Effects of streamflow variation on critical water quality for multiple discharges of decaying pollutants

The assumption that the worst water quality occurs at the lowest streamflow may not always hold in instances involving multiple discharges and nonconservative pollutants. The additional dilution resulting from increased streamflow may be offset by adverse changes in the parameters that govern water quality and in decreased residence time, which allows the stream less time to recover from the effect of one discharge before receiving another. This paper addresses the question of whether, with multiple sources of decaying pollutants, water quality might worsen with increasing streamflow. For an isothermal uniform stream it is shown that the pattern of discharge that maximizes the derivative with respect to streamflow of critical dissolved oxygen deficit or the concentration of a substance exhibiting a first‐order decay is an infinite uniform distributed load. Whether the maximum value of the derivative is positive or negative depends on the values of the parameters that characterize the hydraulic geometry of the channel and the dependence of reaeration on flow. Theoretical results presented here indicate that for most natural streams the traditional assumption, that the lowest streamflow is the worst from a water quality perspective, will usually be valid for first‐order pollutants. Nevertheless, they also lead to the expectation that increases in impacts with increasing streamflow might occur for dissolved oxygen, especially in highly polluted and regulated streams (pollution, water quality models, rules and regulations, and management).