1 Introduction

Drought, among the most pervasive, frequent, and devastating extreme climatic events worldwide, could impose detrimental effects on regional water resource management, terrestrial ecosystem health, and socio-economic sustainability (Pedro-Monzonís et al. 2015; AghaKouchak et al. 2020; Zhang et al. 2022a). During the summer of 2022, the Yangtze River Basin (YRB) experienced an unprecedented meteorological drought characterized by historically low precipitation levels since 1961. The drought affected an area exceeding 8000 hm2 across 10 provinces, resulting in substantial socio-economic consequences (Wang et al. 2022; Xia et al. 2022; Liang et al. 2023). With projections indicating increased drought risk and severity in many regions, there is urgent demand to implement preventive measures to minimize the impacts of droughts (Carrão et al. 2018; Cook et al. 2018; Hao et al. 2018; Yao et al. 2020). Investigating the evolving dynamics and underlying mechanisms of drought can enhance our comprehension of relevant physical processes, thereby facilitating more effective drought prevention and mitigation strategies (Blöschl et al. 2019).

Drought evolution is a dynamic process encompassing both spatial and temporal dimensions (Wen et al. 2020). Compared with other hydroclimatic extremes, it exhibits greater spatiotemporal complexity, which can endure from several months to years and span expansive geographical extents, ranging from hundreds to thousands of kilometers (Herrera-Estrada et al. 2017; Konapala and Mishra 2017; Apurv and Cai 2020). To quantify the severity of diverse drought types, various drought indices based on water deficit have been applied, including the Standardized Precipitation Index (SPI) (McKee et al. 1993), Standardized Precipitation Evapotranspiration Index (SPEI) (Vicente-Serrano et al. 2010), Standardized Runoff/Streamflow Index (SRI/SSI) (Shukla and Wood 2008), Standardized Soil Moisture Index (SSMI) (Hao and AghaKouchak 2013), Standardized Groundwater Index (SGI) (Bloomfield and Marchant 2013), along with several multivariate drought indices (Rajsekhar et al. 2015; Xu et al. 2021). These drought indices can effectively reflect drought statuses and attributes for multiple temporal scales (e.g., 1, 3-, 6-, 9-, 12-months accumulations), enabling the quantification of temporal variability such as frequency and duration of drought events at specific regions/grids (Mishra and Singh 2010; Gocic and Trajkovic 2014; Wu and Chen 2019). Nevertheless, research aimed at quantifying the spatial behaviors of drought evolution remains limited (Konapala et al. 2022). Existing studies primarily focused on aspects like the affected area, centroid, and trajectory of drought evolution at the spatial scale (Herrera-Estrada et al. 2017; Zhou et al. 2019; Dikshit et al. 2022). These studies often lack in-depth quantification of drought spatial propagation. The spatial propagation of drought refers to the prevailing evolving processes of drought events from source to sink regions, which can aid in unraveling the formation and disaster-causing mechanisms of drought and hold the potential to enhance the accuracy of drought forecasting. For a large area, there may exist distinct spatial scales for drought spatial propagation (Zhou et al. 2020, 2023; Mondal et al. 2023). As a result, the classification of localized regions exhibiting coherent spatial propagation patterns of drought becomes a prime.

To quantify drought spatial propagation, it is essential to analyze the synchronized and time-delayed properties of drought events at different locations (Konapala and Mishra 2017; Jha et al. 2022). The synchronization signifies the co-occurrences of drought events within a certain time period at different locations. Regions with significant synchronization typically display certain spatial correlations, and thus understanding the synchronized patterns of drought at a regional level facilitates the characterization of regions where drought events co-occur and co-evolve. The delay elucidates the sequential order of drought occurrences at various locations, which can offer crucial insights into the dynamics of drought spatial propagation and enable the forecast of its evolutionary trends. However, analyzing the two properties is challenging and requires specific statistical and dynamical methods (Fan et al. 2021). In recent years, the integration of event synchronization (ES) and complex networks (CN) has provided new possibilities and perspectives (Boers et al. 2013, 2019; Konapala and Mishra 2017; Mondal et al. 2020). ES, as a nonlinear method, is utilized to measure the time-lagged correlation between drought event sequences and is able to capture both the synchronized and time-delayed properties (Quiroga et al. 2002). CN, as a graph-based theory, is used to construct the interconnected network among different nodes within drought systems. In the networks, geographical locations often serve as nodes, and the existence of an edge between two nodes is determined by whether the synchronized or time-delayed performance of their drought occurrences exceeds a given threshold (Tsonis and Roebber 2004; Donges et al. 2016; Donner et al. 2017; Dijkstra et al. 2019). In recent research, Jha et al. (2022) utilized the ES and CN methodologies to construct an undirected network and assessed the spatiotemporal characteristics of Indian precipitation-driven meteorological droughts in past and future climatic scenarios. In the study by Konapala and Mishra (2017), a directed network and network-based metrics (i.e., intensity, direction, and distance) were introduced to identify the spatiotemporal evolutions of droughts in the continental United States. Konapala et al. (2022) further constructed regional drought networks and explored the spatiotemporal structure and driving mechanisms of drought evolution in North America. In summary, the synthesis of ES and CN holds vast potential for quantifying various aspects of drought spatial propagation. However, there is currently limited research specifically investigating these aspects in the context of China (Gao et al. 2023). Moreover, there exists a lack of clarity concerning the driving mechanisms and influencing factors that contribute to drought spatial propagation.

As one of the largest river basins and the most flourishing economic areas in China, the YRB holds paramount significances owing to its water resources endowment and economic productivity (Zeng et al. 2008; Birkinshaw et al. 2017). Given the increasing frequency of drought occurrences in the YRB, along with potential exacerbation in the future (Sun et al. 2019; Wang et al. 2020), it is imperative to understand the spatial propagation patterns of drought in this basin. Meteorological drought in the YRB would often transition into agricultural, hydrological and socioeconomic droughts (Wang et al. 2011; Meresa et al. 2023; Zhang et al. 2023). Hence, analyzing the spatial propagation of meteorological drought within the YRB can also help get knowledge of other types of drought in this basin. Moreover, it is crucial to recognize that the spatial propagation of meteorological drought is usually closely linked with persistent deficits in atmospheric moisture, which are in turn influenced by large-scale drought-inducing climate systems (Masih et al. 2014; Konapala et al. 2022). Given the distinct atmospheric circulation patterns governing the YRB during the wet season and dry season, it is likely that the driving mechanisms of meteorological drought spatial propagation differ between these two distinct periods (Ma and Zhou 2015). Additionally, other factors like teleconnection effects originating from sea surface temperature anomalies may also potentially influence the spatial propagation of meteorological drought within the YRB (Jin et al. 2013; Zhang et al. 2013; Nikraftar et al. 2021). Consequently, it is indispensable to conduct an in-depth analysis of the relevant driving mechanisms and potential influencing factors during both wet and dry seasons.

