## Info

number of successive moving averages would have been 8 minus 2 plus 1 = 7. In general, if the total number of elements is Z and the number of moving elements being averaged in each moving average is k, the number of successive moving averages % is

One way to derive sustained flow rates is through the use of moving averages. In the field survey data, a number of moving averages or sustained flow rates can be formed. For example, a 7-element, 14-element, and any-element sustained flow rate can be formed. The peak or the minimum of these flow rates can be found by the usual method of probability distribution analysis. To be descriptive, substitute the type of element such as hour, day, and so on. Thus, 7-element sustained flow rate becomes 7-day sustained flow rate, 14-element sustained flow rate becomes 14-day sustained flow rate, and so on.

Let us now arbitrarily derive the 14-day sustained flow rates from the field survey data. From Equation (1.36), %, the number of successive moving averages, is equal to 61 - 14 + 1 = 48. Each of these averages will have equal likelihood of occurring with a probability of 1/48. Table 1.20 contains the 14-day sustained flow rates derived from Figures 1.6 and 1.7. Tables 1.21 and 1.22 contain the probability distribution analyses for the sustained peak and the sustained minimum flow rates, respectively.

As in previous analyses, the sustained peak flow rate has a probability of zero in an array of descending order; the sustained minimum flow rate also has a probability of zero but in an array of ascending order. From Table 1.21, the sustained peak flow rate may be extrapolated at 0 as follows (with x representing the maximum daily flow rate): 