S OURCE I DENTIFICATION

The source identification of groundwater contamination involves the determination of the source location or the source release history based on the measured contaminant concentrations at the sampling points. Atmadja and Bagtzoglou (2001) divided the problems of groundwater contaminant source identification into two categories. With the measured concentrations, the first category is to recover the release history at a known source location and the second one is to determine the source location with a constant release concentration and period. They also reviewed the methods that had been developed during the past 15 years in identifying the source location and release history. They classified the contaminant transport inversion methods into four categories, optimization approaches, probabilistic and geostatistical simulation approaches, analytical solution and regression approaches, and direct approaches. Optimization approaches run forward simulations first and then use an optimization method to obtain the best-fit solution. Probabilistic and geostatistical simulation approaches employ probabilistic techniques to identify the probability of the location of the sources. Analytical solution and regression approaches provide a complete estimate of parameters of the

pollutant. Based on the deterministic methods, the direct approaches solve the governing equations reversely and reconstruct the release history of the contaminant concentration plumes. As employed optimization approach to solve the inverse problem, the gradient-type approach or non-gradient-type approach with an iterative scheme is commonly employed to find the solution of nonlinear least-square equations involved in the problem.

For identifying the release history problems, Liu and Ball (1999) further classified these problems into following two types: function fitting problem and full-estimation problem. Function fitting problem initially assumes the release history as a particular function and reformulates it as an optimization problem. Then a gradient-type approach or non-gradient-type approach is employed to estimate the best-fit parameters of the release function (Gorelick et al. 1983; Wagner 1992). The full-estimation approach is to reconstruct the release history by matching the simulated concentrations with the measured concentrations (Skagg and Kabala 1994, 1995, 1998; Samarskaia 1995; Woodbury and Ulrych 1996; Snodgrass and Kitanidis 1997; Woodbury et al. 1998; Liu and Ball 1999; Neupauer and Wilson 1999, 2001;

Neupauer et al. 2000).

For the source information estimation problem, Gorelick et al. (1983) employed groundwater transport simulation model incorporated with the linear programming

and multiple regressions to estimate the source information. Define the error as the difference between measured concentration and simulated concentration. They minimize the sum of the absolute errors for the linear programming model and minimize the sum of the square errors for the multiple regressions model. The two methods both properly identified the source but contain some errors in the determination of release concentration in transient state case. Hwang and Koerner (1983) employed a modified finite element model with limited monitoring well data to minimize the sum of the square errors to identify the pollution source. National Research Council (1990) suggested using the trial-and-error method incorporated with a forward model to solve the problem of source information estimation. Bagtzoglou et al. (1992) proposed an approach using particle methods to provide probabilistic estimates of source location and time history in a heterogeneous site. Their study indicated that the simulation with conditional conductivity field performs as well as the simulation with perfectly known conductivity field. Mahar and Datta (1997, 2000, 2001) provided a serial investigation to different types of source information estimation problems. In their study, the finite differences method was employed to simulate two-dimensional groundwater flow and transport. They formulated the source estimation problem as a constrained optimization form and solved the objective function by nonlinear programming. Their study successfully identified

the source information for flow in steady and transient states Sciortino et al. (2000) developed an inverse procedure based on the Levenberg-Marquardt method and three-dimensional analytical model to solve the least squares minimization problem for identifying the source location and the geometry of a DNAPL pool. Their study showed that the result is highly sensitive to the hydrodynamic dispersion coefficient.

In addition to the gradient-type methods, GA was also employed to solve the source information estimation problems recently. Aral and Gaun (1996) proposed an approach called improved genetic algorithm (IGA) to determine the contaminant source location, leaky rate, and release period. The results obtained from the IGA agreed with those obtained from the linear and nonlinear programming. Aral et al.

(2001) proposed a new approach, named as a progressive genetic algorithm (PGA) in which the GA is incorporated with the groundwater simulation model for source identification problem. Their results indicated that the initial guess doesn’t influence the obtained solution.

Except for the source information estimation problems, the heuristic methods are also applied in other fields. Zheng and Wang (1996) treated the problem of identifying optimal parameter structure as a large combinatorial optimization problem.

They employed the tabu search and SA to solve the combinatorial optimization problem. Their result indicated that the proposed approaches perform extremely

well than those obtained from the grid search or descent search. Tung et al. (2003) developed an optimal procedure for applying SA and the short distance method with MODFLOW to determine the best zonation of hydraulic conductivity. They determine the best zonation of hydraulic conductivity by minimizing the errors of hydraulic head. Their results illustrated that the procedure can effectively determine and delineate the hydrogeological zone. Tung and Chou (2004) proposed a procedure for identifying the spatial pattern of groundwater pumping rates by integrating TS and pattern classification. Their procedure is successfully applied to a simulated problem based on real conditions. They also mentioned that the procedure can also be applied to different problems of pattern classification.