WMOD00459

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

Fujiyoshi et a1. (1990) used 3-minutl~ radar measurements and I-minute sensitive
electrobalance observations of snowfall intensity only 8.7 kIn from a 3.2-cm radar. They
arrived at values of a = 427 and ~ = 1.09 for the range 0.1 to 3.0 mm h-l (0.004 to 0.118 inch
h-l). Unfortunately, in this generally well-done study, the accuracy of snowfall measurements
is questionable. The authors note that the snowfall amount was 50 percent lower at the
western end of their line of three measurement sites where the wind "blew harder." The
three sites were spaced only 100 m apalt, and only data from the center site were finally
used. Although a windbreak was used to protect the electrobalance, how this windbreak
affected snowfall onto the balance in the reported 5- to 6-m S-l winds is not clear. As
discussed in section 3.1, wind speeds of that magnitude can cause significant undercatch by
shielded gages. The question of snowfall accuracy is not well addressed in numerous studies.

Fujiyoshi et al. (1990) group together values based on both calculations of Z and
measurements of Ze in their figure 7, wh:lch shows published a values for snowfall ranging
from as low as 50 to almost 4000. Not all the references cited are readily available, but it
seems likely that most if not all of the h:lghest values are from studies which calculated Z
(e.g., equation (4) is included). But even limiting a values to those based on measured Ze
would result in a large range. Values of ~ in the same figure range from 0.9 to 2.3, also a
considerable range.

Published values of both a and ~ vary considerably. Although no unique Z-S relationship can
be expected, what is not clear is how much of the published variation in coefficients is caused
by natural differences in snowfall characteristics and how much is related to experimental
shortcomings. Developing the "best" valu€!s for a and ~ for snowfall in any given geographical
region is clearly a challenge. And adding to the challenge is the need for large numbers of
data pairs for calculation as discussed by Krajewski and Smith (1991) (see their fig. 6
simulating synchronous observations). Ideally, hundreds of pairs of observations would be
used to establish Ze-S relationships, a difficult and expensive undertaking at any single
location much less at many geographic regions.

One of the reasons that determining the "best" a and ~ coefficients for snowfall is difficult can
be illustrated by figures 1 and 2. . Figure 1 shows the effect of varying the ~ value between
1.0 and 2.0 while holding the a value constant at 300, all reasonable values according to the
literature. The lower the ~ value, the more rapidly the curve rises with increasing radar
returns. The 3 curves barely deviate for values of Ze lower than the 25-dBZ crossover point
where all 3 predict 0.04 inch h-l. As discussed in section 5, most S observations in this study
were below 0.04 inch h-l. Only for Ze values above 30 dBZ do the curves deviate markedly
from one another. But this region of relatively high snowfall rates is where data points
become infrequent because of the highly skewed nature of precipitation intensities. So the
Ze-S relation is relatively insensitive to changes in ~ for the large majority of hours with
snowfall, a point made by Wilson (1975).

On figure 2, the a value of equation (1) is doubled from 150 to 300 and then doubled again
to 600, while ~ is left constant at 1.5, again reasonable values according to the literature.
Lower a values cause the curves to rise more rapidly as Ze increases. So a rapid rise in
predicted snowfall with increasing Ze can be achieved with either a decrease in a or ~ or both.

In the case of figure 2, the curves begin to deviate from one another above 20 dBZ, so the
chance of determining the "best" a value may be better than the chance of determining the
"best" ~ value with typical snowfalls.

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