Volume 46, Issue 9 p. 4573-4580
Research Letter
Free Access

Impact of Data Assimilation on Thermal Tides in the Case of Venus Express Wind Observation

Norihiko Sugimoto

Corresponding Author

Norihiko Sugimoto

Research and Education Center for Natural Sciences, Department of Physics, Keio University, Yokohama, Japan

Correspondence to: N. Sugimoto,

[email protected]

Search for more papers by this author
Toru Kouyama

Toru Kouyama

Artificial Intelligence Research Center, National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

Search for more papers by this author
Masahiro Takagi

Masahiro Takagi

Faculty of Science, Kyoto Sangyo University, Tokyo, Japan

Search for more papers by this author
First published: 16 April 2019
Citations: 11

Abstract

Impacts of horizontal winds assimilation on thermal tides are investigated by using the Venus atmospheric general circulation model for the Earth Simulator local ensemble transform Kalman filter data assimilation system. The assimilated data are horizontal winds derived from Venus ultraviolet images taken by the Venus Monitoring Camera onboard the Venus Express orbiter. The results show that three-dimensional structures of the thermal tides are significantly improved not only in the horizontal winds but also in the temperature field, even though the observations are available only at the cloud top level on the southern dayside hemisphere approximately once an Earth day. The reproduced temperature fields agree well with recent radio occultation measurements of the Venus Climate Orbiter Akatsuki. The zonal mean fields of the zonal wind and temperature are also improved globally. This study would enable reanalysis of past Venus observations.

Key Points

  • Three-dimensional structures of the thermal tides are significantly improved by the data assimilation of horizontal winds derived from Venus UV images
  • Reproduced temperature fields agree well with those obtained by radio occultation measurements of Akatsuki
  • Zonally averaged atmospheric structures are improved globally even though the observations are very limited in space and time

1 Introduction

Thermal tides are planetary scale atmospheric waves excited by the solar heating, which move with the Sun. Since about 60% of the solar flux incident on Venus is absorbed in the cloud layer (45–70 km; Tomasko et al., 1980), the thermal tides are considered to be strongly excited there and have important roles on the Venus atmospheric general circulation (e.g., Fels & Lindzen, 1974). The Venus thermal tides were first detected in temperature fields (Taylor et al., 1980). The semidiurnal tide, which is a tidal component with a zonal wave number of 2, predominates near the equator, whereas the diurnal tide with a zonal wave number of 1 has large amplitudes in middle and high latitudes above the cloud top level (~70 km). Because of the breaking of thermal tides, it is considered that the super rotation decreases with altitude above the cloud layer (~80–90 km; Ando et al., 2018).

There are several Venus general circulation model (GCM) studies in which the thermal tides are taken into account (Kido & Wakata, 2009; Lebonnois et al., 2010, 2016; Takagi & Matsuda, 2007; Yamamoto & Takahashi, 2009). However, the structure of the thermal tides was not fully investigated nor compared with observations, because the generation mechanism of the super rotation was focused on and long-term GCM simulations with relatively low resolutions were performed in these studies. Recently, we have developed a Venus GCM named AFES-Venus (Sugimoto et al., 2014a) on the basis of AFES (an atmospheric GCM for the Earth Simulator; Ohfuchi et al., 2004), in which a weakly stratified layer observed in the cloud layer (Tellmann et al., 2009) is taken into account. AFES-Venus has enabled us to reproduce the realistic super rotation under the solar heating based on observations, planetary scale waves (Sugimoto et al., 2014b), a polar vortex surrounded by a cold latitude band called “cold collar” (Ando et al., 2016, 2017), and planetary scale streak features found in the lower cloud levels (Kashimura et al., 2019). We also investigated the thermal tides and pointed out that they are important for material transports in the cloud layer (Takagi et al., 2018). However, Ando et al. (2018) showed that the thermal tides reproduced in the AFES-Venus simulations were not consistent with equatorial thermal structures obtained by radio occultation measurements of Venus Express (VEX) and Akatsuki; namely, the temperature distribution at the cloud levels was shifted by about 30° in the zonal direction. The reason for this discrepancy is not clear, but it may be ascribed to differences in the zonal wind distribution, by which the thermal tides are strongly affected (Takagi & Matsuda, 2006). The other possibility is uncertainty in the radiative processes. Haus et al. (2015) showed that the solar heating and radiative cooling, which are also important for the thermal tides, depend on the cloud and unknown ultraviolet (UV) absorber. However, because their distributions remain unclear, it is difficult to take their effects into GCMs precisely. In order to correctly interpret the VEX and Akatsuki observations and elucidate the material transport due to the thermal tides, we need to reproduce their structures quantitatively and qualitatively consistent with the observations.

