Water erosion is one of the main processes responsible for soil degradation and sediment transport at the watershed scale. It causes the detachment and downstream transport of soil particles, organic matter and nutrients. It also contributes to the siltation of rivers, lakes, and reservoirs, as demonstrated by Lal [1] and Kinnell [2]. In regions where water resources are under increasing pressure, these processes can simultaneously affect soil conservation, the storage capacity of hydraulic structures, and the long-term sustainability of water resources.

This issue is particularly important in Senegal, where increasing demand for drinking water and agricultural uses is placing greater pressure on major groundwater and surface water resources. The Hors de Diass aquifer, which makes an important contribution to the water supply of Dakar and its surrounding areas, is experiencing a decline in groundwater levels. The Mont Rolland dam watershed is located within the recharge area of this aquifer. However, water erosion on the hillslopes and sediment accumulation in the reservoir may reduce the hydrological functions of the watershed. These processes are therefore important issues to consider in measures aimed at protecting and recharging the aquifer.

Lac de Guiers is one of Senegal’s main freshwater reserves and a strategic resource for drinking water supply, irrigated agriculture, and ecosystems. It provides a significant share of the water supplied to Dakar and its surrounding areas. It is also expected to meet increasing water demand, particularly through water-transfer projects toward inland areas of the country. Protecting this resource requires consideration of several degradation processes, including watershed erosion, sediment inputs, siltation, and deterioration of water quality. Mont Rolland Dam and Lac de Guiers watershed have different soil, geomorphological, and hydrological conditions, but they share a common challenge: improving the understanding and control of erosion and sediment transport processes to support the long-term protection of water resources.

The spatial assessment of these processes can be carried out using models such as the Universal Soil Loss Equation (USLE), the Revised Universal Soil Loss Equation (RUSLE), and the Unit Stream Power-based Erosion Deposition model (USPED). However, their application depends on several parameters whose accuracy directly affects estimated soil loss. Among these parameters, the soil erodibility factor K represents the intrinsic susceptibility of soil to detachment and transport by rainfall and runoff, according to the work of Wischmeier and Smith [3] as well as Renard et al. [4]. Its determination mainly depends on soil particle-size distribution, organic matter content, structure, and permeability.

Soil erodibility datasets and maps are available at global and regional scales. However, their spatial resolution and level of generalization may limit their use for detailed assessments of local watersheds. In addition, several empirical and semi-empirical formulations have been developed to estimate K from soil properties. These formulations do not use the same variables or functional relationships and may therefore produce substantially different K values for the same soil. The choice of the K formulation is thus a potential source of uncertainty in estimating soil loss and sediment transport with USLE, RUSLE, or USPED. A comparison based on local soil data is therefore needed before selecting a K formulation for spatial erosion modelling.

In this context, the present study compares six approaches for estimating the K factor, including those of Wischmeier [3], EPIC [5], Renard et al. [4], Torri-Poesen-Borselli method [6], Auerswald et al. [7], and the Römkens-Renard relationship using the geometric mean particle diameter Dg derived according to the approach of Shirazi et al. [8][9]. The analysis is based on geotechnical investigations conducted in the two watersheds, including 20 soil samples from Mont Rolland Dam watershed and 28 samples from the Lac de Guiers watershed. The parameters required by the different formulations are derived from particle-size distributions, organic matter content, soil structure observations, and in situ infiltration measurements using a double-ring infiltrometer. Additional interpolation or estimation is limited to parameters that cannot be obtained directly. These values are explicitly identified to assess their potential influence on the results.

The main objective of this study is to quantify and compare the variability in K values produced by the six approaches and to evaluate their behaviour under two contrasting soil conditions. The study also aims to identify the methods that are most consistent with local soil characteristics and to provide a basis for spatial mapping of the K factor in both watersheds. In a subsequent stage, the spatially distributed K values will be integrated into the USPED model to estimate erosion and deposition processes. The Mont Rolland dam watershed is particularly useful for this purpose because available bathymetric data provide an independent estimate of sediment accumulation in the reservoir. Comparing simulated sediment transport with observed sediment volumes will therefore provide a validation criterion for assessing the different K formulations. The method showing the best agreement with these observations may then be further examined for estimating soil loss in the Lac de Guiers watershed, while accounting for the differences in soil characteristics between the two study areas.

