Along the aim of COSMO-SP to consider missing interactions · hyperbolic -profile at stable stratification uf Scalar profile for a SYNOP-station lawn linear -profile at non-stable

Separation Turbulence Circulations

Parameterizations of source terms

Parameterizations of SGS processes

integrated in

Cloud-microphysics

Radiationtransfer

interaction

Local parameterizations:

GS parameterizations:

Along the aim of COSMO-SP to consider missing interactions:

STIC

Increased set of diagnostic or prognostic

variables:

Mass fraction and number concentration of- cloud constituents, - precipitation and

- passive tracers (aerosols)

Optical properties:- optical thickness, - single scattering albedo,- asymmetry factor and- delta-transmission function

feed-back with SGS-processes

modified by SGS-processes

PP T2(RC)2

Surface and Soil-processes

PT ConSAT

new focus

new focus

direct analysis of T_2m and TD_2m

operational configuration

revised TURBDIFFimported from ICON

nocturnal warm bias reduced

but perhaps a new nocturnal dry bias

still much too cold during day-time

still much too moist in the afternoon

Case study: 23.06.2016

COSMO-DE with lateral boundaries from ICON-EU

ü only for rather smooth surfaces; applied filterü almost saturated soil due to long standing rain period beforeü almost no clouds due to high pressure situation; + applied filter

T_2m TD_2m

Matthias Raschendorfer Offenbach 2017

ICON-EU-Simulations: Same Testcase

Nocturnal effect of minimal diffusion coefficients in ICON

without minimal diff.-coeff.active minimal diff.-coeff. (operational)

laminar layer

0zk

fu0

Azk

linear -profileat stablestratification

roughness layer

z

fSf

lowest model main level

upper boundary of the lowest model layer

lower boundary of the lowest model layer

h

Pzk

!

m10hA »

0D0z

Turbulent velocityprofile

fu

f0u

Az

STIC-effect on the Profile-Function on near-surface values:

ff

f

d= 00u

k

Dz

m2h m2 »

( )SASA

m200SSm2 r

rrf-f×

++f=f f

ff

0z

m20hp »Pzfrom turbulence-schemef

Pu

Matthias RaschendorferDWD

hyperbolic -profile at stable stratification

fu

Scalar profile for a SYNOP-station lawn

linear -profile at non-stable stratification

fu

COSMO-GM 2018

ò fff

×k==

A

0SASA u

d1u1r

!

!! ( )SAp

HSASS TˆcuSHF

d-q×r=

( )SvAvevHSASS qqLuLHF -×r=

§ Effect of Kmin:

Ø Increased transfer-velocity

Ø Non-stable profile shape

Nocturnal effect of hyperbolic profile for stable turbulent velocity scale

with hyperbolic profile for stable startif.always with linear profile (operational)


with hyperbolic profile for stable startif.always with linear profile (operational)assimilation


with hyperbolic profile for stable startif.always with linear profile (operational)

§ Right correction for nocturnal couplingØ Smaller transfer velocities

Ø Reduction of too excessive nocturnal BL-cooling

§ Below clouds and at vegetated surfaces during summertime

Ø positive nocturnal T2m-bias gets even larger!

Effect of hyperbolic profile for turbulent velocity at stable stratification:

Matthias RaschendorferDWD COSMO-GM 2018

§ Attention:- Nocturnal surface-temperature during the

assimilation run is warmer than measured T2m!- Not only below some sheltering clouds - But correlated with the amount of leaves

Ø Missing decoupling of plant-surfaces with the still warm soil mass!?

Ø Radiative cooling is almost compensated by heat form the soil

Ø Warmer nocturnal BL with hyperbolic profiles causes (although this is an improvement) an even increased positive T2m-bials.


Ø Semi-transparent and decoupled cover-layer in TERRA -> is being done

after sun riseAtlantic sea

§ An lessen from previous ConSAT tasks:

‒ Pure modifications in the description of the turbulent Prandtl-layer can hardly correct the main sources of current model-errors of the diurnal cycle of near

surface variables and of numerical instability of near-surface temperatures!

