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

2. Matthias Raschendorfer DWD COSMO Cracow 2008 Motivation: The moist turbulence scheme is combined with a statistical SGS condensation scheme for non precipitating clouds excluding the ice phase Heat release of SGS freezing does not effect turbulence (not a dominating effect) This should be substituted by statistical SGS condensation scheme We use a different scheme for SGS condensation for radiation and general diagnosis of fractional cloud cover - based on relative humidity 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

3. Matthias Raschendorfer DWD COSMO Cracow 2008 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?

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

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

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

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

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

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

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

11. Matthias Raschendorfer DWD COSMO Cracow 2008

12. Matthias Raschendorfer DWD COSMO Cracow 2008

13. Matthias Raschendorfer DWD COSMO Cracow 2008 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 Only the liquid phase is effected by the adjustment – > inconsistency Clouds by SGS condensation are destroyed again and can’t be seen by micro phys. 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.

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

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

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

17. Matthias Raschendorfer DWD COSMO Cracow 2008

18. Matthias Raschendorfer DWD COSMO Cracow 2008

19. Matthias Raschendorfer DWD COSMO Cracow 2008 Related problems for the aim of a consistent model setup: We use a GS water condensation scheme for saturation adjustment at the end of a time step Should be substituted by statistical scheme We use a different scheme for SGS condensation based on relative humidity for radiation Perhaps tuning of some parameters in radiation scheme Only the liquid phase is effected by the adjustment – no cloud ice Clouds by SGS condensation are destroyed again and can’t be seen by micro phys. 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

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 water  Sommeria/Deardorff ): -Normal distribution of saturation deficiency -Expressing variance of by variance of and, both generated from the turbulence scheme EMS Matthias Raschendorfer AG-Grenzschicht August 2008

21. 1.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 { } Flux gradient representation of the only relevant vertical flux densities: turbulent diffusion coefficient stability function turbulent master length scale TKE 2.Using general boundary layer approximation: Single column solution for turbulent flux densities: EMS Matthias Raschendorfer surface area function (only inside the roughness layer) - neglect derivatives of mean quantities along filtered topographic surfaces compared to derivatives normal to that surfaces AG-Grenzschicht August 2008

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

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

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

25. Matthias Raschendorfer DWD 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 AG-Grenzschicht August 2008 2. Alternative ohne explizite Korrektur:

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

27. Matthias Raschendorfer DWD 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:alternative implicit 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) INPUT-parameters for the turbulence scheme: CLM-Training Course 2008

28. Matthias Raschendorfer DWD 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 CLM-Training Course 2008

29. Matthias Raschendorfer DWD 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)  CLM-Training Course 2008

30. Matthias Raschendorfer DWD Length scale (factors) for turbulent transport: tur_len= 500.0asymptotic maximal turbulent length scale [m] pat_len= 500.0length scale of subscale surface patterns over land [m] (scaling the circulation term) c_diff = 0.20length 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= 0.5cloud cover at saturation q_crit= 4.0critical value for normalized over-saturation (original setting q_crit=0.16) c_scld= 1.00factor for liquid water flux density in sub grid scale clouds Minimal diffusion coefficients in [m^2/s]: tkhmin= 1.0for scalar (heat) transport tkmmin= 1.0for momentum transport CLM-Training Course 2008 to avoid too much low level cloud over ocean

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