VI Workshop Brasileiro de Micrometeorologia

Transcription

1 Validation of a statistic algorithm applied to LES model Eduardo Bárbaro, Amauri Oliveira, Jacyra Soares November 2009

2 Index Objective 1 Objective 2 3 Vertical Profiles Flow properties 4

3 Objective 1 The main objective of this work is to develop a statistical algorithm to process the data generated by the Large-Eddy-Simulation model (LES) in real time. 2 Use the LES model to characterize the Convective and Stable PBL properties in order to validade the algorithm.

4 Objective 1 The main objective of this work is to develop a statistical algorithm to process the data generated by the Large-Eddy-Simulation model (LES) in real time. 2 Use the LES model to characterize the Convective and Stable PBL properties in order to validade the algorithm. 3 Investigate the Energy Budget vertical profile.

5 Objective 1 The main objective of this work is to develop a statistical algorithm to process the data generated by the Large-Eddy-Simulation model (LES) in real time. 2 Use the LES model to characterize the Convective and Stable PBL properties in order to validade the algorithm. 3 Investigate the Energy Budget vertical profile.

6 Numerical Modeling Basis - A Short Review Main Techniques Reynolds-Averaged Navier-Stokes - RANS Direct Numerical Simulation - DNS Large Eddy Simulation - LES

7 Modeling Basis Short Review - RANS and DNS RANS & DNS RANS - Navier-Stokes statistics ensemble. RANS - Turbulent fluxes simplified solution.

8 Modeling Basis Short Review - RANS and DNS RANS & DNS RANS - Navier-Stokes statistics ensemble. RANS - Turbulent fluxes simplified solution. DNS - The Navier-Stokes equations are resolved explicitly (Large-eddies to Kolmolgorov Scale).

9 Modeling Basis Short Review - RANS and DNS RANS & DNS RANS - Navier-Stokes statistics ensemble. RANS - Turbulent fluxes simplified solution. DNS - The Navier-Stokes equations are resolved explicitly (Large-eddies to Kolmolgorov Scale). DNS - More difficult to use in large areas due to computational problems.

10 Modeling Basis Short Review - RANS and DNS RANS & DNS RANS - Navier-Stokes statistics ensemble. RANS - Turbulent fluxes simplified solution. DNS - The Navier-Stokes equations are resolved explicitly (Large-eddies to Kolmolgorov Scale). DNS - More difficult to use in large areas due to computational problems.

11 Modeling Basis Short Review - LES model LES model - the best of the two worlds! The major eddies are geometry dependent. The minor eddies present a more universal characteristics.

12 Modeling Basis Short Review - LES model LES model - the best of the two worlds! The major eddies are geometry dependent. The minor eddies present a more universal characteristics. The LES model explicity resolve the major eddies and parameterize the minors, using a subgrid SGS model.

13 Modeling Basis Short Review - LES model LES model - the best of the two worlds! The major eddies are geometry dependent. The minor eddies present a more universal characteristics. The LES model explicity resolve the major eddies and parameterize the minors, using a subgrid SGS model.

14 Modeling Basis Short Review - LES model Figure: Energy Cascade; Three regions: (A) production, (B) Inertial Sub-interval and (C) dissipation. k is the wave number, λ m the wavelength associated with the most energetic eddy and η the Kolmogorov s microescale. The max wave number explicitely resolved by the LES is represented by k max (LES).

15 Modeling Basis Short Review - LES main properties Using this kind of model is possible to understand the PBL most important behaviors like momentum, temperature and humidity turbulent fluxes. The LES code used in this work was proposed by Moeng, 1984 and improved by Sullivan, 1994, mainly in the subgrid scheme.

16 Modeling Basis Short Review - LES main properties Using this kind of model is possible to understand the PBL most important behaviors like momentum, temperature and humidity turbulent fluxes. The LES code used in this work was proposed by Moeng, 1984 and improved by Sullivan, 1994, mainly in the subgrid scheme. Understanding this kind of model is possible to simulate several PBL conditions: stable (not very stable...), neutral or convective situation.

17 Modeling Basis Short Review - LES main properties Using this kind of model is possible to understand the PBL most important behaviors like momentum, temperature and humidity turbulent fluxes. The LES code used in this work was proposed by Moeng, 1984 and improved by Sullivan, 1994, mainly in the subgrid scheme. Understanding this kind of model is possible to simulate several PBL conditions: stable (not very stable...), neutral or convective situation. The particulates, momentum, temperature and humidity fields, develop a critical role in the environment and can be simulated using LES.

