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Io has one of the most dynamic atmospheres in the solar system due in part to an orbital resonance with Europa and Ganymede that causes intense tidal heating and volcanism. The volcanism serves to create a myriad of volcanic plumes across Io's surface that sustain temporally varying local atmospheres. The plumes primarily eject sulfur dioxide (SO₂) that condenses on Io's surface during the relatively cold night. During the day, insolation warms the surface to temperatures where a global partially collisional atmosphere can be sustained by sublimation from SO₂ surface frosts. Both the volcanic and sublimation atmospheres serve as the source for the Jovian plasma torus which flows past Io at ~57 km/s. The high energy ions and electrons in the Jovian plasma torus interact with Io's atmosphere causing atmospheric heating, chemical reactions, as well as altering the circumplanetary winds. Energetic ions which impact the surface can sputter material and create a partially collisional atmosphere. Simulations suggest that energetic ions from the Jovian plasma cannot penetrate to the surface when the atmospheric column density is greater than 10¹⁵ cm⁻². These three mechanisms for atmospheric support (volcanic, sublimation, and sputtering) all play a role in supporting Io's atmosphere but their relative contributions remain unclear. In the present work, the Direct Simulation Monte Carlo (DSMC) method is used to simulate the interaction of Io's atmosphere with the Jovian plasma torus and the results are compared to observations. These comparisons help constrain the relative contributions of atmospheric support as well as highlight the most important physics in Io's atmosphere. These rarefied gas dynamics simulations improve upon earlier models by using a three-dimensional domain encompassing the entire planet computed in parallel. The effects of plasma heating, planetary rotation, inhomogeneous surface frost, molecular residence time of SO₂ on the exposed non-frost surface, and surface temperature distribution are investigated. Circumplanetary flow is predicted to develop from the warm dayside toward the cooler nightside. Io's rotation leads to a highly asymmetric frost surface temperature distribution (due to the frost's high thermal inertia) which results in circumplanetary flow that is not axi-symmetric about the subsolar point. The non-equilibrium thermal structure of the atmosphere, specifically vibrational and rotational temperatures, is also examined. Plasma heating is found to significantly inflate the atmosphere on both the dayside and nightside. The plasma energy flux causes high temperatures at high altitudes, but plasma energy depletion through the dense gas column above the warmest frost permits gas temperatures cooler than the surface at low altitudes. A frost map (Douté et al., 2001) is used to control the sublimated flux of SO₂ which can result in inhomogeneous column densities that vary by nearly a factor of four for the same surface temperature. A short residence time for SO₂ molecules on the non-frost component is found to smooth lateral atmospheric inhomogeneities caused by variations in the surface frost distribution, creating an atmosphere that looks nearly identical to one with uniform frost coverage. A longer residence time is found to agree better with mid-infrared observations (Spencer et al., 2005) and reproduce the observed anti-Jovian/sub-Jovian column density asymmetry. The computed peak dayside column density for Io agrees with those suggested by Lyman-[alpha] observations (Feaga et al., 2009) assuming a surface frost temperature of 115 K. On the other hand, the peak dayside column density at 120 K is a factor of five larger and is higher than the upper range of observations (Jessup et al., 2004; Spencer et al., 2005). The results of the original DSMC simulations of Io's atmosphere show that the most important and sensitive parameter is the SO₂ surface frost temperature. To improve upon the original surface temperature model, we constrain Io's surface thermal distribution by a parametric study of its thermophysical properties. Io's surface thermal distribution is represented by three thermal units: sulfur dioxide (SO₂) frosts/ices, non-frosts (probably sulfur allotropes and/or pyroclastic dusts), and hot spots. The hot spots included in the thermal model are static high temperature surfaces with areas and temperatures based on Keck infrared observations. Elsewhere, over frosts and non-frosts, the thermal model solves the one-dimensional heat conduction equation in depth into Io's surface and includes the effects of eclipse by Jupiter, radiation from Jupiter, and latent heat of sublimation and condensation. The best fit parameters for the SO₂ frost and non-frost units are found by using a least-squares method and fitting to observations of the Hubble Space Telescope's Space Telescope Imaging Spectrograph (HST STIS) mid- to near-UV reflectance spectra and Galileo photo-polarimeter (PPR) brightness temperature. The thermophysical parameters are the frost Bond albedo, and thermal inertia, as well as the non-frost surface Bond albedo, and thermal inertia. The best fit parameters are found to be [equations] for the SO2 frost surface and [equations] for the non-frost surface. These surface thermophysical parameters are then used as boundary conditions in global atmospheric simulations of Io's sublimation-driven atmosphere using DSMC. The DSMC simulations show that the sub-Jovian hemisphere is significantly affected by the daily solar eclipse. The SO₂ surface frost temperature is found to drop ~5 K during eclipse but the column density falls by a factor of 20 compared to the pre-eclipse column due to the exponential dependence of the SO₂ vapor pressure on the SO₂ surface frost temperature. Supersonic winds exist prior to eclipse but become subsonic during eclipse because the collapse of the atmosphere significantly decreases the day-to-night pressure gradient that drives the winds. Prior to eclipse, the supersonic winds condense on and near the cold nightside and form a highly non-equilibrium oblique shock near the dawn terminator. In eclipse, no shock exists since the gas is subsonic and the shock only reestablishes itself an hour or more after egress from eclipse. Furthermore, the excess gas that condenses on the non-frost surface during eclipse leads to an enhancement of the atmosphere near dawn. The dawn atmospheric enhancement drives winds that oppose those that are driven away from the peak pressure region above the warmest area of the SO₂ frost surface. These opposing winds meet and are collisional enough to form stagnation point flow. The simulations are compared to Lyman-[alpha] observations in an attempt to explain the asymmetry between the dayside atmospheres of the anti-Jovian and sub-Jovian hemispheres. A composite "average dayside atmosphere" is formed from a collisionless simulation of Io's atmosphere throughout an entire orbit. The composite "average dayside" atmosphere without the effect of global winds indicates that the sub-Jovian hemisphere should have lower average column densities than the anti-Jovian hemisphere (with the strongest effect at the sub-Jovian point) due entirely to the diurnally averaged effect of eclipse. Lastly, a particle description of the plasma is coupled with the sophisticated surface thermal model and a final set of global DSMC atmospheric simulations are performed. The particle description of energetic ions from the Jovian plasma torus allows for momentum transfer from the ions to the neutral atmosphere. Also, the energetic ions (or solar photons) can dissociate the neutral atmosphere and cause sputtering of SO₂ on the surface. SO₂ remains the dominant dayside species (>90%) despite being dissociated by ions and photons to form O, O₂, S, and SO. SO₂ remains the dominant atmospheric species on the nightside between dusk and midnight due to sputtering of SO₂ surface frosts by energetic ions as well as the high thermal inertia of SO₂ frosts that cause the surface temperature to cool slowly and thus sublime a thicker SO₂ atmosphere. O₂ becomes the dominant atmospheric species above coldest areas of the surface because it is non-condensable at Io's surface temperatures and other species are sticking to the surface. SO and O are present in similar gas fractions because they are created together via the same ion and photo-dissociation reactions. Sulfur column densities are the lowest throughout the atmosphere because S is created slowly via direct dissociation of SO₂; it is instead created primarily through dissociation of SO. The momentum transfer from the plasma is found to have substantial effect on the global wind patterns. The interaction between the plasma pressure and day-to-night pressure gradient is highly dependent on Io's subsolar longitude. Similar to previous simulations, the westward winds reach higher Mach numbers and wind speeds than the eastward winds. This is because the westward winds are accelerated by a larger day-to-night pressure gradient due to the very cold surface temperatures that exist prior to dawn. Eastward equatorial winds on the nightside are accelerated by the plasma pressure and condense out near the dawn terminator after traveling ~3/4 of the circumference of Io. O₂ is pushed to the nightside by the circumplanetary winds where it builds-up until it reaches an equilibrium column density. On the nightside, O₂ is destroyed by ion dissociation. On the nightside, a shear layer develops between the equatorial eastward winds and stagnant non-condensable species at mid-latitudes. This shear layer generates lateral vorticity which is especially visible in O₂ streamlines. Large cyclones develop in the northern and southern hemispheres and are most apparent in the O₂ wind patterns because other species condense out on the nightside. / text

