# Spatio-temporal assessment of rainfall erosivity in Ecuador based on RUSLE using satellite-based high frequency GPM-IMERG precipitation data

Daniel Delgado, Mahrez Sadaoui, Wolfgang Ludwig, Williams Méndez

► To cite this version:

Daniel Delgado, Mahrez Sadaoui, Wolfgang Ludwig, Williams Méndez. Spatio-temporal assessment of rainfall erosivity in Ecuador based on RUSLE using satellite-based high frequency GPM-IMERG precipitation data. CATENA, 2022, 219, pp.106597. 10.1016/j.catena.2022.106597. hal-05109998

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Distributed under a Creative Commons Attribution 4.0 International License
1 Spatio-temporal assessment of rainfall erosivity in Ecuador based on RUSLE using satellite-

2 based high frequency GPM-IMERG precipitation data

3

4 D. Delgado<sup>a,b*</sup>, M. Sadaoui<sup>a</sup>, W. Ludwig<sup>a</sup>, W. Méndez<sup>b,c</sup>

5

6 <sup>a</sup> Centre de Formation et de Recherche sur les Environnements Méditerranéens, Université de Perpignan, Via Domitia, UMR 5110, 52 Avenue Paul Alduy, F-66860 Perpignan CEDEX, France

7 <sup>b</sup> Departamento de Construcciones Civiles, Facultad de Ciencias Matemáticas, Físicas y Químicas, Universidad Técnica de Manabí, Avenida José María Urbina, Portoviejo EC130105, Manabí, Ecuador

8 <sup>c</sup> Centro de Investigación Estudios del Medio Físico Venezolano, Instituto Pedagógico de Caracas, Universidad Pedagógica Experimental Libertador, El Paraíso 1020, Caracas, Distrito Capital, Venezuela University

12 *Corresponding author.

13 E-mail address: daniel.delgado@utm.edu.ec (D. Delgado)

14

15 ABSTRACT

16

17 Soil erosion caused by rainfall is one of the main soil degradation problems in Ecuador and has major
18 implications on conservation and management of water and soil resources, disaster control, agricultural
19 protection and other applications in the Ecuadorian territory. Extensive precipitation time series are required to
20 estimate the rainfall erosivity as a triggering element of soil erosion, however, meteorological stations
21 distribution in Ecuador is not homogeneous over the national territory (greater concentration in coastal basins)
22 and present high lack of data, generating an incorrect rainfall distribution that requires resorting to other types of
23 available information. The objective of this work was to analysis the spatio-temporal distribution of potential soil
24 erosion through rainfall erosivity in Ecuador, through an innovative method based on the Revised Universal Soil
25 Loss Equation (RUSLE) employing GPM-IMERG rainfall data. Our methodology considered the delimitation
26 and evaluation of the watersheds environmental characteristics, GPM-IMERG, GPCC and ERG-data evaluation
27 as providers of rainfall databases, and calculation of the erosive force of the rain (R-Factor) over the period
28 2001-2020. Basins delimitation and layers of environmental characteristics were obtained from regional
29 literature; GPM-IMERG and GPCC from web servers; ERG-data from INAMHI-Ecuador; R-Factor (30
30 minutes) calculation was made from GPM-IMERG parameters and its was validated with RIST software using a
31 representative subset of pixels, revealing an excellent compatibility of almost 1% average difference. New
32 information was obtained from spatial, interannual and seasonal R-Factor distribution considering environmental
33 characteristics, even though the satellite image products (GPM-IMERG) still underestimate the high values of R-
34 Factor compared to Literature. New models for Ecuador have been established to estimate the R-Factor from
35 annual rainfall, which allow it to be calculated since the beginning of the last century as well as generate
36 projections of future soil erosion. This helps territory managers to take new measures to deal with soil loss.
37

38 **Keywords:** Soil erosion, rainfall erosivity, spatial R-Factor modeling, high temporal rainfall resolution,
39 Ecuadorian drainage basins
40

41 **1. Introduction**
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43 Soil erosion is considered one of the most serious environmental crises today at a global level (Hoyos et al.,
44 2005). Soil erosion can reduce crop yields by up to 50%, being considered the number one threat to global food
45 security (Sparovek & Schnug, 2001), in addition to being responsible for generating an approximate loss of 10
46 million ha of cropland annually (Pimentel, 2006). This problem is among the main global environmental risks
47 and generates significant economic losses (Panagos et al., 2018). It is predicted that by 2050, more than 90% of
48 the soil in the world will probably deteriorate due to erosion problems (Keesstra et al., 2016). With a loss of 3000
49 tons per year, China is one of the countries that suffers from the greatest problems of soil erosion in the world
50 (Liang et al., 2020). In South America, studies related to soil loss are applied to a lesser extent in relation to the
51 other regions of the world, with only 123 methodological applications compared to 976 in Asia, 929 in Europe,
52 or 537 only in the United States of America (Borrelli et al., 2021). Especially in Ecuador, the lack of studies on
53 soil erosion is more alarming, generating misunderstanding of the consequences that this natural phenomenon
54 can cause at the national level, being limited only to certain sectors of the coast (Pacheco et. al., 2019), from the
55 southern Ecuadorian Andes (Ochoa et al., 2015) or small sectors of the Amazon (DMEVA-SNGRE, 2021).
56

56 The degree of complexity that exists in Ecuador with respect to its very peculiar climate and geography,
57 make it a much more interesting study area to analyze soil erosion in relation to other tropical countries
58 (Zehetner & Miller, 2006; Romero et al., 2007). Among its characteristics, its location stands out, which is
59 distributed in three continental regions with marked changes in relief (Coast, Sierra/Andes and Amazon), the
existence of two tropics and the equinoctial line (Pourrut, 1983; 1994). This means that the distribution of rainfall be very irregular throughout its territory, identifying only two periods, one dry and one wet (Pourrut, 1994).

Rainfall is considered the external factor triggering soil erosion (Lai et al., 2016; Tian et al., 2021) and its variation depends on its spatio-temporal distribution (Huang et al., 2013). This factor, which generates the movement of soil particles when its impact force exceeds the cohesive forces of the soil particles, is known as the R-Factor (Bryan, 2000). The R-factor, included in many soil erosion prediction models (Wischmeier & Smith 1978; Renard et al. 1997; Ochoa et al., 2015; Pacheco et. al., 2019; de Sousa et al., 2021; Aouichaty et al., 2022; Bahadur & Praveen, 2022; Ke & Zhang, 2022), is known as one of the best indicators to define the erosive potential of a storm as it combines the effects of duration, magnitude and rainfall intensity (Renard et al., 1991). R-Factor is also considered a highly reactive factor to modifications in climatic conditions and, therefore, a key element to estimate potential soil erosion changes in response to climate change (Panagos et al., 2017).

The rainfall erosivity factor along with five other factors that universally affect soil erosion are applied in the RUSLE and USLE (Universal Soil Loss Equation) mathematical models to determine soil erosion. Although the specific equations used by each method are different (Renard & Ferreira, 1993), both models refer to the same factors: 1) R-Factor (rain erosivity factor); 2) K (soil erodibility factor); 3,4) LS (topographic factor combining slope length and slope steepness); 5) C (cover-management factor); and 6) P (supporting practices factor). Among these factors, the first one requires high temporal resolution data to obtain an accurate estimate of rainfall erosivity and its robustness increases with finer in the temporal resolution data (ex. from 60 to 1 min) (Panagos et al., 2015).

However, the lack of a good and extensive rainfall database with high temporal resolution is a limiting factor for the application of a soil erosion model through the analysis of rainfall erosivity. Nowadays, the R-Factor is generally estimated using various methods adapted to the different temporal resolutions of the rainfall data. Among a long list, several studies based on sub-hourly (Padulano et al., 2021), hourly (Chang et al., 2022), daily (Alves et al., 2022), monthly (Ballabio et al., 2017), and yearly (Diodato & Bellocchi, 2010) were developed from rainfall-gauged data at different spatial scales in the world (national, regional, basin, etc.). The R-Factor estimated via these methods is generally calculated based on the time series of each gauge station. Subsequently, linear interpolation approaches will be applied to map the results in ungauged areas (Panagos et al., 2017). However, these methodologies also have disadvantages: irregular data distribution (Ballabio et al., 2017),
difficulty for continuous data (Panagos et al., 2017; Bezak et al., 2021), difficulty in accessing and obtaining data (de Mello, 2015), poor spatial coverage and non-accessible terrains (Angulo & Beguería; 2009), among others.

Alternative methods exist, very recent studies have already attempted to estimate the R-Factor at a sub-hourly temporal scale (30 min) using satellite-based rainfall products in some regions (Kim et al 2020; Bezak et al, 2021; Das et al., 2022). Nevertheless, the application of this type of method is very recent, which therefore requires other studies to be applied in other regions and to explore more deeply the different satellite-based rainfall products in the future.

Ecuador has the same restriction as other regions. The available rainfall data provided by the National Institute of Meteorology and Hydrology of Ecuador (INAMHI) has a maximum monthly time scale, a high lack of data, a scarce and irregular distribution of gauging stations (greater concentration in basins on the Andean-Pacific slope and very little presence in basins of the Andean-Amazonian slope) and restricted access to information (especially for the recent years). The use of this information can generate an overestimation or underestimation of the results generated by the rainfall erosivity, which could mask certain realities that are occurring in Ecuador based on this phenomenon. All these restrictions have allowed us to reflect deeply on the search for other types of data. We have thought of using data from Satellite Images.

Technology advances, and currently, there are three main methods to measure precipitation: rainfall gauges, weather radars and satellite sensors. Spatialized precipitation data products have existed since a long time, such as, Climatic Research Unit (CRU), Global Precipitation Climatology Centre (GPCC) and WorldClim, among other. This makes it possible to obtain precipitation products with a long recording period and with very high spatial or temporal resolution, such as, TerraClimate, Rainfall Estimates from Rain Gauge and Satellite Observations Version 2 (CHIRPSv2) and/or Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks - Climate Data Record (PERSIANN-CDR).

Recently, engineers and researchers have been able to develop very powerful algorithms which allow to combine the different types of precipitation data, which makes it possible to produce precipitation products at a finer temporal resolution.

Currently, there are two products, Climate Prediction Center with Morphing Technique (CMORPH) and Global Precipitation Measurement with the Integrated Multi-satellite Retrievals (GPM-IMERG), with sub-hourly time resolution, around 10 km of spatial resolution, with information available for more than two decades, free access and coverage of almost the entire world. GPM-IMERG database has been applied and validated in different regions of the world, from Europe (Navarro et al., 2019; Tapiador et al., 2020; Kazamias et
al., 2022), Asia (Kim et al., 2017; Hosseini-Moghari & Tang, 2020; Das et al., 2022), Africa (Lawal et al., 2021), Oceania (Islam & Cartwright, 2020) and even in South America (Rozante et al., 2018; Almagro et al., 2021; Rojas et al., 2021).

