# 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

- Douinot, A.; Roux, H.; Garambois, P.A.; Larnier, K.; Labat, D.; Dartus, D. Accounting for rainfall systematic spatial variability in flash flood forecasting. J. Hydrol.
**2016**, 541, 359–370. [Google Scholar] [CrossRef] [Green Version] - Hou, J.; Guo, K.; Wang, Z.; Jing, H.; Li, D. Numerical simulation of design storm pattern effects on urban flood inundation. Adv. Water Sci.
**2017**, 28, 820–828. [Google Scholar] - Yin, S.; Wang, Y.; Xie, Y.; Liu, A. Characteristics of intra-storm temporal pattern over China. Adv. Water Sci.
**2014**, 25, 617–624. [Google Scholar] - Dunkerley, D. Effects of rainfall intensity fluctuations on infiltration and runoff: Rainfall simulation on dryland soils, Fowlers Gap, Australia. Hydrol. Process.
**2012**, 26, 2211–2224. [Google Scholar] [CrossRef] - Jain, S.K.; Singh, R.D.; Seth, S.M. Design flood estimation using GIS supported GIUH approach. Water Resour. Manag.
**2000**, 14, 369–376. [Google Scholar] [CrossRef] - Máca, P.; Torfs, P. The influence of temporal rainfall distribution in the flood runoff modelling. Soil Water Res.
**2009**, 4, S102–S110. [Google Scholar] [CrossRef] [Green Version] - Lin, M.; Chen, X.; Chen, Y. Regression Analysis of Flood Response to the Spatial and Temporal Variability of Storm in the Jinjiangxixi Watershed. Resour. Sci.
**2011**, 33, 2226–2231. [Google Scholar] - Bezak, N.; Sraj, M.; Mikos, M. Copula-based IDF curves and empirical rainfall thresholds for flash floods and rainfall-induced landslides. J. Hydrol.
**2016**, 541, 272–284. [Google Scholar] [CrossRef] - Forestieri, A.; Caracciolo, D.; Arnone, E.; Noto, L.V. Derivation of rainfall thresholds for flash flood warning in a Sicilian basin using a hydrological model. In Proceedings of the 12th International Conference on Hydroinformatics, Incheon, Korea, 21–26 August 2016; Kim, J.H., Kim, H.S., Yoo, D.G., Jung, D., Song, C.G., Eds.; Elsevier Science B.V.: Amsterdam, The Netherlands, 2016; pp. 818–825. [Google Scholar]
- Norbiato, D.; Borga, M.; Esposti, S.D.; Gaume, E.; Anquetin, S. Flash flood warning based on rainfall thresholds and soil moisture conditions: An assessment for gauged and ungauged basins. J. Hydrol.
**2008**, 362, 274–290. [Google Scholar] [CrossRef] - Yuan, W.L.; Liu, M.Q.; Wan, F. Study on the impact of rainfall pattern in small watersheds on rainfall warning index of flash flood event. Nat. Hazards
**2019**, 97, 665–682. [Google Scholar] [CrossRef] - Zhai, X.Y.; Guo, L.; Liu, R.H.; Zhang, Y.Y. Rainfall threshold determination for flash flood warning in mountainous catchments with consideration of antecedent soil moisture and rainfall pattern. Nat. Hazards
**2018**, 94, 605–625. [Google Scholar] [CrossRef] - Li, J.; Wu, S.; Zhao, X.; Yin, W.; Zhang, S.; Li, M.; Li, J. Analysis on the effect of rain type selection on LID measures. Water Wastewater Eng.
**2018**, 44, 21–27. [Google Scholar] - Pedrozo-Acuna, A.; Moreno, G.; Mejia-Estrada, P.; Paredes-Victoria, P.; Brena-Naranjo, J.A.; Meza, C. Integrated approach to determine highway flooding and critical points of drainage. Transp. Res. Part D Transp. Environ.
**2017**, 50, 182–191. [Google Scholar] [CrossRef] - Rahman, A.; Weinmann, P.E.; Hoang, T.M.T.; Laurenson, E.M. Monte Carlo simulation of flood frequency curves from rainfall. J. Hydrol.
**2002**, 256, 196–210. [Google Scholar] [CrossRef] - Rahman, A.; Islam, M.; Rahman, K.; Khan, S.; Shrestha, S. Investigation of design rainfall temporal patterns in the Gold Coast region of Queensland. Australas. J. Water Resour.
**2006**, 10, 49–61. [Google Scholar] [CrossRef] - Liu, Z.; Yang, D.; Hu, J. Dynamic critical rainfall-based torrential flood early warning for medium-small rivers. J. Beijing Norm. Univ. Nat. Sci. (China)
**2010**, 46, 317–321. [Google Scholar] - Hapuarachchi, H.A.P.; Wang, Q.J.; Pagano, T.C. A review of advances in flash flood forecasting. Hydrol. Process.
**2011**, 25, 2771–2784. [Google Scholar] [CrossRef] - Cheng, W. A review of rainfall thresholds for triggering flash floods. Adv. Water Sci.
