Decomposing Titan’s far-infrared Haze B feature with PCA and NMF analysis

(2026)

Authors:

Joshua S Ford, Nicholas A Teanby, Patrick GJ Irwin, Conor A Nixon, Lucy Wright

Abstract:

During its flyby of Titan in 1980, Voyager 1 unveiled an atmosphere thick with an opaque, orange haze that completely obscured the surface, and provide  the first close-up images of its vertical layering (Smith et al. 1981, Hanel et al 1981). Subsequent observations from the Cassini-Huygens mission (Flasar et al. 2004) expanded this view, revealing a world dominated by photochemical hydrocarbons and nitriles with lakes of methane  (Stofan et al. 2007, Mastrogiuseppe et al. 2019), tholin-like organic sand (Lorenz et al. 2006), and seasonally evolving ice clouds (Jennings et al. 2012, West et al. 2016) as seen in Figure 1. While recent observations and laboratory studies (Anderson et al. 2011, Chatain et al. 2020) have provided greater insights into the physical properties of these aerosols and how they form, their composition and complexity remain a mystery.Figure 1: Image taken by Cassini Imaging Science Subsystem (Credit: NASA/JPL-Caltech/Space Science Institute) showing a large ice cloud possibly made of HCN at 300km in Titan’s south pole, 2012 (West et. 2016, Vinatier et al. 2018)In the upper atmosphere, nitrogen and methane are photodissociated by UV radiation and energetic particles to produce ions which act as embryos for the growth of large organic molecules (Vuitton et al. 2024). As these molecules sink through the atmosphere, they recombine, coagulate, and accumulate into larger aerosol particles, onto which trace species can condense, forming both photochemical hazes and stratospheric ice clouds (Vuitton et al. 2024). Cassini CIRS (Composite Infrared Spectrometer) far infra-red spectra (FP1) exhibit four types of hazes: Haze 0, Haze A, Haze B (otherwise known as the “Haystack”) and Haze C (de Kok et al. 2007). While Haze 0 is present throughout the CIRS spectral range and affects the spectral continuum, Haze A, B and C appear as broad features in the far-infrared range. Relatively little is known about these hazes, making their features difficult to fit and estimate. In addition, their signatures overlap with H2O, C4H2, C2N2 and CH4 rotational lines, complicating retrievals of these gases (Sylvestre et al.2017).  Among these hazes, Haze B exhibits the strongest spectral signature. Anderson et al. 2018 suggested that the composition must be a mixture of more than one chemical compound due to its magnitude, breadth and opacity. Haze B is observed to only be present at the winter poles, forming and dissipating with the changing seasons, most likely caused by reduced sunlight and temperature (Jennings et al. 2012a,b , Anderson et al 2018).To enable accurate fitting of water features, Ford et al. (in review) retrieved an effective spectral cross-section of Cassini CIRS FP1 spectra between 147-257cm-1 of 156 FIRNADCMP 0.5cm-1 observations (Figure 2) across different latitudes and times (see also Ford et al. 2025). This was achieved by scaling gaussian basis functions to fit Haze A, B and C (and any other unknown aerosols) in the spectra baselines using the NEMESIS radiative transfer code (Irwin et al. 2008). Previous aerosol cross-sections did not account for latitude or time variation and therefore this technique empirically and agnostically modelled the changing baseline.  