On the spatial variability of parameters of the unsaturated hydraulic conductivity

In situ measurements of discharge-head (steady state rate of water discharge and water head (Q, H)) pairs were used to estimate the saturated conductivity K-s and the parameter alpha of the Gardner [1958] model of local unsaturated hydraulic conductivity at N = 152 observation points in a field plot (40 m long, 6 m wide, and 2 m deep) by means of the Geulph permeameter method. Twenty-two of these (Q, H) pairs yielded negative K-s and were excluded from the subsequent analyses. Estimates of In K-s and In alpha from N = 130 observation points were used to estimate parameters of the spatial covariance and the drift functions of the two soil properties, using the restricted maximum likelihood estimation procedure and the weighted least squares procedure, respectively. For both soil properties a deterministic drift was identified, suggesting that in the site under investigation, approximately 59% and 37% of the total variability off = In K-s and a = In alpha, respectively, may stem from large-scale variations. Results of the analyses of the uncorrelated residuals of In K-s and In alpha suggest that both follow an approximately normal distribution and are moderately cross-correlated (rho(fa) = 0.68). The fitted covariance models of both soil properties exhibited slight statistical anisotropy in the horizontal plane and a significant anisotropy in the vertical planes. Components of the range of In K-s were 2.5 m and 0.6 m in the horizontal and the vertical directions, respectively, while those of In alpha were 1.4 m and 0.4 m, respectively. Estimates of the correlation scales of both properties in the horizontal plane were associated with relatively large uncertainty, which probably stemmed from the less than optimum selection of the number and locations of the observation points in this plane. The results of the model validation test, however, indicated that the fitted covariance and drift models were theoretically consistent with the observations of both soil properties.