Work Status: • The project implementation is somewhat delayed due to the uncertainty about the future of some project participants
• A review about analogies between turbulence and convection parameterization (a basis for the development) is ca. half-way through (the work is foreseen in the framework of the UTCS Task 1, performed by Dmitrii Mironov)
•An extended documentation of the existing LM turbulence scheme, including a review of turbulence parameterization and basic ideas for further development in particular toward an UTCS, is to a large extent ready (Task 1, Matthias Raschendorfer)
• Various aspects of the treatment of the sub-grid scale cloudiness with the statistical cloud scheme, including its relation to the treatment of the grid-scale water vapour, cloud water and cloud ice, and its consistent use within various physical parameterisation schemes of the LM, are (being) explored (Tasks 1 and 5, Euripides Avgoustoglou and Paola Mercogliano)
• With the aim to slow down cumulus convection scheme, a number of modifications in the cumulus convection scheme (Tiedtke 1989), which have been successfully tested in the GME, are being tried out within the LM (Task 4, Axel Seifert, Jan-Peter Schulz, Detlev Majewski, Dmitrii Mironov)
Outlook:
• The project is (expected) to proceed as scheduled
• However, some changes in the project plan may have to be introduce, both in terms of FTEs and in terms of schedule (hopefully minor changes), due to unavailability of human resources
Priority Project UTCS
Changes in the T89 Cumulus Convection Scheme:
• Saturation adjustment in the T89 is performed with due regard for the cloud water-cloud ice mixed phase (in the original T89, the cloud condensate is either water or ice as dependent on temperature)
• Modified evaporation of convective precipitation (with the 80% environment air humidity threshold compared to 95% before)
• Modified generation of convective precipitation(no detrained cloud condensate is added to the updraught precipitation flux)
• Modified turbulent entrainment (E) / detrainment (D) formulation (now dependent on potential temperature difference between the updraught and the environment) • Modified convective trigger function(convective test parcel now originates from the lowest well mixed sub cloud layer, before from the lowest model level)
• Detrained convective cloud condensate is passed to the microphysics scheme in the form of tendencies (in the original T89, detrained convective cloud condensate is evaporated instantaneously)
About UTCS Task 4. “... with the UTCS in LM, the mass-flux deep convection scheme should be slowed down.”
Research team members: Axel Seifert, Jan-Peter Schulz, Detlev Majewski, Dmitrii Mironov
Priority Project UTCS
Curves are the results of averaging over the area “Germany” (47N-55N, 6E-15E) and over 20 00 UTC forecasts over the period from 01.04.2006 to 20.04.2006.
Left panel: operational GME vs. Exp_1009 (with changes in the microphysics scheme and in the Tiedtke convection scheme, first of all, the water-ice mixed phase). Dot-dashed lines show convective precipitation, dashed lines - grid-scale precipitation, and solid lines - total precipitation.
Right panel: observations.
Precipitation: GME vs. Exp_1009
Convective precipitation
LME
COSMO Bucharest 2006Matthias Raschendorfer
Matthias Raschendorfer
DWD
About UTCS Task 1: “Analytical derivation…of the unified Turbulence-shallow convection scheme”
A first non local extension of the current turbulence scheme:
The circulation term in the TKE equation derived by spectral separation
COSMO Bucharest 2006Matthias Raschendorfer
Turbulence closure:
• Considering 2-nd order budgets:
prs
tt
QQQ
eeD
ee
vveevv ˆˆˆˆˆ:
neglected outside the laminar layer
shear production
molecular dissipation
sub grid scale macroscopic transport
iii ppp
jjii vp0
vp0
,
H,
,
H,
pressure transport pressure destruction
buoyancy source
a:emolecular flux density
vv
g
ˆ
phase change production
COSMO Bucharest 2006Matthias Raschendorfer
Neglect of tD , in particular all transport terms (equilibrium) except the in SKE equation
Neglect of sub grid scale phase change production QQ
Neglect of pressure transport pi
Bernoulli approximation constgz2
pp tot
vv
:
Confluence/diffluence model of local isotropy for a single mode of wave length kL : k
jj vsign
What is the idea of turbulence closure?
1. Primary turbulent closure assumptions:
COSMO Bucharest 2006Matthias Raschendorfer
2. Secondary turbulent closure assumptions:
- spectral density of contributing modes follows a power law in terms of wave length in each direction:
- whole spectrum in a given direction is determined by a single peak wave length
- the peak wave length is the same for samples in all directions: isotropic length scale
- pressure correlation and dissipation can be closed using a single turbulent master length scale for each location
inertial sub range spectrum
COSMO Bucharest 2006Matthias Raschendorfer
What is the remaining difficulty with circulations (beside sub grid icing and precipitation)?
