Analysis of Gravity‐Driven Infiltration With the Development of a Saturated Region. Issue 11 (7th November 2022)

• Record Type: Journal Article
• Authors: Shadab, Mohammad Afzal; Hesse, Marc Andre
• Is Part Of: Water resources research. Volume 58:Issue 11(2022)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-11-07
• Subjects: one‐dimensional infiltration -- extended kinematic wave approximation -- decaying soil conductivity -- perched groundwater table -- analytic solutions -- Hydrus‐1D and experimental validation; Hydrology -- Periodicals; 333.91
• DOI: 10.1029/2022WR032963
• Languages: English
• ISSNs: 0043-1397

Abstract

Abstract: Understanding the controls on the infiltration of precipitation into soil is an important problem in hydrology and its representation in heterogeneous media is still challenging. Here we investigate the reduction of gravity‐driven infiltration by the development of a saturated region due to the downward decrease in porosity and/or hydraulic conductivity. The formation of a saturated region chokes the flow and leads to a rising perched water table that causes ponding even when rainfall intensity is lower than the surface infiltration capacity. Mathematically this problem is interesting, because its governing partial differential equation switches from hyperbolic in the unsaturated region to elliptic in the saturated region. To analyze this coupled unsaturated‐saturated flow we develop an extended kinematic wave analysis in the limit of no capillary forces. This theory provides a general framework to solve gravity‐dominated infiltration problems for arbitrary downward decrease in porosity and/or conductivity. We apply the framework to three soil profiles (two‐layer, exponential and power‐law decay with depth) and develop (semi‐) analytic solutions for evolution of the water saturation. For the case of a two‐layer soil the saturated flux, and therefore the front speeds, are constant which allows explicit analytic solutions that agree well with Hydrus‐1D. All solutions show excellent agreement with our numerical solutions of the governing equations in the limit of no capillary forces. Similarly, our solutions compare well with experimental data for infiltration into a multi‐layer soil with declining hydraulic conductivity. Plain Language Summary: Understanding the rainfall into a heterogeneous medium is crucial to estimate the time when rainwater will pond on the surface and begin to form runoff. Previous work has focused on the limiting cases: limited rainfall where the soil is always unsaturated and water never ponds on the surface and excessive rainfall where the soil is always saturated but ponding is initially prevented by capillary suction. Here we focus on the case of transitional rainfall where soil dynamically switches from unsaturated to saturated if hydraulic conductivity declines with depth. In this case, all rainwater initially infiltrates until a perched water table forms in the soil. If rainfall is sustained long enough this perched water table rises to the surface and water begins to pond and runoff is generated. The dynamics can be compared to filling a leaking bucket, where rise of the water level in the bucket depends on the rate of leakage through the base. The motion of such water fronts is studied by extending an established mathematical theory, which ultimately yields simple analytical solutions. Key Points: Formulated an extended kinematic wave analysis for one‐dimensional infiltration with coupled unsaturated and saturated regions Transitional infiltration into soil with decaying conductivity leads to the formation of a saturated region and rising perched water table Semi‐analytic solutions with formation and evolution of a saturated region provide challenging benchmarks for numerical solutions (Hydrus)