Geophysical Fluid Dynamics Laboratory
Ming Zhao GFDL/NOAA
GFDL Summer School July 18, 2012
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Geophysical Fluid Dynamics Laboratory 2
A view of trade wind shallow cumulus cloud fields
Geophysical Fluid Dynamics Laboratory 3
Hadley CirculaDon and shallow cumulus clouds (Figure courtesy of Pier Siebesma, KNMI)
Subsidence
~0.5 cm/s
10 m/s inversion
Cloud base
~500m
Tropopause 10km
Stratocumulus
Interaction with radiation
Shallow Convective Clouds
No precipitation
Vertical turbulent transport
No net latent heat production
Fuel Supply Hadley Circulation
Deep Convective Clouds
Precipitation
Vertical turbulent transport
Net latent heat production
Engine Hadley Circulation
Geophysical Fluid Dynamics Laboratory 4
subsidence ~0.6 cm/s
SHF~10W/m^2 LHF~150W/m^2 SST~300K 1015mb
950mb
850mb
800mb
radiation ~2K/day
Trade wind cumulus boundary layer physics
Geophysical Fluid Dynamics Laboratory 5
Outline
Conceptual models of shallow cumulus clouds
Results from Large Eddy Simulation
UW Shallow Cu scheme (Bretherton et. al 2004)
Geophysical Fluid Dynamics Laboratory 6
Adiabatic/Undilute cloud model
LCL
LNB
LCT
LFC
The Paradox Cumulus cloud-‐top is
determined by the neutral buoyancy level of nearly undilute sub-‐cloud air.
Cumulus clouds are highly dilute; the mass of a cumulus cloud is composed mostly of entrained air.
Cumulus clouds are highly inhomogeneous, nearly undilute sub-‐cloud air is observed throughout all levels of cumulus clouds.
Geophysical Fluid Dynamics Laboratory 7
Entraining plume model
LCL
LFC
LNB
LCT
The Paradox Cumulus cloud-‐top is
determined by the neutral buoyancy level of nearly undilute sub-‐cloud air.
Cumulus clouds are highly dilute; the mass of a cumulus cloud is composed mostly of entrained air.
Cumulus clouds are highly inhomogeneous, nearly undilute sub-‐cloud air is observed throughout all levels of cumulus clouds.
Geophysical Fluid Dynamics Laboratory 8
Episodic mixing and buoyancy-sorting model (Raymond and Blyth 1986, Emanuel 1991, Zhao and Austin 2003)
LCL
LFC
LNB
LCT The Paradox Cumulus cloud-‐top is
determined by the neutral buoyancy level of nearly undilute sub-‐cloud air.
Cumulus clouds are highly dilute; the mass of a cumulus cloud is composed mostly of entrained air.
Cumulus clouds are highly inhomogeneous, nearly undilute sub-‐cloud air is observed throughout all levels of cumulus clouds.
Geophysical Fluid Dynamics Laboratory 9
AnimaDon of LES simulated shallow cumulus cloud life cycle (Zhao and Aus4n 2005a,b)
Shallow Cu parameterization needs to account for the convective fluxes averaged over the cumulus ensemble which is at any time composed of a spectrum of clouds of different depths and different stages in their life-cycle.
Geophysical Fluid Dynamics Laboratory 10
AnimaDon of LES simulated shallow cumulus cloud life cycle (Zhao and Aus4n 2005a,b)
Geophysical Fluid Dynamics Laboratory
University of Washington -‐ Shallow Cu Scheme (Bretherton et. al 2004)
Cloud model: Single bulk entrainment-detrainment plume Buoyancy-sorting determination of entrainment/detrainment rate Explicit vertical momentum equation Cumulus cloud-top penetrative mixing
Closure: Cloud-base mass flux is determined by convective inhibition (CIN) and boundary layer TKE.
