WMOD00482

• Title: Microphysical Observations Over the Atlas Mountains in Morocco
• Date: 12/23/1988
• Weather Modification - Doc Type: Report

l V2,q:!,02
fAP2

Zz

Vo,qo,Oo

} VI,q ,,0.
API

Z,

APO

Zo
Xo

X,

X2

~: Symbolic two-dimensional flow
across a barrier.

1 [ t.n^ V^
r (q + Qo) ~g
0,1 = Pwt.x 0

~]
- (ql+Qd g

\.

where:

ro,], = average precipitation rate over
the distance t.x

q = layer mean water vapor specific
humi dity

Q = layer mean cloud water (liquid
or solid) specific humidity

t.p = layer thickness (in pressure
units)

v = mean horizontal velocity of
1 ayer

9 = gravity

Pw = density of water (1 g cm-3)

For two-dimensional, steady-state,
hydrostatic flow, the continuity equation
can be written (assuming water substance
changes negligible):

t.Po Vo = t.PIVl = t.P2V2
---
g g g

Therefore (2) can be written. in general

~[
rl,I+l = (qI+QI)
pt.xg

(qI+l+QI+l)}

where

q dqs Ah
1+1 - qI = dz U 1,1+1

dqs!dz was defined in (1) and t.hI 1+1 is
the parcel vertical displacement &etween
point 1 and 1+1 and t.hI.I+l can be written
as

t.hI,I+l = d(zI+l - II)

where

d = 1 - (1 - ~~:)G~ = ~n

is the vertical displacement factor
depending on the degree of stability and
moisture of the parcel.

If we define:

( 2)

qI - qI+l = t.CI.I+1 (5)

as condensation per unit mass. occurring as
the parcel moves from point I to point 1+1.
and specify that a constant fraction E of
the sum of condensate formed and "imported"
precipitates over t.x. the remaining cloud
water, QI+l at point 1+1 is:

QI+l = (I-E)QI + (I-E)t.CI,I+l (6)

Now, substituting (5) and (6) into (2)
yields:

- Vot.Po [ 1
rI.I+1 = Pw(gt.x)E QI + t.CI.I+1 (7)

The term [QI + t.CI 1+1] can be either
>0 (condensation) 'or < 0 (evaporation).
In the latter case. rI.I+l = o.

The model uses. as input:

. Rawinsonde data analyzed and
interpolated for 15 evenly
spaced pressure layers.

. A fine mesh topography grid of
35 x 45 points with t.X = 10.0 km
(see Fig. 2).

. The stations' coordinates for
which estimates of precipitation
are to be made.

( 3)

.

.

.

(4)

I ·
-
.
~.
...
C1

.

Fir. 2: Model topography obtained using
a 0 km grid interval.