Introduction

Tropical cyclones (TCs) are among the most destructive weather systems on Earth, which cause strong winds, heavy rain, and storm surges, and thus greatly threaten the safety of human life and property1. Therefore, the investigation of TCs is an issue of considerable interest1,2,3,4,5,6,7. With global warming, specifically, an increasing trend in the number of globally intense TCs has been noted5,6,7, highlighting the growing importance of precise monitoring and prediction of TCs.

Among the studies of the TCs, the investigation of the stratospheric gravity waves generated by TCs (TC-SGWs) is a novel but important topic. As strong and organized convection systems, TCs are natural sources for the stratospheric gravity waves8,9,10,11, which can be used as a potential proxy to monitor the TCs12,13,14. The TC-SGWs, which can reach upper-stratospheric altitudes in ~20 min after their generation under suitable background wind and stability conditions13 are mainly induced by the deep convection and hot towers in the eyewall12; meanwhile, deep convection and hot towers typically form several hours prior to TC intensification12. Therefore, changes in the corresponding TC intensity could be theoretically diagnosed by the TC-SGWs in the stratosphere on time scales relevant to forecasting needs12,13,14. Using the 13.5-year satellite nadir and 15-year satellite limb observations, respectively, both Hoffmann et al.12 and Wright15 found that the TC-SGWs are indeed statistically associated with the intensification of the TCs. Wu et al.14 used numerical simulations to further verify the argument that TC-SGW activity is more frequent during the intensification of the TCs. Based on those statistical results, Tratt et al.13 introduced a new mission concept, Geostationary Hosted Observatory for Storm Tracking, to investigate the relationship between the TC-SGWs and the TCs for further monitoring of the TCs.

TC-SGWs can also provide feedback to influence the evolution of the TCs16,17. Kim et al.16 found that the gravity waves generated by TCs can decrease and increase vertical wind shear around the outflow during the developing and decaying stages of the TC, respectively, and the intensity of the TCs can thus be influenced. Kim et al.17 further investigated the impact of the gravity waves generated by TCs in the upper troposphere and lower stratosphere and found that the waves can influence the intensity of the TCs by modifying the upper-level horizontal divergence. Therefore, the TC-SGWs may also be significant for more precise simulation and prediction of the TC intensity.

Moreover, the TC-SGWs can also influence the global atmospheric circulation through the momentum flux budget8,9,10,11,16,17,18. Kawatani et al.18 investigated the relationship between the gravity waves (GWs, unless otherwise noted, GWs hereafter denote stratospheric GWs) and the Quasi-Biennial Oscillation, which is a significant large-scale zonal wind oscillation in the tropic lower stratosphere. They found that the GWs are important in driving the Quasi-Biennial Oscillation, and the GWs “with zonal wavelength ≤1000 km are the main contributors to the westward wind shear phase of the simulated Quasi-Biennial Oscillation”18. Because the TCs are important weather systems in the tropics, the TC-SGWs might influence the Quasi-Biennial Oscillation. The wavelength of the GWs spans a wide range of scales16,17,18,19,20,21, and the GWs with small horizontal wavelength cannot be resolved directly and need to be parameterized in the current general circulation models19,20. The GW parameterization in the current general circulation models has some assumptions on GW propagation and sources20 (e.g., the GWs only propagate vertically and the convection sources generate the GWs only by diabatic heating). However, the assumptions may not be realistic because of both the limitations of the computing resource and the poor understanding of the GWs, which thus motivates the investigation of the GWs, including the TC-SGWs.

Considering the importance of the TC-SGWs, Wang et al.21 used the European Centre for Medium-Range Weather Forecasts Reanalysis version 5 (ERA5) data to carry out the 30-year statistical research to reveal the climatology of the TC-SGWs on the Northwest Pacific Ocean, and also found that there is a certain degree of positive correlation between the intensity of TCs and GWs. On this basis, they further revealed that because of the effect of the background wind, the TC-SGWs show a significantly anisotropic distribution with intense waves mainly located in the southeast quadrant of the TCs. Note that Wang et al.21 only reveal a narrow range of the TC-SGW spectra, since ERA5 is only sensitive to the GWs with horizontal wavelength longer than about 400 km22,23,24 which carry relatively less momentum flux during their vertical propagation25, while the spectra range of the TC-SGWs is very wide in the real atmosphere16,17,18,19,20,21. In fact, GWs in the stratified atmosphere are, in essence, mainly with short horizontal wavelength and long vertical wavelength26, which tend to propagate upward faster and carry relatively more momentum flux. The GWs in this spectral range thus deserve more attention not only because these waves can reach upper-stratospheric altitudes on time scales relevant to forecasting needs while the waves with longer horizontal wavelength need more time to reach stratosphere, but also because of their potentially greater impact on the evolution of atmospheric circulation, which were not covered in the study of Wang et al.21. Moreover, since their study was confined to the Northwest Pacific Ocean, there is a lack of global surveys on TC-SGWs21.

As mentioned above, satellites have the advantage of providing long-term and quasi-global observations, which can cover the weather systems over the ocean (e.g., TCs) that are difficult to detect by conventional methods. Furthermore, with the development of the related technology, satellites can offer more and more refined observations. As a result, satellite observations are increasingly used to investigate the TC-SGWs12,15,27,28,29,30,31,32,33,34,35. For example, Wright15 carried out a global survey of the TC-SGWs based on the 15-year satellite limb observation from three sounders, but these limb sounders are also only sensitive to the gravity waves with long horizontal wavelength and short vertical wavelength.

