Developing scientific software, for example for climate modeling or medical research, is a highly challenging task. Domain scientists are often deeply involved in low-level programming details just to make their code run sufficiently fast. These tedious, but important, optimization steps significantly reduce the productivity of scientists. Domain specific languages (DSLs) revolutionize the productivity of domain scientists by enabling them to focus on scientific questions rather than making their code run fast. Sophisticated DSL compilers automatically generate high-performance code from domain-specific high-level problem descriptions. While there are individual successes, the existing landscape of DSLs is scattered and the reuse of software components in DSL compiler implementations is limited as traditionally DSL compilers are built in isolation. This results in high development costs of new DSLs and prevents many DSLs from ever achieving a level of maturity and sustainability that enables uptake by the scientific community. This project revolutionizes the design of DSL compiler implementations by leveraging the breadth and cross-industry support of the MLIR compiler and Python ecosystems. Python is the tool of choice for application developers in many domains, such as machine learning, data science, and - we believe - an important component of the future of High Performance Computing software. This project establishes MLIR as a common representation for code at multiple levels of abstraction in DSL compiler development. DSLs embedded in various host languages, including Python and Fortran, will be easily built on top of MLIR. Instead of building DSL compilers as isolated monolithic towers, our research will build a toolbox that enables developers to build DSLs using a rich ecosystem of shared intermediate representations IRs and optimizations. This project evaluates, drives, and demonstrates the DSL design toolbox to build the next generation of DSLs for Seismic and Climate Modelling as well as Medical imaging. These will share common software components and make them available for other DSLs. An extensive evaluation will show the scalability of DSL software towards exascale. Finally, this project investigates how future disruptors, including artificial intelligence, data science, and on-demand HPC-as-a-service, will shape and influence the next generations of high performance software. This project will work towards deeply integrating modern interactive data analytics and machine learning methods from the Python ecosystem with high-performance scientific code.

If CO2 emissions continue to rise, climate change will adversely affect global food and water availability, ecosystems, cities, and coastal communities. While reduction of fossil fuels will be an essential step for reducing atmospheric CO2, Negative Emission Technologies (NETs) can help meet emission targets. During combustion, CO2 can be extracted, transported, and stored in geologic repositories - this is the process of Carbon Capture and Storage (CCS). Combining bioenergy with CCS (BECCS) could result in negative emissions of CO2. BECCS is attractive since it results in a net removal of CO2 from the atmosphere while also providing a renewable source of energy. However, BECCS requires a large commitment of land and will have impacts on food and water availability. This work focuses on BECCS and addresses the challenges for planning a global and nationwide distribution of bioenergy crops. The vast majority of IPCC scenarios that remain below 2 degrees C makes use of NET in the 21st century. Although bioenergy crops and BECCS are an essential component of the scenarios (produced by Integrated Assessment Models, or IAMs), the crops in even the most sophisticated IAMs only respond to mean changes in climate. This results in an inconsistency in the modelling framework: the IAMs can assume bioenergy crops are effective at drawing down CO2 and producing energy in a region where actually climate change will reduce their effectiveness. Earth System Models (ESMs) represent the dynamics of the atmosphere, oceans, sea ice, and land surface. They can account for biophysical (i.e. changes to albedo and latent heat fluxes) and biogeochemical (i.e. uptake or release of greenhouse gases) feedbacks due to land use change. They are the only tool available to investigate future impacts of spatial and temporal variability in climate on the food, energy, and water nexus. However, the ESMs used in the last IPCC report only accounted for a generic crop type at best, not differentiating between bioenergy and food crops. Without an explicit representation of bioenergy crops in ESMs, the effects of climate change do not feedback to affect the food, energy, and water resources assumed to be true in the IAMs. There is an urgent need for predicting the productivity of bioenergy crops in a coupled climate simulation, to see the impact of a range of climate change on the productivity, and associated impacts on food crop productivity, energy production, and water availability. In this project, I will include representations of first and second generation bioenergy crops in the UK ESM, and investigate the impacts of climate change on the productivity at the global and regional (for the UK) level. This work will assess the viability of negative emissions of CO2 through bioenergy crops as an effective climate mitigation strategy under a changing climate, and provide data to support decisions that will minimize the impacts of both climate change and climate change mitigation on bioenergy production, food, and water availability. The outcomes of this project will enhance the resilience of the food/water/energy nexus to climate change and climate variability through better planning, and providing socially responsible recommendations for balancing the challenges of reducing climate change with feeding our growing global population.

