Rain Erosivity Factor (R) and Topographic Factor (LS) of the Universal Soil Loss Equation (USLE) in a Semi-Desert Area

Abstract

Water erosion is a critical degradation process that reduces fertility and agricultural sustainability, especially in semi-arid regions. The Universal Soil Loss Equation (USLE) allows for the quantification of this phenomenon using factors such as rainfall erosivity (R) and topography (length-slope, LS). In this study, both factors were estimated and analyzed in the Cañitas sub-basin, located in the semi-desert area of the state of Zacatecas, Mexico, characterized by irregular precipitation and limited data availability. The objective of this study is to estimate and analyze the R factor and LS factor to evaluate their influence on soil water erosion processes. Records from five meteorological stations (1986–2022) were used, along with the Modified Fournier Index (MFI) and Geographic Information Systems (GIS) tools, generating spatial maps of rainfall erosivity and topography. An average R factor of 81.69 MJ∙mm/ha∙h∙year was estimated, consistent with the values obtained using the MFI. The LS factor shows that the northwestern area of the study zone has the most extensive and steepest slopes (up to 20). This study analyzes the R and LS factors to identify areas vulnerable to water erosion and to understand the influence of climate and topography in a semi-arid region, which can serve as a reference for planning conservation actions and managing watersheds in semi-arid areas with high climatic variability.

1. Introduction

One of the main environmental problems globally is soil erosion [1], due to its economic and social impact [2]. Loss of biodiversity, soil degradation, nutrient loss, and water and soil pollution are negative impacts of erosion. In 2018, the International Resolution on Soil and Water Conservation established that in different types of land cover and uses, “the global average soil erosion is estimated to be between 12 and 15 t/ha/year” ([3], meaning that, globally, the Earth’s land surface loses between 0.90 and 0.95 mm of soil annually, assuming a soil density of 1.4–1.5 $\mathrm{g} {\mathrm{c}\mathrm{m}}^{-3}$.

Its economic, social, and ecological impacts, which affect fertility, biodiversity, and water quality, have made soil erosion one of the main environmental problems. Precipitation, topography, and land use are fundamental factors in water erosion, which also exhibits high spatial and temporal variability. In this context, the integration of models such as USLE/RUSLE with geospatial tools has allowed for progress in identifying critical areas; however, limitations persist in the detailed representation of these factors, especially in semi-arid regions with limited data. In particular, understanding the spatial distribution of the R factor and the heterogeneity of the LS factor remains a significant challenge for accurately interpreting erosional processes under conditions of climatic variability. The R and LS factors represent two of the main mechanisms controlling the water erosion of soil: the capacity of rainfall to detach particles and the influence of topography on their transport [4].

In 2015, a 20 m Digital Elevation Model (DEM) [5] and the Desmet and Govers model were used [6] in southern Italy, with the authors finding that for slopes greater than 15–20%, erosion can be up to 10 times higher than for slopes gentler than 15%, with the topographical factor being the main geomorphological control [5]. Using the RUSLE method and GIS, in 2015, LS was identified as one of the fundamental factors in the erosion process [6]. In 2016, using high-precision precipitation data, the R factor was analyzed in Europe using the RUSLE method, revealing high variability and elevated values associated with extreme events in the Mediterranean region [7]. In 2016, using the GAM statistical model and the RUSLE method, it was found that erosivity is concentrated in autumn and winter, with a clear relationship between the distribution of rainfall and the spatial distribution of the erosivity factor [8]. In Rwanda in 2016, the USLE method, GIS, and remote sensing were used to determine that water erosion is very severe in Rwanda, and is concentrated in agricultural areas with steep slopes [9]. In the Koga Basin in 2016, using RUSLE, GIS, and remote sensing, severe erosion was found to be related to topography, rainfall, and intensive land use for agriculture [10]. In 2017, a collaborative study was conducted on a global R factor using high-density climate databases, concluding that rainfall erosivity is highly variable in space and time, concentrating in the tropics and in specific seasons [11]. In 2017, erosion risk was assessed by integrating RUSLE and GIS, concluding that it is a powerful tool for diagnosing erosion and prioritizing areas for ecological restoration [12].