This study focuses on two watersheds in Senegal that exhibit different hydroclimatic and geomorphological conditions: the Mont Rolland Dam watershed and the Lac de Guiers watershed (Figure 1). The first, located in the Thies region, lies southwest of the village of Tiwin Tanghor. The area of the watershed directly influenced by the dam is approximately 311 hectares. It is part of a larger hydrographic network covering approximately 129.98 km², which feeds Lake Tanma. Its topography is quite rugged, with elevations ranging from 30 to 118 meters, which promotes the accumulation of runoff and the transport of sediments toward the dam. Over the period from 2005 to 2025, the average annual rainfall is approximately 475 mm. This terrain contributes to soil erosion and the gradual filling of the dam.

The Lac de Guiers, meanwhile, is located in northern Senegal, primarily in the Saint-Louis and Louga regions (Figure 2). The lake is a large natural depression,

Figure 1. Topographic map of the Mont Rolland Dam watershed.

Figure 2. Topographic map of the Lac de Guiers watershed.

fed mainly by the Senegal River via the Taouey Canal. This watershed is characterized by relatively gentle topography, a variety of sandy and clayey formations, and a relatively arid Sahelian climate. The runoff and erosion processes occurring there can generate significant sediment inputs into the lake, which is an essential resource for drinking water supply, irrigated agriculture, and the maintenance of local ecosystems.

Soil erodibility characterization in the Mont Rolland Dam and Lac de Guiers watersheds is based on geotechnical studies conducted both in the field and in the laboratory, supplemented by in situ infiltration measurements. Samples collected at various sampling points were analyzed to determine the key physical characteristics essential for evaluating the erodibility factor K. In the laboratory, equipment was used to perform particle-size analyses, which made it possible to quantify the proportions of sand, silt, and clay. In addition, other devices were used to obtain additional parameters necessary for soil characterization. Field observations, as well as photographs of the samples, also played a crucial role in identifying their structure and surface condition. The infiltration capacity of the soils was measured directly on-site using a double-ring infiltrometer [10][11], consisting of two concentric metal cylinders driven into the ground and supplied with water. By monitoring the decrease in the water level over time, it is possible to estimate the infiltration rate, with the outer ring limiting lateral flow. All of these geotechnical and hydrodynamic data serve as an empirical basis for calculating and comparing the K-factor using various empirical formulas. Soil infiltration was measured in situ using a double-ring infiltrometer operated under falling-head conditions [12]. The device consisted of concentric steel rings, 15 cm and 33 cm in internal diameter and 20 cm high, inserted approximately 4 - 5 cm into the soil. The outer ring was used to reduce lateral flow beneath the inner ring and promote predominantly vertical infiltration. Water-level changes were measured using millimetre-graduated scales fixed inside both rings. The initial ponding depth was approximately 15 cm.

The methodology is based on an experimental approach that combines field investigations, geotechnical laboratory analyses, and a comparative calculation of the erodibility factor K. This approach is applied to soils in the watersheds of the Mont Rolland Dam and Lac de Guiers to assess the spatial variability of their susceptibility to water erosion.

Prior to the field investigations, the main soil units within the two study areas were identified from available national soil maps. These mapped soil units provided the initial basis for planning the field investigations and selecting representative sampling areas. During field reconnaissance, this preliminary soil-unit identification was verified and complemented by direct observations of surface conditions and local soil characteristics. Sampling locations were then selected to ensure that each identified soil unit was represented by at least one sampling point, while also accounting for the diversity of surface conditions encountered in the field. At each sampling location, apparent soil texture, soil structure, vegetation or organic debris, surface condition, and visible signs of erosion were examined and documented. Surface soil samples were collected mainly from the 0 - 20 cm layer, which is directly exposed to rainfall, runoff, and erosion processes. Twenty samples were collected and analyzed in the Mont Rolland Dam watershed and twenty-eight (28) samples in the Lac de Guiers watershed.

At the same sampling locations, infiltration tests were conducted in situ using a double-ring infiltrometer. At each sampling location, three infiltration tests were performed within a radius of approximately 5 m. The two rings were filled simultaneously and maintained at comparable initial water levels. Under falling-head conditions, the decrease in water level in the inner ring was recorded as a function of time. Successive filling-infiltration cycles were performed until quasi-steady conditions were reached. Quasi-steady state was assumed when the slopes of the water-level-time relationships for two successive cycles differed by less than 5%, following the criterion used by Arriaga et al. [12]. The final stable cycle was retained for calculation.

The quasi-steady infiltration rate q_s was determined from the absolute slope of the water-level decline in the inner ring during the final stable cycle. Since q_s represents the measured infiltration flux under ponded conditions, it was converted to field-saturated hydraulic conductivity K_fs using the relationship proposed by Reynolds et al. [11] and applied to falling-head double-ring measurements by Arriaga et al. [12]:

where q_s is the quasi-steady infiltration rate (cm/s), H is the mean ponding depth during the final cycle (cm), a is the inner-ring radius (cm), d is the ring insertion depth (cm), α is the inverse macroscopic capillary length (0.12 cm⁻¹), C1 and C₂ are dimensionless quasi-empirical constants. Following Reynolds et al. [11], C₁ = 0.316π and C₂ = 0.184π for d ≥ 3 cm and H ≥ 5 cm.

