Review and Enhancement of Cautious Parameter Estimation for Model Based Control: A Specific Realisation of Regularisation

[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,

Section: Introductionmentioning

confidence: 99%

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

Pokhrel

Gupta

2010

“…In its broadest sense, regularization is a technique that facilitates the inclusion of additional information, in the form of regularization relationships or constraints, to help in the stabilization and solution of ill‐posed problems [ Doherty and Skahill , 2005; Linden et al , 2005]. There are two general approaches by which this can be achieved.…”

Section: Regularizationmentioning

confidence: 99%

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

Pokhrel

Gupta

Wagener

2008

[1] 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 Hydrologic 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.Citation: Pokhrel, P., H. V. Gupta, and T. Wagener (2008), A spatial regularization approach to parameter estimation for a distributed watershed model, Water Resour. Res., 44, W12419,

“…In general, the resolution of dynamic flow and transport data seldom lends itself to characterization of heterogeneity at small scales, often necessitating a coarse‐scale description of rock properties for model calibration. Examples of coarse‐scale model parameter representations include upscaling/zonation, low‐rank parameterization, and regularization techniques [see e.g., Jacquard and Jain , ; Jahns , ; Tikhonov and Arsenin , ; Gavalas et al ., ; Shah et al ., ; Lawson and Hanson , ; Weiss and Smith , ; Chavent and Bissell , ; Grimstad et al ., ; Linden et al ., ; Tonkin and Doherty , ; Doherty and Skahill , ; Jafarpour and McLaughlin , , ]. One of the key issues in formulating model calibration problems is reconciling the discrepancies between model and data resolutions so that the parameters of interest properly represent the salient and relevant information (to fluid flow and transport processes) while enabling the estimation of parameters from available (often low‐resolution) pressure and flow rate measurements.…”

Section: Introductionmentioning

confidence: 99%

A distance transform for continuous parameterization of discrete geologic facies for subsurface flow model calibration

Hakim-Elahi

Jafarpour

2017

Construction of predictive subsurface flow models involves subjective interpretation and interpolation of spatially limited data, often using imperfect modeling assumptions. Hence, the process can introduce significant uncertainty and bias in predicting the flow and transport behavior of these systems. In particular, the uncertainty in the facies distribution in complex geologic environments, such as alluvial/fluvial channels, can be consequential for forecasting the dynamic response of these systems to perturbations due to pumping and development activities. Conventional model calibration techniques that are designed to update continuous model parameters cannot be used to estimate discrete parameters from flow and pressure data. We present a distance transform approach for converting discrete facies models to continuous parameters that can be updated using continuous model calibration methods. Distance transforms are widely used in discrete image processing, where the discrete values in each pixel are replaced with their distance (i.e., a continuous variable) to the nearest boundary cell. After updating the continuous distance maps during model calibration, a back transformation is applied to retrieve the updated facies maps. To preserve large‐scale facies connectivity, truncated singular value decomposition (SVD) parametrization may be used to represent the distance maps with low‐rank parameters. A variant of the ensemble smoother, ES‐MDA is used to update the continuous parameters of the inversion (either distance maps or their SVD coefficients if used). The distance transform method addresses an important problem in facies model calibration where model updating can result in losing facies connectivity and discreteness.