Volume 124, Issue 5 p. 1143-1156
Research Article
Free Access

Formation of the Y Feature at the Venusian Cloud Top by Planetary-Scale Waves and the Mean Circulation: Analysis of Venus Express VMC Images

Y. Nara

Corresponding Author

Y. Nara

Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba, Japan

Correspondence to: Y. Nara,

[email protected]

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T. Imamura

T. Imamura

Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba, Japan

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S. Murakami

S. Murakami

Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Sagamihara, Kanagawa, Japan

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T. Kouyama

T. Kouyama

National Institute of Advanced Industrial Science and Technology, Koto-ku, Tokyo, Japan

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K. Ogohara

K. Ogohara

Department of Electronic System Engineering, School of Engineering, The University of Shiga Prefecture, Hikone, Shiga, Japan

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M. Yamada

M. Yamada

Planetary Exploration Research Center, Chiba Institute of Technology, Narashino, Chiba, Japan

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M. Takagi

M. Takagi

Faculty of Science, Kyoto Sangyo University, Kyoto, Japan

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H. Kashimura

H. Kashimura

Center for Planetary Science/Department of Planetology, Graduate School of Science, Kobe University, Kobe, Hyogo, Japan

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N. Sato

N. Sato

Natural Science Division, Tokyo Gakugei University, Koganei, Tokyo, Japan

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First published: 09 April 2019
Citations: 10

Abstract

The relationship between the planetary-scale ultraviolet contrast known as the Y feature and the wind field at the Venusian cloud top was investigated by using images obtained by Venus Monitoring Camera (VMC) on ESA's Venus Express. Spectral analyses of the ultraviolet reflectivity and the wind field revealed common periodicities of 4–5 Earth days, which are attributed to Kelvin and Rossby waves with a zonal wave number of unity. Combined with the morphological relationship between the dark streaks and the enhancement of poleward flow, we propose a mechanism for the formation of the Y feature: The dark materials are supplied to the cloud top in the equatorial region by a Kelvin wave, subsequently advected poleward by the mean meridional circulation and a Rossby wave, and then stretched by the midlatitude jet to the tilted band structures. A simplified transport model was developed to demonstrate the scenario.

Key Points

  • The role of planetary-scale winds in the formation of the Y feature was investigated using UV images taken by Venus Express
  • 4- and 5-day periodicities were found in the UV brightness and the wind velocity, suggesting the roles of atmospheric waves
  • The tilted dark bands can be created by the transport of dark materials by Kelvin and Rossby waves and the mean circulation

Plain Language Summary

The albedo feature of Venus' cloud top is important for radiative energy budget and atmospheric chemistry. The Venus' cloud frequently exhibits planetary-scale, equatorially symmetric dark patterns in ultraviolet, called the horizontal Y feature, which is composed of tilted dark bands extending from the equator to high latitudes and a dark equatorial band at the root of the Y. The generation mechanism of the feature has been unclear for more than 40 years since its discovery. This study proposes a mechanism based on an analysis of cloud images obtained by ESA's Venus Express. We have identified planetary-scale waves with periods of 4–5 Earth days in the ultraviolet reflectivity and the wind field. The combination of those planetary-scale waves and the mean circulation was shown to produce the Y feature using a simplified transport model.

1 Introduction

Ultraviolet (UV) images of Venusian cloud top exhibit various planetary-scale features because of the presence of unidentified UV absorbers (Mills et al., 2007; Moroz et al., 1985). One of the significant features is the dark horizontal Y feature (e.g., Rossow et al., 1980), which often shows equatorially symmetric dark pattern with a zonal wavenumber of unity accompanying tilted dark midlatitude bands extending from the equator to high latitudes and a dark equatorial band at the root of the Y. Though the Y feature is frequently observed with some variability in the structure, its generation mechanism has been unclear for more than 40 years since its discovery (Boyer & Guerin, 1969). The phase-angle dependence of the UV contrast suggests that the absorbers are deep in the cloud (Esposito, 1980) and the tendency of decreased albedo near the subsolar suggests the supply of absorbers by upwelling or the evaporation of the upper haze (Titov et al., 2012). Therefore, the formation of the Y feature should be strongly related to the transport of materials absorbing sunlight, and thus its understanding would provide clues to the mechanism determining the planetary albedo and the solar heating in the cloud layer.

