016O49.3049.27 49.27122.83 122.88 122.93 122.98 123.03 123.08 123.13 123.18 123.23 123.28Fig. 7.17. Undisplaced water flux (mm) for August 30, 1991(00:00 UTC)198Chapter 7. APPUCATION OF A METEOROLOGICAL MODEL122.83 122.88 122.93 122.98 123.03 123.08 123.13 123.18 123.23 123.28i i i r 1’T 1’iIIIIll4953 . 495349.50 -- 49.5049.47 -- 49.4749.43- 49.43:::: ::::49.33 -- 49.3349.30 - 49.3049.27 I I I I I 49.27122.83 122.88 122.93 122.98 123.03 123.08 123.13 123.18 123.23 123.28Fig. 7.18. Displaced water flux (mm) for August 29, 1991 (12:00 LJTC)199Chapter 7. APPUCATION OF A METEOROLOGICAL MODEL122.8349.5749.5349.5049.4749.4349.4049.3749.3349.3049.27122.83122.88 122.93 122.98 123.03 123.08 123.13 123.18 123.23 123.2849.57I I I I I49.6349.4749.4349.4049.37I I49.3049.27122.88 122.93 122.98 123.03 123.08 123.13 123.18 123.23 123.28Fig. 7.19. Displaced water flux (mm) for August 30, 1991 (00:00 UTC)200z000LULU00LULU0.Chapter 7. APPLICATION OF A METEOROLOGICAL MODEL18016014012010080604040 60 80 100 120 140 160 180II5004504003503002502001501:1 line— — —— Regression liner = 0.690IIII.I150 250 350 450OBSERVED PRECIPITATION (mm)Fig. 7.20. Scattergraphs of observed and predicted precipitation for verificationfor a) August 29, 1991 and b) total storm period between August 26-30, 1991201CHAPTER 8A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FOR THEESTIMATION OF FLOOD RUNOFF8.1 IntroductionIn the previous Chapters the distribution of precipitation in space and time has been analyzedwith statistical methods. However, the estimation of the precipitation is, for hydrologists, justthe first of many stages of the analysis of the watershed response and the estimation of therunoff. An important practical application of hydrology is the estimation of extreme floodevents since the planning and design of water resources projects depend on the frequency andmagnitude of peak discharges. In this Chapter the findings on precipitation distribution andprevious results on watershed modeling wifi be integrated into a physically based procedurefor the estimation of flood frequency from ungauged watersheds of coastal British Columbia.The approaches used to analyze extreme events can be classified as purely statistical,simulation, and derived distribution techniques. The purely statistical methods attempt to fitextreme value probability distributions to measured peak flow records. The method isextremely data intensive and can be applied only to gauged watersheds. For ungaugedwatersheds two other statistical methodologies can be applied. The first methodologyincludes the regional techniques (Watt et al, 1989; Chapman et al, 1992) namely the IndexFlood Method, the method of Direct Regression of Quantiles, and the method of Regressionfor Distribution Parameters. The second method is the combination of single site and regionaldata. This can be done either analytically (Watt et al, 1989) or numerically using the Bayes’2ZChapter 8. A PHYSICALLYBASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFtheorem (Russell, 1982). More details about the regional and combination techniques will begiven in a later section of this Chapter.Simulation techniques use rainfall-runoff models of varying degrees of complexity togenerate synthetic discharges knowing the precipitation. For ungauged watersheds therainfall-runoff models should be calibrated with regional data. Furthermore, the simulationcan be either continuous when long time-series of rainfall are available or event-based whenonly certain large rainfall events are simulated. In the case of continuous simulation the peakdischarges are ranked and the flood frequency is estimated. In the event rainfall-runoffsimulation, it is assumed that the return period of a flow is the same as the return period of therainfall producing the flow. This assumption is often criticized and has occasionally beenstudied (Reich, 1970; Larson and Reich, 1972; Dickinson et a!, 1992). An event rainfall-runoff simulation has been applied in Chapter 5 for the estimation of the peak runoff from theJamieson Creek watershed, where the assumptions underlying the application of the methodhave been discussed.The derived distribution approaches are based on relatively simple rainfall-runoffmodels that are used to derive the cumulative distribution function of the flood runoff andsubsequently obtain a relationship between discharge and recurrence interval. The method ofderived distributions uses a model for the rainfall generation which is usually stochastic, aninfiltration model and a watershed response model. The derivation of the CumulativeDistribution Function (CDF) of the peak flow can be found either analytically or numerically.In the next paragraphs detailed information about this relatively new method of the deriveddistributions will be presented.Hebson and Wood (1982) and Diaz-Granados et a!. (1984) derived analytically theCDF of the peak flow. These two methods use the same rainfall model of Eagleson (1972).According to this model the intensity and duration of the storm are assumed to be independent203Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFrandom variables and their joint probability is exponential. Hebson and Wood (1982) usedthe geomorphologic instantaneous unit hydrograph developed by Rodriguez-Iturbe and Valdes(1979). Diaz-Granados et a!. (1984) used the geomorphoclimatic instantaneous unithydrograph proposed by Rodriguez-Iturbe et al. (1982). Both methods were applied to realwatersheds and obtained reasonable results when compared to observed data.Moughamian et al. (1987), however, applied the above two methods to the samewatersheds and reported that the two methods perform poorly when compared to the Log-Pearson type III extreme value analysis of 40 years of data. Sensitivity analysis showed thatthe two models are extremely sensitive to small variations in the parameters of the rainfallgeneration model as well as to the variation of the infiltration parameters. Furthermore,Moughamian et al. (1987) showed that the models of Hebson and Wood (1982) and DiazGrenados et a! (1984) performed poorly even when the infiltration parameter values wereestimated by least squares optimization. Finally, Moughamian et al. (1987) concluded that“...the results indicate that fundamental qualitative improvements are needed before derivedflood frequency methods can be applied with any confidence.”Another attempt to analytically estimate flood frequency using the deriveddistributions was performed by Cadavid et al. (1991). Their method incorporates theEagleson’s (1972) rainfall model, Philip’s infiltration equation (Philip, 1960), and kinematicoverland flow mechanics. They applied their method to two urban watersheds, whereoverland flow is the predominant runoff mechanism and found that their method estimated thehigh frequency flows (lower flows) better than the most extreme flows. They identified theinaccurate values of the rainfall model parameters as a possible reason for the poorperformance of the method.Haan and Edwards (1988) analytically derived the peak flow probability distributionusing the Extreme Value type I (EVI) distribution to describe the rainfall probabilities and the204Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFU.S. Soil Conservation Service (1972) Curve Number (CN) model to simulate the infiltrationand watershed response. They tested the method on seven small agricultural watersheds andthey found that when the U.S. Weather Bureau TP 40 (Hershfield, 1961) 2-year and 100-year24-hour rainfall depths were used for the estimation of the EVI distribution, the methodoverestimated the peak flow. However, when the parameter values of the EVI distributionwere estimated by observed rainfall data the results improved significantly.The most recent attempt to analytically estimate the flood probability distribution withthe derived distributions methodology is by Raines and Valdes (1993). Raines and Valdes(1993) used Eagleson’s (1972) rainfall model, the CN model to estimate the infiltration andgeomorphoclimatic instantaneous unit hydrograph to simulate the watershed response(Rodnguez-Iturbe et al, 1982). They applied their method to four small watersheds and theyshowed that their method is an improvement over the earlier methods of Hebson and Wood(1982) and Diaz-Grenados et al. (1984). However, they concluded that “the parameterestimation procedure needs to be improved to provide more reproducible parameters to yieldmore consistent results. However, the estimation of rainfall parameters is the most subjectivetask and seems to be responsible for major source of error...”All attempts for the analytical derivation of the flood probability distribution showedthat although the method gives a physical insight in the flood generation process, theassumptions needed to simplify the problem usually result in poor performance of the method.The oversimplifications are mainly done in the rainfall generation model since the temporaland spatial distribution of rainfall are not considered. To overcome these problems the floodprobability distribution can be derived numerically. Consuegra et al. (1993) used regionaldata to derive storm patterns, the CN method to estimate the infiltration, and thegeomorphologic unit hydrograph to describe the watershed response. They fitted the storageparameter of the CN model to an Antecedent Precipitation Index (API) and, considering the205Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFprobability of the rainfall and API, they simulated a large number of scenarios for thegeneration of the peak flow. Then they were able to calculate the frequency of a given flowby integrating the probability of the flow for all possible scenarios. They applied their methodto a 51 km2 Swiss mountainous watershed and compared the results with the results of astatistical analysis of simulated flows by a continuous deterministic model for a period of 20years. The comparison showed that their method could reproduce the simulated flows. Theymade, however, no attempt to compare the estimated peak flows with observed data.Another recent attempt to analytically derive the distribution of the flood flow wasmade by Muzik (1993). He used Monte Carlo simulation to generate the rainfall depth,duration, and time distribution and the parameters of the CN model were used to model theinfiltration process. Muzik used a regionally derived dimensionless unit hydrograph tosimulate the watershed response. This regional unit hydrograph was developed from ananalysis of flows from 30 watersheds in the Alberta foothills (Muzik and Chang, 1993).Application of the method to two Alberta watersheds showed that the method can simulate theflood probability distribution fairly well.The above results showed that the numerical derivation of the flood probabilitydistribution gives better results than the analytical method. The reason for the poorperformance of the analytical method is the poor representation of the rainfall characteristicsas has already been mentioned. In the numerical method, the storm time and spacedistribution, the storm duration and the storm depth can be simulated, whereas the Eaglesonmodel, used in most of the analytical studies, considers only the duration and the intensity ofthe storm and assumes that these two parameters are independent.This Chapter presents an improved method for the estimation of design floodparameters for mountainous and rural ungauged watersheds. The proposed procedure uses thenumerical derivation of the flood probability distribution approach and incorporates the206Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFfindings of the research on the rainfall spatial and temporal distribution as well as the responseof the watersheds of the region. The procedure is based on a rainfall simulator, and thewatershed response model developed in an earlier study (Loukas, 1991) and applied inChapter 5. Firstly, the proposed procedure will be presented and its components, the rainfallsimulator and the watershed response model, and their parameters will be discussed in detail.Then, the procedure will be applied to eight representative catchments located in coastalBritish Columbia with varying basin characteristics and compared with historical steamfiowdata. The sensitivity of the procedure to the variation of its parameters will be analyzed nextand finally, the procedure will be compared with regional techniques and conclusions will bestated.8.2 ProcedureThis section describes the derived flood frequency procedure. As has been noted above, theprocedure is based on a rainfall simulator, and a watershed model which simulates theinfiltration process and the watershed response. The intention in developing this procedure isto provide hydrologists with a method for the estimation of flood frequency that requires verylimited data. The problem of data limitation is especially evident in the mountainous area ofcoastal British Columbia and the coastal region of Pacific Northwest where the hydrologistusually has to estimate the flood frequency with very limited precipitation and runoff data. Inthe next paragraphs the rainfall and watershed response models will be discussed.207Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF8.2.1 Rainfall modelA rain storm is characterized by its duration, depth, time and space distribution. It isimportant to incorporate all these characteristics in a simulation to have a reliablerepresentation of the rainfall process. The minimum data for the rainfall depth can be foundin the Rainfall Frequency Atlas for Canada (Hogg and Carr, 1985). This publication byEnvironment Canada contains maps for all the Canadian Provinces showing the isopleths ofthe mean and the standard deviation of the annual extreme rainfall of various durations (Fig.8.1 and 8.2). These storm durations range from 5 minutes to 24 hours. The