ATMO: Multi-Domain Atmospheric & Robotic Models

• ATMO is a one-dimensional, radiative–convective atmospheric model that computes self-consistent temperature–pressure profiles, chemical abundances, and spectra for bodies like exoplanets and brown dwarfs.
• It underpins exoplanet forward models and Bayesian retrievals by integrating advanced opacity treatments and non-equilibrium chemistry to predict observable spectral features.
• Beyond atmospheric science, ATMO’s framework extends to high-energy astroparticle detectors and morphing aerial robotics, highlighting its multifaceted applications in both astrophysical and engineering domains.

ATMO most commonly denotes a one-dimensional, plane-parallel radiative–convective atmosphere model used to compute self-consistent temperature–pressure structures, chemical abundances, and spectra for exoplanets, brown dwarfs, and giant exoplanets. In the literature represented here, the name also appears in the high-energy astroparticle context through the AtmoHEAD workshop on atmospheric monitoring, and in robotics as the Aerially Transforming Morphobot, a system for dynamic ground–aerial transition (Phillips et al., 2020, Bernlöhr et al., 2014, Mandralis et al., 1 Mar 2025).

1. Scope of the term and adjacent meanings

In high-energy astroparticle instrumentation, the atmosphere is described as “an integral component of many high-energy astroparticle detectors.” Imaging atmospheric Cherenkov telescopes and cosmic-ray extensive air shower detectors use the atmosphere “as a giant calorimeter where cosmic rays and gamma rays deposit their energy and initiate EASs”; it is also “the medium through which the resulting Cherenkov light propagates.” The AtmoHEAD 2013 workshop was convened because “uncertainties in real-time atmospheric conditions and in the fixed atmospheric models typically dominate all other systematic errors,” and because upgraded facilities such as H.E.S.S.-II and MAGIC-II and future facilities such as CTA and JEM-EUSO were expected to reduce statistical uncertainties enough that “the atmosphere” would remain “the limiting factor in the determination of astroparticle spectra” (Bernlöhr et al., 2014).

That usage is distinct from ATMO as an atmospheric-physics code. It is also distinct from ATMO in robotics, where the acronym denotes the Aerially Transforming Morphobot, a ground–aerial robot that transforms near the ground and exploits near-ground aerodynamics during morphing (Mandralis et al., 1 Mar 2025). The shared acronym therefore spans at least three technical domains: atmospheric monitoring for detectors, radiative–convective atmosphere modeling, and morphing aerial robotics.

2. Core architecture of the atmospheric model

ATMO is described as “a one-dimensional, plane-parallel radiative–convective–chemical equilibrium model” that solves hydrostatic equilibrium, radiative–convective energy balance, and either chemical equilibrium or kinetics. In one formulation, the monochromatic radiative-transfer equation is written as

$$\mu \frac{dI_\nu(\tau_\nu,\mu)}{d\tau_\nu}=I_\nu(\tau_\nu,\mu)-S_\nu(\tau_\nu),$$

with $S_\nu$ reducing to the Planck function in LTE. In transmission geometry, ATMO also uses the formal relation

$$R_{\rm eff}^2(\lambda)=R_{p,\mathrm{opq}}^2+2\int_{b=R_{p,\mathrm{opq}}}^{R_{\rm TOA}}[1-\exp(-\tilde{\tau}(b,\lambda))]\,b\,db,$$

so that wavelength-dependent effective radius follows from the total slant optical depth along the limb (Goyal et al., 2017).

Chemical equilibrium is computed by minimizing the total Gibbs free energy subject to element-conservation constraints,

$G_{\rm tot}=\sum_i x_i g_i(T,P),$

or, equivalently, through mass-action relations such as

$K_p(T)=\exp[-\Delta G^\circ(T)/(RT)].$

For retrieval-style exoplanet applications, ATMO was also adapted as “a one-dimensional, line-by-line radiative-transfer and atmospheric-chemistry code” for Bayesian inference, with parameterized temperature–pressure profiles and Gaussian-error likelihoods of the form

$$\ln L=-\frac12\sum_i\left[\frac{(D_i-M_i(\theta))^2}{\sigma_i^2}+\ln(2\pi\sigma_i^2)\right]$$

(Fu et al., 2020).

