Features of the TC-SGW pattern
Composite analysis of the SGWs at 30 hPa (~ 23 km) was carried out for TCs formed over the northwest Pacific Ocean during 1991–2020. The distribution pattern of TC-SGWs is shown in Fig. 1. The azimuths shown in Fig. 1 are measured counterclockwise from 0° to 360°, with east of the TC center at 0° and north of the TC center at 90°. The distribution pattern at other altitudes in the lower stratosphere is similar (not shown).
The TC-SGWI is defined by the absolute value of the band-passed vertical velocity (see “Methods”). The TC-SGWI is highest in the azimuth band from 270° to 10° (Fig. 1a). Because the drag of SGWs on the circulation is calculated from the momentum flux, the momentum flux of SGW is a critical variable for GCMs. Composite analyses of the wave momentum flux are shown in Fig. 1b–d. The pattern of absolute momentum flux (MF, Fig. 1b) is similar to that of TC-SGWI. The eastward zonal momentum flux (MFu, Fig. 1c) is also co-located with the MF and the TC-SGWI, which indicates that the TC-SGWs mainly carry zonal momentum flux. The northward (southward) meridional momentum flux (MFv, Fig. 1d) is located to the north (south) of the TC center, but the MFv is one order weaker than the MFu, which is in agreement with Wei et al.37 Therefore, we focus on the TC-SGWI in the following discussion of TC-SGW characteristics.
The traditional viewpoint is that SGWs are closely related to the wave sources6. To reveal the relationship between TC intensity and the TC-SGWI, a composite analysis based on TC intensity category (supplementary Table 1) 43 is shown in Fig. 2. The TC-SGWs are mainly found in the azimuth range from 270° to 10°, which is consistent with the pattern in Fig. 1a. The composite analyses of MFu, MFv and MF are similar (Supplementary Fig. 1–3).
As the TC intensifies, the TC-SGWI (especially that in the southeastern parts of the TC) intensifies significantly (Fig. 2a–f), indicating that the TC-SGWI depends on TC intensity. The maximum TC-SGWI at TD (Fig. 2a) is ~ 9.5 × 10− 3 m s− 1, and that at STY and SuperTY is ~ 11 × 10− 3 m s− 1, which is an increase of 16%. Furthermore, the areas of significant TC-SGWs have also expanded.
This result is unsurprising because the TC-SGWs are induced by the TC and have a robust relationship with the TC intensity20. However, the pattern of the TC-SGWs varies little with TC intensity, which suggests that the pattern of the TC-SGWs is not determined by TC intensity.
Both the intensity and position of the TC can change, and they are related. The intensity and track of the TCs during 1991–2020 are shown in Fig. 3. Most TCs form north of 5°N (Fig. 3b) and then move northward and westward, accompanied by an increase in their intensity. Most TCs reach their maximum intensity at about 15°N–30°N. When they move north of ~ 30°N, the intensity of most TCs decreases.
The northward movement occurs across a wide range of latitudes, and the background circulation can change over such a large region. Therefore, the background wind at 30 hPa is also shown in Fig. 3; the background wind is easterly and varies with latitude (Fig. 3a, b). Accordingly, we now focus on the meridional movement of the TC. As the TCs move northward, the easterly wind strengthens, reaching a maximum at the tropical easterly jet at ~ 15°N (Fig. 3a). The background easterly wind then weakens northward until it becomes westerly at ~ 45°N. The meridional shear of the zonal wind is negative south of 15°N and positive from ~ 15°N to ~ 55°N, although most TCs do not reach this latitude. The most intense positive meridional shear of zonal wind is found at 30°N. The small number of TCs that move north of ~ 40°N into the no zonal wind or weak westerly wind zones, where both the positive meridional shear of the zonal wind and the intensity of the TCs decrease.
In general, both the background wind and TC intensity (wave source) that vary with the movement of the TC can influence the TC-SGWs. Therefore, it is important to identify the main factors influencing TC-SGWs.
Influencing factors
To evaluate the factors that influence the TC-SGW distribution pattern objectively, “neural network” (NN, hereafter) artificial intelligence algorithms are utilized to reconstruct the TC-SGWI pattern based on 28 explanatory variables, including the background wind and vertical velocity at different heights and 2-min mean maximum sustained wind of the corresponding TCs (Vmax). Details are given in the Methods section. After adjusting the parameters of the NN (not shown), the relative error of the NN is 30%, close to the 32% obtained in A236 using random forests. The azimuthal variations of the TC-SGWI from both ERA5 and the NN are shown in Fig. 4a, b. The most intense TC-SGWs in both ERA5 and NN are located at ~ 0° and ~ 315°, and the TC-SGWI from 45° to 135° is weak in both cases, which is consistent with the southeast pattern in Fig. 1a. The mean TC-SGWI at each azimuth is shown as a blue solid line in Fig. 4a, b. The correlation coefficient between the ERA5 and NN results is 0.81 and passes the 99% significance test. This also indicates that the NN can reproduce the pattern of the TC-SGWI, although the extreme value of the TC-SGWI in ERA5 is not fitted well by the NN.
