# Flood Risk Evaluation in the Middle Reaches of the Yangtze River Based on Eigenvector Spatial Filtering Poisson Regression

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

#### 2.1. Study Area

#### 2.2. Data Source

#### 2.3. Derivation of Hazard Factors

#### 2.3.1. Frequency of Flood Alarming Events

#### 2.3.2. Topological Factors

#### 2.3.3. Hydrological Factors

#### 2.3.4. NDVI

#### 2.3.5. Trigger Factors

## 3. Methodology

#### 3.1. Factors Selection

#### 3.2. Eigenvector Spatial Filtering Poisson Regression

#### 3.2.1. Construction of Spatial Weight Matrix

#### 3.2.2. Calculation of Eigenvectors

#### 3.2.3. Z-Score Normalization

#### 3.2.4. Eigenvector Selection

#### 3.2.5. Coefficient Calculation

#### 3.3. Model Assessment

#### 3.3.1. Accuracy of Model Fitting

#### 3.3.2. AIC

#### 3.3.3. Leave-One-Out Cross Validation (LOOCV)

#### 3.4. Flood Risk Mapping

## 4. Results

#### 4.1. Factor Selection

#### 4.2. Results of Model Coefficients

*******,

******,

*****and

**·**represent that the p-value is less than the threshold of 0, 0.001 and 0.05, respectively.

#### 4.3. Model Assessment

#### 4.4. Spatial Pattern of Flood Risk

## 5. Discussion

#### 5.1. Improvement in the Accuracy of the Flood Risk EVALUATION Model

#### 5.2. Determination of Significant Factors

#### 5.3. Limitations and Future Enhancements

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Petrucci, O.; Aceto, L.; Bianchi, C.; Bigot, V.; Brázdil, R.; Pereira, S.; Kahraman, A.; Kılıç, Ö.; Kotroni, V.; Llasat, M.C.; et al. Flood fatalities in Europe, 1980–2018: Variability, features, and lessons to learn. Water
**2019**, 11, 1682. [Google Scholar] [CrossRef] - Schelske, O.; Sundermann, L.; Hausmann, P. Mind the Risk—A global Ranking of Cities Under Threat from Natural Disasters; Swiss Reinsurance Company Ltd.: Zurich, Switzerland, 2013. [Google Scholar]
- Zhang, L.; Geng, J.; Fan, C. The comprehensive analysis of flood disasters losses in china from 2000 to 2010. IOP Conf. Ser. Mater. Sci. Eng.
**2018**, 466, 012023. [Google Scholar] [CrossRef] - Snedaker, S.; Rima, C. Chapter 4—Risk assessment. In Business Continuity and Disaster Recovery Planning for It Professionals, 2nd ed.; Snedaker, S., Rima, C., Eds.; Syngress: Boston, MA, USA, 2014; pp. 151–224. [Google Scholar]
- He, Y.; Pappenberger, F.; Manful, D.; Cloke, H.; Bates, P.; Wetterhall, F.; Parkes, B. 5.16—Flood inundation dynamics and socioeconomic vulnerability under environmental change. Clim. Vulnerability
**2013**, 241–255. [Google Scholar] [CrossRef] - Pei, F.; Wu, C.; Qu, A.; Xia, Y.; Wang, K.; Zhou, Y. Changes in extreme precipitation: A case study in the middle and lower reaches of the yangtze river in China. Water
**2017**, 9, 943. [Google Scholar] [CrossRef] - Hsieh, S.-H.; Liu, L.-W.; Chung, W.-G.; Wang, Y.-M. Sensitivity analysis on the rising relation between short-term rainfall and groundwater table adjacent to an artificial recharge lake. Water
**2019**, 11, 1704. [Google Scholar] [CrossRef] - Hashizume, M. 1.10—precipitation and flood hazards: Health effects, risks, and impacts. Clim. Vulnerability
**2013**, 115–124. [Google Scholar] [CrossRef] - Legesse, D.; Vallet-Coulomb, C.; Gasse, F. Hydrological response of a catchment to climate and land use changes in tropical africa: Case study south central ethiopia. J. Hydrol.
**2003**, 275, 67–85. [Google Scholar] [CrossRef] - Chen, Y.R.; Yeh, C.-H.; Yu, B. Integrated application of the analytic hierarchy process and the geographic information system for flood risk assessment and flood plain management in Taiwan. Nat. Hazards
**2011**, 59, 1261–1276. [Google Scholar] [CrossRef] [Green Version] - Chau, K.W.; Wu, C.L.; Li, Y.S. Comparison of several flood forecasting models in yangtze river. J. Hydrol. Eng.
