A Lagrangian model for soil water dynamics during rainfall-driven conditions
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2016-09-01
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| Series: | Hydrology and Earth System Sciences |
| Online Access: | http://www.hydrol-earth-syst-sci.net/20/3511/2016/hess-20-3511-2016.pdf |
| _version_ | 1818898249842425856 |
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| author | E. Zehe C. Jackisch |
| author_facet | E. Zehe C. Jackisch |
| author_sort | E. Zehe |
| collection | DOAJ |
| description | 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.
<br><br>
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. |
| first_indexed | 2024-12-19T19:29:05Z |
| format | Article |
| id | doaj.art-6cb10d237fd544d6ae90cf4d72ae4470 |
| institution | Directory Open Access Journal |
| issn | 1027-5606 1607-7938 |
| language | English |
| last_indexed | 2024-12-19T19:29:05Z |
| publishDate | 2016-09-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Hydrology and Earth System Sciences |
| spelling | doaj.art-6cb10d237fd544d6ae90cf4d72ae44702022-12-21T20:08:40ZengCopernicus PublicationsHydrology and Earth System Sciences1027-56061607-79382016-09-012093511352610.5194/hess-20-3511-2016A Lagrangian model for soil water dynamics during rainfall-driven conditionsE. Zehe0C. Jackisch1Karlsruhe Institute of Technology (KIT), Karlsruhe, GermanyKarlsruhe Institute of Technology (KIT), Karlsruhe, GermanyWithin 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. <br><br> 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.http://www.hydrol-earth-syst-sci.net/20/3511/2016/hess-20-3511-2016.pdf |
| spellingShingle | E. Zehe C. Jackisch A Lagrangian model for soil water dynamics during rainfall-driven conditions Hydrology and Earth System Sciences |
| title | A Lagrangian model for soil water dynamics during rainfall-driven conditions |
| title_full | A Lagrangian model for soil water dynamics during rainfall-driven conditions |
| title_fullStr | A Lagrangian model for soil water dynamics during rainfall-driven conditions |
| title_full_unstemmed | A Lagrangian model for soil water dynamics during rainfall-driven conditions |
| title_short | A Lagrangian model for soil water dynamics during rainfall-driven conditions |
| title_sort | lagrangian model for soil water dynamics during rainfall driven conditions |
| url | http://www.hydrol-earth-syst-sci.net/20/3511/2016/hess-20-3511-2016.pdf |
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