# Spatial Heterogeneity Analysis of Short-Duration Extreme Rainfall Events in Megacities in China

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}. Thus, more specific analysis in rainfall spatial heterogeneity is required for hydrological analysis in cities [22,23,24].

## 2. Study Areas and Data

#### 2.1. Study Areas

#### 2.2. Data

## 3. Methodology

#### 3.1. Trend Analysis

#### 3.2. Spatial Heterogeneity Analysis

#### 3.2.1. CV in Space

#### 3.2.2. Global Moran’s I and Local Moran’s I

#### 3.2.3. Semi-Variance Analysis

## 4. Results and Discussion

#### 4.1. Temporal Characteristics of Rainfall Series

#### 4.2. Spatial Heterogeneity of Extreme Rainfall

#### 4.2.1. Rainfall Clustering Analysis

#### 4.2.2. Distribution of Rainfall Centroids

#### 4.3. Discussion

#### 4.3.1. Influence of Urban Growth on Spatial Heterogeneity of Rainfall

#### 4.3.2. Influence of Rainfall Spatial Heterogeneity on Design Storm

## 5. Summary and Conclusions

- (1)
- Though there is no significant change in the magnitude of short-duration extreme rainfall, pronounced rainfall spatial heterogeneity can be found in the four megacities in China. SZ has the largest magnitude of rainfall, while GZ has the largest spatial heterogeneity. It was no significant positive correlation between magnitude and spatial heterogeneity of rainfall. The spatio-temporal analysis of extreme rainfall should attach importance to not only rainfall magnitude but also to the spatial heterogeneity.
- (2)
- The short-duration extreme rainfall exhibit four different patterns of spatial variability in SH, BJ, GZ, SZ. The extreme storm in SH clusters in the central portion, keeping a balance between transverse and longitudinal directions. In BJ, extreme storm clusters in the northeast plain with relatively small rainfall magnitude and a smooth process. The extreme storm in GZ shows a highly clustered pattern in the central areas accompanied by large rainfall magnitudes. Rainfall in the east-west attributed more than north-south to spatial clustering here. The clustering feature in SZ is not as significant as other cities, while the variability of rainfall magnitude is remarkable. It shows a transverse clustering pattern on the north side of the city. Due to different climate, topography, and land use, spatial heterogeneity of rainfall shows different characteristics in these four cities.
- (3)
- Urban growth plays a role in the change of rainfall spatial heterogeneity. SH is a city that shows the largest increase in urbanization and rainfall spatial heterogeneity. During its rapid urbanization in the last 20 years, there is an increasing trend in Moran’s I in SH. The rainfall clusters in SH also tend to cluster in the most urbanized areas. Rainfall spatial heterogeneity cannot be neglected in design storms and thus in the design of urban flood mitigation measurements.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**A schematic diagram of the semi-variance analysis with its key parameters [58].

**Figure 4.**A box and whisker plot of Rx3h magnitude in study cities (The whisker range within 1.5IQR, where IQR = Q3 − Q1, Q1 means 25th percentile, Q2 means 50th percentile, Q3 means 75th percentile).

**Figure 5.**Trend analysis of Rx3h series in study cities (The blue dots are the values of Rx3h, and the red lines are the trend lines calculated by Sen’s slope method).

**Figure 6.**Diagram of probability density distribution to analyze the Rx3h occurrence (Point plots in figure means the total rainfall in months).

**Figure 9.**Analysis of locations of clusters (results in LISA) for four study cities. (Gridded cells which outside the scope of study areas are covered by 0 values, zero represents randomness in spatial autocorrelation analysis).

**Figure 10.**Semi-variance analysis for four cities without considering the change of rainfall in different directions.

**Figure 12.**Locations of Rx3h centroids during 2000–2020 (The dot locations are where the Rx3h centroids occur in the cities, and the dot colors indicate the magnitudes of rainfall. The different numbers reveal the occurrence number of the centroids at the marked location, and the number not marked is one time. Geographic location centers in four cities are represented by a red dot. The blue lines for the nearby river).

**Figure 13.**The wind rose to analyze the relative positions between rainfall centroids and geographic location centers (The relative positions between rainfall centroids and geographic location centers are divided into eight directions. The colors of the ribbons indicate the rainfall magnitudes of rainfall centroids, and the length of it indicates the occurrence probability of these magnitudes).

**Figure 14.**Line charts of annual change in Moran’s I based on 3-h extreme rainfall events in study areas.

**Figure 15.**Influence of urban growth on spatial heterogeneity of 3-h extreme rainfall in SH: (

**a**) Land use maps (only focus on impervious) in 2001, 2015, 2017, (

**b**) LISA maps in 2001, 2015, 2017, (

**c**) Semi-variance analysis in 2001, 2015, 2017.

**Figure 16.**Comparison of Intensity-Duration-Frequency (IDF) curves uses non-uniform spatial transposition (heterogeneity) and uniform transposition (homogeneity) scenarios, which are calculated based on the SST method at a 3-h time scale. The blue/green areas indicate the spread of SST estimates with 90th and 10th quantiles as the solid lines.

