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STANDARD INTENSITY-DURATION RELATIONSHIPS To answer a question of whether there are fairly consistent relationships between the average intensity of rainfall for a period of one hour and the average rates of comparable frequency for shorter and longer intervals, regardless of the geographical location of the stations or frequency of I-hour rainfall, rainfall values for various durations and return periods at selected stations must be examined. Rainfall data obtained from the U,S. Weather Bureau Technical Paper No. 40 are used for this purpose. However, before any conclusion can be drawn from the standard intensity-duration relationships formulated by use of 49 isopluvial maps in the Technical Paper No. 40, attention is first called to the procedures with which these isopluvial maps have been constructed. There are 49 lsopluvial maps in the Technical Paper No. 40, among which the following four are the key maps: 2.year I-hour, 2-year 24.hour, 100-year I-hour, and 100.year 24-hour. These four key maps were used jointly with the duration and frequency relationships for obtaining rainfall values for the other 45 maps. Actually, only the 2-year I-hour and 2.year 24.hour key maps were directly plotted from all available rainfall data through smoothing isopluvial lines. The other two 1 DO-year I-hour and 100.year 24-hour maps were plotted by use of rainfall values which were the product of the values from the 2-year maps and the 100-year to 2-year ratio maps. Programming of the duration and return-period relationships plus the four rainfall values for each of 3,500 selected stations permitted digital computer computation for the 45 additional rainfall values from which the other 45 isopluvial maps were constructed. The key device in these mapping procedures apparently lay in the use of the duration.frequency relationships developed at each (or a group) of the stations, Are they unique enough to be standarized? If so, would it not be much simpler to derive the standard intensity-duration formulas than construct 49 isopluvial maps? While the derivation of such standard intensity-duration formulas will be attempted, the basic questions regarding the uniqueness and implications of the results obtained from the isopluvial maps need to be answered. A generalized duration relationship was developed in the Weather Bureau Technical Paper No. 40 to compute the rainfall depth for a selected return period for any duration between 1 and 24 hours when the 1- and 24-hour values for that particular return period are given. This generalization was ob- tained empirically from data for the 200 Weather Bureau first-order stations. The ratio of l-hour to corresponding 24-hour values for the same return period does not vary greatly over a small region. On the windward sides of high mountains in western United States, the 1- to 24-hour ratio is as low as 10 percent. In southern Arizona and some parts of midwestern United States, it is greater than 60 percent. In general, except for Arizona, the ratio is less than 40 percent west of the Continental Divide and greater than 40 percent to the east. A I. to 24-hour ratio of 40 percent is approximately the average for the United States. There is a fair relationship between this ratio and the climate factor, mean annual number of thunderstorm days. The two parameters, 2-year daily rainfall and the mean annual number of thunderstorm days, have been used jointly to provide an estimate of short-duration rainfalls by Hershfield, Weiss, and Wilson (1955). A return-period diagram used in the Technical Paper No. 40 is partly empirical and partly theoretical. From 1 to 10 years it is entirely empirical, based on freehand curves drawn through plottings of partial-duration series data. For the 20-year and longer return periods reliance was piaced on the Gumbel procedure for fitting annual series data to the Fisher-Tippett Type I distribution, The transition was smoothed subjectively between 10- and 20-year return periods. Consequently, if rainfall values for return periods between 2 and 100 years are plotted on either Gumbel or log-normal paper, the points will nearly approximate a straight line, but are found to be independent of duration. Undoubtedly these features in the return.period relationship will manifest themselves in the standard duration-frequency relationships wbich are developed herein. Rainfall depths for various durations and frequency at a number of geographical points in the United States need to be estimated for the construction of the standard intensity-duration relationships. The Technical Paper No. 25 that contains a series of rainfall intensity-duration. frequency curves for the 200 Weather Bureau stations can also be used for this purpose, although the average difference between the two Technical Papers 13