# Flood Risk Analysis of Different Climatic Phenomena during Flood Season Based on Copula-Based Bayesian Network Method: A Case Study of Taihu Basin, China

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

#### 2.1. Study Area

^{2}. The Taihu Lake, with a water surface area of 2336.8 km

^{2}, is located in the center of the basin. The basin lies in a subtropical zone, with the climate being controlled by the summer monsoon. The average annual precipitation is 1177 mm, concentrated mainly in the flood season. The upper reaches of the Taihu Basin are mountainous areas, whereas the lower reaches are mostly plains. In the flood season, this unusual terrain (high on all sides and low in the middle) leads to upstream floods and basin precipitation confluence in the plains (urbanized areas). Consequently, flood disasters can occur easily. According to geographic and hydrological conditions, the Taihu Basin is usually divided into eight hydrological regions [36]. Detailed information on the eight hydrological sub-regions is listed in Table 1.

#### 2.2. Data

## 3. Methodology

#### 3.1. Flood Season Staging Based on the Different Climatic Phenomena

#### 3.1.1. Distribution Function of Plum Rain and Typhoon Occurrence Times

_{i}and y

_{i}represent the empirical frequency, and theoretical frequency, respectively; $\overline{x}$ and $\overline{y}$ are the mean of empirical frequency and theoretical frequency, respectively; and n is the number of samples.

#### 3.1.2. Flood Season Staging and Results Verification

_{1}and α

_{2}are the weight coefficients (α

_{1}+ α

_{2}= 1), μ

_{1}and μ

_{2}are the means of the samples, and σ

_{1}and σ

_{2}are the mean square deviations of the samples.

#### 3.2. Division of Precipitation Sub-Region Based on Hydrological Regionalization

#### 3.2.1. Clustering of Hydrological Sub-Regions Based on the Correlation Analysis of Precipitation

#### 3.2.2. Select Optimal Precipitation Sub-Regions Division by Copula Functions

_{i}(x

_{i}) represents the marginal distribution of the i-th sub-region precipitation, F(y) represents the marginal distribution of the Taihu Lake water level, and C

_{θ}is the copula CDF with parameter θ.

#### 3.3. Flood Risk Management Based on Copula-Based Bayesian Network

#### 3.3.1. Setting of Flood Disaster Situations

#### 3.3.2. Establishment of Bayesian Network

_{Pa(Xi)}= x is a shorthand notation for X

_{Pa1(Xi)}= x

_{Pa1(Xi)}, … , X

_{Pam(Xi)}= x

_{Pam(Xi)}and Pa(X

_{i}) indicate the set containing m parents of node X

_{i}. For nodes without parents, Pa(X

_{i}) is an empty set so that f

_{XiPa(Xi)}= f

_{Xi}.

## 4. Results

#### 4.1. Results of Flood Season Staging

#### 4.2. Results of Hydrological Sub-Region Clustering

#### 4.3. Risk Management Model for Flood Control and Drainage in the Taihu Basin

#### 4.3.1. The Result of Flood Disaster Situation Setting

#### 4.3.2. The Result of Copula-Based Bayesian Network Model

## 5. Discussion

#### 5.1. Rationality Analysis of the Precipitation Sub-Region Division Results

_{i}, and PCP

_{i}, respectively, are the precipitation concentration degree and concentration period in the research time; R

_{i}is the total precipitation in the research time, and r

_{ij}is the precipitation in five days. θ

_{j}is the corresponding azimuth angle in the research time (the entire research time is 360°); i is the year (i = 1954, … ,2011); j is a five day series in the research time.