Recently, we have developed a Venus AFES local ensemble transform Kalman filter (LETKF) data assimilations system named VALEDAS. The system has been tested for AFES-Venus simulations excluding the thermal tides (Sugimoto et al., 2017). The result shows that the data assimilation works well with observation data with periods less than 12 hr, but its impact is quite limited in the case of daily observation data. In the present study, we proceed to the data assimilation with horizontal winds derived from Venus UV images taken by the Venus Monitoring Camera (VMC) onboard the VEX orbiter using AFES-Venus simulations including the thermal tides in order to investigate the impact of the data assimilation on the thermal tides and the general circulation. The effectiveness of VALEDAS and usefulness for future observation missions are also discussed.

2 Experimental Setup

AFES-Venus is a full nonlinear Venus GCM with simplified physical processes (Sugimoto et al., 2014a) based on AFES (Ohfuchi et al., 2004). The horizontal resolution is set to T42, where T denotes the triangular truncation number for spherical harmonics; there are 128 times 64 horizontal grids at each level. The model atmosphere extends from the flat ground to 120 km, which is divided into 60 layers with constant thickness of 2 km. The model includes vertical eddy diffusion with a constant coefficient of 0.15 m2/s. Horizontal eddy viscosity is represented by the second-order hyper viscosity with a damping time for the maximum wave number component of 0.1 Earth days. At the lowest level, Rayleigh friction with a damping time of 0.5 Earth days is employed to take the surface friction into account. In the upper atmosphere above 80 km, a sponge layer with damping times gradually decreasing with height is applied only to the eddy components. Convective adjustment is used to suppress static instability. The solar heating is based on Pioneer Venus observations (Tomasko et al., 1980). The infrared radiative process is simplified by a Newtonian cooling scheme, whose coefficients are based on Crisp (1989). The temperature is relaxed to a prescribed horizontally uniform temperature distribution based on the Venus International Reference Atmosphere (Seiff et al., 1985). Details are described in our previous research (Sugimoto et al., 2014a, 2014b).

We use an idealized super rotating flow in solid-body rotation as an initial state of the velocity field, in which the zonal wind increases linearly with height from the ground to 70 km and reaches 100 m/s at the equator. The initial temperature distribution is in gradient wind balance with the zonal wind. The direction of the planetary rotation is assumed to be eastward (positive). We have confirmed that a fully developed super rotating flow could be obtained from a motionless state with a small vertical viscosity excluding the thermal tide (Sugimoto et al., 2019), and the zonal mean zonal winds reproduced in the different two initial conditions with the super rotating flow and a motionless state were converged to a similar state. However, since an extremely long time (approximately thousands of Earth years) is needed to spin up if we start from the motionless state, we use the idealized super rotating flow as the initial state in the present study. Using this initial state, we perform nonlinear numerical simulations for more than four Earth years. Then quasi-equilibrium data sets sampled at 8-hr intervals are used as initial conditions for each 31-member ensemble for the ensemble run in the LETKF data assimilation.

The LETKF is an efficient method of the data assimilation based on an ensemble Kalman filter, which has been widely used in the terrestrial meteorology (Miyoshi et al., 2007; Miyoshi & Yamane, 2007; Yamazaki et al., 2017). In the current VALEDAS (Sugimoto et al., 2017), we use 31-member ensemble and 10% multiplicative spread inflation. The value of 10% inflation has been checked and used in the Earth atmosphere data assimilation by ALERA and ALERA2 systems (Miyoshi et al., 2007), on which the VALEDAS used in the present study is based. We adopted the same spread inflation, because it has been suggested that the Venus atmosphere at the cloud levels where the wind observations are assimilated is similar to the Earth one in terms of baroclinic instability and front genesis (Kashimura et al., 2019; Sugimoto et al., 2014a, 2014b). We have checked robustness of the results with large ensemble sizes of 63 and 127 (see also supporting information S2). The localization parameters are 400 km in horizontal and logP = 0.4 in vertical, where P is pressure. Random Gaussian errors with a 4.0-m/s standard deviation are assumed for the horizontal winds field based on the observations errors estimated by Kouyama et al. (2013). Although the time interval of the data assimilation cycle is 6 hr in the original version of VALEDAS, it is about 1 Earth day in the present study because of availability of the observation data as noted below. The four-dimensional LETKF comprised 7-hr time slots at each analysis, and the observations are assigned to hourly time slots depending on their availability (Hunt et al., 2004, 2007). While the system is the same as tested by Sugimoto et al. (2017), we use the realistic solar heating including a diurnal component; that is, the thermal tides are included in the AFES-Venus simulations in the present study. Note that the effects of the distributions of the cloud and unknown UV absorber on the solar heating and infrared radiative cooling are not taken into account as mentioned in Introduction. It has been shown by Sugimoto et al. (2014b) that the zonal mean zonal wind reproduced in AFES-Venus including a diurnal component of the solar heating is consistent with observations at the cloud top level (e.g., Khatuntsev et al., 2013; Kouyama et al., 2012; Machado et al., 2012; Moissl et al., 2009).

