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Matthias Raschendorfer DWD

Recent extensions of the COSMO TKE scheme related to the interaction with non turbulent scales. Separation between turbulence and non turbulent sub grid scale circulations. Additional scale interaction terms in the separated TKE budget.

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Matthias Raschendorfer DWD

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  1. Recent extensions of the COSMO TKE scheme related to the interaction with non turbulent scales • 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) Matthias Raschendorfer DWD Offenbach 2009 COSMO Matthias Raschendorfer

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

  3. Additional circulation terms in the turbulent 2-nd order budgets: average of the non linear turbulent shear terms turbulent shear term turbulent shear term circulation shear term Offenbach 2009 COSMO 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. production terms dependent on: specificlength scales and specificvelocity scales (= ) production terms depend on: theturbulent length scale and the turbulent velocity scale (= ) CKE TKE circulation-scale turbulence-scale and other and other statistical moments We need to consider additional length scales besides the turbulent length scale! Offenbach 2009 COSMO Matthias Raschendorfer

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

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

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

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

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

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

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

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

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

  14. Conclusions: • Non turbulent sub grid scale modes interact with turbulence through additionalshear productionin the TKE equation. • 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. • 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”. 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 convectionscheme as well. • 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. COSMO user seminar Matthias Raschendorfer Offenbach: 09-11.03.2009

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

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

  17. Basic scheme of advanced SC-diagnostics: Identical except horizontla operations and w-equation Forced correction run with SC version 3D-run Realistic 3D-run (analysis) or Forced test run with SC version mesdat only with model variables mesdat containing geo.-wind, vert.-wind und tendencies for horizontal advektion outdat with correction integrals 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. outdat with similar results compared to compared test run using the 3D-model Offenbach 2009 COSMO Matthias Raschendorfer

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

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

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

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

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