Aberdeen University Featured PhD Programmes
National University of Ireland, Galway Featured PhD Programmes
University of Kent Featured PhD Programmes
University of Huddersfield Featured PhD Programmes
University of Leeds Featured PhD Programmes

Novel physical and numerical methods for simulating water and heat transfer in land surface models.

Project Description

Meteorological offices worldwide, including the UK Met Office (UKMO), have come to realise that improved land surface modelling is critical for providing better forecasts within a changing climate, for example for flood and drought prediction. This requires a paradigm change in the way that the terrestrial water cycle is represented in these models. Recent attention has focussed on adopting novel approaches from hydrological models. Land surface models, such as UKMO’s Joint UK Land Environment Simulator (JULES), simulate the soil hydrology through a numerical form of the one-dimensional partial differential equation (PDE) attributed to Richards that describes unsaturated flow in soils. Conventional solution methods to this highly non-linear equation inevitably lead to numerical and accuracy issues, which impact on their hydrological performance.

This NERC Industrial CASE studentship in association with the UKMO and Prof. Ogden concerns the implementation and testing of two relatively new 1-D unsaturated zone flow solution methods (Ogden et al., 2015; Lee, Baines and Langdon, 2015) into JULES. The Ogden Soil Moisture Velocity Equation (SMVE) approach uses the hodograph method to transform Richards equation into a differential equation for a velocity while the Baines approach (CMF) generates a velocity directly from Richards equation but using local mass conservation instead. The SMVE method employs a discretisation of the resulting equation in the form of ‘bins’ containing values of the water content, while in the CMF discretisation the corresponding moving intervals contain constant masses.

Each of the resulting systems is approximated using the method of lines with the time stepping carried out by the first order explicit Euler scheme, yielding an approximation to the water content profile in each case. The two schemes are computationally efficient: although the explicit time steps are limited by stability considerations there are no convergence limits as imposed by implicit schemes.

The Ogden paper considers the transport of three regimes of soil moisture in detail, namely infiltration, wetting fronts disconnected from the surface, and groundwater recharge.
The SMVE method offers accuracy comparable to, or in some cases exceeding, that of the Richards PDE numerical solution, but without the numerical complexity and in a form that is robust, continuous, and suitable for use in models of coupled climate and hydrology at a range of scales. The CMF method is more general in nature and needs further specific development hydrologically. Both methods accept boundary fluxes including arbitrary precipitation, bare soil evaporation, and evapotranspiration.

The two approaches consider only water transport and do not solve the thermal processes in the soil, including coupled heat- and water transfer, which is required for representing the phase changes of soil moisture, e.g. to simulate freeze-thaw. Thus, the student will extend both approaches to include a heat ‘bin’ and local heat conservation approach, respectively.

The intellectual challenge will be to derive a consistent method for coupling water and heat transport within the soil, but without degrading the hydrological performance of the scheme. Furthermore, the student will demonstrate the impact of this new scheme, compared to the original JULES model, for hydrological components within both the UK Environmental Prediction (UKEP) model and for the UK Earth System Model (UKEMS).

The studentship offers an outstanding opportunity to apply mathematical and computational modelling to a real problem of considerable practical interest, comparing the two simulation methods with each other and with results from JULES, as well as visiting the UKMO to work with JULES and the possible involvement in field work. This is a challenging but potentially considerably rewarding studentship.

Funding Notes

This project is funded by NERC (Industrial CASE). Normally to be eligible for a full award a student must have no restrictions on how long they can stay in the UK and have been ordinarily resident in the UK for at least 3 years prior to the start of the studentship (with some further constraint regarding residence for education). For further information regarding residence requirements, please see :
View Website

Applicants should hold or expect to gain a minimum of a 2:1 Bachelor degree or equivalent in Mathematics, Computer Science or suitable Physical Science.


Ogden, F. L. et al (2015), A new general 1-D vadose zone flow solution method, Water Resour. Res., 51, 4282–4300. (See also Ogden. F. L. et al (2017), The soil moisture velocity equation. Journal of Advances in Modelling Earth Systems, doi 10.1002/2017MS000931)

Lee, T. E., Baines, M. J. and Langdon, S. (2015), A finite difference moving mesh method based on conservation for moving boundary problems. Journal of Computational and Applied Mathematics, 288. pp. 1-17. (See also Main, B. (2011),

Email Now

Insert previous message below for editing? 
You haven’t included a message. Providing a specific message means universities will take your enquiry more seriously and helps them provide the information you need.
Why not add a message here
* required field
Send a copy to me for my own records.

Your enquiry has been emailed successfully

FindAPhD. Copyright 2005-2019
All rights reserved.