3.1. Time-Altitude Distribution of GW Ep
Figure 6 describes the vertical distribution of the monthly mean GW Ep over the TP with an altitude of 8~38 km from August 2006 to September 2020. It is shown that the GW Ep, zonal winds, and tropopause have periodic changes over TP. At the same altitude, the GW Ep reaches its maximum when the westerly wind is strong around February and reaches its minimum when the westerly wind is weak or easterly around August [
33].
From
Figure 6, the GW Ep over TP has a vertical distribution that decreases first and then increases. In months with no reversal of the wind direction, the GWs propagate upward under the strong westerly winds at altitudes below 20 km and the GW Ep is larger as a whole. At the altitude of 20~36 km, the value of GW Ep is small, which may be related to the weak westerly wind [
34]. These results indicate that the strong westerly winds over TP are conducive to the upward propagation of GWs [
34,
35,
36,
37]. The value of GW Ep above 36 km is larger due to the influence of the strong westerly winds [
25,
34]. In the month of the wind direction reversal, the GWs propagate upward under the strong westerly wind and the GW Ep is large below the zero-speed wind height. With the increase in altitude, the value of GW Ep near the zero-speed wind decreases sharply, which is due to the fact that the quasi-static GWs caused by the topography are filtered out after reaching a critical height [
1,
20]. The result indicates the existence of topographic waves around the TP. At a height above the zero-speed wind, the GWs continue to propagate upward under the easterly wind, and the value of GW Ep is small.
The strong GW activity in the TP is beneficial to the study of GWs’ activity characteristics and the generation and propagation process of topographic waves. Khaykin et al. [
38] pointed out that the wave-induced fluctuations cause abrupt changes in the structure of the tropopause, and the values of the GW Ep of this layer will likely be overestimated. Therefore, the GW Ep at altitudes below the tropopause (~17 km) is not credible, and this study mainly focuses on altitudes above 17 km. As seen in
Figure 6, when the wind direction did not reverse in winter, the height of strong GW activity was mainly concentrated below 20 km. When the wind direction reverses in summer, the GWs’ activity above 18 km is significantly weakened by the influence of zero-speed wind [
35,
37]. Therefore, in order to specifically study the GW’s activity characteristics and the periodic change in GWs around the TP, an altitude of 18~20 km is selected for the following study.
3.3. Correlation between GW Ep and Topography
Topographic waves play a dominant role in GWs around the TP [
9]. In order to specifically analyze the relationship between the topography and the GW Ep, this section draws the zonal change and the zonal change rate of the GW Ep and elevation (
Figure 8) and the meridional change and the meridional change rate of the GW Ep and elevation (
Figure 9) based on the 2° × 2° monthly mean GWs model, respectively.
Table 2 lists the Pearson correlation coefficients between the GW Ep and the elevation for each month corresponding to
Figure 8 and
Figure 9.
It can be seen from
Figure 8 that the zonal topography has a great influence on the zonal GW Ep from October to March with strong background winds (
Figure 7). In these months, the changes between the zonal GW Ep and the zonal elevation are highly consistent. With the increase in elevation, the value of the GW Ep becomes larger and reaches the maximum before the maximum elevation (
Figure 8a,h–l). The correlation coefficients between the change in the zonal GW Ep and the zonal elevation are 0.673, 0.497, 0.465, 0.405, 0.318, and 0.230, respectively (
Table 2). Although the topography has an obvious effect on the zonal GW Ep from November to February, the correlation coefficients are not always larger, such as in February (0.318). In addition, the maximum correlation coefficient (0.673) appears in October (
Table 2), but the influence of topography on the zonal GW Ep is not the greatest (
Figure 8). Therefore, the magnitude of the correlation coefficient between the elevation and the GW Ep may not clearly indicate the impact of topography on the GW Ep in some months. The change rate between the zonal GW Ep and the zonal elevation shows the same trend from October to March. Near the sharp rise or fall in zonal elevation, the zonal GW Ep also rises or falls sharply (
Figure 8m,t–x). The correlation coefficient from October to March is large and the minimum is 0.553 (
Table 2). These demonstrate that the zonal topography has a significant impact on the zonal GW Ep from October to March, and the large elevation or the large topography changes are conducive to promoting GW excitation. Notably, compared with the correlation coefficient between the change in the zonal elevation and the zonal GW Ep, the correlation coefficient between the change rate of the zonal elevation and the zonal GW Ep is larger from November to February when the topography has a strong influence on the GW Ep (
Table 2). In particular, the correlation coefficient between the change in the zonal GW Ep and the zonal elevation is too small to represent the large impact of the topography on the GW Ep in February (0.318) and March (0.230) (
Table 2). This indicates that the correlation coefficient between the change rate of the GW Ep and the elevation seems to better represent the impact of the topography on the GW Ep. It is worth noting that from November to March, the change/change rate of zonal GW Ep always seems to change earlier than the change/change rate of zonal elevation (
Figure 8a,h–l,m,t–x). As can be seen from
Figure 7, these are caused by the large GW Ep excited by the strong background wind in the southern part of the TP.