Cities | SH | BJ | GZ | SZ |
---|---|---|---|---|

Areas (km^{2}) | 6340.5 | 16,410.54 | 7434.4 | 1997.47 |

Terrain types | Plain | Mountains, and plain | Hilly land | Hilly land, and plain |

Elevation (Datum: WGS_1984, m) | 0–101 | −121–2306 | 0–1185 | 0–936 |

Climate | Subtropical monsoon | Continental monsoon | Subtropical maritime monsoon | Subtropical maritime monsoon |

Annual average temperature (°C) | 17.7 | 12.6 | 22.3 | 22.4 |

Annual rainfall (during 2000–2020, mm) | 1320 | 441 | 1915 | 1801 |

Population density (people in per square kilometer) | 3830 | 1312 | 2059 | 6728 |

Urbanization rate (data up to 2019) | 88.1% | 86.6% | 86.1% | 99.7% |

GDP (billion CNY) | 3815.53 | 3537.13 | 2362.86 | 2692.71 |

Cities | Maximum (mm) | Mean (mm) | Minimum (mm) | Standard Deviation |
---|---|---|---|---|

SH | 59.7 | 36.8 | 20.8 | 11.2 |

BJ | 41.6 | 18.9 | 11.2 | 8.4 |

GZ | 82.3 | 50.1 | 30.3 | 14.1 |

SZ | 99.1 | 58.1 | 35.9 | 18.8 |

Cities | Moran’s I | CV | Z-Score |
---|---|---|---|

Shanghai | 0.472 | 0.473 | 5.16 |

Beijing | 0.621 | 0.487 | 12.109 |

Guangzhou | 0.628 | 0.635 | 8.00 |

Shenzhen | 0.215 | 0.631 | 1.771 |

Cities | Orientation | ${\mathit{C}}_{0}$ | ${\mathit{C}}_{0}+\mathit{C}$ | $\mathit{\alpha}$ | $\frac{{\mathit{C}}_{0}}{{\mathit{C}}_{0}+\mathit{C}}$ | ${\mathit{R}}^{2}$ |
---|---|---|---|---|---|---|

Shanghai | - | 0.487 | 211.753 | 4.840 | 0.2% | 0.893 |

E-W | 3.185 | 164.353 | 5.226 | 1.9% | 0.993 | |

N-S | 20.677 | 290.818 | 5.872 | 7.1% | 0.994 | |

Beijing | - | 8.369 | 68.141 | 11.43 | 12.3% | 0.997 |

E-W | 2.554 | 94.107 | 15.532 | 2.7% | 0.999 | |

N-S | 10.574 | 53.445 | 7.991 | 19.8% | 0.996 | |

Guangzhou | - | 9.469 | 792.589 | 7.669 | 1.2% | 0.976 |

E-W | 0.679 | 747.718 | 5.798 | 0.09% | 0.974 | |

N-S | 15.205 | 1191.336 | 11.918 | 1.3% | 0.993 | |

Shenzhen | - | 173.800 | 427.700 | 2.840 | 26.6% | 0.248 |

E-W | 67.589 | 414.419 | 4.098 | 16.3% | 0.987 | |

N-S | 69.477 | 679.700 | 1.980 | 9.9% | 0.999 |

**Table 5.**A dynamic analysis of the Rx3h centroids at a 3-h time scale (temporal resolution = 30 min). “Frequency” represents the percentage of the events during 21-years.

Cities | Mean of Moving Speed (km/h) | Most Frequently Moving Angles (Frequency) | CV |
---|---|---|---|

SH | 12.3 | 270–315 (28.6%) | 0.27 |

BJ | 24.7 | 225–270 (42.9%) | 0.22 |

GZ | 13.7 | 270–315 (28.6%) | 0.24 |

SZ | 11.7 | 0–45 (23.8%), 90–135 (23.8%) | 0.28 |

Cities | 2001 (%) | 2015 (%) | 2017 (%) | The Annual Rate of Increase (2001–2015) (% Per Year) | The Annual Rate of Increase (2015–2017) (% Per Year) | The Annual Rate of Increase (2001–2017) (% Per Year) |
---|---|---|---|---|---|---|

SH | 15.22 | 36.16 | 55.66 | 1.50 | 9.75 | 2.53 |

BJ | 12.34 | 13.69 | 15.46 | 0.13 | 0.89 | 0.20 |

GZ | 13.19 | 14.48 | 24.44 | 0.09 | 4.98 | 0.69 |

SZ | 29.21 | 35.14 | 37.54 | 0.42 | 1.12 | 0.52 |

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**MDPI and ACS Style**

Zhuang, Q.; Liu, S.; Zhou, Z.
Spatial Heterogeneity Analysis of Short-Duration Extreme Rainfall Events in Megacities in China. *Water* **2020**, *12*, 3364.
https://doi.org/10.3390/w12123364

**AMA Style**

Zhuang Q, Liu S, Zhou Z.
Spatial Heterogeneity Analysis of Short-Duration Extreme Rainfall Events in Megacities in China. *Water*. 2020; 12(12):3364.
https://doi.org/10.3390/w12123364

**Chicago/Turabian Style**

Zhuang, Qi, Shuguang Liu, and Zhengzheng Zhou.
2020. "Spatial Heterogeneity Analysis of Short-Duration Extreme Rainfall Events in Megacities in China" *Water* 12, no. 12: 3364.
https://doi.org/10.3390/w12123364