Mathematical modelling of evaporation from sand rivers in Botswana


Prolonged droughts, made worse by climate change, continue to threaten food and water security in dryland Africa. Innovative solutions are required to increase sustainability of water resources (Byakatonda et al., 2018). Sand rivers are an overlooked resource in this context (Walker et al., 2018). During wet seasons, flash floods run through ephemeral rivers and recharge underlying sand aquifers. Farmers exploit this water in the dry season using hand dug wells. However, such activity is sparse due to the low levels of water stored (Quinn et al., 2019). A simple idea to increase water availability is to construct small gabion check dams to slow flows from flash floods and enable more water to infiltrate underlying aquifers (Agoramoorthy et al., 2016). Storing water in aquifers is more effective than storing in surface water reservoirs due to significant reductions in evaporative losses (Hellwig, 1973; Agoramoorthy et al., 2016; Quinn et al., 2019).

Mathematical models can assist in the design of such systems, creating improved confidence and likelihood of funding from international agencies. However, there remains considerable uncertainty about an appropriate level of physical complexity that should be represented when simulating evaporation reductions due to water storage in shallow aquifer systems (Li et al., 2019). Relevant physical processes include land surface energy budget, multi-phase flow in porous media and heat conservation (Vanderborght et al., 2017). Specific areas of uncertainty include how to represent soils at moisture limiting conditions (Ciocca et al., 2014) and how to characterise boundary conditions at the land-surface interface (Smits et al., 2012).

This PhD involves developing a set of numerical modelling tools to describe the process of water evaporation from the Metsimotlhaba sand river in Botswana. The project forms a component of a larger interdisciplinary research project currently in progress at Durham University and the University of Botswana, looking at “Improving water availability for female headed horticultural projects in African drylands using enhanced aquifer recharge in sand rivers”. The project represents a chance to develop a new modelling package for non-isothermal multiphase flow in porous media. The model will be verified by conditioning to experimental data from the literature (e.g., Hellwig, 1973; Quinn et al., 2018; Li et al., 2019). Finally the model will be used to help assess the feasibility of increasing water availability using check dams in Botswana.

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Image Captions

The Metsimotlhaba sand river in Botswana.


The student will attend a fieldtrip along the Metsimotlhaba sand river in Botswana to learn more about arid zone hydrology and water management issues of concern. The student will develop a multi-physics numerical modelling tool using MATLAB, finite elements and ODE solvers. The student will develop models of sequentially increasing physical complexity ultimately leading to a non-isothermal two-phase and two-component flow model in porous media to describe transient evaporation processes. The student will verify the models by reproducing simulation and experimental scenarios from the literature. Finally, the student will incorporate hydro-meteorological field observations from Botswana to forecast the efficacy of check-dams to increase water availability in this context.

Project Timeline

Year 1

Attend fieldtrip in Botswana.
Assemble experimental data base from the literature.
Develop numerical model for isothermal two-phase flow.

Year 2

Develop numerical model for non-isothermal two-component flow.
Benchmark and condition model to data from literature.

Year 3

Acquire hydro-meteorological data from Botswana.
Perform simulations to explore check-dam efficacy.

Year 3.5

Write up and complete PhD thesis.

& Skills

The student will receive significant training in MATLAB programming, partial differential equations, finite element methods, application of thermodynamics, hydrological modelling, uncertainty analysis and working with interdisciplinary teams.

References & further reading

Agoramoorthy, G., Chaudhary, S., Chinnasamy, P., & Hsu, M. J. (2016). Harvesting river water through small dams promote positive environmental impact. Environmental Monitoring and Assessment, 188(11), 645.

Byakatonda, J., Parida, B. P., Kenabatho, P. K., & Moalafhi, D. B. (2018). Influence of climate variability and length of rainy season on crop yields in semiarid Botswana. Agricultural and forest meteorology, 248, 130-144.

Ciocca, F., Lunati, I., & Parlange, M. B. (2014). Effects of the water retention curve on evaporation from arid soils. Geophysical Research Letters, 41(9), 3110-3116.

Hellwig, D. H. R. (1973). Evaporation of water from sand, 4: The influence of the depth of the water-table and the particle size distribution of the sand. Journal of Hydrology, 18(3-4), 317-327.

Li, Z., Vanderborght, J., & Smits, K. M. (2019). Evaluation of model concepts to describe water transport in shallow subsurface soil and across the soil-air interface. Transport in Porous Media, 128(3), 945-976.

Quinn, R., Parker, A., & Rushton, K. (2018). Evaporation from bare soil: Lysimeter experiments in sand dams interpreted using conceptual and numerical models. Journal of hydrology, 564, 909-915.

Quinn, R., Rushton, K., & Parker, A. (2019). An examination of the hydrological system of a sand dam during the dry season leading to water balances. Journal of Hydrology X, 100035.

Smits, K. M., Ngo, V. V., Cihan, A., Sakaki, T., & Illangasekare, T. H. (2012). An evaluation of models of bare soil evaporation formulated with different land surface boundary conditions and assumptions. Water Resources Research, 48(12), W12526.

Vanderborght, J., Fetzer, T., Mosthaf, K., Smits, K. M., & Helmig, R. (2017). Heat and water transport in soils and across the soil‐atmosphere interface: 1. Theory and different model concepts. Water Resources Research, 53(2), 1057-1079.

Walker, D., Jovanovic, N., Bugan, R., Abiye, T., du Preez, D., Parkin, G., & Gowing, J. (2018). Alluvial aquifer characterisation and resource assessment of the Molototsi sand river, Limpopo, South Africa. Journal of Hydrology: Regional Studies, 19, 177-192.

Further Information

Contact Prof Simon Mathias by email

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