Spatial Distribution, Temporal Behaviour, and Trends of Rainfall Erosivity in Central Italy Using Coarse Data

Abstract

This study examines the spatio-temporal dynamics of rainfall erosivity, R, in the Umbria region (central Italy), based on a 20-year dataset of 30 min precipitation records from 54 stations. Using the RUSLE2 framework, models of varying complexity were evaluated to estimate the R-factor: the original model (Model A), and models based solely on event rainfall depth h_e or daily rainfall depth h_d. All the models show consistency in the spatial and temporal patterns of the R-factor: higher erosivity is observed in the southern and northwestern areas, while summer contributes the most to annual erosivity due to the high average intensity of rainfall events. Trend analyses indicate stationarity across most stations. Compared to Model A (mean R-factor: 1840 MJ mm ha⁻¹ h⁻¹ y⁻¹), the models based on h_e underestimate the R-factor by about 15%, whereas the R-factor derived from the h_d-dependent model is almost equivalent. The estimate from Model A is also approximately 20% higher than that of a previous study conducted on a more limited dataset. The most likely reason for this difference appears to be the formula used for estimating the R-factor. The study highlights the practicality of simplified models, which offer a viable alternative in contexts where high-resolution precipitation data are unavailable. It also demonstrates the benefits of denser station networks and longer observation periods, particularly in regions characterised by complex terrains.

1. Introduction

Soil is a vital, non-renewable resource essential for agricultural productivity, ecosystem services, and global sustainability. Its role in carbon sequestration, water regulation, and biodiversity maintenance underpins numerous ecological and economic processes [1]. However, unsustainable land-use practices, such as deforestation, overgrazing, and inappropriate agricultural methods, have led to widespread soil degradation, compromising both food security and ecosystem resilience. Among the various degradation processes, water erosion is particularly significant, as it not only diminishes soil fertility but also accelerates desertification, alters hydrological cycles, and contributes to downstream sedimentation [2].

Water erosion involves the detachment and transport of soil particles through chemical and mechanical mechanisms. This process is influenced by a combination of interrelated factors, including climatic conditions, soil characteristics, topography, vegetation cover, and land management practices [3]. Climatic changes, particularly in regions prone to intense rainfall events, amplify erosion risks by increasing runoff potential and the erosive force of precipitation [4]. In the Mediterranean region, a hotspot for erosion studies, the interplay of steep topographies, erodible soils, and intense rainfall creates a scenario of heightened vulnerability [5,6,7].

Rainfall aggressiveness, a key driver of erosion, is determined by the intensity and duration of precipitation events. This parameter is quantified through the concept of rainfall erosivity, which measures the kinetic energy of rainfall and its ability to generate runoff [8,9]. The interaction of raindrop impact with soil particles initiates the detachment process, while the subsequent overland flow facilitates particle transport [10,11]. The R-factor, central to models like the Universal Soil Loss Equation (USLE) and its successors (RUSLE and RUSLE-2), captures this erosive potential, combining the effects of kinetic energy and maximum 30 min rainfall intensity [12]. These models have become fundamental tools for assessing soil erosion risk, offering insights that extend beyond soil conservation to support flood and landslide risk assessments [13,14,15,16].

The USLE framework estimates annual soil loss (A) using the equation:

$$\mathrm{A}=\mathrm{R}\times \mathrm{K}\times \mathrm{L}\times \mathrm{S}\times \mathrm{C}\times \mathrm{P},$$

where

• A: average annual soil loss (t ha⁻¹);
• R: rainfall erosivity factor (MJ mm ha⁻¹ h⁻¹);
• K: soil erodibility factor (t h ha⁻¹ MJ⁻¹ mm⁻¹);
• L: slope length factor;
• S: slope steepness factor;
• C: cropping and management factor;
• P: erosion control practices factor.

Accurate estimation of the R-factor requires high-temporal-resolution rainfall data, usually recorded at intervals of 1 to 60 min. These data allow for precise results based on the accumulated erosivity of individual rainstorm events [17]. However, in many regions, such data are scarce, requiring the formulation of empirical models that relate erosivity to readily available rainfall metrics, such as daily, monthly, or annual totals [18,19,20].

Rainfall erosivity studies across Europe demonstrate significant spatial and temporal variability. In Slovenia, Mikos et al. [21] used high-resolution precipitation data to assess erosion risks, while in Spain’s Ebro catchment, Angulo-Martínez et al. [22] highlighted the influence of extreme events on sediment transport. Mici’c Ponjiger et al. [23] produced rainfall erosivity maps for the Western Balkans region based on RUSLE and RUSLE2 modelling and ERA5 data, highlighting the presence of well-defined spatial patterns. Petroselli et al. [20], for a small area in central Italy, conducted a comparative evaluation of several simplified formulas that can be used to estimate annual rainfall erosivity in the absence of high-resolution rainfall datasets. In Switzerland, Meusburger et al. [24] produced detailed erosivity maps that informed national conservation strategies. At a continental scale, advancements in geospatial analysis have enabled estimates of rainfall erosivity across Africa and Europe using satellite-derived precipitation data and geostatistical models [25,26]. In the Algarve region of Portugal, these approaches have been further refined by integrating secondary variables like elevation, thus improving spatial predictions of erosivity [27].

In Italy, a comprehensive assessment based on 10 years of pluviographic data from 386 meteorological stations produced a high-resolution (500 m) national map of rainfall erosivity [28]. The study revealed distinct spatio-temporal patterns, underscoring the importance of localised assessments for effective land management. The broader applications of these findings extend to natural hazard mitigation, with rainfall erosivity data aiding in the prediction of floods and landslides caused by high-intensity precipitation events. In Europe, a detailed study [29] leveraging a decade of pluviographic data from over 1500 meteorological stations led to the creation of a high-resolution (500 m) map of rainfall erosivity across the continent. This work highlighted significant spatial variability in erosivity values, shaped by climatic and geographical factors. This framework supports policymakers and stakeholders in implementing sustainable land-use practices. However, previous studies have certain shortcomings, such as the limited length of the historical series used and the density of weather stations, even in areas characterised by high spatial variability in precipitation.

The present study examines rainfall erosivity estimation using four models of varying complexity, focusing on the region of Umbria in central Italy. The reference Model A utilises high-resolution semi-hourly data to compute the R-factor with exceptional accuracy, capturing the detailed dynamics of individual rainfall events. While ideal for focused research, the computational demands and data requirements of Model A limit its applicability in regions lacking detailed records.

Model B introduces a methodological simplification by employing monthly parameters (α_m, β_m) specific to each meteorological station, striking a balance between accuracy and practicality. Model C further reduces computational complexity by segmenting the year into three seasonal periods (winter, humid, and summer) and applying constant parameters for each station. This approach lowers data requirements while preserving the robustness of erosivity estimates. Finally, Model D is designed for contexts where only daily rainfall data are available, establishing a relationship between daily cumulative rainfall (h_d) and daily erosivity (R_d).

The first objective is to analyse the spatiotemporal variability of the R-factor at the regional scale. The resulting isoerosivity maps are essential for land-use planning and soil conservation, as they identify areas of heightened vulnerability, support the prioritisation of mitigation strategies, and contribute to sustainable land management [30]. The second objective is to define and test simplified models to facilitate R-factor estimation through less detailed input data. The resulting models are useful for size remediation and protection solutions for soil conservation at the local scale, and also for when long-time series of detailed meteorological data are unavailable. Finally, by integrating high-resolution precipitation data, simplified modelling approaches, and advanced geospatial techniques, enhance the planning, programming, and management of the soil erosion protection policy.

Spatial resolution is a critical factor in this context. The results obtained are only truly valuable when they can be effectively integrated into areas of a relatively limited size, such as the Umbria region. In larger areas, the use of low-resolution spatial scales can provide general guidance for policy development; however, these scales are insufficient for delivering the detailed and precise information required for more targeted and actionable decision-making. For this reason, a further objective of the study was to compare the R-factor map obtained in this work, based on a dense network of stations, with the one derived from larger-scale studies [29].

Finally, the statistical trend analysis of annual erosivity series allowed for completing the study with valuable insights into the presence of potential long-term changes in erosion risk.

2. Materials and Methods

2.1. Materials

The study refers to the Umbria region, which extends across central peninsular Italy with a surface area of 8465 km². The region is characterised by a predominantly temperate climate, with cool winters and warm summers, although local variability is influenced by the region’s morphology, which includes both hilly and mountainous areas. The average annual precipitation is approximately 857 mm with a relevant interannual variability. Precipitation is primarily concentrated in spring and autumn (40.5%), followed by winter (34.4%). Although summer is the driest season, it still contributes 25.1%. The distribution and intensity of rainfall play a crucial role in erosion processes and the management of regional water resources.

The dataset used for the analysis was defined based on semi-hourly precipitation time series provided by the Regional Hydrological Service, encompassing a total of 94 meteorological stations. Overall, the initial database contained 29,779,498 semi-hourly records, corresponding to approximately 1700 years of observations. However, not all stations in the initial dataset were included in the final analysis. Stations with excessively short historical series were excluded, as well as years with incomplete months characterised by more than 5% of missing data. This filtering process was carried out to avoid underestimation of the annual R parameter.

The final dataset, obtained after these operations, includes 54 meteorological stations (as shown in Figure 1 and

Table 1. Identification codes (ID), name, and altitude above sea level (m a.s.l.).

