Stochastic downscaling method: application to wind refinement

Abstract

In this article, we propose a new stochastic downscaling method: provided a numerical prediction of wind at large scale, we aim to improve the approximation at small scales thanks to a local stochastic model. We first recall the framework of a Lagrangian stochastic model borrowed from S.B. Pope. Then, we adapt it to our meteorological framework, both from the theoretical and numerical viewpoints. Finally, we present some promising numerical results corresponding to the simulation of wind over the Mediterranean Sea.

Existence of pathwise unique Langevin processes on polytopes with perfect reflection at the boundary

“…Note that our results are disjoint to the results by Bossy and Jabir [3] on C 3 -domains, as we consider domains with edges and corners. To put our result into the context of the articles mentioned above, we note that the box domains considered in this article are the natural ones to use in the downscaling problems studied in [1]. The extension of our results to nonlinear Langevin processes is work in progress.…”

“…In particular, Langevin processes are used in probability density function (PDF) methods for simulation of turbulent ‡ows. For the general theory of PDF methods in turbulence, we refer the reader to the monograph by Pope [10] and for an application of the well-posedness results by Bossy et al, the reader is referred to [1].…”

A new downscaling method for sub-grid turbulence modeling

“…Previous studies have already explored stochastic downscaling methods for the fifth-generation Penn State-NCAR mesoscale model MM5 (see Rousseau et al, 2007;Bernardin et al, 2009Bernardin et al, , 2010. Like these studies, our work aims at modeling the wind on very small scales in a limited area.…”

“…Thus, the whole system contains 19 200 particles. This number may be compared to the 800 particles per grid cell used by Bernardin et al (2009) for the same kind of application.…”

Stochastic Lagrangian method for downscaling problems in computational fluid dynamics

“…In this work, we consider a new approach for the downscaling in CFD, although the authors are particularly interested in applications to meteorology, in collaboration with physicists (see [1]). The local model that we propose is inspired from Pope's previous works on turbulence (see [25,28]): it consists in modelling the fundamental equations of fluid motion by a stochastic Lagrangian model describing the behaviour of a fluid particle.…”