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A study of the grid square method for estimating mean annual runoff Obedkoff, William 1970-12-31

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A STUDY OF THE GRID SQUARE METHOD FOR ESTIMATING MEAN ANNUAL RUNOFF by WILLIAM OBEDKOFF B.A.Sc, University of British Columbia, 1967 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of Civil Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April, 1970 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Civil Engineering The University of British Columbia Vancouver 8, Canada - iii -ABSTRACT With the increasing importance of network planning for water resource management and inventory of supply of water there is need for new analytical methods of estimating flows from sparsely gauged regions. A new approach to estimating mean annual runoff was proposed by Solomon et al. and reported in "Water Resources Research" journal, Volume 4, October 1968. In this technique both meteorological and hydrological information are used to assess the mean annual precipitation, temperature and runoff distribution over large areas. The study area is broken up into a large number of squares and physiographic parameters are determined for each square; available meteorological data are used to derive multiple linear regression equations which relate precipitation and temperature to physiographic parameters and from these equations precipitation, temperature and evapo ration are estimated for each square; runoff is obtained by subtracting evaporation from precipitation for each square and the runoff from all the squares is summed to obtain an estimate of the runoff for the entire basin; if the computed runoff disagrees with the recorded runoff, the precipitation for each square is adjusted and the procedure is repeated until the com puted runoff approaches the observed runoff to the desired degree. The method has already been applied to a region in British Columbia with promising results. In the following study, use of the available basic data have been made to develop a seasonal estimate approach to the "grid square" method and in particular to consider the evaporation component and the possible incorporation of snow course data, two components which have not yet been adequately developed for use in the method under British - iv -Columbia conditions. Considering the evaporation component, it was found that apart from Turc's formula, used in the original grid square method, the Thornthwaite evapotranspiration method was the only other practical method for estimating evapotranspiration over wide areas as required by the grid 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 in actual computer trials of the grid square method showed that on basis of the first estimate of runoff distribution the Thornthwaite approach gave significantly better results. To incorporate the snow course data into the grid square method several approaches were taken in which an attempt at estimating on a seasonal basis the melt prior to April 1st, the date of snow surveys, was un successful but showed insignificant melt which was subsequently ignored and an attempt at estimating annual precipitation at snow courses to .• supplement the meteorological station data was also unsuccessful. However, an attempt in which the snow course data was added to a segregated winter precipitation estimate at the meteorological stations proved to be successful and gave a small but significant improvement to the first estimate of regional precipitation and runoff distribution thus amplifying the potential use of snow course data in supplementing meteorological data for defining more clearly the regional variation of precipitation. - 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 Trip 7 2.3 Data Used in 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 Prior to Snow Survey 20 CHAPTER 5 EXPERIMENTAL GRID SQUARE METHOD 5.1 Programming 24 5.2 Estimation of the Temperature Distribution 25 5.3 Estimation of the Precipitation Distribution 26 5.4 Estimation of the Runoff Distribution... 28 5.5 Incorporation of Snow Course Data 32 CHAPTER 6 CONCLUSIONS 9 REFERENCES 42 - vi -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 Distribution 56 B.2 Estimation of Monthly Precipitation Distribution..... 57 B.3 Estimation of Monthly Precipitation Distribution 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 6 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 - vii -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 First Runoff Estimates Using Turc's Method 29 5.2 First Runoff Estimates Using Thornthwaite's Method 30 5.3 First Runoff Estimates Using Thornthwaite's Method With Winter Season Precipitation Estimates 6 5.4 First Runoff Estimates Using Thornthwaite's Method With Snow Courses Added to the Winter Season Precipitation Estimates 37 - viii -ACKNOWLEDGMENT The author wishes to express his sincere thanks to Mr. S.O. Russell for his guidance throughout the course of work of this study and his valuable criticism during the write up. The author also wishes to thank T. Ingledow and Associates for providing the data for this study, without which the study could not have been accomplished. - 1 -CHAPTER 1 INTRODUCTION With the increasing importance of long range planning for water resources development there is an urgent need for an inventory of the available supply of water. However, in British Columbia there are very few water sheds which are adequately gauged. This results mainly from the size and diversity of the province but also to some extent from the fact that there has been little regional network planning and in general the network just "grew" to meet immediate needs. Obviously, it would be very useful to be able to regionalize hydrologic information in British Columbia to reduce the need for stream gauging stations which have high capital costs. Unfortunately most available regionalizing techniques are either not applicable due to the shortage of data or inadequate for the rugged terrain which prevails in most of British Columbia. Hence, there is need for new analytical methods of estimating flows from sparsely gauged regions. A new approach to estimating mean annual runoff was proposed by Solomon et al. and reported in "Water Resources Research" .journal, Vol. 4, October 1968. In this technique both meteorological and hydrological infor mation are used to assess the mean annual precipitation, temperature and runoff distribution over large areas. The study area is broken up into a large number of squares and physiographic parameters are determined for each square; available meteorological data is used to derive multiple linear regression equations which relate precipitation and temperature to physiographic parameters and from these equations precipitations temperature - 2 -and evaporation are estimated for each square; runoff is obtained by subtracting evaporation from precipitation for each square and the runoff from all the squares is summed to obtain an estimate of the runoff for the entire basin; if the computed runoff disagrees with the recorded runoff, the precipitation for each square is adjusted and the procedure is repeated until the computed runoff approaches the observed runoff to the desired degree. A summary of the method is given in Chapter 2 and a more detailed description is given in Reference 3. An attempt has already been made to apply the method to a region in British Columbia (Reference 3) with promising results and it is planned to use the method to estimate the areal variation of runoff in the Nicola-Kamloops area as part of a comprehensive study of water resources in British Columbia now under way in the Department of Civil Engineering at the University of British Columbia. However, there are two potential weaknesses which need to be carefully assessed before the method is widely used in British Columbia. One is the use of Turc's formula, a widely used empirical formula for evaporation but one which has not yet been verified for British Columbia conditions. The other potential weakness is that the precipitation equation is defined for the whole basin only on the basis of existing precipitation data. In British Columbia nearly all meteor ological stations are located in the valleys whereas most of the pre cipitation occurs in the mountains. An obvious improvement would be to use snow course data which give practically the only information on precipitation at the higher elevations. The aim of this study is to develop a seasonal estimate approach to - 3 -the Solomon or "grid square" method and in particular to consider the evaporation component and the possible incorporation of snow course data into the method. An attempt to apply the grid 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 in British Columbia and the basic data have been made available (Reference 3). Since assembly of the basic data for each of the grid squares involves considerable effort it was decided to make use of the available data and use the South Thompson area as the test area for the study. Chapter 2 describes the grid square method, gives details of the size and number of squares, the type of physiographic data considered and describes the adaption of the method to the available computing facilities at U.B.C. In Chapter 3 a review of literature establishes the Thornthwaite method as the only otherrpractical method of estimating evapotranspiration within the scope to which evapo ration methods are used in the grid square method (water balance approach in which runoff is equivalent to precipitation minus evapotranspiration) and an attempt is described to make an independent comparison of the Turc and Thornthwaite methods on an evaporation basis. Chapter 4 describes an attempt to estimate the melt prior to April 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 insignificant. Chapter 5 de scribes the trial runs of the experimental grid square method in which both the Turc and Thornthwaite evaporation approaches are compared on the basis of the first estimate of runoff and in which the snow course data are incorporated. The results are discussed throughout the course of the text and recommendations for further work are given where appropriate. Final conclusions are given in Chapter 6. - 4 -CHAPTER 2 GRID SQUARE METHOD 2.1 Description of the Method In the original grid square method the study area is first divided into a grid consisting of a series of uniform squares, the size of which determines to a large extent the accuracy of the representation. (A finer grid would result in 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 available maps and climatological data for meteorological stations are obtained from available published records. Physiographic data are also determined for each meteorological station. The grid system permits the storage and retrieval of basic data for future processing by means of simple computer operations. The characteristics of the overall area or sub-basins can be obtained by combining the characteristics of each square which lies wholly or partially within the boundaries of the drainage area. The procedure for the iterative computation to develop equations for mean annual runoff at any point within a basin is summarized as follows: (1) Establish a preliminary relationship between mean annual precipitation at meteorological stations and the corresponding physiographic parameters by a standard linear multiple regression technique. (2) Similarly, establish a relationship for mean annual temperature at meteorological stations. (3) Compute evaporation as a function of precipitation and temperature (using a formula such as that derived by Turc) for each square. - 5 -(4) Make an initial estimate of runoff for each square in the study area by estimating precipitation (Step 1), evaporation (Steps 2 and 3) and subtracting evaporation from precipitation. (5) Compute the mean annual runoff for the drainage area above the streamflow gauging station by summing runoff of each square within the watershed. (6) Compute for the overall drainage basin the ratio _ recorded mean annual runoff computed mean annual runoff (7) Adjust the precipitation value for each square by the following formula: Precipitation (adjusted) = (K)(R^) + E1 where R^ represents runoff and E^ represents evaporation obtained from the previous estimates. (8) Using the adjusted value of precipitation for each square and the precipitation data at meteorological stations, establish a new correlation between precipitation and physiographic parameters with the meteorological station data given a weight ten times that given to the estimated precipitation in each square. (9) Compute a second estimate of runoff for each square as in Step 4. (10) Compute a new value of K by repeating Steps 5 and 6. (11) Re-iterate steps 7, 8, 9 and 10 until a value of K as close to unity as practicable is obtained. (12) Obtain the final regression equation between mean annual precipitation and physiographic parameters by repeating steps 7 and 8. - 6 -(13) Correlate the final estimate of the runoff in each of the squares with the physiographic characteristics to establish a final equation relating runoff to physiographic parameters. At this stage, additional physiographic parameters such as area of lakes, which may be correlated with runoff, can be introduced into the regression analysis. The iterative technique described above can only be applied when the grid square method gives a good runoff-distribution and all sub-basins are either overestimated or underestimated. Thus when iteration is applied in these cases the new estimate of sub-basin runoff would approach the actual values with each iteration. For cases in which the first estimate gave both positive and negative sub-basin errors, iteration would increase some sub-basin errors as it decreased the overall basin error by virtue of step 7, above. To circumvent this situation the iterative technique could be adjusted to compute sub-basin K ratios and apply these individual ratios to adjust the precipitation in each square of the respective sub-basin. The errors of runoff estimates will then decrease in each sub-basin as well as in the overall basin with each iteration. Iteration in this sense is a useful tool, in that, all available hydrologic information is efficiently used and successive runs tend to eliminate some of the inherent errors in the regression technique as well as errors of measurement in meteorological observations. The main strength of the grid square method lies in 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 it makes use of direct correlation of meteorological data with physiographic data for each square rather than average values for entire basins. It can thus cope with physically diverse regimes, an important consideration in an area such as British Columbia. Another advantage of the method is that the process of determining the physiographic character istics and compiling the hydrologic estimates for each square provides an extremely simple computerized method of information storage and re trieval for large drainage areas. The method, however, has the disadvantage that when there are large errors in the first estimate of flows, the precipitation in each square has to be adjusted and the iteration process destroys the statistical independence of the first estimate. The only meaningful correlation is that of the first multiple correlation of temperature and of precipitation; all subsequent correlations are sta tistically meaningless because they are derived from functions which have already been defined by a least squares fit. Standard statistical tests therefore cannot be applied. However, the physical meaning of this approach can be preserved if an independent check is made of the areal distribution of runoff by comparing the computed values with those measured in the sub-basins of the total basin. 2.2. UBC Trip The University of British Columbia Computing Center, in one of their many computer services, provides a subroutine package (Reference 2), called UBC Trip, which performs a series of statistical tests and manipulations on observed data. One of the routines, called Stpreg, in this package makes use of a standard stepwise regression technique for linear multiple - 8 -correlation analysis. During the regression analysis Stpreg considers the significance of each independent variable in turn and either includes or excludes that variable from the regression equation depending on the significance level defined by the user. If desired, an independent variable can be included in the regression equation regardless of its significance. The independent variables to be considered in the regression equation can be fed into Stpreg in any desired form by the user. For example, if the user wanted a curvilinear component of a variable he would feed in the square of the variable in addition to the variable itself and may obtain squared independent variables in 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 in the programs in the study of the grid square method. At the present time there is no provision for iteration in this routine package. 2.3 Data Used in Grid Square Method The South Thompson River Basin was used in the development of the grid square method since data from this basin was processed and compiled by T. Ingledow and Associates Limited in a hydrometric network study in which they applied the grid square method in its original form. The South Thompson River Basin is also one of the few areas in British 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, is shown in Figure A-l of Appendix A. The grid system covering the study area has a 10 kilometer interval (standard on the 1:250,000 scale maps used in Canada) with a total of 212 squares which fall within or on the boundaries. The grid square system is shown in - 9 -Figure A-2 and the areas of squares in each sub-basin are listed in Table A-3 of Appendix A. The time base period used for the study was 10 years (1956-1966) since adequate streamflow records are available from four gauging stations for this period. The location of these stations are shown in Figure A-l and station 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 precipitation records for the selected time base period are available from 37 meteorological stations in 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 peripheral stations which presumably reflect climatic conditions in the basin. Adequate temperature data are available for 28 of the 37 meteorological stations. The locations of these stations are shown in Figure A-l and the 10 year mean values of precipitation and temperature at these stations are listed -10-in Table A-l of Appendix A. Detailed description of compilation of data is given on page 6-6 of Reference 3. The physiographic characteristics that were considered are: (a) Elevation: The mean elevation of a square was obtained by averaging the elevations at the grid square corners, the center and the intermediate 5 kilometer points. (b) Land Slope: Slope is determined by Horton's method which consists of counting the number of contour lines crossing two perpendicular center lines of the square which are parallel to the sides. (c) Distance to Barrier: The index that was adopted was the distance from the center of a square to a straight line drawn along the divide of the Coast Mountains, measured in a west-southwest direction, the predominant wind direction of moisture inflow for the area. (d) Latitude: The latitude index was defined as the distance measured from the U.S. border to the center of a grid square. (e) Shield Effect: The shield effect was determined by summing the average barrier heights along the center line of each square extending for 28 kilometers in a west-southwest direction. The physiographic data for the meteorological stations were extracted from 10 kilometer squares centered over each station. The published elevation characteristic for each station was used instead of the average elevation of the square. A more detailed description of the physiographic characteristics and their 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 for 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 precipitation and the outflow of water by evapotranspiration. The general procedure is to estimate the evapotranspiration loss E, subtract it from the precipi tation P and consider the "moisture surplus" (P-E) as representative of the runoff. This procedure is better suited for climatological rather than hydrological use where time-lag influences (e.g., ground-water storage and snow melt) predominate. However, this water balance procedure can be satisfactorily applied to hydrological estimates of mean monthly and mean annual water balances in which time lag effects are of little influence. For the evaporation component of water balance estimates two estimates of evaporation are generally made, that of potential evaporation and actual evaporation. Potential evaporation is defined as the evaporation that would occur were there an adequate moisture supply at all times. Actual evaporation is equal to potential when the precipitation exceeds the potential evaporation but is less than the potential evaporation when precipitation falls below potential evaporation. In the original grid square method mean annual evapotranspiration is calculated by Turc's evaporation formula which was developed on the basis of a statistical study of 254 watersheds in all climates of the world. - 12 -The formula is very simple to apply and is given as follows: L(t) = 300 + 25t + 0.05t3 (3.1) (3.2) where E = Actual annual evaporation (mm) P = Annual Precipitation (mm) t = Mean annual temperature (°C) A translation of the resume of Turc's original paper (which is in French) is given in Appendix D. A brief review of research literature was made to determine which methods were widely used to estimate evapotranspiration in water balances of watersheds. It was concluded that Penman's method produced the most accurate results but required data which are not readily available over wide-areas for which the grid square method is proposed. For the available data, Thornthwaite's evapotranspiration method was found to be the one most widely used. R.C. Ward, in his paper on potential evapotranspiration, compares the Penman and Thornthwaite methods with an evapotranspirometer (Reference 11). His study showed that there was generally close similarity among the results of the three methods. Both the Penman and Thornthwaite methods showed slight discrepancies in the spring and autumn but the dis crepancies were complementary in each case and the annual results were similar. - 13 -The Thornthwaite method was derived from a statistical study of available observations in the central and eastern United States. The method involves first calculating potential evapotranspiration and then, on the basis of a series of assumptions and empirical rules (formulas or tables), monthly runoff from rainfall and snowmelt. The monthly water balance is calculated with regard to a running total of soil moisture storage from which calculations of moisture deficit and surplus as well as runoff are derived. Basic data used in the method are mean monthly temperature and precipitation and estimates of water holding capacity of the soil. The Thornthwaite formulae used in 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 Ck antilog [ 0.204 + F (1 - log I) + F log tfc] (3.6) antilog [log S - (A) (PE)] (3.7) - 14 -where: E, = adjusted potential evapotranspiration for month k (cm) it = coefficient depending on the month and the latitude (Reference 8) t^ = mean monthly temperature (°C) M = soil moisture retained in the soil (in.) S = water holding capacity of the soil (in.) A = rate of change of M with different 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 = potential evapotranspiration (in.) The first four formulae were taken from G.S. Cavadias' paper on evaporation (Reference 4). The last formula was developed from Thornthwaite's tables starting on page 245 of Reference 9. In the programs of the study of the grid square method 'Formula 3.7 was used with S = 14 inches only since a preliminary study showed essentially no difference in evapotranspiration estimates using the four different values of S (see Program C-l of Appendix C). The extent to which the water balance method of Thornthwaite was used, was in calculation of actual evapotranspiration (see Reference 9). A simplified version of surface runoff was then estimated from precipitation - 15 -minus actual evapotranspiration for each month and summed to obtain the annual runoff estimate. Thornthwaite determines surplus runoff in a more detailed analysis in which moisture deficit and surplus are both estimated and detention periods are used for both water and snow runoff estimates. However, this analysis is beyond the present scope of the grid square method. 