*2.3. The Definition of the Pattern and Indices*

#### 2.3.1. The Uniform NDVI Pattern and Its Index

We found two NDVI patterns dominating the TP in JJAS through the empirical orthogonal function (EOF) decomposition. The first dominant EOF mode features a uniform variation in NDVI anomalies on the TP, which is called the uniform NDVI pattern [35]. In this study, we used the REOF analysis to capture the prevalent and homogeneous patterns of the TP NDVI on inter-annual timescales, since the REOF analysis is more appropriate for the high-resolution and inhomogeneous distribution of the TP NDVI datasets.

The dominant modes obtained based on the EOF and REOF analyses highly resemble each other, and both show a uniform NDVI pattern. Moreover, their corresponding time series are significantly and positively linked. Their distinction is that the uniform pattern based on the REOF analysis does not show larger loadings on the southeast of the TP, which may be due to the high vegetation coverage and insignificant reactions to anomalous climate change over this region. Therefore, the first REOF mode of NDVI anomalies on the TP in JJAS from 1982 to 2020 is called the uniform NDVI pattern (Figure 2a), and its corresponding PC index is called the uniform NDVI pattern index (UNPI).

**Figure 2.** (**a**) The first REOF mode (REOF1) of NDVI anomalies on the TP in JJAS from 1982 to 2020. (**b**) Vertical shear of JJA zonal winds (unit: m/s) over the region (40–110◦E, 0–20◦N) from 1982 to 2020.

#### 2.3.2. The Indian Summer Monsoon Index

In earlier studies, the Indian summer monsoon (ISM) index was defined as the all-Indian summer monsoon rainfall (AISMR) [71]. With the deepening of research, other indices representing the ISM were also proposed, such as the Webster–Yang index (WYI) [72], the monsoon Hadley circulation index (MHI) [73], the extended Indian monsoon rainfall index (EIMRI) [73], the Indian monsoon index (IMI) [74], and the Indian monsoon trough index (IMTI) [75]. Before exploring the influence of the ISM on the TP vegetation, the definitions and features of the abovementioned ISM indices were compared. Using the singular value decomposition and linear correlation, the WYI was most closely related to the uniform NDVI pattern (figures omitted). Therefore, following Webster and Yang [72], the area-mean vertical shear (U850-U200) of zonal winds over the region (40–110◦E, 0–20◦N) in June–August (JJA) was referred to as the ISM index (Figure 2b).

#### **3. Results**

#### *3.1. Correlations between the ISM and TP Precipitation and Vegetation*

Precipitation is one of the main climatic factors affecting TP vegetation in the main growing season [35]. As mentioned in Section 1, the ISM is highly associated with TP precipitation. As such, the ISM should influence the inter-annual variability of vegetation on the TP by modulating precipitation over the TP. Moreover, the ENSO and IOBM can modulate the onset time and intensity of ISM [37,38,48,76,77]. This implies that the ENSO and IOBM may influence the TP precipitation by adjusting the ISM.

Figure 3 reveals the contribution of ENSO, IOBM, and ISM to the TP vegetation on inter-annual scales. A clear and significant positive correlation between the JJA ISM and JJAS TP NDVI appears over most of the TP, manifesting a similarly uniform NDVI pattern (Figure 3a). Moreover, the correlation coefficient between the UNPI and the ISM is 0.45, exceeding the confidence level of 99%. The JJAS TP NDVI is negatively correlated with the spring IBOM/previous winter ENSO, with large loadings (coefficients) roughly distributed on the southwestern TP/northeast–southwest oriented region (Figure 3b,c). These negative correlations reveal that corresponding to positive IOBM/El Niño, the ISM weakens [77]. The correlation coefficient between the UNPI and the spring IBOM is −0.25 and that between the UNPI and the previous winter ENSO is −0.26, which are lower than that between the UNPI and ISM (0.45). After removing the influence of the ISM via the partial correlation, the negative correlation between the spring IBOM (previous winter ENSO) and the JJAS TP NDVI significantly decreased (Figure 3e,f),and the coefficient dropped to −0.09 (−0.23) not reaching the 90% confidence level. To some extent, this implies that the ISM fulfills a "bridge" role linking the influence of ENSO and IOBM with the vegetation growth on the TP. The contribution of ENSO and IOBM to the TP vegetation becomes weaker due to the absence of the bridge effect of ISM.