ID	Metereological Station	Elevation (m a.s.l.)	ID	Metereological Station	Elevation (m a.s.l.)
1	Allerona	153.2	28	Norcia	691.3
2	Amelia	319.5	29	Orvieto	311.4
3	Armenzano	707.7	30	Orvieto Scalo	109.3
4	Azzano	235.2	31	Passignano sul Trasimeno	327.8
5	Bastardo	331.5	32	Perugia Fontivegge	308.5
6	Bastia Umbra	203.3	33	Perugia Santa Giuliana	433.8
7	Bevagna	211.5	34	Petrelle	341.9
8	Cannara	191.4	35	Petrignano del Lago	303.9
9	Carestello	517.8	36	Pianello	231.5
10	Casacastalda	730.1	37	Piediluco	370.0
11	Casigliano	272.5	38	Pierantonio	239.0
12	Castel Cellesi	362.8	39	Ponte Felcino	191.6
13	Cerbara	310.0	40	Ponte Nuovo Torgiano	170.0
14	Città di Castello	304.0	41	Ponte Santa Maria	240.1
15	Compignano	240.2	42	Ponticelli	244.9
16	Foligno	220.0	43	Ripalvella	453.1
17	Forsivo	963.2	44	San Benedetto Vecchio	729.4
18	Gualdo Tadino	596.5	45	San Biagio della Valle	257.0
19	Gubbio	471.5	46	San Gemini	297.1
20	La Cima	790.8	47	San Savino	260.0
21	Lago Corbara	128.0	48	San Silvestro	379.9
22	Massa Martana	327.9	49	Spoleto	353.2
23	Moiano	270.3	50	Terni	123.0
24	Monte Cucco	1087.2	51	Todi	326.1
25	Montelovesco	634.1	52	Umbertide	305.7
26	Narni Scalo	108.9	53	Vallo di Nera	306.7
27	Nocera Umbra	535.7	54	Verghereto	1069.2

), each with a sufficiently long historical precipitation series. To enhance the representativeness of the areas near the regional boundaries, stations from Verghereto (ID54) and Castel Cellesi (ID12), located in neighbouring areas outside of Umbria, were also included in the analysis. The density of the monitoring network, with one station every 156.8 km² (equivalent to a grid of approximately 12.5 km × 12.5 km), ensures high spatial coverage, which is crucial for an accurate representation of erosive dynamics at the regional scale.

The altitude of the stations ranges from 109 to 1087 m above sea level (mean: 382 m a.s.l.). Of the total number of monitored stations, 46% are in hilly areas (300–700 m a.s.l.), 42% in flat areas (0–300 m a.s.l.), and 13% are situated in mountainous regions (>700 m a.s.l.). Two stations are located at altitudes exceeding 1000 m a.s.l.

2.2. Methods

2.2.1. Isoerosivity Maps

Isoerosivity maps are generated through a zonation process based on cluster analysis of the R parameter, which is estimated using the following models. The visualisation is achieved through Inverse Distance Weighting (IDW) interpolation of the mean annual R values recorded at individual stations.

2.2.2. Model A

According to the definition by Wischmeier and Smith [8], the calculation of the rainfall erosivity factor (expressed in MJ mm h⁻¹ ha⁻¹ y⁻¹), requires precipitation data with a temporal resolution of at least semi-hourly intervals. Given the limited availability of such high-resolution data, simplified calculation models or those requiring precipitation data with lower temporal resolution are often used.

In this study, several models were parameterized using as reference data the erosivity calculated with the RUSLE 2 model [31], referred to in the text as Model A, as follows:

$${\mathrm{R}}_{\mathrm{e}}={\mathrm{E}}_{\mathrm{e}}\times {\mathrm{I}}_{30},$$

(1)

where R_e (MJ mm h⁻¹ ha⁻¹) denotes the erosivity of single erosive event; E_e (MJ ha⁻¹) is the total energy of the event; and I₃₀ (mm h⁻¹) is the maximum semi-hourly intensity during the event e.

In the rainfall dataset, following the methodology of Wischmeier and Smith [8], individual events are identified as rainy periods preceded and followed by at least six non-rainy hours. Each event is then subdivided into elementary events i, for which the specific energy e_i (MJ ha⁻¹ mm⁻¹) is calculated as follows:

$${\mathrm{e}}_{\mathrm{i}}=(1-0.72\times {\mathrm{e}}^{\left(-0.082\times {\mathrm{I}}_{\mathrm{i}}\right)}),$$

(2)

where I_i (mm h⁻¹) denotes the erosivity of single erosive event.

The total energy of the event is given by the summation of the individual e_i values as follows:

$${\mathrm{E}}_{\mathrm{e}}={\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathrm{e}}_{\mathrm{i}},$$

(3)

where k is the total number of elementary events within the rainfall event.

R_e, calculated using Equation (1), serves as the reference value for subsequent evaluations and model parameterization. Specifically, the annual value (R_y) is defined as the summation of the erosivity of all individual events occurring between 1 January and 31 December:

$${\mathrm{R}}_{\mathrm{y}}={\sum }_{\mathrm{e}=1}^{\mathrm{n}}{\mathrm{R}}_{\mathrm{e}},$$

(4)

where n is the total number of erosive events in the given year.

The mean annual erosivity R for each station is considered as the multi-year average:

$${\displaystyle \raisebox{1ex}{$\mathrm{R}=(\sum _{\mathrm{y}=1}^{\mathrm{N}}{\mathrm{R}}_{\mathrm{y}})$}\!\left/ \!\raisebox{-1ex}{$\mathrm{N}$}\right.},$$

(5)

where N is the total number of years analysed.

2.2.3. Simplified Models for Erosivity Estimation Based on the Event Rainfall Depth h_e

Accurate estimation of rainfall erosivity through derived USLE models necessitates semi-hourly precipitation records. However, reconstructing long-term historical series with this level of detail remains impractical. While gridded datasets (e.g., E-OBS or ERA5-Land) offer a potential alternative, their temporal resolution is typically inadequate for this purpose. Consequently, it becomes essential to develop models that simplify the estimation of the R factor using rainfall data with lower temporal resolution, which are more widely available.

To reduce the computational burden of calculating R_e in terms of the required temporal resolution of the data, a literature-based model was evaluated [32,33,34,35]. In this model, the rainfall erosivity index for a single event is assumed to be proportional to the power of the rainfall depth of the event h_e (mm):

$${\left[{\mathrm{R}}_{\mathrm{e}}=\mathrm{\alpha }\times {\mathrm{h}}_{\mathrm{e}}^{\mathrm{\beta }}\right]}_{\mathrm{t},\mathrm{s}},$$

(6)

where α is the scale factor; β is the model parameter; t is the temporal reference; and s is the spatial reference.

The parameters α and β assume different values based on the selected temporal reference t and spatial reference s.

If the temporal reference t is not specified, the parameters are determined using the sample of all events available in the historical series of station s. Conversely, when t is specified (e.g., the month of January, the period from June to September, etc.), the following procedure is applied.

The sample of all events occurring during the specified t periods in the historical series is extracted (e.g., all events in January). For each event, h_e and R_e are calculated using the procedure described for Model A. The parameters α and β are then determined through regression analysis between the two variables. This procedure is repeated for each t and for each spatial reference.

Model B

With reference to Equation (6), the erosivity of a single event R_e is calculated by taking the temporal reference as the month t = m and the spatial scale as the individual station s. With S representing the number of stations and M the number of months m in a year, $\mathrm{S}\times \mathrm{M}$ parameter pairs {α_m,s, β_m,s; m = 1, … M; s = 1, … S} are determined and employed in Equation (6) to estimate the erosivity R_e of rainfall events with depth h_e in the month m and station s. As in the case of Model A, the annual erosivity R_y and the average annual erosivity R_m are subsequently calculated using Equations (4) and (5).

Although it represents a simplification compared to the estimation procedures of USLE and RUSLE-2, Model B remains highly complex due to the variability, and consequently, the large number of parameters required.

Model C

With reference to Equation (6), the erosivity of a single event R_e is calculated by taking the temporal reference as the period p, while the spatial scale remains focused on individual stations. With S representing the number of stations and P the number of periods p in a year, $\mathrm{S}\ast \mathrm{P}$ parameter pairs {α_p,s, β_p,s; p = 1, … P; s = 1, … S} are determined using the procedure described for Model A, and employed in Equation (6) to estimate the erosivity R_e of rainfall events with depth h_e for period p and station s. The total number of periods is three: 1, the winter period (January, February, March, December); 2, the humid period (April, May, October, November), and 3, the summer period (June, July, August, September). As in the case of Model A, the annual erosivity R_y and the average annual erosivity R_p are subsequently calculated using Equations (4) and (5).

2.2.4. Simplified Model for Erosivity Estimation Based on the Daily Rainfall Depth h_d (Model D)

In this model (Model D), the daily erosivity R_d is expressed as a function of the daily rainfall depth h_d (cumulative rainfall from 00:00 to 23:30 on day d). R_d is derived from the daily cumulative erosivity of individual rainfall events occurring on day d. Events are defined based on Wischmeier’s six-hour criterion, with additional consideration given to events spanning two days. For example, an event starting at 22:00 on day d and ending at 02:00 on day d + 1 is divided into two separate events: the first covering the time interval 22:00–23:30 on day d, and the second covering 00:00–02:00 on day d + 1.

