Abstract
Abstract. Within this study we propose a stochastic approach to simulate soil water dynamics in the unsaturated zone by using a non-linear, space domain random walk of water particles. Soil water is represented by particles of constant mass, which travel according to the Itô form of the Fokker–Planck equation. The model concept builds on established soil physics by estimating the drift velocity and the diffusion term based on the soil water characteristics. A naive random walk, which assumes all water particles to move at the same drift velocity and diffusivity, overestimated depletion of soil moisture gradients compared to a Richards solver. This is because soil water and hence the corresponding water particles in smaller pore size fractions are, due to the non-linear decrease in soil hydraulic conductivity with decreasing soil moisture, much less mobile. After accounting for this subscale variability in particle mobility, the particle model and a Richards solver performed highly similarly during simulated wetting and drying circles in three distinctly different soils. Both models were in very good accordance during rainfall-driven conditions, regardless of the intensity and type of the rainfall forcing and the shape of the initial state. Within subsequent drying cycles the particle model was typically slightly slower in depleting soil moisture gradients than the Richards model. Within a real-world benchmark, the particle model and the Richards solver showed the same deficiencies in matching observed reactions of topsoil moisture to a natural rainfall event. The particle model performance, however, clearly improved after a straightforward implementation of rapid non-equilibrium infiltration, which treats event water as different types of particles, which travel initially in the largest pore fraction at maximum velocity and experience a slow diffusive mixing with the pre-event water particles. The proposed Lagrangian approach is hence a promising, easy-to-implement alternative to the Richards equation for simulating rainfall-driven soil moisture dynamics, which offers straightforward opportunities to account for preferential, non-equilibrium flow.
Highlights
A tiny amount of water is stored in the unsaturated zone: with an estimated volume of about 16 500 km3 (Dingman, 1994), soil moisture represents 0.05 % of total fresh water
In the following we present final soil moisture profiles simulated with the Darcy–Richards and the particle model for selected runs and compare the temporal evolution of soil moisture profiles in the form of 2-D colour plots
In terms of computing time we noted no remarkable difference between the particle model and the Richards solver
Summary
A tiny amount of water is stored in the unsaturated zone: with an estimated volume of about 16 500 km (Dingman, 1994), soil moisture represents 0.05 % of total fresh water. This tiny storage amount exerts first-order control on the partitioning of net radiation energy in latent and sensible heat flux (Kleidon and Renner, 2013a, b; Gayler et al, 2014; Turner et al, 2014) – possibly the key process in land surface atmosphere exchange. The standard approach to represent capillary- and gravity-controlled soil water dynamics
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have