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<br />various durations and frequencies obtained from the
<br />present method with those obtained from the 49
<br />isopluvial maps in the Technical Paper No. 40.
<br />
<br />EXAMPLE. The values of the storm
<br />parameters, a, b, and c for New York, N.Y. (40.40 N"
<br />74.00 W.) are required in the formulation of design
<br />storm patterns. The 1O.year l.hour, lO-year 24-hour,
<br />and 100-year I-hour rainfall values are estimated
<br />from the maps (Figs. 6,7, and 8) to be 2.15, 5.20,
<br />and 3.11 inches, respectively (see also Table A-I in
<br />Appendix A). The ratios of 2.15/5.20 and 3.11/2.15
<br />are 0.413 and 1.447 (= x), respectively. (Note that
<br />the ratio of 2.year I-hour and 2-year 24-hour rainfall
<br />values is 1.43/3.38 = 0.423 from Table A-I in
<br />Appendix A.) From Fig. 4, corresponding to the ratio
<br />of 0,413, one can readily find a1= 23.9, b (= bl) =
<br />7.85, and c (= c J = 0.75, which are within the
<br />accuracy of the values directly computed from the
<br />corresponding standard intensity-duration
<br />relationships (Table C-l in Appendix C), as tabulated
<br />in Appendix E (see Table E-l). Because rl~J (=
<br />RIO,I) = 2.15 in./hr, from Eq. 45, on substitution of
<br />the x value, the parameter, a, is now expressed as
<br />
<br />a = 51.3910glO(l00.553 T0.447), ....,. (46)
<br />
<br />For various return periods, T .years, the
<br />corresponding values of a can thus be computed from
<br />Eq. 46. For instance, the a values so computed for T
<br />= 1,2, 5, 10, 25,50, and 100 years are 28.42,35.33,
<br />44.48,51.39,60.53,67.45, and 74.36, respectively,
<br />Substituting the a, b, and c values so obtained into
<br />Eq. 6 yields the following intensity-duration
<br />relationships for various return periods:
<br />
<br />28.42
<br />rav = (td + 7,85)0,75
<br />
<br />35.33
<br />rav = (td + 7.85P,75
<br />
<br />44.48
<br />rav = (td + 7,85P.75
<br />
<br />51.39
<br />rav = (td + 7.85p.75
<br />
<br />60.53
<br />rav = (td + 7.85P.75
<br />
<br />67.45
<br />rav = (td + 7.85p.75
<br />
<br />74,36
<br />rav = (td + 7,85)0.75
<br />
<br />T = I ..... . . , . (47)
<br />
<br />T = 2 .. .. .. .. . (48)
<br />
<br />T = 5 ........ (49)
<br />
<br />T = 10 . .. .. .. . (50)
<br />
<br />T= 25........ (51)
<br />
<br />T= 50 ....... (52)
<br />
<br />T = 100 .. .. . .. (53)
<br />
<br />Average rainfall intensities for durations of 5
<br />lOin, 10 min, 15 lOin, 30 min, 60 min,2 hrs, 3 hrs, 6
<br />
<br />hrs, 12 hrs, and 24 hrs are computed by using Eqs. 47
<br />through 53 for various return periods, one at a time,
<br />and tabulated in Table 5. A comparison of Table 5
<br />with Table B-1 in Appendix B reveals that the average
<br />rainfall intensities computed from Eqs. 47 through 53
<br />(or, in general, from Eq. 44) are about of the same
<br />magnitudes as those obtained directly from the 49
<br />isopluvial maps within the tolerable accuracy. This
<br />comparison in a sense leads to the conclusion that Eq.
<br />44 or, more specifically for New York City, the
<br />relationship
<br />
<br />51.3910glO(100,553 fl.447)
<br />r =
<br />av (Id + 7,85P,75
<br />
<br />, . . . . . (54)
<br />
<br />can be used to compute the average rainfall intensity,
<br />r.,(in,/hr), for any duration, t (min), the return
<br />period, T (years). Consequently, tlie a, b, and c values
<br />so determined are believed to be as accurate as those
<br />computed directly from the 49 isopluvial maps.
<br />
<br />The advantage of using Eq. 54 over the 49
<br />isopluvial maps is obvious because Eq. 54 can
<br />compute the average rainfall intensity for any
<br />duration and any return period including those which
<br />do not belong to one of those specified in the 49
<br />maps. Thus, Eq. 54 (only for New York City) or a
<br />general form thereof, Eq, 44, (for any location) is
<br />believed to be in the most suitable form for use in the
<br />computer modeling of the rainfall intensity-duration-
<br />frequency relationship,
<br />
<br />Ifthe value of x defined in Eq. 41 is assumed to
<br />be always 1.5, as portrayed as the "center" line
<br />relationship in Fig. 5, Eq. 54 can be further simplified
<br />and hence a new set of intensity-duration
<br />relationships for various return periods corresponding
<br />to Eqs. 47 through 53 can be obtained. However,
<br />average rainfall intensities computed from this new
<br />set of the relationships based on x = 1.5 were found
<br />to be not so accurate as those obtained from Eqs. 47
<br />through 53; therefore they are not tabulated herein
<br />for comparison.
<br />
<br />For further exammmg the Wlidity of the
<br />present method, data of several major cities obtained
<br />directly from the Technical Paper No, 40, as
<br />appended to this report, are compared with those
<br />computed by using the present method. The rainfall
<br />data for cities representing typical meteorological
<br />localities of the northeast, southwest, midwest, south-
<br />east, deep south, Rocky Mountains, and northwest
<br />areas in the United States, one from each area,
<br />are investigated. The general rainfall intensity-
<br />duration.frequency relationship, Eq, 54, for New
<br />York City which represen ts the northeast region
<br />was already developed and tabulated in Table 5.
<br />Other cities investigated include Los Angeles,
<br />Chicago, Miami, Houston, Denver, and Olympia. The
<br />
<br />22
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