The representation of stratocumulus with eddy diffusivity closure models
Stephan de Roode
KNMI
Global stratocumulus presence
Motivation of the problem
ECMWF underestimates stratocumulus
ECMWF underpredicts stratocumulus Liquid Water Path (LWP)
Duynkerke and Teixeira (2001)
RACMO uses ECMWF physics!
Entrainment of relatively warm and dry inversion air into the cloudy boundary layer
Bjorn Stevens
Entrainment: the holy grail in stratocumulus research
"Dogma": solve the stratocumulus problem by getting the entrainment rate right in a model
Topics:
1. Dogma is not true
2. Entrainment rates from a TKE scheme compared to parameterizations
Tendency equation for the mean
Computation of the flux
Turbulent transport in closure models
zK''w
S
z''w
t
Eddy diffusivities diagnosed from LES results - Results from the FIRE I stratocumulus intercomparison case
LES result
0 100 200 300 400 500 6000
100
200
300
400
500
600
Kl
Kqt
Eddy diffusivity K [m 2s-1]
heig
ht [m
]
● LES: Eddy diffusivities for heat and moisture differ
Eddy diffusivities in K-closure models - Results from the FIRE I stratocumulus intercomparison case
LES result 6 single-column models (SCMs)
0 100 200 300 400 500 6000
100
200
300
400
500
600
Kl
Kqt
Eddy diffusivity K [m 2s-1]
heig
ht [m
]
0 10 20 30 40 50 60 70 800
100
200
300
400
500
600
heig
ht [m
][m2 s-1]
Kq
● LES: Eddy diffusivities for heat and moisture differ
● SCM: typically much smaller values than LES
Kheat = Kmoisture
Should we care about eddy diffusivity profiles in SCMs?
Simple experiment
1. Prescribe surface latent and sensible heat flux
2. Prescribe entrainment fluxes
3. Consider quasi-steady state solutions
fluxes linear function of height
Consider mean state solutions from 'dz
'zK'z''w z
z'z
0'z
0
Use fixed flux profiles from LES results(so we know the entrainment fluxes)
'dz
'zK'z''w z
z'z
0'z
0
Vary eddy diffusivity profiles with a constant factor c
0 200 400 600 800 10000
100
200
300
400
500
600
Kref x 0.2Kref x 0.5KrefKref x 2Kref x 5
Eddy diffusivity K [m 2/s]
heig
ht [m
]
● Kref is identical to Kqt from LES
● Multiply Kref times constant factor c
'dz
'zK'z''w z
z'z
0'z
0
Remember the dogma?
Dogma: solve the stratocumulus problem by getting the entrainment rate right in a model
If we prescribe the entrainment fluxes, do we get the right cloud structure?
Mean state solutions
287.6 287.7 287.80
100
200
300
400
500
600
c=0.35c=0.5c=1c=2adiabatl (LES)
heig
ht [m
]
l [K]
8.6 8.8 9 9.2 9.4 9.6 9.8q
t [g kg-1]
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7q
l [g kg-1]
Liquid Water Path and cloud transmissivity
0
20
40
60
80
100
0
0.2
0.4
0.6
0.8
1
0.4 0.8 1.2 1.6 2 2.4 2.8
LWP
Fdown,surface
/Fdown,cloud top
LWP
[g
m-2
]Fdown,surface /F
down,cloud top
eddy diffusivity multiplication factor c
LWP and cloud transmission VERY sensitive to eddy-diffusivity profile
ECMWF low eddy diffusivities explain low specific humidity
0 10 20 30 40 50 60 70 800
100
200
300
400
500
600
heig
ht [m
]
[m2 s-1]
Kq
ECMWF eddy diffusivity from Troen and Mahrt (1986)
p
3*
3*h h
z1hzhkcwuK
0v
0
3* ''w
Tghw
Computation of the flux
Representation of entrainment rate we
ECMWF K-profile K = we z , we from parametrization
RACMO TKE model K(z) = TKE(z)1/2 l(z) , we implicit
Question
Does we from a TKE model compare well to we from parametrizations?
