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Matthias Raschendorfer DWD Treating implicit vertical diffusion as a part of the turbulence module Using a common subroutine for all species Including half-level variables (TKE) Including passive tracers Allowing treatment of non-gradient fluxes in the same framework Options for treatment of explicit tendencies Optional preconditioning Options for the treatment of the lower boundary (input of explicit surface fluxes possible) In case of surface tiles: flux aggregation (tile structure outside the turbdiff module so far) Diffusion of conserved variables and subsequent turbulent saturation adjustment possible Some technical issues preparing the common module: Easier exchange of complete turbulence/diffusion framework Code is much easier to handle; avoiding code repetitions Facilitates testing the effect of different numerical treatment Common tile structure not yet defined Easiest way to consider turbulent condensation in GS budgets COSMO Sibiu 2013 Forcing with prescribed surface fluxes possible Mainly present in ICON; a private test version with 2 horizontal indices exists Strategy: Generating interface for COSMO and using ICON-Module for further development!!
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COSMO Sibiu 2013Matthias Raschendorfer
Towards a consolidated turbulence and surface coupling
for COSMO and ICON:
• Technical issues preparing the common module for COSMO and ICON
• Revision of security limits and the problem with the stable boundary layer (SBL)
• Foreseen modifications within the first PT ConSAT
Matthias Raschendorfer COSMO Sibiu 2013DWD
Some technical issues preparing the common module:
Call of organize_turbdiff by a long parameter list
Only one horizontal index of variable fields
Extraction of horizontal operations from the turbulence code
Horizontal shear; interpolations due to grid staggering
Stronger modularization (common subroutines for turbdiff and turbtran)
moist physics; turbulence model; initialization
Removing obsolete parts of the code
Different options for gaining positive definiteness of TKE, avoiding singularities in solution for stability functions and other security limits for future testing (stable boundary, SAT)
Trying to generate a somehow more systematic logic of switches and options
Requirement by ICON design
More flexibility to adapt to hardware architecture
Due to different horizontal ICON grid
Clearer code structure; extensions easier to apply
Facilitating future testing (SBL)
More user friendly for testing procedure
Matthias RaschendorferDWD
Treating implicit vertical diffusion as a part of the turbulence module
Using a common subroutine for all species
Including half-level variables (TKE)
Including passive tracers
Allowing treatment of non-gradient fluxes in the same framework
Options for treatment of explicit tendencies
Optional preconditioning
Options for the treatment of the lower boundary (input of explicit surface fluxes possible)
In case of surface tiles: flux aggregation (tile structure outside the turbdiff module so far)
Diffusion of conserved variables and subsequent turbulent saturation adjustment possible
Some technical issues preparing the common module:
Easier exchange of complete turbulence/diffusion framework
Code is much easier to handle; avoiding code repetitions
Facilitates testing the effect of different numerical treatment
Common tile structure not yet defined
Easiest way to consider turbulent condensation in GS budgets
COSMO Sibiu 2013
Forcing with prescribed surface fluxes possible
Mainly present in ICON; a private test version with 2 horizontal indices exists Strategy: Generating interface for COSMO and using ICON-Module for further development!!
The problem with the stable boundary layer (SBL):
Matthias RaschendorferDWD
Almost no production term in a classical TKE equation
wg
uwuTKED vv
zt ˆ
vertical shear by the mean flow
buoyancy dissipation
almost zero for low wind conditions
negative for downward heat flux
always a sink
almost no vertical mixing even though it is usually present in nature
complete decoupling of the surface
almost no dissolution of fog and inversion layer clouds
singularities in turbulence model
model solution is strongly dependent on numerical details
considerable problems with numerical stability
CUS 2013
Possible solutions of the problem:
Matthias RaschendorferDWD
Introduction of artificial background mixing
- minimal value of TKE
- restriction of thermal stability
- minimal value for turbulent diffusion coefficients (tkm[m,h]min)
Problems with these measures
- not physically based (except some additional laminar diffusion)
- often too much mixing in the lower nocturnal BL
- either too fast or too slowly dissolution of inversion layer clouds
- either too strong or too weak nocturnal temperature decrease at the surface
- danger of smoothing out vertical jet structure (e.g. of the low level jet)
Alternatives
- Adopted numerical schemes
-inherent vertical smoothing without explicit minimal diffusion coefficients
-prognostic TKE equation guaranteeing positive definiteness without explicit limits
CUS 2013
momentum
scalars (heat)
Ready in test version and ICON
Matthias RaschendorferDWD
More physical based TKE and mixing in the stable BL
- Additional TKE sources are already beneficial for EDR-forecast (for aviation)- Should be beneficial for near surface SBL as well.
