Coastal hazards pose a significant risk to people, property, and infrastructure worldwide and in the UK. For example, over 1.8 million homes are at risk of coastal flooding and erosion in England alone and coastal flooding is recognized as one of the top two environmental hazards in terms of impact in the 2020 National Risk Register. The occurrence, intensity and impacts of coastal flooding and erosion are projected to increase with climate change and will have major socio-economic consequences. Historically, coastal protection has relied on overwhelming use of hard engineered defence schemes, but adverse effects and high costs of these schemes have driven advocacy of coastal practices that are based on Working with Natural Processes (WWNP). However, future changes in regional sea level, storms, pluvial and fluvial inputs, coastal habitats, and their interrelations lead to significant epistemic uncertainties (due to limited knowledge) about controls on flooding and erosion and limit the implementation of WWNP schemes. Questions remain on how multiple terrestrial and marine drivers of extreme hydrodynamic conditions will combine to control coastal flooding and erosion in the future, on the vulnerability and efficacy of protective services afforded by coastal habitats, and on the performance of WWNP solutions on coasts that already have partial protection by traditional engineered coastal defences. Event-scale coastal flooding and erosion mainly occur in response to synoptic scale meteorological events. These meteorological events can result in a series of individual hazard components to coastal environments, such as storm surges, extreme waves, extreme rainfall, and extreme river flows. However, these hazard components are not independent of each other, and coastal flooding and erosion commonly arise from the collective impact due to interrelated and/or successive hazard components. In other words, coastal flooding and erosion are controlled by multi-hazards. The CHAMFER project will characterise how multi-hazards at the coast control coastal flooding and erosion and determine how these multi-hazards will respond to climate change and coastal management. We will deliver a new community modelling system coupled across terrestrial and marine sectors, numerical simulations of which will be used to support multi-hazard analyses under present and future scenarios. This will be combined with an assessment of the role of coastal habitats resulting in national maps for protective services and vulnerabilities of coastal habitats to climate-driven multi-hazards. We will provide tools to analyse the efficacy of future WWNP schemes. CHAMFER will rely on a multi-scale approach both spatially, by considering UK/GB scales and more local spatial scales, and temporally, by considering responses to meteorological events under long-term climate-related or management-related changes. CHAMFER includes significant elements of co-design with stakeholders and we will work with government departments, public sector organisations, and industry users to inform and support coastal protection and adaptation options.

Natural hazard events claim thousands of lives every year, and financial losses amount to billions of dollars. The risk of losing wealth through natural hazard events is now increasing at a rate that exceeds the rate of wealth creation. Therefore natural hazards risk managers have the potential, through well-informed actions, to significantly reduce social impacts and to conserve economic assets. By extension, environmental science, through informing the risk manager's actions, can leverage research investment in the low millions into recurring social and economic benefits measured in billions. However, to be truly effective in this role, environmental science must explicitly recognize the presence and implications of uncertainty in risk assessment. Uncertainty is ubiquitous in natural hazards, arising both from the inherent unpredictability of the hazard events themselves, and from the complex way in which these events interact with their environment, and with people. It is also very complicated, with structure in space and time (e.g. the clustering of storms), measurements that are sparse especially for large-magnitude events, and losses that are typically highly non-linear functions of hazard magnitude. The tendency among natural hazard scientists and risk managers (eg actuaries in insurance companies) is to assess the 'simple' uncertainty explicitly, and assign the rest to a large margin for error. The first objective of our project is to introduce statistical techniques that allow some of the uncertainty to be moved out of the margin for error and back into an explicit representation, which will substantially improve the transparency and defensibility of uncertainty and risk assessment. Obvious candidates for this are hazard models fitted on a catalogue of previous events (for which we can introduce uncertainty about model parameters, and about the model class), and limitations in the model of the 'footprint' of the hazard on the environment, and the losses that follow from a hazard event. The second objective is to develop methods that allow us to assess less quantifiable aspects of uncertainty, such as probabilities attached to future scenarios (eg greenhouse gas emissions scenarios, or population growth projections). The third objective is to improve the visualisation and communication of uncertainty and risk, in order to promote a shared ownership of choices between actions, and close the gap between the intention to act (eg, to build a levee, or relocate a group of people living in a high-risk zone) and the completion of the act. In natural hazards this gap can be large, because the cost of the act is high, many people may be affected, and the act may take several years to complete. Ultimately, everyone benefits from better risk management for natural hazards, although the nature of the benefits will depend on location. In the UK, for example, the primary hazard is flooding, and this is an area of particular uncertainty, as rainfall and coastal storm surges are likely to be affected by changes in the climate. A second hazard is drought, leading to heat stress and water shortages. Our project has explicit strands on inland flooding, wind-storms, and droughts. Other parts of the world are more affected by volcanoes or by earthquakes, and our project has strands on volcanic ash, debris flows as found in volcanic eruptions (ie lahars; avalanches are similar), and earthquakes. In the future, new hazards might emerge, such as the effect of space weather on communications. A key part of our project is to develop generic methods that work across hazards, both current and emerging.

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.