HR: 1340h
AN: H13A-0395    [Abstracts]
TI: A Gibbs Sampler for Constrained Geostatistical Interpolation and Inverse Modeling
AU: * Michalak, A M
EM: amichala@umich.edu
AF: Dept. of Civil and Environmental Engineering, 119 EWRE, University of Michigan, Ann Arbor, MI 48109-2125 United States
AB: Interpolation and inverse modeling techniques are gaining increased exposure as researchers and practitioners strive to make optimal use of limited data. In stochastic approaches, unknown parameters are described through statistical distributions, and meaningful uncertainty bounds can often be identified. One of the challenges of stochastic approaches is the need to select a statistical model that is consistent with our conceptual understanding of the problem. In addition, for most environmental applications, data are limited and any information available about an unknown parameter or function should be used to improve the analysis. One useful piece of information is that, in many cases, the unknown parameter has known physical constraints. Examples from environmental applications include solubility limits for chemical concentrations, nonnegativity constraints on hydraulic conductivity, and minimum or maximum hydraulic head constraints when screened portions of sampling wells do not capture the location of the water table. Geostatistical interpolation and inverse modeling techniques have often been applied for estimating such parameters, but these methods typically cannot enforce physical constraints, instead imposing an assumption of Gaussianity on estimates, confidence bounds and conditional simulations. This presentation describes a novel, mathematically rigorous and computationally efficient Gibbs sampler (a Markov chain Monte Carlo technique) which allows for multiple and variable physical constraints to be enforced within a geostatistical framework. Sample interpolation and inverse modeling applications confirm that estimates, uncertainty bounds and conditional simulations reflect the specified constraints, leading to conclusions that are more consistent with the underlying conceptual model and provide a more accurate measure of the posterior uncertainty of the parameters to be estimated. In addition, especially in inverse modeling applications, a posteriori confidence bounds are narrower even in areas where constraints are not imposed, as a result of the additional information introduced into the system. Finally, the method can be directly applied in multiple dimensions and with any variogram model, without sacrificing the statistical rigor of the geostatistical approach.
UR: http://www-personal.engin.umich.edu/~amichala/
DE: 3260 Inverse theory
DE: 1829 Groundwater hydrology
DE: 1831 Groundwater quality
DE: 1832 Groundwater transport
DE: 1869 Stochastic processes
SC: Hydrology [H]
MN: 2004 AGU Fall Meeting