School of Mathematical Sciences

Water projects

A list of currently available water projects within the MASS doctoral training centre. For queries in relation to a particular project, please contact the supervisors associated with that project. Click on a project name to view more details below.

Multi-scale modelling of flow through heterogeneous geo-materials

Supervisors: Dr Kris van der Zee (Mathematical Sciences), Dr Xia Li (Engineering)

Permeability of geomaterials is critical in predicting pollutant contamination and nitriation transport in groundwater. However, geo-materials are often heterogenous. The micro-defects and rock fractures provide channels for rapid groundwater flow, and consequently, the effective in-situ permeability could be larger than the lab measurement by several orders of magnitude.

This research will develop mathematical models to simulate the groundwater flow through heterogeneous geo-materials and the multi-scale homogenisation techniques that connects the field-scale permeability to intact rock properties and the statistics of micro-defects and fractures. The findings will inform and support effect groundwater management.


Dynamic socio-hydrology modelling: mathematical approaches for adaptive co-evolution

Supervisors: Dr Nick Mount (Geography), Prof Markus Owen (Mathematical Sciences)

Socio-hydrology is an emerging focus of hydrological science that views social and hydrological systems as co-evolutionary, governed by an array of complex feedbacks.  The International Association of Hydrological Sciences (IAHS) decadal Science Plan (2013-2023) asserts that the most pressing challenges associated with water resources globally (e.g. resilience to drought and flood, adequate water availability and quality) can only be properly addressed if the co-evolution of the socio-hydrologic system can be adequately represented and understood.  A key challenge facing those tasked with managing the world’s water resources is to develop a new modelling paradigm that moves away from isolated representation of the physical, hydrologic system towards a fully coupled representation of both social and hydrologic systems.

Preliminary attempts to do this have focussed on the issue of flooding and have progressed using relatively simple mathematical models built on differential equations.  These models seek to describe the co-evolution of hydrologic (flood height), technologic (flood defence infrastructure), societal (risk awareness), economic (wealth and defence funding) and political (planning policy) variables. These models have been very useful in revealing the likely influence of socio-hydrologic phenomena such as ‘collective flood memory’ on a community’s overall flood risk and in projecting the role that social behaviour might have on flood risk under a changing climate. However, the static nature of existing socio-hydrologic models limits their capacity to represent critical, dynamic co-evolutionary processes.  We know that major ‘shocks’ to the hydrologic and/or socio-economic sub-systems often change the rules by which the whole system co-evolves. Examples of such shocks include large shifts in the course of a river (e.g. the course of the Kosi River in India has shifted by 120 km in the last 250 years), and wholesale changes to the governance of flood risk management (e.g. following the UK summer floods of 2007).

The objective of this PhD is to advance the field of socio-hydrology by developing mathematical approaches to support adaptive causal pathways in socio-hydrologic modelling.  It will examine the potential of alternative approaches to delivering adaptive model structures (e.g. model switching and dynamic causal models) as well as methods for supporting dynamic parameter adjustment.  It is anticipated that, initially, the project will build upon existing examples of socio-hydrologic models of flood risk.  However, it is expected that the successful candidate will wish to expand the application domain to include alternative socio-hydrologic phenomena such as irrigated agriculture models.


Mechanical modelling of the stability of Earth's peatland carbon reservoirs

Supervisors: Dr David Large (Chemical & Environmental Engineering), Dr Matthew Hubbard (Mathematical Sciences), Dr Donald Brown (Mathematical Sciences), Dr Bagus Muljadi (Chemical & Environmental Engineering), Professor Neil Crout (Biosiences).

The project involves the development of mechanical models of peatland growth and restoration. Peat is a soft multiphase (solid, liquid, gas) material that stores 1/3 of earth’s terrestrial carbon. Current models combine mass balance and hydrology but none consider the mechanical stability of the peat.  This is a huge oversight as the extremely weak multiphase peat body should deform with ease and this deformation must influence gas emissions and long term stability. The project will develop novel numerical models of peat growth and the mechanical response of peat to the changes in loading, mass balance and hydrology. The student will have the opportunity to visit peatlands in the UK and Malaysia and to link their work to geospatial observations.


School of Mathematical Sciences

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