Post on 03-Jan-2016
transcript
Matthias Raschendorfer
DWD
About the results of UTCS Tasks (ii)a,c and (iii)a
As far as attended by
COSMO Offenbach 2009Matthias Raschendorfer
3D-run
mesdat only with model variables
Forced correction run with SC version
outdat with correction integrals
Identical except horizontla operations and w-equation
mesdat containing geo.-wind, vert.-wind undtendencies for horizontal advektion
Realistic 3D-run (analysis)
Forced test run with SC version
outdat with similar results compared to compared test run using the 3D-model
Basic scheme of advanced SC-diagnostics:
COSMO Offenbach 2009Matthias Raschendorfer
or
Component testing:
outdat or mesdat may contain 3D-corrections and arbitrary measurements (like surface temperature or surface heat fluxes) the model can be forced by.
COSMO Offenbach 2009Matthias Raschendorfer
interpolated measurements
free model run starting wit 3D analysis
free model run starting with measurementsforced with prognostic variables from 3D-run
forced with 3D corrections
forced with 3D corrections and measured surface temperature
forced with 3D corrections and measured surface heat fluxes
Stable stratification over snow at Lindenberg
Potential temperature profile
atmosphere
soil
Potential temperature profile
atmosphere
soil
too much turbulent mixing
Turbulent fluxes of the non conservative model variables:
vcw
ccp
ww
2
1
qqq
qrTthermodynamic
non conservative model variables
mznmnmH
nzH
n cKKwf n ~~:
flux-gradient form explicit flux correction
cTcpTc
cTcpTc
cccTcTc
nm
rrrrrrr1rr1rrr
r1rrr1r1c
dp
d
cR
3phPa10
pTr
dp
cT
cL1
1r
:
vsTq :
dpp
cc cr
L :
cr cloud fraction
steepness of saturation humidity
Exner factor
Conversion matrix:
ˆzKww
c
v
3
2
1
thermodynamic conservative model variables
fg
cvz
vvz
czcz
z
qqqq
q
,ˆ,ˆ,ˆˆ
:~
Explicit moisture correction:
COSMO Offenbach 2009Matthias Raschendorfer
should vanish due to grid scale saturation adjustment!
Matthias RaschendorferDWD AG-Grenzschicht Oktober 2008
1. Ursachen für die Wirkung der expliziten Feuchtekorrektur
1)
waren kein reinen Kondensationskorrekturen
Bei impliziter Berechnung der Vertikaldiffusion von
g werden die mit benutzt.
Tridiagonal-Matrix für die Temperaturdiffusion enthält Quotienten aus Exner-Faktoren
Die durch erzeugten Beiträge verschwinden daher nicht bei der Bildung der Erhaltungsvariablen
Bei skaliger Sättigungsadjustierung wurde nur eine Iteration durchlaufen
Dadurch war die Adjustierung nicht genau
Kondensationskorrekturen veränderte das Ergebnis der Adjustierung
3)
2)
Im Modell wurde statt die Differenz
f
~zKff gebildet
Das entspricht dann nicht exakt dem Korrekturfluss“cor”: kleiner Effekt
“it5”: kleiner Effekt
“cor2” : großer Effekt TqrTqqq ttcptvtctvt ; vor impliziter Vertikaldiffusion
ˆzKf
Matthias RaschendorferDWD
Implizite Vertikaldiffusion für Temperatur:
old
kT
kpkT
kpzkt HSrcHrHAdvNfrHT
t
HTHTHT
kkkt
old
k1k
k1kkz NN
NfNfHf
1kk
1k1
pk1
pk
Hk
1pz
Hk HH
HTrHTrNKNTrKNf
kH
keH
kN
1kN
keN
1keN Elemente der Tri-Diagonal-Matrix des resultierenden linearen Gleichungssystems enthalten Faktoren der Form:
kp
kp
Hr
Nr
Weil diese Faktoren nicht im Diffusionsterm für cq stehen, verschwinden die Beiträge der Feuchtekorrekturennicht bei Bildung von wT
AG-Grenzschicht Oktober 2008
COSMO Offenbach 2009Matthias Raschendorfer
But there are differences … … due do numerical effects with the Exner-factor treatment of the T-equation
Time series of model domain averages
less low level clouds
Matthias RaschendorferDWD AG-Grenzschicht Juni 2009
explicit TKE-diffusion with restriction proper for 50 layer configuration
SC simulations with 80 layers and “implicit TKE diffusion”:
numerically unstable!