Opacity treatment is a defining feature. ATMO uses line-by-line cross sections or, more commonly for speed, the correlated-$k$ method. Its opacity database draws on “the newest high-temperature line lists” from ExoMol, HITEMP, VALD, and HITRAN; includes H$_2$–H$_2$ and H$_2$–He collision-induced absorption; and may include Rayleigh scattering, parameterized haze, and grey cloud scattering opacity. In the hot-Jupiter transmission grid, opacities were pre-computed on a $S_\nu$0 grid in $S_\nu$1–$S_\nu$2 from $S_\nu$3–$S_\nu$4 K and $S_\nu$5–$S_\nu$6 Pa, then combined “on-the-fly” via the random-overlap method with resorting and rebinning (Goyal et al., 2017).

Benchmarking against Exo-REM and petitCODE showed that opacity and line-shape choices are not secondary details. Differences between spectra calculated with HITRAN and ExoMol “exceed the expected uncertainties of future JWST observations,” and uncertainties on alkali and molecule line shape induce spectral effects “also larger than the expected JWST uncertainties.” The same benchmark identified PH$S_\nu$7, NH$S_\nu$8, CO sub-bands, and alkali far-wing treatments as persistent sources of inter-model differences (Baudino et al., 2017).

3. ATMO 2020 and the cool brown-dwarf and giant-exoplanet grids

ATMO 2020 was introduced as “a new set of solar metallicity atmosphere and evolutionary models for very cool brown dwarfs and self-luminous giant exoplanets.” The atmosphere models were generated with the 1D radiative–convective equilibrium code ATMO and used as surface boundary conditions to calculate the interior structure and evolution of $S_\nu$9–$$R_{\rm eff}^2(\lambda)=R_{p,\mathrm{opq}}^2+2\int_{b=R_{p,\mathrm{opq}}}^{R_{\rm TOA}}[1-\exp(-\tilde{\tau}(b,\lambda))]\,b\,db,$$0 objects. Two improvements were emphasized. First, “the use of a new H-He equation of state including ab initio quantum molecular dynamics calculations has raised the mass by $$R_{\rm eff}^2(\lambda)=R_{p,\mathrm{opq}}^2+2\int_{b=R_{p,\mathrm{opq}}}^{R_{\rm TOA}}[1-\exp(-\tilde{\tau}(b,\lambda))]\,b\,db,$$1-$$R_{\rm eff}^2(\lambda)=R_{p,\mathrm{opq}}^2+2\int_{b=R_{p,\mathrm{opq}}}^{R_{\rm TOA}}[1-\exp(-\tilde{\tau}(b,\lambda))]\,b\,db,$$2 at the stellar-substellar boundary and has altered the cooling tracks around the hydrogen and deuterium burning minimum masses.” Second, updated molecular opacities “lead to warmer atmospheric temperature structures,” changing both cooling curves and predicted spectra (Phillips et al., 2020).

ATMO 2020 also introduced “significant improvement for the treatment of the collisionally broadened potassium resonance doublet,” and generated “three different grids of model simulations, one using equilibrium chemistry and two using non-equilibrium chemistry due to vertical mixing, all three computed self-consistently with the pressure-temperature structure of the atmosphere.” Phillips et al. further highlighted “how the $$R_{\rm eff}^2(\lambda)=R_{p,\mathrm{opq}}^2+2\int_{b=R_{p,\mathrm{opq}}}^{R_{\rm TOA}}[1-\exp(-\tilde{\tau}(b,\lambda))]\,b\,db,$$3-$$R_{\rm eff}^2(\lambda)=R_{p,\mathrm{opq}}^2+2\int_{b=R_{p,\mathrm{opq}}}^{R_{\rm TOA}}[1-\exp(-\tilde{\tau}(b,\lambda))]\,b\,db,$$4 flux window can be used to calibrate vertical mixing in cool T-Y spectral type objects” (Phillips et al., 2020).

