| OCR Text |
Show the Aspen area, and the six months winter precipitation at the Leadville station of the Weather Bureau. With rounded coefficients, the formula is: Ys = X2 + 45X3 + 30X4 - 245 (±77) (1) Ys - estimated 6 months summer flow, May-September in units of 1,000 acre-feet X2 - observed 6 months winter flow, October-March in units of 1,000 acre-feet X3 - water equivalent of snow in inches on April 1st in the Aspen area X4 = winter precipitation, October-March, at Leadville in inches depth. Or, for the estimated total flow for the water year, Yyi Yy = 2X2 + 45X3 + 30X4 - 245 (±77) (2) With formula (1) the flow of Roaring Fork can be estimated for the six summer months of May through September and the forecast of the outflow from this tributary basin will account for about 78 % of the possible variations in inflow and depletions along the stream. Furthermore the chances are 2 out of 3 that the actual outflow for any year will fall between values not greater than the estimate plus 77,000 acre-feet or less than the estimate minus 77,000 acre-feet. For example, the formula was based on the fifteen years of records 1936 to 1950 inclusive, and the summer flow in 1951 was 719,000 acre-feet at Glenwood Springs. By formula (1) the estimated summer flow was 819,000 acre-feet, with a 2 to 1 probability that it would lie between 896,000 and 742,000 acre-feet. As a forecast this would have been 100,000 acre-feet more than actually occurred last summer and the lower value of the range indicated by the standard error (742,000 acre-feet) is also greater than the observed flow. When values computed by formula for all the other 15 years are also compared with the observed quantities, in addition to 1951 the estimates differed from the true values by more than the standard error of 77,000 .acre-feet in 1937, 1939 and 1947. Hence, 12 out of 16 times or with the slightly greater frequency of 3 out of 4 instead of 2 out of 3, the estimates came within the limits of ± the standard error. The accompanying diagram shows how the computed forecasts vary from the observed values of the summer discharges of Roaring Fork. The central diagonal passes through the point for 1951 if the the forecast had been exact and indicates the trend relating forecasts and observations. The other two lines indicate the range of values between which two-thirds of the forecast should fall. -40- |