Model D functions were obtained by interpolating the scatter plots of the pairs (R_d,h_d) using third-degree polynomial functions. Different relationships were derived for each combination of temporal scale (period, p) and spatial division (regional subareas, z; z = 1, … Z). The sub-zones were identified at the regional level based on the zoning represented in Figure 2a. In the northwestern and southern areas, “red-orange” zones (z = r), 27 stations with an annual average R lower than the regional average (R = 1863.6 MJ mm ha⁻¹ h⁻¹ y⁻¹) are located, while in the northern, eastern, and southwestern areas, “blue-green zone”, (z = b), 27 stations with R values higher than the regional average are located. The temporal resolution remains that of the three periods p = 1, … P as for Model C. This approach resulted in $\mathrm{Z}\times \mathrm{P}$ functions.

2.2.5. Trend Analyses

The Mann–Kendall test [36,37] was employed to evaluate the presence of trends within the dataset. The null hypothesis posits the absence of a trend in the population from which the dataset is drawn, while the alternative hypothesis suggests the presence of a monotonic increasing or decreasing trend. Being a non-parametric test, it does not rely on the distribution of the variable under analysis and is less sensitive to outliers in the time series [19].

While the Mann–Kendall test is effective in detecting monotonic trends, it does not quantify their magnitude. To address this limitation, the non-parametric Theil–Sen estimator [38,39] was utilised to estimate the slope of regression lines interpolating the data.

The Zyp [40] and Kendall [41] packages in the R-statistical software (https://www.r-project.org/) were employed to calculate the Theil–Sen estimator and to determine the p-value associated with the Mann–Kendall test, respectively [19].

3. Results

The analysis of the 54 stations revealed that the duration of the historical series (column 2,

Table 2. For each station: ID (1); series length, years (2); average annual event count (3); mean h_e, mm (4); 95th percentile of h_e, mm (5); multi-year average of annual rainfall depth, mm (6); multi-year average percentage of rainfall during the winter period, % (7); multi-year average percentage of rainfall during the humid period, % (8); multi-year average percentage of rainfall during the summer period, % (9); mean R_e, MJ mm ha⁻¹ h⁻¹ (10); 95th percentile of R_e, MJ mm ha⁻¹ h⁻¹ (11); multi-year average annual erosivity, MJ mm ha⁻¹ h⁻¹ y⁻¹ (12); multi-year average percentage of erosivity during the winter period, % (13); multi-year average percentage of erosivity during the humid period, % (14); multi-year average percentage of erosivity during the summer period, % (15).

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
ID	Series Length	Mean n° of Distinct Events	Mean he	95th Percentile he	P	Pw	Ph	Ps	Mean Re	95th Percentile Re	R	Rw	Rh	Rs
1	21	133.7	6.0	24.4	804.7	36.7	40.0	23.3	13.7	50.5	1823.7	14.8	39.2	46.0
2	19	146.8	6.4	27.2	940.4	37.9	40.2	21.9	16.1	74.6	2421.3	16.9	39.3	43.8
3	15	125.5	9.0	34.6	1130.4	36.3	40.7	22.9	21.9	103.9	2738.2	23.2	36.1	40.6
4	24	128.2	5.9	24.3	754.3	31.3	41.5	27.2	12.1	51.9	1567.4	14.7	34.8	50.6
5	23	127.1	6.7	27.2	845.0	34.7	40.1	25.3	16.9	71.1	2113.0	17.4	34.7	47.9
6	21	129.2	5.8	23.3	748.7	33.9	40.5	25.6	12.8	48.4	1655.3	15.7	32.8	51.5
7	24	144.0	5.1	21.9	734.4	32.1	41.1	26.8	10.0	41.6	1452.5	13.8	34.4	51.8
8	24	126.8	6.1	25.0	778.5	33.2	40.6	26.2	14.5	55.0	1904.5	16.2	34.7	49.1
9	24	162.9	6.2	27.0	1011.7	37.5	39.1	23.4	12.6	61.6	2087.2	17.7	32.4	49.9
10	23	134.1	7.5	29.3	1009.6	33.3	39.7	26.9	17.7	82.1	2361.5	16.5	32.0	51.5
11	24	135.4	6.2	26.0	839.8	34.1	41.6	24.3	16.0	67.6	2159.1	14.6	36.9	48.5
12	19	127.8	5.9	24.4	757.6	38.2	41.5	20.4	14.0	54.7	1885.0	15.4	44.5	40.1
13	21	140.6	5.7	23.6	806.5	34.4	40.8	24.8	11.1	45.8	1563.4	14.5	36.4	49.1
14	23	139.1	6.0	24.7	838.0	35.8	40.9	23.3	11.0	52.1	1525.8	17.6	34.8	47.6
15	24	139.1	5.4	22.5	755.1	33.3	39.3	27.4	12.8	51.0	1780.0	12.5	33.5	54.0
16	23	129.1	5.8	24.1	752.5	31.9	41.1	27.0	12.3	51.4	1624.2	14.1	36.6	49.3
17	24	143.2	6.1	24.4	869.5	32.1	40.7	27.2	11.7	44.2	1667.7	11.1	31.0	58.0
18	20	142.3	7.4	30.0	1057.2	34.5	40.2	25.3	14.4	66.3	2014.7	15.3	31.7	53.0
19	23	146.0	6.5	27.0	955.6	35.6	39.5	24.9	14.0	59.3	2051.1	15.1	30.7	54.2
20	23	152.9	5.6	24.2	845.6	32.3	41.3	26.4	12.4	54.6	1850.9	14.6	34.7	50.7
21	20	125.3	6.4	24.8	805.3	36.9	41.0	22.1	13.1	57.7	1635.6	18.1	36.4	45.4
22	19	143.8	6.1	26.5	881.6	34.3	40.2	25.5	14.2	62.3	2055.7	14.7	34.4	50.9
23	17	181.8	4.2	19.0	769.2	33.1	42.7	24.2	8.5	33.0	1620.7	12.1	40.5	47.5
24	23	171.7	7.7	32.9	1327.3	33.4	41.3	25.3	14.6	64.7	2522.2	13.9	35.3	50.8
25	23	133.2	6.2	24.6	830.8	31.1	41.4	27.4	14.3	56.7	1936.2	10.8	33.7	55.5
26	24	133.7	6.6	26.7	872.8	34.2	40.3	25.5	18.1	72.2	2399.1	13.5	36.4	50.1
27	22	139.8	6.8	27.4	946.1	34.8	38.5	26.7	13.3	58.0	1841.2	16.4	30.1	53.5
28	19	170.2	4.6	19.4	778.9	36.0	39.3	24.7	5.9	24.8	1004.4	16.3	40.9	42.8
29	22	125.6	6.8	27.0	855.4	37.3	39.5	23.2	15.3	62.2	1957.0	15.3	32.1	52.6
30	23	133.3	5.6	23.9	758.3	36.1	39.6	24.3	12.0	47.6	1634.8	14.5	32.4	53.0
31	21	129.2	5.7	22.6	739.9	34.1	40.7	25.2	11.1	50.3	1432.4	13.7	34.5	51.9
32	24	156.6	5.7	25.4	893.2	35.8	39.8	24.4	12.0	50.4	1841.7	15.6	30.2	54.2
33	21	139.4	4.8	19.8	674.0	33.8	41.8	24.4	8.9	38.5	1247.0	13.5	39.0	47.5
34	23	119.0	6.5	25.4	781.6	33.4	39.0	27.6	13.6	56.8	1649.5	13.6	32.0	54.4
35	23	130.2	6.7	25.1	870.0	32.5	40.1	27.3	14.8	57.2	1931.5	12.4	32.8	54.8
36	20	141.5	6.3	25.2	897.9	33.6	38.4	28.1	13.2	58.4	1929.4	13.5	27.2	59.3
37	21	142.8	6.9	28.3	993.5	36.3	41.2	22.6	14.7	71.7	2104.2	16.7	39.5	43.8
38	20	135.0	6.5	27.8	879.7	36.5	38.7	24.9	13.4	58.3	1852.8	17.5	30.1	52.4
39	19	133.3	6.3	25.8	852.0	35.3	39.0	25.8	14.2	60.9	1940.6	14.7	31.0	54.2
40	22	134.6	5.4	22.4	728.8	33.9	39.8	26.4	10.4	46.0	1404.5	15.3	33.2	51.4
41	24	147.8	5.2	22.1	772.0	35.9	39.6	24.5	12.4	48.1	1881.6	15.2	34.1	50.7
42	17	150.0	5.1	22.4	769.5	34.7	41.9	23.4	10.9	43.7	1650.6	11.9	40.3	47.8
43	24	127.5	7.2	27.2	917.0	36.0	41.4	22.6	16.9	74.1	2186.3	17.2	35.1	47.8
44	24	134.3	6.2	25.0	828.6	31.6	40.9	27.5	12.4	49.0	1624.1	12.2	31.4	56.4
45	24	128.1	5.4	21.3	691.8	32.8	40.6	26.7	11.2	47.2	1449.6	12.7	34.9	52.4
46	19	122.5	6.9	26.1	839.2	33.9	40.6	25.5	18.4	78.8	2188.5	12.9	45.1	42.0
47	20	133.1	5.2	21.4	699.4	32.3	43.2	24.5	9.7	41.2	1316.4	14.1	36.0	49.9
48	22	133.7	6.8	27.6	900.8	33.0	40.2	26.8	17.9	75.6	2375.0	14.7	30.4	54.8
49	21	135.2	6.9	28.0	927.6	34.2	40.3	25.5	14.2	75.2	1912.7	16.7	37.2	46.2
50	19	125.6	6.6	24.8	828.6	33.7	40.9	25.4	17.0	57.9	2095.2	13.6	42.7	43.7
51	22	133.9	5.8	24.3	773.6	33.8	41.4	24.8	12.3	55.1	1660.8	14.8	37.3	47.8
52	21	172.9	5.2	22.7	900.2	36.3	38.7	25.1	11.4	42.6	2005.9	15.6	33.2	51.2
53	23	145.7	6.4	26.7	930.2	33.9	39.5	26.6	13.7	54.3	2001.9	14.1	31.6	54.3
54	20	149.9	7.8	31.0	1166.8	31.7	42.7	25.5	14.1	63.0	2097.0	12.3	35.6	52.1
mean	21.6	139.2	6.2	25.3	857.7	34.4	40.5	25.2	13.4	57.1	1863.6	14.9	35.0	50.2
min	15	119.0	4.2	19.0	674.0	31.1	38.4	20.4	5.9	24.8	1004.4	10.8	27.2	40.1
max	24	181.8	9.0	34.6	1327.3	38.2	43.2	28.1	21.9	103.9	2738.2	23.2	45.1	59.3
CV	0.10	0.10	0.14	0.12	0.14	0.05	0.03	0.07	0.21	0.24	0.18	0.14	0.11	0.08

) varies between a minimum of 15 years, recorded at the Armenzano station (ID 3), and a maximum of 24 years. The average length of the series per station is over 21.5 years. The extensive temporal range of the data provides a robust statistical foundation for the analysis, enabling the calculation of means and percentiles with high stability and reliability.