**2005**, 10, 485–491. [Google Scholar] [CrossRef] - Bisht, D.S.; Chatterjee, C.; Kalakoti, S.; Upadhyay, P.; Sahoo, M.; Panda, A. Modeling urban floods and drainage using swmm and mike urban: A case study. Nat. Hazards
**2016**, 84, 749–776. [Google Scholar] [CrossRef] - Sharma, S.K.; Kwak, Y.J.; Kumar, R.; Sarma, B. Analysis of hydrological sensitivity for flood risk assessment. ISPRS Int. J. Geo-Inf.
**2018**, 7, 51. [Google Scholar] [CrossRef] - Neelz, S.N.; Pender, G. Benchmarking of 2d Hydraulic Modelling Packages; Environment Agency: Bristol, UK, 2010. [Google Scholar]
- Lu, C.; Zhou, J.; He, Z.; Yuan, S. Evaluating typical flood risks in yangtze river economic belt: Application of a flood risk mapping framework. Nat. Hazards
**2018**, 94, 1187–1210. [Google Scholar] [CrossRef] - Malczewski, J. A gis-based approach to multiple criteria group decision-making. Int. J. Geogr. Inf. Syst.
**1996**, 10, 955–971. [Google Scholar] [CrossRef] - Wang, Y.; Li, Z.; Tang, Z.; Zeng, G. A gis-based spatial multi-criteria approach for flood risk assessment in the dongting lake region, Hunan, central China. Water Resour. Manag.
**2011**, 25, 3465–3484. [Google Scholar] [CrossRef] - Chen, Y.; Liu, R.; Barrett, D.; Gao, L.; Zhou, M.; Renzullo, L.; Emelyanova, I. A spatial assessment framework for evaluating flood risk under extreme climates. Sci. Total Environ.
**2015**, 538, 512–523. [Google Scholar] [CrossRef] [PubMed] - Tehrany, M.S.; Pradhan, B.; Mansor, S.; Ahmad, N. Flood susceptibility assessment using gis-based support vector machine model with different kernel types. Catena
**2015**, 125, 91–101. [Google Scholar] [CrossRef] - Xiong, J.; Li, J.; Cheng, W.; Wang, N.; Guo, L. A gis-based support vector machine model for flash flood vulnerability assessment and mapping in China. ISPRS Int. J. Geo-Inf.
**2019**, 8, 297. [Google Scholar] [CrossRef] - Xiao, Y.; Yi, S.; Tang, Z. Integrated flood hazard assessment based on spatial ordered weighted averaging method considering spatial heterogeneity of risk preference. Sci. Total Environ.
**2017**, 599–600, 1034–1046. [Google Scholar] [CrossRef] - Kourgialas, N.N.; Karatzas, G.P. A national scale flood hazard mapping methodology: The case of Greece—Protection and adaptation policy approaches. Sci. Total Environ.
**2017**, 601–602, 441–452. [Google Scholar] [CrossRef] - Leggett, D.J.; Jones, A. The application of gis for flood defence in the anglian region: Developing for the future. Int. J. Geogr. Inf. Syst.
**1996**, 10, 103–116. [Google Scholar] [CrossRef] - Dawod, G.M.; Mirza, M.N.; Al-Ghamdi, K.A. Gis-based estimation of flood hazard impacts on road network in Makkah city, Saudi Arabia. Environ. Earth Sci.
**2012**, 67, 2205–2215. [Google Scholar] [CrossRef] - Mandallaz, D.; Ye, R. Prediction of forest fires with poisson models. Can. J. For. Res.
**1997**, 27, 1685–1694. [Google Scholar] [CrossRef] - Wahiduzzaman, M.; Yeasmin, A. Statistical forecasting of tropical cyclone landfall activities over the north Indian ocean rim countries. Atmos. Res.
**2019**, 227, 89–100. [Google Scholar] [CrossRef] - Betts, M.G.; Diamond, A.W.; Forbes, G.J.; Villard, M.A.; Gunn, J.S. The importance of spatial autocorrelation, extent and resolution in predicting forest bird occurrence. Ecol. Model.
**2006**, 191, 197–224. [Google Scholar] [CrossRef] - Tobler, W. On the first law of geography: A reply. Ann. Assoc. Am. Geogr.
**2004**, 94, 304–310. [Google Scholar] [CrossRef] - Getis, A. Spatial Filtering in a Regression Framework: Examples Using Data on Urban Crime, Regional Inequality, and Government Expenditures; Springer-Verlag: Berlin, German, 2010. [Google Scholar]
- Getis, A.; Griffith, D.A. Comparative spatial filtering in regression analysis. Geogr. Anal.
