# 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

## References

- Arabameri, A.; Pradhan, B.; Pourghasemi, H.R.; Rezaei, K. Identification of erosion-prone areas using different multi-criteria decision-making techniques and gis. Geomat. Nat. Hazards Risk
**2018**, 9, 1129–1155. [Google Scholar] [CrossRef][Green Version] - Apollonio, C.; Petroselli, A.; Tauro, F.; Cecconi, M.; Biscarini, C.; Zarotti, C.; Grimaldi, S. Hillslope erosion mitigation: An experimental proof of a nature-based solution. Sustainability
**2021**, 13, 6058. [Google Scholar] [CrossRef] - Sholagberu, A.T.; Mustafa, M.R.; Yusof, K.W.; Hashim, A.M. Geo-statistical based susceptibility mapping of soil erosion and optimization of its causative factors: A conceptual framework. J. Eng. Sci. Technol.
**2017**, 12, 2880–2895. [Google Scholar] - Fox, G.A.; Sheshukov, A.; Cruse, R.; Kolar, R.L.; Guertault, L.; Gesch, K.R.; Dutnell, R.C. Reservoir Sedimentation and Upstream Sediment Sources: Perspectives and Future Research Needs on Streambank and Gully Erosion. Environ. Manag.
**2016**, 57, 945–955. [Google Scholar] [CrossRef][Green Version] - Zabihi, M.; Mirchooli, F.; Motevalli, A.; Darvishan, A.K.; Pourghasemi, H.R.; Zakeri, M.A.; Sadighi, F. Spatial modelling of gully erosion in Mazandaran Province, northern Iran. Catena
**2018**, 161, 1–13. [Google Scholar] [CrossRef] - Odunuga, S.; Ajijola, A.; Igwetu, N.; Adegun, O. Land susceptibility to soil erosion in Orashi Catchment, Nnewi South, Anambra State, Nigeria. Proc. Int. Assoc. Hydrol. Sci.
**2018**, 376, 87–95. [Google Scholar] [CrossRef][Green Version] - Slimane, A.B.; Raclot, D.; Evrard, O.; Sanaa, M.; Lefevre, I.; Bissonnais, Y.L. Relative contribution of rill/interrill and gully/channel erosion to small reservoir siltation in mediterranean environments. Land Degrad. Dev.
**2016**, 27, 785–797. [Google Scholar] - Issaka, S.; Ashraf, M.A. Impact of soil erosion and degradation on water quality: A review. Geol. Ecol. Landsc.
**2017**, 1, 1301053. [Google Scholar] [CrossRef][Green Version] - Borrelli, P.; Robinson, D.A.; Fleischer, L.R.; Lugato, E.; Ballabio, C.; Alewell, C.; Meusburger, K.; Modugno, S.; Schütt, B.; Ferro, V.; et al. An assessment of the global impact of 21st century land use change on soil erosion. Nat. Commun.
