# An Ensemble of Weight of Evidence and Logistic Regression for Gully Erosion Susceptibility Mapping in the Kakia-Esamburmbur Catchment, Kenya

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## Abstract

**:**

## 1. Introduction

^{2}[13], and is too big to be removed by ordinary tillage practices [16]. Gully erosion is a threshold process and therefore several studies have put emphasis on defining the topographic as well as hydraulic conditions to predict gully erosion susceptibility [16,17].

## 2. Materials and Methods

#### 2.1. Study Area

^{2}and 15.7 km

^{2}, respectively (Figure 1), and are located in Narok County, South-West of Kenya. It lies between longitudes 35.83$\xb0$ E and 35.93$\xb0$ E and between latitudes 1.00$\xb0$ S and 1.10$\xb0$ S. The region’s elevation ranges from 1828 to 2147 m above sea level [37]. The main drainage channel is the permanent Enkare Narok River, which rises from the Mau Forest and flows through Narok town. The Enkare Narok has two tributaries, which are the seasonal Esamburmbur and Kakia streams that flow through Narok town and converge a few meters before draining into it [38]. The catchment experiences bimodal rainfall in a year [36]. The long rainy season is usually between the months of March and May, while the short rainy season occurs between October and December. The mean annual rainfall for the area is 750 mm while the temperature range for the area is between 8 °C and 28 °C [39]. The main land use/cover in the catchment includes cropland, forests, built-up areas and shrubs. Cropland, which is the main land use, is made up of crops such as maize and wheat [38].

#### 2.2. Methodology

#### 2.2.1. Gully Erosion Inventory

#### 2.2.2. Conditioning Factors

^{2}) and

^{2}) and $\mathsf{\beta}$ is slope gradient (°). The SPI values of the study area range between 0 and 13,639 (Figure 5c).

^{2}) and $\mathsf{\beta}$ is slope gradient (°). The STI values in the study range from 0 to 246 and were classified into five classes (Figure 5d).

#### 2.3. Multi-Collinearity Test

#### 2.4. Weight of Evidence Model

^{+}and negative, W

^{-}weights are used to calculate the WoE model. The weight for each B is calculated based on the presence or absence of A as shown in Equations (6) and (7).

#### 2.5. Logistic Regression Model

#### 2.6. Model Evaluation

## 3. Results

#### 3.1. Conditioning Factor’s Effect

#### 3.1.1. Multicollinearity Test

#### 3.1.2. Weight of Evidence Model

_{final}value, indicating that such areas in the study area are most vulnerable to gully erosion. From the results it can be seen that higher values of TWI indicate a higher chance of gully erosion occurrence while lower values indicate lower chances of gully erosion occurrence, thus there is a positive association. This can be attributed to the fact that at low TWI, less runoff is generated and at higher TWI, gully development is encouraged [54].

_{final}= 4.1). This can be explained by the fact that the development of roads leads to soil disturbance which exacerbates gully formation [47].

_{final}values while the highest TPI values had the lowest W

_{final}values. Table 3 shows that higher values of SPI are associated with higher chances of experiencing gully erosion and vice versa.

_{final}values while higher STI values have higher W

_{final}values. There is a positive association between STI and gully erosion. It indicates that gully occurrence increases with an increase in STI. This can be attributed to the fact that STI accounts for topographic effect on erosion. Similar results were also found in research carried out by [23].

_{final}= 4.0) while the built-up area has the highest negative final weight (W

_{final}= −2.2).

#### 3.1.3. Logistic Regression Model

#### 3.1.4. LR–WoE Ensemble Model

#### 3.2. Gully Erosion Hazard

#### 3.2.1. Weight of Evidence Model

_{final}) values presented in Table 2 and Table 3, is shown in Figure 7. The total weighted map was converted into five classes: very low, low, moderate, high and very high hazard. It can be seen from the map that the areas around the forests have very low susceptibility levels. This implies that increasing forest cover in the Kakia-Esamburmbur catchment can be carried out in order to reduce soil erosion. The majority of the catchment that has moderate to high susceptibility levels is agricultural land.

