Aeolus: Atmospheric Mapping, Wind, and Erosion

• Aeolus is a multifaceted research label covering Bayesian inversion codes for ultracool atmosphere mapping, ESA wind lidar missions, aerodynamic erosion, and benchmark datasets.
• In atmospheric mapping, Aeolus employs MCMC with Bayesian Information Criterion to retrieve spot geometries and brightness contrasts from rotational light curves, validated against planetary observations.
• In wind and erosion studies, Aeolus encompasses the ALADIN Doppler wind lidar for global wind profiling and models gas-induced erosion in protoplanetary and white-dwarf disks.

Searching arXiv for the relevant “Aeolus” papers and associated contexts. Aeolus is a research name used for several technically distinct entities. In the cited literature it denotes a Markov–Chain Monte Carlo code for mapping the top-of-the-atmosphere structure of brown dwarfs and other ultracool atmospheres from rotational light curves, the European Space Agency wind mission built around the Atmospheric LAser Doppler INstrument (ALADIN), a multi-structural flight delay dataset, a speech re-use prevention overlay, and, in disk-physics studies, the gas “wind” responsible for aeolian erosion of solids (Karalidi et al., 2015, Collaboration et al., 2023, Xu et al., 30 Oct 2025, Zhang et al., 2021, Rozner et al., 2019). Several of these usages are explicitly tied to wind, while others use the name for inversion, benchmarking, or security systems.

1. Aeolus as a Bayesian mapping code for ultracool atmospheres

Aeolus was introduced as a Markov–Chain Monte Carlo inversion code that maps the top-of-the-atmosphere structure of brown dwarfs and other ultracool atmospheres from time-resolved photometric light curves. It represents the top-of-the-atmosphere brightness field as a uniform background atmosphere plus a set of non-overlapping elliptical spots. In the original formulation, each spot is parameterized by longitude $l_i$, latitude $\phi_i$, angular size $s_i$, and contrast $f_i = I_i/I_{\rm bg}$, with a maximum number of spots $N_{\rm max}=5$. In the later Luhman 16AB application, the code was used in a slightly extended form with the number of spots free up to a maximum of 7 and selected via the Bayesian Information Criterion (Karalidi et al., 2015, Karalidi et al., 2016).

The forward model computes the disk-integrated flux as a function of rotational phase for a rotating sphere whose variability is produced only by rotation. In the Luhman 16AB formulation, the model flux is written schematically as

$$F_{\rm model}(t_k \mid \theta)=F_{\rm bg}(t_k \mid \theta)+\sum_{j=1}^{N_{\rm spot}} \Delta F_j(t_k \mid \theta),$$

with Gaussian errors,

$$\chi^2(\theta)=\sum_k \frac{[d_k-m_k(\theta)]^2}{\sigma_k^2},$$

and posterior

$$p(\theta|d)\propto \exp\left[-\frac{1}{2}\chi^2(\theta)\right].$$

The code uses uniform priors over physically reasonable ranges, a Gibbs sampler combined with a random-walk Metropolis-within-Gibbs scheme, multiple chains, burn-in removal, Gelman–Rubin convergence checks with $\hat R<1.2$, and BIC-based model selection (Karalidi et al., 2016).

A central feature of the code is its explicitly parametric treatment of the brightness distribution. This yields posterior distributions for spot geometry and contrast rather than a purely harmonic brightness map. The approach is therefore best understood as light-curve inversion under a low-dimensional spot prior, not as a general nonparametric imaging method.

Validation was performed on HST/WFC3 light curves of Jupiter, where independent imaging provides a ground truth. Aeolus accurately retrieved the properties of the major features of the jovian atmosphere such as the Great Red Spot and a major 5 $\mu$m hot spot, and it was described as the first mapping code validated on actual observations of a giant planet over a full rotational period (Karalidi et al., 2015).

2. Luhman 16AB and the mapping of evolving cloud structures

In "Maps of Evolving Cloud Structures in Luhman 16AB from HST Time-Resolved Spectroscopy" (Karalidi et al., 2016), Aeolus is the central tool used to convert time-resolved HST/WFC3 G141 and G102 light curves into quantitative two-dimensional maps of top-of-the-atmosphere inhomogeneities. The datasets were treated band-by-band and epoch-by-epoch: Luhman 16B was mapped in 2013 from G141 J and H bands and in 2014 from integrated G102 light curves, while Luhman 16A was mapped from the 2014 G102 data. The paper fit only the first complete rotation in each light curve because the atmosphere evolves even within a rotation.

