Atmospheric gravity waves in Venus dayside clouds from VIRTIS-M images

Icarus 415 (2024) 116076 Available online 3 April 2024 0019-1035/© 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Contents lists available at ScienceDirect Icarus journal homepage: www.elsevier.com/locate/icarus Research Paper Atmospheric gravity waves in Venus dayside clouds from VIRTIS-M images José E. Silva a,∗, Javier Peralta b, Alejandro Cardesín-Moinelo c,d,f, Ricardo Hueso e, Daniela Espadinha f, Yeon Joo Lee a aPlanetary Atmospheres Group, Institute for Basic Science, 55, Expo-ro, Yuseong-gu, Daejeon, 34126, Republic of Korea bDepartamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, San Fernando, 4, Sevilla, Andalucía, Spain cEuropean Space Astronomy Centre, Camino Bajo del Castillo s/n, Villafranca del Castillo, Madrid, 28692, Spain dInstitute of Astrophysics of Andalucia, Glorieta de la Astronomía s/n, Granada, 18008, Spain eDepartamento de Física Aplicada, Escuela de Ingeniería de Bilbao, Universidad del País Vasco/Euskal Herriko Unibertsitate, Universidad del País Vasco/Euskal Herriko Unibertsitatea Barrio Sarriena s/n Leioa Bizkaia, Bilbau, 48940, Spain fInstitute of Astrophysics and Space Sciences, University of Lisbon, Astronomical Observatory of Lisbon, Tapada da Ajuda, East Building – 2nd floor, Lisbon, 1349-018, Portugal ARTICLE INFO Keywords: Atmospheres Dynamics Ultraviolet observations Venus Atmosphere ABSTRACT We perform a survey of the Visible and Infrared Thermal Imaging Spectrometer-Mapper (VIRTIS-M) images onboard the Venus Express space mission, at four narrow wavelength bands that target different altitude regions on the cloud deck of Venus’ atmosphere (280–320, 365–400, 580–600, 900–920 nm). Our goal was to detect and characterize atmospheric gravity waves, using several processing techniques based on high-pass filtering to enhance features in low-contrast images. The period of our selected dataset was between August 2007–October 2008 on the dayside hemisphere, identical to a previous study of waves located on the nightside lower cloud, so that a temporally overlapped comparison could be established, although over different longitudinal locations. We retrieved the morphological properties of these waves including horizontal wavelength and packet width along with several orientations of the identified waves. We retrieved properties for 69 wave packets across all analysed wavelength ranges, and dynamical parameters for 16 wave packets. Waves observed across the four wavelength ranges examined here have similar properties, with horizontal wavelengths of a few hundred kilometres and full length of wave-trains going up to 1000 km. Although these wave properties do not seem to depend on latitude, we notice an increase in the values of several of these parameters close to the evening terminator. Considering our results and a comparison with previous studies of stationary features interpreted as gravity waves, we argue that forcing from topography is not the main cause of the wave packets observed here, whose properties are better supported by a convective generation scenario. The retrieved properties show a consistent agreement between waves on the upper and lower cloud, suggesting a similar forcing mechanism based on convection from a neutral stability layer between the lower and middle-upper cloud. Despite the similar properties, we find no evidence of any correlation between wave packets propagating in the lower cloud and upper cloud, based on their shape and relative position. 1. Introduction Gravity waves are a recurring phenomenon in planetary atmospheres. They are formed when a stably stratified layer is disturbed, leaving buoyancy of the displaced air parcel acting as the restoring force of this oscillation (Sutherland,2010). Being governed by such a fundamental force, they remain an intriguing feature in planetary atmospheres and their role in energy and momentum exchange can be influential in atmospheric circulation (Alexander et al.,2010), which holds particular interest for the case of Venus due to unanswered ∗Corresponding author. E-mail address: [email protected] (J.E. Silva). questions regarding superrotation in the cloud layer (Sanchez-Lavega et al.,2017;Horinouchi et al.,2018). Different arguments have been made regarding the influence of mesoscale (10–1000 km) gravity waves on the superrotation of the atmosphere. On a planet like Venus, changes in static stability and background wind velocity with height produce processes that modify the propagation of these waves at different altitudes (Hou and Farrel, 1987). These would provoke momentum exchanges between different atmospheric layers which can generally act to reduce the velocity https://doi.org/10.1016/j.icarus.2024.116076 Received 5 November 2023; Received in revised form 29 March 2024; Accepted 1 April 2024 Icarus 415 (2024) 116076 2 J.E. Silva et al. difference between the two regions (Sanchez-Lavega et al.,2017). Even though this can imply that gravity waves do not have a large impact on the maintenance of superrotation, their role in the vertical distribution of angular momentum is still uncertain, and they can be one of the elements behind the dynamics of the upper cloud (Horinouchi et al., 2020). Furthermore, the attenuation of waves at different heights, depending on their intrinsic phase velocities, can provide retrograde acceleration (Hou and Farrel,1987) and friction from momentum deposition which is expected to influence circulation as well. This may elucidate the dynamical conditions in the transition region between the Hadley cell circulation and the sub-solar to anti-solar circulation in Venus’ atmosphere (Seiff,1982;Gilli et al.,2021). Stationary features interpreted as gravity waves have also been reported, manifesting both on reflected sunlight at ultraviolet (UV) wavelengths (283–365 nm) and on brightness temperature images of the upper cloud at mid-infrared (8–12 μm), further reinforcing a connection between the surface and the cloud layer (Fukuhara et al., 2017;Fukuya et al.,2022;Kitahara et al.,2019;Kouyama et al.,2017; Peralta et al.,2017b). Previous observations of waves in the upper cloud with the Visual Monitoring Camera (VMC) instrument onboard the European Space Agency’s (ESA) Venus Express (VEx) space mission showed periodic structures interpreted as gravity waves on the northern hemisphere of Venus, possibly