# Temporal Pattern Analysis of Local Rainstorm Events in China During the Flood Season Based on Time Series Clustering

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Rainfall Data

#### 2.2. Methods

#### 2.2.1. Standardization and Grouping of Rainfall Time Series

#### 2.2.2. Time Series Clustering

- (1)
- Each element in the time series set is taken as an initial cluster. For a set with $m$ elements $D=\left\{{x}_{1},{x}_{2},\dots ,{x}_{m}\right\}$, the initial cluster $C=\left\{{C}_{1},{C}_{2},\dots ,{C}_{m}\right\}$, in which ${C}_{j}=\left\{{x}_{j}\right\}$;
- (2)
- Calculate the distance matrix $M$, whose element $M\left(i,j\right)=d\left({C}_{i},\text{}{C}_{j}\right)$ and $M\left(i,j\right)=M\left(j,i\right)$, $d\left({C}_{i},\text{}{C}_{j}\right)$ is the distance between cluster ${C}_{i}$ and ${C}_{j}$;
- (3)
- Find the closest two clusters ${C}_{i\ast}$ and ${C}_{j\ast}$ and merge them: ${C}_{i\ast}={C}_{i\ast}{{\displaystyle \cup}}^{\text{}}{C}_{j\ast}$. Renumber the clusters and delete the $j\ast $th row and $j\ast $th column of matrix $M$;
- (4)
- Repeat the previous step until all clusters merge into one cluster, and then a clustering tree is obtained.

#### 2.2.3. Extraction of Representative Temporal Patterns

## 3. Results and Discussion

#### 3.1. Representative Temporal Patterns

#### 3.2. Statistical Characteristics of the Clusters and Temporal Patterns

#### 3.3. Regional Analysis of Rainstorm Characteristics

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**Matching patterns of Euclidean distance and dynamic time warping (DTW). (

**a**) Matching based on trace points by Euclidean distance; (

**b**) matching based on trace points by DTW.

Geographical Zones | Latitude and Longitude Range of Stations | Scope of Flood Season | No. of Stations | No. of Events |
---|---|---|---|---|

Northeast China | 41.1° N–47.9° N 123.4° E–132° E | June–September | 18 | 1255 |

North China | 36.1° N–42.5° N 111.2° E–118.6° E | June–September | 21 | 1384 |

Central China | 25° N–30.1° N 110.9° E–112.9° E | April–October | 6 | 1150 |

East China | 24.5° N–33.2° N 114.9° E–121° E | April–September | 26 | 4958 |

South China | 22.9° N–26° N 109.1° E–114.1° E | April–October | 8 | 2027 |

Northwest China | 32.4° N–39° N 107.1° E–110.4° E | June–October | 9 | 782 |

Southwest China | 23.4° N–32.5° N 99.3° E–108.3° E | May–October | 11 | 1743 |

Duration Section | Clusters | No. of Events (Percentage) | Intensity /mm | Peak Value /mm | Rainfall Depth /mm | Ratio of Peak Value to Rainfall Depth |
---|---|---|---|---|---|---|

[3, 6) | Cluster I | 432 (17.9%) | 3.8 | 7 | 15.5 | 41.70% |

Cluster II | 658 (27.2%) | 4.8 | 10 | 18 | 54.50% | |

Cluster III | 334 (13.8%) | 5.2 | 13.1 | 20 | 65.80% | |

Cluster IV | 454 (18.8%) | 4.8 | 13.5 | 18 | 73.90% | |

Cluster V | 537 (22.2%) | 5.1 | 16 | 18 | 88.70% | |

[6, 12) | Cluster I | 1805 (44.7%) | 2.3 | 6.5 | 19 | 34.8% |

Cluster II | 1023 (25.3%) | 2.4 | 9 | 20.4 | 44.8% | |

Cluster III | 342 (8.5%) | 2.4 | 13 | 19.8 | 67.8% | |

Cluster IV | 554 (13.7%) | 2.6 | 12 | 20 | 63.3% | |

Cluster V | 312 (7.7%) | 2.6 | 16.5 | 19 | 85.7% | |

[12, 24) | Cluster I | 2775 (64.8%) | 1.5 | 6 | 24.5 | 23.80% |

Cluster II | 854 (19.9%) | 1.7 | 11 | 26.8 | 38.70% | |

Cluster III | 150 (3.5%) | 1.8 | 14.5 | 25.8 | 56.10% | |

Cluster IV | 438 (10.2%) | 1.7 | 10.5 | 25.5 | 42.10% | |

Cluster V | 64 (1.5%) | 1.8 | 19.8 | 24.8 | 78.60% | |

[24, 48) | Cluster I | 1828 (84.4%) | 1.3 | 7 | 43 | 16.50% |

Cluster II | 208 (9.6%) | 1.6 | 15 | 46.3 | 30.80% | |

Cluster III | 74 (3.4%) | 1.2 | 12 | 37.8 | 33.60% | |

Cluster IV | 39 (1.8%) | 1.2 | 17.5 | 36 | 45.60% | |

Cluster V | 16 (0.7%) | 1.5 | 18.8 | 42.4 | 55.70% | |

[48, 96) | Cluster I | 320 (84%) | 1.5 | 9.2 | 92.2 | 10.3% |

Cluster II | 36 (9.4%) | 1.5 | 12.8 | 75 | 17.2% | |

Cluster III | 25 (6.6%) | 1.8 | 19 | 105 | 20.9% |

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**MDPI and ACS Style**

Wang, F. Temporal Pattern Analysis of Local Rainstorm Events in China During the Flood Season Based on Time Series Clustering. *Water* **2020**, *12*, 725.
https://doi.org/10.3390/w12030725

**AMA Style**

Wang F. Temporal Pattern Analysis of Local Rainstorm Events in China During the Flood Season Based on Time Series Clustering. *Water*. 2020; 12(3):725.
https://doi.org/10.3390/w12030725

**Chicago/Turabian Style**

Wang, Fan. 2020. "Temporal Pattern Analysis of Local Rainstorm Events in China During the Flood Season Based on Time Series Clustering" *Water* 12, no. 3: 725.
https://doi.org/10.3390/w12030725