Io, the innermost Galilean satellite of Jupiter, exhibits a wide variety of complex phenomena such as interaction with Jupiter’s magnetosphere, volcanic activity, and a rarefied multi-species sublimating and condensing atmosphere with an ionosphere. Io’s orbital resonance with Jupiter and the other Galilean satellites produces intense tidal heating. This makes Io the most volcanically active body in the solar system with plumes that rise hundreds of kilometers above the surface. In the present work, the interaction of Io’s atmosphere with the Jovian plasma torus is simulated via the Direct Simulation Monte Carlo (DSMC) method and the aurora produced via electron-neutral excitation collisions is examined using electron transport Monte Carlo simulation. The electron-transport Monte Carlo simulation models the electron collisions with the neutral atmosphere and their transport along field lines as they sweep past Io, using a pre-computed steady atmosphere and magnetic field. As input to the Monte Carlo simulation, the neutral atmosphere was first modeled using prior 2D sunlit continuum simulations of Io’s atmosphere produced by others. In order to justify the use of a sunlit atmosphere for eclipse, 1D two-species (SO2 and a non-condensable) DSMC simulations of Io’s atmospheric dynamics during and immediately after eclipse were performed. It was found that the inclusion of a non-condensable species (SO or O2) leads to the formation of a diffusion layer which prevents rapid collapse. The degree to which the diffusion layer slowed the atmospheric collapse was found to be extremely sensitive to both the initial non-condensable mole fraction and the reaction (or sticking) probability on the surface of the “non-condensable”. Furthermore, upon egress, vertical stratification of the atmosphere occurred with the non-condensable species being lifted to higher altitudes by the rapid sublimation of SO2 as the surface warms. Simulated aurorae (specifically the [OI] 6300 Å and the S2, SO, and SO2 molecular band emission in the middle ultraviolet) show good agreement with observations of Io in eclipse and an attempt was made to use the simulations to constrain the upstream torus electron temperature and Io’s atmospheric composition, structure, and volcanic activity. It is found that the position of the bright [OI] 6300 Å wake spot relative to Io’s equator depends on the position of Io relative to the plasma torus’ equator and the asymmetric electron number flux that results. Using HST/STIS UV-Vis spectra, the upstream electron temperature is weakly constrained to be between 3 eV and 8 eV depending on the flux of a low energy (35 eV), non-thermal component of the plasma (more non-thermal flux requires lower thermal plasma temperatures to fit the spectrum). Furthermore, an upper limit of 5% of the thermal torus density (or 180 cm−3 based on the Galileo J0 plasma density at Io) is obtained for the low energy non-thermal component of the plasma. These limits are consistent with Galileo observations of the upstream torus temperature and estimates for the the non-thermal component. Finally, plume activity and S2 content during eclipse observations with HST/STIS were constrained by examining the emission intensity along the spatial axis of the aperture. During the August 1999 UV-Vis observations, the auroral simulations indicate that the large volcanoes Pele and Surt were inactive whereas Tvashtar was active and that Dazhbog and possibly Loki were also actively venting gas. The S2 content inferred for the large Pele-type plumes was between 5% (Tvashtar) and 30% (Loki, if active), consistent with prior observations (Spencer et al., 2000; Jessup et al., 2007). A 3D DSMC simulation of Io’s sublimation and sputtered atmosphere including photo- and plasma-chemistry was developed. In future work these atmospheric simulations will replace the continuum target atmosphere in the auroral model and thus enable a better match to the observed high altitude auroral emission. In the present work, the plasma interaction is modeled by a flux of ions and electrons which flow around and through Io’s atmosphere along pre-computed fields and interact with the neutral gas. A 3D DSMC simulation of Io’s atmosphere assuming a simple thermal model for the surface just prior to ingress into eclipse and uniform frost coverage has been performed in order to understand how Io’s general atmospheric dynamics are affected by the new plasma model with chemistry and sputtering. Sputtering was found to supply most of the nightside atmosphere (producing an SO2 column of ~5×1013 cm−2); however, the dense dayside sublimation atmosphere was found to block sputtering of the surface. The influence of the dynamic plasma pressure on the day-to-night circumplanetary flow was found to be quite substantial causing the day-to-night wind across the dawn terminator to flow slightly towards the equator. This results in a region of high density near the equator that extends far (~2000 km for the condensable species) onto the nightside across the dawn terminator. Thus, even without thermal lag due to rotation or variable surface frost, highly asymmetric equatorial column densities relative to the subsolar point are obtained. The non-condensable O2, which is a trace species on the dayside, is the dominant species on the nightside despite increased SO2 sputtering because the loss rate of O2 is slow. Finally, a very intriguing O2 flow feature was observed near the dusk terminator where the flow from the leading hemisphere (pushed by the plasma) meets the flow from the dayside trailing hemisphere. Since the O2 does not condense on the surface, it slowly convects towards the poles and then back onto the nightside, eventually to be dissociated or stripped away by the plasma. / text

