Analysis of multifractal scaling laws describing satellite observations of continental surfaces ; Etude des lois d’échelle multifractales caractérisant les observations satellitaires des surfaces continentales

Considering the strong spatial and temporal heterogeneity of continental surfaces, remote sensing has proved to be an indispensable means for conducting regular, local and global monitoring of the physical and biophysical processes governing these surfaces. The factors on which they depend, such as soil moisture, surface temperature, vegetation, or topography, are variable over wide ranges of scales that only satellites can access. Thus, over the last fifty years, we have seen a growing number of satellite observations defined at multiple spatial scales and based on multiple technologies. Various methods were then developed to analyze and extract the rich and consistent information acquired by satellites. Methods based on multi-scale analysis can provide an effective means to describe the heterogeneity of these observations and thus better understand the complexity of surface processes. In particular, one possibility is to focus on the existence of statistical scaling laws offering a generic tool applicable to the characterization of any type of geometry. The demonstration of specific scaling behaviors can help to characterize surface processes using a multi-scale approach that is rarely taken into account in current surface models.In this context, the objective of this thesis is to demonstrate the potential of a method dedicated to the characterization of the behaviors of surface geophysical variables on several spatial scales. For this, different complementary satellite observations were analyzed using the Universal Multifractal model (Schertzer and Lovejoy, 1987). Two case studies helped to meet this objective. The first application concerns the multifractal analysis of the products involved in the soil moisture disaggregation algorithm called DisPATCh (Disaggregation based on Physical And Theoretical scale Change; Merlin et al., 2008; Molero et al., 2016), on the southeastern part of Australia. In the second case study, we studied the multi-scale behavior of surface reflectances and optical indices acquired ...