OCR Text |
Show this linear multiple correlation formula showed that it was quite satisfactory for the range of elevation or altitude included between Lake Mead, with an elevation of 1,200 feet and latitude of 36 degrees, up to an elevation of about 7,000 feet and latitudes of 40 to 42 degrees. However, if extrapolation was considered, it appeared that, while some lower elevations could be used with reasonable results, when higher elevations were inserted in this formula, results became more and more inaccurate. After quite extensive investigation it was found that increase in elevation up to 10 or 12 thousand feet had decreasing influence upon evaporation from open water surfaces. The amount of total annual evaporation appeared to approach some finite limit at these higher elevations. This study also indicated that as elevations were decreased toward sea level the amount of evaporation also approached a limit in that direction, as indicated by formula (2), which reduces to- E = 86.4 + 46cos 2x at sea level. Finally it was found that a curve of the second degree, based on the equation of the hyperbola, would give quite satisfactory results for a range of 500 to 9,000 feet elevation. The final equation which has been developed, hereinafter referred to as formula (3), is- E = 57cos2x + 548(A+1.275)~1/2- 387(A + 1.275)-1-123 (3) This formula reduces to E = 60 -f- 57cos 2x for locations at sea level. The standard error for formula (3), based on the data for 24 stations, is about ± 3 inches in the depth of evaporation while the square of the coefficient of correlation is about 98 %. These factors may be compared with those for the revised formula (2) which were: standard error ± 2.5 inches and square of coefficient of correlation 98.5%. The results of computations for either equation showed differences between observed and computed quantities up to about double these standard errors in some cases, so that either equation might be used with reasonable results within the smaller range of elevations that is, from 1,200 to 7,000 feet, while above that range the use of the longer equation is recommended. Estimates of evaporation were made by the two formulas (2) and (3) and the results compared both arithmetically and graphically. Considering the relatively small differences in the two sets of results, there is no advantage to be gained by the use of the longer formula within the range of elevations and latitudes to be expected for reservoir sites in the Upper Colorado River Basin, and, therefore, formula (2) was used in computing the following table. |