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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.

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Stephan de roode 1 2 alexander los 2

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

improve albedo bias calculations in large-scale models 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

Outline


Albedo for a homogeneous cloud layer
Albedo for a homogeneous cloud layer improve albedo bias calculations in large-scale models

homogeneous stratocumulus

cloud layer

cloud layer depth = 400 m

cloud droplet size = 10 mm

optical depth t = 25 albedo = 0.79


Albedo for a inhomogeneous cloud layer
Albedo for a inhomogeneous cloud layer improve albedo bias calculations in large-scale models

mean

albedo

in homogeneous stratocumulus

cloud layer

cloud layer depth = 400 m

cloud droplet size = 10 mm

optical depth t = 5 and 45, mean = 25

mean albedo = 0.65 < 0.79


Albedo bias effect
Albedo bias effect improve albedo bias calculations in large-scale models

observed spatial variability in

stratocumulus albedo


Albedo for a inhomogeneous cloud layer1

homogeneous improve albedo bias calculations in large-scale models

albedo

Albedo for a inhomogeneous cloud layer

mean

albedo

inhomogeneous stratocumulus

cloud layer

teffective

tmean

Simple parameterization of the inhomogeneity effect:

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



Factor c diagnosed from all hourly 3d cloud fields for fixed solar zenith angle q 53 0
Factor case)c diagnosed from all hourly 3D cloud fieldsfor fixed solar zenith angle q=530

factor c > 0.7


Factor c depends on the optical depth variance s t
Factor case)c depends on the optical depth variance (st)


Analytical results for the inhomogeneity factor c assumption gaussian optical depth distribution
Analytical results for the inhomogeneity factor case)cAssumption: Gaussian optical depth distribution

c isolines

c not smaller than ~ 0.8



Les fields
LES fields case)

Is temperature important for liquid water fluctuations?


Total humidity liquid water pdfs
total humidity-liquid water PDFs case)

liquid water

total water

Differences in PDFs: temperature effect (Clausius-Clapeyron)



Vertical structure of fluctuations
Vertical structure of fluctuations case)

In a cloudy subcolumn the mean liquid water fluctuation can

be approximated to be constant with height


Model from q t to lwp
Model: from q case)t' to LWP'

ql' ≈ 0  b = 0.4

T' ≈ 0  b = 1



Effect of domain size
Effect of domain size middle of the cloud layer


Conclusion

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

- They used time series of LWP

2. In stratocumulus ql fluctuations are typicall small

- ql' = bqt' , b ≈ 0.4

3. Parameterizations for the variance of LWP and t

- compute total water variance according to Tompkins (2002)

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

Conclusion