This study focuses on quantitatively investigating the spatial propagation patterns of meteorological drought events (MDEs) in the YRB during both wet and dry seasons by employing the integrated ES and CN methods, and further elucidating the underlying mechanisms and potential influencing factors that govern MDE spatial propagation by diagnosing the relevant drought-inducing climate systems. The primary objectives of this study are: (1) to identify the MDE synchronized regions where MDEs co-occur and co-evolve in the YRB, (2) to quantify the spatial propagation patterns of MDEs in the whole YRB and its subregions, and (3) to explore the driving mechanisms and potential influencing factors of MDE spatial propagation. The proposed methodology and findings are expected to contribute significantly to comprehensively understanding the spatial evolutions of MDEs, enhancing the drought forecasting and resilience strategies, and achieving the purpose of mitigating the impacts of drought on socio-economic activities in the YRB.

2 Study area and data

As the third-largest basin globally and the largest in China, the YRB, depicted in Fig. 1, is selected as the study area in this work. Its drainage area covers approximately 1.8 million km2, constituting around one-fifth of China's mainland area. This basin’s unique geographical location, i.e., spanning the Qinghai-Tibet Plateau, the Southwest Monsoon Region, and the Central Subtropical Monsoon Region of China, situates it within a humid and semi-humid region with variable spatiotemporal precipitation distributions. Consequently, the YRB is susceptible to recurring seasonal drought events (Tian et al. 2022). Mainly affected by East Asian monsoon circulation, the annual precipitation pattern in this basin exhibits two distinct phases: the wet season, prevailing from April to September, and the dry season, spanning from October to March (Cao et al. 2017; Ding et al. 2018). As illustrated in Fig. 1a, the YRB is characterized with four prominent water vapor transport pathways: the pathway from the Western Pacific into the eastern parts of the basin, the pathway from the South China Sea into the southeastern reaches, the pathway from the Bay of Bengal into the southwestern expanses, and the pathway from the westerlies affecting the western domains (Wang and Ding 2008; Sun et al. 2020; Guan et al. 2022). These pathways are influenced by monsoon atmospheric circulations, leading to varying contributions of water vapor between the wet season and dry season. Throughout the wet season, there is strong water vapor transport, predominantly originating from the Bay of Bengal and the Western Pacific Ocean (Wang et al. 2018; Shi et al. 2020; Zhang et al. 2021). During the dry season, there is a significant reduction in the water vapor transport fluxes, with the westerlies and the Western Pacific emerging as the dominant contributors of water vapor (Jiang et al. 2009; Zhang et al. 2022b). Overall, these hydroclimatic characteristics of the YRB exert a pivotal influence on the occurrences and evolutions of MDEs within this basin.

Fig. 1
figure 1

(a) location (in purple), (b) elevation and rivers and (c) grid points of the Yangtze River Basin (YRB). The green arrows in (a) visually depict the prominent water vapor transport pathways into the YRB

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In this study, the Standardized Precipitation Evapotranspiration Index (SPEI) is adopted to describe the meteorological drought conditions. In comparison to the traditional Standardized Precipitation Index (SPI), the SPEI also includes the influence of evapotranspiration on drought severity, rendering it more capable of reflecting the impacts of drought on hydrological systems and ecosystems (Vicente-Serrano et al. 2010). Similar to SPI, the SPEI can also be computed for different time scales and the SPEI-3 (SPEI at a time scale of 3 months) delineates seasonal-scale variations of dry and wet conditions, is particularly suitable for characterizing the spatiotemporal evolutions of MDEs (Huang et al. 2018; Zeng et al. 2021). The calculation of SPEI-3 mainly uses the difference between the monthly cumulative precipitation and potential evapotranspiration (PET) and then fits the data to the log-logistic probability distribution function (PDF) (Thornthwaite 1948; Hosking 1990; Wang et al. 2015). The detailed procedure for estimating the SPEI-3 is summarized in Text S1. To calculate the SPEI-3 series in the YRB, the CN05.1 gridded meteorological dataset was utilized in this study, including monthly mean precipitation and monthly mean temperature over the period 1961 − 2021. The CN05.1 dataset, with a spatial resolution of 0.25° × 0.25°, can accurately capture the spatio-temporal distribution characteristics of precipitation in China (Lu et al. 2024). It is released by the National Climate Center and constructed using thin plate spline interpolation and angular distance weighting methods based on observation data from over 2400 national stations (Wu and Gao 2013). In the YRB, a total of 2666 grid points were extracted, which is presented in Fig. 1c. To further investigate the drought-inducing climate systems during MDE spatial propagation, several key atmospheric variables are also selected in this study, including the composite anomalies of the geopotential height field at 500 hPa, the wind field at 750 hPa, and the integrated water vapor flux and its divergence from 1000 to 300 hPa. These variables are sourced from the ERA5 monthly mean reanalysis data, characterized by a spatial resolution of 0.25° × 0.25° and a temporal range of 1961 − 2021 (Hersbach et al. 2020).

3 Methodology

The detailed framework of this study, as depicted in Fig. 2, consists of five sequential steps: (i) Extraction of gridded MDEs in the YRB from the corresponding SPEI-3 series throughout the entire year, wet season, and dry season, respectively. (ii) Construction of MDE synchronization networks for the whole YRB throughout the entire year, wet season, and dry season, respectively. As the undirected networks, these MDE synchronization networks are established based on the extracted MDEs using ES and CN, aimed at identifying the MDE synchronized regions where MDEs co-occur and co-evolve. (iii) Construction of MDE spatial propagation networks for the whole YRB throughout the entire year, wet season, and dry season, respectively, as well as for previously identified subregions during both wet and dry seasons. These MDE spatial propagation networks are directed networks used to derive relevant network metrics, including network divergence, indegree, outdegree, inward orientation, and outward orientation. (iv) Quantization of the MDE spatial propagation patterns across the whole YRB and subregions, including the identification of source/sink zones, direction, and strength of MDE spatial propagation. (v) Exploration of driving mechanisms and influencing factors behind the MDE spatial propagation patterns by diagnosing the drought-inducing climate systems during typical MDE spatial propagation periods. The flowchart of the proposed methodology is illustrated in Fig. 2.

Fig. 2
figure 2

Flowchart of the methodology used in this study

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3.1 Extraction of gridded MDEs in the YRB

Numerous studies demonstrate that SPEI values below the threshold of − 1 represent moderate or more severe drought levels (Bachmair et al. 2016; Ma et al. 2023). Furthermore, short-term droughts (e.g., droughts lasting for 1 or 2 months) may signify less severe drought conditions (Mishra and Singh 2010; Konapala et al. 2022). Hence, MDEs in this study are defined as SPEI-3 values falling below − 1 with a persistent duration of no less than the seasonal scale (i.e., 3 months), and the sequences of MDEs are subsequently extracted for each grid point in the YRB. The occurrence time of each MDE is defined as the first occurrence month of SPEI-3 values less than − 1, as illustrated by the red line depicted in Fig. 3. Besides extracting gridded MDEs throughout the entire year, this study also extracts MDEs specifically for both the wet and dry seasons. The MDE occurrence months are designated to specific time intervals: April to September for the wet season and October to March for the dry season. Considering the delay of MDE spatial propagation within a 3-month period, as detailed in subsequent sections, the wet season is extended from April to November, while the dry season spans from October to May, facilitating a thorough investigation into MDE spatial propagation patterns during respective seasons.