From April to September, the zonal GW Ep did not change significantly in the region with the large zonal elevation and showed a downward trend with increasing latitude (
Figure 8b–g). In addition, the change rate of the zonal GW Ep is negative when the zonal elevation increases sharply (
Figure 8n–s). These factors indicate that the weak background wind is not conducive to the excitation of GWs (
Figure 7), and these phenomena are related to the poleward propagation of the GW generated by the tropical convection [
20,
34,
36]. Notably, the correlation coefficient between the change/change rate of the zonal GW Ep and the zonal elevation was mainly negative from April to September, and the maximum negative correlation coefficient between the change in the zonal GW Ep and the zonal elevation was −0.494 in July, which may be caused by the fact that the elevation increases and the GW Ep decreases with the increase in latitude in the 20–35°N latitude zone (
Figure 8e). Furthermore, the maximum negative correlation coefficient between the change rate of the zonal GW Ep and the zonal elevation was −0.778 in August (
Table 2), which is because the change rate of the elevation and the GW Ep showed an opposite trend (
Figure 8r). Above all, the zonal topographic influence on the zonal GW Ep was small from April to September.
Figure 9 shows the meridional change and the meridional change rate of the GW Ep and the elevation. The GW Ep in
Figure 9a–l shows the same periodicity as
Figure 7 with the maximum from November to March and the minimum from July to September, which may be related to the periodic changes in the background wind. From November to February, the meridional topography has a significant effect on the meridional GW Ep, and the value of meridional GW Ep is large when the area has a high meridional elevation (
Figure 9i–l). From
Table 2, the correlation coefficients between the change/change rate of the meridional GW Ep and the meridional elevation were large from November to February, except for January (0.305/0.223). In addition, the maximum correlation coefficient between the change in the meridional GW Ep and the meridional elevation appears in October (0.835) when the effect of the meridional topography on the meridional GW Ep is not obvious. This proves, once again, that the magnitude of the correlation coefficient between the elevation and the GW Ep may not clearly indicate the impact of topography on the GW Ep in some months. From
Figure 9u–x, within the longitude range of 73–86°E where the meridional elevation changes sharply, the meridional GW Ep also shows the same trend with correlation coefficients of 0.95, 0.96, 0.81, and 0.80, respectively. These demonstrated that large topographic changes are conducive to the generation of GWs, and the GWs in the 73–86°E longitude zone of the TP are strongly excited by the topography and the strong background wind (
Figure 7). Furthermore, the excited GWs may be influenced by the strong zonal winds and propagate upward into the lower stratosphere. In addition, it was found that the change/change rate of the meridional GW Ep from November to February also showed significant changes from 95–105°E, which was caused by the maximum of GW Ep in the southeast of TP (
Figure 7).
From April to September, the meridional GW Ep is affected by the weak background wind (
Figure 7) with a value of less than 2 J/kg and does not show obvious change with the meridional elevation (
Figure 9b–g), and the change rate of the meridional GW Ep fluctuated around 0 (
Figure 9n–s). However, the correlation coefficient between the change in the meridional GW Ep and the meridional elevation is larger in May (0.548) and September (0.583) (
Table 2). This phenomenon does not correspond to that in
Figure 9c,g, which indicates the change in the meridional GW Ep is only slightly affected by the meridional elevation. From
Table 2, the correlation coefficients between the change rate of the meridional GW Ep and the meridional elevation are small, which shows, once again, that the correlation coefficient between the change rate of the GW Ep and the elevation better represents the impact of the topography on the GW Ep. These indicate that the meridional topography has little influence on the meridional GW Ep from April to September.
