Developing a rainfall time series and, subsequently, a rainfall erosivity database is challenging in both spatial and temporal terms. The large diversity of topographic conditions (i.e., two principal mountain ranges and a large latitudinal extent) and proximity to large water bodies from the Pacific Ocean and the Gulf of Mexico make Mexico a contrasting scenario for rainfall patterns and hydrological-related processes (e.g., rainfall erosivity). Accurate benchmarks for understanding typical climate conditions and characterizing climate trends require a rainfall database long enough to represent its corresponding climate normal (CN), i.e., a statistical product computed over 30 years of rainfall time series . The CNs are widely used to compare recent observations, create anomaly-based datasets, and provide context for future climate projections. Considering local patterns across different CNs, these characteristics will contribute to an unprecedented rainfall time series dataset for estimating rainfall erosivity in Mexico.

On the other hand, climatology studies, such as erosivity, need a complete and reliable rainfall time series database . Therefore, a whole scheme of quality assurance, gap-filling, and homogenization process of the rainfall time series is needed . This quality control and homogenization process has been widely applied before rainfall erosivity analysis, in order to avoid incoherent rainfall amounts that could affect the long-term rainfall erosivity estimates . Consequently, with a reliable rainfall database, it is possible to represent the actual rainfall characteristics in a particular region and allow soil erosion monitoring at the local and national scales in Mexico.

The rainfall time series database was developed through four steps: first, compilation, selection, and quality assurance of the rainfall time series. Second, the clustering of the rainfall time series based on their geographical and data attributes. Third, homogenization and data gap-filling of monthly and daily rainfall time series. Fourth, quality control of the data gap-filling process.

In this step, we identified the best empirical relationship to calculate the R factor according to the erosivity characteristics of Mexico. To achieve this, we evaluated three combinations of parameters α and β in a power law model and used three databases with EI30 information on a global , national , and local (EI30 calculated from sub-hourly rainfall time series) scale.

We estimated the R factor for each weather station on the Mexican rainfall time series database. First, we identified the days with erosive rainfall as those with cumulative precipitation greater than 12.7 mm, an extension of the suggestion by , and . Second, we calculated daily erosivity Rd using the best coefficient combination identified in the previous step (Sect. ). Finally, we estimated the mean annual rainfall erosivity, R factor, as described in the previous step (Sect. ).

At this point, it is essential to highlight that we did not consider the erosivity due to the snowmelt because there is a pint-sized area covered with snow (or risk of snowfall), and no monitoring system for snowfall is publicly available in Mexico. To estimate the surface covered by snow, we explored the climate classification developed by , a modified Köppen classification system to better fit Mexico's climate conditions. According to the Köppen classification, only 83 km² (0.004 % of the total area of Mexico) can be classified as E climates in the format of ET (tundra: temperature of warmest month greater than 0 °C but less than 10 °C) and EF (snow/ice: temperature of the warmest month 0 °C or below), both only produced by high altitudes. Additionally, the National Center for Disaster Prevention of Mexico developed a national snowfall danger index at a municipality level based on the occurrence of snowfall during the centuries XV to XXI . They found that in the study period, snowfall had never occurred in 93.8 % of Mexico's municipalities. Additionally, the municipality with the highest snowfall frequency is Juarez (Chihuahua state), with just 30 events over five centuries.

Finally, to provide an overview of the sensitivity associated with the gap-filling and homogenization procedures, the complete rainfall time series were modified according to the percentage change in the mean value of each rainfall time series before and after these procedures. As established in the quality control section (Sect. 2.1.3), the mean change in the rainfall time series did not exceed 10 %. The modified series were subsequently used to recalculate daily rainfall erosivity values, from which new R factors were estimated for each station and climate normal. The percentage change between the recalculated R factor and the R factor estimated from the complete rainfall time series after the gap-filling and homogenization procedures was then computed to evaluate the sensitivity of rainfall erosivity estimates to alterations introduced during these procedures. This analysis provides a first-order assessment of the propagation of uncertainties associated with modifications in the rainfall time series into long-term erosivity estimates.