shorter stormdurations are more important for the generation of floods in small, highly impermeable urbanwatersheds. Since this study is focused on the mountainous and rural watersheds the largerstorm durations of 6, 12 and 24 hours should be more suitable. Simulation has beenperformed using the 6-hour, the 12-hour and the 24-hour extreme storms and the watershedmodel proposed in an earlier study (Loukas, 1991) and used in Chapter 5 for the simulation ofthe peak flow from the Jamieson Creek watershed. The simulation has been performed for theCarnation Creek watershed, which will be presented later in this Chapter, and the results showthat the 6-hour and the 12-hour storm durations are adequate for the generation of the smallreturn period and more frequent floods but they are incapable of producing the more extremepeak flows (Fig. 8.3). On the other hand, the 24-hour storm gave reasonably good simulationof the low and high frequency floods (Fig. 8.3). This result is in accordance with the floodproducing mechanisms in the coastal British Columbia. The most severe floods in this regionare generated by frontal storms that have durations that range around 24 hours as alreadydiscussed in Chapters 4 and 6. Furthermore, the choice of the 24-hour storm duration is apragmatic one. Of the 269 precipitation stations located in the coastal British Columbia, 173are storage gauges which are used to measure the daily precipitation. These stations have208Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFlonger records than the recording stations (Fig. 5.1), which implies more reliable frequencyanalysis, and hence, the use of the 24-hour design storm can expand the usable data both inspace and time resulting in better estimation of flood runoff from ungauged watersheds. As aresult the 24-hour storm was selected as the representative storm.The storm depth of the 24-hour storm is assumed to follow the Extreme Value type I(EVI) distribution. This extreme value distribution has been extensively used for the analysisof rainfall in Canada (Watt et al., 1989). Furthermore this probability distribution is twoparameter distribution and so it limits the number of the parameters required.The mean and the standard deviation of the annual extreme 24-hour rainfall, the twoparameters required for the estimation of the EVI, are estimated either from the records ofexisting data stations or from the Rainfall Frequency Atlas for Canada (Hogg and Carr, 1985)or from mean annual precipitation data because as has been shown in Chapter 5 this can beused as an index of the 24-hour rainfall of various return periods. Especially, the valuesderived from the Rainfall Frequency Atlas for Canada are representative only for the low levelareas. The study of long-term and storm precipitation in Chapters 3 and 4 showed that in thecoastal British Columbia the precipitation increases up to an elevation of about 400-800 m andthen either decreases or levels off. This particular spatial distribution is evident even for themost extreme storms, as shown in Chapter 6.The average increase of the rainfall over the watershed from the lower to the higherlevel areas was estimated to be about 1.5 times. This average increase will be used in thesimulation procedure and no attempt has been made to describe the rainfall spatial distributionin more detail since the watershed response model used in this procedure is a lumped modeland only the average rainfall over the watershed is needed. It is important to mention thatjudgment is necessary at this point to better estimate the rainfall over the watershed. Also,this average fudge factor of 1.5 seems to be representative for watersheds that have an209Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFelevation range similar to that of the Seymour River and Capilano River watersheds which is0-1800 m. For higher level basins a larger factor may be used and a value of 2 may berepresentative whereas for low level basin a lower value may be used. However, for thewatersheds tested the average value of 1.5 seems to be reasonably representative because allhave an elevation range similar to that of the two study watersheds.In Chapter 5 another useful way to estimate the rainfall over the watershed has beenproposed. It has been shown that the extreme 24-hour rainfall of various return periods is acertain percentage of the mean annual precipitation. Hence, if there are any long-termprecipitation data in the region the hydrologist can easily estimate the rainfall depthparameters.The time distribution is another important characteristic of a storm. A way ofmodeling the variability of rainfall within the 24-hour rainy periods is through the cumulativedimensionless hyetograph. Such an analysis has been presented in Chapter 5 where timeprobability curves have been proposed for the coastal British Columbia. For this cumulativedimensionless hyetograph, the rain at each of the twenty four time steps is the cumulativepercentage of the total storm rainfall from the beginning of the storm, R(t). A statisticalmodel for the cumulative dimensionless hyetograph has to take into account, in addition to therandom nature of R(t), that its successive values are dependent and constrained to:0= R(0) R(1) ... R(24) =100% (8.1)It is proposed to model R(0),. ..,R(24) as a random sample of size 24 from a continuousdistribution. Since R(t) ranges between zero and one or 100%, any continuous densitydistribution in this interval could be an appropriate choice. The triangular distribution isproposed because it is simple and fits our data reasonably well, as will be shown later. The210Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFquantiles of 10%, 50% and 90% are necessary to define the density function of the triangulardistribution. These quantiles, for the simulation of the 24-hour storm time distribution, can beestimated from the results of the analysis of the time distribution of the 24-hour design stormas presented in Chapter 5.Under the assumption of an ordered sample from a continuous random sample rangingbetween zero and one, all the conditions stated above are fulfilled because dependence is alsoa property of order statistics and no extra parameters are necessary to fit correlations. Asimilar model has recently been developed and tested in Spain with very good results (GarciaGuzman and Aranda-Oliver, 1993).The proposed model is tested against observed data. As mentioned above the resultsof the previous analysis of the time distribution of the 24-hour storm for the coastal BritishColumbia are used in the proposed model to define the triangular distribution. The simulatedtime distribution probability curves are compared to the observed curves in Figure 8.4. Theobserved and simulated 10% cumulative probability curves are in good agreement whereas thesimulated 50% and 90% curves deviate from the observed ones. Probably a moresophisticated model should be more suitable. However, application of the non-parametricKolmogorov-Smyrnov test (Haan, 1978) showed that observed and simulated time probabilitycurves are not significantly different at the 5% level. Hence, for each one of the 24 hourlytime steps the rainfall is distributed according to the triangular probability distribution withincreasing order.The most important characteristics of a storm, precipitation amount, duration, and timedistribution, have been incorporated in the procedure. This increases the reliability of thestorm estimation and is an improvement over the popular Eagleson’s method (1972), whichconsiders only the average intensity of the storm for a given duration. The proposed methodincorporates the time distribution of the storm and up to a certain degree the storm spatial211Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFdistribution. In the next paragraphs the other component of the procedure, the watershedresponse model will be considered.8.2.2 Watershed response modelThe watershed response model used in the procedure has been developed in a previous study(Loukas, 1991). The same model has been applied to the Jamieson Creek watershed for theestimation of peak flow in Chapter 5. This particular model is used because it requires verylittle information about the watershed and its parameters can be estimated from thegeomorphology of the catchment. Furthermore, it was found that the model gives a goodsimulation of the watershed response. The model has been presented in Chapter 5 andreference will be made to that Chapter of the Thesis whenever necessary.The above model has been applied to the Jamieson Creek for the study of itshydrologic behaviour and response (Loukas and Quick, 1993a). This application showed thatthe storage factor of the slow runoff (KS) (Fig. 5.13) is constant and equal to 750 hours. Thisvalue is consistent with the value used in the simulation of runoff from watersheds of theregion using the U.B.C. watershed model (Quick, 1993), which uses a similar linear routingtechnique.Another result of the previous application of the model was that the infiltrationabstractions (Fig. 5.13) were constant (P5=If) for most of the events. The only exception wasthe rainfall-runoff events during intense summer storms over dry soil conditions. However,these events are not capable of producing the highest annual flows since large volume of rainwater is infiltrated into the dry soil so, flow significantly delayed. Excluding these events, theparameter If was found to be normally distributed with a mean value of 1.37 mm/h and acoefficient of variation of 30%. Furthermore, it was also found that the storage factor of the212Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFfast runoff is normally distributed around a mean value KFm and a coefficient of variation of30%.From the Nash theory of linear routing, the storage factor, KF, is related to the timelag of the watershed as:t,=n•KF (8.2)where n is the number of the linear reservoirs or the shape parameter of the Nash unithydrograph.Recent research (Rosso, 1984; Chutha and Dooge, 1990) has shown that the shapeparameter, n, of the Nash model is a function only of the geomorphology of the watershed andit is related to Horton order ratios. Hence, for a given watershed the shape parameter remainsthe same for all types of storm events and is independent of the storm characteristics.On the other hand, Rosso (1984) and Chuptha and Dooge (1990) showed that the scaleparameter or storage factor, KF, is a function not only of the geomorphology of the watershedbut also of the precipitation characteristics. So, the parameter KF changes from storm tostorm. As a result and according to Equation 8.3 the time lag of the watershed will change aswell. Furthermore, Sarino and Serrano (1990) and Yang et al (1993) showed that the mostuncertain parameter of the Nash cascade of linear reservoirs model is the storage parameterKF. Sarino and Serrano (1990) expressed the uncertainty of the hydrograph only to theuncertainty of the storage factor KF using Stochastic Differential Equations. They also foundthat either the Normal or the Log-normal probability distributions can be fitted to the valuesof KF, but they used the Normal distribution in their study. As a secondary result of this workSarino and Serrano (1990) found that the scale parameter, n, ranged around a mean value of213Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF2.24. A similar result has been found in the analysis of the runoff from a Czechoslovakianwatershed (Blazkova, 1992). For this reason a value of n equal to 2 was used.Yang et a!. (1993) used the Bootstrap sampling method to study the uncertainty of thehydrograph and they found that this uncertainty can be accounted for if only the uncertainty ofthe storage factor KF is considered. Also, from the simulations, they found that the KFparameter is normally distributed around a mean value.From the above discussion, it is possible to assign certain probability distributions andvalues to the parameters of the model. In the application of the procedure, it is assumed thatKS is constant and equal to 750 hours, the infiltration abstractions to slow runoff can bedescribed only by a parameter If which is constant for a certain event but is normallydistributed around a mean equal to 1.37 mm/h with a coefficient of variation equal to 30%.Furthermore, it is assumed that two reservoirs for the simulation of the fast runoff areadequate. This is in accordance with the previous application of the model (Loukas andQuick, 1993a) and the results of the other studies mentioned above. Finally, the storage factorof the fast runoff KF is assumed to follow the Normal distribution with a mean of KFm andcoefficient of variation of 30%.The mean of the storage factor of fast runoff, KFm, can be found using Equation 8.2.The time lag of the watershed, t1, can be estimated by the modified Snyder method (Linsley eta!, 1986),t1=C.