In the ATMO 2020 framework as used for ultracool dwarfs, the “NEQ Weak” grid is cloudless, uses solar metallicity as the baseline, implements non-equilibrium chemistry for H$$R_{\rm eff}^2(\lambda)=R_{p,\mathrm{opq}}^2+2\int_{b=R_{p,\mathrm{opq}}}^{R_{\rm TOA}}[1-\exp(-\tilde{\tau}(b,\lambda))]\,b\,db,$$5O, CO, CO$$R_{\rm eff}^2(\lambda)=R_{p,\mathrm{opq}}^2+2\int_{b=R_{p,\mathrm{opq}}}^{R_{\rm TOA}}[1-\exp(-\tilde{\tau}(b,\lambda))]\,b\,db,$$6, CH$$R_{\rm eff}^2(\lambda)=R_{p,\mathrm{opq}}^2+2\int_{b=R_{p,\mathrm{opq}}}^{R_{\rm TOA}}[1-\exp(-\tilde{\tau}(b,\lambda))]\,b\,db,$$7, N$$R_{\rm eff}^2(\lambda)=R_{p,\mathrm{opq}}^2+2\int_{b=R_{p,\mathrm{opq}}}^{R_{\rm TOA}}[1-\exp(-\tilde{\tau}(b,\lambda))]\,b\,db,$$8, and NH$$R_{\rm eff}^2(\lambda)=R_{p,\mathrm{opq}}^2+2\int_{b=R_{p,\mathrm{opq}}}^{R_{\rm TOA}}[1-\exp(-\tilde{\tau}(b,\lambda))]\,b\,db,$$9 through a relaxation scheme parameterized by an eddy diffusion coefficient, adopts updated ExoMol line lists for CH$G_{\rm tot}=\sum_i x_i g_i(T,P),$0 and NH$G_{\rm tot}=\sum_i x_i g_i(T,P),$1, includes H$G_{\rm tot}=\sum_i x_i g_i(T,P),$2–H$G_{\rm tot}=\sum_i x_i g_i(T,P),$3 and H$G_{\rm tot}=\sum_i x_i g_i(T,P),$4–He CIA and improved pressure broadening for Na I and K I, and uses the hydrogen/helium EOS of Chabrier et al. (2019). That version was described as “suited to T and Y dwarfs, where clouds have largely rained out” (Sanghi et al., 2023).

An earlier physical interpretation for cloudless ATMO models was developed in the context of T and Y dwarfs. Tremblin et al. used ATMO with equilibrium and out-of-equilibrium chemistry and found that “the spectra of Y dwarfs can be accurately reproduced with a cloudless model if vertical mixing and NH$G_{\rm tot}=\sum_i x_i g_i(T,P),$5 quenching are taken into account.” T-dwarf spectra still retained reddening relative to cloudless models, and this reddening could be reproduced “by slightly reducing the temperature gradient in the atmosphere.” The proposed explanation was “the onset of fingering convection, triggered by the destabilizing impact of condensation of very thin dust” (Tremblin et al., 2015).

