WMOD00289 ‎(2)‎

• Title: Observations and Numerical Simulations of Precipitation Mechanisms in Natural and Seeded Convective Clouds
• Prepared By: Lroen D. Nelson
• Date: 3/1/1979
• State: IL
• Weather Modification - Doc Type: Report

14

aMc
at = mass rate of condensation on ice
C = specific heat of water
w

~Ma
a-r- = mass rate of accretion of liquid water on ice

From this point the freezing probability in a specific time of a hailstone in an

Eulerian system can be expressed as:

~MO
- at
P f = MO

at

O~Pf::1

(eq. 13)

Here the development will digress from pure Eulerian notions of transport in the

interests of physical realism. As hailstones melt it will be assumed that they all

decrease in mass at the same rate d MO/~t given above. Thus, the melting of ice

is a purely advective term (in mass) similar to condensation. A problem arises in

specifying the sink for liquid water produced as a result of melting. In the Eulerian
.

system, two-phase particles are not allowed and thus melted water must be stripped

from hailstones to reappear as liquid particles. A variety of possible schemes were

tried and discarded. For example, if the mass melted from each hailstone in a

time step were to reappear as a liquid drop of that mass, then the size spectra of

melted particles would be time-step dependent and the produced drops would be

so small (for practical time steps) that they would evaporate before reaching the

ground as rain. The best scheme was found to be one in which hailstones melt

away in mass at constant number density as described above while melted mass

reappears as raindrops having the same mass as their parent hailstone but at a

~,