#### 3.2.2. LR Model and WoE–LR Ensemble Model

#### 3.3. Model Validation

## 4. Discussion

## 5. Conclusions and Recommendations

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Map of Kakia-Esamburmbur catchment showing the training and testing datasets for modeling.

**Figure 2.**Flowchart for the research methodology on gully erosion susceptibility mapping in Kakia-Esamburmbur catchment, Narok.

**Figure 3.**Map of the observed gullies (

**a**) and pictures of some of the gullies identified in the Kakia-Esamburmbur catchment (

**b**,

**c**).

**Figure 4.**Gully erosion conditioning factors: (

**a**) slope (percent), (

**b**) curvature, (

**c**) topographic wetness index (TWI) and (

**d**) distance to stream/channel.

**Figure 5.**Gully erosion conditioning factors: (

**a**) distance to road, (

**b**) topographic position index (TPI), (

**c**) stream power index (SPI) and (

**d**) sediment transport index (STI).

**Figure 10.**Prediction rate curve for gully erosion susceptibility map using WoE in Kakia-Esamburmbur catchment: (

**a**) training and (

**b**) validation.

**Figure 11.**Prediction rate curve for gully erosion susceptibility map using LR in Kakia-Esamburmbur catchment: (

**a**) training and (

**b**) validation.

**Figure 12.**Prediction rate curve for gully erosion susceptibility map using WoE–LR in Kakia-Esamburmbur catchment: (

**a**) training and (

**b**) validation.

Parameter | Collinearity statistics | |
---|---|---|

Tolerance | VIF | |

Curvature | 0.85 | 1.17 |

Distance to road | 0.83 | 1.20 |

Distance to stream | 0.92 | 1.09 |

Landcover | 0.94 | 1.06 |

Slope | 0.88 | 1.14 |

SPI | 0.96 | 1.04 |

STI | 0.41 | 2.41 |

TPI | 0.88 | 1.14 |

TWI | 0.40 | 2.49 |

**Table 2.**Weights of conditioning factors Slope, Curvature, TWI, Distance to stream and Distance to road as analyzed using WoE method.

Factors | Class | W^{+} | W^{-} | W_{final} |
---|---|---|---|---|

Slope (%) | 0–4.4 | −0.8852 | 0.0099 | −0.8951 |

4.5–8.1 | −0.5559 | 0.0441 | −0.6000 | |

8.2–11.2 | −0.3376 | 0.0359 | −0.3735 | |

11.3–16.0 | −0.2115 | 0.1523 | −0.3638 | |

16.1–42.1 | 0.4138 | −0.3441 | 0.7579 | |

Curvature | Concave | −0.1319 | 0.0420 | −0.1739 |

flat | 0.1961 | −0.2273 | 0.4233 | |

convex | −0.3327 | 0.0938 | −0.4266 | |

TWI | 3–6.1 | −0.4293 | 0.2090 | −0.6383 |

6.1–7.7 | −0.1982 | 0.0832 | −0.2814 | |

7.7–9.6 | 0.0501 | −0.0105 | 0.0606 | |

9.6–11.8 | 0.4188 | −0.0441 | 0.4629 | |

11.8–18.7 | 1.8308 | −0.1672 | 1.9979 | |

Distance to stream (m) | 0–38 | −0.2149 | 0.2410 | −0.4559 |

38–89 | −0.6371 | 0.1579 | −0.7949 | |

89–150 | 1.3807 | −0.3503 | 1.7310 | |

150–224 | −0.7861 | 0.0261 | −0.8122 | |

224–539 | −0.5384 | 0.0051 | −0.5434 | |

Distance to road (m) | 0–204 | 3.8957 | −0.2429 | 4.1387 |

204–434 | 0.5204 | −0.0521 | 0.5725 | |

434–683 | −0.7537 | 0.1270 | −0.8807 | |

683–959 | −0.9306 | 0.2262 | −1.1568 | |

959–1511 | 0.0563 | −0.0442 | 0.1005 |

^{+}is positive weight, W

^{−}is negative weight, W

_{final}is W

^{+}− W

^{−}.

