# Flash Flood Hazard Susceptibility Mapping Using Frequency Ratio and Statistical Index Methods in Coalmine Subsidence Areas

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}. The general topography of this area is characterized by hills with elevations ranging from 150 to 1170 m above sea level. The study area experiences a temperate, humid-semi-arid continental monsoon climate. It is cold and dry in winter, and hot and wet in summer. The annual precipitation is 600–800 mm. The bedrock in this region mainly consists of sandstone (Zq), limestone ($\in $), dolomite (O), carboniferous (C), siltstone (P) and sandstone conglomerate (J). The annual temperature range is −22.9 °C to 40.2 °C, while annual average temperatures range between 4 °C and 11.7 °C. The early Jurassic period was important for coal formation in this area. The boundary of the XQG and its location is shown in Figure 1. Four small villages are located within the XQG. This catchment used to be a coal-mining region.

#### 2.1. Flash Flood Hazard Inventory

#### 2.2. Conditioning Parameters

_{s}is the specific catchment area (m

^{2}/m), and β (radian) is the slope gradient (in degrees) [52].

## 3. Data Collection

^{2}and was produced using the 5 m interval contours from a geomorphologic map generated using Geographic Information System (GIS). The DEM is the ideal source from which to derive topographic parameters of elevation, slope, curvature, SPI, and TWI. The DEM and its derivatives play a major role in determining which areas are susceptible to flood occurrence [56]. The geology parameter was obtained using a geological map of Beijing, which has a scale of 1:10,000. The land use parameter was extracted from remotely-sensed imagery. Both the land use data and soil texture data were provided by the Beijing Institute of Geology. The subsidence risk level parameter was obtained from Zhang [53]. Short-term heavy rain data were collected from 187 weather stations in Beijing during 2006–2010 and summarized by Wang [55].

## 4. Methods

#### 4.1. Frequency Ratio

#### 4.2. Statistical Index

_{ij}is the weight given to the i-th class of the j-th parameter. D

_{ij}is the flash flooding hazard density within the i-th class of the j-th parameter. D is the total flash flooding hazard density within the study area. N

_{ij}is the number of pixels with flash flooding hazard in the i-th class of the j-th parameter. M

_{ij}is the number of pixels in the i-th class of the j-th parameter. N is the total number of flash flooding hazards in the study area. M is the total number of pixels in the study area. Since the natural logarithm (ln) is not defined, the weighting value (W

_{ij}) can only be calculated for classes that contain flash flooding hazards.

_{ij}and n represent the flash flood hazard susceptibility index, the weighting values of the i-th class of the j-th parameter using the SI model and the number of conditioning parameters, respectively.

_{ij}(SI) shows the flash flooding hazard susceptibility index using the statistical index method. N

_{ij}represents the number of flash flooding hazards in the i-th class of the j-th parameter. M

_{ij}represents the number of pixels in the i-th class of the j-th parameter. N is the total number of flash flooding hazards, out of the 60 hazard locations. M represents the number of pixels in the domain. Because there are no flash flooding hazards in the study area between 994 m and 1170 m elevation, the W

_{ij}(SI) for this class is set to −1 to indicate the extremely low possibility of flash flood hazard occurrence [60].

## 5. Results and Discussion

#### 5.1. Application of the Frequency Ratio Model

^{2}.

#### 5.2. Application of the Statistical Index Model

^{2}.

#### 5.3. Validation

#### 5.4. Discussion

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Field survey: (

**a**) coalmine caves; (

**b**) subsidence; (

**c**) ground fissures and (

**d**) coalmine slag.

**Figure 3.**Flash flood hazards in the field: (

**a**) landslide; (

**b**) roadbed scouring; (

**c**) lateral erosion and (

**d**) ground erosion.

**Figure 4.**Input thematic layers: (

**a**) elevation; (

**b**) slope; (

**c**) curvature; (

**d**) SPI; (

**e**) TWI; (

**f**) geology; (

**g**) land use; (

**h**) soil texture; (

**i**) subsidence risk area and (

**j**) short-term heavy rain.

**Figure 5.**Flash flood hazard susceptibility using (

**a**) Frequency Ratio-natural breaks method (FR.1) (

**b**) Statistical Index-natural breaks (SI) and (

**c**) Frequency Ratio-manual classification (FR.2).

**Figure 6.**Success and prediction rate curves using Frequency Ratio-natural break (FR.1), Frequency Ratio-manual classification (FR.2) and Statistical Index-natural breaks (SI): (

