## Retrieval of the Albedo and Phase Function from Exiting Radiances with Radiative Perturbation Theory

Applied Optics, Vol. 38, Issue 9, pp. 1636-1643 (1999)

http://dx.doi.org/10.1364/AO.38.001636

Acrobat PDF (202 KB)

### Abstract

We use radiative perturbation theory to develop a retrieval technique for determining the radiative properties of a scattering medium, such as the Earth’s atmosphere, based on measurements of the radiation emerging at either the top or bottom of the medium. In a previous paper [J. Quant. Spectrosc. Radiat. Transfer <b>54,</b> 695 (1995)] we have shown the capacity of radiative perturbation theory to describe variations in exiting intensity as a linear combination of the parameters that characterize the scattering medium. Here we show that it is possible to set up a matrix relation such that the matrix inversion solves the inverse scattering problem. Using simulated data, we observe that the quality of the solution can be controlled by studying the singular values associated with the kernel matrix, obtaining in this way a stable solution, even in the presence of noise.

© 1999 Optical Society of America

**OCIS Codes**

(010.1110) Atmospheric and oceanic optics : Aerosols

(010.1280) Atmospheric and oceanic optics : Atmospheric composition

(280.1100) Remote sensing and sensors : Aerosol detection

(280.1310) Remote sensing and sensors : Atmospheric scattering

(290.3200) Scattering : Inverse scattering

(290.4210) Scattering : Multiple scattering

**Citation**

Michael A. Box and Claudia Sendra, "Retrieval of the Albedo and Phase Function from Exiting Radiances with Radiative Perturbation Theory," Appl. Opt. **38**, 1636-1643 (1999)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-9-1636

Sort: Year | Journal | Reset

### References

- K. Kamiuto, “A constrained least-squares method for limited inverse scattering problems,” J. Quant. Spectrosc. Radiat. Transfer 40, 47–50 (1988).
- K. Kamiuto, “Application of the emergency-intensity fitting method for inverse scattering problems to a system bounded by transparent plates,” J. Quant. Spectrosc. Radiat. Transfer 46, 159–164 (1991).
- L. G. Henyey and J. L. Greenstein, “Diffuse light in the galaxy,” Astrophys. J. 93, 70–83 (1941).
- K. Kamiuto, “An iterative method for inverse scattering problems,” J. Quant. Spectrosc. Radiat. Transfer 49, 1–13 (1993).
- M. A. Box, S. A. W. Gerstl, and C. Simmer, “Application of the adjoint formulation to the calculation of atmospheric radiative effects,” Beitr. Phys. Atmos. 61, 303–311 (1988).
- M. A. Box, S. A. W. Gerstl, and C. Simmer, “Computation of atmospheric radiative effects via perturbation theory,” Beitr. Phys. Atmos. 62, 193–199 (1989).
- M. A. Box, B. Croke, S. A. W. Gerstl, and C. Simmer, “Application of the perturbation theory for atmospheric radiative effects: aerosol scattering atmospheres,” Beitr. Phys. Atmos. 62, 200–211 (1989).
- M. A. Box and C. Sendra, “Sensitivity of exiting radiances to details of the scattering phase function,” J. Quant. Spectrosc. Radiat. Transfer 54, 695–703 (1995).
- S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, New York, 1977).
- R. L. Parker, Geophysical Inverse Theory (Princeton U. Press, Princeton, N.J., 1994).
- A. E. S. Green, A. Deepak, and B. J. Lipofsky, “Interpretation of the sun’s aureole based of atmospheric aerosol models,” Appl. Opt. 10, 1263 (1971).
- A. Deepak, G. P. Box, and M. A. Box, “Experimental validation of the solar aureole technique for determining aerosol size distributions,” Appl. Opt. 21, 2236–2243 (1982).
- H. Yang and H. R. Gordon, “Retrieval of the columnar aerosol phase function and single-scattering albedo from sky radiance over land: simulations,” Appl. Opt. 37, 978–997 (1998).
- R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, and D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 255, 423–430 (1992).
- J. Lenoble, ed, Radiative Transfer in Scattering and Absorbing Atmospheres: Standard Computational Procedures (Deepak, Hampton, Va., 1985).
- C. Sendra and M. A. Box, “Information content of the kernal matrix for the phase function retrieval problem,” Appl. Opt. 38, 1644–1647 (1999).
- F.-M. Breon, J.-L. Deuze, D. Tanre, and M. Herman, “Validation of spaceborne estimates of aerosol loading from sun photometer measurements with emphasis on polarization,” J. Geophys. Res. 102, 17,187–17,195 (1997).
- M. Herman, J. L. Deuze, C. Devaux, P. Goloub, F. M. Breon, and D. Tanre, “Remote sensing of aerosols over land surfaces including polarization measurements and application to POLDER measurements,” J. Geophys. Res. 102, 17,039–17,049 (1997).
- W. Wanner, A. H. Strahler, B. Hu, P. Lewis, J.-P. Muller, X. Li, C. L. Barker Schaaf, and M. J. Barnsley, “Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: theory and algorithm,” J. Geophys. Res. 102, 17,143–17,161 (1997).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.