INTRODUCTION

UV (365 nm) images of Venus cloud cover obtained by the VMC/Venus Express camera (Titov et al., 2006; Svedhem et al., 2009) of the European Space Agency (ESA) from 2006 to 2013 and the UVI/Akatsuki camera (JAXA) (Nakamura et al., 2016) of the Japan Aerospace Agency from 2015 to the present time have provided a unique opportunity for an almost continuous study of the atmospheric dynamics at the cloud top level (70 ± 2 km). The Venus Express spacecraft operated on a highly elliptical polar orbit with a periapsis near the north pole of Venus, so only the southern hemisphere of the planet was available for horizontal wind measurements. Akatsuki, with its highly elliptical equatorial orbit, observes both hemispheres of the planet, allowing comparison of wind velocities at southern latitudes for both missions.

Based on an analysis of UV VMC images from 2006 to 2012, Khatuntsev et al. (2013) found an increase in the average zonal wind speed at the cloud top in equatorial latitudes. Analysis of UVI images, on the contrary, showed a decrease in the average zonal speed. In total, using results from both missions, long-term quasi-periodic variations in the average wind speed with a period of 12.5 ± 0.5 years were identified (Khatuntsev et al., 2022).

Analysis of the VMC results obtained with the visual method from UV images of the southern hemisphere of Venus (Khatuntsev et al., 2013) made it possible to detect correlation of the zonal wind speed with the topography of the underlying surface in the latitude interval of 10° ± 5° S (Bertaux et al., 2016). It was shown that the location of the minimum zonal wind speed correlates with the highlands of western Aphrodite Terra (Ovda Regio), a vast “continental” area extending along the latitudes of 10° ± 30° S from 50° to 210° E. Following Lindzen (1981) and Young et al. (1987), Bertaux et al. (2016) explained the deceleration of the zonal flow by the influence of gravity waves that emerge when the horizontal flow interacts with a surface obstacle, and subsequently propagate upward with a transfer of momentum to the zonal flow. It was suggested that the mean zonal wind speed increased during the mission period due to the sub-satellite point longitude slowly drifting from orbit to orbit in the western direction, from the mountainous region of Ovda to the lowlands.

Patsaeva et al. (2019) confirmed the dependence of the zonal wind speed on the topography of the underlying surface, as well as discovered the dependence of the minimum zonal speed location on local time. The authors utilized VMC data together with an automated cloud tracking method (Khatuntsev et al., 2013; Patsaeva et al., 2015). However, by analyzing wind speeds obtained from UV (365 nm) UVI images from December 2015 to March 2017, Horinouchi et al. (2018) on the contrary found an increase in the average zonal wind speed above Ovda Regio, and thus questioned influence of the underlying surface topography on the atmospheric dynamics at the cloud top of Venus.

This work examines variations in the dependence of average wind velocity on longitude at the cloud top in the equatorial latitudes from 2006 to 2022 for limited measurement intervals. Longitudinal variations of the zonal wind speed were studied in the latitude band of 10° ± 5° S, corresponding to the highest altitude of Ovda Regio. Longitudinal and latitudinal variations of the zonal and meridional components of wind velocity depending on the phase of the 12.5-year Solar cycle are also considered. To capture solar-induced variations in horizontal flow velocity, the local time interval was limited from 11 to 13 hours. Due to the orbital characteristics of Venus Express, the vast majority of velocity vectors in near-equatorial latitudes obtained from VMC images have phase angles in the range from 60° to 90°. In order to exclude the possible dependence of the zonal speed on the phase angle, the selection of vectors obtained from UVI images was also limited to this range.

DATA AND METHODS

This work analyzes wind velocity vectors obtained from VMC/Venus Express (Markiewicz et al., 2007; Titov et al., 2012) and UVI/Akatsuki (Nakamura et al., 2016; Yamazaki et al., 2018) cameras using automated cloud tracking method on Venus dayside in UV channel of 365 ± 20 nm.

The Venus Express spacecraft operated on a highly elliptical polar orbit around Venus from April 2006 to January 2015 with an apocentre of 63 000 km and a pericenter close to the North Pole, with an altitude of 250–350 km. The orbital period was approximately 24 h (Svedhem et al., 2009). To obtain wind velocity vectors, images from the ascending branch of the orbit with a resolution of 50 to 10 km per pixel were used. The original data (images with corresponding observation geometry) are available online at the ESA Planetary Science Archive (PSA), https://archives. esac.esa.int/psa/ftp/VENUS-EXPRESS/VMC/. The method for obtaining velocity vectors from the displacement of cloud details using an automated algorithm from a pair of consequent UV images is described in Khatuntsev et al. (2013) and Patsaeva et al. (2015).

During the entire period of Venus Express’s orbital operation, VMC acquired images for more than 3000 orbits, approximately half of which were taken on the dayside and are suitable for tracking the cloud features in the UV channel. Some of the images could not be used due to a large number of errors and problems associated with orbital dynamics. Vector fields were obtained from the remaining images. In order to avoid errors when interpreting the results, for our previous study of the longitudinal dependence of the zonal wind speed (Patsaeva et al., 2019), certain orbits were selected for which it was possible to obtain the most complete longitude-latitude coverage. This sample consisted of 262 orbits and was uneven in observation time. The image quality deteriorated in the second half of the mission, so 2/3 of the sampled orbits were concentrated in the first half of the mission. Fewer quantity and lower quality of images in the second half of the mission resulted in poorer spatial coverage by velocity vectors, especially in the low and equatorial latitudes. In particular, coverage of the highland region of Aphrodite Terra turned out to be noticeably worse than that of the surrounding areas.

