Representation of basin scale in flood peak distributions

Abstract

A lognormal cascade model is developed for representing basin scale in flood peak distributions. The model is developed from the multiplicative cascade modeling framework developed by Gupta and Waymire (1990) for spatial hydrologic processes. The lognormal cascade model has a simple parameterization of basin scale that can represent either simple scaling or multiscaling processes. Likelihood‐based statistical inference procedures are developed for parameter estimation and hypothesis testing for the lognormal cascade model. The lognormal cascade model is used to examine scale properties of annual flood peaks from 104 stations in the central Appalachian region of Maryland and Virginia. Drainage area for the basins ranges from 0.3 square miles (0.78 km2) to nearly 10,000 square miles (26,100 km2). The empirical results suggest two hypotheses concerning scaling properties of central Appalachian flood peaks: (1) the multiscaling hypothesis holds over the entire range of scales (for this hypothesis, some anomalous properties of flood peaks in small basins must be dealt with), and (2) scaling properties of rainfall and the channel/floodplain system impose a peak in variability of flood magnitudes for basins with drainage area between 10 and 100 square miles (between 26 and 260 km2).