Anthropogenic disturbance and land-use change in the tropics is leading to irrevocable changes in biodiversity and substantial shifts in ecosystem biogeochemistry. Yet, we still have a poor understanding of how human-driven changes in biodiversity feed back to alter biogeochemical processes. This knowledge gap substantially restricts our ability to model and predict the response of tropical ecosystems to current and future environmental change. There are a number of critical challenges to our understanding of how changes in biodiversity may alter ecosystem processes in the tropics; namely: (i) how the high taxonomic diversity of the tropics is linked to ecosystem functioning, (ii) how changes in the interactions among trophic levels and taxonomic groups following disturbance impacts upon functional diversity and biogeochemistry, and (iii) how plot-level measurements can be used to scale to whole landscapes. We have formed a consortium to address these critical challenges to launch a large-scale, replicated, and fully integrated study that brings together a multi-disciplinary team with the skills and expertise to study the necessary taxonomic and trophic groups, different biogeochemical processes, and the complex interactions amongst them. To understand and quantify the effects of land-use change on the activity of focal biodiversity groups and how this impacts biogeochemistry, we will: (i) analyse pre-existing data on distributions of focal biodiversity groups; (ii) sample the landscape-scale treatments at the Stability of Altered Forest Ecosystems (SAFE) Project site (treatments include forest degradation, fragmentation, oil palm conversion) and key auxiliary sites (Maliau Basin - old growth on infertile soils, Lambir Hills - old growth on fertile soils, Sabah Biodiversity Experiment - rehabilitated forest, INFAPRO-FACE - rehabilitated forest); and (iii) implement new experiments that manipulate key components of biodiversity and pathways of belowground carbon flux. The manipulations will focus on trees and lianas, mycorrhizal fungi, termites and ants, because these organisms are the likely agents of change for biogeochemical cycling in human-modified tropical forests. We will use a combination of cutting-edge techniques to test how these target groups of organisms interact each other to affect biogeochemical cycling. We will additionally collate and analyse archived data on other taxa, including vertebrates of conservation concern. The key unifying concept is the recognition that so-called 'functional traits' play a key role in linking taxonomic diversity to ecosystem function. We will focus on identifying key functional traits associated with plants, and how they vary in abundance along the disturbance gradient at SAFE. In particular, we propose that leaf functional traits (e.g. physical and chemical recalcitrance, nitrogen content, etc.) play a pivotal role in determining key ecosystem processes and also strongly influence atmospheric composition. Critically, cutting-edge airborne remote sensing techniques suggest it is possible to map leaf functional traits, chemistry and physiology at landscape-scales, and so we will use these novel airborne methods to quantify landscape-scale patterns of forest degradation, canopy structure, biogeochemical cycling and tree distributions. Process-based mathematical models will then be linked to the remote sensing imagery and ground-based measurements of functional diversity and biogeochemical cycling to upscale our findings over disturbance gradients.