[’oc]m (8.3)where C and m are coefficients, L is the length of the main stream (kin), L0 is the distancefrom the mouth of the watershed to the centroid of the watershed (usually is taken as L=L/2)(kin), S is the mean slope of the main stream (m/m).214Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFThe value of the coefficient C depends on the average resistance to flow through thedrainage network. The U.S. Bureau of Reclamation (Cudworth, 1989) recommendsC=18.2K and the U.S. Army Corps of Engineers (1990) uses C=16.8K where K is theaverage resistance to flow through the drainage network. There is not a definite value of Cthat can be used. For this reason, the value of C is assumed equal to 0.42. According to U.S.Army Corps of Engineers relationship this value of C represents an average resistance over thewatershed of about 0.025 which seems reasonable for rural and mountainous watersheds.The value of the exponent, m, in Equation 8.3 generally has been assigned within therange of 0.30 to 0.38 (Sabol, 1993). The U.S. Army Corps of Engineers (1990) typically usesm=0.38. This value has been used in this study.Equation 8.3 has been tested against an independent sample of 44 basins. These datawere taken from a paper of Watt and Chow (1985). The data cover a wide range of basinsizes from 0.5 ha to 5,840 km2. The basins are located across North America from themidwest United States to Quebec in Canada. The characteristics of the basins used in theanalysis are shown in Table Cl in Appendix C.The modified Snyder method, as given by Equation 8.3, is found to perform very wellexcept for the largest basin (5,840 km2). This basin is flat and has a time lag of 40 hours.Figure 8.5 shows the scattergraph between the observed and estimated time lag for theremaining 43 basins. The regression line is very close to the line of perfect agreement (1:1line) and their slopes and intercepts are not significantly different at the 5% level. Thestatistical parameters R2 and Standard Error of Estimate (SEE) show that Equation 8.3 fits thedata well and so it is used for the estimation of the parameter KFm.In summary the proposed method requires very little information about the hydrologyof the watershed area. The only necessary input parameters of the procedure are the mean andthe standard deviation of the extreme 24-hour storm depth over the watershed and the mean215Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFvalue of the storage parameter KF which can be found by the Equations 8.2 and 8.3 andtopographical data. Figure 8.6 shows the flow chart of the procedure. Monte Carlosimulation is used to generate the large number of parameters (5,000). At the end of everysimulation a flood hydrograph is estimated and from that the hydrograph parameters arecalculated. The 5,000 values of the flood hydrograph parameters are then ranked and plottedon probability paper as synthetic frequency curves.The above procedure has been programmed in a 123-Lotus (Lotus Develpment Co.,1989) spreadsheet. A recently developed attached-in program, the @RISK (Palisade Co.,1991), is used to generate the large number of the parameters by using a random numbergenerator.The application of the procedure to coastal British Columbia watersheds will bepresented next.8.3 Application and ResultsThe proposed procedure has been applied to eight coastal British Columbia watersheds (Fig.8.7). The watersheds used in the simulation had to meet the following criteria:• they must be mainly rain-fed watersheds,• they should have natural flow and no man-made storage impoundment should exist intheir area,• they should have negligible natural lake storage, and• they should have long enough flow records to allow statistical analysis.Table 8.1 shows the topographical characteristics of the eight watersheds used in thesimulation. For these watersheds, the hourly peak discharge, the daily peak discharge and theflood volume are simulated. It is considered that these parameters of the flood hydrograph are216Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFthe most important and can be used for the estimation of other design parameters as riverflood stage, reservoir level, etc.The mean and the standard deviation of the annual extreme 24-hour rainfall are mainlyestimated using the Rainfall Frequency Atlas for Canada (Hogg and Carr, 1985). Whererainfall gauges were located in the area of the watershed the estimates from the Atlas werecompared with the actual data and, after engineering judgment, the best estimate of the rainfallwas used. More specifically, for the Capilano River watershed the results of the analysis ofthe rainfall data from the adjacent Seymour River watershed are transposed and used. In thecase of the Carnation Creek, the data from a station at the lower elevations were analyzed andthen extrapolated according to observed long-term precipitation distribution at the higherelevations (Hetherington, personal communication). For Chapman Creek no actual data areavailable so the mean and the standard deviation of the 24-hour rainfall are estimated from theRainfall Frequency Atlas for Canada and then are increased by a factor of 1.5 to represent theaverage rainfall over the watershed. The isopleths of both mean and standard deviation of the24-hour extreme rainfall in the Rainfall Frequency Atlas for Canada are wide apart in the areaaround Zeballos River watershed because of the very limited number of stations. The nearestrainfall station to the watershed is the Talisis station which is a storage gauge. In Chapter 5 itwas shown that the 24-hour rainfall depth of various return periods is a certain percentage ofthe mean annual precipitation of the location. Hence, estimates of the rainfall parameters aremade from the Tahsis station data which compare well with the estimates from the RainfallFrequency Atlas for Canada. For the other four watersheds, the North Allouette River, theOyster River, the Hirsch Creek and the San Juan River, the mean and the standard deviation ofthe 24-hour extreme annual rainfall are estimated using the Rainfall Frequency Atlas forCanada. Finally, the estimates are increased by 1.5 times to represent the average watershedrainfall and are used for the simulation.217Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFThe topographical characteristics of the watersheds necessary for the estimation of themean value of the time lag from Equation 8.3, were measured from 1:50,000 scaletopographic maps.The observed flows were obtained in hourly time steps from the Water Survey ofCanada, Environment Canada. From these data, the annual maximum hourly and daily peakflows and the flood volumes were estimated. The Extreme Value type I (Gumbel) and theLog-normal probability distributions are fitted to the observed data. These two probabilitydistributions have been extensively used for flood flows in Canada, the United States andGreat Britain (Watt et al, 1989).218Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFTable 8.1. The characteristics of the eight watersheds used in the study.Watershed Location Area Stream Stream Slope Land Use(km2) Length (1cm) (rn/rn)SouthCapilano Mainland 175 26.0 0.040 ForestedWestCarnation Vancouver 10.1 7.8 0.085 ForestedIslandSouthChapman Mainland 64.5 20.7 0.052 ForestedWestZeballos Vancouver 181 22.0 0.022 ForestedIslandNorth South 37.3 13.0 0.035 ForestedAllouette MainlandEastOyster Vancouver 298 37.6 0.022 ForestedIslandNorthHirsch Mainland 347 36.5 0.053 ForestedSouth-WestSan Juan Vancouver 580 41.97 0.010 ForestedIslandFigures 8.8-8.15 show the results of the simulation for the eight study watersheds. Theresults are, in general, very good except for some simulations of the flood volume. For theflood volume the simulated frequency curve deviates more than the frequency curves of thehourly and daily peak flow from the observed data and the fitted probability distributions.This does not necessarily mean that the method gives poor simulation of the flood volume219Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFfrequency because the estimation of the peak flood volume from the hydrograph record ishighly judgmental and subjective. The overall performance of the method is very good ascan be seen from these figures.8.4 Sensitivity AnalysisTo have a better understanding the effects of the parameter uncertainties, a sensitivity analysiswas performed on the impact of the parameter variation on the resulting flood frequencies. Toquantify the sensitivity of the flood frequency curves to parameters a sensitivity index, SI,similar to that of Raines and Valdes (1993) was defined as,xlOO (8.4)Q0where Q and Q are the old and new 100-year peak discharges, respectively. Furthermore,the sensitivity analysis results have been plotted on probability paper along with the observeddata and the base simulation results. The sensitivity analysis is performed for the CarnationCreek watershed.The sensitivity analysis is first performed for the uncertainty of the model parametervalues (parameter value sensitivity). The effect of assuming that the parameters follow adifferent probability distribution from the one initially used is examined next (parameter formsensitivity).For the parameter value sensitivity the mean annual rainfall depth and its standarddeviation, the mean of storage parameter of the fast runoff(1<m) and the rainfall abstractions(If) were increased and decreased by 10% and 20% of their values used in the simulation220Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFabove. Furthermore, the coefficients of variation of KF and I were varied from 20% to 40%instead of the assumed value of 30% used in the base simulation.For the sensitivity of the method to the form of the parameters the storage factor KFand the rainfall abstractions I are assumed constant and equal to their mean value, instead ofnormally distributed around their mean values. The parameter KF is also assumed to varyaccording to a Log-normal probability distribution with the same mean and standarddeviation.The results show that the sensitivity of the procedure to the variation of the parametervalues and form is usually small (Tables 8.2-8.8 and Figures 8.16-8.22). The simulatedhourly and daily peak flow and the flood volume vary less than the model parameters. Themost insensitive model parameter seems to be the rainfall abstractions, I, and the mostsensitive parameter is the mean rainfall depth of the 24-hour annual extreme storm. Hourlypeak flow is most sensitive to the variations of the mean annual extreme 24-hour rainfall andto the variation of the mean value of the storage parameter of the fast runoff, KFm, and isaffected by the form of KF, as well (Table 8.8). The daily peak flow and the flood volume areless sensitive to the parameter variations and their form. These two parameters of the floodhydrograph are the most sensitive to the variations of the mean annual 24-hour rainfall and itsstandard deviation (Fig. 8.16 and 8.17).The above sensitivity of the procedure is significantly less than the sensitivity of themethod of Raines and Valdes (1993) for which 13% variation of the Curve Number parameterresulted in a maximum 180% underestimation of the 100-year discharge.221Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTiMATiON OF FLOOD RUNOFFTable 8.2. Sensitivity Index values (SI, %) for the mean annual extreme 24-hour rainfall(Rm) for Carnation Creek.HydrographParameter Rm - 20% Rm - 10% Rm + 10% Rm + 20%Hourly Peak -14.2 -7.1 10.2 16.1FlowDaily Peak -12.9 -8.3 4.1 10.5FlowFlood Volume -11.8 -8.0 5.2 11.6Table 8.3. Sensitivity Index values (SI, %) for the standard deviation of the annual extreme24-hour rainfall (CYR) for Carnation CreekHydrographParameter - 20% - 10% + 10% OR + 20%Hourly Peak -4.0 -2.5 4.0 4.0FlowDaily Peak -9.0 -6.0 1.1 5.6FlowFlood Volume -10.2 -4.8 5.7 6.7222Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFTable 8.4. Sensitivity Index values (SI, %) for the mean of storage factor (KFm) forCarnation CreekHydrographParameter KFm - 20% KFm - 10% KFm + 10% KFm + 20%Hourly Peak 10.9 6.7 -7.4 -5.2FlowDaily Peak -4.3 -2.9 -2.5 -0.03FlowFlood Volume 0.03 -1.5 -1.9 -0.09Table 8.5. Sensitivity Index values (SI, %) for the coefficient of variation of KF (CV) forCarnation CreekHydrographParameter CVKF = 20% CVKF = 25% CVKF = 35% CV1 = 40%Hourly Peak -7.8 -7.1 7.3 32.1FlowDaily Peak -0.8 -1.5 -0.7 -0.8FlowFlood Volume -1.0 0.4 -0.3 -0.2223Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFTable 8.6. Sensitivity Index values (SI, %) for the mean of infiltration abstractions parameter(Ii) for Carnation CreekHydrographParameter If - 20% If - 10% If + 10% If + 20%Hourly Peak 4.2 -2.5 0.2 -1.7FlowDaily Peak -1.7 -2.0 -0.9 -1.3FlowFlood Volume -0.3 -2.4 -3.9 -2.0Table 8.7. Sensitivity Index values (SI, %) for the coefficient of variation of I (CV1f) forCarnation CreekHydrographParameter CVTf= 20% CVJf = 25% CVTf= 35% CVTf = 40%Hourly Peak -4.8 1.2 0.5 -1.4FlowDaily Peak -3.3 -5.4 -2.2 -2.3FlowFlood Volume 0.1 -3.2 0.6 -1.8224Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCED URE FORTHE ESTIMATION OF FLOOD RUNOFFTable 8.8. Sensitivity Index values (SI, %) for the form of the parameters for CarnationCreekHydrograph KF and I KFParameter KF constant I constant constants Log-normalHourly Peak -14.2 1.7 -13.5 -10.1FlowDaily Peak -2.6 -2.4 -1.3 -3.5FlowFlood -1.9 -2.3 -1.6 -3.0Volume8.5 Comparison with Regional TechniquesRegional techniques have been broadly used for the estimation of peak runoff in Canada (Wattet aL, 1989), Great Britain (Hoskings et al., 1985) and elsewhere (Inna et al., 1993). In thissection the proposed method will be compared with the most popular regional techniques.Furthermore, regional equations relating floods and physiographic and climatic variables, willbe developed for the coastal British Columbia. Finally the results of the various methods willbe compared with observed data from a real watershed.225Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF8.5.1 MethodsThe methods of flood frequency estimation that will be compared with the proposedprocedure, are presented in this section. These methods fall into the categories of regionaltechniques, statistical methodologies as they have been classified in the Introduction section ofthis Chapter. The methods used are the Index Flood method, method of Direct Regression ofQuantiles, method of Regression for Distribution Parameters, the B.C. Environmentmethodology (regional methods), and Russell’s Bayesian methodology (statistical method). Abrief description of each one of these methods will be presented next.8.5.1.1 Index flood methodThe Index Flood method involves the development of a regression equation expressing the“index” flood - usually the mean annual - in terms of independent physiographic and/orclimatic variables. Then, the index flood is related to the