‒ The description of surface processes promises to provide by far the largest

potential for improvement!

Efforts towards a substantial, semi-transparent cover-layer (canopy) thermally loosely coupled to the dense soil:

Bi TT ==0

( )BRBi TTniTT -×+==1

CRBB

RBRni TaTaTT +===

CTCCBBS TaTaT +=

000 zd +=s=s0T

ATAs=s

0=s=s S

functions of SAI only

RC

RBC aaaa +==+ 1B

GHF

THF

HAr0

SHF

LHF

d,uSRFPHF

d,uLRF

BT

v A canopy-extension of TERRA has been developed already 2 years ago in COSMO-TERRA:

Sequence of connected semi-transparent and substantial cover layersØ Coupled by long-wave radiation and atmospheric heat-transferØ Linear cover-layer T-profileØ Without consideration of snowØ Common heat-budget of the cover-layers with implicit surface temperatureØ The direct coupling of surfaces with the atmosphere becomes as smaller as

more surface-layers are aboveØ The soil-surface is the lowest surfaceØ Controlled by present external parameters and 2->3 tuning parameters

Matthias Raschendorfer EWGLAM/SRNPW , Reading, 2017

§ A more advanced semi-transparent C-layer extension (by M. Raschendorfer) with parameterized heat-conduction and heat storage of the full roughness cover (e.g. plant canopy) is being adapted from an existing test-version prepared last year within COSMO. o The final combination with the reformulated budgets will include all related partial development!

full C-layer treatment : semi-transparent + loosely coupled + heat-storage + adapted evapo-transpiration

amplitude slightly overestimated

removed cold bias in the afternoon!

almost perfect double wave!

still some problemspossibly due to not resolved inversion-layer/mixed-layerafter swap of net radiation

T_2m TD_2m

direct analysis of T_2m and TD_2m

revised TURBDIFFimported from ICON

2) Experiment with the existing test-version in COSMO:o COSMO-DE with lateral boundaries from ICON-EUo domain averaged daily cycles of near-surface variableso almost saturated soil due to long standing rain period beforeo only for rather smooth surfaces: applied filtero almost no clouds due to high pressure situation + applied filter

already shown last year

conditional diagnostic

1. Additional thermal equation for snow-free skin2. Linearization of surface processes3. Thermal equations for skin, snow and soil coupled through implicit

temperatures => extended linear system of equations4. Related adaptations for snow-cover diagnostic, dynamic tiles, initialization

(of nested domains) and organization of model-restart5. Cleaning the code from detrimental limitations6. Necessary restructuring of code7. Correction of various inconsistencies with respect to the treatment of water

interception and phase transitions of surface water8. Merge with various work-arounds and extensions in ICON-TERRA9. Including phase-transitions of precipitation (as well as soil water and the

snow-cover) into the implicit treatment10. Merge with canopy-extension, prepared 2 years ago in COSMO-TERRA11. Canopy-interception of snow and related adaptation of snow-tiles12. Transfer of ICON-development into COSMO?

a very large effort!

v Implementation strategy for ICON:

Solving the problem of oscillating surface-temperatures first

Ø Necessary implicit treatment of surface-temperature is also matches with the structure of the heat-budget for the cover-layer

Ø Treatment of a partial snow-cover is includedØ Separation of formal modifications from physical extensions

already prepared!

