along the aim of cosmo-sp to consider missing interactions · hyperbolic -profile at stable...
TRANSCRIPT
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)
Nocturnal effect of hyperbolic profile for stable turbulent velocity scale
with hyperbolic profile for stable startif.always with linear profile (operational)assimilation
Nocturnal effect of hyperbolic profile for stable turbulent velocity scale
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.
Nocturnal effect of hyperbolic profile for stable turbulent velocity scale
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 -
-
-
-Ȧ ( )
SnSnSfSns TfTf:T ×+×-= 1
[ ] [ ]0evsatvT
redSx
HSAS
0SxT LqdfuLHF
Sx×××r×-=¶
Matthias Raschendorfer Offenbach 2018
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
Matthias Raschendorfer Offenbach 2018
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
Matthias Raschendorfer Offenbach 2018
§ 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 :
Matthias Raschendorfer Offenbach 2018
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 !!
Matthias Raschendorfer Offenbach 2018
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.
Matthias Raschendorfer Offenbach 2018
: 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
Matthias Raschendorfer Offenbach 2018
§ 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