Fig. 3
figure 3

Hypothetical demonstration for identifying meteorological drought events (MDEs) based on 3-month standardized precipitation evapotranspiration index (SPEI-3) series. The upper and lower subplots represent the SPEI-3 series of grid locations i and j, respectively. The red-shaded regions denote the extracted MDEs with a duration of no less than 3 months. The red lines indicate the occurrence time of MDEs. The gray-shaded regions show three distinct groups of MDEs occurred synchronously within 3 months at grid locations i and j, where MDE at grid point i occurs later than MDE at grid point j in the first group, MDEs at both grid points occur simultaneously in the second group, and MDE at grid point i occurs earlier than MDE at grid point j in the third group

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3.2 Event synchronization (ES)

The ES method employed in this study is a nonlinear algorithm to quantify the strengths of synchronization and delay between gridded MDE sequences. It represents a valuable tool for discerning correlations between all pairs of grid points (Quiroga et al. 2002). In comparison with other correlation methods such as Pearson correlation, ES offers two key advantages: 1) it is well-suited to treat event series with unequal spacing between events, thanks to the fact that the time lag is not set a priori but it is dynamically computed. This is especially pertinent since MDEs may occur at irregular intervals due to varying climatic conditions or other factors. 2) it does not assume any specific probability distribution for the event sequences to follow. Given these advantages, ES is in general appropriate for event-like time series and has extensively used to construct climate networks (Malik et al. 2010, 2012; Agarwal et al. 2020; Fan et al. 2021; Giaquinto et al. 2023). In this study, ES is utilized to measure the MDE synchronized and delayed strengths between any two sequences of MDE occurrences by calculating the number of time-coincident MDEs with dynamic lags. Let Ei = \(\left\{{t}_{l}^{i}\right\}\), (\({t}_{l}^{i}<{t}_{l+1}^{i}\), l = 1,2,…,ni) and Ej = \(\left\{{t}_{m}^{j}\right\}\), (\({t}_{m}^{j}<{t}_{m+1}^{j}\), m = 1,2,…,nj) represent MDE occurrence time series at grid locations i and j, respectively, where \({t}_{l}^{i}\) and \({t}_{m}^{j}\) denote the occurrence time of the lth MDE in Ei and the mth MDE in Ej, respectively. Furthermore, ni and nj represent the total number of extracted MDEs for grid locations i and j, respectively. The dynamic time lag \({\tau }_{lm}^{ij}\) of MDEs occurring at \({t}_{l}^{i}\) and \({t}_{m}^{j}\) are defined as follows:

$${\tau }_{lm}^{ij}=\frac{min\left\{{t}_{l+1}^{i}-{t}_{l}^{i},{t}_{l}^{i}-{t}_{l-1}^{i},{t}_{m+1}^{j}-{t}_{m}^{j},{t}_{m}^{j}-{t}_{m-1}^{j}\right\}}{2}$$
(1)

where \({\tau }_{lm}^{ij}\) is adaptive. In order to exclude unreasonable long dynamic lags, a maximum time lag of 3 months (i.e., \({\tau }_{max}\) = 3) is set (Konapala and Mishra 2017; Konapala et al. 2022). When \(\left|{t}_{l}^{i}-{t}_{m}^{j}\right|\in \left[0,{\tau }_{lm}^{ij}\right]\cap \left[0,{\tau }_{max}\right]\), it is considered that the lth MDE at grid point i occurred synchronously with the mth MDE at grid point j. Accordingly, three groups of synchronized MDEs are identified in Fig. 3.

Based on variable time lags, the MDE synchronized strength Qij between grid locations i and j can be defined as follows:

$${Q}_{ij}=\frac{c\left(i|j\right)+c\left(j|i\right)}{\sqrt{{n}_{i}{n}_{j}}}$$
(2)

where \(c\left(i|j\right)={\sum }_{l=1}^{{n}_{i}}{\sum }_{m=1}^{{n}_{j}}{J}_{ij}\) represents the number of MDEs that occurred at grid point i are after those at grid point j, and \(c\left(j|i\right)\) is the contrary. Jij is defined as:

$${J}_{ij}=\left\{\begin{array}{cc}1& if\;0<{t}_{l}^{i}-{t}_{m}^{j}<{\tau }_{lm}^{ij}\;and\;0<{t}_{l}^{i}-{t}_{m}^{j}\le {\tau }_{max}\\ 0.5& if\;{t}_{l}^{i}={t}_{m}^{j}\\ 0& if\;otherwise\end{array}\right.$$
(3)

According to the above definition, Qij is normalized to \(\left[\text{0,1}\right]\). \({Q}_{ij}=1\) indicates complete synchronization of MDE occurrences between grid locations i and j, while \({Q}_{ij}=0\) stands for the absence of synchronization. By repeating the above procedure for all pairwise grid locations within the YRB, the MDE synchronized matrix Q can be obtained. This matrix is square and symmetric, representing the synchronized strengths of MDE occurrences between different grid locations without direction information.

Similarly, the delayed behavior between grid locations i and j can be expressed with qij, which is shown as below:

$${q}_{ij}=\frac{c\left(i|j\right)-c\left(j|i\right)}{\sqrt{{n}_{i}{n}_{j}}}$$
(4)

where \({q}_{ij}\in \left[-\text{1,1}\right]\). \({q}_{ij}=1\) indicates that MDEs at j always precede those at i, and vice-versa for \({q}_{ij}=-1\). This procedure is repeated for all pairwise grid points within the YRB to obtain the MDE delayed matrix q. Similar to Q, q is also square; however, it is antisymmetric, thus representing the delayed strengths of MDE spatial propagation with direction information.

Based on the MDE synchronized matrix Q and MDE delayed matrix q, the MDE synchronization networks and spatial propagation networks of MDEs are respectively constructed to encode the synchronized or delayed relationships between various grid points over the period 1961 − 2021. Each grid point is considered as a node and the edge placed between a pair of nodes is established when there exists a significant connected relationship (synchronization or delay) between them. The MDE synchronization networks provide the information of synchronization without any sense of direction while the MDE spatial propagation networks supply a sense of direction through the information of delay. The detailed illustration on how these two networks are constructed can be found in the following sections.