At the end of this step, we obtained three datasets with R factor values for the three CNs: Mexico-CN1 (1968–1997), Mexico-CN2 (1978–2007), and Mexico-CN3 (1988–2017).

The initial number of rainfall time series for the gap-filling, homogenization and quality control process was 1479; 1774; and 1721 for CN1, CN2, and CN3, respectively (Table ). After data gap-filling, homogenization, and quality control, we discarded 4.8 % of the rainfall time series. Hence, Table  shows that the largest number of rainfall time series corresponds to CN1 (1968–1997), with 7.4 % (110 rainfall time series), which is followed by CN2 (1978–2007), with 5.4 % (96 rainfall time series), and CN3 (1988–2017), with 2.6 % (45 rainfall time series). Likewise, the most significant proportion of discarded rainfall time series corresponded to Mediterranean California (3 rainfall time series, 21.4 %) and North American Deserts (29 rainfall time series, 15.84 %) in CN1; Mediterranean California (2 rainfall time series, 11.11 %) and Great Plains (7 rainfall time series, 12.72 %) in CN2; and Great Plains (5 rainfall time series, 10.86 %) in CN3. Additionally, in the data gap-filling processes, we identified that none of the 5 rainfall time series available for Mediterranean California, in CN3, had a rainfall records for three consecutive years, which did not allow us to carry out the data gap-filling process for the complete study period; however, CN1 and CN2 provide a robust basis for assessing rainfall erosivity in this ecoregion. Finally, we obtained a database with 1369; 1678; and 1676 rainfall time series for CN1, CN2, and CN3, respectively. The available rainfall time series are distributed across the Mexican territory for the three CNs and represent the seven ecoregions (Fig. ).

The percentage of variation in the mean of the rainfall time series by ecoregion and CN using the two-step clustering is shown in Table . The CN2 (1978–2007) showed the highest average change in the mean, with -1.80 %, where it is also noted that four of the seven ecoregions present relatively high average changes. Notably, in CN1 (1968–1997), for North American Deserts, the highest average change in the mean is -1.50 %. In the CN3 (1988–2017), for Tropical Dry Forest and for Temperate Sierras, it is -3.38 % and -1.61 %, respectively. Additionally, Table  shows the Root Mean Square Error (mm) of the monthly accumulated rainfall by ecoregion. It can be seen that the highest RMSE was found for Tropical Rain Forest in the three CNs (6.12, 5.72, 6.78 mm, respectively), followed by Great Plains in CN2 and CN3 (5.72, 6.78 mm, respectively).

Figure  shows the monthly rainfall distribution for the seven ecoregions for CN1 (1968–1997), CN2 (1978–2007), and CN3 (1988–2017). The results indicate that Mexico exhibits a unimodal rainfall regime, with a marked peak and a well-defined dry season across all ecoregions; however, the characteristics of the wet period vary among them. In the Tropical Rain Forest, rainfall increases rapidly from May to June and peaks in September, with monthly values exceeding 300 mm. The Tropical Dry Forest and the Temperate Sierras show a similar annual pattern, with a persistent and evenly distributed wet season from June to September, reaching monthly values of around 200 mm. In the Semi-arid Elevations, the wet period begins in May, peaks in July (approximately 150 mm), and declines gradually until October. The Great Plains ecoregion exhibits a wet season that begins in March, followed by a gradual increase in rainfall, sustained precipitation through July (around 100 mm), and a peak in September (approximately 150 mm). In contrast, the North American Deserts ecoregion is characterised by low rainfall throughout the year, with only a modest increase during the summer months (around 50 mm), and no clear peak. The Mediterranean California ecoregion shows a markedly different pattern, with rainfall concentrated between November and March, reaching monthly values of approximately 50 mm. Overall, the general behavior of rainfall distribution across ecoregions is consistent among the three climate normals. However, slight differences are observed in CN3, where the North American Deserts show an increase in accumulated precipitation in September, and the Great Plains show an increase in July precipitation.

This section presents the results of identifying the best empirical relationship between EI30 and the R factor calculated from three models. To achieve this, we built linear models to identify the rate of change between the EI30 factor and the R factor estimated with the three models (Fig. ). In this context, a slope of 1 indicates perfect agreement between estimated R factors and EI30 values, whereas deviations from 1:1 slope reflect fewer agreement.

