A tunable Monte Carlo method for mixing correlated-k opacities. PRAS: polynomial reconstruction and sampling

Abstract: Accurately accounting for mixed-gas opacities is critical for radiative-transfer (RT) calculations in sub-stellar atmospheres. To produce the total k-coefficients of an arbitrary mixture of gases and their associated volume mixing ratios (VMRs), several methods are applied in the literature with various levels of overall accuracy and ease of computation. We propose a simple, tunable random overlap method, polynomial reconstruction and sampling (PRAS). PRAS is a Monte Carlo-based technique, sampling polynomial approximations of the opacity cumulative distribution function (CDF) in a wavelength band for each species requiring mixing. The method enables control over the end accuracy of the opacity mixture through choices in CDF fitting and number of random samples used in the mixing scheme. We find PRAS is typically as accurate, or more accurate, than other methods at recovering individual, pre-mixed k-coefficients. In an emission spectrum comparison test, PRAS, even with a small number of samples (100), is within ~2% of the reference 16+16 Legendre quadrature node random overlap with resorting and rebinning (RORR) results, and is typically more accurate than the 4+4 and 8+8 Legendre node schemes. In the vertical flux and heating rate tests, we also find that PRAS is generally more accurate than other schemes, and an improvement over the adaptive equivalent extinction (AEE) method. Overall, our current tests show PRAS is a generally viable alternative for the calculation of randomly overlapped opacities, especially in scenarios where increased accuracy of the RT calculation is required and when larger numbers of quadrature points are used. PRAS may therefore provide a benefit in performance and accuracy for high-precision retrieval modelling of JWST data.