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

Abstract

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 κD (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 κD≤1, and becomes negligible when κD≥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∼ aQb, is 1 and independent of κD, 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.

Quantification of the seasonal hillslope water storage that does not drive streamflow

“…Interpretation of discharge generation and direct/indirect storage dynamics at Dry Creek, however, presents a more significant challenge for the conceptual hydrologic modeller. Few process‐oriented, lumped ecohydrologic modelling frameworks account for a dynamic boundary between saturated and unsaturated moisture layers (e.g., Liang, Zhan, Zhang, & Schilling, ; Seibert, Rodhe, & Bishop, ).…”

Comment on “Base Flow Recession from Unsaturated‐Saturated Porous Media considering Lateral Unsaturated Discharge and Aquifer Compressibility” by Liang, X., H. Zhan, Y.‐K. Zhang, and K. Schilling (2017)

“…Liang et al (, hereinafter LZZS) presented an illuminating treatment of the impacts of unsaturated zone processes on streamflow recession. While the focus of LZZS was to derive semianalytical solutions for hydraulic head and discharge accounting for lateral unsaturated flow and aquifer compressibility, this comment only addresses the field data analysis, interpretation, and related conclusions used in LZZS.…”

“… Liang et al () computed the derivative for –dQ/dt using a constant time step, a method that produces artifacts We and many others have provided estimated recession parameters on discharge data eliminating these artifacts (Roques et al, ; Rupp & Selker, ) We highlighted a dramatic impact on the interpretation of the recessions …”

“… Abstract Liang et al () presented an analysis of the impacts of unsaturated zone processes on streamflow recession using methodology from Brutsaert and Nieber () with a constant time step in computation of the time derivative of flow. Over the past 10 years, many authors have demonstrated that this method may produce artifacts that lead to incorrect interpretations.…”

“…Over the past 10 years, many authors have demonstrated that this method may produce artifacts that lead to incorrect interpretations. To demonstrate the impact of the choice of analysis methods, this comment presents an estimation of recession parameters using the Liang et al () discharge data that eliminates artifacts introduced through the constant time step. Here we use the exponential time step method, which revealed recession coefficient b greater than 1 which is inconsistent with the fitting framework used in Liang et al ().…”