#### 5.2. Risk Analysis of Flood Disaster in the Taihu Basin During Different Periods

#### 5.2.1. Flood Analysis in the Plum Rain Period

#### 5.2.2. Flood Analysis in the Typhoon Period

## 6. Conclusions

- Due to meteorological reasons, the occurrence time of plum rain and typhoon present regularity, resulting in uneven distribution of precipitation during the flood season. Our flood season staging indicated that the plum rain period is from June 24 to July 21 and the typhoon period is from July 22 to September 22.
- The spatial heterogeneity of precipitation is different under the influence of the different climatic phenomena. In the plum rain period, the Taihu Basin is divided into three precipitation sub-regions (P-I, P-II, and P-III). In the typhoon period, the Taihu Basin serves as a whole for flood risk analysis.
- In future, the occurrence probability of adverse drainage situations in the Taihu Basin during the plum rain period and the typhoon period is 2.4%, and 0.8%, respectively. Furthermore, the risk increases rapidly as the Taihu Lake water level rises.
- Although the annual precipitation of the Taihu Basin is concentrated in the flood season, the precipitation heterogeneous varies with the differing climatic phenomena. This implies that the risks of flood disaster also differs. Consequently, appropriate emergency plans should be developed to prevent and manage flood disasters occurring in the different periods during the flood season.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Probability density functions of random variables. (

**a**) start time of the plum rain period (STP); (

**b**) plum rain period (ETP); (

**c**) initial time when typhoon begins to affect the Taihu Basin (ITT); (

**d**) Taihu Lake exceeds the warning water level (TWL).

**Figure 4.**Correlation results of precipitation between eight hydrological regions. (

**a**–

**c**) are the results for the plum rain period. (

**d**–

**f**) are the results for the typhoon period; (

**a**,

**d**) are Pearson correlation results; (

**b**,

**e**) are Spearman correlation results; (

**c**,

**f**) are Kendall correlation results.

**Figure 5.**Correlation results of precipitation between four precipitation sub-regions. (

**a**–

**c**) are the results for the plum rain period; (

**d**–

**f**) are the results for the typhoon period; (

**a**,

**d**) are Pearson correlation results; (

**b**,

**e**) are Spearman correlation results; (

**c**,

**f**) are Kendall correlation results.

**Figure 6.**Precipitation sub-region divisions and the probability-probability plots of regional precipitation and the Taihu Lake water level in the typhoon period (

**a**) and plum rain period (

**b**). C is short for Clayton copula; G is short for Gumbel copula; F is short for Frank copula; J is short for Joe copula.

**Figure 7.**Results of precipitation sub-region division in the plum rain period (

**a**) and typhoon period (

**b**).

**Figure 10.**Isogram of precipitation amount (

**a**–

**c**), precipitation concentration degree (PCD) (

**d**–

**f**), and precipitation concentration period (PCP) (

**g**–

**i**) in the Taihu Basin.

**Figure 11.**The priori reasoning of Bayesian network (

**a**), and the posterior probability of various precipitation situations (

**b**–

**d**) in the plum rain period.

**Figure 12.**Priori reasoning of the Bayesian network (

**a**), and the posterior probability of various precipitation situations (

**b**), (

**c**), (

**d**) in the typhoon period.

ID | Name | Areas | Annual Precipitation |
---|---|---|---|

I | Hu Xi | 7897 km^{2} | 1169.1 mm |

II | Wu Cheng Xi Yu | 3615 km^{2} | 1118.5 mm |

III | Yang Cheng Dian Mao | 4314 km^{2} | 1142.0 mm |

IV | Pu Xi | 2165 km^{2} | 1159.9 mm |

V | Pu Dong | 2301 km^{2} | 1153.2 mm |

VI | Hang Jia Hu | 7480 km^{2} | 1247.0 mm |

VII | Zhe Xi | 5931 km^{2} | 1430.4 mm |

VIII | Taihu Lake | 3192 km^{2} | 1183.4 mm |

Family | Parameter Space θ | Generator $\mathit{\phi}(\mathit{t})$ | Expression $\mathit{C}({\mathit{u}}_{1},{\mathit{u}}_{2},\cdots ,{\mathit{u}}_{\mathit{d}})$ |
---|---|---|---|

Clayton | [0, ∞) | $\frac{1}{\theta}({t}^{-\theta}-1)$ | ${\left[({\displaystyle \sum _{j=1}^{d}{u}_{j}^{-\theta}})+1-d\right]}^{-\frac{1}{\theta}}$ |

Gumbel | [1, ∞) | ${(-\mathrm{ln}t)}^{\theta}$ | $\mathrm{exp}\left\{-{\left[{\displaystyle \sum _{j=1}^{d}{(-\mathrm{ln}{u}_{j})}^{\theta}}\right]}^{\frac{1}{\theta}}\right\}$ |

