Matthias Raschendorfer

1. Mixed water/ice phase in the SGS condensation scheme and the moist turbulence scheme Matthias Raschendorfer DWD COSMO Cracow 2008 Matthias Raschendorfer

2. Motivation: The moist turbulence scheme is combined with a statistical SGS condensation scheme for non precipitating clouds Heat release of SGS freezing does not effect turbulence (not a dominating effect) excluding the ice phase We use a different scheme for SGS condensation for radiation and general diagnosis of fractional cloud cover - based on relative humidity This should be substituted by statistical SGS condensation scheme Perhaps tuning of some parameters in radiation or the statistical SGS condensation Cloud ice needs somehow to be included, if it is a model variable Estimate of zero order: total cloud cover, if GS (prognostic) cloud ice is present unrealistic high cloud fraction (always total cloud cover, if GS ice is present) Solution: Introducing a mixed water/ice phase - into the statistical condensation scheme similar to the procedure in the scheme based on relative humidity - into the moist turbulence scheme for consistency and for a higher level of generalization DWD COSMO Cracow 2008 Matthias Raschendorfer

3. Outline: How is the moist turbulence scheme working? How is the mixed phase introduced? How does cloud cover of the statistical scheme look like? What are the crucial remaining problems? DWD COSMO Cracow 2008 Matthias Raschendorfer

4. Numerical solution of model equations generates additional variables: These are second order moments (e.g. SGS flux densities) filtered budget above the roughness layer: DWD COSMO Cracow 2008 Matthias Raschendorfer

5. 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

6. 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

7. 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

8. turbulent kinetic energy [m^2/s^2] Lon -5 5.5 Lat -5 6.5 DWD COSMO Cracow 2008 Matthias Raschendorfer

9. total cloud cover due to GS ice DWD COSMO Cracow 2008 Matthias Raschendorfer

10. Statistical cloud scheme can be tuned away from normal distribution of saturation deficiency • to get a broader or smaller range of broken clouds: • ‘q_crit’ • to get more or less clouds cover at saturation: • ‘clc_diag’ DWD COSMO Cracow 2008 Matthias Raschendorfer

11. DWD COSMO Cracow 2008 Matthias Raschendorfer

12. DWD COSMO Cracow 2008 Matthias Raschendorfer

13. Further problems related with SGS generation of clouds constraining the aim of a consistent model setup: We use a GS water condensation scheme for saturation adjustment at the end of a time step Clouds by SGS condensation are destroyed again and can’t be seen by micro phys. Only the liquid phase is effected by the adjustment – > inconsistency GS saturation adjustment should be substituted by SGS mixed water/ice phase scheme Microphysics should use the additional statistical information We use a convection scheme producing its own clouds and precipitation There is no clear concept of combination and interaction between Turbulent, convective and grid cell production of clouds (and precipitation) Possible solution: - Interaction between convection and turbulence using the concept of scale separation, excluding precipitation - Combination of normal distributed turbulent and bimodal distributed convective clouds in statistical saturation adjustment - Microphysics has to use statistical information of adjustment scheme for precipitation calculation. DWD COSMO Cracow 2008 Matthias Raschendorfer

14. Combination of convection and turbulence in a SGS condensation and precipitation scheme: from normal distribution of turbulence precipitation calculation for separate classifications of the turbulent distribution one for each convective bin from bimodal distribution of convection DWD COSMO Cracow 2008 Matthias Raschendorfer

15. Conclusion: Using a mixed water/ice phase - the moist turbulence scheme is more general valid - the statistical condensation scheme can in principle be used for cloud diagnostics in general Objective validation and possible tuning of the radiation scheme is needed Some principal problems remain in order to get a consistent treatment of clouds DWD COSMO Cracow 2008 Matthias Raschendorfer

16. Thank You for attention! DWD CLM-Training Course 2008 Matthias Raschendorfer

17. DWD COSMO Cracow 2008 Matthias Raschendorfer

18. DWD COSMO Cracow 2008 Matthias Raschendorfer

19. Related problems for the aim of a consistent model setup: We use a different scheme for SGS condensation based on relative humidity for radiation Should be substituted by statistical scheme Perhaps tuning of some parameters in radiation scheme We use a GS water condensation scheme for saturation adjustment at the end of a time step Clouds by SGS condensation are destroyed again and can’t be seen by micro phys. Only the liquid phase is effected by the adjustment – no cloud ice Should be substituted by statistical mixed ice phase scheme Microphysics should use the additional statistical information We use a convection scheme producing its own clouds and precipitation There is no clear concept of combination and interaction between turbulent and convective and grid cell production of clouds and precipitation Possible solution: Convective and turbulent tendencies using the concept of scale interaction excluding precipitation Combination of normal distributed turbulent and bimodal distributed convective clouds in statistical saturation adjustment Microphysics using statistical information of adjustment scheme for precipitation calculation DWD COSMO Cracow 2008 Matthias Raschendorfer

20. The moist extension: • Inclusion of sub grid scale condensation achieved by: • Using conservative variables with respect to condensation: Correlations with condensation source terms are considered implicitly for non precipitating clouds. • Solving for water vapor and cloud fraction by using the statistical condensation scheme (according to cloud waterSommeria/Deardorff): • Normal distribution of saturation deficiency • Expressing variance of by variance of and , both generated from the turbulence scheme EMS AG-Grenzschicht August 2008 Matthias Raschendorfer

21. Single column solution for turbulent flux densities: • Using closure assumptions valid for pure turbulence: 2-nd order budgets reduce to a 15X15 linear system of equations built of all second order moments of the variable set { } • Using general boundary layer approximation: • neglect derivatives of mean quantities along filtered topographic surfaces • compared to derivatives normal to that surfaces Flux gradient representation of the only relevant vertical flux densities: turbulent master length scale TKE turbulent diffusion coefficient surface area function (only inside the roughness layer) stability function EMS AG-Grenzschicht August 2008 Matthias Raschendorfer

