A spatial regularization approach to parameter estimation for a distributed watershed model

Environmental models have become increasingly complex with greater attention being given to the spatially distributed representation of processes. Distributed models have large numbers of parameters to be specified, which is typically done either by recourse to a priori methods based on observable physical watershed characteristics, by calibration to watershed input-state-output data, or by some combination of both. In the case of calibration, the high dimensionality of the parameter search space poses a significant identifiability problem. This article discusses how this problem can be addressed, utilizing additional information about the parameters through a process known as regularization. Regularization, in its broadest sense, is a mathematical technique that utilizes additional information or constraints about the parameters to reduce problems related to over-parameterization. This article develops and applies a regularization approach to the calibration of a version of the Hydrology Laboratory Distributed Hydrologie Model (HL-DHM) developed by the US National Weather Service. A priori parameter estimates derived using the approach by Koren et al. (2000) were used to develop regularization relationships to constrain the feasible parameter space and enable existing global optimization techniques to be applied to solve the calibration problem. In a case study for the Blue River basin, the number of unknowns to be estimated was reduced from 858 to 33, and this calibration strategy improved the model performance while preserving the physical realism of the model parameters. Our results also suggest that the commonly used parameter field "multiplier" approach may often not be appropriate.