Frank | [0, ∞) | $-\mathrm{ln}\frac{{e}^{-\theta t}-1}{{e}^{-\theta}-1}$ | $-\frac{1}{\theta}\mathrm{ln}\left[1+({\displaystyle \prod _{j=1}^{d}{e}^{-\theta {u}_{j}}}-1)/{({e}^{-\theta}-1)}^{d-1}\right]$ |

Joe | [1, ∞) | $-\mathrm{ln}(1-{(1-t)}^{\theta})$ | $1-{\left\{1-{\displaystyle \prod _{j=1}^{d}\left[1-{(1-{u}_{j})}^{\theta}\right]}\right\}}^{\frac{1}{\theta}}$ |

Param | Normal | Lognormal | Gamma | Weibull | Logistic | Beta | |
---|---|---|---|---|---|---|---|

STP | Param#1 | 189.10 | 5.24 | 414.96 | 21.10 | 189.02 | 200.10 |

Param#2 | 9.27 | 0.05 | 2.19 | 193.52 | 5.27 | 186.15 | |

ETP | Param#1 | 165.50 | 5.11 | 407.16 | 22.62 | 166.03 | 227.00 |

Param#2 | 8.09 | 0.05 | 2.46 | 169.15 | 4.39 | 273.66 | |

ITT | Param#1 | 220.86 | 5.38 | 39.76 | 6.83 | 220.92 | 15.05 |

Param#2 | 34.49 | 0.16 | 0.18 | 235.55 | 19.65 | 9.80 |

Statistic | Normal | Lognormal | Gamma | Weibull | Logistic | Beta | |
---|---|---|---|---|---|---|---|

STP | acceptance | accept | refuse | accept | accept | accept | refuse |

D | 0.116 | 0.122 | 0.120 | 0.083 | 0.095 | 0.126 | |

ETP | acceptance | accept | accept | accept | refuse | accept | accept |

D | 0.079 | 0.070 | 0.071 | 0.120 | 0.074 | 0.080 | |

ITT | acceptance | accept | accept | accept | refuse | accept | refuse |

D | 0.050 | 0.056 | 0.051 | 0.075 | 0.053 | 0.064 |

**Table 5.**Goodness-of-fit tests for start time of the plum rain period (STP), plum rain period (ETP), and initial time when typhoon begins to affect the Taihu Basin (ITT).

Distribution | PPCC | MAE | RMSE | DC | |
---|---|---|---|---|---|

STP | Normal | 0.93806 | 0.07608 | 0.00664 | 0.99884 |

Lognormal | 0.86239 | 0.08376 | 0.00793 | 0.99834 | |

Gamma | 0.87721 | 0.08127 | 0.0075 | 0.99852 | |

Weibull | 0.98716 | 0.05248 | 0.00314 | 0.99974 | |

Logistic | 0.92573 | 0.0717 | 0.00616 | 0.999 | |

Beta | 0.89938 | 0.07707 | 0.0068 | 0.99878 | |

ETP | Normal | 0.97582 | 0.04382 | 0.00245 | 0.9998 |

Lognormal | 0.98705 | 0.0401 | 0.00201 | 0.99987 | |

Gamma | 0.98544 | 0.04088 | 0.00212 | 0.99985 | |

Weibull | 0.81086 | 0.08068 | 0.00728 | 0.99825 | |

Logistic | 0.98186 | 0.05228 | 0.00358 | 0.99958 | |

Beta | 0.97941 | 0.04404 | 0.00248 | 0.9998 | |

ITT | Normal | 0.97432 | 0.02271 | 0.00069 | 0.99995 |

Lognormal | 0.94455 | 0.0288 | 0.00105 | 0.99987 | |

Gamma | 0.96392 | 0.02624 | 0.00064 | 0.99991 | |

Weibull | 0.93664 | 0.03021 | 0.00109 | 0.99985 | |

Logistic | 0.9652 | 0.02909 | 0.00112 | 0.99985 | |

Beta | 0.97077 | 0.02275 | 0.00085 | 0.99994 |

Time | Copulas | AIC | BIC | ||||||
---|---|---|---|---|---|---|---|---|---|

Scheme 1 | Scheme 2 | Scheme 3 | Scheme 4 | Scheme 1 | Scheme 2 | Scheme 3 | Scheme 4 | ||