In 2021 erosivity and its trend were monitored in Juliaca, calculating R using the USLE and the Mann–Kendall method. It was concluded that rainfall erosivity in Juliaca is high and variable, directly linked to annual precipitation, with no clear trend during the evaluated period, but with a potentially significant impact on soil erosion [13]. In 2022, USLE and GIS methods were used to estimate soil loss in the Estibaná River sub-basin, comparing different types of vegetation cover and their effects, as well as agricultural management practices. It was concluded that erosion in the Estibaná River sub-basin is a serious problem caused mainly by intense rainfall and rugged topography [14]. In Argentina in 2022, a study was conducted using the USLE, demonstrating the spatial and temporal interactions between different factors (precipitation, slope, soil, crops, and management) [15]. In Cuba, local precipitation data (20 years) were used, and edaphic and topographic factors were estimated using the RUSLE method. Indices such as rainfall erosivity were validated, and the Modified Fournier Index was used to estimate erosion risk in the Los Palacios River sub-basin. This reflected the spatial and temporal interactions between natural factors (rainfall, slope, soil) and anthropogenic factors (crops, management), where rainfall exhibits very high erosive aggressiveness [16].

In 2023, a watershed in northwestern Morocco was analyzed using GIS, DEM, and RUSLE, identifying risk areas and highlighting the LS and R factor importance of the RUSLE as the most relevant factors in the spatial variability of erosion [17]. In China, in 2024 the improved USLE methodology was applied with global climatic, soil, topographic, and satellite data from 1992 to 2015, analyzing temporal trends and regional variations. The authors also validated the results by comparing them with previous global studies, concluding that global potential water erosion is highly sensitive to precipitation and changes in land cover [18]. A 2025 study demonstrates a robust application of the USLE integrated with GIS to assess soil loss and its economic impact in an agricultural watershed, highlighting the effectiveness of conservation practices. Critical areas associated with slope and position in the landscape are identified [19].

This research aims to determine and evaluate the rainfall erosivity factor (R) using the Modified Fournier Index (MFI) and the LS factor through a 20 m DEM. ArcGIS 10.8 software was used, utilizing available data from five meteorological stations of Comisión Nacional del Agua (CONAGUA) spanning 37 years, from 1986 to 2022. The study area is located in the Cañitas sub-basin within the Fresnillo–Yesca basin in the semi-arid region of the state of Zacatecas, Mexico.

This study provides new evidence on the spatial distribution of rainfall erosivity and the topographic influence on soil erosion in a semi-arid watershed in northern Zacatecas State, Mexico. It demonstrates the applicability of the Modified Fournier Index combined with GIS techniques in data-scarce environments.

This research expands knowledge about the dynamics of water erosion in semi-arid regions of northern Mexico by spatially characterizing the R and LS factors. Furthermore, it provides evidence on the usefulness of the Modified Fournier Index for estimating rainfall erosivity in basins with limited meteorological data.

Selected studies conducted between 2015 and 2025 are presented [

Table 1. Some of the studies carried out in the period 2015–2025.

Reference	Country/ Region	Methodology	Main Focus	Main Findings	Limitations
[7]	Morocco	RUSLE + GIS	Spatial analysis.	LS as a fundamental factor.	Without temporal analysis of R factor.
[8]	Greece	RUSLE + DEM high resolution + GAM	Spatiotemporal erosivity (R factor).	High spatial and temporal variability.	Dependence on high-resolution pluviographic data. Approach with Mediterranean dictions.
[9]	Rwanda	RUSLE+GIS	Erosion assessment.	High erosion in sloping agricultural areas.	Tropical context.
[10]	Ethiopia	RUSLE + DEM (30 m)	Critical erosion zones.	Identification of vulnerable areas.	Without methodological validation.
[11]	Global	RUSLE + climatological data	Global R factor.	High spatial and temporal variability.	Global scale without local detail.
[12]	Algeria	RUSLE + GIS	Risk of erosion.	A useful tool for planning.	Without validation of the R factor or long time series.
[13]	Perú	USLE + Mann–Kendall	R Factor	High erosivity and decreasing erosivity trend	Short series (2013–2017); LS not calculated
[20]	Colombia	Empirical models of R	Erosivity assessment	Significant differences between methods	Data dependency; does not include LS.
[21]	Mexico	RUSLE + SWAT + HIT	Agricultural basins.	Integration of hydrological models.	Not validated in semi-arid zones.
[22]	Tunisia	RUSLE	R and LS factors.	Interaction between factors in the Mediterranean Basin.	Without methodological comparison.
[23]	China	Rainfall Temporal Resolution Analysis + USLE (R factor)	R factor accuracy.	Erosivity decreases when using low-temporal-resolution data; errors increase > 15 min.	Dependence on high-resolution data; methodological approach.
[24]	Europe (Czech Republic, Germany, Austria)	USLE/RUSLE comparative + SIG	Comparison of model implementations.	Differences of up to 75% in erosion estimates depending on implementation. Even greater variability at the plot scale.	Lack of standardization between countries.
[14]	Panama	USLE + plots + GIS	Soil use	Influence of soil cover and management.	No methodological validation of the R factor.
[15]	Argentina	USLE (monthly scale)	Spatiotemporal analysis.	Interaction of natural and anthropogenic factors.	Monthly scale.
[25]	Ecuador	MCDA + GIS	Risk zoning.	Identification of critical areas by slope and cover.	Subjectivity in weightings; no physical model or validation.
[18]	China	USLE + DEM + GIS	Global trends.	High sensitivity to climate and land use.	Global scale.
[26]	Brazil	RUSLE + GIS + MLR	Identification of priority areas and geomorphometric control.	Predominantly low risk, with localized critical areas. Topographic factors explain much of the variability. Identification of key geomorphological variables (curvature, humidity index, etc.).	The model partially explains the variability. Dependence on spatial data. Tropical regional focus.

