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Mathematical challenges in climate science
Mathematical challenges in climate science
March 9-13, 2009
Climate science is a field that harbors great challenges for applied mathematics. The aim of this workshop was 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 was impossible to cover all mathematical aspects of climate science in a single workshop, we focused on two of the most urgent topics: 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).
As the amount of observations of the climate system rapidly increases, data assimilation becomes more important than ever. Already a classical research theme in weather forecasting, the importance of data assimilation for climate research topics such as paleoclimatology and biogeochemical modeling has now also been recognized. However, these emerging research fields may need different assimilation tools than 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.
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 workshop drew nearly 40 registered participants from various countries (
The first two days of the workshop were devoted to data assimilation, with presentations covering topics such as data assimilation in paleoclimate studies and biogeochemical modeling, numerical aspects and validation of algorithms, assimilation of Lagrangian data and Bayesian approaches to ill-posed inverse problems. The rest of the week was dedicated to subgrid scale modeling, with presentations focussing on parameterization of clouds and convection, stochastic methods for parameterization, regularized Navier-Stokes equations, cascades and spectral energy transfer, multiscale methods and parameterizations in ocean models.
The workshop program consisted of 16 presentations (lasting either 60 or 45 minutes), moderated group discussions (one each day) and a poster session. There was a wine and cheese party on the first day of the workshop and a dinner in the historic "Regentenkamer" in
Some of the topics that came up regularly during the discussions were (i) the need for systematic approaches to calibrate climate models using observational datasets, (ii) how to initialize climate models, (iii) what measures to use for assessing model performance, (iv) the current lack of a mathematical framework to guide the development of subgrid parameterizations and (v) the potential use of multiscale methods based on scale separation for parameterization. We recommend the discussion on these issues be continued in future workshops. During the wrap-up session that concluded the week, some further topics for future meetings were suggested, going beyond the themes of the current workshop: characterization of structure in data, design of observation systems, uncertainty analysis and identification of model error, predictability.
Overall, the workshop was succesfull in reaching both applied mathematicians and climate scientists and in stimulating interactions between these groups. Several participants reported back to us on the good organization, the excellent presentations, and the interesting discussions. New ideas generated during the workshop will find their ways into the scientific community and are already being considered for new research proposals.
It is a pleasure to thank the
Daan Crommelin (CWI,
Rachel Kuske (
Peter Jan van Leeuwen (University of Reading, UK)