Multiscaling and Skew Separation in Regional Floods

Matalas et al. (1975) (MSW) found that the simulated values of flood peaks in a region using various common forms of flood frequency distributions did not reproduce the empirical skew statistics for 14 different regions covering the conterminous United States. Specifically, the field data always demonstrated a higher value of standard deviation of skew for a given sample value of mean skew than did the simulations. MSW termed this difference “separation” and further showed that it could not be explained either by autocorrelation of flood peaks or as a small sample property. In this paper, we discuss an explanation of this property using the recently developing scaling theories of regional floods. It is shown that in a homogeneous region, recently defined by us, separation would result from the multiscaling structure of flood peaks. Separation would not occur if floods obey simple scaling, nor would separation necessarily occur with heterogeneity or mixing among different homogeneous regions. Mixing must be of a particular kind in order to cause separation. The use of normalized flood frequencies having mean of zero and variance of 1 in the simulations carried out by MSW is shown to be consistent with the assumption of index flood or simple scaling but not multiscaling. In the 14 “megaregions” analyzed by MSW, mixing among subregions within each megaregion may add to the magnitude of separation. The separation in 14 regions is physically interpreted based on different physical mechanisms that have been recently hypothesized by us to be responsible for the presence of simple scaling or multiscaling in floods.