Smith and Gierasch (1996) argued that the horizontal stretching and advection of cloud parcels by the combination of the mean zonal wind, Hadley circulation, and thermal tides produce streak structures and that thermal tides are responsible for the local time dependence of the streak orientation. Though their model seems to explain the characteristics of small-scale streaks, the formation process of the tilted dark bands composing the Y feature is not addressed.

Del Genio and Rossow (1990) showed that the propagation of the equatorial UV contrast with a zonal wavenumber of unity tends to be faster than the mean zonal velocity based on the analysis of the cloud-tracked wind speed and the periodicity of the brightness, although the faster propagation than the mean flow is not very clear due to the large dispersion of cloud-tracked velocities. This suggests that planetary-scale waves propagating relative to the background wind are responsible for the Y feature. Analysis of wind fields deduced by cloud tracking indeed showed existence of planetary-scale waves that are interpreted as Kelvin waves, Rossby waves, and thermal tides (Kouyama, Imamura, et al., 2013; Kouyama et al., 2015; Limaye, 1988; Limaye & Suomi, 1977; Rossow et al., 1990). Covey and Schubert (1982) and Smith et al. (1993) argued that the Kelvin wave might be a preferred global mode of the Venus atmosphere and can be generated by random forcing somewhere below the cloud top. Covey and Schubert (1982) and Yamamoto and Tanaka (1997) suggested that the superposition of a Kelvin wave and a hemispherically symmetric Rossby wave can explain the Y feature, although the mechanism of the transport of UV absorber along the tilted dark bands is not studied. Sugimoto et al. (2014) pointed out that the observed hemispherically symmetric Rossby waves could be explained by baroclinic waves generated at cloud heights and that their horizontal structures are reminiscent of the Y feature. Peralta et al. (2015) argued that the Y feature could be produced by the vertical transport of absorbers by a Kelvin wave distorted in the sheared flow and the subsequent zonal advection by the background wind; since the zonal advection continues to distort the pattern, the mechanism for the long-lasting feature needs to be studied.

To understand the role of spatially and temporally varying winds in the formation of the Y feature, comparison between the cloud morphology and the wind field is essential. Patsaeva et al. (2015) studied the relationship between the cloud motion vectors and the cloud morphology using Venus Express Venus Monitoring Camera (VMC) images and suggested that the deflection of the wind orientation from latitude circles in the midlatitude depends on the presence of dark streaks. However, the mechanism of the formation of dark streaks and the cause of the varying midlatitude wind field are still unclear.

In this study, we analyze the relationship between the periodical variations of the cloud-top wind field and the planetary-scale UV pattern to propose a new hypothesis about the formation of the Y feature, in which advection of the absorbing material by planetary-scale waves plays an important role. The data used are the cloud images taken by VMC on ESA's Venus Express spacecraft, which accumulated a great number of images during its 8 years of observation (Markiewicz et al., 2007; Svedhem et al., 2007). Section 2 describes the data set, section 3 gives the details of the analysis procedures, section 6 shows the results, section 10 discusses the generation mechanism of the planetary-scale streak feature, and section 11 presents a simple numerical simulation which demonstrates the transport of an unidentified absorber leading to a Y feature-like pattern. Section 12 gives conclusion.

2 Data Set

UV images obtained by VMC on Venus Express were used in this study. Venus Express observed Venus from April 2006 until December 2014 in a polar orbit having a period of 24 hr, the apocenter located at 66,000 km altitude above the South pole, and the pericenter located at 250–400 km altitudes above the North pole. Among the four wavelength channels of VMC with the center wavelengths of 365, 513, 965, and 1,010 nm, we analyzed the 365 nm channel, in which absorption by unidentified materials dominates (Moroz et al., 1985). The pixel format of the CCD detector is 512 × 512 pixels and the field of view is 17.5° × 17.5°. Images that contain the entire Venus disk were used in this study; such images were acquired when the spacecraft altitude was higher than about 30,000 km, and mostly the southern hemisphere were covered from such high altitudes because of the orbit shape. The pixel resolution of the images analyzed in this study ranges between 30 and 50 km at the subspacecraft point. The details of Venus Express are given in Svedhem et al. (2007) and the specifications of VMC are given in Markiewicz et al. (2007).