**2017**, 8, 1–13. [Google Scholar] [CrossRef][Green Version] - Hassen, G.; Bantider, A. Assessment of drivers and dynamics of gully erosion in case of Tabota Koromo and Koromo Danshe watersheds, South Central Ethiopia. Geoenviron. Disasters
**2020**, 7, 5. [Google Scholar] [CrossRef] - Bui, D.T.; Shirzadi, A.; Shahabi, H.; Chapi, K.; Omidavr, E.; Pham, B.T.; Asl, D.T.; Khaledian, H.; Pradhan, B.; Panahi, M.; et al. A novel ensemble artificial intelligence approach for gully erosion mapping in a semi-arid watershed (Iran). Sensors
**2019**, 19, 2444. [Google Scholar] [CrossRef][Green Version] - Arabameri, A.; Pourghasemi, H.R. Spatial Modeling of Gully Erosion Using Linear and Quadratic Discriminant Analyses in GIS and R. In Spatial Modeling in GIS and R for Earth and Environmental Sciences; Elsevier: Amsterdam, The Netherlands, 2019; pp. 299–321. [Google Scholar] [CrossRef]
- Poesen, J.; Nachtergaele, J.; Verstraeten, G.; Valentin, C. Gully erosion and environmental change: Importance and research needs. Catena
**2003**, 50, 91–133. [Google Scholar] [CrossRef] - Zakerinejad, R.; Maerker, M. An integrated assessment of soil erosion dynamics with special emphasis on gully erosion in the Mazayjan basin, southwestern Iran. Nat. Hazards
**2015**, 79, 25–50. [Google Scholar] [CrossRef] - Arabameri, A.; Cerda, A.; Tiefenbacher, J.P. Spatial pattern analysis and prediction of gully erosion using novel hybrid model of entropy-weight of evidence. Water
**2019**, 11, 1129. [Google Scholar] [CrossRef][Green Version] - Angileri, S.E.; Conoscenti, C.; Hochschild, V.; Märker, M.; Rotigliano, E.; Agnesi, V. Water erosion susceptibility mapping by applying Stochastic Gradient Treeboost to the Imera Meridionale River Basin (Sicily, Italy). Geomorphology
**2016**, 262, 61–76. [Google Scholar] [CrossRef] - Javidan, N.; Kavian, A.; Pourghasemi, H.R.; Conoscenti, C.; Jafarian, Z. Gully erosion susceptibility mapping using multivariate adaptive regression splines-replications and sample size scenarios. Water
**2019**, 11, 2319. [Google Scholar] [CrossRef][Green Version] - Conoscenti, C.; Angileri, S.; Cappadonia, C.; Rotigliano, E.; Agnesi, V.; Märker, M. Gully erosion susceptibility assessment by means of GIS-based logistic regression: A case of Sicily (Italy). Geomorphology
**2014**, 204, 399–411. [Google Scholar] [CrossRef][Green Version] - Han, F.; Ren, L.; Zhang, X.; Li, Z. The WEPP Model Application in a Small Watershed in the Loess Plateau. PLoS ONE
**2016**, 11, e0148445. [Google Scholar] [CrossRef][Green Version] - Langendoen, E.J.; Wells, R.R.; Ursic, M.E.; Vieira, D.A.N.; Dabney, S.M. Evaluating sediment transport capacity relationships for use in ephemeral gully erosion models. IAHS-AISH Proc. Rep.
**2014**, 367, 128–133. [Google Scholar] [CrossRef] - Pourghasemi, H.R.; Yousefi, S.; Kornejady, A.; Cerdà, A. Performance assessment of individual and ensemble data-mining techniques for gully erosion modeling. Sci. Total Environ.
**2017**, 609, 764–775. [Google Scholar] [CrossRef][Green Version] - Wu, Z.; Wu, Y.; Yang, Y.; Chen, F.; Zhang, N.; Ke, Y.; Li, W. A comparative study on the landslide susceptibility mapping using logistic regression and statistical index models. Arab. J. Geosci.
**2017**, 10, 187. [Google Scholar] [CrossRef] - Dube, F.; Nhapi, I.; Murwira, A.; Gumindoga, W.; Goldin, J.; Mashauri, D.A. Potential of weight of evidence modelling for gully erosion hazard assessment in Mbire District–Zimbabwe. Phys. Chem. Earth
**2014**, 67–69, 145–152. [Google Scholar] [CrossRef] - Kornejady, A.; Ownegh, M.; Bahremand, A. Landslide susceptibility assessment using maximum entropy model with two different data sampling methods. Catena
**2017**, 152, 144–162. [Google Scholar] [CrossRef] - Rahmati, O.; Haghizadeh, A.; Pourghasemi, H.R.; Noormohamadi, F. Gully erosion susceptibility mapping: The role of GIS-based bivariate statistical models and their comparison. Nat. Hazards
**2016**, 82, 1231–1258. [Google Scholar] [CrossRef] - Rahmati, O.; Pourghasemi, H.R.; Melesse, A.M. Application of GIS-based data driven random forest and maximum entropy models for groundwater potential mapping: A case study at Mehran Region, Iran. Catena
**2016**, 137, 360–372. [Google Scholar] [CrossRef] - Gómez-Gutiérrez, Á.; Conoscenti, C.; Angileri, S.E.; Rotigliano, E.; Schnabel, S. Using topographical attributes to evaluate gully erosion proneness (susceptibility) in two mediterranean basins: Advantages and limitations. Nat. Hazards
**2015**, 79, 291–314. [Google Scholar] [CrossRef] - Jaafari, A.; Najafi, A.; Pourghasemi, H.R.; Rezaeian, J.; Sattarian, A. GIS-based frequency ratio and index of entropy models for landslide susceptibility assessment in the Caspian forest, northern Iran. Int. J. Environ. Sci. Technol.
