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Matthias Raschendorfer DWD

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. Basic scheme of advanced SC-diagnostics:. Identical except horizontla operations and w-equation. Forced correction run with SC version.

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Matthias Raschendorfer DWD

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  1. 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

  2. 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

  3. 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

  4. 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

  5. 1. Ursachen für die Wirkung der expliziten Feuchtekorrektur 1) Im Modell wurde statt die Differenz gebildet Das entspricht dann nicht exakt dem Korrekturfluss “cor”: kleiner Effekt waren kein reinen Kondensationskorrekturen 2) Bei skaliger Sättigungsadjustierung wurde nur eineIteration durchlaufen Dadurch war die Adjustierung nicht genau “it5”: kleiner Effekt Kondensationskorrekturen veränderte das Ergebnis der Adjustierung 3) Bei impliziter Berechnung der Vertikaldiffusion von werden die mit benutzt. Tridiagonal-Matrix für die Temperaturdiffusion enthält Quotienten aus Exner-Faktoren erzeugten Beiträge verschwinden daher nicht bei der Bildung der Erhaltungsvariablen Die durch vor impliziter Vertikaldiffusion “cor2” : großer Effekt DWD AG-Grenzschicht Oktober 2008 Matthias Raschendorfer

  6. Implizite Vertikaldiffusion für Temperatur: Elemente der Tri-Diagonal-Matrix des resultierenden linearen Gleichungssystems enthalten Faktoren der Form: stehen, verschwinden die Beiträge der Feuchtekorrekturen Weil diese Faktoren nicht im Diffusionsterm für nicht bei Bildung von DWD AG-Grenzschicht Oktober 2008 Matthias Raschendorfer

  7. 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

  8. DWD AG-Grenzschicht Juni 2009 Matthias Raschendorfer

  9. 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

  10. 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 for 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) turbulent budgets Offenbach 2009 COSMO Matthias Raschendorfer

  11. 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

  12. Physical meaning of the circulation term: • Budgets for the circulation structures: Circulation term is the scale interaction term shifting SKE or any other variance 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- turbulence- moments and other scale Offenbach 2009 COSMO Matthias Raschendorfer

  13. 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 shear production by the mean flow buoyancy production labil: neutral: stabil: Offenbach 2009 COSMO Matthias Raschendorfer

  14. 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

  15. = (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

  16. 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

  17. = (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 Appalachien mountains 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

  18. 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 vanish Solution even for strong stability Offenbach 2009 COSMO Matthias Raschendorfer

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

  20. A first parameterization of the thermal circulations term: • Previous approximations 1-4 in the circulation scale 2-nd order budgets : Circulation term ~ circulation scale temperature variance ~ circulation scale buoyant heat flux square for Brunt-Väisälä-frequency virt. temperature of ascending air separated thermals virt. temperature of descending air pattern length scale • Combination with a max flux approach: bottom level horizontal updraft scale horizontal updraft fraction vertical velocity scale of circulation scaling factor boundary layer height turbulent velocity scale Offenbach 2009 COSMO Matthias Raschendorfer

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

  22. For a solution we deal with budget equations for the 2-nd order moments: shear production mol. and pressure prod. source term correlation cloud water (liquid and ice) icing factor Mixed phase condensation heat DWD COSMO Cracow 2008 Matthias Raschendorfer

  23. We need a decomposition of conservation variables: pressure production contains buoyancy term for mixed phase saturation humidity: linearization of saturation humidity: dependent on: and cloud fraction: normal distribution of saturation deficiency: SGS (statistical) condensation (saturation adjustment) scheme: DWD COSMO Cracow 2008 Matthias Raschendorfer

  24. turbulent kinetic energy [m^2/s^2] Lon -5 5.5 Lat -5 6.5 Effect of SGS release of icing heat DWD COSMO Cracow 2008 Matthias Raschendorfer

  25. 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

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