Cokriging estimation of the conductivity field under variably saturated flow conditions

A linear estimator, cokriging, was applied to estimate hydraulic conductivi ty, using pressure head, solute concentration, and solute arrival time meas urements in a hypothetical, heterogeneous vadose zone under steady state in filtrations at different degrees of saturation. Covariances and cross-covar iances required by the estimator were determined by a first-order approxima tion in which sensitivity matrices were calculated using an adjoint state m ethod. The effectiveness of the pressure, concentration, and arrival time m easurements for the estimator were then evaluated using two statistical cri teria, L-1 and L-2 norms, i.e., the average absolute error and the mean squ are error of the estimated conductivity field. Results of our analysis show ed that pressure head measurements at steady state flow provided the best e stimation of hydraulic conductivity among the three types of measurements. In addition, head measurements of flow near saturation were found more usef ul for estimating conductivity than those at low saturations. The arrival t ime measurements do not have any significant advantage over concentration. Factors such as variability, linearity, and ergodicity were discussed to ex plain advantage and limitation of each type of data set. Finally, to take a dvantage of different types of data set (e.g., head and concentration), a c omputationally efficient estimation approach was developed to combine them sequentially to estimate the hydraulic conductivity field. The conductivity field estimated by using this sequential approach proves to be better than all the previous estimates, using one type of data set alone.