Among the conclusions obtained through the application of these measurements were obtained: underestimation in high areas and overestimation in low areas at the European level, good precision in special rainfall patterns in Asia, minimum seasonal variability in relation to other databases in Africa, better rainfall database in Australia-Oceania, display of the spatial pattern of orographic precipitation in various regions of South America, among others. These conclusions, together with the free access to information, the availability of homogeneous data, and its application in any region, make it an ideal database to be applied in Ecuador, although certain technical limitations must also be considered, caused by the lack of vertical or horizontal resolution, atmospheric effects, scaling processes (truncation or rounding of satellite image properties by increasing or decreasing the scale), among others.

The main objective of this study is to propose a new approach to estimate rainfall erosivity in Ecuadorian basins, both for the Ecuadorian Coastal Basins (ECB) that flow into the Pacific Ocean, and for the Amazonian Tributary Basins (ATB) that flow into the Amazon.

The approach needs to: collect environmental and rainfall data from Ecuadorian basins; homogenize the projection (WGS84-UTM zone 17S) and resolution (4km x 4km) of data; compare the GMP-IMERG product with GPCC database and Ecuadorian Rain Gauge data (ERG-data); calculate and validate the R-Factor; obtain the distribution of rainfall and R-Factor along with its other subfactors at different time scales (monthly and annual) and space (per pixel and per basin) and; establish precipitation classes with intervals of 500 mm together with the median of R-Factor values generated in each range, to generate two new models (ECBs and ATBs) that allow estimating the R-Factor from annual precipitation data available in any database.

Among the major results of this work is the possibility of modeling the R-Factor from the past (since 1900) and testing scenarios in the future from precipitation data, and, therefore, will have an impact on better estimates for soil loss, getting a better planning of the Ecuadorian territory in terms of the generation of measures aimed at stop or reduce the effects generated by the loss of soil due to the erodibility of rain, whose methodology can be replicated in other sectors worldwide.

## 2. Materials and methods
## 2.1. Ecuadorian drainage basin characteristics

The study area spans within the latitudes of 5.04°S - 1.48°N and longitudes of 81.03°W - 75.16°W, covering most of the Ecuadorian territory (Fig. 1) which is delimited to the North with Colombia, to the South and East with Peru and to the West with the Pacific Ocean. Continental Ecuador is in the northeast of South America and is crossed by the Equinoctial Line, dividing it into two hemispheres, North and South. Its capital is Quito, located in the Andes region of the country. It presents different climates, varied geography, and a great concentration of rivers per each square kilometer. These characteristics place it as one of the countries with the greatest biodiversity in the world (Batlle, 2020).

According to the basin delineation procedure determined in the study of Delgado et al. (2021), the entire Ecuadorian basin can be divided into 32 basins. It should be noted that in this procedure the basins have been delineated from an aggregated DEM at 4 km of resolution using the modules of GRASS GIS software based on the multiple flow direction algorithm (MFD, Holmgren, 1994). Only the basins with areas greater than 500 km² have been considered. This condition was applied to eliminate the basins that contain few pixels, considering the use of several databases in the present investigation, which have an approximate spatial resolution between 10 km and 25 km (e.g., there would only be a maximum of 5 pixels for the GPM-IMERG product based on 10 km in basins <500 km²). Even after resolutions have been homogenized to 4 km, the correct presentation of small basins (<500 km²) remains difficult, which can lead to errors.

The area of each basin varies from 542 km² (Id 11 in Fig. 1, Ayampe basin in Supplementary material 1) to 38000 km² (Id 31 Fig. 1, Napo basin in Supplementary material 1) and the totality covers more than 227000 km² which is equivalent to 80% of the Ecuadorian area (Fig. 1).

Among all selected basins, 24 basins locate on the left side of the Andes Mountain and are named ECBs. Among these later, 21 directly discharge into the Pacific Ocean within the Ecuadorian territory (basins in yellow, Fig.1). The other 3 basins also discharge into the Pacific Ocean, but outside to the Ecuadorian territory (basins in pink, Fig. 1). On the right side of the Andes Mountain, 8 basins have been delineated and correspond to the Amazonian territory and are named ATBs (basins in green, Fig. 1).

Within the Ecuadorian coast, there are two basins that stand out for their size, representing approximately 24% of the study area and correspond to the Guayas (Id 12 in Fig. 1, 32103 km²) and Esmeraldas basin (Id 4 in Fig. 1, 21103 km²), respectively. The basins that discharge into the Pacific Ocean in territory outside of Ecuador are relatively small, representing approximately 8% of the study area and of which two ends in Peru (to the
south) and one in Colombia (to the north). The 8 basins of the Amazon territory represent more than half of the study area, with approximately 54% of the total area. The largest basin in the study area corresponds to Napo (Id 11 in Fig. 1, Supplementary material 1), with approximately 17% of the total area, which represents more than 38000 km².

<figure><img src="image_2.png" /><figcaption>Fig. 1. Location map of the studied river basins (32 basins, areas >500 km²) in the Ecuadorian territory. The ECBs (in yellow and pink colors) and ATBs (in green color) located, respectively, on the left and right side of the Andes Mountain. The numeration shows the Id of each basin.</figcaption></figure>

Morphology, lithology, and land cover/land use characteristics of the Ecuadorian basins have been processed and extracted in the study of Delgado et al. (2021) from a series of global data sets. Native spatial resolutions of the considered data sets are variable and were consequently transformed (upscaling/ downscaling) into a common 4 km grid point resolution.

Through the analysis of the hypsometric characteristics, the presence of the Andes Mountains generates a varied distribution of slopes and altitudes, being also a dividing barrier between the coast and the east. The basins closest to the Andes Mountain begin with average heights above 2000 m (Fig. 2a), both for ECBs and ATBs. The range of average elevations per basin is between 2200 m (Id 1 in Fig. 2a) and 60 m (Id 15 in Fig. 2a), while the range of elevations per pixels is between more than 5000 m in the Andes and less of 1 m in the
197 discharge areas of the ECBs to the Pacific Ocean. The ATBs have higher elevation, averaging 1048 m compared to the 722 m average elevation of the ECBs.
198

199 The land cover in the Ecuadorian basins (Fig. 2b) was classified in 13 types distributed in 3 main groups: 200 closed forests, open forests and others. Through this analysis, it was determined that 84% of the study area is 201 covered with forests, of which 60% correspond to closed forests (a continuous set of trees that represent more than 40% of the area) and 14% correspond to open forests (set of discontinuous trees representing between 10% and 40% of the area). The presence of forests such as land cover is more noticeable in the ATBs, where 4 of its 8 202 basins (Id 27, 29, 30 and 32 in Fig. 2b) are made up of 100% closed forests. Within the analysis of the land cover 203 "other", the subclassifications of herbaceous vegetation and cropland are the main ones, representing 59% and 204 21% of this group, respectively. Herbaceous vegetation predominates in the vicinity of the Andes Mountain, 205 while cropland is concentrated in a higher percentage within the Taura and Guayas ECBs (Id 17 and 12, Fig. 2b), 206 representing 39% and 28% of their areas, respectively. 207

209 The lithological classification (Fig. 2c) covered 13 groups of rock types. Within this analysis, it was 210 determined that the sedimentary rocks in general cover more than 70% of the study area and are distributed in a 211 higher percentage in the ATBs. 30% of the remaining area presented a more varied lithological outcrop, where 212 the 12 required lithological classes coexist. This varied distribution is more noticeable in the Andes Mountain 213 and its surroundings, due to the presence of volcanoes.
213
<figure><img src="image_3.png" /><figcaption>Fig. 2. Map show the spatial environmental characteristics in the Ecuadorian basins. (a) Topography; (b) Land cover classification and (c) Lithology classification. The data has already been processed and published in Delgado et al. (2021) in order to evaluate some conditioning factors in soil erosion and present contributions for the construction of a spatial model.</figcaption></figure>

## 2.2. Precipitation data collection

### 2.2.1. GPM-IMERG Version 6B-Final

GPM is an international network of satellites initiated by the National Aeronautics and Space Administration (NASA) and Japan Aerospace Exploration Agency (JAXA) programs dedicated to rainfall measurement (rain and snowfall). As a global successor to Tropical Rainfall Measuring Mission (TRMM), GPM has been strengthened by other international space agencies, such as: the Centre National d'Études Spatiales (CNES), the National Oceanic and Atmospheric Administration (NOAA), and others. The GPM concept integrates the deployment of a Core Observatory satellite carrying an advanced radar / radiometer system to measure precipitation from space. GPM freely distributes a wide range of products and brings a valuable contribution to
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improve the knowledge around the earth's water cycle and its link to climate change, the agricultural crop
forecasting and monitoring of freshwater resources, the forecasting of extreme events that cause natural hazards
and disasters, and the forecasting abilities for natural hazards, including floods, droughts and landslides (GPM
Website: https://gpm.nasa.gov/).

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GPM-IMERG is the combined product from the processing chain consisting in the intercalibration, fusion
and interpolation of all satellite microwave precipitation estimates. The data are combined together with
microwave-calibrated infrared (IR) satellite estimates and precipitation gauge analyses using the 2017 version of
the Goddard Profiling Algorithm (GPROF2017) to produce a quasi-global (60°S-60°N) homogeneous
precipitation measurement. The actual product from this algorithm is the IMERG Version 6B Level 3, covering
the period from June 2000 to present. The data are available at several temporal resolution (30 minutes, 3 hours,
1 day and 1 month) and gridded into 0.1° × 0.1° (roughly 10x10 km) fields (Huffman et al., 2019).

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IMERG has three types of products, first giving a quick estimate in quasi-near-real-time (IMERG Early Run,
minimum latency: 4 hours) gridded only from a global multi-satellite precipitation estimate, and successively
providing better estimates as more data arrive (IMERG Late Run, minimum latency: 12 hours) gridded from
global multi-satellite precipitation estimates with quasi-Lagrangian time interpolation. The last step produced the
final version, named “IMERG Final Run” and released 3.5 months later uses monthly gauge data to create
research-level products (Huffman et al., 2019).

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In the present study, the IMERG Version 6B-Final data were used and the "precipitationCal" variable
(primary unit: mm/hr), calibrated with gauge stations, was chosen. The data in "NetCDF" format with a temporal
resolution of 30 minutes were downloaded only for our study area from GES DISC server link, located at the
GPM website (https://gpm.nasa.gov/). The OpeNDAP service of GES DISC was used from the "Subset/Get
Data" interface to better configure the data download. It allows to generate file links supporting geo-spatial
search and crop and selection of variables, dimensions and formats. At the end, this service generates a list of
links and the data can be downloaded automatically using terminal-wget interface and some code lines. Our
download date range extends from 2000-06-01 00H:00MM to 2020-12-31 23H:30MM, one day contains 48
layers which corresponds to a download of 360864 layers over our study period.

