Discharge indices for water quality loads

[1] Effective discharge has been used to describe the streamflow level that is responsible for transporting the most sediment over the long term. Careful inspection reveals that this concept may not have been well defined, and different interpretations have led to conflicting representations. Because total load is ultimately the quantity of interest, we define a new index, the half-load discharge, which is that discharge above and below which half the total long-term load is transported. The value of the half-load discharge is derived for a reasonable model of flows and constituent concentration. The effective discharge has generally been thought to be a relatively common or frequent flood. The half-load discharge is generally a much greater and less frequent flow than commonly used estimators of the effective discharge. Relations provided here for the frequency and magnitude of the half-load discharge provide evidence that it is relatively rare floods that transport most of the sediment over the long term. These ideas apply to other constituents as well.