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

29

limation) for the same reasons. Stability and error analyses for this scheme are

given by Richtmyer (1957).

Mollenkamp (.1968) gives an analytic expression for the pseudodiffusion error

terms of the upstream difference numerical advection technique under the assumption

'f-

of a constant advective velocity. He points out that u~t/~x must be kept large

(approaching 1) as is done in this model to minimize the effects of pseudodiffusive

errors due to the upstream difference particle advection scheme. Contrary to in-

tuition, making At smaller while leaving other model parameters the same will

significantly increase pseudodiffusive numerical errors. As will be shown later

(equations 44, 45 and 46), the model simulations presented here continually re-

calculate At to maintain UMAXb./Ax as large as possible and typically greater

than 0.5. In spite of these precautions, the upstream differencing particle advection

scheme results in numerical pseudodiffusion coefficients of 200 to 400 m2/s, values

as large or larger than naturally observed particulate diffusion coefficients in

cumulus clouds. For example, Lawson (1978), in an observational study of the

dispersal of artificially generated ice particles inside towering cumulus clouds

finds natural turbulent particle diffusion coefficients of about 180 to 220 m2/s.

While anomalous, the artificially high vertical model particulate pseudo-

diffusion results in vertical mixing that the natural cloud achieves via spatially

and temporally coexisting large-scale updrafts and downdrafts that cannot be other-

wise adequately simulated in this model which has only one (vertical) space

dimension.