In contrast, the correlation between the ISM and JJAS TP NDVI slightly decreases after removing the influence of ENSO and IOBM via the partial correlation, but a significantly positive correlation still covers the eastern TP (Figure 3d), showing a closer relationship than the ENSO-UNPI and IOBM-UNPI ones. After removing the influence of ENSO and IOBM, the correlation coefficient between the UNPI and ISM still reaches 0.29, significant at the 95% confidence level. This suggests that the ISM is not only a "bridge" relaying the influence of the ENSO and IOBM on the TP vegetation growth but also has a significant and direct effect on vegetation growth on the TP, albeit in the absence of ENSO and IOBM. Thus, we focus on the relationship between the ISM and the TP precipitation and NDVI in the following study.

**Figure 3.** Correlations of the JJA ISM (**a**), MAM IOBM (**b**), and D(−1)JF Niño 3.4 (**c**) indices with the JJAS NDVI anomalies on the TP, respectively. (**d**) Partial correlations of the JJA ISM index with the JJAS NDVI anomalies on the TP, where the influences of the IOBM and ENSO were linearly removed. Partial correlations of the MAM IOBM (**e**) and D(−1)JF Niño 3.4 (**f**) indices with the JJAS NDVI anomalies on the TP, where the influence of the ISM index was linearly removed. Black dots indicate coefficients exceeding the confidence level of 95%. The "MAM" and "D(−1)JF" denote the spring (March–May) and previous winter (December–February), respectively.

Figure 4a presents the correlations of the ISM with the TP precipitation in May– August (MJJA). Note that the periods for the correlations are different from Figure 3c since precipitation has a one-month-lagged effect on the TP NDVI [24,25,29,35]. The ISM is highly positively linked with precipitation over the southwestern TP, exhibiting a central coefficient of 0.52, which reaches the confidence level of 95%. Based on the key region with significant correlations (Figure 4a), we referred to the area-mean precipitation anomaly over the southwest of the TP (80–92◦E, 28–35◦N) in MJJA as the precipitation index (PRE index). Time series of the ISM index, PRE index, and UNPI are compared in Figure 4b–d. In these figures, we can detect a slightly better correlation between the ISM and precipitation (0.50) than that between the ISM and NDVI (0.43), but both reach the confidence level of 99% (Figure 4b,c). Since precipitation directly affects the TP vegetation growth, the correlation between precipitation and the NDVI was expected to be greater than that between the ISM and NDVI. However, the former exceeds the 95% confidence level by 0.34 (Figure 4d), lower than the latter (Figure 4c). Note that all three indices exhibit a clear upward trend (Figure 4b–d); these correlations could be influenced by global warming. Therefore, their linear trends are removed in the subsequent sections.

After removing their linear trends, the ISM still maintains a significant correlation with the other two indices, which has an approximate coefficient of 0.49 (0.41) with the PRE index (UNPI) exceeding the confidence level of 99%. The PRE index mainly represents the ISM, exhibiting a regional correlation with precipitation over the TP (Figure 4a), while the UNPI represents the variation in vegetation on the overall TP. Thus, the PRE index's correlation with the UNPI decreases from 0.34 to 0.16, which is significantly lower than the correlation between the ISM and UNPI (Figure 4c,d). Such a result implies that the influence of the ISM on the TP vegetation does not depend merely on precipitation, while other ISM-induced climatic factors may contribute to the TP vegetation growth. Clearly, the influence of the ISM on the TP vegetation requires further analysis.

**Figure 4.** Correlation between the ISM and the MJJA precipitation ((**a**); unit: mm) anomalies. (**b**) Correlation between the ISM index (black lines) and the PRE index (blue lines). The other two figures are as (**b**), but correlations are between the UNPI (red lines) and the ISM index (**c**), and between the UNPI and the PRE index (**d**). Dashed lines indicate the trend of the indices. The R outside the parentheses is the coefficient between these time series of the unremoved trend, while the R in parentheses is removed. Black dots indicate variables exceeding the 95% confidence level.