**a**) success rate curve (

**b**) prediction rate curve.

Parameter | Class | No. of Pixels in Domain | Percentage of Domain | No. of Flash Flood Hazard | Percentage of Flash Flood Hazard | FR | SI |
---|---|---|---|---|---|---|---|

Elevation/m | 150–250 | 202,955 | 15.86 | 24 | 40 | 2.52 | 0.92 |

250–338 | 248,232 | 19.40 | 17 | 28.33 | 1.46 | 0.38 | |

338–422 | 237,960 | 18.60 | 16 | 26.67 | 1.43 | 0.36 | |

422–506 | 187,934 | 14.69 | 3 | 5.00 | 0.34 | −1.08 | |

506–594 | 148,022 | 11.57 | 0 | 0 | 0 | −1 | |

594–686 | 86,181 | 6.74 | 0 | 0 | 0 | −1 | |

686–782 | 68,821 | 5.38 | 0 | 0 | 0 | −1 | |

782–882 | 50,616 | 3.96 | 0 | 0 | 0 | −1 | |

882–994 | 34,910 | 2.73 | 0 | 0 | 0 | −1 | |

994–1170 | 13,795 | 1.08 | 0 | 0 | 0 | −1 | |

Slope angle/° | 0–7 | 74,593 | 5.83 | 7 | 11.67 | 2.00 | 0.69 |

7–15 | 112,220 | 8.77 | 16 | 26.67 | 3.04 | 1.11 | |

15–22 | 154,270 | 12.06 | 12 | 20 | 1.66 | 0.51 | |

22–28 | 179,982 | 14.07 | 6 | 10 | 0.71 | −0.34 | |

28–34 | 203,349 | 15.89 | 7 | 11.67 | 0.73 | −0.31 | |

34–39 | 188,388 | 14.72 | 8 | 13.33 | 0.91 | −0.10 | |

39–45 | 169,838 | 13.28 | 1 | 1.67 | 0.13 | −2.08 | |

45–51 | 113,501 | 8.87 | 3 | 5.00 | 0.56 | −0.57 | |

51–58 | 61,356 | 4.80 | 0 | 0 | 0 | −1 | |

58–77.65 | 21,929 | 1.71 | 0 | 0 | 0 | −1 | |

Curvature | Concave | 600,834 | 46.96 | 25 | 41.67 | 0.89 | −0.12 |

Flat | 89,550 | 7.00 | 9 | 15.00 | 2.14 | 0.76 | |

Convex | 589,042 | 46.04 | 26 | 43.33 | 0.94 | −0.06 | |

SPI | 0–1.03 | 136,354 | 10.66 | 19 | 31.67 | 2.97 | 1.09 |

1.03–2.14 | 256,501 | 20.05 | 18 | 30 | 1.50 | 0.40 | |

2.14–3.16 | 310,560 | 24.27 | 11 | 18.33 | 0.76 | −0.28 | |

3.16–4.10 | 257,690 | 20.14 | 8 | 13.33 | 0.66 | −0.41 | |

4.10–5.04 | 164,815 | 12.88 | 2 | 3.33 | 0.26 | −1.35 | |

5.04–6.07 | 86,211 | 6.74 | 2 | 3.33 | 0.49 | −0.70 | |

6.07–7.44 | 41,725 | 3.26 | 0 | 0 | 0 | −1 | |

7.44–9.32 | 17,318 | 1.35 | 0 | 0 | 0 | −1 | |

9.32–12.05 | 6520 | 0.51 | 0 | 0 | 0 | −1 | |

12.05–21.8 | 1732 | 0.14 | 0 | 0 | 0 | −1 | |

