1. Matthias Raschendorfer DWD Recent extensions of the COSMO TKE scheme related to the interaction with non turbulent scales COSMO Offenbach 2009 Matthias Raschendorfer  Separation between turbulence and non turbulent sub grid scale circulations  Additional scale interaction terms in the separated TKE budget  Parameterization and effect of 3 important scale interaction terms with separated: -Horizontal shear modes (e.g. at frontal regions) -Wake modes from SSO blocking (over mountains) -Buoyancy forced thermal circulations (e.g. due to shallow convection or sub grid scale katabatic flows)  Considering of non turbulent sub grid scale circulations in the statistical condensation scheme (including non Gaussian effects)

2.  Turbulence closure is only valid for scales not larger than - the smallest peak wave length L p of inertial sub range spectra from samples in any direction, where - the largest (horizontal) dimension D g of the control volume  Spectral separation by - averaging these budgets along the whole control volume ( double averaging ) Partial solution for turbulence by spectral separation: Turbulence is that class of sub grid scale structures being in agreement with turbulence closure assumptions! - considering budgets with respect to the separation scale generalized turbulent budgets including additional scale interaction terms COSMO Offenbach 2009 Matthias Raschendorfer

3. average of the non linear turbulent shear terms circulation shear term Additional circulation terms in the turbulent 2-nd order budgets: turbulent shear term COSMO Offenbach 2009 Matthias Raschendorfer

4. Physical meaning of the circulation term:  Budgets for the circulation structures : Circulation term is the scale interaction term shifting Co-Variance (e.g. SKE ) form the circulation part of the spectrum ( CKE ) to the turbulent part ( TKE ) by virtue of shear generated by the circulation flow patterns. CKE TKE production terms dependent on: specific length scales and specific velocity scales (= ) production terms depend on: the turbulent length scale and the turbulent velocity scale (= ) circulation -scale turbulence -scale statistical moments COSMO Offenbach 2009 Matthias Raschendorfer and other We need to consider additional length scales besides the turbulent length scale!

5. Separated semi parameterized TKE equation (neglecting molecular transport): buoyancy production eddy- dissipation rate (EDR) labil: neutral: stabil: time tendency of TKE transport of TKE shear production by sub grid scale circulations expressed by turbulent flux gradient solution to be parameterized by a non turbulent approach COSMO Offenbach 2009 Matthias Raschendorfer shear production by the mean flow

6.  Separated horizontal shear production term: effective mixing length of diffusion by horizontal shear eddies velocity scale of the separated horizontal shear mode scaling parameter  Equilibrium of production and scale transfer towards turbulence: scaling parameter horizontal shear eddy isotropic turbulence horizontal grid plane TKE-production by separated horizontal shear modes: grid scale ……….effective scaling parameter separated horizontal shear additional TKE source term COSMO Offenbach 2009 Matthias Raschendorfer

7. out_usa_shs_rlme_a_shsr_0.2 Pot. Temperature [K] SN 06.02.2008 00UTC + 06h -92 E out_usa_shs_rlme_a_shsr_1.0 COSMO Offenbach 2009 Matthias Raschendorfer = (dissipation) 1/3 frontal zone

8.  SSO-term in filtered momentum budget: blocking term  SSO-term in SKE-equation: TKE-production by separated wake modes due to SSO: separated sub grid orography currently Lott und Miller (1997) COSMO Offenbach 2009 Matthias Raschendorfer

9. moderate light SN 06.02.2008 00UTC + 06h -77 E mountain ridge SSO-effect in TKE budget out_usa_rlme_tkesso out_usa_rlme_sso out_usa_rlme_tkesso – out_usa_rlme_sso MIN = 0.00104324 MAX = 10.3641 AVE = 0.126079 SIG = 0.604423MIN = 0. 00109619 MAX = 10.3689 AVE = 0.127089 SIG = 0.804444 MIN = -0.10315 MAX = 0.391851 AVE = 0.00100152 SIG = 0.00946089 COSMO Offenbach 2009 Matthias Raschendorfer = (dissipation) 1/3

10. 2.In the CKE budget : scale interaction loss = buoyant production 3.In the budget for circulation scale heat and moisture flux : scale interaction loss + pressure destruction = buoyant production 4.In the budget for circulation scale temperature variance : scale interaction loss = vertical flux divergence from the surface 1.In all circulation scale budgets: flux gradient form of temperature variance flux with a vertical constant circulation scale diffusion coefficient a vertical constant circulation time scale for expressing scale interaction loss and pressure destruction thermal circulation structures are negligible during neutral stratification shear production of (not by ) thermal circulations is negligible : TKE-production by separated thermal direct circulations: COSMO Offenbach 2009 Matthias Raschendorfer  In a simplified 2-nd order framework:

