COSMO Sibiu 2013Matthias Raschendorfer

Towards Separated Turbulence Interacting with Circulations (STIC):

kln

dkdk

kln

32

- slope in case of TKE

gD1

ln

turbulence

microphysicsresolvedstructures

pL : largest turbulent wave length

convective peak

neutralstabile

labile

pL1

ln

Spectral characteristics of turbulence and circulations:

- circulations generally are related with …………………………………… additional spectral peaks

- or they cause different peak wavelengths in vertical direction compared to the horizontal directions: ….

• larger peak wavelength in vertical direction in case of labile stratification at least a two-scale-problem

anisotropic peak wave length

catabatic peak

unresolved structures

BL workshop Matthias Raschendorfer

circulations

• smaller peak wavelength in vertical direction in case of stabile stratification

COSMO Sibiu 2013

Principle of a general valid GS parameterization by scale separation:

Closure of the 2-nd order budget equations closure assumptions = further information

Limited (not general valid ) solution:

e. g. for sub grid scale turbulence

General valid sub grid scale closure:

General valid 2-nd order closure assumptions can’t exist!

Assumptions can only be valid for special conditions:

or for sub grid scale convection!

Separation of sub grid scale flow in different classes

Application of specific (rather easy) closure assumptions for each class

Combination of particular parameterizations

Consideration of interaction between different classes

use of different schemes for turbulence, convection or SSO blocking

usually missing in current models!

Spectral separation by

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

- considering budgets with respect to the separation scale

gp DLL ,min

turbulent budgets

Matthias RaschendorferDWD

Separated Turbulence Interacting with Circulations

COSMO Sibiu 2013

LLLLLtD ˆˆ vv

LLL ˆˆ vv

average of the non linear turbulent shear terms

circulation shear term

Additional circulation terms in the turbulent 2-nd order budgets:

BL workshop Matthias Raschendorfer

turbulent shear term

CQ

ˆˆLLL vv

turbulent shear term

COSMO Sibiu 2013

Separated semi parameterized TKE equation (including scale interaction sources):

buoyancy production

eddy-dissipationrate (EDR)

0labil:neutral:stabil: 0

00

time tendency

transport(advection + diffusion)

shear production by sub grid scale circulations

0

2

t Lq

21

3

1i

2i

2

L

L

v

q

21

v

v

~

~

3

1ii

Li vv ˆ~vLv

v

wg

3

1iiLi L

vv ˆ~v

MM

3

Lq

expressed by turbulent

flux gradient solution to be parameterized by a non turbulent approach

v

shear production by the mean flow

0

v

L : with respect to the separation scale L buoyant part

of Lp v

buoyant and wake part

of LL

p v

mean (horizontal) shear production of circulations,

3

1i

2iv

according Kolmogorov

MC

ML FSq :MM

L FSq :HHL FSq :

: correction factor in case of sloped model layers

Matthias RaschendorferDWD COSMO Sibiu 2013

222

211

21221gHHSHSC vv2vvDqQ :_

vv

Separated horizontal shear production term:

effective mixing length of diffusion by horizontal shear eddies

velocity scale of the separated horizontal shear mode

1H scaling parameter

Equilibrium of production and scale transfer towards turbulence:

gH

3HM

HgHH Dq

FDq

MHF:

1H scaling parameter

23

MH

2g

23

H21

HMHgHHSHSC FDFDqQ vv

_2S:

horizontal shear eddy

isotropic turbulence

z

x

y zvh

xvh

xvh

horizontal grid plane

TKE-production by separated horizontal shear modes:

zvh

grid scale

21

pL

gD

……….effective scaling parameter

separated horizontal shear

additional TKE source term

Matthias RaschendorferDWD

Already used for EDR forecast ; to be tuned and verified for operational use

COSMO Sibiu 2013

p

pgvvvvv

i

iiiiit

ˆˆˆˆ v

SSO-term in filtered momentum budget:

ivSSOQblocking term

TKE-production by separated wake modes due to SSO:

currently Lott und Miller (1997)

Pressure term in kinetic energy budget:

pv

p

ppp

p

p

v

v

vv

v

v ˆ

wake source

sources of mean kinetic energy MKE p v

buoyancy production

sources of sub grid scale kinetic energy SKE

pressure transport

expansion production

vp v p

from inner energy

DWD Matthias Raschendorfer

Q

nhv

21x ,

3x

B

vvSSO_CQ

Contribution taken form SSO scheme : already operational

COSMO Sibiu 2013

02

vvC

v

V

v

STH_CV wˆgˆw

ˆg

QˆLLLLL

vv

virtual potential temperature of ascending air

circulation scale temperature variance ~ circulation scale buoyant heat flux TKE source term

TKE-Production by thermal circulations:

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

separated thermals

virtual potential temperature of descending air

vertical velocity scale of circulation

buoyant production of sub grid scale kinetic energy can be derived directly form current mass flux convection scheme

Matthias RaschendorferDWD

Two contributions:

- one taken form convection scheme: already used for EDR forecast ; to be verified

- one being a crude estimate of surface induced density flows: active since years

COSMO Sibiu 2013

Matthias RaschendorferDWD

pot. temperature [K]Wind speed [m/s]

referenceincluding horizontal shear – and SSO-production

including horizontal shear –, SSO- and convective production

mountain ridge

COSMO-US: cross section across frontal line and Appalachian mountains

COSMO Sibiu 2013

A single 2-nd order scheme for the whole SGS range requires horizontal grid scales being sufficient small to allow turbulence closure as a general valid asumption.

We can’t do it without a convection scheme, in particular if we think for global simulations (ICON)

A 2-nd order scheme for non precipitating (shallow) convection only, might be an option.

