Scattering of Radiation by Moderately Nonspherical Particles

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  • 1 National Center for Atmospheric Research, Boulder, CO 80307
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Abstract

The nonsphericity of many atmospheric particles is often raised as an objection to radiative transfer analyses which assume sphericity. This paper studies the behavior of extinction and absorption cross sections, as well as direct backscattering, for rotationally symmetric nonspherical particles of the form r=r0[1+εTn(cosθ)], where ε is a deformation parameter and Tn a Chebyshev polynomial. For n=2 and 4, −0.2≤ε≤0.2 and size parameters up to 10, we compare the various nonspherical scattering parameters in both fixed and random orientation (calculated exactly using the Extended Boundary Condition Method) with those for equal-volume and equal-projected-area spheres.

We find that:

1) The equal-volume-sphere approximation becomes increasingly poor above size parameter 5 unless the oscillations in the spherical curves are smoothed out, either by high absorption or size-averaging.

2) Orientation-averaging of extinction and absorption cross sections reduces spherical-nonspherical differences by an order of magnitude; size-averaging also reduces these differences, but not nearly as much.

3) Equivalent spheres give a better approximation to non-spherical absorption cross section than to extinction cross section or backscattering.

4) Concavity systematically elevates the cross section for larger particles.

5) Backscattering exhibits a magnified sensitivity to particle shape for nearly transparent particles, e.g., a 10% deviation from sphericity may produce a 100% change in backscattering; but this sensitivity is dramatically reduced when the particles have significant absorption.

6) Increasing the absorption always improves the agreement with equivalent spheres.

Abstract

The nonsphericity of many atmospheric particles is often raised as an objection to radiative transfer analyses which assume sphericity. This paper studies the behavior of extinction and absorption cross sections, as well as direct backscattering, for rotationally symmetric nonspherical particles of the form r=r0[1+εTn(cosθ)], where ε is a deformation parameter and Tn a Chebyshev polynomial. For n=2 and 4, −0.2≤ε≤0.2 and size parameters up to 10, we compare the various nonspherical scattering parameters in both fixed and random orientation (calculated exactly using the Extended Boundary Condition Method) with those for equal-volume and equal-projected-area spheres.

We find that:

1) The equal-volume-sphere approximation becomes increasingly poor above size parameter 5 unless the oscillations in the spherical curves are smoothed out, either by high absorption or size-averaging.

2) Orientation-averaging of extinction and absorption cross sections reduces spherical-nonspherical differences by an order of magnitude; size-averaging also reduces these differences, but not nearly as much.

3) Equivalent spheres give a better approximation to non-spherical absorption cross section than to extinction cross section or backscattering.

4) Concavity systematically elevates the cross section for larger particles.

5) Backscattering exhibits a magnified sensitivity to particle shape for nearly transparent particles, e.g., a 10% deviation from sphericity may produce a 100% change in backscattering; but this sensitivity is dramatically reduced when the particles have significant absorption.

6) Increasing the absorption always improves the agreement with equivalent spheres.

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