The representation of stratocumulus with eddy diffusivity closure models
description
Transcript of The representation of stratocumulus with eddy diffusivity closure models
![Page 1: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/1.jpg)
The representation of stratocumulus with eddy diffusivity closure models
Stephan de Roode
KNMI
![Page 2: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/2.jpg)
Global stratocumulus presence
![Page 3: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/3.jpg)
Motivation of the problem
ECMWF underestimates stratocumulus
![Page 4: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/4.jpg)
ECMWF underpredicts stratocumulus Liquid Water Path (LWP)
Duynkerke and Teixeira (2001)
RACMO uses ECMWF physics!
![Page 5: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/5.jpg)
Entrainment of relatively warm and dry inversion air into the cloudy boundary layer
Bjorn Stevens
![Page 6: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/6.jpg)
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
![Page 7: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/7.jpg)
Tendency equation for the mean
Computation of the flux
Turbulent transport in closure models
zK''w
S
z''w
t
![Page 8: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/8.jpg)
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
![Page 9: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/9.jpg)
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
![Page 10: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/10.jpg)
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
![Page 11: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/11.jpg)
Use fixed flux profiles from LES results(so we know the entrainment fluxes)
'dz
'zK'z''w z
z'z
0'z
0
![Page 12: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/12.jpg)
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
![Page 13: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/13.jpg)
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?
![Page 14: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/14.jpg)
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]
![Page 15: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/15.jpg)
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
![Page 16: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/16.jpg)
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
![Page 17: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/17.jpg)
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
![Page 18: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/18.jpg)
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)
![Page 19: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/19.jpg)
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
![Page 20: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/20.jpg)
Entrainment rate [cm/s] sensitivity to inversion jumps -Boundary conditions as for ASTEX A209
1. Note differences2. Buoyancy reversal3. Moisture jump sensitivity
![Page 21: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/21.jpg)
Entrainment rate [cm/s] sensitivity to inversion jumps -Boundary conditions as for ASTEX A209
1. Note differences2. Buoyancy reversal3. Moisture jump sensitivity
![Page 22: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/22.jpg)
Entrainment rate [cm/s] sensitivity to inversion jumps -Boundary conditions as for ASTEX A209
1. Note differences2. Buoyancy reversal3. Moisture jump sensitivity
![Page 23: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/23.jpg)
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
![Page 24: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/24.jpg)
RACMO
How does a TKE model represent entrainment?
● Some model details
● Run ASTEX stratocumulus, and check sensitivity to entrainment jumps
![Page 25: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/25.jpg)
• 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
![Page 26: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/26.jpg)
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
![Page 27: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/27.jpg)
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
![Page 28: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/28.jpg)
FIRE I stratocumulus observations of the stratocumulus inversion structure
de Roode and Wang : Do stratocumulus clouds detrain? FIRE I data revisited. BLM, in press
![Page 29: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/29.jpg)
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/
![Page 30: The representation of stratocumulus with eddy diffusivity closure models](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167a7550346895ddcf367/html5/thumbnails/30.jpg)
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