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<br />in which f(T) is the function relating temperature <br />to saturation vapor pressure which is represented <br />by Program 1. This is the basis of the idealized <br />model developed by Program 2. It computes <br />incremental decreases in evaporation as a function <br />of changes in surface temperature only. <br /> <br />Program 2 simply uses the third order <br />equation derived by Program I to compute the <br />evaporation surrogate, EMOD (saturation vapor <br />pressure) for any given natural water temperature <br />T and the lower evaporation surrogate EMIX for <br />any desired lower surface water temperature TMIX <br />obtained by destratification. The ratio EMIX/ <br />EMOD is then subtracted from unity to determine <br />the resulting percent decrease in evaporation <br />(SUPP). <br /> <br />The temperature decrease (TDlFF) is in cre- <br />mented as desired to obtain the idealized <br />suppression for any given combination of water <br />temperature and temperature decrease. The values <br />computed were used to develop Figure 12. Program <br />2 is listed in Appendix D. <br /> <br />Program 3: <br />Reservoir Depth-Volume Funcdon <br /> <br />Program 3 requires as input a function <br />relating reservoir water surface eJevation to water <br />storage capacity. This information is needed in the <br />form of a continuous function rather than simply <br />data at certain discrete depths. Such a function will <br />allow computation of the quantity of water and <br />heat contained between any particular depths at <br />which temperature profile data are available. It will <br />also provide a convenient way of computing surface <br />area at any depth as follows: <br /> <br />A=Vi-Vi+1 <br /> <br />where A is the surface area in acres and Vi and <br />V I + I are the storage volumes at draw down i and <br />at draw down i plus I fool. <br /> <br />Program 3 derives the depth-volume functions <br />by means of the same orthogonal polynomial sub- <br />routine (POLY) used in Program I. The program <br />input consists of discrete values of water depths in <br />feet and related storage capacities below that <br />depth. Depth is defined as zero at the spillway crest <br />and increases to maximum depth at the reservoir <br />bottom. Total capacity is used, as opposed to active <br />storage above the outlet. The data for Utah <br />reservoirs were obtained from elevation-capacity <br />tables or curves on file at the State Division of <br />Water Rights or from tables published by the <br />USBR in the case of most federally constructed <br />reservoirs. <br /> <br />Fourth order equations were selected for use in <br />Program 4. These functions matched the input <br />data with R' values which varied from .995 to <br />1.0000. Even so. some problems (such as negative <br />volumes) occur at very low water depths. The <br />accuracy obtained is considered adequate. how- <br />ever, since the error in heat quantities represented <br />by slices of water volume ne~r the bottom are <br />usually negligible when aggregated with the total <br />heat in the reservoir. Draw downs to depths <br />representing small fractions of maximum capacity <br />are no problem because thermal mixing is simply <br />not useful under these conditions. <br /> <br />The program (except for POLY) and the <br />output for a number of Utah reservoirs is included <br />in Appendix E. The output includes polynomial <br />coefficients for the function: Vol = f (Depth); the <br />correlation coefficient; and a comparison of the <br />input and fourth order equation values of volume. <br /> <br />Program 4: <br />IdeaUzed Suppression Rates for Period <br />of Temperature ProIDe Data <br /> <br />Program 4 interfaces the previously described <br />evaporation-temperature function and the depth- <br />volume function with temperature profile data. It <br />computes idealized suppression (no secondary <br />effects) for each date on which temperature profile <br />data are available. <br /> <br />The program allows temperature data to be <br />input as either OF or oc. It then checks the <br />temperature range and converts the OF portion to <br />oc. <br /> <br />The program assumes that the thermocline is <br />completely removed by perfect thermal mixing. <br />The resulting mixed temperature for any particular <br />date is computed as follows: The program input <br />includes the depth and corresponding measured <br />temperature for each point on the profile and the <br />reservoir draw down below spillway crest on that <br />date. The reservoir is mathematically divided into <br />slices of water volume between each of these <br />depths. The amount of heat included in each slice <br />is determined by subtracting the total volume <br />below the lower boundary depth VoI(J) , from the <br />total volume below the upper boundary depth <br />Vol (I) and multiplying this slice volume by the <br />average of the two related temperatures. The sum <br />ofthis product for each slice is then divided by total <br />volume to obtain the weighted mixed temperature. <br /> <br />The evaporation suppression for each date is <br />then computed by using the evaporation- <br />temperature function from Program I for both <br />natural (EMOD) and mixed (EM IX) conditions <br />and subtracting the ratio from unity. <br /> <br />24 <br />