] ([7,8,9,10,11,12,13,14,15,18,20,21,22,23,24,25,26]).

2. Materials and Methods

2.1. Study Area

The study area is located in the Cañitas sub-basin, situated between −102°4′49.888564″ longitude and 23°27′47.102213″ latitude, within the Fresnillo–Yesca Basin in the State of Zacatecas, Mexico. This region is located in a semi-desert zone, characterized by high-intensity rainfall over short periods, high hydroclimatic variability, and erosivity associated with high-intensity rainfall events [22].

The Cañitas sub-basin demonstrates the predominant influence of the R and LS factors on the dynamics of water erosion, as also seen in several international studies; however, it is distinguished by its semi-arid condition, limited data availability, and high climatic variability, which modifies the erosion generation mechanisms. In Cañitas it is associated with intense but sporadic rainfall events. Furthermore, the use of different techniques to validate the R factor represents a significant contribution compared to previous studies. The Cañitas sub-basin (Figure 1) has an area of 4949 km² and a perimeter of 428.12 km (SIATL, the water flow simulator for watersheds was developed by the Instituto Nacional de Estadística y Geografía (INEGI, 2010). Within the sub-basin, different land uses are observed, associated with soil degradation processes. The Cañitas sub-basin contributes to surface runoff and the recharge of local aquifers, which is fundamental to the sustainable management of water resources in the northern part of the state of Zacatecas [27]. Analyzing the R (rainfall erosivity) and LS (topography) factors in the Cañitas sub-basin is fundamental to understanding the mechanisms that control water erosion in this environment, characterized by high climatic variability and rainfall concentrated between June and September. This favors short-duration, high-kinetic-energy erosion events. The R factor quantifies the energy and intensity of precipitation, while the LS factor shows the influence of topography on the erosion process. Evaluating both factors allows us to identify the spatial distribution of erosion risk and distinguish areas where climatic or topographic effects predominate. Furthermore, this approach helps reduce uncertainty in erosion estimation using the USLE (Universal Soil Loss Equation), particularly in contexts with limited information, thus strengthening the analysis of the erosion process at a local scale.

The climatic, edaphic, and topographic characteristics of the Cañitas sub-basin, represented by the presence of Leptosols, Calcisols, Phaeozems, and Regosols, and the information derived from the 20 m Digital Elevation Model (DEM) make it an area of interest for evaluating water erosion and the potential effects of climate change on soil loss in semi-arid environments [28].

Table 2. General characteristics of climatological stations (National Meteorological Service).

Weather Station	Name	Basin	Municipality	Latitude	Longitude	AE	Years of Service
32001	Agua Nueva	Fresnillo–Yesca	Villa de Cos, Zac.	23°46′58″	−102°09′37″	1932	1964–2022
32005	Cañitas de Felipe Pescador	Fresnillo–Yesca	Cañitas de Felipe Pescador	23°36′08″	−102°44′02″	2046	1941–2022
32040	Nuevo Mercurio	Camacho–Gruñidora	Mazapil, Zac.	24°13′38″	−102°09′09″	1706	1969–2022
32076	Col. Grever La Colorada	Fresnillo–Yesca	Villa de Cos, Zac.	23°48′34″	−102°28′19″	1950	1971–2023
32142	Tierra y Libertad	Fresnillo–Yesca	Villa de Cos, Zac.	23°27′00″	−102°23′32″	2030	1982–2023