Factors | Class | W^{+} | W^{−} | W_{final} |
---|---|---|---|---|

TPI | −6.8–−1.5 | 0.4019 | −0.0427 | 0.4446 |

−1.5–−0.5 | 0.2975 | −0.1021 | 0.3996 | |

−0.5–0.5 | 0.0118 | −0.0067 | 0.0185 | |

0.5–1.6 | −0.3065 | 0.0890 | −0.3955 | |

1.6–7.1 | −0.8978 | 0.0529 | −0.9507 | |

SPI | 0–160 | −0.1122 | 1.3792 | −1.4915 |

160–750 | −1.3833 | 0.0208 | −1.4041 | |

750–1925 | 2.1774 | −0.0437 | 2.2211 | |

1925–4120 | 3.9965 | −0.0769 | 4.0735 | |

4120–13640 | 2.9584 | −0.0065 | 2.9649 | |

STI | 0–4 | −0.1340 | 0.6750 | −0.8090 |

4–11 | 0.2549 | −0.0254 | 0.2803 | |

11–27 | 1.0322 | −0.0511 | 1.0834 | |

27–60 | 1.7170 | −0.0346 | 1.7516 | |

60–247 | 1.7125 | −0.0056 | 1.7181 | |

LULC | Trees | −1.3375 | 0.0196 | −1.3570 |

Shrubs | −0.9576 | 0.0343 | −0.9918 | |

Grassland | −0.8827 | 0.0098 | −0.8925 | |

Cropland | 0.1143 | −1.0517 | 1.1660 | |

Vegetation aquatic/regularly flooded | 3.1360 | −0.0066 | 3.1425 | |

Bare | 4.0024 | −0.0067 | 4.0091 | |

Built-up areas | −2.1744 | 0.0553 | −2.2296 |

^{+}is positive weight, and W

^{−}is negative weight, W

_{final}is W

^{+}− W

^{−}.

Estimate | Standard Error | Z Value | Pr (>|z|) | ||
---|---|---|---|---|---|

(Intercept) | −7.025994 | 741.6681 | −0.009 | 0.99244 | |

Curvature | −0.003545 | 0.002803 | −1.265 | 0.20593 | |

Distance to road | 0.00677 | 0.001605 | 4.218 | 2.46 × 10^{−5} | *** |

Distance to stream | 0.002653 | 0.001544 | 1.719 | 0.08569 | . |

Land use/cover | 0.007804 | 0.003642 | 2.143 | 0.03214 | * |

Slope | 0.004048 | 0.00634 | 0.639 | 0.52313 | |

SPI | 0.008114 | 0.030244 | 0.268 | 0.78847 | |

STI | −0.023267 | 0.006674 | −3.486 | 0.00049 | *** |

TPI | −0.00194 | 0.002445 | −0.793 | 0.42765 | |

TWI | 0.061095 | 0.014213 | 4.299 | 1.72 × 10^{−5} | *** |

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## Share and Cite

**MDPI and ACS Style**

Nkonge, L.K.; Gathenya, J.M.; Kiptala, J.K.; Cheruiyot, C.K.; Petroselli, A.
An Ensemble of Weight of Evidence and Logistic Regression for Gully Erosion Susceptibility Mapping in the Kakia-Esamburmbur Catchment, Kenya. *Water* **2023**, *15*, 1292.
https://doi.org/10.3390/w15071292

**AMA Style**

Nkonge LK, Gathenya JM, Kiptala JK, Cheruiyot CK, Petroselli A.
An Ensemble of Weight of Evidence and Logistic Regression for Gully Erosion Susceptibility Mapping in the Kakia-Esamburmbur Catchment, Kenya. *Water*. 2023; 15(7):1292.
https://doi.org/10.3390/w15071292

**Chicago/Turabian Style**

Nkonge, Lorraine K., John M. Gathenya, Jeremiah K. Kiptala, Charles K. Cheruiyot, and Andrea Petroselli.
2023. "An Ensemble of Weight of Evidence and Logistic Regression for Gully Erosion Susceptibility Mapping in the Kakia-Esamburmbur Catchment, Kenya" *Water* 15, no. 7: 1292.
https://doi.org/10.3390/w15071292