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

2. non precipitating clouds
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
Matthias Raschendorfer
COSMO Cracow 2008

3. How is the moist turbulence scheme working?
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
Matthias Raschendorfer
COSMO Cracow 2008

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
Matthias Raschendorfer
COSMO Cracow 2008

5. source term correlation
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
Matthias Raschendorfer
COSMO Cracow 2008

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
Matthias Raschendorfer
COSMO Cracow 2008

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

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

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

10. to get a broader or smaller range of broken clouds: ‘q_crit’
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
Matthias Raschendorfer
COSMO Cracow 2008

11. DWD
Matthias Raschendorfer
COSMO Cracow 2008

12. DWD
Matthias Raschendorfer
COSMO Cracow 2008

13. consistent model setup:
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
Matthias Raschendorfer
COSMO Cracow 2008

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
Matthias Raschendorfer
COSMO Cracow 2008

15. Using a mixed water/ice phase
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
Matthias Raschendorfer
COSMO Cracow 2008

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

17. DWD
Matthias Raschendorfer
COSMO Cracow 2008

18. DWD
Matthias Raschendorfer
COSMO Cracow 2008

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
Matthias Raschendorfer
COSMO Cracow 2008

20. AG-Grenzschicht August 2008
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. AG-Grenzschicht August 2008
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
turbulent diffusion coefficient
TKE
surface area function
(only inside the roughness layer)
stability function
EMS
Matthias Raschendorfer
AG-Grenzschicht August 2008

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

23. AG-Grenzschicht August 2008
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
Matthias Raschendorfer
AG-Grenzschicht August 2008

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

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
Matthias Raschendorfer
AG-Grenzschicht August 2008

26. AG-Grenzschicht August 2008
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
Matthias Raschendorfer
AG-Grenzschicht August 2008

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: 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)
DWD
Matthias Raschendorfer
CLM-Training Course 2008

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
Matthias Raschendorfer
CLM-Training Course 2008

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
Matthias Raschendorfer
CLM-Training Course 2008

30. Length scale (factors) for turbulent transport:
tur_len = asymptotic maximal turbulent length scale [m]
pat_len = length scale of subscale surface patterns over land [m] (scaling the circulation term)
c_diff = 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 = 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
Matthias Raschendorfer
CLM-Training Course 2008

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