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<br />REVIEW OF LITERATURE
<br />
<br />Because the rainfall inten,ity-dur-
<br />ation-frequency relationships will be utilized to de-
<br />velop the design storm patterns, existing formulas
<br />used in the description of such relationships were first
<br />extensively reviewed, After the review of the rainfall
<br />intensity-duration-frequency formulas, the design
<br />storm patterns based on such formulas are appraised
<br />in terms of theoretical concepts behind their deveiop-
<br />ments.
<br />
<br />Rainfall Intensity-Duration-Frequency
<br />Formulas
<br />
<br />A design hyetograph for a station under study
<br />can be formulated from the corresponding rainfall
<br />intensity.duration.frequency relationship that may be
<br />either graphically portrayed as a family of curves or
<br />expressed as a formula, Very often a formula, though
<br />derived from a mere exercise in curve fitting, looks
<br />more advantageous than a family of curves for use on
<br />an electronic computer, Several formulas have been
<br />proposed for expressing intensity-frequency relations.
<br />Most of the early ones were simple in form and were
<br />summarized by Gilman (1964),
<br />
<br />The earliest formula was probably the one
<br />developed by Meyer (1917, 1921, 1928) who ana-
<br />lyzed excessive precipitatIon data from 1,962 storms,
<br />at 43 stations (east of Rockies) from 1896 to 1914.
<br />This was a hyperbolic-type formula simplest in form,
<br />but with a limitation in application,
<br />
<br />a
<br />rav= td +b
<br />
<br />, . . . . . (1)
<br />
<br />in which r av is the average rainfall intensity in inches
<br />per hour, td is the time duration of rainfall in
<br />minutes, and a and b are parameters, the values of
<br />which depend upon specific localities under consider-
<br />ation, The formula can be alternatively expressed in
<br />terms of the total rainfall depth, R, by multiplying
<br />Eq. I by td as follows:
<br />
<br />a td
<br />R - , . . . , . . , , . .. . (2)
<br />- 60(td + b)
<br />
<br />which according to Schafmayer and Grant (1936) and
<br />Williams (1950) was first devised by Talbot in 1891.
<br />Bernard (1932), after analyzing data of Meyer (1928)
<br />
<br />and Morgan (n.d,), found that Eq, 1 was suitable only
<br />for rainfall intensities of short durations such as from
<br />5 to 120 minutes. Grunsky (1922) applied Eq. 1 to
<br />New York City data with the values of a and b found
<br />to be 150 and 20, respectively, Grunsky's formula
<br />was later referred to as the New York formula,
<br />
<br />In view of inaccuracy resulting from the use of
<br />Eq, I for estimating rainfall intensities of long
<br />duration, Bernard (1932) proposed a parabolic type
<br />formula which was applicable to duration from 120
<br />to 1,440 minutes,
<br />
<br />C
<br />fav=-n
<br />td
<br />
<br />. ' , , . . , , . , , . . . (3)
<br />
<br />in which C is the coefficient and n is the exponent
<br />ranging from 0.70 to 0.82 with the data of Meyer and
<br />Morgan. If n = 1, Eq, 3 was Nipher's formula of 1885
<br />for St. Louis, Mo, (Schafmayer and Grant, 1936),
<br />Actually Sherman (1931) in 1905 applied Eq. 3 to
<br />Boston data with the values of C and n found to be
<br />38,64 and 0,687, respectively, for 50-year ,tormand
<br />25.12 and 0,687, respectively, for lO-year storm.
<br />Sherman (1931) further proposed that the coeffi.
<br />cient, C, in Eq, 3 could be expressed in terms of
<br />frequency, F, as
<br />
<br />C = kFx "..........,.. (4)
<br />
<br />in which k is the coefficient and x is the exponent.
<br />The value of x was suggested to be 0.27 for Boston,
<br />Mass., by Sherman (1931). Powell (1932), however,
<br />in his discussion of Bernard's (1932) paper suggested
<br />that because the exponent, x, would probably vary so
<br />little with the location, an average value of x could be
<br />used. In view of the inaccuracies inherent in the
<br />raInfall records and the method of compiling them,
<br />the refinement gained in varying the exponent value
<br />of x was not judged to be warranted when many
<br />other greater discrepancies were still accepted in the
<br />course of design. Bernard (1932), nevertheless, on
<br />combination of Eqs. 3 and 4, proposed the following
<br />general intensity-duration-frequency formula for rain-
<br />fall intensities of long duration such as 2 hours to 6
<br />days,
<br />
<br />3
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