In this study, we decomposed those 156 effective spectral cross-sections and extrapolated unique Haze B cross-sections for latitudes of -89° to 88° from June 2004 to April 2017.  We used principal component analysis to determine the number of complete hazes present in the spectral range, finding that Haze B accounts for 98% of the observed variation. We then applied non-negative matrix factorisation to seperate the spectra into two unique and stable components: one representing Haze B, and a second representing a mixture of other haze contributions, along with numerical and spectral noise.Figure 2: Effective spectral cross-section of all 156 Cassini CIRS FIRNADCMP 0.5cm-1 observations before decomposition. Each colour represents a different observation. The plot shows the variation extent of the Haze B feature at ~220cm-1. Using the maximum Haze B cross-section of each observation as proxy, we find a large increase at the winter poles with the increase during northern spring being nearly twice that of northern winter, consistent with previous investigations. We also find Haze B extends to 60°, different to 70° proposed by Anderson et al. 2018. The results also give an insight into the time of formation/dispersion of Haze B at the poles. We see that Haze B at the south pole forms around 2013, reaching its peak during the summer solstice. The final dissipation of Haze B at the north pole cannot be determined due to limited data. ReferencesAnderson, C.M. et al. (2011), Icarus,  212.2, 762-778. DOI: 10.1016/j.pss.2010.10.009Anderson, C.M. et al. (2018), Organic Ices in Titan’s Stratosphere in Space Science Reviews, 214.8, 125  DOI: 10.1007/s11214-018-0559-5Chatain, A.  et al. (2020), Icarus, 345, 113741. DOI: 10.1016/j.icarus/2020.113741Coustenis, A. et al. (1999), Planet Space Science, 47, 1305-1329. DOI:  10.1016/S0032-0633(99)00053-7de Kok, R. et al. (2007), Icarus, 191, 223. DOI:10.1016/j.icarus.2007.04.003Flasar, F.M. et al. (2004), Space Science Reviews, 115, 169–297. DOI: 10.1007/s11214-004-1454-9Ford, J.S. et al. (2025),  EGU General Assembly 2025, Vienna, Austria, EGU25-3741. DOI: 10.5194/egusphere-egu25-3741Ford, J.S. et al. In review. Titan’s Stratospheric Water: Latitudinal and Seasonal Variation from Cassini CIRS Data and Implications for External Oxygen Sources. PSJHanel, R.A. et al. (1981), Science, 212, 192–200. DOI: 10.1126/science.212.4491.192Irwin, P.G.J et al. (2008), JQSRT, 109, 1136. DOI: 10.1016/j.jqsrt.2007.11.006Jennings, D.E. et al. (2012), The Astrophysical Journal Letters, 754, L3. DOI: 10.1088/2041-8205/754/1/L3Khanna, R.K. (2005), Icarus, 178,165-170. doi:10.1016/j.icarus.2005.03.011Lorenz, R. et al. (2006), Science, 312, 724–727. DOI: 10.1126/science.1123257Mastrogiuseppe, M. et al. (2019), Nature Astronomy, 3, 535, DOI: 10.1038/s41550-019-0714-2Samuelson, R.E. Clouds and aerosols of Titan’s atmosphere, in The Atmospheres of Saturn and Titan. Proc.Int. Workshop, vol. ESA SP-241 (1985)Smith, B.A. et al. (1981), Science, 212, 163–191. DOI: 10.1126/science.212.4491.163Stofan, E.R. et al. (2007), Nature, 445, 61–64. DOI: 10.1038/nature05438Sylvestre, M. et al. (2017), A&A, 609:A64. DOI: 10.1051/0004-6361/201630255Vinatier, S. et al. (2018),  Icarus, 310, 89-104. DOI: 10.1016/j.icarus.2017.12.040Vuitton, V. et al. (2024), Chapter 6:Titan’s Atmospheric Structure, Composition, Haze, and Dynamics in Titan after Cassini–Huygens, COSPAR Scientific Symposium Series.West, R.A. et al, (2016), Icarus, 270, 399-408. DOI: 10.1016/j.icarus.2014.11.038 

