WMOD00459

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

sampled by radar. Although several uncertainties exist, this method has produced the
majority of published Z-S relationships.

The alternative method, with its own set of uncertainties, is to relate radar measurements
of Ze to surface observations of snowfall. Equivalent reflectivity factor, Ze' is essentially equal
to Z for spherical drops with diameters small compared to the radar wavelength (i.e., rain).
However, Smith (1984) makes the important and often overlooked point that Ze and Z are
unequal for snowfall. Smith shows that if melted drop diameters are used as the particle
sizes in calculating Z (a common practice), then:

Ze = 0.224 Z

(3)

Therefore, Z values are over a factor of 4 higher than Ze for the same snowfall conditions, and
the two quantities should not be grouped together.. But they often are, accounting for some
of the published wide ranges of values for the coefficient a in equation (1) (~ is unaffected).

7.2 Review of Some Z-S Relationships

For simplicity, the common approach of using the term "reflectivity" for measured equivalent
reflectivity factor (Ze) will be used in the remainder of this report. It should be understood
that reflectivity is not the same as reflectivity factor (Z), a calculated quantity.

Published values of a and ~ for equation (1) applied to snowfall are scarce. Sekhon and
Srivastava (1970) reanalyzed four previous studies based on snow particle data in arriving
at one commonly used expression for snowfall:

Z = 1780 R2.21

(4)

The pioneering study by Wilson (1975) compared 5-cm radar observations of Ze, converted to
snowfall by equation (4), with measurements from a special network of Universal gages
generally located in small clearings in coniferous forests near Oswego, New York.
Unfortunately, Wilson did not attempt to develop a "best fit" Ze-S relationship for the
specially-collected snowfall observations, which are probably some of the best ever obtained
for relating to radar measurements. Climatological gage data were also used which clearly
produced more scatter than the special network. Equation (4) does not appear to have been
converted from Z to Ze which, using equation (3), would have resulted in:

Z = 399 R2.21
e '

(5)

Wilson found a marked range dependence in gage/radar ratios using a 1.70 beamwidth tilted
at a 0.90 elevation angle. Ratios increased from about 3.4 for the nearest gages, about 30 kIn
from the radar, to values well over 20 at ranges beyond 100 kIn. Besides making it obvious
that some sort of range correction scheme is needed with snowfall, Wilson pointed out the
importance of keeping the radar beam narrow and close to the ground.

The ratios reported by Wilson (1975) (see his fig. 2) would be reduced by about half if
equation (5) were applied rather than equation (4). Nevertheless, the radar estimates would
still have been significantly lower than the protected gage observations. This difference
suggests that one or both coefficients in equations (4) and (5) may be too high for (mostly lake
effect) snowfall near Oswego, New York.

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