The importance of carbonatite lavas in outgassing Venus’ modern-day atmosphere

Abstract

Venus diverged from Earth’s evolutionary path through the development of a carbon dioxide (CO₂)–dominated atmosphere, although studies dispute whether this atmosphere arose shortly after accretion or after a protracted period of surface habitability. Widespread volcanic features suggest that volcanic outgassing may have played a pivotal role in the transformation of Venus. However, the formation of volcanic units on Venus by basaltic lavas can only outgas a minor fraction of the CO₂ in the current atmosphere. Here, we model the erosion of long, meandering channels on Venus called canali and show that carbonatite lavas have the unique properties required to erode the canali. Our results suggest that eruption of these carbonatites may have delivered a total mass of CO₂ comparable to that of the modern atmosphere, resolving challenges to the formation of Venus’ atmosphere within the recent past and suggesting that exoplanets in the “Venus zone” may exhibit the potential for prolonged habitability.

The erosion of canali on Venus by carbonatite lavas transformed Venus’ atmosphere within the recent past.

INTRODUCTION

Despite being Earth’s closest twin, the atmosphere of Venus contains mostly CO₂, with a surface pressure ~90 times that on Earth (1). The amount of carbon in Venus’ current atmosphere nearly equals that in Earth’s lithosphere and atmosphere combined (2). Climate simulations suggest that Venus may have experienced a temperate period with liquid water for ~3 billion years, which ended when the brightening Sun created a runaway greenhouse. Past studies invoke a subsequent large igneous province (LIP) period to outgas the modern atmosphere (3). Venus has a geologically young surface with a cratering age of ~250 million years (Myr) (4–6). On Earth, LIPs are most commonly associated with mafic magmatism (7). However, mafic magmatism alone is insufficient to outgas the mass of CO₂ now in Venus’ atmosphere unless the total volume of magmatism exceeded that of the crust (8). Instead, researchers have proposed that the present-day atmosphere may be inherited from before the surface record, diminishing the possibility of a long-lived, temperate period (8, 9). Here, we suggest that carbonatite lavas formed the enigmatic channels known as canali and outgassed a substantial proportion of Venus’ current atmosphere within the age of the surface. Our results illustrate a possible mechanism for how Venus’ atmosphere could have formed in the recent past, allowing Venus to experience an extended period of habitability (1, 9–11) before its runaway greenhouse.

Venus’ surface hosts volcanic features that reflect a diversity of volcanic compositions and eruption styles (12, 13), suggesting that nonmafic magmas may contribute to atmospheric outgassing. Canali are channels in the plains of Venus that were first discovered in Magellan radar images (14). Canali are noteworthy for their extreme lengths, ranging from a few hundreds of kilometers to more than 6800 km for Baltis Vallis, the longest known channel in the solar system. Unlike sinuous rilles, another type of volcanic channel found on the Moon and Venus, canali do not have obvious source regions and exhibit longer meander wavelengths. Whereas sinuous rilles usually follow regional slopes consistent with lava flowing downhill, canali often exhibit topographic undulations that indicate deformation by tectonic or volcanic events postemplacement, possibly due to their longer lengths and/or older ages than sinuous rilles (15, 16). Canali also display morphological features comparable to fluvial landforms on Earth, such as cutoff meanders, deltas, and streamlined islands (Fig. 1C and fig. S1A), but the present-day surface temperature of Venus (~740 K) prohibits the presence of liquid water on the surface (17, 18). Instead, it has been hypothesized that these long channels were formed via erosion by low-viscosity lavas such as carbonatites, komatiites, and tholeiitic basalts (18–20).

Fig. 1. Canali on Venus.

(A) Canali mapped in this study displayed on a Magellan Global C3-MDIR Topographic Mosaic 6600 m. (B) Potential origin of Morongo Valles from a fissure source (white arrow), centered at −22.7°N, 113.8°E. (C) Section of Sati Vallis traced in cyan that is covered by younger lava flows (white arrows), centered at 2.9°N, 24.4°W. Both (B) and (C) are oriented with north to the top.

Terrestrial lava channels are primarily constructional features, but erosion is thought to contribute to the formation of some lava channels on terrestrial bodies. Thermomechanical erosion is credited for the formation of sinuous rilles on the Moon (21), channels in volcanic terrains on Mars (22–24), and at least one channel on Io (25). Cases of pure mechanical erosion by lava are not well-documented, but mechanical erosion has been proposed for the formation of a 220-m-long lava channel on Mount Etna (26).Thermal erosion occurs when the temperature of a lava exceeds the solidus temperature of the substrate, enabling the lava to melt and chemically assimilate the substrate material. Mechanical erosion involves the physical removal and possible entrainment of solidified substrate material (Fig. 2A). Depth profiles of lava channels reveal whether thermal or mechanical erosion is the dominant process. For example, sinuous rilles exhibit depths that decrease along track, indicating slower erosion as the lava cools downstream consistent with thermal erosion (15). In contrast, Baltis Vallis (>6800 km long) has a roughly constant depth along its exceptional length, which is most consistent with mechanical erosion (20). Chemical analyses from the Venera 14 and Vega 2 landing sites are consistent with a tholeiitic basalt bedrock (27). Therefore, only low-temperature lavas such as carbonatites will cause mechanical erosion of the surface, hinting that carbonatites are a better candidate for the canali-forming lava than tholeiitic basalts and komatiites.