Mass flux approach is better adapted to coherent flows than 2-nd order closure

Convection may be partly resolved (grey zone) and fundamental assumptions applied to classical mass flux schemes are no longer fulfilled.

Mass flux convection scheme needs to be reformulated to be scale adaptive.

What’s about the turbulence interaction in the convection scheme?

Matthias RaschendorferDWD COSMO Sibiu 2013

Matthias RaschendorferCOSMO

Conditional domain closure (CDC) :

sdttG

1t

tGG

,

,,

:,rs

sr

r d

G : domain of dimension d

G

G

GG

:ˆ

tttGG

,,:,, rsrs tttGG

,ˆ,:,, rsrs

Q

Ga : : volume fraction of 0GGGG ,,

QQaaˆa surt v

sdG1

QB

2tsur

s

nsv:

1 : mass budget (continuity equ.) Bnt

B

2tt s

G

Bsd

G1

a s

nsln

nt s

x

0GG

Q

gD

0z

QGB :

BQG :

G

dd

0

w

w

ss d2L

Ls: largest non-convective wave length

H

sd zn

n

Foundation of alternative mass flux equations Solvable also for volume fraction, if conditions

for sub –domain definition are used Turbulent properties can be used for lateral

mixing and triggering Separation against turbulence and grid scale

possible

COSMO Sibiu 2013

Non-turbulent (convective) modulation of normal distributed patterns in a statistical condensation scheme:

0

vsq

vs0q

sLdL vsq

cloud

dLs

turbulent variation

normal distr. non turbulent variation

bi/tri-modal convective variation

gD grid scale

horizontal direc. vsq

vsq

PDF

range of up to L-scale patterns

range of up to Ls-scale pat-terns

a0a a

multimodal common

PDF

gp DLL ,min : separation scale for turbulence

sL : horizontal scale of largest normal distr. patterns (turbulence, wakes, gravity waves, etc)

vswvs qqq : local over saturation

Matthias RaschendorferDWD COSMO Sibiu 2013

Conclusion:

Matthias RaschendorferDWD

Generalization of the closure scheme by scale separation

- Classical turbulence closure will only be valid, if all sub-grid structures are in accordance with turbulence closure assumptions

- Usually other sub-grid processes are present and in the near surface SBL they are even dominant

The presence of non-turbulent sub-grid scale structures needs to be considered

Physical reason for the problems with a classical scheme

- Separation of turbulence by a sub-filter only smoothing “turbulence” provides variance equations for turbulence automatically

containing shear production terms by non-turbulent sub-gird processes (scale transfer terms)

The non-turbulent structures can’t be described by turbulence closure, rather we necessarily need separate schemes for

them with specific closure assumptions, in particular specific length scales.

The additional production terms can’t be introduced only by treating all scalar variances by prognostic equations that

introduce turbulent transport of them (UTCS-extension) but no additional sources for TKE.

Turbulent fluxes remain in flux gradient form, those by non-turbulent flow structures do not.

Already (partly) implemented TKE-production by scale transfer from kinetic energy of …

- wakes generated by surface inhomogeneity (from SSO-blocking scheme) already operational

- thermal circulation by surface inhomogeneity (due to differential heating/cooling) only crude

approximation

- horizontal eddies generated by horizontal shear (e.g. at frontal zones) not yet verified

- Convection circulation (buoyant production from convection scheme) not yet verifiedCOSMO Sibiu 2013

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

Considering TKE-transport by circulations

Setting up a first estimate of convective modulation of a turbulent saturation adjustment

Integration of prognostic equations for scalar variances (and skewness of oversaturation) as an option

Implementation of a scale separated mass flux convection interacting with turbulence and providing volume fractions of convective sub domains (final step of STIC)

All further implementations in the common CÓSMO/ICON module not before this is ready for use in COSMO!

Next steps:

Matthias Raschendorfer COSMO Sibiu 2013DWD

Matthias Raschendorfer Moscow: 06-10.09.2010COSMO

x

0GG

Q

gD

0z

QGB :

BQG :

G

dd

0

w

w

ss d2L Ls: largest non-convective wave length

• Simplified diagnostic budgets in advection form do not contain volume fractions and are solved by vertical integration

• Substitute pure mass flux equation (continuity equation) of traditional mass flux scheme by equation for vertical velocity- Direct buoyancy impact using Boussinesq-approximation instead of dynamical de- and entrainment parameterization using grid scale humidity

convergence

• Boundary values from largest non convective mode- No parameterization of boundary mass flux using humidity convergence- No artificial vertical displacement or lateral mixing for boundary values - No distinction between shallow and deep convection; each level can be a starting point for updrafts or downdrafts- Automatic trigger of convection by turbulence using largest non convective wave mode

• Solving for volume fractions by using construction constraints for the convective sub domains- Explicit expression of convective flux densities and total source terms (clouds and precipitation) by convective averaging

• Performing scale interaction and scale separation against turbulence and grid scale convection

Q

Ga i

i :

0iia1

,,

iGiG vf ~:

iG

iGQQad entt

lnˆ ff

- Stopping integration when single cell diameter > horizontal grid scale: cut off against grid scale convection

,i

- Reducing separation scale when single cell diameter < separation scale: reduction of turbulence due to convection- Identification of the lateral mixing sink of convective kinetic energy (detrainment) to be the convective source of TKE

- Stopping integration when vertical velocity < that of turbulence triggered initial cell: cut off of against turbulence

: generalized velocity including molecular and slope effects

vv ~

Hi

in

ient

Q

QiBiGv

D1

Q

ˆˆ~

ii

i

g

2iz2

gi

i

i

i

i

i

i d4

a

m

D2

aDa

m2

G

B

D1

S

d

q1

ln

ii QwwH