WMOD00563

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

by 0.1 over sufficiently wide ranges to "capture" the "best" combination of ex and p. In this approach that
best combination was presumed to be the one with the smallest absolute difference between the hourly
means regardless of the CTF value. In practice it turned out that this difference was usually very near
zero, not greater than 0.001 inches, and sometimes less than 0.0001 inches of hourly S accumulation. In
effect, this alt~rnative approach also resulted in equality of the means for all practical purposes.
Therefore, the main difference between the two approaches is that the alternative approach did not
require a minimum value of CTF in equation (7).

Values shown by regular font in table 3 are from the primary optimization approach using equation: (7).
Bold fonts in shaded cells depict results from the alternative approach just described. Values of ex
corresponding to p=2.0 from the equation (7) optimization approach are also listed for all locations as a
further basis of comparison.

6.5 Limited f3 Variation

The smallest p value in table 3 is 1.8. Values greater than 2.5 were not permitted as they are considered
unrealistic from all previously published evidence and from our own. Only 2 of the 24 values in table 3
were as large as 2.5 and they resulted from the alternative optimization approach. The median value of
the 24 p values of table 3 is 2.25 using both approaches. However, the median was 2.0 for the 10 gages
and least-range Albany snow board group that provided reasonable CTF minimums by equation (7).
These are considered the most reliable estimates. Moreover, as shown in table 4 for grouped
observations, the primary optimization scheme provided a median p value of2.1, ignoring the limited
range and hours of S accumulation data from Minnesota.

A means of using storm totals to estimate "best fit" Ze-S relations, using the alternative approach
discussed above, was recently developed for another project. It was applied to Minnesota gages 1 ~md 2
of table 2 using their hourly data to define storm total periods. The resulting ex and p was 190 and 1.8
determined by the least difference between mean gage and mean radar storm totals. Using the minimum
CTF of equation (7) to choose the "best" pair resulted in ex = 230 and p = 2.0. So even with the limited
snowfall rates of Minnesota this new approach indicates a p near 2.0 is most appropriate. The ex values
by this approach are similar to that found with the primary optimization scheme applied to Minnesota
hourly data for P = 2.0 (see table 4 or 5).

Based on the evidence presented from this and previous work, it is believed there is little reason to lllse
anything but P = 2.0 for the 5 data sets under discussion. As discussed by Smith and Joss (1997) for rain,
a change in the P exponent of:l: 0.2 has little practical significance. A most likely "middle" value can be
used as a fixed exponent (they suggest 1.5 for rain). The important challenge is then to select an
appropriate ex coefficient for particular conditions. Use of equation (3) reveals that for a typical ex of 150,
and typical Ze values during snowfall in the 10 to 20 dBZ range, a difference of:l: 0.2 from (3 = 2.0
changes S only by 0.001 inch h-l.

6.6 Range Dependence in a

Figure 5 shows the ex values of table 3, all for P = 2.0, plotted as functions of range from each ofthe:
5 radars. The lowest beam tilt of 0.5 deg was used with the 4 exceptions previously noted. The
approximately linear fit to each data set is remarkable when all the sources of variance in the data sets are
considered. While the KGJX gages are not totally compatible, all having been related to 2.4 deg rather
than 0.5 deg Ze data, even they show a decrease in ex over the limited range of 6-21 km. Slope is se(m to

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