COSMO Offenbach 2009Matthias Raschendorfer
Dew point profiles 50 layers
considerable difference
Dew point profiles 80 layers
implicit TKE-diffusion being unconditional stable
almost no difference
Turbulence closure is only valid for scales not larger than
- the smallest peak wave length Lp for samples in any direction, where - the largest (horizontal) dimension Dg of the control volume
Spectral separation by
- averaging these budgets along the whole control volume (double averaging)
Partial solution for turbulence by spectral separation:
Turbulence is that class of sub grid scale structures being in agreement with turbulence closure assumptions!
- considering budgets with respect to the separation scale
gp DLL ,min
turbulent budgets
pp LL
COSMO Offenbach 2009Matthias Raschendorfer
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:
turbulent shear term
CS
ˆˆLLL vv
turbulent shear term
COSMO Offenbach 2009Matthias Raschendorfer
Physical meaning of the circulation term:
Budgets for the circulation structures:
LLLLLtD ˆ~ˆ~ 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.
CKE TKE
production terms dependent on:
specific length scales and specific velocity scales (= )
production terms depend on:
the turbulent length scale and the turbulent velocity scale (= )CKE TKE
21
CL
CL
21
pL
pL
and other circulation- turbulence-scale
moments
vvCS
COSMO Offenbach 2009Matthias Raschendorfer
Separated semi parameterized TKE equation (neglecting molecular transport):
shear production by the mean flow
buoyancy production
eddy-dissipationrate (EDR)
0 0labil:neutral:stabil: 0
00
time tendency of TKE
transport of TKE
v
shear production by sub grid scale circulations
0
2
Lt q21
v
2Lq
21
3
1iiLi vv ˆv Lv
v
wg ̂
3
1iLiLi vv ˆv
MM
3
Lq
expressed by turbulent flux gradient solution
to be parameterized by a non turbulent approach
v
COSMO Offenbach 2009Matthias Raschendorfer
222
211
21221gHHSHSC vv2vvDqS :_
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 FDFDqS 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
COSMO Offenbach 2009Matthias Raschendorfer
out_usa_shs_rlme_a_shsr_0.2
20
40
60
Pot. Temperature [K]
S N
06.02.2008 00UTC + 06h -92 E
out_usa_shs_rlme_a_shsr_1.0
COSMO Offenbach 2009Matthias Raschendorfer
= (dissipation)1/3
frontal zone
B
2iiiiiit sdnp
G1
pgvvvvvs
sv ˆˆˆˆ
SSO-term in filtered momentum budget:
Q
n
ivSSOQblocking term
SSO-term in SKE-equation:
2
1i
vSSOi
B
2h
hhhSSOC
iQvsdnpG
pS ˆˆ
_s
vv sv
v
hv
21x ,
3x
TKE-production by separated wake modes due to SSO:
Bseparated sub grid orography
currently Lott und Miller (1997)
COSMO Offenbach 2009Matthias Raschendorfer
moderate light
S N
06.02.2008 00UTC + 06h -77 E
Appalachien mountains
SSO-effect in TKE budget
out_usa_rlme_tkessoout_usa_rlme_sso
out_usa_rlme_tkesso – out_usa_rlme_sso
MIN = 0.00104324 MAX = 10.3641 AVE = 0.126079 SIG = 0.604423 MIN = 0. 00109619 MAX = 10.3689 AVE = 0.127089 SIG = 0.804444
MIN = -0.10315 MAX = 0.391851 AVE = 0.00100152 SIG = 0.00946089
COSMO Offenbach 2009Matthias Raschendorfer
= (dissipation)1/3
Effect of the thermal circulation term for stabile stratification:
z
x
z
w 0
x
ˆzturb Kw
circw
wg
uwuTKED vv
zt ˆ
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
COSMO Offenbach 2009Matthias Raschendorfer
2. In the CKE budget:• scale interaction loss = buoyant production
3. In the budget for circulation scale heat and moisture flux :• scale interaction loss + pressure destruction = buoyant production
