Data fusion modeling for groundwater systems

Engineering projects involving hydrogeology are faced with uncertainties because the earth is heterogeneous, and typical data sets are fragmented and disparate. In theory, predictions provided by computer simulations using calibrated models constrained by geological boundaries provide answers to support management decisions, and geostatistical methods quantify safety margins. In practice, current methods are limited by the data types and models that can be included, Ž . computational demands, or simplifying assumptions. Data Fusion Modeling DFM removes many of the limitations and is capable of providing data integration and model calibration with quantified uncertainty for a variety of hydrological, geological, and geophysical data types and models. The benefits of DFM for waste management, water supply, and geotechnical applications are savings in time and cost through the ability to produce visual models that fill in missing data and predictive numerical models to aid management optimization. DFM has the ability to update field-scale models in real time using PC or workstation systems and is ideally suited for parallel processing implementation. DFM is a spatial state estimation and system identification methodology that uses three sources of information: measured data, physical laws, and statistical models for uncertainty in spatial heterogeneities. What is new in DFM is the solution of the causality problem in the data assimilation Kalman filter methods to achieve computational practicality. The Kalman filter is generalized by introducing information filter methods due to Bierman coupled with a Markov random field representation for spatial variation. A Bayesian penalty function is implemented with Gauss–Newton methods. This leads to a computational problem similar to numerical Ž . simulation of the partial differential equations PDEs of groundwater. In fact, extensions of PDE solver ideas to break down computations over space form the computational heart of DFM. State estimates and uncertainties can be computed for heterogeneous hydraulic conductivity fields in multiple geological layers from the usually sparse hydraulic conductivity data and the often more ) Corresponding author. Present address: Applied Physics Laboratory, The Johns Hopkins University, Laurel, MD 20723, USA. Fax: q1-410-451-4736; e-mail: [email protected] 0169-7722r00r$ see front matter Published by Elsevier Science B.V. Ž . PII: S0169-7722 99 00081-9 ( ) D.W. Porter et al.rJournal of Contaminant Hydrology 42 2000 303–335 304 plentiful head data. Further, a system identification theory has been derived based on statistical likelihood principles. A maximum likelihood theory is provided to estimate statistical parameters such as Markov model parameters that determine the geostatistical variogram. Field-scale application of DFM at the DOE Savannah River Site is presented and compared with manual calibration. DFM calibration runs converge in less than 1 h on a Pentium Pro PC for a 3D model with more than 15,000 nodes. Run time is approximately linear with the number of nodes. Furthermore, conditional simulation is used to quantify the statistical variability in model predictions such as contaminant breakthrough curves. Published by Elsevier Science B.V.