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.

We live in the critical decade for climate change. The world increasingly experiences the damages and losses from extreme weather events caused by human-made climate change. Crop losses, devastating floods, catastrophic wildfires and rising sea levels cannot be ignored. If we do not achieve a balance between our greenhouse gas emissions and removals from the air, these impacts will become considerably worse and more dangerous. The UK has legally committed to achieving a net zero greenhouse gas balance by 2050. However, it is currently hotly debated how this goal can be achieved. The Land Use for Net Zero (LUNZ) Hub brings together researchers, policy-makers, industry leaders, innovators and rural community representatives from all four nations of the UK. Our 33 member organisations include researchers and practitioners from green finance, agricultural advisory organisations, NGOs, and an arts collective. The goal of the LUNZ hub is to accelerate positive land use change that reduces harmful greenhouse gas emissions, increases food security and restores a healthy environment for plants, animals and people. The Hub will equip UK policy-makers, industry and stakeholders with the advice they need, in the format and timeframe they require, to take policy decisions to help avert dangerous climate change and lead to a better future. We will bring together scientific evidence and stakeholder perspectives to define shared, net zero scenarios (plausible alternative futures)and credible pathways (steps including policies and incentives) to achieve them by 2050. The Hub will establish an Agile Policy Centre, a Net Zero Futures Platform, and a Creative Methods Lab. Within the Hub, our four National Teams will work together with our Topic Expert Groups to build capacity for a Just Transition to net zero that benefits people and planet alike. The Hub will support the UK Government and the devolved administrations in achieving multiple environmental goals by understanding the impacts of policy decisions on all relevant aspects, including renewable energy, agriculture, planning frameworks, afforestation, water management, nature conservation, biodiversity, and rural economies. The Hub will work on several priority policy areas: 1. Land use change that benefits the environment and is socially just, leading to ecosystem co-benefits such as biodiversity, soil health, human health and wellbeing, and green growth at national, regional and local levels; 2. Future agricultural, environmental and food policies that deliver a net zero future, building on the Agriculture Act 2020, Environment Act 2021, Agriculture Bill 2022 (Wales) and 2023 (Scotland), including future sources of finance, payment schemes and measures to reduce greenhouse gas emissions and increase removals while strengthening food security, biodiversity and land-based businesses (e.g. farms, crofts, forestry); 3. Integrating policy with carbon and natural capital markets, to ensure that the drivers and mechanisms for on-the-ground transformation work together for optimal outcomes. Achieving net zero by 2050 will require new technologies and practices which lower greenhouse gas emissions. These will include soil improvement practices, peatland protection and restoration, removal of greenhouse gases from the air and decarbonising our economy, large-scale tree-planting to take up carbon from the air, creation and restoration of habitats, transitioning to a circular economy, and significantly reduce food waste and consumption of higher emitting foodstuffs. To cover these diverse areas the Hub is comprised of the primary players in the UKRI AgriFood for Net Zero Network+, Landscape Decisions Programme, and principal investigators from Greenhouse Gas Removals, Changing the Environment, Digital Environment, AI for Net Zero, and Treescapes Programmes. This team have the experience and expertise to bring together a single voice of authority for Net Zero transformation in the UK.

Sea and society interact most strongly at the coast where communities both benefit from and are threatened by the marine environment. Coastal flooding was the second highest risk after pandemic flu on the UK government's risk register in 2017. Over 1.8 million homes are at risk of coastal flooding and erosion in England alone. Extreme events already have very significant impacts at the coast, with the damage due to coastal flooding during the winter 2013/14 in excess of £500 million, and direct economic impacts exceeding £260 million per year on average. Coastal hazards will be increasing over the next century primarily driven by unavoidable sea level rise. At the same time, the UK is committed to reach net zero carbon emissions by 2050. It is therefore essential to ensure that UK coasts are managed so that coastal protection is resilient to future climate and the net zero ambition is achieved. Protecting the coast by maintaining hard 'grey' defences in all locations currently planned is unlikely to be cost-effective. Sustainable coastal management and adaptation will therefore require a broader range of actions, and greater use of softer 'green' solutions that work with nature, are multifunctional, and can deliver additional benefits. Examples already exist and include managed realignment, restoration of coastal habitats, and sand mega-nourishments. However, the uptake of green solutions remains patchy. According to the Committee on Climate Change, the uptake of managed realignment is five times too slow to meet the stated 2030 target. Reasons are complex and span the whole human-environment system. Nature-based solutions often lack support from public opinion and meet social resistance. Despite removing long-term commitment to hard defences, the economic justification for green approaches remains uncertain due to high upfront costs, difficulty in valuing the multiple co-benefits offered, and uncertainties inherent to future environmental and socio-economic projections. The frameworks used to support present day coastal management and policy making (e.g. Shoreline Management Plans) do not provide comprehensive and consistent approaches to resolve these issues. Consequences are that the effectiveness of these policy approaches is reduced. Delivering sustainable management of UK coasts will therefore require new frameworks that embrace the whole complex human-environment system and provide thorough scientific underpinning to determine how different value systems interact with decision making, how climate change will impact coastal ecosystem services, and how decision support tools can combine multiple uncertainties. Co-Opt will deliver a new integrated and interdisciplinary system-based framework that will effectively support the required transition from hard 'grey' defences to softer 'green' solutions in coastal and shoreline management. This framework will combine for the first time a conceptual representation of the complex coastal socio-ecological system, quantitative valuation of coastal ecosystem services under a changing climate, and the characterisation of how social perceptions and values influence both previous elements. Our new framework will be demonstrated for four case studies in the UK in collaboration with national, regional, and local stakeholders. This will provide a scalable and adaptive solution to support coastal management and policy development. Co-Opt has been co-designed with project partners essential to the implementation and delivery of coastal and shoreline management (e.g. Environment Agency, Natural Resources Wales, NatureScot, coastal groups) and will address their specific needs including development of thorough cost-benefit analyses and recommendations for action plans when preferred policy changes. Co-Opt will further benefit the broad coastal science base by supporting more integrated and interdisciplinary characterisation of the complex coastal human-environment system.