Fig. 2. Thermal and mechanical erosion by lava.

(A) Cross section of a dike-fed lava flow thermally and mechanically eroding the substrate. Flow transitions from turbulent to laminar downstream. Crust can form further downstream as the lava cools and becomes less turbulent. (Artist credit: H. Cañellas.) (B) Probability density functions for total lava volume required to erode the 70 observed canali if they have a depth of 35 m. Lavas that only mechanically erode are shown with solid lines, while lavas that thermally and mechanically erode are shown with dashed lines. The volume estimate from a previous study that extrapolated meander wavelengths (19) is indicated by the line with arrows. Channel depth profiles for 6 m thick (C) tholeiitic basalt and (D) carbonatite flows eroding a 35-m-deep channel. Carbonatite flows travel roughly an order of magnitude longer than basalt flows before solidifying.

Previous studies have also argued against the formation of canali by basaltic and komatiitic lavas. Several studies predicted that basaltic and komatiitic lavas cool too rapidly to thermally erode the observed lengths of the canali (18, 19, 28). In particular, tholeiitic basalt lavas would require high discharge rates (>10⁶ m³/s) and thick flows (>80 m thick) (28). While the lava flow thicknesses required for basaltic lavas to erode the canali are within the ranges reported for LIPs on Earth, the discharge rates exceed those reported for even the largest eruptions on Earth (29). Furthermore, these flow thicknesses exceed the reported depths of the canali and would lead to channel overflow. Although reported canali depth measurements are uncertain, channel overflow has not been consistently observed in Magellan images of the canali (17, 30). While a crust may in principle insulate these high-temperature lavas, allowing them to flow ~10³ km, turbulence in such thick flows with large channel widths would inhibit the formation of an insulating crust (31). In contrast, previous studies have favored carbonatite lavas for their rheological properties and their potential to be more common on Venus, possibly due to the presence of rift zones and a CO₂-enriched mantle (19, 31). However, no study has yet demonstrated that they can erode the canali to their observed depths and lengths.

One prior study estimated the volume of canali-forming lavas based on their sinuosity alone, without modeling the cooling and crystallization of the flowing lava. They extrapolated a relation between meander wavelength and bank-full discharge rates to infer a volume of ~10¹³ to 10¹⁵ m³ of lava per canale and eruption timescales of ~1 to 100 Earth-years (19), consistent with later arguments about the rate of lateral migration from mechanical erosion (18). That study concluded that if the 40 canali mapped on the surface by 1993 were formed by a lava made entirely of CaCO₃, then this lava could outgas ~0.1 to 10% of the mass of CO₂ in Venus’ modern atmosphere. Although this is only a small portion of the modern atmosphere, the true amount of atmospheric CO₂ attributable to canali formation could be much larger. First, nearly twice as many canali have been discovered since 1993. Second, the number of canali observable now could be a small fraction of the total number that ever formed, since canali are relatively shallow and thus easily obscured.

RESULTS

Canali mapping and geologic context

In this study, we mapped 70 canali using radar images and altimetry from the Magellan mission (Fig. 1A). Canali have an average length of ~600 km (median of ~400 km) and an average maximum width of ~3 km (median of ~2 km). These lengths are minimum values since segments of canali disappear and reappear, indicating burial of portions of the canali by younger lava flows or regions too smooth to be detected by Magellan radar (Fig. 1C). We found that present-day, average ground slopes range from ~4 × 10⁻⁵ to 0.1 radians, with a mean slope of ~0.01 radians. However, the paleo-slopes were likely steeper and shallowed over time by tectonic deformation, and the measured present-day slope will be underestimated because of the low resolution of Magellan topography data (32). The global survey conducted in this study (Fig. 1A) and in (33) indicate that canali are globally distributed. From current geologic maps (34), canali are not restricted to particular volcanic or tectonic units but are most common on smooth plains that are surrounded by shield plains or densely lineated plains. We found that younger lava flows bury portions of ~40% of the identified canali, as exhibited by their cross-cutting relationships with the canali (Fig. 1C).

