302 MONTHLY WEATHER REVIEW DECEYBEB 1955
AN EMPIRICAL INDEX OF SEASONAL VARIATION
OF INTENSE PRECIPITATION OVERLARGE AREAS
R. W. SCHLOEMER
U. S. Weather Bureau, Washington, D. C.
[Manuscript received May 16, 1955; revised November 10, 1955]
ABSTRACT
Adequate design and sound operational procedures for levees, spillways, and multiple-purpose reservoirs require
a knowledge of seasonal variation of precipitation of high intensity as well as soil infiltration capacities, antecedent
rainfall, and snow melt. The problem of seasonal variation is approached by indirect methods since there is an
inadequacy of data on large storms. A Oechnique ofareal smoothing is introduced and used to overcome lack of
suitable areal distribution of large storms studied in detail. A set of bi-weekly charts is developed giving approxi-
mately equal likelihood of occurrence of high rates of rainfall over areas of 20,000 square miles in 72 hours.
1. INTRODUCTION
The role of the hydrometeorologist in engineering de-
sign is to provide the engineer with as much meteorological
information as possible which may contribute to safe and
economical aonst,ruction of a particular structure. In the
design of levees, spillways, or multiple-purpose reservoirs
the meteorological problem is not alone one of amounts
of precipitation but, because of varying infiltration capac-
ities of the soil, antecedent rainfall, snow melt, and other
variables, it is also a problem of seasonal variations of
precipitation of great intensity. To date the storm study
program of the Corps of Engineers, Department of the
Amy [l] has encompassed about 600 storms of intense
precipitation. This program is designed to study the
depth-duration-area characteristics of major storms in the
United States. Results are tabulated and published as
pertinent data sheets as illustrated by figure 1. As yet,
too few fall, winter, and spring storms have been studied
to provide a suitable approximation to the true seasonal
characteristics of large-area precipitation. Until such
time that the meteorologist can set down a theoretical
solution to the problem of precipitation, its causes and its
seasonal characteristics, or until such time that an ade-
quate portrayal of precipitation distributions can be pre-
sented by synoptic climatological means, approximations
of the desired information will have to be made by engi-
neering techniques. This paper presents one such engi-
neering technique that serves as a partial solution to the
problem of seasonal variation of intense precipitation over
large areas.
J. B. Kincer [2] plotted the monthly State averages of
precipitation for the 55-year period 1886-1940 and tabu-
lated by States the percentages of years having averages
of0-.99,1.00-1.99,2.00-2.99,3.00-3.99, 4.004.99, and
5.00+ inches. In the interest of utility, S. S. Visher [3]
plotted some of the categories tabulated by Kincer and
ventured to draw isolines on the charts to make the data
easier to grasp. Under the direction ofW. F. McDonald
an activity of the Works Projects Administration reviewed
and tabulated daily precipitation records from all stations
operated by the Weather Bureau (seefig. 2) during the
30-year period, 1906-1935. These 24-hour amounts were
summarized within standard weekly intervals beginning
on January 1. The 29th of February once every four
years and the last day of each year were included in the
encompassing week, but the values for such periods were
proportionally adjusted to a 7day basis.Individual
stat.ion weekly averages were plotted on charts and
smoothed, as were average daily intensities. These
charts are in published form [4] and are also printed on
the back of The Daily Weather Map periodically. These
data were also summarized and tabulated at3 weekly aver-
ages over each of the climatological divisions of the United
States. Although most of the divisions are about 20,000
square miles in area their size varies considerably as can
be seen in figure 3.
The Hydrometeorological Section of the Weather
Bureau has from time to time studied portions of the
seasonal variation of prechitation over particular drainage
areas [5] :'and the seasonal variation of precipitation over
small areas [SI. The data tabulated for climatological
divisions serve as a basis for a generalized evaluation of
the seasonal variation of precipitation over moderately
large areas. It would be preferable to study seasonal
variation of 72-hour rainfall directly. Since such data
are not available the assumption is made that seasonal
variation of weekly amounts and 72-hour amounts are
reasonably consistent.