Before analysis, the original image data are processed with the procedure described in the next section, and then projected onto longitude-latitude maps. Radiance values are given on the dayside only. During the projection the pointing direction is corrected by a limb fitting method proposed by Ogohara et al. (2012) and the optical distortion is corrected by the method of Kouyama, Yamazaki, et al. (2013), although Limaye et al. (2015) proposed another image correction scheme. The grid interval of the longitude-latitude maps is 0.25° both in latitude and longitude. The details of the overall data processing pipeline are given in Ogohara et al. (2017). The data we used were obtained in orbits 436–490 (1 July 2007 to 23 August 2007), 659-710 (8 February 2008 to 30 March 2008) and 883-938 (19 September 2008 to 14 November 2008).

3 Analysis Methods

3.1 Photometric Correction and Noise Reduction

To observe variations of the UV reflectivity, we first applied Minnaert's law, which relates the observed brightness I and the brightness at zero incident angle and zero emission angle I0, as
urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0001(1)
where μ is the cosine of the emission angle and μ0 is the cosine of the incidence angle (Minnaert, 1941). This photometric correction has been widely used for images of the planets covered with thick clouds including Venus (Lee, Imamura, et al., 2015; Lee, Titov, et al., 2015; Titov et al., 2012). The parameter k was estimated by fitting pairs of ln (μμ0) and ln (μI) in each image to a linear function; the slope of the fitted line gives k. Since fitting becomes worse for emission or incidence angles near 90°, we restricted the analysis to regions where both the emission and the incidence angles are less than 80°. An example of the photometric correction is shown in Figure 1.
Details are in the caption following the image
An example of photometric correction using Minnaert's law. (a) Original image, (b) corrected image, and (c) scatter plot of ln (μμ0) and ln (μI). The data were taken from orbit 458. In (c), the red line shows the result of fitting; the slope of this line gives k.

The images contain streaky noise along one dimension of the detector, which is created during charge transfer in the CCD as reported in VMC Calibration Report (VMC-MPAE-RP-SS011-001, 2008). For images to be used for cloud tracking, the streaky noise was reduced by differentiating the brightness along the axis of the charge transfer. This procedure at the same time enhances small-scale cloud patterns. Then, the entire area in each image was smoothed by a 5 × 5 pixels moving average to suppress high-frequency noises emphasized by the differentiation. After these corrections the images were projected onto the longitude-latitude coordinate.

3.2 Cloud Tracking

To deduce velocity fields, we used a cloud tracking method based on cross correlation as given below. First, a pair of images observed at different times are prepared. A square area with a particular dimension called a template is selected in the first image. By assuming possible maximum displacements along the longitude and the latitude during the time interval between the two images, an area called a search area is determined. Then, the correlations between the template and areas with the size same as the template in the search area are calculated, composing a cross-correlation surface. The point of maximum correlation in the cross-correlation surface is regarded as the location to which the air parcel was displaced during the time interval. In this study, the size of the template was set to 10° × 10° and the search area was determined by assuming that the zonal velocity is between 0 and 150 m/s and the meridional velocity is between −50 and 50 m/s. Kouyama, Imamura, et al. (2013), Kouyama, Yamazaki, et al. (2013) systematically investigated the template size dependence of cloud-tracked velocities using VMC data set. The zonal velocities deduced from template sizes of 2–10° do not show significant differences while the standard deviation becomes larger and the correlation coefficients tend to be lower for smaller template sizes. We have deduced velocities every 5° in both longitude and latitude.

To reduce erroneous determinations of the displacement caused by multiple peaks that frequently appear in cross-correlation surfaces, we have applied the method of averaging cross-correlation surfaces proposed by Ikegawa and Horinouchi (2016). In this method, three or more images are prepared, and cross-correlation surfaces between multiple combinations with different time intervals are calculated and averaged on the coordinates of the longitudinal and latitudinal velocities. In this study, three images obtained sequentially were used to prepare two pairs of images; one pair is composed of the first image and the second image, and the other is composed of the first image and the third image.

Correlation surfaces sometimes have elongated peaks due to streak features and/or rather featureless structures. To exclude velocity vectors obtained from such correlation surfaces, we adopted the following criteria for acceptable vectors: On the cross-correlation surface, a subregion of 1° × 1° size in longitude and latitude is placed centered at the correlation peak, and the fractional area in the subregion where the difference in the correlation coefficient from the peak value is less than 0.05 is evaluated; the fractional area should be smaller than 80%.

