# Applying a Series and Parallel Model and a Bayesian Networks Model to Produce Disaster Chain Susceptibility Maps in the Changbai Mountain area, China

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## Abstract

**:**

## 1. Introduction

## 2. Methodologies

#### 2.1. Study Area

^{2}and is situated in Jilin Province, China (Figure 2). In the study area, the terrain is generally high in the center, low in northeast, northwest, and southwest, with a stepped topography descending to the south and southwest. Mountains and hills also exist in the area with v-shaped gullies producing significant relief. The rock types in the area consist mainly of basalt, granite, alkali trachyte, and trachyte breccia, with the basaltic rocks accounting for three-quarters of the surface area. The study area belongs to the North Temperate Zone with a continental monsoon climate. The climate is characterized by four seasons with long, cold winters and short, wetter summers. The average temperature is 2.1−3.3°C, the extreme minimum temperature is 36.4°C, and the extreme maximum temperature is 40.5°C. The average rainfall is 632−1407.6 mm, with about 60% of annual rainfall. Large and concentrated rainfall events have created favorable conditions for triggering landslides.

^{2}and the maximum is 324,000 m

^{2}. If the volcano erupts in the future, associated earthquakes and other geological processes may result in a disaster chain. Based on the locations, types and other features such as degree of damage and occurrence frequency of past events, the earthquake-landslide-debris flow disaster chain was selected as the focus of this study.

#### 2.2. Series and Parallel Model

#### 2.2.1. Circuit Principle

_{1}, R

_{2}, and R

_{3}represent the resistance values of three electrical appliances. S represents a closed switch. R

_{2}and R

_{3}form a parallel circuit and R

_{1}forms a series circuit again. When S is closed, the circuit is connected, there is current in the circuit and it is in the path state, the resistance and current in the circuit can be calculated using formulas (1)–(3):

_{1}, R

_{2}, R

_{3}are the resistance values of the electrical appliances, R

_{23}is the parallel circuit resistance, U is the voltage in the circuit, and I is the electric current in the circuit.

#### 2.2.2. Analysis of Disaster Development Conditions

#### 2.2.3. Evaluation of the Series and Parallel Model of Disaster Chain Susceptibility

_{i}and R

_{j}are the resistance values of every parameter in the system.

#### 2.3. Bayesian Networks Model

#### 2.3.1. Bayesian Networks Principle

#### 2.3.2. Bayesian Network Model Construction for the Earthquake Disaster Chain

## 3. Results

#### 3.1. Disaster Chain Susceptibility Assessment from the Series and Parallel Model

#### 3.2. Disaster Chain Susceptibility Assessment of Bayesian Networks Model

^{2}is due to software limitations and this is a drawback that needs to be addressed in future research. The attributed values (earthquake intensity, precipitation, elevation, slope, slope aspect, lithology, distance to rivers, distance to faults, land use and NDVI) for each cell center point were extracted using spatial analysis tools in ArcGIS software. The grid cell data were then converted into case file format and input into the BN model in the Netica software, and the probabilities of the earthquake-landslide and earthquake-landslide-debris flow disaster chains were obtained from the BN model. The susceptibility maps of the earthquake-landslide and the earthquake-landslide-debris flow disaster chains are shown in Figure 8a,b, respectively. The susceptibility zones from the BN model are broadly similar to those from the series and parallel model. According to the two maps, 52.9%, 24.45%, 8.38%, 8.81%, and 5.45% of the studied area is characterized by very low, low, medium, high, and very high susceptibility to an earthquake-landslide disaster chain, respectively. In the same way, 49.51%, 26.04%, 9.84%, 8.76% and 5.84% of the studied area are characterized by very low, low, medium, high, and very high susceptibility to an earthquake-landslide-debris flow disaster chain, respectively.

#### 3.3. Relative Analysis of the Susceptibility Evaluation Results

#### 3.4. Verification of the Different Susceptibility Evaluation Models

## 4. Discussions

## 5. Conclusions

- (1)
- Visual analysis of the four disaster chain susceptibility maps showed that the susceptibility zones obtained from the series and parallel model and the Bayesian Networks model are broadly similar. Very high and high susceptibility are predominantly located within a 10 km radius of the Tianchi volcano, whereas the northern and southwestern sections of the study area were identified as low and very low susceptibility zones.
- (2)
- The basic linear correlation and cross-correlation methods were applied to compare the series and parallel model and the Bayesian Networks model, and the correlation coefficients, Cramer’s V and kappa index showed that the two models were similar and approximately compatible.
- (3)
- The verification results of the ROC curve for the two models were found to be 0.7727 and 0.8062 respectively, showing that two models have great potential for forecasting and early warning, and could be applied in emergency management for earthquake disaster chains in the future.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Condition parameters: (

**a**) Elevation, (

**b**) Slope, (

**c**) Slope aspect, (

**d**) Lithology, (

**e**) Distance to river, (

**f**) Distance to fault, (

**g**) Land use, (

**h**) NDVI, (

**i**) Rainfall.

**Figure 7.**Series and parallel model disaster chain susceptibility maps for the chains: (

**a**) Earthquake-landslide, and (

**b**) Earthquake-landslide-debris flow.

**Figure 8.**BN model disaster chain susceptibility maps for the chains: (

**a**) Earthquake-landslide and (

**b**) Earthquake-landslide-debris flow.

**Figure 9.**The ROC curve of the susceptibility assessment results for (

**a**) The series and parallel model, (

**b**) The Bayesian Networks model.

**Table 1.**The relative analysis results between the series and parallel model and the Bayesian Networks model.

Earthquake-landslide | Earthquake-landslide-debris flow | |
---|---|---|

Correlation coefficients | 0.8267 | 0.9384 |

Cramer’s V | 0.71 | 0.782 |

Chi-square | 11941.334 | 14497.015 |

Kappa index | 0.602 | 0.757 |

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**MDPI and ACS Style**

Han, L.; Zhang, J.; Zhang, Y.; Lang, Q. Applying a Series and Parallel Model and a Bayesian Networks Model to Produce Disaster Chain Susceptibility Maps in the Changbai Mountain area, China. *Water* **2019**, *11*, 2144.
https://doi.org/10.3390/w11102144

**AMA Style**

Han L, Zhang J, Zhang Y, Lang Q. Applying a Series and Parallel Model and a Bayesian Networks Model to Produce Disaster Chain Susceptibility Maps in the Changbai Mountain area, China. *Water*. 2019; 11(10):2144.
https://doi.org/10.3390/w11102144

**Chicago/Turabian Style**

Han, Lina, Jiquan Zhang, Yichen Zhang, and Qiuling Lang. 2019. "Applying a Series and Parallel Model and a Bayesian Networks Model to Produce Disaster Chain Susceptibility Maps in the Changbai Mountain area, China" *Water* 11, no. 10: 2144.
https://doi.org/10.3390/w11102144