The global ocean is populated by a vigorous and dynamic eddy field. This eddy field has a significant impact on the wider structure of the ocean circulation, but it is computationally extremely expensive to resolve directly. While recent simulations have allowed for direct eddy resolving calculations to be performed, equilibrated eddy resolving calculations are unlikely to become routine at any point in the near future. There therefore remains an urgent need for eddy parameterisation schemes, which aim to capture the aggregated effects of the eddy field in coarse resolution numerical models. The development of ocean eddy closures remains a formidable challenge. However, one can apply fundamental principles in order to rule out eddy closures which lead to unphysical behaviour. For example, the eddies require energy in order to mix ocean properties, and must observe the principle of conservation of momentum. A somewhat more subtle property is that ocean eddies must, on average, mix out gradients in the fluid potential vorticity. Eddy parameterisations which fail to observe these constraints can be ruled out as a possible solution for the underlying eddy dynamics. A particularly important challenge for ocean eddy parameterisations is the accurate reproduction of ocean sensitivities to forcing changes. These responses have implications for the long term ocean response to climate change. Recent studies indicate that the Southern Ocean may exhibit reduced responses to wind forcing changes when the influence of the eddies is well sufficiently resolved. Coarse resolution models, which parameterise the eddies and do not resolve them directly, often give wildly incorrect predictions for the ocean responses. This study proposes the implementation of a suite of new and existing ocean eddy parameterisations. The parameterisations are to be implemented in a simplified context (in a "quasi-geostrophic" model), and then in a full ocean circulation model. This research has three key novel aspects. First, optimisation techniques will be employed in order to assess the performance of the closures in the simplified quasi-geostrophic case. These techniques can be used to identify the best possible configuration of a given eddy parameterisation scheme, enabling the best-case performance of the scheme to be rigorously identified. This will provide a robust comparison of a broad range of possible approaches for eddy parameterisation. Secondly, the research aims to impose the three physical principles, imposed by energetic constraints, momentum conservation, and the need to mix potential vorticity, simultaneously. Thirdly, the research will investigate the performance of a broad range of parameterisations in determining the ocean sensitivity to wind forcing changes. Particularly important questions to be addressed are: How important are the fundamental physical constraints in controlling the ocean eddy dynamics? Can the restoration of these constraints in ocean eddy parameterisation schemes lead to improved coarse resolution simulations?

Effective prediction, for example of project cost, is an essential aspect of software engineering. Although considerable research has been devoted to this topic, the role of human experts has been under-emphasised. Our aim is to investigate the impact of enhanced metacognitive awareness on prediction and confidence (uncertainty assessment) to improve the prediction practices of software professionals. This will be accomplished by developing metacognitive awareness during a series of experiments with software professionals as participants. The major outcomes will be a better understanding of (i) the factors that influence prediction and uncertainty assessment skills and (ii) how industry practice can be enhanced. The findings will impact the software industry, its clients and other sectors where accurate predictions are required in uncertain environments.

Optimisation problems appear across all areas of engineering. Optimisation consists of maximising the performance or minimising the cost of a system, subject to some constraints. For example, an aeronautical engineer will want to choose the best shape for a wing to maximise its efficiency, subject to the constraint that the wing will lift the aircraft, while a civil engineer will want to design the cheapest bridge that will support its load. An important class of optimisation problems is where the constraint is given by the laws of physics, such as the physical laws for fluids (in the wing case) and structures (in the bridge case). These problems can be very hard, and usually require massive supercomputers to solve them. A significant amount of mathematical research has gone into investigating techniques for solving them. Engineers currently face a major practical difficulty when trying to solve new kinds of such optimisation problems. The software required to solve these is very intricate, and often takes months or years to develop. This poses a very formidable barrier. This matters a lot, because these problems appear everywhere in engineering, and if we could solve them then we could design many things in a better way. I propose to do this by developing a software framework to generate optimisation codes, rather than have engineers develop them by hand. While the optimisation software is very complex, it has a compact mathematical structure: I propose to generate the optimisation software from a simple high-level description of this mathematical structure. By generating the necessary software, engineers can spend their time on using it to solve real problems. This framework will provide engineers with the necessary optimisaton software in days or weeks instead of months or years. Generating the optimisation codes from simple high-level input has another major advantage. The high-performance supercomputers necessary to solve these optimisation problems are extremely difficult to program efficiently, and are changing rapidly. Code must be tailored for a particular hardware architecture. As each new kind of computing platform comes out, an engineer must adapt the code. Instead, with my new approach, the engineer can simply re-generate the code from the same mathematical input, and the framework will specialise the code to best exploit the different platform. By updating the framework once, many engineers working on many different codes in many different areas can benefit quickly from advances in computational hardware. I will apply the software developed to two important engineering problems. The first engineering problem is found in the design of marine turbine farms for renewable energy. Marine renewable energy is very important to the UK. The government predicts that the industry will be worth £76 billion to the UK economy by 2050. A major problem facing the industry is how to position the turbines to extract the maximum possible energy from the tide. Choosing the best design is very important, as it can greatly change the efficiency. Solving this problem will directly contribute to the UK's energy security and carbon reduction goals. The second engineering problem is identifying regions of the heart that are damaged (ischaemic). Ischaemic heart disease is the most common cause of death in Western countries. When a doctor suspects that a patient has ischaemia, it would be very beneficial to know its location and extent. One possible approach to rapidly identify ischaemia is to extract information from electrocardiograms (ECGs). The optimisation problem is to identify the ischaemia that best explains the ECG measured from the patient. Solving this problem will directly contribute to better healthcare decisions, reducing the mortality rate and improving the long-term prognosis of survivors.

