The SPDE approach for spatio-temporal datasets with advection and diffusion - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

The SPDE approach for spatio-temporal datasets with advection and diffusion

(1) , (2) , (1) , (1)
Lucia Clarotto
  • Function : Correspondent author
  • PersonId : 1113622

Connectez-vous pour contacter l'auteur
Denis Allard
  • Function : Author
  • PersonId : 1136613
Thomas Romary
Nicolas Desassis


In the task of predicting spatio-temporal fields in environmental science, introducing models inspired by the physics of the underlying phenomena that are numerically efficient is of growing interest in spatial statistics. The size of space-time datasets calls for new numerical methods to efficiently process them. The SPDE (Stochastic Partial Differential Equation) approach has proven to be effective for the estimation and the prediction in a spatial context. We present here the advection-diffusion SPDE with first order derivative in time to enlarge the SPDE family to the space-time context. By varying the coefficients of the differential operators, the approach allows to define a large class of non-separable spatio-temporal models. A Gaussian Markov random field approximation of the solution of the SPDE is built by discretizing the temporal derivative with a finite difference method (implicit Euler) and by solving the purely spatial SPDE with a finite element method (continuous Galerkin) at each time step. The "Streamline Diffusion" stabilization technique is introduced when the advection term dominates the diffusion term. Computationally efficient methods are proposed to estimate the parameters of the SPDE and to predict the spatio-temporal field by kriging. The approach is applied to a solar radiation dataset. Its advantages and limitations are discussed.
Fichier principal
Vignette du fichier
main.pdf (1.96 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03762403 , version 1 (29-08-2022)
hal-03762403 , version 2 (16-12-2022)


Attribution - CC BY 4.0



Lucia Clarotto, Denis Allard, Thomas Romary, Nicolas Desassis. The SPDE approach for spatio-temporal datasets with advection and diffusion. 2022. ⟨hal-03762403v1⟩



24 View
14 Download



Gmail Facebook Twitter LinkedIn More