Matthias Raschendorfer

Matthias RaschendorferDWD

Mixed water/ice phase in the SGS condensation scheme and the moist turbulence scheme

Matthias Raschendorfer

COSMO Cracow 2008

Matthias RaschendorferDWD 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


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?


Qt Fˆ

jjjj cvvF ˆˆ

filtered budget

iijijji

xjj vmomentumforpvv

Tqscalarsforkc

,,

coeff.diffusionmoleculark :

viscositykinimatic:

FFabove the roughness layer:

Numerical solution of model equations generates additional variables:

These are second order moments (e.g. SGS flux densities)


QQ

t

cc

vvvv ˆˆˆ

momentumv2g watertotalqqqionprecipitat no0

temp. pot. watertotalqcrL

onidealizatiadiab.moistfor0c

Q

ii3i

cvw

cpp

cw

pd

,

,

,

vΩ

S

ilc qqq : cloud water (liquid and ice)

Mixed phase condensation heat

c

ii q

qTr : icing factor

iilic LrLr1L :

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:


pressure production contains buoyancy term vv

g

ˆfor w

wwwv rq

rw , dependent on: xqpT ,, and cloud fraction: cr

2

w2

pwwp2

w2

Tc2

vs rqr2qr1r1q

linearization of saturation humidity: pvsvsv rTTqTqq ˆ

mixed phase saturation humidity: lvsi

ivsivs qr1qrq

normal distribution of saturation deficiency: svwsv qqq :

vsq

x

0

SGS (statistical) condensation (saturation adjustment) scheme:

cx rqT ,,ww q,cq

We need a decomposition of conservation variables:


turbulent kinetic energy [m^2/s^2] Lon -5 5.5 Lat -5 6.5

Effect of SGS release of icing heat


turbulent kinetic energy [m^2/s^2] Lon -5 5.5 Lat -5 6.5


total cloud cover due to GS ice


-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




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.


x

vsqfrom normal distribution of turbulence

Combination of convection and turbulence in a SGS condensation and precipitation scheme:

0

from bimodal distribution of convection

precipitation calculation for separate classifications of the turbulent distribution

one for each convective bin


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


Thank You for attention!

CLM-Training Course 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 precipitationCombination of normal distributed turbulent and bimodal distributed convective cloudsin statistical saturation adjustmentMicrophysics using statistical information of adjustment scheme for precipitation calculation

The moist extension:

• Inclusion of sub grid scale condensation achieved by:

-Using conservative variables with respect to condensation: vcw qqq cpp

cw q

crL

d

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 schemesatq w wq

satq

x

0

EMS Matthias Raschendorfer

cqcr

satq

vq

AG-Grenzschicht August 2008

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:

zKww turbulent diffusion coefficient

stability function

turbulent master length scale

TKE2q21

2. Using general boundary layer approximation:

Single column solution for turbulent flux densities:

wvuqww ,,,,

EMS Matthias Raschendorfer

SqK :

surface area function(only inside the roughness layer)

- neglect derivatives of mean quantities along filtered topographic surfaces compared to derivatives normal to that surfaces



Implizite Vertikaldiffusion für quasi-Erhaltungsvariablen:

old

nnnkkkknzknt HSrcHHDifHAdvHwH

t

HHH

knkn

kntold

k1k

kn1knknz NN

NwNwHw

1kk

1knknk

Hknz

H

HHHH

NKNK

kH

keH

kN

1kN

keN

1keN Invertierung einer Tri-Diagonal-Matrix



Turbulent fluxes of the non conservative model variables:

vcw

cpp

cw

2

1

qqq

qcrL

d

thermodynamic non conservative model variables

mznmnmH

nzH

n cKKw

flux-gradient form explicit correction

cTcpTc

cTcpTc

cccTcTc

nm

rrrrrrr1rr1rrr

r1rrr1r1c

dp

d

cR

3phPa10

pTr

dp

cT

cL1

1r

:

vsTq :

dpp

cc cr

L :

cr cloud fraction

steepness of saturation humidity

Exner factor

Conversion matrix:


zKww

c

v

3

2

1

qq

thermodynamic conservative model variables


1. Alternative ohne explizite Korrektur:

0HwH knzknt kn HVdif

Vdif

c

Vdif

c

VdifVdif

2

1r

w

lr

c

v

3

2

1

fq

fqq

::

Neue Erhaltungsvariable auf Grund der Vertikaldiffusion

Mit Hilfe des statistischen Kondensationsschemas konvertierte zugehörige Modellvariablen

t

HHHwH

knkn

knzkntoldVdif

Vdif

Vertikaldiffusionstendenz der Modellvariablen



tqKcrL

KtHw czH

pp

cz

Hzkwz

d

tqKqKtHqw czH

vzH

zkwz

w

lr

c

v qf

qq

c

Corr

Integrieren Diffusionstendenzen der nichterhaltenden Modelvariablen mit Hilfe der reinen Gradient-Flussdichten:

c

vzH

qqK

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


2. Alternative ohne explizite Korrektur:

Matthias RaschendorferDWD AG-Grenzschicht August 2008

wq

WasserDampf

vq

z

satq

vzH qK cz

H qK 0qK wzH

Innerhalb einer Wolke:

•Nach der Diffusion der nicht erhaltenden Variablen ist das Sättigungsgleichgewicht gestört.

•Dies sollte durch die expliziten Feuchtekorrekturen gerade wieder aufgehoben werden.

zwz


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:



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



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)



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


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


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Matthias Raschendorfer