Separation of year and site effects by generalized linear models in regionalization of annual floods

This paper explores the utility of generalized linear models (GLMs) and gen eralized linear mixed models (GLMMs) for regionalization and record augment ation of flood data. Because both models allow the separation of site and y ear effects, each gives an estimate of a site's mean annual flood free from effects of the particular years in which floods were recorded. In addition , a GLM gives a measure of the extent to which a short flood record can be regarded as representative of a longer period. The way in which GLMs and GL MMs are formulated effectively unites two problems that have largely been r egarded as separate: namely, regional regression and data augmentation. GLM M model structure implicitly includes correlation between flood records at neighboring sites, and both models contain facilities for testing whether t ime trends exist in flood data, for testing whether such trends are regiona lly uniform when they are found to exist, and for testing which climatologi cal and/or physiographic variables are useful for information transfer. By appropriate selection of probability distribution and link function, biases are avoided that arise where log transformed data are back transformed to the scale on which flood flows are recorded. The paper illustrates GLMs and GLMMs by fitting them to flood records of variable length from 12 sites in the Ibicui drainage basin in southern Brazil. While the models are extreme ly flexible and are easily fitted for gamma-distributed data land to data f ollowing certain other probability distributions), the assumptions on which they are based are arguably more complex than in more familiar methods, re quiring careful checking procedures.