Soil texture | Rock | 291,686 | 22.80 | 14 | 23.33 | 1.02 | 0.02 |

Gravel soil | 239,501 | 18.72 | 2 | 3.33 | 0.18 | −1.73 | |

Clay | 214,029 | 16.73 | 5 | 8.33 | 0.50 | −0.70 | |

Silt clay | 356,685 | 27.88 | 19 | 31.67 | 1.14 | 0.13 | |

Sandy soil | 177,553 | 13.88 | 20 | 33.33 | 2.40 | 0.88 | |

TWI | 0–1.53 | 165,076 | 12.90 | 2 | 3.33 | 0.26 | −1.35 |

1.53–1.94 | 372,711 | 29.13 | 8 | 13.33 | 0.46 | −0.78 | |

1.94–2.34 | 334,742 | 26.16 | 13 | 21.67 | 0.83 | −0.19 | |

2.34–2.80 | 203,450 | 15.90 | 12 | 20 | 1.26 | 0.23 | |

2.80–3.37 | 100,444 | 7.85 | 11 | 18.33 | 2.34 | 0.85 | |

3.37–4.08 | 45,022 | 3.52 | 8 | 13.33 | 3.79 | 1.33 | |

4.08–5.15 | 13,918 | 1.09 | 3 | 5.00 | 4.60 | 1.53 | |

5.15–6.74 | 3638 | 0.28 | 0 | 0 | 0 | −1 | |

6.74–10.32 | 1073 | 0.08 | 0 | 0 | 0 | −1 | |

10.32–13.08 | 39,352 | 3.08 | 3 | 5.00 | 1.63 | 0.08 | |

Geology | Limestone | 348,705 | 27.25 | 15 | 25.00 | 0.92 | −0.09 |

Dolomite | 122,721 | 9.59 | 16 | 26.67 | 2.78 | 1.02 | |

Sandstone conglomerate | 574,689 | 44.92 | 19 | 31.67 | 0.71 | −0.35 | |

Sandstone | 119,291 | 9.32 | 6 | 10 | 1.07 | 0.07 | |

Siltstone | 114,116 | 8.92 | 4 | 6.67 | 0.75 | −0.29 | |

Land use | Coal gangue | 33,827 | 2.64 | 9 | 15.00 | 5.67 | 1.74 |

Construction | 45,244 | 3.54 | 8 | 13.33 | 3.77 | 1.33 | |

Farmland | 53,228 | 4.16 | 8 | 13.33 | 3.21 | 1.16 | |

Orchard | 28,997 | 2.27 | 2 | 3.33 | 1.47 | 0.39 | |

Forest | 1,118,128 | 87.39 | 33 | 55.00 | 0.63 | −0.46 | |

Subsidence risk level | I | 586,314 | 45.83 | 23 | 38.33 | 0.84 | −0.18 |

II | 389,059 | 30.41 | 25 | 41.67 | 1.37 | 0.31 | |

III | 241,660 | 18.89 | 13 | 21.67 | 1.15 | 0.14 | |

IV | 26,043 | 2.04 | 0 | 0 | 0 | −1 | |

V | 36,419 | 2.85 | 0 | 0 | 0 | −1 | |

Short-term heavy rain | Piedmont | 864,744 | 67.60 | 59 | 98.33 | 2.79 | 0.37 |

Mountainous | 414,622 | 32.41 | 1 | 1.67 | 1.39 | −2.97 |

Parameter | Class | No. of Pixels in Domain | Percentage of Domain | No. of Flash Flood Hazard | Percentage of Flash Flood Hazard | FR | SI |
---|---|---|---|---|---|---|---|

