SpeCT: Mixed-Gas Spectral Opacity Tool

• SpeCT is an open-source Fortran tool that computes high-resolution spectra for mixed-gas planetary atmospheres involving CO2, H2O, and N2.
• It employs explicit mixed-gas pressure broadening and empirical far-wing corrections to overcome limitations of additive single-species opacity methods.
• The tool converts detailed spectral data into correlated‑k tables, facilitating accurate climate and radiative-transfer simulations for a range of planetary environments.

SpeCT is an open-source Fortran tool for generating high-resolution spectra, correlated-$k$ tables, and continuum files for planetary atmospheres involving $\mathrm{CO_2}$, $\mathrm{H_2O}$, and $\mathrm{N_2}$. Its central purpose is to make mixed-gas opacity production more physically realistic than additive single-species workflows by accounting for inter-species broadening and empirically corrected far-wing line shapes, while keeping the resulting products usable in climate and radiative-transfer models through downstream conversion to correlated-$k$ form with Exo_k (Chaverot et al., 25 Aug 2025).

1. Scientific role and scope

SpeCT is designed for a specific bottleneck in atmospheric modeling: line-by-line opacity calculations are too expensive to repeat inside 1-D or 3-D climate models, yet simplified additive methods can neglect collision-partner effects that matter for radiative balance. The tool therefore computes high-resolution spectra for specified pressure–temperature–composition states, with explicit treatment of mixed-gas pressure broadening and empirically corrected far-wing line shapes, and these spectra are then converted into correlated-$k$ tables (Chaverot et al., 25 Aug 2025).

The targeted domain is terrestrial-planet and rocky-exoplanet atmospheres, especially mixtures involving $\mathrm{CO_2}$, $\mathrm{H_2O}$, and $\mathrm{N_2}$. This emphasis reflects a specific physical point: total opacity in a gas mixture is not, in general, captured well enough by summing isolated-species opacities or by online mixing of precomputed single-species $k$-tables. In the regimes emphasized by the paper, line shifts, Lorentz half-widths, continuum strength, and especially the far wings of strong $\mathrm{CO_2}$0 bands depend on the broadening species. SpeCT is therefore narrower in chemistry than generic opacity engines, but more explicit about collision-partner-dependent spectroscopy for the targeted mixtures (Chaverot et al., 25 Aug 2025).

A plausible implication is that SpeCT is most relevant precisely where atmospheric composition is neither close to a pure-gas limit nor well approximated by additive opacity rules. The paper links this regime to Earth paleoclimate, Mars, Venus, magma-ocean planets, and telluric exoplanets (Chaverot et al., 25 Aug 2025).

2. Spectroscopic formulation

SpeCT starts from standard line-by-line absorption theory, using line intensities, pressure shifts, collisional widths, and line-shape convolution between Lorentz and Gaussian components. Near line center, the Lorentz half-width for absorber $\mathrm{CO_2}$1 in a mixture is written as

$\mathrm{CO_2}$2

so mixture composition enters directly through the broadening partners $\mathrm{CO_2}$3 (Chaverot et al., 25 Aug 2025).

Species absorption is then accumulated over transitions, and the absorption coefficient is expressed as

$\mathrm{CO_2}$4

with the paper noting that, at sufficiently high pressure, the ideal-gas density factor should be replaced by a real-gas density from an equation of state (Chaverot et al., 25 Aug 2025).

This formulation makes the collision partner part of the opacity model rather than a secondary correction. That distinction is central to the tool’s scope. SpeCT is not presented as a broad chemistry platform; it is presented as a mixed-gas spectroscopic framework in which $\mathrm{CO_2}$5-$\mathrm{CO_2}$6, $\mathrm{CO_2}$7-$\mathrm{CO_2}$8, and $\mathrm{CO_2}$9-$\mathrm{H_2O}$0 broadening are modeled explicitly, and in which high-resolution spectra are the intermediate product from which correlated-$\mathrm{H_2O}$1 tables are later derived (Chaverot et al., 25 Aug 2025).

For high temperature, the implementation uses hybrid line-list logic: HITRAN 2020 for temperate conditions, HITEMP 2010 for $\mathrm{H_2O}$2 above $\mathrm{H_2O}$3, and HITEMP 2024 for $\mathrm{H_2O}$4 above $\mathrm{H_2O}$5. This is a practical feature because it avoids forcing users to manage line-list transitions themselves when generating opacity data over wide thermodynamic ranges (Chaverot et al., 25 Aug 2025).

3. Far-wing treatment and updated $\mathrm{H_2O}$6-factors

The most distinctive spectroscopic component of SpeCT is its treatment of far wings through empirical $\mathrm{H_2O}$7-factors. The paper states that a Voigt profile alone overestimates absorption in the windows between $\mathrm{H_2O}$8 bands, and that there is no fully self-consistent physical profile valid from line core to far wing. SpeCT therefore adopts the Hartmann/Tran/Perrin tradition and multiplies the line shape by mixture-specific far-wing corrections (Chaverot et al., 25 Aug 2025).