Statistical retrievals of lava volumes

We used a model of channel formation to retrieve the volumes of lava required to erode the canali to their observed cross-sectional areas. Our lava erosion models are directly adapted from models of lava erosion on Earth (see Materials and Methods) but take into consideration the effects of Venus’ higher surface temperature, higher atmospheric pressure, and lower gravity. In addition, we used the Markov chain Monte Carlo (MCMC) method to calculate the posterior probability distribution of the lava volume required to erode the canali, given naïve priors for the several model parameters with relatively large uncertainties (see Materials and Methods). Our priors are not strongly correlated with the total lava volumes required, suggesting that our median estimates are not sensitive to these uncertainties (figs. S2 and S3). While canali widths are relatively easy to measure, channel depths have only been inferred for Baltis Vallis (46 ± 16 m) and two shorter canali (24 and <50 m) because of the low spatial resolution of Magellan radar altimetry and stereo topography (19, 20, 28). We modeled canali with depths of 24, 35, and 46 m to account for this range in reported depths. We assumed that the substrate is tholeiitic basalt, consistent with measurements by the Venera and Vega landers (27) but tested erosion by multiple low-viscosity lava types.

The volume of carbonatite lava required to erode the canali to their measured depths exceeds that required for basalt and komatiite lavas. This is because the volume of lava required to erode the canali through combined thermal and mechanical erosion is less than the case of mechanical erosion only (Fig. 2B). If all 70 mapped canali have a depth of 35 m, then a total of 10^16.12±0.75 m³ of carbonatite lava is required to mechanically erode the canali. This volume corresponds to a global layer of carbonatite with a thickness of ~29 m. In contrast, 10^15.40±0.76 m³ of tholeiitic basalt lava, or a ~5.5-m-thick global layer, is required to thermally and mechanically erode the canali. For carbonatite, we calculated total volumes of 10^15.87±0.73 and 10^16.31±0.77 m³ if all canali have a depth of 24 or 46 m, respectively (fig. S4). Canali-forming lavas thus compose a small fraction of Venus’ crust (35), which has a total volume of ~10¹⁹ m³. Critically, the lava type that yields the smallest total volume is not the best candidate to form the canali because we must also explain the extreme lengths of the canali.

Forward modeling of lava erosion

Last, we conducted one-dimensional (1D) forward models (15, 36) to determine the lava flow thicknesses and effusion rates necessary to reproduce the cross-sectional areas and lengths of the canali. Lavas on Venus should flow longer than on Earth due to the high surface temperature and the dense CO₂ atmosphere that leads to the coupling of the radiative and convective heat fluxes (37). That is, the atmosphere absorbs thermal radiation emitted by the lava flow, thereby diminishing the local thermal gradient and thus the efficiency of convective cooling (38). Basaltic and komatiitic lavas have higher liquidus and solidus temperatures than carbonatites, so they cool and solidify more rapidly (see Materials and Methods) (28). Previous models of canali formation [e.g., Williams-Jones et al. (18)] did not account for the coupling of the radiative and convective heat fluxes and did not directly calculate the volumes of different lava types required.

We found that carbonatite lavas can erode the canali to their observed lengths with more realistic effusion rates than those required by komatiites and tholeiitic basalts (Fig. 2C). For a typical canale that is 24 m deep, 3 km wide, and has a slope of 10⁻³ radians, we found that a 6-m-thick carbonatite lava with 10% crust can flow for ~620 km with an effusion rate of ~2.1 × 10⁸ kg/s, whereas basaltic and komatiitic lavas under the same conditions only reach lengths of ~21 and ~70 km, respectively (fig. S5). Eroding Baltis Vallis (~6800 km long) mandates, for example, a carbonatite flow with a thickness of ~12.6 m, ~10% crust, and an effusion rate of ~2.3 × 10⁹ kg/s, over a slope of ~10⁻² radians. Under the same conditions, basaltic lava travels a mere ~490 km, and komatiite lava travels only ~830 km (fig. S6).

To reach the length of Baltis Vallis, basalts require high flow thicknesses (>40 m), almost-complete crust coverages (>90%), and high discharge rates (>10¹⁰ kg/s). On Earth, recent lava flows typically have effusion rates of <10⁷ kg/s (i.e., <10⁴ m³/s) (39). Even discharge rates for terrestrial flood basalt eruptions do not reach 10¹⁰ kg/s. For example, the Roza flow in the Columbia River flood basalt province has an estimated average effusion rate of ~10⁷ kg/s (~0.3 km³/day) spanning approximately a decade of eruption (40). Thus, achieving the observed canali lengths implies that volcanism on Venus may have effusion rates at or above the upper end of the terrestrial range, which is possibly consistent with the large volumes required for lava flows visible on the surface (41, 42). Alternatively, recent studies have shown that lower effusion rates (~10³ m³/s) can produce long (~100 km) basaltic lava flows observed on Venus due to the coupling of convective and radiative heat loss (37). Although effusion rates of ~10⁹ kg/s for carbonatites forming Baltis Vallis may seem high, other lava types would require even higher effusion rates. The longest channel in the Solar System may require a superlative eruption. Overall, our erosion models confirm that carbonatites are the best-fit lava type to explain the observed dimensions of canali.