DECEMBEB 1955 M O N T H L Y W E A T H 303
P u n u l l OF T* rn COWS OF IMCIILLR
STORM STUDIES - PERTINENT DATA SHEET
Storm of 12-20 clay 190
Awlrnment sw 2-21
Location Oklahma t o Great Leks
Stu Prepared by: so~dXwsstern Division
hrlsa-District Office
Part I Reviewed by H. M. k c . of
Weather Bureau. 10/7/L6
Part It Approved by W k e . Chlef
o f Englnaers for Dlstrlbutlon
o f Factual Data, 8/15/L9 pmarkr: Center. near
,.lourds, Okla. kqt. 71 - Ref. Pt. bo FSE
Grid C-15
PATA AND COMPUTATIONS COMPILED
PART I
Prelimhry loohyetal map. in 1 sheet , scale 1: 1,000,000
Pmclpitatlon dnta and mas8 curve@: (Numkr o f Shertr)
Form 5001-C (Hourly prrclp. data) _____ - - - __.___ . _____- 531
Form 5001-1) (hour  1- - - - - - - - - - - - - - - - . - - - - Form 5001-D (  )  - 147
Miscl. preclp. records, mrteorologiul data, etc .___________ __ 10
Form 5002 (Mars rainfall curves) __ 251

e a u
FlnaI isohyetd maps, In 1 sheet , scale 1: l,O&om
Dat& and computation rhcetr:
Form S-IO (Data from mass rainfall curves) ______________ 42
Form 5-11 (Dcpth-area data from isohyetal map) ___________ 8
Form S-I2 (Maximum depth-duration data) ______________-_ 12
Maximum duratlon-depth-ores curves ___________________ 1
Data relatlng t o perlods of maxlmum rainfall _____________ 1
MAXIMUM AVERAGE DEPTH OF RAINFALL IN INCHES
FIGURE 1.-Example of data sheet for Corps of Engineers storm
studies.
FIGURE 2.-Stations with 30-year precipitation records, 1906-1935,
used in preparing weekly precipitation averages and 4-week
charts of average daily precipitation intensity.
2. SEASONAL VARIATION OF INTENSE PRECIPITATION
AS PERCENTAGE OF MAXIMUM
For each climatological division east of the Rockies all
weekly averages greater than one inch were plotted at
the appropriate weekon a seasonal graph. It was felt
that the sparsity of data, irregularities in size and shape
of areas, and topographic influences precluded generalized
studies of this sort for the western States. Figure 4 shows
such a plot for western Tennessee, one of the 94 divisions
studied. (The circled values are associated with storms
already studied in the Corps of Engineers storm study
program. Charts of this sort serve as good indicators of
storms worthy of further study in the program.) On each
such chart were drawn three curves; the highest curve
representing an envelopment of observed weekly average
rainfalls over the particular division, and the lowest repre-
senting the smoothed weekly averages obtained for the
30-year period. It will be noted that the smoothed
weekly means indicate peaks of rainfall on the 13th and
14th weeks and again on the 52dweek, whereas the
enveloped values indicate a single peak on the 3dweek.
It is apparent from the plotted values that the double
peak on the smoothed average curve results from a greater
frequency of 2- and %inch amounts during that time of
year-a significant fact in connection with water supply
problems. However, from the viewpoint of spillway,
flood reservoir, or levee design, the variations of the
extreme or near extreme values are of primary interest.
Figure 5 shows the weekly precipitation over eastern
Texas for the period 1906-1935, and again the highest
curve represents envelopment of all observed values and
the lowest curve represents the smoothed weekly means.
The latter curve indicates two peak periods of rainfall-
the 17th and the 49th and 50th weeks, again resulting
from a predominance of weeks having 2- and 3-inch
amounts of precipitation. In sharp contrast, the envelop-
ing curve shows a marked peak a t the 33d week with indi-
cations of secondary peaks on the 13th and 49th weeks.
The peak on the enveloping curve is a result of weak
tropical storms moving inland over the Texas area-
infrequent for a particular area but not uncommon for
the region adjacent to or just inlend from the Gulf of
Mexico. Such chance occurrences over a particular divi-
sion tend to create an unstable curve of envelopedob-
served values which is highly dependent upon the com-
bination of length of record and chance occurrences.
From an engineering design viewpoint it is desirable to
have a more stable curve upon which to base design
estimates.
The middle curves in figures 4 and 5 , labeled 99 per-
cent, represent a seasonal distribution of intense rain-
storms of unusual but not rare occurrence. Considerable
judgment has gone into the drawing of these curves.
Certain general rules can be enumerated as follows:
1 . The data should serve as basic guides.
304 MONTHLY W E A T H E R R E V I E W DECEMBER 1955
Limit of 5 Isohyet
. .. Storm o f Aug. 10-17, 1940
2. The curves should be fairly smooth, exhibiting no
sharp discontinuities from one week to the next. The
intent of this rule is not to deny the existence of singu-
larities, but rather, to recognize t,he extreme difficulty in
the proof of such singularities-a good number of which
a.ppeared to be indicated over the span of 30 years.
