# Novel Machine Learning Approaches for Modelling the Gully Erosion Susceptibility

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}and lies between 37°30′00″ to 37°50′00″ N, and 55°31′40″ to 56°2′10″ E in the northeast part of Golestan province. Elevation ranges between 160 and 1490 mt. mean sea level (MSL) (Figure 1). More than half of the basin has mountainous morphology with gentle slopes and is a part of the Alborz Mountains. The slope angle at steep slopes reaches up to 118%. The average annual rainfall varies from 346 to 610 mm, with the maximum rainfall conducted in southern parts. The minimum and maximum temperatures are 8 and 16 °C. Three main climatic characteristics of semi-humid, semi-arid, and Mediterranean are evident in the study area. Agriculture, as the predominant land cover, is conducted in most of the study area (i.e., 45.35%), followed by rangelands (38.07%), forests (15.95%), and residential areas (0.64%) (Table 1). Geologically, the largest portion of the region corresponds to the grey to black shale and thin layers of siltstone and sandstone (73.94%), followed by Ammonite bearing shale with the interaction of limestone (12.48%), grey thick-bedded limestone, and dolomite (6.26%), and the remaining area is dominated by other formations described in detail in Table 2.

#### 2.2. Methodology

- (i)
- The gully erosion inventory map and gully erosion causality factors preparations: In the current study, a total of 1115 gully head cut locations were identified using the high-resolution images, field investigation, global positioning system (GPS), and a number of gullies were received from Natural Resources and Watershed Management Organization of the Golestan Province. The 20 environmental factors were considered for the modeling purpose.
- (ii)
- Multi-collinearity analysis among the gully erosion factors using the variance inflation factor (VIF) and tolerance limit was done using SPSS software.
- (iii)
- The significance and effectiveness of factors was carried out using the MaxEnt model (Jackknife test).
- (iv)
- GES maps were prepared using the MaxEnt, ANN, SVM, and GLM models.
- (v)
- The GESM model’s performance was validated through the area under receiver operating characteristic curve (AUROC).

#### 2.3. Gully Inventory Map

#### 2.4. Data Preparation

**Topography position index (TPI):**

**Plan curvature:**

**Elevation:**

**Slope aspect:**

**Slope:**

**Height above nearest drainage (HAND):**

**Drainage density:**

^{2}(Figure 4f):

^{2}.

**Distance from stream:**

**Terrain ruggedness index (TRI):**

**Distance from road:**

**Bulk density:**

**Mineral soil, clay content, and sand content:**

**Relative slope position (RSP):**

**Silt content and valley depth:**

**Land use:**

**Soil texture and lithology:**

#### 2.5. Multi-Collinearity Assessment

#### 2.6. Methods for Gully Erosion Susceptibility

#### 2.6.1. Artificial Neural Network (ANN)

#### 2.6.2. General Linear Model (GLM)

#### 2.6.3. Maximum Entropy (MaxEnt)

#### 2.6.4. Support Vector Machine (SVM)

#### 2.7. Measuring the Importance of GECFs by the Jackknife Test

#### 2.8. Validation and Accuracy Assessment

## 3. Results

#### 3.1. Multi-Collinearity Assessment

#### 3.2. Gully Erosion Susceptibility Modelling

#### 3.2.1. Gully Erosion Susceptibility Modelling Using Artificial Neural Network (ANN)

#### 3.2.2. Gully Erosion Susceptibility Modelling Using the General Linear Model (GLM)

#### 3.2.3. Gully Erosion Susceptibility Modelling Using Maximum Entropy (MaxEnt)

#### 3.2.4. Gully Erosion Susceptibility Modelling Using Support Vector Machine (SVM)

#### 3.3. Assessing the Importance of the Factors

#### 3.4. Validation of the Models

## 4. Discussion

#### Models Prioritization

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Some of the mapped gullies in the study area. (

