Exploring the Added Value of Sub-Daily Bias Correction of High-Resolution Gridded Rainfall Datasets for Rainfall Erosivity Estimation

Abstract

This study evaluates the impact of sub-daily bias correction of gridded rainfall products (RPs) on the estimation rainfall erosivity in Burkina Faso (West African Sahel). Selected RPs, offering half-hourly to hourly rainfall, are assessed against 10 synoptic stations over the period 2001–2020 to appraise their accuracy. The optimal product (the integrated multi-satellite retrievals for GPM, IMERG) is further used as a reference for bias correction, to adjust the rainfall distribution in the remaining RPs. RPs-derived rainfall erosivity is compared to the global rainfall erosivity database (GloREDa) estimates. The findings indicate that bias correction improves the rainfall accuracy estimation for all RPs, in terms of quantitative, categorial metrics and spatial patterns. It also improved the distributions of rainfall event intensities and duration across all products, which further significantly improved the annual rainfall erosivity estimates at various timescales along with spatial patterns across the country, as compared to raw RPs. The study also highlights that bias correction is effective at aligning annual trends in rainfall with those in rainfall erosivity derived from RPs. The study therefore underscores the added value of bias correction as a practice for improving the rainfall representation in high-resolution RPs before long-term rainfall erosivity assessment, particularly in data-scarce regions vulnerable to land degradation.

1. Introduction

Land degradation is a significant problem in the Sahel region, where this effect is worsened by its semi-arid climate, high climatic variability, and the irregular rainfall patterns prevalent in the region. The pre-dominantly rural population is highly dependent on natural resources and are therefore exposed to land degradation-associated threats [1,2]. The progressive degradation of land has resulted in a decline in soil fertility and crop yields, limiting agricultural productivity, which is still, however, the backbone of the economy for most of the Sahelian countries [3,4,5,6]. The implications of land degradation on agriculture are dire, as farmers are unable to produce enough crops to meet the demands of the growing population [2,7].

Rainfall erosivity is acknowledged as a pivotal factor of land erosion and degradation and is integral to shaping landscape vulnerability to soil loss [4,5,8,9,10,11]. As emphasised in the Universal Soil Loss Equation (USLE), rainfall erosivity acts as a driving force in the detachment and transport of soil particles [9,10,12,13,14]. Various methods are used for its estimation, which primarily rely on detailed and high-resolution rainfall measurements at sub-daily timescales, optimally reaching resolutions as fine as 30 min [15,16,17,18,19,20]. These methods essentially use empirical equations to relate rainfall intensities over short timesteps to quantify the erosive potential of rainfall events [21,22,23,24]. Yet, the applicability of such approaches is very limited in poorly gauged environments, especially in countries in the West African Sahel, where meteorological time series are seldom and rarely gap-free. Moreover, when available, rainfall data is generally recorded at the daily timescale [25,26]. The scarcity of high-resolution rainfall data in this context poses a considerable challenge to accurate and comprehensive assessments of rainfall erosivity, impeding our ability to understand and manage soil erosion dynamics effectively in these regions [17,27,28]. Addressing this data gap becomes crucial for advancing our understanding of land degradation processes and implementing targeted mitigation strategies in West African landscapes [29].

In recent years, the growing availability of rainfall products (RPs) has presented a significant opportunity for poorly gauged contexts to benefit from the estimation and mapping of rainfall erosivity using such products [30]. RPs provide high-resolution gridded rainfall data at timesteps of 30 min, 1 h, and up to 3 h, with quasi-global spatial coverage at spatial resolutions of 0.1° (~11 km) to 1° (~111 km) [31,32,33]. RPs come from either reanalysis data or the merging of multisource satellite data, ground observations, and various satellite rainfall measurements [34]. Leveraging these products can substantially improve the accuracy of rainfall erosivity estimation in regions with limited access to detailed rainfall data, facilitating a robust quantification and assessment of soil erosion processes [5,29,35]. However, rainfall estimates provided in RPs are often not accurate. According to several studies, which have critically compared the reliability of different RPs for rainfall estimation in West Africa, RPs show varying degrees of accuracy and reliability in estimating rainfall, depending on the region and the temporal scale, and site-specific assessment should be carried out to identify the optimal product in a given context [31,36,37,38,39,40,41,42,43,44].

