Severe weather, with heavy rainfall and strong winds, has been the cause of recent dramatic land and coastal flooding, and of strong beach and cliff erosion along the British coast. Both the winters of 2012-2013 and 2013-2014 have seen severe environmental disasters in the UK. The prediction of severe rainfall and storms and its use to forecast river flooding and storm surges, as well as coastal erosion, poses a significant challenge. Uncertainties in the prediction of where and how much precipitation will fall, how high storm surges will be and from which direction waves and wind will attack coast lines, lie at the heart of this challenge. This and other environmental challenges are exacerbated by changing climate and need to be addressed urgently. As the latest IPCC reports confirms, sea level rise and storm intensity combined are very likely to cause more coastal erosion of beaches and cliffs, and of estuaries. However, it is also clear that there remains considerable uncertainty. To address the challenges posed by the prediction and mitigation of severe environmental events, many scientific and technical issues need to be tackled. These share common elements: phenomena involving a wide range of spatial and temporal scales; interaction between continuous and discrete entities; need to move from deterministic to probabilistic prediction, and from prediction to control; characterisation and sampling of extreme events; merging of models with observations through filtering; model reduction and parameter estimation. They also share a dual need for improved mathematical models and for improved numerical methods adapted to high-performance computer architectures. Since all these aspects are underpinned by mathematics, it is clear that new mathematical methods can make a major contribution to addressing the challenges posed by severe events. To achieve this, it is crucial that mathematicians with the relevant expertise interact closely with environmental scientists and with end-users of environmental research. At present, the UK suffers from limited interactions of this type. We therefore propose to establish a new Network - Maths Foresees - that will forge strong ties between researchers in the applied mathematics community with researchers in selected strategic areas of the environmental science community and governmental agencies. The activities proposed to reach our objectives include: (i) three general assemblies, (ii) three mathematics-with-industry style workshops, in which the stakeholders put forward challenges, (iii) focussed workshops on mathematical issues, (iv) outreach projects in which the science developed is demonstrated in an accessible and conceptual way to the general public, (v) feasibility projects, and (vi) workshops for user groups to disseminate the network progress to government agencies.

Coastal and estuarine areas are under constant erosion/sedimentation pressure. The sustainable development of these areas depends on our understanding of and ability to predict the effect of complex sediment transport and morphodynamic processes and the development of effective applied engineering solutions. Coastal protection is an important issue in the implementation of successful Integrated Coastal Zone Management (ICZM) plans. The objective of the intrersectoral Network SEDIMARE is the interdisciplinary training and award of a PhD degree to Researchers in coastal processes and engineering, aiming towards a sustainable coastal use and protection. The Network comprises 6 universities, 4 private sector beneficiaries (1 Applied Research Institute, 1 corporation, and 2 SMEs), and 1 industrial associated partner. The Network will provide a training-through-research program to 10 Researchers, which comprises comprehensive academic training including web-based teaching, inter-institutional co-supervision, intersectoral secondments, summer/winter schools, workshops, complementary activities, dissemination, and outreach activities. The research plan is organized into 3 Work Packages (WP): (1) Sediment Transport Processes, (2) Coupling of Flow, Sediment Transport, and Morphodynamics, and (3) Sustainable Coastal Engineering Solutions. Each WP includes several projects, whose implementation is based on the strong interaction between all beneficiaries. The topics include: complex sediment transport processes involving sandmud mixtures, mixed-size sands, and granular-fluid mixtures; coupling between hydrodynamics (waves, storm surges, and tides), sediment transport, and morphological changes; and engineering solutions to issues/problems related to erosion/sedimentation with emphasis on sustainability and resilience. The research methods include effective process-based engineering modeling, advanced numerical simulations, and innovative experiments.

The combined effect of population growth and industrialisation in the UK is such that coastal land areas are increasingly occupied by multiple user groups with diverse and competing needs (e.g. environmental, tourism, industrial). An important aspect of climate change is the increased likelihood of storms, and hence storm-surges and flooding, and this will have obvious impact upon low lying areas. There is thus an increased need to improve our capacity to predicti (especially over a wide range of spatial scales - a few meters to many kilometres) flooding. Improved modelling ability will inform policy makers, rescue services and scientists involved with ocean, climate change and risk reduction strategies. Data assimilation techniques are extremely valuable in compensating for lack of information about our oceans. Observed data is assimilated into models to produce an accurate estimate (in some optimal sense) of the state of the ocean. However, applications of efficient data assimilation approaches (e.g., variational data assimilation) are hampered by two major difficulties: the often complex code (implementation and maintainability) required; and the high computational costs. To address these issues, the proposed work will improve the existing models by using: 1) a newly developed data assimilation formulation to dramatically reduce the code complexity and increase maintainability; 2) a new highly stable and accurate wetting and drying method capable of resolving multi-scale physics and uniquely designed for use with a next generation ocean model; 3) model reduction in which large-scale models are reduced down to a few hundred unknowns so that the resulting models are orders of magnitude faster than the original model. Our overall aim is the accurate prediction of free surface dominated flows in coastal regions. Prediction will be achieved by developing a variational data assimilation (in the content of the time dependent problems solved here) framework within our advanced adaptive mesh ocean model. This framework will be capable of quantifying the effect of model uncertainties, performing sensitivity analysis, and capturing abruptly changing fields such as wetting and drying fronts in free surface dominated regional flows. This will pave the way towards an open source, community, next generation regional ocean model with multi-scale adaptive finite element meshing features and predictive capability. The overall deliverable will be a model capable of resolving free surface dominated flows from ocean to estuary (and smaller scale) scale. The proposed combination of recently developed techniques is the only feasible way of resolving these demanding multi-scale flows. The proposed research is also expected to have a substantial impact on the future development of operational implementation of variational data assimilation in both meteorology and oceanography. The reduction in computational effort and memory requirements will render data assimilation a more affordable research and operational tool. Society as a whole will benefit from this research through improved prediction of multi-scale coastal flows, especially the prediction of storm flooding. In particular, government, regulatory bodies and stakeholder, companies/industries, meteorology, oceanography communities and institutes would benefit from the new technologies that could be used for prediction and impact assessment of natural disasters, pollution and rapid emergency response.

