# Quantitative Agricultural Flood Risk Assessment Using Vulnerability Surface and Copula Functions

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## Abstract

**:**

## 1. Introduction

^{5}km

^{2}and lead to 2 × 10

^{5}million yuan in annual losses in China [10]. The bulletin of flood and drought disasters in China reported on floods and extreme precipitation, with both showing a synchronous increase since 2008, and the total flood disaster area of the crops associated with extreme precipitation increased from 2006–2013 [11]. This means that the effect of flood disasters is closely related to the intensity of the precipitation, and the extreme precipitation can be used to some extent to analyse the evolution and influence of the flood. The study area is located in the Midwest Jilin province (MJP), which is part of the mollisol region of northeastern China and includes one of the three famous maize belts of the world. However, the MJP is also an area influenced by flood disasters and this often results in yield reduction. In the 1990s, floods occurred almost every three years in the area, with high intensity, wide range, and heavy losses [12]. The most serious one is extensive rainfall, which caused floods in the region in July 2010, and affected tens of thousands of families. It was estimated that the total direct economic loss exceeded 1.03 billion yuan [13]. Therefore, it is important to assess the risk of flood disasters to develop strategies to mitigate flood hazards and reduce losses.

## 2. Materials and Methods

#### 2.1. Study Region

^{4}km

^{2}, accounting for 44.23% of the Jilin Province. The MJP is one of the main distribution areas of black soil and maize in China. The so-called golden maize zone has a good reputation because of the good quality, properties, and starch content [31]. The total cereal and oilseeds area is 4.79 × 10

^{6}ha, which accounts for 83.10% of the total area. Crops include maize, rice, potatoes, soybeans, sunflower seeds, fruits, tobacco, and beet. The main types of crops are maize, rice, and soybeans. The proportions of these individual crops of the planted area in the MJP in 2014 were as follows: 71.01%, 11.07%, and 4.20%, respectively [32]. In addition to soybeans, the acreage of maize and rice volatility is increasing. The yield of maize and rice has been declining in recent years due to the occurrence of disastrous weather. On the contrary, the total area of grain and oil crops is increasing. The maize and soybean yields are increasing at a rate of 13.56 kg/ha and 3.8 kg/ha per ten years, respectively (Figure 2).

#### 2.2. Data Source and Processing

#### 2.2.1. Multifractal Detrended Fluctuation Analysis Method

#### 2.2.2. Marginal Distribution Functions

#### 2.2.3. Joint Distribution Function of the Flood Indicators

_{i}denotes the bivariate joint empirical probability of the extreme precipitation factors, P

_{i}is the probability of the copula joint distribution function, and i represents the number of parameters in the model.

#### 2.2.4. Joint Return Period of Flood Indicators

#### 2.2.5. The Vulnerability Surface Model

#### 2.2.6. Quantitative Agricultural Flood Risk Assessment

_{0}, a series of points (x) indicates the intensity of the flood that satisfies Equation (10):

## 3. Results

#### 3.1. Determining the Threshold of Extreme Precipitation Events

_{j}DFA index deviates from the original DFA value. When the rearrangement of the interval data decreases, the y

_{j}DFA exponential converges to the original DFA value. Based on the threshold of the extreme precipitation event variance, the threshold of the extreme precipitation events in Baicheng and Changchun is 38.5 mm and 47.8 mm, respectively (Table 2) [38].

#### 3.2. Joint Return Period of Flood Hazards

#### 3.3. Vulnerability Surface Model

^{2}at the 0.05 significance level is 0.6778, which indicates that the model on behalf of the vulnerability of the region is effective and quantitatively signifies the level of agricultural flood vulnerability in the MJP. Figure 6 shows that the extent of the flood damage in the agricultural area increases with TEP and CDEP. The main reason for this was found in the statistical data. The CDEP increase is mainly due to the continuous non-cumulative number of days due to extreme precipitation when TEP and CDEP increase, while the intensity of extreme precipitation in a single events trend to huge. However, the intensity of the extreme events poses greater risks for crops than that of non-extreme precipitation events. The greater the intensity of the extreme precipitation and quantity of ground water are, the greater is the probability of flooding. The weather was not conducive to sustained rainfall and the growth of crops, and could easily lead to crop reduction.

#### 3.4. Risk Curves

^{4}hm

^{2}. The comparison of the simulated values and historical statistics indicates seven or eight flood disasters for each county. In other words, flood disasters occurred every seven to eight years between 1960 and 2014 in the MJP. Although the simulated values were smaller than the observed data, this implies that the proposed model for the flood risk assessment is highly accurate and efficient.

## 4. Discussion

## 5. Conclusions

- (1)
- The CDEP and TEP both had a tendency of increase in the MJP. The threshold of extreme precipitation events gradually decreases from east to west, and their spatial distribution is similar to that of the precipitation in this region. The CDEP highly correlates with the TEP at each station and all correlation coefficients pass the 0.05 significance test;
- (2)
- The shortest joint return period was determined for Fuyu and Changchun, which indicates that the flood hazard level of the two regions is higher. On contrary, the longest joint return period was obtained for Tongyu and Qianguo at the same intensity of flood indicators; and
- (3)
- We found that the agricultural flood risk of the MJP gradually decreases from east to west, and the spatial distribution of risk in the area with the same spatial pattern of that of the flood hazard, which further illustrates that the amount and duration of extreme precipitation are the important factors affecting agricultural losses in the region.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**Temporal variations of the main types of crops in the MJP. (

**a**) variation characteristics of maize yield; (

**b**) variation characteristics of rice yield; (

**c**) variation characteristics of soybean yield; (

**d**) the proportions of individual crops area.

Copula Function | $\mathit{C}\left({\mathit{u}}_{1},{\mathit{u}}_{2}\right)$ | Parameter Space |
---|---|---|

