PROGRAMS AND PLANS - Study of Surface-Water Data Programs - Adjustments for zero-flow items In Reply Refer To: September 20, 1969 EGS-Mail Stop 415 SURFACE WATER BRANCH TECHNICAL MEMORANDUM NO. 70.07 To: Regional Hydrologists and Districts, WRD From: Chief, Surface Water Branch Subject: PROGRAMS AND PLANS - Study of Surface-Water Data Programs - Adjustments for zero-flow items The STREAMFLOW STATISTICS program provides statistics for high and low flows of various durations. Part of the output data shows the exceedance (or non-exceedance) probabilities, the equivalent recurrence intervals, and the associated discharges. In the regression studies to be made as part of the study of the surface-water data program, the discharges for specified recurrence intervals will be determined on the basis of the output of the STREAMFLOW STATISTICS program. It must be noted that the computations have been made omitting all zero values, both for highs and lows. If a series originally contained zero values, it is essential that the output should not be used directly, but that it should be adjusted to include the effect of the zero values. The number of zero items is counted by inspection of the lists of highs and lows for various numbers of consecutive days. For high flows, for which exceedance probabilities are printed out, the adjustment is made as explained in, "Frequency Curves for Annual Flood Series with Some Zero Events or Incomplete Data," by M. E. Jennings and M. A. Benson. The paper was published in Water Resources Research, v. 5, no. 1, 1969, p. 276-280, and was also issued identically in preliminary form to all Survey offices. Note that the Log-Pearson Type III program for peaks also handles only non-zero values and needs adjustment when zero values are present. The adjustment for highs is simple and requires only that the computed exceedance probability be multiplied by n/N, the percentage of non-zero items. It will be noted that after adjustment the desired even-valued probabilities are no longer available and it is necessary to replot a frequency curve with the adjusted values and then to pick off the discharges corresponding to the even-valued probabilities or recurrence intervals. In the case of low flows, it has not been specified that Log- Pearson Type III fitting must be used, yet this fitting, as computed in the STREAMFLOW STATISTICS program, has been found satisfactory in many cases. However, if zero items exist, the adjustment (to non-exceedance probabilities) is somewhat different than that for exceedance probabilities. The non-exceedance probabilities can be simply adjusted in the following manner: Adj. P = n Pn + N-n N N where Pn is the non-exceedance probability shown in the program output, n/N is the percent of non-zero values, and (N-n)/N is the percent of zero values. Again, a frequency curve will have to be plotted using the adjusted probabilities, from which the discharges corresponding to even-valued probabilities will be selected. It is hoped that both the LOG-PEARSON Type III program and the STREAMFLOW STATISTICS program can be rewritten to incorporate the adjustments for zero items. However, this will take some time, and meanwhile the adjustments will have to be made by hand. It is essential that each set of output data be examined to see whether or not zero items have been omitted, and if they have, to make the necessary adjustments. Rolland W. Carter WRD Distribution: A, B, S, FO Addendum to SW Branch Memorandum 70.07 On the present printout of the graphs in the STREAMFLOW STATISTICS program, both the calculated values and the data values are plotted using only non-zero values. Therefore, a valid comparison of the data and the calculated values cannot be obtained by adjusting only the calculated probabilities. It is necessary to recalculate also the probabilities of the data values, by using the total number of items, (n), including the zero items, in the formula m/(n + 1); or recalculate the recurrence intervals as (n + 1)/m. The same applies if adjustments are made, because of zero items, to results from the LOG-PEARSON Type III program. R. W. Carter