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

2. Budgets of second order moments for cloudy boundary layers 2 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: MotivationLES ResultsSummary Outlook

3. Budgets of second order moments for cloudy boundary layers 3 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 or MotivationLES ResultsSummary Outlook

4. Budgets of second order moments for cloudy boundary layers 44 x z | Production | Inertial subrange | Dissipation | Introduction Scales of turbulence –Large eddies: 10 3 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 LES: volume average Resolved scale Subgrid scale  MotivationLES ResultsSummary Outlook

5. Budgets of second order moments for cloudy boundary layers 5 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 MotivationLES ResultsSummary Outlook

6. Budgets of second order moments for cloudy boundary layers 6 mixed layer cloud layer inversion 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 3.0km 3, grid spacing: Δ=10m, time: 6h MotivationLES ResultsSummary Outlook

7. Budgets of second order moments for cloudy boundary layers 7 BOMEX − TKE and its budget MotivationLES ResultsSummary Outlook

8. Budgets of second order moments for cloudy boundary layers 8 BOMEX − temperature variance and its budget MotivationLES ResultsSummary Outlook

9. Budgets of second order moments for cloudy boundary layers 9 BOMEX − variance of total water content and its budget MotivationLES ResultsSummary Outlook

10. Budgets of second order moments for cloudy boundary layers 10 BOMEX − temperature flux and its budget MotivationLES ResultsSummary Outlook

11. Budgets of second order moments for cloudy boundary layers 11 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 1.5km 3, grid spacing: Δ=35m, Δz=5m, time: 4h MotivationLES ResultsSummary Outlook

12. Budgets of second order moments for cloudy boundary layers 12 Summary Budgets for all second order moments (16 equations) for cloud topped boundary layers are determined with very high 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 MotivationLES ResultsSummary Outlook

13. Budgets of second order moments for cloudy boundary layers 13 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 MotivationLES ResultsSummary Outlook Benefit for COSMO community

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

15. Budgets of second order moments for cloudy boundary layers 15 Systematische Untersuchung höherer statistischer Momente und ihrer Bilanzen 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 SGS stress SGS TKE Continuity equation

16. Budgets of second order moments for cloudy boundary layers 16 Conservation equation 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) First principle Potential liquid water temperature: SGS temperature flux: Total water content SGS humidity flux

17. 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 mit und

18. Budgets of second order moments for cloudy boundary layers 18 The prognostic equation for is 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 mit und

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

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

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

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