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Updated: Jun 8, 2026

Near-Infrared Temperature Measurement Technique for Water Surrounding an Induction-heated Small Magnetic Sphere

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Published on: April 30, 2018

Numerical technique for solving the radiative transfer equation for a spherical shell atmosphere.

B M Herman, A Ben-David, K J Thome

|October 2, 2010

Summary

A new numerical method accurately solves radiative transfer in spherical atmospheres. Ignoring spherical effects causes significant errors, especially at high solar zenith angles.

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Scattering And Absorption of Light in Planetary Regoliths

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Scattering And Absorption of Light in Planetary Regoliths

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Published on: July 1, 2019

Area of Science:

Atmospheric science
Radiative transfer theory
Numerical modeling

Background:

Accurate modeling of radiative transfer is crucial for understanding Earth's climate and atmospheric processes.
Traditional models often simplify atmospheric geometry, potentially limiting accuracy in specific scenarios.

Purpose of the Study:

To present a novel numerical method for solving the radiative transfer equation in a spherical shell atmosphere.
To assess the accuracy of the proposed method and compare it with existing flat-atmosphere models.

Main Methods:

Developed a numerical method incorporating a conical boundary and Gauss-Seidel iteration.
Solved for all orders of scattering along a single radial line.
Validated the model against benchmark cases and compared with flat-atmosphere approximations.

Main Results:

The method achieves better than 1% accuracy for most Earth-atmosphere conditions.
Comparisons reveal that neglecting spherical effects leads to over 5% error at optical depths of 0.10 for solar zenith angles > 85°.

Conclusions:

The proposed numerical method provides a highly accurate solution for radiative transfer in spherical atmospheres.
Spherical effects are significant and cannot be ignored for accurate radiative transfer calculations, particularly under specific solar illumination conditions.