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A study of the grid square method for estimating mean annual runoff 1970

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A STUDY OF THE GRID SQUARE METHOD FOR ESTIMATING MEAN ANNUAL RUNOFF by WILLIAM OBEDKOFF B.A.Sc, University of B r i t i s h Columbia, 1967 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of C i v i l Engineering We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1970 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s thesis for s c h o l a r l y purposes may be granted by the Head of my Department or by h i s representatives. I t i s understood that copying or p u b l i c a t i o n of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of C i v i l Engineering The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada - i i i - ABSTRACT With the increasing importance of network planning f or water resource management and inventory of supply of water there i s need f o r new a n a l y t i c a l methods of estimating flows from sparsely gauged regions. A new approach to estimating mean annual runoff was proposed by Solomon et al. and reported i n "Water Resources Research" j o u r n a l , Volume 4, October 1968. In this technique both meteorological and h y d r o l o g i c a l information are used to assess the mean annual p r e c i p i t a t i o n , temperature and runoff d i s t r i b u t i o n over large areas. The study area i s broken up i n t o a large number of squares and physiographic parameters are determined for each square; a v a i l a b l e meteorological data are used to derive multiple l i n e a r regression equations which r e l a t e p r e c i p i t a t i o n and temperature to physiographic parameters and from these equations p r e c i p i t a t i o n , temperature and evapo- r a t i o n are estimated for each square; runoff i s obtained by subtracting evaporation from p r e c i p i t a t i o n f o r each square and the runoff from a l l the squares i s summed to obtain an estimate of the runoff f o r the e n t i r e basin; i f the computed runoff disagrees with the recorded runoff, the p r e c i p i t a t i o n for each square i s adjusted and the procedure i s repeated u n t i l the com- puted runoff approaches the observed runoff to the desired degree. The method has already been applied to a region i n B r i t i s h Columbia with promising r e s u l t s . In the following study, use of the a v a i l a b l e basic data have been made to develop a seasonal estimate approach to the " g r i d square" method and i n p a r t i c u l a r to consider the evaporation component and the possible incorporation of snow course data, two components which have not yet been adequately developed for use i n the method under B r i t i s h - i v - Columbia conditions. Considering the evaporation component, i t was found that apart from Turc's formula, used i n the o r i g i n a l g r i d square method, the Thornthwaite evapotranspiration method was the only other p r a c t i c a l method f o r estimating evapotranspiration over wide areas as required by the g r i d square method. An attempt at an independent comparison of the two methods on an evaporation basis alone proved to be inconclusive due to the lack of adequate data but a comparison i n actual computer t r i a l s of the g r i d square method showed that on basis of the f i r s t estimate of runoff d i s t r i b u t i o n the Thornthwaite approach gave s i g n i f i c a n t l y better r e s u l t s . To incorporate the snow course data i n t o the g r i d square method several approaches were taken i n which an attempt at estimating on a seasonal basis the melt p r i o r to A p r i l 1st, the date of snow surveys, was un- successful but showed i n s i g n i f i c a n t melt which was subsequently ignored and an attempt at estimating annual p r e c i p i t a t i o n at snow courses to .• supplement the meteorological s t a t i o n data was also unsuccessful. However, an attempt i n which the snow course data was added to a segregated winter p r e c i p i t a t i o n estimate at the meteorological stations proved to be successful and gave a small but s i g n i f i c a n t improvement to the f i r s t estimate of regional p r e c i p i t a t i o n and runoff d i s t r i b u t i o n thus amplifying the p o t e n t i a l use of snow course data i n supplementing meteorological data f o r defining more c l e a r l y the regional v a r i a t i o n of p r e c i p i t a t i o n . - V - TABLE OF CONTENTS PAGE NO. CHAPTER 1 INTRODUCTION 1 CHAPTER 2 GRID SQUARE METHOD 2.1 Description of the Method 4 2.2 UBC Tri p 7 2.3 Data Used i n Grid Square Method 8 CHAPTER 3 EVAPORATION 3.1 Introduction 11 3.2 Comparison of Evaporation Methods 15 CHAPTER 4 SNOW 4.1 Snow Courses 20 4.2 Melt P r i o r to Snow Survey 20 CHAPTER 5 EXPERIMENTAL GRID SQUARE METHOD 5.1 Programming 24 5.2 Estimation of the Temperature D i s t r i b u t i o n 25 5.3 Estimation of the P r e c i p i t a t i o n D i s t r i b u t i o n 26 5.4 Estimation of the Runoff D i s t r i b u t i o n . . . 28 5.5 Incorporation of Snow Course Data 32 CHAPTER 6 CONCLUSIONS 39 REFERENCES 42 - v i - LIST OF APPENDICES PAGE NO. APPENDIX A DATA Figure A - l South Thompson River Basin and Hydro- meteorological Stations 44 Figure A-2 Grid Square Layout.. 45 Table A - l Meteorological Station Data and Snow Course Data 46 Table A-2 Grid Square Physiographic Data 48 Table A-3 Grid Square Sub-Basin Areas 52 APPENDIX B MONTHLY REGRESSION EQUATIONS FOR THE THORNTHWAITE APPROACH OF THE GRID SQUARE METHOD B . l Estimation of Monthly Temperature D i s t r i b u t i o n 56 B.2 Estimation of Monthly P r e c i p i t a t i o n D i s t r i b u t i o n . . . . . 57 B.3 Estimation of Monthly P r e c i p i t a t i o n D i s t r i b u t i o n 58 APPENDIX C COMPUTER PROGRAMS Program C - l Comparison of Thornthwaite's and Turc's Evaporation Methods 60 Program C-2 Snow-Melt Model and Plot 66 Program C-3 Experimental Grid Square Method 71 Program C-4 Experimental Grid Square Method With Snow Courses Added 78 APPENDIX D TRANSLATION OF THE RESUME OF THE PAPER, "CALCUL DU BILAN DE L'EAU, EVALUATION EN FONCTION DES PRECIPITATIONS ET DES TEMPERATURES" BY L.C. TURC 85 - v i i - LIST OF TABLES TABLE TITLE PAGE NO. 3.1 Preliminary Comparison of Turc and Thornthwaite Evaporation Methods 16 3.2 Programmed Comparison of Turc and Thornthwaite Evaporation Methods 17 3.3 Carrs Landing Study Comparison 18 5.1 F i r s t Runoff Estimates Using Turc's Method 29 5.2 F i r s t Runoff Estimates Using Thornthwaite's Method 30 5.3 F i r s t Runoff Estimates Using Thornthwaite's Method With Winter Season P r e c i p i t a t i o n Estimates 36 5.4 F i r s t Runoff Estimates Using Thornthwaite's Method With Snow Courses Added to the Winter Season P r e c i p i t a t i o n Estimates 37 - v i i i - ACKNOWLEDGMENT The author wishes to express h i s sincere thanks to Mr. S.O. Ru s s e l l for h i s guidance throughout the course of work of this study and his valuable c r i t i c i s m during the write up. The author also wishes to thank T. Ingledow and Associates for providing the data f o r t h i s study, without which the study could not have been accomplished. - 1 - CHAPTER 1 INTRODUCTION With the increasing importance of long range planning f o r water resources development there i s an urgent need for an inventory of the available supply of water. However, i n B r i t i s h Columbia there are very few water sheds which are adequately gauged. This r e s u l t s mainly from the s i z e and d i v e r s i t y of the province but also to some extent from the fac t that there has been l i t t l e r egional network planning and i n general the network j u s t "grew" to meet immediate needs. Obviously, i t would be very useful to be able to r e g i o n a l i z e hydrologic information i n B r i t i s h Columbia to reduce the need for stream gauging stations which have high c a p i t a l costs. Unfortunately most a v a i l a b l e r e g i o n a l i z i n g techniques are either not applicable due to the shortage of data or inadequate for the rugged t e r r a i n which p r e v a i l s i n most of B r i t i s h Columbia. Hence, there i s need for new a n a l y t i c a l methods of estimating flows from sparsely gauged regions. A new approach to estimating mean annual runoff was proposed by Solomon et a l . and reported i n "Water Resources Research" .journal, V o l . 4, October 1968. In t h i s technique both meteorological and h y d r o l o g i c a l i n f o r - mation are used to assess the mean annual p r e c i p i t a t i o n , temperature and runoff d i s t r i b u t i o n over large areas. The study area i s broken up into a large number of squares and physiographic parameters are determined f o r each square; a v a i l a b l e meteorological data i s used to derive multiple l i n e a r regression equations which r e l a t e p r e c i p i t a t i o n and temperature to physiographic parameters and from these equations p r e c i p i t a t i o n s temperature - 2 - and evaporation are estimated f o r each square; runoff i s obtained by subtracting evaporation from p r e c i p i t a t i o n f o r each square and the runoff from a l l the squares i s summed to obtain an estimate of the runoff f o r the entir e basin; i f the computed runoff disagrees with the recorded runoff, the p r e c i p i t a t i o n f or each square i s adjusted and the procedure i s repeated u n t i l the computed runoff approaches the observed runoff to the desired degree. A summary of the method i s given i n Chapter 2 and a more de t a i l e d d e s c r i p t i o n i s given i n Reference 3. An attempt has already been made to apply the method to a region i n B r i t i s h Columbia (Reference 3) with promising r e s u l t s and i t i s planned to use the method to estimate the a r e a l v a r i a t i o n of runoff i n the N i c o l a - Kamloops area as part of a comprehensive study of water resources i n B r i t i s h Columbia now under way i n the Department of C i v i l Engineering at the Un i v e r s i t y of B r i t i s h Columbia. However, there are two p o t e n t i a l weaknesses which need to be c a r e f u l l y assessed before the method i s widely used i n B r i t i s h Columbia. One i s the use of Turc's formula, a widely used empirical formula for evaporation but one which has not yet been v e r i f i e d f or B r i t i s h Columbia conditions. The other p o t e n t i a l weakness i s that the p r e c i p i t a t i o n equation i s defined f o r the whole basin only on the basis of e x i s t i n g p r e c i p i t a t i o n data. In B r i t i s h Columbia nearly a l l meteor- o l o g i c a l stations are located i n the v a l l e y s whereas most of the pre- c i p i t a t i o n occurs i n the mountains. An obvious improvement would be to use snow course data which give p r a c t i c a l l y the only information on p r e c i p i t a t i o n at the higher elevations. The aim of th i s study i s to develop a seasonal estimate approach to - 3 - the Solomon or " g r i d square" method and i n p a r t i c u l a r to consider the evaporation component and the possible incorporation of snow course data into the method. An attempt to apply the g r i d square method to the South Thompson drainage area has been made by T. Ingledow and Associates as part of a study of hydrometric network planning i n B r i t i s h Columbia and the b a s i c data have been made a v a i l a b l e (Reference 3). Since assembly of the b a s i c data f o r each of the g r i d squares involves considerable e f f o r t i t was decided to make use of the a v a i l a b l e data and use the South Thompson area as the test area f o r the study. Chapter 2 describes the g r i d square method, gives d e t a i l s of the s i z e and number of squares, the type of physiographic data considered and describes the adaption of the method to the a v a i l a b l e computing f a c i l i t i e s at U.B.C. In Chapter 3 a review of l i t e r a t u r e establishes the Thornthwaite method as the only o t h e r r p r a c t i c a l method of estimating evapotranspiration within the scope to which evapo- r a t i o n methods are used i n the g r i d square method (water balance approach i n which runoff i s equivalent to p r e c i p i t a t i o n minus evapotranspiration) and an attempt i s described to make an independent comparison of the Turc and Thornthwaite methods on an evaporation bas i s . Chapter 4 describes an attempt to estimate the melt p r i o r to A p r i l 1st, the date of snow surveys (snow course data), and shows that the snow melt model assumed was inadequate on a seasonal basis but that the melt was i n s i g n i f i c a n t . Chapter 5 de- scribes the t r i a l runs of the experimental g r i d square method i n which both the Turc and Thornthwaite evaporation approaches are compared on the basis of the f i r s t estimate of runoff and i n which the snow course data are incorporated. The r e s u l t s are discussed throughout the course of the text and recommendations f o r further work are given where appropriate. F i n a l conclusions are given i n Chapter 6. - 4 - CHAPTER 2 GRID SQUARE METHOD 2.1 Description of the Method In the o r i g i n a l g r i d square method the study area i s f i r s t divided into a g r i d consisting of a se r i e s of uniform squares, the s i z e of which determines to a large extent the accuracy of the representation. (A f i n e r g r i d would r e s u l t i n greater accuracy on the one hand, but would increase computer costs of extracting and processing information on the other hand.) Physiographic data for each square are then extracted from a v a i l a b l e maps and c l i m a t o l o g i c a l data f o r meteorological stations are obtained from ava i l a b l e published records. Physiographic data are also determined f o r each meteorological s t a t i o n . The g r i d system permits the storage and r e t r i e v a l of basic data f o r future processing by means of simple computer operations. The c h a r a c t e r i s t i c s of the o v e r a l l area or sub-basins can be obtained by combining the c h a r a c t e r i s t i c s of each square which l i e s wholly or p a r t i a l l y within the boundaries of the drainage area. The procedure for the i t e r a t i v e computation to develop equations for mean annual runoff at any point within a basin i s summarized as follows: (1) E s t a b l i s h a preliminary r e l a t i o n s h i p between mean annual p r e c i p i t a t i o n at meteorological stations and the corresponding physiographic parameters by a standard l i n e a r multiple regression technique. (2) S i m i l a r l y , e s t a b l i s h a r e l a t i o n s h i p for mean annual temperature at meteorological s t a t i o n s . (3) Compute evaporation as a function of p r e c i p i t a t i o n and temperature (using a formula such as that derived by Turc) for each square. - 5 - (4) Make an i n i t i a l estimate of runoff f o r each square i n the study area by estimating p r e c i p i t a t i o n (Step 1), evaporation (Steps 2 and 3) and subtracting evaporation from p r e c i p i t a t i o n . (5) Compute the mean annual runoff f o r the drainage area above the streamflow gauging s t a t i o n by summing runoff of each square w i t h i n the watershed. (6) Compute f o r the o v e r a l l drainage basin the r a t i o _ recorded mean annual runoff computed mean annual runoff (7) Adjust the p r e c i p i t a t i o n value f o r each square by the following formula: P r e c i p i t a t i o n (adjusted) = (K)(R^) + E 1 where R^ represents runoff and E^ represents evaporation obtained from the previous estimates. (8) Using the adjusted value of p r e c i p i t a t i o n f o r each square and the p r e c i p i t a t i o n data at meteorological s t a t i o n s , e s t a b l i s h a new c o r r e l a t i o n between p r e c i p i t a t i o n and physiographic parameters with the meteorological s t a t i o n data given a weight ten times that given to the estimated p r e c i p i t a t i o n i n each square. (9) Compute a second estimate of runoff f o r each square as i n Step 4. (10) Compute a new value of K by repeating Steps 5 and 6. (11) Re-iterate steps 7, 8, 9 and 10 u n t i l a value of K as close to unity as p r a c t i c a b l e i s obtained. (12) Obtain the f i n a l regression equation between mean annual p r e c i p i t a t i o n and physiographic parameters by repeating steps 7 and 8. - 6 - (13) Correlate the f i n a l estimate of the runoff i n each of the squares with the physiographic c h a r a c t e r i s t i c s to e s t a b l i s h a f i n a l equation r e l a t i n g runoff to physiographic parameters. At t h i s stage, a d d i t i o n a l physiographic parameters such as area of lakes, which may be correlated with runoff, can be introduced in t o the regression a n a l y s i s . The i t e r a t i v e technique described above can only be applied when the gr i d square method gives a good r u n o f f - d i s t r i b u t i o n and a l l sub-basins are either overestimated or underestimated. Thus when i t e r a t i o n i s applied i n these cases the new estimate of sub-basin runoff would approach the actual values with each i t e r a t i o n . For cases i n which the f i r s t estimate gave both p o s i t i v e and negative sub-basin e r r o r s , i t e r a t i o n would increase some sub-basin errors as i t decreased the o v e r a l l basin error by v i r t u e of step 7, above. To circumvent t h i s s i t u a t i o n the i t e r a t i v e technique could be adjusted to compute sub-basin K r a t i o s and apply these i n d i v i d u a l r a t i o s to adjust the p r e c i p i t a t i o n i n each square of the respective sub-basin. The errors of runoff estimates w i l l then decrease i n each sub-basin as w e l l as i n the o v e r a l l basin with each i t e r a t i o n . I t e r a t i o n i n this sense i s a useful t o o l , i n that, a l l a v a i l a b l e hydrologic information i s e f f i c i e n t l y used and successive runs tend to eliminate some of the inherent errors i n the regression technique as w e l l as errors of measurement i n meteorological observations. The main strength of the g r i d square method l i e s i n the simultaneous use of meteorological and hydrometric data, two types of data that have - 7 - not previously been used together. The method also has the advantage that i t makes use of d i r e c t c o r r e l a t i o n of meteorological data with physiographic data for each square rather than average values f o r e n t i r e basins. I t can thus cope with p h y s i c a l l y diverse regimes, an important consideration i n an area such as B r i t i s h Columbia. Another advantage of the method i s that the process of determining the physiographic character- i s t i c s and compiling the hydrologic estimates for each square provides an extremely simple computerized method of information storage and re- t r i e v a l f o r large drainage areas. The method, however, has the disadvantage that when there are large errors i n the f i r s t estimate of flows, the p r e c i p i t a t i o n i n each square has to be adjusted and the i t e r a t i o n process destroys the s t a t i s t i c a l independence of the f i r s t estimate. The only meaningful c o r r e l a t i o n i s that of the f i r s t multiple c o r r e l a t i o n of temperature and of p r e c i p i t a t i o n ; a l l subsequent c o r r e l a t i o n s are s t a - t i s t i c a l l y meaningless because they are derived from functions which have already been defined by a l e a s t squares f i t . Standard s t a t i s t i c a l tests therefore cannot be applied. However, the p h y s i c a l meaning of t h i s approach can be preserved i f an independent check i s made of the a r e a l d i s t r i b u t i o n of runoff by comparing the computed values with those measured i n the sub- basins of the t o t a l basin. 