22. Implizite Vertikaldiffusion für quasi-Erhaltungsvariablen: Invertierung einer Tri-Diagonal-Matrix DWD AG-Grenzschicht August 2008 Matthias Raschendorfer

23. Turbulent fluxes of the non conservative model variables: thermodynamic non conservative model variables thermodynamic conservative model variables flux-gradient form explicit correction Conversion matrix: cloud fraction steepness of saturation humidity Exner factor DWD AG-Grenzschicht August 2008 Matthias Raschendorfer

24. 1. Alternative ohne explizite Korrektur: Neue Erhaltungsvariable auf Grund der Vertikaldiffusion Mit Hilfe des statistischen Kondensationsschemas konvertierte zugehörige Modellvariablen Vertikaldiffusionstendenz der Modellvariablen DWD AG-Grenzschicht August 2008 Matthias Raschendorfer

25. 2. Alternative ohne explizite Korrektur: Integrieren Diffusionstendenzen der nichterhaltenden Modelvariablen mit Hilfe der reinen Gradient-Flussdichten: Bilden die zugehörigen Erhaltungsvariablen, die dann trotzdem die richtigen Diffusionsinkremente besitzen: Konvertieren in Modellvariablen mit (statistischer) Sättigungsadjustierung: Berücksichtigung der expliziten Feuchtekorrekturen = Statistische Sättigungsadjustierung nach Integration allein der Diffusionstendenzen + numerische Fehler DWD AG-Grenzschicht August 2008 Matthias Raschendorfer

26. Innerhalb einer Wolke: Dampf Wasser • Nach der Diffusion der nicht erhaltenden Variablen ist das Sättigungsgleichgewicht gestört. • Dies sollte durch die expliziten Feuchtekorrekturen gerade wieder aufgehoben werden. DWD AG-Grenzschicht August 2008 Matthias Raschendorfer

27. INPUT-parameters for the turbulence scheme: itype_turb: type of turbulence parameterisation 1: former calculation of the turbulent diffusion coefficients in the atmosphere using subroutine “parura” 3: new turbulence scheme with prognostic TKE equation, using subroutine “turbdiff” 5_8: different versions of a more simple Prandtl/Kolmogorov-approach introduced for comparison imode_turb: modus for calculation of vertical turbulent flux divergences 0: implicit treatment of the dry part of vertical diffusion like before, using a concentration condition at the lower boundary 1: like 0, but with a flux condition at the lower boundary 2: explicit treatment of vertical diffusion 3: alternativeimplicit treatment of vertical diffusion based on the fluxes in conservative variables (going to be changed in order to get rid of explicit SGS condensation corrections) DWD CLM-Training Course 2008 Matthias Raschendorfer

28. icldm_turb: treatment of clouds with respect to turbulence -1: ignoring cloud water completely (pure dry scheme) 0: no clouds considered (all cloud water is evaporated) 1: only grid scale condensation possible 2: sub grid scale condensation by one of the two versions of subroutine “coud_diag” itype_wcld: type of new cloud diagnostics in subroutine “coud_diag” 1: diagnosis of water clouds, using subroutine “cloud_diag“ with that version based on relative humidity (similar to the procedure of the radiation scheme but without special tuning) 2: diagnosis of water clouds, using the statistical cloud scheme in subroutine “cloud_diag “. icldm_rad: treatment of clouds with respect to radiation 0: radiation does not “see” any clouds 1: radiation “sees” only grid scale clouds 2: radiation “sees” clouds, being diagnosed by one of the two versions of subroutine “coud_diag” 3: radiation “sees” clouds, being diagnosed with the former scheme but with a correction concerning the convective cloud cover 4: radiation “sees” clouds, being diagnosed exactly with the former scheme DWD CLM-Training Course 2008 Matthias Raschendorfer

29. lexpcor: switches on the above mentioned explicit correction ----------------------------------------------------------------------------------------------------------------------------------------------- ltmpcor: switches on the calculation of temperature tendencies related to conversions of inner energy to TKE, (should be FALSE, because the effect is very small) lnonloc: switches on the non local option (is not tested yet and should be FALSE) lcpfluc: switches on the effect of fluctuating humidity on the heat capacity of air in the calculation of the sensible heat flux (should be FALSE, because the effect is only small) --------------------------------------------------- DWD CLM-Training Course 2008 Matthias Raschendorfer

30. Length scale (factors) for turbulent transport: tur_len = 500.0 asymptotic maximal turbulent length scale [m] pat_len = 500.0 length scale of subscale surface patterns over land [m] (scaling the circulation term) c_diff = 0.20 length scale factor for vertical TKE diffusion (c_diff=0 means no diffusion of TKE) Dimensionless parameters used in the sub grid scale condensation scheme (statistical cloud scheme): clc_diag = 0.5 cloud cover at saturation q_crit = 4.0 critical value for normalized over-saturation (original setting q_crit=0.16) c_scld = 1.00 factor for liquid water flux density in sub grid scale clouds Minimal diffusion coefficients in [m^2/s]: tkhmin = 1.0 for scalar (heat) transport tkmmin = 1.0 for momentum transport to avoid too much low level cloud over ocean DWD CLM-Training Course 2008 Matthias Raschendorfer

31. Numerical parameters: epsi = 1.0E-6 relative limit of accuracy for comparison of numbers tkesmot = 0.15 time smoothing factor for TKE and diffusion coefficients wichfakt = 0.15 vertical smoothing factor for explicit diffusion tendencies securi = 0.85 security factor for maximal diffusion coefficients DWD CLM-Training Course 2008 Matthias Raschendorfer