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<br />Z = 318 81.5 <br />. <br /> <br />(8) <br /> <br />The best estimates of a and ~ should be from gage No.1, nearest the radar. However, the <br />optimization scheme was applied to all 5 gages east-northeast of Cleveland as summarized <br />in table 8. Applying the optimi~ation scheme' at more distant ranges provides some insight <br />into expected underestimation of 8 by the radar as range increases and the beam becomes <br />broader and higher above the terrain. At some far range, the radar beam will be above snow- <br />producing clouds, and returns will be negligible even when heavy snowfall is occurring below <br />the beam. <br /> <br />~ <br />1 <br /> <br />Both the "optimum" values of a and ~ change with range in table 8. The optimization scheme <br />caused a to decrease and ~ to increase with range as the calculations attempted to match the <br />observations with the constraint that the average radar estimate must equal the average S <br />value at each gage. Eventually, absurd values resulted at gage No.5, 146 km from the radar. <br /> <br />1 <br />~ <br /> <br />Table 8. - Summary of results of applying the optimization scheme to the five gages located east- <br />northeast of Cleveland. Only hours with gage amounts of 0.005 or more inches are included. <br /> <br />1 <br /> <br /> Distance Beam Standard Error Average <br />Gage from Radar Height* Hours of Estimate S <br />No. (km) (m) Observation ex P R (in h'l) (in h'l) <br />1 36 390 143 318 1.50 0.73 0.0136 0.0196 <br />2 61 750 235 248 1.45 0.81 0.0139 0.0204 <br />3 87 1205 187 147 1.85 0.67 0.0226 0.0260 <br />4 115 1780 202 48 2.20 0.72 0.0179 0.0232 <br />,5 146 2530 218 8 8.50 0.50 0.0169 0.0196 <br /> <br />* Height of 0.50 tilt beam center above gage assuming standard refraction. <br /> <br />The average hourly S values were consistent along the line of gages, ranging only between <br />0.0196 and 0.0260 inch. Table 7 showed that the median was near 0.01 inch h-1 at each gage, <br />and average accumulations varied only between 0.019 and 0.025 inch hot. The Cleveland line <br />of gages appears to have produced a reasonably similar data set, providing the opportunity <br />to examine range effects on radar estimates. <br /> <br /> <br />A linear least-squares regression line (hereafter regression line), linear correlation coefficient, <br />R, and standard error of estimate were calculated for each gage using the a and ~ values of <br />table 8 and the same data sets to which the optimization scheme was applied. The standard <br />error of estimate measures the scatter in the Y-direction of the observed points about the <br />regression line and is analogous to the standard deviation. For a large normal distribution, <br />68 percent (95 percent) of the population would fall within plus or minus 1 (2) standard error <br />of estimate of the regression line. Limited variation of the standard error appears to occur <br />with range although the two gages closest to the radar have the smallest standard errors. <br /> <br />The R values in table 8 are encouraging. In spite of generally low precipitation <br />accumulations typical of snowfall, the correlations between the hourly gage observations and <br />radar estimates are generally at least as high as the 0.68 reported by Smith et al. (1975) for <br />. hourly rainfall on the northern Great Plains. The notable exception is the most distant gage <br />at the 146-km range. No time delay to allow for snowflakes to settle from the illuminating <br />radar beam to the surface has yet been applied to these data. Neither has the advection <br /> <br />26 <br />