New Model of Variogram of Groundwater Hydraulic Heads

Kriging is a powerful tool for interpolation and network design. A necessary prerequisite for a kriging application is the variogram that describes the variation of the semivariance with distance. Variograms are routinely derived from the measurements of the concerned variable. Presented herein is a model of the variogram of groundwater hydraulic heads that permits the estimation of the semivariance corresponding to any distance in terms of the transmissivity $\left(T\right)$ and standard deviation $\left({\sigma }_W\right)$ of the flux. The model thus evolves the variogram from the aquifer attributes rather than from the measured heads. Treating the flux as a normally distributed random variable, with zero mean and an assigned standard deviation, synthetic discrete steady-state stationary head fields are generated by the Monte Carlo simulation. The fields so generated are employed to evolve experimental variograms, and hence to estimate the parameters of the Gaussian model for various values of $T$ and ${\sigma }_W$ . Closed form functional relations between the Gaussian parameters and the independent variables viz. $T$ and ${\sigma }_W$ are arrived at by regression. This provides a new model capable of yielding variograms of groundwater hydraulic heads without invoking the head measurements.