The observational data used in the present study are horizontal winds at approximately 70 km derived by the cloud tracking of a pair of UV images captured by the VMC (Kouyama et al., 2013). It should be noted that the horizontal winds are available approximately once a Earth day only on a dayside region approximately from 60°S to 30°N between 07:00 local time (LT) and 17:00 LT due to the polar long elliptical orbit of the VEX orbiter. Since the region where the winds can be derived also depends on the orbit and observation time, we could have only one pair of Venus cloud images suitable for the cloud tracking in a wider area in every orbit. Though the apparent size of Venus image also depends on the orbit, the winds were derived every 3° both in the zonal and meridional directions. Typical observation data used in the present study include ~1,500 horizontal wind vectors at each time. We have 73 observations for the data assimilation in VALEDAS during a period of about 3 months from 28 January 2008 to 26 April 2008 (Epoch 4). The assimilated data obtained in the last 30 Earth days are analyzed. We have also assimilated the whole 59 observations in Epoch 3 during a period from 1 July to 17 September 2007 (about 80 days). The results are quite similar to those obtained in Epoch 4 (see also supporting information S3), which indicates that the present results obtained for the thermal tides are robust.

3 Results

Figure 1 shows horizontal distributions averaged over Epoch 4 of the zonal and meridional winds fields derived from the VMC UV images. Because the composite means over 73 observations are calculated in solar-fixed coordinates, these winds consist mainly of the zonal mean and the thermal tide components. The subsolar point (12:00 LT) is located at 0°E longitude. Again, the directions of the planetary rotation and the zonal wind are assumed to be eastward (positive) in the present study. Since the VMC observations had been done on dayside of the southern hemisphere only, the horizontal winds are available on about one-fourth area of the whole Venus. Nevertheless, wind distributions associated with the thermal tides are clearly observed; the zonal wind, which has a local minimum around noon, is faster in morning (6–9 LT) and evening (15–18) regions. The meridional wind has local maximum of southward wind around noon in midlatitudes of the southern hemisphere.

Details are in the caption following the image
Horizontal distributions of (a) zonal and (b) meridional winds at the cloud top level derived from the ultraviolet images taken by Venus Monitoring Camera averaged over 73 observations (Epoch 4) in solar fixed coordinates where the subsolar point is fixed at the center of each panel. The units are meters per second. Note that direction of the planet rotation is from left to right in the plots.

In an original run of AFES-Venus (without data assimilation), the thermal tides are excited by a diurnal component of the solar heating. However, their horizontal structures at the cloud top level are not consistent with the VMC observations. Figure 2 shows horizontal distributions of the zonal and meridional winds and the temperature deviations associated with the thermal tides at the cloud top level (~70 km) reproduced by AFES-Venus (a–c) and VALEDAS (d–f). These distributions are calculated by the composite means at the subsolar point (fixed at the center of each panel) over 30 Earth days. In the zonal wind field obtained by AFES-Venus (Figure 2a), positive and negative signs change around noon, and local minimum appears at ~30–45°E longitudes (14–15 LT) around the equator; that is, phases of the zonal wind of the thermal tides are different from those observed by the VMC (Figure 1). In the temperature field (Figure 2c), negative and positive signs change around noon, and the local maximum appears at ~30–45°E longitudes (14–15 LT) around the equator, as in the zonal wind field. This temperature distribution is also not consistent with recent temperature observations of the radio occultation of the Venus Climate Orbiter Akatsuki [Figure 2a in Ando et al., 2018].

