June 15, 2011

Melchior van Wessem &Stephan de Roode

Mixed-Layer Model Solutions ofEquilibrium States of

Stratocumulus-Topped Boundary Layers

Equilibrium states of stratocumulus with a mixed layer model

Stevens 2002

Both temperature and humidity jumps are important for the evolution of a stratocumulus cloud deck

Exploring phase space with a stratocumulus mixed-layer model to investigate stratocumulus cloud-

climate feedback

• Tool: Mixed Layer model

• Set up: Boundary conditions

• Changing parameters: Free atmosphere potential temperature θ and humidity q

• Climate change: SST + 2K

Perturbing the “phase space” with SST+2K.

What happens with LWP ~ (zi-zb)2 ?

Mixed Layer Model

radiative cooling

surface flux surface flux

entrainment fluxentrainment flux

Radiative cooling

zi

zb

zi

zb

q

t∂∂θ

θmoisture temperature

zi∂qT,ML

∂t= Cd U qsat,sst − qT,ML( )+ w eΔqT

zi∂θL,ML

∂t= Cd U θ0,sst − θL,ML( )+ w eΔθL − Qrad

∂zi

∂t= w e + w ; w = −Dz

Radiative cooling

zi

zb

Equilibrium Solutions (Stevens 2006):

qT,ML = qsat,sst +w e(qfa − qsat,sst )

Cd U + w e

θL,ML = θ0,sst +w e(θfa − θ0,sst ) − Qrad

Cd U + w e

w e = Dzi

( )2

21

biql zzLWP −Γ=Liquid water path:

−≅

SST

ml

dv

vb q

qLSSTRz ln

2

γ

Entrainment we from Nicholls & Turton (1986)

Free atmosphere conditions

hei

ght

z

qT θL

qT,MLθL,ML

qT0

θ0

Γq =∂q∂z

FA

Γθ =∂θ∂z

FA

qref θref

qT,FA = qref + δq + Γqz θL,FA = θref + δθ + Γθz

Change free atmosphere conditions. Note: Free atmosphere is assumed to be constant with time

hei

ght

z

qT θL

qT,MLθL,ML

qT0

θ0qref θref

δq δθ

qT,FA = qref + δq + Γqz θL,FA = θref + δθ + Γθz

Γq =∂q∂z

FA

Γθ =∂θ∂z

FA

Change free atmosphere conditions. Free atmosphere is assumed to be constant with time

hei

ght

z

qT θL

qT,MLθL,ML

qT0

θ0qref θref

δq δθ

qT,FA = qref + δq + Γqz θL,FA = θref + δθ + Γθz

Γq =∂q∂z

FA

Γθ =∂θ∂z

FA

Free atmosphere conditions

Steady-state solutions for a range of

different free atmosphere conditions (change δq and δθ)

Boundary conditions

Θfa-ΘSST

qfa-qSST

fog

Decoupling

warmer free atmosphere

moister free atmosphere

Equilibrium solutions as a function of free atmosphere conditions:Inversion height (zi)

Θfa-ΘSST

qfa-qSST

fog

Decoupling

warmer free atmosphere

moister free atmosphere

Equilibrium solutions as a function of free atmosphere conditions:Cloud base height (zb)

Equilibrium solutions as a function of free atmosphere conditions:The Liquid Water Path (LWP)

Θfa-ΘSST

qfa-qSST

fog

Decoupling

warmer free atmosphere

moister free atmosphere

Equilibrium solutions as a function of SST and horizontal wind velocity:The Liquid Water Path (LWP)

Decoupling

SST + 2K, free atmosphere conditions the same

hei

ght

z

qT θL

qT,MLθL,ML

qT0 (SST+2)

Γq =∂q∂z

FA

Γθ =∂θ∂z

FA

qref

θref

qT,FA = qref + δq + Γqz θL,FA = θref + δθ + Γθz

θ0+2 K

SST = 2K, free atmosphere state not changedChanges in LWP

Θfa-ΘSST

qfa-qSST

warmer free atmosphere

moister free atmosphere

SST = 2K, free atmosphere state not changedChanges in LWP

Θfa-ΘSST

qfa-qSST

warmer free atmosphere

moister free atmosphere

1Thicker

SST = 2K, free atmosphere state not changedChanges in LWP

Θfa-ΘSST

qfa-qSST

warmer free atmosphere

moister free atmosphere

1Thicker

2

Thinner

SST = 2K, free atmosphere state not changedChanges in LWP

∼ Θfa-ΘSST

qfa-qSST

warmer free atmosphere

moister free atmosphere

1Thicker

2

Thinner3

Cumulus

θ L,M

L[K

]

[g/k

g]

qT,ML

qsat

Climate change (constant free atmosphere)

Mixed layer θL and qT ~ linearly dependent on SST

Saturation specific humidity increases exponentially

case + : cloud thickeningcase - : cloud thinning

Climate change (constant free atmosphere)

Inversion and cloud base increase for increasing SST

For red line zi increases more than zb

→ cloud thickens

For blue line zi increases slighty less than zb

→ cloud thins

case + : cloud thickeningcase - : cloud thinning

SST + 2K, free atmosphere conditions the same

hei

ght

z

qT θL

qT,MLθL,ML

qT0 (SST+2)

Γq =∂q∂z

FA

Γθ =∂θ∂z

FA

qref

θref+2

qT,FA = qref + δq + Γqz θL,FA = θref + δθ + Γθz

θ0+2 K

ΔLWP/ΔSST

Small increase of LWP

(small negative feedback)

Transition from Scu to Cu (strong positive feedback)

Free atmosphere increased with ΔSST

Conclusions

• Mixed Layer model shows (small) negative feedback if free atmosphere is also

becoming warmer (ΔθFA = ΔSST)

• Results depend on many factors: entrainment formulation, strength of radiative

cooling, lapse rate in free atmosphere, horizontal advection, horizontal wind

velocity

• Phase space gives very much useful information about cloud regime

• Similar excercise can be performed with SCM (see RACMO/EC-EARTH results by

Sara Dal Gesso)