**2014**, 11, 909–926. [Google Scholar] [CrossRef][Green Version] - Hong, H.; Chen, W.; Xu, C.; Youssef, A.M.; Pradhan, B.; Tien Bui, D. Rainfall-induced landslide susceptibility assessment at the Chongren area (China) using frequency ratio, certainty factor, and index of entropy. Geocarto Int.
**2017**, 32, 139–154. [Google Scholar] [CrossRef] - Chen, W.; Pourghasemi, H.R.; Kornejady, A.; Zhang, N. Landslide spatial modeling: Introducing new ensembles of ANN, MaxEnt, and SVM machine learning techniques. Geoderma
**2017**, 305, 314–327. [Google Scholar] [CrossRef] - Nhu, V.-H.; Mohammadi, A.; Shahabi, H.; Bin Ahmad, B.; Al-Ansari, N.; Shirzadi, A.; Clague, J.J.; Jaafari, A.; Chen, W.; Nguyen, H. Landslide Susceptibility Mapping Using Machine Learning Algorithms and Remote Sensing Data in a Tropical Environment. Int. J. Environ. Res. Public Health
**2020**, 17, 4933. [Google Scholar] - Chen, W.; Li, H.; Hou, E.; Wang, S.; Wang, G.; Panahi, M.; Li, T.; Peng, T.; Guo, C.; Niu, C.; et al. GIS-based groundwater potential analysis using novel ensemble weights-of-evidence with logistic regression and functional tree models. Sci. Total Environ.
**2018**, 634, 853–867. [Google Scholar] [CrossRef][Green Version] - Roodposhti, M.S.; Safarrad, T.; Shahabi, H. Drought sensitivity mapping using two one-class support vector machine algorithms. Atmos. Res.
**2017**, 193, 73–82. [Google Scholar] [CrossRef] - Shafizadeh-Moghadam, H.; Valavi, R.; Shahabi, H.; Chapi, K.; Shirzadi, A. Novel forecasting approaches using combination of machine learning and statistical models for flood susceptibility mapping. J. Environ. Manag.
**2018**, 217, 1–11. [Google Scholar] [CrossRef][Green Version] - Kadavi, P.R.; Lee, C.W.; Lee, S. Application of ensemble-based machine learning models to landslide susceptibility mapping. Remote Sens.
**2018**, 10, 1252. [Google Scholar] [CrossRef][Green Version] - Tehrany, M.S.; Pradhan, B.; Jebur, M.N. Flood susceptibility mapping using a novel ensemble weights-of-evidence and support vector machine models in GIS. J. Hydrol.
**2014**, 512, 332–343. [Google Scholar] [CrossRef] - Tchouateu, O.T.; Mwangi, H.M.; Sang, J.K.; Ngugi, H.N. Impacts of climate change on peak streamflow in Kakia-Esamburmbur Sub-catchment of Enkare Narok River catchment, Kenya. J. Sustain. Res. Eng.
