Multiscale Analysis: Methods of Analysis (An Introduction to Complex Systems in Environment)

Mezemate Yacine, Schertzer Daniel

We gave in the courses Multifractal the meaning of the universal multifractal (UM) parameters and , in this courses we will introduce some techniques of estimation of UM parameters based on the scale invariance property of geophysical fields. The first method is the Trace Moment (TM) method which uses the allows to estimate the statistical moment function in the first step and after that to estimate the UM parameters either by the geometrical characteristic of the function or by its mathematical proprieties. The second method, called the Double Trace Moment which is a generalization of the TM method will be introduced and some of its characteristics will be highlighted. We introduce also the Structure Function Analysis which allows us to study the statistics of a non conservative field and estimate the different scaling exponent. In this courses we will also introduce the Empirical Modal Decomposition in order to separate the effects of large scale on the smallest one, which can affect the estimation of the UM parameters. Module 8 of the course set "An Introduction to Complex Systems in Environment"