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PBL transports and clouds 3-2007 Martin Köhler 1
An integral approach to modeling PBL transports and cloudsMartin Köhler, ECMWF
• EDMF @ ECMWF now and future– dry PBL– stratocumulus– shallow cumulus
• stratocumulus: evaluation against observations– EPIC marine stratus field experiment– GLAS cloud and cloud top height
• ongoing work– parcel numerics– stratocumulus down-drafts – shallow cumulus
PBL transports and clouds 3-2007 Martin Köhler 2
ARPEGE
EquatorDateline
California
GCSS Pacific Cross-Section Intercomparison Project
pres
sure
[hPa
]
100200300400500600700800900
1000
pres
sure
[hPa
]
100200300400500600700800900
1000
GFLD AM2 NCAR CAM3 NCEP
HadGAM ERA-40
liquid water [g/kg]
0.30.150.080.040.030.020.010
JJA1998Joao Teixeira
EquatorDateline
California
ECMWF
EquatorDateline
California EquatorDateline
California
PBL transports and clouds 3-2007 Martin Köhler 3
Integral appraoch to PBL transports: EDMF
M1M
K
M2
Shallow cumulus Deep cumulusStratocumulusdry BL
zcb
zi
zi
KbotM
Ktop
KbotKbot
operational
PBL transports and clouds 3-2007 Martin Köhler 4
EDMF: two box M/K decomposition(Siebesma and Cuijpers, 1995)
)()1( φφφφφ −+′′−+′′=′′ uu
e
e
u
u wawawaw
M
M-fluxenv. fluxsub-core flux
zK∂∂
−φ
PBL transports and clouds 3-2007 Martin Köhler 5
A statistical mass flux framework for organized eddies
( )' ' φφ φ φ∂= − + −
∂ uw K Mz
dry PBL
PBL transports and clouds 3-2007 Martin Köhler 6
A statistical mass flux framework for organized eddies
( )' ' φφ φ φ∂= − + −
∂ uw K Mz
Stratocumulus UP
PBL transports and clouds 3-2007 Martin Köhler 7
A statistical mass flux framework for organized eddies
( ),' ' φφ φ φ∂= − + −
∂ ∑ i u ii
w K Mz
Stratocumulus UP / DOWN
PBL transports and clouds 3-2007 Martin Köhler 8
A statistical mass flux framework for organized eddies
( ),' ' φφ φ φ∂= − + −
∂ ∑ i u ii
w K Mz
Shallow Convection
Roel Neggers
PBL transports and clouds 3-2007 Martin Köhler 9
Shallow ConvectionRoel Neggers, Martin Köhler, Anton Beljaars
PBL transports and clouds 3-2007 Martin Köhler 10
Shallow ConvectionRoel Neggers , Martin Köhler, Anton Beljaars
moist
dryK
PBL transports and clouds 3-2007 Martin Köhler 11
Stratocumulus UP: EPIC column from 3D forecasts
PBL transports and clouds 3-2007 Martin Köhler 12
ECMWF vs GLAS cloud fraction
ECMWF
GLASres: 76m
Maike AhlgrimmITCZ off ChileARM
SGP
PBL transports and clouds 3-2007 Martin Köhler 13
ECMWF vs GLAS observations: cloud top height
SC top too low!
GLAS cloud top heightGLAS strcu fraction
ECMWF cloud top heightECMWF strcu fraction
cloud top < 2km, cld > 80% Maike Ahlgrimm
PBL transports and clouds 3-2007 Martin Köhler 14
EDMF PBL: analytical updraft(with Peter Janssen)
• Parcel dominates PBL height (wu=0) and updraft properties (θu, qu, uu).• PBL height dominates mixing.• Parcel is dominated by entrainment.• Entrainment rule gives infinite entrainment at surface and PBL top.