#### *3.2. Physical Process of the ISM Affecting the TP Vegetation*

As an external climatic factor, the ISM plays a role in modifying the vegetation growth on the TP NDVI by stimulating atmospheric circulation to alter the thermal and moisture conditions over the TP. In this section, the process of the ISM influencing the JJAS TP NDVI is explored by linear regression and partial correlation analyses in terms of the atmospheric circulation (Figure 5), water vapor transportation, convection (Figure 6), and thermal conditions over the TP (Figure 7).

In June, the climatological South Asia high (SAH) [78] in the upper troposphere (200 hPa) is situated south of 30◦N, with its center around the southern TP. A strong positive geopotential height anomaly appears over the Iranian Plateau, indicating that the SAH significantly strengthens and shifts northwestward to the western TP (Figure 5a). In the middle-lower troposphere (500–850 hPa), two cyclonic convergences occur around the Indian and Indo-China Peninsulas where air pressure significantly decreases (Figure 5e,i). The enhanced SAH induces the ISM onset, which drives a significant increase in the transportation of water vapor from the Indian Ocean to the lower latitudes and accordingly facilitates water vapor converging over the southern TP (Figure 6e). The strengthened upward motion is induced by the low-pressure convergence and high-pressure divergence in the lower and upper troposphere, which occurs over the southern TP to the south of 30◦N (Figure 6a). A negative outgoing longwave radiation (OLR) anomaly over the southern TP coincides with the entry of water vapor (Figure 6i).

**Figure 5.** Geopotential height (HGT; unit: gpdm; shading) anomalies at 200 hPa (**a**–**d**), 500 hPa (**e**–**h**), and 850 hPa (**i**–**l**) regressed upon the ISM from June to September, respectively. The brown contours indicate the climatological SAH. Black vectors indicate horizontal wind (UV; unit: m/s) anomalies. White dots indicate variables exceeding the confidence level of 95%.

By July, the location of the SAH in the upper troposphere essentially remains unmoved, but its area and intensity are significantly enhanced (Figure 5b). From June to July, the cyclonic convergence over the Indo-China Peninsula moves eastward to the northwest Pacific in the middle-lower troposphere. During the same period, the low pressure over the Indian Peninsula intensifies and slightly moves eastward (Figure 5f,j). Water vapor fluxes are shifted significantly northward, and then large quantities of water vapor are carried to the lower-latitude TP, where they then converge (Figure 6f). The enhanced upward motion over 25◦–35◦N and downward motion on either side (Figure 6b) promote convection, featuring a significant negative OLR anomaly over the southwestern TP (Figure 6j). This sufficient water vapor and strengthened convection contribute to the increase in precipitation.

**Figure 6.** (**a**–**d**) Vertical pressure velocity (unit: hPa/s) anomalies regressed upon the ISM from June to September in latitude vertical cross section (averaged for 80–90◦E), with negative values for upward motion. (**e**–**h**) Integrated water vapor flux from surface to 300 hPa (unit: kg/(m·s); blue vector) and water vapor flux divergence (unit: 10 <sup>×</sup> <sup>10</sup>−7kg/(m2·s·hPa); shading) anomalies regressed upon the ISM from June to September. (**i**–**l**) Outgoing longwave radiation (OLR; unit: W/m2) anomalies regressed upon the ISM from June to September. White dots indicate variables exceeding the confidence level of 95%.

As the SAH intensity decreases slightly in August (Figure 5c), the corresponding cyclonic convergences at 500 hPa and 850 hPa move westward to the Indo-China Peninsula, resulting in a weakening low pressure over the Bay of Bengal (Figure 5g,k). Changes in atmospheric circulation reduce the transportation of water vapor, which causes a consequent reduction in water vapor flux convergence to the southern TP (Figure 6g). The significant upward motion still appears over the overall TP (Figure 6c). Correspondingly, the negative OLR anomaly still appears over the central and western TP (Figure 6k), but the intensity begins to decrease, with the numerical value of the maximum OLR anomaly decreasing from approximately 9 W/m2 to 6 W/m2.

In September, the SAH intensity weakens substantially (Figure 5d), and a cyclonic circulation develops near the Arabian Sea in the mid-troposphere (Figure 5h). This causes the entire circulation system to move westward, with a significant downward motion (Figure 6d) and reduced convection (Figure 6l) over the TP.