associated with the large Ishtar Terra mountain range (Piccialli et al.,2014). Radio occultation data from the Venus Radio Science instrument (VeRa) on board Venus Express captured small fluctuations on temperature profiles which were interpreted as gravity waves propagating in the upper cloud (Tellmann et al., 2012). Gravity waves have also been studied previously at both the upper and lower cloud simultaneously, showing a large diversity of properties and morphologies, unfortunately, limited to the southern hemisphere due to observational constraints (Peralta et al.,2008). A larger survey of gravity waves was made using both data from the Visible and Infrared Thermal Imaging Spectrometer (VIRTIS-M) instrument on VEx and data from the 2 μm Camera (IR2) onboard Akatsuki targeting the lower cloud (44–56 km). The wide range of wave properties suggested different forcing mechanisms, although convection seems the most plausible source for the structures that were characterized (Silva et al.,2021). Higher up in the atmosphere, structures interpreted as gravity waves have also been catalogued from non-LTE (Local Thermal Equilibrium) CO2emissions (Garcia et al.,2009). Given that gravity waves have been detected at several altitude levels, we investigated how their properties might change depending on altitude within the cloud layer of Venus and how transport of these waves might occur between the lower and upper clouds. We use data from the VIRTIS instrument covering the period between August 2007 and October 2008. We present our results of the search and characterization of atmospheric waves interpreted as gravity waves at three slightly different regions in the upper cloud, based on image observations on the dayside at selected wavelengths and sensitive to cloud layers between approximately 60–74 km (Peralta et al.,2017a). In this work, we expand the search of mesoscale waves over previous results obtained in Peralta et al. (2008). Since the period of observations of the upper clouds analysed here overlaps with a previous study of the lower cloud (Silva et al.,2021), we also compare the wave properties on these different altitudes. Additionally, we performed a first inspection of VEx/VIRTIS images at UV wavelengths characteristic of SO2absorption (280–320 nm), which allow us to sense altitudes above the top of the clouds (Horinouchi et al.,2018;Machado et al.,2021). We attempt to explore a possible connection between dayside clouds observed at visible/near UV wavelengths (60–74 km) and the nightside opacity patterns captured at infrared wavelengths (44–56 km) (Silva et al., 2021), by searching for wave packets that can be observed at two vertical levels simultaneously, as the single case reported by Peralta et al. (2008). 2. Data acquisition and selection We used VIRTIS-M on board the Venus Express (VEx) space mission, whose details are presented by Drossart et al. (2007) and Piccioni et al. (2007). Our observations focus on the southern hemisphere due to the high eccentricity of the spacecraft, which leads to high velocities near the pericenter, rendering effective mapping of the disk at these stages challenging (Svedhem et al.,2007). Given one of our primary goals of this work, this analysis serves as a natural progression from the results presented in Silva et al. (2021), where a systematic search for waves was conducted using the IR channel of VIRTIS-M. In turn, we held similar detection and characterization efforts during the same period, specifically the VEX orbits ranging from 467–921, which roughly corresponds to the time interval between August 2007 to October 2008. During this period we surveyed all available images at four wavelength ranges: 280–320 nm (hereafter, W1) (67–74 km); 365–400 nm (hereafter, W2) (63–70 km); 580–600 and 900–920 nm, both sensitive to the same altitude range (60–65 km), and hereafter referred as W3. The W1 range is mainly sensitive to SO2absorption, while also showing reflected light from the top of the clouds, while the W2 range matches the maximum absorption by the unknown UV absorber (Jessup et al.,2015;Perez-Hoyos et al.,2018). The visible range included in W3 shows generally lower contrast features from reflected solar radiation, but at a slightly lower altitude range (Hueso et al.,2015). The near-IR band included in W3 (900–920 nm) was used to complement the data selection procedure since this wavelength region targets approximately the same altitude range (Peralta et al.,2017a). We discuss the altitude of sounded regions at the different wavelength ranges in greater detail in Section 5.1. Thus, by observing wave features at these three four wavelength ranges it becomes possible to analyse the impact of waves propagating on the dayside hemisphere of Venus and evaluate their vertical extent and influence on the atmospheric circulation. Even though we were concerned with analysing the same period as in Peralta et al. (2008) and Silva et al. (2021) who examined VIRTIS-IR data, note that the visible channel of VIRTIS was able to provide data for a much longer period than the infrared channel, observing Venus until 2014. Although the data set used for this work is substantial, even if it represents only a fraction of VEx’s mission, the number of images where wave patterns could be recognized was significantly reduced, especially when we consider shorter VIRTIS wavelengths. At wavelengths W1 and W2, about half of the images were either not rendered in a way suitable to our search or were affected by an ’odd-even’ defect that produces artificial stripes in the images that interfere with the real waves in the images at small spatial scales. This effect was first observed in ground tests of VIRTIS and it occurs when there are large differences of responsivity between adjacent rows or columns in the detector (Cardesin-Moinelo et al.,2010). Even though this effect is negligible for long exposure times (>1 s), it becomes significant for shorter exposures and is exacerbated by high-pass filtering which we use to highlight wave features. Images at the W3 range were less affected by this problem, hence both the number of usable images and consequently the number of detected waves increased proportionally, even if the dayside at visible ranges has less contrasting features than W1 and W2 ranges (Hueso et al.,2015;Sanchez-Lavega et al.,2008). Fig. 1 shows an example of this effect. 