3.1. Model A

The dataset of identified rainfall events includes a total of over 175,000 events. On average, approximately 139 events occur per year, with a maximum of 181 events at the Moiano station (ID 23) and a minimum at Petrelle (ID 34). The number of events is not correlated with either annual cumulative rainfall (r = 0.3) or event volume (r = 0.33).

The average annual number of events (column 3, Table 2) varies moderately (CV = 9.7%) between stations, suggesting differences in local rainfall regimes. Notable variations in the mean event rainfall depth, h_e (column 4, Table 2), are observed, with stations such as Armenzano (ID 3) (9.0 mm) characterised by high volumes and Moiano (ID 23) (4.2 mm) showing values reduced by up to 50%. The 95th percentile (column 5, Table 2), indicative of extreme events, ranges from 19.0 mm (Moiano, ID 23) to 34.6 mm (Armenzano, ID 3). The latter, located in the south and north-west, shows a higher predisposition to extreme events, likely due to specific topographical or microclimatic conditions.

The multi-year average annual rainfall, P (column 6, Table 2), varies significantly, with minimum values at Perugia Santa Giuliana (ID 33) (674.0 mm) and maximum values at Monte Cucco (ID 24) (1327.3 mm). Rainfall is unevenly distributed throughout the year, with the contribution during the humid period (P_h, column 8 in Table 2) representing the main share, ranging regionally from 38.4% to 43.2%, highlighting the greater importance of precipitation during transitional seasons compared to summer and winter periods.

The summer period (P_s, column 9 in Table 2) is the driest, with percentages ranging from 20.4% to 28.1%. Pianello (ID 36) shows the highest summer contribution, indicating less concentrated rainfall in transitional seasons. Winter precipitation (P_w, column 7 in Table 2) contributes one-third of the annual total (34.4%).

The average event erosivity (column 10, Table 2) and the 95th percentile (column 11, Table 2) reveal a differentiated potential risk of soil erosion across various areas. The mean R_e value ranges from a minimum of 5.9 MJ mm ha⁻¹ h⁻¹ (Norcia, ID 28) to a maximum of 21.9 MJ mm ha⁻¹ h⁻¹ (Armenzano, ID 3). The 95th percentile of R_e, reflecting the erosive capacity of the most intense events, again highlights Armenzano (ID 3) as the station with the highest value (103.9 MJ mm ha⁻¹ h⁻¹).

The multi-year average erosivity (R, column 12, Table 2) was determined for the 54 stations using the Model A procedure and exhibits significant spatial variability. Stations such as Armenzano (ID 3) and Amelia (ID 2) stand out for high values, indicative of greater erosive potential, while others, such as Norcia (ID 28) and Perugia Santa Giuliana (ID 33), show lower values.

Although erosivity shows significant variations, its distribution across periods does not mirror that of rainfall regimes, which follow an opposite trend. The highest values are observed during the dry period (R_s, column 15 in Table 2), with an average multi-year erosivity of 50.2%. This is particularly noteworthy, considering that summer has the lowest rainfall among the analysed periods. This phenomenon is attributed to the frequency of intense storms, which significantly increase erosivity.

Winter erosivity (R_w, column 13 in Table 2) is the lowest among the analysed periods, likely due to the nature of typical winter meteorological events, often characterised by less intense precipitation. The multi-year average for the period is 14.9%, significantly lower than the average rainfall for the same interval, which stands at 34.4%.

The humid period, on the other hand, contributes 35% of the annual erosivity (R_h, column 13 in Table 2). This value reflects the transitional role of this period, positioned between the extremes of the dry and winter periods.

An interesting case is represented by the Pianello station (ID 36). During summer, the station records the highest regional erosivity value (59.3%), while during the humid period, it shows the lowest regional erosivity value (27.2%).

Figure 2a shows the isoerosivity map obtained. These values, calculated using Model A, are reported in column 12 of Table 2. IDW determines the cell values by applying a linearly weighted combination of the R values associated with a set of sample points, represented here by the 54 stations. The weight of each point is a function of the inverse distance, and the surface to be interpolated corresponds to the spatially dependent variable, in this case, R.

The southern and northwestern areas, are characterised by higher annual mean erosivity values (2116, 2738, and 1881 MJ mm ha⁻¹ h⁻¹ y⁻¹, respectively, for the mean, maximum, and minimum) compared to the northern, eastern, and southwestern areas, where rainfall erosivity is generally lower (1591, 1852, and 1004 MJ mm ha⁻¹ h⁻¹ y⁻¹, respectively, for the mean, maximum, and minimum). The regional annual mean value is 1863.6 MJ mm ha⁻¹ h⁻¹ y⁻¹, with a standard deviation of 336.4 MJ mm ha⁻¹ h⁻¹ y⁻¹.

3.2. Model B

The model was applied starting from the same dataset of individual rainfall events determined and used for the application of Model A (over 175,000 events).

With reference to Equation (6), the erosivity of a single event R_e was calculated considering the temporal reference as the month t = m = 1, …, 12, and the spatial scale as the specific station s.

The 54 × 12 pairs (α_m,s, β_m,s) are displayed in Figure 3, where the trends of the two parameters throughout the 12 months of the year for the 54 stations can be observed. In both cases, a summer peak is evident during July and August, which tends to decrease towards the Gaussian extremes of the winter months; spring and autumn months exhibit intermediate values. For the same rainfall depth in an event h_e, summer events are thus characterised by a higher degree of erosivity compared to events occurring in the other periods of the year. The monthly values of α and β for each station are presented in

Table A1. α values used in Equation (6) for each month and each station to calculate mean annual erosivity (R_m) in Model B.

