A statistical log piecewise linear model of at‐a‐station hydraulic geometry

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Abstract
A new log piecewise linear model of at‐a‐station hydraulic geometry and a statistical methodology for fitting the model to observed data are described. The proposed parameterization provides a continuity relationship between the model parameters and allows the model to reduce to the Leopold and Maddock power function model when one of the parameters is set equal to zero. Applications of the new model, the Leopold and Maddock model, and the Richards log quadratic model are made to 22 gauging stations in New South Wales, Australia. Ordinary least squares (OLS) procedures are used to fit the models to the data. Results indicate that the new model is superior to the existing models in that it allows the identification of the points at which there are breaks in the slopes of the width‐, mean depth‐, and mean velocity‐discharge relations. In addition, it often produces smaller residual variances and residuals that more frequently conform with the OLS error assumptions. However, more sophisticated procedures for parameter estimation may be needed in some instances if statistical inferences are to be drawn from these regression models.