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<br />surface or measured Ze at limited range where the beam is near the surface. When Ze measurements are <br />made at greater ranges, higher in snow-producing clouds, they will usually be less than near-surface <br />values. Equation (3) requires a smaller a to match weaker reflectivities with a given surface S <br />accumulation. Therefore, it might be expected that the cited studies produced a values greater than will <br />be shown for Reclamation gages and NWS snow board observations located at ranges of about 20 to <br />60 km (ground clutter contamination usually prevented sampling closer than 20-30 km). That has proven <br />to be the case, with the surface observations used in this study resulting in lesser a values than most <br />previously published values. <br /> <br />For reference, table 1 shows some sample results for typical snowfall reflectivities and a range of a <br />values. For the stated conditions, it can be seen that doubling a reduces S to about 70 percent of its <br />initial value. Conversely, reducing a by half increases S by only about 40 percent. These results indicate <br />that an error in the true a of 25 percent or so has limited practical significance. <br /> <br />Table 1.-Summary of some S rates, in inch h-1, for noted a and Ze values (in dBZ). <br />The power law exponent in equation (3) is assumed to be 2.0 in all cases <br />dBZ a =50 a = 100 a = 200 a = 400 <br />5 .010 .007 .005 .004 <br />10 .018 .012 .009 .006 <br />20 .056 .039 .028 .020 <br />30 .176 .125 .088 .062 <br /> <br />6.3 Optimization Technique <br /> <br />The primary optimization scheme used to determine the "most likely" a and p values for the data sets <br />available to this study has been discussed in detail by Super and Holroyd (1996). It is based on earlier <br />work by Smith et al. (1975). Briefly, the approach requires that, for a given population of hourly <br />observations from one or more surface observing sites, the average radar-estimated S directly overhead <br />(nearest neighbor range bin) must equal the average surface-observed S. It is reasonable to expect a <br />useful precipitation algorithm to produce radar estimates that, on average, match "ground truth." <br /> <br />The assumption of equality between average radar-estimated and surface-observed S accumulations <br />results in a unique a value for each specified p value to be tested. Values of P (with corresponding a <br />values) were tested over a sufficiently wide range (1.2 to 2.6) to find any physically realistic value. The <br />minimum value of the CTF (criterion function) was searched for where: <br /> <br />CTF = L Igage-radarl <br /> <br />(7) <br /> <br />This function was used to determine the expont~nts and coefficients at the various individual Universal <br />gages, and for the four KENX snow board groupings, for the radar sites shown in table 2. KFTG site 7 is <br />the only snow board listed outside of the many used near KENX. <br /> <br />21 <br />