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


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

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

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