A PROCEDURE OF SHORT-RANGE WEATHER FORECASTING 
illustrated schematically below: 
APsgro-1ax 
Xy 
Ho ny 
Wi 
AP. are) 
Xs 
Psxo j W; 
Tr00 
Xs 
ID scox0) 
A complete discussion of the physical reasoning in- 
volved in the selection of these variables has been 
given by Thompson. 
Tasie Il. Prepicrors UsEp FOR OBJECTIVELY PREDICTING 
THE RatnraLL Amount At Los ANGELES 
. eviation symbol Part of Fig. 
Predictor pe aes ap an Blcheprer 
1. The sea-level pressure 
difference, San Francisco 
(SFO) minus Los Angeles 
(LAX) COC SP CH OAD OOO GO Oe O6 APsro-nax a 
2. The 700-mb height at 
@ allan: aah dels oan eles sss 700 a 
3. The sea-level pressure 
difference, Los Angeles 
minus Phoenix (PHX).... APyax-pux b 
4. The sea-level pressure at 
San Francisco............. Psro b 
5. The 700-mb temperature 
at Santa Maria........... T 700 c 
6. The surface wind direc- 
tion at Sandberg (SDB)... Dens Cc 
The parameter W; from Fig. 10e is used as the fore- 
cast criterion. Corresponding to each integral value 
of this criterion, the percentage frequency of rainfall 
is listed in Table III. This frequency is tabulated for 
Tas_e III. ReLation BETWEEN Wy; AND THE PROBABILITY 
Tat Ratn Witt Occur In THE INDICATED CATEGORIES 
(Abbreviated from Thompson [79].) 
Wy Noein Tuk ae ei BRST uit ce 
0 100 = — 
3 88 9 3 — 
4.1 69 23 8 — = 
6 28 36 28 6 2 
6.6 24 26 36 11 3 
§) — — 25 55 20 
each of five rainfall intervals, namely, no rain, 0.01— 
4.00 mm, 4.01-12.50 mm, etc. For example, suppose 
that by applying Fig. 10 the value of the forecast 
criterion has been found to be 4.1. Then, according to 
Table III, there are eight chances out of every hundred 
that the occurrence of rainfall will exceed 4 mm. If on 
the other hand W; = 6.6, then the probability is 
36 + 11 + 3 = 50 per cent, or the chances are even 
791 
that the rainfall will be greater than 4 mm. Finally 
we mention that objective methods for predicting pre- 
cipitation also have been applied at Atlanta by Beebe 
[7] and at Washington, D. C. by Rapp [65]. 
Wind. The prognostic upper-air maps give a general 
picture of the future distribution of geostrophic and 
gradient winds aloft. The extent to which the wind 
deviates vectorially from the geostrophic wind has 
been investigated by Houghton and Austin [42], Machta 
[51], Bannon [6], Durst and Gilbert [22], Emmons [25], 
and Godson [84]. They found that, on the whole, the 
magnitude of this deviation is from about one-fourth 
to one-third of the wind speed. With increasing speed, 
this ratio first decreases and then increases. The mini- 
mum value of this ratio occurs with winds around 
sixty knots. At 700 mb the geostrophic speed is, on the 
whole, as accurate as the gradient speed. However 
the gradient wind-speed becomes more accurate than 
the geostrophic wind-speed whenever 
KVZ < 105? m secs, 
for example, at troughs with strong pressure gradients. 
The geostrophic angular deviation of fast winds (for 
example, at 300 mb) is negligible. In this case, the 
absolute isohypses (or the absolute prohypses of the 
prognostic maps) may be considered as streamlines. 
For slow winds (e.g., on the 700-mb map), there may 
be, under certain circumstances, appreciable differences 
in the direction of the absolute isohypses and stream- 
lines. We shall now (1) indicate where on the constant- 
pressure map the forecaster should expect large, geo- 
strophic angular deviations of the wind to occur, as 
well as (2) make some remarks on the nature of these 
deviations. In making an accurate upper-winds fore- 
cast from the prognostic constant-pressure maps, he 
must take (1) and (2) into account. 
The normal equation for horizontal frictionless mo- 
tion may be written as V = a cos 8 Vq. (In this expres- 
sion, V = | V| is the wind speed; Ve = | Va| is the 
geostrophic wind speed; a = f/(f + dw/dt), » being 
the wind direction, f the Coriolis parameter; and the 
angle 8 of geostrophic deviation is measured counter- 
clockwise from Vg to V.) For sufficiently small angles 
of geostrophic deviation the normal equation may be 
written approximately as V = aV,. Assuming @ con- 
stant, V = aVe. But Ve & OVe/dt + aVe(dVe/dse + 
BOV¢/One). (In this differentiation sin 8 has been re- 
placed by 8, and the value of cos 8 has been taken as 
unity.) For this expression, sg is measured in the direc- 
tion of the geostrophiec wind, and ng normal to it. 
Thus, V = adV¢/dt + a2? Ve(AVe/dse + BAVG/ANg). In- 
troducing the tangential equation of horizontal motion 
V =fsinBVe & {Vc for the left member and solving 
for B, we have finally 
ve) 
a 
OSG 
1 OVe 
(- ayia) 