Outgassing of CO₂ by carbonatite

The substantial volumes of carbonatite lava required to erode the canali can change the bulk composition of the atmosphere. Carbonatites are typically at least ~30 wt % carbonate and release CO₂ to the atmosphere primarily via outgassing (43). Carbonatites may also react with SO₃ in the atmosphere and release minor amounts of CO₂, but this decarbonation reaction is limited today by the low abundance of SO₃ in the atmosphere. On Earth, carbonatite lavas typically outgas at least 10% of their carbon as CO₂, while the remainder crystallizes as carbonate minerals (44, 45). However, the fraction of carbon that would be outgassed as CO₂ by carbonatite lavas under the higher surface pressures and temperatures of Venus is unknown. To account for this uncertainty, we investigated a range of carbonate fractions that would be released as CO₂ by carbonatite lavas. We calculated a steady-state rate of CO₂ delivery for the canali-forming carbonatites and thus an outgassing timescale for the atmosphere (t_atm). Figure 3 reports the probability that t_atm is less than or equal to a given time before the present. In the paradigm of equilibrium resurfacing, the oldest areas of the surface should have ages of up to roughly four times the mean cratering age (i.e., reaching ~0.7 to 1 billion years) (46). We found that the cumulative probability is >0.5 for ${\mathrm{\tau }}_{\text{atm}}$ > 550 to 790 Myr, depending on the assumed channel depth. In other words, if the underlying assumptions are true, then there is a >50% chance that canali-forming lavas helped produce the modern atmosphere within the age of the surface (Fig. 4) Speculatively, the surface of Venus could have been habitable until a few hundred Myr ago. Other volcanic processes could have outgassed sizeable amounts of greenhouse gases at earlier times and shortened any habitable period. Ultimately, the volumes of carbonatite lava required to erode canali are substantial and plausibly critical to explaining how Venus may have transitioned from a habitable to a hellish surface.

Fig. 3. Outgassing timescale for Venus’ modern atmosphere.

Cumulative distribution functions for the time required for canali-forming lavas to release the extra mass of CO₂ in Venus’ modern atmosphere, relative to Earth’s atmosphere. Labels indicate the assumed median depth of canali, tied to the required volumes of lava shown in Fig. 2 and fig. S4. Gyr, billion years.

Fig. 4. Erosion of canali by carbonatite lavas.

Artist’s depiction of canali formation with black, turbulent carbonatite flows that form a white crust as they solidify downstream. Streamlined islands and branching of channels are also portrayed. (Artist credit: H. Cañellas.)

DISCUSSION

Carbonatites are rare on Earth. Generating >10⁵ km³ of carbonatite magma to explain features such as Baltis Vallis therefore poses a challenge. We propose a mechanism for voluminous carbonatite generation on Venus driven by resurfacing, burial, and remelting of carbonate-rich lithologies (Fig. 5). At Ol Doinyo Lengai, the only known, active carbonatite volcano on Earth, eruption temperatures (47) have been measured at 490° to 550°C, only a few tens of degrees higher than venusian surface temperatures of ~470°C. The thermal gradient in the venusian crust varies globally (48) between ~5° and 90°C/km. Only a few hundred meters to a few kilometers of burial would therefore be necessary to reheat solidified surface carbonatite and carbonate lithologies to the temperatures at which Ol Doinyo Lengai carbonatites are molten. Burial of these flows would primarily occur through volcanic resurfacing, as evidenced by our observations of lava flows burying portions of the canali (Fig. 1C). This cycle of resurfacing, burial, modest reheating, and remelting of solidified carbonatite lavas and carbonate minerals could drive voluminous shallow carbonatite magmatism on Venus. The initial source of carbon in these lavas may have originated from carbonates precipitated in an ocean that were later buried or carbon sourced directly from the mantle (19).

Fig. 5. Carbonatite generation on Venus due to resurfacing, burial, and remelting.

(A) Superposition of venusian lithospheric thermal gradients (48) of 5° to 90°C/km on Venus’ elevated surface temperatures will strongly favor melting of carbonatites and carbonate lithologies upon burial, depending on alkali and volatile enrichment (49). Carbonatite eruption temperatures at Ol Doinyo Lengai, the only active carbonatite volcano on Earth, are only a few tens of degrees warmer than venusian surface temperatures (47). If venusian carbonatites have alkali and volatile enrichment similar to magmas at Ol Doinyo Lengai, remelting could occur after only a few hundred meters of resurfacing and burial, based on melting curves bounding the yellow shaded region calculated as in (53). (B) Schematic cartoon illustrating the proposed burial mechanism for voluminous carbonatite generation on Venus.