Model I was the coefficient combination with the best overall performance across the three datasets, with slopes closest to 1 (1.07, 0.92, 0.83, and 0.43 for GloREDa vs. Mexico-CN3, Cortés vs. Mexico-CN1, Cortés vs. México-CN2 and for the Michoacán database, respectively) and the lower RMSE values (1524; 2438; 2628; and 4978 MJ mm ha⁻¹ h⁻¹ yr⁻¹ for GloREDa vs. Mexico-CN3, Cortés vs. Mexico-CN1, Cortés vs. México-CN2 and for the Michoacán database, respectively). Whereas, Model II obtained the poorest performance for GloREDa vs. Mexico-CN3, Cortés vs. Mexico-CN1, and Cortés vs. México-CN2 with the highest RMSE values (6176; 4088; and 4554 MJ mm ha⁻¹ h⁻¹ yr⁻¹, respectively). Model III showed intermediate RMSE values, but consistently underestimated EI30 values in all datasets (negative ME values). For the Michoacán dataset, all three models underestimated EI30, with Model I still providing the best performance (ME = -3699; RMSE = 4978 MJ mm ha⁻¹ h⁻¹ yr⁻¹), followed by Models II and III, which showed progressively larger errors.

On the other hand, the distance of each point of the GloREDa and Cortés (Mexico-CN1 and Mexico-CN2) database to the nearest weather station varied in a range of 0.6 to 42.0 km (mean: 11.6 km), 0.3 to 73.4 km (mean: 12.17 km), and 0.3 to 76.5 km (mean: 10.7), respectively. It is important to highlight that there is no correlation between error and the distances between points in the validation datasets and the weather stations of our Mexican database.

In this section, we present the results of rainfall erosivity estimates for the three climate normals considered. First, we describe the statistical distribution of erosivity values, followed by their annual distribution and, finally, their spatial distribution.

Figure  shows the mean number of locations with erosive rainfall for each day of the year for the three climate normals. In all CNs, erosive rainfall is concentrated within a single annual erosive season extending approximately from days 150 to 280, corresponding to the summer rainfall period in Mexico. For CN1, the erosive period is relatively stable, with the highest number of locations with erosive rainfall occurring between days 170 and 260. Similarly, CN2 exhibits a well-defined erosive season, although with slightly greater variability and higher peaks than CN1. In contrast, CN3 is characterised by a more pronounced intra-seasonal variability, with two distinct peaks occurring between days 173–190 and 229–261. These peaks correspond to periods when the number of locations reporting erosive rainfall exceeds the 90th percentile. Additionally, the 90th percentile threshold of the number of locations with erosive rainfall increases from 211 in CN1 to 227 in CN2 and 238 in CN3, representing increases of 7 % and 12 %, respectively, relative to CN1.

The mean values of rainfall erosivity for CN1, CN2, and CN3 were 5276 (SD 5662) MJ mm ha⁻¹ h⁻¹ yr⁻¹, 4832 (SD 5266) MJ mm ha⁻¹ h⁻¹ yr⁻¹, and 5067 (SD 5071) MJ mm ha⁻¹ h⁻¹ yr⁻¹, respectively (Table ). The statistical distribution of the rainfall erosivity values was right-skewed with skewness of 2.7, 3.0, and 2.9 for CN1, CN2, and CN3, respectively. So the median was less than the mean with values of 3245; 3070; and 3327 MJ mm ha⁻¹ h⁻¹ yr⁻¹ for CN1, CN2, and CN3, respectively. The Krustal–Wallis test showed that the erosivity median value for CN2 differed from CN1 and CN3 at a 95 % confidence level. The kurtosis values of 12.6, 15.1, and 15.3 for CN1, CN2, and CN3, respectively, indicate large tails with the presence of outliers. In this case, the outliers are high erosivity values reaching more than 12 000 MJ mm ha⁻¹ h⁻¹ yr⁻¹ for the three CNs (Fig. ).

