# Synchronized Structure and Teleconnection Patterns of Meteorological Drought Events over the Yangtze River Basin, China

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

^{2}, constituting around one-fifth of China’s mainland territory [43]. This basin is situated within a humid and semi-humid region with a remarkable monsoon climate. This implies that its response to climate change is intricate and volatile, as reflected in drought events with short-term fluctuations [44]. Consequently, it is susceptible to recurring seasonal drought events [45].

## 3. Methodology

#### 3.1. Extraction of Grid-Based MDEs and Relevant MDE Characteristics over the YRB by Run Theory

#### 3.2. Calculation of the MDE Synchronized Matrix over the YRB by Event Synchronization (ES)

_{i}and the mth occurrence time of MDEs in E

_{j}, respectively. Furthermore, n

_{i}and n

_{j}represent the total number of extracted MDEs for grids i and j, respectively. The dynamic delay ${\tau}_{lm}^{ij}$ of MDEs occurring at ${t}_{l}^{i}$ and ${t}_{m}^{j}$ is defined as follows:

_{ij}between grids i and j is defined as follows:

_{ij}= 1 indicates complete MDE synchronization between grids i and j, while Q

_{ij}= 0 stands for the absence of MDE synchronization. Repeat the procedure described above for all pairwise grids within the YRB, and the MDE synchronized matrix Q can be obtained. This matrix is square and symmetric, representing the MDEs’ synchronized patterns between different grid locations.

#### 3.3. Construction of the MDE Synchronized Network over the YRB by a Complex Network (CN)

^{Q}[51]. In other words, only the highest5% MDE synchronized strength values between all node pairs remained and were utilized to build the undirected adjacency matrix A

^{Q}, which is expressed as follows:

^{Q}is 0.865. Furthermore, to assess the statistical significance of these linked edges, a test based on independent and uniformly random distribution of events from the work of Boers et al. [52] was employed. The test yielded probability values of 0.01 for Ɵ

^{Q}. Thus, all linked edges corresponded to significant values of ES. Based on the A

^{Q}matrix, the MDE synchronized network over the YRB was constructed, which contained the synchronized MDE information between grid pairs within the YRB.

#### 3.4. Quantification of MDEs’ Synchronized Structure over the YRB by Network-Based Metrics

- (1)
- Degree k
_{i}measures the number of edges that node i has in the network; these connected nodes make up the adjacent nodes of node i. Degree centrality DC_{i}is the normalized result of k_{i}, which is formulated as follows:

- (2)
- MSD represents the average geographic distance between a node and its adjacent nodes in the network. MSD
_{i}can be mathematically expressed as follows:

_{ij}represents the geographic distance between node i and its adjacent node j. In the network, the MSD of a node provides insights into its spatial extent of MDE synchronization.

- (3)
- BC is a metric that identifies nodes that act as intermediaries or bridges in the network. BC
_{i}is defined as the proportion of the shortest path number between node pairs passing through node i to the total number of the shortest paths of these node pairs in the network, which is shown as follows:

- (4)
- The CC of a node measures the proportion of its neighbors that are also connected to one another, which is defined as follows:

_{i}is the degree of node i, while β and ${k}_{i}({k}_{i}-1)/2$ represent the actual number of edges and the maximum possible number of edges among the adjacent nodes of node i, respectively. In the MDE synchronized network, a high CC value for a node suggests that the nodes in its neighborhood are closely interconnected, displaying spatial coherence in the MDE occurrences. However, events in such regions are less likely to synchronize with geographically distant neighbors.

_{c}was obtained by dividing the uncorrected (original) metric M

_{u}by the boundary-affected metric from the 100 surrogate networks M

_{b}, as shown below:

#### 3.5. Partitioning of MDE Synchronized Subregions within the YRB by the Leiden Algorithm

^{Q}; k

_{i}and k

_{j}are the numbers of edges adjacent to nodes i and j, respectively (i.e., the degree of nodes i and j); S

_{i}and S

_{j}are the communities to which nodes i and j belong, respectively; $\delta ({S}_{i},{S}_{j})$ is 1 if nodes i and j belong to the same community and 0 otherwise. Higher modularity values indicate denser intracommunity links and sparser intercommunity links. This suggests that the network is effectively divided into distinct and non-overlapping communities, revealing meaningful association patterns between nodes within each community. By maximizing the modularity, the Leiden algorithm is capable of achieving a more effective partitioning of the network, enabling the identification of MDE synchronized subregions within the YRB.