The $\mathrm{H_2O}$9-factor is piecewise exponential in the distance from line center, $\mathrm{N_2}$0:

$\mathrm{N_2}$1

with temperature-dependent coefficients

$\mathrm{N_2}$2

The paper updates these parameters for pure $\mathrm{N_2}$3, $\mathrm{N_2}$4-$\mathrm{N_2}$5, and $\mathrm{N_2}$6-$\mathrm{N_2}$7 (Chaverot et al., 25 Aug 2025).

The updated factors are organized around three $\mathrm{N_2}$8 band systems centered near $\mathrm{N_2}$9 ($k$0), $k$1 ($k$2), and $k$3 ($k$4). Operationally, the paper applies the $k$5 corrections from $k$6 to $k$7, the $k$8 corrections from $k$9 to $k$0, and the $k$1 corrections from $k$2 to $k$3; above $k$4, because of missing data, the $k$5 factors are reused for overtone bands such as $k$6 (Chaverot et al., 25 Aug 2025).

The paper also makes the asymmetry of the evidential base explicit. For pure $k$7, the $k$8 factors are materially updated using additional continuum constraints between $k$9 and $\mathrm{CO_2}$0. For $\mathrm{CO_2}$1-$\mathrm{CO_2}$2, new $\mathrm{CO_2}$3 factors are derived from Niro et al. data, while the $\mathrm{CO_2}$4 treatment is recast into the same formalism for consistency. For $\mathrm{CO_2}$5-$\mathrm{CO_2}$6, only $\mathrm{CO_2}$7-band laboratory constraints exist, so the previous parameterization is reformulated into the same $\mathrm{CO_2}$8 form and then applied over the whole spectrum as a pragmatic approximation (Chaverot et al., 25 Aug 2025).

This suggests two interpretive points. First, SpeCT is intentionally laboratory-driven rather than purely parametric. Second, its far-wing treatment is empirical and mixture specific, which improves targeted realism but also ties the accuracy of the products to the available measurements and to the underlying line lists (Chaverot et al., 25 Aug 2025).

4. Continua, CIA, and computational workflow

SpeCT aligns its water-continuum treatment with MT_CKD. The line core and far wing are separated at $\mathrm{CO_2}$9 from line center, following the historical MT_CKD convention. Line-center absorption is computed at high resolution, while continua are computed separately as the sum of far-wing contributions, including the “plinth,” with the same plinth removed from the line-core calculation to avoid double counting (Chaverot et al., 25 Aug 2025).

For $\mathrm{H_2O}$0-$\mathrm{H_2O}$1 and $\mathrm{H_2O}$2-$\mathrm{H_2O}$3, continua are taken from MT_CKD v4.0.1, with supplementary $\mathrm{H_2O}$4-$\mathrm{H_2O}$5 CIA from Hartmann et al. and Baranov et al. because MT_CKD foreign broadening is for air rather than pure $\mathrm{H_2O}$6. For $\mathrm{H_2O}$7-$\mathrm{H_2O}$8, the continuum is recomputed following Tran et al., using a HITRAN-based line list complemented with $\mathrm{H_2O}$9-broadening coefficients, extended to $\mathrm{N_2}$0, with temperature dependence from Ma and Tipping up to $\mathrm{N_2}$1. The recently measured simultaneous $\mathrm{N_2}$2 CIA band near $\mathrm{N_2}$3 is also included and assumed temperature-independent because no temperature dependence is available (Chaverot et al., 25 Aug 2025).

The continuum/CIA absorption coefficient for a collision pair $\mathrm{N_2}$4-$\mathrm{N_2}$5 is parameterized as

$\mathrm{N_2}$6

which makes explicit the $\mathrm{N_2}$7 scaling of binary-collision absorption under ideal-gas conditions (Chaverot et al., 25 Aug 2025).

On the computational side, SpeCT is highly parallelized with MPI and OpenMP. It reads HITRAN or HITEMP line lists, distributes the requested $\mathrm{N_2}$8 states across processes, computes line profiles, and sums them into high-resolution spectra. The line-center region is sampled at $\mathrm{N_2}$9 spacing, continua are computed on a $k$0 grid, and the far-wing domain is truncated at $k$1 after sensitivity tests. This cutoff is an explicit modeling choice: shorter cutoffs suppress weak-region continuum absorption, whereas extending farther has negligible effect (Chaverot et al., 25 Aug 2025).

