# Hybrid Computational Intelligence Models for Improvement Gully Erosion Assessment

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}, where the maximum variation in elevation is in the NE–SE axis. Specifically, the average altitude in the NE part is 2160 m.a.s.l., while in the SE it is 680 m.a.s.l. Since the catchment is relatively small, the associated slope significantly varies between flat conditions and 70°, but the average steepness is approximately 3 degrees. Due to the predominantly flat conditions, water stagnation prevails rather than runoff, which is generally the case under the local meteorological conditions responsible for a mean yearly discharge confined to between 48 and 206 mm during the wet season from January to March [27]. The associated temperature regimes reach a peak of 42 °C during summer, especially in the South. It decreases to below 0 °C during winter, towards the Northern regions. The temperatures during the rest of the year range from 14 °C to 24 °C. Overall, these are already indicators of meteorological stress with high variations and local spikes. This may generate freezing and thawing processes in soils as well as expansion and contractions also in the soils, which in turn can open cracks along the regolithic profile.

#### 2.2. Data Collection

#### 2.2.1. Gully Phenomena and Inventory Map

#### 2.2.2. Predisposing Factors

#### 2.3. Multicollinearity Assessment

#### 2.4. Models

#### 2.4.1. Predisposing Factors’ Effects Via EBF Model

#### 2.4.2. Susceptibility Mapping Via FLDA model

_{i}is the i-th sample with multiple attributes, y

_{i}is the corresponding result, which is obtained by linear projection and w denotes the weight vector.

_{b}is “between classes scatter matrix”, and S

_{w}is defined as “within classes scatter matrix”. Finally, the optimization of J

_{F}(w) can be realized using the Lagrange multiplier method.

#### 2.4.3. Susceptibility Mapping Via LMT Model

#### 2.4.4. Susceptibility Mapping Via NBTree Model

_{i}. |D| and |D

_{i}| represent the number of cases in D and D

_{i}, respectively. A denotes one corresponding attribute.

#### 2.4.5. Random SubSpace (RS) Mata Classifier Model

^{’}(x) is the output classifier; C

_{i}(x) denotes the weak classifier, which is produced by the single i-th replicate; t is the total number of bootstrapped training datasets and y is the dichotomous (0/1) target of each model, in our case defined as 0 for the absence of gullies and 1 for the presence of gullies.

#### 2.5. Performance Assessment

_{o}) was calculated. This is known as the overall agreement. However, in order to disregard an agreement due to randomness, Cohen’s kappa includes a measure called agreement by chance (A

_{c}), which is computed as follows:

## 3. Results

#### 3.1. Predisposing Factors’ Effects

^{2}) ranks second with a Bel value of 4.2; third is the stream power index (11.9 > SPI > 14.9) with a Bel value of 4.1 and fourth is the topographic wetness index (TWI > 12.0) with a Bel value of 4.0. These hydrological factors indicate a clear hydrological control on whether an area is prone to gully occurrence that far surpasses the effects of all other factor considered in this study. In fact, the four Bel values reported above far exceed the Bel values retrieved for the other factors, sometimes by one order of magnitude. This is an important finding that places the importance of hydrology above geomorphology and the other thematic properties in terms of contributing to gully erosion.