18 Modeling Basis Short Review - LES main properties Using this kind of model is possible to understand the PBL most important behaviors like momentum, temperature and humidity turbulent fluxes. The LES code used in this work was proposed by Moeng, 1984 and improved by Sullivan, 1994, mainly in the subgrid scheme. Understanding this kind of model is possible to simulate several PBL conditions: stable (not very stable...), neutral or convective situation. The particulates, momentum, temperature and humidity fields, develop a critical role in the environment and can be simulated using LES. The TKE budget can be simulated using LES technique.

19 Modeling Basis Short Review - LES main properties Using this kind of model is possible to understand the PBL most important behaviors like momentum, temperature and humidity turbulent fluxes. The LES code used in this work was proposed by Moeng, 1984 and improved by Sullivan, 1994, mainly in the subgrid scheme. Understanding this kind of model is possible to simulate several PBL conditions: stable (not very stable...), neutral or convective situation. The particulates, momentum, temperature and humidity fields, develop a critical role in the environment and can be simulated using LES. The TKE budget can be simulated using LES technique. These features become LES an excellent choice to simulate the PBL phenomena.

20 Modeling Basis Short Review - LES main properties Using this kind of model is possible to understand the PBL most important behaviors like momentum, temperature and humidity turbulent fluxes. The LES code used in this work was proposed by Moeng, 1984 and improved by Sullivan, 1994, mainly in the subgrid scheme. Understanding this kind of model is possible to simulate several PBL conditions: stable (not very stable...), neutral or convective situation. The particulates, momentum, temperature and humidity fields, develop a critical role in the environment and can be simulated using LES. The TKE budget can be simulated using LES technique. These features become LES an excellent choice to simulate the PBL phenomena.

21 - Some limitations but...there s no free lunch! In the Surface Layer the grid imposes some limitations; The small eddies are not well resolved near walls;

22 - Some limitations but...there s no free lunch! In the Surface Layer the grid imposes some limitations; The small eddies are not well resolved near walls; Regions with high instability levels present intermittent eddies.

23 - Some limitations but...there s no free lunch! In the Surface Layer the grid imposes some limitations; The small eddies are not well resolved near walls; Regions with high instability levels present intermittent eddies. Clouds and radiation put uncertainties in the LES results.

24 - Some limitations but...there s no free lunch! In the Surface Layer the grid imposes some limitations; The small eddies are not well resolved near walls; Regions with high instability levels present intermittent eddies. Clouds and radiation put uncertainties in the LES results.

25 Objective LES in this work In this work we use a LES parallel version, modified by Moeng and Sullivan. The code was improved by Professor PhD. Umberto Rizza, Istituto di Scienze dell Atmosfera e del Clima - (CNR-ISAC), Lecce - Italy and DSc. Edson Marques Filho, UFRJ (IGEO), RJ - Brazil.

26 Objective LES in this work In this work we use a LES parallel version, modified by Moeng and Sullivan. The code was improved by Professor PhD. Umberto Rizza, Istituto di Scienze dell Atmosfera e del Clima - (CNR-ISAC), Lecce - Italy and DSc. Edson Marques Filho, UFRJ (IGEO), RJ - Brazil. The USP Group of Micrometeorology, (PhD. Amauri Oliveira - head), implemented the LES code in 2008 in a DELL-Cluster Tupandora R900 Intel 2-quad (8 cores) 12Gb RAM and 1.2 Tb HD. The Cluster runs 8 hours convective-pbl (128 3 points) in 40 hours.

27 Objective LES in this work In this work we use a LES parallel version, modified by Moeng and Sullivan. The code was improved by Professor PhD. Umberto Rizza, Istituto di Scienze dell Atmosfera e del Clima - (CNR-ISAC), Lecce - Italy and DSc. Edson Marques Filho, UFRJ (IGEO), RJ - Brazil. The USP Group of Micrometeorology, (PhD. Amauri Oliveira - head), implemented the LES code in 2008 in a DELL-Cluster Tupandora R900 Intel 2-quad (8 cores) 12Gb RAM and 1.2 Tb HD. The Cluster runs 8 hours convective-pbl (128 3 points) in 40 hours.

28 - Some details LES code Uses a pseudo-spectral method to resolve the momentum equations (horizontal components); Uses a FFT to the horizontal derivatives and a finite-difference method to the vertical ones;

29 - Some details LES code Uses a pseudo-spectral method to resolve the momentum equations (horizontal components); Uses a FFT to the horizontal derivatives and a finite-difference method to the vertical ones; The temporal derivatives are solved by a 2-order Adams-Bashforth scheme;

30 - Some details LES code Uses a pseudo-spectral method to resolve the momentum equations (horizontal components); Uses a FFT to the horizontal derivatives and a finite-difference method to the vertical ones; The temporal derivatives are solved by a 2-order Adams-Bashforth scheme; The model stability is checked in all time-steps.