For Luhman 16B, the rotation period was fixed to $\phi_i$0 hr, and Aeolus retrieved $\phi_i$1, consistent with earlier constraints $\phi_i$2 from Doppler imaging. For Luhman 16A, the rotation period was uncertain, and two cases were explored. With a 5 hr period, Aeolus found $\phi_i$3; with an 8 hr period, it retrieved $\phi_i$4. The inferred spot configuration depended on the assumed period, so the paper treated the inclination sensitivity as physically consequential rather than a minor nuisance parameter.

The retrieved maps contained three or four spots in the top-of-the-atmosphere of Luhman 16A and B. Surface coverage for Luhman 16A was $\phi_i$5, depending on an assumed rotational period of 5 hr or 8 hr, and for Luhman 16B it was $\phi_i$6, depending on the observational epoch. The brightness temperature of the spots of the best-fit models was $\phi_i$7 K hotter than the background top-of-the-atmosphere. For Luhman 16B in 2014, the temperature contrast was smaller, $\phi_i$8 K, while the inferred surface coverage increased to $\phi_i$9. The paper interpreted the hotter regions as areas of reduced cloud opacity, analogous to Jupiter’s 5 $s_i$0m hot spots.

A more flexible multi-contrast test was used to compare directly with the Doppler map of Crossfield et al. In that test, Aeolus retrieved four spots, including a large, cool spot with $s_i$1 K at low latitude. This agreed with the previously published Doppler map, which also showed a large low-latitude cool feature. However, the BIC of the multi-contrast model was worse than that of the single-contrast model, so the HST data statistically preferred the simpler single-component interpretation.

Temporal behavior was central to the paper’s interpretation. Slight changes in fitted phase windows altered the third spot, which the authors used as evidence for short-term evolution over roughly one rotation. Between 2013 and 2014, spot positions and contrasts changed substantially over $s_i$2 rotations. At the same time, a visually similar trough recurred near rotational phase $s_i$3 in 2013 HST J/H light curves, the 2014 HST G102 light curve, and some TRAPPIST $s_i$4 light curves. The paper referred to this recurrent feature as PPCS-1 and concluded that it was related to atmospheric structures rather than to an exoplanet transit (Karalidi et al., 2016).

3. Aeolus as the ESA Doppler wind-lidar mission

Aeolus was also the name of the European Space Agency wind mission that carried a single payload, ALADIN, the Atmospheric LAser Doppler INstrument. Launched on 22 August 2018, with nominal operations ending on 30 April 2023 and reentry on 28 July 2023, the mission provided global vertical profiles of horizontal wind in the troposphere and lower stratosphere (Collaboration et al., 2023).

ALADIN was the first Doppler wind lidar in space and the first European space lidar. It was a pulsed, frequency-stabilized ultraviolet Doppler wind lidar operating at 354.8 nm from a sun-synchronous orbit at roughly 320 km altitude. The telescope line of sight was 35° off nadir, corresponding to about $s_i$5-$s_i$6 zenith at the surface intersection. The system used a diode-pumped, injection-seeded Nd:YAG master-oscillator power-amplifier with frequency tripling to the ultraviolet, two redundant lasers denoted FM-A and FM-B, a repetition rate of 50.5 Hz, and a 1.5 m monostatic Cassegrain telescope. After a quarter-wave plate and beam expansion to roughly 36 mm at the telescope relay optics, telescope magnification of 41.7 produced a beam diameter in the atmosphere of about 0.92 m and divergence of about 18–20 $s_i$7rad, with a ground footprint of about 8 m at 320 km altitude.

The receiver separated atmospheric returns into Rayleigh and Mie channels. Rayleigh retrievals used molecular backscatter with an approximate 3.8 GHz FWHM backscatter spectrum at 355 nm and 293 K, while the Mie channel used particle backscatter with an approximate 50 MHz FWHM. Operationally, the measurement principle was Doppler shift of the backscattered light, conventionally expressed as

$s_i$8

These wind profiles were assimilated in operational numerical weather prediction by ECMWF, Deutscher Wetterdienst, Météo-France and others.

A defining issue of the mission was progressive loss of atmospheric backscatter signal. FM-A delivered about 65 mJ per pulse early in the mission but dropped to about 40 mJ by May 2019. ESA switched to FM-B in late June 2019; FM-B initially delivered about 67 mJ and was later tuned above 100 mJ, yet the atmospheric backscatter signal measured at the receiver still declined by more than 70% over three years of FM-B operation. This established the key diagnostic question of whether the dominant degradation was located in the emit path, the receive path, or both (Collaboration et al., 2023).