3. The number of points undercut on each seasonal
graph should be approximately 15, 16 or 17 (approxi-
mately 1 percent of the total, 1,560 weeks). Some Iati-
tude had to be allowed in order to permit smoothing of
curves to avoid sharp irregularities.
4. The points undercut should be fairly evenly dis-
tributed throughout the year.
5. The amount of undercutting of a particular point
shouldbe dependent upon the number of other high
intensity values for that season and especially upon the
clustering of points on or just below the tentat8ive curve.
6. The curve for a particular division should be con-
sistent with the curves of adjacent divisions with due
consideration for topographic variation, geographic loca-
tion with respect to moisture source, and variation in
area of the climatological divisions.
The 99 percent curves represent a first approxima-
tion to the seasonal variation of intense weekly precipita-
tion over particular large areas. It is believed that a
reasonable representation has been achieved in spite of
the considerable degree of subjectivity required forthe
final lines. Furthermore, i t is believed that, giventhe
same basic data, another analyst following the general
rules prescribed would obtain approximately the same
curve. As an additional check upon the shape of the
99-percent curve, an additional curve was drawn under-
cutting approximately 78 points throughout the year (95
percent) whenever doubts arose concerning the shape of
the 99-percent curve.
The size, shape, and orientation of storm isohyetal
patterns as related to the topographic, geographic, and
areal characteristics of the divisions play an important
DECEMIBFS 1955 MONTHLY WEATHER REVIEW 305
9
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0 1 1 1 1 I 1 I I I I I I I I I I I t i I I r l I l l J 4 8 12 16 2 0 2 4 20 32 36 40 4 4 4 8 52
WEEK OF YEAR
FIGUBE 4."Western Tennessee weekly precipitation greater than 1 inch, 1906-35.Circled dots are weekly totals greater than 4.5
inches, studied by Corps of Engineers.
role in the evaluation of seasonal variation. From
figure 3, i t is seen that a particular storm may be a good
or poor match for selected areas of study such as States,
climatological divisions, counties, or other arbitrarily
bounded regions. Actually, the only completely ade-
quate way of handling such a problem is to examine
different orientations, shapes, and sizes separately as is
done in the Corps of Engineers Storm Study Program.
For hydrologic studiesindividual river basins are examined
in detail as the problem arises. Because of the depth-
area relationships, comparison of average amounts of
precipitation in inches loses much of its meaning whether
on a State, division, or county basis.
Therefore, a set of charts (dashed lines in figures 6-31)
is presented as a generalized portrayal of seasonal varia-
tion of precipitation over large areas. These charts
are the result of an additional step in smoothing which
partly compensates for the differences in shape, size, and
orientation. For each division, at bi-weekly intervals
the ratio of the value of the 99 percent curve to the maxi-
mum value of the 99 percent curve of that division was
computed. These values were plotted and smoothed
percentage lines drawn. Considerable judgment was
again applied in drawing these lines since the meal
irregularities became more noticeable. Again certain
general rules were adopted as follows:
1. In non-orographic areas smoothness of pattern was
considered desirable. For example, a percentage value
of 80 surrounded by 90's was considered a result of shape
irregularity and was enveloped. The net effect of this
procedure was to modify the basic 99 percent curve for
the particular division by increasing its value at that
particular time of year.
2. Major orographic features (Appalachians and slopes
of Rockies)wereallowed to play dominant roles and
became boundaries of rather sharp discontinuities. Minor
meteorological controls (Ozarks and Great Lakes) were
given less consideration.
306 M O N T H L Y W E A T H E DECEMBEB 1955
I. I .I I 1 I I I I I I I I I I I I ' I I I I I I I I I
4 8 12 16 20 24 28 32 36 4 0 4 4 48 52
WEEK OF YEAR
FIGURE 6.-Percent of maximum value of seasonal variation of
precipitation over large areas (dashed lines) and index of intense
precipitation in inches (solid lines) for the week January 8-14.
FIGURE 7.-Week of January 22-28.
DECEMBEB 1955 MONTHLY REVIEW 307
FIGURE 8.-Week of February 5-11.
FIGURE 9.-Week of February 19-25.
I .-
FIGURE 10.-Week of March 5-11.
FIGURE 11.-Week of March 19-25.
FIGURE 13.-Week of April 16-23.
308 MONTHLY WEATHER REVIEW DECEMBEB 19%
FIGURE 14.-Week of April 30-May 6.