4 Results

4.1 Periodicities in the Radiance

Figure 2a shows the temporal variation of the radiance after photometric correction at 10°S averaged for the local solar time of 11:00–13:00 during orbits 436–490. Figure 2b shows its periodogram obtained by Lomb-Scargle method (Scargle, 1982), which can be applied to unevenly sampled data. Periodicities of 4 and 5 Earth days, exceeding the statistical significance of 99%, are identified. Figure 3 shows the latitudinal profiles of the Lomb-Scargle periodogram obtained for three different periods; the first period, orbits 436–490, shows the most coherent periodicity of about 4 Earth days from the equator to midlatitudes. The second period, orbits 659–710, shows a distinct periodicity of ~5 Earth days in the middle latitude and weak periodicities of ~4 Earth days near the equator. The third period, orbits 883–938, exhibits a periodicity of ~4.5 Earth days in the low latitude and marginally significant periodicities over wide frequencies. Though Lomb-Scargle periodograms can be contaminated by erroneous peaks caused by periodical data gaps (e.g., Kouyama, Imamura, et al. (2013)), the data set used in this study does not have such data gaps, and thus the obtained periodograms should be free from such erroneous peaks. Figure 4 shows examples of the mosaic images created from data obtained every 24 hr for the three periods. The longitudinal shifts between images are determined by the background flow velocity on the equator obtained by cloud tracking later in section 7. We consider that the period of orbits 436–490 shows the most coherent periodicity and the most distinct, tilted dark band representative of the Y feature; we focus on this period in later analysis.

Details are in the caption following the image
(a) Temporal variation of the radiance at 10°S averaged over the local solar time of 11:00–13:00. (b) Lomb-Scargle periodogram of the variation of the radiance. The dashed line shows the 99% statistically significant level. The images used to deduce the periodogram are listed in Table S1.
Details are in the caption following the image
Latitudinal profiles of the Lomb-Scargle periodogram of the radiance for different periods. (a) Orbits 436–490, (b) orbits 659–710, and (c) orbits 883–938. Dashed contours show the 99% statistically significant level. The images used to deduce the periodogram are listed in Table S1.
Details are in the caption following the image
Examples of the mosaic images. Images taken with a time interval of about 24 hr are shifted by (a) 62°, (b) 76°, and (c) 75° in longitude on the assumption that the ultraviolet contrasts are advected westward with a rotational period of (a) 5.4, (b) 4.7, and (c) 4.8 Earth days, respectively. These periods correspond to the recurrence periods of the background flow obtained by cloud tracking.

4.2 Velocity Fields

Figure 5 shows a typical example of the deduced velocity field superimposed on the corresponding image. The background zonal velocity in solid body rotation corresponding to the dayside-mean angular velocity at the equator was subtracted from each vector. Comparison of the velocity field with the brightness distribution suggests that poleward flow is enhanced around the boundary between the tilted dark band on the west side and the white band on the east side, both of which extend in the northeast-southwest direction. Such a tendency has already been suggested by Patsaeva et al. (2015).

Details are in the caption following the image
An example of the velocity field obtained from images taken in orbit 458 superimposed on the ultraviolet image. The background zonal velocity in solid body rotation corresponding to the dayside-mean angular velocity at the equator was subtracted from each vector. The vectors whose meridional components exceed 15 m/s are shown in red.

The latitudinal profiles of the dayside-mean zonal velocity and the rotation period of the atmosphere for orbits 436–490 are shown in Figure 6. This mean velocity, obtained by averaging cloud-tracked velocities on the dayside, is different from the zonal-mean velocity, which is the velocity averaged over the whole latitudinal circle, because of the existence of local time-dependent structures including the thermal tides. The dayside-mean zonal velocity has a maximum of 96 m/s at the latitude of 45°S, which is known as the midlatitude jet. The mean rotation period is ~5.4 Earth days around the equator and decreases to ~2.7 Earth days at 60°S; the period is shorter than the period of the brightness variation (~4 Earth days) on the south of 30°S and longer on the north of 30°S. The dayside-mean zonal velocity obtained in this study are almost consistent with those obtained by other studies including the existence of midlatitude jets (Hueso et al., 2015; Khatuntsev et al., 2013; Rossow et al., 1990).

Details are in the caption following the image
Latitudinal variations of (a) the dayside-mean zonal velocity, (b) the atmospheric rotation period, and (c) the number of averaged vectors. Data from orbits 436–490 are used. Horizontal bars show standard deviations.