**Figure 7.** Partial correlations of the ISM with latent heat flux ((**a**–**d**); unit: W/m2) and sensible heat flux ((**e**–**h**); unit: W/m2) anomalies over the TP from June to September, where the influence of the PRE index was linearly removed. White dots indicate coefficients exceeding the confidence level of 95%.

As mentioned in Section 3.1, the ISM can influence vegetation on the TP through other climatic factors induced by the ISM besides precipitation, such as thermal factors (e.g., latent and sensible heat fluxes). Vegetation dynamics could largely affect the thermal conditions over the TP [12–15]. For example, the greening of TP vegetation can reduce surface albedo and thus increase sensible heat flux [14,15]. Based on that, we examined the partial correlation of the ISM with surface latent and sensible heat flux over the TP after removing the influence of the PRE index (Figure 7). Due to the annual cycle of vegetation growth on the TP, its coverage gradually increases from June to July. The consequently enhanced evapotranspiration of vegetation leads to substantial heat absorption, which promotes the transportation of latent heat across the TP and cools some regions of the TP. Meanwhile, the decrease in surface albedo induced by the substantial vegetation leads to an

increase in sensible heat over most of the TP. Thus, the latent heat flux over the TP exhibits a distinct positive anomaly in JJA (Figure 7a,b), as does the sensible heat flux (Figure 7e,f). When the TP vegetation reaches its maximum coverage in August, the positive latent heat flux anomalies over the TP manifest the greatest magnitude, and the range of negative sensible heat anomalies also increases (Figure 7c,g). With the reduction in the TP vegetation in September, a significant decrease in the positive latent heat anomaly occurs over the TP, whereas the increased albedo leads to a wide range of negative sensible heat flux anomalies (Figure 7d,h).

Based on the above sections, we suggest the ISM may change air and ground temperature over the TP through varying vegetation growth. Additionally, the ISM-induced precipitation can affect the sunshine duration over the TP. Anomalous changes in these ISM-induced climatic factors jointly affect the NDVI inter-annual variability on the TP. Considering the one-month-lagged impact of precipitation on vegetation, the JJA precipitation anomaly, and the JAS surface air temperature, ground surface temperature and sunshine duration anomaly were regressed upon the ISM index (Figure 8).

**Figure 8.** Precipitation (PRE) anomalies in JJA ((**a**); unit: mm) and surface air temperature (SAT) ((**b**); unit: ◦C), ground surface temperature (GST) ((**c**); unit: ◦C), and sunshine duration (SSD) ((**d**); unit: hours) anomalies in JAS regressed upon the ISM index. White dots indicate variables exceeding the confidence level of 95%.

Regulated by the ISM, precipitation increases significantly over the southwest of the TP and decreases over the Pamir Plateau and the southeast of the TP (Figure 8a). Surface air and ground temperatures exhibit significant warming over the northeastern TP to the north of 33◦N (Figure 8b,c), which can contribute to higher NDVI across almost the entire TP. In fact, sunshine duration over the TP is not affected by the ISM, and the shorter sunshine duration should be attributed to the simultaneously increased precipitation. Precipitation increases abnormally over the southwest of the TP, where the sunshine duration is significantly shortened (Figure 8d). This finding is consistent with Mao et al. [35].

To examine the impact of the ISM-induced climatic factors on the NDVI inter-annual variability on the TP, we defined the corresponding indices in accordance with the significant regions (Figure 8) affected by these climatic factors. The JAS area-mean surface air temperature (ground surface temperature) anomalies over the north of the TP (70–104◦E, 34–40◦N) are referred to as the SAT (GST) index. The SSD index is determined in the same definition as the PRE index in Section 3.1, but in JAS. Based on the ISM and these indices, the following regression equation was established to estimate the UNPI.

$$\text{UNPI}\_{t} = 9.9 \times 10^{-9} - 0.15 \times \text{PRE} - 0.39 \times \text{SAT} + 0.69 \times \text{GST} - 0.12 \times \text{SSD} + 0.28 \times \text{ISM} \tag{1}$$

in which the term on the left represents the estimate of UNPI (*UNPIe)*, and the terms on the right represent the effect of these indices (*PRE*, *SAT*, *GST*, *SSD* and *ISM*) with different weights. For ease of calculation, the estimated intercept of 9.9 × <sup>10</sup>−<sup>9</sup> in Equation (1) is usually negligible.

