Traveling 10-day Waves at Mid-latitudes in the Troposphere and Lower Stratosphere Revealed by Radiosonde Observations and MERRA-2 Data in 2020

Although the characteristics of the traveling 10-day waves (10DWs) above the middle stratosphere have been well explored, little research has been performed on the counterpart in the troposphere and lower stratosphere (TLS). In the present study, we use radiosonde observations and MERRA-2 data in 2020 to characterize traveling 10DWs in mid-latitudes in the TLS. Single-site observations in both hemispheres show that strong 10DW activities are always accompanied by strong eastward jets (10-13 km). MERRA-2 data indicates that in the troposphere the eastward-propagating modes with larger wavenumbers, i.e., E3, E4, E5 and E6 are dominant. While in the lower stratosphere the eastward- and westward-propagating modes with small zonal wavenumbers e.g., 1 and 2, are dominant. Further research on E3, E4, E5 and E6 modes in the troposphere of both hemispheres shows that all the wave activities are positively correlated to the background zonal wind. The refractive index squared reveal that a strong eastward jet is suitable for these four modes to propagate. However, just above the jet, the eastward wind decreases with altitude, and a thick evanescence region emerges above 15 km. E3, E4, E5 and E6 10DWs cannot propagate upward across the tropopause; as such this can explain why these four modes are weak or even indiscernible in the stratosphere and above. In the troposphere, E5 10DW at 32°S is the most dominant mode in 2020. A case study of the anomalously strong E5 10DW activity on May 12, 2020 indicates that the wave amplication resulted from the upward and equatorward transmission of wave energy ows. Moreover, the tropopause and equatorial region can prevent the propagations of wave energy ows of E5 10DW. local and key there are two sources of the E5 one source originates from the extratropical surface at mid-latitudes and shows rst upward and then equatorward/poleward movement; the other source is located at 39-49°S and 8-12 km, and its energy ows horizontally to the equator/poles, leading to the formation of a bimodal structure in the latitude-altitude that the EP ux and its divergence reect only the source and energy ow of waves, the generation mechanism remains unclear. the energy ow of E5 10DW cannot propagate upward across the tropopause and equatorward across the equator. there is a thick region of evanescence around the equator, the E5 10DW generated in one does not affect the in the The high-resolution radiosonde data used and analyzed in the present study are available The MERRA-2 data used and analyzed in the present study are available from


Introduction
Atmospheric waves, including planetary waves (PWs), gravity waves (GWs) and tides (Forbes & Garrett, 1979;Salby, 1984;Fritts & Alexander, 2003), are periodic disturbances of the atmosphere with respect to the mean background state; these disturbances are detected in the elds of atmospheric meteorological parameters, e.g., the wind velocity, temperature, geopotential height and pressure. Atmospheric waves dominate throughout the atmosphere and play pivotal roles in determining local and global atmospheric variations and transient structures (Lieberman & Hays, 1994;Alexander et al., 2010;Irving & Simmonds, 2015).
PWs are large-scale atmospheric oscillations that can be divided into quasi-stationary PWs and traveling PWs (Hirooka, 1986;Pancheva et al., 2008), where the latter can be classi ed either as free modes or as forced waves. The free modes, also known as Rossby normal modes, can be obtained from the solutions of Laplace's tidal equation (Ahlquist, 1982). Free modes propagate westward with periods (zonal wavenumbers) near 2 (s = 3), 5 (s = 1), 10 (s = 1), and 16 (s = 1) days, and waves with these periods are often referred to as quasi-2-day waves (QTDWs), quasi-5-day waves (Q5DWs), quasi-10-day waves (Q10DWs), and quasi-16-day waves (Q16DWs), respectively (Salby, 1984). Normal modes with these typical periods have been observed in the stratosphere, mesosphere and lower thermosphere (Wu et al., 1994;Pancheva et al., 2004;McDonald et al., 2011;Forbes & Zhang, 2015) and have been the topic of theoretical investigations for many decades (Ahlquist, 1982 & Zhang, 2015). Interestingly, many scholars discovered that the actual wave elds associated with these quasi-periodic waves contain a number of other modes, e.g., the eastward-propagating modes and westward-propagating modes with zonal wavenumbers different from those of the abovementioned normal modes. These traveling modes also play key roles in and interact with other waves or the mean ow, thereby affecting atmospheric dynamics (Pancheva et  Compared with the research on other quasi-periodic PWs, investigations speci cally considering traveling 10DWs have been relatively sparse, and almost all of these studies were focused on the stratosphere and above. For instance, the normal mode of the 10DW was clearly observed in the global stratosphere by using satellite observations, which suggested that it always persisted for 1-2 months and was stronger in the Northern Hemisphere (NH) than in the Southern Hemisphere (SH) (Hirooka & Hirota, 1985). In addition, dominant 10DWs were detected in the mid-latitude lower ionosphere and were considered to be caused by PWs coming from below (Laštovička, 1996). Ionospheric sounding data revealed that the Flayer electron density pro les were modulated by PW-type oscillations, e.g., modes with 2-day, 5-day, 10day and 16-day periods (Fagundes et al., 2005). As revealed by the Canadian Middle Atmosphere Model (CMAM), the normal mode of the 10DW is strongly correlated with variations in the chemical species between 30 and 60 km (Pendlebury et al., 2008). Moreover, PWs play an important role in ozone transport throughout the stratosphere. For instance, the 10DWs found in ozone pro le data and medium-frequency radar (MFR) wind data were both consistent with the normal mode (Chen et al., 2011). Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) temperature measurements were employed to provide a comprehensive perspective of the westward-propagating 10DW (zonal wavenumber of 1) between 20 and 100 km at latitudes of 50°S-50°N (Forbes & Zhang, 2015). The W1, W2, E1 and E2 10DWs were studied in detail by using Thermosphere, Ionosphere, Mesosphere, Energetics and Dynamics (TIMED) SABER observations, which are all strong at high latitudes and during winter (John & Kumar, 2016). Moreover, the eastward-propagating 10DWs were found to be governed by different mechanisms from those responsible for the normal modes. Using the long-term Modern Era Retrospective-Analysis for Research and Applications version 2 (MERRA-2) database, Huang et al. (2021) found that W1, E1 and E2 10DWs are the dominant traveling waves below the middle mesosphere, and reach their peaks near the stratopause. The E1 and E2 10DWs in the stratosphere might come from those downward-propagating waves excited in the mesosphere by the mean ow instability. Additionally, the enhanced PW activity in the middle atmosphere is a typical phenomenon during or after sudden stratospheric warming (SSW).
Consequently, the association of 10DWs with SSW events has received some attention over the past two decades (Palo et  the abovementioned studies demonstrated that the 10DW eld in the stratosphere and above is dominated by modes with small zonal wavenumbers, i.e., W1, W2, E1 and E2. Nevertheless, PWs in the troposphere and lower stratosphere (TLS), the main source region of atmospheric waves, have not been adequately studied. Baroclinic instability, the forcing action of zonally asymmetric heating, and topography could all serve as sources of PWs in the troposphere (Charney & Drazin, 1961). It is worth noting that PWs in the TLS have greater wind amplitudes (usually larger than 10 ms −1 ) than tides and GWs and thus deserve more attention (Zhang et al.,2008;Huang et al., 2009;Wang et al., 2010). As such, a few studies involved the 10DWs in the TLS. As revealed by intensive radiosonde observations over Yichang (111°18'E, 30°42'N), 10DWs can exert great impacts on the tropospheric jet in winter and the tropopause in both summer and winter months and can obviously modulate diurnal tidal amplitudes (Huang et al., 2009). The proximity of strong 10DWs near the tropospheric subtropical jet stream led some researchers to conclude that the jet stream strengthened the propagation of 10DWs and might even be their excitation source (Wang et al., 2012). Huang et al. (2017) studied the characteristics of PWs in the lower atmosphere over Xianghe (117.00°E, 39.77°N), China, by utilizing Beijing mesospherestratosphere-troposphere (MST) radar measurements and found 10DWs and 16DWs displaying similar seasonal and height variations, implying the same excitation source; in addition, these waves exhibited prevailing eastward propagation in the meridional direction and a quasi-standing structure in the vertical direction. These studies revealed some local characteristics of 10DWs in the TLS. From the perspective of their temporal and spatial resolutions and height coverage, radiosonde and MST radar data are quite suitable for studying local PWs in the TLS. However, the limitations of these data are obvious: the spatial distributions of radiosondes and MST radar stations are incredibly sparse, and the amount of observation data from these sources is still insu cient. Certainly, data from such a limited number of observation sites cannot provide accurate zonal wavenumber information for 10DWs. Moreover, the above studies revealed the characteristics of 10DWs in the TLS of only the NH. Accordingly, a number of . Hence, we devote this paper to addressing the above questions by combining radiosonde observations with MERRA-2 data.
In this paper, our main objective is to characterize the mid-latitudes 10DWs in the TLS of both the NH and the SH from both local and global perspectives. After exposing the local characteristics of the complex 10DWs in both hemispheres by using radiosonde observations, we reveal the characteristics of the dominant modes of traveling 10DWs in the TLS of both hemispheres by leveraging MERRA-2 data.
The datasets utilized in this paper are described in detail in the following section. The background zonal wind is presented in section 3. Local 10DWs revealed by radiosonde observations are illustrated in section 4. The dominant traveling 10-day modes are studied in section 5. A case study of the most dominant mode in the SH is provided in section 6. In the last section, we will give summary and conclusions of our investigation.

Data Description
The Integrated Global Radiosonde Archive (IGRA) consists of radiosonde and pilot balloon observations from more than 2,800 globally distributed stations. Until January 2018, IGRA provided atmospheric soundings, including pressure, temperature, humidity and wind measurements, at approximately 445 radiosonde sites across the globe. The sampling rate of a high-resolution radiosonde is 1 s or 2 s, which correspond to a vertical resolution of approximately 5-10 m throughout the atmosphere. Synoptic radiosonde measurements are taken twice per day at 0000 and 1200 UTC (Guo et al., 2021). We choose the radiosonde observations at Santa Teresa (

Background Mid-latitude Zonal Wind In The Tls
PW activities are closely related to the background structure, especially the activity of the zonal-mean zonal wind. Before revealing the characteristics of the 10DWs at the two abovementioned radiosonde observation stations, we rst present the background zonal winds at these two locations. To display the day-to-day variations in the background zonal wind, we adopt a sliding 30-day window with an increment of 1 day to extract the background zonal wind on the central date of each window; then, the temporally averaged zonal wind within each window is regarded as the background component. Since there exist time gaps in the utilized observation data, no calculation is attempted if fewer than 18 days of data are present in a given 30-day window.
As visualized in the left panels of Figure 1, the background zonal winds at Santa Teresa (-106.7°W, 31.9°N) and Perth Airport (116.0°E, 31.9°S) deduced from the radiosonde observations show characteristics that are highly similar to those revealed by previous observations at mid-latitudes (Wang et al., 2012;Huang et al., 2017). In the troposphere, the background zonal wind manifests as a strong, predominantly eastward-propagating tropospheric jet at heights of approximately 10-13 km in spring and winter months in both hemispheres, reaching maximum values of 54.1 ms −1 at 12.1 km in April in the NH and 54.5 ms −1 at 11.9 km in August in the SH. The zonal wind increases with altitude from 3.5 km up to approximately 12-13 km and then decreases with altitude; this is the typical tropospheric zonal wind structure at mid-latitudes. In the tropospheric jet stream area in summer and autumn, the eastward background zonal winds in the NH are evidently weaker than those in the SH. In the lower stratosphere, the westward background zonal wind mainly appears in summer with maximum values of -24.1 ms −1 at 32 km in July in the NH and -24.3 ms −1 at 30.1 km in January in the SH. Compared to its counterpart in the NH, the westward background zonal wind in the SH persists over a longer time.
For comparison, the background zonal winds deduced from the MERRA-2 data at the two grid nodes nearest the observation stations ((-106.875°W, 32°N) and (116.25°E, 32°S)) are also provided in the right panels of Figure 1. The background zonal winds deduced from the MERRA-2 data have similar spatial and temporal distributions to those deduced from the radiosonde observations. Nevertheless, slight differences are still observed.

Mid-latitude Local 10dws In The Tls
Previous studies revealed that PW-scale perturbations exist at the mid-latitudes in the TLS of the NH . We aim to investigate 10DWs in this paper; however, the other oscillations might be within the scope of our future research. Signi cant 10DWs appear in two layers (5-15 km and 25-32 km), and these oscillations are stronger in the troposphere than in the lower stratosphere. In the NH, the strongest spectral peak of 3.2 ms −1 is situated at ~11 km with a period of 10.2 days; in the SH, the strongest spectral peak of 4.2 ms −1 is located at ~11 km with a period of 9.1 days.
For comparison, the Lomb-Scargle periodograms of the zonal winds deduced from the MERRA-2 data at the same grid nodes as mentioned above are also provided in the right panels of Figure 2 and exhibit similar spatial and temporal distributions to those deduced from the radiosonde observations. However, slight differences are detected. For instance, the radiosonde observation-derived spectral magnitude with a period of 10.2 days at ~11 km in the NH is slightly weaker than that derived from the MERRA-2 data. In addition, the radiosonde-derived spectra above 25 km in the SH are slightly different from those obtained from the MERRA-2 data. In summary, we nd signi cant 10DWs in the zonal winds.
The above Lomb-Scargle periodogram analysis shows that 10DWs exist in the zonal winds. To display the day-to-day variations in the 10DWs, we again adopt a sliding 30-day window with an increment of 1 day to extract the 10DWs on the central date of each window. Within each window, the time average and the linear trend are removed from the raw data as the background component. Then, the residuals are harmonically tted within the period range from 8.0 to 12.0 days in increments of 0.5 days. Since 10DWs are quasiperiodic, they are classi ed using the period band from 8.0 to 12.0 days rather than a single period. The formula used for the tting is as follows: where t is the time in days and A, T, and θ are the amplitude, period, and phase of the 10DWs, respectively. Since the utilized observation data contain time gaps, no t is attempted if fewer than 18 days of data are present in a given 30-day window. The wave amplitude at any given height on the central date of each window corresponds to the one t among these periods that has the largest amplitude. Moreover, because the data from a single sounding site cannot provide the zonal wavenumber information of 10DWs, the tted amplitude corresponds to synthesized multimodal 10DWs, i.e., the superposition of multiple modes with different zonal wavenumbers.
The zonal wind amplitudes of the 10DWs deduced from the radiosonde observations at Santa Teresa , and December (10 ms −1 ) in the NH and in May (9 ms −1 ), July (7 ms −1 ), and August (9 ms −1 ) in the SH. Hence, in this layer, mid-latitude 10DWs with notable amplitudes exist in the NH during winter and spring and in the SH during winter and autumn, and the 10DWs in the NH have a stronger amplitude than those in the SH.

( )
For comparison, the zonal winds of the 10DWs deduced from the MERRA-2 data at the same grid nodes as mentioned above are also provided in the right panels of Figure 3 and display very similar spatial and temporal distributions to those deduced from the radiosonde observations. However, subtle differences are still present. In particular, the radiosonde-derived 10DWs above 25 km in the NH are more intensive than those from the MERRA-2 data in January and March.

Dominant Modes Of The Mid-latitude 10dws In The Tls
The 10DWs shown in the above section are the combination of multiple modes of 10DWs with different zonal wavenumbers. Some observational studies also con rmed these 10DWs in the troposphere of NH of those 10DWs, we use the MERRA-2 data along the same lines of latitude to calculate the frequencywavenumber spectra. The results in the above section demonstrate that the 10DWs are the strongest at 11 km in the troposphere and ~31 km in the lower stratosphere, so we plot the frequency-wavenumber spectra at these two heights. To identify the prevailing modes of the 10DWs in 2020, a sliding 30-day window is adopted, this time with an increment of 10 days. Within each window, the time and zonal averages are removed from the raw data as the background component. Then, the frequencywavenumber spectra are calculated for the residuals, and 34 amplitude spectra are acquired throughout the whole year. Finally, we calculate and normalize their arithmetic average.
The normalized frequency-wavenumber spectra of the zonal wind disturbance at ~11 km in 2020 are provided in the top row of Figure 4. The left panels show the results at 32°N, while the right panels show the results at 32°S. It should be noted that the horizontal axis, where positive zonal wavenumbers represent eastward propagation and negative zonal wavenumbers signify westward propagation. In the following, the westward-propagating and eastward-propagating modes with zonal wavenumber n are referred to as Wn and En, respectively, for simplicity. In the troposphere, the eastward-propagating modes are stronger than the westward-propagating modes. Among the eastward-propagating modes, those with larger wavenumbers are stronger than those with smaller wavenumbers. Furthermore, the eastwardpropagating modes in the NH are weaker than those in the SH. In the NH, E3 and E6 are almost as strong. In the SH, E5 is obviously stronger than the other modes. Likewise, the normalized frequencywavenumber spectra of the zonal wind disturbance at ~31 km in 2020 are provided in the bottom row of Figure 4. The left panels show the results at 32°N, while the right panels show the results at 32°S. Only the modes with small wavenumbers, e.g., 1 and 2, exist in the lower stratosphere. The strongest mode in the NH is W1, while the strongest mode in the SH is E2.
The westward-propagating and eastward-propagating modes in the stratosphere and above with small wavenumbers, e.g., 1 and 2 were widely revealed by previous studies ( Figure 4 only provides average intensity of each mode at ~11 km in 2020; as such to reveal the temporal and spatial evolution characteristics of the eastward-propagating modes with large wavenumbers (E3-E6), the MERRA-2 data are harmonically tted along the same lines of latitude using a sliding 30-day window with an increment of 1 day. Within each window, harmonic ts are performed on the residuals in the period range from 8.0 to 12.0 days in increments of 0.5 days. The formula used for the tting is as follows: where t, A, T, and θ are the same quantities as in Eq. (1). In addition, λ is the longitude in radians, and s is the zonal wavenumber, where positive zonal wavenumbers represent eastward propagation and negative zonal wavenumbers signify westward propagation. For a certain mode of a 10-day wave, its amplitude at any given height in each window corresponds to the one t among these periods that has the largest amplitude.
To ensure that the tting result represents the actual signal rather than noise, we replace the zonal wind from the MERRA-2 data with values from a randomly generated Gaussian distribution with zero mean and a standard deviation associated with the values deduced from the MERRA-2 data. Then, the same method is utilized to t the random data, and the largest amplitude values of the tted waves are used to estimate the worst-case noise levels (McDonald et al., 2011). The largest worst-case noise level among E3, E4, E5 and E6 10DW at 32°N and 32°S is ~1 ms −1 .
Classic PW studies indicate that the atmospheric background state affects planetary-scale wave propagation by altering the refractive index (Charney & Drazin, 1961); hence, the planetary-scale wave amplitude and phase strongly depend on the background wind conditions. Therefore, we whether these eastward-propagating modes with large wavenumbers propagate freely in the atmospheric background by calculating the refractive index. The formula is as follows (Andrews et al., 1987): where the parameter N refers to the buoyancy frequency, u is the zonal-mean zonal wind, φ is the latitude in radians, a is the mean Earth radius, f is the Coriolis parameter (f = 2Ωsinφ; Ω = 7.292 × 10 −5 rad −1 ), H is the scale height, s is the zonal wavenumber, c is the phase velocity, and − q y is the basic northward potential vorticity gradient, which can be written as follows (Andrews et al., 1987): In the above formulas, the overbars denote zonal averages, while the subscripts denote partial derivatives. The parameter β is the Rossby parameter (β =2Ωsinφ/a; a, φ and Ω are the same quantities as those in Eq. (3)), and ρ 0 is the basic state density. We obtain all parameters from the MERRA-2 data.
Refractive index squared diagnoses the in uence of the zonal mean ow on planetary-scale wave propagation in the meridional and vertical plane. The wave propagates meridionally and/or vertically in the regions where n 2 > 0 but are evanescent or re ected in the regions where n 2 < 0. Negative values of n 2 (indicating regions of evanescence) are shaded in red. Figure 5 shows time-altitude contours of zonal wind amplitudes for E3, E4, E5 and E6 10DW at 32°N in 2020. The time variations of these four waves show both similarities and differences. They are all strong in the spring and winter, and weak or even indiscernible in the summer and autumn, which is consistent with the seasonal variation of the subtropical jet (top row of Figure 1). This indicates that these wave activities and the eastward jets might be positively correlated. However, the strongest activities of these four waves occurs in different months, and their magnitudes is also somewhat different. The largest amplitudes of the E3, E4, E5, and E6 10DWs are respectively about 5.6, 5.5, 6.2, and 5.4 ms −1 , which occur in November, February, March, and January respectively.
Likewise, the time-altitude contours of zonal wind amplitudes for E3, E4, E5 and E6 10DW at 32°N in 2020 are provided in Figure 6. Just like those in the NH, the time variations of these four waves display some similar and different characteristics. They are all no negligible throughout the year, and the amplitudes in spring, autumn and winter are greater than those in summer, which agrees well with the seasonal variation of the subtropical jet in the SH (bottom row of Figure1). This also implies a positive correlation between the wave activities and the eastward jet. E5 is obviously the strongest mode, and E4 is stronger than E3 and E6. Similar to the situation in the NH, the strongest activities of these four waves in the SH occurs in different months. The largest E3, E4, E5, and E6 10DW amplitudes in zonal wind are respectively about 4.9, 8.2, 10.5, and 5.6 ms −1 , which appear in September, June, May, and July respectively.
We highlight the evanescence regions, where wave propagation is prohibited, with red shadow in these two gures. The wave amplitude is large in the freely propagating region, while small in the evanescence region, obviously. In both hemispheres, there are very thick evanescence regions above the freely propagating regions at ~15 km, which prevent these waves from propagating upward across the tropopause; as such these eastward-propagating modes with large wavenumbers are weak or even disappear in the stratosphere and above. Since the background zonal wind within the whole display height range (0-32 km) at 32°N from July to August is westward or weakly eastward, there is no freely propagating region.
The above result implies a positive correlation between the wave activities and the eastward jet. Then the correlation coe cients between the amplitudes of E3, E4, E5 and E6 10DWs and the zonal-mean zonal wind at ~11 km in 2020 is calculated. Figure 7 and Figure 8 show the zonal wind amplitudes of the eastward-propagating 10DWs with zonal wavenumbers from 3 to 6 at ~11 km deduced from MERRA-2 data at 32°N and 32°S, respectively. Yellow line marks the zonal-mean zonal wind. For a better representation, the zonal-mean zonal wind is scaled by 7. In both hemisphere, the seasonal variations of E3, E4, E5 and E6 10DWs are consistent with those of the zonal-mean zonal wind. The correlation coe cients between the E3/E4/E5/E6 10DW and the zonal-mean zonal wind are 0.57/0.68/0.71/0.67 in the NH, while 0.31/0.64/0.09/0.17 in the SH. All the coe cients except the one for the E5 10DW in the SH are far greater than the value corresponding to the 99% con dence level of a test of statistical signi cance, which implying strong and positive correlations. The coe cient for the E5 10DW also signi es a positive correlation, but not as strong as the others. We speculate that there are other reasons for the time variation of the E5 10DW in addition to the background zonal wind.
6. Case Study Of The Most Dominant Mode In The Sh Figure 7 and Figure 8 show that in the troposphere, the predominant 10DW mode in the SH, i.e., E5, is much stronger than the predominant 10DW mode in the NH. And, its correlation with the background zonal wind indicates a complex time variation mechanism. Therefore, we further investigate the E5 10DW in the following. The results in the Figure 8 show that the E5 10DW was strongest on May 12, 2020, at 11 km in the SH. To con rm that this phenomenon was an enhanced event rather than a climatological variation, the amplitudes of the E5 10DW at 32°S and ~11 km on May 12 in each year from 2006 to 2020 are obtained using the abovementioned tting method, and the arithmetic average of these 15 amplitudes is taken as the climatological mean amplitude. We then ascertain whether the strength of the E5 10DW was due to a climatological variation or an enhanced event by comparing the climatological mean amplitudes plus twice the standard deviation with the amplitudes in 2020. The results of the signi cance test are presented in Figure 9, which demonstrates that the E5 10DW amplitude on May 12, 2020, is signi cantly different from the climatology at the 95% con dence level because the amplitude in 2020 is larger than the climatological mean amplitude plus twice the standard deviation (red line).
