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

Abstract

Mixed-gas opacities are critical for radiative transfer in stellar and substellar atmospheres. Several approaches exist to obtain net k-coefficients for arbitrary mixtures, each trading accuracy against computational cost. I introduce a tunable Polynomial (or spline) Reconstruction And Sampling (PRAS) method to compute randomly overlapped opacities within a wavelength band. For each species and band, PRAS fits the opacity cumulative distribution function (CDF) with a polynomial or spline, then performs a Monte Carlo convolution to form the mixed distribution. A tunable trade-off between accuracy and speed of computation is controlled by the quality of the CDF fit and the total number of random samples used in the Monte Carlo integration scheme. PRAS is typically as accurate as, or more accurate, than other methods at recovering individual, pre-mixed k-coefficients with the random overlap assumption. In an exoplanet atmosphere outgoing spectral flux comparison test, PRAS, even with a small number of samples (250), is at worse within $\lesssim$20\% of the pre-mixed (PM) reference and typically within $\approx$5\% of the resorting and rebinning method (RORR). In the vertical flux and heating rate tests, PRAS produces similar results to RORR, and an improvement over the adaptive equivalent extinction (AEE) method. In the limit of exact CDF representation and infinite samples, PRAS converges to the exact, convolved randomly overlapped opacity distribution. Given its accuracy and scalability to larger quadrature sets at comparable cost to RORR, PRAS is a practical alternative for retrievals and post-processing applications.