Impact of Gravity Fingering on Deep Drainage in Arid Environments

Gravity fingering is a powerful hydrodynamic instability that sets in during infiltration of water in dry soil, leading to the emergence of vertical channels of preferential flow that conduct virtually all the infiltration water. This phenomenon has been characterized in detail in controlled laboratory experiments, and has been documented in the field. Mathematical and computational modeling of gravity fingering has proved challenging, but recent progress has allowed us to simulate this process quantitatively. Building on earlier work, we model unsaturated flow following a thermodynamic approach, which leads to a partial differential equation with a nonlinear, singular fourth-order term—a formulation that is endowed with an entropy function.

Here, we assess the impact of gravity fingering on deep drainage, that is, the infiltration water that bypasses evaporation and reaches deep groundwater bodies. We do so by coupling our model of unsaturated flow with evapotranspiration, which we model as a spatially- and temporally-variable nonlinear sink term in the equation. We apply the model of coupled infiltration and evapotranspiration to the soil and climatic conditions of the Kalahari transect. We reproduce not only the mean annual precipitation (MAP) and potential evapotranspiration (PET), but also the rainfall statistics that characterize the intensity and frequency of the precipitation events. We conduct unprecedented simulations of infiltration that are decades long (to capture the long-term rainfall statistics and system's deep drainage behavior), with sub-minute temporal resolution (to capture the infiltration flux during storms) and with sub-centimeter spatial resolution (to resolve the gravity fingers accurately).

We compare the predictions of two models: the classic infiltration model based on Richards equation (which cannot reproduce the gravity-fingering instability) and our proposed model capable of reproducing fingered flow. We find that the wetting front instability has a dramatic impact on deep drainage fluxes. Fingered flow causes water to quickly traverse the shallow root zone, by-passing most of the soil column and effectively reducing losses due to evaporation and transpiration from shallowly-rooted plants. As a result, water may be expected to percolate below the topsoil, and be found at depth in arid and semiarid climates, where PET far exceeds MAP. Water from subsequent infiltration events tends to be diverted towards the fingering channels, which may thus persist over many rainfall cycles. Our results suggest that models of vegetation dynamics based on simplified estimates of infiltration depth may underestimate root biomass and groundwater recharge in dryland environments, and that gravity fingering moderates the response of water-stressed ecosystems to climate variability, increasing their resilience to a future scenario of higher aridity.