In this study, similar to Khatuntsev et al. (2022), additional orbits that did not have full longitude-latitude coverage were brought into consideration, which made it possible to approximately double the total number of orbits (see Khatuntsev et al., 2022, Supplementary Materials, Table s1). As a result, this provided an opportunity to study the longitudinal dependence of the zonal wind speed in the equatorial latitudes near noon (12 ± 1 h) for time-limited intervals throughout the entire duration of the Venus Express mission.

The Akatsuki spacecraft has been in a highly elliptical equatorial orbit (inclination less than 10°) with a period of 10.5 days since December 2015 (Nakamura et al., 2016). Thus, both hemispheres of Venus, Northern and Southern, are available for study. The apocenter altitude is ~375 000 km, and the pericenter ~65 000 km. Images with resolutions from 13 to 78 km/pixel were used for processing. Calibrated 365 nm UV images VCO-V-UVI-3-CDR (Murakami et al., 2017) and the corresponding geometry version 3× (Murakami et al., 2018) are available on the website of the Japanese Space Agency (JAXA AKATSUKI Ultraviolet Imager (UVI) Data Archive, https:// darts.isas.jaxa.jp/planet/project/akatsuki/uvi.html.en). Although version 3× of geometry took into account the discrepancy between the real and calculated positions of the limb, this correction was not always successful. Therefore, we visually checked the limb coincidence for images with the best resolution obtained from a relatively close distance. If the limbs did not match, the image was discarded.

As previously noted in Khatuntsev et al. (2022), unlike UV VMC images, the contrast of cloud details was enhanced in the UV UVI images. Brightness correction of each pixel was performed taking into account Minnaert’s law (Minnaert, 1941; Limaye and Suomi, 1977; Limaye 1984) and subsequent application of a 2D-wavelet filter. RegiStax software (http://www.astronomie.be/registax/) was used for 2D wavelet filtering (Berrevoets et al., 2012; Lim et al., 2004). Increasing the contrast of UV images allows to increase the number of wind velocity vectors obtained and improve the longitude-latitude coverage. This method was previously used for low-contrast images of the near-IR (965 nm) (Khatuntsev et al., 2017) and visible (513 nm) (Khatuntsev et al., 2022) channels of the VMC camera, as well as for nightside VIRTIS-M 1.74 μm images (Gorinov et al., 2021).

The same automated method was used to obtain velocity vectors from UVI images. In accordance with a previously developed algorithm, images obtained during one day were divided into pairs with time intervals of 2–4 hours. To interpolate paired images onto a unified longitude-latitude grid, a step of 0.7 or 0.5 degrees was used, depending on the distance to the apocenter. The correlation area, which was selected on the first image in the pair, had dimensions of 15 × 15 and 15 × 10 degrees, respectively. According to the developed methodology, each selected area of a given image was compared with all possible areas of the same size in the second image in the pair by calculating the correlation function. Each subsequent area of interest in the first image was selected with an offset of 2.5 degrees relative to the previous one, which increased the number of results compared to VMC, where the offset was 5 degrees. The resulting correlation functions were filtered by the value of the correlation maximum and depending on the quality of the correlation function. In most cases, functions for which the value of the correlation maximum exceeded 0.7 were taken into account. In some cases, with insufficient longitude-latitude coverage of velocity vectors obtained per day, this value could be lowered to 0.6. Thus, the criterion for selecting correlation functions based on the value of the correlation maximum for UVI was weakened compared to VMC, where this criterion was equal to or greater than 0.8. The high quality of the UVI images, together with contrast enhancement, allowed us to obtain correlation functions with well-defined peaks. Additionally, restrictions were used for zonal (u) and meridional (v) speed: –250 m/s < u < 0 m/s, –50 m/s < v < +50 m/s, |u/v| ≥ 3.5. Local time was in the range from 7 to 17.5 hours.

The number of velocity vectors per day depended on the local time interval available for study and the observed latitude range, and varied on average from several hundred to ~10 thousand. Due to the polar orbit of Venus Express, the vast majority of velocity vectors obtained in the equatorial region from VMC images were in the phase angle range from 60° to 90°. Thus, when compared with VMC, the results obtained from UVI images were also limited to this range. In this case, the number of vectors is comparable for both missions, that is, ~5000 for VMC and ~6000 for UVI. Longitudinal coverage from 2006 to 2022 in the latitude band 10° ± 5° S, corresponding to the highest altitude of Aphrodite Terra, is presented in Fig. 1.

Fig. 1.
figure 1

Longitudinal coverage of wind velocity vectors from 2006 to 2022 in the latitude bin 10° ± 5° S and local time bin 12 ± 1 h for phase angles 60°–90°. Blue circles indicate VMC measurements, green squares—UVI.

