COSMO

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):


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:


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


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


Experiment - Routine Experiment - Routine

before moister

now moister

before more TKE:

Initiating cloud dissolution

now more TKE (within the clouds)


time-height cut

vertical profile

Routine

Experiment


now cooler day-time BL

now much more BL clouds now more intense

low level jet


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:


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


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


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

0

0u

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

uud

rAA

Aneutral

A

A

HA

A

11

11

1

11

00

0

0

0

00

0 ln

lnln

1

0

0

s

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:


• 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 D

nHD 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


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


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)


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)

Documents

COSMO