Mountain Waves in the Upper Atmosphere of Venus

Planetary‐scale mountain waves have been observed at the cloud top of Venus and throughout the cloud deck. As they propagate from the surface to the cloud layers, multiple observations and numerical simulations have shown that they grow in size and do not break. However, the fate of mountain waves in the transition region and thermosphere, above the super‐rotating atmosphere, has only been addressed with two‐dimensional models. We conduct for the first time a simulation of mountain waves with a state‐of‐the‐art Venus climate model that includes the thermosphere. We find that mountain waves can propagate up to at least 150 km altitude, well above the transition region. They affect the circulation of the transition region, by reducing winds speeds, and the subsolar‐to‐antisolar circulation.


Introduction
Prominent features of Venus are the superrotation of its clouds and the slow rotation of its solid body.This manifests as largely different rotation periods in the cloud deck (4-5 Earth days at its top) and the surface (243 Earth days), with vastly different dynamical regimes and atmospheric conditions in the deep atmosphere, cloud deck, and thermosphere.Perhaps due to these differences, the influence of surface atmospheric dynamics was thought to be limited, if not negligible, on the atmospheric layers above.In-situ observations of the VEGA balloon measured a decrease of the lower clouds' wind speed above Aphrodite Terra (Blamont et al., 1986).Equatorial highlands were found to be correlated with wind measurements by cloud tracking of Venus Express (Bertaux et al., 2016;Patsaeva et al., 2019), and also H 2 O and UV albedo (Bertaux et al., 2016), although Khatuntsev et al. (2013) interpreted them as a long-term trend over the mission span, correlated to the 12-year solar cycle (Khatuntsev et al., 2022).Blamont et al. (1986) and Bertaux et al. (2016) postulated that small-scale gravity waves created at the surface are responsible for changes at the cloud deck level.Analysis of winds derived from the Akatsuki images also found a long-term trend, but no correlation of lower deck (Peralta et al., 2018) or cloud top (Jessup et al., 2020) winds with topography.Horinouchi et al. (2018) did not find any such correlation with Akatsuki winds, while Lee et al. (2020) attributed the finding of Bertaux et al. (2016) to an artifact in the longterm trends in their data set.
During its successful orbit insertion in December 2015, the Akatsuki spacecraft (Nakamura et al., 2016) imaged the brightness temperature of the cloud top of the full Venus disk for the first time.It observed an unexpected planetary-scale bow-shaped feature above Aphrodite Terra at the cloud top level in the infrared (Fukuhara et al., 2017), fixed with the surface rather than the background super-rotating winds.Similar features reappeared at the cloud top over five highlands during afternoons (Kouyama et al., 2017), with oscillations extending horizontally both upstream and downstream of the source regions (Fukuya et al., 2022), and were seen in UV (Kitahara et al., 2019).It was soon reproduced by global (Navarro et al., 2018) and mesoscale (Lefèvre et al., 2020) atmospheric models, and interpreted as an atmospheric mountain wave, thus challenging the previously held view that the different atmospheric layers of Venus have little or no direct dynamic connection.Simultaneously, multiple small scale features fixed with the surface were observed with Venus Express (Peralta et al., 2017).
While Venusian mountain waves are seen at the cloud top (Fukuhara et al., 2017;Kitahara et al., 2019;Kouyama et al., 2013), and modeled from the surface to the cloud top (Lefèvre et al., 2020;Navarro et al., 2018;Suzuki et al., 2023;Yamamoto, 2019), their impacts above the clouds are poorly known.Gorinov et al. (2018) measured the apparent motion of the O 2 recombination airglow seen by Venus Express in the upper atmosphere, and suggested a possible correlation between surface features and the airglow motion.Hickey et al. (2022) simulated Venusian mountain waves with a 2D spectral model, from the surface to the ionosphere, and found that they grow in amplitude up to an altitude of 200-250 km at Local Time (LT) 16 hr.The reason that mountain waves reach such high altitudes is the combined effects of an atmospheric scale height (∼13 km) smaller than the vertical wavelength (50 km), large horizontal wind fields (>200 m s 1 ) in the upper atmosphere, and lack of a critical level, at least for the afternoon.This results in a strong acceleration (up to 10 5 m s 1 hr 1 for some cases) and heating rate (up to 50 K hr 1 ).However, this model did not take into account dynamical effects of the atmospheric flow, but was rather based on outputs from a General Circulation Model (GCM) output.The recent improvements in atmospheric modeling for the upper atmosphere of Venus (Gilli et al., 2017(Gilli et al., , 2021;;Navarro et al., 2021) let us now simulate mountain waves with a GCM, benefiting from the surface parameterization of Navarro et al. (2018).In this article we present, in Section 2, the first 3D GCM of mountain waves in the upper atmosphere of Venus.The resulting simulations are discussed in Section 3, and conclusions are given in Section 4.