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Just as for VMC, the longitudinal dependence of velocity for UVI was studied near noon 12 ± 1 h. The Akatsuki orbits which form the basis for this study can be found in Khatuntsev et al., 2022 (Supplementary Materials, Table s2). This work uses additional orbits from the first and last Venusian years of UVI observations (nos. 1, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199).

RESULTS

Mean Zonal Wind Speed Variations in 10°± 5° S Bin

Khatuntsev et al. (2022) studied long-term variations of mean zonal and meridional wind speed around noon from 2006 to 2021 in the 20° ± 2.5° S latitude bin. A periodicity with a period of 12.5 ± 0.5 Earth years was discovered using Lafler-Kinman method (Lafler and Kinman, 1965). The magnitude of the approximating sine function was 10.0 ± 1.6 m/s for the zonal component of wind velocity with the mean value of –98.6 ± 1.3 m/s. The meridional component also showed periodic behavior. Khatuntsev et al. (2022) did not take into account phase angle limitations for UVI data.

Figure 2 presents long-term variations in the average zonal and meridional wind speed from 2006 to 2022 in the latitude band 10° ± 5° S around noon and with a phase angle limitation of 60°–90° obtained using automated cloud tracking on VMC/Venus Express and UVI/Akatsuki data. For the zonal wind, the “−” sign indicates westward flow direction (retrograde superrotation). For meridional wind, the “+” sign means northward flow, the “−” sign means southward flow along the meridian. Each marker on the figure represents a value averaged over one Venusian year (224.7 Earth days) within the considered latitudinal bin. With these limitations, the first and the last year of VMC observations have relatively little data left. First year of UVI observations is a result of averaging over only two Earth days. Periodicity analysis similar to that presented in Khatuntsev et al. (2022), also found a period of 12.5 ± 0.5 years.

Fig. 2.
figure 2

Long-term variations of the mean zonal (a) and meridional (b) wind speed from VMC (blue) and UVI (green) for 10° ± 5° S latitudes. Each marker is a result of averaging across one Venusian year. Vertical bars indicate confidence interval 99.6% (\(3{\kern 1pt} {{\sigma }_{{\bar {x}}}}\)). Light blue and light green areas correspond to the standard deviation σ. The approximating sine function is shown as a red dashed line.

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Figure 2. shows approximating functions of the average zonal and meridional components of wind velocity. The zonal component approximation has a magnitude of 10.6 ± 1.0 m/s relative to the average ‒98.9 ± 0.7 m/s, while the magnitude of the meridional component is 3.4 ± 0.4 m/s relative to the average –0.8 ± 0.3 m/s. Some possible causes for the long-term quasi-periodicity, such as periodic changes in the state of the atmosphere and in solar activity, were considered in Khatuntsev et al. (2022).

Longitudinal Dependence of the Zonal Flow

Bertaux et al. (2016) studied longitudinal dependence of the zonal wind speed in the latitude band 10 ± 5° S, which corresponds to the highest altitudes of Ovda Regio, western Aphrodite Terra, using wind velocity vectors from manual cloud tracking (Khatuntsev et al., 2013). They discovered deceleration of the zonal flow which correlates with the surface topography. The authors attempted to explain this effect with the atmospheric gravity waves which are generated near the surface and then transport momentum upwards to the cloud top level (70 ± 2 km), slowing down the zonal flow. The increase of the mean zonal wind speed during Venus Express mission was explained by the lowering average surface elevation due to gradually changing longitudes under the spacecraft. Insufficient number of velocity vectors in the second half of the mission did not allow to investigate this subject in details.

The extended dataset for VMC considered in this work, together with data for UVI, provided the opportunity to study the longitudinal dependence of the zonal velocity at equatorial latitudes for limited intervals of the 12.5-year dependence presented in Figs. 3a, 3c, 3e, 3g shows the longitudinal variations of the average zonal wind speed for VMC and UVI within 10° ± 5° S latitude, 12 ± 1 h local time, 60°–90° phase angle constraints. Figures 3b, 3d, 3f, 3h presents the longitudinal variations of the residual series u–u12.5 of the zonal speed after subtracting the sine function (see Results, “Mean Zonal Wind Speed Variations in 10° ± 5° S Bin”). It shows that dependence of the zonal speed on longitude is preserved in all cases. Each curve for both VMC and UVI is the result of averaging over six Venusian years: 2007–2010 (Figs. 3a, 3b), 2010–2013 (Figs. 3c, 3d), 2016–2019 (Figs. 3e, 3f), 2017–2020 (Figs. 3g, 3h). This averaging time interval was selected to secure complete longitudinal coverage. The X axis covers 1.5 complete longitudinal intervals (540°) for better visualization. In the case of VMC, the time interval is related to the longitudinal movement of the subsatellite point during the Venus Express mission. This interval allows us to compare on average the behavior of the zonal wind speed in the first and second half of the mission and to trace the evolution of the minimum zonal speed over time. With an increase in absolute value of the mean zonal speed in the ascending part of the long-term dependence (VMC), the minimum of the mean zonal speed above the highest part of Aphrodite Terra (Fig. 3a) changes into a maximum (Fig. 3c). Despite the fact that in the case of UVI the time intervals overlap by 4 years, considered longitudinal variations also make it possible to detect a change in the longitudinal dependence. With a decrease in absolute value of the mean zonal speed in the descending part of the long-term dependence (UVI), the observed maximum of the zonal speed on the longitudinal curve (Fig. 3e) turns into a minimum (Fig. 3g).