- Previous artificial security measures needs to be adopted!
First candidate: the minimal diffusion coefficient
- Previous value: tkv[h,m]min = 1.0 m2/s (same for scalars and momentum)
- Seems to dissolve BL clouds much to early now (and was presumably always a bit too large)
- Previous attempts to decrease it has not been successful.
- After lots of general numerical improvement of the model and the introduction of the SSO-source term a further
attempt has now been tried: New value: tkv[h,m]min = 0.4 m2/sCUS 2013
Physical based solution
Introduction of additional turbulence production via scale interaction - thermal density circulations; wake production; horizontal shear
Deardorff-reduction of the turbulent length scale
Turbulent transport of turbulent scalar variances (TKESV)
Considering circulation transport of GS and turbulent
Considering turbulent condensation in GS budgets
In official version; only wake production runs operational so far
In official version; verification has been delayed
In test version; needs to be introduced as an option verified against current development
not yet implemented
GS saturation adjustment needs to be substituted by statistical approach including turbulence ad convection
15.11.2012 12 UTC
Low level cloud cover CLCL
RoutineExperiment
s
TKE/[m2/s2]TKE/[m2/s2]
diffusion-coefficient/[m2/s]:time-height cut
all values are area averages
Routine Experiment
Theta/[°C]
Vel/[m/s]
cloud-water-content/[Kg/Kg]:
time-height cutRoutine Experiment
all values are area averages
Experiment - Routine Experiment - Routine
before moister
now moister
before more TKE:
Initiating cloud dissolution
now more TKE (within the clouds)
all values are area averages
time-height cut
vertical profile
Routine
Experiment
all values are area averages
now cooler day-time BL
now much more BL clouds now more intense
low level jet
Matthias RaschendorferDWD
Conclusion:
In the SBL pure turbulence would completely disappear, unless non-turbulent sub-grid processes are interacting.
Introduction of scale interaction terms was the reason that previous security measures for the SBL could and must be degraded.
Reduction of tkv[h,m]min diminishes excessive dissolution of inversion layer clouds that seemed to get increasingly worse lately and causes more BL clouds now.
Less often completely wrong simulation of BL clouds
cooler BL also during daytime => slightly negative BIAS of T2m_max
we expect also less systematic radiative cooling of the soil during winter time
(needs to be verified; experiment has been canceled due to technical problems)
Reduction of tkv[h,m]min diminishes night-time heat transfer towards the soil.
cooler clear sky surface layer during night => reduction of positive BIAS of T2m_min
Operational at DWD since December 2012
CUS 2013
Next steps:
Matthias RaschendorferDWD
Investigation of the other security measures in the scheme
CUS 2013
- Reformulation of the numerical sub schemes to allow for less restrictions (ready in a test
version)
- Less restrictive security measures to avoid singularities in the turbulent budget equations (ready in a test
version)
Further development of the scheme
- Reformulation of the thermal circulation term into a thermal SSO-source term (prepared)
- Implementation of missing circulation transport of GS and turbulent properties (additional non-gradient diffusion)
- Reformulation of the surface-to-atmosphere transfer in order to be more sensitive
for stable stratification (ConSAT)
Testing/Adapting/Verification of various implementations
- The not yet activated scale interaction terms (by convection and horizontal shear) (ready in official version)
- Deardorff-restriction of turbulent length scale for stable stratification (ready in official version)
- Turbulent transport of scalar variances (TKESV) (ready in test version; to be adapted to official code as an option)
- Turbulent saturation adjustment in grid scale budgets (in principle already possible)
Strategy: Generating interface for COSMO and using ICON-Module for further development!!
