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Stochastic downscaling method: application to wind refinement

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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 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.

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References

  • Benamou JD, Brenier Y (2000) A computational fluid mechanics solution to the Monge–Kantorovich mass transfer problem. Numer Math 84(3):375–393

    Article  Google Scholar 

  • Bertsekas DP (1991) Linear network optimization: algorithms and codes. MIT Press, Cambridge

    Google Scholar 

  • Bertsekas DP (1992) Auction algorithms for network flow problems: a tutorial introduction. Comput Optim Appl 1:7–66

    Google Scholar 

  • Bossy M (2005) Some stochastic particle methods for nonlinear parabolic pdes. ESAIM Proc 15:18–57

    Google Scholar 

  • Bossy M, Jabir JF (2008) Confined Langevin processes and mean no-permeability condition (preprint)

  • Bossy M, Jabir JF, Talay D (2008) Mathematical study of simplified lagrangian stochastic models (preprint)

  • Carlotti P, Drobinski P (2004) Length-scales in wall-bounded high reynolds number turbulence. J Fluid Mech 516:239–264

    Article  Google Scholar 

  • 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)

  • Cuxart J, Bougeault P, Redelsperger J (2000) A multiscale turbulence scheme apt for LES and mesoscale modelling. Q J R Meteorol Soc 126:1–30

    Article  Google Scholar 

  • Das SK, Durbin PA (2005) A Lagrangian stochastic model for dispersion in stratified turbulence. Phys Fluids 17(2):025109

    Article  CAS  Google Scholar 

  • Deardorff J (1980) Stratocumulus-capped mixed layers derived from a three-dimensional model. Bound-Layer Meteorol 18:495–527

    Article  Google Scholar 

  • Dreeben T, Pope S (1997) Wall-function treatment in PDF methods for turbulent flows. Phys Fluids 9(9):2692–2703

    Article  Google Scholar 

  • 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)

  • 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 121:1493–1513

    Article  Google Scholar 

  • 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 17:708–720

    Google Scholar 

  • Guermond JL, Quartapelle L (1997) Calculation of incompressible viscous flows by an unconditionally stable projection FEM. J Comput Phys 132(1):12–33

    Article  CAS  Google Scholar 

  • Krettenauer K, Schumann U (1992) Numerical simulation of turbulent convection over wavy terrain. J Fluid Mech 237:261–299

    Article  CAS  Google Scholar 

  • Mass FC, Ovens D, Westrick K, Colle B (2002) Does increasing horizontal resolution produce more skillful forecast? Bull Am Meteorol Soc 83:407–430

    Article  Google Scholar 

  • McCann RJ (1995) Existence and uniqueness of monotone measure-preserving maps. Duke Math J 80(2):309–323

    Article  Google Scholar 

  • Mohammadi B, Pironneau O (1994) Analysis of the k-epsilon turbulence model. Masson, Paris

    Google Scholar 

  • Mora CM (2005) Weak exponential schemes for stochastic differential equations with additive noise. IMA J Numer Anal 25(3):486–506

    Article  Google Scholar 

  • Øksendal B (1995) Stochastic differential equations. Springer, Heidelberg

  • Piper M, Lundquist J (2004) Surface layer turbulence measurements during a frontal passage. J Atmos Sci 61:1768–1780

    Article  Google Scholar 

  • Pope S (1985) PDF methods for turbulent reactive flows. Prog Energy Comb Sci 11:119–192

    Article  Google Scholar 

  • Pope S (1993) On the relationship between stochastic Lagrangian models of turbulence and second-moment closures. Phys Fluids 6:973–985

    Article  Google Scholar 

  • Pope S (1994) Lagrangian PDF methods for turbulent flows. Annu Rev Fluid Mech 26:23–63

    Article  Google Scholar 

  • Pope S (2003) Turbulent flows. Cambridge University Press, Cambridge

  • Pryor SC, Schoof JT, Barthelmie RJ (2006) Empirical downscaling of wind speed probability distributions. J Geophys Res 110. doi:10.1029/2005JD005899

  • 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 21:509–530

    Article  Google Scholar 

  • 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 101:375–408

    Article  Google Scholar 

  • 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 526–528

  • 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 11:2271–2291

    Article  Google Scholar 

  • Salameh T, Drobinski P, Vrac M, Naveau P (2008) Statistical downscaling of near-surface wind over complex terrain in southern france (in preparation)

  • Schmidt H, Schumann U (1989) Coherent structure of the convective boundary layer derived from large-eddy simulation. J Fluid Mech 200:511–562

    Article  Google Scholar 

  • 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 148–196

  • Villani C (2003) Topics in optimal transportation. Graduate Studies in Mathematics, vol 58. American Mathematical Society, Providence

    Google Scholar 

  • Xu J, Pope S (1999) Assessement of numerical accuracy of PDF/Monte Carlo methods for tubulent reacting flows. J Comput Phys 152:192–230

    Article  CAS  Google Scholar 

  • 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:445–455

    Google Scholar 

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Acknowledgments

This work was partially supported by ADEME.

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Correspondence to Antoine Rousseau.

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Bernardin, F., Bossy, M., Chauvin, C. et al. Stochastic downscaling method: application to wind refinement. Stoch Environ Res Risk Assess 23, 851–859 (2009). https://doi.org/10.1007/s00477-008-0276-9

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