1038 
across a rectangular area of size A and length Y. The 
inflow wind V,; blows into the model at low levels, 
through a depth Ap;, above which zero wind movement 
is defined. The outflow wind V»2 blows out of the model 
at high levels, through a depth Aps, above and below 
which there is no wind movement. There is assumed to 
be no net accumulation of air or atmospheric water 
content through duration D. Values used are all as- 
sumed to be averages through D. The quantities V; 
and V» are taken as averages through the respective 
Ap’s, and the averages with respect to dp are assumed 
to be equal to the averages with respect to gdp. With 
these assumptions, equations (5) and (6) can be in- 
tegrated. Elimination of the outflow wind results in the 
so-called “‘storage equation,” 
si ViD es Api 
mye G 1 Ap» Ws) (7) 
in which W, and W; are the precipitable-water depths 
at the inflow and outflow ends, respectively. The quan- 
tity within parentheses is frequently referred to as Wz, 
the ‘‘effective precipitable water.”’ For each flow model 
chosen, it represents the amount of rain falling from 
each unit column processed in the model. In the prac- 
tical use of the storage equation, the precipitable water 
is estimated from the surface dew points, and the Ap’s 
are assumed according to the flow model being studied; 
Y is a function of wind direction and drainage-basin 
dimensions, and V, is estimated from either surface or 
pilot-balloon observations. For estimation of the maxi- 
mum possible precipitation that can fall from a given 
model over a project basin, envelopments of wind-speed 
and dew-point statistics, for each wind direction, are 
used in the equation. 
OROGRAPHIC RAINFALL 
Empirical Approaches. Much of the rain which falls 
in mountainous regions is due directly to the lifting of 
moist air up the mountain slopes. For purposes of the 
present discussion, this percentage of the total rainfall 
in a storm is defined as the orographic component, while 
the remainder is called the nonorographic component. 
The orographic component is amenable to fairly 
simple theoretical derivation since the slope and the 
elevation of the ground surface—the factors which 
control the lift of the air per unit wind speed—are 
fixed and known. For certain noncomplex mountain 
systems, it is possible to calculate the rainfall with con- 
siderable success under the principal assumptions that 
(1) all of the rain is orographically produced, and (2) the 
upper-air flow pattern is deducible from surface ob- 
servations. As the topography becomes more complex, 
however, not only does the problem become harder to 
handle mechanically, but also the vertical and horizontal 
distributions of winds become more difficult to estimate 
with assurance. Present deficiency in theoretical knowl- 
edge of the effects of topography upon the space distri- 
bution of wind leads to the conclusion that an empirical 
approach must serve for many problems involving 
orographic rainfall until adequate theory is developed. 
HYDROMETEOROLOGY 
Such an approach may be based upon a rational se- 
lection of topographic parameters, for example, slope, 
exposure, and elevation. Use of multiple-correlation 
techniques may then produce a regression equation in 
which rainfall is expressed as a function of the topo- 
graphic parameters. The equation would also contain a 
residual term, partly resulting from incomplete selection 
of parameters and partly giving the nonorographic 
component of rainfall. 
The approach described above is not adaptable to 
computation of single-storm rainfall unless the meteor- 
ological parameters of wind and humidity are also con- 
sidered. It is well suited, on the other hand, for deriva- 
tion of long-duration rainfalls over orographic regions 
of meteorological homogeneity. The method has been 
used by Russler and Spreen [17] to estimate average 
seasonal precipitation at points between the relatively 
sparse network of recording gages in the Colorado 
River drainage area. Excellent correlations were ob- 
tained in this study, in which a graphical multiple- 
correlation technique was employed. 
In a study of rainfall potentialities in the Willamette 
River Basin, Oregon, Platzman [16] employed an essen- 
tially empirical method. Lack of suitable data, in this 
case, precluded a theoretical investigation. Platzman 
reasoned that the speed and moisture content of the air 
passing over the basin from the Pacific were the domi- 
nant meteorological factors and, further, that these 
parameters were representable by observations made at 
a surface weather-reporting station. He made statistical 
studies which led to selection of an index station, and 
from available DDA data from five of the greatest 
Willamette Basin storms of record, he determined the 
coefficients in the empirical equation 
R = (a+ bT.z)(c + dV), (8) 
where 7’; was dew point and V was wind speed at the 
index station. Envelopes of the rainy-season wind and 
dew-point observations at the index station provided 
values to be placed in equation (8) for estimation of the 
maximum possible rainfall. 
Where theory is inadequate, as in problems associ- 
ated with highly complex topographic regions, em- 
piricism probably offers the only approach which will 
produce the required answers. This approach is usually 
based upon rain which fell in important storms of 
record and assumes that the model of the average large 
storm is the same as that of the maximum possible one. 
Theoretical Barrier Models. For special, simple topo- 
graphic regions it is possible to derive expressions based 
largely upon physical reasoning and yielding computed 
values which agree well with observed ones. When the 
outstanding feature of the basin is the existence of one 
or two mountain barriers which intercept rain-bearing 
winds, the storage equation (7) may be adapted to the 
problem. It is usually necessary to make assumptions 
regarding the vertical distributions of temperature and 
humidity, since radiosonde observations are inevitably 
Missing in the great storms of record which offer the 
only checks on the suitability of models to be chosen. 
Although the assumption of a saturated, pseudo- 