#### 3.2. Susceptibility Mapping

#### 3.3. Model Performance

## 4. Discussion and Conclusions

#### 4.1. General Overview and Novelty

#### 4.2. Methodological Considerations

#### 4.3. Applicability

#### 4.4. Interpretability

#### 4.5. Summary and Relevance in Arid to Semi-arid Environments

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Study area. (

**a**) Location of Iran in the world, (

**b**) location of study area in Iran and (

**c**) location of training and validation gullies in the study area.

**Figure 3.**Gully erosion conditioning factors. (

**a**) elevation, (

**b**) slope, (

**c**) aspect, (

**d**) plan curvature, (

**e**) convergence index (CI), (

**f**) slope length (LS), (

**g**) stream power index (SPI), (

**h**) topography position index (TPI), (

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

**j**) topographical wetness index (TWI), (

**k**) distance to stream, (

**l**) drainage density, (

**m**) rainfall, (

**n**) distance to road, (

**o**) NDVI (normalized difference vegetation index), (

**p**) lithology, (

**q**) land use/cover (LU/LC) and (

**r**) soil type.

ID | Predisposing Factor | Reference |
---|---|---|

1 | Elevation | -- |

2 | Slope | Zevenbergen and Thorne, 1987 |

3 | Aspect | Zevenbergen and Thorne, 1987 |

4 | Planar Curvature | Heerdegen and Beran, 1982 |

5 | Convergence Index | Olaya and Conrad, 2009 |

6 | Topographic Wetness Index (TWI) | Beven and Kirkby, 1979 |

7 | Stream Power Index (SPI) | Moore et al., 1991 |

8 | Slope Length Factor (LS) | Desmet and Govers, 1996 |

9 | Terrain Ruggedness Index | Riley et al., 1999 |

10 | Topographic position Index | De Reu et al., 2013 |

11 | Drainage Density | -- |

12 | Distance to Stream | -- |

13 | Rainfall | -- |

14 | Distance to Road | -- |

15 | Normalized Difference Vegetation Index (NDVI) | -- |

16 | Land Use/Cover | -- |

17 | Lithology | -- |

18 | Soil Type | -- |

Code | Lithology Description |
---|---|

A | Marl, gypsiferous marl and limestone, dacitic to andesitic volcano sediment, well bedded green tuff and tuffaceous shale, dacitic to andesitic volcanic, dacitic to andesitic volcano breccia Andesitic volcanic breccia, sandstone, marl and limestone, granite, pale-red, polygenic conglomerate and sandstone |

B | Phyllite, slate and meta-sandstone, Jurassic dacite to andesite lava flows |

C | Cretaceous rocks in general |

D | Light-red to brown marl and gypsiferous marl with sandstone intercalations, red marl, gypsiferous marl, sandstone and conglomerate |

E | Fluvial conglomerate, piedmont conglomerate and sandstone. |

F | Salt flat, high-level piedmont fan and valley terrace deposits, low-level piedmont fan and valley terrace deposits, salt lake |

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

Tolerance | VIF | Tolerance | VIF | ||

Distance to road | 0.370 | 2.702 | Distance to Stream | 0.596 | 1.677 |

Rainfall | 0.321 | 3.098 | Slope | 0.612 | 1.525 |

Convergence index | 0.586 | 1.707 | Aspect | 0.948 | 1.055 |

Plan curvature | 0.656 | 1.524 | NDVI | 0.658 | 1.520 |

Terrain Ruggedness Index | 0.558 | 2.286 | Topography wetness index | 0.357 | 2.911 |

Elevation | 0.438 | 2.545 | Slope length | 0.874 | 1.144 |

Stream power index | 0.419 | 2.346 | Lithology | 0.749 | 1.335 |

Drainage density | 0.362 | 2.766 | Topographic Position Index | 0.564 | 1.772 |

Soil type | 0.431 | 2.318 | Land use/land cover | 0.621 | 1.611 |

**Table 4.**Spatial Analysis of Gully Erosion Conditioning Factors and Gully Locations using the Evidential Belief Function (EBF) Model.

Factors | Classes | Pixels in Domain | Number of Gullies | Bel |
---|---|---|---|---|