4. External calibration, geolocation, and wind-data intercomparison

A distinctive development in Aeolus research was the use of the Pierre Auger Observatory as an external calibration system for ALADIN. The Auger fluorescence detector, with ultraviolet sensitivity from roughly 310–410 nm, registered the side-scattered 354.8 nm laser pulses emitted from space. Over the mission, 16 Aeolus overpasses were recorded, and three clean overpasses—3 August 2019, 27 June 2020, and 17 July 2021—were used for detailed energy analysis. Geometric reconstruction employed standard shower-detector-plane methods and an improved monocular reconstruction constrained by the near-constant Aeolus pointing (Collaboration et al., 2023, Unger et al., 6 Aug 2025).

From these data, the pulse energies at the ALADIN telescope exit were reconstructed as

$s_i$9

Relative to 2019, the ground-based estimates gave $f_i = I_i/I_{\rm bg}$0 in 2020 and $f_i = I_i/I_{\rm bg}$1 in 2021, while the receiver-measured Rayleigh clear-air return decreased by $f_i = I_i/I_{\rm bg}$2 and $f_i = I_i/I_{\rm bg}$3, respectively. The small excess loss in the receiver signal was interpreted as additional degradation in the receive path, likely clipping at the field stop, whereas the dominant loss was attributed to optics specific to FM-B in the emit path. The later switch back to FM-A in late 2022 increased the receiver signal by a factor of 2.2, which reinforced that diagnosis (Collaboration et al., 2023, Unger et al., 6 Aug 2025).

The Auger reconstruction also constrained Aeolus pointing and exposed a geolocation bug. A systematic across-track offset of about 0.075° in longitude, or about 6.8 km at 10 km altitude, was traced to an incorrect combination of time stamps and time-system identifiers in the Level-1A geolocation processor. After a processor fix in version 7.12 (Baseline 14), the offset relative to Auger decreased to 0.8 km across-track. For 17 July 2021, Baseline 14, the inferred pointing accuracy was 0.06 km along-track and 0.82 km across-track, with 2$f_i = I_i/I_{\rm bg}$4 precision of 1.28 km along-track and 0.93 km across-track (Collaboration et al., 2023, Unger et al., 6 Aug 2025).

External validation also proceeded through the System for Analysis of Wind Collocations (SAWC), a multi-year archive and collocation software application for global 3D winds from Aeolus, sondes, aircraft, stratospheric superpressure balloons, and satellite-derived atmospheric motion vectors (Lukens et al., 2023). In SAWC, Aeolus appears as Level-2B horizontal line-of-sight winds in two principal observing modes: Rayleigh-clear, retrieved from molecular backscatter, and Mie-cloudy, retrieved from aerosol and cloud particle backscatter. The lidar looked off-nadir to the right of the sub-satellite track with incidence angle about $f_i = I_i/I_{\rm bg}$5, and HLOS winds were represented as positive away from the satellite.

For a one-year evaluation covering September 2019 to August 2020 and using Baseline 11 reprocessed Level-2B winds, SAWC applied recommended Aeolus quality controls. Mie-cloudy observations were rejected for $f_i = I_i/I_{\rm bg}$6 hPa or $f_i = I_i/I_{\rm bg}$7 m s$f_i = I_i/I_{\rm bg}$8. Rayleigh-clear observations were rejected for $f_i = I_i/I_{\rm bg}$9 hPa, $N_{\rm max}=5$0 m s$N_{\rm max}=5$1 for $N_{\rm max}=5$2 hPa, $N_{\rm max}=5$3 m s$N_{\rm max}=5$4 for $N_{\rm max}=5$5 hPa, $N_{\rm max}=5$6 km, or integration length $N_{\rm max}=5$7 km. Collocated reference winds were projected onto the Aeolus HLOS azimuth before statistical comparison.