3.4. Periodic Variation of the GW Ep in the Lower Stratosphere
The GW Ep in the lower stratosphere of the TP show periodic changes (
Figure 8 and
Figure 9). In the area with strong background wind and large topography, the GW Ep is larger and has obvious periodic changes. In order to specifically analyze the reasons for the periodicity of the GW Ep in the lower stratosphere of the TP, as shown in
Figure 10, seven typical regions are selected in this section. Regions #1 and#2 represent the regions with weak background wind and strong background wind, respectively. From
Figure 10, Region #3 is selected due to its special topography with weak background wind due to being blocked by the surrounding topography, and the elevation of the southern topography of Region #3 is large. Regions #4 and#5 represent the regions of the small GW Ep and the large GW Ep, respectively. Regions #6 and#7 represent the regions of the small topography and the large topography, respectively. The specific ranges of these regions are shown in
Table 3.
The GWs in the lower stratosphere of TP mainly come from the upward propagation of the topographic waves generated by the interaction between the background wind and topography. Therefore, the periodic variation of the GW Ep in the lower stratosphere may be related to the periodic background winds that were blocked by the topography to generate the topographic wave and then propagated upward into the lower stratosphere. In addition, the correlation coefficient between the GW Ep and the background wind was influenced by the proportion of topographic waves in GWs.
Figure 11 shows the monthly mean time series of the background wind, the zonal wind, and the GW Ep for each region, and the correlation coefficients between the GW Ep and the background wind and the correlation coefficients between the GW Ep and the zonal wind in each region are shown in
Table 3. From
Figure 11a,b, although the zonal wind in Region #1 is stronger than that in Region #2, a large GW Ep occurs in Region #2 with strong background wind and the small GW Ep in Region #1 corresponds to the weak background wind. The correlation coefficient between the GW Ep and the background wind in Region #1 (Region #2) is larger than the correlation coefficient between the GW Ep and the zonal wind (
Table 3), indicating that the periodicity of the GW Ep in the lower stratosphere is greatly affected by background wind in Regions #1 and #2. Furthermore, the correlation coefficients between the GW Ep and the background wind in Regions #1 and #2 are 0.422 and 0.621, respectively. This indicates that the GW Ep excited by strong background wind propagates upward to the lower stratosphere, therefore, the correlation between the GW Ep and the background wind in Region #2 is stronger than that in Region #1. Notably, the background wind is weak in Region #3 (
Figure 11c) but the correlation coefficient between the GW Ep and the background wind is greater than that in Region #2. On the one hand, the GWs also have horizontal propagation in the process of upward propagation, and Region #3 is near the larger GW Ep. On the other hand, Region #3 is close to the edge of the TP with large topographic changes, which is conducive to the excitation of GWs (
Figure 7). From
Table 3, we can observe the zonal wind in Region #4 is stronger than that in Region #5 (
Figure 11), and the large correlation coefficient between the GW Ep and the background wind and the large correlation coefficient between the GW Ep and the zonal wind both appear in Region #5 with the large GW Ep (
Figure 11d,e). This indicates that the GW Ep in the lower stratosphere is mainly affected by the background wind in Regions #4 and #5, and the proportion of topographic waves in Region #5 excited by the interaction between the background wind and the topography is larger in GWs. The intensity of the background wind in Regions #6 and #7 is similar (
Figure 11f,g), and the elevation of Region #7 is larger (
Figure 10), indicating the stronger excitation between the background wind and the larger topography in Region #7 to generate the GWs. However, the correlation coefficient between the GW Ep and the background wind in Region #7 (0.822) is smaller than that in Region #6 (0.828). In addition, the correlation coefficient between the GW Ep and the zonal wind (0.838) is larger than the correlation coefficient between the GW Ep and background wind (0.828) in Region #6. These results indicate that the GW Ep in Region #6 is strongly influenced by the zonal wind during its upward propagation, which promotes the topographic waves to reach the lower stratosphere.
3.5. Relationship between GW Ep and Background Wind and Zonal Wind
The main mechanism of GW generation around the TP is the blocking of background wind by topography, and the GWs are affected by the zonal wind during its upward propagation [
35,
37]. Therefore, the differences in topography, background wind, and zonal wind are important factors for the spatial distribution of the GWs in the lower stratosphere. In order to analyze the specific reasons for the spatial distribution of the GW Ep in the lower stratosphere around the TP, this paper presents the time series of the background wind, the zonal wind, and the GW Ep in
Figure 12 for each region based on the 2° × 2° monthly mean GW model.