Fig. 3.
figure 3

Long-term variations of mean zonal wind speed from VMC (a, c) and UVI (e, g) images, in the 10° ± 5° S latitude bin, averaged over time intervals corresponding to six Venusian years. Longitudinal variations of the residual zonal speed series u–u12.5 after subtracting the sine function for VMC (b, d) and UVI (f, h). Error bars indicate a 99.6% confidence interval (\(3{\kern 1pt} {{\sigma }_{{\bar {x}}}}\)). Light blue and light green areas indicate standard deviation σ. Mean topographic altitude in the same latitude bin is shown in black curve.

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In both VMC and UVI cases, an increase in zonal wind speed above Ovda and Tethys Regio was found near the maximum of the long-term dependence. The amplitude of longitudinal variations in zonal speed is higher for VMC. The difference between the maximum and minimum of the longitudinal variations of the residual zonal speed series is about 15 m/s for VMC and about 10 m/s for UVI (Figs. 3b, 3d, 3f, 3h).

The dependence of the horizontal flow velocity on longitude can be clearly demonstrated if we introduce additional data selection for this parameter. Two test areas were selected: above Ovda Regio (10° ± 5° S, 60°–120° E), where the maximum deceleration of the horizontal flow is observed, and above the lowlands of Navka and Tinatin Planitia (10° ± 5° S, 330°–30° E) (see longitudinal profile of the surface relief, for example in Fig. 3). The maximum height difference between the considered longitudes is about 4.5 km, which corresponds, according to VIRA (Seiff et al., 1985), to a pressure difference of 23.4 bar, from 92.1 bar at the surface to 68.7 bar at 4.5 km. The dataset of single measurements used in this work, sampled for local time constraints of 12 ± 1 h and phase angle constraints of 60°–90°, allows us to study long-term variations above these areas (Fig. 4). The total number of points averaged over the Venusian year using test areas was reduced due to insufficient observation coverage. For the same reason, the errors of the mean increased for some points. Approximating sine functions similar to those presented in Fig. 2 were introduced for both datasets and periods of 12.5 ± 0.5 years. Above Ovda Regio, the sine function amplitudes for the zonal and meridional components increased relative to the average sine functions (see Results, “Mean Zonal Wind Speed Variations in 10° ± 5° S Bin”). For the zonal speed, an increase to 16.7 ± 2.4 m/s with an average speed of –101.2 ± 1.9 m/s was observed, and for the meridional speed the increase was up to 5.3 ± 1.4 m/s with an average of +1.6 ± 1.1 m/s. At the same time, a decrease in amplitude is observed above the lowlands: for the zonal component to 9.7 ± 4.5 m/s with an average of –99.5 ± 3.2 m/s, for the meridional component to 1.6 ± 0.7 m/s with an average of –1.0 ± 0.7 m/s.

Fig. 4.
figure 4

Long-term variations of the zonal (a) and the meridional (b) components of the mean horizontal wind velocity in the 10° ± 5° S bin above highlands (black) and lowlands (red). Markers indicate wind speed averaged over one Venusian year. Error bars indicate confidence interval 99.6% (\(3{\kern 1pt} {{\sigma }_{{\bar {x}}}}\)). Dashed line shows sine functions with a period of 12.5 ± 0.5 years.

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Despite the increased error, we can conclude that highland surface areas have a more significant impact on long-term quasiperiodic variations of the wind velocity field at the cloud top.

Longitude-Latitude Dependence of Zonal Wind Speed

The change in zonal wind speed observed above Aphrodite Terra (Fig. 3) is not limited to the latitudinal band of 10° ± 5° S. Figure 5 shows the longitude-latitude variations of the zonal speed averaged over the first 6 and last 6 Venusian years of VMC observations, as well as the first 6 and last 6 years of UVI observations. The six-year intervals correspond to those presented in Fig. 3 and in the case of UVI overlap by 4 Venusian years. VMC results (Figs. 5a, 5b) show only Southern hemisphere, UVI results (Figs. 5c, 5d) show both hemispheres. Because longitudinal variations in zonal speed persist for the residual series, the subsequent study was conducted on data without sine function subtraction. In each of the considered cases, the area of minimum (Figs. 5a, 5d) and maximum (Figs. 5b, 5c) extends from the equator to the middle latitudes, up to approximately 40 degrees. Slow zonal speed at longitudes 30°–180° E at the beginning of the Venus Express mission (Fig. 5a) changes into fast in the second half of VMC observations (Fig. 5b). In the spatial distribution, for the first 6 years of UVI observations at longitudes from 30° to 180° E an area of maximum zonal speed is observed (Fig. 5c). The area of maximum contains a smaller area of relatively lower zonal speed, which expands as the long-term variations approaches the minimum, extending into mid-latitudes (Fig. 5d). This area of relative minimum zonal wind speed indicates flow deceleration and remains localized at approximately 75° E, i.e. close to Ovda Regio, which is the highest elevation of the western part of Aphrodite Terra (Fig. 3, black curve). Thus, the presence of this deceleration area even during the general acceleration of the horizontal flow above the highlands indicates the persistence of the influence of Ovda Regio during the observation period.

