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

26

Where the terms retain the same meaning given' in the untransformecl equa-

tion. The other equations transform in a directly analogous fashion 0 There are

thus 44 ice particle sizes and 44 liquid drop sizes at each vertical grid nodE! in the

model universe. The vertical dimension will be represented by a grid of 52 levels

spaced 300 meters apart, a vertical depth of 15.6 km. In addition to the particulate

size distributions, the model retains the three state parameters; potential temperature,

mixing ratio, and vertical velocity at each grid node. The model universe is thus

a closed system of 52 (44+44+3) = 4,732 integral-differential equations which must

be simultaneously solved by iterative techniques in time (forward time differencing)

to specify the evolution of the precipitation processes in the model cloud.

The finite difference schemes used to obtain solutions to this closed set of

model equations were chosen to provide a practical compromise between spE!ed,

accuracy, and flexibility.

State Parameter Advection Scheme

Advection of state parameters is approximated numerically via the second

order conservation formulation of Crowley (1968) which can be represented as:

n+ 1 n [ b" x ]
I/JJ =I/JJ 1 + b"t (U J+1/2 - UJ-1/t

b"t ( N N)
- b"x F J+1/2 - F J-l/2

(eq. 30)

where:

2
N Ax p:r:o+l/2 ex J+1/2 ]
FJ+1/2 = b"t [12 (I/JJ+1 +I/J} - 2 (l/Jj+1 -I/J}

(eq. 31)