Kein Folientitel

1
Recent extensions of the COSMO TKE scheme related
to the interaction with non turbulent scales

• Separation between turbulence and non turbulent
  sub grid scale circulations

• Additional scale interaction terms in the
  separated TKE budget

• Parameterization and effect of 3 important scale
  interaction terms with separated

• Horizontal shear modes (e.g. at frontal regions)

• Wake modes from SSO blocking (over mountains)

• Buoyancy forced thermal circulations (e.g. due to
  shallow convection or sub grid scale katabatic
  flows)

• Considering of non turbulent sub grid scale
  circulations in the statistical condensation
  scheme (including non Gaussian effects)

Matthias Raschendorfer DWD
Offenbach 2009
COSMO
Matthias Raschendorfer
2
Partial solution for turbulence by spectral
separation
Turbulence is that class of sub grid scale
structures being in agreement with turbulence
closure assumptions!

• Turbulence closure is only valid for scales not
  larger than
• the smallest peak wave length Lp of inertial
  sub range spectra from samples in any direction,
  where
• the largest (horizontal) dimension Dg of the
  control volume

• Spectral separation by

• considering budgets with respect to the
  separation scale

• averaging these budgets along the whole control
  volume (double averaging)

generalized turbulent budgets including
additional scale interaction terms
Offenbach 2009
COSMO
Matthias Raschendorfer
3
Additional circulation terms in the turbulent
2-nd order budgets
average of the non linear turbulent shear terms
turbulent shear term
turbulent shear term
circulation shear term
Offenbach 2009
COSMO
Matthias Raschendorfer
4
Physical meaning of the circulation term

• Budgets for the circulation structures

Circulation term is the scale interaction term
shifting Co-Variance (e.g. SKE) form the
circulation part of the spectrum (CKE) to the
turbulent part (TKE) by virtue of shear generated
by the circulation flow patterns.
production terms dependent on specific length
scales and specific velocity scales (
)
production terms depend on the turbulent
length scale and the turbulent velocity
scale ( )
CKE
TKE
circulation-scale
turbulence-scale
and other
and other
statistical moments
We need to consider additional length scales
besides the turbulent length scale!
Offenbach 2009
COSMO
Matthias Raschendorfer
5
Separated semi parameterized TKE equation
(neglecting molecular transport)
to be parameterized by a non turbulent approach
expressed by turbulent flux gradient solution
eddy-dissipation rate (EDR)
shear production by sub grid scale circulations
time tendency of TKE
buoyancy production
transport of TKE
shear production by the mean flow
labil
neutral
stabil
Offenbach 2009
COSMO
Matthias Raschendorfer
6
TKE-production by separated horizontal shear
modes
horizontal grid plane

• Separated horizontal shear production term

separated horizontal shear
effective mixing length of diffusion by
horizontal shear eddies
velocity scale of the separated horizontal shear
mode
grid scale
isotropic turbulence
scaling parameter
horizontal shear eddy

• Equilibrium of production and scale transfer
  towards turbulence

scaling parameter
additional TKE source term
.effective scaling parameter
Offenbach 2009
COSMO
Matthias Raschendorfer
7
(dissipation)1/3
out_usa_shs_rlme_a_shsr_0.2
Pot. Temperature K
out_usa_shs_rlme_a_shsr_1.0
S
N
frontal zone
06.02.2008 00UTC 06h -92 E
Offenbach 2009
COSMO
Matthias Raschendorfer
8
TKE-production by separated wake modes due to SSO

• SSO-term in filtered momentum budget

blocking term
currently Lott und Miller (1997)

• SSO-term in SKE-equation

separated sub grid orography
Offenbach 2009
COSMO
Matthias Raschendorfer
9
(dissipation)1/3
out_usa_rlme_sso
out_usa_rlme_tkesso
moderate light

S
N
MIN 0.00104324 MAX 10.3641 AVE 0.126079
SIG 0.604423
MIN 0. 00109619 MAX 10.3689 AVE 0.127089
SIG 0.804444
out_usa_rlme_tkesso out_usa_rlme_sso
mountain ridge
SSO-effect in TKE budget
06.02.2008 00UTC 06h -77 E
MIN -0.10315 MAX 0.391851 AVE 0.00100152
SIG 0.00946089
Offenbach 2009
COSMO
Matthias Raschendorfer
10
TKE-production by separated thermal direct
circulations

• In a simplified 2-nd order framework

1. In all circulation scale budgets

• thermal circulation structures are negligible
  during neutral stratification

shear production of (not by) thermal circulations
is negligible

• a vertical constant circulation time scale for
  expressing scale interaction loss and pressure
  destruction

1. In the CKE budget

• scale interaction loss buoyant production

1. In the budget for circulation scale heat and
   moisture flux

• scale interaction loss pressure destruction
  buoyant production

1. In the budget for circulation scale temperature
   variance

• scale interaction loss vertical flux
  divergence from the surface

• flux gradient form of temperature variance flux
  with a vertical constant circulation scale
  diffusion coefficient

Offenbach 2009
COSMO
Matthias Raschendorfer
11
A first parameterization of the thermal
circulations term