Specific problems of SAT:
CLM-Training Course
ˆ:ˆ~zz zzuqSkzf
• The total effective vertical flux density can be written as:
molecular diffusion coefficient
effective velocity scale
turbulent length scale
ku 0• It is
squared surface area index
zvzqSzu :
TKE2 pure turbulent velocity scale
• Above the laminar layer, where molecular diffusion is negligible and above the roughness layer it holds:
only laminar diffusion at the surface
Matthias RaschendorferDWD
Close to the surface 2 additional difficulties arise:
- Laminar diffusion can’t be neglected
- Roughness layer effects (SGS terms due to non-linearity of
spatial differentiation):
- form drag
- effect of increased surface
- modification of turbulent length scaleearth
roughness layer
000 zd :
0
displacement height
roughness length
0zz
.constz
• Vertical gradients increase significantly approaching the surface.
• Therefore the vertical profile of is not linear and can only be determined using further information.
• Integration yields:
Sz z ˆ
SA
SAS
r
zzzf
ˆˆ~
A
S
z
zSA zzu
dzr
:
transfer layerresistance
roughness layer resistance
free atmospheric resistance
specific roughness length
z
A
0
0
S
z
z
z
z zzu
dz
zzu
dz
The constant flux layer:
Sz
A0r
0Sr
0rM0S 0
M0 zz
• In our model we assume that does not change significantly within the transfer layer
between the surface and the lowest full model level .
zf ~
Szz Azz constant flux layer
A
0
z
z zzv
dz:
elser
vvrHSA
21MSA
,,,
turbulent velocity scale
Matthias RaschendorferDWD CLM-Training Course
Az
squared surface area index
laminar layer
0z
u0
Az
logarithmic Prandtl-layer profile
unstable stable
linear interpolated
Prandtl layer
roughness layer
z
(expon. roughness-layer profile)
m2 S
lowest model main level
upper boundary of the lowest model layer
lower boundary of the lowest model layer
h
Pz
Ahm10
0
m2
D0z
SYNOP station lawn profile
Mean GRID box profile
Effective velocity scale profile
u
0u
SA00
SA0z
ruz
turbulence-scheme
A
S
z
zSA zzu
dzr
Az
no storage capacity
A S
Transfer scheme and 2m-values with respect to a SYNOP lawn:
Lm2
• Exponential roughness layer profile is valid for the whole grid box,
• but it is not present at a SYNOP station
00u
k
Lz
Dz
Sz
L
m2hm2
SASA
m200SSm2
r
rr
0z
Phm20 Pzfrom turbulence-scheme
Pu
Matthias RaschendorferDWD CLM-Training Course
Calculation of the transport resistances:• The current scheme in COSMO explicitly considers the roughness layer resistance for scalars:
zd- applying and an effective SAI value 0S for the whole roughness layer
- using the laminar length scale 00
0 zu
k
: and a proper scaling factor for
scalars
H
H00H
H00
H0S
k
uz
uS
1r ln
- assumingH0
H uu 0H0 z for
0H
, it can be written:
• The current scheme in COSMO explicitly considers the free atmospheric resistance:
- applying a linear u -profile between level 0z (top of the roughness layer)and level Pz (top of the lowest model layer)
stas
zh
zz
labszz
hz
z
uu
dr
AA
Aneutral
A
A
HA
A
11
11
111
00
0
0
0
00
0 ln
lnln
1
0
0s
P
P u
uhz:0zzh :- using the atmospheric height and the stability parameter
it can be written:
new branch
Matthias RaschendorferDWD May.2013
• Can be expressed by surface layer variables only, increasing sensitivity on thermal stratification
Investigation of numerical security limits in the related turbulence model
Implementation, verification and documentation of the revised transfer formulation
Detailed investigation of the problems with daily cycle of near surface variables using measurements and COSMO-SC
Next steps:
Matthias RaschendorferDWD
• Extension of the profile function towards an universal one that includes the laminar limit, thus getting rid of using a virtual laminar layer.