floods of various return periods forthe whole region. It implies that within a region, all frequency curves can be approximatedwith the same shape curve, or in other words the regional flood frequency curve is an averageover the region. As a result a dimensionless regional frequency curve is determined.When the flood frequency of an ungauged watershed is to be found the index flood isestimated by the regional equation, knowing the characteristics of the area and then it ismultiplied with the dimensionless regional frequency curve to give the flood frequency curvefor the ungauged watershed.The physiographic factors used as predictor variables for the index flood are usuallythe basin area, basin surface storage by lakes and swamps, main channel slope, main channel226Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFlength, mean basin elevation, drainage density, basin shape factor, soil and cover type. Theclimate of the area is of major consideration and it can be represented as a predictor in theregression equation by the mean annual precipitation, mean annual extreme rainfall or otherparameters.The index flood method is very popular among hydrologists. In Canada for examplethere are twelve studies for the various regions of the country that use the index flood method(Watt et al., 1989).8.5.1.2 Method of direct regression of quantiles (DRQ)Within a hydrologically and climatically homogeneous region the floods of various returnperiods can be assumed that depend on physiographic and climatic characteristics of theindividual watersheds. With the DRQ method not only the index flood is related to thecharacteristics of the watershed but also all the flood quantiles. This method is the secondmost popular regional technique in Canada (Watt et a!., 1989).8.5.1.3 Method of regression for distribution parameters (RDP)The RDP method assumes that a standardized flood frequency distribution can be applied overa homogeneous region. It is hypothesized that the parameters of the flood frequencydistribution for each individual watershed will change according to the physiographiccharacteristics. Usually a two parameter probability distribution is assumed to fit the floods ofthe region. The mean and the standard deviation or the coefficient of variation of the floodsfor the gauged watersheds are related through regression to physiographic and climatic227Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFparameters. Then, using the predictor equations it is possible to estimate the probabilitydistribution parameters and so, the flood frequency for an ungauged watershed.8.5.1.4 B.C. Environment methodThe British Columbia Ministry of Environment, Lands and Parks proposed a method for theflood frequency estimation based on the Index Flood method (Reksten, 1987). The wholeprovince was separated into homogeneous subregions, and the mean annual daily flood, Qmd,of the watershed in these subregions was plotted against the basin area. No attempt was madeto relate the mean annual flood to other physiographie and climatic parameters because thesedata were not available (Reksten, 1987).The ratios of the floods for various return periods to the mean annual daily flood, C,were calculated for the gauged watersheds of the subregions. Knowing the area of anungauged watershed the mean annual daily flood, Qmd’ can be estimated from graphs and thenis multiplied by the values of C to give an estimation of the daily flood for various recurrenceintervals.The B.C. Environment method also estimates the instantaneous flood. In eachsubregion of British Columbia the mean ratio of instantaneous to daily flood, LID, is estimatedfor the gauged watersheds and plotted against the area of the watersheds. So, the lID value fora given area multiplied by the daily flood gives the instantaneous flood of the same returnperiod. The above method averages the response of each watershed, and so the lID ratio, toonly one value which is questionable since the response of the same watershed even for thelargest floods can vary significantly.228Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF8.5.1.5 Russell’s Bayesian methodologyRussell (1982) proposed a procedure which involves the use of a compound distribution whichis a weighted combination of individual probability distributions. The initial values areassigned to the parameters of the component distributions and their weights on the basis ofsubjective or regional estimates of the mean and the standard deviation of flood peaks. Theweights of the component distribution can be updated using the Bayes’ theorem in light of anyadditional measurements or even subjective information, such as the largest flood in a numberof years or a flow which was not exceeded in a given number of years. The method requiresthe low, probable, and high estimates of the mean and the standard deviation. The low valueis the one for which there is 90% probability that it wifi be exceeded, probable is the bestestimate and high is the estimate with 90% probability that will not be exceeded.The model developed based on the above procedure estimates the values of the meanand the standard deviation half way between the low and the probable estimates, and theprobable and the high estimates. The marginal probabilities assigned for each one of thesevalues are 0.169, 0.206, 0.250, 0.206, 0.169 for the low to the high estimates.The compound distribution is made up of 25 component distributions each specifiedby a mean and a standard deviation and a weight or marginal probability. The probability ofany particular combination of mean and standard deviation is obtained by multiplying theindividual probabilities and normalizing to make the sum of all the weights equal to 1.0. Thefrequency of a given flood is simply the weighted sum of all the component distributions. Iffurther information is available the weights or marginal probabilities of the componentdistributions are updated by using the Bayes’ theorem.229Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF8.5.2 ApplicationIn this section the application of the various methods to a coastal British Columbia watershedwill be presented. The study watershed is the Santa River watershed on the west coast ofVancouver Island and its area is 162 km2. The majority of the flow is generated as for the restof the coastal watersheds by strong frontal systems formed above the North Pacific Ocean.The west coast of the Vancouver Island is actually in the path of these frontal systems. As aresult, the highest values of the unit discharge (discharge over area) in British Columbia havebeen observed in that area (Environment Canada, 1982). The results of the various techniquesare compared with twelve years of instantaneous peak flow data and thirty seven years of peakdaily flow.The various methods are applied to rainfed watersheds, because the majority of thefloods recorded at about 74% of the coastal British Columbia streamflow stations are rainfall-induced floods (Melone, 1986). Also the rainfall-induced floods should be separated from thesnowmelt-induced floods because snowmelt-induced floods have much flatter frequency curvethan the rainfall-induced floods (Jarrett, 1987). Also, in watersheds where both rainfall andsnowmelt induce peak flows the rainfall usually produces the larger flood for the mostextreme conditions. The application of each one of the methods will be presented next.Although the coastal British Columbia has distinct climatic and physiographic featuresfrom the rest of the province, a homogeneity test is applied to eliminate non-conformingstations. The homogeneity test described in Hydrology of Floods in Canada (Watt et al.,1989) has been applied. This homogeneity test has been proposed by Gumbel (1958), and isbased on the assumption that the EVI (Gumbel) distribution fits all the regional data andinvolves the following procedural steps.230Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF• The ratio of the 10-year flood to the mean annual flood is computed for all stations andaveraged over the region.• Each station mean annual flood is multiplied by the regional average ratio to yield aregionally estimated 10-year flood. The return period of this flood is then estimatedfrom the stations frequency curve.• This estimated return period of each station’s flood is plotted against the station lengthof record. The 95% confidence bands approximated (Kite, 1978) by yE = 2.25 ±where y is the reduced variable equal to y6 = _ln[_th(l_ J], n is the years ofstation record and 7 is the estimated return period of the flood.Twenty eight stations are used to test the homogeneity of the instantaneous peak flow recordsand thirty seven stations are used for the daily peak flows (Table 8.9). All stations used havepassed the test as can be seen from Figures 8.23 and 8.24.In this study, the Index Flood method and the DRQ and RDP methods are used todevelop regional equations. The Index Flood method presented in this study, is different fromthe B.C. Environment methodology even though they both use the same technique. The IndexFlood method of this study includes only the rainfall generated flows of rivers that have noman-made impoundment. Furthermore, the regional equations developed, use not only thebasin area as a predictor but also other physiographic as well as climatic parameters. Also,separate equations have been developed for the instantaneous and daily peak flow.The physiographic parameters used for the development of the regional equations arebasin area, A, main stream length, L, main stream slope, 5, mean basin elevation, E, and lakestorage, St. These physiographic parameters were measured from maps of 1:50,000 scale.The mean annual 24-hour rainfall, Rm, is used for the representation of the climaticcharacteristics and it is estimated from the Rainfall Frequency Atlas for Canada (Hogg andCarr, 1985). The watershed characteristics can be seen in Table 8.9.231Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFTable 8.9. Characteristics of coastal British Columbia watersheds used in the study.Mean Mean MeanArea Stream Stream Mean Lake Annual Annual AnnualWatershed (1cm2) Length Slope Elevation Area 24-h Instant. Daily(1cm) (rn/rn) (m) (1cm2) Storm Flow Flow(mm) (m3/sec) (m3lsec)Capilano 172 25.97 0.040 782 - 120 317.8 224.1Carnation 10.1 7.80 0.085 765 - 135 31.2 13.7Chapman 64.5 20.65 0.044 680 - 78 80.0 47.5Hirsch 347 36.47 0.020 820- 80 350.5 207.1N.Allouette 37.5 13.00 0.035 478 - 110 76.0 44.3Oyster 298 37.60 0.022 701- 60 180.3 145.1San Juan 580 41.97 0.010 414 - 120 776.4 619.6Sumas 149 32.91 0.005 414- 55 25.93 23.3Zeballos 181 22.00 0.022 725 - 190 552.1 338.5Exchaniiskis 370 47.98 0.005 785- 80 491.2 354.9Zymagotitz 376 35.77 0.016 772- 70 272.8 178.2Pallant 76.7 15.60 0.012 519 8.63 90 70.3 49.4Canaka 47.7 15.16 0.045 732- 90 77.8 41.2Lit. Wedeena 188 23.33 0.022 855 - 70 192.0 127.1Mackay 3.63 2.45 0.105 497- 110 6.95 3.61Murray 26.2 9.00 0.0095 60 - 55 22.8 10.8Noons 2.59 5.47 0.131 409- 85 7.46 4.02Yakoun 477 62.82 0.0025 351 8.50 75 291.1 270.6Ucona 185 28.50 0.052 834 4.88 160 394.01 233.9Stawamus 40.4 13.53 0.032 785 - 140 63.51 37.7Bings 15.5 5.40 0.045 359 - 60- 6.93Browns 86 24.25 0.039 626- 70- 77.2Chemainus 355 55.90 0.0105 644- 80- 243.9Englishman 324 34.40 0.019 828- 80- 228.8Haslam 95.6 16.54 0.036 451- 60- 38.6Koksilah 209 35.80 0.011 493- 60- 133.7Tsable 113 25.30 0.037 681- 70- 143.2Kokish 290 36.20 0.0185 799- 80 130.9 96.9Tsitika 360 37.15 0.018 792- 80 412.0 249.6Jacobs 12.2 3.50 0.025 483- 75 17.83 10.96Mashiter 38.9 12.20 0.084 872 - 100 43.7 22.1Salloomt 161 22.10 0.030 883 - 100 90.6 62.2Mamquam 334 30.95 0.036 911- 110 223.3 152.01Nusatsum 269 32.00 0.029 897 - 100 151.4 100.4Kemano 583 30.55 0.018 912- 85 502.1 323.1Anderson 27.2 13.50 0.0075 47- 60- 10.4Yorkson 5.96 10.6 0.003 35- 60- 2.88Santa 162 20.32 0.0175 442- 190 357.7 313.7232Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFThe stepwise multiple regression analysis is conducted as linear analysis using log-transformed data. Only the statistically significant parameters at the 95% level were includedin the equations. For all the equations only the basin area, A, the mean stream slope, S, andthe mean annual extreme 24-hour storm depth, Rm, are included.For the index flood method the mean instantaneous flood is given from the equation:— (11 1 A°•823 ‘°,039 R 1.226m ( . )withR2=O.91 and See=9.O1%.The respective equation for the mean daily peak flood is:Qm,d = O.014• A°934 . S°°89 Rm°987 (8.6)withR2=O.91 and See=l9.3%.Data from all the stations are used to develop dimensionless regional frequency curvesfor instantaneous and daily peak flows. The ratio of the flows for various return periods to themean annual flood Qm are calculated using the EVI distribution. Figures 8.25 and 8.26 showthe dimensionless frequency curves for the instantaneous and daily flows, respectively.Multiplication of the mean annual flood with the dimensionless frequency curves gives thefrequency curves for a given watershed.The regional equations for the floods of the 2, 5, 10, 25, 50, and 100 years recurrenceinterval are developed for the DQR method. The EVI distribution has been used. Theequations for the instantaneous flow are shown in Table 8.10. The equations for the dailyfloods are shown in Table 8.11.233ChapterS. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFTable 8.10. Regional equations of instantaneous peak flow for the method of DirectRegression of Quantiles (Q =K.Ac.Sd.R).ReturnPeriodT K c d e R2 See(years)100 0.0648 0.861 1.085 0.171 0.90 8.150 0.0518 0.856 1.106 0.157 0.90 8.125 0.0422 0.853 1.119 0.144 0.90 8.210 0.0252 0.841 1.178 0.110 0.90 8.45 0.0186 0.835 1.196 0.085 0.91 8.62 0.0097 0.819 1.237 0.084 0.90 9.2234Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTiMATiON OF FLOOD RUNOFFTable 3. Regional equations of daily peak flow for the method of Direct Regression ofQuantiles (QT =K.Ac.Si.R).Return K c d e R2 SeePeriod T(years)100 0.0483 0.9442 0.9374 0.11214 0.93 8.350 0.0424 0.9439 0.9407 0.1085 0.93 8.425 0.0364 0.9434 0.9453 0.1035 0.93 8.510 0.0275 0.9369 0.9583 0.0847 0.93 8.75 0.0223 0.9413 0.9614 0.0844 0.93 8.82 0.0134 0.9378 0.9818 0.0574 0.94 9.4For the RDP method the regional equations for the mean instantaneous and the meandaily flows are the Equations 8.5 and 8.6 developed for the Index Flood method. The EVIdistribution was tested for the estimation of the flow. The equation for the standard deviationof the instantaneous peak flow is:= 0.0156A0872 NO.248.Rm’°59 (8.7)with R2=0.87 and See=12.8%.The equation of the standard deviation of the daily peak flow is:235Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFOQ 0.0l13A°946S°1Rm°05 (8.8)with R2=0.91 and See=114.1%.The B.C. Environment method (Reksten, 1986) has been applied to the varioussubregions in which the province of British Columbia has been divided. In this study, theresults of the analysis for the Vancouver Island subregion (Chapman et al., 1992) are used.Two watersheds located in the west coast of the Vancouver Island have similarcharacteristics to the Santa River. The Zeballos River and the Ucona River watersheds havesimilar areas, 181 and 185 km2, respectively. From the diagrams provided in the B.C.Environment report (Chapman et a!., 1992) the mean annual flood is estimated as 300 m3/secif the Zeballos River is used and 210 m3lsec if the Ucona River is considered.The ratios of the floods of the various return periods to the mean annual flood areestimated from the results of the analysis of peak daily flows using Log-Pearson type Illdistribution. The values of the ratios, C, for the 2-, 5-, 10-, 25-, 50-, 100-year floods are0.89, 1.28, 1.58, 1.95, 2.28, and 2.55, respectively if the Zeballos River is used and 0.81, 1.34,1.75, 2.27, 2.65, 3.09, respectively if the Ucona River is used.The daily floods of various return periods then can be estimated from the equation:Qr,dQm,dc (8.9)The average ratio of the instantaneous to daily flow, LID is estimated from the B.C.Environment report using the Zeballos River as 1.32 and 1.7 when the Ucona River is used.The instantaneous flood can then be found if the daily flow is multiplied by the lID factor as:Q:=Q:AIID (8.10)236Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFThe results for Santa River watershed are shown in Tables 8.12 and 8.13.In order to use the Russell’s Bayesian method, it is necessary to determine the low,probable, and high estimates of mean annual flow and its coefficient of variation. Only thewatersheds located on the west coast of the Vancouver Island (Zeballos, Ucona, Carnation,San Juan in Table 8.9) are used. The low, probable, and high values of the mean annual floodand its coefficient of variation are estimated as the smaller, the average and the larger valuesof these parameters for the above four watersheds. The estimated low, probable, and highvalues of the mean annual instantaneous flow and its coefficient of variation are: 340 m3/sec,447 m3/sec, 502 m3/sec and 0.3, 0.5, 0.7, respectively. The estimates for the mean annualdaily flood and its coefficient of variation are: 194 m3/sec, 243 m/sec, 308 m3/sec and 0.35,0.50, 0.65, respectively. The results for the Santa River watershed using the Bayesianmethodology are shown into the Tables 8.12 and 8.13.Finally, for the proposed stochastic-deterministic procedure, the mean and the standarddeviation of the mean annual 24-hour storm are estimated from the Rainfall Frequency Atlasfor Canada (Hogg and Carr, 1985). The mean of the storage factor of fast runoff, KFm, isfound by using Equations 8.3 and 8.4 and topographical data. After estimating the parametervalues and 5,000 Monte Carlo simulations the flood frequency of the hourly peak flow anddaily peak flow are estimated for the Santa River watershed (Tables 8.12 and 8.13). It shouldbe noted that the other techniques estimate the frequency of the instantaneous peak flowwhereas the proposed procedure estimates the frequency of the hourly peak flow. The hourlypeak flow is similar to instantaneous peak flow for large and medium size basins but for smallcatchments it could be substantially different from instantaneous. Examination of the ratio ofhourly to instantaneous peak flow for the Santa River watershed (162 km2), showed that thisratio is close to one so that the hourly peak flow of the proposed procedure is compared with237Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFthe observed and estimated instantaneous peak flows for the Santa River watershed in Table8.12 and Figure 8.27.8.5.3 ResultsThe results of the various techniques are compared in Tables 8.12 and 8.13 and are shown inFigures 8.27 and 8.28. The comparison shows that for the instantaneous peak flow all thetechniques give flows larger than the observed flows. This incompatibility is the result of thesmall number of years of record. It should be mentioned that the largest daily peak flow of 37years of record is 677 m3/sec and the largest instantaneous peak flow of 12 years of record isonly 486 m3/sec. Examination of the data of the Santa River showed that the ratio of theinstantaneous peak flow to the daily peak flow ranges between 1.11 to 1.55 with a mean of1.35. Applying these ratios to the largest daily flow in record indicates that the instantaneouspeak flow of the same day should have been between 750 to 1050 m3/sec. If these flows wereextrapolated then the 100-year instantaneous flood should range between 1000 and 1300m3/sec. As can be seen from Table 8.12 and Figure 8.27, only three techniques haveestimated flows that are close to these values. These techniques are the proposed stochastic-deterministic procedure presented earlier, the Bayesian method, and the B.C. Environmentmethod. In Figure 8.27 and Table 8.12 the estimate using the upper 95% confidence level ofthe regional dimensionless frequency curve (Fig. 8.25) is also presented. This estimate iswithin the above range of 1000 to 1300 m3/sec for the 100-year flood. This is not surprisingsince the west coast of Vancouver Island receives large amounts of rain from the PacificOcean storms and so the watersheds located in that area exhibit a response that is higher thanthe average response of the coastal British Columbia watersheds.238Chapter 8. A PHYSICALLYBASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFThe estimates of the 100-year flood using the other regional techniques are well belowthe range of 1000 to 1300 m3lsec. This is mainly because the regional equations developed inthis study average the watershed response over the coastal region of British Columbia whereasas it has been mentioned above the watersheds located on the west coast of the VancouverIsland respond at a much higher rate than the rest of the coastal watersheds.The results of the analysis of the peak daily flow are compared with the estimatesderived from the fitted Extreme Value type I distribution to the observed data in Table 8.13and Figure 8.28. As it can be seen the estimates of the proposed procedure, the Bayesianmethod and the B.C. Environment methodology are closer to the estimates of the fitted EVIdistribution. The estimates of the Index Flood method, RDP and DRQ methods are below theobserved values. The discussion presented above for the peak instantaneous flow is also validfor the daily peak flow as well.239Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFTable 8.12. Comparison of estimated instantaneous peak flow (m3/sec) for various returnperiods using various methods for Sarita River.Return Period (years)2 5 10 25 50 100Stochastic- 470 646 773 946 1100 1256DeterministicSimulationBayesian 497 688 816 945 1095 1213MethodB.C.Environment 289 478 626 811 947 1103MethodUconaB.C.Environment 352 523 626 811 947 1103MethodZeballosIndex Flood 369 505 596 710 795 880MethodIndex Flood 381 593 755 960 1110 1259Method -95%RDP 374 484 557 650 718 786DRQ 372 495 564 641 708 769240Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFTable 8.13. Comparison of estimated daily peak flow (m3lsec) for various return periodsusing various methods with the fitted Extreme Value type I distribution to the observed flowsfor Santa River.Return Period (years)2 5 10 25 50 100Fitted EVI 275 399 481 584 662 738Stochastic- 315 424 496 591 679 773DeterministicSimulationBayesian 282 391 463 551 622 690MethodB.C.Environment 170 281 368 477 557 649MethodUconaB.C.Environment 267 396 474 585 684 765MethodZeballosIndex Flood 194 271 322 387 435 483MethodIndex Flood 199 294 371 466 533 604Method -95%RDP 191 270 321 387 435 483DRQ 216 296 350 415 463 512241Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF8.6 SummaryFlood frequency curves for ungauged watersheds are very difficult to obtain. This isespecially important for coastal British Columbia where both rainfall and streamfiow data arelimited both in space and time. The physically based stochastic-deterministic procedureproposed in this study provides an alternative to the more traditional methods. The procedureuses the derived distributions method and incorporates the findings of the research on rainfalland watershed response in the region of coastal British Columbia. The input datarequirements are minimum and can be derived from a topographical map and the RainfallFrequency Atlas for Canada.The application of the procedure to eight coastal British Columbia watersheds andcomparison with the observed data and the fitted EVI and Log-normal probabilitydistributions showed that the method is reliable and efficient. Especially, the estimation of thefrequency of instantaneous and daily peak flow is very good, whereas the estimation of thefrequency of flood runoff volume is not as good as the estimation of the frequency of theother two flood hydrograph parameters. The subjective derivation of the peak flood volumefrom the hydrograph record is a probable reason for the poor estimation of its frequency.Sensitivity analysis also showed that the proposed procedure is not very sensitive tothe uncertainty in the values and form of the model parameters. The analysis showed that themethod is the most sensitive to the variation of the mean annual extreme 24-hour rainfall andless or not sensitive at all to the variation of the other parameters.The proposed procedure was applied to a real watershed, the Santa River watershed,along with the most popular regional techniques that were either developed in the course ofthis study or proposed in the literature. The frequency of the hourly and daily peak flows arecompared. The results show that the proposed procedure, the B.C. Environment regional242Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFmethodology (Relcsten, 1987), and the Bayesian methodology (Russell, 1982), give goodresults which fit the observed flow well. It should be mentioned that the other regionaltechniques, the Index Flood, RDP, and DRQ methods, failed to give good results mainlybecause they have been developed for the whole coastal British Columbia but they wereapplied to a watershed on the west coast of Vancouver Island. The response of the watershedslocated in that area is much higher than the response of the other coastal British Columbiawatersheds because they receive large amounts of rainfall from the highly moist frontalstorms. Hence, for this region, probably the equations developed for the extreme conditionsshould be applied. This has been shown with the use of the 95% confidence limit of thedimensionless frequency curve for the Index Flood method. It would be helpful if regionalequations could be developed for the west coast of the Vancouver Island but this is notfeasible because there are only four watersheds in the area with long enough records.In summary, on the basis of the comparison made in this Chapter, it has been shownthat the proposed procedure can be applied to ungauged watersheds in coastal BritishColumbia with very limited data and give results that either are better or comparable to otherregional procedures. The value of this procedure is that it utilizes the results on precipitationdistribution and incorporates these results along with previous results on watershed modelingfor the estimation of flood frequency so that it integrates the findings of the Thesis.243Fig.8.1.Isoplethsofthemeanannual24-hourrainfallinBritishColumbia.(AfterRainfallFrequencyAtlasforCanada,HoggandCarr,1985)t)Fig.8.2.Isoplethsofthestandarddeviationof themeanannual24-hourrainfallinBritishColumbia.(AfterRainfallFrequencyAtlasforCanada,HoggandCart,1985)0•OBSERVEDFLOWHT[EDEVIRUEDLOGNORMALa) U) Ui C) U)90 80 70-60-50-40 30 20 100SIMULATEDUSING24-HOURSTORMxSIMULATEDUSING12-HOURSTORMvSIMULATEDUSING6-HOURSTORMI.IsxxxxxxxVxVV•25102050100RECURRENCEINTERVAL(years)Fig.8.3Comparisonof thefrequencyof theobservedandsimulatedhourlypeakflowusingthe24-hour,the12-hourandthe6-hourstormsfor theCarnationCreekwatershed100z Q90I 380w a-070o60o504OoC-,30w >2010o00TIME(hours)Fig.8.4.CompansonoftheobservedandsimulatedcumulativetimeprobabilitydistributionsforthecoastalBritishColumbia.048121620248tCD-,0.00.3CDCOz0>3IHG)Cl)mIIc’)z0COMPUTEDTIMELAG(hours)--‘C) 0.0)0.0)0Izm•I.0‘.1mCl)z-<mU.IU0mm-•1C.) 0b1ONfTh’UOO7J1ONOLLVWLLSH11O11flI33OM3LLSINII?V1313c1-311SvH301SI3SVgA77V3ISAHJgUChapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFRmRAINFALL SIMULATIONWATERSHED RESPONSESIMULATIONR%KFPeak Hourly Flow Peak Daily Flow Flood Volume+I+/Probability ProbabilityFig. 8.6. Flow chart of the Monte Carlo simulation.INPUTRm‘0RKFmDERIVED DISTRIBUTIONS249Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFFig. 8.7 Map showing the location of the eight coastal British Columbiawhere the proposed procedure has been appliedPACIFIC OCEAN Hirsch Creek AlbertaZeballosOysterCarnationSan Juan0 100 200km U.S.A.250Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFwI00280w 240309U-200160120OBSERVEDSIMULATEDEVI (GUMBEL)LOG-NORMAL8040-ea)10009000a)U)— 7006005004003002001000600e2 5 10 20 50 100• OBSERVEDe SIMULATED b)-— EVI(GUMBEL)— LOG-NORMAL5004003002001000320.2 5 10 20 50 100•OBSERVED• SIMULATED C)EVI(GUMBEL)—— LOG-NORMALe..