1034 
average depth and the catchment area of the measuring 
equipment. 
Depth-Duration-Area Data. The user of hydro- 
meteorological advices primarily requires information 
in the form of average depths of precipitation, duration 
by duration, over the areas of specified drainage basins. 
The areas may be as large as, for example, the 145,500 
square miles of the Colorado River drainage basin 
above the Bridge Canyon dam site [26] or they may be 
small as in the case of the design of storm sewers over 
a few city blocks. For large areas, the total amount of 
water which can collect over a period of days is the 
dominant factor in most design problems. For small 
areas, design is controlled by high intensities for du- 
rations measured in hours or even minutes. The hy- 
drometeorologist is, accordingly, required to determine 
values of average depth over duration for areas of a 
larger order of magnitude than those of the catchments 
of rain gages. He deals with what can be considered as 
the uniquely hydrometeorological ‘“‘depth-duration- 
area”’ (DDA) values derived from the processing of the 
essentially ‘“‘point-rainfall’”? measurements of the rain 
gage. Because of the peculiarities of hydrologic needs, 
most DDA data and estimates are either for large areas 
and long durations or for small areas and short du- 
rations. Because the other two types of combinations 
are rarely needed, few storms critical as to such combi- 
nations have been processed. 
In each storm of record, for each standard area (¢.g., 
10, 100, or 10,000 square miles) and for each duration 
(e.g., 6, 12, 48, or 120 hr), there exists a maximum depth of 
rainfall. An array of such data is called the set of 
“maximum DDA values” for the storm. The Corps of 
Engineers, in cooperation with the Weather Bureau, is 
conducting a continuing program of developing maxi- 
mum DDA values for major rainstorms of record in the 
United States. Approximately 600 storms have been 
processed up to the present time. Table I contains the 
greatest depths together with a list of the storms which 
produced them. Glasspoole [7] has presented similar 
data for the United Kingdom, processed by a method 
slightly different from that used in this country. 
Mass Curves of Rainfall. Graphs of accumulated 
precipitation versus time, called ‘‘mass curves” of rain- 
fall, may be prepared in considerable detail in the case 
of data from recording gages. From 24-hr observation 
stations, or from stations recording only total-storm 
amounts, mass curves can be synthesized by referring 
to the records of nearby recording-gage stations, to 
synoptic meteorological analysis, and to ‘‘double-mass 
analysis” [11]. The set of mass curves for a single storm 
is basic to the development of the maximum DDA 
values, and for the construction of isohyetal maps—for 
increments of six hours, say, as well as for the total 
storm. Obviously, the more mass curves available, the 
more accurate the results will be. DDA values may be 
derived by planimetering of the isohyetal maps, or by 
employment of area-weighting procedures such as the 
“Thiessen polygon” method [24]. A combination of the 
two methods is now in standard use in the United 
States. 
HYDROMETEOROLOGY 
Conversion of point-rainfall to DDA values involves 
the assumption that each rain-gage measurement is 
representative of a more or less large increment of area 
surrounding it. In its report on thunderstorm rainfall, 
the Hydrometeorological Section [27] has discussed in 
detail the reliability of areal rainfall determination. 
Taste J. Maximum OBSERVED RAINFALL DEPTHS IN THE 
UNITED StatTEs* 
Duration 
Area (hr) 
(sq mi) 
6 12 18 24 36 48 72 
in. in. in. mn. mn. in. in. 
10] 24.7a 29 .8b 35.06 |36.5b |37.66 |37.6b |37.6b 
100) 19.66 26 .2b 30.76 |31.9b |82.9b |32.9b |35.2c 
200) 17.96 24.36 28.76 |29.7b |30.7b |81.9c |34.5c 
500} 15.46 21.46 25.66 |26.66 |27.6b |30.3c |33.6c 
1,000) 13.46 18.8) 22.9b |24.0b |25.6d |28.8c |82.2c 
2,000) 11.26 15.76 19.56 |20.6b |23.1d |26.8c |29.5¢ 
5,000} 8.16,7 | 11.16 14.16 |15.06 |18.7d |20.7d |24.4d 
10,000} 5.77 7.9k 10.le |12.le |15.1d |17.4d |21.3d 
20,000} 4.07 6.0k 7.9e | 9.6e |11.6d |13.8d |17.6d 
50,000} 2.5¢,h 4.29 5.3e | 6.3e | 7.9e | 8.9e |11.5f 
100,000} 1.7h 2.5h,t 3.5¢ | 4.3e | 5.6e | 6.6f | 8.9f 
* The letter after the rainfall depth identifies the particular 
storm which gave that depth according to the following key: 
Storm Date Location of rainfall center 
a July 17-18, 1942 Smethport, Pa. 
6 Sept. 8-10, 1921 Thrall, Tex. 
c Aug. 6-9, 1940 Miller Island, La. 
d June 27—July 1, 1899 Hearne, Tex. 
e March 13-15, 1929 Elba, Ala. 
f July 5-10, 1916 Bonifay, Fla. 
g April 15-18, 1900 Eutaw, Ala. 
h May 22-26, 1908 Chattanooga, Okla. 
t Nov. 19-22, 1934 Millry, Ala. 
i June 27—July 4, 1936 Bebe, Tex. 
April 12-16, 1927 Jeff. Plag. Sta., La. 
Figure 1, reproduced from this report, illustrates the 
variation in isohyetal-pattern analysis which can result 
from a variation in the number of reporting stations. For 
large-area and/or long-duration storms, existing rain- 
gage networks are usually adequate for computations 
of DDA values. But only rarely can detailed isohyetal 
patterns—and thus, accurate DDA values—be deter- 
mined for the intense, local, short-duration bursts of 
rainfall which sometimes occur in thunderstorms. 
PHYSICAL BACKGROUND OF 
HYDROMETEOROLOGY 
Empiricism and Theory. It has long been recognized 
that maximum intensities of point rainfall decrease as 
the durations through which they are computed in- 
crease. A number of empirical formulas expressing re- 
lations between duration and maximum intensity have 
been developed, differences between them being ascrib- 
able to the availability and type of data used in the 
formulation of the relationships, geographical regions of 
application, and similar factors. Since it is also recog- 
nized that maximum average depths of rainfall decrease 
‘as the area over which they are averaged increases, 
other empirical relations have been derived to include 
the factor of area. 
Empirical formulas can represent, with an accuracy 
