Determination of the optical thickness
and effective radius from reflected
solar radiation measurements
David Painemal
MPO531
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Outline
•
•
•
•
Theory
Applications
Results
Conclusions
Theory
• 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. S= 0: conservative scattering
s
1  0 
1  0 g
•S=0 for 1m.
  16


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•1.65m2.16
m, S sensitive to re.
re
S as a function of wavelength for
selected values of the effective radius
Theory
• We chose the wavelengths: 0.75m and 2.5m
– Outside of water vapor and oxygen absorption.
•Reflection at 2.16m:
sensitive to re
• Reflection at 0.75m:
sensitive to 
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 We can estimate re and
separately
Theoretical relationships between the reflection
function at 0.75m and 2.16 m for various values
of  and r
Theory
• Optical thickness at 0.75m does
not depend strongly on re.
• Reflection function at 2.16m is
independent of the optical
thickness.
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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
• Minimizing , we obtain  and r.
  ln R
2
i
meas
i

(, 0,  )  ln R
i
calc
( ,re, 0,  )
2
Determination of  and re
Measurements of
reflectance
albedo, 
0.75
Rcalc
( ,r, , 0 ,  )
2.16
Rcalc
( ,r, , 0 ,  )

0.75
Rmeas
(, 0 ,  )
R 2.16 (,  ,  )
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
Minimum  , re
Determination of  and re
 at 0.75, 1.65
and 2.16m

at 0.75
and 2.16m
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 at 0.75 and
3.7 m
 at 0.75, 1.65
2.16 and 3.7m
Determination of  and re
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• Two minima regardless of the
number of channels.
• The introduction of a third channel
at 1.65m 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.
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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
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•Remote sensing based
on reflectivity is
insensitive to drizzle.
Optical thickness
• Geometric thickness assumed constant
3 LWPin situ
2  rin situ
LWPin situ  w JW  z
w JW : LWC - Johnson - Williams probe
 in situ 
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
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.
g (2.16m)  0.6km1
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 'ext 
 ext
1 0.33 ce0.26
c
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 2.16m.