*.00*I I I I I2 5 10 20RECURRENCE INTERVAL (years)50 100Fig. 8.8. Flood frequency curves for Capilano River watershed.a) hourly flows b) daily flows and c) flood volume.251Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF90.8070OBSERVEDSIMULATEDEV1 (GUMBEL)LOG-NORMAL6050a)64403020 0—IwIC)0wDI.e2 5 10 20 50 100• OBSERVED• SIMULATED b)EV1(GUMBEL) ——— LOG-NORMAL0. I I I I2 5 10 20 50 100. OBSERVED• SIMULATED—e C)EVI (GUMSEL) — ———LOG-NORMAL —0 —0 ——0103228242016128432028024020016012080400 2 5 10 20 50 100RECURRENCE INTERVAL (years)FIg. 8.9. Flood frequency curves for Carnation Creek watersheda) hourly flows b) daily flows and c) flood volume..I.I I252FIg. 8.10. Flood frequency curves for Chapman Creek watersheda) hourly flows b) daily flows and C) flood volume.253Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF- eOBSERVEDSIMULATEDEVI (GUMBEL)LOG-NORMALee — —.a)200180160140120wci3 100806040200110100080w70C-!,60=C)03020180160140w 1203 100800940U-200b)2 5 10 20 50 100• OBSERVED• SIMULATEDEVI(GUMBEL)- —— LOG-NORMAL.—C).2 5 10 20 50 100. OBSERVEDe SIMULATED— EVI (GUMBEL)—— LOG-NORMAL.eee.e0...2 5 10 20 50 100RECURRENCE INTERVAL (years)Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF14001200 -1000 -800 -600 -400 -200900800700g. 600wc. 5004003002001000600Fig. 8.11. Flood frequency curves for Zeballos River watershed.a) hourly flows b) daily flows and C) flood volume..eOBSERVEDSIMULATEDEV1 (GUMBEL)LOG-NORMALw=C)0a)e—• b).02 5 10 20 50 100• OBSERVED. 0 SIMULATEDEVI (GUMBEL)- —— LOG-NORMAL0. 000I I I I I2 5 10 20 50 100• OBSERVEDe SIMULATED c): EVI(GUMBEL) —#—— LOG-NORMAL —wDI500400300200100000..0I I I I2 5 10 20RECURRENCE INTERVAL (years)50 100254Chapter 8, A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF.eOBSERVEDSIMULATEDEVI (GUMBEL)LOG-NORMALa)...••2 5 10 20 50 100200180160- 140120w1008060402001101009080‘—‘ 70w 6050Io 40020100280260240E 220w 200180—I 1601408 1209 100806040b),.0.e0• OBSERVED• SIMULATED-— EVI(GUMBEL)—— LOG-NORMAL2 5 10 20 50 100• OBSERVED° SIMULATED— EVI(GUMBEL)— LOG-NORMALC)-0.0.000e00.2 5 10 20RECURRENCE INTERVAL (years)50 100Fig. 8.12. Flood frequency curves for North Allouette River watershed.a) hourly flows b) daily flows and c) flood volume.2555505000400350Lii30025020015010050Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF4.a)• OBSERVED• SIMULATED— EVI(GUMBEL)—— LOG-NORMALae0e.0Lii=0Cl)450400350300250200150100502 5 10 20 50 100• OBSERVED- b)•SIMULATED -EVI(GUMBEL)— LOG-NORMAL-a00000e200180- 160140>80o 6040200C)—2 5 10 20 50 100• OBSERVEDSIMULATED-— EVI(GUMBEL)— LOG-NORMAL.000•000•2 5 10 20RECURRENCE INTERVAL (years)50 100Fig. 8.13. Flood frequency curves for Oyster River watershed.a) hourly flows b) daily flows and C) flood volume.256Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF.eOBSERVEDSIMULATEDEVI (GUMBEL)LOG-NORMALa)e.eeI I I I I11001000900800,g. 70060050040030020010007006005004003002001000200180160140120100> 800 60402002 5 10 20 50 100• OBSERVED b)• SIMULATEDEVI(GUMBEL)——LOG-NORMALI I I I2 5 10 20 50 100OBSERVED c)* SIMULATEDEVI(GUMBEL)—— LOG-NORMAL.e0I I I I2 5 10 20 50 100RECURRENCE INTERVAL (years)Fig. 8.14. Flood frequency curves for Hirsch Creek watershed.a) hourly flows b) daily flows and C) flood volume.257Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFa)LUC)C,)LUIeOBSERVEDSIMULATEDEV1 (GUMBEL)LOG-NORMAL1bUU160C -1400 -12001000800 -600 -• a)000400140012001000800600400200000.e0.2 5 10 20 50 100• OBSERVED• SIMULATED-—EVI(GUMBEL)— LOG-NORMAL2 5 10 20 50 100• OBSERVEDe SIMULATED CEVJ(GUMBEL)—— LOG-NORMAL28024020016012080400.00I I I2 5 10 20RECURRENCE INTERVAL (years)50 100Fig. 8.15. Flood frequency curves for San Juan River watershed.a) hourly flows b) daily flows and c) flood volume.258Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF100— 9080w 60050I00201038..z’ 3430— 26Ui22x 18C)14106UiDOBSERVED FLOWRmRm-1O%Rm+1O%Rm-20%Rm+20%a).— _.— _.. _I I-.—-.—2 5 10 20 50 100B OBSERVED FLOW b)—Rm- - -- Rm-1O%Rm+1O%—— Rm.20%——• Rm+20%—. I I I2 5 10 20 50 100B OBSERVED FLOOD VOLc)- --- Rm-1O%Rm+1O%—— Rim2O%—•— Rm+20%— ... I I3202802402001601208040.-——2 5 10 20RECURRENCE INTERVAL (years)50 100Fig. 8.16. Sensitivity of the procedure to the change of mean 24-hour rainfalldepth (Rm) for a) hourly flow, b)daily flow and c) flood volumefor Carnation Creek watershed.259Ia)LUC!,0Cl)RECURRENCE INTERVAL (years)Fig. 8.17. Sensitivity of the procedure to the change of standard deviation ofthe 24-hour annual rainfall ) for a)hourly flow, b)daily flowand C) flood volume for Carnation Creek watershed.Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF• OBSERVED FLOW—L’-- L-20%9080706050403020 -10a).b).--—••••I....363228242016128432028024020016012080402 5 10 20 50 100• OBSERVED FLOW-—-----10%---q-20%-.2 5 10 20 50 100• OBSERVED FLOOD VOL—q-----10%. q, +10%-- L-20%——.q+20%LUDIc)———.....••...•2 5 10 20 50 100260Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF9080a, 70C.,w 5040C)ci)10034302622w18z 14C)106228024020016012080400Fig. 8.18.OBSERVED FLOWKFmKFm-1O%KFm+1O%KFm-20%KFm+20%a)50 1002 5 10 20b)• OBSERVED FLOW—KFm- - -- KFm-1O%KFm+1O%—••— KFm-20%—— KFm+20%.•e••.•••.awDc).2 5 10 20 50 100• OBSERVED FLOOD VOL.— KFm- - -- KFm-1O%KFm+1O%—..—• KFm-20%—— KFm+20%..B.BB•_•B.••B—B2 5 10 20 50 100RECURRENCE INTERVAL (years)Sensitivity of the procedure to the change of mean storage factor offast runoff (KFm) for a)hourly flow, b)daily flow and c) flood volumefor Carnation Creek watershed.261Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF110• OBSERVED FLOW a)100-—90- - - -- C=2O%80 -70 -— CcF’35%LiiCV4O%C! 60-50-40-30-20103430C)26w18= 14C.)1062wD3002 5 10 20 50 100• OBSERVED FLOW-— C\3O%- - -- CV=2O%CV,25%--- GcF35%-CV=4O%B2 5 10 20 50 100• OBSERVED FLOOD VOL- — C\(3O%- - -- C=2O%-—— C35%--..-. CO%B- ..B.BB- B..BB••.B•••••B•B.mB..b)C)26022018014010060202 5 10 20 50 100RECURRENCE INTERVAL (years)Fig. 8.19 Sensitivity of the procedure to the change of coefficient of variationof storage factor (CVKF) for a)hourly flow, b)daily flow and c) flood volumefor Carnation Creek watershed.262RECURRENCE INTERVAL (years)Fig. 8.20 Sensitivity of the procedure to the change of mean final infiltrationabstractions (I,j for a) hourly flow, b)dally flow and c) flood volumefor Carnation Creek watershed.Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF• OBSERVED FLOWIIfr•’lO%+10%‘fm +20%a)/U.•2 5 10 20 50 1009080a)Co60w50IC)O 302010322824w20I 160084300__260Eg. 220w1801408 1006020b).• OBSERVED FLOW—‘ftn- - -- I-10%I+10%——•• I+20%.I....•_••c)U2 5 10 20 50 100U OBSERVED FLOOD VOL. ‘fm- - -- I-10%I+10%—— I-20%Ifrfl+2O%. U.•B.....2 5 10 20 50 100263Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCED URE FORTHE ESTIMATION OF FLOOD RUNOFFOBSERVED FLOWCVff =30%CV1f=20%CV =25%CV1=35%CVf=4O%90 -807060504030a,wIC)0a).b)2 5 10 20 50 100• OBSERVED FLOW-— CVK=30%- - - -- OV—20%CV=25%.—— CVw=35%CV=40%.2 5 10 20 50 100•e....•a•••201034302622w18z 14C.)1062300260. 22018014006020C)..• OBSERVED FLOOD VOL-— CV=30%- - -- CV=20%- CV,=25%—— CV=35%--- CV=4O%. ••••••.....•••2 5 10 20 50 100RECURRENCE INTERVAL (years)Fig. 8.21 Sensitivity of the procedure to the change of coefficient of variationof Infil. abstr. (CV ) for a)hourly flow, b)daily flow and c) flood volumefor Carnation Creek watershed.264wC-I,IC)0wIC)02 5 10 20 50 100RECURRENCE INTERVAL (years)Fig. 8.22 Sensitivity of the procedure to the form of procedure parameters fora) hourly flow, b) daily flow and c) flood volume for Carnation Creek watershed.Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFF• OBSERVED FLOW-— BASE SIMULATION- --. CONSTANT KFCONSTANTb—— CONSTANTKF&b- KF LOGNORMALa)—9080706050403020103228242016128428024020016012080400b)••_U•••••2 5 10 20 50 100- • OBSERVED FLOW— BASE SIMULATION---- CONSTANTKFCONSTANTb- CONSTANTKF&b——• KFLOQNORMAL.2 5 10 20 50 100• • OBSERVED FLOW— BASE SIMULATION- - - -- CONSTANT KFCONSTANTb. CONSTANTKF&KFLOGNORMA.••.......wD265500200(‘S 0 1000 j550Q a:20z a: t10a:5 2 10120LENGThOFRECORD(years)Fig.8.23.HomogeneitytestforpeakinstantenousflowforthecoastalBritishColumbiastations.20406080100500!b0050Q 20z.LENGTHOFRECORD(years)Fig.8.24.Homogeneitytestfor peakdailyflowfor coastalBritishColumbiastations..95%Confidencelimit••••••‘.....••bChapter 8. A PHYSICALLYBASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFcdE.5C.)Cl)0o‘8\a) 0.‘S ,CnS0 <S‘S‘SLU LU“S5’ ‘ZZ It)W W C)zzzLI • LUSC-) ‘S‘SW W SQ_ 0D .J d)OSS1 EI I IIt) C) It) CJ It) IS) 0it268Chapter 8. A PHYSICALLY BASED STOCHASTIC-DETERMINISTIC PROCEDURE FORTHE ESTIMATION OF FLOOD RUNOFFSSSSSSSSSSS.SZZLii LiiLL00It)0)Lii UiSSEooCl)oU,8oa) 0>5 =_10<0)‘-,I•I— cz •c—It)C) a)Ui zC)Dt —__11SSI I::I I I I• U C) It) CJ It) It)C., 102691400•OBSERVEDFLOW1300PROPOSEDMETHODpo1200-++BAYESIANMETHOD(RUSSEll..1982)1ioo-xB.C.ENViRONMENTMEflIOD(REKSTEN,1987)x>INDEXFLOODMETHOD1O0O-INDEXFLOODMErHOD-95%x-900-——-RDPMETHODEVDROMETHOD+xw800-C(I,4—----700-600-.--500-+••400-300-$-•x0III25102050100RECURRENCEINTERVAL(years)Fig.827.Comparisonof thefrequencyoftheobservedinstantaneouspeakflowwiththefrequencyofthesimulatedinstantaneouspeakflowusingvariousmethodsforSantaRiver.I...GRECURRENCEINTERVAL(years)Fig.8.28.ComparisonofthefrequencyoftheobserveddailypeakflowwiththefrequencyofsimulateddailypeakflowusingvariousmethodsforSaritaRiver.•OBSERVEDFLOWPROPOSEDMETHOD+BAYESIANMETHOD(RUSSELL,1982)xB.C.ENViRONMENTMETHOD(REKSTEN, 1987)INDEXFLOODMETHODINDEXFLOODMEFHOD-95%——-RDPMETHODvDRQMETHODa, go w C, C) Co900800700600500400300200100 0V—&—ri V—.——H 02IIIII5102050100CHAPTER 9CONCLUSIONS AND RECOMMENDAflONS9.1 ConclusionsThe primary goal of this Thesis is to study the precipitation distribution in the mountainouscoastal British Columbia and to use the results for the development of techniques for thereliable estimation of flood frequency for ungauged watersheds. This goal is achieved bycombining results from each of the Chapters presented in this Thesis. Study componentsinclude the analysis of the long-term and short-term precipitation in two study watersheds, theSeymour River and Capilano River watersheds; generalization of the findings of the analysisto coastal British Columbia; study of extreme historical storms; application of ameteorological model for the estimation of short-term precipitation; and development of aphysically-based stochastic-deterministic procedure which incorporates the findings of theprevious research on precipitation and runoff generation for the estimation of the floodfrequency from ungauged watersheds of the region. To illustrate the continuity between thestudy components, an overview of the results is included below.The background information about the climate of coastal British Columbia and thetopography of the study area have been presented in Chapter 2. It has been shown that mostof the precipitation in the region is generated during winter and fall months from frontalsystems that are developed over the North Pacific Ocean and travel eastward towards the coastof British Columbia.The study begins with the analysis of the distribution of the long-term precipitation,namely annual, seasonal, and monthly and its distribution with elevation. The analysis showsChapter 9. CONCLUSIONS AND RECOMMENDATIONSthat the annual and the wet period October to March precipitation increases with elevation upto about 400 m in the Capilano River watershed whereas the topography of the Seymour Riverwatershed reduces the elevation to about 260 m. The position of the maximum precipitation isthe middle of the watersheds. After that point the precipitation either decreases as in theSeymour River watershed or levels off as in the Capilano River watershed. On the other hand,the dry period April to September precipitation is more uniformly distributed over the studywatersheds and it is not affected by the elevation.The Bergeron two-cloud mechanism has been identified as the mechanism whichgenerates most of the precipitation in the region, and can explain the distinctive precipitationdistribution observed in this study.Another important finding of the study is that the valley and the adjacent mountainslope precipitation is similar at the same distance from the beginning of the mountain region.This result is very significant because most of the precipitation stations are located in theeasily accessible river valleys. However, this distribution pattern has been observed in the twostudy watersheds only for the initial topographic rise because of the absence of high elevationdata in the back range. It is therefore important that high elevation stations should be installedon the mountain slopes beyond the front range in order to confirm or deny the observationsfor the front mountains.Regional precipitation and runoff data were used to examine the generality of thefindings of the study of the precipitation distribution in the two study watersheds. Thisanalysis showed that the initial results of the study are more general and regional in scale, andthat long-term precipitation follows a similar pattern to that in the two study watersheds,increasing up to about 400-800 m elevation and then either leveling off or even decreasing athigher elevations. This finding is very important because it is usually assumed (Barry, 1992)that the precipitation in the mid-latitude mountainous areas increases almost linearly with273Chapter 9. CONCLUSIONS AND RECOMMENDATIONSelevation up to the top elevation. This result has a very strong impact on the design andplanning procedures of water resources of the region.The next step was to study the short-term or storm precipitation in the Seymour Riverwatershed. This short-term precipitation is one of the