Among various satellite instruments, the Atmospheric Infrared Sounder (AIRS) has the ability to effectively detect the TC-SGWs with short horizontal wavelength and long vertical wavelength12,27,28,29,30,31, which can carry relatively more momentum flux25. AIRS observation is commonly used in many case studies of the TC-SGWs32,33,34,35, which all revealed a clear wavelike structure around the TC center with a horizontal wavelength of dozens to hundreds of kilometers32,33,34,35. Cullens et al.35 also found that the difference in the amplitude of the TC-SGWs among 5 TCs grows during the upward propagation of the waves, which highlighted the importance of background wind on the TC-SGW intensity. However, those studies were all based on one or a few TCs, which led the results to be case-dependent. To our knowledge, Hoffmann et al.12 were the only ones so far to carry out the statistical study on the TC-SGWs based on the AIRS observation from a global perspective. However, they only showed the relation between the TC intensity and the area-variance TC-SGW intensity around the TCs. The global distribution and anisotropic structure of the TC-SGWs, as well as the effect of the background wind, were not investigated. Recently, some studies21,35,36,37 continually emphasized the important impact of the background wind on the intensity and distribution of TC-SGWs. On the one hand, in order to construct an accurate and reliable relationship to guide the monitoring of TCs by detecting the TC-SGWs, it is necessary to consider the modification of the background wind on the distribution and structure characteristics of the waves. On the other hand, the TC-SGWs with short horizontal wavelength cannot be resolved by general circulation models and thus need to be parameterized, which leads a comprehensive understanding of their global distribution to be a crucial prerequisite for more precise gravity-wave paramaterization19,20. Therefore, a more detailed global survey of the TC-SGWs is urgently needed.

In this paper, the global distribution and local structure of the TC-SGWs are obtained, and the impacts of the background wind on them are also given based on 21 years of AIRS observation and the International Best Track Archive for Climate Stewardship (IBTrACS)38 from 2003 to 2023. IBTrACS provides global tropical cyclone best-track data and helps us determine the location and time of the TCs. This dataset has also been used by the other TC-SGW studies, e.g., Hoffmann et al.12 and Wright15. Our results provide a preliminary guide for both TC monitoring, gravity-wave parameterization of the general circulation models, and TC-SGW research interests in certain regions.

Results

Global distribution of the TC-SGWs

To obtain the TC-SGWs, a simple algorithm is used to match the snapshots of the perturbation brightness temperatures from AIRS observation representing the GWs with the TC data from IBTrACS data. The TC-SGWs observed by AIRS are mainly located at z = 30 ~ 40 km vertically, and in swaths within 890 km of the known TCs' center horizontally. Further details can be found in the “Methods” section.

Globally, TC-SGWs are mainly located at three hotspots, namely, North Atlantic-Northeast Pacific region (NAEP), Northwest Pacific region (WP), and South Pacific-Southern Indian region (SPSI), shown as the three red boxes in Fig. 1a. The range of the hotspots is generally from 40°S to 40°N in latitude apart from the equator (Fig. 1a), which corresponds with the locations of the TC activity (contours in Fig. 1a). Generally, the regions with intense TC-SGWs and high-density TC activity are well matched (Fig.1a–e).

Fig. 1: Global distribution of the TC-SGWs.
figure 1

a Composite global distribution of acumulative TC-SGW intensity over all samples after maximum-minimum normalization based on all samples (shading) and TC density [contour, (10° × 10°) −1]. b–e Composite global distribution of normalized accumulative TC-SGW intensity (shading), TC density [contour, (10° × 10°) −1], and 3-hPa background wind (arrow, m s−1) in northern winter, spring, summer, and autumn, respectively. The accumulative TC-SGW intensity is also maximum-minimum normalized based on all samples. The red boxes denote the TC-SGW hotspots. The approximate altitude range of the results is 30 ~ 40 km, and the composite dataset is from AIRS observations and IBTrACS; see the “Methods” section for further details.

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The intensity of the TC-SGWs in various hotspots exhibits obvious seasonal differences, which are stronger in summer and autumn than in winter and spring for the corresponding hemisphere (Fig. 1b–e). The seasonal difference of the TC-SGWs is the response to the TC activities, because the TCs are statistically more numerous and stronger in summer and autumn than in winter and spring39.

TC-SGW activity also exhibits regional differences, with the intensity of the waves being strongest in SPSI and weakest in NAEP. As Fig. 1a, TC-SGW intensity reaches a local maximum at around 20°S and 20°N, respectively.

Local structure of the TC-SGWs

TC-SGWs are mainly generated by the TC eyewall40, and as stated by Nolan41, the waves generated by TCs (i.e., rotation systems with unique structure) “are wrapped into tight spirals by the radial and vertical shear of the tangential wind field”, which causes the characteristics of the TC-SGWs to be closely related to the TCs themselves. Therefore, the local structure of the waves around the TC center in each hotspot is shown in Fig. 2a–c. In Fig. 2, the shadings denote the TC-SGW intensity, the gray circles denote the radius from the center of the TCs, and the gray rays denote the azimuth starting from the eastern edge of the TCs.