Some of Günthers Workarounds:

§ Forcing the effect of a closed snow-cover of melting snow below a snow-free canopy by generation of an artificial sf surface-fraction of the soil and by a reduced snow-albedo

Ø The artificial sf sub-tile can be warmer than Tmelt and can heat the near surface air

Ø Necessary corrections of this measure:

o Avoiding soil-evaporation of this tile, since real soil is snow-covered

o Artificial reduction of day-time snow-temperature (since snow should be colder than the roughness elements), in order to avoid too excessive snow evaporation

o Artificial reduction of heat-capacity of the artificial sf sub-tile, since it has to represent

sf roughness elements being loosely coupled with the compact soilv This had to be adapted and partly substituted

§ Reduction of roughness-length above a snow-coverv This caused jumps in transfer-velocity after aggregation of new dynamic sub-tilesv Now R-elements get sunk in an increasing snow-cover

§ Interception of rime has been consideredØ Larger interception storage and longer lasting potential evaporation

Ø Phase transitions between rime and dew are not considered, which creates artificial heat sources

v This could be adapted by treating super-cooled interception water

AT

2bT

1bT

sfT substantial, loosely coupled, semi-transparent

C-layer

idealized, infinite-thin

S-layerbT

sfb TT ®

snTsnw sfw

THF

snTHF sfTHF

[ ]sxudsx LHFSHFLRFLRFSRFPHFTHF +++++=

[ ] ( )0sxsx0sxuT

0sx TTLHFSHFLRFTHF

sx-×++¶+=

[ ] [ ]030

0 4 sxsxuT TLRFsx

se-=¶

[ ] [ ] p0H

SAs0sxT cuSHF

sx×r-=¶

[ ] ( ) ( )[ ]0sxsxevsxsatvT

redsx

HSAs

0sxT TLTqdfuLHF

sx×××r-=¶

snGHF sfGHF

( )11 bsfbbsf TTGHF -×a-=

( )1bsnb1b

snb

snb

sn TTGHF -×a+a

a-=

[ ] 0tTTcGHFTHF0cmcm0

ccsfsf ®D-

r=-

[ ] 0tTTcGHFTHF

0snh

0smsm0

snsnsnsn ¾¾ ®¾D-

r=-®

snf snf-1

mean cover-temp.(of lin. vert. prof.).

mean snow-temp. (of lin. vert. prof.)

so far substituted by

so far only explicit and resistance of soil-half-layer not

considered

so far only explicit contribution considered

singularity for vanishing

snow-depth

so far no budget equation for in favour of setting sfT 1bsf TT =

1bsf TT =

New linear-implicitly coupled budget equations at the surface :(completely implemented)

Implicit increments of atmospheric transfer velocities:(already implemented)

[ ] [ ] p0H

SAS0SxT cuSHF

Sx×r-=¶

§ Considering the hidden TSx-dependency of the transfer velocity for heat ,which controls the virtual conductivities of SHFSx and LHFSx:

HSAu

[ ] [ ] [ ] ( )0SxSx

0HSAT

0HSA

HSA

0HSA TTuu:uu

Sx-×¶+=®

§ The implicit heat budgets for Sf and Sn become quadratic in :

§ From solutions of the decoupled versions of these implicit quadratic equations:*SxT

[ ] [ ] [ ] ( )0Sx

*Sx

0HSAS

0HSA

*HSA TTuuu

sx-×¶+=

§ This updated transfer velocity is used in the subsequent linear system.

SxT

[ ]*HSAu

§ The factor of the linear TSx-dependency of the transfer-velocity is estimated by registration:

[ ] [ ] [ ]1

s0s

1HSA

0HSA0H

SAT TTuu

usx -

-

-

-»¶ ( )

SnSnSfSns TfTf:T ×+×-= 1

[ ] [ ]0evsatvT

redSx

HSAS

0SxT LqdfuLHF

Sx×××r×-=¶


Sn Sf B1 B2 B3 …

Resulting matrix of the extended linear system:

§ All 2 + k_soil budgets are always present (even for f_sn=0 or f_sn=1)

§ They are linearly coupled in the temperatures:

SnSna 1B

Sna

SfSfa 1b

sfa

SnBa 1

11

BBa 2

1BBa

12

BBa 2

2BBa 1

2BBa

SfT

1BT

2BT

SnT

Sfd

1Bd

2Bd

Snd

§ Can easily be tri-diagonalized by matrix-operations and solved by the standard solver