3.2. Comparison of Evaporation Methods For the comparison of the Turc and Thornthwaite methods of estimating evapotranspiration under British Columbia conditions, several attempts were made. A preliminary examination was first made for a wide range of meteorological stations with mean annual precipitation ranging from 8.15 inches to 179.50 inches. Precipitation data and Thornthwaite evaporation estimates were obtained from Thornthwaite's published results (Reference 1) and temperature data were obtained from the U.B.C. Geography Department. The meteorological stations considered and the results that were obtained are given in Table 3.1. - 16 -TABLE PRELIMINARY COMPARISON OF TURC AND (All 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 Oliver 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 Tranquille 47 8. 15 7. 96 8. 15 0.19 WEST COAST AND VANCOUVER ISLAND Alberni 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 Falls 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 it can be seen that Turc's method gives consistently lower estimates of actual evapotranspiration than Thornthwaite, especially in the South Thompson region. - 17 -In a second examination a program.was written for calculating actual evapotranspiration by the Turc and Thornthwaite methods (see Program C-l of Appendix C). Two meteorological stations were chosen for the trial runs, one for high and one for low precipitation (Reference 7). The results obtained are given in Table 3.2. TABLE 3.2 PROGRAMMED COMPARISON OF TURC AND THORNTHWAITE EVAPORATION METHODS (All 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 Glacier 36.2 57.1 13.8 18.7 The difference between the two methods again appears to be rather significant. In an evaporation study of the Carrs Landing area in the Okanagan, the British 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 in the third examination in an attempt to establish which method gave better evaporation results for British Columbia conditions. The results of the comparison of two sites for 1967 are given in Table 3.3. - 18 -TABLE 3.3 CARRS LANDING STUDY COMPARISON (All figures are mean annual) Thorn. Evapotrans. Turc Actual Penman Evapotrans. Station Temp. Precip. Potential Actual Evapotrans. Potential 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 (April-October) , therefore may be underestimates of total annual evapotranspiration. Calculations for only one year at two sites with the highest observed pre cipitation were made since further examination of the Penman data revealed that in no trial did precipitation exceed evapotranspiration"; In both trials shown above the precipitation was so much lower than the potential evapo transpiration that both the Thornthwaite and Turc methods (except Turc at Station 3) simply showed that actual evapotranspiration was equal to the precipitation. Hence the comparison of the two methods with the Penman method proved to be inconclusive in the third evaporation examination. Although the first two attempts (Tables 3.1 and 3.2) at comparing the Turc and Thornthwaite methods indicated a significant difference in their estimates, no conclusion could be drawn on an evaporation basis alone as to which method gave better results for British Columbia conditions. Hence there was a need for an experimental grid square approach,to establish which method gave better results in water balance estimates. The comparison of the two evaporation methods using a grid square approach is presented in Chapter 5. - 20 -CHAPTER 4 SNOW 4.1 Snow Courses The British Columbia Water Resources Service conducts a snow survey program for purposes of forcasting volumes of snowmelt runoff. Most of the snow courses in operation are located at elevations above 4,000 ft. Since most of the meteorological stations are situated in valleys at elevations below 4,000 feet, the snow survey data provide practically the only observed information on precipitation at the higher elevations. In the study area, all meteorological stations are located below 4,100 feet (except one which is at 4,100 feet) and all snow courses are located at or above 6,000 feet. Hence, the snow course data should provide additional valuable information in the seasonal development of the grid square method. 4.2, Melt Prior to Snow Survey The British Columbia Water Resources Service is also undertaking snow-melt studies in which they have so far, collected two years of snow pillow data at two different sites. This data was examined and a very simplified model was developed to determine the melt prior to the 1st of April, the date of the snow surveys. The method consisted of a program (see Program C-2 of Appendix C) which read in daily 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 plotted the relationship with degree days as the independent variable and the water equivalent loss as the dependent variable. In each computer run of a set of data, four plots were produced where time lags of zero, one, two - 21 -and three days were observed. The best plot was determined and from it a seasonal average melt (accumulated melt from start of snowfall to April 1st) was estimated using a season.average temperature multiplied by the length of season for the seasonal average degree day estimate (see Figure 4.1). With this approach It was hoped to estimate the seasonal premelt and to combine it with the snow course data for an estimate of winter precipitation. The program was tested out on three complete sets of data from Blackwall (1967-68 and 1968-69) and Barkerville (1968-69). The resulting graphs were examined for shape and lags of one and two days were found to give the best plots. A seasonal value of melt was required since a daily estimate is beyond the scope of the grid square method. When a seasonal estimate of degree days was made (season average temperature multiplied by the length of season in days) the seasonal melt was found to be 77% in error for Barkerville (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 plot was that of Barkerville which is shown in Figure 4.1. Since the melt in each case was below 1.5 inches, it was ignored in subsequent use of snow course data. This approach did not prove to have any significant results due most likely to unexplained factors affecting snow melt (e.g., antecedent moisture in soil affecting heat from the ground and effect of humidity), and perhaps the limitation in measuring equipment. The results of the model when applied to snow pillow data on a daily basis showed melt graphs which displayed smooth plots for 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 variation with average accumulated degree days. In further development of the method it is suggested that the same model be applied to the data but with maximum daily temperatures as a basis for a heat index. This would give positive seasonal melt estimates (see section 4.2, page 20) which may or may not be significant on a seasonal basis. Other aspects to be considered would be the effect of antecedent moisture conditions (can be estimated from the rain hydrograph prior to snowfall and the soil conditions), the effect of the snow pillow interfering with the actual natural melt process (e.g., may have a shielding effect from heat from the ground) and the comparison of the precipitation hydrograph with the snow pillow hydro-graph to determine the difference between the actual snow melt runoff and the ripening and storage processes. Dr. Quick of the Civil Engineering Department of U.B.C. is now collecting snow pillow data on Mount Seymour and should have sufficient data for such modelling in the near future. It is also suggested that rain gauges be installed on a yearly basis at the snow pillow sites of the British 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 collected to date. - 24 -CHAPTER 5 EXPERIMENTAL GRID SQUARE METHOD 5.1 Programming Computer programs, using UBC Trip, were initially set up to define regional temperature and precipitation regression equations. Stpreg (see section 2.2, page 7) was used to establish the relationships between temperature and precipitation at meteorological stations (dependent variables) and the corresponding physiographic parameters (independent variables). Mean annual temperature and precipitation equations were used in the Turc approach but mean monthly equations were derived for the Thornthwaite approach. The results of these programs are given in the following sections 5.2 and 5.3. A program was then written for estimating mean annual runoff by the grid square method using lure's formula for estimating mean annual evaporation. Another program was written for estimating mean annual runoff, using the Thornthwaite approach for esti mating mean annual evapotranspiration. Several modified trial runs were made with this program and the modifications and the results are presented in section 5.4. A sample program of one of the trial runs is given in Appendix C (Program C-3). In the Thornthwaite programs both potential and actual evapotranspiration were estimated but only the latter was used in estimating runoff. Mean annual runoff was determined by adding the twelve estimates of mean monthly runoff (precipitation minus actual evapo transpiration) . In both the Turc and the Thornthwaite programs mean annual runoff was determined for each square and summed to obtain the total mean annual runoff for the basin. Provision was made in both programs for checking the areal distribution of the first estimate of basin - 25 -runoff by dividing the total basin into four sub-basins for which published hydrometric data were available. A final set of programs was written to incorporate the snow course data into the grid square system. These trial runs are described in part c of section 5.5 and a sample program is given in Appendix C (Program C-4). 