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<br />There is some scatter of data points around th(~ least squares regression lines, but, to a first <br />approximation, each set of Ze data resulted in a linear vertical profile of S. These preliminary results <br />together with those reported by Super (1998) indicate that this approach of using radar measurements <br />alone should provide a viable means of developing a seasonal range correction scheme for individual <br />radars. It seems likely that the seasonal correction determined for a single radar would be applicable to a <br />number of neighboring radars in a similar climatic regime but further study would be needed to test this <br />hypothesis. This "radar alone" approach has considerable appeal from the standpoint of data availability. <br />Level II Ze data have been archived at the National Climatic Data Center for most WSR-88Ds for a <br />number of winter seasons. These existing data could be utilized in developing seasonal range <br />corrections. <br /> <br />Another approach to developing a seasonal range correction is to use radar/surface observation ratios <br />such as shown later in figure 7. While also a satisfactory method, the problem usually lies in finding <br />sufficiently accurate snowfall data. It is difficult to determine, without on-site visitation, whether <br />individual gages are in protected, semi-protected or exposed and windy locations. Without such <br />determinations one can easily be attempting to match radar reflectivity data to some gages with over <br />50 percent S undercatch (Goodison 1978), some near "ground truth" and the rest somewhere in between. <br />Such an approach is unlikely to result in satisfactory radar estimation of S. <br /> <br />Atlas et al. (1995) make the important point that experimental work with rainfall has established that well <br />calibrated radars perform according to theory under ideal conditions of short ranges and small pulse <br />volumes. The theory for radar and snowfall relations is also reasonably well understood (Smith, 1984). <br />Nevertheless, Atlas et al. (1995) discuss evidelllce from Austin (1987) for a rainfall period which varied <br />from convective to stratiform. They conclude that, "it is an exercise in futility to apply any single Z-R <br />relation to a point in the space-time domain." This is because the actual Z-R varies significantly in space <br />and time. But they also discuss how the spatial and temporal statistics of rain allow for reasonable <br />rainfall accumulation estimates to be made ovt~r time using conventional radar measurements. It will be <br />shown that SAA estimates of S accumulation improve in accuracy with integration over time. For <br />example, storm total estimates are more accurate that hourly estimates. <br /> <br />The authors have chosen the approach of using equation (3) in developing appropriate a and P values. <br />That is, they have sought out accurate hourly ground observations of S and related them to overhead <br />radar measurements of Ze' The Ze data used in this study typically were from the lowest available beam <br />tilt near 0.5 deg elevation angle in order to sample Ze as near the surface as practical. This approach <br />minimizes range underestimation related to the: known vertical profile of Ze for snowfall, with maximum <br />values typically near the surface. In some situations terrain blockage does not permit use of the 0.5 deg <br />beam. <br /> <br />A careful reading of some earlier studies show.s that Ze or even dBZ were averaged over time, sometimes <br />over an hour or more. This practice must causl~ a bias as discussed by Super and Holroyd (1997a) <br />because of the nonlinear nature of equation (3). In this study Ze values (in dBZ) for each range bin and <br />volume scan were always converted to S rates before any averaging. That is, S was often averaged over <br />time but reflectivity was never averaged over time. <br /> <br />6.2 Review of Some Z-S and Ze'.S Relationships <br /> <br />It should be recognized that no unique Z-S or Ze-S relationships exist. In fact, the relationships constantly <br />vary over time and space with changes in snow particle sizes, habits, degrees of riming and aggregation, <br />fall speeds, etc. For example, Ohtake and Henmj (1970) calculated Z-S relations for eight different <br /> <br />19 <br />