1 Introduction

The Southwest China is one of the regions with high frequency of meteorological disaster and severe damage since ancient times (Feng and Luo 1995). The weather and climate are complicated and changeable, and heavy rainfall is prone to trigger all manner of disasters in this region. The Southwest China has abundant rainfall (about 1200 ~ 1800 mm year− 1), which is also regarded as a source of multiple important rivers, including Yangtze River, Lantsang and Nujiang River. These rivers provide 46% of available water resources in China (Wang et al., 2015). There are obvious rainy and dry seasons in Southwest China, which accounts for about 85% and 15% of the total precipitation, respectively (Duan et al. 2000; Qin et al. 1997). The rainy season mainly ranges from May to October, with the heaviest precipitation in June and July (Chen et al. 2006; Peng et al. 2007; Li et al. 2016). In addition, the Southwest China is located at the boundary between Indian monsoon and East Asian summer monsoon, which increasing the variability of precipitation in this region (Cao et al. 2012). The above previous studies indicate that the Southwest China is easily affected by flood and drought, which cause huge economic losses and major casualties. Thus it is significant to illustrate the physical mechanism of the variability of precipitation in different periods in the rainy season, which plays an important role in improving the prediction skill of flood and drought in Southwest China.

Multiple previous studies have analyzed and discussed the temporal and spatial variation of precipitation and related mechanisms in Southwest China (Li et al. 2023; Yan and Zi 2021; Ye et al. 2021; Liu & Liu 2016). The summer precipitation in Yunnan province usually exceeds the normal level during the development period of La Nina, which is close to the climate mean state during El Niño (Liu et al. 2011). In addition, atmospheric circulation anomaly, such as the westwards extending and strengthening of sub-tropical high pressure (Yang et al. 2012), the intensity of the India-Burma trough weakened (Ding and Gao 2020), and the northwards extending of mid-latitude westerlies (Sun and Yang 2012), which have been proven to reduce the precipitation over Southwest China. The recent research shows that the hottest temperatures and droughts in this region may be mainly driven by atmospheric internal variation (Liu et al. 2022). Wang and Li (2010) analyzed the severe drought event in Southwest China in autumn and winter in 2010, and the results show that the beginning, development and weakness of this event are closely associated with the movement of south trough and vertically integrated water vapor transport in the corresponding period. Li et al. (2010) analyzed the reasons for drought-flood disaster in the eastern part of Southwest China, and the results indicate that the water vapor source of the above region comes from the upstream of the Bay of Bengal and the Indian Ocean. Jiang et al. (2007) analyzed the characteristics of water vapor transfer and its effects on the drought-flood in Sichuan Basin, and they found the water vapor mainly originates from Tibetan Plateau, Bay of Bengal and South China Sea. The stronger (weaker) atmospheric heat source over the Tibetan Plateau in summer is in favor of more (less) precipitation in the eastern part of Southwest China (Li et al. 2011). In addition, Cao et al. (2014) found that the similar sea surface temperature mode with subtropical Indian Ocean Dipole (SIOD) is the key forcing factor which is related to the summer precipitation anomalies in mountain area at low latitude in China. On the other hand, the regional precipitation variability is not only affected by both the dynamic factor (wind field), but also modulated by thermodynamic process (Chen and Bordoni 2016; Seager et al. 2010; Walker et al. 2015). The previous studies indicate that Asian monsoon usually results from the change of wind (dynamic component), but which is influenced by both the dynamic and thermodynamic processes in late summer (Chu et al. 2012; Oh et al. 2018; Sampe and Xie 2010; Xie et al. 2008). Walker et al. (2015) determined the interannual variability of South Asian summer monsoon (SASM) and its thermodynamic and dynamic components, and SASM is dominated by dynamic process. For summer precipitation in Southwest China, up to now the effects and relative contributions of these two components have not been discussed and analyzed. Thus we should consider both of thermodynamic and dynamic components in moisture flux convergence (MFC) equation, and investigate each component that modulates the atmospheric circulation and specific humidity distribution, which lead to the interannual variations of precipitation in Southwest China.

Moreover, summer is usually considered as a whole for precipitation study, which may prevent us from improving the precipitation prediction. Considering the uneven and seasonal processes of precipitation in Southwest China, it is necessary to divide the summer into the early (May-June) and late summer (July-August) so that we can improve the understanding of characteristic and mechanism of precipitation variation. On the other hand, compared to previous studies used the dynamics and thermodynamics components to analyze the moisture budget, there are only quite few researches used this method to study the Southwest China. Thus it has important scientific significance to analyze the physical mechanisms of dynamics and thermodynamics components for the Southwest precipitation. Overall, the purpose of this study is to illuminate the relative contributions of dynamic and thermodynamic processes to the SW-MFC in May-June (MJ) and July-August (JA), and investigate the corresponding physical mechanisms. The structure of the paper is arranged as follows: The datasets, analysis methods and atmospheric circulation model used in this study are described in Sect. 2. The dynamic and thermodynamic components of MFC in Southwest China during early and late summer are analyzed in Sect. 3. The corresponding large-scale circulation and SST mode are studied in Sect. 4. The sensitivity experiments based on AGCM are presented in Sect. 5. Section 6 provide the schematic diagram of physical mechanism, conclusion and further discussions.

2 Data and methods

2.1 Datasets

In this study, we use three precipitation datasets from 1979 to 2023, including in situ daily measurements from China automatic weather stations (AWS) of China Meteorological Administration (CMA) (438 operational stations in Yunnan, Guizhou, Sichuan Provinces, Chongqing City and Xizang Autonomous Region in Southwest China, as shown in Fig. 1), the first generation of global daily land surface reanalysis datasets with 0.25°x0.25° resolution (CRA-40) developed by National Meteorological Information Center of CMA (Liu et al. 2023), and monthly precipitation data with 2.5°x2.5° resolution from the Climate Prediction Center Merged Analysis of Precipitation (CMAP) (Xie and Arkin 1997). The historical precipitation dataset has undergone quality control and homogenization processing by the National Meteorological Information Center of CMA. We also use daily CRA-40 atmospheric reanalysis data with 0.25°x0.25° horizontal resolutions and 37 vertical levels from 1000 hPa to 10 hPa (e.g. zonal and meridional wind component, geopotential height, vertical velocity, specific humidity and surface pressure). Compared to other global reanalysis datasets, the multiple remote sensing data (e.g. the atmospheric products from FY-2 satellite, microwave humidity sounder from FY-3 C satellite and Global Positioning System radio occultation) have been successfully assimilated into CRA-40. We also use the monthly 2° × 2° resolution Extended Reconstructed Sea Surface Temperature version 5 (ERSSTv5) from the US National Oceanic and Atmospheric Administration (NOAA) (Huang et al. 2017). We derive the annual atmospheric circulation field after linear detrending is applied, so that the interannual variation will be better discussed. In this study, the SW denotes Southwest China, including Yunnan, Guizhou, Sichuan Provinces, Xizang Autonomous Region and Chongqing City. Xizang Autonomous Region is called Xizang for short, and the areas of SW excluding Xizang are called SW-nonXizang.

Fig. 1
figure 1

Locations of 438 stations (black dots) and topography height (shading, m) in Southwest China used in this paper

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2.2 Methods

To diagnose the contribution of the multiple factors (e.g., circulation and moisture) to anomalous precipitation in Southwest China, we analyze the moisture budget based on the moisture budget equation as follows (Peng and Zhou 2017; Dai et al. 2020):

$$MFC = - \left\langle {{\partial _t}q} \right\rangle - \left\langle {\nabla \bullet \left( {Vq} \right)} \right\rangle - \left\langle {{\partial _p}\left( {\omega q} \right)} \right\rangle$$
(1)

Where MFC is moisture flux convergence, V is horizontal winds, q is specific humidity, and \(\omega\) is vertical pressure velocity. ⟨•⟩ denotes a mass weighted vertical integral based on 37 pressure-level data from 1000 hPa to 100 hPa. Ignoring water vapor storage in the atmosphere and vertical velocity at the surface, the Eq. (1) is decomposed as follows (Qu et al. 2014; Chen and Bordoni 2016):

$$MFC = - \left\langle {\nabla \bullet \left( {Vq} \right)} \right\rangle = - \left\langle {\nabla \bullet {\rm{(}}\bar V\bar q{\rm{)}}} \right\rangle - \left\langle {\nabla \bullet \left( {\overline {V{^{\prime}}p{^{\prime}}} } \right)} \right\rangle$$
(2)

The overbar denotes the time average in early summer (MJ) or late summer (JA). Using moisture budget equation to deepen understanding of the mechanism of dynamics (DY) and thermodynamics (TH) processes, we further decompose the Eq. (2) for the purpose of revealing the contribution of each component as follows (Oh et al. 2018):

$$\eqalign{& \delta MFC = - \left\langle {\delta \bar V \bullet \nabla {{\bar q}_{clim}}} \right\rangle - \left\langle {{{\bar q}_{c\lim }}\nabla \bullet \delta \bar V} \right\rangle \cr & - \left\langle {{{\bar V}_{c\lim }} \bullet \nabla \delta \bar q} \right\rangle - \left\langle {\delta \bar q\nabla \bullet {{\bar V}_{c\lim }}} \right\rangle - \left\langle {\delta \bar V \bullet \nabla \bar q} \right\rangle \cr & - \left\langle {\delta \bar q\nabla \bullet \delta \bar V} \right\rangle - \left\langle {\nabla \bullet \delta \overline {\left( {V{^{\prime}}q{^{\prime}}} \right)} } \right\rangle \cr}$$
(3)

Where the subscript “clim” denotes the climatological mean from 1979 to 2023, δ denotes the anomaly relative to monthly climatological mean. The summation of the first (ADV(DY)) and second (CON(DY)) terms on the right side of Eq. (3) are dynamics processes, which represent the changes in wind with fixed specific humidity. The summation of the third (ADV(TH)) and fourth (CON(TH)) terms are thermodynamics processes, which represent the changes in specific humidity with fixed wind. The summation of fifth (ADV(QD)) and sixth (CON(QD)) terms is quadratic component, and the last term is transient term. In addition, the ADV(DY) and ADV(TH) terms represent the moisture advection procedure caused by horizontal wind changes and uneven distribution of specific humidity, respectively. The CON(DY) and CON(TH) terms denote the moisture convergence procedure caused by wind changes and uneven specific humidity, respectively. More detailed information about each component is shown in Table 1.