Elevation (m) | <819 | 1373897 | 46 | 1.006 |

819–1000 | 567118 | 29 | 1.536 | |

1000–1206 | 450512 | 9 | 0.600 | |

1206–1500 | 237673 | 6 | 0.758 | |

>1500 | 73829 | 0 | 0.000 | |

Slope (°) | <5 | 2270219 | 81 | 1.072 |

5–10 | 234394 | 6 | 0.769 | |

10–15 | 84199 | 3 | 1.070 | |

15–20 | 43477 | 0 | 0.000 | |

20–30 | 46247 | 0 | 0.000 | |

>30 | 24488 | 0 | 0.000 | |

Aspect | F | 135222 | 4 | 0.888 |

N | 203003 | 4 | 0.915 | |

NE | 244887 | 10 | 1.226 | |

E | 395661 | 25 | 1.898 | |

SE | 496849 | 24 | 1.451 | |

S | 473666 | 13 | 0.824 | |

SW | 342248 | 6 | 0.527 | |

W | 223850 | 3 | 0.402 | |

NW | 187643 | 1 | 0.160 | |

Plan curvature (100/m) | Concave | 894313 | 31 | 1.041 |

Flat | 901103 | 40 | 1.333 | |

Convex | 907612 | 19 | 0.629 | |

Convergence index (100/m) | <–39.6 | 275709 | 14 | 1.523 |

–39.6 to –12.9 | 586976 | 22 | 1.124 | |

–12.9–10.5 | 919934 | 28 | 0.913 | |

10.5–38 | 624756 | 18 | 0.864 | |

>38 | 292694 | 8 | 0.820 | |

LS (m) | <20 | 1531797 | 63 | 1.235 |

20–57.5 | 230099 | 9 | 1.175 | |

57.5–92.1 | 396472 | 9 | 0.682 | |

92.1–128.2 | 339443 | 4 | 0.354 | |

>128.2 | 204840 | 5 | 0.733 | |

<8.2 | 1023818 | 32 | 0.939 | |

SPI | 8.2–9.9 | 1017957 | 30 | 0.885 |

9.9–11.9 | 489089 | 9 | 0.553 | |

11.9–14.9 | 140449 | 19 | 4.063 | |

>14.9 | 31709 | 0 | 0.000 | |

<−8 | 42635 | 3 | 2.113 | |

TPI | –8 to –1.8 | 371266 | 17 | 1.375 |

–1.8–1.9 | 2122669 | 69 | 0.976 | |

1.9–9.6 | 138072 | 1 | 0.218 | |

>9.6 | 28385 | 0 | 0.000 | |

<1.4 | 2031200 | 73 | 1.079 | |

TRI | 1.4–3.9 | 421180 | 12 | 0.856 |

3.9–7.8 | 159763 | 5 | 0.940 | |

7.8–13.5 | 69390 | 0 | 0.000 | |

>13.5 | 21495 | 0 | 0.000 | |

TWI | <6.25 | 1087667 | 24 | 0.663 |

6.25–8.57 | 1013529 | 30 | 0.889 | |

8.57–11.97 | 465805 | 18 | 1.161 | |

>11.97 | 136023 | 18 | 3.975 | |

Distance to stream (m) | <100 | 645017 | 48 | 2.235 |

100–200 | 486406 | 15 | 0.926 | |

200–300 | 435933 | 9 | 0.620 | |

300–400 | 297487 | 7 | 0.707 | |

>400 | 838184 | 11 | 0.394 | |

Drainage density (km/km^{2}) | <0.89 | 670956 | 9 | 0.403 |

0.89–1.25 | 1133824 | 27 | 0.715 | |

1.25–1.73 | 696610 | 26 | 1.121 | |

>1.73 | 201639 | 28 | 4.171 | |

Rainfall (mm) | <66.3 | 615156 | 8 | 0.391 |

66.3–84.9 | 1046810 | 54 | 1.549 | |

84.9–111.5 | 904755 | 28 | 0.929 | |

111.5–149.9 | 86955 | 0 | 0.000 | |

>149.9 | 49353 | 0 | 0.000 | |

Distance to road (m) | <500 | 142666 | 32 | 6.738 |

500–1000 | 134376 | 8 | 1.788 | |

1000–1500 | 129321 | 1 | 0.232 | |

1500–2000 | 125196 | 4 | 0.960 | |

>2000 | 2171485 | 45 | 0.622 | |

NDVI | <0.043 | 1279439 | 29 | 0.679 |

0.043–0.132 | 1417082 | 61 | 1.290 | |

>0.132 | 873 | 0 | 0.000 | |

Lithology | A | 578105 | 11 | 0.571 |

B | 27122 | 2 | 2.213 | |

C | 34563 | 0 | 0.000 | |

D | 439618 | 22 | 1.502 | |