- they are related with at least one additional spectral peak
- or they cause different peak wavelengths in vertical direction compared to the horizontal directions:
anisotropic peak wave length - larger peak wave length in vertical direction in case of labile stratification
kln
dkk
dk2
35
- slope in case of TKE
gD1
ln
Turbulence
Circulations
Microphysics
ResolvedStructures
pL : largest turbulent wave length
convective peak in vertical spectrum
catabatic peak
neutralstabile
labile
pL1
ln
at least a two scale problem
COSMO Bucharest 2006Matthias Raschendorfer
What is the problem?
• In general there are non turbulent, arranged circulation structures present as well:
More general closure assumptions valid for both, turbulence and circulations
Separation of turbulence and circulations with adopted closure assumptions for each class and related quite easy particular solutions
Impossible without knowing moments of as much classes as we have length scales for
-Sub grid phase changes (cloud processes) -> boundary layer clouds
-different length scales of sub grid structures
-Sub grid cloud – radiation interaction
COSMO Bucharest 2006Matthias Raschendorfer
How to find a particular solution for turbulence?
• turbulence closure is only valid for scales not larger than
-the smallest peak wave length Lp
-and the largest dimension Dg of the control volume
Spectral separation by considering budgets with respect to the separation scale gp DLL ,min
and averaging these budgets along the whole control volume
Turbulence is that class of sub grid scale structures being in agreement with turbulence closure assumptions!
COSMO Bucharest 2006Matthias Raschendorfer
- Turbulent budgets:
...ˆˆ...
LLLLLtD vv
LLL ˆˆ vv
LLK ˆˆ
Mean of the non linear turbulent shear term
MM
3
LLv
v31i
2
Li2
zM2
Lt
qw
gvuKq
21
D
ˆ
ˆˆ,
- Partly parameterized TKE equation:
shear by circulation motions
shear turbulent buoyancy
dissipation
First part of the circulation shear term
CS
vvCS
COSMO Bucharest 2006Matthias Raschendorfer
- Physical meaning of the circulation term:
Budgets for the circulation structures:
...ˆˆ...
LLLLLtD vv
CS
Circulation term is the scale interaction term shifting SKE or any other variance form the circulation part of the spectrum (CKE) to the turbulent part (TKE) by virtue of shear generated by the circulation flow patterns.
vvCS
CKE
TKE
COSMO Bucharest 2006Matthias Raschendorfer
- Parameterization of the circulation term for thermal driven (direct) circulations:
1. In the CKE budget:
•scale interaction loss = buoyant production
2. In the budget for circulation scale heat and moisture flux :• scale interaction loss + pressure destruction = buoyant production
3. In the budget for circulation scale temperature variance :
•scale interaction loss = vertical flux divergence from the surface
4) In all budgets:
• flux gradient form of temperature variance flux with a vertical constant circulation scale diffusion coefficient
• a mass flux approach for circulation patterns
• a vertical constant circulation time scale
COSMO Bucharest 2006Matthias Raschendorfer
0Hz
wg
zwg
SC
vCv
Vv
vvC
2
V LLLLL
expˆ
ˆˆˆ
ˆˆ
21
Cv
v
21CC Hg
a21
a1w
ˆ
ˆ
boundary layer height
horizontal updraft fractiondifference between updraft and downdraft
• other circulation scale 2-nd order moments have a similar representation
• turbulent and circulation scale flux densities can be added:
- in the first order budgets- as input for the statistical condensation scheme
Circulation term ~ circulation scale temperature variance ~ circulation scale buoyant heat flux
Effect of the circulation term for stabile stratification:
z
x
z
w0
x
zturb Kw
circw
wg
uwuTKEd vv
zt
0• 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
Simulated midnight profile of potential temperature
COSMO Bucharest 2006Matthias Raschendorfer
Conclusions:
-Due to this extension the turbulence scheme is able to produce a physical solution even for strong stability
1. The main problems with the inclusion of non turbulent circulations is, besides sub grid scale freezing and – precipitation:
•Occurrence of at least one additional length scale
spectral scale separation
2. There is a first simple solution of describing vertical circulation flux densities•actually used only to describe the scale interaction term in the TKE equation
circulation term
-The circulation scale flux densities can be used in the 1-st order budgets and the statistical condensation scheme
-The approach can be extended (prognostic equations for circulation scale variances)