A three-dimensional (3D) steady-state electron modulation model based on Parker (1965) transport equation is applied to study the modelling of – 7 MeV galactic and Jovian electrons in the inner heliosphere. The latter is produced within Jupiter's magnetosphere which is situated at - 5 AU in the ecliptic plane. The heliospheric propagation of these particles is mainly described by the heliospheric diffusion tensor. Some elements of the tensor, such as the diffusion coefficient in the azimuthal direction, which were neglected in the previous two-dimensional modulation studies are investigated to account for the three-dimensional transport of Jovian electrons. Different anisotropic solar wind speed profiles that could represent solar minimum conditions were modelled and their effects were illustrated by computing the distribution of 7 MeV Jovian electrons in the equatorial regions. In particular, the electron intensity time-profile along the Ulysses spacecraft trajectory was calculated for these speed profiles and compared to the 3-10 MeV electron flux observed by the Kiel Electron Telescope (KET) on board the Ulysses spacecraft from launch (1990) up to end of its first out-of-ecliptic orbit (2000). It was found that the model solution computed with the solar wind profile previously assumed for typical solar minimum conditions produced good compatibility with observations up to 1998. After 1998 all model solutions deviated completely from the observations. In this study, as a further attempt to model KET observations more realistically, a new relation is established between the latitudinal dependence of the solar wind speed and the perpendicular polar diffusion. Based on this relation, a transition of an average solar wind speed from solar minimum conditions to intermediate solar activity and to solar maximum conditions was modelled based on the assumption of the time-evolution of large polar coronal holes and were correlated to different scenarios of the enhancement of perpendicular polar diffusion. Effects of these scenarios were illustrated, as a series of steady-state solutions, on the computed 7 MeV Jovian and galactic electrons in comparison with the 3-10 MeV electron observed by the KET instrument from the period 1998 up to the end of 2003. Subsequent effects of these scenarios were also shown on electron modulation in general. It was found that this approach improved modelling of the post-1998 discrepancy between the model and KET observations but it also suggested the need for a time-dependent 3D electron modulation model to describe modulation during moderate to extreme solar maximum conditions. / Thesis (M.Sc.)--North-West University, Potchefstroom Campus, 2004.

A three-dimensional (3D) steady-state electron modulation model based on Parker (1965) transport equation is applied to study the modelling of – 7 MeV galactic and Jovian electrons in the inner heliosphere. The latter is produced within Jupiter's magnetosphere which is situated at - 5 AU in the ecliptic plane. The heliospheric propagation of these particles is mainly described by the heliospheric diffusion tensor. Some elements of the tensor, such as the diffusion coefficient in the azimuthal direction, which were neglected in the previous two-dimensional modulation studies are investigated to account for the three-dimensional transport of Jovian electrons. Different anisotropic solar wind speed profiles that could represent solar minimum conditions were modelled and their effects were illustrated by computing the distribution of 7 MeV Jovian electrons in the equatorial regions. In particular, the electron intensity time-profile along the Ulysses spacecraft trajectory was calculated for these speed profiles and compared to the 3-10 MeV electron flux observed by the Kiel Electron Telescope (KET) on board the Ulysses spacecraft from launch (1990) up to end of its first out-of-ecliptic orbit (2000). It was found that the model solution computed with the solar wind profile previously assumed for typical solar minimum conditions produced good compatibility with observations up to 1998. After 1998 all model solutions deviated completely from the observations. In this study, as a further attempt to model KET observations more realistically, a new relation is established between the latitudinal dependence of the solar wind speed and the perpendicular polar diffusion. Based on this relation, a transition of an average solar wind speed from solar minimum conditions to intermediate solar activity and to solar maximum conditions was modelled based on the assumption of the time-evolution of large polar coronal holes and were correlated to different scenarios of the enhancement of perpendicular polar diffusion. Effects of these scenarios were illustrated, as a series of steady-state solutions, on the computed 7 MeV Jovian and galactic electrons in comparison with the 3-10 MeV electron observed by the KET instrument from the period 1998 up to the end of 2003. Subsequent effects of these scenarios were also shown on electron modulation in general. It was found that this approach improved modelling of the post-1998 discrepancy between the model and KET observations but it also suggested the need for a time-dependent 3D electron modulation model to describe modulation during moderate to extreme solar maximum conditions. / Thesis (M.Sc.)--North-West University, Potchefstroom Campus, 2004.

Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2007.

Accurate knowledge of the centimeter- and millimeter-wavelength absorptivity of ammonia is necessary for the interpretation of the emission spectra of the jovian planets. The objective of this research has been to advance the understanding of the centimeter- and millimeter-wavelength opacity spectra of ammonia under jovian conditions using a combination of laboratory measurements and theoretical formulations. As part of this research, over 1000 laboratory measurements of the 2-4 mm-wavelength properties of ammonia under simulated upper and middle tropospheric conditions of the jovian planets, and approximately 1200 laboratory measurements of the 5-20 cm-wavelength properties of ammonia under simulated deep tropospheric conditions of the jovian planets have been performed. Using these and pre-existing measurements, a consistent mathematical formalism has been developed to reconcile the centimeter- and millimeter-wavelength opacity spectra of ammonia. This formalism can be used to estimate the opacity of ammonia in a hydrogen/helium atmosphere in the centimeter-wavelength range at pressures up to 100 bar and temperatures in the 200 to 500 K range and in the millimeter-wavelength range at pressures up to 3 bar and temperatures in the 200 to 300 K range. In addition, a preliminary investigation of the influence of water vapor on the centimeter-wavelength ammonia absorptivity spectra has been conducted. This work addresses the areas of high-sensitivity centimeter- and millimeter-wavelength laboratory measurements, and planetary science, and contributes to the body of knowledge that provides clues into the origin of our solar system. The laboratory measurements and the model developed as part of this doctoral research work can be used for interpreting the emission spectra of jovian atmospheres obtained from ground-based and spacecraft-based observations. The results of the high-pressure ammonia opacity measurements will also be used to support the interpretation of the microwave radiometer (MWR) measurements on board the NASA Juno spacecraft at Jupiter.

The three-dimensional (3D) steady-state electron modulation model of Ferreira (2002), based on Parker (1965) transport equation, is used to study the modulation of the 7 MeV galactic and Jovian electron anisotropies in the inner heliosphere. The Jovian electrons are produced in Jupiter's magnetosphere which is situated at ~ 5 AU in the ecliptic plane. The propagation of these particles is mainly described by the diffusion tensor applicable for the inner heliosphere. Some of the elements of the diffusion tensor are revisited in order to establish what contribution they make to the three-dimensional anisotropy vector and its components in the inner heliosphere. The 'drift' term is neglected since the focus of this study is on low-energy electrons. The effects on the electron anisotropy of different scenarios when changing the solar wind speed from minimum to maximum activity is illustrated. The effects on both the galactic and Jovian electron anisotropy of changing the polar perpendicular coefficient, in particular, are illustrated. It is shown that the computed Jovian electron anisotropy dominates the galactic anisotropy close to the Jovian electron source at ~5 AU, as expected, testifying to the validity of the3D-model. For the latitudinal anisotropy, the polar perpendicular diffusion plays a dominant role for Jovian electrons close to the source, with the polar gradient becoming the dominant factor away from the electron source. Of all three anisotropy components, the azimuthal anisotropy is dominant in the equatorial plane close to the source. It is found that there is a large azimuthal gradient close to the source because the low-energy electrons tend to follow the heliospheric magnetic field more closely than higher energy particles. The transition of the solar wind speed from minimum to intermediate to maximum solar activity condition was used to illustrate the modulation of the magnitude of the 7 MeV total anisotropy vector along the Ulysses trajectory. It was found that during the two encounters with the planet a maximum anisotropy of 38% was computed but with different anisotropy-timepeaks as the approach to Jupiter was different. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2007.