2.2. UBC T r i p The U n i v e r s i t y of B r i t i s h Columbia Computing Center, i n one of t h e i r many computer se r v i c e s , provides a subroutine package (Reference 2 ) , c a l l e d UBC T r i p , which performs a series of s t a t i s t i c a l tests and manipulations on observed data. One of the routines, c a l l e d Stpreg, i n t h i s package makes use of a standard stepwise regression technique f o r l i n e a r multiple - 8 - c o r r e l a t i o n a n a l ysis. During the regression analysis Stpreg considers the s i g n i f i c a n c e of each independent v a r i a b l e i n turn and e i t h e r includes or excludes that v a r i a b l e from the regression equation depending on the s i g n i f i c a n c e l e v e l defined by the user. If desired, an independent var i a b l e can be included i n the regression equation regardless of i t s s i g n i f i c a n c e . The independent v a r i a b l e s to be considered i n the regression equation can be fed i n t o Stpreg i n any desired form by the user. For example, i f the user wanted a c u r v i l i n e a r component of a v a r i a b l e he would feed i n the square of the v a r i a b l e i n a d d i t i o n to the v a r i a b l e i t s e l f and may obtain squared independent variables i n the resultant regression equation (e.g., Equation 5.1 of section 5.2). This routine was used to define the regression equations that were used i n the programs i n the study of the g r i d square method. At the present time there i s no provision for i t e r a t i o n i n t h i s routine package. 2.3 Data Used i n Grid Square Method The South Thompson River Basin was used i n the development of the g r i d square method since data from t h i s basin was processed and compiled by T. Ingledow and Associates Limited i n a hydrometric network study i n which they applied the g r i d square method i n i t s o r i g i n a l form. The South Thompson River Basin i s also one of the few areas i n B r i t i s h Columbia where there are adequate meteorologic and hydrologic data to perform the regression analysis. The drainage basin, with a catchment area of approximately 6,350 square miles, i s shown i n Figure A - l of Appendix A. The g r i d system covering the study area has a 10 kilometer i n t e r v a l (standard on the 1:250,000 scale maps used i n Canada) with a t o t a l of 212 squares which f a l l w i t h i n or on the boundaries. The g r i d square system i s shown i n - 9 - Figure A-2 and the areas of squares i n each sub-basin are l i s t e d i n Table A-3 of Appendix A. The time base period used f o r the study was 10 years (1956-1966) since adequate streamflow records are a v a i l a b l e from four gauging stations for t h i s period. The l o c a t i o n of these stations are shown i n Figure A - l and s t a t i o n data are as follows: Drainage Area Ten Year Station Station Above Station Mean Flow No. Name (sq. mi.) (cfs) 8LG-3 Shuswap River near 776 1,800 Lumby 8LC-19 Shuswap River at 1,560 2,890 Mable Lake 8LD-1 Adams River near 1,156 2,560 Squilax 8LE-69 South Thompson River 6,350 10,700 near Monte Creek Adequate p r e c i p i t a t i o n records f o r the selected time base period are av a i l a b l e from 37 meteorological stations i n the :;general area of the South Thompson River Basin. However, only 15 of these stations are located within the study basin, while the remaining 22 are peri p h e r a l stations which presumably r e f l e c t c l i m a t i c conditions i n the basin. Adequate temperature data are a v a i l a b l e f o r 28 of the 37 meteorological s t a t i o n s . The locations of these stations are shown i n Figure A - l and the 10 year mean values of p r e c i p i t a t i o n and temperature at these stations are l i s t e d - 1 0 - i n Table A - l of Appendix A. Detailed d e s c r i p t i o n of compilation of data i s given on page 6-6 of Reference 3. The physiographic c h a r a c t e r i s t i c s that were considered are: (a) Elevation: The mean elevation of a square was obtained by averaging the elevations at the g r i d square corners, the center and the intermediate 5 kilometer points. (b) Land Slope: Slope i s determined by Horton's method which consists of counting the number of contour l i n e s crossing two perpendicular center l i n e s of the square which are p a r a l l e l to the sides. (c) Distance to B a r r i e r : The index that was adopted was the distance from the center of a square to a s t r a i g h t l i n e drawn along the divide of the Coast Mountains, measured i n a west-southwest d i r e c t i o n , the predominant wind d i r e c t i o n of moisture inflow for the area. (d) Latitude: The l a t i t u d e index was defined as the distance measured from the U.S. border to the center of a g r i d square. (e) Shield E f f e c t : The s h i e l d e f f e c t was determined by summing the average b a r r i e r heights along the center l i n e of each square extending for 28 kilometers i n a west-southwest d i r e c t i o n . The physiographic data for the meteorological stations were extracted from 10 kilometer squares centered over each s t a t i o n . The published elevation c h a r a c t e r i s t i c f o r each s t a t i o n was used instead of the average elevation of the square. A more d e t a i l e d d e s c r i p t i o n of the physiographic c h a r a c t e r i s t i c s and t h e i r measurement are given on pages 6-6 through 6-9 of Reference 3. - 11 - CHAPTER 3 EVAPORATION 3.1 Introduction Evaporation theory can be used f o r estimating the runoff from un- gauged watersheds by using the water balance approach. Water balance can be defined as the balance between the income of water from p r e c i p i t a t i o n and the outflow of water by evapotranspiration. The general procedure i s to estimate the evapotranspiration loss E, subtract i t from the p r e c i p i - t a t i o n P and consider the "moisture surplus" (P-E) as representative of the runoff. This procedure i s better suited f o r c l i m a t o l o g i c a l rather than h y d r o l o g i c a l use where time-lag influences (e.g., ground-water storage and snow melt) predominate. However, t h i s water balance procedure can be s a t i s f a c t o r i l y applied to hy d r o l o g i c a l estimates of mean monthly and mean annual water balances i n which time lag e f f e c t s are of l i t t l e i nfluence. For the evaporation component of water balance estimates two estimates of evaporation are generally made, that of p o t e n t i a l evaporation and actual evaporation. P o t e n t i a l evaporation i s defined as the evaporation that would occur were there an adequate moisture supply at a l l times. Actual evaporation i s equal to p o t e n t i a l when the p r e c i p i t a t i o n exceeds the p o t e n t i a l evaporation but i s less than the p o t e n t i a l evaporation when p r e c i p i t a t i o n f a l l s below p o t e n t i a l evaporation. In the o r i g i n a l g r i d square method mean annual evapotranspiration i s calculated by Turc's evaporation formula which was developed on the basis of a s t a t i s t i c a l study of 254 watersheds i n a l l climates of the world. - 12 - The formula i s very simple to apply and i s given as follows: L(t) = 300 + 25t + 0.05t 3 (3.1) (3.2) where E = Actual annual evaporation (mm) P = Annual P r e c i p i t a t i o n (mm) t = Mean annual temperature (°C) A t r a n s l a t i o n of the resume of Turc's o r i g i n a l paper (which i s i n French) i s given i n Appendix D. A b r i e f review of research l i t e r a t u r e was made to determine which methods were widely used to estimate evapotranspiration i n water balances of watersheds. It was concluded that Penman's method produced the most accurate r e s u l t s but required data which are not r e a d i l y a v a i l a b l e over wide-areas f or which the g r i d square method i s proposed. For the a v a i l a b l e data, Thornthwaite's evapotranspiration method was found to be the one most widely used. R.C. Ward, i n h i s paper on p o t e n t i a l evapotranspiration, compares the Penman and Thornthwaite methods with an evapotranspirometer (Reference 11). His study showed that there was generally close s i m i l a r i t y among the r e s u l t s of the three methods. Both the Penman and Thornthwaite methods showed s l i g h t discrepancies i n the spring and autumn but the d i s - crepancies were complementary i n each case and the annual r e s u l t s were s i m i l a r . - 13 - The Thornthwaite method was derived from a s t a t i s t i c a l study of ava i l a b l e observations i n the ce n t r a l and eastern United States. The method involves f i r s t c a l c u l a t i n g p o t e n t i a l evapotranspiration and then, on the basis of a serie s of assumptions and empirical rules (formulas or tables ) , monthly runoff from r a i n f a l l and snowmelt. The monthly water balance i s calculated with regard to a running t o t a l of s o i l moisture storage from which c a l c u l a t i o n s of moisture d e f i c i t and surplus as w e l l as runoff are derived. Basic data used i n the method are mean monthly temperature and p r e c i p i t a t i o n and estimates of water holding capacity of the s o i l . The Thornthwaite formulae used i n the computer programs of this study are: 1.514 i k (3.3) 5 I (3.4) F 0.93 (3.5) 2.42 - log I E. 'k C k a n t i l o g [ 0.204 + F (1 - log I) + F log t f c] (3.6) a n t i l o g [ l o g S - (A) (PE)] (3.7) - 14 - where: E, = adjusted p o t e n t i a l evapotranspiration f o r month k (cm) it = c o e f f i c i e n t depending on the month and the l a t i t u d e (Reference 8) t ^ = mean monthly temperature (°C) M = s o i l moisture retained i n the s o i l (in.) S = water holding capacity of the s o i l (in.) A = rate of change of M with d i f f e r e n t amounts of PE (dimensionless) i . e . , when S = 16, A = 0.02719 S = 14, A = 0.03106 S = 12, A = 0.03628 S = 10, A = 0.04331 PE = p o t e n t i a l evapotranspiration (in.) The f i r s t four formulae were taken from G.S. Cavadias' paper on evaporation (Reference 4). The l a s t formula was developed from Thornthwaite's tables s t a r t i n g on page 245 of Reference 9. In the programs of the study of the g r i d square method 'Formula 3.7 was used with S = 14 inches only since a preliminary study showed e s s e n t i a l l y no d i f f e r e n c e i n evapotranspiration estimates using the four d i f f e r e n t values of S (see Program C - l of Appendix C). The extent to which the water balance method of Thornthwaite was used, was i n c a l c u l a t i o n of actual evapotranspiration (see Reference 9). A s i m p l i f i e d version of surface runoff was then estimated from p r e c i p i t a t i o n - 15 - minus act u a l evapotranspiration f or each month and summed to obtain the annual runoff estimate. Thornthwaite determines surplus runoff i n a more detail e d analysis i n which moisture d e f i c i t and surplus are both estimated and detention periods are used f o r both water and snow runoff estimates. However, t h i s analysis i s beyond the present scope of the g r i d square method. 3.2. Comparison of Evaporation Methods For the comparison of the Turc and Thornthwaite methods of estimating evapotranspiration under B r i t i s h Columbia conditions, several attempts were made. A preliminary examination was f i r s t made f o r a wide range of meteorological sta t i o n s with mean annual p r e c i p i t a t i o n ranging from 8.15 inches to 179.50 inches. P r e c i p i t a t i o n data and Thornthwaite evaporation estimates were obtained from Thornthwaite's published r e s u l t s (Reference 1) and temperature data were obtained from the U.B.C. Geography Department. The meteorological stations considered and the r e s u l t s that were obtained are given i n Table 3.1. - 16 - TABLE PRELIMINARY COMPARISON OF TURC AND ( A l l figures are 3.1 THORNTHWAITE EVAPORATION METHODS mean annual) Turc Thorn. Actual Actual Difference Temp. Precip. Evapotrans. Evapotrans. between Thorn. Station (°F) (in.) (in.) (in.) and Turc OKANAGAN Okanagan Centre 48 12. 75 11. 46 12. 75 1.29 Oliv e r 49 8. 65 8. 46 8. 65 . 0.19 Kelowna 47 12. 20 10. 99 12. 20 1.21 Keremeos 49 9. 75 9. 37 9. 75 0.38 SOUTH THOMPSON DRAINAGE AREA Ashcroft 45 9. 45 8. 89 9. 45 0.56 Kamloops 47 10. 20 9. 58 10. 20 0.62 Salmon Arm 46 19. 05 14. 31 18. 00 3.69 Vavenby 43 14. 65 11. 80 14. 65 2.85 Chinook Cove 44 16. 50 12. 82 16. 50 3.68 Tappen 46 21. 10 15. 03 18. 55 3.52 Tra n q u i l l e 47 8. 15 7. 96 8. 15 0.19 WEST COAST AND VANCOUVER ISLAND Alber n i 49 66. 75 21. 66 22. 70 1.04 Anyox 44 78. 40 18. 48 20. 95 2.47 Britannia Beach 50 75. 85 22. 65 23. 60 0.95 Clayoquot 49 106. 50 22. 31 24. 45 2.14 Estevan Point 48 107. 80 21. 54 24. 15 2.61 Holberg 46 101. 80 20. 03 23. 70 3.67 Ocean F a l l s 47 179. 50 21. 02 24. 40 3.38 Ucluelet 48 102. 80 21. 51 23. 70 2.19 Upon examination of the Difference column i t can be seen that Turc's method gives consistently lower estimates of actual evapotranspiration than Thornthwaite, e s p e c i a l l y i n the South Thompson region. - 17 - In a second examination a program.was written f o r c a l c u l a t i n g a c t u a l evapotranspiration by the Turc and Thornthwaite methods (see Program C - l of Appendix C). Two meteorological stations were chosen f o r the t r i a l runs, one f o r high and one for low p r e c i p i t a t i o n (Reference 7). The r e s u l t s obtained are given i n Table 3.2. TABLE 3.2 PROGRAMMED COMPARISON OF TURC AND THORNTHWAITE EVAPORATION METHODS ( A l l figures are mean annual) Turc Actual Thorn. Actual Temp. Precip. Evapotrans. Evapotrans. Station (OF) (in.) (in.) (in.) Armstrong 44.5 17.2 13.2 17.2 Gla c i e r 36.2 57.1 13.8 18.7 The difference between the two methods again appears to be rather s i g n i f i c a n t . In an evaporation study of the Carrs Landing area i n the Okanagan, the B r i t i s h Columbia Water Resources Services has determined some evaporation data based on the Penman method. Using these data as a base (assuming that the data represented true evaporation), the methods of Turc and Thornthwaite were compared i n the t h i r d examination i n an attempt to e s t a b l i s h which method gave better evaporation r e s u l t s f o r B r i t i s h Columbia conditions. The r e s u l t s of the comparison of two s i t e s f o r 1967 are given i n Table 3.3. - 18 - TABLE 3.3 CARRS LANDING STUDY COMPARISON ( A l l figures are mean annual) Thorn. Evapotrans. Turc Actual Penman Evapotrans. Station Temp. Precip. P o t e n t i a l Actual Evapotrans. P o t e n t i a l Actual No. («F) (in.) (in.) (in.) (in.) (in.) (in.) 1 51.0 8.9 27.8 8.9 8.9 27.5 6.3 3 42.4 12.9 21.9 12.9 10.8 22.9 9.0 The Penman "annual" figures are aggregates of summer period only ( A p r i l - October) , therefore may be underestimates of t o t a l annual evapotranspiration. Calculations f o r only one year at two s i t e s with the highest observed pre- c i p i t a t i o n were made since further examination of the Penman data revealed that i n no t r i a l d id p r e c i p i t a t i o n exceed evapotranspiration"; In both t r i a l s shown above the p r e c i p i t a t i o n was so much lower than the p o t e n t i a l evapo- t r a n s p i r a t i o n that both the Thornthwaite and Turc methods (except Turc at Station 3) simply showed that a c t u a l evapotranspiration was equal to the p r e c i p i t a t i o n . Hence the comparison of the two methods with the Penman method proved to be inconclusive i n the t h i r d evaporation examination. Although the f i r s t two attempts (Tables 3.1 and 3.2) at comparing the Turc and Thornthwaite methods indicated a s i g n i f i c a n t d i f f e r e n c e i n t h e i r estimates, no conclusion could be drawn on an evaporation basis alone as to which method gave better r e s u l t s f o r B r i t i s h Columbia conditions. Hence there was a need f o r an experimental g r i d square approach,to e s t a b l i s h which method gave better r e s u l t s i n water balance estimates. The comparison of the two evaporation methods using a g r i d square approach i s presented i n Chapter 5. - 20 - CHAPTER 4 SNOW 4.1 Snow Courses The B r i t i s h Columbia Water Resources Service conducts a snow survey program f o r purposes of f o r c a s t i n g volumes of snowmelt runoff. Most of the snow courses i n operation are located at elevations above 4,000 f t . Since most of the meteorological stations are situated i n v a l l e y s at elevations below 4,000 feet, the snow survey data provide p r a c t i c a l l y the only observed information on p r e c i p i t a t i o n at the higher elevations. In the study area, a l l meteorological stations are located below 4,100 feet (except one which i s at 4,100 feet) and a l l snow courses are located at or above 6,000 feet. Hence, the snow course data should provide a d d i t i o n a l valuable information i n the seasonal development of the g r i d square method. 