<br />is approximately 10 percent with no bias. The
<br />differences were ascribed mainly to the considerable
<br />areal generalization used in the Technical Paper No.
<br />40, ex""pt for the fact that the Technical Paper No.
<br />40 is for the partial-duration series and No. 25 is for
<br />the annual series. In this study, only the isopluvial
<br />maps in Technical Paper No. 40 are used.
<br />
<br />A total of 34 major cities including 23
<br />metropolis in order of population size and 11 capitals
<br />of the western United States were selected and
<br />rainfall depths for 1-, 2-, 5-, 10., 25., 50-, and
<br />100-year return periods for 30.minute, 1-,2-,3-,6-,
<br />12., and 24-hour durations at each city are estimated
<br />from the corresponding isopluvial maps in the
<br />Technical Paper No. 40, as appended to this report
<br />(see Appendix A).
<br />
<br />It is noted in the Technical Paper No. 40 that
<br />the empirical relationship, 0,79 times the 6O-minute
<br />rainfall, was used in the estimation of the 30-minute
<br />rainfall. In the case of those which have duration
<br />shorter than 30 minutes such as the 5-, 10-, and
<br />IS-minute rainfalls, rainfall depths are estimated on
<br />the basis of the average relationships between
<br />30.minute rainfall and shorter duration rainfall for
<br />the same return period, as given in Table 3 of the
<br />Technical Paper No. 40. Because the empirical ratio
<br />between the 30-minute rainfall and the 60-minute
<br />rainfall is 0.79, the 5-, 10-, and IS-minute rainfalls
<br />can also be estimated based on the same 60-minute
<br />rainfall with the modified ratios shown respectively in
<br />Table 1. From the ratios between the 60-minute
<br />rainfall and the shorter-duration rainfalls, the
<br />relationships between the 60-minute intensity and the
<br />shorter-duration intensities can be derived, as listed in
<br />Table 1. These intensity ratios, if derived from the
<br />Technical Paper No. 40, should also appear in the
<br />standard intensity-duration relationships. Any
<br />deviations from these ratios may be attributed to the
<br />smoothing and areal generalization during
<br />construction of the 49 isopluvial maps, errors in
<br />estimation from the maps, or a combination thereof.
<br />
<br />Table 1. Average relationships between 60-minute
<br />rainfall and shorter duration rainfalls for the
<br />same return period.
<br />
<br />Duration Ratio for
<br />(minutes) Rainfall Rain fall
<br />depth intensity
<br />5 0.292 3.51
<br />10 0,450 2,70
<br />15 0,569 2,28
<br />30 0.790 1.58
<br />60 1.000 1.00
<br />
<br />Supplemental rainfall values for 2-,5-, 10-,25-,
<br />50., and 100-year return periods for 6. and 24-hour
<br />durations can be obtained from the NOAA Atlas 2
<br />(Miller, Frederick, and Tracey, 1973) which provides
<br />precipitation-frequency isopluvial maps for the 11
<br />western states, Rainfall values for the selected points
<br />in the NOAA Atlas 2 were estimated and entered in
<br />the same tables in parenthesis for comparison with
<br />those values obtained from the Technical Paper No,
<br />40. However, it appears that the supplemental values
<br />obtained from the NOAA Atlas 2 cannot be used in
<br />the present analysis because of the difficulty in
<br />maintaining the internal consistency between the two
<br />sources of data.
<br />
<br />The rainfall depths in inches obtained for each
<br />station are next converted to the average rainfall
<br />intensities in inches per hour by multiplying (for
<br />shorter than 60-minute durations) or dividing (for
<br />longer than 60-minute durations) the corresponding
<br />rainfall depths by the ratios of their durations to 1
<br />hour. The results are also tabulated and appended to
<br />this report (see Appendix B).
<br />
<br />The so-called standard intensity-duration curves
<br />(Hathaway, 1945; Williams, 1949) were plotted on
<br />the basis of the relations of I-hour rainfall intensity
<br />to those for other durations, The formulation of
<br />these curves is equivalent to fmd the ratios of
<br />various-duration intensities to 60-mmute intensity for
<br />the same frequency at each station, as tabulated in
<br />Appendix C. It is not surprising to see from Appendix
<br />C that the ratios for duration shorter than I hour
<br />have the values very close to those listed in Table 1.
<br />Any deviations from the listed ratios, as reasoned
<br />before, are probably caused by the smoothing and
<br />areal generalization during the construction of the 49
<br />isopluviaJ maps in .the Technical Paper No. 40 or
<br />errors in estimation from the maps, or both.
<br />
<br />In the Technical Paper No. 40, the generalized
<br />duration relationship used in the computation of
<br />rainfall values between 1 and 24 hours is the ratio of
<br />I-hour to corresponding 24.hour values. However,
<br />this ratio, though it appears to be independent of
<br />frequency, varies from 10 to 60 percent with the
<br />average of 40 percent in the United States, as
<br />mentioned previously. Rainfall values for other
<br />durations between I and 24 hours were interpolated
<br />linearly by means of the rainfall depth-duration
<br />diagram given in the Technical Paper No. 40. If the
<br />I-hour rainfall depth is arbitrarily chosen as 1 inch,
<br />the range of the pre""ding 1- to 24.hour ratio can
<br />readily be plotted in the rainfall depth-duration
<br />diagram, as shown in Fig. 2. The range of rainfall
<br />depths and corresponding intensities for durations
<br />between 1 and 24 hours can thus readily be
<br />computed from this diagram (see Table 2). For
<br />convenience in later analysis, the rainfall
<br />
<br />14
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