	Month
ID Station	1	2	3	4	5	6	7	8	9	10	11	12
1	0.094	0.097	0.098	0.115	0.126	0.136	0.159	0.160	0.147	0.118	0.110	0.099
2	0.101	0.105	0.103	0.115	0.119	0.145	0.168	0.162	0.139	0.138	0.116	0.105
3	0.098	0.100	0.100	0.112	0.121	0.122	0.152	0.151	0.142	0.129	0.106	0.103
4	0.087	0.089	0.093	0.110	0.112	0.142	0.153	0.144	0.142	0.117	0.102	0.095
5	0.090	0.097	0.099	0.112	0.116	0.146	0.142	0.161	0.141	0.123	0.109	0.095
6	0.089	0.094	0.097	0.105	0.115	0.131	0.150	0.153	0.142	0.119	0.103	0.095
7	0.097	0.098	0.103	0.112	0.121	0.139	0.157	0.155	0.140	0.124	0.111	0.101
8	0.092	0.095	0.096	0.112	0.119	0.140	0.146	0.160	0.132	0.112	0.101	0.092
9	0.091	0.093	0.097	0.105	0.112	0.133	0.146	0.150	0.137	0.122	0.105	0.095
10	0.082	0.089	0.094	0.096	0.106	0.127	0.144	0.145	0.121	0.115	0.098	0.087
11	0.093	0.095	0.100	0.114	0.122	0.143	0.173	0.161	0.137	0.118	0.110	0.095
12	0.094	0.099	0.105	0.117	0.124	0.145	0.146	0.138	0.144	0.126	0.112	0.098
13	0.082	0.085	0.092	0.105	0.120	0.138	0.156	0.154	0.137	0.122	0.100	0.090
14	0.085	0.084	0.086	0.103	0.114	0.135	0.164	0.143	0.132	0.116	0.101	0.090
15	0.087	0.089	0.093	0.104	0.115	0.127	0.147	0.141	0.126	0.113	0.096	0.090
16	0.088	0.089	0.095	0.100	0.112	0.132	0.141	0.139	0.133	0.113	0.103	0.092
17	0.078	0.090	0.084	0.094	0.102	0.119	0.123	0.145	0.123	0.104	0.087	0.083
18	0.087	0.091	0.092	0.110	0.113	0.126	0.153	0.143	0.128	0.118	0.100	0.095
19	0.086	0.091	0.094	0.111	0.111	0.132	0.145	0.149	0.129	0.121	0.103	0.092
20	0.092	0.098	0.099	0.116	0.129	0.141	0.155	0.153	0.145	0.126	0.109	0.095
21	0.094	0.097	0.101	0.115	0.120	0.138	0.142	0.161	0.132	0.126	0.111	0.098
22	0.092	0.094	0.100	0.114	0.117	0.143	0.147	0.155	0.133	0.129	0.113	0.101
23	0.091	0.097	0.095	0.110	0.119	0.134	0.155	0.142	0.140	0.128	0.109	0.096
24	0.073	0.084	0.083	0.093	0.102	0.123	0.132	0.131	0.118	0.096	0.086	0.077
25	0.084	0.086	0.090	0.106	0.112	0.127	0.147	0.145	0.130	0.116	0.100	0.089
26	0.091	0.092	0.097	0.105	0.124	0.149	0.168	0.161	0.142	0.124	0.111	0.100
27	0.081	0.079	0.087	0.098	0.113	0.129	0.131	0.148	0.134	0.112	0.095	0.083
28	0.084	0.094	0.097	0.104	0.111	0.139	0.146	0.145	0.129	0.117	0.100	0.091
29	0.097	0.100	0.099	0.118	0.120	0.137	0.159	0.148	0.137	0.133	0.108	0.099
30	0.094	0.096	0.102	0.115	0.126	0.142	0.141	0.150	0.139	0.123	0.114	0.099
31	0.096	0.096	0.095	0.116	0.123	0.129	0.144	0.148	0.116	0.123	0.113	0.100
32	0.086	0.089	0.091	0.103	0.119	0.142	0.156	0.156	0.137	0.119	0.101	0.090
33	0.095	0.094	0.096	0.107	0.119	0.135	0.127	0.134	0.127	0.121	0.104	0.093
34	0.082	0.087	0.088	0.100	0.111	0.137	0.135	0.123	0.124	0.108	0.098	0.086
35	0.091	0.097	0.097	0.106	0.122	0.143	0.143	0.143	0.137	0.125	0.110	0.095
36	0.096	0.100	0.101	0.110	0.121	0.131	0.158	0.145	0.138	0.127	0.113	0.097
37	0.082	0.089	0.092	0.095	0.106	0.129	0.144	0.144	0.133	0.116	0.101	0.091
38	0.092	0.096	0.096	0.114	0.113	0.133	0.155	0.150	0.135	0.128	0.110	0.101
39	0.095	0.097	0.104	0.114	0.119	0.144	0.148	0.154	0.140	0.131	0.112	0.096
40	0.097	0.101	0.099	0.112	0.119	0.142	0.149	0.154	0.141	0.123	0.112	0.097
41	0.097	0.102	0.096	0.111	0.120	0.148	0.155	0.163	0.146	0.127	0.108	0.101
42	0.096	0.098	0.099	0.109	0.120	0.147	0.159	0.157	0.148	0.128	0.112	0.097
43	0.080	0.093	0.092	0.108	0.120	0.138	0.141	0.155	0.138	0.117	0.106	0.093
44	0.083	0.087	0.087	0.104	0.111	0.133	0.147	0.145	0.133	0.109	0.099	0.083
45	0.086	0.092	0.095	0.111	0.121	0.135	0.158	0.156	0.135	0.115	0.106	0.090
46	0.103	0.103	0.102	0.116	0.122	0.147	0.155	0.163	0.147	0.138	0.118	0.100
47	0.094	0.093	0.101	0.113	0.111	0.127	0.126	0.142	0.124	0.120	0.109	0.097
48	0.092	0.095	0.097	0.105	0.120	0.144	0.150	0.163	0.142	0.123	0.108	0.097
49	0.093	0.101	0.103	0.108	0.118	0.137	0.141	0.152	0.136	0.121	0.109	0.099
50	0.102	0.098	0.102	0.115	0.125	0.140	0.154	0.156	0.142	0.133	0.110	0.102
51	0.087	0.092	0.096	0.110	0.109	0.139	0.154	0.159	0.131	0.119	0.098	0.090
52	0.093	0.095	0.096	0.109	0.118	0.120	0.144	0.146	0.132	0.131	0.108	0.097
53	0.087	0.089	0.093	0.104	0.110	0.133	0.141	0.151	0.133	0.123	0.103	0.090
54	0.081	0.083	0.088	0.109	0.118	0.134	0.149	0.136	0.126	0.109	0.097	0.084

and

Table A2. β values used in Equation (6) for each month and each station to calculate mean annual erosivity (R_m) in Model B.

	Month
ID Station	1	2	3	4	5	6	7	8	9	10	11	12
1	1.694	1.719	1.727	1.805	1.887	1.975	2.048	2.057	1.981	1.858	1.792	1.713
2	1.717	1.736	1.727	1.843	1.859	2.014	2.072	2.051	1.968	1.936	1.820	1.730
3	1.779	1.801	1.786	1.798	1.815	2.028	1.978	2.066	1.922	1.874	1.804	1.781
4	1.733	1.762	1.793	1.842	1.898	1.993	2.017	2.058	1.942	1.928	1.804	1.777
5	1.764	1.790	1.804	1.857	1.859	2.007	2.037	2.058	1.980	1.924	1.840	1.777
6	1.757	1.757	1.794	1.865	1.872	1.994	2.027	2.040	1.981	1.909	1.815	1.756
7	1.696	1.728	1.740	1.819	1.838	2.003	1.999	1.999	1.922	1.865	1.766	1.708
8	1.762	1.780	1.817	1.875	1.881	1.988	2.019	2.042	1.997	1.915	1.829	1.759
9	1.689	1.724	1.724	1.814	1.797	1.943	2.047	2.025	1.933	1.863	1.767	1.699
10	1.761	1.770	1.797	1.829	1.858	1.991	2.038	2.055	1.975	1.905	1.828	1.763
11	1.758	1.766	1.800	1.851	1.920	2.032	2.075	2.062	1.957	1.910	1.833	1.757
12	1.679	1.711	1.739	1.812	1.860	2.002	2.004	1.929	1.965	1.900	1.809	1.715
13	1.707	1.764	1.758	1.835	1.874	1.982	2.016	2.066	1.979	1.867	1.778	1.741
14	1.734	1.756	1.765	1.827	1.888	2.020	2.037	2.085	1.934	1.914	1.788	1.740
15	1.744	1.772	1.795	1.846	1.879	2.015	2.066	2.061	1.971	1.919	1.816	1.754
16	1.757	1.792	1.792	1.885	1.886	2.008	2.008	2.048	1.982	1.914	1.826	1.770
17	1.734	1.763	1.755	1.823	1.863	2.025	2.048	2.037	1.917	1.869	1.800	1.752
18	1.640	1.698	1.716	1.797	1.826	1.983	1.991	2.059	1.923	1.810	1.747	1.690
19	1.693	1.724	1.716	1.792	1.836	1.999	2.034	2.041	1.968	1.896	1.757	1.706
20	1.701	1.722	1.765	1.806	1.856	1.993	2.009	2.008	1.953	1.872	1.775	1.724
21	1.732	1.735	1.721	1.783	1.915	2.057	2.078	2.055	1.980	1.883	1.786	1.716
22	1.686	1.724	1.754	1.840	1.895	2.013	2.043	2.005	1.932	1.877	1.778	1.703
23	1.651	1.671	1.692	1.782	1.849	1.937	2.010	1.948	1.916	1.858	1.758	1.679
24	1.699	1.736	1.737	1.798	1.838	1.966	2.054	2.005	1.918	1.855	1.764	1.694
25	1.720	1.746	1.765	1.841	1.836	1.962	2.046	2.039	1.950	1.943	1.809	1.756
26	1.741	1.779	1.787	1.850	1.932	2.064	2.036	2.068	1.990	1.895	1.844	1.768
27	1.714	1.746	1.737	1.813	1.826	1.986	2.051	2.061	1.937	1.855	1.766	1.728
28	1.635	1.681	1.697	1.753	1.806	1.941	1.964	1.961	1.862	1.791	1.721	1.639
29	1.702	1.721	1.738	1.819	1.837	2.032	2.052	2.035	1.978	1.872	1.751	1.701
30	1.701	1.737	1.730	1.836	1.851	2.041	2.044	2.054	1.974	1.897	1.772	1.716
31	1.712	1.718	1.728	1.779	1.850	2.032	2.038	2.094	1.965	1.891	1.758	1.702
32	1.718	1.742	1.755	1.812	1.882	2.007	2.023	2.034	1.950	1.880	1.776	1.747
33	1.702	1.710	1.729	1.782	1.849	1.942	1.916	1.928	1.923	1.864	1.762	1.687
34	1.752	1.789	1.775	1.814	1.872	2.019	2.054	2.100	1.978	1.887	1.848	1.769
35	1.712	1.746	1.754	1.832	1.867	2.012	2.030	2.052	1.962	1.863	1.823	1.726
36	1.704	1.722	1.753	1.788	1.839	1.972	1.994	2.021	1.934	1.868	1.768	1.701
37	1.719	1.763	1.771	1.842	1.851	2.011	2.038	2.043	1.972	1.888	1.822	1.740
38	1.690	1.743	1.743	1.791	1.840	1.980	2.024	2.054	1.958	1.866	1.774	1.730
39	1.701	1.743	1.740	1.780	1.839	1.978	2.031	2.045	1.968	1.875	1.785	1.704
40	1.709	1.719	1.763	1.833	1.830	1.992	2.038	2.063	1.952	1.865	1.777	1.702
41	1.697	1.722	1.712	1.797	1.835	1.969	2.015	2.063	1.970	1.855	1.755	1.704
42	1.681	1.703	1.711	1.791	1.859	2.009	2.011	2.022	1.958	1.870	1.785	1.682
43	1.767	1.766	1.799	1.849	1.885	2.033	2.089	2.060	1.977	1.916	1.820	1.765
44	1.720	1.730	1.746	1.821	1.843	1.983	2.011	2.060	1.921	1.883	1.784	1.718
45	1.730	1.756	1.798	1.861	1.874	2.022	2.043	2.053	1.955	1.889	1.817	1.744
46	1.723	1.718	1.756	1.797	1.907	2.038	2.063	2.060	1.997	1.919	1.835	1.747
47	1.715	1.724	1.738	1.766	1.858	1.993	2.009	2.060	1.941	1.858	1.760	1.718
48	1.745	1.770	1.788	1.839	1.887	2.005	2.043	2.042	1.971	1.937	1.804	1.771
49	1.695	1.731	1.729	1.825	1.892	2.011	2.049	2.055	1.949	1.892	1.781	1.720
50	1.739	1.736	1.741	1.819	1.883	2.033	2.080	2.079	1.979	1.940	1.813	1.741
51	1.731	1.756	1.781	1.837	1.853	2.029	2.055	2.070	1.958	1.915	1.781	1.740
52	1.676	1.697	1.715	1.761	1.817	1.902	1.982	2.037	1.877	1.889	1.768	1.700
53	1.724	1.747	1.756	1.818	1.853	2.004	2.032	2.035	1.949	1.874	1.798	1.735
54	1.626	1.682	1.670	1.717	1.803	1.944	2.033	2.035	1.899	1.792	1.708	1.683

in the Appendix A.