3.3 MDE synchronization networks for the whole YRB

To ensure the statistical significance of the established edges in MDE synchronization networks, a locally tailored significance testing scheme is implemented in this study. For a pair of grid locations i and j, a null model is established using the original MDE occurrence sequences for grid point i and 1000 surrogate MDE occurrence sequences for j, preserving the respective number of events nj. It is assumed that the MDEs at grid point j occur independently following a uniform random distribution. Subsequently, the MDE synchronized strength value Qij is computed for each surrogate time series, and an empirical distribution function is derived. Nodes are connected in the network (by setting \({A}_{ij}^{Q}=1\) for an undirected adjacency matrix AQ) if Qij exceeds the 95th percentile of the respective surrogate test distribution (Boers et al. 2019; Vallejo-Bernal et al. 2023), which is expressed as follows:

$${A}_{ij}^{Q}=\Theta \left({Q}_{ij}-{\theta }_{ij}^{Q}\right)-{\delta }_{ij}$$
(5)

where Θ denotes the Heaviside function, \({\theta }_{ij}^{Q}\) is the 95th percentile of the surrogate test distribution for Qij, and Kronecker’s delta δij is used to exclude self-loops. Based on the AQ matrices, the undirected and unweighted MDE synchronization networks are constructed for the entire YRB throughout the entire year, wet season, and dry season, respectively. These networks contain synchronization information between all pairs of grid points within the YRB and can be used to identify the general co-evolving regions of MDEs.

To determine the general co-occurring and co-evolving domains of MDEs in the YRB throughout the entire year, wet season, and dry season, respectively, it is necessary to partition the basin into several subregions, where MDEs occur and evolve more synchronously and is more likely to undergo spatial propagation within these subregions. In recent years, community detection in CN has emerged as a promising avenue for region partitioning based on the event-like data (Fortunato and Hric 2016). Although a wide array of community detection algorithms exists, only a few are applicable to large networks containing hundreds of nodes. In this MDE synchronization network, a community detection approach named Leiden algorithm is adopted to identify the co-evolving regions of MDEs in the YRB. This algorithm, aimed at maximizing modularity, represents an enhancement over the prevalent Louvain algorithm due to its faster running speed and improved partition performance (Good et al. 2010; Lancichinetti et al. 2011; Traag et al. 2019). It boasts enhanced accuracy and robustness for detecting community structures in large networks. The Leiden algorithm identifies the regions within which MDEs are more likely to propagate (maximum number of intra-connections) and less likely to propagate beyond these regions (minimum number of inter-connections) by optimizing modularity (Mod), which is defined by the following expression:

$$Mod=\frac{1}{2M}\sum_{i,j}\left[\left({a}_{ij}^{Q}-\frac{{k}_{i}{k}_{j}}{2M}\right)\delta \left({s}_{i},{s}_{j}\right)\right]$$
(6)

where M is the total number of edges in the network; \({a}_{ij}^{Q}\) is an element of the undirected adjacency matrix AQ; ki and kj are the number of edges connected to nodes i and j, respectively, namely the degree of nodes i and j; si and sj is the community to which nodes i and j belong; \(\delta \left({s}_{i},{s}_{j}\right)\) is 1 if nodes i and j belong to the same community and 0 otherwise. A high modularity value signifies dense intra-community links and sparse inter-community links. By maximizing the modularity, this algorithm is capable of achieving effective partitioning of the YRB.

3.4 MDE spatial propagation networks for the whole YRB and its subregions

Similarly, the connected edges within the MDE spatial propagation networks are established using the locally tailored significance testing scheme. Once the threshold Ɵq is determined, the directed adjacency matrix Aq is converted from q using Eq. 7:

$${A}_{ij}^{q}=\Theta \left({q}_{ij}-{\theta }_{ij}^{q}\right)-{\delta }_{ij}$$
(7)

Based on Aq, the MDE spatial propagation networks for the whole YRB throughout the entire year, wet season, and dry season, respectively, as well as for the respective subregions during both wet and dry seasons are constructed. This network includes time-delayed information of MDEs, which can be used to determine the spatial propagation patterns for MDEs, including the source and sink, as well as the strength and direction. To identify the sources and sinks of MDE spatial propagation, the network divergence (ND) of each node is calculated in the constructed networks. The ND is described as the difference between the indegree (ID) and outdegree (OD) of a node, which are defined as follows:

$$N{D}_{i}=I{D}_{i}-O{D}_{i}$$
(8)
$$I{D}_{i}=\sum_{j=1}^{N}{A}_{ji}^{q}$$
(9)
$$O{D}_{i}=\sum_{j=1}^{N}{A}_{ij}^{q}$$
(10)

where NDi, IDi and ODi denote the ND, ID and OD of node i, respectively. IDi represents the number of other nodes from which MDEs propagate to node i, while ODi is the number of other nodes MDEs propagate to staring from node i, and N is the total number of nodes. Grid points with negative ND values primarily act as propagators of MDEs and are considered as the sources of MDE spatial propagation. Conversely, grid points characterized by positive ND values serve as recipients of MDEs and are identified as the sinks of MDE spatial propagation. In this study, it is assumed that spatially continuous regions with high negative or positive ND values are designated as the source or sink zones (Konapala et al. 2022).

To further explore the dominant directions of the MDE spatial propagation, two metrics are introduced: the inward orientation (IO) and the outward orientation (OO). These two metrics provide insights into the predominant propagation directions from the perspective of individual nodes in the network, where IO indicates the weighted average direction of MDEs propagating from other nodes to the considered node, and OO measures the weighted average direction of MDEs propagating from the node of interest to other nodes (Mondal et al. 2020). Assuming that node j is connected inward to node i, and the azimuth angle from j to i is denoted as ηji, and node i is connected outward to node k, with the azimuth angle from i to k denoted as ηik, then the inward orientation IOi and outward orientation OOi of node i are respectively defined as follows:

$$I{O}_{i}=\frac{\sum_{j=1}^{N-1}{A}_{ji}^{q}{\eta }_{ji}}{\sum_{j=1}^{N-1}{A}_{ji}^{q}}$$
(11)
$$O{O}_{i}=\frac{\sum_{k=1}^{N-1}{A}_{ik}^{q}{\eta }_{ik}}{\sum_{k=1}^{N-1}{A}_{ik}^{q}}$$
(12)

where IOi and OOi represent the weighted average azimuth angle of inward and outward connections linked with node i, respectively.

3.5 Drought-inducing climate systems

The drought-inducing climate systems during MDE spatial propagation are also investigated in this study. To achieve this, three variables related to atmospheric circulation are selected as indicators: (1) the 500 hPa geopotential height field. The 500 hPa level corresponds to the mid-level of the troposphere, and its variations are closely linked to variations in atmospheric pressure and circulation patterns (Chen and Zhai 2014). (2) the 700 hPa wind field. The 700 hPa wind field is selected due to its direct influence on the pathways and intensity of moisture transport in the atmosphere. Wind patterns at this level can directly impact the weather systems that contribute to precipitation in the middle and lower atmosphere levels (Chen et al. 2020). (3) the integrated water vapor flux and its divergence. Moisture transport and moisture convergence/divergence are essential components of the water vapor circulation process in the atmosphere. The integrated water vapor flux assists in characterizing the sources and transport pathways of atmospheric moisture, while the divergence value serves as an indicator of the prevailing regions regarding with moisture convergence or divergence. This information offers a clear distinction between areas that are favorable for precipitation (i.e., moisture converges) and areas where drying conditions predominate (i.e., moisture divergence). In this manner, both variables contribute significantly to comprehensive understanding of atmospheric moisture dynamics and its implications for regional precipitation patterns (Simmonds et al. 1999; Zhou and Yu 2005; Qiao et al. 2022).

