TOUCANS C
TOUCANS: pre-operational
choices
Ivan Bašták Ďurán∗
Jean-François Geleyn∗∗
Filip Váňa∗∗∗
∗
ČHMÚ ONPP Prague, ivanbastak@gmail.com
∗∗
CNRM Météo-France Toulouse
∗∗∗
ECMWF Reading
TOUCANS C
1
Turbulent scheme
2
Length scale
3
Moisture influence
4
Prognostic computations
5
TOMs parametrisation
TOUCANS C
TOUCANS
TOUCANS
T - Third
O - Order moments (TOMs)
U - Unified
C - Condensation
A - Accounting and
N - N-dependent
S - Solver (for turbulence and diffusion)
TOUCANS C
Turbulent scheme
Turbulent scheme
Du
= Su
∂t
−
∂u 0 w 0
Dv
,
= Sv
∂z
∂t
−
∂v 0 w 0
,
∂z
∂s 0 w 0
Dqt
∂q 0 w 0
DssL
= SssL − sL ,
= Sqt − t
∂t
∂z
∂t
∂z
h
i c
u, v , w -wind components,ssL = cpd 1 + cpv − 1 qt T + g z − (Lv ql + Ls qi ) a
pd
diffused moist conservative variable, g gravitational acceleration, z height, cpd and cpv
specific heat values for dry air and water vapour, Lv and Ls latent heats of
vaporisation and sublimation, T temperature, qt total specific water content, ql and
qi specific contents for liquid and solid water, Sψ - external source terms, t - time,
D()
∂t
=
∂()
∂t
∂()
+ u ∂x + v
∂()
,
∂y
() - average, ()0 - fluctuation
TOUCANS C
Turbulent scheme
Exchange coefficients
KM =
√
ν4
eLK ,
χ
(Ri
)
f
C 3
free parameters
stab. functions
given by
turbulence scheme
√
4
KH = C3 Cν φ3 (Rif ) eLK
TKE
length scale
prognostic
quasi-independent,
meassue of intensity may depend on
TKE and BVF
χ3 (Rif ),φ3 (Rif ) - stability functions, ν - free parameter,C3 - inverse Prantl number at
neutrality,LK - length scale, Rif = Ri KKH - flux Richardson number
TOUCANS C
Turbulent scheme
Stability dependency functions χ3 , φ3
and free parameters
derived from Louis stability functions + RMC01 (pTKE)
based on (Bašták Ďurán, Geleyn, and Váňa, 2014
-BGV14) (TOUCANS)
analytical framework given by four free
parameters: C , ν, C3 , Oλ (+ two possible
functional dependencies)
enables emulation of various schemes: EFB,
QNSE, RMC01,..
TOUCANS C
Turbulent scheme
Stability dependency functions χ3 , φ3
1 − RiPf
φ3 (Rif ) =
,
1 − Rif
1 − RiRf
χ3 (Rif ) =
,
1 − Rif
Ri
P(R − Rif )
=
.
Rif
C3 R (P − Rif )
R - variable describing the effect of the flow’s anisotropy on the turbulent momentum
exchange, P - variable describing the joint effect of flow’s anisotropy and TPE
conversion on the turbulent heat exchange with :
critical flux-Richardson number
lim P = Rifc , Rifc = lim Rif -
Ri→∞
Ri→∞
TOUCANS C
Turbulent scheme
Turbulent scheme - switches
LPTKE
LCOEFKTKE
Scheme:
.TRUE.
.TRUE.
.FALSE.
TOUCANS pseudo-TKE
Emulation
model I
model II
TOUCANS ON:
eRMC01
eeQNSE
eeEFB
CGTURS
MD1
MD2
RMC
QNSE
EFB
.FALSE.
Louis scheme
TOUCANS C
Turbulent scheme
Stability dependency functions φ3 and χ3 -BGV14
3
basic model I
basic model II
tuned model II
eeQNSE
eeEFB
2.5
1
0.8
2
χ3
χ3
0.6
1.5
0.4
1
0.2
0.5
0
-5
-4
-3
-2
-1
0
Ri
1
2
3
4
0
0.001
5
basic model I
basic model II
tuned model II
eeQNSE
eeEFB
0.01
0.1
Ri
1
10
5
basic model I
basic model II
tuned model II
eeQNSE
eeEFB
4
basic model I
basic model II
tuned model II
eeQNSE
eeEFB
1
0.8
3
φ3
φ3
0.6
2
0.4
1
0.2
0
-5
-4
-3
-2
-1
0
Ri
1
2
3
4
5
0
0.001
0.01
0.1
Ri
1
10
TOUCANS C
Turbulent scheme
Free parameters -BGV14
Parameter
C3
Oλ
1
ν ≡ (CK C ) 4
C
Parameter name
C3TKEFREE
ETKE OLAM
NUPTKE
C EPSILON
MD1
MD2
MD2
1.183
1.183
1.183
2.0/3.0 2.0/3.0 0.29
0.5265 0.5265 0.5265
0.871
0.871
0.871
Parameter
C3
Oλ
1
ν ≡ (CK C ) 4
C
Parameter name
C3TKEFREE
ETKE OLAM
NUPTKE
C EPSILON
eRMC01 eeQNSE eeEFB
2.38
1.39
1.25
2.0/3.0
0.324
0.113
0.5265
0.504
0.532
0.845
0.798
0.889
TOUCANS C
Turbulent scheme
