WMOD00399

• Title: WMO Training Workshop on Weather Modification for Meteorologists - Lecture Notes
• Date: 12/1/1979
• Weather Modification - Doc Type: Report

- 19-

4

tration change of m particles by collisions of water droplets, ice particles or water drop-
lets with ice particles; the second term results from breakup of drops or ice particles;
the third term indicates category transfers by freezing or melting and the fourth term
the source of particles at size moi by nucleation (N is the nucleation rate, <5 the Dirac
Delta function).

Particle numbers are not conserved since larger particles may capture smaller
ones and grow or breakup in collisions with smaller ones and thus decay in size. However,
the total amount of water substance need be conserved. Thus with:

P.
1.

f f m dm
o

(6)

and

v.
-1.

1
Pi

J f m v dm
-m

(7)

o

it can be stated that:

3p. 3pv
-.-! + \7' p.v. -
at 1._:L at

\7 . Pv v

o

(8)

Thereby Pi is the particle density, Pv the welter vapor density and v is the velocity of
the air.

Nucleation and condensation cancel each other in equation (8) because they
conserve mass.

Integrating over the mass of all particles described by the kinetic equation
also gives their total mass, which - assuming they are falling at terminal speed - is
producing the equivalent to their total drag, Le. the term which has to be entered in the
Navier-Stokes equation.

The H20 conservation equation will affect the vapor component in the gas law.

The evolution of the spectrum of droplets, drops and/or ice particles in a cloud
is determined in the first order by the particle growth equations. As long as the
particles are small (< 10 ]Jm), their fall velocity can be neglected and it can be assumed
that growth from the vapor phase is controlled by processes of molecular diffusion of mass
and heat. The two factors are closely related because condensation, deposition or evapor-
ation of H20 vapor represents - when multiplied by the corresponding latent heats - sources
or sinks of heat, which for (quasi) balance during growth or evaporation need to be com-
pensated by heat conduction to or from the particle under consideration.

These processes control the growth of cloud droplets from CCN or that of ice
crystals from ice nuclei IN.

The molecular transport processes give way to effects for bigger particles which
are controlled by the fall speed in air. Appreciable terminal velocities do not only
affect the exchange of H20 vapor and heat by increasing it considerably, they also allow
another growth process, namely growth by collection of cloud particles. This can be seen
through the following considerations.

The terminal speed of particles can be obtained from setting the particle weight
equal to its drag. For spherical particles \Ire obtain: