Horizontal winds assimilation to reproduce equatorial Kelvin wave in the Venus atmosphere
Authors: Shirasaka Mimo , Sugimoto Norihiko , Fujisawa Yukiko , Hosono Asako , Abe Mirai , Ando Hiroki , Takagi Masahiro , Yamamoto Masaru 
Published: October 2020

&#160;

Abstract
&#160;
Structure of the planetary scale wave, which has been studied for over decades since its discovery in 1980s, is yet to be shrouded in mystery. To clarify this, images by cameras would definitely be necessary. Our team has been assimilating data with AFES LETKF Data Assimilation System for Venus (ALEDAS-V): the first data assimilation system for the Venusian atmosphere, as a pre-experiment before executing the mission. Results show that you can successfully reproduce 4-day planetary scale wave when assimilating data of wind velocity of latitude S15&#176;- N15&#176; every 6 hours at an altitude of 70 km. This discovery will contribute not only to a mission to observe wind velocity of Venus, but also to proposal regarding missions for further understanding of atmospheric structure on other planets, in the future.
&#160;
&#160;
The planetary scale wave, which is considered as 4-day &#8220;equatorial Kelvin wave&#8221; is existing at the cloud top in the equatorial region on the Venus atmosphere [1,2]. The equatorial Kelvin wave is pointed out to have a possibility of contributing to generation and maintenance of what is called &#8220;Super Rotation&#8221;: the wind circulating Venus 60 times faster than the speed of Venusian rotation [3]. However, the equatorial Kelvin wave has not been simulated in any Venusian atmospheric General Circulation Model (VGCM) in the world. We have so far developed AFES-Venus; Atmospheric GCM for the Earth Simulator for Venus, and ALEDAS-V; AFES LETKF Data Assimilation System for Venus, using LETKF; Local Ensemble Transform Kalman Filter, for the first time in the world [4,5]. In this study, we made an observation data regarding the speed of wind, by varying conditions such as altitude, latitudinal range, and frequency of observations, assuming observations with various wavelength cameras. We created the idealized observation data from CCSR/NIES Venus AGCM [6], in which the equatorial Kelvin wave is reproduced at ~70 km by 5.5-day wave forcing from the lowest level (~30 km).
&#160;
&#160;
AFES-Venus solves dry 3-D Primitive equation on sphere. The physical parameters are based on Venus. The latitude-longitude grids (128 times 64) with 60 vertical layers are used. Solar heating is based on Tomasko (1980) and Crisp (1989), and radiative process is simplified by Newtonian cooling. The simulation starts from zonal wind assuming super rotation and spin up for 4 Earth years. ALEDAS-V uses the LETKF [7] to produce an improved estimate (called analysis) by combining observations and short time ensemble forecasts of AFES-Venus. The number of ensemble members is 31. Assimilation cycle is 6 hourly interval. Observation period and error are set to 1 month and 3 m/s, respectively. We first assimilated the wave observation at several altitudes and different frequency, however, the 4-day wave was not perfectly reproduced. Therefore, we conducted sensitivity experiments of observational domain at an altitude of 70 km, where the wave was mostly reproduced. In this experiment, observation with ultraviolet wavelength camera on Akatsuki for example, is assumed to be used for observations.
&#160;
&#160;
We have been conducting various cases of experiments, though, we will show the results partially here.
&#160;

Figure 1: Longitude-time cross sections of wind at the equator at 70 km (deviations from time averages)
(a): free-run-forecast, where data is not assimilated
(b): horizontal winds data assimilated in latitudes of S15&#176;- N15&#176;, every 6 hours at 70 km
&#160;
Figure.1 shows Longitude-time cross section of deviation of zonal wind from its time average at the equator at altitude of 70 km. Black arrows refers 4-day waves, and it is approximately 4-days from bottom-left to upper-right of the arrow. In spite of the vague expression in (a), 4-day wave is apparent in (b). The 4-day wave was reproduced by data assimilation.
&#160;

Figure 2: Time variations of temperature (color) and horizontal winds &#160;(vector) at 70 km.
Horizontal winds data is assimilated in latitudes of S15&#176;- N15&#176;, every 6 hours at 70 km.
&#160;
Figure. 2 is time variations of temperature and horizontal winds at an altitude of 70 km. In this figure, high-pass filter with 10-day running mean subtracted is drawn. The black lines in the images characterize borders between contrasting vectors. The locations of two lines in Day 1 and Day 5 are almost the same, respectively. Therefore, it is explicit that 4-day wave is successfully reproduced.
&#160;
Our team also conducted several other experiments and analyzed their results. By drawing latitude-longitude cross section of averaged zonal wind and temperature, we found that the velocity of wind at 65 km &#8211; 70 km at S45&#176;- N45&#176; is contrasting by assimilating different latitudenal range data. In another experiment, where we drew time-altitude cross section of wind at the equator, we confirmed that 4-day wave was apparent only when assimilating data. Finally, we investigated latitudinal dependency and observation frequential dependency with root-mean-square-deviation. From these, we learned that there is a strong jet in mid-latitude and also reinforced our hypothesis of the best observation latitude. &#160;
&#160;&#160;
&#160;
We sought the reproduction of 4-day wave in Venus atmosphere by assimilating data of an idealized observation with ALEDAS-V. And we discovered that under the following conditions, we can expect to reproduce 4-day wave successfully, using ultraviolet wavelength cameras. First, the altitude of assimilating data would be better to set at 70 km. Also, the most potential frequency for data assimilation would be once in 6 hours, with latitude between S15&#176;- N15&#176;. Our research has an important roll as pre-investigation before executing an actual mission, thus we will carry on a further research to contribute solving the enigma of Venus.
&#160;
Acknowledgements
&#160;
This study was conducted under the joint research project of the Earth Simulator Center and supported by the Japan Science and Technology Agency.
&#160;
References
&#160;
[1] A.D. Del Genio and W.B. Rossow, Icarus, 1982
[2] A.D. Del Genio and W.B. Rossow, J. Atmos. Sci., 1990
[3] M. Yamamoto et al., J. Atmos. Sci., 1997
[4] H. Ando et al., Nature Communications, 2016
[5] N. Sugimoto et al., Scientific Reports, 2017
[6] M. Yamamoto et al., Icarus, 2012
[7] T. Miyoshi and S. Yamane, Mon. Wea. Rev., 2007
&#160;
&#160;