Our environment has a major influence on all aspects of human endeavour ranging from the mundane, such as deciding whether to cycle or take the bus to work, to the exceptional, such as coping with the ever more damaging effects of extreme natural phenomena (tropical storms, inundations, tsunamis, droughts, etc.). In addition, climate change is one of the most pressing challenges that confront humanity today. What was once viewed as something that might happen in the future is now part of daily life. Because most impacts of climate variability and change occur through extreme weather events and spells, the two issues of weather and climate are closely interlinked. We rely on science and technology to provide the means of managing the complex intricacies of the environment and to meet the pressing challenges of climate change. Mathematics plays a central role in this massive undertaking as it provides the fundamental basis of the theory and modelling of weather, oceans and climate. However the nature of the mathematical challenges is changing and the need for scientists trained in risk and uncertainty is growing rapidly. Meeting these needs can only be achieved by training an entirely new generation of scientists to meet the multi-faceted challenges, with all their complex inter-dependencies. These scientists will need extraordinarily broad training in several scientific areas, including geophysical fluid dynamics, scientific computing, statistics, data assimilation and partial differential equations. Above all, they must understand the mathematics that unifies them. The alignment of Imperial College's Mathematics Department and Grantham Institute for Climate Change with Reading University's Departments of Mathematics and Statistics and of Meteorology has put these two institutions into a unique position to offer a CDT focussing on the priority area: Mathematical Sciences for Weather, Ocean and Climate, as a 50-50 joint venture. We propose to bring together, as academic supervisors and stakeholders in the centre, more than 60 world-leading researchers with expertise in a wide spectrum of areas that comprise the mathematical foundation as well as the frontier application areas. The central aim of the proposal is to build a strong cohort of young scientists whose backgrounds will span the breadth of the mathematical sciences from statistics, PDEs and dynamical systems, scientific computing, data analysis, and stochastic processes including relevant application areas from weather, oceans and climate. These young scientists must also acquire problem-specific knowledge through an array of elective courses and supervisory expertise offered by the two institutions and the external partners. A core component of the cohort training will be a ten-week programme hosted by the Met Office in Exeter which will include lectures given by world-leading scientists and research internships with Met Office staff, tackling real-world projects by teamwork. Key partners to the proposed CDT include major international players in research and operational forecasting for weather, oceans, and climate, including the UK Met Office, the European Centre for Medium Range Weather Forecasts, the German DWD, the National Centre for Atmospheric Science and the National Centre for Earth Observation. The EPSRC contribution to the Centre will be heavily leveraged with institutional and external partners, whose financial commitments are estimated to cover 65% of the total costs. The proposal is also in alignment with the global initiative Mathematics of the Planet Earth 2013 which involves scientific societies, universities, institutes and organizations all over the world aiming to learn more about the challenges faced by our planet and to increase the research effort on these issues.

The ocean circulation is dominated by an energetic mesoscale eddy field on spatial scales of 10-100 km, analogous to weather systems in the atmosphere. These eddies are unresolved, or at best inadequately resolved, in the ocean models used for long-range climate projections. Thus it is necessary to parameterise the impacts of the missing mesoscale eddies on the large-scale circulation. The vast majority of numerical ocean circulation models employ the Gent and McWilliams "eddy parameterisation" which acts to flatten density surfaces, mimicking the release of potential energy to fuel the growth of the mesoscale eddies. A key parameter in this eddy parameterisation is the "eddy diffusivity", which is critical as it plays a leading order role in setting global ocean circulation, stratification and heat content, the adjustment time scale of the global circulation, and potentially atmospheric CO2. In this project, we will implement a new closure for the Gent and McWilliams eddy diffusivity, derived from first principles, which depends only on the ocean stratification, the eddy energy and a non-dimensional parameter that is less than or equal to 1. If the eddy energy is known, then there is no freedom to specify explicitly any additional dimensional parameters, such as an eddy diffusivity. For this reason, we argue that existing approaches to parameterising eddies in ocean climate models are fundamentally flawed. Our new approach requires solving an equation for the depth-integrated eddy energy. This is a significant challenge and will form a major component of the present project. However, we believe that solving for the eddy energy is tractable as we have some understanding of the key physical ingredients. These key ingredients include the source of eddy energy through instability of the large-scale flow, westward propagation of eddies, diffusion of eddy energy, dissipation of eddy energy in western boundary "eddy graveyards", and dissipation of eddy energy through bottom drag and lee wave generation. Once a consistent eddy energy budget is incorporated, our new eddy parameterisation leads to three highly desirable results, which serve as important proofs of concept: 1. It reproduces the correct dimensional growth rate for eddies in a simple model of instability of atmospheric and oceanic flows for which there is an exact mathematical solution. 2. Assuming perfect knowledge of the eddy energy, it reproduces the eddy diffusivity diagnosed from high-resolution computer simulations of fully turbulent instabilities. 3. It predicts and explains the physics of "eddy saturation", the remarkable insensitivity of the size of the Antarctic Circumpolar Current to surface wind forcing, and a long standing challenge and known deficiency of current eddy parameterisations. The work plan will consist of four inter-related work packages: 1. Implementation and validation of the new eddy parameterisation framework in the NEMO ocean model, used by NERC and the UK Met Office, along with other European partners. 2. Development and refinement of the parameterised eddy energy budget. 3. Quantifying the impact of the new parameterisation on the oceanic uptake of heat and passive tracers in the UK Earth System Model, used for the UK contribution to the Intergovernmental Panel for Climate Change (IPCC) climate projections. 4. Project management, to ensure that the work is delivered fully and in a timely manner.