4.2, Melt P r i o r to Snow Survey The B r i t i s h Columbia Water Resources Service i s also undertaking snow- melt studies i n which they have so f a r , c o l l e c t e d two years of snow pi l l o w data at two d i f f e r e n t s i t e s . This data was examined and a very s i m p l i f i e d model was developed to determine the melt p r i o r to the 1st of A p r i l , the date of the snow surveys. The method consisted of a program (see Program C-2 of Appendix C) which read i n d a i l y average values of temperature and water equivalent of snow pack, compiled the accumulated degree days (base 32°F) against the accumulated incremental water equivalent losses and plo t t e d the r e l a t i o n s h i p with degree days as the independent v a r i a b l e and the water equivalent loss as the dependent v a r i a b l e . In each computer run of a set of data, four pl o t s were produced where time lags of zero, one, two - 21 - and three days were observed. The best p l o t was determined and from i t a seasonal average melt (accumulated melt from s t a r t of snowfall to A p r i l 1st) was estimated using a season.average temperature m u l t i p l i e d by the length of season for the seasonal average degree day estimate (see Figure 4.1). With t h i s approach I t was hoped to estimate the seasonal premelt and to combine i t with the snow course data for an estimate of winter p r e c i p i t a t i o n . The program was tested out on three complete sets of data from Blackwall (1967-68 and 1968-69) and B a r k e r v i l l e (1968-69). The r e s u l t i n g graphs were examined f o r shape and lags of one and two days were found to give the best p l o t s . A seasonal value of melt was required since a d a i l y estimate i s beyond the scope of the g r i d square method. When a seasonal estimate of degree days was made (season average temperature m u l t i p l i e d by the length of season i n days) the seasonal melt was found to be 77% i n error f o r B a r k e r v i l l e (1968-69) while the seasonal melts for the other two sets of data were found to be meaningless since the seasonal average temperature was below 32°F. The best p l o t was that of B a r k e r v i l l e which i s shown i n Figure 4.1. Since the melt i n each case was below 1.5 inches, i t was ignored i n subsequent use of snow course data. This approach did not prove to have any s i g n i f i c a n t r e s u l t s due most l i k e l y to unexplained factors a f f e c t i n g snow melt (e.g., antecedent moisture i n s o i l a f f e c t i n g heat from the ground and e f f e c t of humidity), and perhaps the l i m i t a t i o n i n measuring equipment. The r e s u l t s of the model when applied to snow p i l l o w data on a d a i l y basis showed melt graphs which displayed smooth plo t s f o r lag times of one 22 0 . 0 10.0 20.0 30 .0 40.0 50.0 60.0 ACCUMULATED DEG-DPYS 100.0 - 23 - and two days. These plots suggest the existence of a melt function or a snow melt v a r i a t i o n with average accumulated degree days. In further development of the method i t i s suggested that the same model be applied to the data but with maximum d a i l y temperatures as a basis f o r a heat index. This would give p o s i t i v e seasonal melt estimates (see section 4.2, page 20) which may or may not be s i g n i f i c a n t on a seasonal bas i s . Other aspects to be considered would be the e f f e c t of antecedent moisture conditions (can be estimated from the r a i n hydrograph p r i o r to snowfall and the s o i l conditions), the e f f e c t of the snow p i l l o w i n t e r f e r i n g with the actual n a t u r a l melt process (e.g., may have a s h i e l d i n g e f f e c t from heat from the ground) and the comparison of the p r e c i p i t a t i o n hydrograph with the snow p i l l o w hydro- graph to determine the differ e n c e between the actual snow melt runoff and the ripening and storage processes. Dr. Quick of the C i v i l Engineering Department of U.B.C. i s now c o l l e c t i n g snow pi l l o w data on Mount Seymour and should have s u f f i c i e n t data f o r such modelling i n the near future. It i s also suggested that r a i n gauges be i n s t a l l e d on a yearly basis at the snow p i l l o w s i t e s of the B r i t i s h Columbia Water Resources Services to obtain information which could lead to the development of snow melt models and thus make wider use of the many snow course data that have been c o l l e c t e d to date. - 24 - CHAPTER 5 EXPERIMENTAL GRID SQUARE METHOD 5.1 Programming Computer programs, using UBC T r i p , were i n i t i a l l y set up to define regional temperature and p r e c i p i t a t i o n regression equations. Stpreg (see section 2.2, page 7) was used to e s t a b l i s h the re l a t i o n s h i p s between temperature and p r e c i p i t a t i o n at meteorological stations (dependent variables) and the corresponding physiographic parameters (independent v a r i a b l e s ) . Mean annual temperature and p r e c i p i t a t i o n equations were used i n the Turc approach but mean monthly equations were derived f o r the Thornthwaite approach. The r e s u l t s of these programs are given i n the following sections 5.2 and 5.3. A program was then written f o r estimating mean annual runoff by the g r i d square method using lure's formula f o r estimating mean annual evaporation. Another program was wr i t t e n f o r estimating mean annual runoff, using the Thornthwaite approach f o r e s t i - mating mean annual evapotranspiration. Several modified t r i a l runs were made with this program and the modifications and the r e s u l t s are presented i n s e ction 5.4. A sample program of one of the t r i a l runs i s given i n Appendix C (Program C-3). In the Thornthwaite programs both p o t e n t i a l and actual evapotranspiration were estimated but only the l a t t e r was used i n estimating runoff. Mean annual runoff was determined by adding the twelve estimates of mean monthly runoff ( p r e c i p i t a t i o n minus act u a l evapo- transpiration) . In both the Turc and the Thornthwaite programs mean annual runoff was determined f o r each square and summed to obtain the t o t a l mean annual runoff f o r the basin. Provision was made i n both programs f o r checking the a r e a l d i s t r i b u t i o n of the f i r s t estimate of basin - 25 - runoff by d i v i d i n g the t o t a l basin i n t o four sub-basins f o r which published hydrometric data were a v a i l a b l e . A f i n a l set of programs was wr i t t e n to incorporate the snow course data into the g r i d square system. These t r i a l runs are described i n part c of section 5.5 and a sample program i s given i n Appendix C (Program C - 4 ) . 5.2 Estimation of the Temperature D i s t r i b u t i o n Using data at 28 meteorological s t a t i o n s , a c o r r e l a t i o n was established between the mean annual temperature and the corresponding physiographic c h a r a c t e r i s t i c s (elevation, land slope, distance to b a r r i e r , l a t i t u d e index, b a r r i e r height, and s h i e l d e f f e c t ) . The r e s u l t i n g regression equation i s : T = 50.8308 - 0.003107E - 0.00003754L2 (5.1) where, T i s mean annual temperature in°F, E i s s t a t i o n elevation i n fe e t , and L i s the l a t i t u d e index i n kilometers. The c o e f f i c i e n t of c o r r e l a t i o n i s 0.96 which i s s i g n i f i c a n t at the one percent l e v e l and the standard error estimate i s 1.0°F. The c o e f f i c i e n t s of the variables included i n the equation have signs corresponding to t h e i r expected p h y s i c a l influence on the mean annual temperature. For the Thornthwaite approach i n the g r i d square method twelve mean monthly temperature equations were needed. Since monthly temperature data were not av a i l a b l e i n Reference 3, the twelve mean monthly values f o r each s t a t i o n were obtained from References 5 and 7, and were* adjusted to the time base period of Reference 3. The cor r e l a t i o n s were established as f o r Equation 5.1. and twelve regression equations were obtained, one for each - 26 - month. The equations are s i m i l a r i n form.and are shown i n Appendix B, section B . l (Equations B . l through B.12). For example, the equation f o r the mean monthly temperature f o r January i s : T l = 28.1903 - 0.002675E - 0.00006324L2 (B.l) where E i s s t a t i o n elevation i n feet and L i s the l a t i t u d e index i n kilometers. The c o e f f i c i e n t of c o r r e l a t i o n ranges from a low of 0.81 f o r T2 (February) to a high of 0.94 f o r T4 ( A p r i l ) , with a s i g n i f i c a n c e at the one percent l e v e l . The standard error of estimate ranges from a low of 1.1°F f o r T10 (October) to a high of 2.2 f o r T l (January). The smaller c o e f f i c i e n t s of v a r i a t i o n f o r the monthly equations suggest that less v a r i - ation was explained i n these than i n the annual equation, which was expected since the time base f or c o r r e l a t i o n was shortened. 5.3 Estimation of the P r e c i p i t a t i o n D i s t r i b u t i o n Using data at 37 meteorological s t a t i o n s , a c o r r e l a t i o n was established between the mean annual p r e c i p i t a t i o n and the corresponding physiographic c h a r a c t e r i s t i c s (elevation, land slope, distance to b a r r i e r , l a t i t u d e index, b a r r i e r height and s h i e l d e f f e c t ) . The r e s u l t i n g regression equation i s : P = 11.7765 - 0.0956L + 0.0000005127E2 + 0.0005778DB2 - 0.00000002558SE2 (5.2) where P i s mean annual p r e c i p i t a t i o n i n inches, L i s the l a t i t u d e index i n kilometers, E i s elevation i n feet, DB i s distance to b a r r i e r i n kilometers and SE i s s h i e l d e f f e c t i n feet . The c o e f f i c i e n t of c o r r e l a t i o n i s 0.97 which i s s i g n i f i c a n t at the one percent l e v e l and the standard error of estimate i s 3.59 inches. - 27 - For the Thornthwaite approach i n the g r i d square method twelve mean monthly p r e c i p i t a t i o n equations were required. As i n the case of the monthly temperature data, the data f o r the twelve mean monthly p r e c i p i t a t i o n values f o r each s t a t i o n were obtained from References 5 and 7 and adjusted to the common time base period (1956-1966). As with the temperature equations, twelve correlations were established f o r mean monthly p r e c i p i - t a t i o n . The equations are s i m i l a r i n form and are shown i n Appendix B, , section B.2 (Equations B.13 through B.24). For example, the corresponding equation f o r the mean monthly p r e c i p i t a t i o n f o r January i s : P l = 5.3639 - 0.0474DB + 0.0001803DB2 - 0.00003784L2 ...(B.13) The c o e f f i c i e n t of c o r r e l a t i o n ranges from a low of 0.68 f o r P8 (August) to a high of 0.96 f o r P3 (March), with a s i g n i f i c a n c e at the one percent l e v e l . The standard error of estimate ranges from a low of 0.25 inches for P4 (Ap r i l ) to a high of 0.80 inches f o r P12 (December). Of the independent variables used i n c o r r e l a t i o n i n t h i s study, the va r i a b l e of elevation was considered the most important since i t i s the only common c h a r a c t e r i s t i c that a l l land areas share which influences the v a r i a t i o n of weather phenomenon. The stepwise regression technique (Stpreg, described i n section 2.2) that was used i n the c o r r e l a t i o n analysis includes i n the regression equations only those independent variables which are s i g n i f i c a n t to the l e v e l defined by the user. Seven of the above twelve regression equations did not r e t a i n elevation as a s i g n i f i c a n t v a r i a b l e and were defined by other s i g n i f i c a n t independent v a r i a b l e s . By using UBC Tr i p with the elevation v a r i a b l e included regardless of s i g n i f i c a n c e , i n t o the regression equations, twelve a d d i t i o n a l c o r r e l a t i o n s were established - 28 - and are shown i n Appendix B, section B.3 (Equations B.25 through B.36). 2 Elevation was forced i n t o the regression equations as E since previous 2 examination of Stpreg revealed that E r e s u l t e d i n higher s i g n i f i c a n c e than E and was generally more r e a d i l y accepted i n t o a regression equation than was E. The corresponding equation f o r the mean monthly p r e c i p i t a t i o n for January i s : PI = - 0.2672 + 0.00000008047E2 + 0.00007911DB2 - 0.00003614L2 (B.25) The c o e f f i c i e n t of c o r r e l a t i o n ranges from.a low of 0.70 for P8 (August) to a high of 0.96 for P3 (March), with a s i g n i f i c a n c e at the one percent l e v e l , the exceptions being the elevation variables i n equations of P8, P10 and P12 where the v a r i a b l e s i g n i f i c a n c e i s 5.5%, 9.15% and 1.2% re s p e c t i v e l y . The standard error of estimate ranges from a low of 0.25 inches f o r P4 (April) to a high of 0.76 inches f o r P12 (December). 5.4 Estimation of the Runoff D i s t r i b u t i o n Regression equations f o r temperature and p r e c i p i t a t i o n that had been derived from the meteorological observations were used to ca l c u l a t e a c t u a l evapotranspiration which was then subtracted from the corresponding pre- c i p i t a t i o n to obtain runoff f o r each square. The runoff values f o r each square were then summed for each sub-basin ( p a r t i a l areas of squares within sub-basins were accounted for) and the t o t a l basin. The sub-basin runoff t o t a l s then represented the f i r s t estimate of the g r i d square technique and were therefore used to compare the Turc and Thornthwaite methods of estimating evaporation. A runoff regression equation comparison was of no b e n e f i t since the c o r r e l a t i o n c o e f f i c i e n t of any runoff regression equation would be 0.999 - 29 - due to the nature of deri v a t i o n of runoff values (observations would be derived from functions which had already been f i t t e d by a l e a s t squares method). In the program f or c a l c u l a t i n g runoff with the Turc approach the mean annual regression equations f o r temperature and p r e c i p i t a t i o n , Equations 5.1 and 5.2, were used since the Turc formula uses only annual values. The r e s u l t i n g f i r s t estimates and t h e i r corresponding recorded flowsfor the sub-basins and t o t a l basin are given i n Table 5.1. TABLE 5.1 FIRST RUNOFF ESTIMATES USING TURC'S METHOD Sub-Basin Recorded Estimated Stream Gauge Drainage Area Flow Flow Percentage River Station (sq. mi.) (cfs) (cfs) Difference Shuswap 8LC-3 776 1800 1940 + 7.8 Shuswap 8LC-19 784 1090 1548 + 42.0 Adams 8LD-1 1156 2560 3281 +28.2 S. Thompson 8LE-69 3634 5250 7063 + 34.6 Tot a l 6350 10,700 13,831 +29.2 In the program f o r c a l c u l a t i n g runoff with the Thornthwaite approach the twelve mean monthly regression equations f o r temperature, Equations B . l to B.12 i n c l u s i v e of Appendix B, and p r e c i p i t a t i o n were used since the Thornth- waite approach uses monthly values. One t r i a l runoff estimate was made with the p r e c i p i t a t i o n Equations B.13 to.B.24 i n c l u s i v e , derived with normal step- wise regression (elevation not included i n a l l regression equations) and another runoff estimate was made with the p r e c i p i t a t i o n Equations B.25 to B.36 - 30 - i n c l u s i v e , derived with the modified stepwise regression (elevation v a r i a b l e included i n a l l the regression equations regardless of i t s s i g n i f i c a n c e ) . The r e s u l t i n g f i r s t estimates and t h e i r corresponding recorded flows are given i n Table 5.2. TABLE 5.2 FIRST RUNOFF ESTIMATES USING THORNTHWAITE'S METHOD River Sub-Basin Estimated Flow Estimated Flow Drainage Recorded Normal Modified Stream Gauge Area Flow Stpreg % Stpreg % Station (sq. mi.) (cfs) (cfs) D i f f . (cfs) D i f f . Shuswap Shuswap Adams S. Thompson 8LC-3 8LC-19 8LD-1 8LE-69 776 784 1156 3634 1800 1090 2560 5250 1262 990 2612 4633 -29.2 - 9.2 + 2.0 -11.8 -1775 1369 3021 6040 - 1.4 +25.6 +18.0 +15.0 To t a l 6350 10,700 9498 -11.2 12,204 +23.4 Examination of the c o e f f i c i e n t s of c o r r e l a t i o n of the two sets of twelve pre- c i p i t a t i o n equations of section? 