SpeCT: A state-of-the-art tool to calculate correlated-k tables and continua of CO$_2$-H$_2$O-N$_2$ gas mixtures

TL;DR

This work addresses the need for accurate opacity data across diverse planetary atmospheres by updating chi-factor corrections for CO$_2$-broadened lines in CO$_2$-CO$_2$, CO$_2$-N$_2$, and CO$_2$-H$_2$O mixtures. It introduces SpeCT, an open-source Fortran tool that efficiently computes high-resolution spectra with inter-species broadening, enabling the generation of eight new correlated-$k$ tables and continua following the MT_CKD framework for H$_2$O. The paper also provides a comprehensive review of laboratory chi-factor measurements and collisional continua, and delivers a set of tables that span a wide range of temperatures (50 K–1000 K for some mixtures) and pressures (1 Pa–10 bar, with extensions for higher regimes). The resulting data products—eight correlated-$k$ tables and CO$_2$ continua—facilitate flexible, composition-dependent radiative transfer in climate models of Earth-like, magma-ocean, and other CO$_2$-bearing worlds, with the SpeCT code and data openly available to the community.

Abstract

A key challenge in modeling (exo)planetary atmospheres lies in generating extensive opacity datasets that cover the wide variety of possible atmospheric composition, pressure, and temperature conditions. This critical step requires specific knowledge and can be considerably time-consuming. To circumvent this issue, most available codes approximate the total opacity by summing the contributions of individual molecular species during the radiative transfer calculation. This approach neglects inter-species interactions, which can be an issue for precisely estimating the climate of planets. To produce accurate opacity data, such as correlated-k tables, chi factor corrections of the far-wings of the line profile are required. We propose an update of the chi factors of CO$_2$ absorption lines that are relevant for terrestrial planets (pure CO$_2$, CO$_2$-N$_2$ and CO$_2$-H$_2$O). These new factors are already implemented in an original user-friendly open-source tool designed to calculate high resolution spectra, named SpeCT. The latter enables to produce correlated-k tables for mixtures made of H$_2$O, CO$_2$ and N$_2$, accounting for inter-species broadening. In order to facilitate future updates of these chi factors, we also provide a review of all the relevant laboratory measurements available in the literature for the considered mixtures. Finally, we provide in this work 8 different correlated-k tables and continua for pure CO$_2$, CO$_2$-N$_2$, CO$_2$-H$_2$O and CO$_2$-H$_2$O-N$_2$ mixtures based on the MT_CKD formalism (for H$_2$O), and calculated using SpeCT. These opacity data can be used to study various planets and atmospheric conditions, such as Earth's paleo-climates, Mars, Venus, Magma ocean exoplanets, telluric exoplanets.

Figures (6)

• Figure 1: Comparison of calculated spectra for 1 bar of pure CO$_2$ gas at 750 K, with (black line) and without (red line) the $\chi$ factors. The blue line is the spectrum calculated for the same pressure and temperature conditions, but using HITEMP 2024 hargreaves_updating_2024 instead of HITRAN 2020 gordon_hitran2020_2021 The vertical dotted black lines illustrate the definition interval of the 3 main bands of CO$_2$ we consider. The horizontal dashed, dot-dashed and dotted gray lines represent the intervals for which measurement of the continuum (excluding CIAs) are available, for CO$_2$-CO$_2$, CO$_2$-N$_2$ and CO$_2$-H$_2$O, respectively.
• Figure 2: Absorption spectrum for a gas mixture including 0.01 bar of H$_2$O, 1 bar of CO$_2$ and 1 bar of N$_2$ at 300 K. Red and grey lines are the spectra containing the centers of absorption lines (of CO$_2$ and H$_2$O respectively) up to $\pm$25 cm$^{-1}$. Other solid lines are the CO$_2$ continua obtained using the original $\chi$ factors from this work, while the dashed lines are the spectra calculated with previously existing factors. The continua calculated with existing $\chi$ factors (dashed lines) are based on tran_measurements_2011, perrin_temperature-dependent_1989 and tran_measurements_2018 for pure CO$_2$, CO$_2$-N$_2$ and CO$_2$-H$_2$O, respectively. For this comparison, we do not use $\chi$ factors from burch_absorption_1969 to calculate the $\nu_1+\nu_3$ band of CO$_2$-N$_2$ as it is based on a different formalism, thus the factors derived for the $\nu_3$ band perrin_temperature-dependent_1989 are applied everywhere (green dashed line).
• Figure 3: Adjustment of the $\chi$ factors of a pure CO$_2$ gas for various temperatures. We include the CIA, near 7050 cm$^{-1}$, from filippov_collision-induced_1997 (black dotted line on the right panel) to adjust the $\chi$ factors at 295 K. Black dashed, solid and dot-dashed lines correspond to experiment data from tran_measurements_2011, tran_collision-induced_2024 and burch_absorption_1969, respectively. Colored lines are the spectra calculated with our model, using the original $\chi$ factors proposed in this work. For visualization reasons, we arbitrary multiplied the spectra by an offset (see offset on the figure) to avoid potential overlapping of the curves.
• Figure 4: Adjustment of the $\chi$ factors of CO$_2$ broadened by N$_2$ for various temperatures. The black dashed and dotted-dashed lines correspond to experiment data from niro_spectra_2004 and burch_absorption_1969, respectively. The black dotted line corresponds to a spectrum computed using the ECS model from niro_spectra_2004, that is the core of the $\nu_2$ band without local bands. The red dotted line is our $\chi$ factor calculation of the $\nu_2$ band without local bands. For visualization reasons, we arbitrarily multiplied the spectra by a factor (see offset on the figure) to avoid potential overlapping of the curves.
• Figure 5: Absorption spectrum corresponding roughly to the surface Earth gas mixture (N$_2$, H$_2$O and CO$_2$). Here we assume 1 bar of total pressure, including 370 ppm of CO$_2$ and 0.01 bar of H$_2$O at 285 K. The CO$_2$ content corresponds to the Earth's atmosphere conditions in 2000.