Flooding is a growing problem in the UK and causes extensive damage to infrastructure, homes and business. Recently, the problem was highlighted again due to severe flooding in 2013/14 winter, causing total economic losses of over £1 billion. Earth dykes, used as major flood defence structures in the UK, can fail in extreme events, as evidenced by the numerous breaches along earth embankments during the December 2013 East Coast surge event. Earth dykes even become more vulnerable due to changing operation conditions caused by climate change. The project addresses strategic issues associated with changing environments and deteriorating flood defence systems at a UK national level, which have been identified by HR Wallingford and the Environment Agency. The outcomes of the project will contribute towards developing next generation risk based performance evaluation and prediction methodology for reducing flood risk, improving resilience of flood defences to changing environments, and determining optimum maintenance strategies. The methods developed in this research will be implemented into flood risk management framework through HR Wallingford who currently lead the technical development of the flood risk assessment methodology used by the Environment Agency.

It is not widely known that the global economy relies on uninterrupted usage of a network of telecommunication cables on the seafloor. Yet these submarine cables carry ~99% of all inter-continental digital data traffic worldwide, as they have far greater bandwidth than satellites. Over 9 million SWIFT banks transfers alone were made using these cables in 2004, totally $7.4 trillion of transactions per day between 208 countries. Our dependence on these cables is growing, for example there were 15 million SWIFT bank transactions last year. Submarine cables thus have considerable strategic importance to the UK because this data traffic includes the internet, defence information, financial markets and other services that underpin daily lives. This project is timely because submarine cable breaks are a notable omission from the UK National Risk Register. It focusses on the industry challenge of why exactly, how often, and where are seafloor cables broken by natural causes, primarily subsea landslides and sediment flows (turbidity currents). These slides and flows can be very destructive. A flow in 1929 travelled at 19 ms-1 and broke 11 cables in the NE Atlantic, running out for ~800 km to the deep sea. A repeat event would break far more cables today. It is difficult to mitigate against multiple breaks from such flows/slides because data traffic cannot be re-routed along adjacent cables. This contrasts with trawling (or other human activities) that break a single cable. This study is in conjunction with Global Marine and the International Cable Protection Committee. The ICPC is the global umbrella body for the submarine cable sector, and hosts Talling's Royal Society Industry Fellowship. This will be the first study to statistically analyse a global database of cable breaks and causes. It will use novel field and laboratory experiments to show how cables abrade or break. The main project impacts are: (1) We will provide our industry partners (ICPC, individual cable companies) with the first global statistical analysis of the frequency and causes (earthquake, typhoons) of cable breaks. (2) We will map geographic "pinch points" in the global seafloor network that are most at risk from specific hazards; thus helping our partners to design cable routes. These results will help to assess where future climate change is most likely to impact upon cable routes. (3) Laboratory experiments and a novel full-scale field experiment will help our industry partners to understand exactly how cables are broken by submarine flows (and why they sometimes fail to break). Results will be presented at workshops with individual cable companies, and at the ICPC's plenary meeting. Such meetings will provide a global forum for discussion of future strategies for reducing cable breaks. (4) A briefing document will be delivered to the UK Natural Hazards Partnership and Cabinet Office that sets out the basis for whether submarine cable breaks should be included in the UK National Risk Register. This project has wide relevance for multiple geographic and geologic settings and the global subsea communications industry. Other type of expensive and strategically important seafloor infrastructure are also susceptible to impacts by submarine flows/slides, including export pipelines and in-field flowline for oil and gas, and umbilicals that transfer chemicals, power and communications. This project's findings will help to assess the risk posed to these other types of subsea infrastructure by submarine flows/slides. Our project partners include those interested in risks to seafloor pipeline used to carry treated water (Carroll at ScottishWater), and oil and gas networks worldwide (Jobe, Sylvester, Armitage). Submarine flows deposit layers of sand that now form many valuable oil and gas reservoirs. We will also communicate insights from our project into these processes to interested partners (e.g. Jobe at Shell, Sylvester at Chevron, Armitage at ConocoPhilips).