Figure 9 presents the regression of the monthly NDVI anomaly upon the UNPIe in JJAS. Positive NDVI anomalies appear on the TP for each month (Figure 9a–d), displaying an approximately uniform NDVI pattern after four-month vegetation accumulation (Figure 9e). This suggests that the inter-annual variability of NDVI on the TP in JJAS can be attributed to the ISM and its induced changes in the local climatic factors in the TP, which can account for more than 52% of the variation in the UNPI.

**Figure 9.** (**a**) NDVI anomalies in June (**a**), July (**b**), August (**c**), September (**d**), and JJAS (**e**), respectively, as regressed upon the UNPIe. Black dots indicate variables exceeding the confidence level of 95%.

#### **4. Discussion**

This paper indicates that the ISM is a significant external factor affecting the interannual variation in TP vegetation in the growing season, and examined the correlations among the ISM, the TP precipitation, and the TP vegetation. The findings reveal that the correlation between ISM and UNPI is much greater than that between UNPI and ISMinduced precipitation, especially when the linear trends of the three indices were removed (Figure 4b–d). The variations in the uniform NDVI pattern on the TP in JJAS on interannual scales are caused by a combination of several local climatic factors [35]. Therefore, instead of precipitation, other ISM-induced climatic factors dominate the inter-annual variations in vegetation on the TP. In addition to regulating the atmospheric circulation and associated precipitation over the TP, the ISM can also influence the inter-annual variability of vegetation by inducing changes in the TP thermal conditions. Figure 10 summarizes the process of the ISM influencing the vegetation growth on the TP.

**Figure 10.** The influence process of the ISM on the inter-annual variability of vegetation on the TP in its main growing season.

In the main growing season (JJAS), changes in the SAH concerning its location and intensity cause higher pressure (positive HGT anomalies) over the TP in the upper troposphere, and lower pressure (negative HGT anomalies) at the lower-latitude TP in the middle-lower troposphere (Figure 5). Such an atmospheric circulation structure, with atmospheric divergence and convergence in the upper and middle-lower troposphere, respectively, enhances the upward motion over the TP (Figure 6a–d). Furthermore, the transport of water vapor through the Indian Ocean entering the lower-latitude TP is facilitated by the strengthened cyclone activity in the lower troposphere (Figure 6e–h). The sufficient water vapor and strengthened convection can increase precipitation over the TP, thus promoting vegetation growth.

Vegetation evapotranspiration modulates thermal conditions over the TP as a result of the physical phase transition of water, as well as altering the local atmospheric water vapor content and associated precipitation. Additionally, the variations in vegetation coverage also can affect surface sensible heat flux by modifying the TP surface elements, such as albedo and roughness. With the gradual increase in vegetation, the enhanced evapotranspiration replenishes the atmospheric water vapor over the TP while absorbing latent heat (Figure 7a–d) and altering surface sensible heat (Figure 7e–h). Due to the interaction between vegetation and temperature, a certain degree of warming promotes vegetation growth. According to earlier studies, changes in thermal conditions over the TP may also

affect vegetation growth [23–26], and moderate warming of the northern TP effectively promotes the growth of local vegetation [35]. Additionally, the ISM-induced increase in precipitation can also lead to the lack of sunshine, which interferes with vegetation growth on the TP [25].

We further explored the joint effects of the ISM and its induced changes in local climatic factors (precipitation, air temperature, ground temperature, sunshine duration, etc.) on the uniform NDVI pattern using multiple regression (Equation (1)). These factors jointly modulate more than 52% of the variation in the UNPI. In other words, the ISM not only influences the TP vegetation growth through precipitation, but also can regulate the TP vegetation growth through modulating the variations in thermal factors in the TP. The current findings are based on statistical analyses, which are insufficient to clarify the influence of the ISM on the TP vegetation. We will further verify the results through numerical experiments in the future.

Various factors have an impact on the ISM, such as the TP diabatic heating, land–sea thermal contrast, ENSO, and internal atmospheric processes [37,47–49,53]. Among these factors, the TP atmospheric heat source directly affects the ISM onset, and its diabatic heating also plays a decisive role in the intensity and location of the ISM [52,53]. Additionally, the increased vegetation on the TP can cause changes in local thermal conditions (Figure 7). This raises an interesting question, that is, can the TP vegetation regulate the ISM through the alteration of TP thermal conditions in its main growing season?