Beach and barrier systems with a substantial gravel fraction, including 'pure', 'composite' and 'mixed sand-gravel', are common globally at mid to high latitudes. These geomorphological features, collectively referred to herein as 'gravel barriers', represent up to 20% of the wave-exposed coastline of Great Britain. They provide natural protection against coastal flooding and erosion, and support unique ecosystems. However, much of our ability to predict their morphodynamics comes from research on sandy coasts, which is flawed in translation. Specifically, our understanding and capability to model the morphodynamics of barriers comprising sand-gravel mixtures is significantly lacking. Fundamental differences in sand and gravel sediment transport processes and morphological response preclude direct application of sandy coastal models to gravel barriers. In mixed sand-gravel systems, the presence of one grain size fraction affects the transport of another through selective entrainment and cascading disturbances. Our understanding of gravel barrier behaviour, especially their response to sea-level rise, storms, and changes in wave conditions related to climate variability, is thus mainly qualitative. We understand, for example, that landward barrier migration occurs due to storm-induced overwash, but the constraints on the migration rate are poorly understood. Whilst migration is likely to increase with sea-level rise, the influence of different sediment grades and accommodation space is unclear. Likewise, changes in the predominant wave direction induce both alongshore and cross-shore response through beach rotation and sediment sorting. This, in turn, changes shoreline position and can create erosion hotspots, but the ability to robustly predict these processes for different climate change scenarios is deficient. Gravel barriers have an important role in providing coastal protection. Traditionally they have been maintained through sediment recycling and beach nourishment. However, evidence indicates that some of these practices negatively impact barrier stability making it unsustainable, particularly under rising sea levels. Thus, this project (#gravelbeach) aims to develop, reliable, consistent and appropriate approaches for working with, and making space for, these natural features, to enable more sustainable and adaptive national-scale management practices.

Glaciers and ice sheets are one of the least explored parts of the Earth's surface, and are now known to harbor significant populations of micro-organisms despite the challenging environmental conditions (e.g. extreme cold, desiccation, freezing and high pressure under ice sheets). Many of these microbes accelerate chemical weathering and supply nutrients to downstream ecosystems. A better knowledge of these processes is widely recognized as important for understanding: 1) global impacts of glaciers/ice sheets on the cycling of carbon and nutrients 2) biodiversity and life in extreme environments (e.g. Antarctic Subglacial Lakes) and 3) water flow beneath ice sheets as inferred from meltwater chemistry. Currently, the toolkits available to glaciologists to advance knowledge in these areas are very limited, and a technological leap is required to engage fully in future science campaigns. Building on previous work, this proposal aims to develop the first generation of compact chemical sensors for use in glaciers and ice sheets. While much of this technology has been evaluated for use in the oceans, it has not been assessed or modified for application in icy environments. We will take this technology and evaluate its performance under icy conditions (e.g. at low temperature, under freeze/thaw, at high pressure and with glacial meltwater sample types). This will be followed by design changes and further testing, culminating in a final demonstration of prototype instruments in Svalbard, Norwegian Arctic. These developments will provide key and rate limiting technology for future glacial science, and will have application in subglacial lake exploration (e.g. Subglacial Lake Ellsworth, Antarctica), in marine under-ice operations (e.g. Autosub under ice), and across a wide range of icy ecosystems where in situ measurements are desirable. This work is a forerunner to high impact international science campaigns requiring the development of purpose-built measuring systems that employ a comprehensive array of chemical sensor (e.g. the Lake Ellsworth Exploration Programme, the 'Basal Conditions on Rutford Ice Stream: Bed Access, Monitoring and Ice Sheet History' (BEAMISH) and the US-funded WISSARD programme, with which we have strong links). It also has strong relevance to water quality monitoring in freshwater environments, which will be explored via collaboration with the Environment Agency, UK.