4.3 Periodicities in the Velocity

Velocity fields were deduced at an interval of about 1 Earth day. Here we apply periodicity analysis to the velocity time series at the local solar time of 12:00. First, the obtained velocity vectors were averaged on the coordinates fixed to the latitude and the local time (Figure 7). In this local time-dependent component, poleward divergent flows are significant in the afternoon region, being consistent with Patsaeva et al. (2015). Next, the local time-dependent component was subtracted from all velocity vectors; the resultant velocity field mostly contains components propagating with respect to the local time. Then, to utilize all velocity measurements including those at local solar times other than 12:00, the time when the atmospheric region corresponding to each velocity vector has passed 12:00 was calculated on the assumption that the velocity field is advected at the dayside-mean zonal velocity, and this “corresponding time” was assigned to each velocity vector. Mathematically, letting the time when the velocity was measured be t (hours), the local solar time of the measurement be l (hours), the background zonal wind be urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0002, the radius of Venus be RV, and the latitude be ϕ, the corresponding time is calculated as urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0003. Similar analyses were conducted by previous studies (Limaye & Suomi, 1981).

Details are in the caption following the image
Brightness distribution and the velocity field averaged on the coordinates fixed to the local solar time in orbits 436–490. The vectors whose poleward components are larger than 15 m/s are shown in red. The background zonal velocity in solid body rotation corresponding to the dayside-mean angular velocity at the equator was subtracted from each vector.

Left panels of Figure 8 show the zonal and meridional velocity time series at 10°S obtained with the procedure above, and the right panels show the Lomb-Scargle periodogram. The analyzed period is orbits 436–465, in which the periodicity around 4 Earth days is most prominent. A measure of the errors in the cloud-tracked velocity when the correlation peak is precisely identified is given by one grid interval divided by the time interval, and is estimated to be 3.7 m/s at 10°S and 2.8 m/s at 40°S for the zonal velocity and 3.7 m/s for the meridional velocity. The uncertainty of the periodogram that originates from this measurement error is much smaller (<5%) than the power of the spectral peak at ~4 Earth days and does not influence the detection of the peak.

Details are in the caption following the image
Temporal variations of the (a) zonal and (c) meridional velocities at 10°S in orbits 436–465 after subtracting the solar-fixed component, and (b and d) their Lomb-Scargle periodograms. The dashed lines show the 99% statistical significant level.

The latitudinal dependences of the periodicities are shown in Figure 9. Dominant periods of ~4 and ~5 Earth days are found both in the zonal and meridional velocities. The dayside-mean zonal velocity is ~82 m/s near the equator and ~84 m/s at 15°S, corresponding to the mean rotation period of 5.4 Earth days and 5.1 Earth days, respectively (Figures 6a and 6b). The mean rotation period is shorter than 5.1 Earth days poleward of 15°S. The 4-day oscillation is attributed to a Kelvin wave because the propagation speed is faster than the dayside-mean zonal velocity if the zonal wavenumber is assumed to be one, the velocity oscillation is predominantly zonal, and the amplitude is large in the low latitude. The 5-day oscillation is prominent in the meridional velocity poleward of 15°S, where the dayside-mean zonal velocity has shorter rotation periods; this feature can be attributed to a Rossby wave. The dayside-mean velocity deduced from the dayside images can be different from the zonal-mean velocity because of the presence of the thermal tide; however, given the amplitude of the thermal tide of ~10 m/s (Newman & Leovy, 1992; Takagi et al., 2018), the sign of the intrinsic phase velocities with respect to the zonal-mean zonal velocity would not change even if such a difference is considered, although the amplitude of the thermal tide shows variability (Limaye, 1988). Considering the hemispherically symmetric nature of the midlatitude oscillation seen in the UV contrast observed by Pioneer Venus (Del Genio & Rossow, 1990), the observed oscillation might represent hemispherically symmetric Rossby waves. The latitudinally broad structures are consistent with the linear theories (Kouyama et al., 2015; Imamura, 2006). The periodograms deduced from the same data set by Kouyama, Imamura, et al. (2013) also show a 4-day periodicity in the zonal velocity and a 5-day periodicity in the meridional velocity, although the peak for the 5-day period does not reach the statistically significant level; the difference is attributed to a smaller number of velocity vectors in Kouyama, Imamura, et al. (2013), where data at a specific local time were used.