The resulting field-saturated hydraulic conductivity K_fs was converted to the permeability class p used in the Wischmeier K-factor equation according to the classification presented in Table 1, following the permeability-class framework associated with the Wischmeier soil-erodibility nomograph [3][4].

The collected samples were subsequently analyzed in the laboratory. The analyses included particle-size distribution by sieving, in accordance with standards NF EN 933-1 and NF P 94-057, as well as organic matter content using the calcination method XP P 94-047. The particle-size distribution curves make it possible to identify the proportions of the various particle size classes required for erodibility calculations, particularly for the sand, silt, and clay fractions. For samples containing a significant fine fraction, the particle size analysis is supplemented by a sedimentometric analysis. The results are then combined with data on organic matter content and visual observations that help assess soil structure. The results were analyzed by calculating the normalized fractions of clay (<0.002 mm), silt (0.002 - 0.050 mm), sand (0.050 - 2 mm), and very fine sand (0.050 - 0.100 mm). The soil structure code (s) and permeability class (p) were also determined for each sample. The geotechnical reports also highlight a wide range of textures, ranging from fine sands and silty sands to sandy silts and more clayey soils, which requires an evaluation of the K factor for each sample.

Table 1. Permeability Classes used to assign the Wischmeier permeability code p from field-saturated hydraulic conductivity Kfs [3][4].

Based on the collected data, the erodibility factor K was calculated individually for each sample using several methods. The Wischmeier-Smith method [3] is based primarily on the erodible grain size fraction, organic matter, and soil structure and permeability classes. The EPIC formulation [5] relies primarily on the contents of sand, silt, clay, and organic carbon. The Römkens-Renard method [4] determines K based on the mean geometric particle diameter Dg. The formulations by Torri, Poesen and Borselli [6] and by Auerswald et al. [7] are also applied using the available granulometric and organic parameters. The results of each method are converted to a single unit of the International System of Units to facilitate comparison of the values. The final step involves examining the variability of the estimates obtained. For each sample, the K values derived from the different methods are compared using descriptive statistics, absolute and relative deviations, inter-method ratios, and, where relevant, correlation analyses. This analysis identifies the formulations most sensitive to texture, organic matter, structure, and infiltration, while assessing their consistency for soils in both basins. The ultimate goal is to propose a single value or a range of K s that is sufficiently representative to improve the parameterization of the USLE, RUSLE, and USPED models applied to the Mont Rolland Dam and Lac de Guiers watersheds.

Field sampling followed by laboratory analyses was conducted in the Mont Rolland Dam watershed. The geotechnical studies carried out in the Mont Rolland Dam area, involving 20 samples (S01 through S20), reveal substantial variability in soil characteristics. The identified materials consist mainly of silty sands, sandy silts, gravels, and lateritic gravels, with the occasional presence of calcareous formations and lateritic concretions. The grain-size analysis shows that silty textures dominate: nine samples are classified as fine silt. Three as silt, three as fine clayey silt, three as sandy silt, one as silty sand, and one as very fine silt. Certain samples, such as S13, exhibit particularly high silt content, while S08 is distinguished by its notable proportion of sand. Organic matter varies significantly among the samples, with levels ranging from approximately 3.3% to 11.5%, which can affect structural stability and, consequently, erodibility. Infiltration measurements corroborate this marked spatial variability, with values ranging from 20 mm/h for S18 to 2,550 mm/h for S06, while S08 and S09 also exhibit very high infiltration rates. The predominance of silty fractions, combined with variations in organic matter, texture, and infiltration, suggests different susceptibilities to water erosion, This justifies the need to determine the K-factor for each sample before mapping it within the watershed. A summary of the particle-size analyses, organic matter estimates and infiltration data for the Mont Rolland Dam watershed is presented in AppendixTable A1. The following graph (Figure 3) presents the classification of materials according to the USDA (United States Department of Agriculture) textural triangle [13].

Figure 3. USDA textural triangle for the soil of the Mont Rolland Dam watershed.

