entrainment rates in stratocumulus computed from a 1d tke model
DESCRIPTION
Entrainment rates in stratocumulus computed from a 1D TKE model. Stephan de Roode KNMI. Turbulent mixing and entrainment in simple closure models. Computation of the flux Representation of entrainment rate w e 1. K-profile K = w e D z , w e from parametrization - PowerPoint PPT PresentationTRANSCRIPT
Entrainment rates in stratocumulus computed from a 1D TKE model
Stephan de Roode
KNMI
Computation of the flux
Representation of entrainment rate we
1. K-profile K = we z , we from parametrization
2. 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
Stability jumps
v,sat = 2 (the CTEI criterion, Randall 1980, Deardorff 1980)
Solve entrainment rate for a stratocumulus-topped boundary layer
we A w*
3
g
0 H v
we 2.5AWNE
v 2.5A T2v,dry T4v,sat
-0.04 -0.02 0 0.02 0.040
0.2
0.4
0.6
0.8
1
<w'v'>
WE
WNE
<w'v'>
norm
alize
d h
eig
ht
solve for entrainment rate
Solve entrainment rate for a stratocumulus-topped boundary layer
we A w*
3
g
0 H v
we 2.5AWNE
v 2.5A T2v,dry T4v,sat
-0.04 -0.02 0 0.02 0.040
0.2
0.4
0.6
0.8
1
<w'v'>
WE
WNE
<w'v'>
norm
alize
d h
eig
ht
solve for entrainment rate
Solve entrainment rate for a stratocumulus-topped boundary layer
we A w*
3
g
0 H v
we 2.5AWNE
v 2.5A T2v,dry T4v,sat
we __________forcing WNE
"jumps"
-0.04 -0.02 0 0.02 0.040
0.2
0.4
0.6
0.8
1
<w'v'>
WE
WNE
<w'v'>
norm
alize
d h
eig
ht
solve for entrainment rate
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
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
Entrainment rate [cm/s] sensitivity to inversion jumps -Boundary conditions as for ASTEX A209
• 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
• Moisture jump sensitivity
• No buoyancy reversal: entrainment rates slightly larger than parameterizations
• Buoyancy reversal: entrainment rates decrease
buoyancy reversal criterion
•ASTEX A209
Eddy diffusivities in K-closure models - Results from the EUROCS stratocumulus case
LES result results from 6 differents 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 (like CBL, Wyngaard and Brost 1980)
● SCM: typically smaller values than LES
Should we care about eddy diffusivity profiles in SCMs?
Simple experiment
1. Prescribe surface latent and sensible heat flux
2. Prescribe entrainment rate
Given jumps of l and qt, fluxes at BL top are fixed
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
Vary eddy diffusivity profiles with a constant factor
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
● 0.2 x Kref is very close to Kql from LES
LWP and shortwave radiation (normalized) solutions as a function of the eddy-diffusivity multiplication factor c
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
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]
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/
Conclusions
TKE model
● appears to be capable to represent realistic entrainment rates
Eddy diffusivity experiments
● stratocumulus may dissappear by incorrect BL internal structure, even for 'perfect'
entrainment rate
● observations often show adiabatic LWPs (Albrecht et al. 1990, Bretherton et al. 2004),
suggesting large values for Kqt
Recommendation
● pay more attention to K-profiles from LES
http://www.knmi.nl/~roode/publications.html
FIRE I stratocumulus observations of the stratocumulus inversion structure
de Roode and Wang : Do stratocumulus clouds detrain? FIRE I data revisited. BLM, in press