SfBa 1

23

bBa 3

3BBa 4

3BBa

degree of corrected implicit coupling of TSn to the soil- and atm. temperatures

ifb

§ Partly reducible by parameters:

degree of considered flux-equilibrium in diagnostics of TSf

isc:

isc

fes

degree of implicitness for effective surface fluxes used in the heat budgets

fes:ifb:

Default for test: isc=1; fes=1; ifb=1 (full implicit solution active) - modified for diagnostic points

altered

created


Scheme for snow-covered fraction and snow-depth :

§ Snow is not equally distributed along the grid-cell surface, due to various sources of inhomogeneity:

snfSnow-covered fraction

snwincreases monotonically with mean snow-water level of a grid cell

snh

until a critical mean snow-water level is reached. csnw

§ Specific snow-water-level is prop. to specific snow-depthsn

snsn f

ww =

snw

csnw

0

snf1

snw

csnw

0

snwcsnw

ssp

§ New control-parameter : ssp: spreading efficiency

ssp=0: so far operational version; not steady; it is always !!csnsn ww ³

ssp

ssp=1: full snow-spreading; always full snow-cover!!

Test-grid-point Kenia (+33.71_+7.89) :

§ Oscillations almost completely eliminated by ifb=1 + itv=1 § Similar result but a bit larger daily amplitudes ifb=1 + itv=1 + fes=1 (not shown)

old-sx-cpl + Ifb=1 + itv=1 old-sx-cpl + Ifb=1 + itv=1

itv=1: full consideration of implicit T_sx-dependency in atmospheric transfer velocity fes=1: full consideration of flux-equilibrium at the sf surface

T_sf LHF_sf

§ After-noon situation; tropical hot with strong radiation forcing§ 3 hour ICON-global test-run (R2B6, dt=6min) with § implicit defaults of the new development version of SAT-formulation (mainly TERRA)§ Emulation of so far operational explicit surface coupling only for a special grid-point


§ Major adaptations in TERRA, TURBTRAN (and related interfaces) introduced into ICON-branch:

o Restructuring the sequence of processes

o Removal of various, now detrimental limitations all over the code

o Reformulations related to variable-redistribution for dynamic snow-tiles

o Generalization of snow-cover diagnostics

o Adaptation and extension of various empirical extension implemented by Günther Z

Current state :


v consistent formulation of a 2-phase interception-store

v together with the so far missing implicit formulation of wSf -evolution

§ Sanity-checks performed:

o numerically stable even for large time steps; a couple of technical ICON-testsuites

o some remaining oscillations due to phase-transitions of snow or soil-water

o almost minor differences compared to operational version

o Technical test-suite of ICON passed

New implicit and simultaneous incrementation of interception water:(partly implemented)

SfSfSfSfSf DWFVWFPWF

tww

++=D- 0

PWF : given precipitation-water flux-density

( ) ( )0Sf

potSfSf

covSfSf TVWFwfVWF ×-= : current water-vapour flux-density

explicit potential evaporation (negative for dew- or rime-fall, where )

linear cover-function: ( ) 1=maxSf

covSf wf

( ) refSfSf

drpSfSf DWFwfDWF ×-= : current drip-water flux-density

explicit reference value at (parameter of the scheme) 1=dprSff

rational drip-function:

( ) 00 =covSff

( ) 00 =dprSff ¥¾¾¾ ®¾

® maxSfSf ww

dprSff

v Quadratic equation for ; automatically positive-definite and limitedmaxSfSf ww ££0

v Simultaneous consideration of all sources and sinksv still depends on previous surface temperature . 0

SfTØ No implicit coupling between hydrological and thermal equations yet!

