Cokriging estimation of the conductivity field under variably saturated flow conditions

A linear estimator, cokriging, was applied to estimate hydraulic conductivity, using pressure head, solute concentration, and solute arrival time measurements in a hypothetical, heterogeneous vadose zone under steady state infiltrations at different degrees of saturation. Covariances and cross-covariances required by the estimator were determined by a first-order approximation in which sensitivity matrices were calculated using an adjoint state method. The effectiveness of the pressure, concentration, and arrival time measurements for the estimator were then evaluated using two statistical criteria, L-1 and L-2 norms, i.e., the average absolute error and the mean square error of the estimated conductivity field. Results of our analysis showed that pressure head measurements at steady state flow provided the best estimation of hydraulic conductivity among the three types of measurements. In addition, head measurements of flow near saturation were found more useful for estimating conductivity than those at low saturations. The arrival time measurements do not have any significant advantage over concentration. Factors such as variability, linearity, and ergodicity were discussed to explain advantage and limitation of each type of data set. Finally, to take advantage of different types of data set (e.g., head and concentration), a computationally 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.