• Circulation scale 2-nd order budgets with proper
  approximations valid for thermals

circulation scale temperature variance
circulation scale buoyant heat flux
circulation term
vertical velocity scale of circulation
square for Brunt-Väisälä-frequency
virtual temperat. of ascending air
separated thermals
current formulation using an additional
assumption about the gradient
virtual temperat. of descending air
pattern length scale
circulation height e.g. BL-height
horizontal updraft scale
scaling factor
bottom level
turbulent velocity scale

• Simplified max flux approach for the circulations

horizontal updraft fraction
Offenbach 2009
COSMO
Matthias Raschendorfer
12
Effect of the thermal circulation term for
stabile stratification
horizontal scale of a grid box

• Even for vanishing mean wind and negative
  turbulent buoyancy there remains a positive
  definite source term

TKE will not vanish
Solution even for strong stability
Offenbach 2009
COSMO
Matthias Raschendorfer
13
measured midnight profile of potential
temperature
simulated midnight profile of potential
temperature
Offenbach 2009
COSMO
Matthias Raschendorfer
14
Convective modulation of turbulence in a
statistical condensation scheme
total oversaturation
from normal distribution of turbulence
turbulent Gaussian saturation adjustment using
average oversaturation of upward flow
cloud
grid scale oversaturation
turbulent Gaussian saturation adjustment using
average oversaturation of downward
flow
horizontal direction
from bimodal distribution of convective
circulation
to be estimated form relevant 2nd order scheme
describing convective circulations
derivable directly from proper mass flux scheme
describing convective circulations
Offenbach 2009
COSMO
Matthias Raschendorfer
15
Conclusions

• Non turbulent sub grid scale modes interact with
  turbulence through additional shear production in
  the TKE equation.

• 3D-shear terms have got a significant effect
  only, when formulated as a scale interaction term
  producing TKE by shear of a separated horizontal
  shear mode with its own length scale.

• Wake production of TKE by blocking can be
  formulated as a scale interaction term as well
  and can be described by scalar multiplication of
  the horizontal wind vector with its
  SS0-tendencies yielding some effect above
  mountainous terrain.

• Buoyancy forced (convective) circulations can be
  described either by a mass flux approach or 2-nd
  order closure. The according TKE production term
  is related to the circulation buoyancy heat flux.
• Interaction of those circulations with the
  statistical saturation adjustment (cloud scheme)
  can be formulated by convective modulation.

Prospect

• We intent to implement the revised formulation of
  the circulation term together with the
  convective modulation of the statistical cloud
  scheme and to derive a similar scale interaction
  term from the current convection scheme as well.

• Further we plan to consider the circulation scale
  fluxes in the 1-st order budgets leading to
  additional non local mixing tendencies of the
  prognostic variables.

COSMO user seminar
Offenbach 09-11.03.2009
Matthias Raschendorfer
16
Thank You for attention!
Offenbach 2009
COSMO
Matthias Raschendorfer
17
About the results of UTCS Tasks (ii)a,c and (iii)a
As far as attended by
Matthias Raschendorfer DWD
Offenbach 2009
COSMO
Matthias Raschendorfer
18
Basic scheme of advanced SC-diagnostics
Identical except horizontla operations and
w-equation
Forced correction run with SC version
3D-run
Realistic 3D-run (analysis)
or
Forced test run with SC version
mesdat only with model variables
mesdat containing geo.-wind, vert.-wind
und tendencies for horizontal advektion
outdat with correction integrals
Component testing outdat or mesdat may contain
3D-corrections and arbitrary measurements (like
surface temperature or surface heat fluxes) the
model can be forced by.
outdat with similar results compared to compared
test run using the 3D-model
Offenbach 2009
COSMO
Matthias Raschendorfer
19
Potential temperature profile
Potential temperature profile
too much turbulent mixing
atmosphere
atmosphere
soil
soil
interpolated measurements
free model run starting wit 3D analysis
free model run starting with measurements
forced with prognostic variables from 3D-run
forced with 3D corrections
forced with 3D corrections and measured surface
temperature
forced with 3D corrections and measured surface
heat fluxes
Stable stratification over snow at Lindenberg
Offenbach 2009
COSMO
Matthias Raschendorfer
20
Explicit moisture correction
Turbulent fluxes of the non conservative model
variables
thermodynamic non conservative model variables
thermodynamic conservative model variables
explicit flux correction
flux-gradient form
should vanish due to grid scale saturation
adjustment!
Conversion matrix
cloud fraction
steepness of saturation humidity
Exner factor
Offenbach 2009
COSMO
Matthias Raschendorfer
21
Time series of model domain averages
less low level clouds
due do numerical effects with the Exner-factor
treatment of the T-equation
But there are differences
Offenbach 2009
COSMO
Matthias Raschendorfer
22
SC simulations with 80 layers and implicit TKE
diffusion
Dew point profiles 50 layers
Dew point profiles 80 layers
explicit TKE-diffusion with restriction proper
for 50 layer configuration
considerable difference
numerically unstable!
implicit TKE-diffusion being unconditional stable
almost no difference
Offenbach 2009
COSMO
Matthias Raschendorfer