Details are in the caption following the image
Horizontal distributions of (a, d) zonal wind, (b, e) meridional wind, and (c, f) temperature deviations associated with the thermal tides at the cloud top level (~70 km) reproduced in AFES-Venus (a–c) and VALEDAS (d–f). These distributions are calculated by the composite means over 30 Earth days at the subsolar point (fixed at the center of each panel). The assimilation data obtained in the last 30 Earth days are used for the VALEDAS results. The units are meters per second for winds and kelvins for temperature, respectively. Note that since the planet rotates from left to right in the present study, the morning and evening terminators are located at 90°W (6 LT) and 90°E (18 LT) longitudes, respectively. VALEDAS = Venus atmospheric general circulation model for the Earth Simulator (AFES-Venus) local ensemble transform Kalman filter (LETKF) data assimilation system; AFES-Venus = Venus atmospheric general circulation model for the Earth Simulator.

As shown in Figures 2d–2f, the phase distributions of the thermal tides are improved by assimilating the horizontal winds by VALEDAS not only for the horizontal winds but also for the temperature field. Both the local minimum of zonal wind and the local maximum of temperature appear around noon at the cloud top level (~70 km) around the equator. Note that the observations are available only on the dayside of the southern hemisphere once an Earth day. Because a north–south symmetry about the equator keeps widely, the present result indicates that the improvement obtained by the data assimilation extends outside of the observed region.

To investigate how the impact of data assimilation spreads in the vertical direction, Figure 3 shows the zonal wind and temperature deviations associated with the thermal tides reproduced by AFES-Venus (a, b) and VALEDAS (c, d) in a longitude-height section at the equator. Again, these distributions are calculated by the composite means over 30 Earth days at the subsolar point (fixed at the center of each panel). Amplitudes are multiplied by a factor of urn:x-wiley:00948276:media:grl58882:grl58882-math-0001 for visibility, where σ is a scaled pressure level defined in the sigma coordinate system. The phase distributions are changed at 65- to 75-km levels both for the zonal wind and temperature deviations, although the horizontal winds are assimilated only at the cloud top (~70 km). It is also shown that the phases of the semidiurnal tide (a tidal component of wave number 2) are significantly modified in these levels, while the diurnal tide in the cloud layer 50- to 60-km levels seems not to change, especially for the zonal wind.

Details are in the caption following the image
Vertical distributions of (a, c) zonal wind and (b, d) temperature deviations associated with the thermal tides at the equator reproduced in AFES-Venus (a, b) and VALEDAS (c, d). These distributions are calculated by the composite means over 30 Earth days at the subsolar point (fixed at the center of each panel). The assimilation data obtained in the last 30 Earth days are used for the VALEDAS results. The units are meters per second for wind and kelvins for temperature, and amplitudes are multiplied by a factor of urn:x-wiley:00948276:media:grl58882:grl58882-math-0002 for visibility, where σ is a scaled pressure level in the sigma coordinate system. VALEDAS = Venus atmospheric general circulation model for the Earth Simulator (AFES-Venus) local ensemble transform Kalman filter (LETKF) data assimilation system; AFES-Venus = Venus atmospheric general circulation model for the Earth Simulator.

Since the thermal tides propagate vertically, it is expected that they could give large impacts on the general circulation of the Venus atmosphere. Figure 4 shows the zonal mean zonal wind and temperature fields (black contours) in a latitude-height cross section averaged over the last 30 Earth days. The colors show deviations from those obtained by an original run of AFES-Venus (without data assimilation) averaged over 60 Earth days. The zonal mean zonal wind and temperature fields are significantly modified as a result of the long-term data assimilation. The zonal mean zonal wind above the cloud top region (~65–85 km) substantially decreases by about 20 m/s (blue tones). The temperature field is also modified especially in high latitudes around the cloud top level (~70 km) so that the thermal wind balance is established. These results are in contrast to those obtained in the previous work in which the thermal tides were not reproduced well in each ensemble AFES-Venus run in VALEDAS (Sugimoto et al., 2017). In the present study, the thermal tides with large amplitude are included in an original run of AFES-Venus (without data assimilation) by using the realistic solar heating. It is inferred, therefore, that the improvement of the three-dimensional structure of the thermal tides by VALEDAS would give large impacts on the general circulation through changes of their momentum and heat transports.

Details are in the caption following the image
Zonal mean zonal wind (a; contours, m/s) and temperature (b; contours, K) in a latitude-height cross section averaged over the last 30 Earth days. The colors show deviations from those obtained by an original run of Venus atmospheric general circulation model for the Earth Simulator (without data assimilation) averaged over 60 Earth days.