Monthly erosivity varies throughout the year in the three CNs (Fig. a). The behavior of the erosivity in the three CNs is monomodal, indicating just one peak and one valley. The month with the highest erosivity is September, reaching values almost to 1300 MJ mm ha⁻¹ h⁻¹ yr⁻¹, followed by August, July, and June with erosivity values around 1000 MJ mm ha⁻¹ h⁻¹ yr⁻¹. It is important to highlight that for June, July, and August, the CN1 (1968–1997) had the highest monthly erosivity values; however, for September, the highest values are found in the CN2 (1988–2017). The months with the smallest erosivity values are February, followed by March with values less than 40 MJ mm ha⁻¹ h⁻¹ yr⁻¹.

As the three CNs had the same behavior throughout the year, we displayed in Fig. b the monthly erosivity for CN3 by ecoregion. The Tropical Rain Forest exhibits the highest erosivity values throughout the year, ranging from a minimum in March (114 MJ mm ha⁻¹ h⁻¹ yr⁻¹) to a maximum in September (3395 MJ mm ha⁻¹ h⁻¹ yr⁻¹). In contrast, the North American Deserts show the lowest erosivity values, generally remaining below 500 MJ mm ha⁻¹ h⁻¹ yr⁻¹. Most ecoregions reach their maximum erosivity in September; however, the Semi-arid Elevations peak earlier, in July. It is important to note that CN3 does not include stations in the Mediterranean California ecoregion. Nevertheless, in CN1 and CN2, this ecoregion shows the lowest erosivity values among all regions.

Regarding the spatial distribution, the erosivity values across Mexican territory look similar for the three CNs (Figs.  and ). Low erosivity values (<1000 MJ mm ha⁻¹ h⁻¹ yr⁻¹) are mainly concentrated in the Baja California peninsula and northern Mexico, corresponding to arid regions such as the North American Deserts and Semi-arid Elevations. Intermediate values (approximately 1600–4300 MJ mm ha⁻¹ h⁻¹ yr⁻¹) are distributed across central Mexico, reflecting transitional climatic conditions. In contrast, the highest erosivity values (>7600 MJ mm ha⁻¹ h⁻¹ yr⁻¹) are concentrated in the southern and southeastern regions of the country. These areas correspond to the upper deciles of the statistical distribution, indicating a strong spatial concentration of high erosive potential in humid tropical environments. This spatial pattern is also reflected in the mean erosivity values calculated for each ecoregion (Table ). The Tropical Rain Forest consistently exhibited the highest mean erosivity values for the three climate normals, followed by the Tropical Dry Forest, Temperate Sierras, and Great Plains. In contrast, the Mediterranean California and North American Deserts ecoregions showed the lowest mean erosivity values. Across the three climate normals, the relative hierarchy among ecoregions remained similar, with tropical and humid regions presenting substantially higher erosivity values than arid and semi-arid regions.

The spatial distribution of percentage changes in rainfall erosivity after the homogenization and gap-filling procedures was heterogeneous across the three climate normals, with positive and negative changes interspersed throughout Mexico (Fig. a for the CN3 and Fig. a for the CN1 and CN2). In all climate normals, most stations exhibited relatively small changes, generally between −5 % and 5 %. CN1 showed a slight predominance of positive changes in northern Mexico, particularly in the Baja California Peninsula and northwestern regions, whereas CN2 displayed a more balanced distribution of positive and negative changes across the country. In contrast, CN3 exhibited a greater occurrence of negative changes in northern and northwestern Mexico. Southern Mexico and the Yucatán Peninsula generally showed lower magnitudes of change across the three climate normals. Overall, the largest positive and negative changes were associated with isolated stations rather than coherent regional clusters.

The scatterplots reveal a consistent inverse relationship between the percentage change in the mean rainfall series after the homogenization and gap-filling procedures and the corresponding percentage change in rainfall erosivity across the three climate normals (Fig. b for the CN3 and Fig. b for the CN1 and CN2). The three climate normals exhibited a similar funnel-shaped distribution, in which the dispersion of erosivity changes increased progressively as the magnitude of rainfall change became larger. Stations with precipitation changes close to 0 % showed relatively small erosivity variations concentrated near zero, whereas stations with larger positive or negative rainfall changes exhibited a wider range of erosivity responses, reaching approximately ±20 %.

