BBOS meeting on Boundary Layers and Turbulence, 7 November 2008De Roode, S. R. and A. Los, QJRMS, 2008.Corresponding paper available from http://www.srderoode.nl/publications.html

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A parameterization for the liquid water path variance to improve albedo bias calculations in large-scale models

Stephan de Roode(1,2)

&Alexander Los(2)

(1)Clouds, Climate and Air Quality, Department of Applied Sciences, TU Delft, Netherlands

(2)KNMI, Netherlands

Outline

What is the albedo bias effect

How is it modeled in large-scale models, e.g. for weather and climate

Albedo bias results from a Large-Eddy Simulation of stratocumulus

Parameterization of liquid water path variance

Conclusion

Albedo for a homogeneous cloud layer

cloud layer depth = 400 mcloud droplet size = 10 m optical depth = 25 albedo = 0.79

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60

Cloud albedo

Cloud optical depth

homogeneous stratocumuluscloud layer

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=32

LWPρ liqreff

, LWP = ρ air

zbase

ztop

∫ q ldz

Albedo for a inhomogeneous cloud layer

cloud layer depth = 400 mcloud droplet size = 10 m optical depth = 5 and 45, mean = 25

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60

Cloud albedo

Cloud optical depth

in homogeneous stratocumuluscloud layer

mean albedo

mean albedo = 0.65 < 0.79

€

=32

LWPρ liqreff

, LWP = ρ air

zbase

ztop

∫ q ldz

Albedo bias effect

observed spatial variability in stratocumulus albedo

Albedo for a inhomogeneous cloud layer

inhomogeneous stratocumuluscloud layer

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60

Cloud albedo

Cloud optical depth

effective mean

mean albedo

homogeneous albedo

Simple parameterization of the inhomogeneity effect:

Inhomogeneity constant: = 0.7 (Cahalan et al. 1994)

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effective = χτ mean

The diurnal cycle of stratocumulus during FIRE I (Cahalan case)LES results

€

LWP = ρ air

zbase

ztop

∫ q ldz

Factor diagnosed from all hourly 3D cloud fieldsfor fixed solar zenith angle =530

factor > 0.7

Factor depends on the optical depth variance ()

Analytical results for the inhomogeneity factor Assumption: Gaussian optical depth distribution

not smaller than ~ 0.8

isolines

Aim: model cloud liquid water path variance

RACMO

LES fields

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q liq = q tot −qsat T( )

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LWP = ρ air

zbase

ztop

∫ q ldz

Is temperature important for liquid water fluctuations?

total humidity-liquid water PDFs

Differences in PDFs: temperature effect (Clausius-Clapeyron)

liquid water

total water

0

10

20

30

40

50

-20 -10 0 10 20 30 40 50

qsaturation

[g/kg]

temperature [0C]

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q liq = q tot −qsat T( )

Temperature-humidity correlations

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l ' = T' −L v

cp

q l ' = 0 ⇒ T' =L v

cp

1+L v

cp

dqs

dT

⎛

⎝ ⎜

⎞

⎠ ⎟q t ' ≈ 1000q t '

Vertical structure of fluctuations

In a cloudy subcolumn the mean liquid water fluctuation can be approximated to be constant with height

Model: from qt' to LWP'

LWP'ρ0

=Hβqt'+12H'βqt'

l' ≈ 0 = 0.4

' ≈ 0 = 1

PDF reconstruction from total humidity fluctuations in the middle of the cloud layer

Effect of domain size

Conclusion

1. Why did Cahalan et al. (1994) found much lower values for the inhomogeneity factor

- They used time series of LWP

2. In stratocumulus l fluctuations are typicall small

- ql' = qt' , ≈ 0.4

3. Parameterizations for the variance of LWP and

- compute total water variance according to Tompkins (2002)

4. Current ECMWF weather forecast model uses LWP variance for McICA approach

LWP'2= ρ0Hβ( )2qt'

2

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'2 =3ρ 0 Hβ2ρ liqreff

⎛

⎝ ⎜

⎞

⎠ ⎟

2

q t '2