Simulated annealing is introduced and applied to the optimization of groundwater management problems cast in combinatorial form. This heuristic, probabilistic optimization method seeks minima in analogy with the annealing of solids and is effective on large‐scale problems. No continuity requirements are imposed on objective (cost) functions. Constraints may be added to the cost function via penalties, imposed by designation of the solution domain, or imbedded in submodels (e.g., mass balance in aquifer flow simulators) used to evaluate costs. The location of global optima may be theoretically guaranteed, but computational limitations lead to searches for nearly optimal solutions in practice. Like other optimization methods, most of the computational effort is expended in flow and transport simulators. Practical algorithmic guidance that leads to enormous computational savings and sometimes makes simulated annealing competitive with gradient‐type optimization methods is provided. The method is illustrated by example applications to idealized problems of groundwater flow and selection of remediation strategy, including optimization with multiple groundwater control technologies. They demonstrate the flexibility of the method and indicate its potential for solving groundwater management problems. The application of simulated annealing to water resources problems is new and its development is immature, so further performance improvements can be expected.

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Analysis of flow in a fractured porous reservoir forms the basis for investigations of chemical and energy transport in such media. Numerical models are often employed to analyze these geohydrologic systems. In this paper a well hydraulics problem is solved using the Laplace transformation and the double‐porosity concept. The transient solution is obtained by numerical inversion of the Laplace transform. Solutions to slug test problems indicate that the head response due to fracturing is distinct from the response due to partial penetration or skin effect. An alternative to the commonly used van Everdingen model of skin effect is given. No method for identifying fractured porous reservoir parameters from slug tests has been developed. The results of this paper may be applied to test numerical models of flow in fractured porous media.

Stochastic reconstruction techniques are developed for mapping the interior optical properties of tissues from exterior frequency-domain photon migration measurements at the air-tissue interface. Parameter fields of absorption cross section, fluorescence lifetime, and quantum efficiency are accurately reconstructed from simulated noisy measurements of phase shift and amplitude modulation by use of a recursive, Bayesian, minimum-variance estimator known as the approximate extended Kalman filter. Parameter field updates are followed by data-driven zonation to improve the accuracy, stability, and computational efficiency of the method by moving the system from an underdetermined toward an overdetermined set of equations. These methods were originally developed by Eppstein and Dougherty [Water Resources Res. 32, 3321 (1996)] for applications in geohydrology. Estimates are constrained to within feasible ranges by modeling of parameters as beta-distributed random variables. No arbitrary smoothing, regularization, or interpolation is required. Results are compared with those determined by use of Newton-Raphson-based inversions. The speed and accuracy of these preliminary Bayesian reconstructions suggest the near-future application of this inversion technology to three-dimensional biomedical imaging with frequency-domain photon migration.

Abstract. The extended Kalman filter (EKF) has long been recognized as a powerful, yet computationally intensive, methodology for stochastic parameter estimation. Three improvements to traditional algorithms are presented and applied to heterogeneous transmissivity estimation. First, the costly EKF covariance updates are replaced by more efficient approximations. Second, the zonation structure of the distributed parameter field being estimated is dynamically determined and refined using a partitional clustering algorithm. Third, a new method of merging first and second moments of random fields that have heterogeneous statistics is introduced. We apply this method, called random field union, as an alternative to conventional random field averaging for the systematic shrinking of covariance matrices as the dimensionality of the parameter space is reduced. The effects of these three improvements are examined. In applications to steady state groundwater flow test problems, we show that the first and second improvements reduce the computational time requirements dramatically, while the second and third can improve the accuracy and stability of the results. The resulting integrated method is successfully applied to a larger, more realistic calibration test case under steady and cyclostationary flow conditions (similar to regular seasonal fluctuations). When flow is steady, the method can be viewed as iterative; when flow is transient, the method is fully recursive.