Very few studies explore the potential of mapping rainfall erosivity from these RPs in West Africa [1,3,4,5]. In general, the accuracy of rainfall erosivity estimates is highly dependent on the ability of a given RP to reproduce rainfall, which is affected by different factors, such as the complexity of the topography [45,46], the effect of elevation (often referred to as the orographic effect) [47], and the type of precipitation [48,49]. The so-called “drizzle effect” [50] in RPs refers to the tendency of these products to overlook light rainfall events and underestimate high rainfall events, particularly those driving rainfall erosivity [20,51]. This, in turn, affects the representation of rainfall and the estimation of soil erosivity from gridded RPs [18].

From a spatial scale perspective, gridded rainfall data differs from gauge measurements: gridded data averages rainfall data over a cell space, the size of which depends on the spatial resolution of the dataset, while gauge measurement is the result of a point sampling [33]. As a result, the intrinsic probability density functions describing gridded rainfall and gauge observations are different and should be further treated to bring gridded rainfall closer to observations. In this view, statistical processing methods, referred to as bias corrections, could help alleviate the inherent biases in RPs, reducing the differences between the two sources of rainfall data [52]. Despite the wide range of bias correction techniques currently available, ranging from simple scaling methods to multivariate distribution mapping approaches [53], the potential benefits of rainfall bias correction on rainfall erosivity estimation have been overlooked in the scientific literature, especially in the Sahelian context. This is further confirmed by the fact that the vast majority of studies involving bias correction generally focused on a daily temporal scale, while impact studies related to rainfall erosivity use sub-daily rainfall data (at 30 min or 1 h timescales), which often need specific considerations when treating biases [52,53,54]. The aspects of the sub-daily rainfall distribution that could be addressed by bias correction techniques are the event duration, maximum intensity, and cumulative amount, which are critical terms for rainfall erosivity evaluation [12], therefore suggesting that there is a need to assess the potential benefits of bias correction for rainfall erosivity estimation.

This study focuses on Burkina Faso, a landlocked country of 272,200 km² in West Africa. This focus holds strategic significance due to the country’s location in the vulnerable Sahelian region, making it a representative case for land degradation challenges [55,56,57,58]. A significant decline in agricultural productivity and the economy, along with alarming rates of deforestation, have been observed, especially between 1992 and 2009 [2,59,60,61]. The country’s population, close to 20 million people according to the latest population census in 2019 [62], largely depends on agriculture and faces significant challenges due to the decline in the provision of ecosystem services, including food availability, soil fertility, wood production, and groundwater recharge [63,64,65,66]. Recently, climate change has further intensified the pressure on arable land [67]. The country has set voluntary targets to achieve Land Degradation Neutrality (LDN) by 2030, but significant obstacles, such as a lack of technical know-how in rural communities and a lack of awareness, are yet to be overcome [57,68]. The highly prevalent scarcity of ground-based rainfall observations at sub-daily timescales highlights the necessity of exploring the added value of bias correction of RPs for accurate assessments of rainfall erosivity. The agrarian economy and rural population further emphasise the practical implications of assessing rainfall erosivity for sustainable land management and livelihoods [69].

In light of these considerations, our study objectives are twofold: (1) to quantify the potential of bias correction in improving the accuracy of rainfall estimation in Burkina Faso across several RPs, and (2) to assess the potential of bias correction to improve the accuracy of rainfall erosivity estimates from RPs. By addressing these objectives, this study contributes to a better understanding of the dynamics and broader challenges of soil erosion in poorly gauged environments, offering insights for effective and sustainable land management.