• Revision of near surface diagnostics in particular with respect to their applicability at grid points with a large roughness length.
Implementation of the vertically resolved roughness layer with roughness terms in all 1-st and second order budgets and considering only the not resolved part in the SAT scheme (reduction of roughness length).
For longer terms:
1-st 1-year task
COSMO Sibiu 2013
2e
1e
R
Re
ee
e
eetur04
112
12 dRR11
RRa1
Ra1
1
R1
1
u
r
*~
:
stableRc1
instableRc11
e
etur :
MO0 Luk
c*
~:
contribution with pure turbulent profile function
k
uR
410
e*
~:
contribution for additional laminar correction
pure neutral contribution
analytically integrable dimensionless resistance
Ae zR Atur0A zuzv ~*and from TKE scheme
c
The general valid resistance:
COSMO Offenbach 2009Matthias Raschendorfer
lowest full level
1 2 5 10 20 50 100
M
eM
R
k
zu*
0
5
10
15
20
Normalized transition profile for wind speed:
according classical measurements form Reichardt 1951
according approximation
1RaRa21
ba
1R2b
aba21
uu M
eM2M
eM
M1M
e
M1
M
lntantanˆ
* MM aa4b :
COSMO Offenbach 2009Matthias Raschendorfer
molecular solution
turbulent solution
0
0
x
0D
21 tan
1
slope of the equivalent topography:
pzatnp mDxm
0
0
mD
m
0
p
iso-surface with constD
i
iD
i
filtered topography nAv Dn
HD ˆ
n
n
n
The general boundary layer approximation GBA:
A substitute of the horizontal boundary layer approximation
0zd
h
For any scale
v
Dd
COSMO Matthias Raschendorfer Offenbach 2009
earth
roughness layer
• At the lowest level, where this is valid, it is: 0zz
Roughness layer properties and the surface flux density:
can be described in the roughness layer and
z
von Kaman constant
-surfaces normal to local turbulent
and molecular flux densities, being a
shifted topography without small
scale modes not contributing to
for any variable . Their area is
times the horizontal projection
000 zd :
0
displacement height
0dz
roughness length
0zz
CLM-Training Course
mean distance form the rigid surface
• Using ,
zd
0
000
11 dS
:
zh
• The flux densities of prognostic model variables at the lower model boundary are affected by
the roughness layer and have turbulent as well as molecular contributions:
ˆ:ˆ~zz zzuqSkzf
• The total effective vertical flux density can be written as:
molecular diffusion coefficient
effective velocity scale
turbulent length scale
ku 0• It is
squared surface area index
zvzqSzu :
TKE2 pure turbulent velocity scale
• Above the laminar layer, where molecular diffusion is negligible and above the roughness layer it holds:
only laminar diffusion at the surface
Matthias RaschendorferDWD
0
00 1
zd
S
• Above the roughness layer, the surface area index is
equal to 1 and can be chosen so that it holds there:0d
Implicit calculation of surface temperature by liniarized surface energy budget, including a decoupled cover layer
Vertically resolved roughness layer (interaction with roughness elements in budet equations)
Further development of scale separation (namely related to convection and cloud processes)
Consistent microphysics including SGS processes (turbulent and convective phase changes)
Matthias RaschendorferDWD
Switching on the implemented scale interaction terms after verification against SYNOP data (operational verification)
Reformulation of the surface induced density flow term (circulation term) in the current scheme to become a thermal SSO production dependent on SSO parameters
Expression of direct sub grid scale transport by SSO eddies and horizontal shear eddies
Introduction of an option for three additional prognostic scalar variance equations (UCTS)
Further development:
Detailed investigation of the problems with daily cycle of near surface variables using measurements and COSMO-SC (ConSAT)
Implementation and verification of the full revised transfer formulation (ConSAT)