Plum rain period | Clayton | −181 | −188 | −189 | −176 | −175 | −182 | −183 | −171 |

Gumbel | −174 | −180 | −175 | −178 | −168 | −174 | −169 | −173 | |

Frank | −164 | −172 | −173 | −176 | −158 | −166 | −167 | −170 | |

Joe | −158 | −167 | −164 | −181 | −152 | −161 | −158 | −175 | |

Typhoo-n period | Clayton | −1124 | −1197 | −1193 | −1775 | −1113 | −1185 | −1181 | −1763 |

Gumbel | −1131 | −1176 | −1179 | −1792 | −1120 | −1164 | −1168 | −1780 | |

Frank | −1045 | −1123 | −1133 | −1753 | −1033 | −1112 | −1121 | −1741 | |

Joe | −989 | −1062 | −1080 | −1803 | −977 | −1051 | −1069 | −1792 |

Conducive Drainage Situation | |||||||||||||||

P-I precipitation | Low | Low | Low | Low | High | Low | High | High | High | ||||||

P-II precipitation | Low | Low | Low | High | Low | High | Low | High | High | ||||||

P-III precipitation | Low | Low | High | Low | Low | High | High | Low | High | ||||||

Taihu Lake water level | ↑ | ↓ | ↓ | ↓ | ↓ | ↓ | ↓ | ↓ | ↓ | ||||||

Encounter probability | 12.183 | 81.978 | 0.956 | 1.019 | 1.142 | 0.143 | 0.17 | 0.052 | 0.001 | ||||||

Adverse Drainage Situation | |||||||||||||||

P-I precipitation | High | Low | Low | High | High | High | Low | ||||||||

P-II precipitation | High | Low | High | Low | High | Low | High | ||||||||

P-III precipitation | High | High | Low | Low | Low | High | High | ||||||||

Taihu Lake water level | ↑ | ↑ | ↑ | ↑ | ↑ | ↑ | ↑ | ||||||||

Encounter probability | 0.021 | 0.878 | 0.411 | 0.171 | 0.58 | 0.157 | 0.137 |

Conducive Drainage Situation | Adverse Drainage Situation | ||||||||
---|---|---|---|---|---|---|---|---|---|

Taihu Basin Precipitation | Low | Middle | Middle | Low | Low | High | High | Middle | High |

Taihu Lake water level | ↓ | ↔ | ↓ | ↔ | ↑ | ↓ | ↔ | ↑ | ↑ |

Encounter probability | 86.52 | 0.74 | 8.44 | 2.25 | 1.21 | 0.04 | 0.01 | 0.75 | 0.05 |

Situation | P-I Precipitation | P-II Precipitation | P-III Precipitation | Taihu Lake Water Level |
---|---|---|---|---|

A | Is High | High or Low? | High or Low? | ↑or↓? |

B | Is High | Is High | High or Low? | ↑or↓? |

C | Is High | Is High | Is High | ↑or↓? |

Situation | Taihu Basin Precipitation | Taihu Lake Water Level |
---|---|---|

A | Is Low | ↑ or ↔ or ↓? |

B | Is Middle | ↑ or ↔ or ↓? |

C | Is High | ↑ or ↔ or ↓? |

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## Share and Cite

**MDPI and ACS Style**

Luo, Y.; Dong, Z.; Guan, X.; Liu, Y.
Flood Risk Analysis of Different Climatic Phenomena during Flood Season Based on Copula-Based Bayesian Network Method: A Case Study of Taihu Basin, China. *Water* **2019**, *11*, 1534.
https://doi.org/10.3390/w11081534

**AMA Style**

Luo Y, Dong Z, Guan X, Liu Y.
Flood Risk Analysis of Different Climatic Phenomena during Flood Season Based on Copula-Based Bayesian Network Method: A Case Study of Taihu Basin, China. *Water*. 2019; 11(8):1534.
https://doi.org/10.3390/w11081534

**Chicago/Turabian Style**

Luo, Yun, Zengchuan Dong, Xike Guan, and Yuhuan Liu.
2019. "Flood Risk Analysis of Different Climatic Phenomena during Flood Season Based on Copula-Based Bayesian Network Method: A Case Study of Taihu Basin, China" *Water* 11, no. 8: 1534.
https://doi.org/10.3390/w11081534