Methods
We employ the Venus Planetary Climate Model (PCM) (Forget et al., 2022;Stolzenbach et al., 2023), formerly known as the Institut Pierre-Simon Laplace Venus GCM (Garate-Lopez & Lebonnois, 2018;Lebonnois et al., 2016).The PCM configuration is the same as in Navarro et al. (2021) and Gilli et al. (2021), with a groundto-thermosphere capability up to ∼150 km that accounts for the change of atmospheric composition, near infrared solar heating rate, thermal conduction and viscosity, non-orographic gravity waves, etc… In addition, the PCM simulation includes the gravity wave drag parameterization of Lott et al. (2012) adapted for Venus in Navarro et al. (2018), letting us simulate mountain waves.In short, the subgrid statistics of the 4 km resolution Magellan topography (Ford & Pettengill, 1992) are used to create idealized, elliptical mountain shapes at each grid point defined by their slope, orientation, anisotropy, and standard deviation.A surface drag parameterization is then applied, resulting in PCM winds corrected at 35 km, the altitude where Venus mountain waves are explicitly resolved at the PCM grid.All in all, these enhanced computational features give the Venus PCM an unmatched capability to simulate mountain waves and their impact with the atmospheric dynamics above the cloud top, in the transition region and the thermosphere.This capability was initially sought for in Navarro et al. (2021) by increasing the horizontal resolution of Gilli et al. (2017) that was too coarse for the subgrid parameterization of mountain waves.However, the increase in resolution resulted in significant qualitative changes in the dynamics of the upper atmosphere that justified a study without mountain waves in Navarro et al. (2021).
Since the gravity wave drag parameterization has been shown to enhance the spurious loss of angular momentum (Navarro et al., 2018) by numerical rounding (Lebonnois et al., 2012), we decided to start the computations from the converged simulation with the upper atmosphere of Navarro et al. (2021) and Gilli et al. (2021), and run for an additional two Venus Solar days after switching on mountain waves following the method described in Navarro et al. (2018).This strategy prevents any significant effect of the long-term loss of angular momentum, and hence superrotation, while allowing the atmosphere to adapt dynamically to mountain waves.

Spatial Structure
In the simulations, the zonal wind structure varies predominantly with altitude.Zonal wind increases from zero at the surface, up to >100 m s 1 near the cloud top (Garate-Lopez & Lebonnois, 2018), in broad agreement with observations (e.g., Sánchez-Lavega et al., 2017).Above 90 km, the superrotation transitions to a Subsolar-to-Antisolar (SS-AS) circulation (Bougher et al., 1990;Schubert et al., 2007), with wind direction varying with local time.Figure 1 shows the average westward wind values over the Beta Regio area during daytime, with a drastic change of wind direction above 90 km past noon.Since the SS-AS flow is directed from the subsolar point toward the antisolar point, upper atmospheric winds become westwards, in the afternoon, in the same direction as the superrotation.In our simulations, we obtain an inflexion point at 90 km with westwards wind of 30 m s 1 in the transition region at 16 hr, meaning that the zonal wind always remains westwards above the cloud top during most of the afternoon.
Planetary-scale mountain waves are preferably generated in the afternoon (Kouyama et al., 2017) when the nearsurface atmospheric stability is optimal for Venus' largest mountain heights (Navarro et al., 2018).Of all the planetary-scale mountain waves, Beta Regio sees the earliest occurrence of one, in both observations and the Venus PCM.Kouyama et al. (2017) report a sighting at local time 11 hr, and no sighting before, whereas our model starts generating one at 7 hr.In Navarro et al. (2018), we attributed this early occurrence to the higher latitude, closer to deep mid-latitude jets and hence stronger surface winds, and the weaker diurnal cycle of this area.The occurrence of the Beta Regio wave too early in the Venus PCM is probably biased by too strong surface winds.
Beta Regio is an interesting case since its mountain wave appears early enough that the upper atmospheric winds are eastwards, instead of westwards.We show in Figure 1 the amplitude of the mountain wave.Taking advantage of the mountain waves on-off PCM experiment, we propose to estimate the wave amplitude with: with w′ the local vertical wind perturbations, the overline denoting averaging, and the index mw denoting the simulation where mountain waves are activated.This formulation has the advantage of removing background structures not due to mountain waves (unlike the quantity (w′ 2 mw ) ) and large-scale differences (unlike ), by comparing the deviations dominated by mountain waves for a given regional domain.As