**2013**, 24, 901–908. [Google Scholar] - Miao, Q.H.; Yang, D.W.; Yang, H.B.; Li, Z. Establishing a rainfall threshold for flash flood warnings in China’s mountainous areas based on a distributed hydrological model. J. Hydrol.
**2016**, 541, 371–386. [Google Scholar] [CrossRef] - Georgakakos, K.P. A generalized stochastic hydrometeorological model for flood and flash-flood forecasting: 1. Formulation. Water Resour. Res.
**1986**, 22, 2083–2095. [Google Scholar] [CrossRef] - Georgakakos, K.P. A generalized stochastic hydrometeorological model for flood and flash-flood forecasting: 2. Case-Studies. Water Resour. Res.
**1986**, 22, 2096–2106. [Google Scholar] [CrossRef] - Mogil, H.M.; Monro, J.C.; Groper, H.S. NWS flash flood warning and disaster preparedness programs. Bull. Am. Meteorol. Soc.
**1978**, 59, 690–699. [Google Scholar] [CrossRef] [Green Version] - Nikolopoulos, E.I.; Anagnostou, E.N.; Borga, M.; Vivoni, E.R.; Papadopoulos, A. Sensitivity of a mountain basin flash flood to initial wetness condition and rainfall variability. J. Hydrol.
**2011**, 402, 165–178. [Google Scholar] [CrossRef] - Yin, S.Q.; Xie, Y.; Nearing, M.A.; Guo, W.L.; Zhu, Z.Y. Intra-Storm temporal patterns of rainfall in china using huff curves. Trans. ASABE
**2016**, 59, 1619–1632. [Google Scholar] - El-Sayed, E.A.H. Development of synthetic rainfall distribution curves for Sinai area. Ain Shams Eng. J.
**2018**, 9, 1949–1957. [Google Scholar] [CrossRef] - Keifer, C.; Chu, H. Synthetic Storm Pattern for Drainage Design. J. Hydraul. Div.
**1957**, 83, 1–25. [Google Scholar] - Hershfield, D.M. Extreme rainfall relationships. J. Hydraul. Div.
**1962**, 88, 73–92. [Google Scholar] - Huff, F.A. Time distribution of rainfall in heavy storms. Water Resour. Res.
**1967**, 3, 1007–1019. [Google Scholar] [CrossRef] - Pilgrim, D.H.; Cordery, I. Rainfall temporal patterns for design floods. J. Hydraul. Div.
**1975**, 101, 81–95. [Google Scholar] - Yen, B.C.; Chow, V.T. Design hyetographs for small drainage structures. J. Hydraul. Div.
**1980**, 106, 1055–1076. [Google Scholar] - USDA. Urban Hydrology for Small Watersheds; Technical Release TR-55; National Resources Conservation Service: Washington, DC, USA, 1986. [Google Scholar]
- Wu, S.J.; Yang, J.C.; Tung, Y.K. Identification and stochastic generation of representative rainfall temporal patterns in Hong Kong territory. Stoch. Environ. Res. Risk Assess.
**2006**, 20, 171–183. [Google Scholar] [CrossRef] - Terranova, O.G.; Iaquinta, P. Temporal properties of rainfall events in Calabria (Southern Italy). Nat. Hazards Earth Syst. Sci.
**2011**, 11, 751–757. [Google Scholar] [CrossRef] [Green Version] - Ghassabi, Z.; Kamali, G.A.; Meshkatee, A.H.; Hajam, S.; Javaheri, N. Time distribution of heavy rainfall events in south west of Iran. J. Atmos. Sol. Terr. Phys.
**2016**, 145, 53–60. [Google Scholar] [CrossRef] - Jun, C.Y.; Qin, X.S.; Lu, W. Temporal Pattern Analysis of Rainstorm Events for Supporting Rainfall Design in a Tropical City. In New Trends in Urban Drainage Modelling: UDM 2018; Mannina, G., Ed.; Springer International Publishing: Berlin/Heidelberg, Germany, 2019; pp. 380–384. [Google Scholar]
- Berndt, D.J.; Clifford, J. Using Dynamic Time Warping to Find. Patterns in Time Series. In Proceedings of the AAAI-94 Workshop on Knowledge Discovery in Databases, Seattle, WA, USA, 31 July–1 August 1994. [Google Scholar]
- Berndt, D.J.; Clifford, J. Finding Patterns in Time Series: A Dynamic Programming Approach. In Advances in Knowledge Discovery and Data Mining; MIT Press: Cambridge, MA, USA, 1996; pp. 229–248. [Google Scholar]
- Gavrilov, M.; Anguelov, D.; Indyk, P.; Motwani, R. Mining the stock market: Which measure is best? In Proceedings of the KDD-2000, Sixth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Boston, MA, USA, 20–23 August 2000; pp. 487–496. [Google Scholar]
- Goldin, D.Q.; Kanellakis, P.C. On similarity queries for time-series data: Constraint specification and implementation. In Proceedings of the Principles and Practice of Constraint Programming—CP ʹ95: First International Conference, Cassis, France, 19–22 September 1995. [Google Scholar]
- Rafiei, D.; Mendelzon, A. Efficient Retrieval of Similar Time Sequences Using DFT. In Proceedings of the 5th International Conference on Foundations of Data Organizations and Algorithms (FODO ʹ98), Kobe, Japan, 12–13 November 1998. [Google Scholar]
- Sakoe, H.; Chiba, S. Dynamic-Programming algorithm optimization for spoken word recognition. IEEE Trans. Acoust. Speech Signal. Process.
