OCR Text |
Show Waddell and Fields- Model for Evaluating the Effects of Dikes on The third step was to compute the pan coefficients in order to convert pan evaporation to freshwater- lake evaporation. The pan coefficients ( Pcf) shown in table 12 were interpolated from the U. S. Department of Commerce ( 1959, pi. 3). The annual freshwater- lake evaporation ( Efw) was then computed for each station as follows ( table 12): Efw = ( E)( Pcf) The fourth step was to develop an equation describing freshwater- lake evaporation ( Efw) as a function of latitude, longitude, and water- surface altitude. This equation was developed by multiple- regression technique using the data input from the 49 sites in table 12. Then, lines of equal freshwater- lake evaporation were drawn for Great Salt Lake using data generated by the equation ( fig. 5). Like precipitation, the mean evaporation is variable over the lake surface; and because the lake- surface area varies with the lake altitude, it was necessary to compute mean values for different areas inundated at various altitudes for the several proposed areas of the lake. The lake surface was broken down in the same way as described for precipitation and the mean evaporation values were computed for areas inundated at water- surface altitudes of 4,205, 4,199, 4,196, and 4,195 ft ( 1,281.7, 1,279.8, 1,278.9, and 1,278.6 m) ( table 1). Then by interpolation, the freshwater- lake evaporation can be computed for the inundated area occurring at any altitude. The pan- evaporation data at Utah Lake Lehi were tested for annual variations by computing the ratio of the annual pan- evaporation values to the 1931- 70 mean. The ratio ranged from 0.84 to 1.19. These ratios were used initially to correct the 1931- 70 means for the evaporation of an individual year. During calibration of the model, however, it was found that these annual variations created a larger error in the mass balance than did a factor of 1.0. So the correction factor for the individual year evaporation was discarded and the mean value for 1931- 70 was used without correction. The annual variations are probably within the range of sampling error and are not indicative of annual fluctuations of evaporation rates. The monthly distribution of evaporation for 1931- 73 was computed similarly to that of precipitation. The monthly distribution was computed as a percentage ( Emi)( 100) of the annual total ( fig. 4). The monthly distribution had only a small variation from year to year during a selected test period ( 1951- 60). An average monthly distribution was computed for the the Water and Salt Balance of Great Salt Lake 9 Table 2. Average annual precipitation and freshwater evaporation from Willard Reservoir and wetland areas between long- term surface- inflow stations and the 4,200- foot shoreline of Great Salt Lake. Precipitation ( in) Evaporation ( in) Bear River Migratory Bird Refuge 13.25 49.4 Willard Reservoir 14.10 49.1 Farmington Bay Waterfowl Management Area 14.08 50.2 Average 13.81 49.6 test period and assumed to be the same for each year of 1931- 73. Thus: Monthly freshwater- lake evaporation = ( Efw)( Emi), The next step was to correct freshwater- lake evaporation ( Efw) for the effect of salt content. The following equations, which were developed during a prior study of Great Salt Lake ( Waddell and Bolke, 1973, p. 33), were adapted for this study: SCE = ( 1- 0.778 CS/ pS) SCEN = ( 1- 0.778 CN/ pN) The equations were then verified with field data obtained from the Morton Salt Co. These data were for brines whose specific gravity indicated that they were near saturation with respect to sodium chloride ( table 3). Saturation in the north part of Great Salt Lake is attained at a specific gravity of approximately 1.225 at a temperature of 20° C ( 68° F). The average specific gravity of the brines observed by the Morton Salt Co. was 1.218 at an average temperature of 24.9° C ( 76.8° F). This adjusts to 1.219 at 20° C ( 68° F). The average ratio of the brine to freshwater, adjusted to 20° C ( 68° F), thus was 0.75. This compares to a ratio of 0.78 which was computed by the equations of Waddell and Bolke ( 1973, p. 33). Thus, the evaporation rate from Great Salt Lake, in inches, was computed by applying the salinity correction factor ( SCE or SCEN) to the freshwater- lake evaporation rate ( Efw) for the concentration ( CS or CN) existing in the lake for each month of the 1931- 73 base period. Then total evaporation, in acre- feet, was computed for each month by applying the rate to the total area as shown in the following equations: Monthly evaporation from south part = ( Efw/ 12)( Emi)( SCE)( A) Monthly evaporation from north part = ( Efw/ 12)( Emi)( SCEN)( A) The annual evaporation from Great Salt Lake ranged from about 2.2 to 4.0 million acre- ft ( 2,712.6 to 4,932.0 hm3) during 1931- 73. The average annual |