3. Methods 3.1. Identification of atmospheric waves The process for wave detection and characterization was similar to what is described in Silva et al. (2021). Since most features have very poor contrast, high-frequency filters are employed to highlight atmospheric features, bringing possible waves to light. To eliminate spurious detections brought by filter artefacts and further enhance Icarus 415 (2024) 116076 3 J.E. Silva et al. Fig. 1. A VIRTIS-M image at wavelengths W1(A), W2(B) and W3(C) both before and after applying our processing routine. The odd-even effect manifests as set of vertical lines, most recognizable at W1 where creating creates stronger noise patterns. With high pass filtering this effect severely affects the visibility of features. image quality, several neighbouring filters of a VIRTIS cube were stacked (added then averaged) and processed together, along with the verification of consecutive images (separated by the shortest possible time difference) that target the same region of the atmosphere (where possible), to confirm the presence and propagation of the detected waves. To ensure consistency when stacking images at wavelengths W1, W2 or W3, we use the same number of frames for each wavelength range. No photometric corrections or normalization were applied to the images as our main concern was our ability to distinguish contrasting patterns in the atmosphere and most corrections of this kind did not improve significantly the images in our data set. Each image within the selected period was individually inspected for each wavelength range, looking for alternating contrasting patterns of bright and dark stripes which formed a localized ‘‘packet’’. As a first step to distinguish between possible wave features and other kinds of morphologies, we searched for wave packets with at least three consecutive bright and dark stripes forming a semi-organized wave train observable in the reflected light from Venus’ atmosphere. For both processing and characterization purposes, we made use of the tools provided by the PLIA (Planetary Laboratory for Image Analysis) software (Hueso et al.,2010) as well as other specialized programs designed for Venus image interpretation (Peralta et al.,2018). Multiple examples of detected wave packets at wavelengths W1, W2, and W3 are shown in Fig. 2. 3.2. Characterization of wave properties A total of 1564 VIRTIS-M-VIS cubes were inspected for this work, and since for each data cube we focused on three wavelength ranges, roughly 4600 images were individually analysed. These images were taken between Venus Express orbit 467 (31st of July 2007) and orbit 921 (27th of October 2008). Navigation of the images (i.e. longitudinal and latitudinal position of each pixel) is provided in geometric cubes, with the data calculated from SPICE kernels. The navigated images can then be projected into cylindrical maps in which longitudes and latitudes are equally spaced facilitating the comparison between images acquired at different times from different perspectives. The following Eq. (1) is used to compute the geometric distance, 𝐷𝑖𝑠𝑡, between two points in the image located at longitudes 𝛬1,𝛬2and latitudes 𝜙1,𝜙2. 𝐷𝑖𝑠𝑡 = 𝜋√(𝛬2−𝛬1)2𝑐𝑜𝑠2( 𝜙𝜋 180 )+ (𝜙2−𝜙1)2 180 (𝑎+ℎ)(1) where  𝜙is the average latitude between measured points, 𝑎is the planet radius and ℎis the altitude of the observed cloud layer. From this calculation, basic morphological properties were measured for each detected packet including horizontal wavelength (𝜆𝑥), packet length (𝑃 𝐿), and packet width (𝑃 𝑊 ), as illustrated in Fig. 3. Measurements for each of these properties are performed several times for the same packet and then averaged for a more robust characterization. Orientation with respect to the parallel was also recorded but here we define several orientation types due to the heterogeneous shape of wave packets — crest tilt (𝜃𝑇), crest orientation (𝜃𝐶) and group orientation 𝜃𝐺.𝜃𝑇is the angle between crest alignment with the equator. 𝜃𝐶is the orthogonal direction to the crest tilt and is positive when the point of highest longitude is northward and negative otherwise. We define 𝜃𝐺as the angle between the equator and the general axis that marks the observable length of the packet. This axis can be marked by having the same orientation as the shortest distance between two parallel lines that encapsulate the entire packet. The calculation of each orientation shares the same formula, where 𝛥𝜙 and 𝛥𝛬 are the angular difference between the latitude and longitude of points 1 and 2: 𝜃=𝑎𝑟𝑐𝑡𝑎𝑛(𝛥𝜙 𝛥𝛬 )(2) To aid in the visualization of these definitions of orientation we present a diagram on a wave example in Fig. 3. For cases where the same wave was observable between consecutive images, we took the opportunity to follow the movement of packets across several images to retrieve the phase velocity of the waves. We used a similar routine as employed in Peralta et al. (2018) to track the displacements of each crest of a wave packet between two images separated by a known time interval, retrieving at least 10 displacement measurements per packet. The local background wind at similar latitudes was also tracked to evaluate the intrinsic phase velocity of these waves and how they relate to the general atmosphere dynamics. Phase velocities of wave packets and background wind velocity were measured individually using wind tracers and the following equation: 𝑈= 𝑐𝑜𝑠( 𝜙)𝑅𝑒𝑞 𝜋 180 𝛥𝐿𝑜𝑛 𝛥𝑡 (3) Where 𝑈is the zonal velocity of the tracer (phase velocity if wave crests are used as tracers, background wind if other cloud features unassociated with the wave are tracked),  𝜙is the latitude average as in Eq. (1),𝑅𝑒𝑞 is the equatorial radius of Venus, 𝛥𝐿𝑜𝑛 is the zonal Icarus 415 (2024) 116076 4 J.E. Silva et al. Fig. 2. Wave packets observed on the dayside hemisphere of Venus by VIRTIS-M, highlighted in red. The wavelength range selected is centred on 288 (A–B), 365 (C–D), 600 (E) and 920 (F) nm, with the last two panels assumed to be monitoring the same altitude of Venus clouds. All images where subject to high-pass filtering and contrast enhancement followed by projection. Other wavy patterns present in the examples here are image artefacts and do not represent any atmospheric formation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Fig. 3. A diagram of the measurement routine for morphological characterization. The red, green and yellow coloured lines represent how the horizontal wavelength (𝜆𝑥), packet width (𝑃 𝑊 ) and packet length (𝑃 𝐿) are measured respectively. The angles 𝜃𝑇,𝜃𝐶and 𝜃𝐺illustrate the crest tilt, crest orientation and group orientation, all relative to the parallel. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) displacement of the tracked feature between images A and B and 𝛥𝑡 the temporal interval between the images. Wave phase speed is measured by tracking individual structures that belong to the wave packet (usually wave crests) between one or more pairs of images, depending on the lifetime and visibility of the packet. Given the observational constraints brought by VEx’s orbit around Venus, usually, the same region of the atmosphere could only be monitored for consecutive periods no longer than 6 h, which only allows for a minimum lifetime of the wave’s propagation to be observed in this way. 3.3. Other wave properties If we assume that the wave packets that were detected in this analysis correspond to atmospheric gravity waves, additional properties can be inferred by applying simple analytical models. Using linear theory to describe wave phenomena, neglecting effects from Venus’ rotation and assuming a Boussinesq flow, we can describe gravity waves as a small perturbation on the mean flow at a specific atmospheric level while considering the local pressure of the layer constant except when coupled with gravity (Nappo,2002;Holton,2004;Sutherland,2010; Sanchez-Lavega,2011;Peralta et al.,2014). Thus, an oscillatory disturbance caused by the buoyancy of neighbouring layers when subject to these small perturbations can be represented by the dispersion relation, which provides a relationship between a wave’s phase speed and its wavenumber: (𝑐𝑥 𝑝−𝑢)2= 𝑐𝑥 𝑝 2= 𝑁2+𝜉2(𝑚2+1 4𝐻2 𝑧 ) 𝑘2+𝑚2+1 4𝐻2 𝑧 (4) Where 𝑐𝑥 𝑝is the zonal component of the phase velocity, 𝑢 is the average zonal wind, 𝑁is the 𝐵𝑟𝑢𝑛𝑡-𝑉 𝑎𝑖𝑠𝑠 𝑎𝑙 𝑎 frequency, 𝑘and 𝑚are the horizontal and vertical wave-numbers, 𝐻𝑧represents the density Icarus 415 (2024) 116076 5 J.E. Silva et al. scale height at altitude 𝑧and 𝜉accounts for the centrifugal force when modified by the meridional shear of the background wind (Schubert and Walterscheild,1984;Peralta et al.,2014). Note here that we reduce absolute phase velocity to the intrinsic phase velocity of the waves (  𝑐𝑥 𝑝) by subtracting the contribution from the background flow. We do not include the meridional component of the phase velocity as its contribution to Venus’ circulation is limited when compared to the zonal flow and more importantly, because the best spatial resolution achieved on these images is often comparable with the absolute values measured for the meridional wind, possibly leading to unreliable results (Hueso et al.,2012,2015). The 𝐵𝑟𝑢𝑛𝑡-𝑉 𝑎𝑖𝑠𝑠 𝑎𝑙 𝑎 frequency can be estimated using the results from radio occultation measurements described in detail in Ando et al. (2020), namely temperature and consequent static stability vertical profiles for the upper/middle clouds: 𝑁=√𝑔.𝑆 𝑇(5) Where 𝑆is the static stability, 𝑔is the acceleration of gravity and 𝑇 is the atmospheric temperature. As both 𝑆and 𝑁vary with altitude and latitude range, multiple values were calculated for each variable. For the latitude range, we considered the intervals suggested by Ando et al. (2020) based on the distributions of zonally and temporally averaged temperatures and static stability. Regarding altitude ranges we considered the definitions summarized in Peralta et al. (2017a) for the wavelength ranges addressed in this work (W1, W2 and W3). We discuss this topic in greater depth in Section 5.1. The estimation of the 𝐵𝑟𝑢𝑛𝑡-𝑉 𝑎𝑖𝑠𝑠 𝑎𝑙 𝑎 frequency is then used to calculate the vertical wavelength of characterized packets. Considering the horizontal and vertical wave-numbers and their relationship with wavelength: 𝑘=2𝜋 𝜆𝑥 𝑚=2𝜋 𝜆𝑧 (6) Where 𝜆𝑥and 𝜆𝑧are the horizontal and vertical wavelengths of packets and introducing these in Eq. (4) we can compute the vertical wavelength of wave-packets with: 𝜆𝑧= 2𝜋√ 𝑐𝑥 𝑝 2−𝜉2 𝑘2 √𝑁2− 𝑐𝑥 𝑝 2𝑘2−1 4𝐻2 𝑧( 𝑐𝑥 𝑝 2−𝜉2 𝑘2)(7) Since this value is sensitive to the 𝐵𝑟𝑢𝑛𝑡-𝑉 𝑎𝑖𝑠𝑠 𝑎𝑙 𝑎 frequency, it is influenced by latitude and altitude range. Further up in Section 5.1.4 we will also discuss the influence of vertical shear of the zonal wind for wave packets with retrieved phase velocities. 3.4. Considerations on sources of uncertainty For both detection and characterization purposes, the spatial resolution of images in the data set is the most important factor when considering uncertainty since it affects the ability to see wave structures in the first place and also is the main contributor to error in distance measurement for various morphological parameters. Table 1 shows the average spatial resolution of images (𝛿𝐷𝑖𝑠𝑡) on the regions where waves were identified. It also shows the average uncertainties for each measured wave property (in square brackets), influenced mainly by spatial resolution and the processing applied to each image, to a lesser degree. Given the smaller sample in W1, the measurement uncertainties across packets are larger. Since the spatial resolution is the most limiting factor in measuring wave properties, the fact that the mean uncertainties 𝜁𝜆𝑥, 𝜁𝑃 𝑊 and 𝜁𝑃 𝐿 are comparable with the spatial resolution at the wave’s region is expected. However, this is less valid for waves in W1 due to the smaller sample size. Regarding the variations between distinct wave packets, we can see from the standard deviations from the average value of each property in Table 1 that values for 𝑃 𝑊 and 𝑃 𝐿 can change considerably between different packets, signalling diversity in waveforms. Also notice the spread of group orientations and crest tilt angles when compared with their mean values as illustrated in Table 1, although the limited number of detected waves at W1 somewhat influences the results presented here. Regarding phase velocities, not only is spatial resolution a factor in determining uncertainty on the wind tracers but the time interval between images as well: 𝛿𝑈 =𝛿𝑠 𝛥𝑡 (8) Where 𝛿U is the velocity error, 𝛿𝑠is the spatial resolution on the wave packet region, and 𝛥t is the time interval between images in the pair used to retrieve wind tracers. It is obvious from Eq. (8) that larger temporal differences between images lead to smaller errors. The mean error for the wind tracers across all dynamically