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Systematische Untersuchung höherer statistischer Momente und ihrer Bilanzen

Budgets of second order moments for cloudy boundary layers derived from LES. 5 September 2011 Rieke Heinze , Siegfried Raasch Institute for Meteorology und Climatology Leibniz University Hannover, Germany Dmitrii Mironov German Weather Service.

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Systematische Untersuchung höherer statistischer Momente und ihrer Bilanzen

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  1. Budgets of second order moments for cloudy boundary layers derived from LES 5 September 2011 Rieke Heinze, Siegfried Raasch Institute for Meteorology und Climatology Leibniz University Hannover, Germany Dmitrii Mironov German Weather Service COSMO General Meeting, Rome, September 2011 LES der atmosphärischen Grenzschichtturbulenz – systematische Untersuchung höherer statistischer Momente und ihrer Bilanzen 1 Budgets of second order moments for cloudy boundary layers Systematische Untersuchung höherer statistischer Momente und ihrer Bilanzen

  2. Results Summary Motivation LES Outlook Background (I) • Atmospheric boundary layer is characterized by turbulent motions • In weather prediction and climate models turbulence and shallow convection have to be parameterized • A lot of closure models are based on the truncated ensemble-mean budget equations for the statistical moments of second order: Budgets of second order moments for cloudy boundary layers

  3. Results Summary Motivation LES Outlook or Background (II) • Budgets are needed for • Estimation of relative importance of the budget terms • Testing of parameterizations and further development • Determination of disposable/tuning parameters • Budgets have a fundamental meaning • So far: lack of systematic and comprehensive analysis for cloudy boundary layers • Usage of large eddy simulation (LES) to determine all the budgets of second order moments and to examine pressure correlation terms like Budgets of second order moments for cloudy boundary layers

  4. Introduction Scales of turbulence Large eddies: 103 m, 1 h Small eddies: 10-3 m, 0.1 s Spectrum of TKE Large scales: production Small scales: dissipation Filtering Large, energy containing eddies are resolved Small eddies are modeled Calculation of a turbulent boundary layer flow Results Summary Motivation LES Outlook z x | Production | Inertial subrange | Dissipation | Resolved scale Subgrid scale D LES: volume average 4 4 Budgets of second order moments for cloudy boundary layers

  5. Results Summary Motivation LES Outlook Budgets from LES • Closure models are often based on ensemble-mean budgets • LES: approximation by averaging over horizontal planes and afterwards over several time steps • LES is based on filtering: • Application to budget equations as well: • Explicit consideration of SGS budgets Budgets of second order moments for cloudy boundary layers

  6. Results Summary Motivation LES Outlook inversion cloud layer mixed layer BOMEX − first order moments • BOMEX LES study (Siebesma et al., 2003, 10 LES models, GCSS) • Stationary case of shallow cumulus convection over ocean (no precip.) • Domain size: 6.4 x 6.4 x 3.0km3, grid spacing: Δ=10m, time: 6h Budgets of second order moments for cloudy boundary layers

  7. Results Summary Motivation LES Outlook BOMEX − TKE and its budget Budgets of second order moments for cloudy boundary layers

  8. Results Summary Motivation LES Outlook BOMEX − temperature variance and its budget Budgets of second order moments for cloudy boundary layers

  9. Results Summary Motivation LES Outlook BOMEX − variance of total water content and its budget Budgets of second order moments for cloudy boundary layers

  10. Results Summary Motivation LES Outlook BOMEX − temperature flux and its budget Budgets of second order moments for cloudy boundary layers

  11. Results Summary Motivation LES Outlook DYCOMS − first results • DYCOMS LES study (Stevens et al., 2005, 10 LES models, 16 sim.) • Homogeneous, nocturnal stratocumulus over ocean (no drizzle) • Domain size: 3.4 x 3.4 x 1.5km3, grid spacing: Δ=35m, Δz=5m, time: 4h Budgets of second order moments for cloudy boundary layers

  12. Results Summary Motivation LES Outlook Summary • Budgets for all second order moments (16 equations) for cloud topped boundary layers are determined with veryhigh resolution LES (2560 x 2560 x 1280 grid points) • PALM is able to simulate GCSS cases • Shallow cumulus (BOMEX) • Budgets of • TKE and scalar variances: production and dissipation largest but transport is also very important • Scalar fluxes: importance of buoyancy and pressure scalar cov. • Stratocumulus (DYCOMS) • First results look promising Budgets of second order moments for cloudy boundary layers

  13. Results Summary Motivation LES Outlook Future plans • Simulation of a SC-CU transition case • Detailed examination of pressure-scalar and -velocity covariance • Testing of existing parameterizations against LES data • LES data set will be made available • Testing and evaluation of currently used closure schemes • Further development of new schemes (→ e.g. TKE-scalar variance scheme) • Data is in netCDF format and preparation of a detailed documentation is ongoing Benefit for COSMO community Budgets of second order moments for cloudy boundary layers

  14. Supplementary material Budgets of second order moments for cloudy boundary layers

  15. LES basic equations (I) Filtering: with Basic system of equations consists of the filtered Navier-Stokes equations in Boussinesq form Volume balance approach (Schumann, 1975) Equations of motion Modified pressure Continuity equation SGS stress SGS TKE 15 15 Budgets of second order moments for cloudy boundary layers Systematische Untersuchung höherer statistischer Momente und ihrer Bilanzen

  16. LES basic equations (II) Filtering: with Basic system of equations consists of the filtered Navier-Stokes equations in Boussinesq form Volume balance approach (Schumann, 1975) Total water content First principle Potential liquid water temperature: SGS humidity flux SGS temperature flux: Conservation equation 16 16 Budgets of second order moments for cloudy boundary layers

  17. LES SGS turbulence parameterization (I) Turbulence closure based on Deardorff,1980 Flux-gradient relationship for SGS fluxes Prognostic equation for SGS TKE Diffusion coefficients The mixing length depends on Grid spacing Distance to nearest solid wall Stratification und mit 17 17 Budgets of second order moments for cloudy boundary layers

  18. LES SGS turbulence parameterization (II) Turbulence closure based on Deardorff,1980 Flux-gradient relationship for SGS fluxes Prognostic equation for SGS TKE Diffusion coefficients und mit • The prognostic equation for is 18 18 Budgets of second order moments for cloudy boundary layers

  19. Buoyancy flux Total water flux BOMEX − second order moments Budgets of second order moments for cloudy boundary layers

  20. BOMEX − skewness (important for e.g. statistical cloud schemes) • Cumulus convection shows strong updrafts of moist and cold air within cloud layer Budgets of second order moments for cloudy boundary layers

  21. BOMEX − covariance and its budget Budgets of second order moments for cloudy boundary layers

  22. BOMEX − flux of total water content and its budget Budgets of second order moments for cloudy boundary layers

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