5.3 on pages 27 and 28 w i l l show that the two sets of equations e s s e n t i a l l y show i d e n t i c a l s t a t i s t i c a l s i g n i f i c a n c e . However, the r e s u l t s shown i n Table 5.2 show a s i g n i f i c a n t d i f f e r e n c e between the two t r i a l runs i n which the normal regression equations underestimate and the modified regression equations overestimate the flow. This r e s u l t i s interpreted as being due to the f a c t that the meteorological stations are mostly situated i n the v a l l e y bottoms while the g r i d squares cover f a i r l y large areas which generally include parts of the higher elevation mountain slopes. This fa c t was investigated further when i n a program, the p r e c i p i - t a t i o n f o r each square was printed out f o r each t r i a l of the normal and the modified regression. Upon examination of the squares with the lowest e l e - - 31 - vations, i t was found that both sets of equations gave.the same p r e c i p i - t a t i o n estimates but at the squares with the highest elevations the normal regression equation set underestimated while the modified regression set overestimated the p r e c i p i t a t i o n . This r e s u l t was i n f e r r e d from the r e s u l t s of Table 5.2 i n which runoff estimates are underestimated i n the f i r s t t r i a l and overestimated i n the second. The reasoning was further s u b s t a n t i a l when the runoff estimates were printed out for each square f o r both t r i a l s and the higher elevation squares were examined to compare the runoff estimates with the p r e c i p i t a t i o n and evaporation estimates. The p r e c i p i t a t i o n values were found to.be much larger than the corresponding evaporation values i n most cases. Temperature d i s t r i b u t i o n did not a f f e c t e i t h e r of these t r i a l s because elevation was s i g n i f i c a n t i n a l l twelve mean monthly temperature regression equations and one set of temperature equations was therefore used i n both t r i a l s . The conclusion to be drawn from this analysis i s that the meteorological s t a t i o n s , being located i n the v a l l e y bottoms, do not ade- quately explain the p r e c i p i t a t i o n v a r i a t i o n , i n terms of elevation at l e a s t . This point i s w e l l brought out i n the next section when snow course data i s used to supplement the meteorological data to define a better p r e c i p i t a t i o n v a r i a t i o n . It appears that the Thornthwaite approach to the g r i d square method gives better r e s u l t s than Turc's evaporation approach since i t gives a better f i r s t estimate of runoff d i s t r i b u t i o n . Obviously both estimates could be improved by i t e r a t i o n to progressively reduce the discrepancies between estimated and recorded runoff (see discussion on page 6 of section 2.1) and this would normally be the next step. However, at other than the f i r s t estimate there would be no basis f o r comparison between a l t e r n a t i v e - 32 - techniques. Hence i n t h i s research study the g r i d square method was not taken beyond the f i r s t estimate. 5.5 Incorporation of Show Course Data To incorporate the snow course data i n t o the g r i d square system several approaches were made as follows: (a) The c l o s e s t r e l a t e d (considering l o c a t i o n and physiographic charac- t e r i s t i c s ) meteorological s t a t i o n was chosen f o r each snow course s t a t i o n and the percentage of annual p r e c i p i t a t i o n that the winter p r e c i p i t a t i o n (October-March) represented was determined at the meteorological s t a t i o n . The two independent estimates, percentage of winter p r e c i p i t a t i o n and the A p r i l 1st snow pack water equivalent were combined f o r an estimate of annual p r e c i p i t a t i o n at each snow course s t a t i o n . These independent (of the p r e c i p i t a t i o n stations) average annual p r e c i p i t a t i o n estimates were combined with the average annual p r e c i p i t a t i o n s t a t i o n observations and data was then a v a i l a b l e for 50 meteorological s t a t i o n s . A c o r r e l a t i o n was established between the mean annual p r e c i p i t a t i o n and the corresponding physiographic c h a r a c t e r i s t i c s . The r e s u l t i n g regression equation i s : P = - 30.9787 + 0.005885E + 0.2302DB - 0.0001832L2 (5.3) where P i s mean annual p r e c i p i t a t i o n i n inches. The c o e f f i c i e n t of c o r r e l a t i o n i s 0.93 which i s s i g n i f i c a n t at the one percent l e v e l and the standard error of estimate i s 7.6 inches. When compared with Equation 5.2, Equation 5.3 with the snow courses added, shows a s l i g h t l y lower s t a t i s t i c a l s i g n i f i c a n c e and adds no refinement to the - 33 - o r i g i n a l p r e c i p i t a t i o n regression Equation 5.2. As an added check, Equation 5.3 was used i n place of Equation 5.2 i n the Turc method of the g r i d square system and the r e s u l t s obtained were much worse than those shown i n Table 5.1 for Equation 5.2. (b) Mean annual p r e c i p i t a t i o n at each snow course s t a t i o n was computed from the regression equation developed from meteorological stations only, Equation 5.2, and the percentage of these values represented by the A p r i l 1st snow course data was determined. The percentage values were then correlated with physiographic parameters and the regression equation thus derived was used to recompute the percentages at the snow course loc a t i o n s . The recomputed.percentage values were combined with the snow course data to estimate an average annual p r e c i p i t a t i o n value at the snow course l o c a t i o n s . These annual p r e c i p i t a t i o n estimates were then combined with the mean annual p r e c i p i t a t i o n s t a t i o n obser- vations and another set of data was a v a i l a b l e f o r 50 meteorological st a t i o n s . A c o r r e l a t i o n was again established between the mean annual p r e c i p i t a t i o n and the corresponding physiographic c h a r a c t e r i s t i c s . The r e s u l t i n g regression equation i s : P = - 3.2011 + 0.003910E + 0.0005573DB2 - 0.0002471L2 (5.4) The c o e f f i c i e n t of c o r r e l a t i o n i s 0.95 which i s s i g n i f i c a n t at the one percent l e v e l and the standard error of estimate i s 6.3 inches. When compared with Equation 5.2, Equation 5.4 with the snow courses added, shows a s l i g h t l y lower s t a t i s t i c a l s i g n i f i c a n c e and, j u s t as Equation 5.3, adds no refinement to the o r i g i n a l p r e c i p i t a t i o n regression Equation 5.2. I t should be noted, however, that the regression equation of - 34 - percentages had a c o r r e l a t i o n c o e f f i c i e n t of 0.36 and a standard error of 13.7% and t h i s t r i a l i s , hence, of very l i t t l e s i g n i f i c a n c e . - The attempts to use snow.course data to estimate annual pre- c i p i t a t i o n at the snow courses by assuming that the percentage of annual p r e c i p i t a t i o n was the same as that at the nearest meteorological s t a t i o n (part a) and by recomputing from a c o r r e l a t i o n equation the percentage that the snow course represented of annual p r e c i p i t a t i o n (part b) were not successful. The resultant p r e c i p i t a t i o n regression equations (Equations 5.3 and 5.4) did not improve upon the p r e c i p i t a t i o n d i s t r i b u t i o n as estimated by the meteorological stations only (Equation 5.2). (c) Mean monthly temperatures for every g r i d square were calculated by the twelve temperature regression equations (B.l to B.12 of Appendix B) and then examined to define the winter period. It was observed that v i r t u a l l y a l l squares had mean monthly temperatures greater than 32°F for the period of A p r i l to October and the winter period was therefore defined as November to March. Actual observed p r e c i p i t a t i o n f o r t h i s period was compiled f o r each meteorological s t a t i o n making a v a i l a b l e data for 37 winter season observations. A c o r r e l a t i o n was established between winter season p r e c i p i t a t i o n and the corresponding physiographic c h a r a c t e r i s t i c s . The r e s u l t i n g regression equation i s : P , . = 27.6898 - 0.0605L - 0.2073DB + 0.0007837DB2 (5.5) (n-m) where P, s i s the mean winter seasonal (November-March) p r e c i p i t a t i o n (n-m; i n inches. The c o e f f i c i e n t of c o r r e l a t i o n i s 0.96 which i s s i g n i f i c a n t - 35 - at the one percent l e v e l and the standard error of estimate i s 2.6 inches. The elevation v a r i a b l e was not retained i n the regression equation as being s i g n i f i c a n t . A-duplicate c o r r e l a t i o n at the f i v e percent l e v e l did not automatically produce elevation as a s i g n i f i c a n t v a r i a b l e . UBC Tr i p was then used with elevation forced at the one 2 percent l e v e l i n t o the regression equation (the v a r i a b l e E was i n - cluded without regard to s i g n i f i c a n c e as discussed at the end of section 5.3) and the following r e s u l t was obtained: P, , = - 2.1805 + 0.0000004381E2 + 0.0003352DB2 (n-m) „ - 0.0001476IT ....(5.6) The c o e f f i c i e n t of c o r r e l a t i o n i s 0.96 which i s s i g n i f i c a n t at the one percent l e v e l and the standard error of estimate i s 2.6 inches. By compiling winter monthly p r e c i p i t a t i o n data i n t o lumped f i v e month season estimate f o r each meteorological s t a t i o n , an opportunity was created i n which snow course data could be added i n i t s unaltered form and i n a comparable sense. Thus, with snow courses included, data were then a v a i l a b l e f o r 50 mean winter seasonal observations f o r corre- l a t i o n with t h e i r corresponding physiographic c h a r a c t e r i s t i c s . The re- s u l t i n g regression equation i s : P, . = - 21.5062 + 0.1647DB + 0.0000005143E2 (wint) - 0.0001474LT (5.7) where P ( w ^ n t ) i - s t n e mean winter seasonal (with snow courses added) pre- c i p i t a t i o n i n inches. The c o e f f i c i e n t of c o r r e l a t i o n i s 0.94 which i s s i g n i f i c a n t at the one percent l e v e l and the standard error of estimate i s 4.8 inches. I t can be noted that the elevation v a r i a b l e was retained i n the c o r r e l a t i o n equation at the usual l e v e l of s i g n i f i c a n c e without f o r c i n g a f i t as i n the case of Equation 5.6. However, a comparison of - 36 - the s t a t i s t i c a l s i g n i f i c a n c e of the above formulae shows:that Equations 5.5 and 5.6 are.very s l i g h t l y better than Equation 5.7. The three equations are again compared a f t e r they were applied i n the g r i d square method. Runoff d i s t r i b u t i o n was estimated by the g r i d square method using the Thornthwaite approach f o r each of the winter seasonal p r e c i p i t a t i o n equations. In the main program each of these regression equations was used as a lumped f i v e month season runoff estimate (no evaporation because a l l temperatures were below 32°F) together with seven separate monthly estimates of runoff to produce an average annual runoff estimate f o r each square. The r e s u l t s of the t r i a l runs of the g r i d square method using Equations 5.5 and 5.6 as the winter season estimates are given i n Table 5.3. TABLE 5.3 FIRST RUNOFF ESTIMATES USING THORNTHWAITE'S METHOD WITH WINTER SEASON PRECIPITATION ESTIMATES River Sub-Basin Estimated Flow Estimated Flow Drainage Recorded Normal Modified Stream Gauge Area Area Stpreg % Stpreg % Station (sq. mi.) (cfs) (cfs) D i f f . (cfs) D i f f . Shuswap Shuswap Adams S. Thompson 8LC-3 8LC-19 8LD-1 8LE-69 776 784 1156 3634 1800 1090 2560 5250 1161 901 2569 4538 -35.5 -17.4 + 0.4 -13.6 1782 1365 3012 6077 - 1.0 +25.2 +17.7 +15.8 T o t a l 6350 10,700 9169 -14.3 12,235 +14.3 The r e s u l t s obtained above, b a s i c a l l y show the same trends as those of Table - 37 - 5.2 where mean monthly p r e c i p i t a t i o n regression equations were used. The same argument, that of p r e c i p i t a t i o n v a r i a t i o n not being explained by the low elevation meteorological s t a t i o n s , can be applied. Runoff d i s t r i b u t i o n was then estimated using Equation 5.7, with added snow course data, and the r e s u l t s are given i n Table 5.4. TABLE 5.4 FIRST RUNOFF ESTIMATES USING THORNTHWAITE'S METHOD WITH SNOW COURSES ADDED TO THE WINTER SEASON PRECIPITATION ESTIMATES Sub-Basin Recorded Estimated Stream Gauge Drainage Area Flow Flow % River Station (sq. mi.) (cfs) (cfs) D i f f . Shuswap 8LC-3 776 1800 1748 - 2.9 Shuswap 8LC-19 784 1090 1361 +24.9 Adams 8LD-1 1156 2560 2852 +11.4 S. Thompson 8LE-69 3634 5250 6142 +17.0 To t a l 6350 10,700 12,103 +13.1 Comparison of these r e s u l t s with those of Table 5.3 shows that the runoff d i s t r i b u t i o n estimate using the snow course data i s s l i g h t l y better than, and f a l l i n g w i t h i n the range of, the previous estimates which did not use snow course data. This improvement i s s l i g h t but r e a l despite the f a c t that the p r e c i p i t a t i o n Equation 5.7 used i n the estimates summarized i n Table 5.4 i s s t a t i s t i c a l l y i n f e r i o r (again s l i g h t l y ) to Equation 5.5 used as a basis of Table 5.3. As pointed out previously, the supporting s t a t i s t i c s f o r Equation 5.7 i s that the elevation v a r i a b l e was retained i n the c o r r e l a t i o n at the usual l e v e l of s i g n i f i c a n c e without f o r c i n g a f i t as i n the case of - 38 - Equation 5.6. Snow course data thus appear to add a d d i t i o n a l valuable information to the meteorological stations located i n the lower elevations. Comparison of the errors of the f i r s t estimates i n the f i n a l run shown i n Table 5.4 with those of the f i r s t estimates of the o r i g i n a l method shown i n Table 5.1 w i l l show that the Thornthwaite method with the snow course data gives a s i g n i f i c a n t l y better f i r s t estimate with errors that approach those inherent i n the observed values of runoff. This can be supported by the f a c t that hydrometric Stations 8LC-3 and 8LC-19 measure small drainage areas with r e l a t i v e l y small annual runoffs and thus the observed values of runoff f o r these stations would probably tend to have larger errors than the observed values f o r say Stations 8LD-1 and 8LE-69. The r e s u l t s of Table 5.4 are s i m i l a r to those of the second t r i a l of Table 5.2 and both estimates could be improved by t h e a p p l i c a t i o n of an i t e r a t i v e technique as described i n section 2.1. CHAPTER 6 CONCLUSIONS This study using data f o r the South Thompson River Basin has demon- strated that a seasonal estimate approach to the g r i d square method i s f e a s i b l e and that the r e v i s i o n of the evaporation component and the i n - corporation of snow course data i n t o the p r e c i p i t a t i o n component have improved s i g n i f i c a n t l y the a r e a l runoff d i s t r i b u t i o n estimate on the basis of the f i r s t estimate, giving the g r i d square method a more sound phy s i c a l ba s i s . Considering the evaporation component i t was found that apart from Turc's formula, the Thornthwaite evapotranspiration method was the only other p r a c t i c a l method for estimating the evapotranspiration over wide areas as required by the g r i d square method. An attempt was made at an independent comparison of the two methods of estimating evapotranspiration on an evaporation basis alone but i t was found inconclusive due to lack of adequate data. A comparison of the two methods i n actual t r i a l s of the gr i d square method showed that on the basis of the f i r s t estimate of runoff d i s t r i b u t i o n the Thornthwaite approach gives s i g n i f i c a n t l y better r e s u l t s lowering on the average the error of estimate i n the t o t a l basin from approximately 30% to 15%. To incorporate the snow course data i n t o the g r i d square method several approaches were made. An attempt was made.at estimating on a seasonal b a s i s , the melt at the snow courses p r i o r to A p r i l 1st, the date of snow surveys, with the aim of adding the estimate to the measured water equivalent of snow pack to give estimates of the t o t a l winter p r e c i p i t a t i o n . The attempt - 40 - was unsuccessful but showed that the melt p r i o r to A p r i l 1st was not s i g n i f i c a n t and was therefore ignored i n subsequent c a l c u l a t i o n s . Attempts were made to compute annual p r e c i p i t a t i o n at the snow courses by f i r s t estimating the percentage of annual p r e c i p i t a t i o n that the A p r i l 1st water equivalents represented and then extrapolating the seasonal to annual estimates. The attempts were not successful and did not improve the pre- c i p i t a t i o n d i s t r i b u t i o n as estimated by the meteorological stations only. A f i n a l attempt was then made to break the annual p r e c i p i t a t i o n i n t o winter and summer season components and to use the snow course data (from the higher mountain elevations) together with meteorological data (from the lower v a l l e y elevations) f o r the winter p r e c i p i t a t i o n estimates and the meteoro- l o g i c a l data alone f o r the summer estimates. This approach of incorporating snow course data when applied to the g r i d square method gave a small but s i g n i f i c a n t improvement to the f i r s t estimate of regional p r e c i p i t a t i o n and runoff d i s t r i b u t i o n . The p o t e n t i a l use of the snow course data i s thus amplified i n i t s a d d i t i o n a l value of information f o r the e x i s t i n g meteoro- l o g i c a l stations i n defining more c l e a r l y the regional v a r i a t i o n of pre- c i p i t a t i o n . The g r i d square method, from i t s o r i g i n a l development and from the study presented here, has demonstrated a f e a s i b l e regression technique f o r estimating mean annual flows f o r sparsely gauged regions. The study has also demonstrated that the method i s f l e x i b l e f o r development on a mean monthly and seasonal approach (mean annual runoff was calculated from a sum of mean monthly values i n the Thornthwaite approach). P o t e n t i a l development therefore, e x i s t s f o r a p p l i c a t i o n of the method to annual flows - 4 1 - i n p a r t i c u l a r years and ultimately to seasonal and monthly flows i n any period of a year. This development would have to be supplemented by a modelling technique to d i s t r i b u t e the seasonal or monthly volume estimates over a time basis (e.g., d a i l y ) . In such modelling, considerations w i l l have to be given to such p h y s i c a l aspects as snow-melt runoff lagging the actual melt process (e.g., estimated by some heat index), basin response to p r e c i p i t a t i o n input (e.g., unit hydrograph) and dependence or independence of events which influence runoff (e.g., i n the Thornthwaite approach monthly flows are i n t e r r e l a t e d ) . Hence, i t i s recommended that further studies be undertaken to develop the p o t e n t i a l of t h i s apparently powerful technique. - 42 - REFERENCES 1. Average Clima t i c Water Balance Data of the Continents. C.W. Thornthwaite Associates, Laboratory of Climatology, Publications i n Climatology, Volume 17, Number 2. 