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The data were subsequently processed under R, the layers were converted to the classic format (.tif), then re-
projected from WGS84 to the local coordinate system (WGS84-UTM zone 17S) and finally these layers were
downscalled from 10 km to 4 km of spatial resolution. The primary unit of layers have been presented in mm/hr
units and were subsequently divided into two seasonal half-year layers to prepare them for the calculation of R-

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Factor at step of 30 minutes (see 2.4 below). Thereafter, the monthly and annually cumulative precipitation has been calculated at the pixel scale and averaged for each basin in order to compare the values with the GPCC and ERG-data (Fig. 3 and Fig. 4) on the one hand and for analysis of their variability in Ecuadorian basins on the other hand.

## 2.2.2. GPCC

GPCC provide high-quality gauge-based gridded precipitations datasets over the global land surface for monitoring and research of the Earth's climate. It has been established in 1989 on request of the World Meteorological Organization (WMO) as German contribution to the World Climate Research Programme (WCRP) and the Global Climate Observing System (GCOS). The database consists of a large amount of daily and monthly data derived from a conventional precipitation gauge (~ 85000) around the world such as national meteorological and hydrological services, global and regional data collections (Schneider et al., 2021).

All gridded GPCC analysis products are freely available in Deutscher Wetterdienst, National Meteorological Service of Germany (DWD) via internet (http://gpcc.dwd.de). Depending on the product, it can be provided at different spatial resolutions (2.5°, 1.0°, 0.5° and 0.25°) and with maximum time coverage (from 1891 to present) (Schneider et al., 2021).

Two of the gridded products released by GPCC are “Monitoring V2020” (quality-controlled data: 7000-9000 stations; spatial resolution: 1.0°, 2.5°; time coverage: 1982 - 2019) and “Full Data Monthly V 2020” (quality-controlled data: all stations; spatial resolution: 0.25°, 0.5°, 1.0°, 2.5°; time coverage: 1891 – 2019). They provide monthly data and serve as bias correction for IMERG Final Run (Huffman et al., 2019).

For this study, we downloaded these two versions in "NetCDF" format. The first product "Full Data Monthly V 2020" has been downloaded at 0.25° of spatial resolution for the majority of time ranges in our study (2000-2019). The second product has been downloaded at 1.0° of spatial resolution "Monitoring V2020" only for the year 2020. We then applied the same processing steps under R as with our GPM-IMERG database in order to homogenize these two products (4 km of spatial resolution). The data were stacked in chronological order to produce a single product over the period of our study (June 2000 - December 2020). Thereafter, the monthly and annually cumulative precipitation are calculated at the pixel scale and averaged for each basin in order to compare the values with the GPM-IMERG product (Fig. 3).

## 2.2.3. Ecuadorian Rain Gauge data (ERG-data)
INAMHI is the entity of Ecuador in charge of generating and disseminating hydrometeorological information throughout the country through on-site observations composed of monthly data obtained from all meteorological stations in Ecuador since 1965. Raw data were obtained from 103 meteorological stations for the period 1965-2019, which were analyzed and evaluated in detail to determine their quality. To begin with this data evaluation process, firstly, we decided to select only the stations that have a maximum of 30% missing data. Based on this condition, the time range is reduced to 1985-2015 and only 52 stations (41 corresponding to ECB and 11 to ATB) fulfilled our data quality standards.

Thereafter, this database had undergone the following additional processing: (1) stations sharing homogeneous climatic zones were identified according to the criteria of Bourrel et al. (2014). The principle is that these stations should have the same rainfall regime and annual rainfall should be pseudo-proportional; (2) Under the previous criterion, correlations were performed over the period 1985-2015 using Pearson's Correlation Coefficient (r) between model stations and stations to be completed. Only the stations that had a correlation index greater than or equal 0.70 were chosen; (3) For the stations that did not meet the minimum correlation index, it was decided to extend their selection range (stations between different regions) and to accept a correlation index between 0.70 and 0.54, but only for stations that had percentages of missing data less than 2%; (4) In the case of the stations that still did not meet the established conditions, correlation has been tested on sub-samples which correspond to shorter period (10 years) and accepting a minimum r coefficient of 0.7; (5) The stations that did not comply with any of the previously established conditions or that were located outside the limits of the study area (2 stations), were not considered suitable to be incorporated into the research, and, therefore, it is not recommended to complete their data.

The result of this processing allows us to have a final database in monthly resolution containing 46 gauging stations over the period 1985-2015. In total, 9% of data of this time series were filled by linear regression. 4 stations are complete and have no data infill and only 18 stations had a maximum of 5% data infill. For the rest of the stations, the percentage of data filling does not exceed 30%. Later, the multilevel B-Spline spatial interpolation method (Lee et al., 1997) was applied to create continuous data over the Ecuadorian basin with missing information from adjacent gauging stations. This allows to establish a precipitation raster stack with a spatial resolution of 4km where each layer presents monthly values. This database is then used to compare and validate the data of GPM-IMERG product over the joint period 2001 – 2015.

2.3. Evaluation of the GPM-IMERG product
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We subsequently evaluated the performance of the GPM-IMERG product at daily temporal resolution (mm/day) from the two databases GPCC and ERG-data using both statistical and graphical methods (section 3.1). Two standard comparison metrics were used: the Pearson correlations coefficient (PCC) and the Root Mean Squared Error (RMSE). The equation of each metric is shown below:

$$PCC = \frac{cov(P^{GPM-IMERG},P^{GPCCVERG})}{\sqrt{var(P^{GPM-IMERG})\sqrt{var(P^{GPCCVERG})}}} \quad (1)$$

$$RMSE = \sqrt{\frac{1}{N} \sum_{i=1}^{n} (Y_{iGPM} - Y_{iGPCCVERG})^2} \quad (2)$$

Where $P^{GPM-IMERG}$ and $P^{GPCC}$ are the rainfall obtained from satellite estimates and gridded climatologies, and $P^{ERG}$ the rainfall obtained through the rain gauges (ERG-data); $n$ is the number in the data set and $Y_i$ is the average daily precipitation for each method. Using equation 1, the level of linear agreement between the satellite estimates and the grid point/ rain gauge data was analyzed and, with equation 2, the typical magnitude of the error product of the satellite readings (GPM-IMERG and GPCC) was evaluated in terms of discrepancies (GPCC) and the possibility of rain gauge outliers (ERG).

## 2.4. RUSLE R-factor calculation

RUSLE is the most frequently used soil loss estimation model which has been used in many regions in the world. Rainfall is one of the main drivers of soil erosion. The erosive force of rainfall is expressed as rainfall erosivity (R-Factor). In this study the original R-Factor equation was applied to create a raster stack of rainfall erosivity database in the Ecuadorian basins.

The R-Factor is the product of kinetic energy of a rainfall event (E) and its maximum 30-min intensity (I30) (Wischmeier and Smith, 1978):

$$R = \frac{1}{n} \sum_{j=1}^{n} \sum_{k=1}^{m} (EI_{30})_{k} \quad (3)$$
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Where R is the average annual rainfall erosivity (MJ mm ha⁻¹ h⁻¹ yr⁻¹), E is the total storm kinetic energy (MJ ha⁻¹), I₃₀ is the maximum rainfall intensity in 30 min (mm h⁻¹), k is the index of number of storms in each year, mj is the number of erosive events of a given year j, m is the number of storms in each year, j is the index of the number of year used for average and n is the number of years covered by the data records.

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The rainfall erosivity index of a single event k, EI30 (MJ mm ha⁻¹ h⁻¹), is defined as:

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$$EI_{30} = \left( \sum_{r=1}^{0} e_r v_r \right) I_{30} \qquad (4)$$

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Where e_r is the unit rainfall energy (MJ ha⁻¹mm⁻¹), v_r is the rainfall volume (mm) during a time period r and I₃₀ is the maximum rainfall intensity in a 30 min period during the event (mm h⁻¹). Equation 4 was also used to estimate rainfall energy (E) as an environmental factor derived from the R-Factor. In this case, rainfall intensity (I₃₀) was not considered as a term in the equation.

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The unit rainfall energy (e_r) is calculated for each time interval as:

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$$e_r = 0.29[1 - 0.72\exp(-0.05i_r)] \qquad (5)$$

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Where i_r is the rainfall intensity during the time interval (mm h⁻¹).

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The R-Factor equation is based primarily on identifying the erosive rainfall events for each pixel. In general, rainfall events are discretized from continuous records using standardized criteria, such as the one proposed by Renard et al. (1997). This criterion identifies 2 possible events: 1) when the accumulated precipitation of an event is greater than 12.70 mm; 2) when the event accumulates a peak greater than 6.35 mm in less than 30 minutes. It is not considered an event when the rainfall accumulation is less than 1.27 mm during a period of 6 hours, dividing a long storm period into two storms. In conclusion, rainfall thresholds of 12.70 mm are defined as events that have erosive potential (Renard et al., 1997). These criteria have been widely applied in many investigations worldwide (Panagos et al., 2015; Kim et al., 2020; Matthews et al., 2022).

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For the present investigation, 3 conditions were established: 1) erosive event, generated when the rainfall accumulation is greater than 12.70 mm; 2) non-erosive event, generated when the rainfall accumulation is greater
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than 1.27 mm but less than 12.70 mm and 3) no event, generated when the rainfall accumulation for 6 hours is less than 1.27 mm (Fig. 3).

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<figure><img src="image_4.png" /><figcaption>Fig. 3. Figure shows the identification of erosive rainfall events in 48 hours</figcaption></figure>

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Based on these considerations, two R-Factor values were obtained: 1) R-Factor, calculated using non-erosive events ($1.27 < \text{accumulated rainfall} < 12.70 \text{ mm}$) and 2) R-Factor$_{erosive-event}$ calculated by using the erosive events only ($\text{accumulated rainfall} > 12.70 \text{ mm}$).

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R-Factor has been calculated under R Software at the 4 km pixel scale on the basis of the precipitation layers at 30 min temporal resolution during the period from June 2000 to December 2020. The primary unit of each precipitation layer is mm/h and the layers were consequently divided by 2 in order to obtain layers in mm/30 minutes.

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First, a routine has been generated in R Software to calculate R-Factor from spatialized data at a temporal resolution of 30min. This routine correctly explains and calculates the R-Factor and its subfactors from equation 3 for the time series of each pixel. It is capable to process, at the same time, approximately 60,000 time series (number of pixels of the surface of our study area).