**2002**, 34, 130–140. [Google Scholar] [CrossRef] - Murakami, D.; Griffith, D.A. Random effects specifications in eigenvector spatial filtering: A simulation study. J. Geogr. Syst.
**2015**, 17, 1–21. [Google Scholar] [CrossRef] - Chun, Y.; Griffith, D.A.; Lee, M.; Sinha, P. Eigenvector selection with stepwise regression techniques to construct eigenvector spatial filters. J. Geogr. Syst.
**2016**, 18, 67–85. [Google Scholar] [CrossRef] - Griffith, D.A. A linear regression solution to the spatial autocorrelation problem. J. Geogr. Syst.
**2000**, 2, 141–156. [Google Scholar] [CrossRef] - Griffith, D.; Chun, Y. Spatial Autocorrelation and Spatial Filtering; Springer-Verlag: Berlin, German, 2003. [Google Scholar]
- Kourgialas, N.N. A flood risk decision making approach for mediterranean tree crops using gis; climate change effects and flood-tolerant species. Environ. Sci. Policy
**2016**, 63, 132–142. [Google Scholar] [CrossRef] - Wu, Y.; Zhong, P.A.; Zhang, Y.; Xu, B.; Ma, B.; Yan, K. Integrated flood risk assessment and zonation method: A case study in huaihe river basin, China. Nat. Hazards
**2015**, 78, 635–651. [Google Scholar] [CrossRef] - Rawat, P.K. Impacts of climate change and hydrological hazards on monsoon crop patterns in the lesser himalaya: A watershed based study. Int. J. Disaster Risk Sci.
**2012**, 3, 98–112. [Google Scholar] [CrossRef] - Jiang, S.; Ren, L.; Hong, Y.; Yang, X.; Ma, M.; Zhang, Y.; Yuan, F. Improvement of multi-satellite real-time precipitation products for ensemble streamflow simulation in a middle latitude basin in south China. Water Resour. Manag.
**2014**, 28, 2259–2278. [Google Scholar] [CrossRef] - Farrar, D.E.; Glauber, R.R. Multicollinearity in regression analysis: The problem revisited. Rev. Econ. Stat.
**1967**, 49, 92–107. [Google Scholar] [CrossRef] - Kutner, M.H.; Nachtsheim, C.J.; Neter, J. Applied Linear Regression Models; McGraw-Hill Irwin: New York, NY, USA, 2004. [Google Scholar]
- Zhu, Q.A.; Zhang, W.C.; Zhao, D.Z. Topography-based spatial daily precipitation interpolation by means of prism and thiessen polygon analysis. Sci. Geogr. Sin.
**2005**, 25, 233–238. [Google Scholar] - Zhang, J.; Li, B.; Chen, Y.; Chen, M.; Fang, T.; Liu, Y. Eigenvector spatial filtering regression modeling of ground PM
_{2.5}concentrations using remotely sensed data. Int. J. Environ. Res. Public Health**2018**, 15, 1228. [Google Scholar] [CrossRef] - Grus, J. Data Science from Scratch: First Principles with Python; O’Reilly Media: New York, NY, USA, 2015. [Google Scholar]
- Hocking, R.R. A biometrics invited paper. The analysis and selection of variables in linear regression. Biometrics
**1976**, 32, 1–49. [Google Scholar] [CrossRef] - Akaike, H. IEEE xplore abstract—A new look at the statistical model identification. IEEE Autom. Control Trans.
**1974**, 19, 716–723. [Google Scholar] [CrossRef] - Kohavi, R. A study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection. In Proceedings of the International Joint Conference on Artificial Intelligence, Montreal, QC, Canada, 20–25 August 1995. [Google Scholar]
- Youssef, A.M.; Pradhan, B.; Sefry, S.A. Flash flood susceptibility assessment in Jeddah city (Kingdom of Saudi Arabia) using bivariate and multivariate statistical models. Environ. Earth Sci.
**2016**, 75, 12. [Google Scholar] [CrossRef] - Tehrany, M.S.; Pradhan, B.; Jebur, M.N. Spatial prediction of flood susceptible areas using rule based decision tree (dt) and a novel ensemble bivariate and multivariate statistical models in gis. J. Hydrol.
**2013**, 504, 69–79. [Google Scholar] [CrossRef] - Kazakis, N.; Kougias, I.; Patsialis, T. Assessment of flood hazard areas at a regional scale using an index-based approach and analytical hierarchy process: Application in rhodope–evros region, Greece. Sci. Total Environ.
**2015**, 538, 555–563. [Google Scholar] [CrossRef] [PubMed]