The analysis was performed on precipitation data from the five meteorological stations (the remaining stations within the sub-basin either ceased operations several years prior or lacked sufficient data for analysis and were therefore excluded) provided by the Comisión Nacional del Agua (CONAGUA) for the period 1986–2022. This period was chosen to provide more comprehensive information. The U.S. National Weather Service method was used to fill in missing data [29].

shows the general characteristics of the five meteorological stations analyzed during the period 1986–2022. It is worth noting that some stations have a longer operating time and greater availability of records.

GIS tools based on the Modified Fournier Index (MFI) were applied, enabling a spatial assessment of rainfall erosivity and topography in the study area.

2.2. Universal Soil Loss Equation (USLE)

The Universal Soil Loss Equation (USLE) is a mathematical model that calculates water erosion of soil [30] based on factors given by Equation (1) [31].

$$\mathit{A}=\mathit{R}·\mathit{K}·\mathit{L}·\mathit{S}·\mathit{C}·\mathit{P}$$

(1)

where A is the annual average soil erosion $\mathrm{M}\mathrm{g}/(\mathrm{h}\mathrm{a}·\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}),$ R is rainfall erosivity (MJ∙mm/ha∙h∙year), K is soil erodibility ($\mathrm{M}\mathrm{g}·\mathrm{h})/\left(\mathrm{M}\mathrm{J}·\mathrm{m}\mathrm{m}\right),$ L is slope length (dimensionless), S is slope grade (dimensionless), C is crop and crop management (dimensionless), and P is soil management practices (dimensionless) [32].

2.3. Modified Fournier Index (MFI)

The R factor, called rainfall erosivity or soil erosivity, is a function of the kinetic energy and intensity of precipitation. The calculation is based on the climatic aggressiveness index or FI (Equation (2)), which is calculated using data from weather stations. The formula for the FI is obtained from Equation (2) [33].

Fournier, in 1960, calculated the precipitation coefficient to estimate erosivity [31]. Lombardi Neto and Moldenhauer (1992) established an empirical equation between precipitation and erosivity using the Fournier Index (FI). This allows erosivity to be calculated [34].

$$\mathit{F}\mathit{I}={\displaystyle \frac{{\mathit{p}}_{\mathit{m}\mathit{a}\mathit{x}}^{{\displaystyle 2}}}{\mathit{P}}}$$

(2)

where FI is the Fournier Index, ${\mathit{p}}_{\mathit{m}\mathit{a}\mathit{x}}$ is the average precipitation of the rainiest month (mm), and P is the average annual precipitation (mm).

The MFI (Equation (3)) is obtained from the ratio of the sum of the squares of the monthly precipitation for a year to the total average annual precipitation [35].

Although the FI is widely used due to its ease of calculation, it does not have much popularity among soil scientists, since it only considers the month with the highest precipitation, while the MFI considers all months and is based on the fact that surface erosion is not only caused by the month with the highest precipitation, but also by months with lower precipitation [20].

$$\mathit{M}\mathit{F}\mathit{I}={\displaystyle {\sum }_{\mathit{i}={\displaystyle 1}}^{{\displaystyle 12}}}{\displaystyle \frac{{\mathit{p}}_{\mathit{i}}^2}{{\mathit{P}}_{\mathit{t}}}}$$

(3)

where MFI is the Modified Fournier Index, ${\mathit{p}}_{\mathit{i}}$ is the mean monthly precipitation (mm), and ${\mathit{P}}_{\mathit{t}}$ is the mean annual precipitation (mm).

2.4. Erosivity Factor (R)

The use of the Modified Fournier Index (MFI) for estimating the rainfall erosivity factor R has been widely supported in the scientific literature, particularly in regions where high-resolution pluviographic records are unavailable. In this context, several studies have demonstrated a strong relationship between the MFI and the R factor. For example, in 2016, it was reported that the Modified Fournier Index shows a high degree of fit with the R factor [34], supporting its use as a surrogate indicator of rainfall erosivity. Subsequently, in 2018, a correlation between the R factor and the MFI was used to recalibrate and improve the representation of erosivity in erosion models [35]. Furthermore, in 2015, the erosivity factor was estimated using Equation (4), developed with data from a Mediterranean region characterized by irregular rainfall and high-intensity rain events [36]. Although Mediterranean climatic conditions differ from those present in semi-arid environments, both contexts share precipitation patterns capable of generating high erosivity, which has favored the use of this type of empirical relationship in water erosion studies carried out in regions with limited availability of rainfall intensity data.

$$\mathit{R}={\displaystyle 1.05}·\mathit{M}\mathit{F}\mathit{I}.$$

(4)

For the spatial estimation of the rainfall erosivity factor, ArcGIS software was used, a geospatial platform widely used in hydrological and environmental studies for the processing, analysis, and interpolation of climatic variables [37]. The calculation of the R factor was based on precipitation records from five meteorological stations located within and in the immediate vicinity of the Cañitas sub-basin, whose distribution allowed for the representation of the spatial variability of precipitation in the study area.

Because the erosivity estimate was based on information from only five meteorological stations heterogeneously distributed within and around the Cañitas sub-basin, the Inverse Distance Weighting (IDW) method was deemed appropriate. This method assumes that the similarity between observations decreases with distance, thus assigning greater weight to stations closer to the estimation point. This approach is particularly suitable for climatic variables such as precipitation and rainfall erosivity, whose spatial variability is often strongly influenced by geographic proximity. Furthermore, comparison with the Kriging method showed very similar spatial patterns, indicating that the spatial structure of the data was consistently represented. In this context, the use of IDW allowed for a robust spatial representation of erosivity with a limited number of stations and without requiring the explicit modeling of the spatial autocorrelation structure necessary in more complex geostatistical methods.

The Modified Fournier Index (MFI) was calculated annually for each station during the study period, allowing for the incorporation of the temporal variability of precipitation. From these values, the R factor was estimated for each year and station, and subsequently, the average erosivity values were determined. This procedure made it possible to characterize both the temporal variability of rainfall erosivity and its spatial distribution within the Cañitas sub-basin, providing a solid basis for the identification of areas with greater erosive potential.

2.5. Topographic Factor LS

The precipitation and topographic surfaces were generated using the Inverse Distance Weighting (IDW) interpolation method in ArcGIS, using a cell size of 100 m × 100 m.

Slope length (L) and slope (S) are two fundamental elements in the USLE for calculating the LS factor in watershed studies, which includes the influence of topography on soil loss [38].

Foster (1977) proposed Equations (5)–(7) for L factor estimation.

$$\mathit{L}={\left({\displaystyle \frac{\mathit{\lambda }}{{\displaystyle 22.13}}}\right)}^{\mathit{m}}$$

(5)

with

$$\mathit{m}={\displaystyle \frac{\mathit{F}}{{\displaystyle 1}+\mathit{F}}}$$

(6)

and

$$\mathit{F}={\displaystyle \frac{\mathit{s}\mathit{i}\mathit{n}\mathit{\beta }/{\displaystyle 0.086}}{{\displaystyle 3}{\left(\mathit{s}\mathit{i}\mathit{n}\mathit{\beta }\right)}^{{\displaystyle 1.8}}+{\displaystyle 0.56}}}$$

(7)

where L is the slope length (m), λ is the surface flow area (m²), F is the slope factor that defines m, m is the exponent influenced by the slope length and angle, and β is the slope angle.

In 2015, Panagos and Meusburger expanded on the approach developed by Desmet and Govers (1996), incorporating GIS techniques to propose Equation (8) [8].

$${\mathit{L}}_{\left(\mathit{i},\mathit{j}\right)}={\displaystyle \frac{{\left[{\mathit{A}}_{(\mathit{i},\mathit{j})}+{\mathit{D}}^{{\displaystyle 2}}\right]}^{(\mathit{m}+{\displaystyle 1})}-{\mathit{A}}_{(\mathit{i},\mathit{j})}^{(\mathit{m}+{\displaystyle 1})}}{{\mathit{x}}^{\mathit{m}}{\mathit{D}}^{(\mathit{m}+{\displaystyle 2})}{\left({\displaystyle 22.13}\right)}^{\mathit{m}}}},$$

(8)

where β is the slope, A is the flow accumulation, D is the grid cell size (m), and x is the shape coefficient (x = 1).

According to Renard et al. (1997), soil loss increases with slope length, hence the importance of the L factor [39].