2. Materials and Methods

2.1. Study Area

Burkina Faso is a landlocked Sahelian country (274,200 km²) located in West Africa (9°20′–15°05′ N, 2°20′ E–5°30′ W, Figure 1). The physical setting is characterised by a diverse geography, with a larger share of the area covered by a peneplain and a gently undulating landscape forming slopes between 0 and 3% while the southwest consists of a sandstone massif. Over 90% of the country is flat, within the 250–300 m range [2,26,38].

According to the Koppen-Geiger climate classification [71], the climate is a hot desert (BWh) or Sahelian climate in the north, transitions to a hot semi-arid (BSh) or Sudano–Sahelian climate in the central region, and to a tropical savanna (Aw) or Sudanian climate in the south. Two contrasting seasons alternate in a year: a rainy season (from June to October) and a dry season (from November to May). The average annual rainfall ranges between 495 mm (in the north) and 1100 mm (in the south), with average annual daily temperatures in the range of 34–37 °C (for maximum daily temperature) and 21–23 °C (for minimum daily temperature) [26].

2.2. Data Sources

2.2.1. Rainfall Observations

Over Burkina Faso’s territory, 300 climatic, agroclimatic, and pluviometric rainfall gauge stations were installed, but only provided daily rainfall measurements. However, due to poor maintenance and technical failures, the data provided by these stations were filled with large gaps scattered throughout the monitoring period, which made the data highly unsuitable for practical applications such as rainfall monitoring and rainfall erosivity assessment [72]. Only 10 stations, referred to as synoptic stations, are properly monitored by the National Meteorology Agency in Burkina Faso (ANAM-BF). These stations provide continuous, gap-free daily rainfall measurements, which were collected in this study over the period 2001–2020 (i.e., 20 years). The location of these stations is presented in Figure 1.

Table 1. Description of the 10 synoptic stations used in this study.

WMO Code 1	Name	Latitude, Longitude (Decimal Degrees)	Altitude (m)	Annual Rainfall (mm) 2	Climate Type 3
1200010000	Dori	14.0333, −0.0333	288	528.2 ± 127.6	BWh
1200024100	Ouahigouya	13.5833, −2.4333	329	764.7 ± 145.0	BSh
1200004300	Bogande	12.9833, −0.1333	250	643.8 ± 121.6	BSh
1200007900	Dedougou	12.4667, −3.4667	308	859.7 ± 115.1	BSh
1200000100	Ouagadougou	12.3500, −1.5167	304	816.1 ± 115.0	BSh
1200010300	Fada	12.0333, 0.3667	308	833.3 ± 103.5	BSh
1200005200	Boromo	11.7500, −2.9333	270	920.1 ± 129.2	BSh
1200004000	Bobo-Dioulasso	11.1667, −4.3167	459	1043.4 ± 197.1	Aw
1200026200	Po	11.1667, −1.1500	326	1024.9 ± 128.0	Aw
1200011200	Gaoua	10.3333, −3.1833	333	1088.4 ± 150.2	Aw

¹ WMO Code = World Meteorological Organization reference station code. ² Annual rainfall ± standard deviation is calculated over the period 2001–2020. ³ Climate type refers to the Köppen-Geiger climate classification system [71].

provides the description, physical characteristics, and climate of all the synoptic stations.

2.2.2. Rainfall Products (RPs)

The rainfall data from 7 RPs were used in this study to evaluate rainfall erosivity in Burkina Faso. The characteristics of the selected RPs are presented in

Table 2. Description of the Rainfall Products (RPs) used in this study.