Table  summarizes the percentage changes in rainfall erosivity by ecoregion for the three climate normals after the homogenization and gap-filling procedures. Overall, mean percentage changes remained low across all ecoregions and climate normals, with most values below 3 %. For CN1, the largest mean positive percentage changes were observed in the North American Deserts (2.3 %) and Mediterranean California (2.1 %). In CN2, mean percentage changes were generally smaller, although the North American Deserts still exhibited the largest positive mean change (1.7 %), while the Great Plains showed a slight negative mean change (−0.6 %). Similarly, in CN3, mean percentage changes remained close to zero across ecoregions, ranging from −0.4 % in the North American Deserts and Great Plains to 0.7 % in the Tropical Dry Forest. Although the mean changes were comparatively small at the ecoregional scale, some individual stations exhibited larger positive and negative percentage changes. The maximum positive changes reached 21.2 %, 19.3 %, and 17.6 % for CN1, CN2, and CN3, respectively, whereas the minimum changes reached −18.8 %, −23.0 %, and −19.3 %. Overall, the range of percentage changes was similar among the three climate normals, with both positive and negative changes occurring within comparable magnitudes.

Improvement over the previous rainfall products in Mexico: Previous national-scale rainfall datasets for Mexico are those produced by and ; they emphasise spatial completeness through interpolation. updated the mean monthly rainfall for 100 years (1910–2009) using around 5000 rainfall time series and used thin-plate smoothing spline interpolation to generate gridded data at 30 arcsec spatial resolution for the continental area of Mexico. Similarly, developed the Mexico High Resolution Climate Database (MexHiResClimDB), a gridded dataset that provides daily, monthly, and annual rainfall for the period 1951–2020, using up to 4000 rainfall records per day. This dataset was generated using kriging with external drift on a local neighbourhood, producing gridded data at 20 arcsec spatial resolution across Mexico.

These approaches prioritize spatial completeness and provide valuable insights into the spatial distribution of climate variables across Mexico. However, previous gridded datasets either did not perform quality control or applied only basic quality control procedures , such as selecting stations with more than 80 % of recorded data for at least 10 consecutive years and discarding unrealistic values (e.g., daily rainfall exceeding 600 mm). However, climatological studies have shown that inhomogeneities in rainfall time series can introduce biases and artificial trends, potentially leading to erroneous interpretations and misleading conclusions . In consequence, guidelines recommend that rainfall data undergo a comprehensive set of quality control tests, including constraint, consistency, rapid change, and domain analysis. These procedures are essential to ensure the reliability of climatic analyses, avoid biases due to measurement or recording errors, and maintain comparability across stations and regions, particularly in long-term rainfall time series.

Therefore, although gridded datasets are important for understanding large-scale ecological processes across Mexico, generating climate data from reliable and quality-controlled time series is equally important. This represents a key strength of our rainfall dataset compared to previous efforts. By providing a robust and quality-controlled rainfall time series database, we ensure greater reliability for climate analyses that depend on the accurate representation of extreme events and temporal variability, including rainfall erosivity estimation, hydrological modeling, and climate extremes assessment.

Evaluation of empirical models for daily erosivity estimation: among the three coefficient combinations evaluated for estimating daily rainfall erosivity, the proposal consistently demonstrated superior performance across the national and local datasets. Although all three models adopt a similar functional structure of the form R=αPβ, differences in the parameterisation of the α and β coefficients have substantial implications for model behavior under diverse rainfall regimes. The equation was developed using rainfall time series across the United States of America, including rainfall conditions of the southern states such as Georgia, Mississippi, and Texas. This equation defines different α coefficients for the cool and warm seasons that occur from October to March and from April to September, respectively; it is very similar for the Mexican climate, where it is seen that the warmest months are those from May to October . Additionally, the β coefficient has no spatial or seasonal pattern, the same as found in the equation and contrary to the one, where the β coefficient is affected by the latitude in the Tropical (A) climate classification according to Köppen–Geiger. However, it is notable that the β coefficient for equation (1.81) is slightly higher than that for and (1.72 and between 1.5 and 2 depending on the latitude, respectively), placing greater weight on high rainfall amounts which may better capture the erosive potential of intense storms. Indeed, this is the reason why the model obtained the highest erosivity estimates for the Michoacán dataset (purple points always over the blue and green dots in Fig. d), because β coefficients for all the Michoacán dataset were 1.81, 1.558 and 1.72 for the three models , , and , respectively.