Therefore, we postulate that the ampli cation of the E5 10DW on May 12, 2020, represents an enhanced event instead of climatological variation.
Because the ampli cation of wave amplitudes is a dynamic process, we choose several dates at equal intervals to analyze the amplitude trend. Accordingly, the refractive index squared and the Eliassen-Palm (EP) ux and its divergence on April 24, April 30 and May 6 are examined to explain the latitude-height structures and investigate the local excitation and dissipation processes.
The EP ux and its divergence are analyzed by using the zonal transformed Eulerian mean momentum equation under the quasi-geostrophic approximation in spherical log (pressure) coordinates (Edmon et al. 1980;Andrew et al. 1987;Andrew 1987) by applying the formula below: The vector F is known as the EP ux, of which the meridional and vertical components are de ned, respectively, as follows: where the prime symbol denotes a perturbation quantity (deviation from the zonal average); v * and w * are the meridional and vertical components, respectively, of the residual mean meridional circulation; u, v, and w are the zonal, meridional and vertical winds, respectively; and θ is the potential temperature. We obtain u, θ, and ρ 0 from the MERRA-2 data, based on which u ′ , v ′ and θ ′ are obtained using the same tting method mentioned above. Since the term proportional to v ′ θ ′ θ z dominates the vertical EP ux component, the term proportional to ū ′ w ′ is omitted from the calculations. In addition, the meridional and vertical components of the EP ux refer to a generalization of the group velocity concept so that their cross-sections can be used to visualize the ow of the wave energy density (Edmon et al. 1980;Andrews 1987;Chen et al., 2005). Because of the density factors in Eqs. (5) and (6), the components of the EP ux have a large dynamic range. For a better height representation, the meridional and vertical components of the EP ux are scaled by the density, namely, F ( φ ) /ρ 0 and F ( z ) /ρ 0 , which we refer to as EPY and EPZ, respectively, and display them as red vectors in the right panels in Figure 10. The zonal force per unit mass acting on the mean state is de ned as DF = ρ 0 acosφ − 1 ∇ ⋅ F, which is shown with color contours in the right panels in Figure 10. Regions of positive (negative) EP ux divergence are sources (sinks) of wave energy, where the wave is ampli ed (dissipated). source of the E5 10DW, as the EP ux divergence is indeed large and positive here with a maximum of 11.9 ms −1 day −1 ; the horizontal energy ow originates from this region. On April 30, this source region moves to 47°S and 10 km, where the EP ux divergence also shows large positive values with a maximum of 7.1 ms −1 day −1 . On May 6, the source at 10 km shifts to 39°S with a maximum divergence of 7.9 ms −1 day −1 . Otherwise, the zonal wind amplitudes of the E5 10DW in the left panel of Figure 9 show a bimodal structure in the latitude-altitude section. In addition to the abovementioned extratropic surface source, the sources at 49°S and 10 km on April 24 and at 47°S and 10 km on April 30 can explain the formation of the peak at 51°S and ~11 km. In addition, the region where n 2 < 0 in the left panels and the red vectors of the EP ux in the right panels of Figure 9 both indicate that the energy ow of E5 10DW cannot propagate upward from the tropospheric jet height to the stratosphere or across the equator into the NH.

