Determination of the optical thickness and effective radius from reflected solar radiation measurements David Painemal MPO531.

Determination of the optical thickness and effective radius from reflected solar radiation

measurementsDavid Painemal

MPO531

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Outline

• Theory

• Applications

• Results

• Conclusions

Theory

S= 0: conservative scattering



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s =1−ω0( )1−ω0g( )

τ =16

•S=0 for 1m.

•1.65m 2.16m, S sensitive to re.

re

S as a function of wavelength for selected values of the effective radius

• The asymptotic theory: The reflection (and transmission) properties of thick layer depend essentially on three parameters of the atmosphere, the scaled optical thickness (’), the similarity parameter (s) and reflectivity of the underlying surface.

Theory

• We chose the wavelengths: 0.75m and 2.5m– Outside of water vapor and oxygen absorption.



Theoretical relationships between the reflection function at 0.75m and 2.16 m for various values of and r

•Reflection at 2.16m: sensitive to re

• Reflection at 0.75m: sensitive to

We can estimate re and separately

Theory

• Optical thickness at 0.75m does not depend strongly on re.

• Reflection function at 2.16m is independent of the optical thickness.



Reflection function as a function of r for different values of , and azimuth angle.

Determination of and re

• We assume that measurements have a relative precision

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χ 2 = lnRmeasi (μ,μ0,φ) − lnRcalc

i (τ ,reμ,μ0,φ)[ ]2

i

∑

• Minimizing χ, we obtain and r.



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Rmeas0.75 (μ,μ0,φ)

Rmeas2.16 (μ,μ0,φ)

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Rcalc0.75(τ ,r,μ,μ0,φ)

Rcalc2.16(τ ,r,μ,μ0,φ)




Measurements of reflectance

Minimum , re

albedo,


χ at 0.75 and 2.16m



χ at 0.75, 1.65 and 2.16m

χ at 0.75, 1.65 2.16 and 3.7m

χ at 0.75 and 3.7 m


• Two minima regardless of the number of channels.

• The introduction of a third channel at 1.65m does not improve the retrieval for liquid water clouds.



Stratocumulus observations:

• Why?– Uniform layer– Dark ocean surface, reducing problems

associated with surface reflection.– Liquid water droplets: Mie scattering by

spherical particles is applicable

Marine Sc observations

• Comprehensive measurements off the coast of California 29 June-18 July

• The intent of this work is to provide comparisons of remote sensing and in situ estimates of cloud properties.



Instrumentation

• Aircraft measurements (7, 10, 13 and 16 July)– ER-2 aircraft: 18 km of altitude.Spectral scanning

radiometer, seven channel narrowband solar flux radiometer, spectral scanning radiometer.

– C-131A aircraft: within the clouds. Measurements of cloud microphysics.

• Satellite measurements on 2 days (7 and 16 July.

Effective radius

• Good spatial correlation

• Overestimation




are needed to see this picture.•Remote sensing based on reflectivity is insensitive to drizzle.

Optical thickness

• Geometric thickness assumed constant



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in situ =3

2ρ

LWPin siturin situ

LWPin situ = wJW ⋅Δz

wJW : LWC - Johnson - Williams probe

Including additional absorption

• Overestimation of effective radius It is necessary to introduce additional absorption for water vapor.

• We can adopt a gaseous volume extinction=0.6km-1.



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β 'ext =β ext

1− 0.33τ ce−0.26τ c




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βg (2.16μm) = 0.6km−1

Conclusions• A statistical technique has been described for inferring optimum

values of r and .• Reflection function at:

– 2.16 m is primarily sensitive to re.– 0.75 m is primarily sensitive to .

• Comparisons between in situ and remote sensing estimates of:– Effective radius

• Correlated variables• Remote sensing overestimates the radius of cloud droplets.

– Optical thickness:• Close agreement.• Problems with Johnson-Williams hot wire probe?

• The discrepancy between in-situ and remote sensing estimates of re can be explained by additional absorption by water vapor at 2.16m.

Determination of the optical thickness and effective radius from reflected solar radiation measurements David Painemal MPO531.

Documents

reflection function

surface reflection

function of r

remote sensing estimates

function of wavelength

s sensitive

comparisons of remote

scaled optical thickness