Frank Copula | $F\left(x,y\right)=C\left({u}_{1},{u}_{2}\right)=-\frac{1}{\theta}ln\left[1+\frac{\left({e}^{-\theta {u}_{1}}-1\right)\left({e}^{-\theta {u}_{2}}-1\right)}{{e}^{-\theta}-1}\right]$ | $\theta \in \mathrm{R}$ |

Clayton Copula | $F\left(x,y\right)=C\left({u}_{1},{u}_{2}\right)={({{u}_{1}}^{-\theta}+{{u}_{2}}^{-\theta}-1)}^{-1/\theta}$ | $\theta \in \left[0,\infty \right]$ |

Gumbel Copula | $F\left(x,y\right)=C\left({u}_{1},{u}_{2}\right)=exp\left\{-{\left[{\left(-ln{u}_{1}\right)}^{\theta}+{\left(-ln{u}_{2}\right)}^{\theta}\right]}^{1/\theta}\right\}$ | $\theta \in \left[1,\infty \right]$ |

Stations | Changchun | Tongyu | Changling | Qianan | Qianguo | Shuangliao | Fuyu | Baicheng | Siping |
---|---|---|---|---|---|---|---|---|---|

threshold | 47.8 | 38.3 | 48.2 | 38.4 | 37.1 | 58.5 | 43 | 38.5 | 56.6 |

Indicators | Parameters | Changchun | Tongyu | Changling | Qianan | Qianguo | Shuangliao | Fuyu | Baicheng | Siping |
---|---|---|---|---|---|---|---|---|---|---|

TEP | k | 0.375 | 0.200 | 0.295 | −0.026 | 0.844 | 0.808 | 0.337 | 0.498 | 0.674 |

s | 45.635 | 45.170 | 39.520 | 44.960 | 29.917 | 44.423 | 37.930 | 47.953 | 45.413 | |

m | 84.566 | 91.208 | 79.495 | 94.979 | 71.990 | 81.112 | 94.069 | 100.317 | 96.017 | |

CDEP | k | 0.302 | 0.250 | −0.183 | 0.171 | 0.469 | 0.527 | 0.606 | 0.319 | 0.539 |

s | 2.464 | 2.149 | 2.485 | 2.039 | 1.709 | 2.241 | 1.577 | 1.967 | 2.248 | |

m | 3.433 | 3.545 | 3.946 | 3.187 | 2.425 | 3.407 | 2.387 | 3.363 | 3.302 |

Stations | Copula Functions | RMSE | AIC | Parameter |
---|---|---|---|---|

Baicheng | Clayton | 0.0653 | −116.9052 | 1.4973 |

Frank | 0.0533 | −125.8407 | 7.1460 | |

Gumbel | 0.0501 | −128.6466 | 2.4672 | |

Qianan | Clayton | 0.0679 | −115.1339 | 0.9138 |

Frank | 0.0529 | −126.1794 | 4.8031 | |

Gumbel | 0.0500 | −128.6915 | 1.8931 | |

Qianguo | Clayton | 0.0541 | −125.2456 | 2.0720 |

Frank | 0.0530 | −126.1135 | 7.4039 | |

Gumbel | 0.0521 | −126.8485 | 2.5475 | |

Tongyu | Clayton | 0.0617 | −119.3877 | 1.8507 |

Frank | 0.0627 | −118.6967 | 6.7939 | |

Gumbel | 0.0712 | −113.0363 | 2.0599 | |

Changling | Clayton | 0.0603 | −120.4239 | 1.8507 |

Frank | 0.0520 | −126.9380 | 6.7939 | |

Gumbel | 0.0511 | −127.7760 | 2.0599 | |

Fuyu | Clayton | 0.0547 | −124.7080 | 2.2624 |

Frank | 0.0510 | −127.7962 | 9.1288 | |

Gumbel | 0.0506 | −128.1797 | 2.8739 | |

Shuangliao | Clayton | 0.0652 | −116.9382 | 0.9143 |

Frank | 0.0566 | −123.1843 | 4.4784 | |

Gumbel | 0.0540 | −125.2837 | 1.8775 | |

Siping | Clayton | 0.0615 | −119.5317 | 1.5214 |

Frank | 0.0578 | −122.2900 | 6.6635 | |

Gumbel | 0.0542 | −125.0960 | 2.4773 | |

Changchun | Clayton | 0.0738 | −111.4586 | 1.3408 |

Frank | 0.0568 | −123.0482 | 7.4784 | |

Gumbel | 0.0551 | −124.3642 | 2.6622 |

Coefficient | a | b | C | d | e | f |
---|---|---|---|---|---|---|

Estimated Value | 3421 | −32.14 | 292.9 | 0.3552 | 0.7325 | −7.738 |

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**MDPI and ACS Style**

Wang, Y.; Liu, G.; Guo, E.; Yun, X.
Quantitative Agricultural Flood Risk Assessment Using Vulnerability Surface and Copula Functions. *Water* **2018**, *10*, 1229.
https://doi.org/10.3390/w10091229

**AMA Style**

Wang Y, Liu G, Guo E, Yun X.
Quantitative Agricultural Flood Risk Assessment Using Vulnerability Surface and Copula Functions. *Water*. 2018; 10(9):1229.
https://doi.org/10.3390/w10091229

**Chicago/Turabian Style**

Wang, Yongfang, Guixiang Liu, Enliang Guo, and Xiangjun Yun.
2018. "Quantitative Agricultural Flood Risk Assessment Using Vulnerability Surface and Copula Functions" *Water* 10, no. 9: 1229.
https://doi.org/10.3390/w10091229