characterized packets was approximately 10 m/s. Another limiting factor concerning wave detection was related to the overall quality of the images. Since we chose the period of observation to overlap with Silva et al. (2021) which focused on the nightside, a non-negligible part of the data set for the visible channel of VIRTIS does not show reflected light, making such images unsuitable for this work. Also, even though Venus’ atmosphere shows overall less contrast at visible wavelength (Hueso et al.,2012), these were the most reliable wavelengths to detect and characterize waves. A possible reason for this situation is the influence of the before-mentioned nonuniformity response of the detector which is more significant at shorter wavelengths and short exposure times. Finally, uncertainties in the geometrical information and timing of the images are estimated to cause navigation errors smaller than 1 km and do not play a significant role in this analysis. 4. Results A total of 69 wave packets were characterized this way across wavelengths W1, W2 and W3. At W1, the odd-even effect was strongest and only 4 detections were confirmed during this period. For W2, 14 images with waves were identified and W3 holds most of the detections with 51 observations. At least 20 of the images with a packet share the same wave formation across wavelength ranges. Two cases with the same packet at W1 and W2 wavelengths, 15 cases with the same packet at W2 and W3 wavelengths, and three cases where the same packet could be seen across the three wavelength ranges. However, note that due to the before mentioned odd-even effect, it becomes challenging to confirm at the wavelength ranges W1 and W2 the simultaneous existence of wave features observed in W3 when exposure times are short (<1 s). The same wave structure can also be observed in consecutive images, thus the total number of detections when referring to wave packets detected might be misleading. As such, we define a distinct wave packet as an independent feature that can be observed on multiple images but has singular coordinates and characteristics. Taking all repeated waves we arrive at 41 characterized distinct waves. As stated in Section 3, consecutively observed packets made their dynamical characterization possible. A total of 16 distinct packets were tracked for their phase speed and approximate trajectory in the atmosphere of Venus. 4.1. Wave properties In Fig. 4 we show the characterized wave packets at W1, W2 and W3. Some of these overlap because the same wave was visible at multiple wavelengths. Since VIRTIS observations during the selected period were not uniform over all geographical locations of Venus we calculated the ratio of detection of waves to the total number of observations for a specific area of the planet, which we show in Fig. 5. The size of the area used in the calculation of the wave occurrence maps is a square area with 10◦latitude and 20◦longitude, centred on the wave’s mean position. Our study is focused on the southern Icarus 415 (2024) 116076 6 J.E. Silva et al. Fig. 4. Distribution of all characterized wave packets between August 2007–October 2008 over the topography of Venus. Dark blue data points represent the detections in W1, magenta in W2 and green in W3. Topographical data was extracted from Magellan data. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Fig. 5. Top:Latitude-Longitude (A) and Latitude-Local Time (B) coverage maps for VIRTIS-M-VIS observations during the selected period of observation. Bottom:Wave frequency maps for Latitude-Longitude (C) and Latitude-Local Time (D), showing the distribution and occurrence of wave packets. The size of the bins in the wave occurrence maps is 10◦ latitude by 20◦longitude centred on the waves mean position. White space signifies lack of data. Icarus 415 (2024) 116076 7 J.E. Silva et al. Table 1 Morphological Properties of wave packets. For each wavelength range ([𝜆]) we list the number of characterized packets in parenthesis. 𝜆𝑥is the horizontal wavelength, PW is the packet width, PL is packet length and 𝜃is the orientation of the packet. Each table entry in 𝜆𝑥, PW, PL is the mean value for that property for packets characterized at that wavelength.𝜃𝐺is the group orientation, 𝜃𝑇is the crest tilt and ‖𝜃𝐺−𝜃𝐶‖is the angle between the crest and group orientations, henceforth referred to as crest skew. Standard deviations of each morphological property are represented next to the average value. Below in square brackets we represent the measurement uncertainty of each morphological property for individual packets, since each packet’s properties are measured several times. [𝜆]𝛿𝐷𝑖𝑠𝑡 𝜆𝑥±𝜎𝜆𝑥PW ±𝜎𝑃 𝑊 PL ±𝜎𝑃 𝐿 𝜃𝐺±𝜎𝜃𝐺𝜃𝑇±𝜎𝜃𝑇‖𝜃𝐺−𝜃𝐶‖ [𝜁𝜆𝑥] [𝜁𝑃 𝑊 ] [𝜁𝑃 𝐿 ] [𝜁𝜃𝐺] [𝜁𝜃𝑇] (nm) km/pix (km) (◦) W1 (#4) 32.0 211 ±47 516 ±159 939 ±567 3.9 ±61.9 −27.3 ±47.9 13.8 [30] [94] [58] [3.2] [6.0] W2 (#14) 23.4 122 ±56 264 ±188 468 ±338 1.8 ±25.3 −14.0 ±47.9 34.5 [19] [35] [35] [2.6] [7.4] W3 (#51) 22.6 107 ±48 289 ±163 405 ±213 3.9 ±17.1 −11.3 ±56.5 23.2 [17] [35] [29] [2.7] [5.2] hemisphere due to the apocenter of Venus Express’ orbit close to the south pole (Titov et al.,2006). In general, wave occurrence is less than 5% (Fig. 5), and wave activity seems to be concentrated close to the evening terminator at local times between 17–18 h. However, caution must be taken when extracting conclusions since this low recurrence might be partially caused by the problem of low contrast in VIRTIS-M images. 