The formula for obtaining the slope is derived from Equations (9) and (10) based on McCool et al. (1987) [39].

$$\mathit{t}\mathit{a}\mathit{n}{\mathit{\beta }}_{(\mathit{i},\mathit{j})}<{\displaystyle 0.09}\to {\mathit{S}}_{(\mathit{i},\mathit{j})}={\displaystyle 10.8}\mathit{s}\mathit{i}\mathit{n}{\mathit{\beta }}_{(\mathit{i},\mathit{j})}+{\displaystyle 0.03},$$

(9)

$$\mathit{t}\mathit{a}\mathit{n}{\mathit{\beta }}_{(\mathit{i},\mathit{j})}\ge {\displaystyle 0.09}\mathbf{\to } {\mathit{S}}_{(\mathit{i},\mathit{j})}={\displaystyle 16.8}\mathit{s}\mathit{i}\mathit{n}{\mathit{\beta }}_{(\mathit{i},\mathit{j})}-{\displaystyle 0.5}.$$

(10)

3. Results and Discussion

3.1. R Factor

The R-factor was calculated based on data from weather stations over the period 1986–2022 (National Meteorological Service), the last year with published data; however, significant changes have been recorded in recent years.

Table 3. R factor for the period 1986–2022.

Year	Agua Nueva	Cañitas	Grever	Nuevo Mercurio	Tierra y Libertad
1986	54.25	71.14	82.42	59.17	75.22
1987	9.64	54.35	68.12	26.40	82.36
1988	84.56	106.47	113.07	68.27	58.91
1989	53.58	52.97	42.05	84.18	45.09
1990	269.37	88.99	70.94	68.90	80.34
1991	132.23	149.41	291.40	156.91	160.18
1992	73.10	61.15	66.01	48.12	92.83
1993	82.18	73.12	93.73	42.59	81.33
1994	74.46	55.09	67.38	74.81	134.43
1995	71.61	73.60	72.00	46.50	36.81
1996	45.90	216.75	78.85	53.77	101.70
1997	33.37	29.60	27.23	39.21	48.97
1998	95.00	136.12	131.38	91.86	134.41
1999	52.46	59.33	58.66	73.30	68.60
2000	65.00	85.32	76.25	44.00	70.83
2001	32.18	46.95	35.51	32.69	50.06
2002	73.87	71.40	58.74	70.15	93.95
2003	113.31	84.40	58.66	132.03	121.63
2004	83.33	91.39	58.66	81.47	146.50
2005	34.58	80.91	49.97	36.35	66.31
2006	66.21	65.54	88.85	57.64	102.73
2007	78.83	86.83	58.66	48.36	149.30
2008	54.25	123.01	132.37	57.30	121.59
2009	63.42	72.15	138.65	100.82	91.28
2010	197.84	70.31	79.09	59.94	132.59
2011	67.01	60.99	48.71	85.32	88.06
2012	57.79	79.22	85.61	100.54	66.00
2013	97.68	122.62	83.26	64.45	140.78
2014	88.60	78.75	83.24	84.63	80.34
2015	102.22	125.58	91.16	87.67	117.41
2016	96.22	123.62	86.99	132.96	91.24
2017	93.74	123.36	121.42	83.62	109.12
2018	73.27	114.42	81.12	116.67	178.85
2019	60.18	44.02	37.13	47.20	73.84
2020	58.02	73.77	61.37	50.77	66.07
2021	113.85	82.05	92.33	72.83	118.69
2022	59.99	103.39	48.79	71.80	76.95

shows the R factor for the five stations analyzed during the period 1986–2022.

Figure 2 shows the average R factor results for the five weather stations analyzed over the period 1986–2022.

Figure 2 shows that the area most influenced by the average R factor is the southeast during the period 1986–2022.

Figure 3 shows the average results of the R factor at the five meteorological stations analyzed in 2000, 2010, 2020 and 2022, showing significant changes in precipitation.

The year 2022 was selected because it corresponds to the most recent period with complete and validated meteorological data for the five stations analyzed. Its selection allows for the characterization of current rainfall erosivity conditions and the evaluation of recent erosion factors in the Cañitas sub-basin, providing an updated basis for soil management and conservation.

Figure 3 shows that the stations exhibiting the highest R factor in 2020 and 2022 are located in the southwest of the sub-basin (Cañitas) and in the southeast (Tierra y Libertad). In 2010, the highest factor was found in the west (Agua Nueva) and in the southeast (Tierra y Libertad). In 2000, the highest R factor was found in the southwest (Cañitas) and in the center of the sub-basin (Grever).