The background wind and the zonal wind have similar periodicity in each region, which is strong around February and weak around August. The GW Ep of each region is obviously different due to the influence of the different background wind and the different zonal wind, but it shows the same periodic change as the background wind and the zonal wind in its region. For example, the background wind and the zonal wind in Region #7 are significantly stronger than that in Region #1 around February when the background wind and the zonal wind are strong, and the background wind and the zonal winds in Region #7 are weaker than those in Region #1 around August when the background wind and the zonal wind are weak. Therefore, the GW Ep of Regions #1 and #7 is also larger around February and smaller around August. Around February, the value of the GW Ep in Region #7 is significantly larger than that in Region #1 on the whole and the value of the GW Ep in Region #7 is smaller than that in Region #1 around August. These results show that the large GW Ep in the lower stratosphere of the TP is related to the strong background wind and the strong zonal wind.
The background wind in Regions #1 and #3 due to being blocked by the surrounding topography leads to significantly weaker wind than that in Region #2 around February when the background wind is strong. In addition, the zonal winds in Region #2 are also significantly stronger than those in Regions #1 and #3 around February. This suggests that around February, not only is the excitation of GWs stronger in Region #2 but the excited GWs are also more conducive to upward propagation. Therefore, the GW Ep of Region #2 in
Figure 12c is larger than that of Regions #1 and #3 on the whole around February. It is worth noting that the magnitude of the background wind and the zonal wind are similar in Regions #1 and #3, but the GW Ep of Region #3 is larger than that of Region #1 as a whole, which may be due to the horizontal spread of the large GW Ep near Regions #2. Around August, the zonal winds in Region #2 are weak easterly winds, indicating that the quasi-static GWs caused by the topography have been filtered by the zero wind speed, but the value of GW Ep is greater than that in Regions#1 and #3. As can be seen from
Figure 7, this may be due to the spread of the GW Ep generated by tropical convection to Region #5.
The background winds in Regions #4 and #5 are similar and strong around February, so the reason the value of the GW Ep in Region #5 is larger than that in Region #4 around February is that the zonal winds in the upward propagation of the GW Ep in Region #5 are stronger than that in Region #4, which explains that the larger GW Ep in the southeast of TP in winter is caused by the strong background wind and the strong zonal wind. The background wind and the zonal wind in Region #5 are weaker than those in Region #4 around August, and the zonal wind in Region #5 is easterly, but the value of the GW Ep in Region #5 is similar to Region #4, which may also be attributed to the GW Ep generated by tropical convection.
The strength of the background wind is similar in Regions #6 and #7 (
Figure 12a), but the topography of Region #7 is larger (
Figure 9), which indicates that Region #7 is more conducive to the generation of GW Ep. The zonal wind in Region #6 is stronger than that in Region #7 around February (
Figure 12b), indicating that the GW Ep in Region #6 is favorable for upward propagation around February, which again proves that the GW Ep in Region #6 mentioned in
Section 3.4 is affected by the strong zonal winds in its upward propagation. Therefore, it can be found from
Figure 12c that around February, when the zonal wind of Region #7 is significantly weaker than that of Region #6, the GW Ep in Region #6 is larger (2011, 2015, 2016, and 2019). When the zonal wind of Region #7 approaches Region #6, the GW Ep is larger in Region #7 (2007–2009, 2012, 2014, 2017, and 2018). This indicates that the GW Ep in the lower stratosphere is influenced by the background wind and the topography at excitation and the zonal wind during upward propagation. It is worth noting that around August, the values of the GW Ep in Regions #6 and #7 are similar, and the values of background wind are also similar. This suggests that in Regions #6 and #7 when the background wind is weak and not conducive to GW excitation, the zonal wind has little influence on the upward propagation of the GWs and the GW Ep in the lower stratosphere is mainly affected by the background wind.
