RESIDUAL MAXIMUM-LIKELIHOOD (REML) METHODS FOR ANALYZING HYDROLOGICALDATA SERIES

Much hydrological data can be displayed as two-way tables with observa tions classified (for example) by years (rows) and sites (columns), co mmonly with many missing entries; data classified by three factors or more (e.g. gauge sites within drainage basins; drainage basins; years) can also be put in this form. On an appropriate scale, the observatio ns in such tables can frequently be represented by linear, additive mo dels of components, some of which can be considered as random variable s. Residual maximum likelihood (REML) is a technique for fitting model s in which each observation is expressed additively in terms of fixed and random effects. When the model contains only one such random effec t, the linear model reduces to a restricted form of multiple regressio n; REML can be regarded as an extension of multiple regression to the case where there are several error terms with different statistical ch aracteristics. Models of this kind are appropriate in the hydrological context where the effects of the-years (or other periods) of observat ion can be regarded as a sample from a hypothetical population of year s (periods), or where sites can be regarded as random. The paper discu sses two examples where REML was used: one in estimating mean areal mo nthly rainfall in Amazonia, using incomplete records from 48 raingauge sites, and the other using incomplete records of annual floods from 1 9 gauging stations on the Rio Itajai-Acu, in southern Brazil. In both cases, the assumptions of the REML model were satisfied and the object ives of the analysis achieved. Given the prevalence of incomplete hydr ological records, the REML method may well have wider application.