Quantification of temporal variability of vertical soil moisture movement through an unsaturated zone

Understanding of the soil moisture movement process in the unsaturated zone is crucial for an accurate estimate of the rate of recharge to the aquifer. The goal of the present research is therefore to quantify the temporal variability of moisture movement through the unsaturated zone. A new framework for quantifying the temporal variability of soil moisture movement over a relatively large space scale through the unsaturated zone is proposed. The unsaturated zone is treated as a nonlinear soil moisture reservoir with a single random input, the effective infiltration, and a single random output, the recharge to the saturated zone, in time. The variation of volumetric soil moisture in response to the variation of effective infiltration is represented by a nonlinear functional series involving generalizations of the convolution integral, which underlies the concept of unit hydrograph. A second order autoregressive model is used to account for the temporal behavior of the input process. The use of Fourier-Stieltjes representation approach enables developing closed-form expressions for the variance of volumetric soil moisture and cross-covariance of the soil moisture and effective infiltration. The variance can be viewed as an index of temporal variability in soil moisture or uncertainty involved in the modeling process. The cross-covariance contains information about how two processes are correlated in time. Focus of analysis is placed on the influence of the controlling parameters on the temporal variability of soil moisture movement.