François Landais
PhD studentGéosciences Paris Sud (GEOPS) Bâtiment 504, Rue du Belvédère Campus Universitaire d’Orsay 91405 Orsay Cedex, FRANCE mail : francois.landais@upsud.fr This thesis aims to characterize the statistical structure of planetary topographies in the solar system. The topographic field of a planet is a highly irregular field that traditional analysis can only partially deal with. With details at every scale, a complex hierarchy of high and low elevations, heavytailed distributions of slopes at different scales and a multiplicity of (scale invariant) spatial features, topographic fields clearly require powerful analysis techniques able to capture in a comprehensive framework its behavior at different scales and the spatial variations of roughness. In this thesis, I make an extensive use of Multifractal analysis is a very general and multidisciplinary approach that consists in describing the statistical properties of any complex system that exhibit a large variability over a wide range of scales. The word « multifractal » was first introduced to tackle the problem of turbulence in atmospheric field (Frisch et al., 1985) that lead to highly heterogenous distribution of cascading energy in the atmosphere. The notion is now involved in many axes of research that must deal with irregular temporal or spatial series of data and span of variety of topics from geophysics (Lovejoy et al., 2013) to astrophysics (Martinez et al., 1990) and image analysis (Combrexelle et al., 2015). The overall goal of multifractal analysis is to reduce the complexity of natural phenomenons to a few relevant statistical parameters that accurately reflect the structuring of data across scales when no characteristic dimensions are present. The first part of my work consist in investigating the mulifractal aspect of topography in the the solar system on a global, regional and local basis. I am also interested in mulitfractal simulation technique, especially simulation on a sphere (see illustration below) Publication :Universal multifractal Martian topography, Landais, F., F. Schmidt, S. Lovejoy, 2015, Nonlin. Processes Geophys. Discuss., 2, 1007–1031, doi:10.5194/npgd210072015. Multifractal topography of several planetary bodies in the Solar System Landais, F., Schmidt, F., & Lovejoy, S. 2017 (Under review). Water Residence Time Distribution Estimation through 1D Deconvolution, Meresescu, Kowalski, Schmidt, Landais, submitted to Computer and Geosciences, 2017 Topography of (exo)planet, Landais, Schmidt, and Lovejoy, in preparation Axes of research : statistical analysis of surfaces
keywords : Topography, Solar system, statistics, fractal Conference : 2017 : LPSC, Multifractal Analysis of the Martian Topography (poster presentation)
Workshop and seminar 2016 : Workshop imageIN (GEOPS), multifractal analysis and spherical simulation (oral presentation)
Teaching at IUT of ORSAY 20152016 :
Optique (1st year),
Acoustic (2nd year),
Electromagnetism (1st year)
multifractal simulation of planetary bodiesExemple of a universal multifractal simulation with parameters H=0.9, C1=0.1, alpha=2. The simulation is performed on a spherical geometry by using 2 successive convolutions in spherical harmonic domain (see Landais et al, topography of exoplanet, in preparation). Elevation data is used to build a 3D model. The shaded reliefs are calculated and then wrapped on the 3D surface. This visualization highlight the local variations of roughness specific to multifractal fields. Being realistic in a statistical sense, such simulations will be useful to infer the photometric properties of various planetary bodies (comets, asteroids, irregularly shaped satellite) Proportion of oceansExemple of a universal multifractal simulation with parameters H=0.5, C1=0.1, alpha=1.7 (similar to the statistics of Earth topography, see Landais, F., Schmidt, F., & Lovejoy, S. 2017 (Under review)). Unlike the above simulation, the planet radius is large resulting in an approximatively spherical body. Still the roughness strongly varies across the global given the value of the intermittency parameter C1. The level of water is fixed in order to obtain 50% of land and 50% of ocean. We can see on the simulation the fractal aspect of coastline. As the planet is rotating, the fraction of visible ocean varies in time and strongly rely on the fractal nature of topography. This method of simulation will possibly contribute to the growing field of rocky exoplanet detection. The first direct detection of earthlike planet will probably be unresolved and will rely on our ability to extract the information from the ligth curve of a single pixel. The proportion of an hypothetic ocean at the surface will be one of key aspect to properly interpret the signal. 