necessary components of the floodestimation procedures. The analysis of 175 storms for seven stations showed that the averageprecipitation follows a distribution pattern similar to the pattern found in the analysis of thelong-term precipitation. This fmding is very important since in coastal British Columbia onlyabout one third of the existing precipitation stations are recording gauges capable ofmeasuring the short-term precipitation. This preliminary result suggests that the long-termprecipitation may be used as an indicator of the shorter-term precipitation, but further study ofthis issue is necessary. Moreover, the distribution pattern of the storm is not affected by thetype of precipitation, whether rain, rain and snow or snow.A part of the storm precipitation study was the analysis of the time distribution of thestorms. This analysis showed that the storm time distribution is reasonably constant and doesnot vary significantly with the type of precipitation, elevation, storm duration, and stormdepth. Also, examination of regional data from sparsely located coastal British Columbiastations showed that the storm time distribution does not change significantly over the region.This result indicates that the storm time distribution found in this study can be transposed overthe whole region.The final goal of the research program is to find techniques to accurately estimate theflood runoff from ungauged watersheds of the region, even when the data are limited. Toassist in the estimation of flood runoff, the 24-hour design storm has been developed. Thechoice of the 24-hour storm duration was based on climatic, hydrological, and pragmaticreasons. The design storm has been developed with data from the Seymour River watershedand then it has been compared with other regional studies and data. This comparison showed274Chapter 9. CONCLUSIONS AND RECOMMENDATIONSthat the results for the Seymour River watershed do not differ significantly from the regionaldata, so that they can be transposed over the region. An event-based rainfall-runoff simulationwas undertaken for a real watershed, the Santa River watershed on Vancouver Island, andshowed that only the 10% time probability distribution curve and the synthetic SoilConservation Services type IA hydrograph are capable of accurately reproducing the floodhydrograph.Another important finding of this analysis was that the 24-hour annual rainfall of agiven return period is a constant percentage of the mean annual precipitation. This result isvery important because it expands the results of this study both in space and in time sincedaily data is available from the storage precipitation gauges in coastal British Columbia. Alsothere are more storage gauges and they have longer records than the recording gauges. Thisresult also suggests that the extreme 24-hour annual rainfall probably follows a similar patternto that of the annual precipitation which is important for the estimation of the spatialdistribution of the design storm.The above findings for the short-term precipitation were examined for five extremeflood producing historic storms that occurred over the two study watersheds. This analysisshowed that the results of the storm precipitation analysis are valid for the extreme storms,which adds confidence in their use in coastal British Columbia.A theoretically-based meteorological model, the BOUNDP model, was tested to checkwhether it could predict the precipitation distribution and to confirm the results of thestatistical analysis. The model was applied for the mountainous area of the two studywatersheds, Seymour River and Capilano River. From the comparison of the model resultswith the observed precipitation, it was evident that the model is incapable, in its present form,of simulating the large precipitation amounts observed in the mountain areas and ofreproducing the distinct precipitation distribution pattern found in this study. As a result, no275Chapter 9. CONCLUSIONS AND RECOMMENDATIONSattempt was made to use the model for hydrologic modeling of the runoff from thesemountainous watersheds, as was initially intended.The final step of the research program was to develop a technique to estimate the floodfrequency for ungauged watersheds with limited data. This was achieved using the method ofderived distributions and the integration of the previous results of the precipitation analysisand the study of the watershed response. The proposed method is a physically-based methodbecause all its parameters can be estimated by using physical variables, and it is stochastic-deterministic because it uses a deterministic watershed response model which has stochasticparameters, along with a stochastic rainfall generation model.The proposed procedure was applied to eight coastal British Columbia watersheds andcompared with other regional techniques. The results showed that the method is easy toapply, requires very limited data, and is efficient and reliable for determining the hourly anddaily peak flows.In summary, this Thesis examines the distribution pattern of precipitation withelevation; provides regional characteristics of long-term and storm precipitation for estimatinginput precipitation data to a hydrologic model; and proposes a physically-based stochastic-deterministic method for the estimation of flood frequency from ungauged watersheds in thecoastal region of British Columbia.9.2 RecommendationsOne of the most important findings of this study is that precipitation does not continue toincrease linearly with elevation, as has often been assumed (Melone, 1986; Barry, 1992).Consequently, water supply and design floods may both be overestimated if the leveling off276Chapter 9. CONCLUSIONS AND RECOMMENDATIONSand even reduction of precipitation above even modest elevations of about 400 to 800 m is nottaken into account.Clearly, this decrease or levelling off of precipitation at higher elevations is a matter ofsuch high economic importance that considerable effort and expenditure should be made toconfirm or deny this result by gathering additional higher elevation data in the region. Thesedata can be used also in the development and testing of more reliable meteorological modelsof mountainous precipitation.Furthermore, these additional high elevation data can also be used to test anotherfinding of this study, namely that the mountain slope and valley precipitation are similar at thesame position. This finding is very important, and needs to be confirmed by expanding thedata base to assist in the reliable evaluation of the areal precipitation, especially as mostprecipitation stations are located in the river valleys.Another topic for further research is the application of the proposed procedure for theestimation of flood runoff to other areas of the coastal Pacific Northwest. Furthermore, theprocedure could be applied to other areas of different climate from that of the coastal BritishColumbia. This application requires appropriate adjustments in the values of the modelparameters. Also, another potential future application of the procedure is in evaluating theimpact of watershed changes on flood magnitudes and frequencies. This evaluation would beproduced for a given watershed with parameter values representing the modified or futureconditions.A last point which is considered significant for further research is the adaptation of theproposed procedure for the estimation of floods generated by rain on snow events. The focusin this research program was on the rain storm produced floods. Melone (1986) has shownthat rain on snow is the second most important mechanism for the generation of peak flow incoastal British Columbia after the rain storms. Also, Melone proved that the increased277Chapter 9. CONCLUSIONS AND RECOMMENDATIONSresponse of the coastal watersheds to these events is not due to a fundamental change of thewatershed behaviour but it is the result of increased water input from the snowmelt.To incorporate these processes in the proposed procedure, a research program shouldbe set up to study the distribution and variation of the snowpack and temperature withelevation. 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Precipitation Stations in coastal British Columbia.Name Station Elevation Period of RecordNumber* (m)ABBOTSFORD 1100030 58 1944-1980AGASSIZ CDA 1100120 15 1889-1966AIYANISH 1070150 229 1924—1971ALBERNIBC 1030180 91 1894-1959ALBERNI LC 1030210 9 1948- 1974ALBERNI ML 1030220 43 1958—1973ALBERNIRC 1030185 75 1962—1969ALDERGROVE 1100240 76 1953-1980ALERT BAY 1020270 52 1913-1980ALICE ARM 1060330 314 1948—1964ALOUETTE L 1100360 117 1924-1970ALTA LAKE 1040390 668 1950—1976ALTALAKE2 1040420 640 1931—1969AMPHITRITEP 1030425 11 1968—1980BALLENAS LIGHT 1020590 11 1966—1980BAMBERTON OC 1010595 85 1961—1980BAMFIELD EAST 1030605 4 1959-1980BEAR CR 1010720 351 1964-1971BECHER BAY 1010780 12 1956—1966BELLA BELLA 1060810 12 1964-1977BELLA COOLA 1060840 18 1939—1980BELLA COOLA BC H 1060842 14 1961-1980BENSON LAKE 1030850 145 1959-1972BLACK CREEK 1020880 46 1976- 1980BLIND CHANNEL 1020885 3 1956- 1980BONILLA ISL 1060902 16 1960-1980BOWEN ISL AB 1040908 23 1959—1965BOWEN ISL BB 104090R 8 1966—1978BRITANNIAB 1041050 49 1913-1974BUNTZEN LAKE 1101140 17 1969-1980BURNABY BR 1101144 125 1959-1970BURNABY CAPITOL 1101146 183 1960-1980BURNABY MTN 1101155 137 1958-1980BURNABY SFU 1101158 336 1965-1980BURQUITLAM 1101200 61 1926-1975CAMPBELL RIV 1021260 79 1936-1969CAMERON LAKE 1021230 198 1924-1980CAMPBELL RIVA 1021261 105 1965-1980CAMPBELL RIV BCFS 1021262 128 1969-1980CAPE LAZO 1021320 38 1935—1962300APPENDIX ATable Al. Precipitation Stations in coastal British Columbia. (cont.)Name Station Elevation Period of RecordNumber* (m)CAPE SCOTT 1031353 72 1965—1980CAPE ST JAMES 1051350 89 1944—1980CARMANAH POINT 1031402 38 1968—1980CARNATION CREEK CDF 1031413 61 1971-1980CENTRAL SAANICH ISL 10114F6 38 1970-1980CENTRAL SAANICH V 1011467 53 1970-1980CHATHAM POINT 1021480 20 1958-1970CHEMAINUS 1011500 53 1934-1979CHILLIWACK 1101530 6 1950-1980CHILLIWACKGR 1101545 12 1961-1980CHILLIWACKRFCR 1101565 457 1966—1980CFIILLIWACK R MT THURSTON 1101N65 198 1963-1980CHILLIWACK RIV CT 1101564 488 1961-1976CLOWHOM FALLS 1041710 23 1932-1980COAL HARB 1031735 57 1970—1980COBBLE HILL 1011745 61 1970—1980COMOX A 1021830 24 1944-1980COQUITLAM L 1101890 161 1924-1980CORDOVA BAY 1011920 37 1951—1980CORTES ISL 1021950 6 1947—1980CORTES ISL TB 1021960 5 1960-1973COURTENAY 1021990 24 1930-1980COURTENAY GR 1021988 81 1972-1980COWICHAN BAY 1012010 104 1953—1980COWICHAN LAKE F 1012040 177 1949-1980COWICHAN LAKE WEIR 1012055 163 1960-1980CULTUS LAKE 1102220 46 1962—1980CUMBERLAND 1022250 159 1922—1980DAISY LAKE DAM 1042255 381 1968-1980DELTA LADNER SOUTH 1102417 2 1971-1980DELTA PEBBLE 1102420 12 1961-1980DELTA TSAWWASSEN 1102424 53 1959-1969DELTA TSAW. BEAC. 1102425 2 197 1-1980DENMAN ISL 1022430 35 1910-1965DUNCAN BAY 1022560 7 1957-1980DUNCAN FOR 1012570 6 1958—1980EAST SOOKE 1012628 37 1966- 1980EGG ISL 1062646 12 1965- 1980ELK LAKE 1012655 114 1957—1978ESQUIMALT M 1012700 12 1872—1950301APPENDIX ATable Al. Precipitation Stations in coastal British Columbia.(cont.)Name Station Elevation Period of RecordNumber* (m)ESTEVAN POINT 1032730 7 1908—1980ETHELDA BAY 1062745 8 1957—1980FALLS R1V 1062790 18 1931—1980GABRIOLA ISL 1023042 46 1967-1980GALIANO ISL 1013045 15 1956—1977GAMBlER HAR 1043048 61 1962-1980GARIBALDI 1043060 381 1921—1980GIBSONS 1043150 126 1949—1980GIBSONS GP 1043152 34 1961-1980GOLD RIV 1033232 117 1966-1980GRAHAM INLET 1203255 660 1973-1980HANEY CI 1103324 142 1960—1980HANEY EAST 1103326 30 1959-1980HANEY UBC RF SP17 1103334 373 1961-1972HANEY UBC RFA 1103332 143 1961-1980HANEY UBC RFLL 1103333 354 1962-1972HANEY UBC RFM 11OCCCC 114 1945-1972HATZICPR 1103342 9 1959-1976HELLS GATE 1113420 122 1951—1980HOLBERG 1033480 52 1956—1980HOLBERG FD 1033483 46 1967—1980HOLLYBURN RIDGE 1103510 951 1954-1980HOPE A 1113540 39 1935—1980HOPEKL 1113550 152 1955—1977HOPKINS L 1043582 8 1969—1980IOCO REF 1103660 53 1955—1980JAMES ISL 1013720 54 1914-1978KEMANO 1064020 70 1951—1980KENSINGTON PR 1104080 27 1953-1978KILDALA 1064138 30 1966—1980KILDONAN 1034170 3 1972-1976KINGCOME INLET 1064227 2 1974—1985KITIMAT2 1064321 17 1966—1980KITIMAT MISSION 1064290 6 1939—1948K1TIMAT TOWN 1064320 128 1954- 1980KLEENA KL 1084350 899 1942- 1968KYUQUOT 1034440 3 1933—1959LADNER 1104470 1 1952—1971LADNER MSTN 1104477 0 1959-197 1LADNER PG 1104484 0 1960-1975302APPENDIX ATable Al. Precipitation Stations in coastal British Columbia. (cont.)Name Station Elevation Period of RecordNumber* (m)LAKELSE LK 1064497 85 1967—1980LANGARA 1054500 41 1936—1980LANGFORD LAKE 1014530 76 1953-1980LANGLEYL 1104555 101 1957-1980LANGLEY PR 1104560 87 1953-1980LOIS RIV DAM 1044680 131 1954—1956LUND 1044732 14 1960—1975MALIBU JERVIS INLET 1044840 8 1974-1980MASSET 1054920 3 1897—1968MASSET CFS 10549BN 12 1971—1980MAYNE ISLAND 1014931 30 1970-1980MCINNES ISL 1064010 23 1954-1980MERRY ISL 1045100 6 1942-1980MESCHOSIN HV 1015107 76 1968—1980MILL BAY 1015134 46 1972—1980MILNERAIC 1105155 8 1967—1979MILNES LANDING 1015160 38 1910-1956MISSION 1105190 56 1957—1980MISSION WA 1105192 221 1962—1980MOUNT SEYMOUR 1105230 823 1958-1968MUD BAY FRB 1025240 11 1971-1980MUIR CR 1015242 30 1970—1980MULE CR 1205248 884 1970-1980NANAIMO 1025340 70 1892-1980NANAIMO A 1025370 30 1947—1980NANAIMO CHUB 10253P0 21 1969-1980NANAIMO DEP BAY 1025C70 8 1970- 1980NEW WESTMINSTER 1105550 119 1894-1980NEW WESTMINSTER BCPEN 1105553 18 1960-1980NEW WESTMINSTER W 1105570 84 1960-197 1N.VANCOUVER 2ND NAR 1105666 4 1957-1980N.VANCOUVER CAPILANO 1105655 67 1955-1980N.VANCOUVER CLEVELAND 110EF56 157 1968-1980N.VANCOUVER CLOVERL. 