I
FIGURE 15.-Week of May 14-20.
i
FIGURE 16.-Week of May 28-June 3.
FIGURE 17."Week of June 11-17.
r
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FIGURE 18.-Week of June 25-July 1.
r
FIGURE IO.-Week of July 9-15.
DECEMBEB 1955 MONTHLY WEATHERREVIEW 309
FIGURE 20.-Week of July 23-29.
1 FIGURE 2l."Week of August 6-12.
,.-
u
FIGUBE 23.-Week of September 3-7.
FIGURE 24.-Week of September 17-23.
,.-.
1-
FIGURE 25.-Week of October 1-7.
310 MONTHLY WEATHER REVIEW DECEMBEB 1956
I
FIGURE 26.-Week of October 15-21.
FIGURE 27.-Week of October 29-November 4.
FIGURE 28.-Week of November 12-18.
FIGURE 29.-Week of November 26-December 2.
FIGURE 30.-Week of December 10-16.
FIGURE 31.-Week of December 24-31.
DEUEMBEB 1955 MONTHLY WEATHER REVIEW 311
3. Experience with major storm studies of the Corps
of Engineers Storm Study Program with regard to
season and place of occurrence of major storms influenced
the final drawing of isolines when doubt existed.
4. From a practical and safety viewpoint there was a
tendency to overdraw rather than underdraw percentages.
For example, values of 95-100 percent may have been
encircled by the 100 percent line in order to catch peaks
which might fall to either side of the bi-weekly.chart dates.
3. EMPIRICAL INDEX OF SEASONAL VARIATION
OF PRECIPITATION
So far, a portayal of the seasonal variation of weekly
precipitation over moderately large areas 'in terms of
percentage of a maximum value has been established.
The next step was to evaluate a base for maximum values
at particular locations. Figure 32 is a plot of all observed
20,000-square-mile, 72-hour storm values from the Corps
of Engineers storm studies regardless of season of occur-
rence. These values can serve as a base for maximum
values provided a suitable portayal of areal variation
can be obtained. The monumental proportions of a
storm study program with the intent of obtaining a
complete array of storm values for all areas of the country
and all seasons of the year has precluded this method of
approach. It should be noted that the selection of storms
studiedin the program is based upon intensities, total
volume of rainfall, associated floods, availability of suit-
312 MONTHLY W E A T H E R R E V I E W DECEMBEB 1955
e.
2-
-
0 I I I I 1 I I I I I I 1 1 1 1 105 103 101 99 97 95 93 91 89 87 85 83 81 79 77 75
L0NGITUD.E I.W)
FIGURE 33.-Average depth of storm rainfall over 20,000 sq. mi. in
72 hours according to longitude for the latitudinal strip 40-42' N.
able rainfall measurements, and work load of the En-
gineersfieldoffices. It can readily beseen that no
frequency or expected-return period could be assigned to
a particular storm. As objective a method as possible
wasdesired to reduce, if possible, the observed storm
values to base values representing approximately equal
Iikelihood of occurrence.
The eastern part of the United States was divided into
2 O strips of latitude and longitude. Storms values from
within each 2' strip of latitude were plotted on a graph
with longitude as abscissa and depth of precipitation as
ordinate, as shown in figure 33. All storms within each
2 O longitude strip were plotted with precipitation as
abscissa and latitude as ordinate (fig. 34). A first approxi-
mation to the distribution of depths was drawn (dotted
line) considering values on adjacent strips by means of
overlay comparison. On these graphs a number of storm
values were undercut since the values were far and away
greater than all other values in the neighborhood. One
limitation placed upon undercutting was that the storms
undercut be fairly evenly distributed over the country.
Values read from the visually fitted curves of latitudinal
strips were than plotted on the longitudinal strips (X's).
Curves of second approximation (dashed lines) were then
&am, roughly splitting the difference between the first
approximation and the points obtained from the latitudinal
strips. From the dashed lines on the longitudinal strips,
then, values were plotted on the latitudinal strips (X's),
providing a basis for a third approximation on the lati-
tudinal strips. Additional approximations reduced the
remaining dXerences to the order of several tenths of an
inch which was considered a sufEcient degree of accuracy.