Summary And Conclusions
Using radiosonde observations and MERRA-2 data, the characteristics of the mid-latitude 10DWs in the TLS of both the NH and the SH in 2020 are simultaneously studied. The main results and conclusions are as follows: 1. Single-site radiosonde observations in both hemispheres show that 10DWs exist in mid-latitudes in the TLS. In the troposphere of both hemispheres, strong 10DW activities are always accompanied by strong eastward jets (10-13 km) implying that the 10DW activities are related to eastward jets; this also implies that the 10DWs in the NH and SH might have a similar formation mechanism. In the lower stratosphere, 10DWs appear in boreal winter and spring as well as austral winter and autumn. It should be noted that the 10DWs observed at a single site are the combination of multiple modes of the 10DWs with different zonal wavenumbers, the magnitude of which is greater than that of a single mode.
2. MERRA-2 data along latitude 32°N and 32°S show that the 10DW eld in the troposphere is very different from the situation in the lower stratosphere. In the troposphere, the eastward-propagating 10DW modes are stronger than the westward-propagating modes, which agrees well with previous work (Huang et al. 2017 3. Further analyses on E3, E4, E5 and E6 modes in the troposphere of both hemispheres shows that these four modes are positively correlated to the background zonal wind. The calculated refractive index squared reveals the control of background wind on these waves. For these four modes, weak eastward jets can cause negative refractive index squared; as such these four modes activities are always accompanied by strong eastward jets. In addition, there are thick evanescence regions above the freely propagating regions at ~15 km ,which prevent these waves from propagating upward across the tropopause; as such these waves are not found in the stratosphere and above. 4. The temporal evolution characteristics of the 10DW modes reveal dramatic E5 10DW activity on May 12, 2020, at 32°S and ~11 km. Then, a detailed case study of this E5 10DW activity indicates that is the most intense in the past 14 years and can be regarded as an enhanced event rather than a climatological variation. The refractive index squared and the EP ux and its divergence on three dates before the central date, i.e., April 24, April 30 and May 6, are further examined to explain the latitude-height structures and investigate the local excitation and dissipation processes. From this case study, we summarize two key conclusions. First, there are two sources of the E5 10DW: one source originates from the extratropical surface at mid-latitudes and shows rst upward and then equatorward/poleward movement; the other source is located at 39-49°S and 8-12 km, and its energy ows horizontally to the equator/poles, leading to the formation of a bimodal structure in the latitude-altitude section. We note that the EP ux and its divergence re ect only the source and energy ow of waves, whereas the generation mechanism remains unclear. Second, the energy ow of E5 10DW cannot propagate upward across the tropopause and equatorward across the equator. Since there is a thick region of evanescence around the equator, the E5 10DW generated in one hemisphere does not affect the atmosphere in the other hemisphere. Background zonal winds at Santa Teresa (top row) and Perth Airport (bottom row) deduced from the radiosonde observations (left panels) and MERRA-2 data (right panels) in 2020.

Figure 2
Lomb-Scargle periodograms of the zonal winds at Santa Teresa (top row) and Perth Airport (bottom row) deduced from the radiosonde observations (left panels) and MERRA-2 data (right panels) in 2020. The three dashed vertical lines denote three periods of 20, 12, and 8 days.

Figure 3
Zonal wind amplitudes of the 10DWs at Santa Teresa (top row) and Perth Airport (bottom row) deduced from the radiosonde observations (left panels) and MERRA-2 data (right panels) in 2020.

Figure 4
Normalized frequency-wavenumber spectra of the zonal wind disturbances at ~11 km (top row) and ~31 km (bottom row) along latitudes of 32°N (left panels) and 32°S (right panels) in 2020.   Zonal wind amplitudes of the 10-day eastward-propagating modes with zonal wavenumber 3 to 6 at ~11 km deduced from the MERRA-2 data at 32°N in 2020. Yellow line marks the eastward zonal-mean zonal wind.

Figure 8
Zonal wind amplitudes of the 10-day eastward-propagating modes with zonal wavenumber 3 to 6 at ~11 km deduced from the MERRA-2 data at 32°S in 2020. Yellow line marks the eastward zonal-mean zonal wind.

Figure 9
Results of the signi cance test. The black dots are the amplitudes of the E5 10DW at 32°S and ~11 km on May 12 in each year from 2006 to 2020. The red line is the climatological mean amplitude plus twice the standard deviation.