**a**) Lat: 377012.3; Long 4183012. (

**b**) Lat: 392812.6; Long 4176965.6. (

**c**) Lat: 389226.2; Long 4173413.5.

**Figure 4.**Gully erosion factors are showing (

**a**) Topography position index (TPI), (

**b**) Plan curvature, (

**c**) Elevation, (

**d**) Aspect, (

**e**) Slope, (

**f**) Height above nearest drainage (HAND), (

**g**) Drainage density, (

**h**) Distance from stream, (

**i**) Terrain ruggedness index (TRI), (

**j**) Distance from road, (

**k**) Bulk density, (

**l**) Mineral Soil, (

**m**) Clay content, (

**n**) Sand content, (

**o**) Relative slope position (RSP), (

**p**) Silt content, (

**q**) Valley depth, (

**r**) Land use, (

**s**) Soil Texture, (

**t**) Lithology.

**Figure 5.**Gully erosion susceptibility mapping using the ANN model: (

**a**) 50/50, (

**b**) 60/40, (

**c**) 70/30, (

**d**) 80/20, and (

**e**) 90/10.

**Figure 6.**Gully erosion susceptibility mapping using the GLM model: (

**a**) 50/50, (

**b**) 60/40, (

**c**) 70/30, (

**d**) 80/20, (

**e**) 90/10.

**Figure 7.**Gully erosion susceptibility mapping using the MaxEnt model: (

**a**) 50/50, (

**b**) 60/40, (

**c**) 70/30, (

**d**) 80/20, (

**e**) 90/10.

**Figure 8.**Gully erosion susceptibility mapping using the SVM model: (

**a**) 50/50, (

**b**) 60/40, (

**c**) 70/30, (

**d**) 80/20, (

**e**) 90/10.

**Figure 11.**Area under the curve based on training datasets in the ANN (

**a**), MaxEnt (

**b**), SVM (

**c**), and GLM (

**d**) model.

**Figure 12.**Area under the curve based on validation datasets in the ANN (

**a**), MaxEnt (

**b**), SVM (

**c**), and GLM (

**d**) model.

Land Use | Area (he) | Area (%) |
---|---|---|

Forest | 12,513.04 | 15.95 |

Residential Areas | 498.6 | 0.64 |

Rangelands | 29,858.8 | 38.07 |

Agricultural | 35,568.2 | 45.35 |

Geo Unit | Description | Age | Area (ha) | Area (%) |
---|---|---|---|---|

Qm | Swamp | Cenozoic | 2169.48 | 2.77 |

Qsw | Grey to block shale and thin layers of siltstone and sandstone | Cenozoic | 58,000.92 | 73.94 |

Ksn | Ammonite bearing shale with interaction of limestone | Mesozoic | 9786.63 | 12.48 |

Ksr | Grey thick—bedded limestone and dolomite | Mesozoic | 4906.5 | 6.26 |

Jmz | Olive—green shale and sandstone | Mesozoic | 1857.68 | 2.37 |

Ekh | Swamp | Cenozoic | 1715.73 | 2.19 |

Sl. No. | Conditioning Factors | Source | Time | Spatial Resolution/Scale |
---|---|---|---|---|

1 | Topography position index (TPI) | ALOSPALSER DEM | 12/08/2012 | 12.5 mt. |

2 | Plan curvature | ALOSPALSER DEM | 12/08/2012 | 12.5 mt. |

3 | Elevation | ALOSPALSER DEM | 12/08/2012 | 12.5 mt. |

4 | Aspect | ALOSPALSER DEM | 12/08/2012 | 12.5 mt. |

5 | Slope | ALOSPALSER DEM | 12/08/2012 | 12.5 mt. |

6 | Height above nearest drainage (HAND) | ALOSPALSER DEM | 12/08/2012 | 12.5 mt. |

7 | Drainage density | ALOSPALSER DEM | 12/08/2012 | 12.5 mt. |

8 | Distance from stream | ALOSPALSER DEM | 12/08/2012 | 12.5 mt. |

9 | Train ruggness index (TRI) | ALOSPALSER DEM | 12/08/2012 | 12.5 mt. |

10 | Distance from road | Google Earth images, Landsat 8 satellite images by USGS and Topographical map by National Geographic Organization of Iran (www.ngo-org.ir) | 17/06/2019 | 30 mt. |

11 | Bulk density | Soil and Water Research Institute (SWRI) (http://www.iran.swri.com) | 18/06/2019 | 1:1,000,000 |

12 | Mineral Soil | Soil and Water Research Institute (SWRI) (http://www.iran.swri.com) | 18/06/2019 | 1:1,000,000 |

13 | Clay content | Soil and Water Research Institute (SWRI) (http://www.iran.swri.com) | 18/06/2019 | 1:1,000,000 |

14 | Sand content | Soil and Water Research Institute (SWRI) (http://www.iran.swri.com) | 18/06/2019 | 1:1,000,000 |

15 | Relative slope position (RSP) | ALOSPALSER DEM | 12/08/2012 | 12.5 mt. |

16 | Silt content | Soil and Water Research Institute (SWRI) (http://www.iran.swri.com) | 18/06/2019 | 1:1,000,000 |