1964. 2. B j e r r i n g , J.H., J.R.H. Dempster and R.H. H a l l . UBC"Trip (Triangular Regression Package). The University of B r i t i s h Columbia, Computing Center. February 1969. 3. B r i t i s h Columbia Hydrometric Network Study. T. Ingledow and Associates Limited, Consulting Engineers, Volumes I and I I . A p r i l 1969. 4. Cavadias, G.S. Evaporation Applications i n Watershed Y i e l d Determination. Proceedings of Hydrology Symposium No. 2, Evaporation, National Research Council of Canada. March 1961. 5. Climate of B r i t i s h Columbia, Tables of Temperature, P r e c i p i t a t i o n and Sunshine. Province of B r i t i s h Columbia, Department of A g r i c u l t u r e . 1965. 6. Solomon, S.J., J.P. D e n o u v i l l i e z , E.J. Chart, J.A. Woolley and C. Cadou. The Use of a Square Grid System f o r Computer Estimation of P r e c i p i t a t i o n , Temperature and Runoff. Water Resources Research, The American Geophysi- c a l Union, Volume 4. October 1968. 7. Temperature and P r e c i p i t a t i o n Tables for B r i t i s h Columbia. Canada, Department of Transport, Meteorological Branch. 1967. 8. Thornthwaite, C.W. An Approach Toward a Rational C l a s s i f i c a t i o n of Climate. Geographical Review, Volume 38. January 1948. 9. Thornthwaite, C.W. and J.R. Mather. Instructions and Tables for Computing P o t e n t i a l Evapotranspiration and the Water Balance. Drexel I n s t i t u t e of Technology, Laboratory of Climatology, Publications i n Climatology, Volume 10, Number 3. 1957. 10. Turc, L.C. C a l c u l du B i l a n de L'Eau, Evaluation en Fonction des Pre- c i p i t a t i o n s et des Temperatures. International Association of S c i e n t i f i c Hydrology, General Assembly of Rome, Volume 38. 1954. 11. Ward, R.C. Observations of P o t e n t i a l Evapotranspiration (PE) on the Thames Floodplain 1959-1960. Journal of Hydrology, Volume 1. 1963. - 43 - APPENDIX A DATA Figure A - l South Thompson River Basin and Hydrometeorological Stations Figure A-2 Grid Square Layout Table A - l Meteorological Station Data and Snow Course Data Table A-2 Grid Square Physiographic Data Table A-3 Grid Square Sub-Basin Areas FIGURE A - l SOUTH THOMPSON RIVER BASIN AND HYDROMETEOROLOGICAL STAT IONS - 45 - FIGURE A - 2 GRID S Q U A R E L A Y O U T TABLE A - l METEOROLOGICAL STATION DATA Station Mean Annual Temp. ( F.) Mean Annual P r e c i p i t a t i o n (inch) Station Elevation • ( f t . ) Land Slope (ft./mi.) Distance to Bar r i e r (km.) Latitude Index (km.) Barrier Height ( f t . ) Shield E f f e c t ( f t . ) 1 Armstrong 45.0 18.82 1,190 506 201 151 4,790 9,600 2 Barriere 44.5 14.23 1,280 ' 695 217 235 6,690 11,100 3 Blue River 40.0 48.67 2,240 822 333 335 6,430 10,300 4 Chase 45.9 15.36 1,160 822 208 193 7,420 7,400 5 Chute Lake 39.1 23.29 3,920 885 127 73 3,380 8,000 6 D a r f i e l d - 16.40 1,250 695 225 249 6,600 11,500 7 Eagle Bay - 24.14 1,180 822 241 204 7,320 7,400 8 Falkland (Salmon R.) 44.6 18.39 1,500 758 194 153 5,210 10,300 9 Faquier 45.8 25.07 1,600 1,454 208 85 4,010 16,400 10 Gerrard 43.2 34.37 2,350 2,149 299 155 4,290 18,100 11 Glacier 37.2 57.11 4,090 2,402 350 239 3,320 12,500 12 Glacier Avalanche 36.5 69.71 3,860 2,655 348 237 3,440 7,400 13 Heffley Creek 42.1 12.87 2,240 442 184 199 6,830 8,300 14 Hemp Creek 39.5 23.77 2,100 822 277 314 7,390 9,600 15 Joe Rich Creek '40.3 22.92 2,870 885 154 86 3,300 7,600 16 Kamloops A 47.4 10.05 1,130 632 164 182 7,510 7,600 17 Kelowna 46.2 11.54 1,590 316 141 86 5,030 6,700 18 Lumby 44.0 17.33 1,700 758 195 128 4,080 7,300 19 Mable Lake - 21.20 1,310 1,138 210 136 3,560 10,600 20 Malakwa - 35.02 1,200 1,074 261 204 5,940 7,500 21 McCulloch 37.0 25.08 4,100 253 147 77 2,920 8,900 22 Monte Lake - 14.51 2,240 822 176 160 5,660 9,000 23 Needles - 26.06 1,420 822 207 85 5,330 16,400 24 Okanagan Centre 48.0 12.66 1,155 506 155 107 4,600 7,300 25 Revelstoke 45.1 43.17 1,500 1,264 295 201 6,470 7,200 26 Richland 43.8 25.53 2,350 948 215 126 3,480 9,600 27 Salmon Arm 46.0 21.29 1,660 822 217 179 7,340 11,000 28 Sicamous 46.0 25.93 1,400 885 243 193 7,240 11,000 29 Sidmouth 43.0 43.16 1,410 1,074 284 180 6,210 17,400 30 Shuswap F a l l s - 21.10 1,450 1,011 206 133 3,990 7,600 31 Sorrento - 21.15 1,280 442 223 199 7,500 7,400 32 Sugar Lake 43.0 30.53 2,000 1,390 224 139 2,700 10,600 33 Tappen 45.1 20.13 1,450 822 221 188 7,030 10,400 34 Vavenby 43.4 17.05 1,465 1,138 269 279 6,310 16,000 35 Vernon (Coldstream) 45.4 15.28 1,580 1,074 182 131 3,810 7,800 36 V i n s u l l a - 12.90 1,170 948 190 206 6,590 9,400 37 Westwold 43.6 12.63 2,025 1,074 176 154 5,290 8,800 TABLE A - l SNOW COURSE DATA A p r i l 1 Distance Water to Latitude B a r r i e r S h i e l d Equivalent E l e v a t i o n Land Slope B a r r i e r Index Height E f f e c t S t a t i o n (inch) ( f t . ) (ft./mi.) (km.) (km.) ( f t . ) ( f t . ) 1 Albreda Mountain 26.8 6,300 2,971 373 381 7,100 14,800 2 Enderby 32.0 6,250 1,201 227 172 4,200 14,800 3 F i d e l i t y Mountain 52.5 6,150 3,097 336 235 5,500 11,000 4 Koch Creek 29.3 6,100 ' 2,402 206 83 6,000 16,400 5 Mission Creek 19.7 6,000 632 174 104 4,300 10,200 6 Mount Abbot 45.5 6,800 2,465 352 241 5,500 11,000 , 7 Mount Cook 54.1 6,000 2,149 335 345 6,800 12,300 8 Park Mountain 33.3 6,200 1,327 231 151 4,900 14,200 9 Revelstnke Mountain 45.6 6,000 1,833 300 216 5,400 10,300 10 S i l v e r Star Mountain 23.0 6,050 1,138 200 141 4,900 14,200 11 Trophy Mountain 25.0 6,250 1,643 285 304 6,600 15,400 12 Up-per Goldstream 43.3 6,300 2,339 340 288 6,600 22,300 13 White Rock Mountain 19.6 6,000 758 137 103 3,000 5,800 TABLE A - l , Page 2 of 2 -= 48 - TABLE A-2 GRID SQUARE PHYSIOGRAPHIC DATA Distance Area of Area of Average to Latitude Shield Lake In Square Square Elevation Land Slope Barrier Index Effect Square In Basin No. (ft .) (ft . /ml.) (km.) (km.) (ft.) (sq. km.) (sq. km.) 1 3,944 190 160 135 6,722 1.00 4.37 2 4,233 316 168 145 6,712 0.00 6.25 3 3,689 126 160 125 6,466 1.05 9.37 4 3,500 126 168 135 6,589 7.26 96.87 5 4,233 695 176 145 6,744 2.42 96.87 6 4,533 316 184 155 6,722 2.42 35.62 7 3,478 695 193 165 7,000 7.66 22.50 8 2,333 632 201 175 7,066 0.80 9.37 9 3,500 506 209 185 7,466 0.00 2.50 10 4,878 885 168 125 6,267 0.80 5.62 11 4,111 1,011 176 135 6,755 0.80 95.62 12 3,700 1,138 184 145 11,211 1.61 100.00 13 3,756 1,264 192 155 6,789 3.63 100.00 14 3,178 695 201 165 6,789 0.00 100.00 15 2,100 . 506 209 175 7,200 6.45 97.50 16 3,189 885 217 185 7,311 3.63 .66.25 17 3,744 1,391 225 195 7,611 2.82 13.75 18 4,578 1,138 234 205 8,234 0.00 7.50 19 4,533 l,-327 242 215 8,522 0.00 7.50 20 3,733 1,138 250 225 11,200 0.80 70.50 21 3,433 569 258 235 10,677 2.82 21.70 22 5,111 1,580 184 135 6,400 1.21 77.50 23 4,211 948 192 145 11,422 1.21 99.37 24 3,011 1,075 200 155 11,068 0.00 100.00 25 3,489 759 209 165 6,789 0.80 100.00 26 3,000 1,075 217 175 7,045 1.21 100.00 27 2,444 1,075 225 185 7,356 10.08 100.00 28 2,856 253 233 195 7,556 9.68 94.37 29 3,889 1,264 241 205 7,900 0.00 95.62 30 3,578 1,327 250 215 8,411 14.11 81.87 31 3,422 2,023 258 225 8,389 17.74 100.00 32 3,933 1,138 266 235 11,100 5.65 37.50 33 4,411 948 200 145 11,289 2.82 13.75 34 3,322 1,391 208 155 6,744 0.00 93.12 35 3,844 1,327 216 165 10,966 2.02 100.00 . 36 3,867 1,580 225 175 6,867 0.00 100.00 37 3,322 1,643 233 185 7,122 0.00 100.00 38 2,022 632 241 195 7,477 21.77 100.00 39 2,633 1,770 249- 205 7,833 5.65 100.00 40 4,056 1,454 258 215 8,278 2.42 100.00 41 3,100 1,201 266 225 8,345 25.00 100.00 42 3,278 948 274 235 10,999 7.50 93.12 43 4,278 1,201 282 245 10,711 0.00 20.00 44 5,256 1,201 299 265 14,333 1.21 21.87 45 3,511 1,643 208 145 11,522 0.00 25.62 46 3,322 1,707 216 155 11,211 0.80 100.00 47 4,211 1,075 224 165 .11,089 4.44 100.00 48 4,222 948 233 175 7,000 1.61 100.00 49 3,689 1,138 241 185 7,156 1.61 100.00 50 2,178 1,327 249 195 7,311 4.44 100.00 51 2,200 1,075 257 205 7,655 18.54 100.00 52 4,067 1,011 265 215 8,167 0.00 100.00 53 4,000 1,201 274 225 • 8,522 0.00 100.00 54 3,089 759 282 235 11,200 28.63 100.00 55 3,222 1,327 290 245 10,633 30.24 88.12 56 4,711 948 298 255 13,411 6.45 53. 75 57 3,589 1,580 307 265 14,477 0.00 96.87 58 4,189 1,011 315 275 11,200 1.21 74.37 59 2,256 695 216 145 11,278 2.02 18.50 60 2,544 758 224 155 11,288 1.21 66.87 61 2,911 1,327 232 165 11,134 1.21 75.00 62 2,600 948 241 175 10,888 1.61 95.62 63 • 2,422 948 249 185 10,901 24.19 100.00 64 2,211 695 257 195 7,389 2.82 100.00 65 1,767 442 265 205 7,556 34.27 100.00 66 3,200 2,212 273 215 7,900 0.00 100.00 67 4,489 1,643 282 225 8,411 0.00 100.00 TABLE A-2, Page 1 of 4 - 49 - TABLE A-2 GRID SQUARE PHYSIOGRAPHIC DATA Distance Area of Area of Average to Latitude Shield Lake in Square Square Elevation Land Slope Barrier Index Effect Square in Basin No. (ft.) (ft . /mi.) (km.) (km.) (ft.) (sq. km.) (sq. km.) 68 5,311 2,023 290 235 8,389 1.21 100.00 69 3,567 1,138 298 245 10,677 6.85 100.00 70 3,078 1,391 306 255 10,441 . 8.87 100.00 71 3,156 1,580 315 265 13,767 2.42 100.00 72 4,200 1,454 323 275 14,734 1.61 71.25 73 • 4,000 1.011 331 285 14,499 0.00 0.62 74 4,578 190 191 105 7,011 10.48 21. 75 75 4,378 253 198 115 7,456 12.90 •32.50 76 2,911 1,075 224 145 11,345 1.21 25.62 77 1,622 569 232 155 11,289 1.21 46.62 78 2,144 759 240 165 11,289 5.65 61.75 79 2,433 859 248 175 10,966 1.61 88.12 80 2,489 1,011 257 185 10,723 ' 24.19 100.00 81 3,000 1,327 265 195 7,122 3.63 100.00 82 2,178 822 273 205 7,589 30.65 100.00 83 4,078 1,643 281 215 7,889 0.00 100.00 84 5,078 1,391 290 225 8,322 0.00 100.00 85 5,500 1,327 298 .235 8,345 0.00 100.00 86 3,656 1,327 306 245 10,999 4.03 100.00 87 4,100 1,580 314 255' 10,488 2.42 100.00 88 3,889 1,011 322 265 13,767 4.84 100.00 89 3,300 1,264 331 275 14,333 2.82 100.00 90 3,867 1,517. 347 285 14,733 0.00 71.87 91 3,733 1,580 347 295 14,678 0.80 40.62 92 3,989 1,580 355 305 15,300 4.84 21.25 93 4,089 1,264 364 315 12,156 2.82 3.12 94 4,978 506 199 105 6,966 3.23 31.10 95 4,289 759 207 115 7,355 9.68 100.00 96 2,744 822 215 125 7,667 0.40 72.50 97 3,378 695 223 135 10,833 0.40 48.12 98 3,933 1,391 232 145 11,223 0.00 95.00 99 2,633 1,201 240 155 11,389 0.00 100.00 100 2,567 1,454 248 165 11,045 5.24 100.00 101 3,189 1,138 256 175 11,144 4.84 100.00 102 2,444 1,327 265 185 11,022 22.18 100.00 103 2,144 379 273 195 7,156 33.87 100.00 104 2,089 442 281 205 7,444 37.09 100.00 105 2,711 569 289 215 7,877 23.39 100.00 106 3,489 1,264 297 225 8,145 17.34 100.00 107 . 3,633 1,264 306 235 8,522 4.84 100.00 108 3,500 1,201 314 245 8,034 5.65 100.00 109 4,522 1,327 322 255 10,633 2.02 " 100.00 110 4,400 1,011 330 265 13,411 1.61 100.00 111 4,811 1,770 339 275 14,477 6.45 100.00 112 4,544 3,224 347 285 11,200 2.42 100.00 113 4,856 2,844 355 295 14,778 0.00 100.00 114 4,378 2,149 363 305 14,955 3.63 100.00 115 4,700 1,517 371 315 12,156 3.63 83.12 116 5,000 2,212 380 325 12,444 2.42 64.37 117 5,378 2,212 388 335 12,133 4.44 20.62 118 5,722 506 207 105 6,956 4.84 ' 49.25 119 4,656 1,327 215 115 7,267 0.80 100.00 120 2,889 569 223 125 7,489 1.61 100.00 121 2,567 948 231 135 10,578 0.80 100.00 122 2,933 632 240 145 10,001 1.21 100.00 123 2,800 1,264 248 155 11,278 0.00 100.00 124 3,078 1,517 256 165 11,288 3.23 100.00 125 4,944 1,517 264 175 11,134 0.00 100.00 126 4,678 1,327 272 185 10,888 2.82 100.00 127 . 3,167 1,517 281 195 7,200 5.24 100.00 128 3,567 1,075 289 205 7,311 3.63 100.00 129 3,356 1,391 297 215 7,556 20.16 100.00 130 2,356 1,517 305 225 7,900 18.95 100.00 131 2,489 1,011 314 235 8,322 16.93 100.00 132 2,800 1,011 322 245 8,389 1.61 100.00 133 3,989 1,770 330 255 10,677 1.61 100.00 134 5,200 1,264 338 265 10,411 1.61 100.00 TABLE A-2, Page 2 of 4 - 50 - TABLE A-2 GRID SQUARE PHYSIOGRAPHIC DATA Distance Area of Area of Average to Latitude Shield Lake in Square Square Elevation Land Slope Barrier Index Effect Square in Basin No. (ft.) (ft . /mi.) (km.) (km.) (ft.) (sq. km.) (sq. km.) 135 5,433 2,781 346 275 13,756 5 24 100.00 136 5,422 1,580 355 285 14,734 4 44 83. 75 137 6,133 2,465 363 295 14,555 0 80 87.50 138 5,756 2,718 371 305 14,900 1 61 47.50 139 6,189 2,908 379 315 15,244 1 61 63.12 140 5,867 2,908 388 325 12,555 1 61 71.25 141 6,033 2,592 396 335 12,267 0 80 35.00 142 5,633 190 215 105 7,289 4 84 38.70 143 4,456 758 . 2 2 3 115 7,011 4 03 100.00 144 3,422 1,138 231 125 7,456 4 84 100.00 145 3,200 1,327 239 135 10,589 3 23 100.00 146 2,789 1,201 247 145 11,011 7 26 100.00 147 3,089 1,580 256 155 11,367 25 40 100.00 148 2,489 1,075 264 165 11,244 19 35 100.00 149 3,089 1,327 272 175 11,090 1 61 100.00 150 4,900 1,833 280 185 10,966 0 80 100.00 151 4,489 1,707 289 195 10,856 0 80 100.00 152 3,356 1,391 297 205 7,333 . 2 42 100.00 153 3,967 2,086 305 215 7,589 0 00 100.00 154 4,300 3,160 313 225 7,889 0 00 100.00 155 5,167 3,097 321 235 8,189 0 00 100.00 156 4,900 2,086 330 245 8,322 2 42 100.00 157 4,222 1,770 338 255 10,655 3 23 100.00 158 5,122 2,149 346 265 10,532 2 82 96.87 159 5,711 1,707 354 275 13,767 6 45 35.00 160 5,633 2,275 36 3 285 14,489 2 42 9.37 161 5,111 1,896 396 325 12,244 0 00 8.12 162 5,422 2,971 404 3-35 12,600 0 00 3.75 163 4,944 569 222 105 7,322 0 00 0.62 164 3,756 1,896 231 115 7,011 0 00 95.00 165 3,089 759 239 125 7,355 1 21 100.00 166 3,444 1,327 247 135 7,667 2 42 100.00 167 4,056 1,391 255 145 10,833 2 02 100.00 168 4,944 1,075 264 155 11,256 0 00 100.00 169 4,467 2,465 272 165 11,389 4 44 100.00 170 3,677 2,339 280 175 11,178 15 32 100.00 171 3,256 1,327 288 185 11,144 1 21 100.00 172 4,489 1,833 297 195 11,022 0 80 100.00 173 3,989 2,023 305 205 7,066 0 00 100.00 174 3,256 1,833 313 215 7,444 0 00 100.00 175 4,500 2,339 321 225 7,877 1 21 100.00 176 6,156 3,413 329 235 8,278 2 02 100.00 177 6,256 3,160 338 245 8,345 0 80 88. 75 178 5,189 1,770 346 255 8,034 6 45 84.37 179 5,467 2,655 354 265 10,633 2 02 26.25 180 3,822 2,149 239 115 6,956 0 00 66.87 181 3,533 1,391 247 125 7,267 0 00 100.00 182 4,422 1,770 255 135 7,489 2 42 100.00 183 4,044 1,391 263 145 10,578 23 79 100.00 184 4,311 . 1,770 272 155 11,001 4. 03 100.00 185 4,822 1,075 280 165 11,522 1 21 100.00 186 5,522 2,212 288 175 11,288 0 80 100.00 187 4,856 1,896 296 185 11,011 1 61 100.00 188 4,144 1,833 304 195 10,922 2 42 100.00 189 4,200 2,086 313 205 7,200 3 23 100.00 190 4,889 1,707 321 215 7,311 2 02 96.87 191 5,956 2,275 329 225 7,556 3 23 65.62 192 7,067 2,149 337 235 8,234 0.00 12.50 193 6,489 2,465 346 245 8,522 0 80 6.25 194 5,178 1,770 247 115 7,289 0 00 38.12 195 5,200 2,592 255 125 7,344 0 00 97.50 196 4,756 1,580 263 135 7,456 0 40 89.37 197 5,089 2,275 271 145 10,589 1 21 93.75 198 4,478 1,707 279 155 11,011 2 02 100.00 199 4,467 2,781 288 165 11,278 0. 40 100.00 200 4,756 1,770 296 175 11,422 2 02 100.00 201 5,578 2,212 304 185 11,068 4 03 100.00 TABLE A-2, Page 3 of 4 - 51 - TABLE A-2 GRID SQUARE PHYSIOGRAPHIC DATA Distance Area of Area of Average to L a t i t u d e S h i e l d Lake i n Square Square E l e v a t i o n Land Slope B a r r i e r Index E f f e c t Square i n Basin No. ( f t . ) (ft./mi.) (km.) (km.) ( f t . ) (sq. km.) (sq. km.) 202 5,344 3,097 312 195 10,922 2.02 92.50 203 4,878 1,959 321 205 10,856 1.61 55.00 204 4,633 2,149 329 215 7,333 0.00 1.87 205 4,711 1,959 254 115 7,322 0.00 1.25 206 5,667 3,540 263 125 7,011 2.42 5.00 207 4,900 2,023 279 145 7,667 0.80 10.00 208 6,244 1,580 287 155 10,922 6.00 47.50 209 5,744 3,287 296 165 11,366 2.02 69.37 210 5,911 2,592 304 175 11,289 4.43 56.25 211 5,467 2,465 312 185 11,233 0.00 20.62 212 4,200 2,592 302 195 10,966 0.80 3.75 TABLE A-2, Page 4 of 4 - 52 - TABLE A-3 GRID SQUARE SUB-BASIN AREAS Area of Square in Sub-Basin (sq. km.) 8LC-3 8LC-19 8LD-1 8LE-69 Sq. No. Sugar Lake Mable Lake Adams Lake Shuswap Lake Total 1 7 9 11 14 26 27 28 29 30 31 32 33 36 37 38 39 40 42 43 44 45 46 47 48 49 50 51 52 53 54 55 57 58 59 60 61 '62 63 64 65 66 67 68 69 70 71 4.37 4.37 2 - - - 6.25 6.25 3 - - - 9.37 9.37 4 - 5 - - 6 - - - 35.62 35.62 96.87 96.87 96.87 96.87 22.50 22.50 9.37 9.37 2.50 2.50 1 0 - - - 5.62 5.62 95.62 95.62 12 - - - 100.00 100.00 1 3 - 100.00 100.00 - - 100.00 100.00 1 5 - - - 97.50 97.50 1 6 - - - 66.25 66.25 13.75 13.75 17 18 - - 0.62 6.88 7.50 19 - - 7.50 - 7.50 20 - - 70.50 - 70.50 21 - - 21.70 - 21.70 22 - - - 77.50 77.50 23 - - - 99.37 99.37 24 - 100.00 100.00 25 - - - 100.00 100.00 100.00 100.00 100.00 100.00 94.37 94.37 20.62 75.00 95.62 81.87 - 81.87 100.00 - 100.00 37.50 - 37.50 13.75 13.75 34 - - - 93.12 93.12 35 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 18.75 81.25 100.00 56.25 43.75 100.00 41 - - 98.13 1.87 100.00 93.12 - 93.12 20.00 - 20.00 21.87 - 21.87 25.62 25.62 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 35.62 64.38 100.00 87.50 12.50 100.00 88.12 - 88.12 56 - - 53.75 - 53.75 96.87 - 96.87 74.37 - 74.37 18.50 18.50 66.87 66.87 75.00 75.00 95.62 95.62 100.00 100.00 100.00 100.00 _ 100.00 100.00 100.00 100.00 100.00 100.00 5.63 94.37 100.00 4.37 95.63 100.00 100.00 - 100.00 100.00 - 100.00 TABLE A-3, Page 1 of 3 - 53 - TABLE A-3 GRID SQUARE SUB-BASIN AREAS Area of Square in Sub-Basin (sq. km.) 8LC-3 8LC-19 8LD-1 8LE-69 3q. No. Sugar Lake Mable Lake Adams Lake Shuswap Lake Total 72 _ _ 71.25 71.25 73 - - 0.62 - 0.62 74 - 21. 