The calculation of integrated water vapor flux and its divergence is relatively intricate, requiring specific humidity, meridional wind speed and zonal wind speed data in the troposphere. The integrated water vapor flux is divided into zonal water vapor flux and meridional water vapor flux and their expressions are as follows:

$${Q}_{u}=\frac{1}{g}{\int }_{{P}_{s}}^{{P}{t}}\left(qu\right)dp$$
(13)
$${Q}_{v}=\frac{1}{g}{\int }_{{P}_{s}}^{{P}{t}}\left(qv\right)dp$$
(14)

where q is the specific humidity; u and v are the zonal wind component and meridional wind component, respectively; Ps and Pt are the pressures at 1000 hPa and 300 hPa, respectively; g is the gravitational acceleration.

The integrated water vapor flux divergence within the zonal layer A is expressed as follows:

$$A=-\frac{\partial }{\partial x}{\int }_{{P}_{s}}^{{P}_{t}}\frac{1}{g}\left(qu\right)dp-\frac{\partial }{\partial y}{\int }_{{P}_{s}}^{{P}_{t}}\frac{1}{g}\left(qv\right)dp$$
(15)

where a positive value of A indicates a situation of moisture divergence. In this case, water vapor disperses outwardly, which is not conducive to the occurrence of precipitation. Conversely, a negative value of A implies moisture convergence, which is favorable for precipitation occurrence.

4 Results and discussions

4.1 MDE synchronized subregions in the YRB

The spatial distributions of MDE synchronized subregions in the YRB throughout the entire year, wet season and dry season, respectively, are depicted in Fig. 4, showcasing certain similarities and differences between each other. The YRB is divided into five subregions during the entire year, with Subregions Y1 and Y2 located in the southern part, while the remaining three subregions are situated in the northern part. During the wet season, the basin is divided into four subregions, where W4 generally overlaps with the ranges of Y4 and Y5. During the dry season, the extents of partitioned subregions resemble those observed throughout the entire year. For each subregion, MDEs are more likely to occur synchronously within 3 months and propagate within the spatial extent of this region, and the probability for MDEs propagating outside of this region is relatively less (Konapala et al. 2022). Notably, the partitioned MDE synchronized subregions in the YRB are the statistical outcomes of all extracted MDEs that represent significant spatial propagation scales within corresponding temporal scales. Thus, for one specific MDE, its spatial propagation scale might not completely align with any subregion. The partition of these subregions could be attributed to the interplay of various climatic and geographical factors specific to each area. Identifying these subregions is a crucial initial step, as it lays a foundation for further investigations into the atmospheric controls and driving mechanisms that govern MDE spatial propagation patterns.

Fig. 4
figure 4

Spatial distributions of MDE synchronized subregions in the YRB throughout the entire year (a), wet season (b) and dry season (c), respectively

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4.2 MDE spatial propagation patterns in the whole YRB

Figure 5 provides valuable insights into the MDE spatial propagation patterns in the YRB throughout the entire year, wet season and dry season, respectively. Figure 5a-c illustrates the source and sink zones of MDE spatial propagation, indicated by large negative and positive ND values, respectively. Throughout the entire year, the source and sink zones exhibit alternating distribution patterns with source zones concentrated in Subregions Y1 and Y3, while sink zones are predominantly located in Subregions Y1 and Y4. The distributions of source and sink zones during the wet season mirror those observed throughout the entire year. However, during the dry season, there are notable differences in the distributions, characterized by an increase of sink zones in D3. For both seasons, although the distributions of source and sink zones in the entire basin appear mixed, but they are more distinctly singular within specific subregions. Figure 5d-i indicates the strengths and directions of MDE spatial propagation across the YRB. According to Fig. 5d-i, OD tends to be larger in the source zones, while ID is more pronounced in the sink zones. Both IO and OO results show that the source zones diffusely propagate MDEs along the directions pointing to sink zones and most grid locations show dominant incoming and outgoing propagation directions pointing towards sink zones. As grid locations get closer to source zones, their indegree values decrease and their outdegree values increase. It can be concluded that the source zones are more likely to affect the MDEs in the output directions, while the sink zones are more susceptible to MDEs in the input directions. As there are differences of source and sink zones between wet season and dry season, the distributions of ID, IO, OD and OO also exhibit certain variations between these two seasons, particularly in the ranges of W3 and D3. Similarly, they are more closely aligned between the wet season and the entire year. The higher similarity between the results during the wet season and those in the entire year can be attributed to the greater number of MDEs occurring during the wet season than the dry season. The distributions of both IO and OO across the entire basin appear dispersed during both wet and dry seasons, yet each subregion displays a discernible trend. This further highlights the necessity of assessing the MDE spatial propagation patterns separately for each subregion. Remarkably, the MDE spatial propagation patterns across different subregions are different, due to the driving action of distinct atmospheric processes. Therefore, a more detailed investigation from the perspectives of these subregions is imperative to unravel the intricate MDE spatial propagation patterns and the underlying mechanisms.

Fig. 5
figure 5

Spatial distributions of network divergence (ND) (a − c), indegree (ID) and inward orientation (IO) (d − f), and outdegree (OD) and outward orientation (OO) (g − i) derived from the MDE spatial propagation networks of the whole YRB for the entire year (left panels), wet season (middle panels), and dry season (right panels), respectively. The IO and OO results are presented using black arrows, sampled uniformly at a proportion of 10% for improved visual clarity

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4.3 MDE spatial propagation patterns within individual subregions

The distributions of metrics derived from the MDE spatial propagation networks of individual subregions during both wet and dry seasons are presented in Fig. 6a-f. It is evident that each subregion exhibits distinctive spatial propagation patterns of MDEs during these two seasons. The spatial distributions of source and sink zones, as well as the strengths and directions within each subregion, closely align with the overall findings across the YRB. Notably, the differences in MDE spatial propagation patterns within individual subregions between wet and dry seasons are evident. For instance, compared to W1, D1 demonstrates more dispersed source zones covering a larger area, while its sink zones are more concentrated. Moreover, D1 exhibits greater diversity in MDE propagation directions beyond the prevailing westward trend. In contrast, W2 shows more intricate patterns of MDE spatial propagation compared to D2. W2 features dispersed source and sink zones, with MDE pathways exhibiting a mix of westerly and easterly directions. Conversely, D2 primarily displays source zones in the northeast and sink zones in the southwest, resulting in southwest-oriented MDE propagation. Despite both W3 and D3 exhibiting westward MDE propagation directions, a notable disparity exists in their northwest regions. In W3, the northwest region comprises predominantly sink zones, whereas in D3, it primarily consists of source zones. Consequently, the MDE propagation directions in this region differ between W3 and D3. W4 displays a complex MDE spatial propagation pattern characterized by multiple source and sink zones and diverse pathways. The source zones primarily lie along the boundary of the central and eastern parts, while the sink zones are concentrated in the western parts and central area of the eastern parts. D4, occupying the eastern parts of W4, features sink zones concentrated in central areas surrounded by source zones. Conversely, D5 occupies the western and central parts of W4 and displays a relatively simpler MDE spatial propagation pattern. In D5, the source zones are primarily located in the northern and southeastern boundary areas, while the sink zones are concentrated mainly in the southwestern and central parts. These observations highlight the diversity of MDE spatial propagation patterns among various subregions between the wet and dry seasons, potentially driven by distinct atmospheric processes during these periods. Further analysis of regional circulation anomalies is imperative to uncover the underlying mechanisms behind these subregion-specific spatial propagation patterns of MDEs.

