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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Benamou JD, Brenier Y (2000) A computational fluid mechanics solution to the Monge–Kantorovich mass transfer problem. Numer Math 84(3):375–393
Bertsekas DP (1991) Linear network optimization: algorithms and codes. MIT Press, Cambridge
Bertsekas DP (1992) Auction algorithms for network flow problems: a tutorial introduction. Comput Optim Appl 1:7–66
Bossy M (2005) Some stochastic particle methods for nonlinear parabolic pdes. ESAIM Proc 15:18–57
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
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
Das SK, Durbin PA (2005) A Lagrangian stochastic model for dispersion in stratified turbulence. Phys Fluids 17(2):025109
Deardorff J (1980) Stratocumulus-capped mixed layers derived from a three-dimensional model. Bound-Layer Meteorol 18:495–527
Dreeben T, Pope S (1997) Wall-function treatment in PDF methods for turbulent flows. Phys Fluids 9(9):2692–2703
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
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
Guermond JL, Quartapelle L (1997) Calculation of incompressible viscous flows by an unconditionally stable projection FEM. J Comput Phys 132(1):12–33
Krettenauer K, Schumann U (1992) Numerical simulation of turbulent convection over wavy terrain. J Fluid Mech 237:261–299
Mass FC, Ovens D, Westrick K, Colle B (2002) Does increasing horizontal resolution produce more skillful forecast? Bull Am Meteorol Soc 83:407–430
McCann RJ (1995) Existence and uniqueness of monotone measure-preserving maps. Duke Math J 80(2):309–323
Mohammadi B, Pironneau O (1994) Analysis of the k-epsilon turbulence model. Masson, Paris
Mora CM (2005) Weak exponential schemes for stochastic differential equations with additive noise. IMA J Numer Anal 25(3):486–506
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
Pope S (1985) PDF methods for turbulent reactive flows. Prog Energy Comb Sci 11:119–192
Pope S (1993) On the relationship between stochastic Lagrangian models of turbulence and second-moment closures. Phys Fluids 6:973–985
Pope S (1994) Lagrangian PDF methods for turbulent flows. Annu Rev Fluid Mech 26:23–63
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
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
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
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
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
Xu J, Pope S (1999) Assessement of numerical accuracy of PDF/Monte Carlo methods for tubulent reacting flows. J Comput Phys 152:192–230
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
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This work was partially supported by ADEME.
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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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DOI: https://doi.org/10.1007/s00477-008-0276-9