Fig. 2: Local structure of the TC-SGWs and those under meridional shear of zonal wind with different signs.
figure 2

a–c Composite local structure of TC-SGW intensity (shading, K2) in SPSI, WP, and NAEP, respectively. d–f Composite local structure of TC-SGW intensity (shading, K2) under positive 3-hPa meridional wind shear in SPSI, WP, and NAEP, respectively. g–i As (d–f), but under negative meridional wind shear. The area-mean and maximum values within r = 600 km of the TC-SGW intensity are presented in the corresponding titles. The black and white arrows in a − c denote the schematic tangential and radial propagation components of the TC-SGWs, respectively. The shadings denote the TC-SGW intensity (K2). The gray circles denote the radius from the center of the TCs, and the radius is marked in each figure as 200, 400 km. The gray rays denote the azimuth starting from the eastern part of the TCs, and the azimuths are marked in each figure as 0°, 45°, and so on. The composite dataset is from AIRS observations and IBTrACS; see the “Methods” section for further details.

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As shown in Fig.1, the TC-SGW intensity in Fig. 2a–c is also, in general, strongest in SPSI and weakest in NAEP. The area-mean values of the TC-SGW intensity within radius (r) = 600 km in SPSI, WP, and NAEP are 0.023 K2, 0.018 K2, and 0.017 K2, respectively. The area maximums of them are 0.031 K2, 0.022 K2, and 0.019 K2, respectively.

In each hotspot, the TC-SGW intensity shows significant anisotropy around the TC center. The active waves are mainly located on the eastern side of the TC center, while the specific quadrant is different among the three hotspots (Fig. 2a–c). The intense TC-SGWs are located in the northeastern, southwestern, and northeastern quadrants of the TC, with the azimuth of the maximum TC-SGW intensity being around 22.5°, 320°, and 45° in SPSI, WP, and NAEP (Fig. 2a–c), respectively. By comparison, the radial ranges of the intense waves around the TC center are similar among the three regions, and the TC-SGWs are mainly located at r < 500 km, which is consistent with the findings of Hoffmann et al.12 and Yue et al.33. We also find that the maximum TC-SGW intensity in SPSI, WP, and NAEP is located around similar r of 200, 200, and 220 km, respectively. In WP, Wang et al.21 also found that the intense TC-SGWs are located in the southeastern quadrant of TC, which is consistent with the AIRS observation in this paper. However, their research was based on ERA5 data, and thus only revealed the characteristics of TC-SGWs with relatively long horizontal wavelengths. In other words, the waves they focused on are in a different spectral range from the waves here.

From the global distribution, the remarkable TC-SGWs are in three hotspots in summer and autumn for the corresponding hemisphere, which are generally consistent with the areas of high-density TC activity. From the local structure, the TC-SGWs show the significant characteristics of an anisotropic structure. The intense waves are generally biased towards the eastern side of the TC center, while the specific azimuth of the waves relative to the TC center is different among the three hotspots. In addition, the TC-SGW intensity is strongest in SPSI and weakest in NAEP from both global distribution and local structure. Hereafter, we will try to investigate the underlying mechanisms responsible for these phenomena.

After their generation, the structure, pattern, and intensity of the GWs can be modified by the background wind and its shear significantly during their upward propagation20,21,22,23,24,42,43. Shown by Wang et al.21, the background wind can even dominate the distribution of the TC-SGWs. Therefore, the 3-hPa wind fields, which can be used as the representative background wind for the GWs observed by AIRS12,27,28,29,35 are shown in Fig. 1b–e. It can be found that the background winds of TC-SGWs are always easterly winds in SPSI and WP, while in NAEP, the background wind of TC-SGWs varies with season, which is westerly in autumn and easterly in summer. Accordingly, the impacts of the background wind on the TC-SGWs in different regions should be investigated separately to avoid the disruption of the background wind direction.

Dominating impacts of easterly wind in WP and SPSI

Figure 3 shows the composite background wind profiles of the TC-SGWs in three hotspots. Regardless of region, the background zonal winds at 3 hPa are always dominated by easterly wind (red solid lines in Fig. 3), while the meridional wind (blue solid lines in Fig. 3) is negligible by contrast. The magnitude of the easterly wind in SPSI is ~40 m s−1 (Fig. 3a), which is obviously larger than that in the other two regions (~20 m s−1; Fig. 3b, c). Theoretically, the stronger background wind can refract the vertical wavelength of the GWs to be longer25, which are more sensitive to the AIRS observation30. This may be an important reason leading to the strongest TC-SGWs in SPSI identified by the AIRS.

Fig. 3: Background wind profiles of the TC-SGWs.
figure 3

a–c Composite area-mean background wind (m s−1) within r = 1000 km around the TC center for SPSI, WP, and NAEP, respectively. The x-axis denotes the magnitude of the background wind, and the y-axis denotes the pressure level. The red and blue solid lines denote the zonal and meridional background wind, respectively. Considering that there are both easterly and westerly winds around the TC-SGWs as Fig. 1b−e, to show the magnitude of the easterly and westerly winds, respectively, and avoid offsetting each other, we composite area-mean easterly or westerly background wind profiles separately according to the direction of area-mean background wind at 3-hPa. The red dashed and dot-dashed lines denote the composited background wind profiles when the 3-hPa area-mean background winds are easterly and westerly, respectively. The light blue vertical and horizontal lines denote the zonal wind speed of −20 m s−1 and height of 3 hPa, respectively. The composite dataset is from ERA5; see the “Methods” section for further details.