Details are in the caption following the image
Latitudinal profiles of the periodograms of the (a) zonal and (b) meridional velocities in orbits 436–465 after subtracting the solar-fixed component. Dashed contours represent the 99% statistical significance.

5 A Scenario for the Formation of the Y Feature

The temporally and zonally oscillating meridional wind can play an important role in distributing the UV absorber. The amplitude of the meridional displacement associated with the 5-day (Rossby) wave is given by
urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0004(2)
where urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0005 is the amplitude of the meridional velocity and T* is the intrinsic period. The amplitude of the meridional velocity is estimated to be urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0006 m/s at 30°S by fitting a sinusoidal function to the data. The intrinsic period is given by (1/Tb − 1/Tw)−1 = 24 ± 7 Earth days at 30°S, where Tb = 4.3 ± 0.1 Earth days is the period of the background velocity at 30°S and Tw = 5.2 ± 0.4 Earth days is the period of the oscillation. The error in Tb is given by the standard deviation (Figure 6) divided by the square root of the number of the averaged vectors. The half width at half maximum of the periodogram of the meridional velocity gives the error in Tw. Substituting these into 2, we obtain urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0007 (1.4 ± 0.5) × 103 km or 13 ± 4° in latitude. The total displacement caused by the wave is twice this amplitude, that is, 27 ± 8° in latitude. This is comparable to the latitudinal extent of the observed dark bands at the cloud top. The occurrence of the strong poleward flow near the prominent streak feature (Figure 5) also implies transport of dark material by the oscillating wind.

As shown in Figure 7, the wind field fixed to the local solar time also shows strong poleward flow in the afternoon region because of the superposition of the thermal tide, whose velocity amplitude is typically ~10 m/s (Newman & Leovy, 1992; Rossow et al., 1990), on the mean meridional circulation. However, because the thermal tide has a relatively short intrinsic period that is close to the rotation period of the mean zonal wind (typically 4-5 Earth days), the associated meridional displacement is around 2 × 10 (m/s) × 4.5 (Earth days) / 2π ~ 1,200 km ~ 11°, which is half of that by the 5-day wave. Furthermore, the thermal tide cannot form patterns that propagate at a velocity faster than the superrotation.

Based on the estimates above, we propose the following scenario. The region of upward flow associated with the Kelvin wave moves westward at a speed slightly faster than the background wind, and the upward wind transports dark material to the equatorial cloud top from below (Del Genio & Rossow, 1990). Then the combination of the mean meridional circulation and the hemispherically symmetric Rossby wave transports the dark material poleward in both hemispheres. Once the dark material reaches the midlatitude, the meridional shear of the zonal wind associated with the midlatitude jet stretches the dark feature in the northeast-southwest (northwest-southeast) direction in the southern (northern) hemisphere, forming the Y shape. Since the meridional velocity amplitude of the Rossby wave is comparable to the mean meridional velocity, which is estimated to be 1–5 m/s (e.g., Lee, Imamura, et al., 2015; Lee, Titov, et al., 2015; Rossow et al., 1990; Takagi et al., 2018), the poleward flow undergoes large oscillation, thereby creating the undulation of the boundary between the dark region on the low-latitude side and the bright region on the high-latitude side (Figure 4). Furthermore, since the velocity of the poleward advection of the dark material is variable depending on the phase relationship between the Kelvin wave and the Rossby wave, the slope of the tilted dark band becomes variable as seen in the mosaic images given by Del Genio and Rossow (1982). The periodicity of the radiance in the midlatitude is determined mostly by the supply of the dark material to the cloud top by the Kelvin wave; though the Rossby wave modulates the efficiency of the poleward transport, it does not seem to change the dominant period (Figure 3).