Figure 2b shows the isoerosivity map determined through IDW interpolation of the mean annual values, R_m, for each station, calculated using Equations (4)–(6) with the pairs (α_m,s, β_m,s) given in Figure 3.

In this case, the northwestern and southern areas are characterised by higher values of mean annual erosivity (2299.0, 2298.9, 1446.7 MJ mm ha⁻¹ h⁻¹ y⁻¹, respectively, mean, maximum, and minimum) compared to the northern, eastern, and southwestern areas, where erosivity values are generally lower (1305.6, 1682.5, 756.0 MJ mm ha⁻¹ h⁻¹ y⁻¹, respectively, mean, maximum, and minimum). The regional mean annual value is 1531.2 MJ mm ha⁻¹ h⁻¹ y⁻¹, with a standard deviation of 318.3 MJ mm ha⁻¹ h⁻¹ y⁻¹.

Model B operates at the event scale temporal resolution, where the parameters α and β are kept constant across the months. This makes the procedure less computationally demanding compared to the semi-hourly scale required by Model A (USLE and RUSLE-2), although despite simplifying the process, Model B remains highly complex due to the variability and number of parameters involved.

3.3. Model C

The analysis of the temporal variability of the parameters {α_m, m = 1, … 12} e {β_m, m = 1, … 12}, shown in Figure 3, reveals a periodic pattern in the annual dynamics, with a maximum value in the summer months, a minimum in the winter months, and intermediate values corresponding to the spring and autumn months. Based on this, a data analysis was conducted for the selection and grouping of months with homogeneous erosivity values. A statistical analysis based on normalisation and clustering of the α and β data showed that these parameters can be considered statistically constant within three distinct periods, p (with p = 1, …, 3): summer period p_s from June to September; the humid period p_h, April, May, October and November; the winter period p_w, January, February, March and December. The period values of α and β for each station are presented in

Table A3. α and β values used in Equation (6) for each period and each station to calculate mean annual erosivity (R_p) in Model C.

	Period				Period
ID Station	1	2	3	ID Station	1	2	3
1	0.098	0.116	0.148	1	1.714	1.830	2.009
2	0.104	0.121	0.150	2	1.728	1.859	2.017
3	0.100	0.116	0.141	3	1.785	1.821	1.996
4	0.092	0.110	0.144	4	1.767	1.861	1.995
5	0.095	0.114	0.147	5	1.785	1.868	2.015
6	0.094	0.109	0.143	6	1.777	1.873	2.016
7	0.100	0.117	0.146	7	1.717	1.814	1.977
8	0.094	0.110	0.143	8	1.778	1.868	2.011
9	0.094	0.111	0.141	9	1.715	1.806	1.980
10	0.088	0.103	0.132	10	1.773	1.853	2.011
11	0.096	0.116	0.149	11	1.770	1.874	2.021
12	0.099	0.119	0.145	12	1.710	1.838	1.985
13	0.087	0.111	0.144	13	1.741	1.831	2.007
14	0.087	0.108	0.142	14	1.745	1.845	2.003
15	0.090	0.106	0.133	15	1.764	1.862	2.025
16	0.092	0.107	0.135	16	1.776	1.872	2.009
17	0.083	0.096	0.127	17	1.752	1.837	1.997
18	0.092	0.109	0.135	18	1.688	1.789	1.981
19	0.091	0.111	0.137	19	1.710	1.813	2.007
20	0.096	0.119	0.147	20	1.726	1.823	1.980
21	0.097	0.117	0.141	21	1.726	1.832	2.035
22	0.097	0.118	0.142	22	1.715	1.839	1.991
23	0.095	0.115	0.140	23	1.673	1.802	1.942
24	0.079	0.093	0.125	24	1.718	1.810	1.971
25	0.087	0.108	0.135	25	1.748	1.855	1.991
26	0.095	0.115	0.153	26	1.767	1.876	2.036
27	0.082	0.104	0.136	27	1.731	1.808	1.996
28	0.091	0.108	0.139	28	1.664	1.768	1.923
29	0.099	0.119	0.143	29	1.713	1.809	2.015
30	0.098	0.119	0.142	30	1.720	1.830	2.021
31	0.097	0.119	0.131	31	1.712	1.813	2.029
32	0.089	0.110	0.146	32	1.741	1.832	1.998
33	0.094	0.111	0.130	33	1.704	1.809	1.927
34	0.086	0.104	0.130	34	1.772	1.854	2.031
35	0.095	0.115	0.142	35	1.735	1.842	2.009
36	0.099	0.118	0.141	36	1.720	1.815	1.972
37	0.088	0.104	0.136	37	1.749	1.844	2.009
38	0.097	0.116	0.142	38	1.726	1.812	2.000
39	0.098	0.119	0.146	39	1.721	1.817	2.003
40	0.099	0.117	0.145	40	1.722	1.821	2.008
41	0.099	0.116	0.152	41	1.707	1.802	1.998
42	0.098	0.117	0.152	42	1.698	1.819	1.993
43	0.090	0.112	0.142	43	1.775	1.861	2.030
44	0.085	0.105	0.137	44	1.728	1.828	1.985
45	0.091	0.113	0.144	45	1.758	1.855	2.013
46	0.101	0.121	0.152	46	1.737	1.861	2.039
47	0.096	0.113	0.130	47	1.723	1.803	2.001
48	0.095	0.114	0.148	48	1.768	1.861	2.011
49	0.099	0.114	0.140	49	1.720	1.840	2.011
50	0.101	0.119	0.146	50	1.739	1.862	2.033
51	0.091	0.108	0.143	51	1.753	1.841	2.020
52	0.096	0.116	0.135	52	1.697	1.807	1.935
53	0.090	0.109	0.138	53	1.741	1.832	1.998
54	0.084	0.108	0.135	54	1.668	1.752	1.964

in the Appendix A.

In addition, he percentage of the total annual rainfall height P_y relative to the three periods (Table 2) are substantially different with an average value at the regional scale of P_s = 211.7 mm, P_w = 286.8 mm and P_h = 339.1 mm, while the corresponding means R_s = 935.5 MJ mm ha⁻¹ h⁻¹ y⁻¹, R_w = 277. 7 MJ mm ha⁻¹ h⁻¹ y⁻¹, R_h = 652.3 MJ mm ha⁻¹ h⁻¹ y⁻¹ show an opposite behaviour with the higher value in summer and the lower in winter period.

Figure 2c shows the isoerosivity map determined through IDW interpolation of the mean annual values, R_p, for each station, calculated using Equations (4)–(6) with the pairs (α_p, β_p).

The data shown in Figure 2c highlight a substantial agreement with the pattern obtained using RUSLE-2 (Model A, Figure 2a). Areas located in the south and north-west are characterised by significantly higher average annual erosivity values compared to other regions. Specifically, the average, maximum, and minimum erosivity are 1699.2, 2272.4, and 1334.7 MJ mm ha⁻¹ h⁻¹ y⁻¹, respectively. In contrast, the areas in the north, east, and south-west show lower average annual values, with an average of 1304.2 MJ mm ha⁻¹ h⁻¹ y⁻¹, a maximum of 1675.3 MJ mm ha⁻¹ h⁻¹ y⁻¹, and a minimum of 772.3 MJ mm ha⁻¹ h⁻¹ y⁻¹. The regional mean value of annual erosivity is 1499.1 MJ mm ha⁻¹ h⁻¹ y⁻¹, with a standard deviation of 294.0 MJ mm ha⁻¹ h⁻¹ y⁻¹, reflecting territorial variability.

In Model C, the complexity related to the calculations and the procedures required is further reduced compared to previous models, as the parameters α and β are considered constant across different periods. Like Model B, Model C requires a temporal resolution of the data at the scale of individual rainfall events.

3.4. Model D

The conducted analysis reveals a clear distinction in the levels of average annual erosivity across different geographical areas and periods. Thus, six functional relationships between the daily rainfall and erosivity were obtained, as shown in

Table 3. Relationships between the daily rainfall (h_d) and erosivity (R_d) for each period and sub-zone processed using the D model.