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Because the easterly wind above 200 hPa increases gradually with altitude (Fig. 3a, b), the upward-propagating TC-SGWs in SPSI and WP are in the background wind with easterly vertical wind shear. According to the filtering theory of the background wind43, the westward-propagating TC-SGWs will be filtered out when their phase speed is equal to the background easterly wind during the upward propagation of the waves. Accompanied by the upward propagation, the TC-SGWs radiate outward from the TC center40,41 (the white arrows in Fig. 2a, b). Therefore, the waves propagating westward in the western side of the TC center are filtered by vertical wind shear, and the intense TC-SGWs are mainly concentrated on the eastern side of the TC center in SPSI and WP, where the waves possess an eastward radial-propagating phase speed (shading in Fig. 2a, b).

According to Nolan41, the gravity waves generated by TCs are wrapped into tight spirals by the tangential wind of the TCs; thus, the TC-SGWs propagate not only outward but also along the same direction as the tangential wind of the TCs, namely, clockwise propagation in the Southern Hemisphere and counterclockwise propagation in the Northern Hemisphere. When the propagation is cyclonic (black arrows in Fig. 2a, b), there are the westward tangential-propagating components of the TC-SGWs on the southern and northern semicircles of the TC center in the SPSI and WP, respectively, which will be filtered out by the easterly vertical wind shear. Consequently, there are intense TC-SGWs on the northern and southern semicircles of the TC center in SPSI (Fig. 2a) and WP (Fig. 2b), respectively.

Apart from the filtering effect of vertical wind shear, there is horizontal shear in the background wind (Fig. 1b–e), which may also influence the structure of the TC-SGWs through the refraction effect of the background wind21,43,44. Theoretically, for the eastward-propagating GWs, the positive easterly meridional wind shear can lead the GWs to propagate southward, and the negative meridional wind shear can lead them to propagate northward43,44, which is opposite for the westward-propagating GWs. Therefore, the composite local structure of the TC-SGWs under positive and negative meridional wind shear at 3 hPa is separately given in Fig. 2d–i. The eastward-propagating TC-SGWs in SPSI (Fig. 2d) and WP (Fig. 2e) under positive meridional wind shear indeed tend to propagate more southward than those under negative meridional wind shear (Fig. 2g, h).

Consequently, under the combined effects of filtering and refraction, the TC-SGWs exhibit a complex anisotropic structure. When the impacts of filtering and refraction effect are in-phase, there will be a distinct meridional bias of the TC-SGWs, which tend to exist on the northeast quadrant of the TC in SPSI under negative meridional wind shear (Fig. 2g) and on the southeast quadrant of the TC in WP under positive meridional wind shear (Fig. 2e). When the impacts of filtering and refraction effect are out-phase, the intense TC-SGWs will tend to exist on just the eastern side of the TC center with little meridional asymmetry in SPSI under positive shear (Fig. 2d) and in WP under negative shear (Fig. 2h).

The combination of filtering and refraction effect related to the easterly wind can well explain the formation of anisotropic structure of TC-SGWs in both SPSI and WP. However, they do not seem to work for TC-SGWs in NAEP (Fig. 2c, f, i), which are supposed to show local structure similar to that in WP (Fig. 2b, e, h), since they are both in the northern hemisphere under easterly background wind (red solid lines in Fig.3b, c) with the same propagation direction of the TC-SGWs (Fig. 2b, c). But the intense TC-SGWs in NAEP are in fact located in the northeastern quadrant of the TC rather than the southeastern quadrant of the TC, as in WP. Therefore, a more meticulous investigation of the background wind in NAEP is conducted to explore the structure there.

Impacts of both easterly and westerly winds in NAEP

Note that only the TC cases with 3-hPa background wind above 20 m s−1 will be selected in this study (see the “Methods” section), while the composite zonal wind at 3 hPa in NAEP is easterly weaker than 20 m s−1 (Fig. 3c). This implies that quite a few cases are under strong westerly wind, which is also consistent with the phenomenon of distinct TC-SGWs under westerly wind in Fig. 1b, e. The background-wind profiles are thus composited separately according to the sign of 3-hPa zonal wind (red dashed and dot-dashed lines in Fig. 3). The percentage of the 3-hPa westerly cases in SPSI, WP, and NAEP is 4.02%, 16.06%, and 19.01% respectively; meanwhile, the magnitude of the westerly wind in SPSI, WP, and NAEP is 28, 25, and 35 m s−1, respectively. The more cases with stronger westerly wind imply that the westerly wind shear also has a potentially important role in shaping the structure of the TC-SGWs in NAEP, and the composite results ignoring the wind direction (Fig. 2c, f, i) may thus not objectively present the real structure of the waves there.