11OEFEF 79 1968-1980N.VANCOUVER HOLYROOD 1105659 183 1958-1968N. VANCOUVER LYNN CR 1105660 191 1964-1980N.VANCOUVER RDR 110N6F5 229 1973-1980N.VANCOUVER SEYMOUR 11OEFFF 9 1968-1980N.VANCOUVER UP.LYNN 1105668 177 1960-1980N.VANCOUVER WHARVES 1105669 6 1962-1980303APPENDIX ATable Al. Precipitation Stations in coastal British Columbia. (cont.)Name Station Elevation Period of RecordNumber* (m)N.VANCOUV. GROUSE 1105658 1128 1971-1980OCEAN FALLS 1065670 5 1924—1980OYSTER RIV UBC 1025915 11 1967-1980PACHENA POINT 1035940 46 1924—1980PARKSVILLE 1025970 82 1915—1960PENDERISL 1016120 15 1924—1965PIERS ISL 1016169 0 1973—1980PITT MEADOWSL 1106177 6 1960-1969PITT POLDER 1106180 2 1951—1980POINT ATKINSON 1106200 9 1968—1980PORT ALBERNI 1036205 59 1917—1962PORT ALBERNI A 1036206 2 1969-1980PORT ALBERNI CCR 1036207 70 1960- 1980PORT ALBERNI RED 1036210 21 1947-1980PORT ALICE 1036240 15 1924-1980PORT CLEMENTS 1056250 8 1967-1980PORT COQUITLAM 1106255 7 1958—1980PORT HARDY A 1026270 22 1944-1980PORT HARDY BHR 1026274 5 1959—1975PORT KELLS 1106300 9 1953-1965PORT MELLON 1046330 8 1942-1980PORT MOODY GRFY 1106CL2 130 1970-1980PORT RENFREW BCFP 1016335 6 1970-1980POWELL RIVER 1046390 52 1924-1980POWELL RIVER A 1046391 130 1953-1980POWELL RIVER W 1046410 55 1960-1980PRINCE RUPERT 1066480 52 1908-1963PRINCE RUPERT A 1066481 34 1961-1980PRINCE RUPERT MC 1066488 85 1959-1980PRINCE RUPERT PARK 1066492 91 1959-1980PRINCE RUPERT SH 1066193 11 1966-1980QUALICUM RFR 1026563 8 1962—1980QUATSINO 1036570 8 1895—1980RIVER JORDAN 1016780 3 1908—1980SAANICH DAO 10169DK 223 1916-1977SAANICH DEN 1016942 38 1963—1974SAANICTON CDA 1016940 61 1914—1980SALT SPRING ISL 1016990 73 1945-1980SALT SPRING IV 1017000 7 1955—1980SANDSPIT A 1057050 5 1945—1980304APPENDiX ATable Al. Precipitation Stations in coastal British Columbia. (cont.)Name Station Elevation Period of RecordNumber* (m)SARDIS 1107080 107 1954-1980SAYWARD BCFS 1027114 15 1973-1980SECHELT 1047170 23 1927- 1968SEWALL MASSET IN 105PA91 3 1974-1980SEWELL INLET 1057192 12 1973—1980SEYMOUR FALLS 1107200 244 1927—1980SHAWNIGANL 1017230 137 1918—1980SOOKE 1017556 27 1970—1980SOOKE LAKE 1017560 173 1913-1966SOOKE LAKE N 1017563 229 1966—1980SOUTH PENDER ISLAND 1017610 61 1966-1980SPRING ISL 1037650 11 1949-1979SQUAMISH 1047660 2 1959-1980SQUAMISH FMC CHEMICALS 1047662 3 1968-1980STAVE FALLS 1107680 55 1959-1989STEVENSON 1107710 1 1896-1980STEWART 1067740 5 1926-1967STEWART A 1067742 7 1974- 1980STEWART BCHPA 1067745 12 1967—1976STILLWATER PH 1047770 24 1931-1980STRATHCONA DAM 1027775 201 1967-1980SUMAS CANAL 1107785 6 1957-1980SURREYKP 1107873 93 1960—1980SURREYMH 1107876 76 1962—1980SURREY N 1107878 73 1960—1980SURREY S 1107879 101 1960-1980TAHSIS 1037890 5 1952- 1980TAHTSA LAKE WEST 1087950 863 1951—1980TASU SOUND 1058003 15 1963—1980TATLAYOKO LAKE 1088010 853 1928-1980TERRACE A 1068130 217 1944-1980TERRACE PCC 1068131 58 1968—1980TEXADA ISL 1048140 24 1960-1980TLELL 1058190 5 1950—1980TOFINO A 1038205 20 1942-1980TUNNEL CAMP 1048310 671 1924-1974UCLUELET KENNEDY CAMP 1038330 12 1914-1948VANCOUVER A 1108447 3 1936-1980VANCOUVER CITY H 1108430 86 1924-1980VANCOUVER DUNBAR 1108435 61 1955—1974305APPENDIX ATable Al. Precipitation Stations in coastal British Columbia.(cont.)Name Station Elevation Period of RecordNumber* (m)VANCOUVER HARBOUR 1108446 0 1925-1980VANCOUVER KERRISDALE 1108449 88 1970- 1980VANCOUVER KITSILANO 1108453 34 1956-1980VANCOUVER OAK 53 1108462 82 1970-1977VANCOUVER PMO 1108465 59 1898-1979VANCOUVER SF 1108475 64 1955-1972VANCOUVER SOUTH 1108436 61 1966-1982VANCOUVER UBC 1108487 87 1957-1980VICTORIA A 1018620 19 1940-1980VICTORIAGH 1018614 43 1959-1980VICTORIA GHTS 1018610 69 1898-1980VICTORIA HIGHLAND 1018616 152 1961—1980VICTORIAL 1038640 29 1953—1962VICTORIA MARINE 1018642 32 1967-1980VICTORIA PS 1O1HFEE 8 1973-1980VICTORIA SHELBOURNE 101QF57 38 1964-1974VICTORIA SS 1O1QEFG 21 1961—1973VICTORIA T 1018660 23 1958-1980WANNOCK RIV 1068677 8 1974-1980WHALLEY FN 1108890 84 1958-1980WHITE ROCK 1108910 61 1929- 1970WHITE ROCK STP 1108914 15 1964-1980WHONNOCK 269 ST 1108927 61 1960—1975WHONNOCK HILL 1108925 213 1957-1969WILLIAM HEAD 1018935 12 1959-1980WOODFIBRE 1048974 6 1960-1980W.VANCOUVERD 1108829 2 1971-1980W.VANCOUVER M 1108840 38 1961-1980W.VANCOUVER P 1108846 122 1961-1972YOUBOU 1019010 174 1959-1967*QfficjaI Environment Canada station number306APPENDIX ATable A2. Streamfiow gauging stations in the coastal British Columbia.Station Basin Mean Area (km2) Years of RecordNumber* Elevation (m)ANDERSON CREEK 08MH104 46 27 1965-1987ATNARKO RIVER 08FB006 1024 2430 1965-1988BELLA COOLA RIVER 08FB002 673 310 1948-1968BELLA COOLA R.BBC 08FB007 920 3730 1965-1988BINGS CREEK 08HA016 207 15.5 1961-1988CAMPBELL RIVER O8HDOO1 589 1400 1910-1949CARNATION CREEK 08HB048 765 10.1 1973-1988CHAPMAN CREEK 08GA060 680 64.5 1971-1988CHEAKAMUS RIVER 08GA024 1010 287 1925-1947CHEMAINUS O8HAOO1 644 355 1915-1988ENGLISMAN RiVER 08HB002 828 324 1915-1988HIRSCH CREEK 08FF002 820 347 1966-1988JACOBS CREEK 08MH108 483 12.2 1966-1978KANAKA CREEK 08MH076 168 47.7 1960-1988KEMANO RIVER 08FE002 912 583 1972- 1988KITIMAT RIVER O8FFOO1 960 1990 1967—1988KOKISH RIVER O8HFOO1 799 290 1927-1941KOKSILAH RIVER 08HA003 493 209 1960- 1988LITTLE WEDEENE R. 08FF003 855 188 1967-1988MACKAY CREEK 08GA061 497 3.63 1974—1988MAHOOD CREEK 08MH020 35 16 1927- 1974MAHOOD CREEK 08MH018 34 18.4 1927-1985MAMQUAM RIVER 08GA054 911 334 1967-1986MURRAY CREEK 08MH129 50 26.2 1970-1982NICOMEKL RIVER 08MH105 29 64.5 1966-1984NIMPKISH RIVER 08HF002 802 1760 1928-1935NOONS CREEK MD 08GA065 382 2.59 1977-1988NOONS CREEK PM 08GA052 253 4.4 1965-1975NORRISH CREEK 08MH058 598 117 1960-1988NORTH ALLOUETTE R. 08MH006 478 37.3 1961-1988NUSATSUM RIVERF 08FB005 897 269 1966- 1988OYSTER CREEK O8HDO11 701 298 1974-1988PALLANT CREEK 08DB002 519 76.7 1968-1987RUBBLE CREEK 080A023 673 74.1 1925-1934SALLOOMT RIVER 08FB004 883 161 1965—1988SAN JUAN RiVER O8HAO1O 414 580 1960— 1988SARITA RIVER 08HB014 442 162 1950—1988SLESSE CREEK 08MH056 1104 162 1957—1988STAWAMUS RIVER 08GA064 785 40.4 1972-1988307APPENDIX ATable A2. Streamfiow gauging stations in the coastal British Columbia.(cont.)Station Basin Mean Area (km2) Years of RecordNumber Elevation (m)TSABLE RIVER 0811B024 681 113 1961—1988TSITIKA RIVER 08HF004 792 360 1975—1988UCONA RIVER 08HC002 589 185 1957—1988YAKOUM RIVER 08DA002 351 477 1963—1987YORKSON CREEK 08MH097 43 5.96 1965-1977ZEBALLOS RIVER 08HE006 725 181 1960-1988ZYMOETZ RIVER 08EF005 858 2980 1964-1988ZYMOETZ RIVER TER. 08EF003 549 100 1953-1963*Qfficjaj Environment Canada station number308APPENDIX BRELATIONSHIP BETWEEN EXTREME 24-HOUR RAINFALL ANDMEAN ANNUAL PRECIPITATION3CAPPENDIX BTable Bi. Characteristics of the sixty—one stations used in the analysisof the 24—hour extreme rainfall.24-hour Extreme RainfallReturn PeriodMean annual Station (mm)Station Precipitation Elevation 2 5 10 25 50 100(mm) (m)ABBOTSFORD A 1562.9 58 61.7 77.8 88.3 101.8 111.6 121.4AGASSIZA 1727.8 15 73 88.6 98.9 111.8 121.4 131ALLOUETE LAKE 2775.3 117 97.7 117.6 130.8 147.6 159.8 172.1ALTA LAKE 1415.4 668 43 56.2 64.8 75.8 84 92.2BEAR CREEK 3513.9 351 141.8 205.2 247.2 300.2 339.4 378.5BELLA COOLA H 2109.3 14 88.3 113.8 130.6 151.9 167.5 183.1BUNTZEN LAKE 2909.5 17 111.4 151 177.4 210.5 235.2 259.7BURNABY MTN BCHPA 1908.9 465 75.1 89.8 99.6 111.8 121 129.8CAMPBELL R. BCFS 1655.9 128 54 65.3 73 82.6 89.8 96.7CAMPBELL R.A. 1409.1 106 60 67.2 76.8 84 91.2 96CAMPELL RIVER BC. 1406 30 60 69.8 76.3 84.5 90.7 96.7CARNATION CREEK 2770.3 61 91.9 119 137.3 159.8 176.9 193.7CHILLIWACK MICR. 1850.5 229 55.2 66.5 73.9 83.5 90.5 97.4CLOWHOM FALLS 2230 23 78 92.9 102.7 115.2 124.3 133.4COMOX A 1187.6 24 58.1 69.4 77 86.4 93.6 100.6COQUITLAM LAKE 3616 161 143.8 174.5 194.6 220.3 239.3 258.2COURTENEY PUNTL. 1464.7 24 66.2 84.5 96.7 112.1 123.4 134.6DAISY LAKE DAM 2054.2 381 66.2 78.7 87.1 97.7 105.4 113ESTEVAN POINT 3180.6 7 131 168.2 193 223.9 247.2 270HANEY MICR. 1763.9 320 78.7 97 109 124.3 135.6 146.9HANEY UBC 2183.5 143 89.3 111.8 126.7 145.4 159.4 173.3HOPE A 1915.7 39 86.4 120 144 165.6 187.2 208.8KITIMAT 2740.1 17 88.8 109.7 123.6 141.1 154.3 167LADNERBCHPA 981.7 2 43.2 56.2 64.6 75.6 83.5 91.4LANGLEY LOCHIEL 1482.2 101 61.2 75.6 85.2 97.2 106.3 115.2MISSION WEST A. 1841.5 221 72.5 85.4 94.1 105.1 113 121.2NANAIMO DEP.BAY 955.6 8 41.3 50.4 56.4 64.1 69.8 75.4N.VANC.LYNN CR. 2695.7 191 120.2 156.5 180.5 211 233.5 255.8PITT MEADOWS STP 1804.7 5 67.7 85.7 97.4 112.6 123.8 134.9PITT POLDER 2326.2 2 98.9 119 132.2 149 161.5 173.8PORT ALBERNI A 1886 2 87.1 108.5 122.9 140.9 154.3 167.5P. COQUITLAM CITY 1930.9 7 81.1 96.7 107 120 129.6 139.2PORT HARDY 1870.6 22 89.5 116.6 134.6 157.4 174.2 190.8PORT MELLON 3307.1 8 142.6 176.6 199.4 222.8 249.4 270.2PORT MOODY G. 1889.3 130 84.5 105.4 119 136.3 149 161.8PORT RENFREW BCFS 3943.2 3 168 197.3 217 241.4 259.7 277.9PRINCE RUPERT A 2551.6 34 89.5 112.3 127.7 146.6 161 175310APPENDIX BTable B 1. Characteristics of the sixty—one stations used in the analysisof the 24—hour extreme rainfall. (cont.)24-hour Extreme RainfallReturn PeriodMean annual Station (mm)Station Precipitation Elevation 2 5 10 25 50 100(mm) (m)SAANICH DENSMORE 928.4 38 49.4 67 78.5 93.1 103.9 115SANDSPIT A 1359.1 5 52.1 59.8 65 71.3 76.1 80.9SEYMOUR 21A 3291.6 640 124.4 161.5 185.9 209.7 240.2 263.3SEYMOUR 25B 3256.6 762 131.7 170.7 196.9 221.3 253.6 278SEYMOUR ELBOW CR 3427.4 305 114 144.5 164 183.5 208.5 226.8SPRING ISLAND 3155.1 11 121.7 156.7 179.8 209 230.9 252.5STAVE FALLS 2296.8 55 83.8 106.3 121.4 140.4 154.3 168.2STRATHCONA DAM 1381.2 201 61.7 88.1 105.4 127.4 143.8 160.1SURREY KWANTLEN P. 1574.6 93 67.9 89.3 103.4 121.4 134.9 148.1SURREY MUNICIPAL H. 1355.9 76 55.4 68.4 77 87.8 96 103.9TERRACE A 1295.3 217 55.7 79.4 95.3 115.2 129.8 144.5TERRACE PCC 1136.9 58 43.9 58.8 68.6 81.1 90.2 99.4TOFINO A 3295.4 20 128.2 157 176.4 200.6 218.6 236.6VANCOUVER A 1167.4 3 62.2 75.8 85 96.2 104.6 113.3VANCOUVER HARBOUR 1540.3 0 52.8 66.5 75.4 86.6 95 103.4VANCOUVER KITS. 1367.1 23 60.2 76.3 86.9 100.1 110.2 120VANCOUVER PMO 1588.9 59 68.6 94.3 111.6 133 149 164.9VANCOUVER UBC 1288.6 87 57.8 74.2 85.2 98.9 109 119VICT. GONZALES H. 619.2 69 45.1 63.8 76.3 91.9 103.7 115.2VICTORIA INT.A 857.9 19 49.4 63.1 72.2 83.8 92.4 101VICTORIA MARINE R. 1226.9 32 64.8 84.5 97.4 114 126.2 138.5VICTORIA SHELBOURNE 790 38 44.9 61.7 73 87.1 97.4 108VICTORIA UVIC 708.2 46 49.9 67.7 79.7 94.6 105.6 116.6WHITE ROCK STP 1098.2 15 50.4 64.8 74.4 86.6 95.5 104.6311180170160150140130-J120-J110z 100 90 80c’J70 60 50 40 30 20R24=0.040R2=0.886SEE=1O.4mm.aaBU.1I.••I.I•2-YEAR24-HOURRAINFALL____REGRESSIONUNEIIIIIIIItI6001000140018002200260030003400MEANANNUALPRECIPITATION(mm)Fig.Bi.Relationshipofthe2-year24-hourrainfallandmeanannualprecipitationforthesixty-onerecordingstationsincoastalBritishColumbia.3800220210200190180170p160150-j :140z100C’J90 80 70 60 50 40 30MEANANNUALPRECIPITATION(mm)Fig.B2. Relationshipofthe5-year24-hourrainfallandmeanannualprecipitationforthesixty-onerecordingstationsincoastalBritishColumbia....1R24—0.050PR2=0.847SEE=15.3mm.. IU•••I•1.1•U•I.•UI••IU•5-YEAR24-HOURRAINFALL____REGRESSIONUNEIIIIII60010001400180022002600300034003800-J-J zFig.B3. Relationshipofthe10-year24-hourrainfallandmeanannualprecipitationfor thesixty-onerecordingstationsincoastalBritishColumbia.260-240-220200180-160140-120-100— 80-60-40 20R24—0.057FR2=0.815SEE=19.4mmB•BB••..IIaB•aB•I ..I•B•B••••10-YEAR24-HOURRAINFALL____REGRESSIONUNEII•.•IIIIIIIII60010001400180022002600300034003800MEANANNUALPRECIPITATION(mm)-J-J zR24=0.066PR2=0.776SEE=24.6mm.320300280260240220200180160140120100 80 60 40....•:I.••••.II25-YEAR24-HOURRstJNFA1i____REGRESSIONUNE60010001400180022002600300034003800MEANANNUALPRECIPITATION(mm)Fig.B4.Relationshipofthe25-year24-hourrainfallandmeanannualprecipitationforthesixty-onerecordingstationsincoastalBritishColumbia.R24=0.073P-R2=0.762SEE=28.6mmI360340320300280__260E 240 220LI.. z200140 120100 80 60 40C’B•B.I..I..B•II••I.I III.I.•600I50-YEAR24-HOURRAINFALL____REGRESSIONUNEIIIIIIIIIIIII10001400180022002600300034003800MEANANNUALPRECIPITATION(mm)Fig.B.5Relationshipofthe50-year24-hourrainfallandmeanannualprecipitationfor thesixty-onerecordingstationsincoastalBritishColumbia.-J-J z 2R24—0.079PR2=0.741SEE=32.8mm400350300250200-150-100 50 0..I..II•1II.”.I.II:..I•100-YEAR24-HOURRPJNFALL____REGRESSIONUNEIIIIIIIIIIIIIII60010001400180022002600300034003800MEANANNUALPRECIPITATION(mm)Fig.86.Relationshipofthe100-year24-hourrainfallandmeanannualprecipitationforthesixty-onerecordingstationsincoastalBritishColumbia.APPENDIX CCHARACTERISTICS OF THE 44 BASINS USED FOR THE TESTING OFTHE MODIFIED SNYDER FORMULA3APPENDIX CTable Cl. Characteristics of the basins used in theindependent test of the modified Snyder formula*.Basin Time Lag Area Length Str.Slope(h) (km2) (km) (mim)1 0.083 0.08 0.372 0.04892 0.167 0.21 0.656 0.03993 0.117 0.05 0.432 0.05444 0.283 0.44 1.2 0.02745 0.025 0.005 0.109 0.09786 0.05 0.01 0.205 0.08537 0.315 0.1 0.445 0.01518 0.443 1.17 1.76 0.01299 0.476 0.34 0.646 0.006610 0.436 0.18 0.838 0.005411 1.87 3.91 3.03 0.005112 1.81 4.01 2.7 0.005813 0.625 0.36 0.579 0.00614 1.9 18.5 7.96 0.005315 0.24 0.31 0.969 0.006516 0.31 1.22 1.36 0.03717 0.286 0.75 1.52 0.011518 0.117 0.03 0.206 0.062519 0.419 1.35 1.76 0.020320 0.116 0.1 0.305 0.047521 0.267 0.7 0.997 0.021722 0.417 1.4 2 0.007623 0.139 0.012 0.173 0.014124 0.165 0.011 0.178 0.014825 1.42 7.8 6.58 0.00626 0.636 1.94 2.74 0.00527 8.3 109 18.5 0.0030228 6.4 58.8 8.21 0.0057429 9 324 24.2 0.0021730 9.3 89.1 19.5 0.0048531 7.4 259 21.6 0.0067132 9.5 165 30.3 0.0043533 10.8 59.6 11.7 0.0026834 6.9 85.5 16.4 0.0067735 19.6 124 27.5 0.0015336 13.5 132 19.8 0.0012137 24 1210 97.4 0.0034319APPENDIX CTable Cl. Characteristics of the basins used in theindependent test of the modified Snyder formula*. (cont.)Basin Time Lag Area Length Str.Slope(h) (km2) (krn) (rn/rn)38 22 1650 77.2 0.004639 22 824 24.1 0.002540 13 1130 85.3 0.004141 40 5850 196 0.001442 21.5 839 61.2 0.004543 13 642 48.3 0.008344 10 210 34.9 0.0058* Data from Watt and Chow, 1985320

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