4.1.1. Morphology For characterization, our first step was to measure the basic properties of detected wave packets. In Table 1 we list the basic morphological properties of the characterized packets for each wavelength range ([𝜆]) along with the average spatial resolution (𝛿𝐷𝑖𝑠𝑡) of images at each wavelength range. We include here spatial properties like horizontal wavelength, packet width and length and several orientations including the crest skew. This last orientation parameter can be seen as an indication of wave deformity from a ’standard shape’ where crests are perfectly perpendicular to the group’s orientation. For each wavelength range, we also note its respective number of characterized packets. Also in Table 1 we show the standard deviations of wave packet dimensions from the mean values. Since several measurements of the same property are taken for a single wave packet, it is also useful to verify that the retrieved measurements are consistent within the same wave packet. On the same table the uncertainties associated with the measuring procedure for each property are written in square brackets. Even though most of the waves detected during this period have scales of hundreds of km, and despite the high spatial resolution at subspacecraft point for most of our images (∼20 km/pix) it is possible that smaller packets also manifest at these wavelengths, similar to what has been reported in Piccialli et al. (2014). Another point to consider is that some of these packets were detected close to the evening terminator, where visibility becomes limited at these wavelengths. As such, the packets in question might be larger (in PW or PL) and for those, we can only provide a minimum value for both wave dimensions. Figs. 6 and 7show how the measured properties of the waves in this study change with latitude and local time. Although most of the waves are located southward of 50◦, the dimensions of wave packets seem to subtly rise as they approach the equator. Changing circulation regimes for higher latitudes (close to the ‘‘cold collar’’) might disturb the formation mechanisms for larger wave structures or aid in their destruction. Alternatively, the cold collar marks the transition from elevated clouds observed in UV to lower clouds descending over 10 km from 74 km in subpolar latitudes to about 65 km around the inner side of the cold-collar (Ignatiev et al.,2009). These large changes in altitude may occur through vertical layers of the atmosphere in which the stability properties change strongly, modifying the conditions for wave propagation. A simpler explanation may reside in the general fact that for VIRTIS-M data, the spatial resolution becomes larger for equatorial latitudes, explaining a lack of smaller wave packets. Another tentative remark concerns the tendency for group orientation to align with parallels, even though the background zonal wind Table 2 Intrinsic Phase Velocity of Dayside Waves with VIRTIS-M. VEx Orbit Lat (◦) LT (h)  𝑐𝑥 𝑝(m/s) 𝛿𝑐𝑥 𝑝(m/s) 694 (W2) −58.4 12.4 −12 9 477 (W2) −69.6 13.4 −16 12 698 (W3) −31.1 14.2 −6 18 468 (W3) −52.3 12.8 −15 3 650 (W3) −53.3 7.2 5 6 694 (W3) −57.3 11.9 −13 9 740 (W3) −63.9 8.4 −23 8 914 (W3) −65.9 14.1 22 7 476 (W3) −66.6 15.0 −11 14 476 (W3) −68.4 14.4 −12 11 891 (W3) −70.4 8.9 −2 7 912 (W3) −72.5 14.6 −9 7 479 (W3) −72.8 16.6 18 11 471 (W3) −74.8 12.7 −1 4 880 (W3) −76.2 10.7 −39 7 885 (W3) −78.3 8.3 15 7 is generally weaker, south of 60◦. The measured properties seem to be more influenced by local time. There is some indication that waves’ spatial scales are enhanced close to the evening terminator, with the group orientation also seemingly affected. 4.1.2. Dynamics — phase velocity For the 16 cases where waves were tracked in sequences of several images, we retrieved the phase velocity of the packets by tracking the movement of wave crests at different times during the observed propagation. The method employed here has many similarities with cloud tracking which has been used extensively to study Venus’ cloud deck (Goncalves et al.,2019;Hueso et al.,2015;Machado et al., 2017). We could not find any example of an image sequence where the dynamics of a wave at W1 could be tracked. Hence, no dynamics data for these packets was retrieved. Fig. 8 shows the retrieved phase speed velocities of 16 wave packets that could be tracked within the observation period. For comparison, we also show the average zonal wind profile obtained by Hueso et al. (2015). Most of the packets follow the average zonal wind profile or move within the boundaries of the errors. However, some wave packets show considerable deviations from this mean flow. Such deviations can be expected since considerable variety in the instantaneous values of the zonal wind with longitude, local time, and period of observation has been reported (Machado et al., 2021;Sanchez-Lavega et al.,2017). For a clearer picture of the waves’ motions in the atmosphere, we subtract the local background wind, retrieved at the same latitude level by tracking cloud features not related to the wave propagation. Table 2 shows the values for the intrinsic phase velocity of waves, where negative velocities imply waves being faster than the background wind since the general zonal circulation on Venus is retrograde. Almost all of the waves dynamically characterized display such values in relation to the background wind, with one case going at speeds that Icarus 415 (2024) 116076 8 J.E. Silva et al. Fig. 6. Morphological properties (A: Horizontal Wavelength, B: Packet Width, C: Packet Length, D: Group Orientation, E: Crest Tilt, F: Crest Skew) with respect to the packet’s latitude on Venus. We ignore the northern hemisphere due to orbital constraints. Packets are also separated in wavelength range showing W1 detections in purple, W2 in blue and the W3 range in red. Approximate altitude ranges for each wavelength range is also represented in square brackets. For orientation parameters we do not include the error bars here because the errors are associated with the spatial resolution (in degrees) which for all cases is less than 1 deg/pix. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) are almost 40 m/s greater than the surrounding winds. The error 𝛿𝑐𝑥 𝑝 is based on the image’s spatial resolution and time interval between them as explained in Section 3.4. Most of the waves were tracked over a relatively short period (approximately 1 h) as shown in Fig. 9 and their trajectory suggests that they mostly follow the zonal direction, possibly because the zonal wind dominates atmospheric circulation in the cloud deck (Sanchez-Lavega et al.,2008). As previously mentioned, the starting and end positions for the waves represented in this work are not directly related to wave generation or dissipation since we were limited by the observing conditions brought by VEx’s orbit around Venus. 