the representation of stratocumulus with eddy diffusivity closure models stephan de roode knmi
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ECMWF underpredicts stratocumulus Liquid Water Path (LWP)
Duynkerke and Teixeira (2001)
RACMO uses ECMWF physics!
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
Sz
''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 [m2s
-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 [m2s
-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 0.2
Kref
x 0.5
Kref
Kref
x 2
Kref
x 5
Eddy diffusivity K [m2/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
287.6 287.7 287.8
0
100
200
300
400
500
600
c=0.35
c=0.5
c=1
c=2
adiabat
l (LES)
heig
ht
[m]
l [K]
8.6 8.8 9 9.2 9.4 9.6 9.8
qt [g kg
-1]
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
ql [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
]F
dow
n,su
rface /F
dow
n,c
lou
d to
p
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
z1
h
zhkcwuK
0v0
3* ''w
T
ghw
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 m
cloud top height = 755 m
sensible heat flux = 10 W/m2
latent heat flux = 30 W/m2
longwave flux jump = 70 W/m2
max liq. water content = 0.5 g/kg
LWP = 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 differences
2. Buoyancy reversal
3. Moisture jump sensitivity
Entrainment rate [cm/s] sensitivity to inversion jumps -Boundary conditions as for ASTEX A209
1. Note differences
2. Buoyancy reversal
3. Moisture jump sensitivity
Entrainment rate [cm/s] sensitivity to inversion jumps -Boundary conditions as for ASTEX A209
1. Note differences
2. Buoyancy reversal
3. Moisture jump sensitivity
Entrainment rate [cm/s] sensitivity to inversion jumps -Boundary conditions as for ASTEX A209
1. Note differences
2. Buoyancy reversal
3. 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'wzz
V'w'v
z
U'w'u''w
g
t
Ev
v
zTKEc''w
du
111
z
qB
zA1
z
qB
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
c
L
LE
H
K/'q'w
K/''w
z/q
z/
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 m
cloud top height = 755 m
sensible heat flux = 10 W/m2
latent heat flux = 30 W/m2
longwave flux jump = 70 W/m2
max liq. water content = 0.5 g/kg
LWP = 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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