Many aspects of physics can be described by mathematical equations, for example, the motion of water in the sea, the expansion and contraction of metal as it is heated and cooled, or the flow of electricity in a radio antenna. Scientists write these equations using mathematical symbols. However, when we wish to model a specific problem with a computer, for example the thermal expansion of a particular engine part, there are several practical things which we need to do. Firstly, we need to be able to describe the shape of the engine part accurately. Usually, the shape can be described by a simple mesh (for example, any two-dimensional shape can be divided into triangles, and three-dimensional shapes can be divided into triangular pyramids, known as tetrahedra). By dividing the complex shape into smaller, simpler shapes the equations can be solved more easily. Secondly, and most importantly, the mathematical equations describing the physics need to be converted to a form the computer can understand. In the past, this has been a tedious task for programmers, but in the FEniCS scientific software library (fenicsproject.org), this has been made much easier by translating from a mathematical language, similar to the equations, directly into computer code. Along with some additional information about the mesh, and the external conditions (e.g. in the example above, the source of heat), a full model can be computed and the results can be plotted and analysed. Not all simulations are so straightforward. For example, the equations for air bubbles moving through water would contain terms for surface tension. Surface tension is sensitive to the curvature of the mesh surface, but a mesh made of triangles always has a flat, faceted surface. In a simulation, as the bubbles move, the mesh would also need to be distorted to take account of the new position of the bubbles. In another context, for noise emitted from jet engines, the equations may require complex numbers, or be highly non-linear. In both of these cases, the computer code needs to be written to take care of the specific issue. Scientists would like to make computer simulations without having to worry about the complexities of programming these details. In this project, I am addressing five main issues: complex numbers, curved surfaces, difficult non-linear problems, mesh deformation, and mesh formats. The FEniCS software framework will be extended to allow users to have access to these features without having to program them directly themselves. It will open up new areas of research, for example in surface tension and liquid-gas interaction, multiphase flow, acoustics, quantum mechanics, and stability analysis, as well as making the software more accessible on HPC platforms. Software developments alone are not enough to drive forward scientific and engineering advances. Another important aspect of this project is to engage with application scientists and help them to get the most out of software libraries, understand their scientific problem, and help them translate it into computer code. I will provide training, in association with EPSRC doctoral training centres, to use the new software developments at large scale, including on supercomputers. Software maintenance is another important aspect of any scientific project, and I will encourage the next generation of scientists to use modern techniques of version control and automatic testing, which will enhance the quality of their software projects, and improve their longevity.

The coastal zone plays a crucial part in addressing two of the most pressing issues facing humanity: energy supply and water resources. Marine renewable energy and desalination are both characterised by the deployment of relatively small-scale technology (for example, tidal turbines, or desalination plant outfalls) in large-scale ocean flows. Understanding the multi-scale interactions between sub-metre scale installations and ocean currents over tens of kilometres is crucial for assessing environmental impacts, and for optimisation to minimise project costs or maximise profits. The vast range of scales and physical processes involved, and the need to optimise complex coupled systems, represent highly daunting software development and computational challenges. Geographically, the UK is uniquely positioned to become a world leader in marine renewable energy, but adequate software will be a key factor in determining the success of this new industry. To address this need, this project will re-engineer a unique CFD to marine scale modelling package to provide performance-portability, future-proofing and substantially increased capabilities. To motivate this we will target two applications: renewable energy generation via tidal turbine arrays and dense water discharge from desalination plants. Both are characterised by a common wide range of spatial and temporal scales, the need for design optimisation and accurate impact assessments, and a current lack of the required software. This project will build upon several world-leading open source software projects from the assembled multi-disciplinary research team. This team already has a long and successful track record of working together on the development of high quality open source software which is able to exploit large-scale high performance computing and has been used widely in academia and industry. In addition, the project has assembled a wide range of suitable project partners to aid in the delivery of the project as well as to promote longer term impact. These include complementary centres of excellence in cutting-edge software development, industry leaders in the targeted application areas, marine consultancies, and those contributing to environmental regulation.