Table 1 Detail definition for the components of moisture flux convergence. The abbreviated form, component name, corresponding term in Eq. (3) and relevant physical process are shown in columns 1, 2, 3 and 4, respectively
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In addition, we utilize the Indian Monsoon Index (IMI) to present the strength of summer monsoon. The IMI is defined as the zonal wind differences at 850 hPa between the region A (5°N -15°N, 40°E -80°E) and region B (20°N -30°N, 70°E -90°E), which reflects the convective activities from the perspective of dynamics in Indian monsoon area (Wang et al. 2001, 2004).

In this study, we also perform a set of numerical experiments with the atmospheric general circulation model (AGCM) to verify diagnostic analysis results. The AGCM originates from the Community Earth System Model version 2.1.3 (CESM2.1.3; Danabasoglu et al. 2020), which is developed by the US National Center for Atmospheric Research (NCAR). For more detail information, please refer to http://www.cesm.ucar.edu/models/cesm2/. For the atmospheric model with “F_2000” component, configuration value “f09_f09_mg17” is set with 0.9°× 1.25° resolution.

3 Dynamic and thermodynamic components of moisture flux convergence in Southwest China during early and late summer

The Southwest China exhibits distinct wet and dry seasons due to its topography and unique geographic position. The rainy season in the Southwest predominantly spans from May to October, typically occurring in mid-May. With the onset of the rainy season, the precipitation increase noticeably in the entire Southwest China. Further, concomitant with the onset and progression of distinct Asian summer monsoon subsystems, the Southwest China precipitation displays notable differences in both the spatiotemporal distribution and its interannual variations during May-August (Wang et al. 2018). The rainfall correlation between May and June is 0.45, and it is 0.41 between July and August, which all passed the significant test at the 99% confidence level, but the correlation between June and July/August did not pass the significant test. In addition, the spatial evolution of daily precipitation over Southwest China from 1 May to 31 August also reflects distinct differences between May-June and July-August (figure not shown). In short, both the time series and spatial evolution of the Southwest precipitation exhibits strong similarities during May-June (July-August), while the interannual variability between June and July is relatively independent. Therefore, this study focuses on the precipitation changes in early (May-June) and late summer (July-August) over Southwest China and its possible physical mechanisms. The Southwest China in early summer experiences an average precipitation of 4.55 mm day− 1, mainly concentrated in southern Yunnan, southern Guizhou and the Nyingchi region in Xizang (Fig. 2a and e). The precipitation shows a decreasing pattern from southeast to northwest, and the areas with significant interannual variances of rainfall are also found in the southern parts of the Southwest China. The regional average precipitation in Southwest China during late summer is 5.84 mm day− 1, which is slightly different from that in early summer. The main rainy regions are present on most part of Yunnan, Guizhou, Sichuan province and Chongqing, and the significant interannual variance of the precipitation occurs in the eastern part of Southwest China (Fig. 2c and g). The spatio-temporal distribution of precipitation from in situ measurements and CRA40 reanalysis in China are almost consistent with each other except for the Nyingchi region with fewer stations. Based on the mean precipitation time series in Southwest from above two datasets (Fig. 2i and j), it can be found that there is a clear increasing trend in early summer, as confirmed by both observation and reanalysis data through a 95% confidence test. On the other hand, the rainfall over Southwest China primarily exhibits interannual variations during late summer period, and observational data shows a slight declining trend. In general, the spatial distribution and temporal evolution of rainfall over Southwest China during early and late summer exhibit distinct disparities.

Fig. 2
figure 2

(a) Climatology (mm day− 1) and (b) variance (mm2 day− 2) of observation precipitation over Southwest China in May-June from 1979 to 2023. Panels (c, d) as in panels (a, b), except for July-August. Panels (e, h) as in panels (a, d), except for CRA40 precipitation. Panels (i, j) denote the normalized time series of precipitation in early and late summer, respectively