4. Observational performance, systematic deviations, and ATMO 2020++

A large empirical stress test was provided by the Hawaii Infrared Parallax Program, which used optical-to-mid-IR SEDs for 1054 ultracool dwarfs to characterize ATMO 2020 systematics as a function of spectral type and position in the near-IR color–magnitude diagram. The study found “the greatest discrepancies between atmospheric and evolutionary model-derived $G_{\rm tot}=\sum_i x_i g_i(T,P),$6 (up to 800 K) and radii (up to 2.0 $G_{\rm tot}=\sum_i x_i g_i(T,P),$7) at the M/L transition boundary.” At the M/L transition, $G_{\rm tot}=\sum_i x_i g_i(T,P),$8 reached up to $G_{\rm tot}=\sum_i x_i g_i(T,P),$9 K, $K_p(T)=\exp[-\Delta G^\circ(T)/(RT)].$0 up to $K_p(T)=\exp[-\Delta G^\circ(T)/(RT)].$1, and $K_p(T)=\exp[-\Delta G^\circ(T)/(RT)].$2 ranged from $K_p(T)=\exp[-\Delta G^\circ(T)/(RT)].$3 dex for blue M/L dwarfs to $K_p(T)=\exp[-\Delta G^\circ(T)/(RT)].$4 dex for red M/L dwarfs. Cloudless ATMO 2020 and BT-Settl both showed a “pile-up” of best-fit objects at $K_p(T)=\exp[-\Delta G^\circ(T)/(RT)].$5–$K_p(T)=\exp[-\Delta G^\circ(T)/(RT)].$6 K with nearly no fits at $K_p(T)=\exp[-\Delta G^\circ(T)/(RT)].$7–$K_p(T)=\exp[-\Delta G^\circ(T)/(RT)].$8 K or $K_p(T)=\exp[-\Delta G^\circ(T)/(RT)].$9–$$\ln L=-\frac12\sum_i\left[\frac{(D_i-M_i(\theta))^2}{\sigma_i^2}+\ln(2\pi\sigma_i^2)\right]$$0 K, which was interpreted as insufficient treatment of condensate opacity in the $$\ln L=-\frac12\sum_i\left[\frac{(D_i-M_i(\theta))^2}{\sigma_i^2}+\ln(2\pi\sigma_i^2)\right]$$1–$$\ln L=-\frac12\sum_i\left[\frac{(D_i-M_i(\theta))^2}{\sigma_i^2}+\ln(2\pi\sigma_i^2)\right]$$2 K regime (Sanghi et al., 2023).

The same work proposed explicit remedies: “Introduce parameterized cloud layers,” “revisit vertical mixing prescriptions to allow thicker residual clouds through L/T transition,” and “incorporate updated optical constants and grain size distributions for Fe and MgSiO$$\ln L=-\frac12\sum_i\left[\frac{(D_i-M_i(\theta))^2}{\sigma_i^2}+\ln(2\pi\sigma_i^2)\right]$$3 condensates.” For mid-T spectra, underestimation of CH$$\ln L=-\frac12\sum_i\left[\frac{(D_i-M_i(\theta))^2}{\sigma_i^2}+\ln(2\pi\sigma_i^2)\right]$$4 and NH$$\ln L=-\frac12\sum_i\left[\frac{(D_i-M_i(\theta))^2}{\sigma_i^2}+\ln(2\pi\sigma_i^2)\right]$$5 band strengths was taken to hint at incomplete line lists or missing CIA opacities, with a recommendation to “fold in the latest ExoMol methane/hydride data and revisit H$$\ln L=-\frac12\sum_i\left[\frac{(D_i-M_i(\theta))^2}{\sigma_i^2}+\ln(2\pi\sigma_i^2)\right]$$6–H$$\ln L=-\frac12\sum_i\left[\frac{(D_i-M_i(\theta))^2}{\sigma_i^2}+\ln(2\pi\sigma_i^2)\right]$$7 collision-induced absorption at low $$\ln L=-\frac12\sum_i\left[\frac{(D_i-M_i(\theta))^2}{\sigma_i^2}+\ln(2\pi\sigma_i^2)\right]$$8” (Sanghi et al., 2023).