Geophysical Research Letters
10.1029/2023GL104922 shown in Figure 1, the amplitude of the mountain wave grows with local time, peaking in the transition region, above 80 km, and maximal at 16 hr.Hickey et al. (2022) found that the amplitudes of afternoon mountain waves keep growing well into the ionosphere, and dissipate between 150 and 250 km, much higher than our simulations suggest in Figure 1.Assessing the causes of this difference is beyond the scope of this study, but it is worth noting that Suzuki et al. (2023) found that the dissipation could happen at a much lower altitude than Hickey et al. (2022), with lower stability values.
The appearance and growth of the mountain wave at various altitudes above the cloud deck is illustrated in Figure 2. Once again, Beta Regio is an interesting case due to its large amplitude in the late afternoon.At the cloud top (70 km), the mountain wave reaches a planetary scale at noon, with 2 cm s 1 amplitude.This value is in agreement with mesoscale modeling (Lefèvre et al., 2020).However, the amplitude has increased to 10 cm s 1 at 16 hr, owing to the higher surface winds of Beta Regio than Aphrodite Terra, Atla Regio, or Phoebe Regio.Consequently, the mountain wave is still clearly visible in the vertical wind maps in the SS-AS region, at 110 and 135 km.The mountain wave merges with the structure described in Navarro et al. ( 2021): a shock-like structure of large vertical wind speeds and intense heating past the terminator.At high Southern latitudes in the late afternoon (LT = 16.2 hr at 135 km in Figure 2), the Beta Regio mountain wave extends past the terminator, into the nightside, where it meets the shock-like structure.

Impact on Dynamics
The extension of mountain waves high into the upper atmosphere raises the question of their impact on atmospheric dynamics and the mean flow, especially on the SS-AS circulation.The Venus PCM is uniquely positioned to begin addressing this topic.We find that, overall, mountain waves can substantially change wind speeds locally, but their impact does not last.Figure 3 shows low-latitude westward zonal wind profiles along the planetary longitude.At 135 km, the SS-AS circulation is clearly apparent, with increasing, positive (i.e., westwards, toward the terminator) afternoon zonal wind speeds, and negative zonal wind speeds in the morning.The shock creates a sudden drop in wind speed, past the terminator at 6 and 18 hr (Navarro et al., 2021).The winds averaged for one solar day are compared for simulations with and without mountain waves.The two simulations are very similar, suggesting that mountain waves have no long-lasting impact on the circulation at 135 km.They only differ slightly by the position of the shock and nightside wind speeds, which is expected due to the strong nightside variability (Navarro et al., 2021).However, the same wind profile averaged when Beta Regio is located between 16 and 18 hr shows the localized impact of one single mountain wave.At 135 km, the zonal wind above Beta Regio (dashed line in Figure 3) is up to 80 m s 1 slower than the average zonal wind (continuous blue line in Figure 3) in the upstream region (between 14 and 16 hr), and up to 80 m s 1 faster in the downstream region (between 16 and 18 hr).At an altitude of 100 km, in the transition region, the impact of mountain waves is different, with a global decrease in wind speeds when mountain waves are activated in the model.Interestingly, the localized impact of Beta Regio is the opposite at 100 km of what it is at 135 km: increased horizontal winds upstream, and decreased downstream.
According to the non-acceleration theorem (Andrews & McIntyre, 1976), mountain waves do not generate meanflow acceleration, as long as they do not dissipate.Therefore, the net acceleration due to mountain waves in the cloud deck and transition region is expected to be null.
In Figure 4, we show the averaged afternoon vertical wind speed.Mountain waves do not break in the cloud deck and transition region and their impact is evident on the vertical wind field.
We find large values of vertical wind speeds: more than 5 cm s 1 in the transition region, and ±15 cm s 1 d 1 for Beta Regio at 135 km and above.By comparison, a simulation without mountain waves gives a VDMF of less than 2 cm s 1 in the whole atmosphere, leaving no doubt that the structures of Figure 4 are due to mountain waves.