Equation	P, Z
${\mathrm{R}}_{\mathrm{d}}=0.00080848·{\mathrm{h}}_{\mathrm{d}}^3-0.03067570·{\mathrm{h}}_{\mathrm{d}}^2+1.35937424·{\mathrm{h}}_{\mathrm{d}}-1.92473511$	p = 1; z = r	(7)
${\mathrm{R}}_{\mathrm{d}}=-0.00022788·{\mathrm{h}}_{\mathrm{d}}^3+0.05795112·{\mathrm{h}}_{\mathrm{d}}^2+0.99900288·{\mathrm{h}}_{\mathrm{d}}-2.06564377$	p = 2; z = r	(8)
${\mathrm{R}}_{\mathrm{d}}=-0.00060982·{\mathrm{h}}_{\mathrm{d}}^3+0.18384798·{\mathrm{h}}_{\mathrm{d}}^2+0.56087557·{\mathrm{h}}_{\mathrm{d}}-1.48459328$	p = 3; z = r	(9)
${\mathrm{R}}_{\mathrm{d}}=-0.00032134·{\mathrm{h}}_{\mathrm{d}}^3+0.05897403·{\mathrm{h}}_{\mathrm{d}}^2+0.04415188·{\mathrm{h}}_{\mathrm{d}}+0.09640815$	p = 1; z = b	(10)
${\mathrm{R}}_{\mathrm{d}}=-0.00024928·{\mathrm{h}}_{\mathrm{d}}^3+0.07843005·{\mathrm{h}}_{\mathrm{d}}^2+0.47441833·{\mathrm{h}}_{\mathrm{d}}-0.80569572$	p = 2; z = b	(11)
${\mathrm{R}}_{\mathrm{d}}=-0.00036687·{\mathrm{h}}_{\mathrm{d}}^3+0.17375462·{\mathrm{h}}_{\mathrm{d}}^2+0.53993365·{\mathrm{h}}_{\mathrm{d}}-1.04597592$	p = 3; z = b	(12)

.

The “blue-green zones” (Figure 2d) exhibit significantly higher erosivity values, with an annual average of 2040.3 MJ mm ha⁻¹ h⁻¹ y⁻¹, a maximum value of 2830.8 MJ mm ha⁻¹ h⁻¹ y⁻¹, and a minimum of 1698.5 MJ mm ha⁻¹ h⁻¹ y⁻¹.

Conversely, the “red-orange zones” (Figure 2d) show lower erosivity levels. In these areas, the average value stands at 2116.7 MJ mm ha⁻¹ h⁻¹ y⁻¹, with a maximum of 2093.8 MJ mm ha⁻¹ h⁻¹ y⁻¹ and a minimum of 1698.8 MJ mm ha⁻¹ h⁻¹ y⁻¹.

Considering the entire study region, the average annual erosivity is 1915.4 MJ mm ha⁻¹ h⁻¹ y⁻¹, with a standard deviation of 328.9 MJ mm ha⁻¹ h⁻¹ y⁻¹.

3.5. Model Validation

To validate the obtained models, the meteorological station of Trestina (43.358 N, 12.237 E), not included in the database of Table 1, was considered. For this station, half-hourly precipitation data are available for the period 2007–2024.

For the application of Models B and C, Equation (6) was used with the parameters α and β derived from the nearest station (Città di Castello, ID14, approximately 9 km away). For Model D, Equations (7)–(9) were applied, as the Trestina station falls within the red zone. The estimated annual values (R_m, R_p, and R_d, corresponding to Models B, C, and D, respectively) were compared with the annual R values of Model A. The results are presented in Figure 4.

As shown, while Models B and C exhibit a general agreement with the reference values, their annual estimates tend to show a slight underestimation. Model D demonstrates a stronger correlation, with values more evenly distributed around the 1:1 line, maintaining this pattern even in the presence of extreme values.

The comparison of annual values between Model A and Model B results in a MAPE of 24.4%, while the difference between Model A and Model C yields a MAPE of 23.3%. The comparison between Model A and Model D shows a slightly lower MAPE of 19.9%.

3.6. Trend Analyses

The trend analysis was conducted on the annual erosivity, R_y, as well as the annual rainfall, P, for each of the 54 stations. The historical series analysed are robust, spanning a total of 1167 years. Their duration ranges from a minimum of 15 years, observed in a single case at the Armenzano station (ID 3), to a maximum of 24 years. The average series length per station exceeds 21.5 years (Column 2, Table 2).

The results of the analysis indicate the absence of significant trends in annual erosivity in most meteorological stations, both for the multi-year average rainfall series and for those related to multi-year average erosivity. For most stations, neither rainfall events nor erosive events exhibit a predictable or consistent pattern over time.

A single exception was identified at the Nocera Umbra (ID 27), where a significant trend in rainfall was observed, with a Theil–Sen slope of 13.5 per year. Regarding erosivity, significant trends were observed in four stations: Armenzano (ID 3), Moiano (ID 23), Nocera Umbra (ID 27), and Ponte Felcino (ID 39). In these cases, the Theil–Sen slope values were 89.5, 109.0, 61.0, and 90.3, respectively.

4. Discussion

4.1. Comparison Between Simplified Models (B, C, D) and Reference Model (A)

Figure 2 presents isoerosivity maps generated through a zonation process based on clustering analysis. These maps depict the multi-year average annual erosivity values of the R parameter, calculated using different predictive models. Despite considering other explanatory factors, such as altitude (r = 0.24), latitude (r = 0.14), and longitude (r = 0.17), their correlations with erosivity were found to be insufficiently significant to provide a representative contribution.

To enhance the clarity and interpretability of the results, each map was constructed using uniform intervals, which were defined based on percentiles corresponding to specific erosivity ranges across the models. Adopting a uniform scale highlighted the peculiarities and differences among the various methods for calculating erosivity. The general pattern is consistently observed in all isoerosivity maps, although predictive models tend to underestimate the final values produced by RUSLE2 (Model A).

The statistics of the multi-year average annual erosivity values calculated using Models A, B, C, and D for individual stations are presented in

Table 4. Statistics of mean annual erosivity (MJ mm ha⁻¹ h⁻¹ y⁻¹) at the Umbria region’s 54 meteorological stations. The mean absolute percentage error, MAPE, and the Pearson correlation coefficient, r, refer to the comparison between the reference (model A) and all the other R estimates at the station level. The description of the models follows that of Figure 2. R_d is distinguished based on the regional mean value into R_db (>R_mean) and R_dr (<R_mean), while R_Panagos is derived from [29].

	Model
	A	B	C	D	D
	R	Rm	Rp	Rd r	Rd b	RPanagos
Minimum value	1004.4	756.0	772.3	992.5	879.2	1125.7
Maximum value	2738.2	2299.0	2272.4	2132.4	2694.4	2151.4
Mean value	1843.6	1531.2	1499.1	1626.3	2040.3	1518.7
Standard deviation	336.4	318.3	294.0	318.4	241.2	217.6
Coefficient of variation (%)	18.2	20.8	19.6	16.1	14.8	14.3
MAPE (%)		18.9	20.1	5.5	5.4	18.6
r		0.81	0.80	0.76	0.73	0.54

. Regional values from the analysis by Panagos et al. [29] are also presented for comparison purposes.

The minimum average value of R is observed at the Norcia station (ID 28), whereas Armenzano (ID 3) exhibits the maximum. These results are consistent for the erosivity estimates of Rm, Rp, and Rd. The highest variability in the estimates is found using Models B and C, whit CV = 20.8% and CV = 19.6%, (Table 4), respectively.

In general, although all models confirm spatial patterns similar to those provided by the reference model (Model A), the annual average erosivity shows a slight underestimation (≈15%) in the case of Models B and C, while it is more comparable in Model D (when averaging the values of R_d,r and R_d,b).

With the increase in the degree of simplification applied to the model, the correlation between the model prediction and the expected value calculated by RUSLE2 (model A) decreases, from r = 0.81 and 0.80 for models B and C, to r = 0.76 and 0.73 for models D. Despite this variation, the explanatory power of the model relative to the reference data remains high considering the lower level of detail in the input data (from 30 min to daily time resolution). The stability and reliability of the Rm, Rp, and Rd estimates in representing the erosive phenomenon are further confirmed by the Mean Absolute Percentage Error (MAPE) between the model predictions and the expected values calculated using RUSLE2 (Model A) (Table 4). In this case, the best performance (i.e., the lowest MAPE) is achieved by Model D, with values around 5–6%, whereas Models B and C exhibit MAPE values of approximately 19–20%.

The simplified models prove to be sufficiently reliable not only at the annual and mean annual R-factor scales (Table 4) but also at the sub-annual level. This evaluation is demonstrated, by way of example, for Models B (R_m) and C (R_p).

The monthly distribution of the R and R_m are plotted in Figure 5a as a box plot to highlight potential seasonal trends and differences between the two estimates, with a particular focus on variability and extreme events characterising different months of the year. During the winter months (January, February, and December) the erosivity is generally low, with contained medians, relative compact distribution and similar values estimated by the two models. This pattern reflects the low intensity and variability of rainfall typical of the winter climate, which tends to have a lower potential erosive power [42].

During the spring and summer, erosivity progressively increases, reaching the maximum in August, and then progressively decreases in autumn toward the winter values. This behaviour corresponds to a marked variability among stations starting from May. This variability remains almost unchanged for R until September; instead, Rm dispersion follows the erosivity trend with a maximum dispersion in August. The R presents a greater variability than Rm, with the difference diminishing in winter months when erosivity values are more similar. This seasonal trend confirms the system’s greater stability in winter, where both models converge, and the heightened sensitivity to the variable summer climate. This behaviour could be attributed to the nature of the Rm parameter calculation, which incorporates reduced sensitivity to short-duration intense rainfall, characteristic of the summer period, better described by a parameter like I30 rather than event-scale cumulative rainfall (he).