**2020**, 5, 194–205. [Google Scholar] - Mireille, N.M.; Mwangi, H.M.; Mwangi, J.K.; Gathenya, J.M. Analysis of Land Use Change and Its Impact on the Hydrology of Kakia and Esamburmbur of the. Hydrology
**2019**, 6, 86. [Google Scholar] [CrossRef][Green Version] - Umukiza, E.; Raude, J.M.; Wandera, S.M.; Petroselli, A.; Gathenya, J.M. Impacts of Land Use and Land Cover Changes on Peak Discharge and Flow Volume in Kakia and Esamburmbur Sub-Catchments of Narok Town, Kenya. Hydrology
**2021**, 8, 82. [Google Scholar] [CrossRef] - Rahmati, O.; Tahmasebipour, N.; Haghizadeh, A.; Pourghasemi, H.R.; Feizizadeh, B. Evaluation of different machine learning models for predicting and mapping the susceptibility of gully erosion. Geomorphology
**2017**, 298, 118–137. [Google Scholar] [CrossRef] - Lombardo, L.; Cama, M.; Maerker, M.; Rotigliano, E. A test of transferability for landslides susceptibility models under extreme climatic events: Application to the Messina 2009 disaster. Nat. Hazards
**2014**, 74, 1951–1989. [Google Scholar] [CrossRef] - Alaska Satellite Facility Data Search Vertex (2020). Available online: https://search.asf.alaska.edu/#/?dataset=ALOS (accessed on 29 January 2023).
- Arabameri, A.; Chen, W.; Loche, M.; Zhao, X.; Li, Y.; Lombardo, L.; Cerda, A.; Pradhan, B.; Bui, D.T. Comparison of machine learning models for gully erosion susceptibility mapping. Geosci. Front.
**2019**, 11, 1609–1620. [Google Scholar] [CrossRef] - Hu, C.; Wright, A.L.; Lian, G. Estimating the Spatial Distribution of Soil Properties Using Environmental Variables at a Catchment Scale in the Loess Hilly Area, China. Int. J. Environ. Res. Public Heal.
**2019**, 16, 491. [Google Scholar] [CrossRef][Green Version] - Trigila, A.; Iadanza, C.; Esposito, C.; Scarascia-Mugnozza, G. Comparison of Logistic Regression and Random Forests techniques for shallow landslide susceptibility assessment in Giampilieri (NE Sicily, Italy). Geomorphology
**2015**, 249, 119–136. [Google Scholar] [CrossRef] - Jenness, J. Topographic Position Index (tpi_jen.avx) Extension for ArcView 3.x, v. 1.2. Jenness Enterprises. 2006. Available online: http://www.jennessent.com/arcview/tpi.htm (accessed on 1 March 2023).
- Chen, W.; Pourghasemi, H.R.; Naghibi, S.A. Prioritization of landslide conditioning factors and its spatial modeling in Shangnan County, China using GIS-based data mining algorithms. Bull. Eng. Geol. Environ.
**2018**, 77, 611–629. [Google Scholar] [CrossRef] - Meinhardt, M.; Fink, M.; Tünschel, H. Landslide susceptibility analysis in central Vietnam based on an incomplete landslide inventory: Comparison of a new method to calculate weighting factors by means of bivariate statistics. Geomorphology
**2015**, 234, 80–97. [Google Scholar] [CrossRef] - Copernicus. Available online: https://scihub.copernicus.eu/ (accessed on 31 August 2020).
- Ozdemir, A. Using a binary logistic regression method and GIS for evaluating and mapping the groundwater spring potential in the Sultan Mountains (Aksehir, Turkey). J. Hydrol.
**2011**, 405, 123–136. [Google Scholar] [CrossRef] - Chen, W.; Sun, Z.; Han, J. Landslide susceptibility modeling using integrated ensemble weights of evidence with logistic regression and random forest models. Appl. Sci.
**2019**, 9, 171. [Google Scholar] [CrossRef][Green Version] - Pourghasemi, H.R.; Moradi, H.R.; Fatemi Aghda, S.M. Landslide susceptibility mapping by binary logistic regression, analytical hierarchy process, and statistical index models and assessment of their performances. Nat. Hazards
**2013**, 69, 749–779. [Google Scholar] [CrossRef] - Xu, C.; Xu, X.; Dai, F.; Xiao, J.; Tan, X.; Yuan, R. Landslide hazard mapping using GIS and weight of evidence model in Qingshui River watershed of 2008 Wenchuan earthquake struck region. J. Earth Sci.
**2012**, 23, 97–120. [Google Scholar] [CrossRef] - Shit, P.K.; Bhunia, G.S.; Pourghasemi, H.R. Gully Erosion Susceptibility Mapping Based on Bayesian Weight of Evidence. Adv. Sci. Technol. Innov.
**2020**, 8, 133–146. [Google Scholar] [CrossRef] - Chen, W.; Reza, H.; Seyed, P.; Naghibi, A. A comparative study of landslide susceptibility maps produced using support vector machine with different kernel functions and entropy data mining models in China. Bull. Eng. Geol. Environ.
**2018**, 77, 647–664. [Google Scholar] [CrossRef] - Youssef, A.M.; Pourghasemi, H.R.; Pourtaghi, Z.S.; Al-Katheeri, M.M. Landslide susceptibility mapping using random forest, boosted regression tree, classification and regression tree, and general linear models and comparison of their performance at Wadi Tayyah Basin, Asir Region, Saudi Arabia. Landslides Landslides
**2015**, 13, 839–856. [Google Scholar] [CrossRef] - Pourtaghi, Z.S.; Pourghasemi, H.R.; Rossi, M. Erratum to: Forest fire susceptibility mapping in the Minudasht forests, Golestan province, Iran. Environ. Earth Sci.
**2015**, 73, 1535. [Google Scholar] [CrossRef][Green Version] - Meliho, M.; Khattabi, A.; Mhammdi, N. A GIS-based approach for gully erosion susceptibility modelling using bivariate statistics methods in the Ourika watershed, Morocco. Environ. Earth Sci.
**2018**, 77, 655. [Google Scholar] [CrossRef] - Mukai, S. Gully Erosion Rates and Analysis of Determining Factors: A Case Study from the Semi-arid Main Ethiopian Rift Valley. Land Degrad. Dev.
**2016**, 28, 602–615. [Google Scholar] [CrossRef] - Chuma, G.B.; Mondo, J.M.; Ndeko, A.B.; Mugumaarhahama, Y.; Bagula, E.M.; Blaise, M.; Valérie, M.; Jacques, K.; Karume, K.; Mushagalusa, G.N. Forest cover affects gully expansion at the tropical watershed scale: Case study of Luzinzi in Eastern DR Congo. Trees For. People
**2021**, 4, 100083. [Google Scholar] [CrossRef] - Kou, M.; Jiao, J.; Yin, Q.; Wang, N.; Wang, Z.; Li, Y.; Yu, W.; Wei, Y.; Yan, F.; Cao, B. Successional Trajectory Over 10Years of Vegetation Restoration of Abandoned Slope Croplands in the Hill-Gully Region of the Loess Plateau. Land Degrad. Dev.
**2016**, 27, 919–932. [Google Scholar] [CrossRef] - Azareh, A.; Rahmati, O.; Rafiei-Sardooi, E.; Sankey, J.B.; Lee, S.; Shahabi, H.; Ahmad, B. Modelling gully-erosion susceptibility in a semi-arid region, Iran: Investigation of applicability of certainty factor and maximum entropy models. Sci. Total Environ.
**2019**, 655, 684–696. [Google Scholar] [CrossRef] - Arabameri, A.; Pradhan, B.; Bui, D.T. Spatial modelling of gully erosion in the Ardib River Watershed using three statistical-based techniques. Catena
**2020**, 190, 104545. [Google Scholar] [CrossRef]

**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