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Uncertainty quantification in hydro-environmental systems models

   School of Engineering

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  Dr A Angeloudis, Prof Lindsay Beevers, Dr A Wilson, Dr Brian Sellar  No more applications being accepted  Competition Funded PhD Project (Students Worldwide)

About the Project


This project seeks to establish generalised strategies to quantify uncertainty in hydro-environmental modelling that is closely linked to the underlying flow hydrodynamics.

This is part of the E4 Doctoral Training Partnership programme based at the University of Edinburgh with the project description and details to apply documented here.

Project background

This project will investigate the sources of uncertainty inherent in riverine, limnological and coastal systems models and will explore statistical approaches for modelling these uncertainties. Methods for calibrating the models against real-world datasets that account for these uncertainties as well as the spatial nature of the models will be developed. The premise of this work regards hydrodynamic modelling at regional scales which has a multitude of applications. The work is motivated by recent projects by the supervisory team on marine energy resource quantification, but is formulated to be extensible given methodological commonalities. Particular examples regard flood risk when presented by uncertain climate trends. Beginning with marine energy, we consider tidal stream energy, which is a natural resource that can deliver major benefits to UK infrastructure as it strives to achieve its low-carbon goals. The UK offers geomorphological characteristics that amplify the available tidal energy resources, yielding some of the most pronounced sustainable energy sources worldwide. As an example, estimates for the size of the tidal stream resource at sites such as the Pentland Firth, Scotland, vary over a wide range (1 GW mean – 18 GW peak) depending on assumptions about environmental conditions, the fraction of flow which can be swept by turbine blades, flow losses, and the flow source impedance. These uncertainties hinder investment to marine renewables. Similar considerations underpin compound flood models that need to reconcile uncertain inputs from riverine and coastal flow observations alongside uncertain parameters that form the basis of the geometric representation. These parameters can lead to deviations in the order of 10s of cm that may easily compromise adaptation measures and population displacement strategies to defend our infrastructure. Effectively, the project targets the delivery of strategies to minimise uncertainty associated with hydrodynamic predictions by optimising model configuration to balance accuracy with computational efficiency.

Research questions

  1. How sensitive are the hydrodynamic model outputs to riverine and marine environment characteristics (geometry, geomorphology)?
  2. How should the main uncertainties be modelled to enhance reliability of hydro-environmental modelling?
  3. How should the key parameters in the models (e.g. mesh parameters) be calibrated to balance computation time with accuracy?
  4. How can the statistical approaches developed be used to improve decision-making in practice?


The project will build on recent hydrodynamic modelling tools (e.g. Thetis, and a preliminary investigation into the use of statistical approaches for modelling uncertainties in marine energy models (e.g. FASTWATER). The project hydrodynamic model applications have been demonstrated for marine energy, sediment transport, tsunami propagation (i.e. coastal flood modelling) and water quality.

  1. Review of literature on shallow-water equation processes and on statistical approaches for uncertainty quantification and calibration - [Months 1-4]
  2. Development of a numerical flow model representative of environmental flow conditions, identifying key uncertain parameters. Examples include riverine flow reaches (quasi-1-D), estuarine or tidal setups (2-D and 3-D) of both idealised and realistic case studies - [Months 4-12]
  3. Develop statistical methodology (e.g. Bayesian emulation) for modelling the impact of the key uncertainties on model outputs and develop a framework to help stakeholders use this uncertainty quantification to take better decisions (e.g. choosing where to take real-world measurements to improve the models) - [Months 12-24]
  4. Explore new methods for calibrating key parameters for underlying model efficiency. For example, this might include the development of an automated procedure for choosing mesh parameters that also captures the key modelling uncertainties previously identified - [Months 24-30]
  5. Examine the value of model down-scaling techniques e.g. Multi-level Monte Carlo (MLMC) models to reduce computational burden of brute-force iterative methods, while preserving uncertainty margins. - [Months 30-36]
  6. Dissemination of findings, aiming for 2 journal and 2 conference papers spanning idealised, methodological and practical research findings as per the preceding steps. [Months 12-36]
  7. Write-up of PhD thesis. [Months 37-42]


A comprehensive training programme will be provided comprising both specialist scientific training and generic transferable and professional skills. The candidate may choose to attend lectures on unsteady flows at the University of Edinburgh. The student will also be encouraged to attend courses on digital mapping given by EDINA and the use of HPC facilities provided by the University of Edinburgh. The School of Engineering requires all its doctoral students to attend a compulsory Health and Safety course, and to undergo training in research methods provided through the University's Postgraduate Transferable Skills

Programme. The latter includes the Institute of Academic Development courses on Communication (including effective writing, conference preparation, writing a literature review, and writing for publication), Professional Development (including time management and goal setting), IT, and Research Planning (including finding academic literature, how to be an effective researcher, managing your own research project, a PhD thesis writing workshop, practical project management, and presenting made easy.) As part of the School of Mathematics the student will be encouraged to attend Statistics seminars and will be supported to attend the Academy for PhD Training in Statistics (APTS) courses.


Candidates should have at least an upper second class degree in Engineering, Mathematics, Physics, or Oceanography, possibly but not necessarily supported by an MSc Degree in a relevant discipline. 

An interest in modern programming techniques (using Python, Matlab, C or FORTRAN) is desirable.


A. L. Baker, R. M. Craighead, E. J. Jarvis, H. C. Stenton, A. Angeloudis, L. Mackie, A. Avdis, M. D. Piggott, and J. Hill. “Modelling the impact of tidal range energy on species communities”. Ocean & Coastal Management 193 (2020), p. 105221. doi: 105221.
S. C. Warder, A. Angeloudis, and M. D. Piggott. “Sedimentological data-driven bottom friction parameter estimation in modelling Bristol Channel tidal dynamics”. Ocean Dynamics 72.6 (2022), pp. 361–382
D. J. Wagenaar , K. M. De Bruijn, L. M. Bouwer, and H. De Moel(2016). "Uncertainty in flood damage estimates and its potential effect on investment decisions. Natural Hazards and Earth System Sciences, 16(1), 1-14.
M. Kreitmair, S. Draper, A. G. Borthwick, and T. S. van den Bremer. “The effect of uncertain bottom friction on estimates of tidal current power”. Royal Society open science 6.1 (2019), p. 180941.
I Vernon, M Goldstein, and R. G. Bower. “Galaxy formation : a Bayesian uncertainty analysis.” Bayesian Analysis 5.4 (2010), pp. 619 –670.

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