WMOD00445

• Title: Implications of Time Dependent Convective Z-R Relations for Radar Precipitation Analysis
• Weather Modification - Doc Type: Report

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IMPLICATIONS OF TI~rn DEPENDENT CONVECTIVE Z-R RELATIONS
FOR RADAR PRECIPITATION ANALYSIS

Loren D. Nelson

Bureau of Reclamation
Denver, CiOlorado

Richard E. Carbone

anI!

National Center for Atmospheric Research.
Boulder, Colorado

1. - INTRODUCTION

Most area-wide convective precipitation enhance:ment
experiments rely upon radar for estimating total
precipitation over the treatment area, because high
spatial resolution using conventional rain gauges
is prohibitively expensive. The accuracy of this
radar precipitation measurement is deoendent on the
applicability of the reflectivity-rainfall (Z-R')
relation assumed for the calculation of rain rate.

During the summer of 1975, radar, aircraft, and
surface observations of convective showers were
conducted as part of the High Plains Coonerativl,
Experiment (HIPLEX). The observations reoorted
here are selected results from the Texas-HIPLEX
site located in the Big Spring-Snyder area, whic:h
is approximately 150 km south of Lubbock in wes':
Texas.

Numerical simulations (Nelson) with a time-
dependent, one-dimensional microphysical Eulerilm
numerical model and cloud microphysical r.leasure..
ments (Carbone) for an intensively studied stonl
(Big Spring, Texas, August 14, 1975) both show non-
standard and time-denendent Z-R relations throul'h-
out the storm's rainfall history. The nwnericaf
model used is described by Nels~n (1976). An ear-
lier version of the model without ice-phase micro-
physi~s has been discussed by Silverman and Gla!.s
(1973). The synoptic situation and field measure-
ments are given in more detail by Carbone et al.
(1976). A more detailed model-observation comp~ir-
ison is being prepared for publication. In thi!.
brief note we wish to concentrate only u~on the
model-predicted and field-observed nonstandard
time and space-dependent raindrop spectra and
reSUlting Z-R relationships and to co~ent upon
their implications for radar precipitation
analysis.

2. MODEL RESULTS AND FIELD OBSERVATIONS

We find the developing rainshaft to be character-
ized by high concentrations of large drops with
respect to conventional Marshall-Palmer (~I-P)

· The National Center for Atmospheric Research
is operated by the National Science Foundation.

distributions. The decaying rain shaft tends to
approach conventional M-P'behavior. This is illus-
trated by figures IA and IB which show the temporal
evolution of the parameters N(O) [cm-4J and
Lambda [em] in the exponential (~larshall-Palmer
type) raindrop size distribution given by Eq.(l).

N(D)-N(O) exp(-Lambda D)

(1)

Strai~ht solid lines in figure I represent the
classical ~-P values. Connected boxes represent
model predictions at times in minutes ~iven by the
numbers adjoinin~ the boxes. Dashed lines repre-
sent objectively smoothed estimates of the mean and
mean !l standard deviation of N(O) and Lambda in
rain cells sampled by the aircraft before reaching
their peak reflectivity on ground-based radar.
Chain-dashed lines are analogous values in decaying
rainshafts having passed their peak reflectivity.
About 4800 7-second running average estimates of
the parameters N(O) and Lambda versus aircraft-
measured cloudbase rainrate derived from a Particle
Measuring Systems Precipitation Probe are involved
in the "early" data, while the "late" data repre-
sent about 1140 estimates of these parameters. The
model predicts that N(O) can be two orders of mag-
nitude lower than the M-P value in develooing rain-
shafts,'while Lambda begins one order of ~agnitude
deficient. As the rainfall intensity builds, the
intercept (N(O)) increases while the slope remains
constant, a behavior opposite to the Marshall-
Palmer distribution. As the rainshaft decays, the
model-predicted behavior in both N(O) and Lambda is
adequately described by the ~larshall-Palmer distri-
bution (fig. I). The excess of large drops in the
early sta~es of the model rainshaft comes about
predominately by size sorting in the time-dependent
updraft, large drops ~eing ahle to fall down to the
cloudbase through the uodraft earlier than small
drops. As the precipitation-enhanced downdraft
develops, this vertical sorting becomes less impor-
tant and the drop spectra become more classical.
As seen in figure I, the observations in decaying
rainshafts (dotted lines) are (based on the !l
standard deviation lines) drawn from a distinctly
different pooulation than the developing rains haft
values. While these "late" observations show the
same trend as the model outout, they never approach
the M-P values as the model predicts. Figure II
shows sample spectra taken from the aircraft data