# Errors induced by the neglect of polarization in radiance calculations for three-dimensional cloudy atmospheres

## TL;DR

This study quantifies the errors caused by neglecting polarization in radiative transfer calculations for complex 3D cloudy atmospheres, revealing errors up to 8% depending on conditions.

## Contribution

It provides a detailed analysis of polarization neglect errors in 3D cloud models using Monte Carlo simulations, highlighting their significance in remote sensing.

## Key findings

- Maximum error of about 8% in clear-sky conditions at 400nm.
- Error reduces to about 6% in cloud-surrounded clear regions.
- Within clouds, errors up to 4%, highest in shadows.

## Abstract

Remote sensing instruments observe radiation being scattered and absorbed by molecules, aerosol particles, cloud droplets and ice crystals. In order to interpret and accurately model such observations, the vector radiative transfer equation needs to be solved, because scattering polarizes the initially unpolarized incoming solar radiation. A widely used approximation in radiative transfer theory is the neglect of polarization which allows to greatly simplify the radiative transfer equation. It is well known that the error caused by multiple Rayleigh scattering can be larger than 10\%, depending on wavelength and sun-observer geometry (Mishchenko et al., 1994). For homogeneous plane-parallel layers of liquid cloud droplets the error is comparatively small (below 1\%) (Hansen 1971). However, in reality clouds are not plane-parallel layers of water droplets but complex three-dimensional (3D) structures and observations of clouds usually include pixels consisting of clear and cloudy parts. In this study we revisit the question of the magnitude of error due to the neglect of polarization in radiative transfer theory for a realistic 3D cloudy atmosphere. We apply the Monte Carlo radiative transfer model MYSTIC with and without neglecting polarization and compare the results. At a phase angle of 90{\deg} and 400nm wavelength we find the maximum overestimation error of about 8% for complete clear-sky conditions. The error is reduced to about 6% in clear-sky regions surrounded by clouds due to scattering from clouds into the clear regions. Within the clouds the error is up to 4% with the highest values in cloud shadows. In backscattering direction the radiance is underestimated by about 5% in clear regions between clouds. For other sun-observer geometries, the error ranges between the two extremes. The error decreases with wavelength and in the absorption bands.