WMOD00459

• Title: Snow Accumulation Algorithm for the WSR-88D Radar, Version 1
• Date: 6/1/1996
• Weather Modification - Doc Type: Report

8. Optimization Scheme for Determination of a and 13 Coefficients

An optimization scheme was developed for detennining the best a and 13 coefficients for
equation (1), repeated below, for any given data set; that is, from the Ze values in an array
of range bins over a particular gage and simultaneous hourly S observations by that gage.

Z = a S~
e

(1)

This scheme is based on the work of Smith et al. (1975) and personal communication with
Dr. Paul Smith. The approach is discussed in more detail in appendix A by Dr. James
Heimbach, who programmed the scheme for use with the Cleveland and Denver data sets.

The average estimated snowfall accumulation for each vertical (or upwind) array of9 or more
range bins was repeatedly calculated as described in section 6. At the suggestion of Dr. Paul
Smith, for any specified value of 13 in equation (1), a unique value of a was established by.
forcing the average radar-derived snowfall accumulation to be equal to the average gage
hourly snowfall accumulation for each data set (e.g., all pairs of hourly accumulations
observed by a particular gage and radar estimates over that gage). This constraint simplified
the optimization process by limiting the solution to one of a set of 13 values, each with only
one a. A more complex scheme might vary both a and 13. Moreover, as pointed out by Smith
et al. (1975), the optimization scheme is not restricted to equation (1) because higher order
tenn equations could be tested. But the work herein has been limited to equation (1) with
the constraint of using only a unique a value for each 13 value.

It is again emphasized that radar estimates of S, not Ze values, were calculated for each
range bin using equation (1), summed, and averaged in each iteration of this optimization
process. This approach avoids the biases resulting from averaging Ze over time and space.

Calculations were made for any input range of 13 and 13 increment. A CTF (criterion function)
was used to judge the fit of each pair of a and 13. Smith et al. (1975) discuss the difficulties
of selecting the most appropriate CTF. The CTF used here is the simple sum of absolute
differences between the gage measurement of precipitation and that estimated by the radar,
again as suggested by Dr. Paul Smith. The combination of a and 13 accepted for any
optimization run was that which yielded the smallest CTF value.

Operator-input values to this scheme include:

· The particular gage to be tested.

· The range of 13 and its increment. Unless otherwise stated, the range was from 0.7 to 3.0
in steps of 0.05.

· The minimum number of volume scans required for 1 hour of data to be accepted, always.
set at 4.

· The minimum number of range bins needed, always set at 5. But in fact, no missing
range bins have been noted so this requirement appears unnecessary.

Range bins commonly had no detectable signal during the beginning and ending portions of
storms and/or over distant gages. The estimated snowfall rates for all such bins were set to

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