Data fusion modeling for groundwater systems

Engineering projects involving hydrogeology are faced with uncertainties be cause the earth is heterogeneous, and typical data sets are fragmented and disparate. In theory, predictions provided by computer simulations using ca librated models constrained by geological boundaries provide answers to sup port management decisions, and geostatistical methods quantify safety margi ns. In practice, current methods are limited by the data types and models t hat can be included, computational demands, or simplifying assumptions. Dat a Fusion Modeling (DFM) removes many of the limitations and is capable of p roviding 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 geotech nical applications are savings in time and cost through the ability to prod uce 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 f or parallel processing implementation. DFM is a spatial state estimation an d system identification methodology that uses three sources of information: measured data, physical laws, and statistical models for uncertainty in sp atial heterogeneities. What is new in DFM is the solution of the causality problem in the data assimilation Kalman filter methods to achieve computati onal practicality. The Kalman filter is generalized by introducing informat ion filter methods due to Bierman coupled with a Markov random field repres entation for spatial variation. A Bayesian penalty function is implemented with Gauss-Newton methods. This leads to a computational problem similar to numerical simulation of the partial differential equations (PDEs) of groun dwater. In fact, extensions of PDE solver ideas to break down computations over space form the computational heart of DFM. State estimates and uncerta inties can be computed for heterogeneous hydraulic conductivity fields in m ultiple geological layers from the usually sparse hydraulic conductivity da ta and the often more plentiful head data. Further, a system identification theory has been derived based on statistical likelihood principles. A maxi mum likelihood theory is provided to estimate statistical parameters such a s Markov model parameters that determine the geostatistical variogram. Fiel d-scale application of DFM at the DOE Savannah River Site is presented and compared with manual calibration. DFM calibration runs converge in less tha n 1 h on a Pentium Pro PC for a 3D model with more than 15,000 nodes. Run t ime is approximately linear with the number of nodes. Furthermore, conditio nal simulation is used to quantify the statistical variability in model pre dictions such as contaminant breakthrough curves. Published by Elsevier Sci ence B.V.