The importance of each explanatory variable can be obtained as Fig. 4c by Layer-wise Relevance Propagation (LRP)45. The background wind in the stratosphere (70–30 hPa), especially at 30 hPa, is the most important variable for the TC-SGWI pattern. Next, the TC Vmax is also important because the TC-SGWs are induced mainly by the eyewall20. Because the wind at 1000 hPa is at almost the same altitude as Vmax at 2 m, the wind at 1000 hPa is also slightly significant, showing the influence of the sources. Therefore, the most important variable is the background wind in the lower stratosphere, especially around the altitude of the TC-SGWs (30 hPa in this case). Hereafter, the wind at 30 hPa is chosen as the background wind in the lower stratosphere. Although the NN can select the main influencing factors, it cannot explain the physical mechanisms of the effect. Therefore, the influence of the mechanisms of the background wind should also be investigated.
Mechanisms of background wind influence
The distinct TC-SGWs are located mainly in the southeast quadrant of the TC, which is the upstream side of the easterly background wind in the stratosphere (Fig. 1e), indicating propagation against the background wind 11,26,40. Because the TC-SGWs with the same phase speed as the background wind will be filtered out at the critical level46, the TC-SGWs propagating eastward can be retained. The meridional wind is much smaller than the zonal wind (Fig. 1e), so the filtration effect of the meridional wind may not be the main cause of the formation of the TC-SGWI pattern.
The background wind at 30 hPa is the most important background wind (Fig. 4c), and it changes with latitude (Fig. 3a, b). The meridional shear of the background wind is negative south of 15°N and turns positive north of 15°N. The meridional shear increases from north of 15°N to 30°N, where the meridional shear is the maximum. Based on the difference of the background wind, the TC-SGWI is divided into three latitude regions for composite analysis, and the corresponding results are shown in Fig. 5. The composite analysis results for MFu, MFv, and MF are similar to those for TC-SGWI (Supplementary Figs. 4–6). The maximum of the TC-SGWI is located north of the TC center when the TC centers are south of 15°N (Fig. 5a) where there is intense negative meridional shear of the zonal wind (Fig. 3a). When the TC centers are north of 15°N, the maximum of the TC-SGWI is located southeast (Fig. 5b) and even farther south (Fig. 5c) of the TC center. The center of maximum TC-SGWI rotates clockwise with increasing center latitude. There are very few samples when the TC centers are at 30°–40°N (Fig. 5c; only 12.0%), and the TC intensity is much weaker (Fig. 3b). Therefore, the pattern in Fig. 5c is not investigated further here.
Dunkerton47 and Forbes et al.48 studied the refraction of SGWs by the horizontal wind shear and gave the relation between wind shear and wavenumber as:
$$\frac{{dl}}{{dt}}= - k\frac{{\partial u}}{{\partial y}}$$
1
,
where k and l are the zonal and meridional wavenumbers of the SGWs, t and y are time and meridional distance, and u is the zonal wind. The easterly wind (red lines in Fig. 1e) can filter out the TC-SGWs propagating westward 46,49, so the TC-SGWs propagate eastward with positive zonal wavenumber.
According to Eq. (1), because of the negative meridional shear of the zonal wind south of 15°N, the TC-SGWs propagating eastward are refracted northward with positive meridional wavenumber. North of 15°N, the meridional shear of the zonal wind becomes positive and the TC-SGWs propagating eastward are refracted southward (Fig. 5b). Therefore, although the meridional background wind is weak in Fig. 1e, refraction by the meridional shear of the zonal background wind can change the propagation direction of the TC-SGWs and result in the southeast pattern of TC-SGWs (Fig. 5b) which is consistent with the previous studies50,51.
The intense TC-SGWs in the composite results (Fig. 1a) are located in the southeastern part of the TC center, similar to the pattern when the TC centers are at 15°N–30°N (Fig. 5b), because the southeast pattern for the TC-SGWI is the most common, as the number of samples and the intensity of TCs with centers in 15°N–30°N are much larger than those in other regions (more than 61.4% of the total samples, see the Methods section). The number of samples of other patterns like those in Fig. 5a and Fig. 5c is smaller (26.6% and 12.0%, respectively). Therefore, the southeast pattern of the TC-SGWI is closely associated with the background wind.