Recursive parameter estimation of hydrologic models

Abstract

Proposed is a nonlinear filtering approach to recursive parameter estimation of conceptual watershed response models in state‐space form. The conceptual model state is augmented by the vector of free parameters which are to be estimated from input‐output data, and the extended Kaiman filter is used to recursively estimate and predict the augmented state. The augmented model noise covariance is parameterized as the sum of two components: one due to errors in the augmented model input and another due to errors in the specification of augmented model constants that were estimated from other than input‐output data (e.g., topographic and rating curve constants). These components depend on the sensitivity of the augmented model to input and uncertain constants. Such a novel parameterization allows for nonstationary model noise statistics that are consistent with the dynamics of watershed response as they are described by the conceptual watershed response model. Prior information regarding uncertainty in input and uncertain constants in the form of degree‐of‐belief estimates of hydrologists can be used directly within the proposed formulation. Even though model structure errors are not explicitly parameterized in the present formulation, such errors can be identified through the examination of the one‐step ahead predicted normalized residuals and the parameter traces during convergence. The formulation is exemplified by the estimation of the parameters of a conceptual hydrologic model with data from the 2.1‐km2 watershed of Woods Lake located in the Adirondack Mountains of New York.