Degradation of plume-deposited organics at Enceladus and implications for future surface missions

Copernicus Publications (2026)

Authors:

Tom Nordheim, Robert Grayson, Leonardo Regoli, Edith Fayolle, Morgan Cable, Shannon MacKenzie, Kevin Hand, Jasmina Wiemann, Carly Howett, Mathieu Choukroun, Christopher Paranicas

Abstract:

Saturn’s ocean moon Enceladus is among the most compelling targets for future astrobiology-focused missions. Material erupted from the moon’s south polar “Tiger Stripe” fractures is thought to originate from a global subsurface ocean, providing a natural pathway for ocean-derived compounds to be sampled without penetrating the ice shell. Cassini observations demonstrated that Enceladus’ plume contains water vapor, ice grains, salts, organics, phosphates, and other compounds of astrobiological interest. Consequently, future landed or plume-sampling missions to Enceladus will seek to determine whether ocean-sourced organic molecules, and potentially biosignatures, can be preserved and detected in plume material.However, once plume grains are erupted and deposited onto the surface, they are exposed to multiple space weathering agents. Solar ultraviolet radiation, Saturnian magnetospheric charged particles, and galactic cosmic rays can alter or destroy organic molecules contained within surface material. The degree of processing depends not only on radiation environment and molecular susceptibility, but also on the rate at which fresh plume fallout buries previously deposited material. Identifying locations and depths where organics may remain minimally processed is therefore key for mission planning and interpretation of future measurements.Here we model the degradation and preservation of plume-deposited organics on Enceladus, using the amino acids glycine and phenylalanine as representative organic molecules and potential biosignature proxies. We combine solar UV photodestruction calculations, Geant4-based charged-particle irradiation simulations, and estimates of local plume deposition rates to produce a coupled model of irradiation and burial across the surface. Solar UV photolysis rates are calculated using experimental rate coefficients adjusted for seasonal variation in photon flux at selected locations on Enceladus, including equatorial and southern-hemisphere sites at leading and trailing longitudes. Because even small abundances of non-water-ice contaminants can strongly influence UV attenuation, we also examine the effect of trace tholin-like material mixed into the ice. Charged-particle processing is estimated using Cassini-derived magnetospheric electron spectra and a numerical transport model for the galactic cosmic ray flux at Saturn.Our results show that preservation of plume-deposited organics is highly sensitive to burial rate and season. At low to moderate surface deposition rates, less than approximately 0.002 mm yr⁻¹, newly deposited surface material is strongly processed by solar UV radiation before burial can shield it from further exposure. In such regions, there may be no practical “safe sampling depth” at which pristine or minimally processed organics can be accessed, because material has already been altered before reaching depth. By contrast, in regions receiving the highest predicted plume deposition rates, especially during local winter when solar UV exposure is reduced, burial can occur rapidly enough to protect a significant fraction of the organic inventory. Under these conditions, the near-surface stratigraphy may consist of millimeter-scale layers that alternate between relatively well-preserved and heavily photoprocessed material, reflecting seasonal variations in irradiation during emplacement.Our findings have implications for the mission design and sampling strategy of future Enceladus missions. A landed mission seeking minimally processed ocean-derived organics should prioritize regions of high plume fallout, where burial is most effective, and should consider the seasonal context of deposition and sampling. The most favorable strategy may be to collect plume grains directly before surface deposition, e.g., from a funnel on the surface or plume fly-through, thereby avoiding prolonged radiolytic and photolytic alteration. If surface sampling is required, targeting the uppermost approximately 0.1 mm of material in high-deposition regions during local winter may maximize the probability of detecting less-processed organics. More broadly, our results demonstrate that preservation potential at Enceladus is governed by the competition between surface irradiation and plume-driven burial, and that this balance should be incorporated into future landing site selection, sampling-depth requirements, and biosignature-detection strategies.

Final results: Jovian upper clouds and hazes from visible and near infrared spectroscopy using CARMENES

(2026)

Authors:

José Ribeiro, Pedro Machado, Santiago Pérez-Hoyos, Asier Anguiano-Arteaga, Patrick Irwin

Abstract:

The origin and vertical distribution of Jupiter’s red coloration remain uncertain, despite multiple proposed aerosol models. Laboratory work (Carlson et al., 2016) showed that photolyzed ammonia and acetylene can form a red compound consistent with Jupiter’s colours, motivating the “universal chromophore” hypothesis (Sromovsky et al., 2017), and the “Crème Brûlée” model (Baines et al., 2019), which places a thin absorber above the ammonia clouds. Later HST and VLT studies (Pérez‑Hoyos et al., 2020; Braude et al., 2020) suggested a more vertically extended, less blue‑absorbing material, while recent analyses of the Great Red Spot and Oval BA indicate the presence of two distinct colouring agents: a universal‑chromophore absorber and a deeper UV‑absorbing aerosol (Anguiano‑Arteaga et al., 2021, 2023). These findings highlight persistent ambiguity in Jovian aerosol composition and structure.To investigate this, we analysed 2019 Jupiter observations from CARMENES (The Calar Alto High-Resolution search for M dwarfs with Exoearths with Near-infrared and optical Échelle Spectrographs), (0.52–1.71 μm). Since no calibration star was available, we calibrated the spectra using Saturn’s B ring and Cassini/VIMS reflectivity (Cuzzi et al., 2009), achieving agreement with published Jupiter spectra to within 10% (Clark, R.N., McCord, T.B., 1979; Mendikoa, I., et al., 2017; Irwin, P.G., et al., 2018).Using 64 VIS–NIR observation pairs, we performed a Minnaert limb‑darkening analysis and generated synthetic spectra for five regions. These were used in NEMESIS retrievals with three aerosol models. Across all models, the highest‑altitude aerosol layer dominated the spectral behaviour, with particle size, cloud‑base abundance, and pressure level strongly influencing the fits. Model B (Braude et al., 2020) produced the lowest χ²/Nfree values, but no model fully reproduced the observations, likely due to the limited wavelength range, which lacks constraints on deeper clouds.The models diverged in retrieved particle sizes and cloud‑base pressures, with several results, such as extremely small tropospheric particles or overly large stratospheric particles, indicating physical inconsistencies. Model A’s tropospheric haze base aligns with Galileo probe measurements (Sromovsky and Fry, 2002); Model C retrieves a cloud base level near the NH₄SH level predicted by Atreya (1998), deeper than CIRS detections (Matcheva et al.,2005) but within the range of Baines et al. (2019), with implausible particle sizes.Overall, the study shows that CARMENES can deliver high‑quality, flux‑calibrated planetary spectra, but also that broader spectral coverage is essential to resolve Jupiter’s chromophore composition and aerosol vertical structure. Figure 1: Location of the spectra used to perform the Minnaert limb-darkening approximation for each region considered in this study. Red for EZ, yellow for NEB, green for SEB, pink for SEB transition and blue for NEB transition. The Jupiter AGC image represented corresponds only to the spectra of the EZ whose longitude was closest to 0º. Figure 2: Comparison between observed and modelled spectra and residuals for EZ using model B]{Comparison between observed (blue) and modelled (red) spectra (left column) and comparison between differences (red) and a priori errors (black) (right column) for the EZ using model B, with the grey shaded areas corresponding to telluric absorption. The top row corresponds to nadir (incidence and emission angle = 0º) and the bottom row to limb (incidence and emission angle = 61.45º). Figure 3: Comparison between the a priori aerosol vertical profiles and the retrieved profiles for every region for models A and B. We compare the optical depth/atm at 0.90 μm of model B with all three aerosol populations considered and model A's stratospheric and tropospheric hazes. The horizontal dashed line corresponds to 0.15 atm, separating model B's deep cloud layer from the haze. References:Carlson, R. W., et al. (2016). Chromophores from photolyzed ammonia reacting with acetylene: Application to Jupiter's Great Red Spot. Icarus, 274, 106–115.Sromovsky, L. A., et al. (2017). A possibly universal red chromophore for modeling color variations on Jupiter. Icarus, 291, 232–244.Baines, K. H., et al. (2019). The visual spectrum of Jupiter's Great Red Spot accurately modelled with aerosols produced by photolyzed ammonia reacting with acetylene. Icarus, 330, 217–229.Pérez-Hoyos, S., et al. (2020). Color and aerosol changes in Jupiter after a North temperate belt disturbance. Icarus, 132, 114021.Braude, A. S., et al. (2020). Colour and tropospheric cloud structure of Jupiter from MUSE/VLT: Retrieving a universal chromophore. Icarus, 338, 113589.Anguiano-Arteaga, A., et al. (2021). Vertical Distribution of Aerosols and Hazes Over Jupiter's Great Red Spot and Its Surroundings in 2016 From HST/WFC3 Imaging. Journal of Geophysical Research: Planets, 126, e2021JE006996.Anguiano-Arteaga, A., et al. (2023). Temporal variations in vertical cloud structure of Jupiter's Great Red Spot, its surroundings and Oval BA from HST/WFC3 imaging. Journal of Geophysical Research: Planets, 128, e2022JE007427.Irwin, P., et al. (2008). The NEMESIS planetary atmosphere radiative transfer and retrieval tool. J. Quant. Spectrosc. Radiat. Transf., 109, 1136–1150.Rodgers CD. (2000). Inverse methods for atmospheric sounding: theory and practice. Singapore: World Scientific.Cuzzi, J., et al., 2009. Ring Particle Composition and Size Distribution. Springer Netherlands, Dordrecht. pp. 459–509.Clark, R.N., McCord, T.B., 1979. Jupiter and Saturn: Near-infrared spectral albedos. Icarus 40, 180–188.Mendikoa, I., et al., 2017. Temporal and spatial variations of the absolute reflectivity of Jupiter and Saturn from 0.38 to 1.7 𝜇m with planetcam-upv/ehu. A&A 607, A72.Irwin, P.G., et al., 2018. Analysis of gaseous ammonia (NH3) absorption in the visible spectrum of Jupiter. Icarus 302, 426–436.Matcheva, K.I., Conrath, B.J., Gierasch, P.J., Flasar, F.M., 2005. The cloud structure of the jovian atmosphere as seen by the Cassini/CIRS experiment. Icarus 179(2), 432–448.Sromovsky, L., Fry, P., 2002. Jupiter’s cloud structure as constrained by Galileo probe and HST observations. Icarus 157 (2), 373–400.

