Literature review

Atmadja and Bagtzoglou (2001) pointed out the groundwater source identification problem is an ill-posed problem because the solution may not be unique

and stable. They also reviewed the available methods for source identification and recovering the release history and classified them under following four categories:

optimization approaches, probabilistic and geostatistical simulation approaches, analytical solution and regression approaches, and direct approaches. Tracking the pollution source location usually needs to give an initial guess solution and run forward simulations first and then to search the best-fitted solution via an optimization approach. Probabilistic and geostatistical simulation approaches employ several probabilistic and statistical techniques to assess the probability of source locations (Sun, 2007). Atmadja and Bagtzoglou (2001) indicated this approach is applicable only when the location of the potential source is known in advance. Analytical solution and regression approaches can estimate all the parameters simultaneously but work well only for simple aquifer geometries and flow conditions. Direct approaches reconstruct the release history by solving governing equation directly.

Generally, the groundwater contaminant source identification problem can be classified into three categories, they are: (1) identifying source location, (2) recovering the release history, (3) identifying source location and recovering the release history simultaneously. For the identifying source location problem, Gorelick et al. (1983) proposed an optimization approach, employing the groundwater transport simulation model to incorporate with the linear programming and multiple

regressions to estimate the source information. In their study, only if the observed concentrations are relatively noise-free, the both two proposed approaches shall perform well. Hwang and Koerner (1983) employed a modified finite element model with a small number of monitoring well data to identify the pollution source by minimizing the sum of the squared errors between the sampling and simulated concentrations. National Research Council (1990) suggested that using trial-and-error method incorporated with a forward model to solve the source identification problem. Bagtzoglou et al. (1992) used particle methods to identify solute sources in heterogeneous site, and provided probabilistic estimates of source location and time history without relying on optimization approaches. Mahar and Datta (1997, 2000, and 2001) provided a serial investigation related to problems of source identification. They formulated the source information estimation problem as a constrained optimization form and used nonlinear optimization models to identify the source information for two-dimensional steady-state and transient groundwater flow problems. Sciortino et al. (2000) developed an inverse procedure based on the Levenberg-Marquardt method and a three-dimensional analytical model to solve the least-squares minimization problem for identifying the source location and the geometry of a nonaqueous pool under steady-state condition. Their study showed that the result is highly sensitive to the hydrodynamic dispersion coefficient.

Mahinthakumar and Sayeed (2005) combined genetic algorithm (GA) with local search methods (GA-LS) to solve the groundwater source identification problem.

Their results exhibited that the GA-LS are more effectively than the individual heurist approaches in the groundwater source identification problem.

For recovering the release history problem, Liu and Ball (1999) classified the problem of recovering the release history into two types: the function-fitting and full-estimation approaches. The function-fitting approach initially assumes that the source function is known and reformulates it as an optimization problem, and then employs the appropriate inverse methods to estimate the best-fit parameters of the source function (Gorelick et al., 1983; Wagner, 1992). The full-estimation approach is to recover the release history by matching the observed sampling concentrations with the simulated concentrations (Skaggs and Kabala, 1994, 1995, 1998; 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 simultaneously identifying source location and recovering the release history problem, Aral and Gaun (1996) proposed an approach called improved genetic algorithm (IGA) to determine the contaminant source information, including source location, leak rate, and release period. They indicated the results obtained from the IGA match with those obtained from linear and nonlinear programming approaches.

Based on GA algorithm and a groundwater simulation model, Aral et al. (2001) further developed a new combinatorial approach, defined as progressive genetic algorithm (PGA), to identify the source location and release history in steady state flow problem. Sun et al. (2006a) employed a constrained robust least squares (CRLS) method to recovery the release history of a single source, and the results of CRLS in their assumed example are better than several classic methods (i.e., ordinary least squares (LS), standard total least squares (TLS), and nonnegative least squares (NNLS)). Sun et al. (2006b) employed the CRLS combined with a branch-and-bound global optimization solver for identifying source locations and release histories. In their study, the results showed their new approach had better performance than a non-robust estimator. Milnes and Perrochet (2007) presented a direct approach method to identify a single point-source pollution location and contamination time under perfectly known flow field conditions. Recently, Yeh et al.

(2007a) developed a novel source identification model, SATS-GWT, which combines simulated annealing (SA), tabu search (TS), and MODFLOW-GWT, to identify the constant source release problem. Their method can estimate the contaminant source information in a three-dimensional transient groundwater flow system. However, the source release history they considered is uniform in their case study.

Ho et al. (1992) presented a new approach called ordinal optimization algorithm

(OOA) which can solve complex optimization problems effectively and accurately.

Complex optimization problems usually require huge amount of computing time in obtaining the solution. The OOA is suitable for solving the complex optimization problem with sifting the most possible solution part for further evaluation (Ho and Larson, 1995; Lau and Ho, 1997; Ho, 1999).