Inverse Methods for Parameter Estimations

Abstract

Estimation of various flow and mass transport parameters can be seen as the inverse problem of groundwater modeling. In this article, current methodologies for parameter estimation are classified according to whether they consider the errors in observation data, in parameter structure, and in model applications. The structures of hydraulic parameters are usually very complex and unknown. This article gives an overview on adaptive parameterization methods for simultaneously identifying the parameter values, the complexity level, and the pattern of parameter structure. Methods for model reliability analysis are described. Finally, a generalized inverse problem is introduced that can find a representative parameter for a given model application. The Inverse ProblemFor a model given by (2), the observed values of state variables, u obs , at observation locations and times x obs can Encyclopedia of Hydrological Sciences. Edited by M G Anderson.

Comparison of deterministic ensemble Kalman filters for assimilating hydrogeological data

“…There can be various sources of model errors in hydrogeological problems [34]. To illustrate the effect of covariance inflation, we assume here that the true Y field has a standard deviation of 1.0.…”

“…Many researchers have attempted the optimization of model structures and parameters in the past (cf., [23,34,39]). However, two types of inherent difficulties complicate the solution of inverse problems in groundwater modeling: (i) the geological structure of a real aquifer is often complex and unknown and (ii) data that can be used for model calibration are usually limited in both quantity and quality.…”

“…Observing and analyzing aquifer responses to system excitements, such as pumping events, can reveal important features of the subsurface formation heterogeneity. Although pressure head data have been the de-facto state observations to use in groundwater model calibration, a number of other observable attributes can also be potentially incorporated to infer model parameters via appropriately coupled models [34]. Examples of such data include, for example, tracer concentration and arrival time, water temperature, infiltration rate, water content, and geophysical data.…”

“…An alternative interpretation for covariance inflation is that it constitutes a regularization technique for inversion under model uncertainty. There is a direct link between covariance inflation and the widely used regularized least squares method for ill-conditioned systems [34]. Covariance inflation can also be tied to robust programming; a hydrogeological application of the latter was presented in [35], where the bound of hydraulic conductivity uncertainty was used to regularize the covariance matrix in a Bayesian-based robust contaminant source identification method.…”

A robust geostatistical approach to contaminant source identification

“…In addition to parameter value uncertainty, the parameter structure of hydraulic conductivity (e.g., the dimension of zonation) can also be subject to uncertainty. For example, Sun and Sun [2005] discussed different strategies for finding the optimal model structure from a model reliability point of view.…”