Fig. 6
figure 6

Spatial distributions of ND (a − b), ID and IO (c − d), and OD and OO (e − f) derived from the MDE spatial propagation networks of individual subregions for the wet season (left panels) and dry season (right panels), respectively. The IO and OO results are presented using black arrows, sampled uniformly at a proportion of 10% for improved visual clarity

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4.4 Driving mechanisms behind MDE spatial propagation within individual subregions

The underlying mechanisms driving the spatial propagation of MDEs in various subregions during both wet and dry seasons are investigated by analyzing relevant circulation anomalies. The analysis involves several steps: (1) For each subregion, months wherein MDEs originate from in the source zones are identified. (2) Among the identified months, only those aligning with the MDE spatial propagation pathways from source zones to sink zones within a 3-month window are selected as the typical occurrence months of MDE spatial propagation. These selected months, along with the subsequent two months, serve as the typical MDE spatial propagation periods. (3) Correspondingly, the 3-month composites of 500 hPa geopotential height, 700 hPa wind vectors, and integrated water vapor flux and its divergence are computed and the anomalies of these three variables relative to the climatology of 1991 − 2020 are estimated.

The detailed representations of typical MDE spatial propagation processes in each subregion are provided in Figs. S1-S9, which depict the spatial migrations of MDE occurrence areas during typical MDE spatial propagation periods in all the subregions, illustrating how MDEs propagate over time. Compared to Fig. 5, it is evident that the spatial migration trajectories closely adhere to the prevailing MDE spatial propagation pathways in respective subregions. This consistency underscores the reliability of the identified typical processes of the MDE spatial propagation in characterizing its representative behaviors. To further investigate the underlying mechanisms driving the MDE spatial propagation in each subregion in both dry and wet seasons, Figs. 7–10 show the anomalies in geopotential height, wind vectors, and integrated water vapor flux and its divergence during typical MDE spatial propagation periods in both two seasons. To compare conveniently, these figures adopt a uniform color gradient and scale ratio with symmetrically center at zero for both positive and negative anomalies. This approach allows for a clear examination of circulation anomalies associated with the MDE spatial propagation across different subregions and seasons.

Fig. 7
figure 7

Anomalous circulation fields during typical MDE spatial propagation periods of Subregions W1 (a − b) and D1 (c − d), respectively. (a) 500 hPa geopotential height (shading, unit: gpm) and 700 hPa wind (vectors, unit: m·s−1) anomalies for W1; (b) integrated moisture flux (vectors, unit: kg·m−1·s−1) and divergence (shading, unit: 10−6 kg·m−2·s−.1) anomalies for W1; (c, d) analogously to (a, b) but for D1

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  1. 1

    Subregions W1 and D1

Figure 7a, b presents the anomalies of atmospheric variables during typical MDE spatial propagation periods of W1. In Fig. 7a, it is observed that the geopotential height in the northeastern side of W1 is notably stronger than the climatological normal level. This heightened geopotential height suggests the reinforcement and westward expansion of the Western Pacific Subtropical High (WPSH). Situated at the southwestern periphery of the anticyclonic circulation anomaly, W1 is characterized by decreasing positive anomalies of geopotential height from its east part to west part. Consequently, this atmospheric condition induces prevalent subsidence and a diminished transport of water vapor within the subregion. Furthermore, an anomalous low-pressure system is evident over northern China. This atmospheric circulation pattern fosters the dominance of westerlies in mid-high latitudes, impeding the southward intrusion of cold air masses. Consequently, the conditions for the convergence of warm and cold air masses are unfavorable, thereby suppressing convective activities and impeding the generation of precipitation within W1 (Wei et al. 2022). Additionally, W1 is located near the southeastern edge of the Tibetan Plateau, where the geographical location coupled with the plateau’s topography and thermal variations frequently products low-level vorticity during summer and contributes to heightened rainfall in this subregion (Yin and Li 2013). The positive geopotential height anomalies observed over the plateau signify a weakening of low-level vorticity, which subsequently curtails precipitation generation within W1. Figure 7b reveals how the WPSH and anticyclonic circulation anomaly obstructs the moisture transport into W1. The anomalous water vapor transport in the southern side of W1 suppresses the influx of water vapor from the Bay of Bengal and the South China Sea, leading to moisture divergence within this subregion. Moreover, the abnormal water vapor transport pathways in W1 align with the observed MDE spatial propagation directions in W1, which suggests that variations in moisture transport significantly contribute to the spatial propagation of MDEs in this subregion.

Figure 7c, d shows the anomalies of atmospheric circulation during typical MDE spatial propagation periods of D1. In Fig. 7c, an evident strengthening and westward shift of the WPSH is also apparent. The persistent weakening of the southern branch trough, i.e., the semi-permanent low-pressure trough over the Bay of Bengal on the south side of the Tibetan plateau during the winter months, induces a reduced moisture transport from the Bay of Bengal, which can be seen in Fig. 7d (Wang and Li 2010). Figure 7c also illustrates that the variations of westerlies in mid-high latitudes influence the intensity and frequency of southward-moving cold air during the dry season, which lead to the northward and eastward shifts of cold air activity. The atmospheric circulation configuration also restricts the moisture transport from the westerlies. Consequently, the moisture divergence prevails over D1, indicating the dry conditions experienced during this period, as depicted in Fig. 7d. Different from westerly wind anomalies within W1, Fig. 7d illustrates that the water vapor transport anomalies in D1 vary slightly, which may be attributed to the multidirectional nature of the MDE spatial propagation in this subregion.

  1. 2

    Subregions W2 and D2

Figure 8a, b displays the atmospheric circulation anomalies during typical MDE spatial propagation periods of W2. In Fig. 8a, it is evident that the WPSH intensifies and extends westward, forming a connected high-pressure belt that breaks through the topographical barrier of the Tibetan Plateau with the eastward extension and northward jump of the South Asian High (SAH). The SAH is a prominent warm high-pressure system in the upper troposphere and plays a crucial role in regulating the atmospheric circulation in China (Zhang 2001). This configuration leads to a weakened moisture transport and prevailing downdraft from the upper air over W2. Furthermore, the westerlies prevailing in mid-high latitudes hinder the southward penetration of cold air and lead to weak conditions for the convergence of warm and cold air masses, which suppresses convective activities and makes it difficult to generate precipitation. The anticyclonic circulation anomaly linked to the high-pressure belt induces anomalous easterly winds over the south of W2, restricting the water vapor transport from the Bay of Bengal, South China Sea, and Western Pacific, and accelerating moisture divergence over this subregion (Fig. 8b). Figure 8b also illustrates the prevalence of northeasterly moisture transport anomalies in W2, which corresponds to the dominant MDE spatial propagation direction and suggest a close relationship between variations in moisture transport and the MDE spatial propagation in this subregion.

