WMOD00474

• Title: The Evolution of Raindrop Spectra in Warm-Based Convective Storms as Observed and Numerically Modeled
• Date: 12/12/1978
• Weather Modification - Doc Type: Report

2308

J 0 URN A L OF THE A T M 0 S P HER I C S C I E NC E S

VOLUME 35

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-I TEMPORALLY STRATIFIED
, AVERAGED SPECTRA _
\ 20<R<40
\ (R) = 27.5 mm/hr
~ , 0 Growth Stage
-2 -: x :, x Dissipation
. l ~ . Mid-stage
~ ~: ,Marshall-Palmer
~ ~ x '^ (R=30).
~ ~ : x \ - Srivastava (1971)
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D(mm)

FIG. 5. Drop spectral densities stratified by stage of echo de-
velopment in high rainfall rate regions (> 10 mm h-1). Marshall-
Palmer distribution and Srivastava (1971) equilibrium solution
,for 30 mm h-1 are shown to bracket the observations, See text for
further explanation.

of one 4.5 mm drop can change Z by as much as 10
dBZ. More typically, however, the uncertainty is
approximately ::1::3 dBZ.
The radar samples shown in Fig. 4 were acquired
within one minute of the aircraft penetration and
within 700 m of the flight altitude. Usually the radar
scanned 300-500 m below the aircraft. Time lapse
video replay of radar data frequently showed aircraft
entrance and exit points with respect to the echo. The
flight path was considered to be a straight line between
these points. For penetrations where the aircraft was
not visible by radar, it was assumed that the path
bisected the 40 dBZ contour with the direction of flight
given by the recorded heading. This assumption was
considered valid since penetration was guided by an
airborne X-band radar with digital display.

5. Temporal evolution of spectral form

Preliminary examination of drop spectra revealed
periods of very low number concentration and high
radar reflectivity factor. The authors hypothesized
systematic temporal changes in drop spectra related to
size sorting by the updraft. In the low-shear environ-
ment with nonstationary storms, this is a plausible
physical mechanism which could produce spectra of
the type measured below cloud base. In order to lend
some substance .to this argument, the data were
temporally stratified. The 10 cm radar data were ex-

amined for the life history of echoes sampled by the
aircraft. The five echoes described in Section 4 were
determined to have nearly complete radar coverage,
and there were at least two aircraft passes through
each. Two echoes were penetrated by the aircraft prior
to the time that precipitation reached its maximum
intensity. Another two storms were principally sampled
during the dissipation stage, when maximum Z values
were decreasing with time. The fifth echo was that of a
multicellular storm with elements of growth and dis-
sipation throughout the echo volume. For the sake of
simplicity (and lacking other criteria) the intensifying
echoes were assumed to have active updrafts prior to
the time of maximum Z and the dissipating echoes were
assumed either to have dying updrafts or no updrafts
at all. The pulsating, multicellular echo data were not.
used for the purpose of determining updraft sorting
effects.
All size distributions from the high-rainfall-rate
regions (> 10 mm h-1) were averaged for each aircraft
penetration. These averaged spectra shown in Fig. 5
are plotted and labeled as to whether they are from a
growing or dissipating storm. Data acquired within 5
min of Zmax are plotted as "mid-stage" echoes. The
data represent approximately 80 km of flight path in
rainrates > 10 mm h-1. This corresponds to a minimum.
sample volume of 5.SX 104 .e in the 4.5 mm diameter
size range and a total volume of 1.5 X 106 .e. The mini-
mum sample volume for any iIldividual point is SX HJ3.e.
The average rainfall rates for all averaged spectra
vary between 20 and 40 mm h-1. Also plotted on Fig. 5
is the MP spectrum for 30 mm h-1 which is close to the
ensemble average rate (27.5 mm h-l~ of all spectra.
Similarly, the numerically derived equilibrium spectrum
determined by Srivastava (1971) for 30 mm h-1 rate
is also shown. It is apparent from Fig. 5 that spectra
from the growing cells (which are presumed to have
updrafts) tend to have lower spectral densities for
drop diameters < 2 mm and larger spectral densities
at diameters >3 mm. Conversely, the spectra from
dissipating echoes tend to have higher spectral density
for small drop diameters, approaching the MP spectrum
as the upper limit. Large drop spectral densities in
dissipating echoes are quite scattered but tend to be
lower than the growth stage echoes.
Fig. 6a shows linear regressions of these same ob-
served spectra together with model results at R= 27.5
mm h-1 in the growth and dissipation stages. The
model, in this case, has been exercized for all physical
processes except collision breakup. It can be seen that
the observed growth and dissipation spectral densities
are separated by approximately two standard devia-
tions at the small and large drop diameter extremes.
This is a convincing statistical indicator that the spectra
are indeed different. The model growth stage spectrum
closely agrees with observations, with low number
density of drops < 2 mm diameter and high density of

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