In mountainous areas orographic effects create strong horizontal gradients of various rainfall statistics such as the frequency of occurrence, the distribution of intensity and the structure of spatial correlation.
To account for these non-stationary statistics this paper presents a non-stationary trans-Gaussian model tailored for daily rainfall over complex topography.
Publications
Spline interpolation is a widely used class of methods for solving interpolation problems by constructing smooth interpolants that minimize a regularized energy functional involving the Laplacian operator. While many existing approaches focus on Euclidean domains or the sphere, relying on the spectral properties of the Laplacian, this work introduces a method for spline interpolation on general manifolds by exploiting its equivalence with kriging.
Gaussian processes are widely used to make spatial predictions and to estimate uncertainty. But they usually assume that the studied phenomenon has a stationary structure —an assumption often violated with today’s large datasets from sensors or satellites. To overcome this, this paper explores a space deformation strategy:
This paper illustrates how progress in spatial statistics is fueled by scientific questions arising from applications in agriculture and environment. The unifying theme is the work that has been carried out at BioSP, a statistics and mathematics research unit mainly affiliated to the ``Mathematics and Digital Technologies" division at INRAE, the French National Research Institute for Agriculture, Food and Environment.
Structural geological modeling is aimed at finding a representation of geological units. This is a complex ill-posed problem, and the data may be sparse and of varying quality, leading to multiple geological models consistent with them. A generative adversarial network is trained to generate two-dimensional unconditional geomodels that are plausible. Then a Metropolis-adjusted Langevin algorithm is used to produce geomodels consistent with field data.
In order to estimate the return period of bivariate CEs, a novel non-parametric approach employing bivariate Generalized Pareto distributions (bi-GPD) is proposed and compared to a copula-based approach. Simulations reveal that this approach is effective in case of positive asymptotic dependence and should be avoided in case of asymptotic independence.
This work leverages the Gaussian mixture perspective to propose extensions of the spectral simulation approach for Gaussian Random Fields covering new classes of covariance functions for nonstationary (univariate or multivariate) spatio-temporal GRFs, as well as simulation algorithms for those that are currently missing in the framework of spectral simulation.
Nous explorons l’utilisation des réseaux génératifs antagonistes et de l’inférence variationnelle profonde pour simuler conditionnellement des réservoirs chenalisés méandriformes. Nous comparons des approches d’apprentissage profond, notamment les W-GAN et un modèle de conditionnement par mélange gaussien, en utilisant des simulations 2D/3D issues du modèle stochastique Flumy. Les résultats montrent que ces réseaux, grâce aux techniques récentes de stabilisation, permettent de reproduire efficacement des distributions complexes avec un réalisme accru.
Nous proposons un nouveau générateur météorologique multivarié spatio-temporel, appelé MSTWeatherGen, qui tire parti de développements récents pour modéliser et simuler différentes variables météorologiques, notamment la température, les précipitations, la vitesse du vent, l'humidité et le rayonnement solaire, dans l'espace et dans le temps.
Nous introduisons une nouvelle méthode d'agrégation des probabilités appelée « alpha pooling » qui construit une fonction de répartition agrégée conçue pour être plus proche d'une fonction de répartition de référence sur la période d'étalonnage (historique). La clé du α- pooling est un paramètre α qui décrit le type de transformation et donc le type d'agrégation, généralisant les méthodes de agrégation linéaires et log-linéaires.