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<br />I-hour average intensity, r Tal, into Eq, 39 gives the
<br />average rainfall intensity for T years and td hours (or
<br />minutes), rT;:d. The method of determining the rTal
<br />value can be simplified if the relationships between
<br />1O.year intensity and those for other return periods
<br />can be established. The possibility of formulating
<br />such relationships is explored herein.
<br />
<br />According to the frequency analysis made in
<br />the Technical Paper No. 40, a semi-empirical
<br />frequency diagram was actually used in the
<br />computation of rainfall values for return periods
<br />other than 2 and 100 years and hence in the con~
<br />struction of the 49 isopluvial maps. Thus, in reverse,
<br />the intensity-frequency relationship to be formulated
<br />from the isop1uvial maps should be independent of
<br />duration and should approximate a straight line
<br />on log-normal paper if the smoothing and areal
<br />adjustment during the construction of the maps
<br />did not take place. To examine this, the ratios of
<br />various.frequency intensities to lO-year intensity for
<br />the same duration at each of the 34 cities are
<br />calculated and listed in Appendix D. An inspection of
<br />the tables given in Appendix D reveals that these
<br />ratios so calculated vary, though slightly with
<br />duration for the same frequency, in a much less
<br />distinguishable manner than with return period for
<br />the same duration on semi-log paper. For illus.
<br />tration, these ratios for 60~minute duration for
<br />the 34 cities are plotted on semi-log paper, as
<br />shown in Fig. 5. The figure demonstrates different
<br />ranges of the ratios for various return periods. In Fig,
<br />5 " straight line is drawn to pass approximately
<br />through the middle ranges of the ratios, but in no
<br />way it represents the average return -period
<br />relationship. Despite these discrepancies, if we still
<br />assume for simplicity that the "standard"
<br />intensity.frequency relationship is independent of
<br />duration and nearly approximate a straight line on
<br />semi-iog paper, the relationship can be expressed
<br />mathematically as
<br />
<br />T, td
<br />r
<br />av 2-x X-I) (40)
<br />JU;ld = 10glO (10 T . . . . .. ... .
<br />r av
<br />
<br />in which x is the ratio of 100-year to corresponding
<br />1O.year intensity for the same duration, dermed as
<br />
<br />100,td
<br />r av
<br />x = -ru:td. . . . . . . . . . .. . . . . . . . . . . . . . (41)
<br />
<br />r av
<br />
<br />For the "center" line shown in Fig. 5, the value of x
<br />is always equal to 1.5 so that Eq. 40 can be further
<br />simplified. However, it is felt that this assumption is
<br />not necessary. We assume that the standard
<br />
<br />intensity-frequency relationship is a straight-line
<br />relationship, but not necessarily a "central" one.
<br />Specifically for l-hour rainfall, Eqs. 40 and 41
<br />become
<br />
<br />rT,1 =rIO, I log10(l02 -XTX-l).,... (42)
<br />av av
<br />
<br />rlOO, 1
<br />x = ~ . . . . . . . . . . . . . . , . . . . . . , , .. . (43)
<br />r av
<br />
<br />respectively. Substituting Eq. 42 into Eq. 39 yields
<br />
<br />T, td
<br />r av
<br />
<br />arlO,llog (10 2 - x TX - I)
<br />I av 10
<br />(td + b)C
<br />
<br />., (44)
<br />
<br />This is the general expression of the rainfall
<br />intensity-duration.frequency relationship. To make
<br />use of Eq. 44, one must first determine the values of
<br />the parameters, a I' b, c, and x from the three
<br />isopluvial maps with the help of Fig. 4. The three
<br />isopluvial maps used in the present study are ones for
<br />lO-year I-hour rainfall (RIO)), lO-year 24.hour
<br />rainfall (R 10,24), and 100-year I-hour rainfall
<br />(RI00,1), In other words, from the ratio of I-hour to
<br />24-hour rainfall depth for lO-year frequency,
<br />RIO, IjRIO,24, the values of aI' bl (= b), and c1 (=
<br />c) can be estimated from Fig. 4. The ratio of 100.year
<br />to lO-year rainfall intensity (or depth) for l.hour
<br />duration rIOO,I{rIO,I =RIOO,I{RIO,l isactually
<br />, av av '
<br />equal to the value of x, as expressed by Eq, 43.
<br />Therefore, use of Eq. 44 with Fig. 4 greatly reduces
<br />the number of the isopluvial maps (from 49 to 3)
<br />needed in the evaluation of the storm parameters, a,
<br />b, and c (Eq. 6) at any location in the United States.
<br />Because Eq. 44 is expressed in the same form as Eq.
<br />6, the parameters, a and aI' must be related by
<br />
<br />a = al rl~~l 10glO (102. x TX - I) . . . . . (45)
<br />
<br />If the 2.year l.hour and 2-year 24-hour key
<br />maps were used in the evaluation of the parameters,
<br />aI' bl (= b), and cI (= c), it would be better to
<br />express the parameter, a, in terms of r2a~ than rl~vl
<br />as shown in Eq. 45. In that case, the standard
<br />intensity-frequency relationship, as portrayed in Fig.
<br />5, should be calculated on the basis of 2-year
<br />intensity rather than lO-year intensity and the
<br />expressions of Eqs. 40 through 45 would change
<br />accordingly, possibly becoming more complicated
<br />than the present forms due mainly to the odd
<br />expression of logt02 instead of logtOlO which is
<br />unity. The validity of the present method using the
<br />three isopluvial maps with the help of Eq. 44 and Fig.
<br />4 is examined by comparing the rainfall intensities of
<br />
<br />20
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