Free parameters - relation to shape of φ3 and χ3
R(C3 , ν), P(C3 , ν, Oλ )
model I, Oλ=2/3
model II, Oλ=2/3
model II, Oλ=0.29
basic model I
basic model II
tuned model II
eeQNSE
0.6
eeEFB
0.5
Pinf
0.4
0.3
0.2
2
1.8
0
0.2
1.6
0.4
Rinf
1.4
0.6
0.8
1.2
1 1
Rinf = lim R, Pinf = lim P
Ri→∞
Ri→∞
C3
TOUCANS C
Length scale
TKE based length scales L
Bougeault a Lacarrère (1989) :
− 4 − 4 − 54
L 5 +L 5
LBL (E ) = up 2 down
Lup (E ) (Ldown (E )) - L upward (downward)
LN =
q
2.E
N2
for stable straification
with possibility to use moist BVF
(computed from Ri ∗ )
prognostic treatment of L (under development)
TOUCANS C
Length scale
Conversion between L and lm
following RMC01:
3
1
LK
C
C f (Ri) 4
χ32
,
L
=
= 3 lm
l
m
1
ν
ν 3 f (Ri) 34
χ2
3
assuming: L ≡ L3K L
L=
14
C
l
ν3 m
we get:
TOUCANS C
Length scale
Length scale choice
CGMIXELEN
EL0
EL1
EL2
EL3
EL4
Ri > 0
LGC
LBL
LBL
min (LN , Lmax )
√LGC2 LN 2
LGC +LN
EL5 min (LBL , LN )
Ri ≤ 0
LGC
LBL √
min LBL LGC , LBL
LGC
LGC
LBL
Lmax - upper limit for mixing length in stable stratification;
LGC is lm converted to TKE type mixing length.
TKEMULT - controls influence of TKE on L:
L(ek ) → L(TKEMULT.ek )
TOUCANS C
Moisture influence
Moisture influence
expansion and latent heat release influences BVF N 2 (→ Ri, Rif , ..) (Marquet and Geleyn, 2013):
N 2 = EssL (SCC , Q)
∂ssL
∂z
+ Eqt ,ssL ,Q (SCC , Q)
∂qt
∂z
SCC - Shallow Convection Cloudiness
c∗ ) - represents the effects of non-Gaussian
Q(SCC ) (or R
distributions (influence of skewness) of fluctuations
LCOEFK SCQ
F (Cn ) = 0.5
q
.TRUE.
Q(SCC ) = SCC
(6.25 Cn )2 + 4 − 6.25 Cn
Cn a skewness-linked parameter.
.FALSE.
Q(SCC ) = SCC F (Cn )
TOUCANS C
Moisture influence
Moist Anti-fibrillation scheme
(currently) required due to SCC compuation from Ri ∗
controlled by XDAMP
turned off by XDAMP=0
automatically turned off in case of prognostic TTE
computation
TOUCANS C
Moisture influence
Hybrid computation
in dry case is Ri(θ) single stability parameter for
indication of well mixed state (entropic considerations)
and also for intensity of turbulent mixing (buoyancy
considerations)
moist case - two stability parameters required:
Rif m = − III (buoyancy considerations)
g M(SCC ) 0 0
w θs(1)
θs(1)
Rif s1 = −
(entropic considerations)
I
θs(1) - moist entropy potential temperature θs(1)
derived by (Marquet, 2011)
I - shear source term, II - buoyancy source term
TOUCANS C
Moisture influence
Hybrid computation
0
w 0 ssL
=
w 0 qt0 =
w 0u0 =
w 0v 0 =
∂ssL
Oλ τk
∂ssL
0
0
w 0 ssL
(Rif s1 )
− KH (Rif m )
N2 +
I
02
∂z
∂z
2 C3 w
+TOMs
∂qt
Oλ τk
∂q
t
0
0
2
0
−KH (Rif s1 )
− KH (Rif m )
w 0 qt N +
II
∂z
∂z
2 C3 w 02
+TOMs
∂u
−KM (Rif s1 )
∂z
∂v
−KM (Rif s1 )
∂z
−KH0
Hybrid computation activated by
LCOEFK RIH=.TRUE.
TOUCANS C
Prognostic computations
Prognostic computations
source terms I and II computation:
(LCOEFK FLX=.F.) from gradients only in
current time step with TKE correction due to
TOMs contribution:
h i
2
∂v 2
+
,
I = KM ∂u
∂z
∂z
t
II = −EssL KH ∂s∂zsL − Eqt ,ssL KH ∂q
∂z
(LCOEFK FLX=.T.) from fluxes and gradients
from previous time step:
I = −u 0 w 0 ∂u
− v 0 w 0 ∂v
,
∂z
∂z
0
II = EssL w 0 ssL + Eqt ,ssL w 0 qt0
prognostic L activated by LCOEFK PL=.TRUE.
prognostic TTE activated by LCOEFK PTTE=.TRUE.
TOUCANS C
TOMs parametrisation
TOMs parametrisation
turned on by LCOEFK TOMS=.TRUE.
contributions
coefficients:
TOM term
w 03
w 0 θ02
w 02 θ0
from TOM terms can be controlled via
Multiplying parameter
ETKE CG01
ETKE CG02
ETKE CG03
TOUCANS C
TOMs parametrisation
Thank you for your attention!
TOUCANS C
TOMs parametrisation