The solidus temperature of carbonatite magma depends strongly on the alkali and volatile contents, both of which depress the solidus (49). The melting behavior of potential venusian carbonatites is thus uncertain, but alkalis and sulfates have been argued to be abundant in venusian surface rocks (19, 50). Measurements from Venera 13 may be consistent with an alkali basalt generated by partial melting of a carbonated mantle source (51). The low abundance of water in Venus’ atmosphere may favor the preservation of alkali elements in the magma (18). Fractional crystallization of carbonated, silica-undersaturated magmas on Venus would theoretically lead to more efficient alkali enrichment than on Earth due to the lower water abundances, requiring smaller volumes of the parent melt. Alternatively, if Venus once had liquid water, then the formation of carbonates, clays, and salts would be expected and would concentrate alkalis in the crust (52). The presence of halogens and sulfur can also lower the viscosity and solidus temperature of carbonatites (49, 53). The low abundance of halogens in Venus’ modern atmosphere suggests that halogens may instead be concentrated in the crust. Degassed halogens in the atmosphere may have reacted with surface minerals to form halogen-bearing salts and metal halides (54). In summary, owing to the very high venusian surface temperatures, if carbonatite lavas or other carbonate lithologies do exist on Venus with alkali and sulfur enrichment comparable to terrestrial carbonatites, then they should undergo melting upon shallow burial (19, 53), providing a source for abundant carbonatite magmas that is unique to Venus.

In addition to burial-driven carbonatite melting, other mechanisms may also operate on Venus. On Earth, carbonatite generation is often linked with continental rifting (55). Rift zones on Earth concentrate carbon in the lithospheric mantle through advection of carbon-enriched mantle into zones of lithospheric thinning and melting (55, 56). Venus’ surface features plentiful rift zones where delamination may occur along zones of lithospheric weakness (57), potentially further favoring carbonatite generation. While there is not a clear spatial association between rift zones and canali, the abundance of rift zones may play a role in concentrating carbon in the lithospheric mantle that can provide a source for the generation of carbonatite magmas. Ultimately, the climate catastrophe on Venus may have been a multistep process. Solar evolution drove a runaway greenhouse that made the surface temperatures incompatible with liquid water. These conditions then invigorated carbonatite magmatism that efficiently cycles the carbon inventory from the lithosphere back to the atmosphere.

Future missions and models will help test the predictions of our study and provide answers to questions about Venus’ atmospheric and surface evolution. For example, 3D simulations of heat transfer from turbulent lava flows with temperature-dependent crystallinity and viscosity will allow us to more rigorously assess the erosion of canali by different lava types. Upcoming missions to Venus will provide a generational leap in our understanding of canali. NASA’s Venus Emissivity, Radio Science, InSAR, Topography, and Spectroscopy (VERITAS) mission and the European Space Agency’s (ESA) EnVision mission (58) will return higher-resolution images of canali and measurements of their depth profiles. These missions will also collect multispectral images that may allow us to infer the composition of canali-forming lavas. Carbonatite on Venus may weather to form patchy coatings of anhydrite in the presence of SO₂ (52, 59). Carbonatites and sulfates would exhibit low near-infrared emissivity, but laboratory studies of their emissivity under Venus’ atmospheric and temperature conditions should be performed to distinguish them from other weathering products. The subsurface radar sounder on EnVision will also elucidate the structure of lava flows in and around canali. We predict that the depth profiles of all canali are relatively constant, consistent with mechanical erosion, rather than shallowing along track as for thermal erosion. We suspect that the small-scale morphology of canali will reveal further signs of open-channel flow, not that canali are collapsed lava tubes. In addition, carbonatites are ionic melts that may be detectable in the subsurface using ground penetrating radar on future missions (53).

Our results have profound implications for our understanding of the evolution of Venus and other rocky planets, including their potential for habitability. Carbonatite magmatism could form a small fraction of the crust but play a pivotal role in the transformation of a planetary atmosphere. Carbonatites on Earth are often enriched in rare earth elements (e.g., lanthanum and neodymium), suggesting that Venus may also contain them. As we enter a new era of exoplanet characterization, Venus serves as an exemplar of terrestrial planet evolution. The prospect of protracted habitability on Venus suggests that not all exoplanets (60) in the “Venus zone” will be hellish wastelands. While stellar evolution may eventually doom planets with relatively close orbits around Sun-like stars, water oceans may survive on their surfaces for an appreciable fraction of their lifetimes.