17 | Valley depth | ALOSPALSER DEM | 12/08/2012 | 12.5 mt. |

18 | Land use | Google Earth images, Landsat 8 satellite images by USGS and Topographical map by National Geographic Organization of Iran (www.ngo-org.ir) | 17/06/2019 | 30 mt. |

19 | Soil Texture | Soil and Water Research Institute (SWRI) (http://www.iran.swri.com) | 18/06/2019 | 1:1,000,000 |

20 | Lithology | Geological Society of Iran (GSI) (http://www.gsi.ir/) | 14/07/2019 | 1:100,000 |

Conditioning Factors | Collinearity Statistics | |
---|---|---|

Tolerance | VIF | |

TPI | 0.923 | 1.079 |

HAND | 0.921 | 1.118 |

Valley depth | 0.916 | 1.124 |

Lithology | 0.915 | 1.127 |

Land use | 0.888 | 1.279 |

RSP | 0.823 | 1.483 |

Bulk density | 0.813 | 1.492 |

Distance from road | 0.778 | 1.532 |

Soil texture | 0.754 | 1.611 |

Plan | 0.745 | 1.721 |

Distance from stream | 0.743 | 1.865 |

Mineral Soil | 0.739 | 1.897 |

Slope | 0.728 | 1.932 |

Drainage density | 0.425 | 2.364 |

TRI | 0.387 | 2.624 |

Elevation | 0.346 | 2.715 |

Aspect | 0.345 | 2.817 |

Silt | 0.233 | 3.534 |

Clay | 0.313 | 3.696 |

Sand | 0.231 | 4.749 |

Row | Models | AUC | Prioritizing | ||
---|---|---|---|---|---|

Training | Validation | Priority Based on Training | Priority Based on Validation | ||

1 | GLM 90/10 | 0.826 | 0.818 | 14 | 10 |

2 | GLM 80/20 | 0.834 | 0.788 | 12 | 16 |

3 | GLM 70/30 | 0.837 | 0.79 | 11 | 15 |

4 | GLM 60/40 | 0.813 | 0.837 | 16 | 4 |

5 | GLM 50/50 | 0.833 | 0.816 | 13 | 11 |

6 | MaxEnt 90/10 | 0.809 | 0.784 | 18 | 17 |

7 | MaxEnt 80/20 | 0.821 | 0.764 | 15 | 18 |

8 | MaxEnt 70/30 | 0.81 | 0.799 | 17 | 13 |

9 | MaxEnt 60/40 | 0.786 | 0.819 | 20 | 9 |

10 | MaxEnt 50/50 | 0.808 | 0.796 | 19 | 14 |

11 | ANN 90/10 | 0.885 | 0.867 | 4 | 2 |

12 | ANN 80/20 | 0.91 | 0.804 | 3 | 12 |

13 | ANN 70/30 | 0.872 | 0.837 | 7 | 4 |

14 | ANN 60/40 | 0.917 | 0.825 | 2 | 8 |

15 | ANN 50/50 | 0.918 | 0.868 | 1 | 1 |

16 | SVM 90/10 | 0.87 | 0.864 | 8 | 3 |

17 | SVM 80/20 | 0.877 | 0.819 | 5 | 9 |

18 | SVM 70/30 | 0.875 | 0.828 | 6 | 7 |

19 | SVM 60/40 | 0.859 | 0.835 | 10 | 5 |

20 | SVM 50/50 | 0.866 | 0.834 | 9 | 6 |

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## Share and Cite

**MDPI and ACS Style**

Arabameri, A.; Asadi Nalivan, O.; Chandra Pal, S.; Chakrabortty, R.; Saha, A.; Lee, S.; Pradhan, B.; Tien Bui, D.
Novel Machine Learning Approaches for Modelling the Gully Erosion Susceptibility. *Remote Sens.* **2020**, *12*, 2833.
https://doi.org/10.3390/rs12172833

**AMA Style**

Arabameri A, Asadi Nalivan O, Chandra Pal S, Chakrabortty R, Saha A, Lee S, Pradhan B, Tien Bui D.
Novel Machine Learning Approaches for Modelling the Gully Erosion Susceptibility. *Remote Sensing*. 2020; 12(17):2833.
https://doi.org/10.3390/rs12172833

**Chicago/Turabian Style**

Arabameri, Alireza, Omid Asadi Nalivan, Subodh Chandra Pal, Rabin Chakrabortty, Asish Saha, Saro Lee, Biswajeet Pradhan, and Dieu Tien Bui.
2020. "Novel Machine Learning Approaches for Modelling the Gully Erosion Susceptibility" *Remote Sensing* 12, no. 17: 2833.
https://doi.org/10.3390/rs12172833