Stochastic downscaling method: application to wind refinement

  • Frédéric Bernardin
  • Mireille Bossy
  • Claire Chauvin
  • Philippe Drobinski
  • Antoine Rousseau
  • Tamara Salameh
Original Paper


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 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.


Stochastic differential equations Downscaling method Wind simulation 



This work was partially supported by ADEME.


  1. Benamou JD, Brenier Y (2000) A computational fluid mechanics solution to the Monge–Kantorovich mass transfer problem. Numer Math 84(3):375–393CrossRefGoogle Scholar
  2. Bertsekas DP (1991) Linear network optimization: algorithms and codes. MIT Press, CambridgeGoogle Scholar
  3. Bertsekas DP (1992) Auction algorithms for network flow problems: a tutorial introduction. Comput Optim Appl 1:7–66Google Scholar
  4. Bossy M (2005) Some stochastic particle methods for nonlinear parabolic pdes. ESAIM Proc 15:18–57Google Scholar
  5. Bossy M, Jabir JF (2008) Confined Langevin processes and mean no-permeability condition (preprint)Google Scholar
  6. Bossy M, Jabir JF, Talay D (2008) Mathematical study of simplified lagrangian stochastic models (preprint)Google Scholar
  7. Carlotti P, Drobinski P (2004) Length-scales in wall-bounded high reynolds number turbulence. J Fluid Mech 516:239–264CrossRefGoogle Scholar
  8. Chauvin C, Hirstoaga S, Kabelikova P, Bernardin F, Rousseau A (2007) Solving the uniform density constraint in a downscaling stochastic model. In: ESAIM Proc (to appear)Google Scholar
  9. Cuxart J, Bougeault P, Redelsperger J (2000) A multiscale turbulence scheme apt for LES and mesoscale modelling. Q J R Meteorol Soc 126:1–30CrossRefGoogle Scholar
  10. Das SK, Durbin PA (2005) A Lagrangian stochastic model for dispersion in stratified turbulence. Phys Fluids 17(2):025109CrossRefGoogle Scholar
  11. Deardorff J (1980) Stratocumulus-capped mixed layers derived from a three-dimensional model. Bound-Layer Meteorol 18:495–527CrossRefGoogle Scholar
  12. Dreeben T, Pope S (1997) Wall-function treatment in PDF methods for turbulent flows. Phys Fluids 9(9):2692–2703CrossRefGoogle Scholar
  13. Drobinski P, Redelsperger J, Pietras C (2006) Evaluation of a planetary boundary layer subgrid-scale model that accounts for near-surface turbulence anisotropy. Geophys Res Let 33(L23806)Google Scholar
  14. Dudhia JA (1993) Nonhydrostatic version of the Penn State-NCAR mesoscale model: validation tests and simulation of an atlantic cyclone and cold front. Mon Weather Rev 121:1493–1513CrossRefGoogle Scholar
  15. Graber H, Terray EA, Donelan MA, Drennan WM, Leer JCV, Peters DB (1999) Asis—a new air–sea interaction spar buoy: design and performance at sea. J Atmos Oceanic Technol 17:708–720Google Scholar
  16. Guermond JL, Quartapelle L (1997) Calculation of incompressible viscous flows by an unconditionally stable projection FEM. J Comput Phys 132(1):12–33CrossRefGoogle Scholar
  17. Krettenauer K, Schumann U (1992) Numerical simulation of turbulent convection over wavy terrain. J Fluid Mech 237:261–299CrossRefGoogle Scholar
  18. Mass FC, Ovens D, Westrick K, Colle B (2002) Does increasing horizontal resolution produce more skillful forecast? Bull Am Meteorol Soc 83:407–430CrossRefGoogle Scholar
  19. McCann RJ (1995) Existence and uniqueness of monotone measure-preserving maps. Duke Math J 80(2):309–323CrossRefGoogle Scholar
  20. Mohammadi B, Pironneau O (1994) Analysis of the k-epsilon turbulence model. Masson, ParisGoogle Scholar