JWST/NIRSpec observations of very young benchmark brown dwarfs exposed a different failure mode. When cloudless ATMO models were matched to $$\ln L=-\frac12\sum_i\left[\frac{(D_i-M_i(\theta))^2}{\sigma_i^2}+\ln(2\pi\sigma_i^2)\right]$$9–$k$0 spectra of TWA 28, TWA 27A, and TWA 27B, they failed to reproduce the depth and shape of the $k$1 H$k$2O band, the FeH band at $k$3, the VO band at $k$4, and several alkali-line and H-band gravity-sensitive features. Both ATMO and BT-Settl predicted a prominent methane $k$5 fundamental band near $k$6 in the $k$7 K L6 atmosphere of TWA 27B, but “JWST/NIRSpec observations of TWA 27B show no detectable CH$k$8 absorption at $k$9.” The authors suggested that “the L/T transition of very young dwarfs starts at later spectral types than for older brown dwarfs” (Manjavacas et al., 2024).

ATMO-2020 models with strong non-equilibrium chemistry also performed well on benchmark eclipsing and directly imaged objects. For LHS 6343 C, the NEQ-strong grid gave “the best overall fit to the full SED” with $_2$0 and $_2$1 K under a Gaia-constrained distance, while a semi-empirical integration of the observed and modelled SED yielded $_2$2 K from the Stefan–Boltzmann law (Frost et al., 2024). For HR 2562 B, the ATMO fit to the full NIR+MIRI SED gave $_2$3 K, $_2$4, $_2$5, $_2$6, and $_2$7 when a Gaussian prior on mass was used; in that study, ATMO fit better than ExoREM and supported a near cloud-free atmosphere (Godoy et al., 2024).

The ATMO 2020++ suite extended the framework to very cold Y dwarfs with a “semi-empirical P–T profile,” a “PH$_2$8-free grid,” updated CH$_2$9, H$_2$0O, NH$_2$1, CO, and CO$_2$2 opacities, updated CIA, Allard et al. (2016) K I far wings, a correlated-$_2$3 approach with ODF sampling over $_2$4 wavelength bins, and “full treatment of scattering” (Leggett et al., 5 Sep 2025). In that regime, the absolute $_2$5 magnitude was found to be an excellent proxy for $_2$6, and the ratio of the $_2$7 flux to the $_2$8–$_2$9 flux became strongly gravity sensitive (Leggett et al., 2024). Applied to WD 0806–661 B, ATMO 2020++ gave a good fit across the observed spectral energy distribution except at the shortest near-infrared wavelengths, and produced atmospheric parameters consistent with evolutionary models, thereby resolving a previously reported discrepancy between atmospheric retrievals and evolution calculations (Leggett et al., 2 Jun 2026).

5. Exoplanet forward models and retrieval applications

For hot Jupiters, Goyal et al. used ATMO to build a large forward-model grid of transmission spectra for 117 planets. The grid adopted an isothermal limb temperature, equilibrium chemistry with rainout, 50 vertical levels from $_2$0 to $_2$1 bar, and five varied parameters: temperature, metallicity, C/O ratio, haze factor, and cloud factor. The resulting five-dimensional space produced “$_2$2 spectra,” or 3920 per planet, and the entire grid was made publicly available and directly compatible with PandExo for JWST observation planning (Goyal et al., 2017).

That grid isolated two transition behaviors. First, there is “a transition value for the metallicity between 10 and 50 times solar, which leads to substantial changes in the transmission spectra.” Second, the C/O transition from H$_2$3O-dominated to carbon-species-dominated infrared spectra is temperature dependent, ranging from $_2$4 at $_2$5 K to $_2$6–$_2$7 at $_2$8 K. HCN and C$_2$9H$S_\nu$00 features, especially in the $S_\nu$01–$S_\nu$02 region, were highlighted as diagnostics for metallicity and C/O with JWST (Goyal et al., 2017).

ATMO has also been used as a retrieval engine on specific exoplanets. For WASP-76b, ATMO was applied to both transit and eclipse spectra as a Bayesian retrieval code. The transmission retrieval returned a cloud-free equilibrium-chemistry fit with reduced $S_\nu$03, and the combined analysis found TiO and H$S_\nu$04O absorption in the transit spectrum, a strong CO emission feature in Spitzer’s $S_\nu$05 band, and a dayside inversion from $S_\nu$06 K at $S_\nu$07 bar to $S_\nu$08 K at $S_\nu$09 mbar. The ATMO retrieval and self-consistent PHOENIX forward models agreed on the presence of “a thermal inversion driven by strong UV/optical absorbers (TiO, metals)” and on “muted water signatures in emission due to thermal dissociation at low pressures” (Fu et al., 2020).

