The Development of Rating Curve Considering Variance Function Using Pseudo-likelihood Estimation Method

Abstract

This paper employs a new estimation method for estimating stage–discharge rating curve parameters. In typical practical applications, the original non-linear rating curve is transformed into a simple linear regression model by log-transforming the measurement without examining the effect of heteroscedasticity of residuals. Therefore, the model with pseudo-likelihood estimation is developed in this study to deal with heteroscedasticity of residuals in the original non-linear model. The parameters of rating curves and variance functions of errors are simultaneously estimated by the pseudo-likelihood estimation (P-LE) method. Also simulated annealing, a sort of global optimization techniques, is adapted to minimize the log likelihood of the weighted residuals. At first, the developed P-LE model was applied to a hypothetical site where stage–discharge data were generated by incorporating various errors for statistical test. Also, the limit of stages for segmentation is estimated in the process of P-LE using the Heaviside function. For the validation of effects of the developed P-LE model, the results of the conventional log-transformed linear regression (LT-LR) model and the P-LE model are estimated and compared. After statistical simulation, the developed P-LE model is then applied to the real data sets from six gauge stations in the Geum River basin. It can be suggested that this new estimation method is applied to real river sites to successfully determine the weights taking into account error distributions from observed discharge data.