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<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 <br />