6 Numerical Modeling of Material Transport

The scenario described in the previous section is examined using a two-dimensional transport model on a Cartesian coordinate for the cloud-top atmosphere. The influence of the vertical shear of the mean zonal wind is not taken into account since the mean zonal velocity has a maximum in this height region. Passive tracers representing the dark material are placed artificially near the equator and the subsequent horizontal transport by the mean circulation, the Rossby wave, and the Kelvin wave is modeled. The Rossby wave field is represented by a simple stream function. Since the physical processes are considered to be symmetric about the equator, the model domain includes the southern hemisphere only. Letting x be the westward distance and y be the southward distance with the origin at the equator, the total wind vector (u, v) is a combination of the Rossby wave field (u′, v′) and the background circulation ( urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0008, urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0009):
urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0010(3)
urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0011(4)
urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0012(5)
urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0013(6)
urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0014(7)
urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0015(8)
where t is the time, u0 = 100 m/s is the mean zonal wind at the equator corresponding to the rotation period of 4.5 Earth days, Lx = 3.8 × 104 km is the zonal span of the model domain corresponding to 360° on the equator, Ly = 6.4 × 103 km is the meridional span of the model domain corresponding to 60° in latitude, and u1 = 50 m/s is the velocity of the midlatitude jet at y = Ly realizing the rotation period of 3.0 Earth days. The latitudinal profile of the rotation period of the background atmosphere is taken from the mean zonal velocity deduced by cloud tracking in the 6 years of observations by VMC (Sánchez-Lavega et al., 2017) because the relatively short period of our analysis might include notable uncertainty in the mean circulation. k = 2π/Lx and l = π/Ly are the wavenumbers in the zonal and meridional direction, respectively, v0 = 2 m/s is the peak velocity of the mean meridional circulation, urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0016 and urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0017 are the velocity amplitudes of the Rossby wave, ωR = 2π/5.0 [days−1] is the frequency of the Rossby wave, urn:x-wiley:21699097:media:jgre21133:jgre21133-math-0018 is the zonal velocity amplitude of the Kelvin wave, ωK = 2π/4.0 [days−1] is the frequency of the Kelvin wave, and ye − fold is the e-folding distance corresponding to the latitudinal distance of 25°, which is comparable to the value estimated by Kouyama et al. (2012). The existence of the horizontal wind associated with the Kelvin wave is not consistent with the two-dimensional model; we have tested model runs without the Kelvin wave and confirmed that the results are largely unchanged (not shown here). The model domain is restricted to equatorward of 60°S, where major dark features exist (e.g., Peralta et al., 2007).

Passive tracers represented by particles are placed every 24 hr at intervals of 10° in longitude and latitude in a rectangular region near the equator (5–25°S) with a longitudinal span of 40° that moves westward at a velocity corresponding to the rotation period of the Kelvin wave (4.0 Earth days), which is expected to supply the dark material to the cloud top. The region where the tracers are supplied is located at the phase of the maximum divergence of the zonal velocity associated with the Kelvin wave, that is, the phase of the maximum upward displacement. The latitudinal width of the rectangular region is taken from the half width of the Kelvin wave. To visualize stretching of air parcels, the tracers are connected in the north-south direction by thin lines when they are first placed. The dark material seems to have a lifetime on the same order of magnitude as the timescale of the meridional advection because the dark air supplied in the equatorial region becomes brighter during poleward advection and creates the bright polar band around 60° latitude (Figure 4). Considering the timescale of the meridional advection of Ly/v0 ~ 37 Earth days in the model, the color of the tracers is changed to lighter colors every 10 Earth days and the tracers are removed from the system when 30 Earth days has passed since their supply to the equatorial region. A test run without the Rossby wave was also conducted to examine the role of the wave.

Figure 10 shows snapshots of the calculation spanning 20 Earth days where the periodical variation has reached a quasi-steady state; because of the 4- and 5-day period forcing, the overall variation is repeated every 20 Earth days. The tracers placed near the equator are transported poleward and westward to form a band structure resembling the observed tilted dark bands. The thin lines connecting the tracers are aligned in the northeast-southwest direction, suggesting that air parcels are stretched in this direction; this feature is consistent with the observed small-scale streaks along the dark bands (Figure 4). Prominent poleward extension of the band structure occurs at the poleward wind phase of the Rossby wave, while the tracers are confined to the equatorial region at the equatorward wind phase of the Rossby wave. The eastern edge of the tracers confined in the equatorial region is stretched zonally by the eastward wind component of the Rossby wave, creating the root of the Y feature. At the leading (western) edge of the Y feature near the equator, the eastward wind component of the Rossby wave pushes the tracers eastward to shape the bow-like structure. Since the phase relationship between the Rossby wave and the equatorial source of the tracers is variable, the overall structure is not steady. Such a variability in the tracer transport leads to the variation of the tilt angle of the dark bands (Del Genio & Rossow, 1982). It should be noted that the magnitude of the mean meridional circulation and the lifetime of the UV absorber are rather uncertain. To examine the sensitivity to these parameters, test runs were performed with the maximum value of the mean meridional circulation of 1–4 m/s (2 m/s in the nominal run), and the tracer lifetime of 15–60 Earth days (30 Earth days in the nominal run). The characteristics of the tracer distribution resembling the Y feature were largely unchanged from the nominal run (not shown here).