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We decompose the moister flux convergence in Southwest China into thermodynamic (TH) and dynamic (DY) components, as well as the seven terms on the right side of Eq. (3). Then we can explore the relationship between each component and precipitation during early and late summer in Southwest China. In general, the interannual variation characteristics of the MFC over Southwest China in early and late summer are mutually independent (with correlation of 0.02; Fig. 3a and b). Notably, the amplitude of the MFC time series is remarkably greater in late summer than in early summer, which corresponds to the increased intensity and variability of precipitation in July-August compared to May-June. The maximum and minimum anomalous MFC in early summer occurred in 1995 and 1986, respectively, while for late summer, these occurred in 1998 and 2022. The discrepancy between the interannual variability of MFC in May-June and that in July-August leads to our hypothesis that the underlying mechanisms of moisture flux convergence in Southwest China in early and late summer are different. Besides, we find that the dynamic component exhibits the strongest similarity to the MFC in both early and late summer compared to other terms. The DY component shows significant positive correlation with precipitation and moisture flux convergence in May-June, and the corresponding correlation coefficients are 0.57 and 0.72, respectively. In July-August, the above correlation coefficients are 0.31 and 0.52, respectively. However, the TH component only shows a significant positive correlation with the precipitation during early summer (with correlations of 0.53 and 0.31 for precipitation and moisture flux convergence, respectively), while it displays a weak negative correlation in late summer (with correlations of -0.23 and − 0.2, respectively). According to the interannual variances of the seven components of the SW-MFC decomposition (Fig. 3c and d), the precipitation during May-June is mainly dominated by the CON(DY) and ADV(TH) terms. The CON(DY) represents the moisture flux convergence caused by horizontal wind changes, and the ADV(TH) represents the water vapor advection caused by uneven distribution of the specific humidity in Southwest China. The CON(DY) and ADV(TH) variances on interannual timescale from 1979 to 2023 are 0.35 and 0.28 mm2 day− 2, respectively. The difference is that the precipitation over Southwest China is obviously dominated by the CON(DY) during July-August, and its variance accounts for 0.75 mm2 day− 2. The results show that the SW-MFC in late summer is mainly influenced by the dynamic process CON(DY), and the contribution of thermodynamic process is minimal. Moreover, in order to verify the interannual variations stability of moisture flux convergence in Southwest China under the influence of dynamic and thermodynamic processes, we divide Southwest China into two subregions: the four provinces including Yunnan, Guizhou, Sichuan and Chongqing, and the Xizang Autonomous Region. For different regions in the Southwest, it is found that the variance proportions of seven components remain consistent and stable with those in the entire region. In conclusion, the moisture flux convergence in Southwest China during early summer is primarily dominated by the CON(DY) component, followed by the ADV(TH) component. Whereas it is notably driven by dynamic processes in late summer, with the majority originating from the CON(DY) component.

Fig. 3
figure 3

Time series of the detrended moisture flux convergence (MFC), dynamic (DY), thermodynamic (TH) and quadratic (QUA) components (mm day− 1) in Southwest China in (a) May-June and (b) July-August from 1979 to 2023. The variances of the seven components of MFC (mm2 day− 2) in (c) May-June and (d) July-August are given, respectively. ADV(DY)/ CON(DY) and ADV(TH)/ CON(TH) represent the moisture advection/ convergence caused by wind changes and uneven specific humidity, respectively. ADV(QD) and CON(QD) are quadratic components, and the last term is transient factor. SW and Xizang denote Southwest China and Xizang Autonomous Region, respectively. SW-nonXizang denotes the areas of SW excluding Xizang

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The correlation coefficient between the dynamic and thermodynamic factors of moisture flux convergence is 0.32 in early summer, and the correlation coefficient is -0.17 in late summer. Therefore, the dynamic and thermodynamic terms are considered to be independent of each other during July-August, and there is a positive correlation between the time series of regional averaged thermodynamic and dynamic in Southwest China during May-June. Moreover, the rainfall contribution areas of the dynamic and thermodynamic components in early summer also reflect prominent spatial differences. The dynamic process in early summer mainly affects precipitation in southern Southwest China, especially in southern Tibetan Plateau and Yunnan province (Fig. 4a and e). This spatial distribution is generally similar to climatic rainfall pattern in Southwest China. Besides, the thermodynamic processes have a positive contribution to precipitation in northern Yunnan and southern Sichuan province (Fig. 4b and f). In terms of the rainfall regression magnitude, the contribution of dynamic processes dominates is significantly larger than that of the thermodynamic components. During late summer period, dynamic processes play a primary role in governing precipitation in Southwest China, especially in Yunnan, Guizhou provinces and Xizang Autonomous Region (Fig. 4c and g). The spatial distribution of dynamic process also determines the primary rainfall pattern. In comparison, the thermodynamic components have a negligible effect on late summer precipitation in this region (Fig. 4d and h).

Fig. 4
figure 4

Regression patterns (shading, mm day− 1) of the (a, e) dynamic (DY) and (b, f) thermodynamic (TH) components of moisture flux convergence against the precipitation over Southwest China in May-June during 1979 to 2023. Panels (a, b) and (e, f) demote observation and CRA40 precipitation dataset, respectively. Panels (c, d) and (g, h) as in panels (a, b) and (e, f), except for July-August. The black dots denote significant values at the 95% confidence level based on the Student’s t test

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Moreover, we regress moisture flux convergence of the Southwest China onto corresponding precipitation and seven components from Eq. (3) to facilitate a comparison of each component contribution (Figs. 5 and 6). During early summer, the moisture flux convergence in Southwest China is primarily influenced by the CON(DY) component, which represents the moisture convergence caused by changes in horizontal wind (Fig. 5c). This pattern closely resembles the precipitation regression. Meanwhile, the ADV(TH) component makes a positive contribution to the central Southwest rainfall (Fig. 5d). The ADV(DY) and CON(TH) exhibit minor negative and positive contributions to precipitation in eastern Southwest China and Xizang autonomous region, respectively. Transient terms also have a negative impact in Yunnan Province. The remaining components have a negligible influence on early summer precipitation in Southwest China. However, the moisture flux convergence during late summer period is primarily controlled by the CON(DY) of dynamic process triggered by changes in wind patterns (Fig. 6c), while the contributions from the remaining components remain quite limited. The CON(DY) component is associated with more rainfall in majority of Southwest China, particularly in Xizang autonomous region, northern Yunnan, Guizhou province and southern Chongqing city.