5.2 Estimation of the Temperature Distribution Using data at 28 meteorological stations, a correlation was established between the mean annual temperature and the corresponding physiographic characteristics (elevation, land slope, distance to barrier, latitude index, barrier height, and shield effect). The resulting regression equation is: T = 50.8308 - 0.003107E - 0.00003754L2 (5.1) where, T is mean annual temperature in°F, E is station elevation in feet, and L is the latitude index in kilometers. The coefficient of correlation is 0.96 which is significant at the one percent level and the standard error estimate is 1.0°F. The coefficients of the variables included in the equation have signs corresponding to their expected physical influence on the mean annual temperature. For the Thornthwaite approach in the grid square method twelve mean monthly temperature equations were needed. Since monthly temperature data were not available in Reference 3, the twelve mean monthly values for each station were obtained from References 5 and 7, and were* adjusted to the time base period of Reference 3. The correlations were established as for Equation 5.1. and twelve regression equations were obtained, one for each - 26 -month. The equations are similar in form.and are shown in Appendix B, section B.l (Equations B.l through B.12). For example, the equation for the mean monthly temperature for January is: Tl = 28.1903 - 0.002675E - 0.00006324L2 (B.l) where E is station elevation in feet and L is the latitude index in kilometers. The coefficient of correlation ranges from a low of 0.81 for T2 (February) to a high of 0.94 for T4 (April), with a significance at the one percent level. The standard error of estimate ranges from a low of 1.1°F for T10 (October) to a high of 2.2 for Tl (January). The smaller coefficients of variation for the monthly equations suggest that less vari ation was explained in these than in the annual equation, which was expected since the time base for correlation was shortened. 5.3 Estimation of the Precipitation Distribution Using data at 37 meteorological stations, a correlation was established between the mean annual precipitation and the corresponding physiographic characteristics (elevation, land slope, distance to barrier, latitude index, barrier height and shield effect). The resulting regression equation is: P = 11.7765 - 0.0956L + 0.0000005127E2 + 0.0005778DB2 - 0.00000002558SE2 (5.2) where P is mean annual precipitation in inches, L is the latitude index in kilometers, E is elevation in feet, DB is distance to barrier in kilometers and SE is shield effect in feet. The coefficient of correlation is 0.97 which is significant at the one percent level and the standard error of estimate is 3.59 inches. - 27 -For the Thornthwaite approach in the grid square method twelve mean monthly precipitation equations were required. As in the case of the monthly temperature data, the data for the twelve mean monthly precipitation values for each station 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 for mean monthly precipi tation. The equations are similar in form and are shown in Appendix B, , section B.2 (Equations B.13 through B.24). For example, the corresponding equation for the mean monthly precipitation for January is: Pl = 5.3639 - 0.0474DB + 0.0001803DB2 - 0.00003784L2 ...(B.13) The coefficient of correlation ranges from a low of 0.68 for P8 (August) to a high of 0.96 for P3 (March), with a significance at the one percent level. The standard error of estimate ranges from a low of 0.25 inches for P4 (April) to a high of 0.80 inches for P12 (December). Of the independent variables used in correlation in this study, the variable of elevation was considered the most important since it is the only common characteristic that all land areas share which influences the variation of weather phenomenon. The stepwise regression technique (Stpreg, described in section 2.2) that was used in the correlation analysis includes in the regression equations only those independent variables which are significant to the level defined by the user. Seven of the above twelve regression equations did not retain elevation as a significant variable and were defined by other significant independent variables. By using UBC Trip with the elevation variable included regardless of significance, into the regression equations, twelve additional correlations were established - 28 -and are shown in Appendix B, section B.3 (Equations B.25 through B.36). 2 Elevation was forced into the regression equations as E since previous 2 examination of Stpreg revealed that E resulted in higher significance than E and was generally more readily accepted into a regression equation than was E. The corresponding equation for the mean monthly precipitation for January is: PI = - 0.2672 + 0.00000008047E2 + 0.00007911DB2 - 0.00003614L2 (B.25) The coefficient of correlation ranges from.a low of 0.70 for P8 (August) to a high of 0.96 for P3 (March), with a significance at the one percent level, the exceptions being the elevation variables in equations of P8, P10 and P12 where the variable significance is 5.5%, 9.15% and 1.2% respectively. The standard error of estimate ranges from a low of 0.25 inches for P4 (April) to a high of 0.76 inches for P12 (December). 5.4 Estimation of the Runoff Distribution Regression equations for temperature and precipitation that had been derived from the meteorological observations were used to calculate actual evapotranspiration which was then subtracted from the corresponding pre cipitation to obtain runoff for each square. The runoff values for each square were then summed for each sub-basin (partial areas of squares within sub-basins were accounted for) and the total basin. The sub-basin runoff totals then represented the first estimate of the grid square technique and were therefore used to compare the Turc and Thornthwaite methods of estimating evaporation. A runoff regression equation comparison was of no benefit since the correlation coefficient of any runoff regression equation would be 0.999 - 29 -due to the nature of derivation of runoff values (observations would be derived from functions which had already been fitted by a least squares method). In the program for calculating runoff with the Turc approach the mean annual regression equations for temperature and precipitation, Equations 5.1 and 5.2, were used since the Turc formula uses only annual values. The resulting first estimates and their corresponding recorded flowsfor the sub-basins and total basin are given in 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 Total 6350 10,700 13,831 +29.2 In the program for calculating runoff with the Thornthwaite approach the twelve mean monthly regression equations for temperature, Equations B.l to B.12 inclusive of Appendix B, and precipitation were used since the Thornth waite approach uses monthly values. One trial runoff estimate was made with the precipitation Equations B.13 to.B.24 inclusive, derived with normal step wise regression (elevation not included in all regression equations) and another runoff estimate was made with the precipitation Equations B.25 to B.36 - 30 -inclusive, derived with the modified stepwise regression (elevation variable included in all the regression equations regardless of its significance). The resulting first estimates and their corresponding recorded flows are given in 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) Diff. (cfs) Diff. 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 Total 6350 10,700 9498 -11.2 12,204 +23.4 Examination of the coefficients of correlation of the two sets of twelve pre cipitation equations of section? 5.3 on pages 27 and 28 will show that the two sets of equations essentially show identical statistical significance. However, the results shown in Table 5.2 show a significant difference between the two trial runs in which the normal regression equations underestimate and the modified regression equations overestimate the flow. This result is interpreted as being due to the fact that the meteorological stations are mostly situated in the valley bottoms while the grid squares cover fairly large areas which generally include parts of the higher elevation mountain slopes. This fact was investigated further when in a program, the precipi tation for each square was printed out for each trial of the normal and the modified regression. Upon examination of the squares with the lowest ele-- 31 -vations, it was found that both sets of equations gave.the same precipi tation estimates but at the squares with the highest elevations the normal regression equation set underestimated while the modified regression set overestimated the precipitation. This result was inferred from the results of Table 5.2 in which runoff estimates are underestimated in the first trial and overestimated in the second. The reasoning was further substantial when the runoff estimates were printed out for each square for both trials and the higher elevation squares were examined to compare the runoff estimates with the precipitation and evaporation estimates. The precipitation values were found to.be much larger than the corresponding evaporation values in most cases. Temperature distribution did not affect either of these trials because elevation was significant in all twelve mean monthly temperature regression equations and one set of temperature equations was therefore used in both trials. The conclusion to be drawn from this analysis is that the meteorological stations, being located in the valley bottoms, do not ade quately explain the precipitation variation, in terms of elevation at least. This point is well brought out in the next section when snow course data is used to supplement the meteorological data to define a better precipitation variation. It appears that the Thornthwaite approach to the grid square method gives better results than Turc's evaporation approach since it gives a better first estimate of runoff distribution. Obviously both estimates could be improved by iteration 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 first estimate there would be no basis for comparison between alternative - 32 -techniques. Hence in this research study the grid square method was not taken beyond the first estimate. 