Optical particle sizing in vertically inhomogeneous turbid media

Alexander A. Kokhanovsky, Vladimir V. RozanovInstitute of Remote Sensing, Bremen University

P. O. Box 330440 Bremen, Germany

alexk@iup.physik.uni-bremen.de

Contents

• Introduction• Functional derivative of reflectance• Algorithm• Application to synthetic data• Conclusions

Functional derivative of reflectance

_

ln,

ln ( )a ef k k kef k

RS z f z

a z

1

_

0

( )

( )a ef efef

RR a z dz

a z

z=Z/H

variation of droplet size at depth z

_ _

1

/ ,kN

ef k ef ka ef a ef k

k ef

a z a zR R S z

a z

efa z

plots

00

,ˆ, , ,

4

dSS P S d B

d

0ˆ, ,surf

AS R S d

,0 0S

Upwelling diffuse radiation at the bottom

Downweling diffuse radiation at the top

0 0 0E I

Solar radiation at the top

Theory

SCIATRAN: software package for the solution of direct and inverse problems of atmospheric optics

(Rozanov et al., 2011)

Free download: www.iup.physik.uni-bremen.de/sciatran

Results of calculations

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

1.0

1.2

1.4

1.6

1.8

2.0 = 1.0a

ef=12m

SZA = 60degreesVZA = 0degrees

z, k

m

|S|, km-1

0.865m 1.24m 1.6m 2.13m 3.7m

0.0 0.1 0.2 0.3 0.4

1.0

1.2

1.4

1.6

1.8

2.0

= 5a

ef=12m

SZA = 60degreesVZA = 0degrees

z, k

m

|S|, km-1

0.865m 1.24m 1.6m 2.13m 3.7m

0.0 0.2 0.4 0.6 0.8 1.0

1.0

1.2

1.4

1.6

1.8

2.0

= 10a

ef=12m

SZA = 60degreesVZA = 0degrees

z, k

m

|S|, km-1

0.865m 1.24m 1.6m 2.13m 3.7m

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

1.0

1.2

1.4

1.6

1.8

2.0

= 20a

ef=12m

SZA = 60degreesVZA = 0degrees

z, k

m

|S|, km-1

0.865m 1.24m 1.6m 2.13m 3.7m

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6

1.0

1.2

1.4

1.6

1.8

2.0

= 50a

ef=12m

SZA = 60degreesVZA = 0degrees

z, k

m

|S|, km-1

0.865m 1.24m 1.6m 2.13m 3.7m

0 2 4 6 8 10

1.0

1.2

1.4

1.6

1.8

2.0

= 100a

ef=12m

SZA = 60degreesVZA = 0degrees

z, k

m

|S|, km-1

0.865m 1.24m 1.6m 2.13m 3.7m

Algorithm

,

,

a z A zB N const C

a A z B N C

1 2 3

1ˆ ˆ ˆ ˆ ˆ ˆ ˆ, , [ ]T T T T

R c A c B c C

y cx c y c cx x c c c y

2 2

1 1

, ,z z

z z

a z N zR K z dz K z dz

a z N z

Results of retrievals for synthetic data

4 5 6 7 8 9 10 11 12 13 14 15 161.0

1.2

1.4

1.6

1.8

2.04 5 6 7 8 9 10 11 12 13 14 15 16

solid lines - exact profiles

he

igh

t, km

effective radius, m

865nm1240nm1600nm2100nmnaidr,SZA=60degA=0

N_t

1/cm3

N_r

1/cm3

COT(true

)

COT

(retrieved)

ER profile

(true),

ER profile

(retrieved),

ER(retrieved

using

SACURA),

40 39.2 9.5 9.7 15-11.25-7.5 14.9-11.4-7.9 13.0

40 39. 11.5 11.5 15-12.5-10 14.9-12.7-

10.5

14.3

LWP(inh)=73.3kg/m^2, LWP(hom)=83.9kg/m^2, difference:16.6kg/m^2

0.5-0.9km

Conclusions

• It is possible to retrieve vertical profiles of effective radius of droplets in clouds using passive spectral measurements in some cases

• The accuracy of the technique is higher for moderately thick clouds (COT=10-30)

• The new approach enables the improvement of the liquid water path estimation