This paper introduces a new algorithm for the solution of the problem of parameter identification associated with a two-dimensional unsteady state groundwater flow. The parameters to be identified are functions of the space variables. It is assumed that some observations on the dependent variable of the governing equation are available. The unknown parameters are directly identified from observations. An implicit finite difference scheme is used to approximate the original partial differential equation. A least squares criterion function is employed. The identification problem is then formulated as a standard quadratic programing representation by quasi-linearization. The formulation is further modified by a simple matrix operation which drastically reduces the dimension of the constraint set. The new algorithm is shown to be very effective in solving the large-scale inverse problem, and it is easily implemented, rapidly convergent, and able to handle any inequality constraints, a feature that is essential for such a problem. In this study a new algorithm is presented which is especially suited for solving the large-scale inverse problem. It is mathematically related to the technique of quasi-linearization. However, it is more versatile in its ability to handle inequalityconstraints and easily implemented on the computer. It is also free from the 'curse of dimensionality' that is usually associated with most large-scale problems. Simultaneous identification of 84 parameters with relative ease is demonstrated by numerical examples. PROBLEM DEFINITIONThe inverse problem under consideration is concerned with an inhomogeneous isotropic confined aquifer and pumping well system. The parameters to be identified are the transmissivities, assumed to be functions of the space variables x and y. Assume that pumping wells completely penetrate the aquifer and that the Dupuit-Forchheimer assumptions hold. The governing equation is easily shown to be

When a series of aerators are used to raise the level of dissolved oxygen in a polluted stream through instream artificial aeration augmentation, the system is governed by the basic dissolved oxygen mass balance equation with the existence of artificial aeration as its boundary conditions. A mathematical model is formulated for the optimization of the allocation of aeration capacity to each of the series of aerators subject to a limitation on total available aeration capacity. The objective function is the minimization of the sum of the squares of the aeration costs and the costs incurred by damaging or unnecessarily improving the system. The original constrained allocation problem is simplified by converting it to an unconstrained one via the use of Lagrange multiplier. A discretized dynamic programming algorithm is formulated for finding the optimal allocation policy. A typical optimal aeration capacity allocation policy and its corresponding dissolved oxygen sag profile for the illustrated numerical example is presented, and the relationship between the total available aeration capacity and Lagrange multiplier is also developed treating weighting factors as parameters.

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