31 - Some details LES code Uses a pseudo-spectral method to resolve the momentum equations (horizontal components); Uses a FFT to the horizontal derivatives and a finite-difference method to the vertical ones; The temporal derivatives are solved by a 2-order Adams-Bashforth scheme; The model stability is checked in all time-steps. LES uses a cyclic lateral boundary, (homogeneous surface) and a radiative top boundary.

32 - Some details LES code Uses a pseudo-spectral method to resolve the momentum equations (horizontal components); Uses a FFT to the horizontal derivatives and a finite-difference method to the vertical ones; The temporal derivatives are solved by a 2-order Adams-Bashforth scheme; The model stability is checked in all time-steps. LES uses a cyclic lateral boundary, (homogeneous surface) and a radiative top boundary.

33 Simulation Description Temporal Scale time-step dt caracteristic velocity scale - surface layer u PBL Height Z i Monin-Obukov Lenght L Stability parameter ζ = Z L Potential Temperature - Surface θ 0 Specific humidity - Surface q 0 Turbulent heat flux - Surface θ w 0 Turbulent latent flux - Surface q w 0 θ MixedLayer <θ w > w

34 Simulation Description Resolved and sub-grid spatial scales Velocities components variances < u 2 >, < v 2 >, < w 2 > θ and q variances < θ 2 >, < q 2 > Vertical flux - Sensible heat < w θ > Vertical flux - Latent heat < w q > Zonal flux - Sensible heat < u θ > Zonal flux - Latent heat < u q > Meridional Flux - Sensible heat < v θ > Meridional Flux - Latent heat < v q > Mean Zonal Velocity < u > Mean Meridinal Velocity < v > Momentum Flux Variance < u w > Momentum Flux Variance < v w > Momentum Flux Variance < u v > Shear Production u w ū z v w v z g Thermal Production θ w θ ( ) Transport z e w + w p ρ 0 Dissipation ɛ

35 The SGS Model Objective SGS The SGS model proposed by Sullivan considers that the turbulence can be split in a isotropic and non-homogeneous part. τ ij = 2ν tγs ij 2ν T S ij S ij = 1 ( ui + u ) j 2 x j x i θ τ θi = 2ν θ x i γ is the isotropy factor. This factor is responsible by the transition between the resolved and SGS scale.

36 Vertical profiles Objective Vertical Profiles Flow properties (a) Potential temperature The vertical profiles present the expected results for a Convective and Neutral/Stable PBLs. In the surface layer, the temperature presents a reduction with the height in the convective case. In the stable one a continuous increase in the temperature is observed. The properties s homogeneity is observed in the mixed-layer for convective and neutral cases. The PBL top is defined when Z/Zi = 1.

37 Momentum fluxes Objective Vertical Profiles Flow properties Figure: Vertical and horizontal second order statistical momentum

38 The subgrid importance Vertical Profiles Flow properties Figure: Thermal Production The SGS thermal production presents a major importance in the surface and in the PBL top. Therefore, is critically necessary to develop good parametrizations to simulate the subgrid phenomena.

39 Turbulent Kinetic Energy Budget Vertical Profiles Flow properties (a) Convective (b) Stable

40 TKE evolution Objective Vertical Profiles Flow properties Figure: Turbulent Kinetic Energy vertical profile for stable and convective PBLs

41 Vertical evolution Objective Vertical Profiles Flow properties Figure: Zonal and meridional wind components vertical profiles The fields present an expected profile, for all of the wind components. The red curves, convective, show an increasing in all the SBL. The mixed layer present constant values and the inversion layer a tendency to geostrophic value. To the neutral part one can see that the wind components present an increase in the mixed layer. The stable part shows the inertial oscilation pattern.

42 Momentum fluxes Objective Vertical Profiles Flow properties Figure: Vertical and horizontal second order statistical momentum

43 Flow properties Objective Vertical Profiles Flow properties Figure: Monin-Obukhov length s Temporal Evolution L The theoretical atmosphere simulated in this work presents a instable/stable conditions with moderate winds. The Monin-Obukhov length gives a good idea about the (in)stability.

44 Objective The statistic analysis was successfully implemented and validated for a known case; The second order fluxes were implemented; The TKE budget was implemented for Convective and Stable cases. The main Convective and stable PBL properties were simulated using the LES model; The post-processing was eliminated; The results presented here indicate that the algorithm is ready to be applied to a diurnal cycle using CO as an inert scalar.