MATERIALS AND METHODS

Canali mapping

We conducted a new survey of canali on Venus using Magellan radar images and elevation data to constrain their lengths, widths, slopes, and geologic contexts. Although the canali were inventoried previously (30), enhanced datasets such as stereo-derived topography allow for higher-resolution measurements of topography (61). In Java Mission-planning and Remote Sensing (JMARS), we digitized canali as polyline segments and traced their paths in the Magellan Synthetic Aperture Radar FMAP Left and Right Look Global Mosaics (~125 m, oversampled to 75 m) (62, 63). We added the lengths of the polyline segments for each canale to give a total length for each canale. We measured canali widths at several locations dispersed along the length of the canale to obtain a maximum width for each canale. Then, we extracted elevation profiles from the polylines using the Venus Global Topography Data Record (GTDR) and stereo-derived topography datasets.

Both the Venus stereo-derived topography and GTDR have a vertical resolution of ~50 to 100 m, but the new stereo-derived topography has an improved horizontal resolution of ~1 to 2 km (20% surface coverage) in contrast to the GTDR’s lower horizontal resolution (61, 64) of ≥10 to 20 km. Of the 70 canali surveyed, ~25 canali had partial or complete coverage by the Venus stereo-derived topography. In these cases, we used the elevation from the stereo-derived topography due to the higher horizontal resolution. We determined the average slope of each canale by calculating the slope between adjacent points along the profile and then averaging these values to obtain an average slope. Since the flow direction is not obvious for many of the canali, we looked for features such as streamlined islands and deltas to indicate flow direction. When these features were not present, we approximated flow direction based on which direction gave a net negative slope. We also reviewed a global geologic map of Venus throughout our mapping to contextualize the tectonic and volcanic settings where the canali occur (34). We found one potential canale with a fissure source (Fig. 1B) and four canali with streamlined islands narrowing in the downstream direction (fig. S1B).

Inversions of lava flow volumes

Once we obtained average dimensions for the canali, we used an MCMC method to sample the posterior probability distributions for each of our model parameters. We obtained a cross-sectional area ( $A$ ) for each canale by multiplying the maximum channel width ( $W$ ) and channel depth ( $D$ ). Because we could not measure channel depths in the topography data, we consulted previously published values of canali depths, derived from radar clinometry, which range from several tens of meters to <50 m. We tested canali depths of 24, 35, and 46 m to encompass the ranges reported in the literature. We ran this model for six different low-viscosity lava types including carbonatite, komatiite, high-Ti basalt, low-Ti basalt, ocean island basalt, and tholeiitic basalt, assuming a tholeiitic basalt substrate. The properties for these lavas are provided in table S1.

Carbonatites and high-Ti basalts are not hot enough to thermally erode the tholeiitic basalt substrate, so we ran a separate model for the case of mechanical erosion only. The mechanical erosion rate (21) ( $U_{\text{me}}$ ) in meters per second is

$$U_{\text{me}}=\left(\frac{b}{Y_{\mathrm{s}}}\right)\mathrm{\rho }g\text{HVsin}\left(\mathrm{\varphi }\right)$$ (1)

where $b$ is a dimensionless erodibility factor; $Y_{\mathrm{s}}$ is the substrate strength in pascals; $\mathrm{\rho }$ is the density of the lava in kilograms per cubic meter; $g$ is the surface gravity of Venus in meters per square second; $H$ is the thickness of the lava flow in meters; $V$ is the velocity of the lava flow in meters per second; and $\mathrm{\varphi }$ is the slope of the canale in radians.

If a canale has a depth $D$ at its source, then the total time ( ${\mathrm{\tau }}_{\text{tot}}$ ) required to form it is

$${\mathrm{\tau }}_{\text{tot}}=\frac{D}{U_{\text{me}}}$$ (2)

and the total volume of lava ( $Q_{\text{to}t}$ ) required to erode the canale is

$$Q_{\text{tot}}=\text{HVW}{\mathrm{\tau }}_{\text{tot}}=\frac{A}{\mathrm{\rho }g\text{sin}\left(\mathrm{\varphi }\right)}\left(\frac{Y_{\mathrm{s}}}{b}\right)$$ (3)

The cross-sectional area of the canale is then

$$A=Q_{\text{tot}}\mathrm{\rho }g\text{sin}\left(\mathrm{\varphi }\right)\left(\frac{b}{Y_{\mathrm{s}}}\right)$$ (4)

Because of the uncertainty in their values, we used log-normal priors for $Q_{\text{tot}}$ , $\mathrm{\varphi }$ , $b$ , and $Y_{\mathrm{s}}$ , where $Q_{\text{tot}}$ ranges from 10⁵ to 10²⁰; $\mathrm{\varphi }$ ranges from 0.001 to 0.1 radians; $b$ ranges from 10⁻⁴ to 10⁻²; and $Y_{\mathrm{s}}$ ranges from 1 kPa to 25 Pa. We defined the standard deviation (SD) for our measured cross-sectional areas as 0.35 $A$ for all three depths tested, which corresponds to the formal uncertainty on the depth estimate from Baltis Vallis but is less than the uncertainty on the average depth of the other two canali with reported average depths.