Fig. 5.
figure 5

Spatial distribution of mean zonal wind speed, averaged over time intervals 2007–2010 (a), 2010–2013 (b), 2016–2019 (c), 2017–2020 (d). Black contours indicate surface features higher than 1 km.

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According to UVI data near the maximum of the long-term variations (Fig. 5c), an increase in the zonal component (acceleration) is observed not only at the longitudes corresponding to the highest areas of Aphrodite Terra (60°–140° E), but also around 270°–300° E, where a mountain chain is located stretching from north to south, including Beta, Phoebe and Themis Regio. In other cases (Figs. 5a, 5b, 5d), there is no noticeable connection between these elevations and changes in zonal wind speed, such as the influence of Aphrodite Terra in the same time period.

Influence of Surface Topography on the Meridional Wind Speed

The influence of surface topography on the dynamics of the atmosphere implies not only a change in the magnitude of the zonal wind, but also a change in the meridional wind, consistent with the topography of the underlying surface. The longitudinal dependence of the meridional velocity for 10° and 25° S, averaged over the entire VMC dataset, showed the presence of variations associated with Aphrodite Terra (Patsaeva et al., 2019). Figure 6 shows longitudinal variations of the meridional wind speed for different latitudes of the equatorial region of Venus, obtained from VMC (Figs. 6a, 6b) and UVI (Figs. 6c, 6d) data for Venusian six-year observation intervals close to the maximum and minimum of the long-term dependence of mean zonal speed. The time intervals correspond to those that were taken to study the zonal speed. Each curve is the result of averaging within the 10-degrees latitude bin and shows the change in meridional speed at 10° and 35° S for VMC. UVI results additionally show variations of the meridional speed at the equator and at 10° S. The changing relief of Aphrodite Terra highlands and slopes extends from 50° to 210° E and from 40° S up to 20° N (see Fig. 5, black outlines). Its highest parts, Ovda and Tethys Regio, are located from 60° to 140° E and from 20° S up to 5° N. In accordance with the dynamics of the Venusian atmosphere, the mean horizontal flow at the upper cloud level on the dayside is directed from the equator to the pole in each hemisphere. The effect that Aphrodite Terra has on the meridional wind speed is expressed in the change of the horizontal flow direction to the north or south in accordance with surface features depending on latitude. For VMC (Figs. 6a, 6b) and UVI near the maximum of the long-term variations (Fig. 6c), a significant difference in the behavior of the curves at the longitudes of Aphrodite Terra is observed in the southern hemisphere of Venus (10° and 35° S, blue and red curves). For UVI near the minimum of the long-term variations (Fig. 6d), the greatest difference is noted between the behavior of the meridional speed at the latitudes north and south of the highest altitudes of Aphrodite Terra (10° N and 35° S, green and red curves). Although the longitude of this greatest difference shifts somewhat from figure to figure, the dependence of the horizontal flow direction on the underlying surface topography is observed in all considered cases.

Fig. 6.
figure 6

Longitudinal variations of the mean meridional wind speed at 10° ± 5° S (blue), 35° ± 5° S (red), 10° ± 5° N (green), equator 0° ± 5° (black). Meridional wind speed is averaged over time intervals 2007–2010 (a), 2010–2013 (b), 2016–2019 (c), 2017–2020 (d). Error bars correspond to a 99.6% confidence interval (\(3{\kern 1pt} {{\sigma }_{{\bar {x}}}}\)).

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The shift of the meridional wind speed towards positive values, detected at 20° S according to VMC data, near the maximum of the long-term variations (Khatuntsev et al., 2022), is observed at all southern equatorial latitudes (Fig. 6b). At 10° S the average meridional speed changes from –1.1 ± 0.1 to +1.7 ± 0.1 m/s, changing the horizontal flow direction from south to north. Due to the lack of data from 2013 to 2015, it is not possible to confirm or refute such an assumed shift of the meridional component.

DISCUSSION

Comparison with UVI/ Akatsuki Observations in 2015–2017

Horinouchi et al. (2018) identified the longitudinal-latitude dependence of the zonal wind speed from UVI/Akatsuki observations from December 2015 to March 2017. The authors found a slight increase in the mean zonal speed at equatorial latitudes above Ovda Regio, and thus did not confirm the conclusions of Bertaux et al. (2016) about the zonal flow deceleration and the influence of surface topography on dynamic processes in the atmosphere. Imai et al. (2019), examining zonal wind during 2017, also did not find a significant dependence of the flow speed on the surface topography. Longitudinal variations of the zonal speed in the latitude band 10° ± 5° S, which we obtained near noon for the same period (Fig. 7), show an increase in the zonal wind speed above Ovda Regio, and, therefore, are consistent with the result presented in Horinouchi et al. (2018). Thus, the apparent discrepancy between the conclusions drawn in Bertaux et al. (2016) and Horinouchi et al. (2018) can be explained by the use of different observation periods.

Fig. 7.
figure 7

Longitudinal variations of the mean zonal wind speed for the latitude bin 10° ± 5° S and local time bin 12 ± 1 h from December 2015 to March 2017 (red). Error bars indicate 99.6% confidence intervals (\(3{\kern 1pt} {{\sigma }_{{\bar {x}}}}\)). Light blue area corresponds to standard deviation σ. Mean surface topographic altitude in the same latitude bin is shown in black curve.

