1042 
joining the warm trough and cold low. It is of interest 
to note that this example is a storm type which can 
produce large rainfall depths for long durations. Exist- 
ence of the warm continental surface (late spring 
through fall) south of Texas tends to retard movement 
of a warm trough; in addition, deep cold lows farther 
to the north are frequently observed to move very 
slowly. Synoptic studies of variations in this and other 
types of major storms will without question throw 
much light on the relationships between rainfall and 
other measurable variables. 
Statistical Relationships. The problem of objective 
forecasting of rainfall has been attacked—sometimes 
quantitatively and sometimes qualitatively—by many 
writers. In the main, the approaches have been statisti- 
cal, although the choice of independent variables has 
usually been made on physical grounds. Jorgensen [9] 
has related upper-air flow patterns to rainfall in Cali- 
fornia. By means of ‘‘composite maps,” Solot [22] has 
developed a method of preparing monthly precipitation 
forecasts for the Hawaiian Islands. Brier [1] and Penn 
[15] have made use of upper-air flow patterns in de-. 
veloping objective methods of quantitative precipita- 
tion forecasting. Through use of mean maps, Klein [10] 
has related five-day precipitation amounts to character- 
istics observed at the 700-mb surface. The statistical 
approaches, of which the above are a selection, yield 
results which show appreciable amounts of skill. Hs- 
pecially for the task of quantitative precipitation fore- 
casting, objective, statistical methods display much 
promise. 
As far as hydrometeorological needs are concerned, 
approaches such as those listed in the previous para- 
graph constitute only the first step. They tend to deal 
with average rather than enveloping values of the 
variables. Forecasts are based on relations derived from 
rainfall depths of lower orders of magnitude than those 
with which the hydrometeorologist is concerned. Fur- 
thermore, the approaches make no provision for extra- 
polation of observed to maximum possible values. They 
have, however, disclosed variables which are important 
as regards rainfall formation and, consequently, suggest 
certain directions for future hydrometeorological re- 
search. 
Enveloping Depth-Duration-Area Relationships. It 
has recently been shown by Fletcher [4] that maximum 
observed point-rainfall depths tend to vary with a 
power of duration so near to 0.50 that the assumption 
that depth varies with the square root of duration 
produces a very close envelopment of all recorded 
values of point rainfall. It was found, in addition to the 
square root of duration variation, that maximum ob- 
served areal rainfall depths vary hyperbolically with 
area. The equation 
266 
Fa ean 
ih =“VD (os + ion 4 Ja 
was found to be a close envelope of all observed rainfall 
depths for durations ranging from one minute to one 
year, and for areas between a point and 200,000 square 
HYDROMETEOROLOGY 
miles. In the equation, R is depth of rainfall in inches, 
D is duration in hours, and A is area in square miles. 
Equation (9) was derived empirically, and it is en- 
tirely possible that future rainfall records may bring 
about revisions in the constants. On the other hand, 
theoretical investigations now under way suggest that 
the form of the equation is correct for maximum possible 
precipitation. 
SPECIAL HYDROMETEOROLOGICAL PROBLEMS 
Rainfall Probabilities. Certain design problems re- 
quire estimates not of the maximum possible precipita- 
tion but rather of the greatest precipitation to be 
expected within a selected number of years. Economic 
factors might dictate, for example, that the design 
criteria for a certain structure should be based upon the 
greatest 6-hr rainfall to be expected once in ten years. 
For some needs point-rainfall estimates suffice, for 
others, estimates of average depths over specified areas 
are required. 
From the Weather Bureau’s tabulations of excessive 
rainfall occurrences, Yarnell [34] has published charts 
of rainfall expectancies in periods of from 2 to 100 years. 
Such charts can answer many questions as to proba- 
bilities of heavy rains. They are confined, however, to 
point-rainfall depths for durations from 5 min to only 
24 hr, and are based upon data which have some vari- 
ation as to criteria of selection. There is great practical 
need for an extension of Yarnell’s work to longer 
durations and to averaging of depths over areas. 
Other writers have made studies of frequencies of 
point-rainfall depths and, occasionally, of averages over 
various sizes of area. When the highest values of rainfall 
are considered, however, the difficulty arises that such 
values occur only once in the period of record of the 
observing station. Thus, the reliability of a “once in a 
hundred years” value, and similar values, is open to 
question. Development in statistical theory will un- 
doubtedly assist as regards the probability aspects of 
high rainfall rates. It is obvious, nevertheless, that 
accumulation of data through the years is necessary for 
the development of the probabilities of extremely high 
rates of rainfall. 
Space and Time Distributions of Rainfall. Estimates 
of maximum possible DDA values do not meet all of 
the needs of the hydrologist, especially for larger drain- 
age basins. It is also necessary that estimates be made 
of the isohyetal patterns and their variations with time. 
As far as river stages at the lower end of a basin are 
concerned, a heavy burst of rainfall occurring upstream 
and followed by another downstream is a more signifi- 
cant sequence than one in which the order is reversed. 
Heavy storms of record exhibit the characteristic 
that the highest ratios of observed to maximum re- 
corded DDA values for the United States tend to cluster 
about only one combination of area and duration, that 
is, each storm is important only within a restricted range 
of the durations and areas over which rain actually fell 
in the storm. Maximum recorded values for the United 
States are therefore determined by a series of “‘con- 
trolling” storms. Since the greatest storms of record all 