Fig. 8
figure 8

Anomalous circulation fields during typical MDE spatial propagation periods of Subregions W2 (a − b) and D2 (c − d), respectively. (a) 500 hPa geopotential height (shading, unit: gpm) and 700 hPa wind (vectors, unit: m·s−1) anomalies for W2; (b) integrated moisture flux (vectors, unit: kg·m−1·s−1) and divergence (shading, unit: 10−6 kg·m−2·s−.1) anomalies for W2; (c, d) analogously to (a, b) but for D2

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The atmospheric circulation anomalies during typical MDE spatial propagation periods of D2 are presented in Fig. 8c, d. It is observed from Fig. 8c that the intensified and eastly extended Mongolian High, located over Mongolian Plateau during the dry season, engenders a stronger East Asian winter monsoon. This phenomenon may be related to the anomalous propagation of Rossby waves in the middle and upper troposphere (Huang et al. 2012). The energy carried by Rossby waves from the North Atlantic can propagate eastward across Eurasia and accumulate in the East Asia–Pacific region, intensifying the East Asian monsoon and influencing the climate in East Asia (Xu et al. 2017). It is worth noting that the East Asian trough is a significant planetary-scale stationary trough positioned in the midlatitude western Pacific Ocean (Leung et al. 2022). Positioned behind the East Asian trough, D2 is affected by recurrent disturbances from the East Asian cold air outbreak. The intersection of robust anomalous northerly winds from the eastern part of the anticyclonic circulation anomaly and the western part of the cyclonic circulation anomaly governs D2, where strong anomalous northerly winds facilitate the southward penetration of cold air. The negative geopotential height anomalies over the Western Pacific indicates the weakened intensity of the WPSH. As a result, the warm and moist air on the western side of the WPSH fails to reach D2, inhibiting its convergence with the incoming cold air. The atmospheric circulation configuration also restricts the moisture transport from the westerlies. The lack of warm and humid air, coupled with the dominance of cold air, impedes the convective activity and the formation of precipitation, thereby contributing to the prevailing moisture divergence in D2 (Fig. 8d). Notably, Fig. 8d also illustrates that the northeasterly water vapor transport within D2 corresponds to the observed MDE spatial propagation pattern in this particular subregion.

  1. 3

    Subregions W3 and D3

For W3, the atmospheric circulation anomalies during its typical MDE spatial propagation periods are depicted in Fig. 9a, b. Situated at the northern boundary of W3, the WPSH intensifies and extends westward. Meanwhile, the anomalous easterly winds on the south side of the anticyclonic circulation anomaly deflecting towards W3. This atmospheric circulation configuration impedes the inflow of warm and humid moisture and the convergence of cold and warm airflows within W3, which in turn contributes to decreased rainfall. Similar to the wind field, the abnormally low water vapor transport into the eastern part of W3 deflects both westward and northward, creating favorable conditions for the MDE spatial propagation.

Fig. 9
figure 9

Anomalous circulation fields during typical MDE spatial propagation periods of Subregions W3 (a − b) and D3 (c − d), respectively. (a) 500 hPa geopotential height (shading, unit: gpm) and 700 hPa wind (vectors, unit: m·s−1) anomalies for W3; (b) integrated moisture flux (vectors, unit: kg·m−1·s−1) and divergence (shading, unit: 10−6 kg·m−2·s−.1) anomalies for W3; (c, d) analogously to (a, b) but for D3

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As for the dry season, Fig. 9c highlights the intensification of the Mongolian High and the deepening of the East Asian trough, which are indicators of strengthening East Asian winter monsoon. D3, positioned behind the East Asian trough, is affected by recurrent disturbances from the East Asian cold air outbreak. Similar to D2, D3 is under the control of strong anomalous northerly winds and consequently facilitates the southward penetration of cold air. Similar to the negative geopotential height anomalies over the Western Pacific in Fig. 8c, those shown in Fig. 9c indicate a weakened and eastward-shifted WPSH. The inability of the warm and moist air from the Western Pacific and westerlies to converge with incoming cold air leads to persistent drought conditions in D3. Moreover, this anomalous moisture transport pattern is also conducive to the MDE spatial propagation in this subregion.

  1. 4

    Subregions W4, D4 and D5

The atmospheric circulation anomalies of W4 during its typical MDE spatial propagation periods are illustrated in Fig. 10a, b. It is found that the variations of the SAH and WPSH differ from those observed in the other subregions. The northward and eastward extension of the SAH, along with the southward and eastward retreat of the WPSH, collectively yield adverse conditions for moisture transport within W4. W4 becomes subject to the northeasterly flow originating from the southeastern part of the anticyclonic anomaly. Figure 10b shows that the anomalous water vapor transport pathways in the southern part of W4 suppress the influx of water vapor from the Bay of Bengal and the South China Sea, exacerbating the water vapor divergence within W4. The abnormally low water vapor transport into W4 also align with the dominant spatial propagation directions of MDEs in this subregion.

Fig. 10
figure 10

Anomalous circulation fields during typical MDE spatial propagation periods of Subregions W4 (a − b), D4 (c − d) and D5 (e − f), respectively. (a) 500 hPa geopotential height (shading, unit: gpm) and 700 hPa wind (vectors, unit: m·s−1) anomalies for W4; (b) integrated moisture flux (vectors, unit: kg·m−1·s−1) and divergence (shading, unit: 10−6 kg·m−2·s−.1) anomalies for W4; (c, d) and (e, f) analogously to (a, b) but for D4 and D5

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Figure 10c, d illustrates the influence of the high-pressure ridge and the weakened East Asian trough on D4, as evidenced by westerly airflows originating from the eastern part of the anticyclonic anomaly. Additionally, the prevailing westerlies in mid-high latitudes result in a reduced ability for cold air to penetrate into D4. These atmospheric conditions suppress the inflow of water vapor from westerlies and hinder the convergence of warm and cold air masses within this subregion. Similar to water vapor transport anomalies observed in D1, Fig. 10d illustrates that the water vapor transport anomalies in D1 vary slightly. This variance may be attributed to the relatively complex MDE spatial propagation patterns observed in this subregion.

Figure 10e, f also demonstrates a weakness in the strength of the East Asian trough in the north side of D5. Located at the northeast side of the anticyclonic anomaly, D5 is controlled by westerly flow anomalies. The surrounding high-pressure ridge similarly restricts the invasion of cold air the input of warm and humid airflow, further resulting in moisture divergence over this subregion. The westerly water vapor transport anomalies into D4 also corresponds to the dominant direction of the MDE spatial propagation in this subregion.

