On the use of spatial regularization strategies to improve calibration of distributed watershed models

Hydrologic models require the specification of unknown model parameters via calibration to historical input-output data. For spatially distributed models, the large number of unknowns makes the calibration problem poorly conditioned. Spatial regularization can help to stabilize the problem by facilitating inclusion of additional information. While a common regularization approach is to apply a scalar multiplier to the prior estimate of each parameter field, this can cause problems by simultaneously changing both the mean and the variance of the distribution. This paper explores a multiple-criteria regularization approach that facilitates adjustment of the mean, variance, and shape of the parameter distribution, using prior information to constrain the problem while providing sufficient degrees of freedom to enable model performance improvements. We also test simple squashing functions to help in maintaining conceptually reasonable parameter values throughout the spatial domain. We apply the method to three basins in the context of the Distributed Model Intercomparison Project (DMIP2), obtaining considerable performance improvements at the basin outlet. However, the prior parameter estimates are found to give much better performance at the interior points (treated as ungauged), suggesting that the spatial information has not been properly exploited. The results also suggest that basin outlet hydrographs may not be particularly sensitive to spatial parameter variability and that an overall basin mean value may be sufficient for flow forecasting at the outlet, although not at the interior points. We discuss weaknesses in our study approach and suggest diagnostically more powerful strategies to be pursued.