optical particle sizing in vertically inhomogeneous turbid media

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