Impact on Angular Momentum
The mountain wave parameterization arbitrarily launches waves as grid point perturbations at an altitude of 30 km (Navarro et al., 2018).Therefore, we do not show, nor try to assess, the local impact of mountain waves on angular momentum transport below the cloud deck, since simulated mountain waves, and the associated results, are probably not realistic in that altitude range.Overall, the total budget of angular momentum between a simulation with and without mountain waves is dominated by the spurious, long term, loss of angular momentum in the dynamical core documented in Lebonnois et al. (2012) and Navarro et al. (2018).).On the average, mountain waves decrease zonal winds of the SS-AS circulation in the transition region at 100 km, but have minimal impact at 135 km.However, the strong Beta Regio mountain wave creates a transient, noticeable impact of 80 m/s in afternoon winds at 135 km.Changes on the nightside are due to the high variability of the nightside past the shock-like structure and do not capture an impact of a mountain wave.

Conclusions
We have made the first simulation of planetary-scale mountain waves in the Venusian upper atmosphere with a GCM.The ground-to-thermosphere capability of the Venus PCM, in our setup, allows for the inclusion of dynamic orographic effects on the circulation up to 150 km altitude.
We find that the net effect of mountain waves is to decrease winds in the transition region from the superrotation circulation to the SS-AS circulation, while creating a noticeable localized weakening of the SS-AS circulation that ceases once the wave vanishes.For instance, the mountain wave centered on Beta Regio can change horizontal winds by up to 80 m s 1 .These effects on the wind suggest an efficient momentum transport from the SS-AS circulation to the transition region, via the general circulation.In agreement with Horinouchi et al. (2018), and contrary to Bertaux et al. (2016), we do not find significant cloud top wind changes associated with the topography.

Geophysical Research Letters
10.1029/2023GL104922 The Venus PCM realistically simulates planetary-scale mountain waves.Ideally we would like to run at a higher horizontal spatial resolution (<100 km).The twin mesoscale model of Lefèvre et al. (2020), extended into the upper atmosphere, would account for high-resolution topography while making minimal physical assumptions.However, assessing the large-scale impact of mountain waves on the circulation may prove to be problematic with a mesoscale model due to its limited spatial domain.Nevertheless, this issue of assessing the global, long-term impact of mountain waves still exists in the Venus PCM due to the non-conservation of angular momentum of its dynamical core, at least in the lower atmosphere.
Another future goal would be to include mountain waves in a model with an upper boundary at 250 km, higher than the model top of 150 km used in Navarro et al. (2021) and Gilli et al. (2021).That model will also include improved non-orographic wave drag, NIR heating rates, EUV solar flux, and photochemistry (Martinez et al., 2023).
In particular, Martinez et al. (2023) found that their improved formulation of non-orographic gravity waves resulted in a drag peaking at higher altitude (140-160 km) than in our PCM version (120-130 km), causing reduced SS-AS winds and the disappearance of the shock-like structure.However, the modeled shock-like structure is likely real since it explained various observations: nightside and terminator variability, spatiotemporal patterns of O UV dayglow and O 2 IR nightglow.Therefore, the impact of non-orographic gravity waves and their parameterization on mountain waves in the upper atmosphere remains to be explored.

Figure 2 .
Figure 2. Maps of downwards vertical wind speed (cm/s) above Beta Regio from the cloud top (70 km) to the thermosphere (135 km) for three local times.Positive (negative) values are downwards (upwards).The location of the Beta Regio mountain is indicated by a green dot.As the mountain wave grows in the afternoon, it reaches higher latitudes and altitudes.The local times are for the Beta Regio mountain (centered at 78°W, 25°N) and the 6 p.m. terminator is indicated by a vertical black line.

Figure 3 .
Figure3.Westward zonal wind (averaged for latitudes 40°S-40°N for data accumulated over one solar day) as a function of local time for altitudes 100 and 135 km.Continuous lines are averaged for one solar day, whereas the dashed line is averaged only for local times 16-18 hr above Beta Regio (longitude 78°W).On the average, mountain waves decrease zonal winds of the SS-AS circulation in the transition region at 100 km, but have minimal impact at 135 km.However, the strong Beta Regio mountain wave creates a transient, noticeable impact of 80 m/s in afternoon winds at 135 km.Changes on the nightside are due to the high variability of the nightside past the shock-like structure and do not capture an impact of a mountain wave.

Figure 4 .
Figure 4. Vertical wind speed for local times 14-16 hr and all latitudes, in m/s above the cloud top.The average underlying 40°S-40°N elevation is shown in gray shadings.