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On a seasonal scale, we calculated the R-Factor month by month. The precipitation input data contains: 1488, 1440, 1392 or 1344 layers, depending on the number of days in each month (31, 30, 29 and 28 days respectively, 48 layers per day).

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At the annual scale, we first calculated the R-Factor on a semester basis (from January to June and from July to December) and then determined the annual value by addition of the two semesters. It should be noted that to calculate the R-Factor for a complete annual series based on a step of 30 min requires importing and processing

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at the same time 17,520 layers of precipitation. Applying our routine to such a large number of data layers holds the risk of facing memory allocation problems with standard PCs. Working on more powerful computers and/ or with more suitable programming languages would be necessary to overcome these problems. However, our routine efficiently calculates the R-Factor for a six-month time series based on a time step of 30 min, which requires the simultaneous treatment of 8,688 (semester 1) and 8,832 (semester 2) input layers. The only inconvenient of our method is that for a given calendar year, an event which starts in June and ends in July might not be properly accounted for. But it should be noticed that calculating R-Factor on a complete annual series or on two complete six-month series has only minimal impacts on our results (see section 3.1.2). Moreover, it should be kept in mind that also R-Factor calculations on complete annual series are not perfect since they cannot properly account for events which stretch over two calendar years neither.

The output data from our R code are the results of the R-Factor on a monthly scale and by semester and were classified into 11 output factors: EI30 all events (MJ mm/ha h), EI30 erosive events (MJ mm/ha h), EI30 percentage (%), accumulated precipitation (p30cum in mm), energy (MJ/ha), maximum rainfall intensity during a 30-min period (I30 mean in mm/h), erosivity density (MJ/ha h; equation 6) (Hijmans et al., 2005), number of events in month (N°), number of erosive events in month (N°), number of erosive events percentage (%) and, duration of erosive events (hours). These results were subsequently aggregated on an annual scale and over the study period for the spatio-temporal analysis (to better understand the definition of each factor and the aggregation method see also section 3.3.2.).

Where ED is erosive density, R is the average annual rainfall erosivity (MJ mm ha⁻¹ h⁻¹ yr⁻¹) and P is the average annual rainfall (mm yr⁻¹)

## 2.5. Comparison with standard RIST software

Rainfall Intensity Summarization Tool (RIST) is a software designed by the U.S. Department of Agriculture (USDA) for the Windows Platform. It facilitates the analysis of rainfall records in general and is available at the following link: https://www.ars.usda.gov/southeast-area/oxford-ms/national-sedimentation-laboratory/watershed-physical-processes-research/research/rist/rist-rainfall-intensity-summarization-tool/.

$$ED = R/P \qquad (6)$$
Among its benefits is the possibility of calculating the original R-Factor with a temporal resolution of 5, 10, 15, 30 and 60 minutes. RIST performs calculations from a data table time series of a single station. As our data is spatialized, it is not possible to directly apply this software to our study region. However, when selecting representative subset data samples, the RIST software can be used for validation of our R-routine for the calculation of R-Factor. To do this, four time series from four pixels were extracted, equally distributed between the ECBs and ATBs. The choice of these stations is based on the location (downstream, mountain) and the intensity of precipitation (low, medium and high) in order to determine a correct comparison and validation of results.

The methodological scheme used in the present investigation can be seen in Fig. 4.

<figure><img src="image_5.png" /></figure>

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Fig. 4. Diagram showing a methodological overview applied in this study to process the different databases used and to evaluate the R-Factor.

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## 3. Results

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3.1. *Intercomparison of precipitation data sets*

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In this section, the mean annual precipitation from GPM-IMERG is compared both with GPCC and ERG-data. Figure 5 shows a comparison of the annual average rainfall classified in mm/day between GPM-IMERG and GPCC over the period 2001-2020.

By the means of both figures (Figs. 5a, b), it can be observed that the greatest amount of rainfall occurs in the Amazon basins, especially in the Conocoto-Curaray (Id 30 in Fig. 5) and Napo (Id 31 in Fig. 5) basins. The driest regions of the country are concentrated in the areas of the basins closest to the Pacific Ocean, starting in the province of Manabí (Coast) and ending in the province of Loja (Andes). The decrease in rainfall in this region of the country is accentuated from North to South.

Compared to GPCC, the GPM-IMERG values are slightly higher in coastal basins and slightly lower in the Amazon basins (Fig. 5c).

In addition, the RMSE parameter allows to demonstrate that GPM-IMERG correctly reproduces the rainfall in several regions of the Ecuadorian basin. The average RMSE is 1.18 mm/day (Fig. 5d). The closest values were observed in the Southwest of the Ecuadorian basin with an initial RMSE of 0.21 mm/day, while the greatest variation in rainfall was generated in some part of the Amazon region which has high values of RMSE, especially in the basin of the Napo River (Id 31 in Fig. 5), with a maximum value of 4.98 mm/day.

Regarding the pixel-wise Pearson's R correlation coefficient (Fig. 5e), a very good correlation index is observed between GPM-IMERG and GPCC in much of the Ecuadorian territory. In contrast, the lowest and insignificant (pixels bordered in white) correlations are concentrated in much of the central region of Ecuador, the sector through which the Andes Mountains cross. Despite the lower presence of GPCC gauging stations in the Amazon basins and high RMSE values produced in some areas (Figs. 5b, d), correlations in this region are generally good between the two databases. In contrast, despite the large number of GPCC stations in the vicinity of the Andes Mountains, a low correlation is observed. Additional information is also shown in the scatter plot of Fig. 5f. Despite the strong correlation (R²=0.85), however, some details can be noticed. GPM-IMERG overestimates low values of annual mean precipitation and underestimates high values.

In general, GPM-IMERG shows better correlations with GPCC on land with low elevations corroborated by high values of PCC and low values of RMSE. In the high regions, the highest values of RMSE exist and correlation indexes are low. This might be related to insignificant measurements in complex areas with limited
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access. The Amazon basin represents high correlation despite high values of RMSE. This area is the rainiest region over the Ecuadorian basin and GPM-IMERG values were underestimated comparing to GPCC.

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Several factors can influence the quality of the two precipitation data sets. Both have different spatial resolutions (0.1° for GPM-IMERG vs 0.25° for GPCC V8 and 1° for GPCC V6) in their original forms, which naturally can affect interoperability. Moreover, frequency, recording time, errors in the station data (including their correct locations) are the major factors that can impact the data quality in databases like GPCC, especially in mountainous regions like the Andes. The quality of satellite-based precipitation estimates as GPM-IMERG depend to a great extent on the visibility of the territory (frequently cloudy) and the type of surface that is generally affected in very irregular terrain, such as the Andes Mountain. This represents a source of error for rainfall estimates using any type of methodology, especially for rainfall estimates from passive microwave (PMW).

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<figure><img src="image_6.png" /></figure>

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<caption>Fig. 5. Comparison of the spatial distribution of annual mean precipitation in the Ecuadorian basin based on mm/day unit over the period 2001 – 2020 from (a) GPM-IMERG, (b) GPCC (gauge station number has been added), c) Difference map between GPM-IMERG and GPCC, (d) Spatial distribution of GPM-IMERG -GPCC Root Mean Squared Error (RMSE), (e) PCC map between GPM-IMERG and GPCC, pixels bordered in white</caption>

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represent insignificant correlations (p-values >0.1), (f) GPM-IMERG - GPCC scatterplot colored by density (bins=100) comparing the annual mean precipitation at pixel scale. The black line is identity line (1:1 line).

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Figure 6 shows the comparison of precipitation in mm/day between the GPM-IMERG and ERG-data during the period between 2001 and 2015. Figure 6a shows the GPM-IMERG mean daily precipitations and the Fig. 6b shows, at the same time, the distribution of mean daily precipitations of ERG-data. In both cases, the maps are based on linear interpolation (in a spatial resolution of 4 km) of the 46 data points which correspond to the ERG-data gauging stations (for correct representation of the GPM-IMERG data set, see Fig. 5a).

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It can be seen that the limited data points does not allow a correct interpolation of GPM-IMERG rainfall, especially in areas where rainfall is greater than 11 mm/day (ATBs and northwestern ECBs). That is, by the means of the GPM-IMERG method restricted to 46 study points, the maximum precipitation obtained is 8.79 mm/day, located in the ATBs region, while the lowest rainfall drops to 1.47 mm/day in the ECBs oriented to the Southwest of Ecuador, in areas near the Pacific Ocean. In contrast, by the means of the ERG-data method, the gauging station interpolation generates higher rainfall compared to the GPM-IMERG method. Maximum rainfall is 13.10 mm/day in ATBs and areas of northwestern Ecuador, while minimum rainfall decreases to 0.91 mm/day in large parts of the Andes Mountains and several areas near the Pacific Ocean. These differences between precipitations can also be observed in Fig. 6c.

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Figure 6d shows both the PCC and RMSE values for the 46 gauging stations of the ERG-data and of the 46 pixels of GPM-IMERG which correspond to same locations. Among these stations, 8 have insignificant PCC (p-value > 0.1). Generally, strong correlations (to green color) and low values of RMSE (to circles with small sizes) are found in the lower regions. The mountainous region shows moderately weak correlations with a strong RMSE (Fig. 6d). The scatter plot also demonstrates that GPM-IMERG underestimates for these locations low precipitation values and overestimates high values. As the number of stations considered in the ERG-data database is reduced, correlation is only weak (PCC = 0.64 with R² = 0.42), but the average value of RMSE remains acceptable (2.04 mm/day) (Fig. 6d). Additional information is shown in the scatter plot of Fig. 6e.

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In general, GPM-IMERG produces similar patterns than the GPCC or ERG-data, even if in the latter data set the number of stations and the comparison period are reduced. It has to be kept in mind, of course, that it is possible that GPCC already includes ERG-data stations.
<figure><img src="image_32.png" /></figure>

Fig. 6. Comparison of the spatial distribution of annual mean precipitation in the Ecuadorian basin based on mm/day unit over the period 2001–2015 from GPM-IMERG (a) and ERG-data from linear interpolation (46 gauges stations have been added) (b). PCC and RMSE map between GPM-IMERG and ERG-data for the 46 stations, the white dots in the center of some stations represent insignificant correlations (p-values> 0.1) (c). Difference map between GPM-IMERG and ERG-data from linear interpolation (d), GPM-IMERG - ERG-data scatter plot for 46 gauges stations and colored by density (bins=2) comparing the annual mean precipitation at pixel scale. The black line is identity line (1:1 line) (e).