**1978**, 26, 43–49. [Google Scholar] [CrossRef] [Green Version] - Jain, A.K. Data clustering: 50 years beyond K-means. Pattern Recognit. Lett.
**2010**, 31, 651–666. [Google Scholar] [CrossRef] - Tian, Z.; Ramakrishnan, R.; Livny, M. BIRCH: An efficient data clustering method for very large databases. ACM Sigmod Rec.
**1996**, 25, 103–114. [Google Scholar] - Darkins, R.; Cooke, E.J.; Ghahramani, Z.; Kirk, P.D.W.; Wild, D.L.; Savage, R.S. Accelerating Bayesian Hierarchical Clustering of Time Series Data with a Randomised Algorithm. PLoS ONE
**2013**, 8, 8. [Google Scholar] [CrossRef] [Green Version] - Schliep, A.; Schonhuth, A.; Steinhoff, C. Using hidden Markov models to analyze gene expression time course data. Bioinformatics
**2003**, 19, i255–i263. [Google Scholar] [CrossRef] - Xiong, Y.M.; Yeung, D.Y. Mixtures of ARMA models for model-based time series clustering. In Proceedings of the 2002 IEEE International Conference on Data Mining, Maebashi City, Japan, 9–12 December 2002; IEEE Computer Soc.: Los Alamitos, CA, USA, 2002. [Google Scholar]
- Begum, N.; Ulanova, L.; Dau, H.A.; Wang, J.; Keogh, E. A General Framework for Density Based Time Series Clustering Exploiting a Novel Admissible Pruning Strategy. IEEE Trans. Knowl. Data Eng.
**2016**. Available online: https://arxiv.org/abs/1612.00637 (accessed on 6 March 2020). - Keogh, E. A Fast and Robust Method for Pattern Matching in Time Series Databases. In Proceedings of the 9th International Conference on Tools with Artificial Intelligence, Newport Beach, CA, USA, 3–8 November 1997. [Google Scholar]
- Wang, Q.; Megalooikonomou, V. A dimensionality reduction technique for efficient time series similarity analysis. Inf. Syst.
**2008**, 33, 115–132. [Google Scholar] [CrossRef] [Green Version] - Chan, K.P.; Fu, A.W.C. Efficient time series matching by wavelets. In Proceedings of the 15th International Conference on Data Engineering, Sydney, Australia, 23–26 March 1999; IEEE Computer Soc.: Los Alamitos, CA, USA, 1999. [Google Scholar]
- Lin, J.; Keogh, E.; Wei, L.; Lonardi, S. Experiencing SAX: A novel symbolic representation of time series. Data Min. Knowl. Discov.
**2007**, 15, 107–144. [Google Scholar] [CrossRef] [Green Version] - Ye, L.X.; Keogh, E. Time Series Shapelets: A New Primitive for Data Mining. In Proceedings of the Kdd-09: 15th Acm Sigkdd Conference on Knowledge Discovery and Data Mining, Paris, France, 29 June–1 July 2009; Assoc Computing Machinery: New York, NY, USA, 2009. [Google Scholar]
- Itakura, F. Minimum Prediction Residual principle applied to speech recognition. IEEE Trans. Acoust. Speech Signal. Process.
**1975**, AS23, 67–72. [Google Scholar] [CrossRef] - Yi, B.K.; Jagadish, H.V.; Faloutsos, C. Efficient retrieval of similar time sequences under time warping. In Proceedings of the 14th International Conference on Data Engineering, Orlando, FL, USA, 23–27 February 1998; IEEE Computer Soc.: Los Alamitos, CA, USA, 1998. [Google Scholar]
- Kim, S.W.; Park, S.; Chu, W.W. An index-based approach for similarity search supporting time warping in large sequence databases. In Proceedings of the 17th International Conference on Data Engineering, Heidelberg/Germany, Germany, 2–6 April 2001; IEEE Computer Soc.: Los Alamitos, CA, USA, 2001. [Google Scholar]
- Keogh, E. Exact indexing of Dynamic Time Warping. In Proceedings of the Twenty-Eighth International Conference on Very Large Data Bases, Hong Kong, China, 20–23 August 2002; pp. 406–417. [Google Scholar]
- Keogh, E.; Ratanamahatana, C.A. Exact indexing of dynamic time warping. Knowl. Inf. Syst.
**2005**, 7, 358–386. [Google Scholar] [CrossRef]

**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