The resulting statistics established the standard mode dependence of Aeolus performance. Rayleigh-clear versus aircraft gave $N_{\rm max}=5$8 and $N_{\rm max}=5$9 m s$$F_{\rm model}(t_k \mid \theta)=F_{\rm bg}(t_k \mid \theta)+\sum_{j=1}^{N_{\rm spot}} \Delta F_j(t_k \mid \theta),$$0; Rayleigh-clear versus sondes and AMVs also had $$F_{\rm model}(t_k \mid \theta)=F_{\rm bg}(t_k \mid \theta)+\sum_{j=1}^{N_{\rm spot}} \Delta F_j(t_k \mid \theta),$$1 with $$F_{\rm model}(t_k \mid \theta)=F_{\rm bg}(t_k \mid \theta)+\sum_{j=1}^{N_{\rm spot}} \Delta F_j(t_k \mid \theta),$$2–7 m s$$F_{\rm model}(t_k \mid \theta)=F_{\rm bg}(t_k \mid \theta)+\sum_{j=1}^{N_{\rm spot}} \Delta F_j(t_k \mid \theta),$$3. Mie-cloudy versus aircraft, AMV, and sonde data yielded $$F_{\rm model}(t_k \mid \theta)=F_{\rm bg}(t_k \mid \theta)+\sum_{j=1}^{N_{\rm spot}} \Delta F_j(t_k \mid \theta),$$4–0.98 and $$F_{\rm model}(t_k \mid \theta)=F_{\rm bg}(t_k \mid \theta)+\sum_{j=1}^{N_{\rm spot}} \Delta F_j(t_k \mid \theta),$$5–5.6 m s$$F_{\rm model}(t_k \mid \theta)=F_{\rm bg}(t_k \mid \theta)+\sum_{j=1}^{N_{\rm spot}} \Delta F_j(t_k \mid \theta),$$6, with biases near zero to $$F_{\rm model}(t_k \mid \theta)=F_{\rm bg}(t_k \mid \theta)+\sum_{j=1}^{N_{\rm spot}} \Delta F_j(t_k \mid \theta),$$7 m s$$F_{\rm model}(t_k \mid \theta)=F_{\rm bg}(t_k \mid \theta)+\sum_{j=1}^{N_{\rm spot}} \Delta F_j(t_k \mid \theta),$$8. The study therefore treated Mie-cloudy winds as more accurate and less noisy than Rayleigh-clear winds, while also documenting time-dependent Rayleigh degradation consistent with instrument signal loss (Lukens et al., 2023).

5. Aeolus as wind-driven erosion in protoplanetary and white-dwarf disks

In another line of work, Aeolus is not a spacecraft or code but the “wind” itself: the gas flow past solid bodies in disks. In protoplanetary-disk studies, aeolian erosion is a mechanical process in which the relative motion of sub-Keplerian gas past a solid body strips grains from the surface once aerodynamic forcing exceeds cohesion and, for large enough objects, self-gravity (Rozner et al., 2019). The threshold was expressed in terms of a critical velocity

$$F_{\rm model}(t_k \mid \theta)=F_{\rm bg}(t_k \mid \theta)+\sum_{j=1}^{N_{\rm spot}} \Delta F_j(t_k \mid \theta),$$9

and the erosion rate in terms of

$$\chi^2(\theta)=\sum_k \frac{[d_k-m_k(\theta)]^2}{\sigma_k^2},$$0

Under a minimum-mass-solar-nebula-like model, bodies in the $$\chi^2(\theta)=\sum_k \frac{[d_k-m_k(\theta)]^2}{\sigma_k^2},$$1-$$\chi^2(\theta)=\sum_k \frac{[d_k-m_k(\theta)]^2}{\sigma_k^2},$$2 m range were found to be highly susceptible to gas-drag aeolian erosion. For $$\chi^2(\theta)=\sum_k \frac{[d_k-m_k(\theta)]^2}{\sigma_k^2},$$3 cm surface grains, erosion is mostly effective inside about 2.7 au. At 1 au, a 1 m body has an erosion timescale of order $$\chi^2(\theta)=\sum_k \frac{[d_k-m_k(\theta)]^2}{\sigma_k^2},$$4 yr, much shorter than typical disk lifetimes, and bodies with initial radii $$\chi^2(\theta)=\sum_k \frac{[d_k-m_k(\theta)]^2}{\sigma_k^2},$$5-$$\chi^2(\theta)=\sum_k \frac{[d_k-m_k(\theta)]^2}{\sigma_k^2},$$6 cm are eroded efficiently down to a final radius $$\chi^2(\theta)=\sum_k \frac{[d_k-m_k(\theta)]^2}{\sigma_k^2},$$7-20 cm. The paper defined this as an aeolian-erosion barrier: rather than permitting growth through the metre to hundreds-of-metres range, gas wind grinds such objects down to decimetre pebbles (Rozner et al., 2019).

