Effects of excess rainfall on the temporal variability of observed peak-discharge power laws

Few studies have been conducted to determine the empirical relationship between peak discharge and spatial scale within a single river basin. Only one study has determined this empirical relationship during single rainfall–runoff events. The study was conducted on the Goodwin Creek Experimental Watershed (GCEW) in Mississippi and shows that during single events peak discharge Q(A) and drainage area A are correlated as Q(A) = αAθ and that α and θ change between events. These observations are the first of their kind and to understand them from a physical standpoint we examined streamflow and rainfall data from 148 events in the basin. A time series of excess rainfall was estimated for each event in GCEW by assuming that a threshold infiltration rate partitions rainfall into infiltration and runoff. We evaluated this threshold iteratively using conservation of mass as a criterion and found that threshold values are consistent physically with independent measurements of near-surface soil moisture. We then estimated the excess rainfall duration for each event and placed events into groups of different durations. For many groups, data show that α is linearly related to excess rainfall depth and that the event-to-event variability in Q(A) is controlled mainly by variability in α through changes in . The exponent θ appears to be independent of for all groups, but mean values of θ tend to increase as the duration increases from group to group. This later result provides the first observational support for past theoretical results, all of which have been obtained under idealized conditions. Moreover, this result provides an avenue for predicting peak discharges at multiple spatial scales in the basin.