Values taken from the very last approximation were
then plotted on a map and a smooth pattern (fig. 35) was
obtained which, it is believed, represents, approximately,
50 -
48 -
46 -
44 -
-
42 -
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238 -
-40 -
Y
0
- +
236 -
34 -
32 -
30 -
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28
r l t l I l l l l l l l l l r
0 2 4 ' ' 6 8 10 12 14
FIGURE 34.-Average depth of storm rainfall over 20,000 sq. mi.
in 72 hours according to latitude for the longitudinal strip 89"-
91 w.
the depths of precipitation having equal likelihood of
occurrence over the country for areas of 20,000 square
miles and duration of 72 hours. Observed storm precipi-
tation undercut by this pattern is shown in figure 35.
It is believed that (having been derived from observed
data) figure 35 represents a picture of precipitation depths
resulting from near-maximum combinations of rainfall-
produc.ing mechanisms regardless of season over the
eastern part of the United States. In a similar sense the
dashed lines of figures 6-31 represent evaluations of
rainfall-producing mechanisms at bi-weeldy intervals.
It is reasonable, then, to presume that the products of
values for the same points on figures 6-31 (dashed lines)
and on figure 35 should produce a reasonable picture of
the seasonal variation of rainfall potential for 20,000
square miles and 72-hour duration. The solid Lines in
figures 6-31 were drawn from products of such values.
They have been smoothed once through seasons and once
for area at each season. Additional smoothings would
result in minor changes in various portions of the charts
but the generalized procedures followed in the development
of the charts would belie the accuracy obtained by
additional smoothings.
4. DISCUSSION
There were many interesting meteorological questions
raised during the drawing of these charts: for example,
the apparent short-lived period of intense rain of hurricane
origin along the Middle Atlantic Coast, the influence of
the Great Lakes on storms of large area and long duration,
the northward migration of zones of intense rainfall during
the spring, and what appears to be a double structure of
areas of intense precipitation in May and June. Synoptic
climatological studies of storms would very likely yield
indications of the more direct causes of such variations.
DECEMBEB 1955 MONTHLY W E A T H E R R E V I E W 313
FXQIJEE 35.-Depths of precipitation having approximately equal
likelihood of occurrence; 20,000 sq. mi., 72 hours, all seasons.
Plotted values show total rainfall amounts for storms which are
undercut by the index.
For a number of years the Hydrometeorological Section
has applied a technique of storm transposition to extend
effectively the storm history of a particular area. On the
basis of synoptic climatology limits are drawn delineating
the area over which the apparent significant factors con-
tributing to the mechanism of a particular rainstorm could
reasonably occur. Areal transpositions of storms with
suitable adjustments for moisture potential have been
made in many studies, but temporal transpositions have
arbitrarily been limited to 15 days. As an indication of
adjustments required for either areal or temporal trans-
position of storms, or both, it appears reasonable to use
the ratio of the index values a t the time and place of
occurrence to the values at the transposed time and
location.
ACKNOWLEDGMENTS
The writer wishes to acknowledge the suggestions and
criticisms of J. F. Appleby of the Hydrometeorological
Section and D. E. Nunn of the Corps of Engineers who
are currently analyzing seasonal variation of rainfall over
small areas. Thanks are also due the sub-professional
staff of the Hydrometeorological Section-A. E. Brown,
A. L. Criss, J. L. Kiester, J. T. Lindgren, C. G. Ludwig,
H. H. Vinnedge and F. C. Robrecht-who a t various
times assisted in the laborious task of plotting and
tabulating the data, and to Miss M. I. Hammer for
the typing.
REFERENCES
1. Corps of Engineers, Department of the Army, Storm
Rainfall in the United States.
2. J. B. Kincer, Normal Weather for the United States,
U. S. Weather Bureau, Washington D. C., 1943.
3. Stephen S. Visher, Maps of Percentage Frequencies of
Very Dry, Moderate and Very Wet Months,
Monthly Weather Review, vol. 72, No. 3, March 1944,
4. W. F. McDona,ld, Average Precipitation in the United
States for the Period 1906 to 1935 Inclusive, U. S.
Weather Bureau, Washington, D. C., 1944.
5. Hydrometeorological Section, U. S. Weather Bureau
HydrometeorologicalReport No. 2, Maximum Pos-
sible Precipitation, Ohio River Basin above Pitts-
burgh, Pa. In cooperation with the Corps of En-
gineers, War Department, Washington, June 1941.
6. Hydrometeorological Section, U. S. Weather Bureau,
HydrometeorologicalReport No. 29, SeasonalVaria-
tion of the Standard Project Storm for Areas of 200
and 1000 Square Miles East of 105th Meridian,
In cooperation with Corps of Engineers, Department
of the Army, Washington, March 1953.
pp. 63-70.