Recursive estimation of a hydrological regression model

The use of the generalised least square (GLS) technique for estimation of hydrological regression models has become good practice in hydrology. Through a regression model, a simple link between a particular hydrological variable and a set of catchment descriptors can be established. The regression residuals can be treated as the sum of sampling errors in the hydrological variable and errors in the regression model. This paper presents a recursive method for estimating a parameterised form of the cross correlation between the regression model errors, the variance of these errors and the regression model parameters. A re-weighted set of regression residuals can be defined such that the covariance of these residuals is essentially similar to that of the model error. The cross products of the re-weighted regression residuals, pooled within bins, can be used to identify a structure and to fit a parameterised form for the cross-correlations of the regression errors. The procedure has been tested successfully on annual maximum flow data from 602 catchments located throughout the UK.