Fig. 5
figure 5

Regression patterns (shading, mm day− 1) of the (a) precipitation, (b, d and f) moisture advection, (c, e and g) moisture convergence for dynamic (DY), thermodynamic (TH) and quadratic components (QD), and (h) transient eddies against moisture flux convergence over Southwest China in May-June, respectively. The black dots denote significant values at the 95% confidence level based on the Student’s t test

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Fig. 6
figure 6

The same as Fig. 5, but for July-August

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4 Atmospheric circulation pattern contributing to the dynamic process and its associated with tropical forcing

We show the large-scale circulation, water vapor transport and sea surface temperature (SST) related to the MFC and CON(DY) in Southwest China during early summer (Fig. 7). It can be seen that the corresponding circulation pattern are consistent with SST spatial distribution. The moisture flux convergence corresponds to a tripole mode of cold, warm, and cold SST pattern within the tropical Pacific-Indian Ocean region (Fig. 7e and f). Specifically, it reveals a cooling (warming) SST over the western Pacific-eastern Indian Ocean warm pool while exhibiting warming (cooling) SST over the eastern Pacific and western Indian Ocean. This SST pattern closely resembles the dominant mode of tropical Pacific-Indian Ocean sea surface temperatures, which is also referred to as the Pacific-Indian Ocean temperature anomaly mode (Zhang and Duan 2021; Yang et al. 2006) or the Indo-Pacific tripole mode (IPT; Chen 2011). The accompanying dominant circulation reveals a significant low pressure over the northern Indian Peninsula in middle and lower troposphere (850-500 hPa). The southerly water vapor transport on the southeast side of the cyclone carries warm water vapor from the tropical Indian Ocean to Southwest China via the Bay of Bengal, resulting in convergence of moisture fluxes over Southwest China in May - June (Fig. 7c and d). In addition, a cyclonic anomaly also presents in lower troposphere over the South China Sea, which is very significant in the circulation pattern corresponding to the CON(DY), while the cyclone intensity of related MFC mode is relatively weak. Furthermore, in the southern part of Southwest China and the northern part of the Indian peninsula, upward motion anomalies appear at 500 hPa which is consistent with the corresponding precipitation modes (Fig. 7a and b).

Fig. 7
figure 7

Correlation coefficients between the Southwest moisture flux convergence and (a) vertical velocity at 500 hPa (shading) overlaid zonal wind at 200 hPa (contour), and (c) geopotential height overlaid water vapor transport flux at 850 hPa, and (e) SST, (g) precipitation from CMAP in May-June during 1979 to 2023. Panels (b), (d), (f) and (h) as in panels (a), (c), (e) and (g), respectively, except for the moisture convergence of dynamic component (CON (DY)). The black dots denote significant values at the 95% confidence level based on the Student’s t test

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The main difference from the SW-MFC circulation mode in early summer is that the SW-MFC and CON(DY) during late summer are affected by the subtropical Pacific-Indian Ocean dipole SST and its large-scale atmospheric circulation pattern (Fig. 8). The increased precipitation in July - August corresponds to widespread warm SSTs in the Bay of Bengal, the Indian Ocean, and the subtropical western Pacific, and abnormally cold SSTs in the central and eastern Pacific (Fig. 8e and f). This large-scale dipole SST mode between the central and eastern Pacific and Indo-Pacific warm pools results in a significant SST gradient between the two regions. The SST gradient between the Indo-Pacific produces significant equatorial easterly anomalies toward the Maritime Continent at 850 hPa. The anomalous low-level winds and associated moisture convergence enhance the rainfall over Maritime Continent. Moreover, the equatorial easterly wind anomalies excite an anticyclonic vorticity band over the subtropical western Pacific, resulting in large-area sinking motion and dry anomalies (Fig. 8c and d). Under the control of the anticyclones, the high-pressure suppresses convective activities and creates a dry zone in South Asia roughly between 10°N and 20°N (Yue et al. 2021; Xie and Wang 1996). In the north of this high-pressure zone, there is an enhanced rainfall belt, which is located from the Southwest China to the Yangtze and Huaihe River basin. Accompanied by the circulation pattern are meridional low-high pressure centers with quasi-barotropic structures distributed over Southwest China and the northern Indian Peninsula. Besides, a strong upward anomaly is shown over Southwest China, which is also consistent with widespread precipitation in this area during late summer (Fig. 8a and b). The water vapor in lower troposphere is mainly transported in the zonal direction, while the upper troposphere over Southwest China corresponds to a strengthening of westerly winds. Thus, the dynamic processes leading to the enhanced precipitation in Southwest China during early and late summer can be summarized as the effect of tropical Indo-Pacific SST anomalies in driving large-scale circulation over the Indian Peninsula. However, it is necessary to be clarified that these SST patterns primarily act as a trigger rather than a direct contributor to the dynamics processes.

Fig. 8
figure 8

The same as Fig. 7, but for July-August

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The above results indicate that the dynamic process CON(DY) dominating the MFC in Southwest China during early and late summer are closely related to the atmospheric circulation system over the northern Indian Peninsula, but the mechanisms in these two periods may be quite different. Since the location of the key circulation is consistent with the area affected by the Indian monsoon, we calculate the monthly Indian monsoon index (IMI) and perform a lead-lag correlation with the precipitation over Southwest China, the MFC, and the CON(DY), in order to obtain the remarkable period of the circulation system in the northern Indian Peninsula affecting the SW-MFC (Fig. 9). The results in May-June and July-August have significant differences. The IMI is positively correlated with the precipitation over Southwest China and CON(DY) in early summer (Fig. 9a). In other words, the IMI from April to June has an in-phase relationship with the early summer precipitation in Southwest China, and the IMI is one month ahead which also has a significant signal. The characteristics in late summer are contrary to those in early summer (Fig. 9b). The IMI has a negative correlation with the SW-MFC, and the out-of-phase relationship reaches its maximum during the same period. This indicates that the IMI in July-August has a significant negative contribution to the rainfall over Southwest China.