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Variations of Equatorial Wind Caused by Surface Topography

The key result of this study is evidence of the surface influence on variations of the horizontal wind field at the equatorial latitudes of Venus, from UV (365 nm) images of VMC/Venus Express and UVI/Akatsuki. Previous analysis revealed global periodicity of zonal circulation of 12.5 ± 0.5 years (Khatuntsev et al., 2022, Fig. 2 therein). This work shows the role of the continental highland of Aphrodite Terra in modulating the zonal flow near noon (12 ± 1 h) (Figs. 3 and 5). In addition to the previously discussed deceleration of zonal flow (Bertaux et al., 2016; Patsaeva et al., 2019), which was observed further downstream, “behind” the highlands, results of this paper indicate long-term variations in the deceleration itself, caused by the topography of the underlying surface.

Figure 3 shows the average longitudinal profiles of wind speed for the first and second half of Venus Express and Akatsuki missions. It highlights the transition from the zonal flow deceleration of about 20 m/s to acceleration of about 10 m/s above Aphrodite Terra. Averaging over six-year intervals does not allow us to completely eliminate the longitude selection bias and carries distortions associated with the assumed long-term variations in the atmosphere. Although the results obtained for individual Venus years tend to have limited longitudinal coverage, they nevertheless provide insight into how the longitudinal dependence of zonal speed changes from year to year. The transition from decelerating to accelerating zonal flow occurred around 2010 and was observed by Venus Express. Acceleration of the flow above Aphrodite Terra from 2010 to 2017 was observed by both Venus Express and Akatsuki (Figs. 3c, 3e). The same conclusion can be drawn from Fig. 4: the “black” sine function curve was obtained for Aphrodite Terra at the latitudes corresponding to the highest altitudes of Ovda Regio.

Despite general acceleration above Aphrodite Terra, data from the beginning of UVI observations points out the presence of relative deceleration near 75° E associated with Ovda Regio (Figs. 3 and 5). The lack of observations from 2013 to the end of 2015 does not allow us to verify the persistence or absence of a similar phenomenon in the earlier period of time. Data from the second half of VMC observations show a pronounced acceleration of the horizontal flow above Ovda Regio with no evidence of flow deceleration at 75° E or any close longitudes. Possibly, the sparse coverage of Aphrodite Terra measurements in the second half of VMC observations does not allow to detect this phenomenon.

At the same time, based on the behavior of the meridional component (see Results, “Influence of surface topography on the meridional wind speed”), one can cautiously suggest persistence of the surface influence on atmospheric dynamics, regardless if a minimum or a maximum of zonal wind speed is observed above the highest part of Aphrodite Terra.

Changes in atmospheric circulation caused by the surface topography are usually associated with gravity waves (buoyancy waves). The presence of such waves in the atmosphere of Venus has been observed in several experiments. Piccialli et al. (2014) identified gravity waves in UV images of the dayside cloud tops obtained by the VMC camera. Mesoscale gravity waves were detected during mapping of the nightside in near-IR with the VIRTIS-M/Venus Express imaging spectrometer, corresponding to the altitudes of the middle and lower cloud layers (Peralta et al., 2008). The presence of gravity waves in the atmosphere of Venus is confirmed by observations in the thermal IR range (Fukuhara et al., 2017), as well as in radio occultation experiments on Venus Express (Tellmann et al., 2012), Magellan (Hinson and Jenkins, 1995) and Akatsuki (Imamura et al., 2017).

Gravity waves caused by the surface topography that reach the upper cloud boundary can have both a direct effect on the wind speed due to the momentum transport, and an indirect one, affecting the cloud parameters. The latter also includes changing the altitude where the UV features are formed. The troposphere of Venus (<60 km) has a complex layered structure with alternating stable and unstable layers and zonal wind speed that increases sharply with altitude (Sánchez-Lavega et al., 2017; Limaye et al., 2018). Both these factors significantly influence the propagation of buoyancy waves. Convectively unstable layers, where the static stability parameter is close to zero, are located in the lower and middle cloud layers (48–57 km), as well as in the lower atmosphere at approximately 15–35 km. The planetary boundary layer (0–5 km) is assumed to have neutral stability. The remaining heights in the troposphere and mesosphere, especially near the cloud tops where the UV features are formed, are highly stable.

Buoyancy waves in the atmosphere of Venus can be formed either from the interaction between surface features and atmosphere (especially in mountainous regions), or be caused by convection in neighboring unstable layers of the atmosphere (Baker et al., 2000). The propagation of buoyancy waves in a homogeneous atmosphere is described by the Taylor–Goldstein equation—a dispersive relation between the vertical m(z) = 2π/λz and horizontal k(z) = 2π/λx wave numbers (Salby, 2012):

$${{m}^{2}}\left( z \right) = \frac{{{{N}^{2}}}}{{{{{\left( {c - \bar {\bar {U}}} \right)}}^{2}}}} - {{k}^{2}}\left( z \right) + \frac{{{{{\bar {\bar {U}}}}_{{zz}}}}}{{c - \bar {\bar {U}}}},$$
(1)

where λx and λz are the horizontal and vertical wave lengths, c is the phase velocity, N(z) is the Brunt-Väisälä frequency, U(z) and Uzz are the mean zonal wind speed and its second derivative. Equation (1) establishes dispersive relation between wave numbers k(z), m(z) and atmospheric properties.

