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374 Chapter 11 Hydrology: Rainfall and Runoff
comes but once in a century or the storm that visits a region but once in a score of years; they
suggest cycles and trends and identify variations in areal distribution of normal and unusual
rainfalls; and they lend form to predictions of runoff in hydraulic systems, such as storm
drains and canals still to be built.

11.8.2 Runoff Records
As soon as serious thought is given to the development of a catchment area, actual
measurements of runoff should be started. Even the first year’s results will tell much
because they can be amplified by feedback; for example, by cross-correlation between
short-term runoff observations of the river basin under study and long-term records of
neighboring or otherwise similar systems. If rainfall records for the watersheds in ques-
tion are long, correlation of rainfall ratios with runoff ratios for the period of recorded
stream flow in each basin provides a reasonable foundation for extending the shorter
record. Generally speaking, comparative studies of hydrographs or duration curves are
more reliable than correlations of precipitation and other hydrologic information, but
there are exceptions.
Records of the intermittent runoff from small areas yet to be drained by storm sewers
are neither numerous nor of much use. Rates of flow change markedly when drainage sys-
tems are constructed and go into operation, and they are bound to change further as commu-
nities grow and age. Accordingly, continuous records supported by imaginative estimates of
runoff to be drained away in stormwater systems in a growing urban complex have much to
commend them.
Flow measurements in existing sewers are hard to translate into design values for
other sewers, unless the new drains are to be situated in similar, normally nearby, catch-
ments. Even then, the uncertainty of future change remains.
Flood-flow estimates must look to unusual as well as normal experience. The range
and number of useful observations is best extended by resorting to as much hydrologic in-
formation as can be assembled. Fortunately, the labor of correlating pertinent data has been
greatly reduced by access to high-speed computers. By combining modern computational
methods with modern statistical procedures, it has become possible to harvest information
in far greater measure than before and, in a sense, to generate operational sequences of hy-
drologic information of great significance.

11.9 HYDROLOGIC FREQUENCY FUNCTIONS

Arrays of many types of hydrologic as well as other measurements trace bell-shaped
curves like the normal frequency distribution shown in Appendix 5 of this book. Arrays
are numerical observations arranged in order of magnitude from the smallest to the
largest, or in reverse order. They are transformed into frequency distributions by subdi-
viding an abscissal scale of magnitude into a series of usually equal size intervals—
called class intervals—and counting the number of observations that lie within them.
The resulting numbers of observations per class interval, by themselves or in relation to
the total number of observations, are called the frequencies of the observations in the in-
dividual sequent intervals. To simplify subsequent calculations, frequencies are refer-
enced to the central magnitudes of the sequent class intervals.

11.9.1 Averages
The tendency of a bell-shaped curve to cluster about a central magnitude of an array,
that is, its central tendency, is a measure of its average magnitude. The arithmetic mean