Flow recession behavior of dendritic subsurface flow patterns

Discharge curves of springs are the fingerprint of aquifers. In particular, the recession of flow after strong recharge events has been widely used for aquifer characterization. While an exponential decay is often found at long time scales, the short-term behavior is less unique and widely used in the context of characterizing karst systems. Several empirical and a few physically-based models describing the short-term recession behavior were proposed.

This study investigates the flow recession behavior of aquifers with preferential flow paths with a structure according to the concept of minimum energy dissipation.
Assuming a power-law relationship between hydraulic conductivity and porosity, the subsurface flow patterns used in our model are organized towards an optimal spatial distribution of these two parameters in a way that the total energy dissipation of the flow is minimized. This leads to two-dimensional dendritic network structures similar to river networks. Starting from a steady-state initial condition with a constant recharge rate we model the decrease of discharge over time, under the assumption of a linear storage behavior.
As expected the long-term flow recession can be approximated by an exponential function. At short times, however, our model predicts a power-law behavior with exponents ranging from 0.7 to 0.9. For the most realistic scenario, a quadratic relationship between hydraulic conductivity and porosity, the power-law exponent approximates 0.8 which corresponds well to what other studies have found for suitable recession events of karst springs.