To more reasonably reveal the impact of background wind on the TC-SGWs in NAEP, the composition based on the direction of both vertical wind shear and meridional wind shear is shown in Fig. 4. The TC-SGWs under easterly vertical wind shear are, in general, weaker (Fig. 4a, c, e) than those under westerly vertical wind shear (Fig. 4b, d, f), which can be explained by the refraction of the waves to longer vertical wavelength25 by the larger magnitude of the westerly wind (Fig. 3c).

Fig. 4: Local structure of the TC-SGWs in NAEP under zonal wind and zonal wind shear with different signs.
figure 4

a, b Composite TC-SGW intensity (shading, K2) under 3-hPa easterly and westerly wind, respectively. c, d As (a, b), but under only positive 3-hPa meridional wind shear. e, f As (a, b), but under only negative 3-hPa meridional wind shear. The area-mean and maximum values within r = 600 km of the TC-SGW intensity are presented in the corresponding titles. The black and white arrows in (a, b) denote the schematic tangential and radial propagation components of the TC-SGWs, respectively. Noted that the magnitudes of the first column are much smaller than those of the second column. The left colorbar at the bottom of this figure corresponds to the left column subplots, and the right colorbar at the bottom of this figure corresponds to the right column subplots. The shadings denote the TC-SGW intensity (K2). The gray circles denote the radius from the center of the TCs, and the radius is marked in each figure as 200, 400 km. The gray rays denote the azimuth starting from the eastern part of the TCs, and the azimuths are marked in each figure as 0°, 45°, and so on. The composite dataset is from AIRS observations and IBTrACS; see the “Methods” section for further details.

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Under the filtering effect of the easterly vertical wind shear, as discussed above, the waves will tend to be located at the eastern semicircle of the TCs because the outward propagation of the TC-SGWs (white arrows in Fig. 4a) can lead the eastward- propagating TC-SGWs to be located at the eastern semicircle of the TCs, and the waves will tend to be located at the southern semicircle of the TCs because the counterclockwise propagation of the TC-SGWs (black arrows in Fig. 4a) can lead the eastward-propagation TC-SGWs to be located at the southern semicircle of the TCs. In the meantime, due to the refraction effect of the meridional wind shear, the eastward-propagating TC-SGWs will tend to propagate southward under the positive meridional wind shear, and propagate northward under the negative meridional wind shear. Therefore, as Fig. 4c, the TC-SGWs with the intensity larger than 0.017 K2 are mainly located at the azimuth of 315°–22.5°, which shows that the intense TC-SGWs in NAEP mainly exist on the southeastern quadrant of the TC under the easterly vertical wind shear with positive meridional wind shear. The TC-SGWs under the easterly vertical wind shear with negative meridional wind shear (Fig. 4e) tends to be located at the further northern side of the TC center than the TC-SGWs under the easterly vertical wind shear with positive meridional wind shear (Fig. 4c). Note that the intense TC-SGWs are more likely to be located at the eastern side rather than the southern side of the TC center in Fig. 4a, which shows the more significant filtering effect on the western side than the northern side in this scenario. Eventually, the TC-SGWs in NAEP present a distinct asymmetric structure in the east-west direction around the TC center under easterly wind (Fig. 4a).

By comparison, when the vertical wind shear is westerly, the TC-SGWs propagate westward because the eastward-propagating TC-SGWs are filtered out by the westerly wind; meanwhile, the refraction effect of the meridional wind shear will cause an opposite meridional-propagating trend of the westward-propagating waves compared with their eastward-propagating counterpart. Consequently, the intense TC-SGWs in NAEP under westerly vertical wind shear with positive meridional wind shear (Fig. 4d) are located further north than those with negative meridional wind shear (Fig. 4f). Note that differing from the zonal-asymmetric structure of the TC-SGWs under easterly vertical wind shear (Fig. 4a), the composite waves present a distinct meridional-asymmetric structure dominated by the northern-side intense component under westerly vertical wind shear (Fig. 4b), which also implies the more significant filtering effect on the southern side than the eastern side in this scenario.

According to the discussion above, it is natural to raise the question of why the waves on the western side of the TCs tend more to be filtered out under easterly and those on the southern side of TCs tend more to be filtered out under westerly vertical wind shear. On the western side, the westward propagation of the waves is predominantly radial (i.e., outward), and on the southern side, the eastward propagation of the waves is mainly tangential (i.e., counterclockwise) (Fig. 4a, b). Note that the TC-SGWs are mainly generated by the diabatic heating of the TCs40, and the waves generated by the idealized diabatic heating mainly propagate radially (i.e., outward) with vertical wavelength around the depth of the heating45, which is around 4–8 km for TCs46. Under the mid-frequency approximation25, the radial phase speed of the TC-SGWs with 4–8 km vertical wavelength is around 20 m s−1. Since the tangential propagation of the TC-SGWs is related to the tangential circulation of the TCs41 with much larger representative velocity than 20 m s−1 1,2,3,4,5,6,7, the tangential phase speed of the TC-SGWs is larger than the radial phase speed of the TC-SGWs. Therefore, the westward-propagating waves on the western quadrant possess a smaller phase speed than the eastward-propagating waves on the southern quadrant. Meanwhile, note that the westerly wind exceeds the easterly wind in strength (Fig. 3c) in their respective scenarios, and only the waves with the same phase speed as the velocity of the background wind can be filtered out42. Consequently, in the easterly scenario, the westward-propagating waves with relatively slow phase speed on the western side are easily to be filtered out by the relatively weak easterly wind; and in the westerly scenario, by comparison, the eastward-propagating waves on the southern side with relatively fast phase speed are easily to be filtered out by the relatively strong westerly wind. Therefore, the difference of the tangential and radial phase speed of the TC-SGWs leads to the zonal- and meridional-asymmetric structure of the waves under easterly and westerly vertical wind shear, respectively.

In brief, the more complex state of background wind in NAEP leads to a more diverse anisotropic structure of the TC-SGWs in different scenarios. Compared to the easterly wind cases with intense waves on the eastern side of the TC center in NAEP (Fig. 4a), the westerly wind cases with intense waves on the northern side (Fig. 4b) possess smaller sample numbers (see the “Methods” section) but stronger TC-SGW intensity, thus not only the shear but also the direction of background wind have important effect on the local structure of the TC-SGWs. Ultimately, the composite intense TC-SGWs in NAEP are located in the northeastern quadrant of the TC (Fig. 2c), with relatively weaker intensity compared with the waves in SPSI and WP (Fig. 2a, b).

Discussion

In this paper, the global distribution and local structure of the TC-SGWs detected by AIRS for the 21-year period of 2003–2023 are investigated. The influence of the vertical wind shear and meridional wind shear on the distribution and structure of TC-SGWs is further revealed systematically.

From a global perspective, the TCs can generate non-negligible intense GWs, which are mainly distributed from 40°S to 40°N in summer and autumn for the corresponding hemisphere, and the global distribution of the TC-SGWs is the obvious response to the region of TC activity, with three hotspots of SPSI, WP, and NAEP being highlighted (red boxes in Fig. 5a). Generally, the TC-SGW intensity in SPSI is strongest, while that in NAEP is weakest. SPSI possesses the largest background easterly wind among the three hotspots, which can refract the waves to longer vertical wavelengths more easily identified by AIRS. This is an important reason for the strongest signal of TC-SGWs in SPSI. The intense TC-SGWs are generally associated with the background easterly wind in the stratosphere, except for those in the northern autumn of NAEP, which are also strongly influenced by the westerly wind (orange arrows in Fig. 5a).

Fig. 5: Conceptual model of the global distribution and local structure of the TC-SGWs.
figure 5

a Global distribution, local structure, and background wind of the TC-SGWs. b TC-SGW structures and/or their formation mechanism under different background winds. The shadings denote the location of the intense TC-SGWs. The red boxes in (a) denote the TC-SGW hotspots. The TC-SGW structures and/or their formation mechanism in the same green box in (b) are identical. The plus signs denote the superposition of the mechanisms on both sides, and the equal signs denote the results of the superposition. The blue and red arrows denote the tangential and radial propagation components of the TC-SGWs, respectively. The brown arrow in Fig. 5b denotes the direction of the vertical wind shear. The group of yellow arrows in Fig. 5b denotes the meridional wind shear. The length and direction of the yellow arrows denote the magnitude and direction of the wind, and the direction of the meridional wind shear can be inferred from the length and direction of the yellow arrows.

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From the perspective of local structure, the TC-SGWs in three hotspots show different anisotropic structure (Fig. 5a), which is found to be caused by the combination of the filtering and refraction effect of background wind shear (Fig. 5b). In SPSI and WP, because of the outward and cyclonic propagation of the TC-SGWs (arrows in boxes 1, 5 in Fig. 5b) the westward-propagating waves are mainly located on the southwestern and northwestern quadrant of the TC center which are filtered out by the easterly vertical wind shear (boxes 1, 5 in Fig. 5b). The meridional wind shear can also refract the TC-SGWs as box 2 and box 3 in Fig. 5b. Consequently, due to the superposition of those effects, the composite TC-SGWs in SPSI are biased towards the northeastern quadrant of the TCs (box 4 in Fig. 5b) and the composite TC-SGWs in WP are biased towards the southeastern quadrant of the TCs (box 6 in Fig. 5b).

For the TC-SGWs in NAEP, under the filtering effect of the easterly vertical wind shear (box 5 in Fig. 5b) and westerly vertical wind shear (box 8 in Fig. 5b), the waves in the northwestern (box 5 in Fig. 5b) and southeastern (box 8 in Fig. 5b) quadrants of the TC center can be filtered out, respectively. Besides, note that the easterly wind prefers to result in the zonal asymmetry (Fig. 4a) of the TC-SGWs and the westerly wind prefers to result in the meridional asymmetry (Fig. 4b) of the TC-SGWs, implying the velocity of the cyclonic propagation of the waves is larger than that of the outward propagation, which may be related to the large tangential velocity of the TCs. At the same time, the easterly and westerly meridional wind shear tends to refract the TC-SGWs to propagate southward and northward as boxes 2, 3, 9, 10 in Fig. 5b. Consequently, due to the superposition and combination of those complex effects (boxes 7, 11, 12 in Fig. 5b), the composite local structure of the TC-SGWs in NAEP is more diverse in different scenarios, which also leads the composite TC-SGW intensity in NAEP to be weakest.