  21. Mora CM (2005) Weak exponential schemes for stochastic differential equations with additive noise. IMA J Numer Anal 25(3):486–506CrossRefGoogle Scholar
  22. Øksendal B (1995) Stochastic differential equations. Springer, HeidelbergGoogle Scholar
  23. Piper M, Lundquist J (2004) Surface layer turbulence measurements during a frontal passage. J Atmos Sci 61:1768–1780CrossRefGoogle Scholar
  24. Pope S (1985) PDF methods for turbulent reactive flows. Prog Energy Comb Sci 11:119–192CrossRefGoogle Scholar
  25. Pope S (1993) On the relationship between stochastic Lagrangian models of turbulence and second-moment closures. Phys Fluids 6:973–985CrossRefGoogle Scholar
  26. Pope S (1994) Lagrangian PDF methods for turbulent flows. Annu Rev Fluid Mech 26:23–63CrossRefGoogle Scholar
  27. Pope S (2003) Turbulent flows. Cambridge University Press, CambridgeGoogle Scholar
  28. Pryor SC, Schoof JT, Barthelmie RJ (2006) Empirical downscaling of wind speed probability distributions. J Geophys Res 110. doi: 10.1029/2005JD005899
  29. Redelsperger J, Sommeria G (1981) Méthode de représentation de la turbulence l’échelle inférieure à la maille pour un modèle tridimensionnel de convection nuageuse. Bound Layer Meteor 21:509–530CrossRefGoogle Scholar
  30. Redelsperger J, Mahé F, Carlotti P (2001) A simple and general subgrid model suitable both for surface layer and free-stream turbulence. Bound Layer Meteor 101:375–408CrossRefGoogle Scholar
  31. Rousseau A, Bernardin F, Bossy M, Drobinski P, Salameh T (2007) Stochastic particle method applied to local wind simulation. In: Proceedings of IEEE international conference on clean electrical power, IEEE, Capri, Italy, pp 526–528Google Scholar
  32. Salameh T, Drobinski P, Menut L, Bessagnet B, Flamant C, Hodzic A, Vautard R (2007) Aerosol distribution over the western mediterranean basin during a tramontane/mistral event. Ann Geophys 11:2271–2291CrossRefGoogle Scholar
  33. Salameh T, Drobinski P, Vrac M, Naveau P (2008) Statistical downscaling of near-surface wind over complex terrain in southern france (in preparation)Google Scholar
  34. Schmidt H, Schumann U (1989) Coherent structure of the convective boundary layer derived from large-eddy simulation. J Fluid Mech 200:511–562CrossRefGoogle Scholar
  35. Talay D (1996) Probabilistic numerical methods for partial differential equations: elements of analysis. In: Talay D, Tubaro L (eds) Probabilistic models for nonlinear partial differential equations. Lecture notes in mathematics, vol 1627. Springer, Heidelberg, pp 148–196Google Scholar
  36. Villani C (2003) Topics in optimal transportation. Graduate Studies in Mathematics, vol 58. American Mathematical Society, ProvidenceGoogle Scholar
  37. Xu J, Pope S (1999) Assessement of numerical accuracy of PDF/Monte Carlo methods for tubulent reacting flows. J Comput Phys 152:192–230CrossRefGoogle Scholar
  38. Žagar N, Žagar M, Cedilnik J, Gregorič G, Rakoveg J (2006) Validation of mesoscale low-level winds obtained by dynamical downscaling of ERA40 over complex terrain. Tellus 58A:445–455Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Frédéric Bernardin
    • 1
  • Mireille Bossy
    • 2
  • Claire Chauvin
    • 3
  • Philippe Drobinski
    • 4
  • Antoine Rousseau
    • 3
  • Tamara Salameh
    • 4
  1. 1.CETE de LyonLaboratoire Régional des Ponts et ChausséesClermont-FerrandFrance
  2. 2.ToscaINRIASophia AntipolisFrance
  3. 3.MoiseINRIAGrenobleFrance
  4. 4.CNRS, Laboratoire de Météorologie DynamiquePalaiseauFrance

Personalised recommendations