Base flow recession from unsaturated-saturated porous media considering lateral unsaturated discharge and aquifer compressibility

Unsaturated flow is an important process in base flow recessions and its effect is rarely investigated. A mathematical model for a coupled unsaturated-saturated flow in a horizontally unconfined aquifer with time-dependent infiltrations is presented. The effects of the lateral discharge of the unsaturated zone and aquifer compressibility are specifically taken into consideration. Semianalytical solutions for hydraulic heads and discharges are derived using Laplace transform and Cosine transform. The solutions are compared with solutions of the linearized Boussinesq equation (LB solution) and the linearized Laplace equation (LL solution), respectively. A larger dimensionless constitutive exponent kappa(D) (a smaller retention capacity) of the unsaturated zone leads to a smaller discharge during the infiltration period and a larger discharge after the infiltration. The lateral discharge of the unsaturated zone is significant when kappa D <= 1, and becomes negligible when kappa(D) >= 100. The compressibility of the aquifer has a nonnegligible impact on the discharge at early times. For late times, the power index b of the recession curve -dQ/dt similar to aQ(b), is 1 and independent of kappa(D), where Q is the base flow and a is a constant lumped aquifer parameter. For early times, b is approximately equal to 3 but it approaches infinity when t -> 0. The present solution is applied to synthetic and field cases. The present solution matched the synthetic data better than both the LL and LB solutions, with a minimum relative error of 16% for estimate of hydraulic conductivity. The present solution was applied to the observed streamflow discharge in Iowa, and the estimated values of the aquifer parameters were reasonable.