Figure 5b compares the values of R and Rp across three main seasonal periods: 1, winter (January, February, March, and December); 2, humid (April, May, October, and November); and 3, summer (from June to September). The comparison confirms all the results discussed above relative to the R and Rm models with a progressive increase in intensity and variability of the rainfall erosivity from the winter to summer, with a particularly pronounced rise during spring and summer, coinciding with the intensification of rainfall phenomena.

These comparisons highlight the significance of factors such as the frequency and intensity of storm events in determining erosivity dynamics. The analysis of stations characterised by different seasonal distributions provides valuable insights into the influence of local factors on rainfall and erosivity properties. These results, enhanced by the integration of geomorphological data such as orography and microclimate, allow for a more accurate assessment of erosion risks and their potential environmental impacts.

Although models B and C offer a simplification in the calculation of erosivity at the event scale, they still require the knowledge of h_e, a variable that is typically not available in meteorological datasets. This significantly limits their practical utility. On the other hand, Todisco et al. [43], in a study based on 18 stations in the Umbria region from 2000 to 2010, demonstrated that the differences between h_e and h_d were not particularly pronounced, as they were found to be less than 5 mm in 95% of the cases analysed. Therefore, a more practical use of models B and C could involve substituting h_d for h_e. The impact of this solution, likely modest, will still require specific investigations.

The validation performed using the Trestina weather station (Figure 4) confirms the reliability of the results obtained through the application of the simplified models (Models B, C, and D). Among these, Model D represents the most effective trade-off between computational efficiency and accuracy. Specifically, the input data, characterised by a daily temporal resolution and a spatial scale at the sub-zone level (for Trestina, corresponding to the red zone), allow for a streamlined and efficient calculation process.

The literature offers several studies assessing the feasibility of obtaining reliable estimates of the R-factor through simplified empirical models. For certain regions of Italy, empirical approaches based on the Modified Fournier Index (MFI) have been shown to be both effective and easy to implement [19,20], as they require only monthly precipitation data as input. However, unlike these methodologies, the simplified models proposed in this study can be applied not only for the estimation of the annual R-factor but also for a (although approximate) assessment of erosivity at the event or daily scale.

4.2. Comparison with Panagos et al. (2015) [29]

The results obtained in this study were compared with the iso-erosivity maps developed in a previous work by Panagos et al. [29], which serve as a well-established reference in the field.

The erosivity map by Panagos et al. [29] (Figure 5b) was obtained through regional scale clipping operations applied to the map developed at the European scale. The erosivity value scale remains consistent with that presented in Figure 2. The comparison of individual values was conducted by sampling erosivity data from the Panagos map at the coordinates of the meteorological stations utilised in this study, using QGIS version 3.34.15.

The R_Panagos are derived from a raster dataset developed at a European scale [29], which may imply a less detailed spatial resolution compared to Model A. The number of stations used at the regional scale is also smaller. Panagos et al. [29] analysed a total of 251 meteorological stations across Italy, with a spatial distribution that accounts for the country’s main climatic conditions (Mediterranean, continental, and alpine) and different altitudinal zones. However, when considering the size of the Umbrian region in comparison to the national territory, only seven meteorological stations are representative of the region in Panagos’ work, whereas this study analyses data from 54 stations. Additionally, the historical series used by Panagos has an average duration of 10 years, significantly shorter than the 21.5-year average in the present study, offering a broader temporal coverage. Furthermore, the use of different approaches for erosivity calculation (RUSLE for Panagos and RUSLE-2 for Model A) introduces another source of discrepancy between the two methods.

From the comparative analysis (Table 4), a relatively weak correlation (r = 0.56) emerged between the annual erosivity values estimated using the RUSLE-2 model, applied in the calculation of Model A, and those derived from the RUSLE model employed in Panagos’s studies, R_Panagos.

The comparison between the R and R_Panagos reveals a systematic tendency for the latter to provide lower estimates, indicating a potential intrinsic underestimation in [29]. This, in addition to the differences between the datasets used, may depend on the known tendency of the RUSLE method to underestimate precipitation energy compared to the RUSLE model2 [43].

Amelia (ID 2) recorded the highest erosivity value R_Panagos = 2151.4 MJ mm ha⁻¹ h⁻¹ y⁻¹ according to Panagos et al. [29], whereas Umbertide showed the lowest value R_Panagos = 1125.7 MJ mm ha⁻¹ h⁻¹ y⁻¹). At the regional level, the average erosivity R_Panagos = 1518.7 MJ mm ha⁻¹ h⁻¹ y⁻¹. The analysis of the distribution of values shows a general consistency across stations, although R highlights significant peaks for certain stations (ID 3, ID 24, and ID 43), while R_Panagos is more uniform, exhibiting lower variability among stations. This behaviour suggests that the method used in Panagos et al. [29] reduces the impact of extreme values, likely due to differences in calculation methodology or the nature and density of the data used.

The differences between the results are particularly pronounced in some stations, such as ID3 and ID43, whereas in other cases, such as ID4, ID31, and ID44, there is an almost complete convergence between the two approaches. The general pattern confirms that Model A tends to produce higher erosivity values compared to those estimated by Panagos et al. [29].

Figure 6a compares the erosivity values (MJ mm ha⁻¹ h⁻¹) across five models: R, R_Panagos, R_m, R_p, and R_d. Among them, R_d stands out with the highest median and the widest interquartile range (IQR), indicating greater variability and higher erosivity estimates. In contrast, R_Panagos exhibits the lowest median and the narrowest IQR, reflecting more consistent and lower values. The R_m and R_p models show similar distributions, with R_p displaying slightly greater variability. The R model, though closer to R_d in median, reveals a broader spread compared to R_Panagos, indicating moderate variability. Outliers are present in all models, emphasising occasional extreme erosivity values.

A direct comparison between R and R_Panagos highlights their differences. The median and mean values of R are notably higher, with R also showing a larger IQR and more extended whiskers, capturing a wider range of data. Conversely, R_Panagos demonstrates lower variability, with a compact box and shorter whiskers. While R_Panagos has an outlier above the upper limit, R spans a broader range without evident outliers but includes a higher maximum value.

The greater variability in R likely stems from increased sensitivity in input data, influenced by the number of analysed stations or differing calculation criteria in RUSLE-2. By contrast, R_Panagos, derived using the RUSLE model, reflects less sensitivity to erosivity peaks, suggesting a more constrained methodology.

The isoerosivity map developed by Panagos [29] in Figure 6b is consistent with that obtained using Model A, despite systematic underestimations observed like in Models B and C. The dataset is projected onto a regular grid with a pixel resolution of 0.006° × 0.006°, which provides less detailed results compared to the models analysed in this study (0.0009° × 0.0009°).

The areas with the lowest R-factor values are in the southeast and along the entire western strip, while erosivity values exceeding 2000 MJ mm ha⁻¹ h⁻¹ are found in the south and northeast. The central part of Umbria is characterised by average values.

5. Conclusions

This study aimed to assess rainfall erosivity in the Umbria region through the analysis of a twenty-year rainfall dataset. By exploring the spatial and temporal dynamics of erosive events, the research uncovered significant differences across areas and seasons, with implications for soil erosion risk. The R-factor was mapped at a 100 m resolution using IDW interpolation, leveraging extensive rainfall intensity data. The application of the RUSLE-2 model to a network of uniformly distributed meteorological stations demonstrated its ability to identify erosion-prone areas, supported by precise erosivity indices calculated from 30 min rainfall data.

Regional Zoning. Isoerosivity maps highlighted a clear spatial gradient, with higher rainfall erosivity values in the southern and north-western areas of Umbria. These patterns reflect the combined effects of topography, climate, and geomorphology, underscoring the importance of region-specific soil conservation plans.

Comparison of Medians, Model Variability, and Recommendation for Model D. Model A demonstrated high sensitivity to local erosivity variations, with values ranging from 1004.4 to 2738.2 MJ mm ha⁻¹ h⁻¹ y⁻¹ and a standard deviation of 336.4 MJ mm ha⁻¹ h⁻¹ y⁻¹. Simplified models (B, C, and D) provided reliable yet slightly underestimated alternatives, making them suitable for contexts with limited data availability. Among these, Model D, which relies on daily rainfall data, emerged as the most practical solution for regions with restricted access to high-resolution pluviometric data. Striking a balance between computational simplicity and accuracy, it represents a robust choice for large-scale applications.

Importance of Station Density and Temporal Resolution. The reliability of Model A, confirmed by comparisons with prior studies (e.g., Panagos et al. [29]), highlights the significance of a dense meteorological network and long-term datasets. These factors enhance the detection of spatial and temporal variability, improving predictive accuracy and erosion management strategies.

Trend Analysis. The Mann–Kendall test applied to Model A revealed temporal stability in rainfall erosivity across most stations, with significant trends in only a few locations. This indicates a largely consistent pattern at the regional scale, though some areas may require intensified monitoring.

Seasonal Variability. The analysis identified pronounced seasonal differences in rainfall erosivity, emphasising the necessity of incorporating seasonal dynamics into erosion risk assessments to optimise soil protection measures during periods of higher erosivity.

By integrating high-resolution data with simplified models, this study provides a comprehensive framework for evaluating rainfall erosivity, contributing to sustainable land management and soil conservation in erosion-prone regions.