75 - - 21. 75 75 - 32.50 - 32.50 76 - - - 25.62 25.62 77 - - - 46.62 46.62 78 - - - 61.75 61.75 79 - - - 88.12 88.12 80 - - - 100.00 100.00 81 - - 100.00 100.00 82 - - - 100.00 100.00 83 - - - 100.00 100.00 84 - - - 100.00 100.00 85 - ' - - 100.00 100.00 86 - - 55.63 44.37 100.00 87 - - 100.00 - 100.00 88 - - 100.00 - 100.00 89 - - 100.00 - 100.00 90 - - 71.87 - 71.87 91 - - 40.62 - 40.62 92 - - 21.25 - 21.25 93 - - 3.12 - 3.12 94 - 31.10 - 31.10 95 - 100.00 - - 100.00 96 - 72.50 - - 72.50 97 - 48.12 - - 48.12 98 - 13.12• - 81.88 95.00 99 - - - 100.00 100.00 100 - - - 100.00 100.00 101 - - - 100.00 100.00 102 - - - 100.00 . 100.00 103 - - - 100.00 100.00 104 - - - 100.00 100.00 105 - - - 100.00 100.00 106 - - - 100.00 100.00 107 - • - - 100.00 100.00 108 - - 3.75 96.25 100.00 109 - - 46.87 53.13 100.00 110 - - 100.00 - 100.00. 111 - - 100.00 - 100.00 112 - - 100.00 - 100.00 113 - - 100.00 - 100.00 114 - - 100.00 100.00 115 - - 83.12 - 83.12 116 - 64.37 -, 64.37 117 - - 20.62. :- ' 20.62 118 - 49.25 - 49.25 119 - 100.00 - 100.00 120 100.00. • - - 100.00 121 93.75 6.25 100.00 122 - 36.25 - 63.75 100.00 123 - 20.00 - 80.00 100.00 124 - - - 100.00 100.00 125 - - - 100.00 100.00 126 - - - 100.00 IOO.OO 127 - - - 100.00 100.00 128 - - - 100.00 100.00 129 - - 100.00 100.00 130 - - - 100.00 . 100.00 131 - - - 100.00 100.00 132 - - - 100.00 100.00 133 - - 1.25 98. 75 100.00 134 . - - 37.50 62.50 100.00 135 - - 33.13 66.87 100.00 136 - - 28.13 55.62 83. 75 137 - - 87.50 - 87.50 138 - - 47.50 - 47.50 139 " - - • 63.12 - 63.12 140 - - 71.25 - 71.25 141 - - 35.00 - 35.00: 142 26.20 12.50 - - 38.70 TABLE A-3, Page 2 of 3 - 54 - TABLE A-3 GRID SQUARE SUB-BASIN AREAS Area of Square in Sub-Basin (sq. km.) 8LC-3 8LC-19 8LD-1 8LE-69 3q. No. Sugar Lake Mable Lake Adams Lake Shuswap Lake Total 143 48.13 51.87 _ 100.00 144 50.62 49.38 - - 100.00 145 40.00 60.00 - - 100.00 146 i 100.00 - - 100.00 147 87.50 - 12.50 100.00 148 - 46.87 - 53.13 100.00 149 - 11.25 - 88.75 100.00 150 - 3.75 - 96.25 100.00 151 - - - 100.00 100.00 152 - - - 100.00 100.00 153 - - - 100.00 100.00 154 _ i - - 100.00 100.00 155 - - - 100.00 100.00 156 - - - 100.00 100.00 15 7 - - - 100.00 100.00 158 - - - 96.87 96.87 159 - - - 35.00 35.00 160 - - - 9.37 9.37 161 - - 8.12 - 8.12 162 - - 3.75 - 3.75 163 .62 - - - 0.62 164 95.00 - - - 95.00 165 100.00 - - - 100.00 166 93.75 6.25 - - 100.00 167 38.13 61.87 - - 100.00 168 21.81 78.19 - - 100.00 169 - 100.00 - • 100.00 170 - 100.00 - - 100.00 171 - 93.75 - 6.25 100.00 172 - 56.25 - 43.75 100.00 173 - 6.25 - 93.75 100.00 174 - - - 100.00 100.00 175 - - - 100.00 100.00 176 - - - 100.00 100.00 177 - - - 88. 75 88. 75 178 - - - 84.37 84.37 179 - - - 26.25 26.25 180 66.87 - - - 66.87 181 100.00 • - - - 100.00 182 100.00 - - - 100.00 183 100.00 - - 100.00 184 98.75 1.25 - 100.00 185 48.12 51.88 - - 100.00 186 8.75 91.25 - - 100.00 187 13.13 86.87 - - 100.00 188 1.25 95.00 - 3.75 100.00 189 - 11.25 - 88.75 . 100.00 190 - - - 96.87 96.87 191 - - 65.62 65.62 192 - - - 12.50 12.50 193 - - - 6.25 6.25 194 38.12 - - - 38.12 195 97.50 - - 97.50 196 89.37 - - 89.37 197 93.75 - - - 93.75 198 100.00 - - - 100.00 199 100.00 - - - 100.00 200 100.00 - - - 100.00 201 96.87 3.13 - - 100.00 202 30.62 45.62 - 16.26 92.50 203 - - - 55.00 55.00 204 - - - 1.87 1.87 205 . 1.25 - - - 1.25 206 5.00 - - - 5.00 207 10.00 - - - 10.00 208 47.50 - - - 47.50 209 69.37 - - - 69.37 210 56.25 - - - 56.25 211 20.62 - - - 20.62 212 1.87 1.88 - - 3.75 16,447.00 TABLE A-3, Page 3 of 3 - 55 - APPENDIX B MONTHLY REGRESSION EQUATIONS FOR THE THORNTHWAITE APPROACH OF THE GRID SQUARE METHOD B . l Estimation of Monthly Temperature D i s t r i b u t i o n B.2 Estimation of Monthly P r e c i p i t a t i o n D i s t r i b u t i o n B.3 Estimation of Monthly P r e c i p i t a t i o n D i s t r i b u t i o n - 56 - B.1 Estimation of Monthly Temperature D i s t r i b u t i o n As discussed i n section 5.2, page 25, the twelve regression equations for mean monthly temperature are: T l = 28.1903 - 0.002675E - 0.00006324L2 ....(B.l) T2 = 29.9052 - 0.0000005027E2 - 0.00004295L2 ....(B.2) T3 = 41.1399 - 0.003314E - 0.00003267L2 ....(B.3) T4 = 54.5055 - 0.003337E - 0.0170DB ....(B.4) T5 = 60.3414 - 0.003647E ....(B.5) T6 = 66.2320 - 0.003410E (B.6) T7 = 71.4715 - 0.003342E ....(B.7) T8 = 70.1207 - 0.003307E - 0.00003050L2 (B.8) T9 = 61.2753 - 0.002820E - 0.00003509L2 ....(B.9) T10 50.0519 - 0.002385E - 0.00003762L2 (B.10) T i l = 41.7830 - 0.003236E - 0.0182L . . . . ( B . l l ) T12 = 35.8599 - 0.003191E - 0.0229L (B.12) where, T l through T12 i n c l u s i v e , are mean monthly temperatures f o r January through December i n c l u s i v e , E i s s t a t i o n elevation i n feet, L i s l a t i t u d e index i n kilometers and DB i s distance to b a r r i e r i n kilometers. - 57 - B.2 Estimation of Monthly P r e c i p i t a t i o n D i s t r i b u t i o n As discussed i n section 5.3, page 27, the twelve regression equations (using normal Stpreg routine of UBC Trip) f o r mean monthly p r e c i p i t a t i o n are: P l = 5. 3639 - 0.0474DB + 0.0001803DB2 - 0.00003784L2 (B.13) P2 = 6. 0267 - 0.0473DB - 0.0111L + 0.0001632DB2 (B.14) P3 = 0. 3673 - 0.009609L + 0.00005179DB2 : + 0.00000009314E2 - 0.0000002140HS2 . (B.15) P4 = 0. 6401 - 0.005257L + 0.00003020DB2 + 0.00000004901E2 - 0.000000001840SE2 (B.16) P5 = 0. 5333 + 0.0003027E + 0.00001089DB2 (B.17) P6 = 1. 1550 + 0.00002069DB2 (B.18) P7 = 0. 3615 + 0.0002073E + 0.00001713DB2 (B.19) P8 = 0. 7460 + 0.00002041DB2 (B.20) P9 = 0. 1776 + 0.0003149E + 0.00002154DB2 (B.21) P10 = 0. 8348 - 0.009903L + 0.00005539DB2 (B.22) P l l = 5. 8083 - 0.0452DB - 0.0119L + 0.0001676DB2 > • • • (B • 23) P12 = 1. 1343 - 0.0173L + 0.00009395DB2 (B.24) where, P l through P12 i n c l u s i v e , are mean monthly p r e c i p i t a t i o n s f o r January through December i n c l u s i v e , DB i s distance to b a r r i e r i n kilometers, L i s l a t i t u d e index i n kilometers, E i s elevation i n f e e t , HS i s average land slope and SE i s s h i e l d e f f e c t i n feet. - 58 - ( B.3 Estimation of Monthly P r e c i p i t a t i o n D i s t r i b u t i o n As discussed i n section 5.3, page 27, the twelve regression equations (using Stpreg with elevation included i n t o the regression equation re- gardless of s i g n i f i c a n c e ) f o r mean monthly p r e c i p i t a t i o n are: P l = :- - 0. 2672 + 0.00000008047E2 + 0 .00007911DB 2 - 0.00003614L2 ....(B.25) P2 = - o. 5433 + 0 .00000009233E 2 + 0 .00006207DB 2 - 0 .00002806L 2 (B .26) P3 = 0 .3673 - 0.009609L + 0.00000009314E2 + 0.00005179DB2 - 0.0000002140HS2 (B.27) P4 = 0. 6401 - 0.005257L + 0.00000004901E2 + 0.00003020DB2 - 0.000000001840SE2 (B.28) P5 = 0. 2283 + 0.005282DB + 0.00000006386E2 (B.29) P6 = - 0. 0397 + 0.009214DB + 0.00000005461E2 (B.30) P7 = - 0. 3860 + 0.008248DB + 0.00000004779E2 (B.31) P8 = - 0. 4172 + 0.009190DB + 0.00000004510E2 (B.32) P9 = - 0. 7209 + 0.0104DB + 0.00000007275E2 (B.33) P10 = 0. 6477 - 0.008663L + 0.00000003493E2 + 0.00005202DB2 (B.34) P l l = - 0. 6099 + 0.00000009757E2 + 0.00006920DB2 - 0.00002810L2 (B.35) P12 = - 0. 5036 + 0.00000008138E2 + 0.00008608DB2 - 0.00003795L2 (B.36) - 5 9 - APPENDIX C COMPUTER PROGRAMS Program C - l Comparison of Thornthwaite's and Turc's Evaporation Methods Program C -2 Snow-Melt Model and Pl o t Program C -3 Experimental Grid Square Method Program C -4 Experimental Grid Square Method With Snow Courses Added - 60 - Program C - l Comparison of Thornthwaite's and Turc's Evaporation Methods Both the Thornthwaite and Turc methods were programmed and the following program gives the d e t a i l s involved i n both methods. Data was taken from Reference 7 ( G l a c i e r , B.C.). Lines 0005 to 0115, i n c l u s i v e , comprise the Thornthwaite method of c a l c u l a t i n g evapotranspiration. The following l i s t describes the h i g h l i g h t s of t h i s part of the program: Lines Description 10 to 21 C o e f f i c i e n t s C^ of Equation 3.6 32 to 44 Equations 3.3 through 3.6 of section 3.1 45 to 115 C a l c u l a t i o n of actual evapotranspiration and runoff. Operations were derived from the descriptions on pages 190 to 193, i n c l u s i v e , of Reference 9 61 to 65 Equation 3.7 i n which S i s given four d i f f e r e n t values i n each of the four t r i a l s Lines 0116 to 0124 i n c l u s i v e , comprise Turc's formula that i s described i n s e c t i o n 3.1 (Formulas 3.1 and 3.2). The output on the fourth page consists of four t r i a l runs, one for each value of s o i l moisture holding capacity S (16, 14, 12 and 10 inches). The format of the output i s s i m i l a r to that used i n Reference 9. - 6 1 - The notation used i s as follows: T(*F) Temperature (degrees Fahrenheit) P P r e c i p i t a t i o n PE P o t e n t i a l Evapotranspiration P-PE P r e c i p i t a t i o n minus P o t e n t i a l Evapotranspiration ACC-P-WL Accumulated P o t e n t i a l Water Loss ST S o i l Moisture Storage CH-ST Change i n S o i l Moisture AE Actual Evapotranspiration P-AE P r e c i p i t a t i o n minus Actual Evapotranspiration FORTRAN IV G COMPILER MAIN 02-18-70 14:29:53 PAGE 0001 ^ 0001 0002 00C3 0004 50 DIMENSION I XI20) READ (5,50) U X U ) , 1 = 1 , 2 0 ) WRITE (6,50) {IXC I) , 1=1,20) FORMAT I20A4) C c c CALCULATION OF EVAPORATION BY THORNTHWAITE•S METHOD 0005 0C06 0007 SMCAP = 16. REAL INDEX,II DIMENSION T(12) ,CTEMP<12) , 1 I ( 1 2 ) , E ( 1 2 ) , C ( 1 2 ) CGC8 0009 DIMENSION P(12) , PERNF{12 ) ,ACCPWL(12),STI12 ) , C H S T I 1 2 ) , A E ( 1 2 ) , 1 AERNF{12) DIMENSION A R G U 2 ) 0010 0011 0012 C U ) = 0.74 C ( 2 ) = 0.78 C(3 3 = 1.02 0G13 0014 0015 .. . C ( 4 ) = 1.15 C ( 5 ) = 1.33 C<6) = 1.36 0016 0017 0018 C(7) = 1.37 C<8) = 1.25 C I 9 ) = 1. 06 0019 002 0 0021 0022 0023 0024 C I 1 0 ) = 0 . 9 2 C U D = 0.76 C(12) = 0.7G INDEX = 0.0 TEVAP = 0.0 TTOT = 0.0 0025 0026 .0.0 2.7 . - 5 PTCT = 0.0 READ (5,5) {T(K } » K=i,12) FORMAT U 2 F 6 . 1 ) 0028 0029 0030 6 READ(5,6) (PtK),K=1,12) FORMAT(12F6 .2 ) DO 10 K=l,12 0G31 C c. CTEMP(K) = ( T ( K ) - 3 2 . ) * ( 5 . / 9 . ) INPUT DATA— TEMP. <*F) 0032 0033 C PREC. UN.) IF ICTEMP(K) .LE.0.0) I K K ) = 0.0 IF (CTEMPIK).LE.0.0) GO TO 10 0 034 0035 0036 _ 10 I K K ) = {CTEMP(K)/5.)**1.514 INDEX = INDEX + I I ( K) DO 11 K=l,12 0037 0038 0039 11 PTOT = PTGT + P(K) TTOT = TTOT + TIK) FAVG = TTOT/12. 0040 0041 .... 0042 ._ F = C.93/12.42 - AL0G10(INDEX)) DO 15 K=l,12 IF (CTEMP(K).LE.0.0) EJK) = 0.0 0043 0044 IF (CTEMPIK).LE.0.0) GO TO 15 E i K ) = C t K ) * EXP{ 2. 303*( 0. 204 + F*<-1. - AL0G10 (I NDEX) ) + F*AL0G10< 1 C T E M P ( K ) ) ) ) / 2 . 5 4 c c c EIK) IS COMPUTED IN CM. BUT CHANGED INTO IN. FORTRAN IV G COMPILER MAIN 02-18-70 14:29:53 PAGE 0002 63 0045 CC46 0047 0048 15 TEVAP = TEVAP + E l K ) 1 CONTINUE J = 0 AETOT = 0.0 0049 0050 .0051 00 5 2 0053 0054 16 AERTGT = 0.0 PERTOT = 0.0 DO. 16..K = U 1.2 PERNF(K) = P(K) - E<K) PERTOT = PERTOT + PERNF(K) IF(PERTOT.LT.O.O) GO TO 30 CG55 0056 _0_0.57_ 0058 0059 0C60 DO 17 K=l,.12 IFIPERNF(K) .GT.C.C) ACCPWHK) = 0.0 IFIPERNF(K) .LT.O.O) ACCPWLIK.) = PERNFIK) 17 IF(PERNFIK).LT.O.O) ACCPWL(K) = ACCPWL(K) + DO 19 K=l,12 IFiACCPHUK).EQ.O.0? GO TO 18 ACCPWLIK-1) 0061 0062 -006 3 0064 0065 0066 IF( SMCAP.EQ. 16. ) ARG(K) = A L 0 G 1 0 U 6 . ) - 0 . 0271 8513* (-ACCPWL I K ) ) IF(SMCAP.EQ.14. ) ARG(K) = AL0G10(14.) IFtSKCAP.EQ.12.) ARG(K) = AL0G10(12.) IFISMCAP.EQ.IO.) ARG(K) = A L O G l O f l O . ) ST(K) = EXP(2.303*ARG(K) ) J = J + 1 0 .0310 5843*(-ACCPWH K)) 0 .03627738*(~ACCPWL(K)) 0.0433C699*(-ACCPWL(K)) 0067 C068 0069_ CC7C 0071 0072 GO TO 19 18 IF{CTEMP(K).GT.O.O) ST{K) = SMCAP IF (CTEMP(K).LT.C.O) ST(K) = SMCAP + PERNF(K) I F ( K . G T . l ) ST(K) = S T ( K - l ) + P<K) I F ( J . G T . O ) ST(K) = S T ( K - l ) + PERNFi K) IF(CTEMP(K).LT.O.O) GO TO 19 0073 0074 0075 0076 0077 0078 19 IFIST(K).GT.StfCAP) ST (K ) = SMCAP CONTINUE D0_ 20 K = l t l 2 I F ( K . E Q . l ) CHST<K) = 0.0 I F ( K . E Q . l ) GO TO 20 CHST(K) = - ( S T ( K - l ) ST{K) ) 0079 0080 OC 8.1 C082 0083 0084 IF(CTE K P C K ) * L E . 0 . 0 ) CHST(K) = 0.0 IF<ST(K-1).GE. SMCAP) CHST(K) = 0.0 .20 . CONTINUE DO 21 K=l,12 AE(K ) = P(K) + {-CHST1K >> IF(CHST(K).GE.O.O) AE(K) = E ( K) 0085 0086 .0087 0088 0089 0C9C 21 CONTINUE DO 22 K=l,12 AEPNF(K) = P(K) - AE(K) 22 AERTOT = AERTOT + AERNF(K) DO 28 K = l i 1 2 28 AETOT = AETOT + AE(K ) 0091 0C92 .CO9 3 0094 0CS5 0C96 GO TO 32 30 00 31 K=l,12 __A EJ K) = P( K l AERNF< K ) = P(K) - AE(K) AETOT = AETGT + AE(K) 31 AERTOT = AERTGT + AERNF(K) 0097 0C98 0099 32 WRITE<6,40) (T(K) , K = l ,12) »FAVG WRITE(6,41) < P ( K ) # K = l f l 2 ) , P T 0 T WRITE<6.42) (£(K> ,K = 1 ,12) ,TEVAP FORTRAN IV G COMPILER MAIN 02-18-70 14:29:53 PAGE 0003 0100 WRITE(6,43) (PERNF(K) ,K = 1,12)» PERTOT 0101 IFCPERTOT.LT.O . O GO TO 33 0102 W R I T E ( 6 » 4 4 ) (ACCPWL{K),K=1,12) 010 3 WRITE(6,45) ( S T ( K ) , K ~ l f 12) 0104 WRITE(6,46) CCHSTCK),K=lt12) 010 5 33 WRITE(6,47) (AECK),K=1,12),AETOT . ._ _ .0 1.C 6 WRITEC6,48) (AERNFCK) ,K=1, 12) •AERTOT 01C7 40 F O R M A T C « T C * F ) • ,12F6. 1,F8.1) o i c e 41 FORMAT(* P • ,12F6.1,F8.1) 0109 42 FORMAT(* PE ' , 12F6. 1 , F 8 . 1 ) o n e 43 FCPMATC'P-PE • ,12F6.1,F8.1) 0111 44 FORMAT!»ACC-P-WL* ,12F6.1) 0112. 45 FORMAT <'ST «,12F6.1) 0113 46 FORMATC'CH-ST »,12F6.1) 0114 47 FORMATC *AE •,12F6.1,F8.1) 0115 48 FGPMATC'P-AE ', 12F6.1,F8.1) C C CALCULATION OF EVAPORATION BY TURC'S METHOD _ C . INPUT I N'T 0 T U R C S EQ'N IS *C € MM. 0116 c CT = I FAVG - 32.)*<5./9.) 0117 PP = PT0T*25.4 0118 FPPT = 300. + 25.*CT + 0.05*CT*CT*CT 0119 EVAP = PP/SQRT C 0.9 + (PP/FPPT )*(PP/FP P T)) .. 0120 EVAP = EVAP/25.4 0121 PREC = PP/25.4 0122 RTUP = PREC - EVAP 0123 WRITE (6,60) PREC»EVAP»RTUR 0124 60 FORMAT C / * P R E C = ',F5.1,* C TURC ) E VAP . = • , F5 . 1 1 • RNF. =• , F 5 . 1/) 0125 SMCAP = SMCAP - 2. _ . . 0126 . IFCSMCAP.E0.8.) STOP 0127 GO TO 1 0128 END EXECUTION TERMINATED 6 5 $RUN -LQADff EXECUTION BEGINS DATA FROM GLACIER (D.G.T. PUBLICATION) _ I 1 « J _ 1.1. .5 18, .4 26 .._§_ 36 .0 45 .4 52 .7 57 .9 55. 8 48 .3 37.4 24 .3 18 .4 36 .2 P 7. 7 6 .1 5 .0 3 . 1 2 .6 3 .3 2 .9 2. 8 3 .7 5.C 6 .7 8 .3 5 7 . 1 PE 0. 0 0 .0 G .C 0 .9 2 .6 3 .8 4 .5 3 . 9 2 .4 0.9 0 .0 0 .0 19 .0 P-PE 7. 7 6 .1 5 .0 2 .2 -0 .C -0 .5 -1 .7 -1. 1 1 . 3 4.2 6 .7 8 .3 38 .1 ACC-P--WL 0. 0 0 .0 0 .0 0 .0 -0 .0 -0 .6 -2 .2 -3. 3 0 .0 0.0 0 .0 0 . 0 ST 23. 7 29 .8 34 . 8 16 .0 16 .0 15 .5 13 .9 1 3 . 0 14 .3 16.0 22 .7 31 .0 . . . . . .. C H - S X . ._0_.. 0 0 *o 0. ..0 0 ..o 0 .c -0 .._5_ _rA .5 -0. 9 1 .3 1.7 0 .0 0 .0 AE 0. 0 0 .0 C .0 0 .9 2 .6 3 .8 4 .4 3. 7 2 .4 0.9 0 .0 0 .0 18 .7 P-AE 7. 7 6 .1 > .0 2 .2 -0 . G -0 . 5 -1 . 5 -0. 9 1 .3 4,2 6 .7 8 .3 38 .4 PREC. = 57 . 1 (TURC)EVAP • — 13. 8 RNF 43. 3 J J *F_)_ .13.. .5 JL.8 •A_ ..2A .5 _36_ .0 45 .4 52 .7 57 .9 55. 8 48 .3 37.4 24 .3 18 .4 36 .2 P 7. 7 6 .1 5 .0 3 . 1 2 . 6 3 .3 2 .9 2 . 8 3 .7 5.0 6 .7 8 . 3 57 . 1 PE 0 . 0 0 .0 0 .0 0 .9 2 .6 3 .8 4 .5 3. 9 2 .4 0.9 0 .0 0 .0 19 .0 P-PE 7. 7 6 .1 5 .0 2 .2 -0 .0 -0 .5 -1 .7 -1. 1 1 . 3 4.2 6 .7 8 .3 38 . 1 ACC-P-•WL 0. 0 0 .0 G . 0 0 .0 -0 .0 -0 .6 -2 .2 -3. 3 0 .0 0.0 0 .0 0 .0 ST 21. 7 27 .8 3 2 .8 14 .0 14 . G 13 • 11 .9 11. 0 12 .4 14. C 20 .7 29 .0 . _ CH-ST .0 _Q. .0 0 . G 0 .0 0 .0 -0 .5 -1 .5 -0. 9 1 .3 1.6 0 .0 0 .0 AE o. 0 C .0 G .0 0 .9 2 .6 3 .8 4 .4 3. 7 2 .4 0.9 0 .0 0 .0 18 .6 P-AE 7. 7 6 .1 5 .0 2 .2 -0 .0 -0 .5 -1 . 5 -0. 9 1 .3 4.2 6 .7 8 .3 38 .5 PREC. • — 57 . 1 (TURC)EVAP 13. 8 RNF * — 43. 3 T ( *F ) .13.. .5. 18. .4 26 . 5 36 .0 45 .4 52 .7 57 .9 55. 8 48 . 3 37.4 24 .3 18 .4 36 .2 P 7. 7 6 . 1 5 .0 3 . 1 2 .6 3 .3 2 .9 2. 8 3 .7 5.0 6 .7 8 .3 57 .1 PE 0. 0 0 .0 0 .0 0 .9 2 .6 3 .8 4 . 5 3. 9 2 .4 0.9 0 .0 0 .0 19 .0 P-PE 7. 7 6 • 1 5 . 0 2 .2 -0 .0 -0 .5 -1 .7 -1 . 1 1 .3 4.2 6 .7 8 .3 38 .1 ACC-P-•WL 0 . 0 0 .0 0 .0 0 .0 -0 .0 -0 .6 -2 .2 -3. 3 0 .0 0. 0 0 .0 0 .0 ST 19. 7 25 .8 30 .8 12 .0 12 .0 11 .5 10 .0 9. 1 10 .4 12*0 18 .7 27 .0 CH-SX. ,0. .0 0. „.jQ__ 0 .0 0 .0 0 . c -0 .5 -1 .5 -0. 9 1 .3 1 . 6 0 .0 0 .0 AE 0 . 0 0 .0 0 . 0 0 .9 2 .6 3 .8 4 .4 3. 7 2 .4 C. 9 0 .0 0 .0 18 .6 P-AE 7. 7 6 .1 5 .0 2 .2 -0 .0 -0 .5 -1 .5 -0. 9 1 .3 4.2 6 .7 8 . 3 38 .5 PREC. • ~ 57 .1 (TURC) EVAP • —- 13. 8 RNF • ™ 43. -3. TI * F.) 13. .5. 18 .4 26 * _ 36 .0. 45 •A _52 .7 57 .9 - 55_. 8 48 .3 37.4 24 .3 18 .4 36 .2 P 7. 7 6 .1 5 .o" 3 . 1 2 .6 3 .3 2 .9 2. 8 3 .7 5. 0 6 .7 8 .3 57 .1 PE 0. 0 0 .0 C .0 0 .9 2 .6 3 .8 4 .5 3. 9 2 .4 0.9 0 .0 0 .0 19 .0 P-PE 7. 7 6 . 1 5 . 0 2 . 2 -0 .0 -0 .5 -1 .7 -1. 1 1 .3 4.2 6 .7 8 .3 38 .1 ACC-P--WL 0. 0 0 .0 0 .0 0 .0 -0 .0 -0 .6 -2 . 2 -3. 3 0 .0 0.0 0 .0 0 .0 ST 17. 7 23 .8 28 .8 10 .0 10 .0 9 .5 8 .0 7. 2 8 .5 10.0 16 .7 25 .0 CH-ST _JCL. 0 0 .0 0 .*XL _Q .0 0 . 0 „_-o .5 -1 .5 -0. 8 1 .3 1 .5 0 .0 0 .0 AE 0. 0 0 .0 0 .0 d .9 2 .6 3 .8 4 -a . — 3. 6 2 .4 0.9 0 .0 0 .0 18 . 5 P-AE . 7. 7 6 . 1 .0 2 .2 -0 .0 -0 .5 -1 .5 -0. 8 1 .3 4.2 6 .7 . 8 .3 38 .6 PREC. 57 .1 (TURC)EVAP 13. 8 RNF • ~ 43. 