Figure 7 shows the comparison of the annual mean precipitation values by drainage basins. GPM-IMERG is compared to GPCC in Fig. 7a and GPM-IMERG to ERG-data in Fig. 7b. By an analysis of Fig. 7a it is shown that the mean values of rainfall by basins between both methods show a strong positive correlation (R²= 0.96), which corresponds to a good quality fit of the model, despite the presence of fewer gauging stations in GPCC. Also, the average RMSE value (0.62 mm/day) is satisfactory. Through this model, maximum dispersion per basin of less than 1 mm / day is observed in relation to the identity line. This is indicating that, by means of the
analysis by basin, a much stronger correlation exists compared to the correlation shown in Fig. 5f, which considers the same values and study periods, but on a pixel scale analysis.

On the contrary, by analyzing Fig. 7b, it can be determined that the positive correlation between GPM-IMERG and ERG-data on the drainage basin scale is lower ($R^2$= 0.71) in relation to what is shown in Fig. 7a. This behavior is the result of the small number of gauging stations used in the ERG-data method (only 46 stations) that were interpolated to obtain a national precipitation layer. The lack of stations is more noticeable in the ATBs, which is the main causes of the dispersion in the data. Despite these limitations, the RMSE value (1.30 mm/day) is still acceptable. This model presented maximum dispersion per basin of more than 2 mm/day (double that shown in Fig. 7a) in relation to the identity line. Nevertheless, a better correlation also exists by the means of an analysis on the drainage basin scale in relation to what is shown in Fig. 6e (pixel-scale analysis).

<figure><img src="image_33.png" /><figcaption>Fig. 7. Scatter plots for 32 Ecuadorian basins comparing the annual mean precipitation based on mm/day unit over the period 2001–2020 from GPM-IMERG - GPCC (a), and 2001-2015 from GPM-IMERG - ERG-data (b). The black line is identity line (1:1 line).</figcaption></figure>

## 3.2. Spatial variability of mean annual and seasonal GPM-IMERG precipitation

The analysis in section 3.1 demonstrated that GPM-IMERG allows a more reliable and accurate picture of precipitation over Ecuador. Figure 5a summarizes the mean annual rainfall from GPM-IMERG over the period 2001-2020, distributed in mm/year. It can be observed that the highest rainfall is concentrated in the ATBs and basins of the Ecuadorian northwest and evidence increasing rainfall patterns from the W to the E and from the S to N. These spatial variations, especially in the Amazon region, highlight the role of the Andes Mountain as an
orographic barrier in the transport of precipitation, thus underlining the unique climate of Ecuador. At the same time, it can be seen how the equatorial line also conditions rainfall, generating its increase in the ECBs that are located within the Northern Hemisphere (Fig. 1, upper part of Ecuador country).

Per-pixel analysis reveals that annual rainfall ranges from 445 mm in ECBs to 3696 mm in ATBs (Fig. 8a). When annual rainfall by basin is considered, it should be noticed that the ECB Zapotal (Id 14 in Fig 8b) is the one with the lowest annual average with 637 mm/year. The basin with the highest average annual rainfall corresponds to the ATB Conocoto-Curaray (Id 30 in Fig. 8b), with 3427 mm/year (more than 500% higher than the ECB Zapotal).

On average, 71% of the rainfall corresponds to ATBs and only 29% to ECBs. The cumulative values are much higher in ATBs than in ECBs, while the total area of ATBs is only slightly higher (see section 2.1).

In general, the mean rainfall in Ecuador according to GPM-IMERG is 1403 mm/year. Only on 3 occasions notable variations from this average could be observed (year 2012, 1805 mm/year; year 2017, 1797 mm/year and year 2020, 1103 mm/year).

<figure><img src="image_34.png" /><figcaption>Fig. 8. Map shows the annual and seasonal variability of GPM-IMERG precipitation in the Ecuadorian basins over the period 2001-2020. (a) Spatial distribution of GPM-IMERG mean annual precipitation. (b) Histogram</figcaption></figure>
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shows GPM-IMERG mean annual precipitation for each basin. Box plot (c) and (d) present the distribution of monthly rainfall in ECBs and ATBs, respectively.

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It is also interesting to analyze the seasonal precipitation variability. Due to the difficulty of defining the periods of the two seasons (wet and dry) for the ECBs and the ATBs, this variability is analyzed on a monthly scale for the period 2000 - 2020 (Fig. 8c and 8d).

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Through these considerations, for the analysis of the ECBs (Fig. 8), the median of the data determined that the period with the greatest presence of rains begins in December and ends in May (6 months), identifying this period as "wet season". For this reason, the dry season occurs during the months of June to November (6 months). In the ECBs, the average rainfall during the wet season was 148 mm/month while the average in dry season was only 31 mm/month (almost 80% less rainfall in relation to the wet season).

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Within the ECBs, the highest monthly mean precipitation (Fig. 8c) was recorded in March with 226 mm/month, while the lowest rainfall was recorded in August with 19 mm/month. When analyzing the monthly rainfall by basins, the highest rainfall (307 mm/month) is recorded in April in the ECB Cayapas (Id 2 in Fig. 8) that is located in the northwest of the country, close to Colombian territory. The lowest rainfall was recorded in November (2 mm/month) in the ECB Guayas (Id 12 in Fig. 8).

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Using the median data in ATBs (Fig. 8d), it is not easy to identify a clear seasonal pattern, i.e. dry and wet seasons. The amounts of rainfall are high throughout the year. According to the months with the highest rainfall, the wet season is a long-lasting season, it starts in October and ends in July (10 months). Only the months of August and September (2 months) might be considered as "dry season". The average rainfall during the wet season is 200 mm/month while the average rainfall for the dry season is 135 mm/month (almost 33% less than in the wet season).

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Within the ATBs, the highest monthly mean precipitation (Fig. 8d) is recorded in March (250 mm/month), and the lowest rainfall in August (130 mm/month). Through an analysis by drainage basin, it can be noticed that the highest precipitation is generated in June (340 mm/month) in the ATB Napo (Id 31 in Fig. 8), while the lowest precipitation occurs in August (16 mm/month) in the ATB Moyo (Id 25 in Fig. 8).

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According to our analysis, the highest rainfall in the ECBs is concentrated in the North, on the western and windward side of the Andes Mountain. On the coastal border, rainfall is lowest in the ECBs and inside the country due to the influence of the SE Pacific anticyclone and the outcrop of cold water from the Humboldt current in the austral winter (Bendix et. al., 2006). Increasing rains begin at the end of November and the

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599 beginning of December, when the Intertropical Convergence Zone begins its movement towards the south,
600 reaching its maximum intensities between March and April (Campozano et. al, 2016). The lowest rains occur at
601 the end of July and mid-September, due to the displacement of the Intertropical Convergence Zone towards the
602 North and the intensified Walker circulation that produces low advective clouds and that, with the occurrence of
603 the El Niño phenomenon, are generated extraordinary disturbances (Campozano et. al, 2016).
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604 ATBs have a more uniform and humid climate, characterized by high temperatures and the distribution of
605 rainfall is remarkably high and regular throughout the year. Here also the continuous vegetation cycle controls
606 the constant occurrence of rainfall (Makarieva et al., 2013). However, a small increase in rainfall is observed
607 from west to east with small irregularities due to local reliefs.
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609 3.3. Validation of the pixel scale R-Routine for R-Factor calculation

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611 Fig. 9a shows the distribution of the pixels chosen for the validation of our R-Factor values (section 2.4) in
612 comparison with the results obtained by using the RIST software (section 2.5). In Fig. 9b the annual rainfall at
613 the study points is depicted, clearly showing that in the ATBs the amounts of rainfall are much higher than in
614 ECBs. In Figs. 9c, d, e and f; R.1M, R.6M and R.A are the results of the R-Factor which was calculated from the
615 R routine developed in this study at three different time resolutions: monthly, half-yearly and annual,
616 respectively. However, RIST. A is the R-Factor calculated via the RIST software at an annual time resolution.
617 By analyzing the factors R. 1M, R. 6M and R. A independently of the pixel, it can be noticed that there is a great
618 similarity in the results, which shows the weak influence of erosive events which overlap the temporal units
619 (especially between R. 6M and R. A, 1 the cut event is very insignificant). In addition, regardless of the
620 difference in the intensity of rainfall (weak, medium, strong) and in the locality (downstream, mountain) of the 4
621 pixels, the annual R-Factor results are very similar between R. A and RIST. A (the difference is only 1,004%). By
622 the means of this analysis, it can be concluded that our R-routine correctly calculates the R-Factor equation of
623 the RUSLE model. It is robust and reliable, providing adequate results to meet the objectives of this work.
623
<figure><img src="image_65.png" /><figcaption>Fig. 9 shows the 4 pixels for annual validation of GMP-IMERG R-Factor with RIST (a) and its precipitations (b) and the values of R-Factor applying each method for the pixel 1 (c), 2 (d), 3 (e) and 4 (f).</figcaption></figure>

### 3.4. Spatial distribution of mean annual GPM-IMERG rainfall erosivity

In this section we present the main results of the mean annual R-Factor and derived factors analysis calculated from GPM-IMERG on the basis of equation 3 and covering the period 2001-2020.

#### 3.4.1. RUSLE R-factor in Ecuadorian basins

Through the long-term EI30 analysis (equation 3) that produces the R-Factor via consideration of rainfall erosive events (Fig. 10), it should be noticed that the distribution of its maximum values is skewed to the east and almost exclusively concentrated on ATBs, with an average of over 4200 MJ mm/ha h. Small pixels with high R-Factor values are also observed in the north of the country, close to Colombia, with values per pixel that exceed 8000 MJ mm/ha h (Id 1 in Fig 10a).

The highest per pixel values exceed 11000 MJ mm/ha h and are located in the ATB Conocoto-Curaray (Id 30 in Fig 10a). The lowest values decreased to almost 300 MJ mm/ha h and are restricted to 8 basins (7 are located
in southwestern Ecuador), both in ATBs and in ECBs (Id 18, 19, 21, 23, 24, 25, 26, 28 in Fig. 10a). When considering the average values by basins (Supplementary material 2) reveals that the ATBs Conocoto-Curaray and Putumayo (Id 30 and 32) are the basins that register the highest R-Factor with 6800 MJ mm/ha and 5900 MJ mm/ha h respectively. Within the ECBs, the Cayapas (Id 2 in Supplementary material 2) shows the highest average R-Factor with 2,600 MJ mm/ha h. The lowest values in ECBs are found in the Puyango (Id 23 in Supplementary material 2) with 475 MJ mm/ha h. In ATBs, Moyo (Id 25 in Supplementary material 2) which shows the lowest value (620 MJ mm/h).

Analyzing Fig. 10b, it can be confirmed that R-Factor<sub>erosive-events</sub> represents the dominant part within the R-Factor. Other information is also shown in histograms (Fig. 10c and d).