5.5 Incorporation of Show Course Data To incorporate the snow course data into the grid square system several approaches were made as follows: (a) The closest related (considering location and physiographic charac teristics) meteorological station was chosen for each snow course station and the percentage of annual precipitation that the winter precipitation (October-March) represented was determined at the meteorological station. The two independent estimates, percentage of winter precipitation and the April 1st snow pack water equivalent were combined for an estimate of annual precipitation at each snow course station. These independent (of the precipitation stations) average annual precipitation estimates were combined with the average annual precipitation station observations and data was then available for 50 meteorological stations. A correlation was established between the mean annual precipitation and the corresponding physiographic characteristics. The resulting regression equation is: P = - 30.9787 + 0.005885E + 0.2302DB - 0.0001832L2 (5.3) where P is mean annual precipitation in inches. The coefficient of correlation is 0.93 which is significant at the one percent level and the standard error of estimate is 7.6 inches. When compared with Equation 5.2, Equation 5.3 with the snow courses added, shows a slightly lower statistical significance and adds no refinement to the - 33 -original precipitation regression Equation 5.2. As an added check, Equation 5.3 was used in place of Equation 5.2 in the Turc method of the grid square system and the results obtained were much worse than those shown in Table 5.1 for Equation 5.2. (b) Mean annual precipitation at each snow course station was computed from the regression equation developed from meteorological stations only, Equation 5.2, and the percentage of these values represented by the April 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 locations. The recomputed.percentage values were combined with the snow course data to estimate an average annual precipitation value at the snow course locations. These annual precipitation estimates were then combined with the mean annual precipitation station obser vations and another set of data was available for 50 meteorological stations. A correlation was again established between the mean annual precipitation and the corresponding physiographic characteristics. The resulting regression equation is: P = - 3.2011 + 0.003910E + 0.0005573DB2 - 0.0002471L2 (5.4) The coefficient of correlation is 0.95 which is significant at the one percent level and the standard error of estimate is 6.3 inches. When compared with Equation 5.2, Equation 5.4 with the snow courses added, shows a slightly lower statistical significance and, just as Equation 5.3, adds no refinement to the original precipitation regression Equation 5.2. It should be noted, however, that the regression equation of - 34 -percentages had a correlation coefficient of 0.36 and a standard error of 13.7% and this trial is, hence, of very little significance.-The attempts to use snow.course data to estimate annual pre cipitation at the snow courses by assuming that the percentage of annual precipitation was the same as that at the nearest meteorological station (part a) and by recomputing from a correlation equation the percentage that the snow course represented of annual precipitation (part b) were not successful. The resultant precipitation regression equations (Equations 5.3 and 5.4) did not improve upon the precipitation distribution as estimated by the meteorological stations only (Equation 5.2). (c) Mean monthly temperatures for every grid 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 virtually all squares had mean monthly temperatures greater than 32°F for the period of April to October and the winter period was therefore defined as November to March. Actual observed precipitation for this period was compiled for each meteorological station making available data for 37 winter season observations. A correlation was established between winter season precipitation and the corresponding physiographic characteristics. The resulting regression equation is: P , . = 27.6898 - 0.0605L - 0.2073DB + 0.0007837DB2 (5.5) (n-m) where P, s is the mean winter seasonal (November-March) precipitation (n-m; in inches. The coefficient of correlation is 0.96 which is significant - 35 -at the one percent level and the standard error of estimate is 2.6 inches. The elevation variable was not retained in the regression equation as being significant. A-duplicate correlation at the five percent level did not automatically produce elevation as a significant variable. UBC Trip was then used with elevation forced at the one 2 percent level into the regression equation (the variable E was in cluded without regard to significance as discussed at the end of section 5.3) and the following result was obtained: P, , = - 2.1805 + 0.0000004381E2 + 0.0003352DB2 (n-m) „ - 0.0001476IT ....(5.6) The coefficient of correlation is 0.96 which is significant at the one percent level and the standard error of estimate is 2.6 inches. By compiling winter monthly precipitation data into lumped five month season estimate for each meteorological station, an opportunity was created in which snow course data could be added in its unaltered form and in a comparable sense. Thus, with snow courses included, data were then available for 50 mean winter seasonal observations for corre lation with their corresponding physiographic characteristics. The re sulting regression equation is: P, . = - 21.5062 + 0.1647DB + 0.0000005143E2 (wint) - 0.0001474LT (5.7) where P(w^nt) i-s tne mean winter seasonal (with snow courses added) pre cipitation in inches. The coefficient of correlation is 0.94 which is significant at the one percent level and the standard error of estimate is 4.8 inches. It can be noted that the elevation variable was retained in the correlation equation at the usual level of significance without forcing a fit as in the case of Equation 5.6. However, a comparison of - 36 -the statistical significance of the above formulae shows:that Equations 5.5 and 5.6 are.very slightly better than Equation 5.7. The three equations are again compared after they were applied in the grid square method. Runoff distribution was estimated by the grid square method using the Thornthwaite approach for each of the winter seasonal precipitation equations. In the main program each of these regression equations was used as a lumped five month season runoff estimate (no evaporation because all temperatures were below 32°F) together with seven separate monthly estimates of runoff to produce an average annual runoff estimate for each square. The results of the trial runs of the grid square method using Equations 5.5 and 5.6 as the winter season estimates are given in 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) Diff. (cfs) Diff. 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 Total 6350 10,700 9169 -14.3 12,235 +14.3 The results obtained above, basically show the same trends as those of Table - 37 -5.2 where mean monthly precipitation regression equations were used. The same argument, that of precipitation variation not being explained by the low elevation meteorological stations, can be applied. Runoff distribution was then estimated using Equation 5.7, with added snow course data, and the results are given in 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) Diff. 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 Total 6350 10,700 12,103 +13.1 Comparison of these results with those of Table 5.3 shows that the runoff distribution estimate using the snow course data is slightly better than, and falling within the range of, the previous estimates which did not use snow course data. This improvement is slight but real despite the fact that the precipitation Equation 5.7 used in the estimates summarized in Table 5.4 is statistically inferior (again slightly) to Equation 5.5 used as a basis of Table 5.3. As pointed out previously, the supporting statistics for Equation 5.7 is that the elevation variable was retained in the correlation at the usual level of significance without forcing a fit as in the case of - 38 -Equation 5.6. Snow course data thus appear to add additional valuable information to the meteorological stations located in the lower elevations. Comparison of the errors of the first estimates in the final run shown in Table 5.4 with those of the first estimates of the original method shown in Table 5.1 will show that the Thornthwaite method with the snow course data gives a significantly better first estimate with errors that approach those inherent in the observed values of runoff. This can be supported by the fact that hydrometric Stations 8LC-3 and 8LC-19 measure small drainage areas with relatively small annual runoffs and thus the observed values of runoff for these stations would probably tend to have larger errors than the observed values for say Stations 8LD-1 and 8LE-69. The results of Table 5.4 are similar to those of the second trial of Table 5.2 and both estimates could be improved by the application of an iterative technique as described in section 2.1. CHAPTER 6 CONCLUSIONS This study using data for the South Thompson River Basin has demon strated that a seasonal estimate approach to the grid square method is feasible and that the revision of the evaporation component and the in corporation of snow course data into the precipitation component have improved significantly the areal runoff distribution estimate on the basis of the first estimate, giving the grid square method a more sound physical basis. Considering the evaporation component it was found that apart from Turc's formula, the Thornthwaite evapotranspiration method was the only other practical method for estimating the evapotranspiration over wide areas as required by the grid square method. An attempt was made at an independent comparison of the two methods of estimating evapotranspiration on an evaporation basis alone but it was found inconclusive due to lack of adequate data. A comparison of the two methods in actual trials of the grid square method showed that on the basis of the first estimate of runoff distribution the Thornthwaite approach gives significantly better results lowering on the average the error of estimate in the total basin from approximately 30% to 15%. To incorporate the snow course data into the grid square method several approaches were made. An attempt was made.at estimating on a seasonal basis, the melt at the snow courses prior to April 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 total winter precipitation. The attempt - 40 -was unsuccessful but showed that the melt prior to April 1st was not significant and was therefore ignored in subsequent calculations. Attempts were made to compute annual precipitation at the snow courses by first estimating the percentage of annual precipitation that the April 1st water equivalents represented and then extrapolating the seasonal to annual estimates. The attempts were not successful and did not improve the pre cipitation distribution as estimated by the meteorological stations only. A final attempt was then made to break the annual precipitation into winter and summer season components and to use the snow course data (from the higher mountain elevations) together with meteorological data (from the lower valley elevations) for the winter precipitation estimates and the meteoro logical data alone for the summer estimates. This approach of incorporating snow course data when applied to the grid square method gave a small but significant improvement to the first estimate of regional precipitation and runoff distribution. The potential use of the snow course data is thus amplified in its additional value of information for the existing meteoro logical stations in defining more clearly the regional variation of pre cipitation. The grid square method, from its original development and from the study presented here, has demonstrated a feasible regression technique for estimating mean annual flows for sparsely gauged regions. The study has also demonstrated that the method is flexible for development on a mean monthly and seasonal approach (mean annual runoff was calculated from a sum of mean monthly values in the Thornthwaite approach). Potential development therefore, exists for application of the method to annual flows - 41 -in particular years and ultimately to seasonal and monthly flows in any period of a year. This development would have to be supplemented by a modelling technique to distribute the seasonal or monthly volume estimates over a time basis (e.g., daily). In such modelling, considerations will have to be given to such physical aspects as snow-melt runoff lagging the actual melt process (e.g., estimated by some heat index), basin response to precipitation input (e.g., unit hydrograph) and dependence or independence of events which influence runoff (e.g., in the Thornthwaite approach monthly flows are interrelated). Hence, it is recommended that further studies be undertaken to develop the potential of this apparently powerful technique. - 42 -REFERENCES 1. Average Climatic Water Balance Data of the Continents. C.W. Thornthwaite Associates, Laboratory of Climatology, Publications in Climatology, Volume 17, Number 2. 