Geophysical Fluid Dynamics Laboratory
Bulk entraining-‐detraining plume model
€
Mu = ρuσ uwu
−∂Mu
∂p= E −D = εMu −δMu, ε =
˜ ε ρug
−∂Muψu
∂p= Eψ −Dψu + MuSψ , ψ ∈ hlf ,qt ,u,v,w}{
−∂ψu
∂p= ε (ψ −ψu) + Sψ
∂ψ∂t
⎛
⎝ ⎜
⎞
⎠ ⎟ shcu
= g ∂Mu(ψu −ψ)∂p
+ gMuSψ
= −gMu∂ψ∂p
+ gD ψu −ψ( )
€
hlf = cpT + gz − Leqcqt = qv + qc = qv + ql + qiqs = qs(T, p)ql = (1− µ)qc, qi = µqc
µ = f (T) = max(min(268 −T20
,1),0)
Le = (1− µ)Lv + µLs
Pc = (qc − qc,crit ), Sqc =ΔqcΔp
=PcΔp
Pl =qlqcPc, Pi =
qiqcPc
∂hlf∂t
⎛
⎝ ⎜
⎞
⎠ ⎟ shcu
= g∂Mu(hlf ,u − hlf )
∂p+ gMu
PcΔp
Le
∂qt∂t
⎛
⎝ ⎜
⎞
⎠ ⎟ shcu
= g∂Mu(qt,u − qt )
∂p− gMu
PcΔp
∂ql∂t
⎛
⎝ ⎜
⎞
⎠ ⎟ shcu
= −gMu∂ql∂p
+ gD ql ,u − ql( )∂qi∂t
⎛
⎝ ⎜
⎞
⎠ ⎟ shcu
= −gMu∂qi∂p
+ gD qi,u − qi( )
€
ρw 'ψ ' ≈ Mu(ψu −ψ)supported by Siebesma and Cuijpers (1995)
Geophysical Fluid Dynamics Laboratory
Lateral mixing, entrainment and detrainment
€
χ : fraction of environment air in mixturesχc : maximum fraction of environment air for mixtures to be entrainedχs : maximum fraction of environment air for mixtures to be saturated
ε = 2ε 0 χ0
χc∫ PDF(χ)dχ = ε 0χc2
δ = 2ε 0 (1− χ)χ c
1∫ PDF(χ)dχ = ε 0(1− χc )
2
virtua
l pote
ntial
tempe
ratur
e
precipitation
€
Pc = (qc − qc,crit ), qc,crit =
qc0 T ≥ 0°C
qc0 1− TTcrit
⎛
⎝ ⎜
⎞
⎠ ⎟ Tcrit < T < 0°C
0 T ≤ Tcrit
⎧
⎨
⎪ ⎪
⎩
⎪ ⎪
⎫
⎬
⎪ ⎪
⎭
⎪ ⎪
entrainment/dilution
Geophysical Fluid Dynamics Laboratory
Plume verDcal velocity equaDon
β: drag due to pressure perturbation and growth of sub-plume turbulence β: parameterized as linear combination of the first 2 terms (Simpson and Wiggert 1969)
Geophysical Fluid Dynamics Laboratory
Cloud-‐top penetraDve mixing
cloud-top (Wu=0)
penetrative entrainment
LNB (Bu=0)
€
−∂Md
∂p= E
−∂Mdψd
∂p= Eψ, ψ ∈ hlf ,qt}{
MdkLNB −1/ 2 = 0
Geophysical Fluid Dynamics Laboratory
Closure at cloud-‐base: Mb ̴ exp (−CIN / TKE)
€
P(w) =1
2πσw
exp(− w2
2σw
), σw = k f eavg
eavg =12u*
3 + c1w*3( )2 / 3
u* = u'w '( )s
2+ v 'w '( )
s
2⎡ ⎣ ⎢
⎤ ⎦ ⎥
1/ 4
w* =gθ v,s
w 'θ v'( )
sh
⎛
⎝ ⎜
⎞
⎠ ⎟
1/ 3
Ab = P(w)dw =wc
∞
∫ 12
erfc( wc2
2k f eavg)
Mb = ρb wP(w)dw =wc
∞
∫ ρbk f eavg
2πexp(− wc
2
2k f eavg)
wb =Mb
ρbAb
wc = max( 2aCIN ,wc,min ),wc,min = c2σw
friction velocity scale
convective velocity scale
Holtslag and Boville (1993), J. Climate
Geophysical Fluid Dynamics Laboratory
Flow chart of UW-‐ShCu
calculation CIN
find LCL of source air
set plume base level
determine CBMF
calculation plume properties
cloud-top penetrative entrainment
flux of heat/moisture/momentum
tendencies to large-scale variables
find source air property
Plume model: cumulus mixing assumptions cloud microphysics assumptions vertical velocity cloud detrainment cumulus penetrative mixing
Adiabatic cloud: LCL, LFC, LNB, CIN, CAPE
CBMF closure: PBL TKE / CIN based alternative choices
Others: source air determination precipitation re-evaporation
Modules
Geophysical Fluid Dynamics Laboratory 18
End
Geophysical Fluid Dynamics Laboratory 19
Episodic mixing and buoyancy-sorting model (Raymond and Blyth 1986, Emanuel 1991, Zhao and Austin 2003)
BOMEX case
Geophysical Fluid Dynamics Laboratory 20
BOMEX case
Episodic mixing and buoyancy-sorting model (Raymond and Blyth 1986, Emanuel 1991, Zhao and Austin 2003)