4.1.3. Dynamics — vertical wavelength Table 3 shows the calculated values of the vertical extent of the waves using Eq. (7). For each distinct packet, we list the calculated value of the vertical wavelength (𝜆𝑧) along with the propagated error Table 3 Vertical Wavelengths for dayside wave packets detected with VIRTIS-M-VIS. VEx Orbit Lat (◦) LT (h) 𝜆𝑧(km) 𝛿𝜆𝑧(km) 694 (W2) −58.4 12.4 4 3 477 (W2) −69.6 13.4 5 4 698 (W3) −31.1 14.2 2 7 468 (W3) −52.3 12.8 6 2 650 (W3) −53.3 7.2 2 2 694 (W3) −57.3 11.9 5 4 740 (W3) −63.9 8.4 7 6 914 (W3) −65.9 14.1 7 5 476 (W3) −66.6 15.0 3 5 476 (W3) −68.4 14.4 4 4 912 (W3) −72.5 14.6 1 2 479 (W3) −72.8 16.6 5 5 880 (W3) −76.2 10.7 11 7 885 (W3) −78.3 8.3 4 3 Icarus 415 (2024) 116076 9 J.E. Silva et al. Fig. 7. Morphological properties versus their Local Time coordinate. Organization of panels is identical to Fig. 6. The morning and evening terminators are approximately at 7–8 h and at 18–19 h. The errors on local time are generally less than 0.5 h, which makes them comparable to the size of the symbols illustrated here. The errors associated with morphological parameters are identical to what is presented in Fig. 6. 𝛿𝜆𝑧which was calculated with the following equation: 𝛿𝜆𝑧=√ √ √ √ √(𝜕𝜆𝑧 𝜕 𝑐𝑥 𝑝)2 𝛿 𝑐𝑥 𝑝+(𝜕𝜆𝑧 𝜕𝑘 )2 𝛿𝑘 +(𝜕𝜆𝑧 𝜕𝑁 )2 𝛿𝑁 +(𝜕𝜆𝑧 𝜕𝐻𝑧)2 𝛿𝐻 (9) As expected, the biggest contributors to the propagated error of the vertical wavelength were the retrieved phase velocities and the 𝐵𝑟𝑢𝑛𝑡- 𝑉 𝑎𝑖𝑠𝑠 𝑎𝑙 𝑎 frequency. From these results, we observe that the vertical extent of waves is rather small when compared with their morphological properties (see Table 1). As demonstrated by Ando et al. (2020), static stability can vary significantly with latitude and altitude, which plays a role in the calculation of vertical wavelength via the 𝐵𝑟𝑢𝑛𝑡-𝑉 𝑎𝑖𝑠𝑠 𝑎𝑙 𝑎 frequency (see Eq. (7)). However, static stability profiles can be generalized for specific latitudinal ranges, namely the equator (0◦–30◦) and midlatitudes (30◦–60◦), while for higher latitudes, narrower ranges become necessary. This generalization is possible since within these latitude ranges the static stability has been observed to not change considerably at the altitudes studied in this work. Even though we calculated the value of 𝜆𝑧for each altitude between 60–74 km, with 1-kilometre bins, we also defined altitude intervals for each wavelength window: W2 - 63–70 km, W3 - 61–65 km. We can then average the 𝐵𝑟𝑢𝑛𝑡-𝑉 𝑎𝑖𝑠𝑠 𝑎𝑙 𝑎 frequency values for each altitude level within range at the appropriate latitudinal window (depending on the wave location) to arrive at the vertical wavelength values in Table 3. Even though this simple approach is powerful enough to calculate approximate values of the vertical wavelength, using the aforementioned approximations, it does not capture the influence of the vertical shear of the background zonal wind. Since the zonal wind is dominant on the cloud layer of Venus, it can have a significant impact on wave propagation. We approach this influence in Section 5.1.4 with a recalculation of the vertical wavelength using a more sophisticated model. 5. Discussion 5.1. Altitude of waves within the cloud layer The observation of Venus’ atmosphere at different wavelengths enables the monitoring of multiple levels of the atmosphere, taking advantage of several ongoing processes. The wavelength range used in this work is concerned with the reflection or absorption of sunlight on Icarus 415 (2024) 116076 16 J.E. Silva et al. Fig. 15. Intrinsic phase velocity of gravity waves propagating on the upper and lower clouds from VIRTIS data within the same observing period. Nightside waves results are taken from Silva et al. (2021) and Peralta et al. (2008). We also include dayside waves data retrieved in Peralta et al. (2008). The average errors associated with dayside waves are approximately 9 m/s and for nightside waves around 6 m/s. Fig. 16. Calculated vertical wavelengths from waves on the upper and lower cloud at their respective latitudes. explored here. As reported in Kitahara et al. (2019), the features have a horizontal extension between 300–500 km and a north–south extension between 2000–3000 km. Considering that these features have a mostly perpendicular orientation to the zonal direction, we relate the before-mentioned values to packet length and packet width respectively. The local distribution of packets found in this study and the stationary features observed by UVI never overlap, which is largely expected due to the equatorial orbit of the Akatsuki spacecraft as opposed to the previously mentioned polar orbit of Venus Express. The horizontal extensions of these stationary waves are overall smaller than the packet length of waves in this survey (see Table 1), although we must acknowledge the difference between the wave trains in this work (which feature a sequence of multiple crests-troughs) and those found by Kitahara et al. (2019) (usually single crest). Regarding meridional extension of the packets when compared to the packet width of the waves found by VIRTIS, there is a stark contrast in dimensions between the two populations of waves, with the crests of the bow-shaped features seen with UVI extending over 4 times the average width of VIRTIS waves. As already mentioned, the group orientation of the stationary waves observed is predominantly close to 0◦however, taking the standard deviation of the group orientation from the mean (see Table 1), the alignment of the packets found in this study is less consistent (average variability of around 25◦between packets at W2). Similar comparisons can be established with stationary features found on brightness temperature images recorded by the Longwave Infrared Camera (LIR) onboard Akatsuki (Fukuya et al.,2022). These images show stationary wave trains, which greatly extend their zonal span, reaching values between 500–1500 km, revealing some consistency between wave populations there and in the present work. Note that the waves detected with LIR can be found on both dayside and nightside and the altitudes associated with these structures are centred at ∼65 km (Taguchi et al.,2007). Stationary and slow-moving features were also reported on the nightside atmosphere using VIRTIS-M at 3.8 and 5 μm, which shows its thermal emission of the upper cloud, on an extensive survey presented in Peralta et al. (2017b). The horizontal wavelengths of these structures are between 100–250 km, with packet lengths around 1000 km and widths extending within 1000–3000 km. Curiously the horizontal wavelengths found on travelling waves both on the day and nightsides (Peralta et al.,2008;Silva et al.,2021) are similar to what was measured for the stationary features seen on thermal emission. However, the packet lengths are on average double the size for stationary features than for travelling waves at the same altitude region on the dayside, even though there