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) = alpha A(0), during single rainfall-runoff events. Observations also show that alpha and theta change between events, and, based on a recent analysis of 148 events, observations indicate that X and 0 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 alpha and theta show that if excess-rainfall depth is fixed then there is a decreasing concave relationship between a and excess-rainfall duration, and an increasing and slightly convex relationship between alpha and excess rainfall duration. These trends are consistent with observations only when hillslope velocity nu(h) is given a physically realistic value near 0.1 m/s. If nu(h) >> 0.1 m/s, then the predicted trends deviate from observed trends. Results also suggest that trends in alpha and theta can be impacted by the dependence of nu(h) and link velocity nu(1) on excess-rainfall rate. (C) 2007 Elsevier Ltd. All rights reserved.