Fig. 9
figure 9

Lead-lag correlations between the Indian Monsoon Index (IMI) and other variables, including the precipitation from station data (PRECsta) and CRA40 (PRECcra) reanalysis datasets, the moisture flux convergence (MFC), and the dynamic component of MFC caused by horizontal wind changes (CON(DY)) in Southwest China in May-June. The Ldj and Lgj (-6 ≤ j ≤ 6) on the abscissa axes denote the IMI leads or lags j months, respectively. Panels (b) as in panels (a), but for July-August

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In order to more intuitively explore the influence of the Indian summer monsoon system on the precipitation over Southwest China in different periods, we present the correlation patterns between the IMI and circulation pattern in early and late summer (Fig. 10). The results are consistent with the above analysis. The IMI in early summer corresponds to a deep low-pressure center over the Indian Peninsula and two heavy precipitation belts from the northern Indian Peninsula and Indo-China Peninsula (Fig. 10a and c). In terms of water vapor transport, it can also reflect the strong meridional water vapor channel transporting to the Southwest China in May-June. However, a weak Indian summer monsoon during July-August corresponds to widespread precipitation in Southwest China and a suppressed convection pattern over southern Indian Peninsula (Fig. 10b and d). These precipitation and circulation patterns in early and late summer are very similar to those obtained from the CON(DY) in Southwest China.

Fig. 10
figure 10

Correlation coefficients between the Indian Monsoon Index (IMI) and (a) precipitation, (c) geopotential height overlaid water vapor transport flux at 850 hPa in May-June during 1979 to 2023. Panels (b) and (d) the same as in panels (a) and (c), except for July-August. The IMI*-1 in July-August corresponds to the increase of precipitation over Southwest China. The black dots denote significant values at the 95% confidence level based on the Student’s t test

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In order to further explore how the Indo-Pacific SST anomaly affects the SW-MFC in early and late summer by modulating the large-scale circulation over the Indian Peninsula, we first show the regression between the CON(DY) in Southwest China and velocity potential, vertical circulation and the regional zonal cells during May-June (Fig. 11). In early summer, consistent with the tripole mode of SST anomalies, large-scale low-level convergence (upper-level divergence) over the western Pacific warm pool has a significant effect on the SW-MFC (Fig. 11a and b). Besides, Abnormal upper-level convergence (lower-level divergence) are observed along east coast of the African continent, the Arabian Sea and the equatorial central-eastern Pacific, indicating abnormal descending motion and suppressed convection over this region. Correspondingly, in upper troposphere (200 hPa), anomalous easterly (westerly) flow from the northern Maritime Continent toward the Arabian Sea (equatorial central-eastern Pacific). In lower troposphere (850 hPa), there is an opposite anomalous westerly (easterly) wind flowing back to the western Pacific warm pool. This can be directly observed in the vertical zonal circulation cells averaged over 0–15°N (Fig. 11c). In other words, an abnormal “double-ring” vertical circulation cells occurs over the tropical Pacific-Indian Ocean, and the Walker circulation is strengthened (Li et al. 2018, 2021; Yuan and Yan 2013; Wang et al. 2006). The large-scale westerly anomalies in lower troposphere over the northern Arabian Sea are crucial for the strengthening of the cyclone system over the Indian Peninsula and the SW-MFC in early summer. The above pattern of velocity potential anomaly is maintained by the tripole mode of tropical Pacific-Indian Ocean SST by stimulating thermally driven large-scale divergent circulation cells.

Fig. 11
figure 11

Regression coefficients between the Southwest CON(DY) and wind potential function (shading; m2 s− 1/ mm day− 1) overlaid its divergence component (vectors; m s− 1/ mm day− 1) at (a) 200 hPa, (b) 850 hPa, and (c) zonal cells averaged along 0°-15°N in May-June during 1979 to 2023. The black dots denote significant values at the 95% confidence level based on the Student’s t test

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In late summer, the circulation patterns closely related to the SW-MFC are an abnormal high-pressure zone from the central and western Pacific to the Indian Peninsula, and the narrow low-pressure belt from the Southwest China to the East Asia. This is accompanied by an enhanced precipitation over Southwest China. In order to explore the possible mechanism of the CON(DY) affecting the MFC during July-August, Fig. 12 shows the correlation of SW-MC and CON(DY) with the local meridional circulation averaged along 75°E − 105° E. The flow rises along 20°N -30°N over the Southwest and descends around 10°N -20°N. The large-scale vertical velocity shows a strong upward motion over Southwest China and an abnormal subsidence motion over South Asia. Therefore, along with the dry zone over South Asia, the water vapor convergence and its transport over Southwest China are enhanced, which in turn leads to an increase in the rainfall.