The same mechanism was then applied to white-dwarf debris disks. There the headwind from sub-Keplerian gas can rapidly destroy sub-kilometre solids and shape the size distribution of debris. The analysis concluded that solid bodies smaller than $$\chi^2(\theta)=\sum_k \frac{[d_k-m_k(\theta)]^2}{\sigma_k^2},$$8 km will be eroded within the short disk lifetime, and that aeolian erosion is the dominant destructive process for objects with radius $$\chi^2(\theta)=\sum_k \frac{[d_k-m_k(\theta)]^2}{\sigma_k^2},$$9 cm at distances $$p(\theta|d)\propto \exp\left[-\frac{1}{2}\chi^2(\theta)\right].$$0 from the white dwarf. The paper positioned aeolian erosion as the main destructive pathway linking fragmentational collisions of large objects with sublimation of the smallest objects and Poynting–Robertson drag, thereby contributing to the production of polluted white dwarfs (Rozner et al., 2020).

A related extension considered wind erosion and transport on $$p(\theta|d)\propto \exp\left[-\frac{1}{2}\chi^2(\theta)\right].$$1 to $$p(\theta|d)\propto \exp\left[-\frac{1}{2}\chi^2(\theta)\right].$$2 km planetesimals in the protosolar nebula. Drag from the headwind was found to be strong enough to loft cm and smaller sized particles off the surface of a 10 km diameter asteroid in the inner solar system, and micron sized particles off the surface of a 10 km diameter object in the Transneptunian region. However, cohesion could be overcome in the inner solar system but not in the outer solar system, so in the outer system impact-driven liberation of grains becomes essential. Using crater-ejecta scaling, the paper estimated that impacts from particles in the headwind lead to erosion of mass rather than accretion for planetesimals below about 6 km in diameter, and it suggested that the Kuiper Belt Object Arrokoth’s smooth undulating terrain could be explained by disk winds only during an epoch of high particle flux and low wind velocity (Quillen et al., 2023).

6. Other technical uses: structured data and speech freshness

Outside astronomy and planetary science, Aeolus has also been used to name a structured-data benchmark. "Aeolus: A Multi-structural Flight Delay Dataset" (Xu et al., 30 Oct 2025) is a multi-structural flight delay dataset built from U.S. flight operations and global weather data for 2016–2024. It contains a tabular flight-level dataset with rich operational, airport, and meteorological features for 54.67M flights across 320 airports, a flight chain modality modeling sequential rotations of the same aircraft over a 24-hour period, and a flight network graph modality encoding delay propagation through shared aircraft, crew, and airport resource connections. The dataset is designed around strict temporal splitting and leakage prevention, and it supports regression, classification, probabilistic prediction, temporal structure modeling, and graph learning. On the reported baselines, FTTransformer was best on arrival-delay regression with $$p(\theta|d)\propto \exp\left[-\frac{1}{2}\chi^2(\theta)\right].$$3 and $$p(\theta|d)\propto \exp\left[-\frac{1}{2}\chi^2(\theta)\right].$$4, TabulaRNN yielded top classification accuracy of about 0.77 for both arrival and departure delays, and graph augmentation improved an AFM baseline from $$p(\theta|d)\propto \exp\left[-\frac{1}{2}\chi^2(\theta)\right].$$5 to $$p(\theta|d)\propto \exp\left[-\frac{1}{2}\chi^2(\theta)\right].$$6 with VGAE embeddings (Xu et al., 30 Oct 2025).

A further usage appears in voice security. AEOLUS, in "Practical Speech Re-use Prevention in Voice-driven Services" (Zhang et al., 2021), is a software-only security overlay that embeds a dynamic acoustic nonce at the time of user interaction and detects the embedded nonce in the recorded speech to ensure freshness. The nonce is generated digitally, encoded by BFSK, and embedded acoustically with a frequency-hopping spread-spectrum design chosen to balance robustness and perceptual non-disruptiveness. Experimental results reported $$p(\theta|d)\propto \exp\left[-\frac{1}{2}\chi^2(\theta)\right].$$7 FRR at $$p(\theta|d)\propto \exp\left[-\frac{1}{2}\chi^2(\theta)\right].$$8 FAR for speech re-use prevention up to a distance of 4 meters in three real-world environments with different background noise levels, and a user study with 120 participants found that the acoustic nonce did not degrade overall user experience for $$p(\theta|d)\propto \exp\left[-\frac{1}{2}\chi^2(\theta)\right].$$9 of speech samples, on average (Zhang et al., 2021).

These non-astronomical uses are technically independent of both the ESA mission and the ultracool-atmosphere mapping code. A plausible implication is that, within contemporary research literature, Aeolus functions as a cross-domain label for systems concerned with propagation, structure, or freshness under realistic dynamical constraints rather than as a single canonical object.