The findings in this study emphasize the intricate interplay between the MDE spatial propagation patterns and varying controlling circulation systems across various subregions during both wet and dry seasons. These anomalous circulation systems give rise to perturbed wind patterns and altered water vapor transport dynamics, consequently leading to a reduction of water vapor supply and unfavorable precipitation conditions within these subregions. It is found that the dominant MDE spatial propagation directions in almost all the subregions are consistent with the trajectories of abnormally low water vapor transport pathways, which further demonstrate that deficient moisture transport plays a crucial role in influencing the MDE spatial propagation within these subregions. These findings are consistent with those in previous studies (Gimeno et al. 2012; Hoerling et al. 2014; Herrera-Estrada et al. 2017, 2019; Konapala et al. 2022), indicating that an insufficient moisture flux, particularly the large-scale deficit of atmospheric water transport over land through oceans, has the potential to lead to a reduction in precipitation downwind and thereby triggers or exacerbates the MDE spatial propagation. These findings contribute to our understanding in the intricate nature of the MDE spatial propagation within these subregions.

4.5 Potential influencing factors for MDE spatial propagation in the YRB

Preliminary large-scale atmosphere–ocean coupling interactions, particularly variations in tropical sea surface thermal conditions such as El Niño-Southern Oscillation (ENSO), the Western Pacific Warm Pool, and Indian Ocean sea surface temperature anomalies, play a crucial role in causing the atmospheric circulation anomalies during MDE spatial propagation periods. These variations exert a notable influence on key atmospheric phenomena including the Asian monsoon, the WPSH, and the SAH (Xie et al. 2009; Wu et al. 2010; Dai 2013; Li and Ting 2015; Zhang et al. 2019). For instance, during El Niño events, the suppressed convective activity spanning from the South China Sea to the Western Indian Ocean hinders the northward transport of warm and moist air towards the Bay of Bengal, the Indochina Peninsula, and the upstream regions of the YRB. Additionally, warm Pacific currents contributes to the dispersion of tropical water vapor away from these target regions. As a result, the reduced water vapor inflow from the South China Sea to the upstream basin increases the likelihood of drought in those areas. Conversely, during La Niña episodes, the Walker circulation intensifies, causing robust ascending motion near the equatorial Western Pacific Warm Pool and relatively weaker ascending motion over the Indian Ocean. This weakens the Hadley circulation and yields a weaker and eastward-shifted WPSH alongside weakened westerly winds prevailing within the mid-latitudes. These atmospheric states facilitate the southward incursion of cold air, engendering downdraft across the middle and lower reaches of the YRB. Consequently, the amount of water vapor originating from the Indian Ocean and the Bay of Bengal to these areas experiences reduction, resulting in diminished precipitation. Furthermore, the negative phases of the Indian Ocean Dipole (IOD) are conducive to the development of anomalous anticyclonic circulation in the Northwest Pacific, which strengthen both the WPSH and SAH and thereby suppress the moisture transport from the South China Sea and affect the summer precipitation in the YRB.

The Tibetan Plateau also plays a critical role in influencing the anomalous circulation systems during MDE spatial propagation. The plateau’s unique topography and thermal characteristics wield substantial impacts on the regional climate and atmospheric circulation dynamics during both wet and dry seasons (Duan et al. 2012). During the wet season, robust radiation over the Tibetan Plateau leads to a pronounced increase in surface temperature, resulting in the formation of a high-temperature and low-pressure center near the ground surface. This center, in conjunction with the Indian Low Pressure, enhances the Indian monsoon and promotes the strengthening of the southwestern monsoon in China. The low-level convergence heating core over the Tibetan Plateau leads to the formation of SAH. When the downdraft on the eastern side of the SAH and the Hadley circulation on the southern side of the WPSH converge and control the middle and lower reaches of the YRB, the high-temperature and dry conditions will occur in these areas. In winter, the elevated altitude and widespread snow cover across the Tibetan Plateau facilitate rapid radiative cooling near the ground surface, creating a high-temperature and high-pressure center. This pronounced temperature gradient between the plateau and the southern atmospheric domain accentuates the intensity of southward intrusion by the southern westerly flow. Along with the Mongolian High, this high-pressure center amplifies the convergence of airstreams from the plateau’s northeast side and southward flow originating from the Mongolian High. This additive effect substantially intensifies the strength of winter monsoon. Furthermore, the reduction of winter-to-spring snow coverage over the Tibetan Plateau would lead to enhanced heating of the plateau during summer, thereby strengthening the following East Asian summer monsoon (Ding et al. 2008, 2018).

The self-propagation of MDEs induced by land–atmosphere feedback is another important driving factor of MDE spatial propagation across the subregions (Seneviratne et al. 2010; Schumacher et al. 2022). It plays a pivotal role in amplifying and prolonging drought conditions within the influenced domains. During the MDE spatial propagation periods, the reduced precipitation in the source zones leads to soil drying. The dry soil surface results in limited evaporation and reduced humidity near the surface and then extends vertically through the lower atmosphere, which finally lead to a reduction in water vapor transport to the downwind sink zones. As a consequence, the sink zones experience decreased precipitation and the occurrences of MDEs. Overall, this feedback loop contributes to the persistence and severity of drought conditions and enhances the spatial propagation of MDEs in the subregions.

5 Conclusions

This study employed the complex network-based methodology to explore the MDE spatial propagation patterns and underlying mechanisms over the YRB. The proposed methodology exhibits good generality and expansibility, positioning it as a promising tool for assessing associated hazard risks and forecasting evolving dynamics of drought events. The key findings are summarized as follows:

  1. 1.

    The MDE synchronized subregions in the YRB, identified by the MDE synchronization networks, differ between the wet and dry seasons. Specifically, in the wet season, the YRB is segmented into four subregions, whereas during the entire year and dry season, it is divided into five subregions.

  2. 2.

    The spatial distributions of source and sink zones, as well as the strengths and directions of the MDE spatial propagation within each subregion, closely align with the overall findings across the YRB, which were identified by the MDE spatial propagation networks. Furthermore, the MDE spatial propagation patterns within individual subregions for the wet and dry seasons are evidently different.

  3. 3.

    The variations of tropical sea surface thermal conditions, coupled with influences of the Tibetan Plateau and MDE self-propagation triggered by land–atmosphere feedback, collectively contribute to the perturbations of large-scale circulation systems. These perturbations manifest as anomalies in wind patterns and water vapor distribution, resulting in conditions of water vapor deficiency or inadequate precipitation in certain subregions during both wet and dry seasons. As a result, conducive circumstances are established for the spatial propagation of MDEs along dominant water vapor transport pathways, irrespective of wet or dry seasons.

This study quantified the MDE spatial propagation patterns and revealed their forming causes in detail at a basin scale, which provides great potential to develop circulation anomaly-based spatial prediction models for meteorological droughts and is capable of making early warning for areas that are at risk of MDEs. In addition, the potential variations in the spatial characteristics of MDE evolutions under the influences of teleconnection factors, such as the ENSO, Pacific Decadal Oscillation (PDO), Arctic Oscillation (AO), North Atlantic Oscillation (NAO), Indian Ocean Dipole (IOD), etc., climate warming and intensified human activities are worthy to be further explored in the future.