Ø Lower atmosph. BC: explicit and corrected !!


potSxVWF

0SxVWF SxSxSx THFSHFSHF D+= 0

(for real evaporation)

( ) 1ºSfcovSf wf

Implicit freezing and melting of interception water and precipitation: (being implemented)

§ At least for liquid and frozen interception-water coexists with a smooth transition. frz

maxSfliqmin TTT ££

SfTliqminT frz

maxTmeltmltSf TT »

: liquid fraction of wSf and its linearization

0

1/2

1

[ ] ( )000SfSfSfTSfSf TTPHFPHFPHF

Sf-×¶+=

( ) ( )[ ]00Sf

liqSfSfSfSflfSf TfSWFRWFRWFLPHF ×+-×=

[ ] ( )00

0Sf

liqSfT

SfSfSflfSxT Tfd

twSWFRWFLPHF

Sx×÷÷ø

öççè

æD

++×-=¶

( ) ( ) ( ) ( )[ ]SfliqSffvSf

liqSflvSfevSfev TfLTfLTLTL -×+×=® 10

[ ] [ ]( )00Sfev

satvT

redSf

HssSfT TLqdfuLHF

Sf×××r×-=¶

[ ] ( )000SxSxSxTSfSf TTLHFLHFLHF

Sx-×¶+=

generalized latent heat of vaporization

( ) ( ) ( ) ( )000SfSfSf

liqSfTSf

liqSfSf

liqSf TTTfdTfTf -×+»

: latent heat flux-density due to rain<->snow transitionincluding implicit extension

: related virtual conductivity including associatedphase transition of present interception water

Ø Correct and implicit treatment of liquid and frozen interception water

Ø Final Tsf is in dynamical accordance with complete turnover of latent heat.


: related explicit part

v Introducing LHFSf and PHFSf in decoupled TSf-equation and solving this in quadratic approximation:

0Sfw

Next steps:

§ Operationalization of my development branch in ICON

§ Adding melting of snow and freezing/melting of soil-ice into the implicit heat budgets

§ Incorporation of a multi-layer snow-model

[ ]tTTcGHFTHF CmCm

ccCC D-

r=-0

0

( )11

1BCB

BCB

BB

CB

C TTGHF -×a+aa×a

-=

o the partitioning of fluxes into those related to B and C

o expressions for the additional conductivity

and the additional heat capacity :

CBacc


§ Introducing the extension with a decoupled, substantial and semi-transparent cover-layer, including

( )BCCm TTT +×=21 linear vertical T-profile of R-layer

CBa due to the exchange of SH and LR between B and C

cc due to the mass of R-elements and interception water

Ø removal of remaining conceptual deficiencies!

Ø significant impact on simulated properties!

Ø based on an already developed prototype, present in an older test-version of COSMO!

Ø largely prepared just by the current implementations into ICON!

v 1-st official ICON-release -> COSMO

v 2-nd official ICON-release -> COSMO

Direct STIC-impact on SAT:

Matthias RaschendorferDWD

§ In TURBTRAN, the SAT-resistance has a two contributions:

úúû

ù

êêë

é-÷÷

ø

öççè

æ=g f

ff 1

0

0s

P

Ps u

uhz:

îíì-

=stable

unstables

11

( ) ( )

( ) ( )ïïî

ïïí

ì

<g+÷÷ø

öççè

æg-

³÷÷ø

öççè

æ¾¾¾¾ ®¾÷÷

ø

öççè

æ×g+g-

×k

=×k

=fff

-f-

ff®gff

ff

f

òstableuu

zh

zzln1

unstableuuzzln

hzzln

11

u1

ud1r

0p0

A1

0

A1

0p0

Aneutral0

A10

A

1

0HA0

1A

0

!

