WMOD00281

• Title: Application of a Simple Local-Scale Numerical Model in the Study of Altered Climate Impacts on Watershed Precipitation
• Prepared By: J. G. Medina
• Date: 1/1/1989
• State: AZ
• Weather Modification - Doc Type: Report

As inputs, the model requires, as a minimum.
estimates of the vertical profiles of wind, temperature,
and humidity at the upwind edges of the geographical
area of interest. When available from sources such as
the LFM or NGM numerical models, estimates of the
large-scale vertical motion can be inserted in the
precipitation model.

T]1e model produces precipitation estimates
integrated over desired time periods at each grid point
of a selected grid array. For estimates at other
locations of interest, such as sites where gauges are
located, an interpolation scheme utilizing surrounding
grid point values is employed. Integrated volume
precipitation for designated watersheds, for periods of
choice, is also produced by the model. With
regression techniques, volume precipitation can be
employed to estimate monthly or seasonal streamflow
(e.g., Medina, 1981).

The basic precipitation formula for the model
(Rhea, 1977) is given as:

R = ~ ft fPz diJ. w dp tit (1)
pwg 0 PI dz

where
R
E

Precipitation amount (em)
Precipitation efficiency (dimensionless)
Vertical motion (em S-I)
= Density of water (1 g cm-3)
Gravitational acceleration (em S-2)

w
P..
g

diJ.
dz

fPz
PI

Specific humidity change with
height (em-I)

Pressure depth of saturated air column
(g cm-1 S-2)

f~

Duration of the process (s)

Figure 1 is a representation of the two.
dimensional flow across a barrier as given by Rhea
(1977).

N_ ~l Vz,qz,Qz
~}} vVI'I,qq""QQ.. \llP2
vo.qo,Qo 6PI
Zz
llPo Z.

Zo
Xo

XI

X2

Fig. 1. Symbolic two-dimensional flow across a barrier
(from Rhea, 1977).

The formula for computation of precipitation
rate - along grid interval .:1x is:
'1.1+1

:- EV,.:1P,
('/'/+1)' = pwg.:1x (Q/+.:1C/,/.I)/

(2)

where
1
V
J1P =
Q:
J1C1,1+1 =
E
PO'

Computational layer in question
Horizontal wind speed in the x direction
at the upwind edge of the grid
Pressure thickness of the inflowing layer
at the upwind edge of the grid
Cloud water content (mixing ratio) of
liquid or solid at grid point I
Additional condensation (or
evaporation) due to vertical
displacement between points I and 1+ 1.
Precipitation efficiency
Density of water

3.

MODEL ADAPTATION

A previously noted, the model requires
36 topographic grids, one for each 100 wind direction
class. Figures 2 and 3 are contoured presentations of
the 10-km model topography for the 27(1' grids for the
Mogollon Rim of Arizona and the Delaware River
watershed.

19
17
16
,J
"
9
7
6
J

Fig. 2. Model topography for the Mogollon Rim area
of Arizona (contours in feet).