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<br />;::: <br /> <br />and approaches in the following sections. A review of some previous Z-S and Ze-S relations can be found <br />in section 7.2 of Super and Holroyd (1996). An important point from that review is that only limited <br />literature exists discussing such snowfall relations. Work with rainfall has been much more extensive <br />than with snowfall. <br /> <br />Estimation of f3 values may be made from snow particle measurements, from theoretical considerations, <br />or from radar observations. For example, the classical paper by Sekhon and Srivastava (1970) presented <br />a reanalysis of four previous particle measurement studies which resulted in a f3 value of 2.21. Support <br />for an exponent of 2.0 for snowfall observed by S-band radar is given by the theoretical treatment of <br />Matrosov (1992). Boucher and WieleI' (1985) compared X-band radar measurements with snow depth <br />observations for six Massachusetts snow storms and derived a f3 value of 1.65. A summary of f3 values <br />from several snowfall studies is given in figure 7 of Fujiyoshi et al. (1990), from both snow particle <br />spectra and Ze measurements, yielding a range of f3values from 0.9 to 2.3. <br /> <br />The wide reported range of f3 values likely results from at least two factors. The first is experimental <br />uncertainty, which can be illustrated by the Fujiyoshi et al. (1990) analysis. The two smallest f3 values <br />in their figure 7 (0.9 and 1.1) are from their own study, which has a number of potential problems, <br />including suspect snowfall observations because of wind effects, averaging of Ze instead of snowfall rates, <br />relatively few measurements less than 15 dBZ, and virtually no measurements less than 10 dBZ. Yet the <br />measurement site was located only 8.7 kIn from a reasonably sensitive X-band radar, so the lack of lower <br />reflectivity values is surprising. Similar experimental uncertainties likely could be found in careful <br />review of a number of the reported studies. <br /> <br />A second area of uncertainty may be the grouping of f3values derived from various wavelength radars. <br />According to the theoretical analysis of Matrosov (1992), for snowflake densities between 0.02 to 0.06 <br />g cm-3, f3values should be 2.0 for S-band, between 1.9 and 2.0 for C-band, and between 1.6 and 2.0 for <br />X-band radars. A Ka-band radar is predicted to have f3values less than unity. If Matrosov's results are <br />correct, they could account for some of the range in f3 values reported in the literature. <br /> <br />Based on the limited existing snowfall literature, one might anticipate that f3 values for S-band radar <br />would be near 2.0, probably no greater than 2.3 or less than 1.7. Fortunately, radar-estimated snowfall <br />rates are not higWy sensitive to f3 values in this range for typical observations of Ze' Table 1 shows SWE <br />rates in the conventional English precipitation units used in the United States, calculated from equation <br />(1) for stated a and P values. Less than a factor of two variation is seen over the f3 range from 1.7 to 2.3 <br />for snowfalls corresponding to 10 dBZ. These very light (but common) rates are near the level of <br />detection of even Universal gages. Little variation occurs near 20 dBZ. No more than a 33-percent <br />change occurs at 30 dBZ, although such variations can begin to be important at these moderate snowfall <br />rates. By 35 dBZ, the f3variations result in significant differences in snowfall rate. Greater reflectivity <br />values are infrequently observed in the absence of bright band effects. <br /> <br />Hourly rates greater than 0.10 inch h-J were infrequent in the Cleveland and Denver areas, making it <br />difficult to optimize the Ze-S relation in the high snowfall range. Although heavier snowfall rates seldom <br />occur in those areas, they can be important. However, Smith and Joss (1997) show the importance of <br />selecting appropriate <<and f3values near the rates at which most precipitation accumulates and, further, <br />that accumulations are rather insensitive to P value selection. <br /> <br />5 <br />