#### 3.6. Identification of MDE Representative Grids in MDE Synchronized Subregions by the Z − P Space Approach

_{i}is the degree of node i in community S

_{i}, $\overline{{K}_{{S}_{i}}}$ is the average degree of all nodes in community S

_{i}, and ${\sigma}_{{K}_{{S}_{i}}}$ is the standard deviation of all degrees in S

_{i}. Since two nodes with similar Z values may play different roles within the community, this measure is often combined with the participation coefficient P for a more comprehensive assessment of node representativeness.

_{i}compares the number of links of node i to nodes in all communities with the number of links within its own community. The P

_{i}of node i is defined as follows:

_{m}represents the number of communities in the network, ${k}_{i{S}_{j}}$ is the number of links of node i to nodes in community S

_{j}, and k

_{i}is the degree of node i in the network. Essentially, P measures how uniformly a node’s links are distributed among all of the communities. If a node’s links are evenly spread across different communities, its p value is close to one. Conversely, if all of its links are confined within its own community, its p value is zero. The grid with the highest number of intracommunity links is designated as the MDE representative grid based on the argument that it shows the strongest MDE synchronization within the subregion [61].

#### 3.7. Evaluation of MDE Teleconnection Patterns of MDE Synchronized Subregions by Wavelet Coherence Analysis (WCA)

_{t}} and Y{Y

_{t}} was defined by Torrence and Compo [66] as follows:

_{scale}(ς

_{time}(W(s,t))), where ς

_{scale}denotes smoothing along the wavelet scale axis and ς

_{time}denotes smoothing over time. W

_{xy}represents the cross-wavelet coefficient between X and Y. W

_{x}(s,t) and W

_{y}(s,t) denote the wavelet coefficients obtained from the wavelet transform of X and Y at scale s and time t, respectively.

_{s}is the number of points with the COI and n

_{s}= t

_{2}− t

_{1}+1. The GWC results are used to characterize the associations between MDEs in individual subregions and the four teleconnection factors at different timescales.

## 4. Results and Discussion

#### 4.1. MDEs’ Synchronized Structure over the YRB

#### 4.2. Synchronized Subregions and Representative Grids of MDEs within the YRB

#### 4.3. MDE Characteristics of MDE Synchronized Subregions

#### 4.4. MDE Teleconnection Patterns of MDE Synchronized Subregions

## 5. Conclusions

- ●
- The northeastern portion of the YRB exhibits significant MDE synchronization, as evidenced by its high DC and MSD values. These characteristics make this region more susceptible to experiencing widespread MDEs. Conversely, specific areas in the upper reaches, characterized by low DC and MSD values, suggest a higher likelihood of localized MDE occurrences. The BC results highlight the propagation of synchronous MDEs along two main pathways: the central pathway and the eastern pathway. These two pathways display relatively low MDE spatial coherence, as indicated by the low CC values.
- ●
- The YRB is partitioned into eight MDE synchronized subregions, and the spatial ranges of the individual subregions are consistent with the MDE synchronized scales identified from the DC and MSD results. Each subregion exhibits distinct characteristics in terms of the frequency, duration, total severity, and peak of MDEs, as well as distinct MDE temporal frequency distributions. Among these subregions, Subregion 3 in the southeast experiences the fewest MDEs, while Subregion 1 in the southwest has the highest MDE duration value and the strongest MDE total severity value. Additionally, Subregions 3, 5, 6, and 7 in the southeast and north show relatively low MDE peak values. In Subregions 1–7, the season with the highest MDE frequency gradually shifts from winter to summer, while Subregion 8 in the northwest exhibits greater month-to-month fluctuations in the MDEs’ temporal frequency.
- ●
- The MDE synchronized subregions exhibit significant variability in MDE teleconnection patterns at multiple timescales. ENSO exerts a strong influence on MDEs in all subregions, whereas the influence effects from other teleconnection factors (i.e., the PDO, NAO, and AO) are relatively weaker. Specifically, the PDO shows a significant association with MDEs in all subregions except for Subregion 3 in the southeast, the NAO displays a significant influence on the MDEs in the southern subregions of the YRB (Subregions 1, 2, and 3), and the AO has a more pronounced influence on the MDEs in the northern subregions of the YRB (Subregions 4, 5, and 6).