5. Released opacity products

The paper emphasizes eight correlated-$k$2 tables and a set of continuum/CIA files. In the detailed product description, the eight correlated-$k$3 tables are two binary-mixture tables and six Earth-like ternary tables, while the work also provides original $k$4 continua for $k$5-$k$6, $k$7-$k$8, and $k$9-$\mathrm{CO_2}$00 (Chaverot et al., 25 Aug 2025).

Product class	Composition coordinate	Thermodynamic range
$\mathrm{CO_2}$01 table	$\mathrm{CO_2}$02	$\mathrm{CO_2}$03–$\mathrm{CO_2}$04, $\mathrm{CO_2}$05–$\mathrm{CO_2}$06
$\mathrm{CO_2}$07 table	$\mathrm{CO_2}$08	$\mathrm{CO_2}$09–$\mathrm{CO_2}$10, $\mathrm{CO_2}$11–$\mathrm{CO_2}$12
Six $\mathrm{CO_2}$13 tables	$\mathrm{CO_2}$14, fixed dry-air $\mathrm{CO_2}$15	$\mathrm{CO_2}$16–$\mathrm{CO_2}$17, $\mathrm{CO_2}$18–$\mathrm{CO_2}$19

For the two binary tables, the volume-mixing-ratio grid spans $\mathrm{CO_2}$20 to $\mathrm{CO_2}$21. For the six ternary Earth-like tables, the fixed dry-air $\mathrm{CO_2}$22 abundances are $\mathrm{CO_2}$23 ppm, $\mathrm{CO_2}$24 ppm, $\mathrm{CO_2}$25 ppm, $\mathrm{CO_2}$26, $\mathrm{CO_2}$27, and $\mathrm{CO_2}$28. The correlated-$\mathrm{CO_2}$29 products use spectral resolution $\mathrm{CO_2}$30, with Exo_k defining the resolution in wavenumber space by $\mathrm{CO_2}$31. The paper does not specify the number of $\mathrm{CO_2}$32-ordinates, the quadrature rule, or the detailed sorting formula (Chaverot et al., 25 Aug 2025).

The accompanying continua are distributed separately rather than embedded in the correlated-$\mathrm{CO_2}$33 tables. The original $\mathrm{CO_2}$34 continua span $\mathrm{CO_2}$35 to $\mathrm{CO_2}$36 and $\mathrm{CO_2}$37 to $\mathrm{CO_2}$38, and are provided in ASCII files containing wavenumber and absorption in $\mathrm{CO_2}$39. The paper also compiles and homogenizes CIA and dimer data from the literature for several collision pairs (Chaverot et al., 25 Aug 2025).

6. Position within opacity modeling, use cases, and limitations

SpeCT is presented as a targeted alternative to more generic opacity engines. The paper explicitly contrasts it with tools such as HELIOS-K: SpeCT is less versatile in species coverage, but more accurate for the targeted mixtures because it explicitly incorporates collision-partner-dependent broadening and empirically updated far-wing corrections (Chaverot et al., 25 Aug 2025).

That specialization also defines its limitations. Chemistry is restricted mainly to $\mathrm{CO_2}$40, $\mathrm{CO_2}$41, and $\mathrm{CO_2}$42, though future inclusion of $\mathrm{CO_2}$43 and $\mathrm{CO_2}$44 is planned. Some broadening and line-shift parameters are missing from HITRAN and HITEMP and must be approximated; for example, missing $\mathrm{CO_2}$45-in-$\mathrm{CO_2}$46 broadening and shift parameters are approximated from air values following Brown et al. The $\mathrm{CO_2}$47-factor formalism is empirical and line-list dependent, so substantial line-list changes may require readjustment (Chaverot et al., 25 Aug 2025).

The paper is also explicit about extrapolation. Experimental constraints are sparse in some spectral regions and above about $\mathrm{CO_2}$48, yet continua are extrapolated up to $\mathrm{CO_2}$49 and binary tables to $\mathrm{CO_2}$50. The MT_CKD-style split at $\mathrm{CO_2}$51 is stated to be suitable below roughly $\mathrm{CO_2}$52, but less robust at extreme pressure. Line mixing is not treated except implicitly through tuned far-wing corrections, so some high-pressure band-center features remain imperfect (Chaverot et al., 25 Aug 2025).

Within those boundaries, the intended applications are clear: Earth paleoclimate calculations with variable $\mathrm{CO_2}$53, early Mars and Venus studies, steam–$\mathrm{CO_2}$54 atmospheres on post-runaway or magma-ocean planets, and terrestrial exoplanets around M dwarfs. The paper’s broader methodological claim is that when atmospheres lie in the intermediate-composition regime—where broadener identity materially alters line wings and continua—SpeCT-generated mixed-gas correlated-$\mathrm{CO_2}$55 tables should be preferred to additive or online-mixed opacity methods (Chaverot et al., 25 Aug 2025).