## Long-Term Programs

## Mathematics for the Fluid Earth

Organized by Mike Cullen (Met Office), Klaus Fraedrich (Hamburg), Valerio Lucarini (Hamburg/Reading), Beatrice Pelloni (Reading) and Sandro Vaienti (Marseilles)

http://www.newton.ac.uk/programmes/MFE/index.html10/21/13 - 12/20/13

Isaac Newton Institute for Mathematical Sciences, Cambridge, UK

The fluid Earth is an excellent example of a forced, dissipative non-equilibrium system dominated by nonlinear processes and featuring multi-scale interactions, so that its understanding can be approached using the tools of dynamical systems theory and non-equilibrium statistical mechanics. The understanding of the statistical properties of a system under consideration is crucial *per se* and in a variety of applications, especially when considering large fluctuations which may result into extreme events of relevant impact. The differential equations that describe mathematically the fluid components, in particular the Navier-Stokes equations and their many variants and reductions, are at the core of the work of any analyst working in nonlinear PDEs. The many fundamental questions still open are often precisely the questions at the heart of the link between analysts and geophysicists.

The purpose of this programme is to bring together scientists from very different perspectives in models of the dynamics of the fluid components of the Earth system. This interest may be directly into the modelling, also numerical, or at a more abstract modelling level in terms of understanding the climate system as a complex dynamical system. This programme aims to prove that there is a close connection between “core” questions and problems of pure and applied mathematics and “core” questions of geophysical fluid dynamics relevant for the investigation of the climate system and of its component, and that these are closely linked to defining rigorously what is a good model for a complex system. The aim of the programme is to provide a common ground for fostering mutually stimulating and inspiring exchanges and for creating opportunities for future research. This programme is part of the international initiative “Mathematics for Planet Earth 2013” supported by mathematical societies and institutes around the world (http://mpe.dimacs.rutgers.edu).

#### Three Streams

The programme features three main macro-themes of interest where the progress has been impressive on the mathematical side and in terms of the investigation – theoretical, model-assisted, and observational – of the planet Earth: *a) Dynamical Systems and Statistical Mechanics; b) Extreme Events; c) Partial Differential Equations*. Work at these interfaces has, realistically, the potential to provide huge breakthroughs in the next years. These themes have mutual connections at mathematical level, which definitely need to be strengthened, with the possibility of obtaining new general results of great significance. Moreover, each theme has a huge potential for future breakthroughs at the boundary between mathematics and natural science. Finally, a crucial thread linking all of these themes is that related to the approaches and methodologies of modelling and analysing model outputs. In complex, multiscale system an ubiquitous issue is the choice of the specific details to model, of how to model them and parametrize the unresolved scales, how to implement efficiently a model, how to validate the model with sparse and uncertain data, how to control the model error, how to define robust observable, how to convincingly perform upscaling and downscaling procedures, and how to deal with coarse-graining.

#### Activities

The programmes at the Isaac Newton Institute benefit from a careful combination of structured, non-structured, and improvised events fostering scientific exchange. As for the first category, the following initiatives are being actively prepared:

- One introductory satellite workshop taking place in Exeter during the week before the start of the programme;
- Two workshops taking place at the Institute during the programme, the first one dedicated to themes more directly relevant for the first two streams of activity, and the second one dedicated to the third stream;
- Tutorial lectures, given by scientists active at the interface between the macro-themes;
- Other events will include seminars, round tables, discussions with non-academic stakeholders, plus, of course, a range of social events;
- Editorial activities, e.g. collection of selected contributions into an edited book or special issue of a journal.