Komatiites, low-Ti basalts, ocean island basalts, and tholeiitic basalts are hot enough to thermally and mechanically erode the tholeiitic basalt substrate. The thermal erosion rate (15, 65) $\left(U_{\text{th}}\right)$ in meters per second is

$$U_{\text{th}}=\frac{h_T(T-T_{\text{sg}})}{\mathrm{\rho }[C_{\mathrm{p}}(T_{\text{sg}}-T_{\mathrm{A}})+L]}$$ (5)

where $h_T$ is the heat transfer coefficient in watts per square meter per kelvin, T is the lava temperature in kelvin, $T_{\text{sg}}$ is the solidus temperature of the substrate in kelvin, $C_{\mathrm{p}}$ is the specific heat capacity of the substrate in joules per kilogram per kelvin, $T_{\mathrm{A}}$ is the ambient temperature (740 K), and $L$ is the latent heat of melting for the substrate in joules per kilogram. We then again solved for the cross-sectional area

$$A=\frac{Q_{\text{tot}}(U_{\text{me}}+U_{\text{th}})}{\text{HV}}$$ (6)

Our thermal and mechanical erosion model has two additional priors compared to the case of mechanical erosion only. First, the lava flow thickness, $H$ ranges from 0 to 20 m. Second, we introduced a dimensionless substrate coefficient, ${\mathrm{\beta }}_{\mathrm{S}}$ , which ranges from 0.001 to 1, in the heat transfer coefficient. Previous studies effectively used β_S ~ 1 in equations for h_T that were benchmarked to studies of homogeneous and well-mixed fluids (e.g., water). However, lava flows are not homogeneous. Crystals can form above the relatively cold substrate. Using β_S < 1 in our models captures how the temperature-dependent crystallinity of lava flows may thicken the thermal boundary layer at the bottom of the flow (66–68). Thickening the boundary layer then decreases the rate of heat transport from the lava into the substrate (see fig. S7). In comparison to previous studies, our models with β_S < 1 thus predict slower thermal erosion for a given lava flow thickness but also that those lava flows can flow for longer distances before crystallizing.

For both types of erosion models, we computed the posterior probability distributions for all model parameters using the MCMC method. We used the open-source package emcee (69), an affine-invariant ensemble sampler implemented in Python. For each MCMC inversion, we used at least 20 walkers with a burn-in of 5000 steps and a chain length of 10⁵ links. We ensured that the chains were at least 50 times as long as the autocorrelation length and manually inspected the trace plots for consistency with convergence. For each lava type, we performed a separate MCMC inversion for each of the 70 canali. We then summed the posterior probability distributions for $Q_{\text{tot}}$ , using Monte Carlo resampling, to obtain the final posterior probability distribution for the total lava volume required to erode all observed canali.

1D lava erosion modeling

Next, we ran forward models to reproduce the lava volumes, corresponding lava flow thicknesses, and effusion rates required to erode the canali. We used a fourth-order Runge-Kutta method to calculate how lava properties such as temperature, crystal fraction, viscosity, velocity, and heat flux to the atmosphere change as a function of distance along the length of a canale. Using these properties, we then calculated the rate of thermal and mechanical erosion along the length of the canale. We assumed that thermal erosion only occurs if the temperature of the lava exceeds the solidus of the alkaline basalt substrate and that each lava erupts at its liquidus temperature. The lava properties used (15, 19, 31, 36, 70–73) are given in table S2. The cooling rate in the direction of flow (15, 23, 65) is

$$\frac{\mathit{dT}}{\mathit{dx}}=\left(\frac{\mathit{dT}}{\mathit{dt}}\right)\frac{1}{V}=\frac{-Q_{\mathrm{A}}-Q_{\mathrm{S}}-Q_{\mathrm{M}}}{\mathrm{\rho }{C}_{\mathrm{p}}\text{HV}\left[1-\frac{L}{C_{\mathrm{p}}}\left(\frac{dX}{dT}\right)\right]}$$ (7)

where x is distance along track, t is the time, $Q_{\mathrm{A}}$ is the heat lost to the atmosphere though coupled radiation and convection, $Q_{\mathrm{S}}$ is the heat transferred to the substrate through conduction, $Q_{\mathrm{M}}$ is the heat used to melt the substrate in the case of thermal erosion, $\mathrm{\rho }$ is the density of the lava, $C_{\mathrm{p}}$ is the specific heat of the lava, $H$ is the lava flow thickness, and $L$ is the latent heat (see the Supplementary Materials) (15, 36, 65). After obtaining the temperature of the lava flow along track, we then calculated the thermal and mechanical erosion rates using Eqs. 1 and 3. Then, we calculated the flow duration ( $\mathrm{\tau }$ ) in seconds for a channel of a given depth (D) by

$$\mathrm{\tau }=\frac{D}{U_{\text{th}}+U_{\text{me}}}$$ (8)

