Articles | Volume 16, issue 2
https://doi.org/10.5194/gmd-16-659-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-16-659-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Development and technical paper
| 
27 Jan 2023
Development and technical paper |
| 27 Jan 2023
| 27 Jan 2023
A simple, efficient, mass-conservative approach to solving Richards' equation (openRE, v1.0)
Global Institute for Water Security, University of Saskatchewan, Saskatoon, Saskatchewan, Canada
School of Environment and Sustainability, University of Saskatchewan, Saskatoon, Saskatchewan, Canada
Raymond J. Spiteri
Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan, Canada
Martyn P. Clark
Department of Geography and Planning, University of Saskatchewan, Saskatoon, Saskatchewan, Canada
Simon A. Mathias
Department of Engineering, Durham University, Durham, UK
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Cited
17 citations as recorded by crossref.
- Revisiting Salvucci’s Semi-analytical Solution for Bare Soil Evaporation with New Consideration of Vapour Diffusion and Film Flow S. Mathias et al. https://doi.org/10.1007/s11242-023-01917-5
- Development of a modified Green–Ampt model considering the unsaturated zone Y. Li et al. https://doi.org/10.1016/j.biosystemseng.2025.104174
- Assessing simplified approaches in modeling rainfall-induced landslides using Richards' equation with Biot poroelasticity R. Abbasov et al. https://doi.org/10.1016/j.enggeo.2025.108481
- Heavy metals in unsaturated urban soils: Experimental insights and stochastic forecasting A. Dell'Oca et al. https://doi.org/10.1016/j.jconhyd.2026.104855
- Research on dynamic fitting models for road performance of self-melting ice surfaces and salt storage slow-release performance L. Zhang et al. https://doi.org/10.1016/j.coldregions.2025.104765
- A unified fractional-order model for soil infiltration X. Guo et al. https://doi.org/10.1016/j.jhydrol.2026.135443
- Two Film Approach to Continuum Scale Mixing and Dispersion with Equilibrium Bimolecular Reaction S. Mathias et al. https://doi.org/10.1007/s11242-024-02091-y
- A novel semi-numerical infiltration model combining conceptual and physically based approaches F. Stanić et al. https://doi.org/10.1016/j.jhydrol.2025.132664
- Why modified Picard works: Mass-conservative and higher-order time integration for the Richardson–Richards equation H. Bootsma et al. https://doi.org/10.1016/j.advwatres.2026.105327
- Dynamic modeling of grounding device impact characteristics considering coupling of river seepage, water velocity and current dispersion J. Li et al. https://doi.org/10.1007/s00202-023-02210-w
- Limitations of temporally linearized soil–water flux gradients in estimating root water uptake H. Fu et al. https://doi.org/10.1111/nph.70889
- Implementing a process-based representation of soil water movement in a second-generation dynamic vegetation model: application to dryland ecosystems (LPJ-GUESS-RE v1.0) W. Verbruggen et al. https://doi.org/10.5194/gmd-18-6623-2025
- MP-FVM: Enhancing finite volume method for water infiltration modeling in unsaturated soils via message-passing encoder-decoder network Z. Song & Z. Jiang https://doi.org/10.1016/j.compgeo.2025.107745
- Partitioning of flows in the unsaturated zone N. Krüger & C. Külls https://doi.org/10.1016/j.jhydrol.2024.132643
- An evaluation of the relationship between fingering flow fraction and water flux in natural field soil Y. Liu et al. https://doi.org/10.1016/j.jhydrol.2025.133783
- HydroCAL: A novel integrated surface–subsurface hydrological model based on the Cellular Automata paradigm L. Furnari et al. https://doi.org/10.1016/j.advwatres.2024.104623
- A multi-scenario multi-model analysis of regional climate projections in a Central–Eastern European agricultural region: assessing shallow groundwater table responses using an aggregated vertical hydrological model L. Koncsos & G. Murányi https://doi.org/10.1007/s13201-023-02097-9
17 citations as recorded by crossref.
- Revisiting Salvucci’s Semi-analytical Solution for Bare Soil Evaporation with New Consideration of Vapour Diffusion and Film Flow S. Mathias et al. https://doi.org/10.1007/s11242-023-01917-5
- Development of a modified Green–Ampt model considering the unsaturated zone Y. Li et al. https://doi.org/10.1016/j.biosystemseng.2025.104174
- Assessing simplified approaches in modeling rainfall-induced landslides using Richards' equation with Biot poroelasticity R. Abbasov et al. https://doi.org/10.1016/j.enggeo.2025.108481
- Heavy metals in unsaturated urban soils: Experimental insights and stochastic forecasting A. Dell'Oca et al. https://doi.org/10.1016/j.jconhyd.2026.104855
- Research on dynamic fitting models for road performance of self-melting ice surfaces and salt storage slow-release performance L. Zhang et al. https://doi.org/10.1016/j.coldregions.2025.104765
- A unified fractional-order model for soil infiltration X. Guo et al. https://doi.org/10.1016/j.jhydrol.2026.135443
- Two Film Approach to Continuum Scale Mixing and Dispersion with Equilibrium Bimolecular Reaction S. Mathias et al. https://doi.org/10.1007/s11242-024-02091-y
- A novel semi-numerical infiltration model combining conceptual and physically based approaches F. Stanić et al. https://doi.org/10.1016/j.jhydrol.2025.132664
- Why modified Picard works: Mass-conservative and higher-order time integration for the Richardson–Richards equation H. Bootsma et al. https://doi.org/10.1016/j.advwatres.2026.105327
- Dynamic modeling of grounding device impact characteristics considering coupling of river seepage, water velocity and current dispersion J. Li et al. https://doi.org/10.1007/s00202-023-02210-w
- Limitations of temporally linearized soil–water flux gradients in estimating root water uptake H. Fu et al. https://doi.org/10.1111/nph.70889
- Implementing a process-based representation of soil water movement in a second-generation dynamic vegetation model: application to dryland ecosystems (LPJ-GUESS-RE v1.0) W. Verbruggen et al. https://doi.org/10.5194/gmd-18-6623-2025
- MP-FVM: Enhancing finite volume method for water infiltration modeling in unsaturated soils via message-passing encoder-decoder network Z. Song & Z. Jiang https://doi.org/10.1016/j.compgeo.2025.107745
- Partitioning of flows in the unsaturated zone N. Krüger & C. Külls https://doi.org/10.1016/j.jhydrol.2024.132643
- An evaluation of the relationship between fingering flow fraction and water flux in natural field soil Y. Liu et al. https://doi.org/10.1016/j.jhydrol.2025.133783
- HydroCAL: A novel integrated surface–subsurface hydrological model based on the Cellular Automata paradigm L. Furnari et al. https://doi.org/10.1016/j.advwatres.2024.104623
- A multi-scenario multi-model analysis of regional climate projections in a Central–Eastern European agricultural region: assessing shallow groundwater table responses using an aggregated vertical hydrological model L. Koncsos & G. Murányi https://doi.org/10.1007/s13201-023-02097-9
Saved (final revised paper)
Latest update: 15 Jun 2026
Short summary
Richards' equation (RE) is used to describe the movement and storage of water in a soil profile and is a component of many hydrological and earth-system models. Solving RE numerically is challenging due to the non-linearities in the properties. Here, we present a simple but effective and mass-conservative solution to solving RE, which is ideal for teaching/learning purposes but also useful in prototype models that are used to explore alternative process representations.
Richards' equation (RE) is used to describe the movement and storage of water in a soil profile...
