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

2304

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 35

MODEL MICROPHYSICAL INTERACTIONS

.--J

FIG. 1. Schematic representation of allowable microphysical interactions. See text
for explanation.

estimates. Data acquisition was performed by a mini-
computer, PMS buffer memory system and a digital
tape recorder. Analyses of aircraft data focused specif-
ically on the evolution of cloud droplet and raindrop
size distributions in conjunction with radar echo
characteristics. Precipitation drop sizes were measured
in 15 size classes of 300 J.lm between 300 and 4500 J.lm.
The size distributions were initially averaged over a
500 m path length in order to obtain a minimally
adequate sample volume of 340 e in the 4500 J.lm size
channel. A least-squares, logarithmic-linear regression
was fit to each distribution which yielded intercept
(N 0) and slope (^-) values, assuming an exponential
form given by (1). In addition, radar reflectivity
factor (Z), total number concentration (NT), median
volume diameter (Do) and rainfall rate were routinely
computed frQm the actual distributions.

c. The model

The model is an extension of the one-dimensional,
time-dependent, microphysical warm cumulus model
of Silverman and Glass (1973). A variety of ice-phase
additions have been made to make the model relevant
to midlatitude convection. These additions include
expressions for the activation of ice nuclei as functions
of temperature and a formulation for drop size, tem-
perature, cooling rate and ice nuclei (concentration-
dependent) contract-freezing of existing supercooled
liquid drops. Allowances are also made for the nucleation
of ice crystals from vapor according to Fletcher (1966).
A detailed riming process is also permitted by means of
a stochastic ice-liquid coalescence equation and a
simplified ice deposition/sublimation process takes
place where all ice particles are assumed to grow as if

having spherical symmetry. Melting and shedding of
liquid water by hailstones falling below the OOC level
is also permitted. The aforementioned ice processes
are listed in the Appendix. A schematic representation
of the allowable microphysical interactions between
hydrometeors is shown in Fig. 1. These interactions take
place in a time-dependent Eulerian framework having
a vertical space dimension. Where drop breakup is
indicated, collision and/or spontaneous breakup is
permitted. All microphysical processes are coupled
with the dynamics which maintains mass continuity
by the method of Asai and Kasahara (1967). The ice
hydrometeor spectra are represented by 47 discrete
size categories which are logarithmically spaced between
12 J.lm and 2.65 cm radius. Similarly, the liquid hydro-
meteors are represented by 47 categories from 2 J.lm
to 4.0 mm radius. The vertical grid consists of 52 levels
separated by 300 m and state parameters are advected
by a second-order Crowley (1968) technique, whereas
hydrometeors are advected by first-order upstream
differencing.
The initial.conditions required by the model are a
conventional rawinsonde sounding, estimates of cloud
condensation nuclei (CCN) and ice nuclei (IN) spectra,
and an initiating pulse of ,vertical motion, temperature
or humidity. It is also necessary to assume an updraft
radius for subsequent entrainment calculations and a
cloud base droplet concentration. The cloud base is then
found by dry convection in the model, and cloud
droplets are activated from the CCN spectra until the
input concentration limit is reached. Having formed
cloud base, the model then iterates forward in time with
a variable time step of approximately 15 s. A variety
of time- and height-dependent (dynamical and micro-