A MONTE CARLO SIMULATION STUDY ON KRIGING AS A WATER TABLE INTERPOLATOR

Abstract

Kriging, a geostatistical numerical method is widely employed as an interpolation tool for water table elevation. This method apart from permitting the interpolation, also leads to the mean square error of interpolation. This renders this method superior to the other methods like spline function, trend surface analysis etc. An important step in conducting a kriging assisted interpolation is to evolve the variogram. The common practice in this regard is to first derive an experimental variogram from the available discrete point data, and subsequently to fit a chosen variogram model. However, the main problem in this approach is that the discrete point data used for building a experimental variogram are theoretically expected to be stationary i.e., devoid of any regional trend. This requirement is very rarely fulfilled in practice. The present work is aimed at evolving closed form equations for the parameters of Gaussian model of the variogram. The parameters are viewed as functions of the aquifer transmissivity (T) and the standard deviation (aw ) of the net vertical recharge. Treating the net vertical recharge as a normally distributed random variable with zero mean and assigned standard deviations, discrete point stationary water table elevations are generated by Monte Carlo simulation. The heads so generated are employed to evolve the variogram and hence the parameters of the Gaussian variogram model. This is repeated for different combinations of T and o .The estimates of the parameter so arrived at are regressed to evolve closed form equations describing the parameters are functions of T and c„, . The proposed equations have been validated by comparing the equation-based and data-based variograms of water table from unconfined aquifer of Yamuna-Hindon doab.