Equation (1) allows to evaluate cloud top properties of the gravity waves, emerging when wind interacts with surface highlands (such as Aphrodite Terra). These buoyancy waves have phase velocity near zero. Known properties of the Venusian atmosphere N2 = 3.8 × 10−4 s−2, U ≈ 100 m/s and Uzz = –0.9 × 10–6 s−1 m−1 at 70 km (Sánchez-Lavega et al., 2017; Limaye et al., 2018) allow us to evaluate length of the vertical wave to be about 40 km, which aligns with the theoretical modeling results (Yamada et al., 2019). The modeling also showed that presence of neutral stability layers in Venusian troposphere does not significantly weaken relatively long waves.

Vertical buoyancy waves exchange momentum with the zonal circulation. Their near-zero phase velocity facilitates deceleration of the superrotation. In linear theory of buoyance waves (Andrews et al., 1987) the decelerating force is written as:

$${{\bar {\bar {X}}}_{1}} = \frac{{{{N}^{2}}K}}{{c - \bar {\bar {U}}}},$$
(2)

where K = 4 m2/s is the turbulent diffusion coefficient at the cloud top. Estimations show that waves generated from the surface can cause flow deceleration at the cloud top up to about 1 m/s per day.

Baker et al. (2000) numerically modeled the emergence of buoyancy waves in a stable layer at 35–48 km using convection in neighboring unstable layers in the clouds at 48–57 km and in the lower troposphere (15–35 km). Although these studies were limited to the troposphere (0–60 km), their results can also be applied to the region of the stable lower mesosphere (60–80 km), making them useful for our work. Baker et al. (2000) showed that convection in unstable layers can generate buoyancy waves in adjacent stable areas through the interaction of convective cells and “columns” with the zonal circulation. This mechanism is similar to the mechanism operating near the surface, where the role of obstacles is played by the surface elevations, however the altitude area of wave generation is located much closer to the layer of our focus. The penetration of convective “columns” into the stable layer generates buoyancy waves with a characteristic length of 25–30 km in the horizontal, and 7–13 km in the vertical direction. Both convection and the buoyancy waves excited by it influence the circulation at the cloud top. According to Baker et al. (2000), ultimately the interaction of convection and buoyancy waves with the zonal flow results in a slowdown of the zonal superrotation both below the clouds and above the tropopause (~60 km).

Asai (1970) numerically modeled the interaction of three-dimensional convection with a wind field varying with altitude and concluded that convective cells can transfer horizontal momentum and energy in the vertical direction, which can result in either deceleration or acceleration of the flow. This process strongly depends on the scale of the disturbances.

The aforementioned results of numerical modeling and evaluation make it possible to qualitatively explain the influence of surface topography on the circulation at the cloud top. Firstly, buoyancy waves with a characteristic length of tens and hundreds of kilometers, emerging from the interaction of the atmosphere with large surface features, such as the continental elevation of Aphrodite Terra, can propagate to the cloud layer heights and transfer their momentum to zonal circulation. This usually results in the zonal flow slowing down at a rate of several meters per second per day. Secondly, convection in the unstable lower and middle parts of the cloud layer can influence the zonal circulation both directly, through the upward propagation of slow convective cells, and indirectly through the generation of buoyancy waves at the boundary between the stable and unstable layers near 57 km (Baker et al., 2000). This mechanism can slow down the zonal circulation at the cloud top, although, as noted by Asai (1970), three-dimensional numerical modeling shows that under certain conditions the flow can accelerate. The direction of buoyancy waves influence depends on the convection parameters, the waves themselves and their interaction, which in turn is determined by the conditions in the cloud layer.

Currently existing models which to a certain extent reproduce the influence of surface topography on Venus’ atmospheric dynamics (Herrnstein and Dowling, 2007; Mingalev et al., 2015; Fukuhara et al., 2017; Navarro et al., 2018; Yamamoto, 2019; Yamamoto et al., 2021; Lefèvre et al., 2020), do not consider any variations of this influence with time.

Correlation of Zonal Circulation with UV Albedo Variations

Lee et al. (2019) showed significant variations in Venus’ albedo at 365 nm between 2006 and 2017. Maximum albedo was observed in 2006–2007, then decreased to a minimum in 2011–2014 and recovered in 2016–2017 to the 2008 level. According to Lee et al. (2020) a pronounced maximum of the average albedo in the latitude band 10° ± 5° S, which was observed in the first half of the Venus Express mission (2006–2009) at the longitudes of Aphrodite Terra at phase angles of 75°–80°, is replaced by a minimum in the second half of the mission (2010–2014). Note that in 2010 the longitudinal wind profile changed from an apparent slowdown above Aphrodite Terra to a slight acceleration, thus demonstrating consistency with the UV albedo. Low albedo is expected to cause increased absorption of solar energy in the upper cloud layer, which should affect the thermal structure and stability of the atmosphere. To better understand the interactions between convection, gravity waves and large-scale dynamics in the Venusian atmosphere, large-scale 3D modeling of the tropospheric and mesospheric circulation is required.