For HAT-P-18b, a free-chemistry ATMO retrieval on JWST NIRISS/SOSS data treated H$S_\nu$10O, CH$S_\nu$11, CO, and CO$S_\nu$12 as free constant-with-altitude mixing ratios, together with a parameterized cloud deck and haze slope. The retrieved abundances were

$S_\nu$13

The methane abundance was therefore “$S_\nu$14 orders of magnitude lower than that of solar composition.” The Bayesian evidence difference was

$S_\nu$15

in favor of the model including CH$S_\nu$16, which was described as “moderate” evidence, even though the spectrum did not display clearly identifiable methane absorption features. The study concluded that vertical mixing and photochemistry are required to remove methane relative to simple equilibrium predictions (Fu et al., 2022).

6. ATMO in morphing aerial robotics

In robotics, ATMO denotes “An Aerially Transforming Morphobot for Dynamic Ground-Aerial Transition.” The system is a $S_\nu$17 kg morphobot that “reuses the same four ‘wheel–thruster’ appendages for both quadrotor flight and differential-drive locomotion.” Its actuation architecture is summarized as “1 tilt + 4 thrust + 2 drive,” replacing the 12 separate posture actuators of an earlier platform (Mandralis et al., 1 Mar 2025).

The robot’s defining maneuver is a “dynamic wheel landing” with three phases: traditional quadrotor flight, morphing flight during descent, and a near-ground “morpho-transition.” A six-axis robotic arm and load-cell study showed that the normalized thrust coefficient

$S_\nu$18

increases monotonically as $S_\nu$19 for $S_\nu$20, peaking at $S_\nu$21–$S_\nu$22 when $S_\nu$23 m, while at $S_\nu$24 it drops below unity to $S_\nu$25 with large thrust fluctuations. The maximum ground effect, about $S_\nu$26 extra thrust, occurs at $S_\nu$27. ATMO used a model-predictive controller that blended a flight-phase cost and a transition-phase cost so that “vertical control is sacrificed near the ground, but attitude terms” remain high; experimentally it landed on its wheels with $S_\nu$28, exceeding the critical angle $S_\nu$29 away from the ground, while keeping maximum mean normalized thrust near $S_\nu$30 (Mandralis et al., 1 Mar 2025).

A later extension added passive wake vectoring. In that system, each thruster-wheel module is paired with a fixed deflector, and the total vertical thrust is written as

$S_\nu$31

with normalized thrust and recovery ratio

$S_\nu$32

For Deflector 2, the reported values were $S_\nu$33 and peak $S_\nu$34 near $S_\nu$35. Full-system hover tests gave a maximum thrust of $S_\nu$36 kgf and “recovering up to 40 % of thrust that would otherwise be zero in extreme tilt.” The passive vectoring increased the feasible hover tilt from $S_\nu$37 without deflectors to $S_\nu$38 with Deflector 2, a $S_\nu$39 improvement (Mandralis et al., 4 Dec 2025).

Across these domains, ATMO denotes either a physically detailed atmosphere-modeling framework or a mechanically and aerodynamically specialized morphobot. In astrophysics and planetary science, the atmospheric code has evolved from 1D radiative–convective equilibrium and equilibrium chemistry to non-equilibrium chemistry, updated alkali line profiles, and semi-empirical non-adiabatic structures in ATMO 2020 and ATMO 2020++; in robotics, the acronym identifies a platform whose central technical problem is the preservation or recovery of vertical thrust during transformation (Phillips et al., 2020, Mandralis et al., 4 Dec 2025).