Elevation/m | 150–250 | 202,955 | 15.86 | 24 | 40.00 | 2.52 | 0.92 |

250–350 | 287,569 | 22.48 | 19 | 31.67 | 1.41 | 0.34 | |

350–450 | 267,293 | 20.89 | 16 | 26.67 | 1.27 | 0.24 | |

450–550 | 196,183 | 15.33 | 1 | 1.67 | 0.11 | −2.22 | |

550–650 | 128,388 | 10.04 | 0 | 0 | 0 | −1 | |

650–750 | 76,584 | 5.99 | 0 | 0 | 0 | −1 | |

750–850 | 56,995 | 4.45 | 0 | 0 | 0 | −1 | |

850–950 | 38,826 | 3.03 | 0 | 0 | 0 | −1 | |

950–1050 | 18,406 | 1.44 | 0 | 0 | 0 | −1 | |

1050–1170 | 6227 | 0.49 | 0 | 0 | 0 | −1 | |

Slope angle/° | 0–10 | 109,916 | 8.59 | 16 | 26.67 | 3.10 | 1.13 |

10–20 | 177,097 | 13.84 | 17 | 28.33 | 2.05 | 0.71 | |

20–30 | 291,007 | 22.75 | 12 | 20.00 | 0.88 | −0.13 | |

30–40 | 359,823 | 28.12 | 11 | 18.33 | 0.65 | −0.43 | |

40–50 | 250,488 | 19.58 | 4 | 6.67 | 0.34 | −1.08 | |

50–60 | 75,640 | 5.91 | 0 | 0 | 0 | −1 | |

60–70 | 14,542 | 1.14 | 0 | 0 | 0 | −1 | |

70–77.65 | 913 | 0.07 | 0 | 0 | 0 | −1 | |

SPI | 0–1 | 132,382 | 10.35 | 19 | 31.67 | 3.06 | 1.12 |

1–2 | 221,816 | 17.34 | 16 | 26.67 | 1.54 | 0.43 | |

2–3 | 299,666 | 23.42 | 11 | 18.33 | 0.78 | −0.25 | |

3–4 | 282,692 | 22.10 | 10 | 16.67 | 0.75 | −0.28 | |

4–5 | 183,961 | 14.38 | 2 | 3.33 | 0.23 | −1.46 | |

5–6 | 87,786 | 6.86 | 2 | 3.33 | 0.49 | −0.72 | |

6–7 | 37,161 | 2.90 | 0 | 0.00 | 0 | −1 | |

7–8 | 15,809 | 1.24 | 0 | 0.00 | 0 | −1 | |

8–9 | 8204 | 0.64 | 0 | 0.00 | 0 | −1 | |

9–21.8 | 9949 | 0.78 | 0 | 0.00 | 0 | −1 | |

TWI | 0–1 | 14,467 | 1.13 | 0 | 0 | 0 | −1 |

1–2 | 585,654 | 45.78 | 14 | 23.33 | 0.51 | −0.67 | |

2–3 | 524,194 | 40.97 | 24 | 40.00 | 0.98 | −0.02 | |

3–4 | 94,915 | 7.42 | 17 | 28.33 | 3.82 | 1.34 | |

4–5 | 15,411 | 1.20 | 3 | 5.00 | 4.15 | 1.42 | |

5–6 | 3171 | 0.25 | 0 | 0 | 0 | −1 | |

6–7 | 1428 | 0.11 | 0 | 0 | 0 | −1 | |

7–8 | 547 | 0.04 | 0 | 0 | 0 | −1 | |

8–9 | 196 | 0.02 | 0 | 0 | 0 | −1 | |

9–13.08 | 39,443 | 3.08 | 2 | 3.33 | 1.08 | 0.08 |

Susceptibility | FR.1 | SI | FR.2 | |||
---|---|---|---|---|---|---|

Area (km^{2}) | Ratio (%) | Area (km^{2}) | Ratio (%) | Area (km^{2}) | Ratio (%) | |

Very Low | 2.53 | 31.63 | 1.25 | 15.62 | 2.69 | 33.68 |

Low | 2.66 | 33.28 | 2.10 | 26.24 | 3.05 | 38.15 |

Moderate | 1.30 | 16.29 | 2.31 | 28.98 | 1.21 | 15.19 |

High | 0.94 | 11.72 | 1.49 | 18.70 | 0.66 | 8.30 |

Very high | 0.56 | 7.03 | 0.84 | 10.46 | 0.37 | 4.68 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Cao, C.; Xu, P.; Wang, Y.; Chen, J.; Zheng, L.; Niu, C. Flash Flood Hazard Susceptibility Mapping Using Frequency Ratio and Statistical Index Methods in Coalmine Subsidence Areas. *Sustainability* **2016**, *8*, 948.
https://doi.org/10.3390/su8090948

**AMA Style**

Cao C, Xu P, Wang Y, Chen J, Zheng L, Niu C. Flash Flood Hazard Susceptibility Mapping Using Frequency Ratio and Statistical Index Methods in Coalmine Subsidence Areas. *Sustainability*. 2016; 8(9):948.
https://doi.org/10.3390/su8090948

**Chicago/Turabian Style**

Cao, Chen, Peihua Xu, Yihong Wang, Jianping Chen, Lianjing Zheng, and Cencen Niu. 2016. "Flash Flood Hazard Susceptibility Mapping Using Frequency Ratio and Statistical Index Methods in Coalmine Subsidence Areas" *Sustainability* 8, no. 9: 948.
https://doi.org/10.3390/su8090948