Mathematics in the climate of global change (Q2473613)

The investigators of the climate and its consequences meet the problem that their object of study - the Earth system, or essential parts of this system - cannot be modeled and studied in detail in the laboratory. It is too large and too complex. Thus, observations and direct measurements, as well as modeling and computer simulations, are of great importance. The author of the article, first discusses two essential sources of the complexity of the Earth's system, the multitude of different physical processes and the interrelation of numerous - small and large - spatial and temporal scales. Modern mathematics, above all numerical mathematics and asymptotic analyses, may essentially contribute to the solution of both problems. The author concentrates in the article on the many-scales problem only. Using the example of the harmonic oscillator with small mass and damping, a two-scale problem with respect of the time is analysed. The sublinear growth condition is explained. It is shown that multi-scale approaches help to identify not only small-scale and large-scale parts of solutions, but also the related physical processes. Finally, a multi-scale model of the synoptic-planetary interactions in the tropes is presented. This model possesses a multi-scale ansatz of the zonal spatial variable.