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-- .-' Z=f%SP . (1) equation (1), the equivalent reflectivity factor, Z., is expressed in mm6 m-3, and S is the instantaneous owfall rate in mm h-I. The hourly SWE accumulation (mm) is numerically equal to S integrated over hour. For simplicity, the term reflectivity is often used in place of equivalent reflectivity factor, and this antity is frequently expressed in units of dBZ, where dBZ = 10 10glO (Z.11 mm6m-3). o unique values of a and p exist, and they may vary from storm to storm or even within a storm. The eoretical development of Matrosov (1992) indicates that avaries markedly with snowflake density for , given radar wavelength. The values of a and P may, on average, vary from one geographical region t another, and investigation of such regional variations is a portion of the SAA work. This work is I i tended to recommend optimum a and pvalues for each major region of the nation that receives frequent ~ ow. I S me confusion exists in the literature about snowfall a values resulting from experiments that calculated . and those that measured Z.o Values of p should be similar with either approach. The confusion likely t suIts in part from the fact that the quantities Z and Z. can be considered numerically equal for spherical I . ater drops that are small compared with the radar wavelength. However, Smith (1984) shows that the t mmon practice of using melted drop diameters as the particles' sizes in calculating Z for snowfall results I i the equation: I I I , s a consequence of this inequality between the two quantities, a values derived from Ze measurements S ould be about a factor of 4.5 less than those based on Z calculations. I Z. = 0.224Z (2) ost published values of a and p for snow are based on Z estimation from snow particle observations. nfortunately, a number of papers incorrectly group a values from Z estimation and Z. measurement ~ gether, accounting for some of the wide range of published values. For example, Fujiyoshi et al. (1990) r port a values from several sources which range from about 50 to over 3000. Presumably, the larger ~ lues resulted from snow particle observations and should be divided by 4.5 for comparison with ~ periments based on Z. measurements. I I common uncertainty in estimating a and p values with any approach is whether a sufficient population i available to obtain stable results. The data set required for stability may be larger than generally t cognized. Krajewski and Smith (1991) performed Monte Carlo simulation experiments to estimate data s t size required to obtain accurate Z-R (where R is rainfall) parameter estimates. Although most of their , ork dealt with climatological (non synchronous) radar and gage observations, their figure 6 presents a s ulation experiment for synchronous observations as used in Reclamation's work. They suggest that ~ timates based on 100 samples would have rather wide uncertainties for both a and p but that quite S able results could be expected with 1000 samples. (Much larger data sets are needed for p nsynchronous observations.) Krajewski and Smith (1991) point out that their results are probably b tirnistic because the power-law model likely does not hold over the entire range of precipitation rates. : eclamation has attempted to obtain at least several hundred samples of radar and snowfall observations ~ each geographical location. Attaining such large sample numbers has often proven difficult, especially d ring dry winters, and resources permit only one winter's sampling at each location. I I I s a prelude to discussion of SAA development and refinement, the exponent (pvalue) in equation (1) ill be considered. We will briefly review some earlier work and then discuss results from our own data 4