WMOD00561

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

taken, an accurate Z-S relation may be obtained for essentially the same particles in a limited spatial
domain. However, the sampling volume for the particle size spectra approach is often small raising
questions of representativeness. Some other problems with this approach are that the most appropriate
size-mass relationships for particular circumstances may be uncertain (e.g., Braham et aI., 1992), and it
may not be clear which of the many published particle-fall velocity relations should be used.

A comprehensive review of attempts to relate Z and Ze to R (rainfall) over almost 50 years was presented
by Atlas et aI. (1995). They refer to Zawadzki (1984) who discussed sources of errors involved in
estimating Ze-R relations beyond short ranges. These include vertical variations of Ze and several
physical effects of falling precipitation between the radar beam and the terrain. Such common reference
to "errors" in Ze-R or Ze-S relationships because of range effects are correct only from a particular point
of view. Such discussion presumes that the "correct" Ze value is that which is expected to exist very near
the surface. In fact, Ze refers to the quantity actually measured by a radar wherever that might be. But
even the lowest available radar observations will be well above the underlying terrain at moderate to far
ranges. Ze-S relationships calculated from such observations and surface S measurements are not
inherently incorrect. They simply combine all the real factors of earth's curvature, beam spreading,
possible lack of beam filling by snow particles, possible errors in radar calibration, etc. Certainly the
resulting Ze-S relation will differ from one that might be calculated if Ze observations were available very
near the surface over the same S measurements. But such near-surface Ze observations do not exist in an
operational setting except very near the radar.

There is no physical reason that a precipitation algorithm could not employ a Ze-S (Ze-R for rain) relation
that varies with range, or perhaps with the vertical separation between the lowest available radar beam
and the local underlying terrain. The approach of using a range dependant Ze-S may offer a superior
technique of accounting for all of the factors involved with range.

However, it has been customary to use a single Ze-R relation (perhaps changed for different storm or rain
types), usually based on near-range radar and gage observations. Range corrections are sometimes
applied to make that single relation more applicable at farther ranges. This SAA follows the custom of
using a set of equation coefficients developed near a radar although the range used for Ze-S relation
estimation is larger than commonly used. We have attempted to determine a set of coefficients that
provide reasonably accurate S estimates within about 60 km of particular radars. A simple range
. correction scheme is then provided for dealing with underestimation at farther range. This scheme uses a
second order polynomial equation applied beyond a stated range (like 60 km). Determining the
appropriate coefficients to use with this correction scheme is then the challenge. However, two practical
approaches will be discussed for determination of the coefficients.

In the case of the standard NEXRAD PPS a default relation,

Z = 300 Rl.4
e ,

(5)

is currently used for all radars nationwide and for all seasons. An exception is allowed for coastal radars
in the presence of large tropical storms and hurricanes. The PPS has the capability for incorporating
range correction but that feature is not used in practice. Use of equation (5) with no range correction
generally provides adequate results with deep convective rainfall where cloud bases are often well above
ground and rain may partially evaporate below cloud. That is, Ze may have maximum values near cloud
base, at or near the radar beam being used for rain estimation. Equation (5) is identical to that developed
for Florida convective rains by Woodley et aI. (1975) Experience using the PPS has been discussed by a
number of investigators including Smith et aI. (1996) and Hunter (1996). Fulton et aI. (1998) provide a
current comprehensive discussion of the PPS.

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