E | 193927 | 13 | 2.011 | |

F | 1427087 | 42 | 0.883 | |

Agriculture | 2353 | 0 | 0.000 | |

LU/LC | Bareland | 20180 | 0 | 0.000 |

Kavir | 806162 | 46 | 1.712 | |

Poorrange | 1460908 | 37 | 0.760 | |

Rock | 296104 | 5 | 0.507 | |

Saltlake | 99897 | 2 | 0.601 | |

Saltland | 13808 | 0 | 0.000 | |

Wetland | 1010 | 0 | 0.000 | |

Bad Lands (a) | 241417 | 3 | 0.373 | |

Rock Outcrops/Entisols (b) | 495473 | 13 | 0.787 | |

Soil type | Rocky Lands (c) | 134508 | 0 | 0.000 |

Salt Flats (d) | 469856 | 8 | 0.511 | |

Aridisols (e) | 3622 | 0 | 0.000 | |

Entisols/Aridisols (f) | 1355545 | 66 | 1.461 |

Model | Classes | Area | % | Model | Classes | Area | % |
---|---|---|---|---|---|---|---|

LMT | Very Low | 570.19 | 23.44 | RS-LMT | Very Low | 460.15 | 18.92 |

Low | 612.51 | 25.18 | Low | 688.42 | 28.30 | ||

Moderate | 543.93 | 22.36 | Moderate | 606.83 | 24.94 | ||

High | 409.67 | 16.84 | High | 432.77 | 17.79 | ||

Very High | 296.42 | 12.18 | Very High | 244.56 | 10.05 | ||

FLDA | Very Low | 267.42 | 10.99 | RS-FLDA | Very Low | 232.46 | 9.56 |

Low | 603.25 | 24.80 | Low | 525.06 | 21.58 | ||

Moderate | 716.31 | 29.44 | Moderate | 749.11 | 30.79 | ||

High | 580.03 | 23.84 | High | 603.13 | 24.79 | ||

Very High | 265.72 | 10.92 | Very High | 322.95 | 13.28 | ||

NBTree | Very Low | 510.48 | 20.98 | RS-NBTree | Very Low | 923.20 | 37.95 |

Low | 805.93 | 33.13 | Low | 693.29 | 28.50 | ||

Moderate | 141.55 | 5.82 | Moderate | 369.36 | 15.19 | ||

High | 423.87 | 17.42 | High | 294.96 | 12.13 | ||

Very High | 550.90 | 22.65 | Very High | 151.59 | 6.23 |

Models | AUC | Kappa | TSS | |||
---|---|---|---|---|---|---|

SRC | PRC | SRC | PRC | SRC | PRC | |

FLDA | 0.763 | 0.755 | 0.657 | 0.650 | 0.571 | 0.50 |

LMT | 0.677 | 0.766 | 0.672 | 0.665 | 0.559 | 0.531 |

NBTree | 0.666 | 0.777 | 0.658 | 0.670 | 0.501 | 0.541 |

RS-FLDA | 0.777 | 0.810 | 0.652 | 0.676 | 0.539 | 0.552 |

RS-LMT | 0.742 | 0.859 | 0.643 | 0.702 | 0.539 | 0.604 |

RS-NBTree | 0.780 | 0.898 | 0.682 | 0.748 | 0.618 | 0.697 |

© 2020 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**

Arabameri, A.; Chen, W.; Lombardo, L.; Blaschke, T.; Tien Bui, D.
Hybrid Computational Intelligence Models for Improvement Gully Erosion Assessment. *Remote Sens.* **2020**, *12*, 140.
https://doi.org/10.3390/rs12010140

**AMA Style**

Arabameri A, Chen W, Lombardo L, Blaschke T, Tien Bui D.
Hybrid Computational Intelligence Models for Improvement Gully Erosion Assessment. *Remote Sensing*. 2020; 12(1):140.
https://doi.org/10.3390/rs12010140

**Chicago/Turabian Style**

Arabameri, Alireza, Wei Chen, Luigi Lombardo, Thomas Blaschke, and Dieu Tien Bui.
2020. "Hybrid Computational Intelligence Models for Improvement Gully Erosion Assessment" *Remote Sensing* 12, no. 1: 140.
https://doi.org/10.3390/rs12010140