Calculated radiance errors induced by neglecting the polarization of the irradiation beam exposed to an atmosphere

Highlights

• Calculated radiance errors induced by neglecting the polarization of the incident irradiation reach up to 94.00%.

• Neglecting the linear polarized component induces much larger errors than neglecting the circularly polarized component of the incident beam.

• Diffuse reflection weakens the calculation errors for the boundary reflected radiance.

Abstract

The radiance calculation via the solution of the scalar approximation form of the rigorous vector radiative transfer equation (VRTE) leads to non-negligible errors in atmospheric radiative transfer problems. In this work, for the first time, a quantitative investigation of the calculated radiance errors induced by neglecting the polarization of incident irradiation beams exposed to a plane-parallel atmosphere is presented. The discontinuous finite element method, which is highly accurate in the spatial and angular spaces, was employed to solve both the VRTE and its scalar approximation. The calculated values of the radiance obtained via the scalar model are compared with the exact solutions calculated via the vector model and their relative errors are analyzed. The results show that neglecting the linearly polarized component of the incident irradiation leads to relative errors up to 94.00%. These values are much larger than the errors induced by neglecting the circularly polarized component.

Introduction

In the radiative transfer community, the full description of a radiation bundle consists of the definition of both its intensity and its polarization state [1]. The polarization state is defined via the Stokes vector, and the equation governing the polarized radiative transfer in a medium is known as the vector radiative transfer equation (VRTE) [2], [3], [4], [5]. In the polarized radiative transfer propagation process, the scattering and the reflection events induce multiple transformations on the components of the Stokes vector. This increases the complexity of the VRTE when compared to the scalar radiative transfer equation.

The scalar approximation, which ignores the polarization, is usually applied to solve the radiative heat transfer problems in participating media at high temperatures [6], [7], [8], [9], [10], [11], [12] because the polarization effect in these situations are marginal and only the radiation intensity is needed to calculate the temperature distributions. Numerical algorithms using the scalar approximation are much more computationally efficient than those considering the full polarization effect. However, in the fields of radiation signal applications, such as astrophysics [13], [14], [15], atmospheric radiative transfer [16], [17], [18], optical imaging [19], [20], [21], and remote sensing [22], [23], [24], the particle scattering are usually strong polarized, the radiance calculation via the scalar approximation introduces non-negligible calculation errors [1], [25], [26], [27], [28], [29], [30], [31]. Early in 1950, Chandrasekhar [1] showed that the polarization effect should be carefully treated to avoid significant errors in addressing atmospheric radiative transfer-related problems. Adams and Kattawar [25] found that these errors may measure up to 11.7% in the case of the calculated transmitted radiance if the polarized scattering events are approximated by the scalar approximation in a Rayleigh scattering atmosphere. Hansen [26] examined the deviation of the scalar approximated radiation intensity from its exact polarized value in a plane-parallel Mie-scattering cloud. The work of Kotchenova et al. [27] shows that ignoring the polarization effect leads to an error up to 7.2% when calculating the reflectance at the top of the atmosphere with a Lambertian surface. By comparing the results obtained via the vector and the scalar models, Lacis et al. [28] and Sromovsky [29] discussed the relative errors for an Earth-like and a Neptune-like atmosphere, respectively. Mishchenko et al. [30] performed a systematic study of the calculation error in a one-dimensional atmosphere-system in 1994. Moreover, Emde et al. [31] have recently studied the errors in the case of a three-dimensional cloudy atmosphere.

The source term in all the previously mentioned investigations is usually modeled as non-polarized sunlight or thermal emission and the errors are induced by neglecting the polarized medium scattering. While the incident beam is usually strongly polarized in some advanced techniques, such as the active remote sensing [32], ocean color observations from the surface radiation intensity [33,34], and laboratory optical imaging [35]. To our best knowledge from the released literature, the estimate of the errors induced by neglecting the polarization effect has not been previously studied when the incident irradiation is polarized. The influence of the polarization state of the incident irradiation on the calculated radiance remains unresolved.

In this work, by employing a previously developed discontinuous finite element method (DFEM) [36], [37], [38], which is highly accurate in both the spatial and the angular domains, the rigorous VRTE and its scalar approximation are solved. A participating medium of Mie scattering atmosphere is considered, and the relative errors of the calculated radiance for the cases with different incident radiation beams with different polarization states are estimated.