Towards a new generation of adaptive climate and weather models

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Wavelet multiresolution analysis is one of the most significant mathematical breakthroughs of the last 30 years. The impact of wavelet methods in both pure and applied mathematics was recognized when Yves Meyer was awarded the 2017 Abel Prize for “his pivotal role in the development of the mathematical theory of wavelets.”******Wavelet methods are now common in analysis, statistics and approximation theory. This proposal applies the multiscale formalism of wavelet analysis to adaptively solve nonlinear partial differential equations (PDEs) on the sphere. In particular, I will use the mathematical tools I develop to build a full climate model. This innovative climate model will be applied to investigate open problems in the physics of atmospheres and oceans. The research program will impact both numerical analysis (adaptive numerical methods for PDEs in spherical topology) and climate modelling.******Weather and climate models use static computational grids which are unable to adapt to resolve rapidly developing storms or coarsen where less accuracy is needed. This means that computational resources are used inefficiently and that the resulting errors are not uniformly bounded in space and time. It is also difficult to increase resolution where more accuracy is needed, for example over densely populated areas. ******The first objective extends our adaptive 2D shallow water model to a 3D multilayer hydrostatic model. At this point it will form a so-called "dynamical core" on which physical effects (e.g. radiation, clouds, the effect of topography, vegetation) can be added to build a true climate model. This will be the first dynamically adaptive dynamical core for both atmospheres and oceans.******The second objective develops a scale aware physics model to account for subgrid scale physical effects, such as cloud formation and solar radiation transfer. These processes occur on scales varying from ten thousand kilometres to submillimeter and from centuries to milliseconds. Weather models use data assimilation to optimally incorporate observations of temperature, wind etc. into the numerical simulation. The third objective is to develop new techniques in data assimilation that take advantage of the dynamic adaptive of our numerical model.******I will train 11 Highly Qualified Personnel (1 post-doctoral fellow, 2 PhD students, 3 MSc students and 5 BSc students) over the five-year span of this research program.******This proposal contributes to an international effort (e.g. by Environment Canada, ECMWF, NCAR, Météo France) to develop the next generation of weather and climate models. Canada has been a world leader in numerical weather prediction and climate modelling, and the knowledge gained in this research project will keep Canada at the forefront as new models are developed to deal with emerging challenges.**************