Details are in the caption following the image
Result of the modeling of tracer transport. Black dots are the tracers within 10 Earth days after supply, gray dots are within 10–20 Earth days, and light gray dots are within 20–30 Earth days. The dots connected by thin lines were aligned in the north-south direction when they were first placed near the equator. The arrows indicate the velocity vectors of the Rossby wave.

Figure 11 shows snapshots of the test run without the Rossby wave. In this case, the tracers supplied near the equator are transported poleward and westward solely by the mean circulation. Though a dark band is created also in this run, the band is tilted in the northeast-southwest direction only in the midlatitude poleward of ~35°, where the latitudinal shear of the zonal wind is large. The root of the Y feature in the equatorial region is not created. The orientation of the dark bands is stable with time. The difference between the nominal case and the test run suggests the key role of the Rossby wave in the formation of the Y feature.

Details are in the caption following the image
Same as Figure 10 but in the absence of the Rossby wave.

7 Summary

We investigated the role of planetary-scale waves and the mean circulation in the formation of the Y feature based on a comparison between the velocity field deduced by cloud tracking and the brightness distribution using 365 nm images obtained by VMC on Venus Express spacecraft. Brightness variations with periods of 4–5 Earth days that are thought to be related to the Y feature are observed most of the time. We focused on orbits 436–490, in which the tilted dark band was clearly observed and the brightness variation had a coherent periodicity of ~4 Earth days independent of the latitude. Spectral analyses of the cloud-tracked velocities revealed existence of ~4 and ~5 Earth day periodicities. The 4-day oscillation was attributed to a Kelvin wave because the phase speed is faster than the background zonal wind, the amplitude is large in the low latitude, and the velocity oscillation is predominantly zonal. The 5-day oscillation was attributed to a Rossby wave because the phase speed is slower than the background zonal wind and the amplitude of the meridional velocity is large in the middle latitude. The meridional displacement of air parcels associated with the Rossby wave was found to be comparable to the latitudinal extent of the Y feature, suggesting a significant contribution.

Based on the observations above, a scenario for the formation of the Y feature is suggested. Dark materials are first supplied to the cloud top by the vertical wind associated with the Kelvin wave from below. The materials are subsequently transported poleward by the combination of the mean meridional circulation and the Rossby wave, and then stretched to the northeast-southwest (northwest-southeast) direction in the southern (northern) hemisphere by the midlatitude jet, forming the tilted dark bands that constitute the Y feature. Because of the contribution of the oscillating winds to the transport, the tilt of the dark bands becomes variable. A simplified two-dimensional numerical simulation was conducted to examine the transport of passive tracers by the mean meridional circulation, the midlatitude jet, and the Rossby wave; a tilted band structure resembling the observed Y feature was created, suggesting the validity of the proposed scenario.

In this study, the analysis of the observational data was restricted to the southern hemisphere because of the orbital configuration of Venus Express. The use of images obtained by JAXA's Akatsuki (Nakamura et al., 2016), which is observing both hemispheres of Venus from an equatorial orbit from December 2015, would allow investigation of the formation of the whole structure of the Y feature. Since multiple wavelength channels in addition to UV are available simultaneously, more detailed analysis of the wave field should be possible. Three-dimensional modeling of tracer transport using Venus GCMs is also needed for comprehensive understanding of the role of atmospheric dynamics in the formation of the planetary-scale brightness contrast. Petrova et al. (2015) pointed out, based on an analysis of UV and near-IR images taken by VMC, that submicron particles also contribute to the formation of the UV contrast; the role of photochemistry and cloud microphysics is left for future studies.

Acknowledgments

Takeshi Horinouchi provided valuable comments on this study. We are grateful to the Venus Express VMC team for releasing the excellent data. The data sets of VMC are available at ftp://psa.esac.esa.int/. The data sets of cloud-tracked wind velocities are available at https://zenodo.org/record/2604932#.XKBItyj7SUk. The two anonymous reviewers provided valuable comments.