1
uwε
τ=
( )2
212
1
uu
u
u
uu
ddz
d gdzw w
w
θ θ
θ
θ
θθ
ε
ε
ετ
= − −
−= − +
=
Updraft equations: ( )2
[m]
[m]
τθθ
τ
θ≡ −
≡ u
ugT
W w
Rescale:
Assume: constθ =
2'' ' 2 ' 1 0+ + + =WW W WThen:
Solution: ln( )β− = − topz zT T
PBL height: 0 0= +top T Wz
PBL transports and clouds 3-2007 Martin Köhler 15
EDMF PBL: analytical updraft(with Peter Janssen)
( )2
[m]
[m]
τθθ
τ
θ≡ −
≡ u
ugT
W w
positive buoyancy branch
1eβ
1β
1e
αβ
−
0z α=
1β
−
T, W
Z0.5
-0.5
0.0
-1.0 -0.5 0.50.0 1.0
PBL transports and clouds 3-2007 Martin Köhler 16
EDMF PBL: analytical updraft(with Peter Janssen)
( )2
[m]
[m]
τθθ
τ
θ≡ −
≡ u
ugT
W w
positive buoyancy branch
1eβ
1β
1e
αβ
−
0z α=
negative buoyancy branch
1β
−
T, W
Z0.5
-0.5
0.0
-1.0 -0.5 0.50.0 1.0
PBL transports and clouds 3-2007 Martin Köhler 17
SiebesmaDryEDMF2006
296 298 300 302 304Potential Temperature [K]
0
500
1000
1500
2000
2500
3000
Hei
ght[m
]
Mod
el L
evel
s
75
80
85
90
EDMF PBL: analytical updraftdry growing PBL case
0
500
1000
1500
2000
297 298 299 300 301
Hei
ght (
m)
Θ (K)
0 hr 1:30 hr 3:30 hr 5:30 hr 7:30 hr 9:30 hr
LES
SiebesmaDryEDMF2006
296 298 300 302 304Potential Temperature [K]
0
500
1000
1500
2000
2500
3000
Hei
ght[m
]
Mod
el L
evel
s
75
80
85
90
analytical 400s
SiebesmaDryEDMF2006
296 298 300 302 304Potential Temperature [K]
0
500
1000
1500
2000
2500
3000
Hei
ght[m
]
Mod
el L
evel
s
75
80
85
90
analytical 500s
numerical 400s
SiebesmaDryEDMF2006
296 298 300 302 304Potential Temperature [K]
0
500
1000
1500
2000
2500
3000
Hei
ght[m
]
Mod
el L
evel
s
75
80
85
90
numerical 500s
ztop(10h) LES=1800m
τ numerical analytical
300 1900m 1800m
400 2200m 1850m
500 2500m 1900m
Siebesma
PBL transports and clouds 3-2007 Martin Köhler 18
stratocumulus organized eddies: DYCOMS-II LES simulation
up-draft
vertical velocity & cloudBjorn Stevens (dx=35m, dz=5m)
down-draft
PBL transports and clouds 3-2007 Martin Köhler 19
stratocumulus down-drafts: scaling arguments
3x zx
up
L L 10 su w
τ ∼ ∼ ∼
IRx
p entr
RT 1Kc z
τρ ∆
∼ ∼IR cooling:
parcel time scale:1/3
top*topv i
v
gw w ' ' z 1m / sθθ⎛ ⎞
= ⎜ ⎟⎝ ⎠
∼
PBL transports and clouds 3-2007 Martin Köhler 20
LES DYCOMS-II: mixing line scatterplot of qt and θl
Steve Krueger, LES, dz=6m
PBL transports and clouds 3-2007 Martin Köhler 21
Steve Krueger, LES, dz=6m
LES DYCOMS-II: mixing line scatterplot of w
PBL transports and clouds 3-2007 Martin Köhler 22
SCM DYCOMS-II: up- and down-drafts
PBL transports and clouds 3-2007 Martin Köhler 23
LES DYCOMS-II: cloud liquid water
Steve Krueger, LES, dz=6m
Cloud Liquid Water
CLW
[g/kg]
PBL transports and clouds 3-2007 Martin Köhler 24
EDMF @ ECMWF
• dry PBL• stratocumulus
– updraft– downdraft
• momentum• plume solution• shallow convection
– dual M– dual cloud
( )' ' φφ φ φ∂= − + −
∂∑ ∑i i uii i
w K Mz