3 STOP 0 EXECUTION TERMINATED - 66 - Program C-2 Snow-Melt Model and Plot The s i m p l i f i e d snow-melt model and plots described i n section 4.2 are presented i n the following two programs. The input of the f i r s t program, shown on the f i r s t page, consists of d a i l y maximum and minimum temperatures and water equivalent of snow pack which are obtained from snow pi l l o w charts. The d e t a i l s of the method can e a s i l y be followed by reading the Fortran statements. The Do Loop ( l i n e s 13 to 27) of statement number 30 picks out both incremental temperature r i s e s and incremental melt but ignores temper- ature f a l l s (below 32 F) and snow pack accumulations. Melt i s compiled as accumulated incremental water equivalent loss with the corresponding accumulated degree-days with lags of zero, one, two and three days. An example of a t r i a l run with data from B a r k e r v i l l e (1968-1969) i s given on the t h i r d page. The output of the f i r s t program i s used as the input of the second program which i s given on the fourth page. This program plots out the i n - put data on graph paper. The Fortran statements conform to the a v a i l a b l e p l o t t i n g routines of the P l o t t e r of the I.B.M. 360 Computer at U.B.C. A sample p l o t of the r e s u l t s f or data from B a r k e r v i l l e (1968-1969) i s given i n Figure 4.1 of section 4.1. FORTRAN IV G COMPILER MAIN 02-18-70 15:28:16 PAGE 0001 C SNOWMELT MODEL TO ESTIMATE MELT PRIOR TO APRIL 1 SNOW COURSE DATA. C METHOD IS OERIVED FROM SNOW PILLOW DATA BY COMPILING INCREMENTAL C TEMP. RISE (DEG-DAYS) WITH INCREMENTAL WATER EQUIVALENT LOSS. C OUTPUT DATA IS SET UP WITH ACCUMULATED DEGREE-DAYS AS THE INDEPEN- C C DENT VARIABLE AND ACCUMULATED MELT U N .) AS THE DEPENDENT VARIABLE N = NO. OF TEMP. DATA 0001 DIMENSION TMA X ( 1 0 0 ) t T H I N ( 1 0 0 ) , T ( 1 0 0 ) , W ( 1 0 0 ) , T A C C U M ( 1 0 0 ) , 1 WACCUM1100) ,TAVG(100) 0002 1 READ (5,5 ) N 0003 5 FORMAT (13) 0004 IF (N.EQ.O) STOP 000 5 NN = N + 1 0CC6 READ (5,10) ( T M A X U ) , T M I N U ) , W U ) , 1 = 2,NN) 0007 10 FORMAT ( 16X,2F6.1,6X,F7.2) 0C08 TAV = 0.0 0CG9 W( 1 ) = 0.0 0010 TACUMM = 0.0 0C11 WACUMM = 0.0 0012 J = 0 0 0 1 3 DO 30 I = 2,NN 0014 T U ) = 0.5*(TMAX(I) + T M I N U ) ) 0015 IF U W ( I - l ) - WU )) .LT.0.005) GO TO 15 0016 WDELTA = W ( I - l ) - W( I) 0017 WACUMM •= WACUMM + WDELTA .0018 0019 ---- — GO TO 2 5 IF ( I T U ) - 32. ).LT.0.005) GO TO 30 - 0C2C 25 TDELTA = T U ) - 32. 0021 IF (TDELTA.LT.O.005) TDELTA = 0.0 0022 TACUMM = TACUMM + TDELTA 0 02 3 J = J + 1 -- 0024 002 5 ... ...... M = J WACCUM!J) =WACUMM 0026 TACCUM(J) = TACUMM 0027 30 CONTINUE 0028 WACCUMlM+l) = 0.0 0029 WACCUMCM+2) = 0.0 ' 0030 WACCUMfM+3) = 0.0 0031 DO 31 I=2,NN 0022 TAVG(I) = 6 . 5 * ( T M A X ( I ) + T M I N U ) ) 0G33 31 TAV = TAV + TAVG( I) 0034 X = N 0035 TAV = TAV/X 0036 PAV = (TAV - 32.)*X 0037 WRITE (6,32) N 0038 3 2 FORMAT (//' PERIOO N = ',I5) 0C39 WRITE (6,33) TAV 004C 3 3 FORMAT (' AVERAGE TEMPERATURE FOR PERIOD I S S F 7 . 2 ) 0041 WRITE (6,34) PAV 1 0042 34 FORMAT (• PERIOD AVG. ACCUM. DEG-DAYS I S * f F 8 . 2 ) 0043 WRITE (6,35) 0044 35 FORMAT (• J ACCUM. ACCUM. ACCUM. ACCUM. ACCUM.'/ 1 • CEG-OAYS MELT MELT MELT MELT'/ 2 ' LAG-OD LAG-ID LAG-2C LAG-30*/) 0045 WRITE (6,40) (J,TACCUM(J),WACCUM<J) ,WACCUM(J+1) fWACCUM(J+2) , _ 1 WACCUM( J+3) , J = 1,M) F O R T R A N IV G C O M P I L E R M A I N 0 2 - 1 8 - 7 C 1 5 : 2 8 : 1 6 P A G E 0 0 0 2 C C 4 6 4 0 F O R M A T { 1 3 , F 7 . 2 , 4 F 9 . 2 ) 0 0 4 7 GO TO 1 0 0 4 8 END EXECUTION TERMINATED 69 $RUN -LOAC# EXECUTION BEGINS PERIOD N = 30 AVERAGE TEMPERATURE FOR PERIOD IS .32.88 PERIOD AVG• ACCUM. DEG-DAYS IS 26.25 J ACCUM. ACCUM. ACCUM. ACCUM . ACCUM. DEG-DAYS MELT MELT MELT MELT LAG-OD LAG-ID LAG-20 LAG-3D 1 3.00 0.0 C .C O.G 0.0 2 5.00 0.0 0 .0 0.0 0.0 3 6.50 0. 0 0.0 0.0 0.0 4 7.50 0.0 0.0 0.0 0.01 5 8.30 0.0 0 .0 0.01 0.33 6 18.00 0.0 C. 01 0.33 0.36 7 29.50 0.01 0 .33 0.36 0.39 8 36.25 0.33 0.36 0.39 0.58 9 41.50 0.36 0. 39 0. 58 1.03 10 57 .00 0.39 0 .58 1.03 1.35 11 . 7.1.00 . 0.58 1.03 1 .35 1 .45 * 12 81.00 1.03 1 .35 1.45 1.45 13 81. CO 1.3 5 1 .45 1.45 1.45 14 82.00 1. 45 1.45 1.45 1.45 15 86 .00 1.45 1.45 1.45 1.45 16 87.00 1.45 1.45 1.45 1 .45 17 .9 0.00 1.45 1.45 1.45 1.45 18 90 .50 1.45 1 .45 1.45 - 0.0 19 92. 50 1.45 1.45 0.0 0 .0 20 95 .50 1.45 C .0 0.0 0.0 STOP 0 EXECUTION TERMJ.NAT.ED. $SIG FORTRAN IV G COMPILER MAIN 0 2 - 1 8 - 7 0 1 5 : 2 5 : 1 1 PAGE 0 0 0 1 0 C 0 1 DIMENSION T < 1 0 0 ) , M ( 1 0 0 ) 0 0 0 2 C A L L PLOTS C C N = J FROM SNOWMELT MODEL 0GG3 C N = 20 0 004 . K_ = C 0 0 0 5 5 READ 1 5 , i o ) tTV ITVW( I ) , 1 = 1 , N ) 00C6 10 FORMAT 1 3 X , F 7.2 , F 9.2> 0007 11 K = K + 1 0 0 0 8 C A L L S C A L E ( T t N i l O . 0 , T M I N , 0 7 f 1 ) 0 0 0 5 CALL S C A L E ( W , N , 1 0 . 0 , W M I N , D W , 1 ) 001G C A L L AX IS ( 0 . 0 , 0 . 0 , ' A C C U M U L A T E D D E G - D A Y S ' , - 2 0 , 1 0 . 0 , 0 . 0,TMIN,OT) 0 0 1 1 CALL AX IS ( 0 . 0 , 0 . 0 , ' A C C U M U L A T E D MELT ( I N . ) • , + 22 , 1 0 . 0 , 9 0 . 0 , W M I N , D W ) 0 0 1 2 C A L L SYMBOL (2.0,9.5,0.35, « F I G . 4 . i « , o . o , 8 ) 0 0 1 3 C A L L SYMBOL ( 2 . 0 , 9 . 0 , 0 . 2 8 , * SNOWMELT PLOT* , 0 . 0 , 1 4 ) 0 0 1 4 C A L L SYMBOL 12.1,8.7,0.14, 3,0.0,-D 0 0 1 5 C A L L SYMBOL ( 2 . 1 , 8 . 4 , 0 . 1 4 , 1 , 0 . 0 , - 1 ) 0 0 1 6 C A L L SYMBOL ( 2 . 1 , 8 . 1 , 0 . 1 4 , 4 , 0 . 0 , - 1 ) 0 0 1 7 C A L L SYMBCL ( 2 . 1 , 7 . 8 , 0 . 1 4 , 5 , 0 . 0 , - 1 ) 0 0 1 8 C A L L SYMBOL ( 2 . 5 , 8 . 6 , 0 . 1 4 , ' L A G O-DAYS* , 0 . 0 , 1 0 ) 0 0 1 9 C A L L SYMBOL ( 2 . 5 , 8 . 3 , C . 1 4 , ' L A G 1 -DAYS * , 0 . G , 1 0 ) 002C C A L L SYMBOL (2 . 5 , 8 . 0 , 0 . 1 4 , ' L A G 2 -DAYS ' , 0 . 0 , 1 0 ) 0 0 2 1 C A L L SYMBOL 1 2 . 5 , 7 . 7 , G . 1 4 , ' L A G 3 - D A Y S ' , 0 . 0 , 10 ) 0 0 2 2 C A L L SYMBOL 1 2 . 1 , 7 . 0 , 0 . 1 4 , ' D A T A - B A R K E R V I L L E • , 0 . 0 , 17) 002 3 C A L L SYMBGL 1 2 . 5 , 6 . 7 , 0 . 1 4 , ' ( 1 9 6 8 - 6 9 ) ' , 0 . 0 , 9 ) 0 0 2 4 C A L L PLOT 1T( 1) , W ( 1 ) , 3 ) 002 5 DO 15 I = 1 , N 0 0 2 6 15 C A L L SYMBOL ( T l I) , W ( I ) , 0 . 0 7 , 3 , 0 . 0 , - 1 ) 0 0 2 7 C A L L L I N E I T ( 1) , W1 1) , N , + 1) 0 0 2 8 C A L L PLOT ( T ( 1 ) , W U ) , 3 ) 0 0 2 9 16 DO 2G 1 = 1 fN 0 0 3 0 IF ( I . E Q . N ) W(1+1) = 0.0 0 C 3 1 20 C A L L SYMBOL (T( I ) , W ( I + 1 ) , 0 . 0 7 , 1 , 0 . 0 , - 1 ) 0 0 3 2 C A L L L I N E 1 T( U ,W( 2) , N-i,+ l ) 0 0 3 3 C A L L PLOT (T 1 1) , W ( 1 ) , 3 ) 0 0 3 4 21 DO 25 1=1 ,N 0 0 3 5 IF ( I .EQ.N) W(1+1) = 0 . 0 0 0 3 6 IF ( I . E Q . N ) W1I-+2) = 0 . 0 0 0 3 7 25 C A L L SYMBCL (T( I) ,W(I+2 ) , 0 . 0 7 , 4 , 0 . 0 , - 1 ) 0 0 3 8 CALL L I N E ( T l l ) , W ( 3 > , N - 2 , + l ) 0 03 9 C A L L PLOT 1 T ( 1 ) , W ( 1 ) , 3 ) 0 0 4 0 26 DO 30 1 = 1 ,N 0 0 4 1 IF ( I . E Q . N ) W1I+1) = 0 . 0 0042 IF (I . E Q . N ) W(1+2) = 0 . 0 0 0 4 3 IF ( I . E Q . N ) WCI+3) = 0 . 0 0 0 4 4 3 0 C A L L SYMBOL 1T( I ) , W ( 1 + 3 ) , 0 . 0 7 , 5 , 0 . 0,-1) 0 0 4 5 C A L L L I N E ( T (1) ,W(4) , N - 3 , + l ) 0 0 4 6 C A L L PLOTND 0 04 7 STOP 0G4 8 END - 71 - Program C-3 Experimental Grid Square Method The following program i s an example of an a p p l i c a t i o n of the experi- mental g r i d square method i n which Thornthwaite 1s evapotranspiration method i s used. The set of p r e c i p i t a t i o n regression equations (Equations B.13 to B.24) used i n t h i s t r i a l run were derived by the normal Stpreg routine of UBC T r i p . The Thornthwaite method of c a l c u l a t i n g evapotranspiration i s represented by l i n e s 34 to 118,inclusive, and i s e s s e n t i a l l y i d e n t i c a l to Program C - l except for adaptation i n t o the g r i d square system of c a l c u l a t i o n s . Lines 119 to 124 represent c a l c u l a t i o n s of runoff for the sub-basin areas and t o t a l area. The f i f t h page shows the output printed f or this run and corresponds to the r e s u l t s of the t r i a l run presented i n Table 5.2. Both p o t e n t i a l and actual runoff were estimated but only actual runoff was analysed i n the development of the g r i d square method, as discussed i n section 3.1. The computer s t a t i s t i c s print-out of t h i s run i s given on the s i x t h page and shows that the t o t a l computer time used i s 22 seconds with a cost of s l i g h t l y over $2.00. Even though Thornthwaite's method seems i n - volved and lengthy on a g r i d square b a s i s , the t r i a l runs i n t h i s study used very l i t t l e computer time and therefore presented a very e f f i c i e n t method of compiling information. FORTRAN IV G COMPILER MAIN 02-18-70 17:00:07 PAGE 0001 72 0CC1 CGC2 REAL LAREA,L,INDEX DIMENSION S GNG ( 2 12 ) , L AR E A (212 ) , GS AF E A ( 21 2 ) , E ( 212 ) , HS ( 2 12 ), 1 S S ( 2 1 2 ) , D B ( 2 1 2 ) , L ( 2 1 2 ) ,HB<212) , S E ( 2 1 2 ) , 2 C T E M P ( 1 2 , 2 1 2 ) , 1 1 ( 1 2 , 2 1 2 ) , INDEXC 2 1 2 ) , F ( 2 1 2 ) , E V ( 1 2 , 2 1 2 ? , I ) T C 1 2 , 2 1 2 ) , P ( 1 2 , 2 1 2 ) , T T O T ( 2 1 2 ) , P T O T C 2 1 2 ) , T P E R N F ( 5 ) , PERNF(12,212),ACCPWL< 21, 2 1 2 ) , C ( 1 2 ) » T E V A P ( 2 1 2 ) , A < 2 1 2 , 5 ) , TAERNFI5) ,_J (212) j AETOT (212),AERTOTJ 212), PE_RTOT! 212) , 7 AERNF(12,212),PERUN(212, 5),AERUNt 212,5),FAVG(212) , 8 P W I N T ( 2 1 2 ) , P D I F ( 5 ) , P E D I F ( 5 ) , E V T 0 T { 2 1 2 ) 0003 READ ( 5 , 5) < S Q N O (I),LAREA(1) , G S A R E A ( I ) , E ( I ) , H S I I ) , S S ( I ) , D B ( I ) , 1 L( I ) , H B ( I ) , S E ( I ) , 1=1, 212) CCC4 5 FORMAT (13,1X,2F8.2,16X,3F6.0,2F5 . 0,2F7.0) 0005 DC 6 1=1 ,212 0 006 6 READ ( 5 , 7) (A(I,M),M=1,5) 0GC7 7 FORMAT (4X,5F8.2) 0008 DO IC 1= 1,212 0C09 T ( 1 , I ) = 28.1903 - 0 .2675D-02*E( I) - 0 . 6 3 2 4 D - 0 4 * L ( I ) * L ( I ) 0010 T ( 2 ,1 ) = 29.9052 - 0. 5 0 2 7 D ~ 0 6 * E ( I ) * E J I) - 0 . 4 2 9 5 D - 0 4 * L ( I ) * L ( I ) 0011 T ( 3, I ) = 41 . 1399 - 0 . 3314D-0 2*E(I ) - C. 3 2 6 7 D - 0 4 * L ( I ) * L ( I ) 0012 T ( 4 , I ) = 54.5055 - C.3337D-02*E(I ) - 0 . 0 1 7 0 * 0 8 ( I ) 0013 T ( 5 , I ) = 60.3414 - C.3647D-02*E(I) 0C14 T ( 6 ,1 ) = 66.2320 - 0.3410D-02*E(I ) 0015 T( 7, I ) = 71.4715 - G.33420-0 2 * E ( I ) 0016 T ( 8 , I ) = 70. 1207 - G.3307D-02*E(I ) - G.3G50D-C4*L( I )*UI) 0017 T ( 9 , I ) = 61.2753 - C.2820D-02*E(I) - 0 . 3 5 0 9 D ~ 0 4 * L ( I ) * L ( I ) 0018 T ( 1 0 , I ) = 50.C51S - 0.2385D-02*E(I) - C . 3 7 6 2 D - 0 4 * L ( I ) * L ( I ) 0C19 T(11 ,1 ) = 41.7830 - 0.3236D-02*E(I) - 0 . 0 1 8 2 * L ( I ) 0020 T<12, I ) = 35.859S - C.3191D-02*E(I) - 0 . 0 2 2 9 * L ( I ) 0021 P ( 1 , I ) = 5.3639 + 0. 180 3D-03*DB(I )*DB(I) - 0.0474*DB(I) 1 - -0.37840-04*1U)*L<I) 002 2 P(2, I) = 6.0267 + 0 . 1632D-03*DB(I)*DB(I) - 0.0473*DB(I) 1 - 0.0111*L ( I ) 0023 P ( 3 , I ) = 0.3673 + C.5179D-G4*DB(I)*DB(I) - 0.96090-02*L(I) 0024 0025 0026 0027 1 + 0.93140-07*E(I )*E( I) - P ( 4 , I ) = 0.6401 + 0.3020D- 1 + 0.4901D-07*E( I ) * E ( I) - P( 5 ,1 ) = 0.5333 + 0.1089D P { 6 , I ) = 1. 15 50 + 0.2C69D- P ( 7 , I ) = 0.3615 + 0.1713D 0.2140D-06*HS(I)*HS(I) 0 4 * D B ( I ) * 0 B ( I ) - 0.5257D-02*L(I ) 0. 1 8 4 G D - C 8 * S E ( I ) * S E ( I ) C 4 * C B ( I ) * C B ( I ) 04*DB(I ) *DBI I) 0 4 * C B ( I ) * D B ( I ) + 0.3027D-03*E( I ) + 0.2073D-03*E(I ) 0028 0029 0C3C 0031 003 2 PC 8 , I) = G.7460 + P (9, I ) = 0. 1776 + PC 10 ,1 ) = _0_. 8348_+ P l l l f l ) = 5.8C83 + 1 - 0. 0119*L ( I ) Pi 12, 1 ) = 1. 1343 + 0.2041D-04*DB(I)* D B{I) 0.2154D-0 4 * D B ( I ) * D B ( I ) _J_55_39JJ -04*DB( I )*DB( I ) 0.1676D-03*DB(I)*DB(I) - + 0.3149D-03*E(I ) - 0.9903D-02*L( IJ_ "~ 6 . 0452*08 U ) 0.9395D-C4*DB( I )*DBCI) - 0.0173*L(I) 0C33 10 C C CONTINUE CALCULATION GF EVAPORATION BY THORNTHWAITE* S METHOD C INPUT DATA- TEMP. (*F) C PREC. (IN.) C OUT PUT- EVAP. (CM.) C C C PREC. (CM.) RUNOFF (CM.) f FORTRAN IV G COMPILER MAIN 02-18-70 17 :00:07 PAGE 0002 73 • • 0034 0G35 0036 0037 C ( 1 ) = 0.74 C(2) = 0.78 C ( 3 ) = 1.02 C ( 4 ) = 1.15 • > 0038 0039 _ 0040 C(5) = 1.33 C< 6 ) = 1 .36 C (7 ) = 1 .37 0C41 0042 0043 C i £) = 1.25 C!9) = 1.C6 C U O J = 0.92 • 0044 0045 0046 C! 11) = 0.76 C( 12 ) = 0.7C DO 15 1=1,212 0C4 7 0048 0G49 INDEX!I) = 0.0 T T O T ( I ) = 0.0 PTCT (I) = 0.0 • • -- - • 00 5 0 0051 . GC5.2 0053 0054 CG55 15 T E V A P ( I ) = C O DO 16 M=l,5 TPERNF(M) = 0 . 0 16 TAERNF(M) = 0.0 DO 66 1=1,212 00 20 K=l,12 '. 0056 CTEMP(K,I) = ( T ( K , I ) - 3 2 . ) * ( 5 . / 9 . ) c - • c C INPUT DATA - TEMP. <*F) C PREC. (IN.) c • 0057 IF (CTEMP(K,I ).LE.0.0 ) I K K , I ) = 0.0 • 0058 0059 0G6C IF (CTEMP(K,I ).LE.O.O) GO TO ZO I K K , I ) = (CTEMP(K, I )/5.)**1.514 20 INDEX(I) = INDEX! I) + I K K , I) • 0061 0062 0063 DO 51 K=l,12 PTGT(I) = PTOT(I) + P ( K , I ) 51 T T O T ( l ) = T T C T ( I ) + T ( K , I ) • • - 0064 . 0065 „ .00 6.6 0067 0068 0069 FAVG(I) = TTOT( I ) /12. F ( I ) = 0.93/(2.42 - ALOG10(INDEX!I))) DO 25 K=l,12 IF(CTEMP(K,I).LE.O.O) E V ( K , I ) = 0.0 I F ( C T E M P ( K , I ) . L E . 0 . 0 ) GO TO 25 E V ( K , I ) = C(K)*EXP(2.303*!0.204 + F ! I ) * ! l . - ALCG10I INDEX!I>)) + • 0C7C 1 F ( I )*AL0G10(CT EMPIK, I) ) ) )/2.54 25 TEVAP(I) = TEVAPII) + EVIK,I) C C E V I K , I ) IS COMPUTED IN CM. BUT CHANGED INTO c IN. 0 07 1 L J ( I ) = C • • --- 007 2 0073 GG74 0075 0076 00 77 AETOT!I) = 0.0 AERTGT! I ) - 0.0 PERTOT!I) = 0.0 DO 56 K = f , 12 " " PEPNF!K,I) = P!K,I) - EV!K,I) 56 PERTOT!I) = PERTOT(I) + P ERNF(K,I) — • 0078 0G7S 008C IF!PERTOT(I ) .LT.0.0) GO TO 64 DO 57 K=l,12 IF!PERNFIK,I).GT.O.O) ACCPWL!K,I) = 0.0 — . . . . ...... — — FORTRAN IV G COMPILER MAIN 02-18-7C 17:00:07 PAGE 0003 0081 I F ( P E R N F ( K , I ) . L T . O . O ) ACCPWLCK,!) = PERNF(K,I I 0082 57 IF(PERNF(K, I ) .LT.C.C) ACCPWL(K,I) = ACCPWLIK,I) + ACCPWL<K~1, 13 CC82 DO 59 K = l , 1 2 0084 IF(ACCPWL(K,I ).EG.O.O) GO TO 58 0085 ARG(K, I ) = A L 0 G 1 0 U 4 . ) - 0.03105843*1-ACCPWLIK ,1)1 00 86 ST ( K , I ) = EXPI2.303*ARG(K,I)) 0087 J ( I) = J I I ) + 1 0088 GO TO 59 0C89 58 IFICTEMPIK,I).GT.O.O) S T ( K , I ) = 14. 0090 I F ( C T E M P ( K , I ) . L T . C . C ) S T ( K , I ) = 14. + PERNF(K, I ) 0C91 I F ( K . G T . l ) ST{K,I) = S T ( K - 1 , I ) + P ( K , I ) 0092 I F ( J I I).GT.O ) S T ( K , I ) = S T ( K - 1 , I ) + PERNF(K,I) 0093 IFiCTEMPtK, D.LT.O.O) GO TO 59 CC94 I F 1 S T ( K , I ) . G T . 1 4 . ) S T ( K , I ) = 14. 0095 59 CONTINUE 0096 DO 60 K=I, 12 0097 I F J K . E Q . l ) CHSTCK.I) = 0 . 0 0098 I F ( K . E Q . l ) GO TO 6C GC99 CHST(K.I) = - < S T ( K - 1 » I ) - S T ( K , D ) ' C1GC IF(CTEMF{K,I}.LE.0.0) CHST(K,I) = 0.0 0101 IF < S T I K - l , I ) . G E . 1 4 . ) CHST(K,I) = O.C 0102 60 CO NT IMJE 0103 DO 61 K = l f 1 2 0104 A E ( K , I ) = P ( K , I ) + (-CHST(K,I)) 0105 I F ( C H S T t K , I ) . G E . 0 . 0 ) AE(K,I) = E V ( K , I ) 0 106 61 ' CONTINUE 0107 DO 62 K=l,12 0108 AERNFIK, I ) = P(K,l> - A E ( K , I ) 0109 62 AERTOTl I ) = A E R T O T U ) + AERNFIK,I) c u e DC 63 K=1,12 0111 63 A E T O T U ) = A E T O T U ) + AE(K,I) 0112 GO TO 66 0113 64 DC 65 K=l,12 0114 AE(K,I) = PtK, I ) 0115 AERNFIK,I) = P ( K , I ) - A E ( K , I ) 0116 AETOT ( I ) = A E T O T U ) + AE( K , I ) 0 117 65..... A ERTOTU) = A E R T O T U ) + AERNF (K, I ) 0118 66 CONTINUE 0119 00 67 M=l,5 0120 DO 67 1=1,212 0121 PERUNII,M) = PERTOKI ) * A ( I ,M ) / 3 5.1577 0122 TPERNF(M) = TPEPNF(M) + PERUN(I,M) 0123 AERUN( I »M ) = AERTOTU ) * A ( I ,M)/35. 1577 0124 67 TAERNFIM) = TAERNF(M) + AERUN(I,M) 0125 DO 68 M = l , 5 0126 PEOIFIM) = ( (TPERNF(M) - TAERNF(M 3)*1CO.) /TAERNF(M) 0127 68 WRITE(6 ,69) M,TPERNF(M),PEOIFIM) G12 8 69 FORMAT! « SUB BASIN ='»I3,» P E RUNOFF = « , F 1 0 . 1 , IT C I F F . FROM AE RUNOFF * ) • CFS',F7.1,« PERCEN 012 9 DO 70 M=l,5 0 130 I F ( M . E Q . l ) PDIF(M) = (ITAERNF(M) - 1800.)*100. 3/1800. 0131 IF(M.EQ.2> PDIF(M) = UTAERNF(M) - 1090.1*100. )/1090. 0132 IFIM.EQ.3) PDIF(M) = (ITAERNF(M) - 2 5 6 0 . ) * 1 0 0 . )/2560. 0133 IFIM.EQ.4) PDIF(M) = ((TAERNFIM) - 5250.)*100. 3/5250. 0134 IF(M.EQ.5I POIF(M) = 1(TAERNF(M ) - I C 7 0 0 . ) * 100. 3/10700. FORTRAN IV G COMPILER MAIN 0 2 - 1 8 - 7 0 17:00:07 PAGE 0004 75 0135 0136 0137 013 8 70 71 WRITE(6,71) M,TAERNF{M),POIF<M) FORMAT{ IT OIFF, STOP END SUB FROM BASIN =•tI3,« AE ACTUAL RUNOFF') RUNOFF = ,,F10.1,' CFS«,F7.1,» PERCEN E X E C U T I O N T E R M I N A T E D 76 $RUN - L O A D S 5 = D A T A ( 5 1 ) E X E C U T I O N B E G I N S SUB B A S I N = Ska_M.SJjN.._=_ SUB B A S I N = SUB B A S I N = S U B B A S I N = 1 P E R U N O F F 2 PE R U N O F F 1 2 0 9 . 6 9 1 2 . 0 C F S C F S - 4 . 2 - 7 . 9 P E R C E N T D I F F , P E R C E N T D I F F , 3 PE R U N O F F 4 PE R U N O F F 5 P E R U N O F F FROM . _ . FROM 2 5 6 2 . 8 C F S - 1 . 9 P E R C E N T D I F F . F R O M 4 2 7 1 . 3 C F S - 7 . 8 P E R C E N T D I F F . FROM 8 9 5 5 . 5 C F S - 5 . 7 P E R C E N T D I F F . FROM A E R U N O F F AE R U N O F F A E R U N O F F AE R U N O F F A E R U N O F F SUB B A S I N = SUB B A S I N = SUBL B A S J N _ = SUB B A S I N = SUB B A S I N = 1 AE R U N O F F 2 A E R U N O F F 3 A E R U N O F F 4 AE R U N O F F 5 A E R U N O F F 1 2 6 2 . 3 C F S - 2 9 . 9 P E R C E N T D I F F . FROM A C T U A L R U N O F F 9 9 0 . 4 C F S - 9 . 1 P E R C E N T D I F F . FROM A C T U A L R U N O F F 2 6 1 _ 2 . 5 _ CjFS __2 .C P E R C E N T D I F F . F R O M A C T U A L R U N O F F 4 6 3 2 . 9 C F S - 1 1 . 8 P E R C E N T D I F F . FROM A C T U A L R U N O F F 9 4 9 7 . 9 C F S - 1 1 . 2 P E R C E N T C I F F . FROM A C T U A L R U N O F F S T O P 0 E X E C U T I O N T E R M I N A T E D $S IG * * * * * * * * * * * * * * * * * * * * * * * * * * * * S i l ! ) ! ! * * * * * ! ! ! * * ! ! : * ? * ) ? * ) ) ; * * * ^ * f 'r*^'*^',--'r^^'r^--r-^-c-f^-.--r-r-r-r--r- R F S N O . 77*3590 U N I V E R S I T Y OF E C C O M P U T I N G C E N T R E M T S < A N 0 5 9 ) J O B 77 U S E R : O E E C D E P A R T M E N T : C . E . * * * * ON AT 1 6 : 5 9 : 5 C **** O F F AT 1 7 : 0 2 : 0 8 **** E L A P S E D T I M E 1 3 8 . 0 2 S E C . **** C P U T I M E U S E D 2 2 . 5 8 5 S E C . **** S T O R A G E U S E D 5 9 1 6 . 0 5 6 P A G E - S E C . **** C A R D S R E A D 1 7 7 * * * * L I N E S P R I N T E D * * * * P A G E S P R I N T E D * * * * C A R D S P U N C H E D 2 1 5 7 0 * * * * DRUM R E A D S * * * * R A T E F A C T O R 2 8 6 0 . 9 * * * * A P P R O X . COST O F T H I S R U N C $ 2 . 1 6 * * * * F I L E S T O R A G E 1 8 P G - H R . C $ . 