An Assessment of and Solution to the Intensity Diffusion Error Intrinsic to Short-Characteristic Radiative Transfer Methods

TL;DR

This paper analyzes the numerical diffusion error in short-characteristic radiative transfer methods used in solar atmosphere simulations, providing an analytical model and practical solutions to improve observational comparisons.

Contribution

It quantifies the diffusion error in short-characteristics methods, derives an analytical model, and proposes a solution to mitigate image degradation for better solar observation simulations.

Findings

Numerical diffusion degrades image resolution away from disk-center.

Diffusion error can be modeled analytically as a function of viewing angle.

Pre-interpolating on a viewing-angle aligned grid avoids diffusion errors.

Abstract

Radiative transfer coupled with highly realistic simulations of the solar atmosphere is routinely used to infer the physical properties underlying solar observations. Due to its computational efficiency, the method of short-characteristics is often employed, despite it introducing numerical diffusion as an interpolation artifact. In this paper, we quantify the effect of the numerical diffusion on the spatial resolution of synthesize emergent intensity images, and derive a closed form analytical model of the diffusion error as a function of viewing angle when using linear interpolation. We demonstrate that the image degradation adversely affects the comparison between simulated data and observations, for observations away from disk-center, unless the simulations are computed at much higher intrinsic resolution than the observations. We also show that the diffusion error is readily avoided by interpolating the simulation solution on a viewing-angle aligned grid prior to computing the radiative transfer. Doing this will be critical for comparisons with observations using the upcoming large aperture telescopes --- the Daniel K. Inouye Solar Telescope and the European Solar Telescope.