WMOD00296 ‎(2)‎

• Contract/Permit #: 14-06-D-5640
• Title: Park Range Atmospheric Water Resources Program Final Report
• Date: 9/30/1969
• Weather Modification - Doc Type: Report

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SECTION 3. 0
SPECIAL SU PPORT STUDIES

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3. I Numerical Models

The advantages of applying numerical studies to experimental cloud seeding
projects come from the ability to separate and study the various physical
processes, and to isolate their effects on precipitation. Evaluation techniques
are enhanced by the predictions of a realistic model that can be compared to
observed values. Various modification techniques can be simulated and the
model used as a tool to optimize the effect of modification procedures. The
basic model used on this project has been d~scribed in previous reports, but
a brief description of the model, as well as present and projected improve-
ments, is included here.

3. 1. 1 Two Dimensional Mountain Airflow

In the flow section of the model the motion is considered to be in an (x, z)
plane with the x-axis along the wind and z -axis in the vertical. The total
flow in this plane can be separated, using perturbation techniques, into a
steady basic current and a small perturbation current. Adiabatic steady
state frictionless motion is assumed. After solving the equations for the
differential form of the perturbation velocity and neglecting the smaller
terms

..,
v

,,2 w
" z2

2
+ (f(z) - k ) w == 0

(7)

where w is the amplitude factor of the vertIcal velocity (sinusoidal with wave
number k) and

f (z)

=~
2
u

+

( :2z~ )

u

(8)

This equation has been used for most of the past work on mesoscale flow over
mountains (Queney 1947, Scorer 1949, Wurtele 1953, Palm 1958, Sawyer
1960). Methods of solving it differ in detail but, in general, some simple
distribution of f (z) has been chosen and Fourier's theorem used.

If the sinusoidal lower boundary condition is of the form

1::0 = f (k) cos kx = ha exp (-ak) cos kx

(9)

the equation may be integrated over all wave numbers to give an ideal moun-

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