HYDROMETEOROLOGY IN THE UNITED STATES 
adjustable by variation of the complexity of the equa- 
tions, the envelopes of rainfall occurrences. Their exten- 
sions to include the maximum possible precipitation 
require adoption of arbitrary measures—the use of 
NOTE: STATION LOGATIONS WHIGH GOINGIDE 
WITH THOSE ON (b) ARE SHOWN ON 
(a) THUS,-© 
(a) 
1035 
where g is the acceleration of gravity, pw is the density 
of water, q is specific humidity, and po is the pressure 
at the bottom of the air column in which W is the 
precipitable water. As has been pointed out by Solot 
Q_5 10 15 20 25 
= S| 
SCALE (MILES) 
(b) 
Fig. 1.—Isohyetal maps of storm of August 3, 1939, Muskingum Basin, Ohio; (a) 449 rain gages (1 gage per 18 sq mi); (6) 22 
rain gages (1 gage per 375 sq mi). 
safety factors, for example. With methods based upon 
meteorological theory, it is possible to derive enveloping 
relationships through the use of meteorological data 
other than those of precipitation, and to develop the 
forms of the extensions of these relationships beyond the 
highest observed depths of precipitation. Such methods 
have been found to be most suitable for the majority of 
hydrometeorological problems. Nevertheless, empirical 
or statistical approaches are still followed whenever 
theoretical knowledge is not sufficiently complete or 
whenever available data are inadequate for the test and 
usage of known theoretical relations. Future advances 
in hydrometeorology therefore hinge upon further de- 
velopment of basic theory and upon the acquisition of 
necessary and sufficient data. 
Precipitable Water. The immediate source of precipi- 
tation is the water-vapor content of the air. For ana- 
lytical purposes, this quantity is customarily expressed 
in terms of the depth of “precipitable water” in a 
column of air, 
w= | G/oe») ap, (1) 
[21], when pressure appears in units of miillibars, W 
(in inches) is closely approximated by 
PO 
W=04] gap. (2) 
0 
Increments of W can be computed when the variation 
of g with pressure is known. 
The basic obstacle in the way of general use of the 
theoretical expression for W is the almost complete 
absence of upper-air sampling in the major rainstorms 
of record. Accordingly, hydrometeorologists have been 
forced to make certain assumptions regarding the re- 
lation between W and other meteorological elements, 
well represented areally and historically. The most 
common such assumption is that, in major rainstorms, 
the air in which the rain is formed is saturated through- 
out its depth and is characterized by a pseudoadiabatic 
lapse rate. Here, the depth of precipitable water in an 
air column above a specified pressure surface is a single- 
valued function of the dew point (or temperature) at 
that surface. Figure 2 shows the relation, based on this 
assumption, between W and surface dew point when 
