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However, for a linear relationship with a reasonably high R value, an approximately equal number of points would be expected on either side of the regression line for any given range of snowfall accumulations. But the large majority of radar-estimated data points lie below the regression lines for figures 3 through 7 for light snowfalls (radar tends to overestimate). The converse is true for the higher snowfalls where the radar tends to underestimate. One possible explanation for the radar underestimating higher snowfall amounts and overestimating lower amounts is related to spatial averaging. The radar's minimum spatial unit is the range bin, 10 by 1 kIn in size. Using Cleveland's gage No. 1 as an example, the single range bin directly over the gage at a 36-km range has an area of 6.3 x 105 m2. But arrays of range bins approximating 3 by 3 kIn of area were used in these analyses. For the same gage, a 50 by 3-kIn array (15 bins) was used, which has a total area of 9.4 x 106 m2. In contrast, the area of an 8-inch-diameter Belfort gage orifice is 0.03 m2, more than 7 orders of magnitude smaller than the single range bin in this example. Clearly, the Belfort gage measures point values of snowfall accumulations which have highly skewed temporal distributions. For example, the frequency distribution for Cleveland gage No.1 hourly totals ranged from 49 h (34 percent) with 0.005 inch, the minimum detectable amount, to 1 h with the a maximum observed total of 0.100 inch. The number of hours with amounts between 0.005 and 0.050 inch was 130 (91 percent). Only 13 hours (9 percent) had amounts between 0.055 and 0.100 inch. But the real question is the degree to which spatial gradients in the snowfall pattern cause these observed skewed temporal distributions. It is well known that convective rainfall has strong spatial gradients, but snowfall patterns would be expected to be much more homogeneous. But dense snow gaging networks are rare, so not much can be said about snow gradients at resolutions smaller than the radar range bin. A test was performed with the existing data by comparing snowfall estimates from the single range bins that make up the averaging array with the array's estimate. This test was done for the array of 15 range bins over Cleveland's gage No.1, used for the radar-estimated hourly amounts of figure 3. For reference, table 8 shows that the R value between the hourly array estimates and gage No.1 observations was 0.73, the average radar-estimated snowfall amount was 0.0196 inch, and the standard error of estimate ~as 0.0136 inch. These values can be compared with the ranges resulting from performing similar calculations with each of the 15 range bins in the array which follow: R-values ranged between 0.69 and 0.73, average radar-estimated snowfall amounts ranged between 0.0190 and 0.0212 inch, and standard errors of estimate ranged between 0.0135 and 0.0144 inch. Even within these limited ranges, the larger R values and smaller standard errors of estimate tended to be located near the array center. These comparisons suggest limited spatial variation over the area of the array. However, although any of the bins within the array would provide reasonable estimates of snowfall, those nearest the array center had the highest association with gage No.1 observations. A plot was prepared (not shown) similar to figure 3 but using the Ze observations from the, single range bin directly over gage No.1; that is, the bin in the center of the array. The plot appeared almost identical to figure 3, which might be expected with an R value of 0.99 between this range bin's hourly amounts and the array amounts. (The R values between the array hourly estimates and those from single bins ranged between 0.96 and 0.99). The above discussion suggests that averaging over an array of range bins may be unnecessary, presuming the data from and over Cleveland's gage No.1 are representative. 31