In this paper, the problem of ill-posedness of solution in identifying multiple groundwater flow parameters from hydraulic head data and other ancillary data was assessed. The solution approach to the parameter identification problem is sought by applying the Least Squares, the Adjoint, the Conjugate Gradient Method and a proposed Parameter Transformation Method. Numerical test for a 1D and 2D flow models governed by PDEs were used to assess the accuracy and stability of the proposed method. The proposed method gave an appreciable solution estimates with minimal error-norm compared with the o ptimisation techniques explored in the study as a measure to the PTM The results revealed that when the adapted methods and the PTM were simulated numerically on a 1D and 2D test problems, the PTM gave a more stable solution estimates with a residual norm-error value of 2.23500 for the 1D test problem compared with that of the Adjoint method which prove to be the comparing solution with a norm-error value of 2.66500. For the 2D test case, the results also revealed that the PTM was stable with a residual norm-error value of 10.98310 compared with that of the Conjugate Gradient method with value of 86.562. Thus in conclusion, the study revealed that the PTM is capable of yielding realistic solution estimates compared with the studied optimisation methods.
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