1964. 2. Bjerring, J.H., J.R.H. Dempster and R.H. Hall. UBC"Trip (Triangular  Regression Package). The University of British Columbia, Computing Center. February 1969. 3. British Columbia Hydrometric Network Study. T. Ingledow and Associates Limited, Consulting Engineers, Volumes I and II. April 1969. 4. Cavadias, G.S. Evaporation Applications in Watershed Yield Determination. Proceedings of Hydrology Symposium No. 2, Evaporation, National Research Council of Canada. March 1961. 5. Climate of British Columbia, Tables of Temperature, Precipitation and  Sunshine. Province of British Columbia, Department of Agriculture. 1965. 6. Solomon, S.J., J.P. Denouvilliez, E.J. Chart, J.A. Woolley and C. Cadou. The Use of a Square Grid System for Computer Estimation of Precipitation, Temperature and Runoff. Water Resources Research, The American Geophysi cal Union, Volume 4. October 1968. 7. Temperature and Precipitation Tables for British Columbia. Canada, Department of Transport, Meteorological Branch. 1967. 8. Thornthwaite, C.W. An Approach Toward a Rational Classification of  Climate. Geographical Review, Volume 38. January 1948. 9. Thornthwaite, C.W. and J.R. Mather. Instructions and Tables for Computing  Potential Evapotranspiration and the Water Balance. Drexel Institute of Technology, Laboratory of Climatology, Publications in Climatology, Volume 10, Number 3. 1957. 10. Turc, L.C. Calcul du Bilan de L'Eau, Evaluation en Fonction des Pre  cipitations et des Temperatures. International Association of Scientific Hydrology, General Assembly of Rome, Volume 38. 1954. 11. Ward, R.C. Observations of Potential 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 STATIONS - 45 -FIGURE A-2 GRID SQUARE LAYOUT TABLE A-l METEOROLOGICAL STATION DATA Station Mean Annual Temp. ( F.) Mean Annual Precipitation (inch) Station Elevation • (ft.) Land Slope (ft./mi.) Distance to Barrier (km.) Latitude Index (km.) Barrier Height (ft.) Shield Effect (ft.) 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 Darfield - 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 Falls - 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 Vinsulla - 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 April 1 Distance Water to Latitude Barrier Shield Equivalent Elevation Land Slope Barrier Index Height Effect Station (inch) (ft.) (ft./mi.) (km.) (km.) (ft.) (ft.) 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 Fidelity 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 Silver 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 . 223 115 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 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.) 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 96.896.87 96.87 22.50 22.50 9.37 9.37 2.50 2.50 10 - - - 5.62 5.62 95.62 95.612 - - - 100.00 100.00 13  100.00 100.0- - 100.00 100.00 15 - -  97.50 97.516  - 66.25 66.25 13.75 13.717 18 - - 0.62 6.88 7.50 19  7.50 - 7.520 - - 70.50  70.50 21  21.70 - 21.722 - - - 77.50 77.50 23  99.37 99.37 24  100.00 100.00 25 - - - 100.00 100.0100.00 100.00 100.00 100.094.37 94.37 20.62 75.00 95.62 81.87 - 81.87 100.00  100.00 37.50 - 37.513.75 13.75 34 - - - 93.12 93.12 35 100.00 100.00 100.00 100.0100.00 100.00 100.00 100.018.75 81.25 100.00 56.25 43.75 100.041 - - 98.13 1.87 100.00 93.12 - 93.12 20.00  20.00 21.87 - 21.87 25.62 25.62 100.00 100.00 100.00 100.0100.00 100.00 100.00 100.0100.00 100.00 100.00 100.0100.00 100.00 35.62 64.38 100.087.50 12.50 100.00 88.12 - 88.12 56 - - 53.75  53.75 96.87 - 96.87 74.37  74.318.50 18.50 66.87 66.87 75.00 75.00 95.62 95.62 100.00 100.00 100.00 100.0_ 100.00 100.00 100.00 100.0100.00 100.00 5.63 94.37 100.04.37 95.63 100.00 100.00 - 100.0100.00  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 Distribution B.2 Estimation of Monthly Precipitation Distribution B.3 Estimation of Monthly Precipitation Distribution - 56 -B.1 Estimation of Monthly Temperature Distribution As discussed in section 5.2, page 25, the twelve regression equations for mean monthly temperature are: Tl = 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) Til = 41.7830 - 0.003236E - 0.0182L ....(B.ll) T12 = 35.8599 - 0.003191E - 0.0229L (B.12) where, Tl through T12 inclusive, are mean monthly temperatures for January through December inclusive, E is station elevation in feet, L is latitude index in kilometers and DB is distance to barrier in kilometers. - 57 -B.2 Estimation of Monthly Precipitation Distribution As discussed in section 5.3, page 27, the twelve regression equations (using normal Stpreg routine of UBC Trip) for mean monthly precipitation are: Pl = 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) Pll = 5. 8083 - 0.0452DB - 0.0119L + 0.0001676DB2 > • • • (B • 23) P12 = 1. 1343 - 0.0173L + 0.00009395DB2 (B.24) where, Pl through P12 inclusive, are mean monthly precipitations for January through December inclusive, DB is distance to barrier in kilometers, L is latitude index in kilometers, E is elevation in feet, HS is average land slope and SE is shield effect in feet. - 58 -( B.3 Estimation of Monthly Precipitation Distribution As discussed in section 5.3, page 27, the twelve regression equations (using Stpreg with elevation included into the regression equation re gardless of significance) for mean monthly precipitation are: Pl = :- - 0. 2672 + 0.00000008047E2 + 0.00007911DB2 - 0.00003614L2 ....(B.25) P2 = - o. 5433 + 0.00000009233E2 + 0.00006207DB2 - 0.00002806L2 (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) Pll = - 0. 6099 + 0.00000009757E2 + 0.00006920DB2 - 0.00002810L2 (B.35) P12 = - 0. 5036 + 0.00000008138E2 + 0.00008608DB2 - 0.00003795L2 (B.36) - 59 -APPENDIX C COMPUTER PROGRAMS Program C-l Comparison of Thornthwaite's and Turc's Evaporation Methods Program C-2 Snow-Melt Model and Plot 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 details involved in both methods. Data was taken from Reference 7 (Glacier, B.C.). Lines 0005 to 0115, inclusive, comprise the Thornthwaite method of calculating evapotranspiration. The following list describes the highlights of this part of the program: Lines Description 10 to 21 Coefficients C^ of Equation 3.6 32 to 44 Equations 3.3 through 3.6 of section 3.1 45 to 115 Calculation of actual evapotranspiration and runoff. Operations were derived from the descriptions on pages 190 to 193, inclusive, of Reference 9 61 to 65 Equation 3.7 in which S is given four different values in each of the four trials Lines 0116 to 0124 inclusive, comprise Turc's formula that is described in section 3.1 (Formulas 3.1 and 3.2). The output on the fourth page consists of four trial runs, one for each value of soil moisture holding capacity S (16, 14, 12 and 10 inches). The format of the output is similar to that used in Reference 9. - 61 -The notation used is as follows: T(*F) Temperature (degrees Fahrenheit) P Precipitation PE Potential Evapotranspiration P-PE Precipitation minus Potential Evapotranspiration ACC-P-WL Accumulated Potential Water Loss ST Soil Moisture Storage CH-ST Change in Soil Moisture AE Actual Evapotranspiration P-AE Precipitation 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) UXU),1=1,20) 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) ,1I(12),E(12),C(12) CGC8 0009 DIMENSION P(12) , PERNF{12 ) ,ACCPWL(12),STI12 ) ,CHSTI12),AE(12), 1 AERNF{12) DIMENSION ARGU2) 0010 0011 0012 CU) = 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 CI10) =0.92 CUD = 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 U2F6.1) 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) - 32.)*(5./9.) INPUT DATA— TEMP. <*F) 0032 0033 C PREC. UN.) IF ICTEMP(K) .LE.0.0) IKK) = 0.0 IF (CTEMPIK).LE.0.0) GO TO 10 0 034 0035 0036 _ 10 IKK) = {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 EiK) = CtK)* EXP{ 2. 303*( 0. 204 + F*<-1. - AL0G10 (I NDEX) ) + F*AL0G10< 1CTEMP(K))))/2.54 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 + ElK) 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) = AL0G10U6.) - 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) = ALOGlOflO.) 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) IF(K.GT.l) ST(K) = ST(K-l) + P<K) IF(J.GT.O) ST(K) = ST(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 = ltl2  IF(K.EQ.l) CHST<K) = 0.0 IF(K.EQ.l) GO TO 20 CHST(K) = -(ST(K-l) ST{K) ) 0079 0080 OC 8.1 C082 0083 0084 IF(CTEKPCK)*LE.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=li12 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( Kl 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=lfl2),PT0T 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 WRITE(6»44) (ACCPWL{K),K=1,12) 010 3 WRITE(6,45) (ST(K) ,K~lf 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 FORMATC«TC*F) • ,12F6. 1,F8.1) oice 41 FORMAT(* P • ,12F6.1,F8.1) 0109 42 FORMAT(* PE ' , 12F6. 1,F8.1) one 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 TURC 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 / * PREC = ',F5.1,* C TURC ) E VAP . = • , F5 . 11 • RNF. =• , F5. 1/) 0125 SMCAP = SMCAP - 2. _ . . 0126 . IFCSMCAP.E0.8.) STOP 0127 GO TO 1 0128 END EXECUTION TERMINATED 65 $RUN -LQADff  EXECUTION BEGINS DATA FROM GLACIER (D.G.T. PUBLICATION) _I1«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 13. 0 14 .3 16.0 22 .7 31 .0 . . ... .. CH-SX. ._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 JJ *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 simplified snow-melt model and plots described in section 4.2 are presented in the following two programs. The input of the first program, shown on the first page, consists of daily maximum and minimum temperatures and water equivalent of snow pack which are obtained from snow pillow charts. The details of the method can easily be followed by reading the Fortran statements. The Do Loop (lines 13 to 27) of statement number 30 picks out both incremental temperature rises and incremental melt but ignores temper ature falls (below 32 F) and snow pack accumulations. Melt is 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 trial run with data from Barkerville (1968-1969) is given on the third page. The output of the first program is used as the input of the second program which is given on the fourth page. This program plots out the in put data on graph paper. The Fortran statements conform to the available plotting routines of the Plotter of the I.B.M. 360 Computer at U.B.C. A sample plot of the results for data from Barkerville (1968-1969) is given in 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 UN.) AS THE DEPENDENT VARIABLE N = NO. OF TEMP. DATA 0001 DIMENSION TMAX(100)tTHIN(100),T(100),W(100),TACCUM(100), 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) (TMAXU), TMINU),WU), 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 0013 DO 30 I = 2,NN 0014 TU) = 0.5*(TMAX(I) + TMINU)) 0015 IF UW(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 (ITU) - 32. ).LT.0.005) GO TO 30 -0C2C 25 TDELTA = TU ) - 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*(TMAX(I) + TMINU)) 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 ISSF7.2) 0041 WRITE (6,34) PAV 1 0042 34 FORMAT (• PERIOD AVG. ACCUM. DEG-DAYS IS*fF8.2) 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) FORTRAN IV G COMPILER MAIN 02-18-7C 15:28:16 PAGE 0002 CC46 40 FORMAT {13,F7.2 ,4F9.2 ) 0047 GO TO 1 0048 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 02-18-70 15:25:11 PAGE 0001 0C01 DIMENSION T<100),M(100) 0002 CALL PLOTS C C N = J FROM SNOWMELT MODEL 0GG3 C N = 20 0 004 . K_ = C 0005 5 READ 15,io) tTVITVW(I) ,1=1,N) 00C6 10 FORMAT 13X,F7.2,F9.2> 0007 11 K = K + 1 0008 CALL SCALE (TtNilO.0,TMIN,07f1) 0005 CALL SCALE (W,N,10.0,WMIN,DW,1) 001G CALL AXIS (0.0,0.0,'ACCUMULATED DEG-DAYS',-20,10.0 ,0.0,TMIN,OT) 0011 CALL AXIS (0.0,0.0,'ACCUMULATED MELT (IN.)