<figure><img src="image_66.png" /><figcaption>Fig. 10. Annual spatial distribution of R-Factor<sub>erosive-events</sub> (a) and its proportion to R-Factor (b) in Ecuadorian basin over the period 2001-2020. (c) and (d) presents both the average value per basin for the factors of Fig. a and Fig. b, respectively (x-axis present the Id of our basins).</figcaption></figure>

### 3.4.2. Subfactors of R-Factor

Soil erosion is a mechanical process that requires energy. Much of this energy comes from raindrops that fall on the ground (Wischmeier et. Al., 1958). Rainfall intensity can be measured directly, but measurement of the
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energy and size of raindrops is seldom available. For this reason, it is necessary to relate the intensity of the rainfall with the generation of energy (Nyssen et. al, 2005).

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For this study, the Fig. 11a and Fig. 11b shown the annual Energy (E) caused by rain and the annual maximum rainfall intensity (I30) during a 30-min period of the rainfall, respectively. All values are averaged over the period 2001-2020. The monthly E presents the cumulative energy of all erosive events for one month and the annual E is calculated by the sum of the energy of two semesters. The monthly I30 and annual I30 present the average I30 of all erosive events of one month and one year, respectively.

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Fig. 11. Map shows the annual spatial distribution of subfactors when applying the original RUSLE equation in the Ecuadorian basins averaged over the period 2001-2020. The sub figures present the annual E (a), annual maximum rainfall intensity (I30) during a 30-min period of the rainfall (b), rainfall erosive event number (c), percentage of the rainfall erosive event number (d), duration of erosive event in hours (e) and, erosive density (f).

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When analyzing the E distribution together with I30 (Fig. 12a and 12b), it can be observed that its generation does not exclusively depend on I30, but it is a very important conditioning factor. Most of the ECBs generate E values less than 200 MJ/ha, despite the fact that in some of them, I30 are very similar to those generated within the ATBs (e.g., Muisne and Napo basins, Id 5 and 31, Fig. 12b). On the other hand, within ATBs, the registered E are much higher compared to ECBs (in some cases higher than 400 MJ/ha) and also present a pattern proportional to their I30.

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<caption>Fig. 12. Histograms show the same factors of Fig. 11 averaged by basins. The sub figures present the E (a), I30 (b), number of rainfall erosive event (c) and percentage (d), erosive event duration (e) and erosive density (f).</caption>

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The x-axis label of each figure presents the Id of our basins.

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A total of 6660 rainfall events were registered within the study period (2001-2020). The ATB Morona (Id. 27, Supplementary material 2) registered the highest number of events (269), while the ECB Daule (Id 15, Supplementary material 2), registered the lowest number of rainfall events (143). Out of the total recorded events, 993 events fulfilled the condition of erosive events (15%) (Fig. 11c, Supplementary material 2), reaching a total duration of 1379 days (Fig. 11e, Supplementary material 2). Within the ECBs, less than 12% of the rainfall events were considered erosive. In the ATBs, more than 22% of the events met this condition (Figs. 11d, 12c and d).

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If E is analyzed (Fig. 11a and Fig. 12a) with the number of erosive events (Fig. 11c and Fig. 12c), it can be observed that, while there is a greater number of erosive events, a greater amount of E is generated, especially for ECBs located closer to the ocean.

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For the rainfall erosive event number/130 ratio (Figs. 11c and 11b), in the Amazon region, which mainly represents the area formed by ATBs, the high number of recorded erosive events generated high rainfall intensities. As in the basins located in the southwest of Ecuador, a direct relationship was identified between these two variables, because they registered few amounts of erosive events that generated low rainfall intensities. However, in central Ecuador, located in the coastal and northwestern region of the country (Id 10, 11, 13, 14 and 16 in Fig. 11), despite an average of almost 160 events, very low rainfall intensities were generated where the percentage of erosive events is even less than 10% (Supplementary material 2).

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When analyzing Fig.11c and Fig.11e, it can be observed that for both ECBs and ATBs, a greater number of hours in the duration of the event also corresponds to a greater number of events. However, in specific cases, such as in the Id 7, 8 and 9 basins, a low number of hours represents a greater number of erosive events. This means that the 12.7 mm of accumulated rainfall that are required to be considered as erosive events are formed in less time compared to other areas of the country. Here, precipitation regimes are characterized by greater intensities and shorter duration.

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To analyze the erosive density (Fig. 11f), the R-Factor (Fig. 10a) and the mean annual precipitation (Fig. 8a) must be considered, which ranged between 299-11789 MJ mm/ha h and 445-3696 mm respectively. The most important erosive density values were concentrated in various portions of 4 ATBs (Id 28, 29, 30, 31). They reach maximum values per pixel of 3.21 MJ/ha hr and an average per basin of 1.79 MJ/ha hr (Supplementary material 2). The areas with less erosive density are located mainly within the Andes region and within a large part of the southwestern part of the country, where the lowest values of the R-Factor were recorded together with the lowest rainfall values. In much of the central-coast and north-coast region, the erosive density values had a range per pixel between 1-2 MJ/ha hr and an average value per basin of 1.17 MJ/ha hr.

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The erosive density showed a mean value per pixel of 1.31 MJ/ha hr, with a high variability ranging from 0.33 MJ/ha hr to 3.21 MJ/ha hr. This high variability shows that, despite registering a proportional relationship with precipitation, it is not possible to calculate the R-Factor exclusively on precipitation values (Panagos et. Al., 2015). However, in section 4.3 we show the results of the R-Factor estimates obtained by means of two empirical equations (for ECBs and ATBs) resulting from the correlation between the GPM-IMERG precipitation data and the R-Factor data obtained by the traditional methodology (equation 3). Erosive density and erosive event duration values by basins can also be observed in Figs. 12e and f.

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## 3.5. Mean seasonal and spatial distribution of R-Factor and its subfactors
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Within the Ecuadorian basins, the distribution of rainfall (Fig. 8c and d) shows a direct impact on the seasonal distribution of E (Figs. 13c and d) and R-Factor generation (Figs. 13a and b). The maximum mean values for the ECBs are recorded in March, with 260 MJ mm/ha h (R-Factor, Fig. 13a) and 23 MJ/ha (E, Fig. 13c). In ATBs, they were registered in June, with 530 MJ mm/ha h (R-Factor, Fig. 13b) and 35 MJ/ha (E, Fig. 13d). In both groups, this corresponds hence to the wet season. When comparing the distribution of the values between ECBs and ATBs for both the R-Factor and E factors, very significant differences can be observed with respect to the monthly patterns. As a common and very general trend, it can be noticed that the record of the lowest values occurs in August, which corresponds to the dry season for both groups of basins.

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When analyzing the two remaining factors, I30 (Figs. 13e and f) and erosive density (Figs. 13g and h), similar trends can be observed within each group of basins. Within the ECBs, the values follow a decreasing trend from January to August, followed by a more irregular increase from September to December. The maximum mean values for the ECBs were recorded in January, with 12 mm/h (I30, Fig. 13e) and 1.6 MJ/ha h (erosive density, Fig. 13g). The minimum mean values were recorded in August with 3 mm/h (I30, Fig. 13e) and 0.2 MJ/ha h (erosive density, Fig. 13g). In the case of ATBs, there is no clear trend in the monthly distribution; the maximum mean values observed for both factors were recorded in June, with 15 mm/h (I30, Fig. 13f) and 1.9 MJ/ha (erosive density, Fig. 13h), while the minimum mean values were recorded in September, with 11 mm/h (I30, Fig. 13f) and 1.4 MJ/ha h (erosive density, Fig. 13h). Within the ECBs, the values of I30 and erosive density still show higher results in the wet season (Fig. 8c), but they do not follow the same distribution than rainfall, contrary to what is observed for the R-Factor and E factors. For the ATBs, the values approach the patterns which are recorded in Fig. 8d, but they do not agree for the two months of the dry season. The data recorded in August (dry season) are even higher than those recorded between October and December (wet season months). When comparing the values between ECBs and ATBs, significant differences are observed in their distributions that confirms the large differences in the general climate conditions of both groups. As a common trend, it can be retained that high average values (not maximum values) occur in January.
<figure><img src="image_74.png" /><figcaption>Fig. 13. Box plots of seasonal variability of GPM-IMERG precipitation in the Ecuadorian basins over the period June 2000 - December 2020. Erosive R-Factor distribution in ECBs (a) and ATBs (b), E in ECBs (c) and ATBs (d), I30 during a 30-min period of the rainfall in ECBs (e) and ATBs (f), Erosive density in ECBs (g) and ATBs (h).</figcaption></figure>

### 3.6. Inter-annual variability of rainfall erosivity (case study based)

After the seasonal analysis, the inter-annual variability of the R-Factor was evaluated. For this case, two basins from two different regions were chosen considering their representativeness for the contrasting sectors in our study area and their territorial size extensions (Fig. 14a). The ECB Guayas (Id 12 in Fig. 14a) is the most
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important fluvial system of the southwestern Pacific coast (Tapia, 2012) and has a warm climate with a marked dry and wet season.

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The ATB Napo (Id 31 in Fig. 14a) is in the region with the greatest hydrographic wealth in the country and is the largest basin of Ecuador (Supplementary Material 1) and has a very hot and humid climate throughout the year (Pourrut, 1944).

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When observing the inter-annual evolution of rainfall (Fig. 14b), in both basins, it can be concluded that in the ATB Napo a more regular trend is maintained with small decreasing trends during the study time, while in the ECB Guayas, the values have remained more dynamic, which is also reflected in a higher rainfall gradient for this basin in comparison to Napo. As it has been stated in the previous sections, higher rainfall occurs in the ATB (Napo), about twice the value compared to the ECB (Guayas). The wettest years were 2012 for the ECB Guayas (1951 mm/year) and 2007 for the ATB Napo (3173 mm/year). In both cases, 2020 registered one of the lowest amounts of rainfall, the year that can be considered as one of the driest years within the study period.

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Through the analysis of Fig. 14c (R-Factor), it is observed that the distribution in both basins is very similar to the distribution of rainfall. For this reason, it can be expected that the highest values of rainfall erosivity should be recorded in 2007 and 2012, for the ATB and ECB respectively. But this is only true for the ATB Napo, where in 2007 the highest R-Factor value exceeded 6600 MJ mm/ha h. On the contrary, in the ECB Guayas the highest R-Factor was recorded in 2002 with more than 3300 MJ mm/ha h. This year had 21% less rainfall in relation to 2012. Likewise, and according to the magnitudes of rainfall, the lowest R-Factor were recorded for both basins in 2020, with 700 MJ mm/ha h (Guayas) and 2800 MJ mm/ha h (Napo).

