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  • Author or Editor: J. T. Twitty x
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J. T. Twitty


An iterative method to invert size distributions from simulated scattered radiance measurements at small angles from the sun has been investigated. The inferred size distributions were represented by piecewise linear and cubic spline functions. Various relevant characteristics were investigated and it was found that:

  1. The inverted size distribution was insensitive to the number of knots in the piecewise linear spine.

  2. Within the range of sensitivity, the choice of initial guess had little effect on the inverted size distribution.

  3. Five percent random noise in the simulated radiances appreciably deteriorated the result but variations are still tolerable when compared with other methods for determining size distributions.

  4. Ale inverted distribution was insensitive to the index of refraction used in the kernel for particle radii r>1 µm.

  5. The choice of wavelength between 0.40µm and 0.70µm has negligible effect on the inverted distribution.

  6. A range of tropospheric aerosol size distributions give acceptable inverted results.

  7. The cubic spline representation can give reasonable inverted distributions, but may become unstable.

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J. A. Weinman
J. T. Twitty
S. R. Browning
, and
B. M. Herman


The intensity of sunlight multiply scattered in model atmospheres is derived from the equation of radiative transfer by an analytical small-angle approximation. The approximate analytical solutions are compared to rigorous numerical solutions of the same problem. Results obtained from an aerosol-laden model atmosphere are presented. Agreement between the rigorous and the approximate solutions is found to be within a few percent.

The analytical solution to the problem which considers an aerosol-laden atmosphere is then inverted to yield a phase function which describes a single scattering event at small angles. The effect of noisy data on the derived phase function is discussed.

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