Although the TC-SGWs in SPSI are the strongest, we should keep in mind that this phenomenon is caused by the observation with AIRS rather than a necessarily physical phenomenon. The AIRS observation is more sensitive to the GWs with long vertical wavelengths. Generally, only the GWs with vertical wavelengths longer than 10 ~ 15 km can be detected by AIRS observation12,27,28. The stronger background wind in the Southern Hemisphere can lead to the vertical wavelength of the TC-SGWs being longer by the refraction25, which makes the TC-SGWs in SPSI easier to be observed by AIRS.

Most previous studies8,9,10,14,16,17,32,33,34,35,37 focused on the TC-SGWs with the easterly wind and found that the intense TC-SGWs are mainly located at the eastern side of the TC center because the TCs are often under easterly wind in the summer stratosphere. However, quite a few TCs in NAEP in autumn are in fact associated with the 3-hPa westerly wind, leading to the distinct meridional asymmetric with intense TC-SGWs located at the northern side of the TC center because of the larger velocity of the westerly wind, which suggests the diverse characteristics of the TC-SGWs in different regions and times. Therefore, a global survey of the TC-SGWs is necessary.

As the number of TCs is limited and most TCs can move over a large area, the importance of TC-SGWs can be obscured by other quasi-stationary sources such as topography when the GWs are investigated in fixed areas and long periods together with other sources27,29. In this paper, the importance of the TC-SGWs is stressed because the coordinate following the TCs is used, and the information from other wave sources is largely avoided. Furthermore, the anisotropic horizontal propagation and local structure of the TC-SGWs are also distinct due to the refraction effect arising from the horizontal shear of the background wind, which is usually ignored in the current gravity-wave parameterization of general circulation models. Therefore, the characteristics and mechanisms of the TC-SGWs analyzed and revealed in this paper imply the necessity of considering the specific wave sources (e.g., TCs) and the more complete effects of background wind (e.g., refraction) in the parameterization for a more precise description of gravity waves in the general circulation models.

Previous studies proposed that the TC-SGWs can serve as an effective proxy for the changes of the corresponding TC intensity12,13,14,15 because of the dynamical connection between TC evolution and the generation of gravity waves13. However, we also find that during the upward propagation of the TC-SGWs, the intensity, structure, and distribution of the TC-SGWs are modified significantly by the background wind and its shear. Therefore, it is not reasonable to establish the relationship between the TCs and TC-SGWs, ignoring the anisotropic structure of the TC-SGWs and the crucial effects of the background wind. We need to pay more attention to the impacts of the background wind on the TC-SGWs for the purpose of more accurate monitoring of the TCs through TC-SGWs observed by the satellites.

The analysis of the global TC-SGW characteristics and formation mechanisms in the present study represents a key step in studying case-by-case TC-SGW samples and their impacts. Our results (1) provide a preliminary guide for global TC-SGW hotspots of research interest in certain regions, (2) show the local structure of the TC-SGWs in each hotspot, and (3) reveal the impacts of the background wind on both global distribution and local structure of the TC-SGWs. Our investigation of the TC-SGWs globally can guide the development of gravity-wave parameterizations in general circulation models and provide decision-makers with TC monitoring from satellites, especially to explore TC-related risks under a changing climate.

Methods

Data

We used 21 years of AIRS observations from 2003 to 2023 in this paper. AIRS is one of the instruments aboard the Aqua satellite, which was launched in May 2002 by the National Aeronautics and Space Administration47,48,49. The orbit of Aqua is Sun-synchronous, nearly polar, low Earth (705 km altitude, 100° inclination, 100 min period). Aqua can cover globally during 14.4 orbits per day. As one of the six instruments aboard Aqua, AIRS can obtain the thermal emissions of atmospheric constituents. Across-track scan of the AIRS covers 1780 km on the ground and 90 footprints. The resolution of the across-track is 13.5 km at the nadir and 41 km × 21.4 km at the scan extremes. Along-track distance of the AIRS scan is 18 km.

The information of the GWs is extracted from spectral mean radiance measurements in the 4.3 μm CO2 waveband, which is most sensitive at 30–40 km of altitude as discussed in Hoffmann et al. 12,27,28,30. The fourth-order polynomial fit to the 4.3-μm brightness temperatures (BTs) along each across-track scan is applied to obtain the background BTs. The perturbation BTs corresponding to the GWs are obtained by removing the background BTs from the original BTs12,27,28,30. GWs with vertical wavelengths longer than 10–15 km can be detected from the AIRS50. The local variances for each footprint based on data of the surrounding footprints within a 100 km radius are commonly used to denote the intensity of the GWs12,27,28.

IBTrACS is used to obtain information about the TCs. It is a collection of best-track estimates of position and intensities of TCs, generated by the various regional forecasting agencies38. The version of the data we used is ver04. The World Meteorological Organization’s standardized portion of the IBTrACS product is used in this paper because it is often regarded as a quality-controlled subset of the full dataset. IBTrACS has been uniformly interpolated to a 6-h regular time scale for convenience in our study. The center of each TC can be directly obtained from this dataset, and the TC center positions are defined at 10 meters above ground level in the dataset. The TC density distribution from the IBTrACS dataset can be found in Supplementary Fig. 1a, and the TCs are mainly located in the three hotspots. The number of snapshots of the TCs from the IBTrACS dataset is 65,320.