• , + 22 ,10 .0,90.0,WMIN,DW) 0012 CALL SYMBOL (2.0,9.5,0.35,« FIG. 4.i«,o.o,8) 0013 CALL SYMBOL (2.0,9.0,0.28,* SNOWMELT PLOT* ,0.0,14) 0014 CALL SYMBOL 12.1,8.7,0.14, 3,0.0,-D 0015 CALL SYMBOL (2.1,8.4,0.14, 1,0.0,-1) 0016 CALL SYMBOL (2.1,8.1,0.14, 4,0.0,-1) 0017 CALL SYMBCL (2.1,7.8,0.14, 5,0.0,-1) 0018 CALL SYMBOL (2.5,8.6,0.14,'LAG O-DAYS* ,0.0,10) 0019 CALL SYMBOL (2.5,8.3,C. 14,'LAG 1-DAYS *,0.G,10) 002C CALL SYMBOL (2 .5,8 .0,0.14,'LAG 2-DAYS ' ,0.0,10) 002 1 CALL SYMBOL 12.5,7.7,G.14,'LAG 3-DAYS' ,0.0 , 10 ) 0022 CALL SYMBOL 12.1,7.0,0.14,'DATA- BARKERVILLE•,0.0, 17) 002 3 CALL SYMBGL 12.5,6.7,0.14,'(1968-69)',0.0,9) 0024 CALL PLOT 1T( 1) ,W(1),3) 002 5 DO 15 I=1,N 0026 15 CALL SYMBOL (Tl I) ,W(I) ,0.07,3,0.0,-1) 0027 CALL LINE I T ( 1) , W1 1) , N , + 1) 0028 CALL PLOT (T(1),WU),3) 0029 16 DO 2G 1 = 1 fN 0030 IF (I .EQ.N) W(1+1) = 0.0 0C31 20 CALL SYMBOL (T( I),W(I+1),0.07,1,0.0,-1) 0032 CALL LINE 1 T( U ,W( 2) ,N-i,+ l) 0033 CALL PLOT (T 1 1) ,W(1),3) 0034 21 DO 25 1=1 ,N 0035 IF (I .EQ.N) W(1+1) = 0.0 0036 IF (I .EQ.N) W1I-+2) = 0.0 0037 25 CALL SYMBCL (T( I) ,W(I+2) ,0.07,4,0.0,-1) 0038 CALL LINE (Tll),W(3>,N-2,+l) 0 03 9 CALL PLOT 1T(1),W(1),3) 0040 26 DO 30 1 = 1 ,N 0041 IF ( I.EQ.N) W1I+1) = 0.0 0042 IF (I .EQ.N) W(1+2) = 0.0 0043 IF (I .EQ.N) WCI+3) = 0.0 0044 30 CALL SYMBOL 1T( I),W(1+3),0.07, 5,0.0,-1) 0045 CALL LINE (T(1) ,W(4) ,N-3, + l) 0046 CALL PLOTND 0 04 7 STOP 0G4 8 END - 71 -Program C-3 Experimental Grid Square Method The following program is an example of an application of the experi mental grid square method in which Thornthwaite1s evapotranspiration method is used. The set of precipitation regression equations (Equations B.13 to B.24) used in this trial run were derived by the normal Stpreg routine of UBC Trip. The Thornthwaite method of calculating evapotranspiration is represented by lines 34 to 118,inclusive, and is essentially identical to Program C-l except for adaptation into the grid square system of calculations. Lines 119 to 124 represent calculations of runoff for the sub-basin areas and total area. The fifth page shows the output printed for this run and corresponds to the results of the trial run presented in Table 5.2. Both potential and actual runoff were estimated but only actual runoff was analysed in the development of the grid square method, as discussed in section 3.1. The computer statistics print-out of this run is given on the sixth page and shows that the total computer time used is 22 seconds with a cost of slightly over $2.00. Even though Thornthwaite's method seems in volved and lengthy on a grid square basis, the trial runs in this study used very little computer time and therefore presented a very efficient 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 SS(212),DB(212),L(212) ,HB<212) ,SE(212), 2 CTEMP(12,212),11(12,212), INDEXC 212),F(212),EV(12,212?, CTEMPI12,212),11(12,212)  212),F(212),EV(12,212)TC12,212),P(12,212),TTOT(212),PTOTC212),TPERNF(5), PERNF(12,212),ACCPWL< 21, 212),C(12)»TEVAP(212),A<212,5), TAERNFI5) ,_J (212) j AETOT (212),AERTOTJ 212), PE_RTOT! 212) , 7 AERNF(12,212),PERUN(212, 5),AERUNt 212,5),FAVG(212) , 8 PWINT(212),PDIF(5),PEDIF(5),EVT0T{212) 0003 READ (5, 5) < SQNO(I),LAREA(1) ,GSAREA(I),E( I),HSII ),SS(I),DB(I) , 1 L( I ),HB(I),SE(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) - 0.6324D-04*L(I)*L(I) 0010 T ( 2 ,1 ) = 29.9052 - 0. 5027D~06*E(I)*EJ I) - 0.4295D-04*L(I)*L(I) 0011 T ( 3, I ) = 41 . 1399 - 0 . 3314D-0 2*E(I ) - C. 3267D-04*L(I)*L( I ) 0012 T(4,I) = 54.5055 - C.3337D-02*E(I ) - 0 .0170*08(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) - 0.3509D~04*L(I)*L(I) 0018 T(10, I ) = 50.C51S - 0.2385D-02*E(I) - C.3762D-04*L(I)*L(I) 0C19 T(11 ,1 ) = 41.7830 - 0.3236D-02*E(I) - 0.0182*L(I) 0020 T<12, I ) = 35.859S - C.3191D-02*E(I) - 0.0229*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) 04*DB(I)*0B(I) - 0.5257D-02*L(I ) 0. 184GD-C8*SE(I)*SE(I) C4*CB(I)*CB(I) 04*DB(I ) *DBI I) 04*CB(I)*DB(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_+ Plllfl)= 5.8C83 + 1 - 0. 0119*L ( I ) Pi 12, 1 ) = 1. 1343 + 0.2041D-04*DB(I)* D B{I) 0.2154D-0 4*DB(I)*DB(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 Ci £) = 1.25 C!9) = 1.C6 CUOJ = 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 TTOT(I) = 0.0 PTCT (I) = 0.0 • • -- -• 00 5 0 0051 . GC5.2 0053 0054 CG55 15 TEVAP(I) = CO 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) - 32.)*(5./9.) c -• c C INPUT DATA - TEMP. <*F) C PREC. (IN.) c • 0057 IF (CTEMP(K,I ).LE.0.0 ) IKK,I) = 0.0 • 0058 0059 0G6C IF (CTEMP(K,I ).LE.O.O) GO TO ZO IKK,I) = (CTEMP(K, I )/5.)**1.514 20 INDEX(I) = INDEX! I) + IKK, I) • 0061 0062 0063 DO 51 K=l,12 PTGT(I) = PTOT(I) + P(K,I) 51 TTOT(l) = TTCT(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) EV(K,I) = 0.0 IF(CTEMP(K,I).LE.0.0) GO TO 25 EV(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 EVIK,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 IF(PERNF(K,I).LT.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,12 0084 IF(ACCPWL(K,I ).EG.O.O) GO TO 58 0085 ARG(K, I ) = AL0G10U4.) - 0.03105843*1-ACCPWLIK ,1)1 00 86 ST(K,I) = EXPI2.303*ARG(K,I)) 0087 J ( I) = JII) + 1 0088 GO TO 59 0C89 58 IFICTEMPIK,I).GT.O.O) ST(K,I) = 14. 0090 IF(CTEMP(K,I).LT.C.C) ST(K,I) = 14. + PERNF(K, I ) 0C91 IF(K.GT.l) ST{K,I) = ST(K-1,I) + P(K,I) 0092 IF(JI I).GT.O ) ST(K,I) = ST(K-1,I) + PERNF(K,I) 0093 IFiCTEMPtK, D.LT.O.O) GO TO 59 CC94 IF1ST(K,I).GT.14.) ST(K,I) = 14. 0095 59 CONTINUE 0096 DO 60 K=I, 12 0097 IFJK.EQ.l) CHSTCK.I) =0.0 0098 IF(K.EQ.l) GO TO 6C GC99 CHST(K.I) = -<ST(K-1»I) - ST(K,D) ' C1GC IF(CTEMF{K,I}.LE.0.0) CHST(K,I) = 0.0 0101 IF <STIK-l,I).GE.14.) CHST(K,I) = O.C 0102 60 CO NT IMJE 0103 DO 61 K=lf12 0104 AE(K,I) = P(K,I) + (-CHST(K,I)) 0105 IF(CHSTtK,I).GE.0.0) AE(K,I) = EV(K,I) 0 106 61 ' CONTINUE 0107 DO 62 K=l,12 0108 AERNFIK, I ) = P(K,l> - AE(K,I) 0109 62 AERTOTl I ) = AERTOTU) + AERNFIK,I) cue DC 63 K=1,12 0111 63 AETOTU) = AETOTU) + 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) - AE(K,I) 0116 AETOT ( I ) = AETOTU) + AE(K,I) 0 117 65..... AERTOTU) = AERTOTU) + 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)/35.1577 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 =«,F10.1, IT CIFF. FROM AE RUNOFF * ) • CFS',F7.1,« PERCEN 012 9 DO 70 M=l,5 0 130 IF(M.EQ.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) - 2560.)*100. )/2560. 0133 IFIM.EQ.4) PDIF(M) = ((TAERNFIM) - 5250.)*100. 3/5250. 0134 IF(M.EQ.5I POIF(M) = 1(TAERNF(M ) - IC700.)* 100. 3/10700. FORTRAN IV G COMPILER MAIN 02-18-70 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 EXECUTION TERMINATED 76 $RUN -LOADS 5=DATA(51) EXECUTION BEGINS SUB BASIN = Ska_M.SJjN.._=_ SUB BASIN = SUB BASIN = SUB BASIN = 1 PE RUNOFF 2 PE RUNOFF 1209 .6 912.0 CFS CFS -4.2 -7.9 PERCENT DIFF, PERCENT DIFF, 3 PE RUNOFF 4 PE RUNOFF 5 PE RUNOFF FROM . _ . FROM 2562.8 CFS -1.9 PERCENT DIFF. FROM 4271.3 CFS -7.8 PERCENT DIFF. FROM 8955.5 CFS -5.7 PERCENT DIFF. FROM AE RUNOFF AE RUNOFF AE RUNOFF AE RUNOFF AE RUNOFF SUB BASIN = SUB BASIN = SUBL BASJN_= SUB BASIN = SUB BASIN = 1 AE RUNOFF 2 AE RUNOFF 3 AE RUNOFF 4 AE RUNOFF 5 AE RUNOFF 1262.3 CFS -29.9 PERCENT DIFF. FROM ACTUAL RUNOFF 990.4 CFS -9.1 PERCENT DIFF. FROM ACTUAL RUNOFF 261_2.5_ CjFS __2.C PERCENT DIFF. FROM ACTUAL RUNOFF 4632.9 CFS -11.8 PERCENT DIFF. FROM ACTUAL RUNOFF 9497.9 CFS -11.2 PERCENT CIFF. FROM ACTUAL RUNOFF STOP 0 EXECUTION TERMINATED $S IG ************************ **** Sil!)!!*****!!!**!!:*?*)?*));***^* f 'r*^'*^',--'r^^'r^--r-^-c-f^-.--r-r-r-r--r-RFS NO. 77*3590 UNIVERSITY OF EC COMPUTING CENTRE MTS<AN059) JOB 77 USER: OEEC DEPARTMENT: C.E. * * * * ON AT 16:59:5C **** OFF AT 17:02:08 **** ELAPSED TIME 138.02 SEC. **** CPU TIME USED 22.585 SEC. **** STORAGE USED 5916.056 PAGE-SEC. **** CARDS READ 177 **** LINES PRINTED **** PAGES PRINTED **** CARDS PUNCHED 215 7 0 **** DRUM READS **** RATE FACTOR 286 0. 9 **** APPROX. COST OF THIS RUN C$2.16 **** FILE STORAGE 18 PG-HR. C$.01 ************************************ * **** ****** *** *************** ****** ************************* **************************** ******************************************************************** ****************************************** *Jr*******************************^ V* *V************^***^ *************************************************************************************^ ************************************************************************************************ ************************************************************************************************ ************************************************************************************************ ************************************************************************************************ ******************************************************************************************** ************************************************************************************************ ************************************************************************************************ ************************************************************************************************ ************************************************************************************************ «**i<c**** ********************************************************************** ****************** ******* * *"*'***"* ******* ** * * *^***** *"** * * ***i «"****! ***^***** * * ********* * ** * * * * ****** ** *** * * * *** ******** ************************************************************************************************ ************************************************************************************************ - 78 -Program C-4 Experimental Grid Square Method With Snow Courses Added The following program is an example of the application of the experi mental grid square method with the Thornthwaite approach and the addition of snow course data. This trial was explained in detail in section 5.5. Individual monthly regression equations for April to November (Equations B.16 to B.23, inclusive) and a lumped winter season regression equation (Equation 5.7) were combined for the mean annual precipitation estimates. Evapotranspiration is calculated for the months of April to November and assumed to be zero in the winter season (see discussion of section 5.5). All steps are essentially the same as in Program C-3 except for the runoff estimates which are segregated in the winter period (lines 110 to 113, 117 to 122 and 127 to 130, inclusive). The fifth page shows the output printed for this run and corresponds to the results presented in Table 5.4 The computer statistics print-out, given on the sixth page, again shows very little 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 212),Ei212),HS(212) , 1 SS(212),DB(212),L(212),HB(212),SE(212), 2 CTEMPt 12, 2 12), IK 12, 212) , INDEX! 212? ,F( 212) ,EVI 12,21 2> ,  3 T(12,212) » P(12 »212 )»TT0T(212)»PTOT1212)»TP ERNFI 5), 4 PERNFI12,212),ACCPWL(21,212),G(12) ,TEVAP(212),A(212,5), . _ 5_ _ J-AEP^F(5),J{2a2),AET0T(212),AERJJ3TI212),PERT0T{212) , 6 ARG(12,212),ST(12,212),CHST{12,212),AE(12,212), 7 AERNF{ 12,212)»PERUN(212,5),AERUN(212,5) ,FAVG(212), 8 PW INT(212 ) ,PDIF (5) ,PEDIF( 5 ), EVTOTI212 )  0003 READ (5,5) (SQNO(I) , LAREA{I),GSAREA(I),E(I),HS(I),SS( 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,Ii = 28.1903 - 0.2675D-02*E(I) - 0.6324D-04*L(I)*L( I) 0010 T(2,I) = 29.9052 - 0.5027D-06*EU)*E( I) - 0.42950-04*L(I )*L <I) oou T(3,I) = 41. 