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When analyzing Fig. 14d (duration of erosive events in hours), it is observed that the differential gap between both basins presents a slight average decrease of more than 10% compared to rainfall, and that, despite the climatological differences in both basins, the peak hours of erosive events that occurred in ECB Guayas in 2017 (1627 hours) have values very similar to those produced in the peak of the ATB Napo in 2011 (1807 hours, only 11% more). Through an analysis with Fig. 14e (number of erosive events), it is shown that, in the ECB Guayas, fewer erosive events generated a greater number of hours, which means that the intensity of rainfall in this basin is much greater than in the ATB Napo (greater precipitation in less time), a situation that comprises a greater risk of flooding (Diodato et al., 2011).

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Figure 14f (erosive density) shows that the values between both basins are very similar, with an average difference of less than 20%. This is true even for the highest values in the ECB Guayas, with 2.44 MJ/ha h (2002) compared to the 2.37 MJ/ha h (2007) recorded in the ATB Napo. This indicates that, in the ECB Guayas,

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as higher values have been generated in the peak of erosive density recorded with precipitation of almost 50% than that registered in the ATB Napo in that same year (2002). The risk of erosion in this basin might therefore be much greater.

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<figure><img src="image_108.png" /><figcaption>Fig. 14. Figure shows inter-annual variability in the ECB Guayas and ATB Napo (a) corresponding to GPM-IMERG precipitation (b), R-Factor values (c), erosive event duration (d) and number (e), and erosive density (f) over the period June 2000 – December 2020. The colors that represent each basin are defined in Fig. a.</figcaption></figure>

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# 4. Discussion

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## 4.1. Comparison of R-Factor from GPM-IMERG with other literature estimates

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In this section the results we obtained with our method for R-Factor based on the GPM-IMERG and the other precipitation data sets used in this study are compared with results obtained by other methods and literature data sources (Fig. 15).
Generally, the GPM-IMERG R-Factor (Delgado et al.) showed a correct spatial variability compared to the two cases of the analyzed literature, but the values were underestimated in some regions where high amounts of precipitation were recorded.

<figure><img src="image_120.png" /><figcaption>Fig. 15. Figure (a) shows difference map between Delgado et al. (GPM-IMERG) – Panagos et al. (2017) R-Factor at daily scale. Figure (b) shows Box plots of R-Factor values to compare R-Factor values with Delgado et al. (GPM-IMERG) and data obtained from Panagos et al. (2017). Figure (c) compares different R-Factor estimations with data from Delgado et al. (GPM-IMERG), Panagos et al. (2017) and Pacheco et al. (2019) for the 8 stations used in the latter study (d).</figcaption></figure>

It is known that satellite images underestimate strong precipitation events and many investigations worldwide corroborate this (Kim et al 2020; Bezak et al, 2021). Das et al. (2022) in the analysis of the R-Factor at a national-scale in India, indicate that the values calculated using satellite data through GPM-IMERG and CMORPH show slightly lower erosivity values in relation to the values of the existing literature in places that receive very low or very high rainfall. For our investigation, comparing the R-Factor of Delgado et al. with the results of Panagos et al. (2017) (Figs. 15a and b) at national-scale in Ecuador, our general results strongly underestimate the values of this literature, especially in the ECBs (Fig. 15a), where the maximum value
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difference reaches -48 MJ mm/ha h per day (in the northwestern) and the average difference is -14 MJ mm/ha h per day (both higher in the available literature).

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Within the ATBs (Fig. 15a), the underestimates tend to decrease, registering a maximum difference of -34 MJ mm/ha h per day (in the south) and an average value of -9 MJ mm/ha h per day (both higher in the R-Factor from Panagos et al., 2017).

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This marked difference between the results is a consequence of the lack of observation stations in Ecuador and the conditions that were established for the interpolation of the literature data. The GloREDa values (Panagos et al., 2017) were obtained from the processing of rainfall data from 3625 stations in 63 countries around the world. No station from Ecuador was included (nearest stations located in Colombia and Brazil, more than 650 km and 1600 km away, respectively). All data for the Ecuadorian territory have been obtained through interpolations applying the Gaussian process regression model (GPR).

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It is possible that the ATBs have presented more approximate values because some stations in the Amazon region of Brazil are included in GloREDa (climatic conditions more similar to the Amazon region of Ecuador, better representation of values through interpolations).

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Figure 15c shows the comparison of our results with other literature estimates, but this time restricted to 8 study points (Fig. 15d) which represent the gauging stations studied by Pacheco et al. (2019) for the province of Manabi on the Ecuadorian coast (initially there are 9 stations, but one station is outside our study area). The results of Pacheco et al. (2019) also present a large overestimation of the average R-Factor values compared to our research, even higher than the ones presented by Panagos et al. (2017). Among the causes of these differences, the use of the INHAMI rainfall database (ERG-data used to calculate the R-Factor), which in addition to presenting a great lack of monthly information, the little information available is characterized by low quality (Erazo et al., 2018). Much of the station database used by Pacheco et al. (2017) were completed using other incomplete databases. On the other hand, the difference could also be the result of the Colombian methodology used by Pacheco et al. (2019). Here the R-Factor is calculated using the Modified Fournier Index (MFI) for the subsequent application of the USLE equation, which is different from the RUSLE (and our) method.

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Therefore, the values of the R-Factor presented by GloREDa (Panagos et al., 2017) and Pacheco et al. (2019), showed a great overestimation of the rainfall erosivity in the Ecuadorian basins that does not reflect the true reality of the country, which can generate erroneous predictions that bring with them problems of greater magnitude. The values of our study should be more in line with the reality of the Ecuadorian basins because they

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are based on information that is more representative of the study area and do not refer to interpolations from other countries or to the use of incomplete and low-quality databases.

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Regarding the sources of uncertainty, the comparison between databases with different spatial resolutions, data recording length, data quality and calibration efforts and correct station locations can affect the GPCC and ERG-data databases. Having only 46 stations suitable for the study of ERG-data (Fig. 6b), and most of which were located within the ECBs, made the comparative processes between methods less meaningful (Fig. 6e, Fig. 7b). The low spatial resolution of GPCC, the combination of two data versions and the smaller distribution of stations within the Ecuadorian territory also caused potential biases in the comparative processes with respect to GPM-IMERG data (Figs. 5d, e and f, Fig. 7a). As for GPM-IMERG, as it is a database with satellite-based precipitation estimates, its quality depends on the visibility of the terrain, and a large part of the Andes region is frequently cloudy. Also, the surface conditions can affect the data quality, and irregular terrains, especially in the Andes Mountains, can represent a considerable error in the measurement of rainfall. For these reasons, the GMP-IMERG values overestimated the low values of mean annual precipitation and underestimated the high values. In addition, several studies recommend a minimum data collection period of 22 years (Verstraeten et al., 2006; Wischmeier & Smith, 1978) which in the case of GPM-IMERG is at the limit of this required limited length. Another limitation is the few literatures available on soil erosion within the Ecuadorian territory, which does not allow more precise comparisons and calibrations of factors with more regional data. The spatial extension of our work together with the important processing capacities it required made it impossible to select a finer spatial resolution (4 km). The uncertainties and their effects analyzed in this paragraph are not considered detrimentally relevant in the application of the model on a national-scale, but it is recommended to implement improvements in future investigations, applying regional studies that arise and that allow better approximations in the future. It is important for INHAMI to improve the data collection methodology and facilitate unrestricted access to existing information (ERG-data) for research institutions in order to generate even more representative results for the Ecuadorian territory that can be used in environmental programs.

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Among its applications, the values obtained for rainfall erosivity by the means of the R-Factor values we calculated are essential for the estimation of the soil loss by erosion through fully application of the RUSLE equation. Among other uses and due to the serious problems in relation to flooding that Ecuador can affect and the lack of rains that periodically occur (Cadier et al., 1994), especially on the Ecuadorian coast, where strong rainfall intensities were recorded in very short periods, it will allow, through the joint application of spatial rainfall climatologies, to generate flood prevention systems, also identifying the areas that are most susceptible

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to highly erosive events that can accelerate the risk of flash floods. The R-Factor could also be applied to determine the erosive potential caused by livestock and crops, which in some areas (such as ECBs Guayas and Taura) are widely practiced activities, also allowing the generation of prevention measures to counteract their harmful effects, such as a crop type rotation plan. The R-Factor has application in geotechnics and geology, to evaluate the susceptibility of land displacements that are not only generated by topographic and seismic conditions (Macias et al., 2021), but also by climatic conditions. Therefore, the importance of knowing the R-Factor is very relevant within many environmental fields and can be used in the prediction of future climate scenarios.

## 4.2. Spatial variability of R-Factor compared to the variability of other environmental characteristics

Fig. 16a show the results of the R-Factor variability analysis compared to the variability of other environmental parameters (elevation, land cover and lithology). It can be noticed (Fig. 16 (a1)) that the elevation class of 300-600m is the class that generates the highest R-Factor values, with an average of almost 6000 MJ mm/ha h and maximum values of almost 12000 MJ mm/ha h. At high elevations (>1600m), the rainfall erosivity index is lower (mean values <1500 MJ mm/ha h) despite having considerable slopes.

From Fig. 16 (a2), forest area accumulates the highest R-Factor values (almost 3000 MJ mm/ha h of average value). This vegetation type has a protection effect that might counteract the erosive effects of rainfall erosion (Arifeen & Chaudhry, 1998). Forest covers more than 80% of the study area and is especially concentrated in the Amazon region, a sector where the highest rainfall intensities are recorded. This implies that, since this type of coverage does not exist in most of the Ecuadorian basins, a given rainfall erosivity index could provoke more erosion in ECBs than in ATBs. On the other hand, when analyzing the remaining 3 classes, it is observed that the mean values of R-Factor are below 1500 MJ mm/ha h. These land use types cover only small areas and are obviously not exposed to elevated R-Factor values. It should be noted that, even though Crop has a very low coverage area, is associated a much higher average R-Factor in relation to Grass, Urban and Water, because this type of coverage is detrimental for soil erosion (Brunel & Seguel, 2011), and would pose major problems in the ECB Guayas (Id 12 in Fig. 2b).

Analyzing Fig. 16 (a3), it is identified that the Sedimentary Rock class is the one that is associated with the highest R-Factor values in the study basins (almost 4500 MJ mm/ha h of mean value). This rock type covers more than 70% of the Ecuadorian territory. It can be composed of sediments (sand, gravel, pebbles, others) with
a low degree of compaction and therefore might be prone to greater erosion rates (Ball et al., 1997). On the other hand, Metamorphic Rocks is the rock type that presented the lowest average R-Factor (less than 1,300 MJ mm/ha h). This rock type can be found in the foothills of the Andes Mountains in ATBs and is not very abundant in the study region. It is expected to better protect soils from surface erosion.

