Work Status:

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


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


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:


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


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


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


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!


- 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


- 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


- 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


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


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)

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