Mathematical challenges in climate science

Description and aim of the workshop

Climate science is a field that harbors great challenges for applied mathematics. Two of the most urgent challenges at present are the issues of data assimilation (incorporating data from observations into model simulations in an optimal way) and subgrid-scale parameterization (how to represent in a numerical model the dynamical and physical processes with spatial scales below the model grid scale). Both topics are studied from theoretical/mathematical as well as more practical/operational perspectives.

As the amount of observations of the climate system rapidly increases, data assimilation (DA) becomes more important than ever. Already a classical research theme in weather forecasting, the importance of DA for climate research topics such as paleoclimatology and biogeochemical modeling has now also been recognized. However, DA in these emerging research fields may need different tools than DA for operational weather forecasting, because the requirements and limitations of models and data can be quite different: typically, models have coarser resolutions, simulations span much longer timescales and observational data have much poorer spatial and temporal resolution. As a consequence, approaches to DA for operational weather forecasting such as 4D-Var need not be very suitable for use in, for example, paleoclimate studies. For subgrid-scale modeling, new strategies are being mapped out, often with a stochastic flavor, as researchers start to acknowledge some of the intrinsic shortcomings of existing approaches. The practical relevance of these new ideas cannot be taken for granted however, as their transfer from simple, idealized toy model environments to the complex models used in climate science often proves to be a difficult task. At the same time, new developments in applied mathematics, regarding for example numerical modeling of multiscale systems, are hardly known among climate scientists in spite of the potential relevance of these new ideas. The purpose of this workshop is to bring applied mathematicians and climate scientists together in order for the latter to learn about new mathematical developments with relevance to practical climate research and for the former to learn about the challenges facing climate scientists at present. As it is impossible to cover all mathematical aspects of climate science in a single workshop, we focus on data assimilation and subgrid-scale parameterization as the main topics of the workshop. Researchers with expertise on either topic are welcome to participate, as are those with a more general applied math or climate science background interested in learning about these topics. There will be room for only a limited number of invited oral presentations, but there will be an opportunity to present posters. Junior researchers in particular are encouraged to participate and to present their work in a poster session. To make the workshop accessible for applied mathematicians as well as for researchers from the climate science community, presentations should try to target both groups.