Appendix A: A Practical Guide to Effective Discharge Calculations
the number of discharge classes; 2) the time base for discharge averaging, and; 3) the length of the period
of record.
Selection of Discharge Class Interval
The selection of class interval can influence the effective discharge calculation. Intuitively, it might
be expected that the smaller the class interval and, therefore, the greater the number of classes, the more
accurate would be the outcome. However, if too small an interval is used, discontinuities appear in the
discharge frequency distribution. These, in turn, produce an irregular sediment load histogram with multiple
peaks. Therefore, the selected class interval should be small enough to accurately represent the frequency
distribution of flows, but large enough to produce a continuous distribution, with no classes having a
frequency of zero.
There are no definite rules for selecting the most appropriate interval and number of classes, but
Yevjevich (1972) stated that the class interval should not be larger than s/4, where s is an estimate of the
standard deviation of the sample. For hydrological applications he suggested that the number of classes
should be between 10 and 25, depending on the sample size. Hey (1997) found that 25 classes with equal,
arithmetic intervals produced a relatively continuous flow frequency distribution and a smooth sediment load
histogram with a well-defined peak. This indicates an effective discharge which corresponded exactly with
bankfull flow. A smaller interval, and correspondingly larger number of classes, produced anomalous
results. Particular care must be exercised on rivers where there is a high incidence of very low flows. In
sand bed rivers, the low flows may be competent to transport the sediment. Under these circumstances,
the effective discharge may be biased towards the lowest discharge class, and caution must be exercised,
therefore, when using arithmetic class intervals.
Flows within the lowest discharge class are seldom normally distributed, being skewed towards
the lower class boundary. The effect is that calculation of the sediment load transported by that class of
flow, based on the median sediment transport rate, will overestimate the actual value. If this is a problem,
it may be necessary to subdivide the lowest class interval into smaller classes.
An alternative approach for determining the class interval is to use the U.S. Geological Survey
(USGS) flow duration procedure that divides the data into 35 classes. The lowest class is zero, with a class
width of 0 to 0. The next class width is 0 to the minimum discharge value. The remaining 33 classes are
determined by subtracting the logarithm of the minimum discharge from the logarithm of the maximum value,
and dividing by 33, to define equal, logarithmic class intervals. The use of log-scale class intervals is
attractive in that it divides the low discharges into more class intervals. This is useful because, on rivers
where the flow duration curve is strongly skewed due to a high incidence of low flows, it generates
approximately equal numbers of events in each. However, the discharge class intervals at the upper end
of the distribution can be extremely large, artificially biasing the value of the effective discharge towards
these flows. Caution must be exercised, therefore, when using logarithmic class intervals.
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