1399 - 0 . 33140-02*E ( I ) - 0.3267D-04*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) - 0.3Q50D-04*L(I)*L(I) 0017 T(9,I) = 61.2753 - 0.2820D-02*E( I ) - 0.3509D-04*L(I )*L(I) 0018 T(10,I)= 50.G519 - 0.2385D-02*E(I) - 0.3762D-04*L(I)*L(I) 0019 T(U,I)= 41.7830 - 0.3236D-02*E ( I ) - 0.0182*L(I) 0020 T(12,1)= 35.8599 - 0.3191D-02*E(I) - 0.0229*L(I) 0 021 P(1,I) = 5.3639 + 0.1803D-03*CB(I )*DB( I) - 0.0474*DB(I) 1 - G.3784D-04*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.490lD-07*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)*DB(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 + 0.21540-04*DB(I)*DB(I) + 0.3149D-03*E<I) 0030 P(10,I)= 0.8348 + 0.5539D-04*D8(I)*DB(I) - 0.9903D-02*L(I ) 0031 P(11,I)= 5.8083 + 0.1676D-G3*DB(I)*DB( I) - 0.0452*DB(I) 1 - 0.0119*LU) 0032 P(12,I)= 1.1343 + 0.9395D-04*DB(I)*DB(I) - 0.0l73*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 ) - 0.1474D-C3*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-lO II ;o if-—i IO 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 Tl 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> Ul Ul ro —i o Ti O o ro H ui m 3 7C TJ II • i—' X -< »—* fU Tl 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 Ul 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 Ul •—1 • CD ~» — O X * * -Sf —H r-4 H O w • ui ro >- o J> o o Ul -J 0000 TJ 70 rn o o 1—1 a > —i j> I —i m T^ TJ ro o o o o o o o o 0 0 o 0 Ul U! Ul Ul U! Ul o* ut J> oj ro r-Ul O —I H O -1 o >'DO m mm < O 70173 1— > O Z|Z 0s TJ Tl — ro II 2 r-i — ro ii ro o o 2 II w II Ul 000000 000000 Ul J> J> J> J> J> O vO OS -0 O Ul I O O o o o o 000000 J> J> J> J> J> UJ J> OJ ru r-. o <£s TJ -I H p OO —4 —4 Z Q — ~> 000! I— I-—i —4 m 1—* ro t—• *-xb' 1 H ~l -<-ri« II II — I ii II il It- O O II o o ;ro -j • • O !•— O O OO • 'N Oi 000000 •-* vO cn |-j o ui ll il !n 11 li o • » • O ro vQ o ui ro OJ OJ 10 -si O OJ o 0 o p 0000 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 Tl O o m TJ —1 < 70 m > m 2 TJ O TJ O i-< * 2 Z Tl FORTRAN IV G COMPILER MAIN 02-18-70 15:29:22 PAGE 0003 81 0G76 C077 0078 0079 AEPTOTM) =0.0 PERTOTU) = 0.0 DO 56 K=l,12 PEPNFtK.I) = P(K,I) - EV(K,I) 0080 0081 0G82 0083 0084 0085 56 57 PERTOT(I) = PERTOTIl) + PERNF(K,I) IFtPERTOTU ).LT.O.O) GO TO 64 DO 57 K=l,12 IF ( P ER N Ft KU).GT.O. 6) ACCPWL(K,l) = 0.0 IF ( PERNF ( K » I ) .LT.0 .0) ACCPWL(K,I) = PERNF(K,II IF! PERNF IK,I ) .LT.O.O) ACCPWLIKU) = ACCPWL(K-I) + ACC PWL ( K-1, I ) 0086 0087 0088 DO 59 K=l,12 IF(ACCPWL(K,I ).EG.0.0) GO TO 58 ARG(K,I) = AL0G10U4.) - 0. 03 105843* (-ACCPWL ( K , I) ) 0089 0090 0091 ST(K,I) = EXP(2.3G3*ARG<K,m J { I ) = J U ) + 1 GO TO 59 0092 0093 0094 58 IFiCTEMPtKt I ) .GT.O.O) STIK,I) = 14. IF(CT£MP(K,I).LT.O.O) ST(K,I) = 14. + PERNF(Kt I > IF(K.GT.l) ST(K,I) = STtK-1,1) + PtK,I) 0095 0096 0097 IF(JII).GT.O) ST(K,I) = ST(K- 1,1) + P ERNFt K , I ) IF1CTEMPIK,I>.LT.O.O) GO TO 59 IF(ST(K,I).GT.14.) ST(K,I) = 14. 0098 0099 0100 0101 0102 0103 5 9 CONTINUE DO 60 K=l,12 IF(K.EQ.l) CHST(K.I) = 0.0 IF(K. EQ.l) GC TO 60 CHST(K,I) = -(ST(K-1,I) - ST(K,I)) IFtCTEMPIK, I ) .LE.0.0) C h:S T { K » I ) = 0.0 0104 0105 0106 60 IFtST(K-l,I).GE.14. ) CHST(K,I) = 0.0 CONTINUE DO 61 K=l,12 0107 0108 01C9 61 AE(K,I) = P(K,I) + (-CHST(K,l)) IF(CHST(K,I).GE.O.O) AE t K,I) = EV(K,I) CONTINUE 0110 0111 0112 .62 00 62 K=4,10 AERNFIK, I) = PtK,I) - AE(K,I) AERTOTU) = AERTOTU) + AERNF(K, I) 0113 0114 0115 63 AERTOT(I) = AERTOTU) + PWINTU) 00 6 3 K=l,12 AETOTU) = AETOTU) + AE(K,I) 0116 0117 0118 _ 64 GO TO 66 DO 6 5 K=4,10 AE(K,I) = PtK,I) 0119 0120 0121 65 AERNFIK,.I) = PtK,I) - A Et K,I ) AETOTU) = AETOTU) + AE(K,I) AERTOTU) = AERTOTU) + AERNF ( K , I ) 0122 0123 0124 66 AERTOTU) = AERTOTU) + PWINTU) CONTINUE DO 92 1=1,212 0125 0126 0127 PEPTOT(I) = 0.0 EVTOTtII = 0.0 DO 72 K=4,1C 0128 0129 0130 72 92 EVTOTU) = EVTGT(I) + EV(K,I) PERTOTU) = PERTOTU) + PERNF t K, I ) PERTOTU) = PERTOTU) + PWINTU) FORTRAN IV G COMPILER MAIN 02-18-70 15:29:22 PAGE 0004 0131 DO 67 M=l,5 0132 O 67 1=1,212 0133 PERUNU.M) = PE R TOT {I) * A ( I , M) / 35. 15 77 0134 TPERNF(M) = TPERNFIM ) + PERUNM,M)  0135 AERUNU.M) = AERTGT(I)*A(I,M)/35.1577 0136 67 TAERNF(M) = TAERNF(M) + AERUNII,M) 0 13 7 DO 68 M = l,5 _ 0138 PEDIF(M) = ( { TP ERNE { M.) - T A E R N F ( M) ) * 1 0 G . ) / T A E R N F ( M ) 0139 68 WRITE<6,69) M,TPERNF(M),PEOIFIM) 0140 69 FORMAT! ' SUB BASIN =',13,' PE RUNOFF =',F10.1,' CFS',F7.1,' PERCEN IT DIFF. FROM AE RUNOFF') 0141 DO 70 M=l,5 0 14 2 IF(M.EQ.l) PDIF(M) = ( ( TAERNFIM) - 1800.)*100.)/1800 . 0143 IFCM.E0.2J PDIF(M) = {(TAERNF ( M} - 1090.)*100.)/1090. 0144 IF(M.EQ.3) PDIF(M) = {(TAERNF(M) - 2560 . )*100 . )/2560. 0145 IF(M.EQ.4) PDIF(M) = ( ( TAERNF IM) - 5250. ) *1 00. )/5250. 0146 IFCM.EQ.5) PDIF(M) = UTAERNF(M) -1C700.)*100.)/10700. 0147 70 WRITE(6,71) M,TAERNF<M),PDIF<M) 0148 71 FO_R_MAT(_«._S_UB BASIN =' , 13, » AE RUNOFF = «,F1Q.1,« CFS,,F7.1,» PERCEN IT DIFF. FROM ACTUAL RUNOFF* ) 0149 STOP 0150 END EXECUTION TERMINATED 83 $RUN -L0AD# 5=DATA(51) EXECUTION BEGINS SUB BASIN = 1 PE RUNOFF SUB .8AS.IN = 2 SUB BASIN = 3 SUB BASIN = 4 SUB BASIN = 5 PE RUNOFF PE RUNOFF PE RUNOFF 1694.8 CFS -3.0 PERCENT DIFF. FROM AE RUNOFF 128_2_A_5 C F_S _-_5 .8_„PEJC E NT _D_I FF . F R 0M_ A E RU NO_F F_ 2802.7 CFS -1.7 PERCENT DIFF. FROM AE RUNOFF 5582.7 CFS -9.1 PERCENT DIFF. FROM AE RUNOFF 11362.6 CFS -6.1 PERCENT DIFF. FROM AE RUNOFF SUB BASIN = SUB BASIN = SUB BASIN =. SUB BASIN = SUB BASIN = 1 AE RUNOFF 2 AE RUNOFF _3_A_E_J?UN0_J_ 4 AE RUNOFF 5 AE RUNOFF 1747.5 CFS -2.9 PERCENT DIFF. FROM 1360.9 CFS 24.9 PERCENT DIFF. FROM __28 5 2 »_4_ C^ S 11.4 PERCENT DIFF. FROM 6142.0 CFS 17.0 PERCENT DIFF. FROM 12102.7 CFS 13.1 PERCENT DIFF. FROM ACTUAL RUNOFF ACTUAL RUNOFF ACTUAL RUNOFF ACTUAL RUNOFF ACTUAL RUNOFF STOP 0 EXECUTION TERMINATED $S IG fc*******************************************************************************^ {c************** ************************************************************************ ********** jc»*»*»********»***» ************************************************************************ ****** ********************** **************************************************************** ********** {c*** *********** **************************************************************** ****************** **********************************************************»*fc********************»***»***»»»»**»* (e*.******* ************************************************************************ **************** ******************************************************************************************«( ****** »******»» ****** ******** ************************************************** ************************ ************************************************************************************************* £************ ************************************************************************* *********** ************************************************************************************************* ************************************************************************************************* ************************************************************* ************************************ ************************************************************************************************* ************************************************************************************************* ************************************************************************************************* ************************************************************************************************* 00* •HH—3d 39V«OiS 3TI3 **** £2*Z$0 Niny S1H1 30 1SD3 'XOaddV **** 6*0 fclOiOVj 3IV« **** T3i savay wnaa **** o L 03H3Nnd sayvo **** OaiNIbd S39Vd **** Q31NI«d S3NIT**** 03S-33Vd *_D3$L •33S *6I eio#ei*s _ *£Z avsy saavo **** Q3Sn 33tf«01S **** oasn 3wii nda **** 3WU 03SdVl3 **** £0:T£:ST IV 330 **** IV NO **** "3*0 :iN3WiaVd30 Q330 :«3Sn *8 s 9or I6S0NV)S1W 3H1N33 DNIiOdWOD 3 9 3D AlISH3MNn 05SSLt *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 translation is included in the thesis to present the general nature of the formula and the following criticism should be regarded as a personal evaluation by the author only. The following translation and a brief inspection of the original paper with a French dictionary will show that the formula was derived from a general and a non-comprehensive approach. The data used is too varied and broad (i.e., climatic data of one half the world and lysimetric data of the other). The formula is probably not adequate and results in large errors when applied to small drainage areas. However, the simplicity of the formula and the relatively good approximate results that it does give is enough to justify further study of the formula in which a slight modification of the formula may give much better useable results for regionalizing hydrologic information on a smaller scale in British Columbia. - 86 -Calculation of Water Balance Evaluation as a Function  of Precipitation and Temperature by Lucien Turc (Laboratoire des Sols, Versailles) Resume Simple formulas enable the evaluation of actual evaporation at different times of the year as a function of precipitation and temperature (and data of which precise knowledge is more available). One can estimate the amount of runoff or perculation through soil and inflow to rivers as well as the variation in humidity of soil. These calculations provide therefore the evaluation of the availa bility of water, within the accuracy of stream gauge measurements; the formulas give runoff if one knows the precipitation and finally one can calculate the dry periods for which water must be adequate for irrigation. The proposed formulas have been established after a systematic study of water balances of 254 rivers located in all climates of the globe of one part and the results of a certain number of lysimetric installations of the other part; these formulas constitute a synthesis of actual knowledge on the subject of water balance in our universe. The relative knowledge of water balance in different lands of the earth - 87 -is by no means complete and the measured data available is sometimes grossly in error. For example, those interested in soil science will often have in sufficient data on: the periods when the soil is saturated and the quantity of water perculating through the soil; the periods of drought, the extent of droughts, the amount of water necessary for irrigation to sustain abundant crops. To overcome these difficulties we have compared the numerical results now available in hydrologic literature in order to make a synthesis of actual knowledge; by this method we have established simple formulas which sum up the results already acquired and permit evaluation of the conditions of water balance as a function of precipitation and temperature, the magnitude of which give relatively satisfactory results for most parts of the world. A detailed write up of this work was published in the "Annales Agronomiques" (1954); we will describe here concisely the general approach and the main results because a more complete discussion would be out of the scope of this article. The first part presents the measures taken by the hydrologists within the overall hydrological systems constituted by the river basins, the second part presents the measures taken by the agriculturalists (agronomists) and soil scientists who made use of small artificial installations, the lysimetric cases; one will see that the proposed formulas show agreement between the - 88 -res ults obtained in these two regions even if different in some respects. 

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