We have also examined the ensemble spreads of the meridional wind and temperature in a latitude-height cross section (see also supporting information S1). The distribution of large spread is similar to that obtained in the previous work (Sugimoto et al., 2017), suggesting that the disturbances excited in VALEDAS would not be changed largely though the zonal mean zonal wind significantly decreases near the cloud top levels. These results also support that the impacts of the data assimilation of horizontal wind at 70 km extend over approximately 10 km in the vertical direction though the observations are very limited in time and space.

4 Summary and Discussion

In the present study, we investigated impacts of the data assimilation of horizontal winds on the thermal tides and the general circulation of the Venus atmosphere by using the data assimilation system named VALEDAS (Venus atmospheric GCM for the Earth Simulator [AFES-Venus] LETKF data assimilation system; Sugimoto et al., 2017). The assimilation data are horizontal winds derived from UV images taken by the VMC onboard the VEX orbiter. The thermal tides obtained in an original run of AFES-Venus are inconsistent with observations in terms of phase distributions at the cloud top level. We showed that this inconsistency was successfully resolved by the data assimilation, though the observed horizontal winds were available only at the cloud top on the dayside on the southern hemisphere approximately once an Earth day. The reproduced temperature fields of the thermal tides also agreed well with recent radio occultation measurements of the Venus Climate Orbiter Akatsuki (Ando et al., 2018). Furthermore, the zonal mean zonal wind and temperature fields were also improved significantly. These results suggest that the improvement of the thermal tides would give large impacts on the general circulation through changes of their momentum and heat transports.

It is rather surprising that the very limited horizontal wind observations, which are available only at a single altitude in a narrow area on the dayside once an Earth day, can improve the global structure of the simulated Venus atmosphere. Because the original assimilation cycle is 6 hr in the present study, we can assimilate the observation data only once every four cycles. It seems, however, that the impact of observations is accumulated in the long-term data assimilation and improves the three-dimensional structure of the thermal tides. This result could be related to a fact that the Venusian thermal tides are long-period waves due to the slow planet rotation (e.g., the diurnal tide has 117-Earth day period). In the previous work (Sugimoto et al., 2017), the zonal mean zonal wind and temperature fields were not significantly modified, though the same horizontal winds were used for the data assimilation. This is because the thermal tides with realistic amplitude were not excited in each ensemble AFES-Venus original run. It is suggested that the realistic reproduction of the thermal tides in an original run of AFES-Venus is a key to achieve the large and effective impacts of the data assimilation obtained in the present study. The deceleration of zonal mean zonal wind, which is caused by the thermal tides, would also contribute to the improvement of the thermal tides.

At the cloud top level (~70 km), relaxation time of the infrared radiative cooling is estimated to be less than 10 Earth days (Crisp, 1989), which is longer than assimilation cycle of about 1 Earth day but much shorter than 3 Earth months over which we have assimilated. This would be one of the reasons that the zonal mean zonal wind and temperature fields are significantly improved. At least around the cloud top level, the present results would help to understand the circulation processes of the Venus atmosphere. Because radiative relaxation time is estimated to be longer (order of 100 Earth days) in the lower cloud layer (~55 km), we need longer time series of observation to improve the lower atmosphere. Nevertheless, the fact that a relatively small number of observations with a large time interval of ~1 Earth days can improve the global structure significantly would encourage to design future Venus missions.

Kouyama et al. (2015) reported that short-period (4–5 Earth days) waves called as Kelvin and/or Rossby waves appear in Epoch 4 used in the present study, which are also expected to play important roles in the Venus atmosphere. However, we could not reproduce such kind of waves in the present assimilation results of VALEDAS. This result suggests that we need more frequent observations to reproduce these short-period waves. The Akatsuki team plans for frequent 2-hourly observations in the near future. It would be interesting to assimilate such high frequent observations by VALEDAS in order to reproduce the short-period waves and investigate their dynamical effects on the Venus general circulation.

Acknowledgments

This study was conducted under the joint research project of the Earth Simulator Center with title “Simulations of Atmospheric General Circulations of Earth-like Planets by AFES.” The work is partly supported by MEXT | Japan Society for the Promotion of Science (JSPS) grants JP15K17767, JP16H02225, JP16H02231, JP17H02961, JP19H00720, and JP19H01971. The GFD-DENNOU Library was used for creating figures. The authors thank Dr. Steven J. Greybush and two anonymous reviewers for useful comments. Results from the GCM simulations performed in this paper are provided as supporting information.