WMOD00561

• Title: Snow Accumulation Algorithm for the WSR-80D Radar: Final Report
• Date: 7/1/1998
• Weather Modification - Doc Type: Report

(mostly aggregated) snowflake types and showed a values ranging from 400 for plates and columns to
3300 for spatial dendrites with a median of 1100. Equivalent values for Ze would be 90 to 740 with a
median of 246. The range of P values for all snowflake types was between 1.5 to 2.3 with a median of
1.6.

Battan (1973) noted that, "There have been few measurements of the radar reflectivity of snow as a
function of precipitation intensity." That situation has not improved substantially since his publication
25 years ago. Battan suggested that on the basis of then published results an appropriate expression
appeared to be:

Z= 2000 S

(6)

which is equivalent to Ze = 450 S using equation (4).

More recently, Fujiyoshi et al. (1990) summarized a values from their own study and ten other
publications which range from about 45 to 3300. They indicated which values were derived from each of
the two basic approaches. The 7 data points of their figure 7 based on Ze have an approximate range of
45 to 550, while the 24 points based on Z are from 400 to 3300. If the latter are multiplied by 0.224 to
compare with Ze-derived values, their range becomes 90 to 740. These approximately order-of-
magnitude ranges indicate a need for refinement in a values for practical use at particular locales.

Fujiyoshi et al. (1990) also reported P values which range between 1.1 to 2.3 for the Z-based studies and
0.9 to 2.1 for the Ze-based investigations. For reference, the median of all 31 values of P was 1.6. As
with the a values, these are large ranges for P and refinement is needed for practical application.

Most published results on Ze-S relationships for snowfall are based on 3.2 cm (X-band) radars. The
theoretical study by Matrosov (1992) suggests that not only are a and P dependent upon the snowflake
density but also upon the microwave wavelength used to monitor snowfall. For example, for a snowflake
density of 0.04 g cm-3, Matrosov calculates that a (for Ze) will range from 570 for a 10 cm radar to 340
for a 3.2 cm radar. Corresponding P values would range from 2.01 and 1.75. Ifthese theoretical results
approximate reality it is inappropriate to group a and P values from studies using different wavelength
radars. The Ze-Sresults summarized by Fujiyoshi et al. (1990) all used 3.2 cm radar. Matrosov's work
suggests that results based on the 10 cm (S-band) WSR-88D radar would yield greater a and P values
than most published results.

Matrosov (1992) calculates that a for a 10 cm radar will range from 870 to 460 for falling snowflake
densities of 0.02 and 0.06 g cm-3, respectively. The observations noted in section 4.3 indicate only the
upper limits offalling snow density, since the sampledfallen snow may have already begun to compact.
But it appears that most falling snow will have densities less than about 0.06 g cm-3. Matrosov's
calculations therefore suggest that a will generally be greater than 460 while P will be near 2.0 for the
WSR-88D. It will be shown that our studies made in support of the SAA agree with the P value being
near 2.0 but they suggest a values much less than 460 for the WSR-88D.

Based on the above publications and additional studies not cited here (e.g, see Super and Holroyd, 1996),
and ignoring the possible dependence of a and P values on radar wavelength, one would expect that a
values would be within the range 100 to 800 with a most likely value near 400 to 500. Values of P would
be expected between 1.2 to 2.2 with most likely values in the 1.6 to 2.0 range.

As will be shown, a is a function of range. As beam height increases values of Ze become less because
snow usually continues to grow as it falls to the surface. The studies cited above calculated Z at the

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