Fig. 12
figure 12

Correlation coefficients between the Southwest moisture flux convergence and zonal averaged (75°E-105°E) vertical velocity (shading) and the meridional circulation in July-August during 1979 to 2023. Panel (b) as in panel (a), except for the moisture convergence of dynamic (CON (DY)) component. The vertical velocity in the meridional circulation is amplified 100 times for better illustration. The black dots denote significant values at the 95% confidence level based on the Student’s t test

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5 Numerical experiments

To elucidate the physical mechanisms in Sect. 4, we performed two numerical experiments with the AGCM from CESM2.1.3, including a control run and a sensitivity run. The control run (CTRL) is forced by the monthly climatological SST with the external forcing fixed at the year-2000 level. The CTRL is integrated for 60 years, and the first 5 years are used as spin-up. Then we use the last 55 years’ outputs as the initial conditions to restart the sensitivity experiments. Since the initial conditions have some different weather disturbances (Schneider and Fan 2007), in order to remove the influence of these atmospheric noises, the sensitivity experiment consists of 55 members with the initial conditions provided by the last 55 years’ outputs of the CTRL run. The precipitation and circulation responses are provided by the ensemble mean of all members. Each member of sensitivity experiments consists of an early summer experiment and a late summer experiment, and they are integrated from March 1 to June 30 and from May 1 to August 31, respectively. The forcing SSTA patterns are set to the regression of SW-MFC over the tropical Indo-Pacific (20°S–25°N, 40°E − 80°W), and the imposed SSTA are shown in Fig. 13. To emphasize the possible influence of the tropical Indo-Pacific SSTA on precipitation in Southwest China, we imposed a double SST anomaly within the tropical region. The SST forcing in the sensitivity experiments is the model climatology plus the above SSTA, while the SST in other ocean is kept the same as the model climatology. As shown in Fig. 13, the SST modes corresponding to the SW-MFC in early summer show a triple SSTA pattern from March to June (Fig. 13a, c, e and g). Besides, the relationship between the late summer MFC and tropical SST from May to August shows the enhanced SST gradient in the subtropical Indian Ocean and the Central-East Pacific (Fig. 13b, d, f and h).

Fig. 13
figure 13

The SST forcing fields in the tropical Pacific and Indian Ocean (20°S–25°N, 40°E–80°W) in the AGCM sensitivity experiments. The imposed SST patterns used in early summer experiments are the regressions of SST (℃) in (a) March, (c) April, (e) May and (g) June against the SW-MFC in May-June. The imposed SST patterns used in late summer experiments are the regressions of SST (℃) in (b) May, (d) June, (f) July and (h) August coefficients against the SW-MFC in July- August

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In early summer, the model response of precipitation and circulation (Fig. 14) can reproduce the similar observed patterns in Fig. 7. Enhanced precipitation occurs over Southwest China, the Bay of Bengal and the western Pacific warm pool (Fig. 14a). The circulation response at lower troposphere can simulate large-scale low pressure over the Indian Peninsula to the western Tibetan Plateau, as well as the cyclone over the South China Sea (Fig. 14b). The difference between the simulation and observation is mainly reflected in the westward shift of the southerly wind response at 850 hPa from the Bay of Bengal to the Southwest China. Besides, the position of the simulated lower-tropospheric cyclone over the Indian peninsula is shifted westwards and northwards, which may be caused by the model’s underestimation of mean easterly vertical shear over the Bay of Bengal (Wang et al. 2003; Xie and Wang 1996). In the late summer sensitivity experiment, the imposed SST gradient between the Indian Ocean and the Pacific in the Northern Hemisphere can trigger an increase in rainfall over Southwest China and a dry belt between 10°N − 20° N over South Asia (Fig. 15a). The circulation response show a high-pressure zone associated with anomalous anticyclones at 850 hPa over the subtropical northwest Pacific and the northern Bay of Bengal (Fig. 15b). An enhanced cyclone center appear over the southern Tibetan Plateau. The lower-tropospheric anticyclone over the Bay of Bengal enhances the northward moisture transport to Southwest China and can promote upward motion through vertical meridional circulation (Fig. 15c).

Fig. 14
figure 14

Simulated precipitation and circulation responses to imposed Indo-Pacific SST anomalies in the tropics in the AGCM early summer experiments. (a) The precipitation (mm day− 1), (b) geopotential height (gpm) overlaid wind at 850 hPa (m s− 1) and (c) vertical velocity (Pa s− 1) at 500 hPa. The responses are the ensemble mean of CESM2.1.3 55-member runs. The black dots denote the significant differences between sensitivity and control experiments based on the two-sample t-test, p < 0.05

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Fig. 15
figure 15

The same as Fig. 14, but for late summer (July-August).

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6 Conclusion and discussion

The above analysis demonstrates that the dynamic component of moisture flux convergence plays a dominant role in precipitation over Southwest China in both early and late summer. In addition, the thermodynamic factor (i.e. local specific humidity changes) also contributed to the enhanced rainfall in the central part of the Southwest China in early summer (Fig. 4b and f). We present the correlation patterns of the SW-MFC and ADV(TH) with 700 hPa specific humidity advection and 500 hPa specific humidity meridional gradient (Fig. 16), in order to discuss the ADV(TH) affecting the Southwest moisture flux convergence in May-June. The results show that ADV(TH) affects the SW-MFC mainly due to the spatial distribution of specific humidity differences between the southern and northern Southwest China in early summer (Fig. 16a and b). The proportion of water vapor in Yunnan, Guizhou province and southern Xizang autonomous region is higher than that in areas north of 30°N. The meridional gradient extremes of specific humidity appear in the southern-central region of the Southwest China, and the climatological southwesterly flow can promote the precipitation anomalies over this region (Fig. 16c and d). This is the main process in which the thermodynamic component ADV(TH) affects the SW-MFC in early summer.