11. virtual temperat. of ascending air circulation scale temperature variance ~ circulation scale buoyant heat flux circulation term A first parameterization of the thermal circulations term:  Circulation scale 2-nd order budgets with proper approximations valid for thermals: pattern length scale square for Brunt-Väisälä- frequency separated thermals  Simplified max flux approach for the circulations: virtual temperat. of descending air COSMO Offenbach 2009 Matthias Raschendorfer scaling factor circulation height: e.g. BL-height bottom level turbulent velocity scale horizontal updraft scale horizontal updraft fraction vertical velocity scale of circulation current formulation using an additional assumption about the gradient

12. Effect of the thermal circulation term for stabile stratification: Even for vanishing mean wind and negative turbulent buoyancy there remains a positive definite source term TKE will not vanishSolution even for strong stability COSMO Offenbach 2009 Matthias Raschendorfer horizontal scale of a grid box

13. simulated midnight profile of potential temperature measured midnight profile of potential temperature COSMO Offenbach 2009 Matthias Raschendorfer

14. from normal distribution of turbulence Convective modulation of turbulence in a statistical condensation scheme: from bimodal distribution of convective circulation cloud turbulent Gaussian saturation adjustment using average oversaturation of upward flow turbulent Gaussian saturation adjustment using average oversaturation of downward flow grid scale oversaturation to be estimated form relevant 2nd order scheme describing convective circulations total oversaturation COSMO Offenbach 2009 Matthias Raschendorfer horizontal direction derivable directly from proper mass flux scheme describing convective circulations

15. 3D-shear terms have got a significant effect only, when formulated as a scale interaction term producing TKE by shear of a separated horizontal shear mode with its own length scale. Wake production of TKE by blocking can be formulated as a scale interaction term as well and can be described by scalar multiplication of the horizontal wind vector with its SS0-tendencies yielding some effect above mountainous terrain. Conclusions: Prospect: We intent to implement the revised formulation of the circulation term together with the “convective modulation” of the statistical cloud scheme and to derive a similar scale interaction term from the current convection scheme as well. COSMO user seminarOffenbach: 09-11.03.2009 Matthias Raschendorfer Non turbulent sub grid scale modes interact with turbulence through additional shear production in the TKE equation. Buoyancy forced (convective) circulations can be described either by a mass flux approach or 2-nd order closure. The according TKE production term is related to the circulation buoyancy heat flux. Interaction of those circulations with the statistical saturation adjustment (cloud scheme) can be formulated by “convective modulation”. Further we plan to consider the circulation scale fluxes in the 1-st order budgets leading to additional non local mixing tendencies of the prognostic variables.

16. Thank You for attention! COSMO Offenbach 2009 Matthias Raschendorfer

17. DWD About the results of UTCS Tasks (ii)a,c and (iii)a As far as attended by COSMO Offenbach 2009 Matthias Raschendorfer

18. 3D-run mesdat only with model variables Forced correction run with SC version outdat with correction integrals Identical except horizontla operations and w-equation mesdat containing geo.-wind, vert.-wind und tendencies for horizontal advektion Realistic 3D- run (analysis) Forced test run with SC version outdat with similar results compared to compared test run using the 3D-model Basic scheme of advanced SC-diagnostics: COSMO Offenbach 2009 Matthias Raschendorfer or Component testing: outdat or mesdat may contain 3D-corrections and arbitrary measurements (like surface temperature or surface heat fluxes) the model can be forced by.

19. COSMO Offenbach 2009 Matthias Raschendorfer interpolated measurements free model run starting wit 3D analysis free model run starting with measurements forced with prognostic variables from 3D-run forced with 3D corrections forced with 3D corrections and measured surface temperature forced with 3D corrections and measured surface heat fluxes Stable stratification over snow at Lindenberg Potential temperature profile atmosphere soil Potential temperature profile atmosphere soil too much turbulent mixing

20. Turbulent fluxes of the non conservative model variables: thermodynamic non conservative model variables flux-gradient form explicit flux correction cloud fraction steepness of saturation humidity Exner factor Conversion matrix : thermodynamic conservative model variables Explicit moisture correction: COSMO Offenbach 2009 Matthias Raschendorfer should vanish due to grid scale saturation adjustment!

21. COSMO Offenbach 2009 Matthias Raschendorfer But there are differences … … due do numerical effects with the Exner-factor treatment of the T-equation Time series of model domain averages less low level clouds

22. explicit TKE-diffusion with restriction proper for 50 layer configuration SC simulations with 80 layers and “implicit TKE diffusion”: numerically unstable! COSMO Offenbach 2009 Matthias Raschendorfer Dew point profiles 50 layers considerable difference Dew point profiles 80 layers implicit TKE-diffusion being unconditional stable almost no difference