ERA5 data is used to obtain the background wind. ERA5 can be accessed hourly, and its resolution is 0.25° and 137 model vertical levels51. To match the temporal resolution with the IBTrACS, the ERA5 is also used every 6 h, corresponding to the IBTrACS.

Algorithm to calculate the distribution and structure

To obtain the global distribution and local structure of the TC-SGWs, we developed a simple algorithm and offer an example, i.e., Freda (2012), to show this algorithm. The algorithm can be divided into three steps as follows:

The first step is to match the AIRS and IBTrACS data. Firstly, we assume that the TCs don’t move very fast and are regarded as motionless for 6 h so that the TC center can be obtained from IBTrACS. Then, the mean time of each footprint is calculated. For each time of the TC, only the footprints with a difference between the mean time of them and the time of the TC less than 3 h are selected. Finally, following Hoffmann et al.12, we also calculate the minimum distance between the TC center and each selected footprint. If the minimum distance was less than 890 km, the footprint is selected as Hoffmann et al.12. The footprints for Freda (2012) at 12:00 UTC on 30 December 2012, after matching, can be found as Supplementary Fig. 2a, and there are distinct concentric semicircular waves centered around TCs in Supplementary Fig. 2a. The TC density after matching can be found in Supplementary Fig. 1b, and the number of snapshots of the TCs from the IBTrACS dataset after matching is 21,935.

The second step is to interpolate the AIRS data into a global distribution and local structure using the inverse distance weighting interpolation method. The resolution is 0.5° × 0.5° and 30 km × 5° for the global distribution and local structure, respectively. One snapshot of the data after interpolation is called a sample. The local structure for Freda (2012) at 12:00 UTC on 30 December 2012 after interpolation can be found in Supplementary Fig. 2b. Although the intensity of the TC-SGWs is weaker after interpolation, the main pattern of the waves is similar to the TC-SGWs before interpolation as Supplementary Fig. 2a, and the noise of the observation can be alleviated to some certain extent. The global distribution for Freda (2012) at 12:00 UTC on 30 December 2012, after interpolation, can be found in Supplementary Fig. 3. The AIRS data is also interpolated to a 0.5° latitude-longitude grid to obtain the global distribution for Freda (2012) at 12:00 UTC on 30 December 2012. The pattern is also similar to Supplementary Fig. 2b, but the intensity weakens again.

The final step is to filter the samples. As Hoffmann et al.12, a minimum background wind speed of about 20 m s−1 is required for AIRS to be able to detect the TC-SGW activity related to the TCs, so the samples with 3 hPa wind speeds below 20 m s−1 are filtered out. The TC density after this filter can be found in Supplementary Fig. 1c, and the number of those snapshots is 11,795. To test the reliability of the background wind threshold (20 m s−1), the local structures of the TC-SGWs with different ranges of the background wind are also shown in Supplementary Fig. 4. The number of the samples can be found in Table 1. The TC-SGWs with background wind weaker than 20 m s−1 are very weak (Supplementary Fig. 4a, b). The patterns of the TC-SGWs with different background wind ranges are the same (Supplementary Fig. 4c-f), while the intensity of the TC-SGWs with weaker background wind is weak, and the sample number of the TC-SGWs with stronger background wind is smaller. Therefore, the 20 m s−1 background wind threshold is reasonable for the filtering of the GWs observed by AIRS

Table 1 The sample numbers of the composite analysis in each figure
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Furthermore, the extremely weak TCs with a maximum sustained wind speed less than 17 m s−1 are also filtered out. The TC density after this filtering can be found in Supplementary Fig. 1d, and the number of those snapshots is 15,552. After those two filtering, there are 8035 snapshots used in this paper, and the corresponding TC density can be found in Fig. 1a.

After the above three steps, the TC-SGWs can be extracted from the AIRS observation. The global distribution of the TC-SGWs of winter in the Northern Hemisphere in 2013, including the GWs generated by TC Freda (2012), can be found in Supplementary Fig. 5. The TC-SGWs in other seasons and years can also be obtained using the same algorithm.

The 50 strongest TC-SGW events are shown in Supplementary Fig. 6, and the GW intensity is the mean TC-SGW intensity within a radius smaller than 600 km. From a visual inspection of GW patterns from Supplementary Fig. 6, there are only 8 GW events in which the waves are not semicircular ring around the TC center which may be not TC-SGWs while the patterns of those GWs in other events are semicircular ring around the TC center, so we conclude that the algorithm works quite well in detecting TC-SGWs, with a success rate of about 84%.

The algorithm to obtain the TC-SGWs from the AIRS observation is simple and suitable for statistical research on the observation over long-time spans. Although the TC-SGWs extracted through our algorithm may be influenced by the other sources (such as orography or convection), the patterns of most of the strong GWs are the semicircular ring around the TC centers (Supplementary Fig. 6), which indicates that most of the GWs we investigated are TC-SGWs.

Sample number and TC density

The sample number is the number of snapshots of the local structures after the matching, interpolation, and filtering. The sample numbers of the composite analysis can be found in Table 1in each figure.

In this paper, we used the TC density to describe the distribution of the TC. The TC density is calculated by dividing the globe into 10° × 10° grids, and the TC density is the TC number matching the TC-SGWs in each 10° × 10° grid. The TC density in Fig. 1 is denoted by the contour.