Solution techniques of groundwater management models

A groundwater management model should include the groundwater simulation model as constraint along with other managerial constraints. Incorporation of groundwater simulation model ensures that the obtained management strategies are physically feasible. The simulation model simulates the physical processes of the aquifers. Generally embedding technique and response matrix approach (Gorelick, 1983) are used for incorporating the governing equations within the management model. The embedded optimization technique incorporates finite difference or finite element approximation of the governing equations as equality constraints within the management model, along with the other physical and managerial constraints. Some of the application of embedding technique for groundwater management problems are seen in Das, 1995; Das and Datta 1999, etc. However, this approach is not suitable for large aquifer systems. The approach may be numerically inefficient especially when applied to large aquifer systems with considerable heterogeneity. The response matrix approach is based on the principle of superposition and linearity. The performance of response matrix approach is not suitable for highly nonlinear systems (Rosenwald and Green, 1974).

As an alternative to the embedding technique and the response matrix approach, the simulation model may be incorporated with the management model as an external module. In this approach, an external simulation model is linked to the optimization model (Finney at el., 1992; Emch and Yeh, 1998; Bhattacharjya and Datta, 2009). The optimization model calls the simulation model as and when it requires any information from the simulation model. The methodology has been applied effectively for large scale groundwater management models. The main disadvantage of this approach is that numerous repetitive iterations between the simulation model and the optimizer are required to arrive at an optimal solution. The computational time can be substantially reduced by utilizing parallel processing capabilities of advanced computers. This would enable use of rigorous numerical models for simulation and its linkage to an optimization model. Also the time requirement for iterative solutions of the optimization model and the simulation model can be drastically reduced. However, this requires appropriate computer hardware and numerical simulation models specially tailored to explicit parallel processing capabilities.

An optimization technique has to be used for solving the management model. Classical optimization techniques have been applied for solving groundwater management problems. Most of the classical optimization methods use gradient search technique for finding the optimal solution. The performance of the gradient based classical optimization methods is not satisfactory when response surface is highly irregular. In such a situation, it is very likely that the solutions obtained would be local optimal solutions. One possible remedy is the use multiple solution points as initial solutions. Some people have also used global search techniques, such as Genetic Algorithm, Simulated Annealing, Differential evolution, etc. for solving groundwater management models.