Table 1 exhibits the correlation coefficients between the monthly ISM from June to September and the one-month-lagged, simultaneous, and summer (JAS) UNPIs. The ISM and the one-month-lagged (summer) UNPI are positively correlated, with the highest association between the July ISM and August (summer) UNPI. The finding indicates the response of the TP NDVI to the influence of the ISM in its main growing season. The ISM is closely correlated with the simultaneous UNPI in June–July. However, the correlation between the ISM and the simultaneous UNPI is insignificant in August–September. These imply the possible influence of the UNPI on the ISM. The September ISM is hardly relevant with summer UNPI with a coefficient of only −0.03, which suggests the ISM-UNPI correlation has vanished at this time.

**Table 1.** Correlation of the monthly ISM with different months of the UNPI. The superscript "\*" denotes the coefficients that significantly exceed the confidence level of 95%.


The differences in latent and sensible heat fluxes over the TP, and the vertical shear of zonal winds over the region (40–110◦E, 0–20◦N), are analyzed for typical positive and negative UNPI years (Figure 11), where the changes in the ISM intensity can reflect the correlation between the ISM and UNPI. The typical UNPI years are characterized as having an absolute value of the UNPI larger than a threshold of 0.5 standard deviations (see Table 2). In June–July, the substantial growth and increased coverage of the TP vegetation result in enhanced evapotranspiration and transportation of latent heat (positive anomalies) over the central and northern TP (Figure 11a,b). A clear decrease in sensible heat fluxes (negative anomalies) appears there, while the sensible heat fluxes increase significantly over the northwest corner and southeast of the TP due to the reduced surface albedo (Figure 11e,f). During this period, the relationship between the ISM and UNPI gradually becomes stronger (Figure 11i,j). When the NDVI reaches its maximum coverage in August, positive latent heat flux anomalies keep increasing due to the vegetation evapotranspiration (Figure 11c), and the magnitude of negative sensible heat flux anomalies increases throughout the whole TP except for the southeast (Figure 11g). In contrast, there is no significant increase in the sensible heat fluxes over the southeastern TP because the vegetation coverage (albedo)

no longer increases (decreases) (Figure 11g). The overall TP exhibits cooling, while the correlation between the UNPI and ISM is somewhat weakened (Figure 11k). In September, the vegetation still shows strong overall evapotranspiration over the TP despite the decrease in TP vegetation coverage. Most of the TP experiences significantly increased latent heat flux (Figure 11d), and the western TP to the west of 90◦E experiences a significant decrease in sensible heat flux (Figure 11h). Meanwhile, the ISM-UNPI correlation seems to disappear (Figure 11l).

**Figure 11.** Differences in latent heat flux ((**a**–**d**); unit: W/m2), sensible heat flux ((**e**–**h**); unit: W/m2) anomalies over the TP, and vertical shear of zonal wind (U850-U200) anomalies ((**i**–**l**); unit: m/s) over the region (40–110◦E, 0–20◦N), composited for positive and negative UNPI years. White dots indicate variables exceeding the confidence level of 95%.

**Table 2.** Typical years of the UNPI in positive and negative phases.


Comparing Table 1 and Figure 11, we speculate that the influence of the NDVI on the TP thermal conditions could play a de-correlation role between the ISM and the TP vegetation in late summer and early autumn. However, our current findings are insufficient to confirm the above opinion. The specific physical mechanism requires further study. The current findings reveal a closer relationship of the TP vegetation with the ISM than that with the IOBM and ENSO on inter-annual scales, explore the influence of the ISM on the TP vegetation, and preliminarily present the speculation of the potential physical process. However, as a "bridge" linking the potential contributions of ENSO and IOBM with vegetation growth on the TP, the effect of the ISM on the growth of the TP vegetation needs to be further quantified. Therefore, a series of numerical experiments should be performed in the future to quantify the specific contributions of several external climatic factors (e.g., the ISM, IOBM, ENSO) to the inter-annual variability of the TP NDVI, especially the role of the ISM. These studies may further deepen our understanding of the relationship between the TP vegetation and regional and global climate change and facilitate future predictions of vegetation activity on the TP on inter-annual scales.
