Diagnosing peak-discharge power laws observed in rainfall–runoff events in Goodwin Creek experimental watershed

Observations from the Goodwin Creek experimental watershed (GCEW), Mississippi show that peak-discharge Q(A) and drainage area A are related, on average, by a power law or scaling relationship, Q(A) = αA^θ, during single rainfall–runoff events. Observations also show that α and θ change between events, and, based on a recent analysis of 148 events, observations indicate that α and θ change because of corresponding changes in the depth, duration, and spatial variability of excess-rainfall. To improve our physical understanding of these observations, a 5-step framework for diagnosing observed power laws, or other space-time patterns in a basin, is articulated and applied to GCEW using a combination of analysis and numerical simulations. Diagnostic results indicate how the power laws are connected to physical conditions and processes. Derived expressions for α and θ show that if excess-rainfall depth is fixed then there is a decreasing concave relationship between α and excess-rainfall duration, and an increasing and slightly convex relationship between θ and excess rainfall duration. These trends are consistent with observations only when hillslope velocity v_h is given a physically realistic value near 0.1 m/s. If v_h ? 0.1 m/s, then the predicted trends deviate from observed trends. Results also suggest that trends in α and θ can be impacted by the dependence of v_h and link velocity v_l on excess-rainfall rate.