Turbulent mixing and entrainment in simple closure models
zK''w
Entrainment parameterizations designed from LES of stratocumulus (Stevens 2002)
• Nicholls and Turton (1986) we 2.5AWNE
v,NT 2.5A T2v,dry T4 v,sat
• Stage and Businger (1981) Lewellen and Lewellen (1998) VanZanten et al. (1999)
we AWNE
T2v,dry T4 v,sat
• Lilly (2002) we ADLWNE,DL
v,DL ADL L2v,dry L4v,sat
• Moeng (2000)
l
pLb
LlMe
c/e3F''wAw
m
• Lock (1998)
v
pLWtNEALe
c/FAWA2w
we = fct (H, LE, zb, zi, Fl, qt, l, LWP or ql,max)
Simulation of ASTEX stratocumulus case
ASTEX A209 boundary conditions_________________________________cloud base height = 240 mcloud top height = 755 msensible heat flux = 10 W/m2
latent heat flux = 30 W/m2
longwave flux jump = 70 W/m2
max liq. water content = 0.5 g/kgLWP = 100 g/m2
l = 5.5 K
qt = -1.1 g/kg
fill in these values in parameterizations, but vary the inversion jumps l and qt
Entrainment rate [cm/s] sensitivity to inversion jumps -Boundary conditions as for ASTEX A209
1. Note differences2. Buoyancy reversal3. Moisture jump sensitivity
Entrainment rate [cm/s] sensitivity to inversion jumps -Boundary conditions as for ASTEX A209
1. Note differences2. Buoyancy reversal3. Moisture jump sensitivity
Entrainment rate [cm/s] sensitivity to inversion jumps -Boundary conditions as for ASTEX A209
1. Note differences2. Buoyancy reversal3. Moisture jump sensitivity
Entrainment rate [cm/s] sensitivity to inversion jumps -Boundary conditions as for ASTEX A209
1. Note differences2. Buoyancy reversal3. Moisture jump sensitivity
vertical lines
sensitivity to moisture jumps qt
RACMO
How does a TKE model represent entrainment?
● Some model details
● Run ASTEX stratocumulus, and check sensitivity to entrainment jumps
• TKE equation
• Flux
• 'integral' length scale (Lenderink & Holtslag 2004)
• buoyancy flux weighed with cloud fraction
• ASTEX A209 forcing and initialization
• t = 60 s , z = 5 m
• Mass flux scheme turned off, no precipitation
Some details of the TKE model simulation
'p'w'E'w
zzV'w'v
zU'w'u''wg
tE
vv
zTKEc''w
du
111
zqB
zA1
zqB
zAEc''w t
dl
dt
wl
wHv
Entrainment sensitivity to inversion jumps from a TKE model
buoyancy reversal criterion
•ASTEX A209
entrainment rates decrease in this regime
many parameterizations predict rates that go to infinity
slightly larger values than Stage-Businger
Entrainment rate depends on moisture jump
Conclusions
Eddy diffusivity experiments
● stratocumulus may dissappear by incorrect BL internal structure, even for 'perfect'
entrainment rate
TKE model● appears to be capable to represent realistic entrainment rates
FIRE I stratocumulus observations of the stratocumulus inversion structure
de Roode and Wang : Do stratocumulus clouds detrain? FIRE I data revisited. BLM, in press
Similar K profiles for heat and moisture -Interpretation
Gradient ratio: (K drops out)
Typical flux values near the surface for marine stratocumulus:
H=10 W/m2 and LE = 100 W/m2
Then a 0.1 K decrease in l corresponds to a change of 0.4 g/kg in qt
The larger the latent heat flux LE, the larger the vertical gradient in qt will be!
p
v
t
l
t
l
cL
LEH
K/'q'wK/''w
z/qz/
GCSS stratocumulus cases
-10
-5
0
0 5 10 15
q t [g
/kg]
l [K]
buoyancy reversal criterion
DYCOMS II RF01
FIRE I (EUROCS)
initial jumps for differentGCSS stratocumulus cases
ASTEX A209 ASTEX RF06 (EUCREM)
DYCOMS II RF02
ASTEX A209 boundary conditions_________________________________cloud base height = 240 mcloud top height = 755 msensible heat flux = 10 W/m2
latent heat flux = 30 W/m2
longwave flux jump = 70 W/m2
max liq. water content = 0.5 g/kgLWP = 100 g/m2
l = 5.5 K
qt = -1.1 g/kg
fill in these values in parameterizations, but vary the inversion jumps l and qt
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