MultiScale Analysis: Fractal (An Introduction to Complex Systems in Environment)

Mezemate Yacine, Schertzer Daniel

In meteorology, oceanology, climatology, hydrology and more generally in geophysics, the researches (turbulence, chaos, global climate evolution understanding, tectonic, seismology...), in studies (strategies definition of sampling for the next generation satellite, estimation of extreme fluctuations of fields, cyclones trajectory or pollutants...), faced by a fundamental difficulty : the extreme variability at large scale range in time and space of the measured fields. This variability coming from the non linear interaction not only at different scale but also between different processes. In order to face on this difficulty, without using artifacts, it has been necessary to develop a specific tools, concepts and technical, to achieve both simple theoretical representations and quantitative assessment of this variability which can be repeated in a simple manner at different scales. These tools have been developed either from the analysis of symmetries of evolution equations when these are known, or on simple phenomenological considerations (self-similar models cascade) or even just empirical (spectra, structure functions...). These approaches have led to develop and renew the concepts of scale invariance or fractals, and releasing from the nonlinear variability a unifying issue geophysics. Module 6 of the course set "An Introduction to Complex Systems in Environment"