4. In the budget for circulation scale temperature variance :
• scale interaction loss = vertical flux divergence from the surface
1. In all circulation scale budgets:
• flux gradient form of temperature variance flux with a vertical constant circulation scale diffusion coefficient
• a vertical constant circulation time scale for expressing scale interaction loss and pressure destruction
• thermal circulation structures are negligible during neutral stratificationshear production of (not by) thermal circulations is negligible:
TKE-production by separated thermal direct circulations:
COSMO Offenbach 2009Matthias Raschendorfer
In a simplified 2-nd order framework:
0FLwg
zwg
S 23
H3patzvvC
vV
vSTHC
2
V LLLLL
ˆˆˆ
ˆˆ
_vv
virt. temperature of ascending air
Circulation term ~ circulation scale temperature variance ~ circulation scale buoyant heat flux
A first parameterization of the thermal circulations term:
Previous approximations 1-4 in the circulation scale 2-nd order budgets :
pattern length scale
square for Brunt-Väisälä-frequency
separated thermals
Combination with a max flux approach:
v
vv
vv
vv
bC
b2
1
Cv
vv
21CC q
gLH
Hga21
a1aw
ˆ
ˆˆˆexp
ˆ
virt. temperature of descending air
turbulent velocity scale
horizontal updraft fraction horizontal updraft scale
boundary layer heightscaling factor
vertical velocity scale of circulation
bottom level
COSMO Offenbach 2009Matthias Raschendorfer
simulated midnight profile of potential temperature
measured midnight profile of potential temperature
COSMO Offenbach 2009Matthias Raschendorfer
Matthias RaschendorferDWD
t
cc
vvvv ˆˆˆ
momentumv2g watertotalqqqionprecipitat no0
temp. pot. watertotalqcrL
onidealizatiadiab.moistfor0c
Q
ii3i
cvw
cpp
cw
pd
,
,
,
vΩ
S
ilc qqq : cloud water (liquid and ice)
Mixed phase condensation heat
c
ii q
qTr : icing factor
iilic LrLr1L :
COSMO Cracow 2008
shear production
mol. and pressure prod.
source term correlation
For a solution we deal with budget equations for the 2-nd order moments:
Matthias RaschendorferDWD COSMO Cracow 2008
pressure production contains buoyancy term vv
g
ˆfor w
wwwv rq
rw , dependent on: xqpT ,, and cloud fraction: cr
2
w2
pwwp2
w2
Tc2
vs rqr2qr1r1q
linearization of saturation humidity: pvsvsv rTTqTqq ˆ
mixed phase saturation humidity: lvsi
ivsivs qr1qrq
normal distribution of saturation deficiency: svwsv qqq :
vsq
x
0
SGS (statistical) condensation (saturation adjustment) scheme:
cx rqT ,,ww q,cq
We need a decomposition of conservation variables:
Matthias RaschendorferDWD COSMO Cracow 2008
turbulent kinetic energy [m^2/s^2] Lon -5 5.5 Lat -5 6.5
Effect of SGS release of icing heat
x
vsqfrom normal distribution of turbulence
Convective modulation of turbulence in a statistical condensation scheme:
0
from bimodal distribution of convective circulation
cloud
turbulent Gaussian saturation adjustment using average oversaturation of upward flow
vsuq
turbulent Gaussian saturation adjustment using average oversaturation of downward flow
vsdq
vsuq
vsdq
a a1
vsgq
grid scale oversaturation vs
gq
vsd
vsu
vsg qa1qaq
,a ,vsuqto be estimated form
relevant 2nd order scheme describing convective circulations
total oversaturation
vsdq
COSMO Offenbach 2009Matthias Raschendorfer
2vsd
vsu
vsC qqa1aqVar
a1a
a21qSkew vsC
horizontal
direction
derivable directly from proper mass flux scheme describing convective circulations