Ground water model calibration using pilot points and regularization

Use of nonlinear parameter estimation techniques is now commonplace in ground water model calibration. However, there is still ample room for further development of these techniques in order to enable them to extract more information from calibration datasets, to more thoroughly explore the uncertainty associated with model predictions, and to make them easier to implement in various modeling contexts. This paper describes the use of pilot points as a methodology for spatial hydraulic property characterization. When used in conjunction with nonlinear parameter estimation software that incorporates advanced regularization functionality (such as PEST), use of pilot points can add a great deal of flexibility to the calibration process at the same time as it makes this process easier to implement. Pilot points can be used either as a substitute for zones of piecewise parameter uniformity, or in conjunction with such zones. In either case, they allow the disposition of areas of high and low hydraulic property value to be inferred through the calibration process, without the need for the modeler to guess the geometry of such areas prior to estimating the parameters that pertain to them. Pilot points and regularization can also be used as an adjunct to geostatistically based stochastic parameterization methods. Using the techniques described herein, a series of hydraulic property fields can be generated, all of which recognize the stochastic characterization of an area at the same time that they satisfy the constraints imposed on hydraulic property values by the need to ensure that model outputs match field measurements. Model predictions can then be made using all of these fields as a mechanism for exploring predictive uncertainty.

An advanced regularization methodology for use in watershed model calibration

A calibration methodology based on an efficient and stable mathematical regularization scheme is described. This scheme is a variant of so-called Tikhonov regularization in which the parameter estimation process is formulated as a constrained minimization problem. Use of the methodology eliminates the need for a modeler to formulate a parsimonious inverse problem in which a handful of parameters are designated for estimation prior to initiating the calibration process. Instead, the level of parameter parsimony required to achieve a stable solution to the inverse problem is determined by the inversion algorithm itself. Where parameters, or combinations of parameters, cannot be uniquely estimated, they are provided with values, or assigned relationships with other parameters, that are decreed to be realistic by the modeler. Conversely, where the information content of a calibration dataset is sufficient to allow estimates to be made of the values of many parameters, the making of such estimates is not precluded by preemptive parsimonizing ahead of the calibration process. White Tikhonov schemes are very attractive and hence widely used, problems with numerical stability can sometimes arise because the strength with which regularization constraints are applied throughout the regularized inversion process cannot be guaranteed to exactly complement inadequacies in the information content of a given calibration dataset. A new technique overcomes this problem by allowing relative regularization weights to be estimated as parameters through the calibration process itself. The technique is applied to the simultaneous calibration of five subwatershed models, and it is demonstrated that the new scheme results in a more efficient inversion, and better enforcement of regularization constraints than traditional Tikhonov regularization methodologies. Moreover, it is argued that a joint calibration exercise of this type results in a more meaningful set of parameters than can be achieved by individual subwatershed model calibration. (c) 2005 Elsevier B.V. All rights reserved.