Limitations of the rainfall and erosivity databases: models based on coarser rainfall time series can underestimate and overestimate EI30 values, as observed in this study. Although calculated at a coarser temporal resolution, underestimations have already been indicated by while evaluating the effect of modifying the time interval for calculating EI30 using 5, 15, 30, and 60 min rainfall time series. The authors concluded that increasing the time interval leads to underestimating erosivity values. Similarly, identifies that using a monthly model underestimates EI30. However, the same author found an overestimation of the R values regarding EI30 using annual models. However, no matter under or overestimation, it has been reported that when coarser time intervals are used instead of high temporal resolution, the relationship between E and I30 remains consistent, but a larger calibration coefficient is needed . Therefore, having more detailed information is arguably the best way to estimate the erosivity factor with greater certainty and to know which model explains the greatest variance of EI30.

In this study, the best-performing coefficient combination was that proposed by . However, we did not differentiate parameter coefficients by ecoregion due to the limited availability of sites with EI30 values. In regions with high-intensity rainfall events, such as the Pacific coastal zone of Mexico, rainfall tends to exhibit greater erosivity than in regions with lower-intensity rainfall, even when total rainfall amounts are similar. Under these conditions, coefficient parameters are expected to vary across regions , reflecting differences in the erosive power of rainfall. Additionally, the choice of model and its associated coefficients constitutes an important source of uncertainty in subsequent soil loss estimation, which should be taken into account by users .

Now, we present our perspective on future directions for cost effective modeling and mapping rainfall erosivity patterns and trends across Mexico along with four main interoperability barriers: (a) transitioning into high temporal resolution and to sub hourly dynamics, (b) climate change projections and non stationarity, (c) integration with digital soil mapping and soil organic carbon sequestration models and (d) uncertainty quantification and the role of citizen science.

First, while the current database provides a robust baseline for the R factor in Mexico, future research could prioritise the integration of sub-hourly rainfall intensity data. The increasing availability of automated weather station networks and high-resolution satellite products (such as GPM-IMERG) offers a pathway to characterise soil erosivity with increased accuracy . Transitioning from daily aggregates to event-based modeling will allow for a deeper understanding of how extreme, short-duration convective storms, which are common in Mexico's complex topography, contribute disproportionately to annual soil loss.

Second, rainfall erosivity projections are commonly based on stationarity assumptions ; a critical frontier involves the incorporation of non-stationarity into erosivity mapping. As climate change alters the frequency and intensity of tropical cyclones and North American Monsoon patterns, static historical averages may become less predictive . Future modeling efforts could couple the current R factor baseline with CMIP6 climate projections to develop digital scenarios of future erosivity patterns and trends. This will be essential for designing long-term sustainable land management strategies and adapting hydraulic infrastructure to a more aggressive erosive environment.

Third, there is a significant opportunity to integrate rainfall erosivity databases with digital soil mapping frameworks to evaluate the positive and negative feedbacks between erosion and soil organic carbon dynamics . Future studies could focus on the soil carbon losses in response to soil erosion and sediment transport across different geomorphic positions . By coupling high-resolution erosivity maps with national soil property grids, researchers can better quantify the role of water erosion in carbon redistribution, moving Mexico toward a more comprehensive National Soil Monitoring System .

Fourth, future iterations of the Mexican rainfall erosivity database should focus on rigorous uncertainty quantification e.g., using Bayesian frameworks or ensemble modeling. Given the uneven distribution of primary weather stations across Mexico's complex and diverse terrain, identifying regions with high predictive uncertainty is paramount. Furthermore, the integration of “Citizen Science” and low-cost IoT (Internet of Things) recording rain gauge could serve as a useful validation tool. Engaging local communities in data collection would not only fill geographic gaps but also bridge the divide between high-level modeling and on-the-ground soil conservation practices .