! !!

operationally deactivated

0XX zz:h -=

úúû

ù

êêë

é×

k=÷÷ø

öççè

æ k+l×

×k= HHH

HH

HHS z

zuk

uzuS

r0

0

0

00

000

11lnln

o Roughness-layer resistance with a laminar and a turbulent part(only for scalars):

o Turbulent Prandtl-layer resistance with an unstable and a stable branch:

earth

roughnesslayer

000 :zd s=+=s

0s =s=s

displacementheight

roughnesslength

Azz = k=ke

k=ke-1

Pzz =

{ }M,HÎf!X

XK:u =f

turbulent velocity

0zz = k=ke+1

fff

+=

A00SSA rr

1:u transfer velocity( )SAp

HSASS TˆcuSHF

d-q×r=

( )SvAvevHSASS qqLuLHF -×r=

COSMO-GM 2018

( ) ( ) MCzz

MT Fvu:F +¶+¶= 22

11061600c080c740920 HHMMHMHM .,.,.,.,.,. =a=a===a=a

MHHMMMHH

HMMMMHH

aaaaababS

--

=MHHMMMHH

MHHHHMM

aaaaababS

--

=

vp

c

d

vw r

r1RR

J×+q×÷÷ø

öççè

æ-=J ˆ: vcv rrr aJ-=q :÷÷

ø

öççè

æ-J×=J T

RRrr

d

vcvTv

ˆ:

( )

( )[ ] MMM

a:

MT

MMHHMM

H

a:

HMHH

HHM

a:

MT

MMH

a:

HMHHHH

b:cSGrGrSGr

b:cSGrSGr

MMHM

MHHH

=-=×úûù

êëé a+a+a

+××a+a

=-=×a+×úûù

êëé ×a+a+a

==

==

31691129

3161231

!!!!! "!!!!! #$!!! "!!! #$

!%!&'!!!!! %!!!!! &'

( )whwhwv

H ˆrqˆg:F q¶+¶J×q

= q

02

2

³×= MT

MT F

q:G !

normal to grid scale surface normal to horizontal surface

cvd

vv qq1

RR1r ˆˆ: -÷÷

ø

öççè

æ-+= ( )TqvsT

ˆ: ¶=a cT T1

1ra+

=:

dp

cc c

LT =dp

dcR

rp p

pr ÷÷ø

öççè

æ=

saturation fraction

( ) qFa1

z1

z1 H

stabm++

k»

!!

HH Fq

:G ×= 2

2![ ]!

!! MMHHM

TMM

zq

ztqFSFrSqqqSqa

--×r=úû

ùêë

é÷øö

çèæ¶r-¶+÷

øö

çèæ r¶

322

21

21

additional shear

Iterative solution for TKE and the stability-functions:

COSMO Matthias Raschendorfer CLM-Training Course

( )îíì

=f+f

×÷÷ø

öççè

æ+×G= f

ff

iid v,scscalara,

Kk:r 21

11

LCFSAI

DAI

( ) ( ) ( )[ ] 2MM0HHM

TM

00

20

2

qαqqFSFSqDifqAdv

Δt2qq

!! -×-×++»

×-

diagnostic (linear) system dependent on TKE=q2/2and mean vert. gradients

(for all other 2-nd order moments) => stability functions:

Implicit vertical diffusion update for mean vert. gradients using vertical diffusion coefficients

MTF

( )MCMM FFr +×

H,MSq!

• SHS circulation• SSO wakes, • SSO density currents• plumes of SGS convection

additional SGS shear by :

STIC-impact:

HFMS HS

artificial treatment of possible singularities

minimal diffusion coefficients

includingnon-gradient diffusion

The STIC-scheme including empirical parameterization extensions:

{ }q,vmaxq min=

minimal turbulent velocity scale

0<0³

MTF HF

optionally contributing to physical horizontal diffusion

Matthias Raschendorfer, Günther Zängl (DWD)

laminar- , tilted surface-and roughness-layer-correction

=H,MK { },kmax H,M

with optional positive definite solution of prognostic TKE-equation and optional vertical smoothing of

potentially reducing stable stratification-damping

partly substituting artificial security limits and related stratification damping

Ri.number dependent

with a stability dependent correction (near the surface)

restrictions for very stable stratification

now more flexible

scaling factorRi-number dependent

restricted

Documents

Along the aim of COSMO-SP to consider missing interactions · hyperbolic -profile at stable stratification uf Scalar profile for a SYNOP-station lawn linear -profile at non-stable