The three-dimensional (3D) steady-state electron modulation model of Ferreira (2002), based on Parker (1965) transport equation, is used to study the modulation of the 7 MeV galactic and Jovian electron anisotropies in the inner heliosphere. The Jovian electrons are produced in Jupiter's magnetosphere which is situated at ~ 5 AU in the ecliptic plane. The propagation of these particles is mainly described by the diffusion tensor applicable for the inner heliosphere. Some of the elements of the diffusion tensor are revisited in order to establish what contribution they make to the three-dimensional anisotropy vector and its components in the inner heliosphere. The 'drift' term is neglected since the focus of this study is on low-energy electrons. The effects on the electron anisotropy of different scenarios when changing the solar wind speed from minimum to maximum activity is illustrated. The effects on both the galactic and Jovian electron anisotropy of changing the polar perpendicular coefficient, in particular, are illustrated. It is shown that the computed Jovian electron anisotropy dominates the galactic anisotropy close to the Jovian electron source at ~5 AU, as expected, testifying to the validity of the3D-model. For the latitudinal anisotropy, the polar perpendicular diffusion plays a dominant role for Jovian electrons close to the source, with the polar gradient becoming the dominant factor away from the electron source. Of all three anisotropy components, the azimuthal anisotropy is dominant in the equatorial plane close to the source. It is found that there is a large azimuthal gradient close to the source because the low-energy electrons tend to follow the heliospheric magnetic field more closely than higher energy particles. The transition of the solar wind speed from minimum to intermediate to maximum solar activity condition was used to illustrate the modulation of the magnitude of the 7 MeV total anisotropy vector along the Ulysses trajectory. It was found that during the two encounters with the planet a maximum anisotropy of 38% was computed but with different anisotropy-timepeaks as the approach to Jupiter was different. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2007.

On se propose dans un premier temps d'étudier des jeux de données topographiques sur la lune glacée de Jupiter Ganymède et d'estimer l'impact de la topographie sur les performances du futur radar sondeur. Les principaux résultats sont présentés dans [1]. Une seconde partie est dédiée à l'expression mathématique du problème direct du sondage radar planétaire (physique et instrumentation). On rappelle ainsi comment dériver à partir des formulations de Stratton-Chu les formulations volumiques classiques et surfaciques (i.e. Huygens-Fresnel). On s'attache ensuite à détailler un algorithme performant basé sur la formulation surfacique pour simuler des échos radar à partir d'une surface planétaire maillée. Cette approche est largement inspirée par le travail de J.-F. Nouvel [2]. Une troisième partie s'intéresse à l'inversion des paramètres géophysiques de surface à partir des mesures radar. On écrit ainsi le problème dans un cadre probabiliste (c.f. [3]) et on présente trois grandes familles d'algorithmes : (i) une approche avec une linéarisation du problème, (ii) une approche itérative basée sur une méthode de gradient et (iii) une approche statistique pour estimer les densités de probabilités a posteriori. Ces algorithmes sont appliqués à des jeux de données synthétiques pour illustrer leurs performances. [1] Y. Berquin, W. Kofman, A. Herique, G. Alberti, and P. Beck. A study on ganymede's surface topography: Perspectives for radar sounding. Planetary and Space Science, (0), 2012. [2] J.-F. Nouvel, A. Herique, W. Kofman, and A. Safaeinili. Radar signal simulation: Surface modeling with the Facet Method. Radio Science, 39:RS1013, February 2004. [3] A. Tarantola. Inverse problem theory and methods for model parameter estimation. SIAM, 2005. / The manuscript details the work performed in the course of my PhD on planetary sounding radar. The main goal of the study is to help designing and assessing the sounding radar performances. This instrument will be embarked on the ac{ESA}'s large class mission ac{JUICE} to probe Jupiter's environment and Jupiter's icy moons Callisto, Ganymede and Europa. As an introduction to the problem, a study on Ganymede's surface ac{DEM} and its implications with regard to the radar performances was performed. The results of this work put forward issues due to a hostile environment with important surface clutter which eventually lead to a decrease in the radar signal bandwidth to 8--10 MHz. A first section is then dedicated to the formulation of the direct problem of sounding radar with a focus on surface formulations. This section eventually leads to a novel algorithm for radar surface echo computation from meshed surfaces which proves to be both efficient and accurate. A second section studies the possibility to use surface formulation to recover geophysical surface parameters from sounding radar data. For that purpose, three main approaches are discussed namely (i) a linear approach, (ii) a gradient-based approach and (iii) a statistical approach. These techniques rely on a probabilistic view of the inverse problem at hand and yield good result with different setups. Although we mainly focus on surface reflectivity, we also discuss surface topography inversion. Finally, a last section discusses the work presented in the manuscript and provides perspectives for future work.