The results indicate that the highest R-value recorded in 2000 was 85 MJ∙mm/ha∙h∙year; in 2010 it was 197 MJ∙mm/ha∙h∙year, while in 2020 it was 73 MJ∙mm/ha∙h∙year and in 2022 it was 103 MJ∙mm/ha∙h∙year. The Cañitas station (southwest of the sub-basin) had the highest R factor in 2000, 2020, and 2022. In 2010, the highest R factor was recorded at the Agua Nueva station (east of the sub-basin). This area shows increased susceptibility to water erosion due to several intense rainfall events, which increase runoff and the erosive power of surface flow. The spatial distribution of this maximum value suggests the influence of intense, short-duration storms during the analyzed period, a typical behavior in semi-desert regions where storms occur in localized areas and with high kinetic energy (Figure 3).

The highest erosivity index in 2022 in the Cañitas sub-basin was obtained in the southwest (Figure 4).

The western part of the study area has the highest erosivity values, while the southern part has the lowest. Similarly, low erosivity values predominate in the central and eastern parts of the sub-basin, while average values are recorded in the north and center.

During the period 1986–2022, the rainfall erosivity values ranged from 68 MJ∙mm/ha∙h∙year in 1986 to 72 MJ∙mm/ha∙h∙year in 2022. This allows us to evaluate the temporal evolution of rainfall erosivity in the Cañitas sub-basin, using the first and last years of the analyzed series as a reference. This approach facilitates the identification of long-term changes associated with climate variability and the potential effect of climate change on precipitation and, therefore, on the risk of water erosion. The difference between the two years (4 MJ∙mm/ha∙h∙year) is relatively insignificant; however, some years show more marked variations, such as 1991, when erosivity reached considerably higher values than the historical average for the period studied (Figure 5).

Table 4. Classification of R factor values.

R Factor	R Factor Classification
0–50	Light
50–500	Moderate
500–1000	High
>1000	Very high

shows the classification of the R factor according to its values [40].

In 1990 and 2010, the eastern part of the sub-basin had an R index of 387.81 and 358.31 MJ∙mm/ha∙h∙year, respectively. In 2018, the southern part had an R index of 374.29 MJ∙mm/ha∙h∙year; in all these cases, the index was classified as moderate. However, in 1991 the index had a value of 607.91 MJ∙mm/ha∙h∙year, which is classified as high.

3.2. LS Factor

High values for the LS factor indicate a combination of slope length and gradient that increases the erosive potential of surface runoff. However, the LS value does not allow for the identification of the relative contribution of each component separately.

Figure 6 and Figure 7 show significant spatial differences in the influence of topography within the Cañitas sub-basin. The LS values range from 0.03 to 20.78. This indicates a wide topographic variability derived from length and slope, demonstrating the significant influence of topography on erosion.

The northwest zone is characterized primarily by steep slopes and long hillsides, where surface runoff acquires greater energy and transport capacity, creating critical areas with erosion potential, especially during heavy rainfall. The eastern part of the sub-basin exhibits a low-to-moderate topographic intensity factor (0.94–3.77). Conversely, most of the sub-basin presents very low LS values (≤1), corresponding to gentle terrain with short slopes and relatively flat areas.

Table 5. Classification of LS factor.

Class	LS Factor Classification	Value
1	<1.5	Very low
2	1.6–3	Low
3	3–5	Moderate
4	5.1–7	High
5	>7	Very high

shows the classification of the LS factor values [40].

The results show that erosion depends on the interaction of the R and LS factors. This analysis provides valuable information for the delimitation of priority conservation areas, decision-making, and the calibration of erosion models at a regional scale.

4. Discussion

The R factor depends on the energy and intensity of rainfall; therefore, a reduction in annual accumulations or in the frequency of erosive events tends to be reflected in lower erosivity values. In Zacatecas, some studies have reported evidence of a reduction in annual precipitation and changes in climatic extremes, which coincides with the behavior observed in the Cañitas sub-basin. In 2014, annual precipitation trends were analyzed in Zacatecas [41].

From a climate change perspective, this decrease in the R factor should not necessarily be interpreted as a reduction in erosion risk. In semi-arid regions, climate change can reduce average precipitation but increase temporal irregularity, the duration of droughts, and the occurrence of concentrated, intense rainfall events. Therefore, although the annual average of R tends to decrease, isolated extreme events can still generate significant erosion, indicating that erosion may be dominated by intense episodes rather than by total annual precipitation.