0 1 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * J r * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ^ V * * V * * * * * * * * * * * * ^ * * * ^ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ^ ************************************************************************************************ ************************************************************************************************ ************************************************************************************************ ************************************************************************************************ ******************************************************************************************** ************************************************************************************************ ************************************************************************************************ ************************************************************************************************ ************************************************************************************************ « * * i < c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * " * ' * * * " * * * * * * * * * * * * * ^ * * * * * * " * * * * ***i « " * * * * ! * * * ^ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * - 78 - Program C-4 Experimental Grid Square Method With Snow Courses Added The following program i s an example of the a p p l i c a t i o n of the experi- mental g r i d square method with the Thornthwaite approach and the addition of snow course data. This t r i a l was explained i n d e t a i l i n section 5.5. Individual monthly regression equations for A p r i l to November (Equations B.16 to B.23, i n c l u s i v e ) and a lumped winter season regression equation (Equation 5.7) were combined for the mean annual p r e c i p i t a t i o n estimates. Evapotranspiration i s calculated f o r the months of A p r i l to November and assumed to be zero i n the winter season (see discussion of section 5.5). A l l steps are e s s e n t i a l l y the same as i n Program C-3 except for the runoff estimates which are segregated i n the winter period (l i n e s 110 to 113, 117 to 122 and 127 to 130, i n c l u s i v e ) . The f i f t h page shows the output printed f or t h i s run and corresponds to the r e s u l t s presented i n Table 5.4 The computer s t a t i s t i c s p r i nt-out, given on the s i x t h page, again shows very l i t t l e computer time used. FORTRAN IV G COMPILER MAIN 02-18-70 15:29:22 PAGE 0001 79 0001 REAL LAREA,L,INDEX 0002 DIMENSION SQN0(212),LAREA(212),GSAPEAC 2 1 2 ) , E i 2 1 2 ) , H S ( 2 1 2 ) , 1 S S ( 2 1 2 ) , D B ( 2 1 2 ) , L ( 2 1 2 ) , H B ( 2 1 2 ) , S E ( 2 1 2 ) , 2 CTEMPt 12, 2 12), I K 12, 212) , INDEX! 212? ,F( 212) ,EVI 12,21 2> , 3 T(12,212) » P(12 »212 ) » T T 0 T ( 2 1 2 ) » P T O T 1 2 1 2 ) » T P ERNFI 5 ) , 4 PERNFI12,212),ACCPWL(21,212),G(12) , T E V A P ( 2 1 2 ) , A ( 2 1 2 , 5 ) , . _ 5_ _ J-AEP^F(5 ) , J{2a2),AET0T(212),AERJJ3TI212),PERT0T{212) , 6 A R G ( 1 2 , 2 1 2 ) , S T ( 1 2 , 2 1 2 ) , C H S T { 1 2 , 2 1 2 ) , A E ( 1 2 , 2 1 2 ) , 7 AERNF{ 1 2 , 2 1 2 ) » P E R U N ( 2 1 2 , 5 ) , A E R U N ( 2 1 2 , 5 ) ,FAVG(212), 8 PW INT(212 ) ,PDIF (5) ,PEDIF( 5 ), EVTOTI212 ) 0003 READ (5,5) (SQNO(I) , L A R E A { I ) , G S A R E A ( I ) , E ( I ) , H S ( I ) , S S ( I ) ,DB(I) , 1 L( I ), HB ( I ),SE( I ), 1=1,212) .0004 _ 5 FORMAT (I 3,1X,2F8.2 ,16X,3F6.0,2F5.0 ,2F7 .0) 0005 DO 6 1=1,212 0006 6 READ (5,7) (A(I,M),M=1,5) 0007 7 FORMAT (4X,5F8.2) 0008 DO 10 1=1,212 0009 T ( l , I i = 28.1903 - 0.2675D-02*E( I ) - 0 . 6 3 2 4 D - 0 4 * L ( I ) * L ( I) 0010 T ( 2 , I ) = 29.9052 - 0.5027D-06* E U ) * E ( I) - 0.42950-04*L(I )*L <I) o o u T ( 3 , I ) = 41. 1399 - 0 . 33140-02*E ( I ) - 0 . 3 2 6 7 D - 0 4 * L ( I ) * L { I ) 0012 T ( 4 , I ) = 54.5055 - 0. 3337D-02*E(I) - 0.0170*08(1) 0013 T ( 5 , I ) = 60.3414 - 0.3647D-02*E(I) 0014 T ( 6 , I ) = 66.2320 - 0.34100-02*E{ I ) 0015 T ( 7 , I ) = 71.4715 - 0.3342D-02*E(I) 0016 T ( 8 , I ) = 70.1207 - 0.3307D-02*E(I) - 0 . 3 Q 5 0 D - 0 4 * L ( I ) * L ( I ) 0017 T ( 9 , I ) = 61.2753 - 0.2820D-02*E( I ) - 0.3509D-04*L(I ) * L ( I ) 0018 T ( 1 0 , I ) = 50.G519 - 0.2385D-02*E(I) - 0 . 3 7 6 2 D - 0 4 * L ( I ) * L ( I ) 0019 T ( U , I ) = 41.7830 - 0.3236D-02*E ( I ) - 0 . 0 1 8 2 * L ( I ) 0020 T(12,1)= 35.8599 - 0.3191D-02*E(I) - 0 . 0 2 2 9 * L ( I ) 0 021 P ( 1 , I ) = 5.3639 + 0.1803D-03*CB(I )*DB( I) - 0.0474*DB(I) 1 - G . 3 7 8 4 D - 0 4 * L ( I ) * L ( I) 0022' P ( 2 , I ) = 6.0267 + 0. 1632D—03*DB(I)*DB(I) - 0.0473*DB(I) 1 - 0.01 U * L ( I ) 0023 P ( 3 , I ) = 0.3673 + 0.5179D-04*DB(I)*DB(I) - 0.9609D-02*L(I) 1 + 0.9314D-07*E( I ) * E ( I) - 0 .2140D-06*HS(I)*HSII) 0024 P ( 4 , I ) = 0.6401 + 0.302 0D-04*DB(I)*DB( I) - 0.5257D-02*L(I ) 1 + C . 4 9 0 l D - 0 7 * E ( I )*E( I) - 0. 1840D-08*SE11)*SE(I) 0G25 P<5,I) = 0.5333 + 0.1089D-04*DB<I )*0B( I ) + 0.3027D-03*E(I ) 0026 P ( 6 , I ) = 1. 1550 + 0 . 2C69D-04*DB(I)*DB(I) 0027 P ( 7 , I ) = 0.3615 + 0.17130-04*DB( I ) * D B ( I ) + 0.2073D-03*E(I ) 0028 P ( 8 , I) = 0.7460 + 0.20410-04*DB(I)*D8I I) 0029 P ( 9 , I ) = 0.1776 + 0.2 1 5 4 0 - 0 4 * D B ( I ) * D B ( I ) + 0.3149D-03*E<I) 0030 P ( 1 0 , I ) = 0.8348 + 0.5539D-04*D8(I)*DB(I) - 0.9903D-02*L ( I ) 0031 P ( 1 1 , I ) = 5.8083 + 0.1676D-G3*DB(I)*DB( I) - 0.0452*DB(I) 1 - 0 . 0 1 1 9 * L U ) 0032 P ( 1 2 , I ) = 1.1343 + 0.9395D-04*DB(I)*DB(I) - 0 . 0 l 7 3 * L ( I ) C c PWINT(I) IS STANDARD REGRESSION PREC. E Q« N. (NOV. - MAR.) c INCLUDING SNOW COURSE DATA 0 033 c PWINT(I) = - 21.5062 + 0.5143D~06*E( I )*E( I ) - 0 . 1 4 7 4 D - C 3 * L { I ) * L ( I ) 1 + 0.1647*DB( I) 0 034 10 c CONTINUE L c CALCULATION OF EVAPORATION BY THORNTHWAITE•S METHOD o o o o , o o -0 - J - J UJ : ro >— o o m o a -a cr o 2 CD c o X > z o m a z o ro I m <. t» TJ :•— w 'r- l O II ;o if - —i I O m !«-. <r!o J>I—i TJ im in < I-I 7N O II O •K- m x TJ m a *•»!—• ro m;«— <c.|— *-> ro o T l I I— a a 2 O m x o o o o o o o o o o o o -J o o o o o O vD no -0. f> U l U l ro —i o T i O o ro H ui m 3 7C TJ II • i—' X - < »—* fU T l O i • ro r* • m J> a o ui ro T li J> O I T> r~ o o ! + ITJ IS TJ —s Z «• O ! — ~ z a o —• o - » o o o o o o o o o o o o o o o a- t> ui J> uo ro i — o vo o o U l 00 ui .ro o o ii ii I-* ro o a ro z H n o *» m 7; —• X •» o *— r-# —4 i—i —' m — 2 il TJ li — — 7s 1—1 O Z *H 1—1 o m —- m 3 : • X TJ r- — m »-« 7? • ~ - - O 1—1 • + — o l - H U l •—1 • CD ~ » — O X * * -Sf —H r-4 H O w • ui ro >- o J> o o U l - J 0 0 0 0 TJ 70 rn o o 1—1 a > —i j> I —i m T̂ T J ro o o o o o o o o 0 0 o 0 U l U ! Ul U l U ! U l o* ut J> oj ro r- U l O —I H O - 1 o > ' D O m m m < O 70173 1— > O Z | Z 0 s TJ T l — ro II 2 r-i — ro ii ro o o 2 II w II U l 0 0 0 0 0 0 0 0 0 0 0 0 U l J> J> J> J> J> O vO OS -0 O U l I O O o o o o 0 0 0 0 0 0 J> J> J> J> J> UJ J> OJ ru r-. o <£s T J - I H p O O —4 —4 Z Q — ~> 0 0 0 ! I— I- —i —4 m 1—* ro t—• * - x b ' 1 H ~ l - < - r i « II II — I ii II il It- O O II o o ;ro - j • • O !•— O O O O • 'N O i 0 0 0 0 0 0 •-* vO cn |-j o ui ll il !n 11 li o • » • O ro v Q o ui ro OJ OJ 10 -si O OJ o 0 o p 0 0 0 0 OJ OJ UJ OJ 00 -<J o ui i o o o o o o 1— o ui ro -O l-sl 00 O cr TJ C Z TJ c > — I 1> I 70 o T l O o m T J —1 < 70 m > m 2 TJ O TJ O i-< * 2 Z T l F O R T R A N IV G C O M P I L E R M A I N 0 2 - 1 8 - 7 0 1 5 : 2 9 : 2 2 P A G E 0 0 0 3 81 0 G 7 6 C 0 7 7 0 0 7 8 0 0 7 9 A E P T O T M ) = 0 . 0 P E R T O T U ) = 0 . 0 DO 5 6 K = l , 1 2 P E P N F t K . I ) = P ( K , I ) - E V ( K , I ) 0 0 8 0 0 0 8 1 0 G 8 2 0 0 8 3 0 0 8 4 0 0 8 5 56 5 7 P E R T O T ( I ) = P E R T O T I l ) + P E R N F ( K , I ) I F t P E R T O T U ) . L T . O . O ) GO TO 6 4 DO 5 7 K = l , 1 2 I F ( P ER N Ft K U ) . G T . O . 6) A C C P W L ( K , l ) = 0 . 0 I F ( P E R N F ( K » I ) . L T . 0 . 0 ) A C C P W L ( K , I ) = P E R N F ( K , I I I F ! P E R N F I K , I ) . L T . O . O ) A C C P W L I K U ) = A C C P W L ( K - I ) + ACC PWL ( K - 1 , I ) 0 0 8 6 0 0 8 7 0 0 8 8 DO 59 K = l , 1 2 I F ( A C C P W L ( K , I ) . E G . 0 . 0 ) GO TO 5 8 A R G ( K , I ) = A L 0 G 1 0 U 4 . ) - 0 . 0 3 1 0 5 8 4 3 * ( - A C C P W L ( K , I ) ) 0 0 8 9 0 0 9 0 0 0 9 1 S T ( K , I ) = E X P ( 2 . 3 G 3 * A R G < K , m J { I ) = J U ) + 1 GO TO 5 9 0 0 9 2 0 0 9 3 0 0 9 4 5 8 I F i C T E M P t K t I ) . G T . O . O ) S T I K , I ) = 1 4 . I F ( C T £ M P ( K , I ) . L T . O . O ) S T ( K , I ) = 1 4 . + P E R N F ( K t I > I F ( K . G T . l ) S T ( K , I ) = S T t K - 1 , 1 ) + P t K , I ) 0 0 9 5 0 0 9 6 0 0 9 7 I F ( J I I ) . G T . O ) S T ( K , I ) = S T ( K - 1 , 1 ) + P E R N F t K , I ) I F 1 C T E M P I K , I > . L T . O . O ) GO TO 5 9 I F ( S T ( K , I ) . G T . 1 4 . ) S T ( K , I ) = 1 4 . 0 0 9 8 0 0 9 9 0 1 0 0 0 1 0 1 0 1 0 2 0 1 0 3 5 9 C O N T I N U E DO 6 0 K = l , 1 2 I F ( K . E Q . l ) C H S T ( K . I ) = 0 . 0 I F ( K . E Q . l ) GC TO 6 0 C H S T ( K , I ) = - ( S T ( K - 1 , I ) - S T ( K , I ) ) I F t C T E M P I K , I ) . L E . 0 . 0 ) C h :S T { K » I ) = 0 . 0 0 1 0 4 0 1 0 5 0 1 0 6 6 0 I F t S T ( K - l , I ) . G E . 1 4 . ) C H S T ( K , I ) = 0 . 0 C O N T I N U E DO 6 1 K = l , 1 2 0 1 0 7 0 1 0 8 0 1 C 9 6 1 A E ( K , I ) = P ( K , I ) + ( - C H S T ( K , l ) ) I F ( C H S T ( K , I ) . G E . O . O ) AE t K , I ) = E V ( K , I ) C O N T I N U E 0 1 1 0 0 1 1 1 0 1 1 2 . 6 2 0 0 6 2 K = 4 , 1 0 A E R N F I K , I ) = P t K , I ) - A E ( K , I ) A E R T O T U ) = A E R T O T U ) + A E R N F ( K , I ) 0 1 1 3 0 1 1 4 0 1 1 5 6 3 A E R T O T ( I ) = A E R T O T U ) + P W I N T U ) 0 0 6 3 K = l , 1 2 A E T O T U ) = A E T O T U ) + A E ( K , I ) 0 1 1 6 0 1 1 7 0 1 1 8 _ 6 4 GO TO 6 6 DO 6 5 K = 4 , 1 0 A E ( K , I ) = P t K , I ) 0 1 1 9 0 1 2 0 0 1 2 1 6 5 A E R N F I K , . I ) = P t K , I ) - A Et K , I ) A E T O T U ) = A E T O T U ) + A E ( K , I ) A E R T O T U ) = A E R T O T U ) + A E R N F ( K , I ) 0 1 2 2 0 1 2 3 0 1 2 4 6 6 A E R T O T U ) = A E R T O T U ) + P W I N T U ) C O N T I N U E DO 9 2 1 = 1 , 2 1 2 0 1 2 5 0 1 2 6 0 1 2 7 P E P T O T ( I ) = 0 . 0 E V T O T t I I = 0 . 0 DO 7 2 K = 4 , 1 C 0 1 2 8 0 1 2 9 0 1 3 0 7 2 9 2 E V T O T U ) = E V T G T ( I ) + E V ( K , I ) P E R T O T U ) = P E R T O T U ) + P E R N F t K , I ) P E R T O T U ) = P E R T O T U ) + P W I N T U ) F O R T R A N IV G C O M P I L E R M A I N 0 2 - 1 8 - 7 0 1 5 : 2 9 : 2 2 P A G E 0 0 0 4 0 1 3 1 DO 6 7 M = l , 5 0 1 3 2 DO 6 7 1 = 1 , 2 1 2 0 1 3 3 P E R U N U . M ) = PE R TOT { I ) * A ( I , M) / 3 5 . 1 5 7 7 0 1 3 4 T P E R N F ( M ) = T P E R N F I M ) + P E R U N M , M ) 0 1 3 5 A E R U N U . M ) = A E R T G T ( I ) * A ( I , M ) / 3 5 . 1 5 7 7 0 1 3 6 6 7 T A E R N F ( M ) = T A E R N F ( M ) + A E R U N I I , M ) 0 13 7 DO 6 8 M = l , 5 _ 0 1 3 8 P E D I F ( M ) = ( { TP ERNE { M.) - T A E R N F ( M) ) * 1 0 G . ) / T A E R N F ( M ) 0 1 3 9 6 8 W R I T E < 6 , 6 9 ) M , T P E R N F ( M ) , P E O I F I M ) 0 1 4 0 6 9 F O R M A T ! ' SUB B A S I N = ' , 1 3 , ' PE R U N O F F = ' , F 1 0 . 1 , ' C F S ' , F 7 . 1 , ' P E R C E N I T D I F F . FROM AE R U N O F F ' ) 0 1 4 1 DO 7 0 M = l , 5 0 14 2 I F ( M . E Q . l ) P D I F ( M ) = ( ( T A E R N F I M ) - 1 8 0 0 . ) * 1 0 0 . ) / 1 8 0 0 . 0 1 4 3 I F C M . E 0 . 2 J P D I F ( M ) = { ( T A E R N F ( M} - 1 0 9 0 . ) * 1 0 0 . ) / 1 0 9 0 . 0 1 4 4 I F ( M . E Q . 3 ) P D I F ( M ) = { ( T A E R N F ( M ) - 2 5 6 0 . ) * 1 0 0 . ) / 2 5 6 0 . 0 1 4 5 I F ( M . E Q . 4 ) P D I F ( M ) = ( ( T A E R N F IM) - 5 2 5 0 . ) * 1 0 0 . ) / 5 2 5 0 . 0 1 4 6 I F C M . E Q . 5 ) P D I F ( M ) = U T A E R N F ( M ) - 1 C 7 0 0 . ) * 1 0 0 . ) / 1 0 7 0 0 . 0 1 4 7 7 0 W R I T E ( 6 , 7 1 ) M , T A E R N F < M ) , P D I F < M ) 0 1 4 8 7 1 FO_R_MAT(_«._S_UB B A S I N = ' , 1 3 , » A E R U N O F F = « , F 1 Q . 1 , « C F S , , F 7 . 1 , » P E R C E N I T D I F F . FROM A C T U A L R U N O F F * ) 0 1 4 9 S T O P 0 1 5 0 END E X E C U T I O N T E R M I N A T E D 83 $ R U N -L 0 A D # 5 = D A T A ( 5 1 ) E X E C U T I O N B E G I N S SUB B A S I N = 1 P E R U N O F F SUB . 8 A S . I N = 2 SUB B A S I N = 3 SUB B A S I N = 4 SUB B A S I N = 5 P E R U N O F F P E R U N O F F P E R U N O F F 1 6 9 4 . 8 C F S - 3 . 0 P E R C E N T D I F F . FROM AE R U N O F F 128_2_A_5 C F_S _ - _ 5 . 8 _ „ P E J C E NT _D_I F F . F R 0M_ A E RU NO_F F_ 2 8 0 2 . 7 C F S - 1 . 7 P E R C E N T D I F F . F R O M AE R U N O F F 5 5 8 2 . 7 C F S - 9 . 1 P E R C E N T D I F F . FROM A E R U N O F F 1 1 3 6 2 . 6 C F S - 6 . 1 P E R C E N T D I F F . FROM A E R U N O F F SUB B A S I N = SUB B A S I N = SUB B A S I N =. SUB B A S I N = SUB B A S I N = 1 AE R U N O F F 2 A E R U N O F F _3_A_E_J?UN0_J_ 4 AE R U N O F F 5 AE R U N O F F 1 7 4 7 . 5 C F S - 2 . 9 P E R C E N T D I F F . FROM 1 3 6 0 . 9 C F S 2 4 . 9 P E R C E N T D I F F . FROM _ _ 2 8 5 2 »_4_ C ^ S 1 1 . 4 P E R C E N T D I F F . FROM 6 1 4 2 . 0 C F S 1 7 . 0 P E R C E N T D I F F . FROM 1 2 1 0 2 . 7 C F S 1 3 . 1 P E R C E N T D I F F . FROM A C T U A L R U N O F F A C T U A L R U N O F F A C T U A L R U N O F F A C T U A L R U N O F F A C T U A L R U N O F F S T O P 0 E X E C U T I O N T E R M I N A T E D $S IG fc*******************************************************************************^ { c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * j c » * » * » * * * * * * * * » * * * » * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * { c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * » * f c * * * * * * * * * * * * * * * * * * * * » * * * » * * * » » » » * * » * ( e * . * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * « ( * * * * * * » * * * * * * » » * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * £ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 00* •HH—3d 3 9 V « O i S 3 T I 3 * * * * £ 2 * Z $ 0 Niny S1H1 3 0 1 S D 3 ' X O a d d V * * * * 6*0 fclOiOVj 3 I V « * * * * T3i savay wnaa **** o L 03H3Nnd sayvo **** O a i N I b d S39Vd **** Q31NI«d S 3 N I T * * * * 0 3 S - 3 3 V d *_D3$L •33S *6I e i o # e i * s _ *£Z avsy saavo **** Q3Sn 3 3 t f « 0 1 S * * * * oasn 3wii nda **** 3 W U 0 3 S d V l 3 * * * * £ 0 : T £ : S T IV 3 3 0 * * * * IV NO * * * * " 3 * 0 : i N 3 W i a V d 3 0 Q330 :«3Sn *8 s 9or I 6 S 0 N V ) S 1 W 3H1N33 DNIiOdWOD 3 9 3D A l I S H 3 M N n 0 5 S S L t *0N S3tt - 85 - APPENDIX D TRANSLATION OF THE RESUME OF THE PAPER, "CALCUL DU BILAN DE L'EAU EVALUATION EN FONCTION DES PRECIPITATIONS ET DES TEMPERATURES" BY L.C. TURC (REFERENCE 10). This t r a n s l a t i o n i s included i n the thesis to present the general nature of the formula and the following c r i t i c i s m should be regarded as a personal evaluation by the author only. The following t r a n s l a t i o n and a b r i e f inspection of the o r i g i n a l paper with a French dict i o n a r y w i l l show that the formula was derived from a general and a non-comprehensive approach. The data used i s too var i e d and broad ( i . e . , c l i m a t i c data of one h a l f the world and l y s i m e t r i c data of the other). The formula i s probably not adequate and r e s u l t s i n large errors when applied to small drainage areas. However, the s i m p l i c i t y of the formula and the r e l a t i v e l y good approximate re s u l t s that i t does give i s enough to j u s t i f y further study of the formula i n which a s l i g h t modification of the formula may give much better useable re s u l t s f o r r e g i o n a l i z i n g hydrologic information on a smaller scale i n B r i t i s h Columbia. - 86 - C a l c u l a t i o n of Water Balance Evaluation as a Function of P r e c i p i t a t i o n and Temperature by Lucien Turc (Laboratoire des Sols, V e r s a i l l e s ) Resume Simple formulas enable the evaluation of actual evaporation at d i f f e r e n t times of the year as a function of p r e c i p i t a t i o n and temperature (and data of which precise knowledge i s more a v a i l a b l e ) . One can estimate the amount of runoff or perculation through s o i l and inflow to r i v e r s as w e l l as the v a r i a t i o n i n humidity of s o i l . These ca l c u l a t i o n s provide therefore the evaluation of the a v a i l a - b i l i t y of water, within the accuracy of stream gauge measurements; the formulas give runoff i f one knows the p r e c i p i t a t i o n and f i n a l l y one can calculate the dry periods for which water must be adequate for i r r i g a t i o n . The proposed formulas have been established a f t e r a systematic study of water balances of 254 r i v e r s located i n a l l climates of the globe of one part and the r e s u l t s of a c e r t a i n number of l y s i m e t r i c i n s t a l l a t i o n s of the other part; these formulas constitute a synthesis of actual knowledge on the subject of water balance i n our universe. The r e l a t i v e knowledge of water balance i n d i f f e r e n t lands of the earth - 87 - i s by no means complete and the measured data a v a i l a b l e i s sometimes grossly i n error. For example, those inter e s t e d i n s o i l science w i l l often have i n - s u f f i c i e n t data on: the periods when the s o i l i s saturated and the quantity of water perculating through the s o i l ; the periods of drought, the extent of droughts, the amount of water necessary f o r i r r i g a t i o n to sustain abundant crops. To overcome these d i f f i c u l t i e s we have compared the numerical r e s u l t s now a v a i l a b l e i n hydrologic l i t e r a t u r e i n order to make a synthesis of actual knowledge; by t h i s method we have established simple formulas which sum up the r e s u l t s already acquired and permit evaluation of the conditions of water balance as a function of p r e c i p i t a t i o n and temperature, the magnitude of which give r e l a t i v e l y s a t i s f a c t o r y r e s u l t s f o r most parts of the world. A d e t a i l e d write up of t h i s work was published i n the "Annales Agronomiques" (1954); we w i l l describe here concisely the general approach and the main r e s u l t s because a more complete discussion would be out of the scope of t h i s a r t i c l e . The f i r s t part presents the measures taken by the hydrologists within the o v e r a l l h y d r o l o g i c a l systems constituted by the r i v e r basins, the second part presents the measures taken by the a g r i c u l t u r a l i s t s (agronomists) and s o i l s c i e n t i s t s who made use of small a r t i f i c i a l i n s t a l l a t i o n s , the l y s i m e t r i c cases; one w i l l see that the proposed formulas show agreement between the - 88 - res u l t s obtained i n these two regions even i f d i f f e r e n t i n some respects.

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