Multi-Scale Mathematics for Mitigating Severe Environmental Events

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.

The central aims of the Network "Maths Foresees" are to exchange knowledge, set up collaborations, stimulate breakthroughs in science and policy and, finally, communicate this clearly to the public. The members in the Network are:
- mathematical scientists;
- environmental scientists with expertise in weather forecasting, hydrology, flood forecasting and urban pollution spreading; as well as
- environmental and risk agencies and companies as stakeholders.

The scientific and technological focus of the Network concerns advanced mathematical techniques and their practical use in local weather (storm, precipitation and fog) forecasting coupled to overland flood forecasting models, coastal flooding and erosion models, as well as urban air pollution spreading. The outcomes will be advances in the following areas: assessment of probabilistic forecasting, multi-scale numerical methods used in coupling weather and hydrological models etc., dispersed multiphase modelling (air and water regarding clouds and precipitation, air and water in breaking waves, water and sediment/grains at beaches, aerosols and urban pollution), mathematical control theory (of floods), and understanding extreme (flooding) events.

The beneficiaries of these advances will be, in order of immediacy of impact:
- environmental researchers, in industry and in universities, whose work relies on mathematical and numerical models;
- environmental agencies and companies which will be able to deliver or exploit better forecasts of severe events, e.g., to design better prevention and adaptation measures;
- decision makers in the public and private sectors, the insurance sector in particular, who will benefit from improved advice;
- the general public, through better protection and information.

Vigorous interactions with the beneficiaries are central to the Network and will be primarily achieved through the close involvement of industrial/public agency stakeholders. The following activities have been designed to drive these interactions and maximise the Network's impact.
- General assemblies will provide an annual overall knowledge exchange between the members (all academics and stakeholders). Our collaborative style of network management will ensure productive interactions between the mathematics and environmental science communities.
- The math-with-industry style workshops give stakeholders explicitly the opportunity to put forward their challenges to the mixed mathematical and environmental academic community. Where practical popular science summaries will involve exemplar applications to real world problems.
- Smaller workshops (10 to 15 people) will be held with a specific mathematical theme.
- Specific user workshops (10 people) will disseminate knowledge and deal with (policy) questions from the stakeholders as the end users through face-to-face communication.
- The findings of the feasibility projects will be promoted through webinars and promoted via the network website.
- Finally, outreach projects will be defined by the members with the aim to reach the general public and demonstrate a proof-of-concept. The interest of two stakeholders (Penine Prospects and the Environment Agency) was specifically kindled by these outreach opportunities (regarding use in high schools and neighbourhood centres). Furthermore, we have discussed the potential to integrate these outreach projects within the Doctoral Training Centres (in Edinburgh, Imperial/Reading, Leeds) that embraced our Network.