Geotechnical studies conducted on the 28 soil samples (S01 through S28) collected from the Lac de Guiers watershed reveal a high degree of heterogeneity in properties that may influence soil erodibility. The grain-size analysis, combined with the plotting of the samples on the textural triangle (Figure 4), indicates a predominance of sandy and sandy-silty textures, with the majority of samples falling into the categories of sand, silty sand, and sandy silt. However, a few samples, such as S28, contain a significant proportion of fine particles and are distinguished by their position in the silt range. Organic matter content also varies, being generally low in sandy soils and higher in certain fine-textured soils. Infiltration measurements taken in the field confirm this diversity: infiltration rates range from 36 to 816 mm/h, with the highest values generally observed in sandy materials, while soils richer in fine particles exhibit more limited infiltration. This variability—in terms of both grain size, structure, and hydrodynamics—leads to notable differences in susceptibility to detachment and runoff. The results therefore suggest that the erodibility of soils in this watershed cannot be represented by a single value for the K factor. They highlight the need for a localized and comparative assessment of K using multiple formulations, such as those by Wischmeier, EPIC, Römkens-Renard, Torri-Poesen-Borselli, and Auerswald, to determine the method best suited to the region’s specific pedological characteristics. A summary of the grain-size analyses, organic matter estimates and infiltration data for the Lac de Guiers watershed is presented in AppendixTable A2. The following graph (Figure 4) shows the classification of the materials according to the USDA textural triangle.

Figure 4. USDA soil textural triangle for the Lac de Guiers watershed.

Soil loss in watersheds is estimated using the original RUSLE formula (Equation (2) [3][4]). It includes several factors that must be quantified.

where

A = Average annual soil loss (t/ha/year);R = Precipitation erosivity factor (MJ·mm/ha·h·year); K = Soil erodibility factor (t·ha·h/ha·MJ·mm);LS = Slope length and slope factor (dimensionless);C = Cover management factor (dimensionless);P = Support-practice factor.

Among these parameters is the soil erodibility factor K. Several methods are used to calculate the erodibility factor K, which has the unit t·ha·h·ha⁻¹·MJ⁻¹·mm⁻¹ in SI units.

This comparative study confirms that soil erodibility cannot be represented by a K value considered independently of its estimation method. The results show substantial method effects in both watersheds. At Lac de Guiers, mean K ranges from 0.01079 to 0.02274, whereas at Mont Rolland it ranges from 0.01014 to 0.05007. The magnitude, dispersion, and relative ranking of samples therefore depend strongly on the formulation used.

The comparison does not support a single site-wide ordering common to all six approaches. At Lac de Guiers, Wischmeier and Auerswald et al. show very similar spatial patterns (r = 0.988), while Torri-Poesen-Borselli produces a narrower range of K values and weaker correlations with the other methods. At Mont Rolland, Wischmeier and Auerswald et al. are also strongly correlated (r = 0.963), whereas the other formulations show substantially different patterns of variability. These results confirm that the choice of K formulation constitutes an important source of uncertainty in subsequent erosion modelling.

The Römkens-Renard relationship using a Shirazi-derived geometric mean diameter was included as a comparative approach to evaluate the sensitivity of K estimates to an alternative characterization of particle-size distribution. Although fractions greater than 2 mm were incorporated into the calculation of the generalized Dg, the present study does not demonstrate that this treatment provides a more accurate estimate of soil erodibility. Similarly, the coarse-fragment-cover term included in the Auerswald et al. formulation could not be evaluated because surface coarse-fragment cover was not measured and was therefore fixed at frf = 0. The influence of coarse fragments on soil erodibility consequently requires specific field characterization and further validation.

The conclusions of this study primarily apply to the sampled soils and to the soil conditions represented by the sampling design. Therefore, rather than selecting a single K equation solely on the basis of its mean value or conventional use, a multi-method sensitivity analysis is recommended for subsequent RUSLE or USPED applications. Independent field observations are required to determine which formulation best represents actual erosion processes under local conditions.

For the Mont Rolland Dam watershed, the available sedimentation information provides an opportunity for such validation. A subsequent comparison between simulated soil loss and observed sediment accumulation in the reservoir may help assess the predictive performance of the different K formulations. Sediment volumes, runoff information, and other field-based erosion indicators should therefore be used, where available, to calibrate and validate the modelling framework before extrapolating the selected K formulation to the Lac de Guiers watershed.

Conceptualization, S.B.; methodology, S.B. and M.B.; geotechnical investigations, S.B.; validation of results, M.B., M.C., and S.N.; writing—original draft preparation, S.B.; writing—review and editing, S.B., M.C., S.N. and M.B.; manuscript validation, M.C., S.N., and M.B. All authors have read and agreed to the published version of the manuscript.

Table A1. Geotechnical measurements in the Mont Rolland Dam Watershed.

Table A2.Geotechnical measurements in the Lac de Guiers Watershed.