Fine Layering Effects on Thermal Infrared Emissivity of CI Simulant Materials 

(2026)

Authors:

Emma-Catherine Belhadfa, Neil Bowles, Katherine Shirley

Abstract:

Introduction: Thermal infrared emissivity measurements of asteroid regolith analogs are challenging owing to atmospheric water vapor absorption, sample heating requirements, and the need for controlled atmospheric conditions [1], yet they provide fundamental constraints on surface thermal properties that cannot be obtained from reflectance spectroscopy alone [1]. While diffuse reflectance measurements have demonstrated that minimal fine dust coverage can dominate spectral signatures [2], spacecraft-based thermal emission instruments like the OSIRIS-REx Thermal Emission Spectrometer (OTES) observe different physical processes related to thermal emission rather than scattered light [3]. The disconnect between laboratory studies and spacecraft observations has thus limited our ability to interpret thermal infrared spectra of asteroid surfaces. Previous work using Space Resource Technology's CI simulant showed that 7-10 wt% fine dust coverage could impose fine-dominated reflectance features on coarse substrates [2], but the corresponding thermal emission properties remained uncharacterized. To bridge this gap, we conducted systematic thermal emissivity measurements of layered CI simulant materials using Oxford’s PASCALE instrument [4] under nitrogen atmosphere, constraining how dust deposition mechanisms affect the thermal emission processes observed by spacecraft instruments at airless bodies like asteroid (101955) Bennu. Methods: We measured thermal emission of layered CI simulant [5] samples using PASCALE under nitrogen atmosphere across 2000-400 cm⁻¹ (5-25 µm), eliminating atmospheric water vapor interference. Six layering configurations were tested, using 10 wt% fines (5% emissivity variations from unity), while the fluffy group shows more subdued but consistent spectral signatures. All method-dependent variations exceed the 2% measurement precision, demonstrating that dust deposition mechanism leaves diagnostic thermal emission signatures that can distinguish (and potentially identify) natural surface processes on airless body surfaces. Discussion: The separation between fluffy and compact layering methods demonstrates that thermal emission spectroscopy can distinguish surface formation processes on airless bodies. These results provide constraints missing from reflectance-only studies, by characterizing thermal emission properties relevant to spacecraft observations like OTES. The ability to spectrally distinguish between natural deposition processes offers new frameworks for understanding regolith evolution and thermophysical properties on asteroid surfaces. Summary: This study establishes thermal emissivity as a diagnostic tool for identifying dust deposition mechanisms on asteroid surfaces, demonstrating that layering processes leave distinct spectral signatures. References: [1] Salisbury et al. (1991) Icarus 92, 280-297. [2] Belhadfa et al. (2026) MaPs, In Prep. [3] Christensen P. R. et al. (2018) Space Science Reviews (Vol. 214, Issue 5). [4] Donaldson Hanna et al. (2019) Icarus 319, 701-723. [5] Landsman Z. et al. (2020) EPSC.  

Galileo PPR Thermal Inertia & Albedo Measurements of Europa, Ganymede and Callisto

Copernicus Publications (2026)

Authors:

Sarah Howes, Carly Howett, Duncan Lyster

Abstract:

IntroductionThe presence of endogenic hotspots provides a measure of the level of geologic activity of icy moons, since they are indicative of ongoing resurfacing processes. However, to avoid misinterpreting thermal abnormalities, it is first necessary to understand passive thermal emission that is governed by the physical structure of materials. Two important thermophysical properties in such analysis are bolometric Bond albedo and thermal inertia: if diurnal temperature variations can be accurately modeled by adjusting these two parameters, a passive rather than endogenic origin is possible. In this work, we aim to constrain the thermal inertia and Bond albedo across the surfaces of Europa, Ganymede, and Callisto using brightness temperature observations recorded by the Galileo Photopolarimeter-Radiometer (PPR) instrument [1]. By presenting estimated values and their uncertainties for these thermophysical properties, we prepare for future thermal measurements carried out by both Europa Clipper and JUICE.MethodsWe first take average diurnal temperatures of the surfaces of Europa, Ganymede, and Callisto using brightness temperatures recorded by PPR. In this analysis, we use 29 datasets for Europa, notably increased beyond previous efforts [2], comparable to [3].  With less observations available, only 7 datasets each were used for both Ganymede and Callisto. By translating the observed radiance into brightness temperatures, the variation in temperature with local time is determined for latitude and longitude bins across each of the three moons. These diurnal curves are compared to those predicted by a 1-D thermal model [4] to determine what thermal inertias and Bond albedos can fit the data within a reduced chi-squared cut-off of χ2red ≤1.0. This analysis is used to extensively quantify the uncertainty of the two thermophysical parameters derived from PPR data.ResultsEuropa: Ensuring closed upper and lower limits within our χ2red cut-off, we map albedo and thermal inertia for 33% and 24% of Europa's surface area into 6°x6° latitude/longitude bins (Fig. 1, left). We find a range of 0.375-0.75 for albedo and 20-110 J m-2 K-1 s-1/2 (MKS) for thermal inertia, agreeing with [2] and [3]. Our uncertainty analysis indicates well-constrained estimates for albedo, with the average higher and lower ranges overlapping within their uncertainties: Ahigh = 0.11 ± 0.06 and Alow = 0.18 ± 0.12. Uncertainties for thermal inertia remain poorly constrained, with average higher and lower ranges being ­Γhigh = 103(+153/-103) MKS and Γ­low = 17 ± 9 MKS.Ganymede: Due to less available surface coverage, Ganymede’s surface is divided into 18°x6° longitude/latitude bins in order to meet the diurnal fitting routine requirements (Fig. 1, right). Preliminary results indicate the Bond albedo remains nearly uniform, with an average of 0.42 ± 0.07 across the surface and agreeing well with previous work [6]. Specifically, our χ2red-deduced higher and lower uncertainty ranges of albedo are: Ahigh = 0.10 ± 0.06 and Alow = 0.14 ± 0.08. No apparent distinct surface variations in thermal inertia are as of yet discerned, with global values distributed across a range of 20-70 MKS. Upper limit thermal inertia estimates align with [6] within χ2red-deduced uncertainty ranges of ­Γhigh = 57 ± 35 MKS and Γ­low = 25 ± 11 MKS.Callisto: With less PPR coverage available, Callisto fits are performed across grouped hemispheric regions, where the Jovian and anti-Jovian hemispheres are analyzed separately. Each hemisphere is divided into 10° latitude strips. Preliminary results for thermal inertia and Bond albedo indicate an overall agreement with lower-bound estimations from previous literature [5,6]. Further constraints are expected to be obtained at the time of the conference.ConclusionThese results give an indication of the albedo and thermal inertia variation across Europa, Ganymede and Callisto. They aid in preparing for the arrival of Europa Clipper and JUICE to the Jupiter system by improving estimates for passive surface thermal properties and providing uncertainties of their values. This will enable future work to help discern what temperatures may lie above those expected from passive emission alone, providing a critical first step in the search for endogenic heating anomalies. Future work aims to refine the Ganymede and Callisto calculations using a two-component (ice and non-ice) analysis, and characterize the causes behind thermal inertia variations by modeling microphysical ice states for the three Galilean moons.Fig. 1: Thermal Inertia (top) and Bond albedo (bottom) map of Europa (left) and preliminary results for Ganymede (right).[1] Russell, E.E. et al., 1992. Space Sci Rev 60, 531-563.; [2] Rathbun, J.A. et al., 2010. Icarus 210, 763-769.; [3] Lange, L. et al., 2026. arXiv:2604.14374; [4] Lyster, D. et al., 2025. pp. EPSC-DPS2025-1479; [5] Meyer, C. et al., 2026. Planet. Sci. J. 7, 10; [6] Spencer, J.R. et al., 1989. Icarus 78(2), 337-354.