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

Abstract

[1] 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.Citation: Pokhrel, P., and H. V. Gupta (2010), On the use of spatial regularization strategies to improve calibration of distributed watershed models, Water Resour. Res., 46, W01505,

Toward seamless hydrologic predictions across spatial scales

“…Parameter fields derived from basin-wise "calibrated" lumped models lack spatial seamlessness and thus are "inadequate representations of real-world systems" (Savenije and Hrachowitz, 2017). Moreover, excessive reliance on parameter calibration leads to deficient performance at interior points of the basin or at other locations at which the model was not calibrated (Pokhrel and Gupta, 2010;Lerat et al, 2012;Brynjarsdottir and O'Hagan, 2014).…”

“…According to Samaniego et al (2010b), these approaches can be broadly classified into post-regionalization and simultaneous regionalization approaches, depending on if the regionalization function parameters (or global parameters) are estimated after (Abdulla and Lettenmaier, 1997;Seibert, 1999;Wagener and Wheater, 2006;Livneh and Lettenmaier, 2013) or during the model calibration (Fernandez et al, 2000;Hundecha and Bárdossy, 2004;Gotzinger and Bárdossy, 2007;Pokhrel and Gupta, 2010). None of these procedures consider the subgrid variability of the model parameters or geophysical characteristics.…”

“…There are potential methods available in the literature that may lead toward coherent parameterizations and prediction of water and energy fluxes in LSMs/HMs. For example, (1) sidestepping the scaling problem of key model parameters by assuming scale-independent distribution functions with regionalized distribution parameters (Intsiful and Kunstmann, 2008), (2) finding strong links between model parameters to mapped geophysical attributes via regularization procedures (Pokhrel and Gupta, 2010), and (3) finding strong links between of observed functional responses of hydrological systems and geophysical characteristics (Yadav et al, 2007). These methods, however, alone may not satisfy the flux-matching criteria.…”

“…Parameterizations require variables called predictors, effective parameters and constants also called transfer, global, or super parameters (Pokhrel and Gupta, 2010). Super parameters are often parameters in empirical relationships that have been found with measurements in the field or in the laboratory, e.g., regression parameters in pedotransfer functions (Cosby et al, 1984).…”

Bayesian joint inference of hydrological and generalized error models with the enforcement of Total Laws

“…For this reason, 2 these parameters must be estimated indirectly by an inverse process (also called calibration) that conditions the parameter 3 estimates and the model response on historically observed input-output data (Pokhrel and Gupta, 2010). Model parameter 4 inferences are based on a likelihood function which quantifies the probability that the observed data were generated by a 5 particular parameter set (Box and Tiao, 1992).…”