MATHEMATICAL MODELLING OF GROUNDWATER SYSTEM

Abstract

Mathematical models of groundwater system have become an important compontnt of water resources planning. These models assist the planners in arriving at optimal ground water development policies either by studying large number of alternatives and choosing the best one or by more objective optimisation methods. Inspite of intensive research in recent years, the use of groundwater modelling techniques in real si tuations is ridden with many problems relating either to an inadequacy of data or to the unrealistic assumptions. In the present work an attempt has been made to provide solutions to a few of these problems. The spacing and orientation of the observation wells are very rarely adequate to meet the data input requirements of a distributed model directly. In addition to this the irregularly spaced data points render the estimation of the hydraulic gradients and the second spatial derivatives of piezometric head, almost unacceptably subjective. The Lagrangian methods of func tional approximation are generally not suitable due to the re quirement of a high degree polynomial. A least square approxi mation can cut down the degree and the size ( number of terms; of the polynomial. In the present study the capability of a least square polynomial to attenuate the data noise and a need to restrict its degree and size have been demonstrated by a simu lation study. The use of the statistical tests of significance -IVfor arriving at an optimal form of the approximating polynomial has been suggested. These polynomials are amenable to the di fferentiation and integration, necessary for the estimation of spatial derivative of piezometric heals and the ground water storages. The estimation of aquifer parameters by Solving inverse problem generally requires a prior knowledge of the directions of principal permeabilities and the distribution of the net ver tical accretion in space and time. The available field data are generally too inadequate to provide a direct estimation of the directions of principal permeabilities. The rainfall recharge, an important component of the net vertical accretion is generally estimated from the rainfall records employing certain empirical or semi-empirical relations. These relations involve certain parameters which are not directly measurable quantities. In the present work an inverse problem model has been developed which affords an explicit estimation of principal permeability direc tions and the recharge parameters. The linear programming based model for arriving at the optimal cropping and groundwater withdrawal patterns neglects the distributed nature of groundwater system. It can in no way incorporate the constraints of restricting the watertable ele vations at all the space points during all thy periods, within an acceptable range. In the present work, a model has been de veloped which overcomes these limitations, by incorporating -Va spatially distributed aquifer response model in the scheme of computations and solving the problem by nonlinear optimisation. The applicability of these models to field situations has been demonstrated by using the data of Daha area(India)