3.6. Reconstruction of GW Ep in Lower Stratosphere
The GWs’ activity in the lower stratosphere around the TP is mainly influenced by the background wind at excitation and the zonal wind during upward propagation (
Figure 12). In order to quantitatively analyze the influence of the background wind and zonal wind on the GW Ep, a multivariable linear regression model [
39,
40] was adopted to reconstruct the GW Ep of the TP in the lower stratosphere. The formula is as follows:
where
is the time series of the GW Ep (18~20 km) on the TP,
is the constant term of the model,
is the trend term, and
and
are the coefficients of the background wind and the zonal wind, respectively.
and
represent the time series of the background wind and the zonal wind over the TP, respectively. The background wind is the average value of the background wind over the elevation range of TP (3–8 km), and the zonal wind is the average value of the zonal wind over the elevation range from TP to the lower stratosphere (8~18 km).
The
p-value of the F-test in this model is 8.03 × 10
−60 and the goodness of fit is 0.811, indicating that the model fit is effective and 81.1% of the GW Ep of TP in the lower stratosphere can be determined by this model.
Figure 13 shows the fitting curve and the corresponding residuals of the model. The true value is essentially on or near the fitted curve and the corresponding residual fluctuates around 0, which indicates that the model is well fitted. The coefficients of the fitted curves were 2.14, 0.0023, 0.607, and −0.139, respectively, denoting that the GW Ep in the lower stratosphere over the TP shows an increasing trend of 0.0023 J/kg per month, and the influence of background wind on the GW Ep in the lower stratosphere is greater than that of the zonal wind. Energy dissipation occurs in the upward propagation of the GWs. This process is mainly affected by the zonal winds, and the strong zonal westerly winds will reduce energy dissipation in this process [
37]. Therefore, the negative correlation coefficient of zonal wind indicates the influence of the energy attenuation of the GWs during upward propagation on the GW Ep in the lower stratosphere.
3.7. General Process of Topography Wave Excitation and Propagation
Based on the above analysis, we can know that the GWs in the TP are generated by the interaction between the topography and the background wind and are then propagated upward to the lower stratosphere under the influence of the zonal wind. Zeng et al. [
9] pointed out that the existence of the topographic waves can be proven by the spatial distribution of the GW Ep (
Figure 7), the relationship between the GW Ep and the topography (
Figure 8 and
Figure 9), and the obvious filtering by the zero-speed wind as it propagates upward (
Figure 6). The obvious filtering of the GW Ep by the zero-speed wind and the high correlation between the distribution of the GW Ep and the topography indicate that topographic waves play a dominant role over the TP in the lower stratosphere.
Figure 14 shows the general process of the excitation and propagation of topographic waves around the TP. Firstly, the mountain blocks the background wind to excite the GWs (topographic waves) (
Figure 14a). The strong background wind and the large elevation or the large topography changes will intensely motivate GWs, especially in the southeast of the TP. Then, the motivated GWs propagate upward (
Figure 14b). The GWs will dissipate energy during upward propagation, which is affected by the zonal wind. The strong westerly wind reduces the energy dissipation in this process and promotes the GWs to propagate upward to the middle and upper atmosphere. The westerly wind with a stronger wind speed will promote the GWs to propagate upward. When the west wind turns into the east wind, the zero-speed wind will filter the quasi-static GWs motivated by the topography, and the GWs decrease sharply above the zero-speed wind. Then, the reduced GWs continue to propagate upward under the east wind.
In this section, we provide an example to describe the specific process of the GWs’ excitation when the background wind is blocked by the TP and the upward propagation of GWs around the TP. The spatial distribution of the topography of TP, the background wind (3 km), the zonal wind (8~18 km), and the GW Ep (18~20 km) was drawn based on the annual average of the observed data in March (
Figure 14c–f). There are strong background winds and large topographic changes in the southern part of the TP (
Figure 14c,d). The strong background wind is blocked by the topography, which promotes the excitation of GWs. The strong zonal westerly winds in the southeastern part of the TP (25–30°N, 95–105°E) promote the upward propagation of GWs (
Figure 14e), which makes the GW Ep largest in the lower stratosphere in this region (
Figure 14f). In contrast, the GW Ep is relatively small in the northwestern plateau (35–40°N, 75–86°E). The background wind in this area is weak due to being blocked by the high surrounding topography (
Figure 14c,d), which is not conducive to GWs’ excitation. In addition, the zonal winds in the upward propagation of GWs are weak (
Figure 14e). Thus, the GW Ep reaching the lower stratosphere in this region is small (
Figure 14f).