On the other hand, the spatial heterogeneity of the LS factor is due to geomorphological causes such as slope length and gradient; therefore, its values increase in areas where the topography favors greater concentration and velocity of surface runoff. In the Cañitas sub-basin, the higher values located toward the northwest are explained by steeper slopes and longer gradients. Conversely, the central, eastern, and southern areas show low LS values due to gentler topography and gradients, and a lower capacity for runoff concentration.

Compared to the studies in Table 1, the Cañitas sub-basin provides an intermediate approach between global or continental studies and local analyses of soil loss. For example, in 2016, researchers worked with high-resolution pluviographic data in Greece, which allows for greater accuracy in R values, but limits its replicability in data-scarce regions. In contrast, the Cañitas sub-basin study validates the use of the Modified Fournier Index under semi-arid conditions with limited information.

Table 1 shows that several studies focus on national, continental, or global scales, while the present study works at the sub-basin scale, allowing for greater spatial detail. Furthermore, it uses an extensive series, from 1986 to 2022, and integrates R and LS analysis. Although the R factor calculation was not performed using high-resolution rainfall data, the use of monthly and annual precipitation records over a 37-year period provided a sufficiently long timescale to assess the variability and evolution of rainfall erosivity. The use of the Modified Fournier Index (MFI) allowed for leveraging this available climate information and obtaining consistent estimates of the R factor in a region where rainfall intensity data are limited.

The study of the Cañitas sub-basin stands out for combining temporal analysis of the R factor, spatial evaluation of the LS factor, and methodological validation in a semi-arid region. While comparative studies confirm the importance of slope, vegetation cover, and data resolution in erosion estimation, this study provides local evidence of how climatic variability and geomorphology control erosion risk differently: the differentiation of critical zones within the Cañitas sub-basin is due to the predominant influence of different erosion factors. The southwest sector showed the highest values of the R factor, indicating greater rainfall erosivity associated with more intense precipitation and, consequently, a greater capacity of rain to generate soil particulate detachment and transport. In contrast, the northwest sector registered the highest values for the LS factor, reflecting more favorable topographic conditions for the concentration of surface runoff. Although the LS factor incorporates the effects of slope length and slope, its high values demonstrate greater susceptibility of the terrain to erosive processes. Therefore, while in the southwest the erosive potential is mainly controlled by rainfall energy, in the northwest it is primarily determined by the topographic characteristics of the terrain.

5. Conclusions

Analysis of the rainfall erosivity factor (R) revealed marked spatial and temporal variability among the meteorological stations in the Cañitas sub-basin. The highest values were recorded in specific years associated with high-intensity rainfall events, while most records corresponded to moderate erosivity levels. The observed heterogeneity confirms that rainfall erosivity is not uniformly distributed within the sub-basin and that its behavior is strongly influenced by precipitation variability.

On the other hand, the LS factor results show marked spatial heterogeneity within the sub-basin. The northwest region has the most extensive slopes and the steepest gradients (LS up to 20.78), where surface runoff generates greater energy and transport capacity, creating critical areas of erosive potential. Conversely, most of the sub-basin area has low values (LS ≤ 1), associated with gentle relief and small slopes, where the topography has a minimal impact on erosion.

The analysis of the R and LS factors shows that the R factor in the southwest area indicates a greater tendency toward erosion, while the LS factor indicates a higher probability of erosion by transport in the northwest area due to the local topography. This identifies two critical areas susceptible to erosion from different causes. This provides empirical validation of the MFI as an alternative method for estimating rainfall erosivity in semi-arid environments with limited pluviographic data, strengthening the regional calibration of the USLE/RUSLE model. This contribution assesses the influence of rainfall on water erosion processes. The LS factor shows marked spatial heterogeneity within the sub-basin, associated with the influence of topography on water erosion.

The results suggest that the identified critical areas are more susceptible to water erosion due to a combination of climatic and topographic conditions that favor surface runoff.

Estimating the R factor allowed for the identification of the spatial and temporal distribution of rainfall erosivity in the Cañitas sub-basin, providing key information on areas where precipitation exerts the greatest pressure on erosive processes. These findings support the planning of soil conservation strategies and integrated watershed management in the semi-arid regions of northern Mexico and constitute a technical basis for formulating land-use and management recommendations aimed at reducing soil degradation.