Fig. 16
figure 16

Correlation coefficients between the Southwest moisture flux convergence and (a) specific humidity advection (shading) overlaid climatological wind at 700 hPa, and (c) specific humidity meridional gradient at 500 hPa in May-June during 1979 to 2023. Panels (b) as in panel (a), except for the moisture advection of thermodynamic (ADV (TH)) component. The black dots denote significant values at the 95% confidence level based on the Student’s t test

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In summary, the schematic diagram illustrating the impact of Pacific-Indian Ocean SST anomalies on the SW-MFC during early and late summer is shown in Fig. 17. In May-June, the SW-MFC corresponds to a tripole mode of tropical Pacific-Indian Ocean SST, characterized by a negative-positive-negative SST anomaly. The atmospheric response to warm pool SST is more sensitive than that of the equatorial cold tongue (Palmer and Owen 1986; Ju and Slingo 1995), and the positive SST anomaly in northern Maritime Continent can directly enhance local convection. Besides, the increased SST gradient on both sides of the Maritime Continent lead to abnormal “double-ring” vertical zonal circulation cells over the Pacific and Indian Oceans, and the Walker circulation is strengthened (Tokinaga et al. 2012; Liu and Huang 1997). The low-level westerly anomalies in northern Arabian Sea are significant, which in turn generates cyclonic shear on both sides of the equator and triggers cyclonic circulation over northern Indian Peninsula and the South China Sea. Therefore, the southerly anomalies in lower troposphere over the Indian peninsula transports warm moisture from the Indian Ocean to the southern part of Southwest China, causing the moisture fluxes convergence over this region (Fig. 17a). This is the dynamic mechanism that affects the SW-MFC in early summer and also the main process, which is also confirmed in previous reanalysis evidence and numerical experiments. In addition, the specific humidity distribution in the south and north of Southwest China is quite different in early summer. The meridional gradient extremes of specific humidity appear over south-central Southwest. The climatological southwesterly wind promote precipitation anomalies in central Southwest China. This is the thermodynamic processes affecting the SW-MFC during May-June.

In late summer, the subtropical Indo-Pacific SST which affects the SW-MFC exhibits a dipole mode. Specifically, the SST in tropical Indian Ocean and the subtropical Western Pacific is a positive anomaly, while the SST in the East-Central Pacific shows a negative anomaly. The SST gradient between the Indian Ocean and the Pacific increases, which directly leads to significant equatorial easterly anomalies toward the Maritime Continent. Moreover, the convective precipitation increased over the Maritime Continent, while an abnormally dry zone appears over the tropical west-central Pacific. The easterly anomalies and large scale convection caused by the above SST pattern stimulate westward propagating Rossby waves (Sun et al. 2022), causing an anticyclonic shear zone from tropical western Pacific to the central Indian Peninsula, and an abnormal low-pressure belt to its north (Yue et al. 2021). The anticyclonic anomaly leads to a dry zone between 10°N − 20° N over South Asia, while the cyclones to its north brought precipitation over Bangladesh, Southwest China and Southern China. Furthermore, the deep meridional low-high pressure centers over Southwest and South Asia forms a vertical circulation circle, which intensifies the widespread precipitation over Southwest China (Fig. 17b). This is how the dynamic component CON(DY) affects the SW-MFC in late summer, while the thermodynamic components have minimal impact.

Fig. 17
figure 17

A schematic diagram illustrating the mechanisms of precipitation during (a) early and (b) late summer in Southwest China

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Our study reveals the dynamic and thermodynamic components of moisture flux convergence over Southwest China during early and late summer, and confirms that tropical Pacific-Indian Ocean SST modes can further modulate the large-scale atmospheric circulation patterns, ultimately leading to droughts or floods over Southwest China. Compared with previous studies on the mechanisms of individual basins SST anomalies such as the Pacific, Indian Ocean or Bay of Bengal on Southwest China rainfall, this study emphasizes the role of joint SST anomalies in the tropical Indo-Pacific. This is because the SST gradient in the tropical Indo-Pacific may have a synergistic effect in modulating large-scale convection, energy disturbance and divergence circulation, thereby altering the atmospheric circulation pattern. Considering that many internal climate variabilities, such as the Tibetan Plateau snow cover, the strength of the plateau atmospheric heat source, Atlantic SST anomalies and even Arctic sea ice may regulate the Southwest China precipitation (Bi et al. 2022; Xu et al. 2012; Li et al. 2011). The rainfall during different periods must be a result of the synergistic effect from multiple internal and external forcings. How the synergistic effect of SST anomalies in the three oceans leads to droughts and floods in Southwest China, and the interaction between the Tibetan Plateau thermodynamic effects and SST in various ocean basins are both issues worthy studying.