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

'l

DECEMBER 1978

R. E. CARBONE AND LOREN D. NELSON

2303

MP) distributions, the intercept parameter No re-
mains constant and the slope parameter .\ decreases
with increasing rainfall rate, where

, N(D) = No exp( -.\D)

and N (D) represents number density (cm-4) by drop
diameter D(cm). Waldvogel (1974) observed temporal
changes in drop spectra by means of vertically pointing
radar and a ground-based disdrometer. Spectra fitted
to the exponential form revealed large variation of No
which he attributed in part to ice phase growth mecha-
nisms associated with the presence or absence of con-
vection. Atlas and Plank (1953) crudely measured the
history of drop spectra at the ground in a weak rain-
shower. They speculated that a combination of sedi-
mentation, coalescence and evaporative effects were
responsible for relatively monodisperse spectra which
evolved from large to small drops as the shower passed
overhead. Srivastava (1971l) modeled the evolution of
warm raindrop spectra, considering stochastic coales-
cence and spontaneous breakup processes. He used the
datR. of Komobayasi et at. (1964) for specification of
the fragment distribution and probability of drop
breakup. Srivastava's results showed equilibrium
spectra which departed significantly from the ex-
ponential form, having a deficit of small drops and an
excess of large drops relative to MP distributions. He
attributed the deviations from MP form to the absence
of collisional breakup and condensation in the calcula-
tions. Young (1975) modeled the major physical pro-
cesses except sedimentation and found that collisional
breakup dominated over spontaneous breakup for the
case where rainfall rate was ~225 mm hel. Young's
results also showed spectral form to be approximately
exponential when collisional breakup was invoked but
roughly uniform when only spontaneous breakup was
permitted. Based on laboratory work by McTaggart-
Cowan and List (1975), List and Gillespie (1976)
modeled the evolution of drop spectra in stili air, in-
cluding some warm rain processes. List and Gillespie
assumed spontaneous breakup to be effectively non-
existent in nature and did not include that process in
their calculations. Their results show high concentra-
tion of small I drops and spectra of exponential form
with few drops in excess of 2.5 mm diameter. They
attributed previous observations of large drops solely
to the predominance of ice phase precipitation mecha-
nisms. Srivastava (1978) formulated equations for the
parameterization of evolving drop spectra by assuming
the exponential form. Numerical solution of the differ-
ential equations yielded evolving No and .\ parameters
for a variety of initial conditions. Srivastava found that
collisional breakup dominates over spontaneous breakup
in cases where the initial number concentration of small
drops is within the commonly observed range. In cases
where number concentrations were one to two orders of
magnitude lower, spontaneous breakup was shown to
playa significant role. For high number concentration

(1)

and liquid water content cases, there was considerable
agreement with the results_of Young (1975) and List
and Gillespie (1976).
In addition to the aforementioned studies, laboratory
work by Alusa (1975) and Blanchard and Spencer
(1970) have yielded spectra with relatively high con-
centrations of large drops and non-exponential form
for very high rainfall rates; however, the limited fall
distance involved in such experiments casts doubt on
the true equilibrium condition. Numerous investigators
have measured or deduced drop spectra in connection
with radar rainfall estimation studies. The results
(usually expressed in terms of reflectivity factor versus
rainfall rate relationships) imply a wide variation of
size distributions.

2. ThE~ observations and the model

a. Radar

Radar observations consisted of continuous 10 cm
low elevation (1.50) PPI scans intended for quantita-
tive precipitation estimation. Digitally programmed
PPI scan sequences (3-180 elevation) were performed
by 3 cm radar from which early echo top climatolo-
gies were obtained. The 10 em observations were
taken during June, July and August of 1975 and
the 3 em observations were taken during July and
August. Both sets of radar data (log video) were re-
corded on video tape and the 10 ern data were digitized
on a special purpose computer at the Illinois State
Water Survey. Pulse-to-pulse integration was achieved
by uniform weighting of 128 linearized samples.
Digitized data consisted of 1024 1.0 J.l.S (150 m) con-
tiguous range gates every 0.90 in azimuth. Complete
spatial independence of 10 em data is defined by the
pulse duration of 1.3 J.l.S (195 m) and beamwidth of 1.50.
The 3 em data were not digitized; however, the resolu-
tion factors are beamwidth of 1.00 and pulse duration
of 0.25 J.l.s. The 10 cm radar was calibrated by means of
a tethered aluminum sphere, resulting in a system gain
(antenna gain minus losses) of 37.0 dB. Peak trans-
mitted powers were typically 340 and 140 kW for the
10 and 3 cm systems, respectively.

b. Airel'aft

Aircraft observations were acquired in the VICInIty
of cloud base on 13, 14 and 15 August 1975. The air-
craft was a twin engine turbo-charged Piper Navajo
instrumented and operated by Meteorology Research,
Inc. It commonly flew at altitudes corresponding to 300
m above and below cloud base during nonprecipitating
and pr,ecipitating stages of cloud development, re-
spectively. The measurements included state param-
eters, particle measuring systems (PMS) optical
spectrometers (2-4500 J.l.m), cloud condensation nuclei
(CCN), ice nuclei, and linear accelerometer, rate-of-
climb and attitude measurements for vertical velocity