ming%zhao% - gfdl's data portal · geophysical)fluid)dynamics)laboratory) 8 episodic mixing...

Geophysical Fluid Dynamics Laboratory

Ming Zhao GFDL/NOAA

GFDL Summer School July 18, 2012

1

Geophysical Fluid Dynamics Laboratory  2

A view of trade wind shallow cumulus cloud fields


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


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


Outline

 Conceptual models of shallow cumulus clouds

 Results from Large Eddy Simulation

 UW Shallow Cu scheme (Bretherton et. al 2004)


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.


Entraining plume model

LCL

LFC

LNB

LCT

The Paradox   Cumulus cloud-‐top is





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





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.


AnimaDon of LES simulated shallow cumulus cloud life cycle (Zhao and Aus4n 2005a,b)


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.


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)


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


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)


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


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


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


End



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