We then used the flow duration to calculate the total volume of lava required and corresponding effusion rates. We tested this model on variable lava flow thicknesses (1 to 50 m), canale slopes (0.001 to 0.1 radians), canale depths (25 to 50 m), canale widths (1 to 5 km), and crust coverage (0 to 90% crust) to reproduce the observed dimensions of the canali.

CO₂ outgassing rate

Our models also introduce an equation for calculating the CO₂ outgassing rate, using a scaling relation between the depths of canali and craters to infer the number of generations of canali that may have formed. We calculated a steady-state rate of CO₂ delivery from canali-forming carbonatites as

$$\frac{{\mathit{dM}}_{\mathrm{C}{\mathrm{O}}_2}}{\mathit{dt}}=\frac{f_{\mathrm{C}{\mathrm{O}}_2}{\mathrm{\rho }}_{\mathrm{l}}{V}_{\text{tot}}}{{\mathrm{\tau }}_{\text{ca}}}$$ (9)

where $f_{\mathrm{C}{\mathrm{O}}_2}$ is the mass fraction of CO₂ in the lava (~0.3), ${\mathrm{\rho }}_{\mathrm{l}}$ is the lava density (~2200 kg/m³), $V_{\text{tot}}$ is the volume of lava that eroded the observed canali, and ${\mathrm{\tau }}_{\text{ca}}$ is the average age of the canali. Assuming that that the resurfacing of Venus has occurred at a steady rate, the canali could be younger than impact craters with the ratio of their average ages equal to the inverse of the ratio of their depths, such that ${\mathrm{\tau }}_{\text{ca}}$ = ( $D_{\text{ca}}$/$D_{\text{cr}}$ ) ${\mathrm{\tau }}_{\text{cr}}$ where $D_{\text{ca}}$ is the depth of the canali, $D_{\text{cr}}$ is the average rim-floor depth for impact craters (~750 m), and ${\mathrm{\tau }}_{\text{cr}}$ is the average age of impact craters. Like impact craters, we expect that the observed canali have a range of ages up to several times their average age. Some could have formed very recently. Others, such as Baltis Vallis, may have ages of ~100 Myr or more, long enough for mantle convection to produce dynamic topography (74, 75). This scaling relation is a first-order approximation to estimate the age of the canali and assumes that (i) canali are globally distributed (Fig. 1A) and that (ii) formation and burial of the canali occur at a constant rate over time. These processes are likely not spatially and temporally constant, but canali are easily removed because of their stratigraphic thinness, and the assumptions fit into the equilibrium resurfacing model for Venus (4). This approach could overestimate the contribution from canali to the atmosphere if canali only ever formed in certain areas or over a restricted time span. In any case, we calculated an effective time ( ${\mathrm{\tau }}_{\text{atm}}$ ) required to deliver this extra mass of CO₂ to the atmosphere

$${\mathrm{\tau }}_{\text{atm}}=\frac{\mathrm{\Delta }{M}_{\mathrm{C}{\mathrm{O}}_2}{\mathrm{\tau }}_{\text{cr}}}{f_{\mathrm{C}{\mathrm{O}}_2}{\mathrm{\rho }}_{\mathrm{l}}{V}_{\text{tot}}}\left(\frac{D_{\text{ca}}}{D_{\text{cr}}}\right)$$ (10)

Relative to Earth, Venus’ atmosphere contains an extra ∆$M_{\mathrm{C}{\mathrm{O}}_2}$ = 4.6 × 10²⁰ kg. We used Monte Carlo sampling of the variables in Eq. 8 to assemble cumulative distribution functions for ${\mathrm{\tau }}_{\text{atm}}$ . For each value of $D_{\text{ca}}$ (24, 35, and 46 m), we draw $V_{\text{tot}}$ from the log-normal distributions derived above (Fig. 2B and fig. S4). We sample ${\mathrm{\tau }}_{\text{cr}}$ = 240 ± 13 Ma from a normal distribution (6) and $f_{\mathrm{C}{\mathrm{O}}_2}$ from a uniform distribution ranging from 0.1 to 0.5 to account for uncertainties in the amount of CO₂ that could be outgassed from potential venusian carbonatites.

Supplementary Materials

This PDF file includes:

Supplementary Text

Figs. S1 to S7

Tables S1 to S2