might reside here an observational bias, as the sample from Peralta et al. (2017b) was much more numerous. Regardless, we observe the same tendency on the packet widths, extending far beyond what is observed for travelling waves. Given the unexpected discovery of the large bow-shaped stationary wave reported in Fukuhara et al. (2017) and the later additional detections of more stationary features on the atmosphere of Venus, modelling efforts were readily directed to reproduce these observations. One such effort (Lefèvre et al.,2020) was able to convincingly replicate the characteristics of the stationary waves detected by the Japanese space mission, with wave features that possess horizontal wavelengths with comparable values to those observed in this study. However, other morphological aspects and vertical wavelengths are remarkably different, the latter which exceeds more than 5 times the average observed here, along with the fact that these calculations model stationary features, unlike our detections. Although differential coverage challenges interpretations over the distribution of packets between UVI and VIRTIS-M on the dayside reflected clouds, both wave populations seem disconnected in terms of their generating mechanisms, further emphasized by their different properties with particular attention to the packet width. For the waves found on the nightside thermal emission, we can find a better agreement between both populations and their distributions partially overlap. However, the large difference between the sample size of both data sets and the same contrast regarding packet widths reinforce the argument that the waves found in this study are not generated by flow over topography. 6. Conclusions We have explored atmospheric waves on the dayside upper cloud of Venus by observing four narrow wavelength bands to characterize wave activity across different altitudes within the upper cloud. This survey took data from an analogous period on which nightside lower cloud waves were characterized (Silva et al.,2021) to investigate how wave properties change with altitude within the cloud deck of Venus and if there is any communication of mesoscale wave activity between lower and upper clouds. This search was partially compromised by data quality issues brought by the small contrast of VIRTIS images, which made it challenging to evaluate wave activity, especially at W1 wavelengths (280– 320 nm). Although this fact made it difficult to verify the threedimensional structure of wave packets by observing across the three wavelength ranges chosen, a substantial number of waves was still characterized, especially at the visible range where fewer atmospheric features have been described in the past. Dayside upper cloud wave packets share similar orientations and many properties with their siblings on the lower cloud, both in terms Icarus 415 (2024) 116076 17 J.E. Silva et al. of their spatial sizes and intrinsic dynamics and trajectories, although waves on the upper cloud seem to have a different distribution of wavelengths and tend to move faster relative to the background wind than waves in the lower layer. It is also noticeable that some morphological properties of waves are enhanced close to the evening terminator where wave activity is slightly increased as well. Continuous analysis of the extended VIRTIS data set (until the end of the mission in 2014) would yield more concluding results in this matter. Waves on the lower and upper clouds, at 44–56 and 60–74 km respectively and observed on the nightside and dayside on different images, have similar mean properties in terms of their wavelengths and orientations. This suggests a similar origin even if both layers are separated by a neutrally stable layer at approximately 50–55 km. Convection in the intermediate neutrally stable layer could be the source of gravity waves in both layers. From comparisons with waves associated with topographical features, we additionally make the tentative conclusion that the waves found in this study are probably not forced by topography. However, we encourage further exploration of the VIRTIS-M dayside data to bridge the gap between past and present missions to Venus and also expand the search for waves to its fullest. Acronyms VIRTIS-M: Visible and Infrared Thermal Imaging Spectrometer- Mapper; VMC: Venus Monitoring Camera; VEx: Venus Express; ESA: European Space Agency; IR2: 2 μm Camera; UV: Ultraviolet; IR: Infrared; W1: 280–320 nm; W2: 365–400 nm; W3: 580–620/900–920 nm; PLIA: Planetary Laboratory for Image Analysis; PL: Packet Length; PW: Packet Width; LT: Local Time; Lat: Latitude; UVI: Ultraviolet Imager; LIR: Longwave Infrared Camera; VeRa: Venus Radio Science; CRediT authorship contribution statement José E. Silva: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Javier Peralta: Writing – review & editing, Validation, Software, Investigation, Formal analysis. Alejandro Cardesín-Moinelo: Writing – review & editing, Validation, Data curation. Ricardo Hueso: Writing – review & editing, Visualization, Validation, Software. Daniela Espadinha: Writing – review & editing, Visualization. Yeon Joo Lee: Writing – review & editing, Validation, Supervision, Resources, Project administration, Funding acquisition. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability Data will be made available on request. Acknowledgements This work was supported by the Institute for Basic Science, South Korea (IBS- R035-C1). We also acknowledge the support of the European Space Agency and the associated funding bodies Centre National d’Etudes Spatiales (France) and Agenzia Spaziale Italiana (Italy) as well as the full team behind the VIRTIS instrument, Venus Express space mission and the PSA archives (ESAPlanetaryScienceArchive). R.Hueso was supported by Grant PID2019-109467GB-I00 funded by MCIN/AEI/10.13039/501100011033, Spain/ and by Grupos Gobierno Vasco, Spain IT1742-22. J. Peralta thanks EMERGIA funding from Junta de Andalucia in Spain (code: EMERGIA20_00414). J.S. acknowledges that J.P. and R.H. contributed greatly with the software used to carry out this work and A.C. for help with interpreting the VIRTIS data set. J.S. also acknowledges the leadership and supervision of Y.J.L. Finally, J.S. acknowledges that all co-authors contributed in the review of this work before its submission. 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