UV albedo variations imply changes in the UV absorber concentration and its vertical distribution. Can the observed long-term fluctuations in wind velocity, as well as the accompanying longitudinal fluctuations, be explained by corresponding fluctuations in the altitude of the high-contrast UV features? For a change in zonal wind speed of 30 m s–1 and its vertical gradient of 2 m s–1 km–1, the corresponding altitude change should be about 15 km. Cloud top height from CO2 IR band Venus Express observations from 2006 to 2014 (Fedorova et al., 2016) did not experience any significant changes that could correlate with changes in speed during the same period. Certainly, the UV absorber can be, and apparently is, located above the cloud top altitude in the IR range (defined as the level of unit optical depth, or, more precisely, the level τ(1 – g) ≈ 1, where g is the parameter asymmetry of the scattering phase function), and experience long-term variations not visible in the IR range. Indeed, Venus Express solar occultation observations have revealed significant long-term variations in the concentration of particles above the cloud haze. However, these changes were abrupt from 2006 to 2007, with aerosol extinction at the altitude of 80 km at low latitudes increasing by more than an order of magnitude, and after that above-cloud haze concentration was relatively constant (Wilquet et al., 2012). An increase in density means an increase in the altitude level of a unit optical thickness. If the high-contrast UV features are attributed to this level, then the observed mean wind speed in the period from 2006 to 2010 should have decreased (since the wind speed decreases with increasing altitude above the cloud top: see, for example, Schubert, 1983), which contradicts to our measurements. Moreover, considering the observed particle sizes of the above-cloud haze, which is probably associated with the UV-absorber (see, for example, Pollack et al., 1980; Perez-Hoyos et al., 2018), namely particles with an effective radius of about 0.1 μm (for example, Pollack et al., 1980; Luginin et al., 2016), the above-cloud haze is not completely transparent in the IR range. Hence, the required changes in the altitude of the τ ≈ 1 level in the UV range would lead to corresponding noticeable variations (at least on the order of several kilometers) of this level in the IR range, which, as mentioned above, are not observed. Thus, the long-term variations in the zonal wind speed observed from high-contrast UV features, as well as the accompanying longitudinal fluctuations, cannot be explained by possible changes in the particle density of the above-cloud haze and the characteristic altitude of the UV features.

CONCLUSIONS

This paper continues the joint analysis of UV (365 nm) Venus’ cloud cover images from both VMC/Venus (ESA) (Titov et al., 2006: Svedhem et al., 2009) 2006–2013 and UVI/Akatsuki (JAXA) (Nakamura et al., 2016). These observations provided a unique opportunity for an almost constant study of the atmospheric dynamics at the upper cloud boundary (70 ± 2 km) during more than 15 years (about 24 Venusian years). With the automated correlation method, we obtained more than 5000 wind velocity vectors from VMC and 6000 from UVI UV images near noon (12 ± 1 h) in the latitude band 10° ± 5° S, which corresponds to the highest areas of western Aphrodite Terra (Ovda Regio). To exclude the phase angle bias, only observations with 60°–90° phase angles were selected for study.

Overall, the analysis confirmed the results we previously presented for the full range of phase angles (Fig. 2, Khatuntsev et al., 2022) as well as the findings of Horinouchi et al. (2018). At 10° S long-term quasi-periodic variations in the average zonal and meridional wind speed are observed with a period of 12.5 ± 0.5 years. The main result of this work is the discovery of modulation of these long-term variations by the underlying surface. In particular, the deceleration of the zonal flow is observed above the highest part of Aphrodite Terra, Ovda Regio, near the minimum of the mean speed in 2007–2010 (Figs. 3a, 3b), while in 2010–2013, when the mean speed is at maximum, the flow experiences acceleration. This trend continues up to 40° S (Fig. 5) and is also present in UVI/Akatsuki observations (Figs. 3c, 3d). The modulation amplitude of the average quasi-periodic dependence (Fig. 2) lies in the range of 10–20 m/s.

It seems unlikely to us that the variations in observed wind speed described above could be caused by changes in cloud top altitude. To explain variations in speed of 10–20 m/s it would require a change in cloud layer altitude of ten kilometers, which contradicts the generally accepted model of the cloud layer and wind fields. On the other hand, the results of numerical modeling and evaluations make it possible to qualitatively explain the influence of surface topography on the circulation at the cloud top. Firstly, buoyancy waves with a characteristic horizontal size of tens and hundreds of kilometers, emerging from the interaction of atmosphere with large surface features, such as, for example, the highland regions of Aphrodite Terra, can propagate to the cloud layer and transfer their momentum to zonal circulation. This can lead to a slowdown of the zonal flow at a rate of several meters per second per day. Secondly, convection in unstable cloud layers can influence the zonal circulation in neighboring stable layers (Baker et al., 2000) both by decelerating the flow and accelerating it, depending on the convection parameters and the waves themselves, which, in turn, is determined by conditions in the cloud layer (Asai, 1970). To more fully understand the interaction of buoyancy waves, surface topography and convection, three-dimensional modeling of these processes is necessary.