Data Product Name | Resolution | Data Source |
---|---|---|

GDEMDEM 30 M | 30 m | http://www.gscloud.cn/ |

MODIS NDVI | 500 m | http://www.gscloud.cn/ |

Hydrological Observation Data | daily | http://61.187.56.156/wap/index_sq.asp |

TRMM_3B42RT | 0.25 degree | https://precip.gsfc.nasa.gov/index.html |

River Network | vector | http://ngcc.sbsm.gov.cn/ |

Moran’s I | Expectation | Variance | p-Value | R Squared | |
---|---|---|---|---|---|

Frequency | 0.3246 | −0.0097 | 0.0040 | $1.547\times {10}^{-7}$ | |

OLS residual | 0.2255 | −0.039 | 0.0043 | $2.743\times {10}^{-5}$ | 0.2623 |

Factor | ELE | SLO | ESD | DEN | RAIN | EXE | DIST | ACC | NDVI |
---|---|---|---|---|---|---|---|---|---|

VIF | 1.299 | 10.944 | 10.460 | 1.783 | 2.678 | 6.095 | 1.156 | 5.339 | 1.090 |

Factor | ELE | ESD | DEN | RAIN | EXE | DIST | ACC | NDVI |
---|---|---|---|---|---|---|---|---|

VIF | 1.331 | 1.236 | 1.837 | 2.804 | 5.980 | 1.155 | 5.265 | 1.099 |

Model | PS | NB | ESFPS | |||
---|---|---|---|---|---|---|

Factors | Coefficient | p-Value | Coefficient | p-Value | Coefficient | p-Value |

ELE | −1.58272 | 0 *** | −0.9996 | 0.001683 ** | −0.0066 | 0 *** |

ESD | −0.25210 | 0 *** | −0.19299 | 0.368332 | −0.0769 | 0.28752 |

DEN | −0.06189 | 0.11095 | 0.07266 | 0.749230 | 0.0630 | 0.000915 ** |

DIST | −0.56152 | 0 *** | −0.79702 | 0.000618 *** | −0.0187 | 0 *** |

RAIN | −0.11253 | 0.00136 ** | −0.03248 | 0.897488 | 0.0006 | 0.5612 |

EXE | 0.59830 | 0 *** | 0.58400 | 0.053373 | 1.0334 | 0 *** |

ACC | 2.876 | 0 *** | −0.70197 | 0.014845 * | 5.6894 | 0 *** |

NDVI | −0.2313 | 0 *** | −0.18582 | 0.252906 | −2.3345 | 0 *** |

Intercept | 1.7188 | 0 *** | 1.8193 | 0 *** | 1.4003 | 0 *** |

Eigenvectors | Coefficient | p-Value |
---|---|---|

EV1 | 4.1934 | 0.039604 * |

EV2 | 8.3770 | 0.000133 ** |

EV7 | −4.0476 | 0.002899 *** |

Model | AIC | Pseudo R Squared | LOOCV | Moran’s I (Expectation) |
---|---|---|---|---|

PS | 1979.4 | 0.56 | 817.9884 | −0.01929 (−0.0097) |

NB | 944.86 | 0.47 | 608.1647 | 0.05737 (−0.0097) |

ESFPS | 1040.3 | 0.78 | 430.4137 | 0.01958 (−0.0097) |

Factor | Weight | Rank |
---|---|---|

ACC | 5.6894 | 1 |

NDVI | −2.3345 | 2 |

EXE | 1.0334 | 3 |

DIST | −0.0187 | 4 |

DEN | 0.063 | 5 |

ELE | −0.0066 | 6 |

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**MDPI and ACS Style**

Fang, T.; Chen, Y.; Tan, H.; Cao, J.; Liao, J.; Huang, L.
Flood Risk Evaluation in the Middle Reaches of the Yangtze River Based on Eigenvector Spatial Filtering Poisson Regression. *Water* **2019**, *11*, 1969.
https://doi.org/10.3390/w11101969

**AMA Style**

Fang T, Chen Y, Tan H, Cao J, Liao J, Huang L.
Flood Risk Evaluation in the Middle Reaches of the Yangtze River Based on Eigenvector Spatial Filtering Poisson Regression. *Water*. 2019; 11(10):1969.
https://doi.org/10.3390/w11101969

**Chicago/Turabian Style**

Fang, Tao, Yumin Chen, Huangyuan Tan, Jiping Cao, Jiaxin Liao, and Liheng Huang.
2019. "Flood Risk Evaluation in the Middle Reaches of the Yangtze River Based on Eigenvector Spatial Filtering Poisson Regression" *Water* 11, no. 10: 1969.
https://doi.org/10.3390/w11101969