stephan de roode , irina sandu, johan van der dussen, pier siebesma, bjorn stevens,

LES results of the EUCLIPSE Lagrangian transitions:

Entrainment, decoupling and low cloud transitions

Stephan de Roode, Irina Sandu, Johan van der Dussen,

Pier Siebesma, Bjorn Stevens,

Andy Ackerman, Peter Blossey, and Adrian Lock

Schematic of cumulus penetrating stratocumulus

by Bjorn Stevens (based on ATEX intercomparison)

Cloud layer

Entrainment

Boundary layer is decoupled

Subcloud layer dynamics scale like dry convective boundary layer

Contents

Determining the degree of decoupling

Moisture and heat fluxes in the decoupled subcloud layer

Evolution of the subcloud layer state

Entrainment scaling

Stratocumulus cloud layer rises with timeSlow increase in cumulus cloud base height

Total water content for ASTEX

- binned mean + (all data) mean horizontal legs

Bulk structure of a decoupled boundary layer

Park et al., 2004, Wood and Bretherton 2004

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αq =qT z i

−( ) − qT,0

qT z i+

( ) − qT,0

αq = 0 if vertically well mixed

Quantification of decoupling from observations

Wood and Bretherton 2004

larger αq for deeper boundary layers

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αq =qT z i

−( ) − qT,0

qT z i+

( ) − qT,0

Decoupling parameter αq consistent between LES models

Example: Turbulent fluxes in ASTEX from DALES at t=23 hr

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w'w' m2s−2( )

€

w'θv ' mKs-1( )

€

ρcpw'qT ' Wm-2( )

Next step: quantify buoyancy and total specific humidity flux at the cumulus base height

Buoyancy flux ratio rv becomes similar to CBL

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rθv=

w'θv 'cu base

w'θv 'sfc

CBL value -0.2

Moisture flux ratio rq exhibits clear diurnal cycleMean value rq slightly smaller than unity

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rq =w'qT '

cu base

w'qT 'sfc

Virtual potential temperature evolution in the subcloud layer

h

€

w'θv '0 = cDUML θv,0 − θv,ML( )

€

w'θv 'h = rθvw'θv '0

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∂v,ML

∂t= −

∂w'θv '

∂z=

1 − rθv

h

⎛

⎝ ⎜

⎞

⎠ ⎟cDUML θv,0 − θv,ML( )

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w'θv ' flux profile

Virtual potential temperature evolution in the subcloud layer

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∂v,ML

∂t=

θv,0 − θv,ML

τθv

h

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w'θv ' flux profile

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τv=

h

cDUML 1 − rθv( )

If h = 500 m, rv = -0.2, cD=0.001, UML = 10 m/s then

τv ≈ 0.5 day

Assume SST increases linearly with time (and likewise v,0)

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v,0 t( ) = θv,00 + γtTime-dependent BC

Solution

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v,ML t( ) = γtlinear term

{ + θv,00 − γτθv+ γτθv

+ θv,ML t =0− θv,00( )e

−t / τθv

"memory term"1 2 4 4 4 4 4 3 4 4 4 4 4

Assume constant subcloud layer height h

Similar approach for the subcloud humidity

Time scale:€

∂qv,ML

∂t=

1 − rq v

h

⎛

⎝ ⎜

⎞

⎠ ⎟cDUML qs,0 − qv,ML( ) =

qs,0 − qv,ML

τq

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τq =h

cDUML 1 − rq v( )

If rqv = 1, τq ∞ (then steady-state qv,ML)

Surface forcing obeys Clausius-Clapeyron

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qs,0 t( ) = qs,0 t =0e t / τ cc

Clausius-Clapeyron time scale:

€

τcc =Rv T0 t =0( )

2

L vγ≈ 5 days

Solution

Time-dependent BC

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qv,ML t( ) =qs,0 t( )

1+τq

τcc

+ qv,ML t =0−

qs,0 t =0

1+τq

τcc

⎛

⎝

⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟

e−t / τq

"memory term"1 2 4 4 4 4 3 4 4 4 4

As τq > 0 , subcloud humidity tendency typically smaller than surface saturation value

Subconclusion

Decoupled subcloud layer:

v,ML increases in accord with changes in the SST

Question: what about cloud layer?

Net cooling due to longwave radiative loss

->

will lead to a destabilization

Idea: entrainment is "needed" to prevent destabilization

What is the entrainment rate needed to give a quasi-steady state

(this means LV tendency in the cloud is similar to the subcloud layer)

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∂VL,CLD

∂t=

∂θVL

∂t

⎛

⎝ ⎜

⎞

⎠ ⎟subcloud

≈w eΔθVL

z i − h−

1

ρcp

ΔF

z i − h

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∂VL

∂t= −

∂w'θ'VL

∂z−

1

ρcp

∂F

∂z , θVL = θL 1+ 0.61qv − qL( )

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w e =z i − h

ΔθVL

∂θVL

∂t

⎛

⎝ ⎜

⎞

⎠ ⎟subcloud

+1

ρcp

ΔF

ΔθVL

Nighttime quasi-steady state entrainment value is rather close to the actual entrainment rate in solid stratocumulus

Conclusions

Dynamics in a decoupled subcloud layer similar to the dry CBL

Decoupling makes it easier to understand subcloud layer dynamics

-> subcloud temperature dictated by time-varying SST

Humidity flux exhibits a distinct diurnal cycle

-> Max during the night, nearly all evaporated moisture in transported to the stratocumulus

During night-time quasi-steady state boundary layer

-> entrainment rate controled by SST tendency

To do

Scaling behavior of drizzle in LES runs (how does it depend on the LWP?)