By analyzing Fig. 16a, R-Factor is unequally distributed over the different environmental factors which are supposed to control soil erosion. The highest mean values are often associated with intermediate to higher elevations. This underlines the need for a joint evaluation of these factors together with the values presented in the Supplementary material 2 for a more efficient evaluation of soil erosion potentials.

<figure><img src="image_121.png" /><figcaption>Fig. 16. Figure (a) shows box plots of R-Factor values by analyzing the environmental parameters cross-values with elevation (a1), land cover (a2) and lithology (a3). The x-axis label of each figure presents the classification for each category. Figure (b) shows the principal Soil Erosion conditioning factors per region (basins IDs are shown only in affected areas).</figcaption></figure>

In a first order and more qualitative approach, Fig. 16b identifies the areas of the Ecuadorian basins that are prone to soil erosion through the cross-study of environmental parameters together with the R-Factor values we produced. Zone 1 considers the terrains which can be derived from the crossing between the maximum values of the R-Factor (>5200 MJ mm/ha h), high slopes >0.5 ° and a lithology made up of sedimentary rocks in an area
927 clearly composed of a forest-type coverage without the presence of cropland. Zone 2 considers the most 928 prominent values of cropland-type soil cover, lithologies composed of sedimentary rocks, R-Factor values 929 between 1500-3382 MJ mm/ha h and slope <0.5°. Zone 3 considers areas with high slopes (>2°), grass-type land 930 cover, R-Factor between 1500-3237 MJ mm/ha h in a region with the lithological presence of volcanic and 931 plutonic rocks, without the presence of sedimentary rocks. Zone 1 hence represents an enhanced soil erosion risk 932 because of the high rainfall erosivity, zone 2 because of missing soil protection in relation to land use, and zone 3 933 because of the steepness of terrains. 934

934 It can be seen from Fig. 16b that the areas with the greatest rainfall erosion possibilities (zone 1) are in the 935 Amazon region. Despite the fact that they are mostly covered by forest (a coverage that generates fewer erosion 936 problems), it is in an area with the continuous presence of significant rainfall that impacts on a soil with 937 lithological presence of sedimentary rocks, which could increase the magnitude of erosive problems. In zone 2, 938 mainly corresponding to coastal region, the areas most prone to soil erosion are in regions where land cover is 939 cropland type, an activity that generates soil degradation, causing a higher rate of erosion, in addition to having 940 also lithologies which are prone to soil erosion (sedimentary rocks), but with low slopes. On the other hand, zone 941 3, the Andes region, presents its greatest erosion possibilities in areas with highest slopes, composed of a grass- 942 type land cover, which could generate an intermediate impact on soil erosion, and with lithologies which are 943 more protective to erosion (volcanic and plutonic rocks). This zone probably causes erosion phenomenon which 944 might be a little less significant among the 3 zones, due to its better land cover and lithological composition. 945

945 The presence of sedimentary rocks in zone 1, a coverage composed mainly of cropland in zone 2 and the 946 presence of high slopes in zone 3 are the parameters with the highest incidence in combination with elevated R- 947 Factor values. These zones could be subjected to serious soil erosion problems. Of course, our results only 948 supply qualitative indicators for this hypothesis, and further research is needed to confirm this, either by fully 949 application by RUSLE including its additional parameters or by conducting field measurements on soil erosion 950 processes. 951

952 **4.3. A new relationship for estimating the R-Factor from annual precipitation in the Ecuadorian basins** 953

954 In this section, we present the relationship between mean R-Factor annual and mean annual precipitation 955 from GPM-IMERG. 956
To better refine the model and better predict the modeled values, we have opted to establish the rating curve from the medians of each precipitation class. This method has already been applied for the modeling of suspended particulate matter fluxes from water discharge in the coastal rivers of the Gulf of Lion - France (Sadaoui et al., 2016).

The purpose of this method is to provide two first generic models (due to the high climatic variability existing between ECBs and ATBs) to calculate the R-Factor from precipitation data of low annual resolution over a long period in the Ecuadorian basins, using databases such as CRU or GPCC since 1901 (Fig. 17d). This can be helpful, for example, to study trends in past and future projections.

<figure><img src="image_122.png" /><figcaption>Fig. 17. Scatterplot of ECBs (a) and ATBs (b) models to calculate R-Factor from low resolution data precipitation. Figure (c) shows R-Factor GPM-IMERG obs (calculated with original RUSLE equation) – R-Factor GPM-IMERG model (calculated with models) scatterplot colored by density (bins=300) comparing the R-Factor at pixel scale (black line is identity line, 1:1 line). Figure (d) shows Box plots of R-Factor values to compare R-Factor values with GPCC data precipitation (1901-2020), GPM-IMERG obs (2001-2020), GPM-IMERG mod (2001-2020) and ERG-data (2001-2015) (the red square represents the validation of the research period).</figcaption></figure>
For the ECBs (Fig. 17a), the model was based on 8 precipitation classes, in a range of 0-4000 mm in 500 mm intervals. A degree two polynomial relationship was identified due to the best statistical approximations obtained (R²= 0.99 and p.value=99.99%) and is shown in equation 7.

$$y = 0.0004x^2 + 0.3618x + 156.73) \quad (7)$$

For the ATBs (Fig. 17b), the model needed 9 precipitation classes (unlike the ECBs, the initial precipitation in this group of basins exceeds 800 mm), in a range of 500-3800 mm. For this model, intervals of 500 mm up to 3500 mm of precipitation were considered. For precipitation >3500 mm, it was necessary to establish finer class intervals to improve the model and its statistical approximations (R²=0.99 and p.value=99.95%) through an exponential relationship (equation 8).

$$y = 187.94096 * \exp(0.00111x) \quad (8)$$

For both models (equations 7 and 8), y is the annual R-Factor in MJ mm/ha h and x is the annual GPM-IMERG precipitation in mm. The equation 7 and 8 allows us to calculate the appropriate R-Factor value only based on annual precipitation.

Important differences between the two groups of basins also affected their models. The ECBs were based on a polynomial relationship of order two while the ATBs on an exponential relationship. Rainfall difference influenced the number of classes established in each group of basins for model generation. ATBs needed further class refinement for high rainfall (>3500 mm) to improve the model. Comparing the two models (Figs. 17a and b), it can be verified that the high rainfall values (3600 mm) generate approximately 6000 MJ mm/ha h in the ECBs, while in the ATBs, the same rainfall value (3600 mm) generates approximately 9800 MJ mm/ha h, that is, 61% more than the ECBs. The rainfall energy required for soil erodibility is different between ECBs and ATBs, which probably depends on the intensity of the rainfall event.

To evaluate the benefits of the generated models, Fig. 17c shows the comparison of the R-Factor values obtained by means of the classic RUSLE equation (equation 3) with those obtained by applying the models shown in Figs. 17a and b using the GPM-IMERG database between 2001-2020. Excellent results were obtained that are supported by a coefficient R²=0.94 and an RMSE= 683 MJ mm/ha h, which represent an excellent
correlation and a very low squared error considering that the maximum values of the R-Factor even exceed 12000 MJ mm/ha h.

In Fig. 17d (red box), in the period 2001-2020, we compared and validated the R-factor values of the model calculated from 3 different precipitation products (except ERG-data that was calculated during the period 2001-2015 because data after 2015 were not considered) with the R-Factor obs (Delgado et al.). The results are generally very similar (both the mean and the median), except for their extreme values. In GPCC and ERG-data, higher values can be recorded, due to the underestimation of the GPM-IMERG product in the precipitation values.

A reconstruction of the R-Factor was also carried out during the previous century (1901-2000) using the GPCC values (Fig. 17d), where the results continue to be very similar both in the mean and in the median, with decreases in their extremes values unlike what is observed in the red box of Fig. 17d. For this procedure, the precipitation data from GPCC V2020 were downloaded, allowing us to verify the benefits of our models with information available from the year 1901 to the year 2000 (in 20-year intervals). This models also allows us to generate R-factor projections into the future.

Additionally, these two models are easy to apply and allow generating a general idea of soil erosion through rainfall erosivity without using a complex calculation such as the original RUSLE R-Factor equation.

## 5. Conclusions

The spatial and temporal (monthly and annual) variation of rainfall erosivity at a national-scale in Ecuador was evaluated for the first time. The spatial distribution of precipitation, modeled with information from the GPM-IMERG database, and the average rainfall erosivity, calculated using the RUSLE R-Factor, showed great variability among the Ecuadorian basins considered in this work. This was very noticeable and contrasting, particularly in the ATBs, due to the peculiar meteorological dynamics at a synoptic scale, typical of intertropical latitudes, which determines the climatic types (thermal and pluviometric regimes) prevailing in the Ecuadorian territory. Precipitation ranges from 445 mm/year on average, observed in ECB Chira (Id 24), to 3696 mm/year on average, recorded for ATB Conocoto-Curaray (Id 30). On average, 71% of the rains were recorded in the ATBs. 15% of the rainfall events met the condition of erosive events, which contributed with a weight of 92% on the estimated magnitudes for the R-Factor. The R-Factor showed a range of values between 312.71 MJ mm/ha h and 12865.81 MJ mm/ha h, with an average of 3172.60 MJ mm/ha h, registering, in general, higher values at lower altitudes. The R-Factor values showed a spatial distribution similar to the existing literature. However, our
rainfall erosivity values based on GPM-IMERG underestimated the values obtained from the literature in some sectors of the country. The spatial variability of the R-Factor considering environmental parameters through a qualitative analysis, allowed us to identify that the areas most prone to soil erosion are composed mainly of sedimentary rocks, croplands and high slopes. The results of the R-Factor, estimated for each of the defined precipitation ranges, allowed to obtain two quite precise models to calculate the R-Factor quickly and efficiently, both for the ECBs and for the ATBs, from the data of annual precipitation from any database. Among the benefits of the statistical models obtained, they allow estimating and/or predicting trends in future R-Factor values, as well as retrospectively extrapolating them. The results presented provide support for the comprehensive management and sustainable use of the soil, making it possible to generate spatial models of soil loss due to rainfall erosivity, water conservation and management, disaster control, agricultural protection and other applications in the Ecuadorian territory.

1043

1044 Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

1047

1048 Acknowledgement

Authors thank the FSPI - Doctoral Schools Project of the French Embassy in Ecuador, funded by the Ministry of Europe and Foreign Affairs; INAMHI (Meteorological and Hydrological National Institute of Ecuador) for providing the hydrometeorological raw dataset and Bruno CHARRIERE (CEFREM laboratory staff) for the logistical support. A special acknowledgment to the researcher Panos Panagos for the suggestions made.

1054

1055

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