Appendix A: A Practical Guide to Effective Discharge Calculations
The effectiveness of this correction can be illustrated by reference to effective discharge calculations
for stations at Marmarth and at Medora on the Little Missouri River reported by Hey (1997). Initially, the
effective discharge was in the lowest class interval at both sites with values of 16.5 and 22.8 m s-1,
respectively. However, following sub-division of the lowest class, the effective discharge at each site
corresponded to bankfull flow, with values of 68 and 90 m3s-1, respectively.
Problems with Outliers
Discharge records, especially those based on mean daily values, can contain distinct gaps in the
higher discharge categories due to the averaging process. This is particularly likely on rivers with flashy
hydrographs or if there has been an extremely large flood event during a relatively short period of record.
The use of arithmetic discharge class intervals can produce a discontinuous flow frequency distribution that,
in turn, generates an irregular bed material load histogram with outliers that reflect the transport associated
with individual flood events. The danger is that the wrong peak may be selected to represent the modal
class, leading to serious overestimation of the effective discharge. Under these circumstances, it is advisable
to modify the flow frequency distribution using one of the two approaches outlined below.
Reduce the Number of Class Intervals
Outliers are readily apparent when using arithmetic class intervals through the presence of gaps
in the bed material load histogram and excessively proportions of the load being transported in an isolated,
high discharge class. They can be removed by increasing the class interval and reducing the number of
classes to reduce the number of discharge classes with zero bed material load and smooth the histogram.
For example, Hey (1997) reported that use of 40 class intervals for the White River upstream of Mud
Mountain Dam, resulted in an effective discharge that was unrealistically high (387 m3s-1). Reducing the
number of classes to 25, resulted in an effective discharge of 81 m3s-1, which corresponded to bankfull flow
Use Logarithmic Class Intervals
Reducing the number of classes while maintaining an acceptable arithmetic class interval does not
always eliminate all zero flow frequencies. In this case, the option of using logarithmic class intervals should
be considered, as this will almost certainly solve the problem.
Checking the Effective Discharge
Guidance on Return Periods for the Effective Discharge
Return periods for effective discharges are expected to vary between study sites depending on the
flow and sediment transport regime of the individual river or reach. For sites where annual maximum series
flood flow data are available, the return period of the calculated effective discharge may be checked to
ensure that it lies within acceptable bounds. Unfortunately, there is very limited information available