Use of parameter transformations in nonlinear, discrete flood event models

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The use of parameter transformations in calibration and post-calibration studies of conceptual rainfall-runoff models is often justified on the basis of their ability to speed the convergence of automatic parameter estimation algorithms, improve the sampling properties of the parameter estimates, and improve statistical inferences that are based on conventional linear model theory. An examination of the abilities of parameter transformations was undertaken using a nonlinear flood event model, rainfall-runoff data from six Australian catchments, a Gauss-Newton optimization algorithm, three measures of statistical nonlinearity, and three types of joint confidence regions (exact, likelihood and linear theory) for the model parameters. Results indicate that the ‘expected-value’ transformation of Ross and the power transformation of Tsai can lead to improved sampling properties and statistical inferences on model parameters. However, it is clear that the effect of model reparameterization on the convergence of optimization algorithms may only be slight, and that care must be taken when applying parameter transformations to nonlinear flood event models.