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Hypothetical demonstration for extracting meteorological drought events (MDEs) based on the series of 3-month standardized precipitation evapotranspiration index (SPEI-3) of grids i and j. The upper and lower subplots represent the SPEI-3 series of grids i and j, respectively. The orange-shaded regions denote the extracted MDEs with a duration of no less than 3 months. The numbers of MDEs at grid i and grid j are 4 and 6, respectively. The red lines indicate the occurrence time of the MDEs. The gray-shaded regions show three groups of synchronously occurring MDEs at grids i and j, where the first group presents the MDE at grid i occurring later than that at grid j, the second group shows the MDEs at both grids occurring simultaneously, and the last group exhibits the MDE at grid i occurring earlier than that at grid j. The identified duration, total severity, and peak of the first MDE of grid i are also represented in the upper subplot.

**Figure 4.**Spatial distributions of (

**a**) uncorrected degree centrality (DC) values obtained from the original MDE synchronized network over the YRB, (

**b**) boundary-affected DC values obtained from 100 surrogate networks, and (

**c**) corrected DC values calculated by dividing the uncorrected DC values by the boundary-affected DC values.

**Figure 5.**Spatial distribution of mean synchronized distance (MSD) obtained from the MDE synchronized network over the YRB.

**Figure 6.**Spatial distributions of (

**a**) uncorrected betweenness centrality (BC) obtained from the original MDE synchronized network over the YRB, (

**b**) boundary-affected BC obtained from 100 surrogate networks, and (

**c**) corrected BC calculated by dividing the uncorrected BC values by the boundary-affected BC values.

**Figure 7.**Spatial distributions of (

**a**) uncorrected clustering coefficient (CC) obtained from the original MDE synchronized network over the YRB, (

**b**) boundary-affected CC obtained from 100 surrogate networks, and (

**c**) corrected CC calculated by dividing the uncorrected CC values by the boundary-affected CC values.

**Figure 8.**Spatial distribution of MDE synchronized subregions and MDE representative grids over the YRB.

**Figure 9.**Spatial distributions of (

**a**) frequency, (

**b**) duration, (

**c**) total severity, and (

**d**) peak for grid-based MDEs over the YRB during 1961–2021.

**Figure 11.**Global wavelet coherence (GWC) results between four teleconnection factors (ENSO, PDO, NAO, and AO) and the SPEI-3 series of MDE representative grids within all of the MDE synchronized subregions. GWC values are shown as black lines, and significant influences (at the 95% significance level) are marked in red.

Teleconnection Factors | Time Frame | Data Source | Access Date |
---|---|---|---|

ENSO | 1961–2021 | http://www.esrl.noaa.gov/psd/data/correlation/nina34.data | 22 October 2023 |

PDO | 1961–2021 | http://www.ncdc.noaa.gov/teleconnections/pdo/ | 22 October 2023 |

NAO | 1961–2021 | https://www.ncdc.noaa.gov/teleconnections/nao/ | 22 October 2023 |

AO | 1961–2021 | https://www.ncdc.noaa.gov/teleconnections/ao/ | 22 October 2023 |

Subregion | Frequency | Duration | Total Severity | Peak |
---|---|---|---|---|

1 | 17.8 | 4.4 | −44.1 | −2.6 |

2 | 18.3 | 3.9 | −38.8 | −2.5 |

3 | 16.1 | 3.9 | −36.3 | −2.8 |

4 | 17.8 | 3.8 | −36.5 | −2.6 |

5 | 18.1 | 3.7 | −38.2 | −3.4 |

6 | 17.8 | 3.9 | −38.5 | −2.9 |

7 | 18.2 | 3.8 | −36.5 | −2.8 |

8 | 18.0 | 4.0 | −41.2 | −2.6 |

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**MDPI and ACS Style**

Liu, L.; Gao, C.; Zhu, Z.; Tang, X.; Zhang, D.; Zhang, S.
Synchronized Structure and Teleconnection Patterns of Meteorological Drought Events over the Yangtze River Basin, China. *Water* **2023**, *15*, 3707.
https://doi.org/10.3390/w15213707

**AMA Style**

Liu L, Gao C, Zhu Z, Tang X, Zhang D, Zhang S.
Synchronized Structure and Teleconnection Patterns of Meteorological Drought Events over the Yangtze River Basin, China. *Water*. 2023; 15(21):3707.
https://doi.org/10.3390/w15213707

**Chicago/Turabian Style**

Liu, Lei, Chao Gao, Zhanliang Zhu, Xiongpeng Tang, Dongjie Zhang, and Silong Zhang.
2023. "Synchronized Structure and Teleconnection Patterns of Meteorological Drought Events over the Yangtze River Basin, China" *Water* 15, no. 21: 3707.
https://doi.org/10.3390/w15213707