Source	Type 1	Spatial Resolution	Temporal Resolution	Spatial Coverage	Temporal Coverage	References
CMORPH (CPC MORPHing technique)	S	0.25° × 0.25° (~28 km)	1 h	60°N/S	1998-present	[74,75]
ERA5 (5th generation of the European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric reanalysis)	R	0.25° × 0.25° (~28 km)	1 h	Global	1940-present	[76,77]
IMERG (Integrated multi-satellite retrievals for the global precipitation measurement)-Late run (v6)	S	0.1° × 0.1° (~11 km)	0.5 h	Global	2000-present	[78]
MERRA-2 (modern-era retrospective analysis for research and applications, Version 2)	R	0.5° × 0.685° (~60 km)	1 h	Global	1980-present	[79]
PERSIANN-PDIR-Now (precipitation estimation from remotely sensed information using artificial neural networks-dynamic infrared rain rate near real-time)	S + G	0.04° × 0.04° (~4.44 km)	1 h	60°N/S	2000-present	[80,81]
PERSIANN (precipitation estimation from remotely sensed information using artificial neural Networks)	S + G	0.25° × 0.25° (~28 km)	1 h	60°N/S	2000-present	[80,82]
PERSIANN-CCS (precipitation estimation from remotely sensed information using artificial neural networks-cloud classification system)	S + G	0.04° × 0.04° (~4.44 km)	1 h	60°N/S	2003-present	[80,82]

¹ R: reanalysis; S: satellite; G: Gauge measurement.

. The selected RPs include reanalysis data, satellite estimates, and satellite measurements merged with gauge data. These RPs were chosen based on their high temporal resolution, providing rainfall data at timescales of 30 min to 1 h, and also for their popular use in the literature [31,38,40,43,44]. The rainfall data were collected from all the RPs for the period 2001–2020. The data were downloaded under the NetCDF file format and processed under the R programming language [73].

2.3. Steps of the Methodology

2.3.1. Selection of a Reference RP for Bias Correction of Rainfall Data

To assess the added value of bias correction in the representation of rainfall and rainfall erosivity in Burkina Faso, a reference dataset was needed. This reference dataset should provide sub-daily rainfall to match the timescale of the gridded RPs in this study. Therefore, the gauge observation data at the synoptic stations could not be considered here for reference because of their daily timescale.

In this study, the rainfall data provided by the selected RPs were aggregated to a daily timescale over the period 2001–2020, then to monthly and annual timescales. For the daily timescale, only erosive events (cumulative rainfall over the 12.7 mm threshold [13]) were retained. The data were further pooled for all the 10 synoptic stations and compared in Figure 2 to the rainfall observations at similar timescales to identify the closest RP to gauge observations at the daily, monthly and annual timescales.

Figure 2 compares rainfall across the RPs to gauge observations in terms of normalised standard deviation, correlation, and centred root mean square (RMS) error. It further reveals that ERA5, PDIR-Now, and MERRA-2 generally have the lowest correlation at all timescales. PERSIANN-CCS shows inconsistent behaviour, with a good performance at the daily timescale (Figure 2a), which becomes poor at the monthly (Figure 2b) and annual (Figure 2c) timescales, most likely because of the large occurrence of drizzle (low rainfall events) in this product, ignored at the daily timescale. IMERG, however, shows consistently good performance at all timescales, with the highest correlation to observed data, followed by CMORPH, which performs slightly less.

We also compared the performance of RPs against a short sample of available 15 min rainfall observations, aggregated at the hourly timescale, at the station of Ouagadougou, over the period 2019–2020, which further confirmed that IMERG is optimal at simulating 60 min rainfall intensities (see Supplementary Material, Figures S1 and S2).

Given its superior and consistent performance at all timescales, the IMERG RP was selected as the reference product in this study for further bias correction of the remaining RPs.

2.3.2. Sub-Daily Bias Correction of RPs

The inherent biases present in high-resolution RPs tend to cause poor representation in observed rainfall patterns. Alleviating such biases using statistical bias correction methods can improve the dynamics and patterns of simulated rainfall, allowing for better estimates in further applications [52,83]. All the RPs were first reprocessed to the hourly timescale. Then, the quantile delta mapping (QDM) method [84] was applied to treat biases in hourly rainfall using the MBCn R package [85]. QDM is selected in this study since it is a quantile-based bias correction method, which tries to convey all aspects of the distribution of reference data to the corresponding distribution from the biased data (i.e., RPs to be treated). Moreover, it is a trend-preserving bias correction method, which allows for the preservation of existing trends for all quantiles in the data to be treated [61,72].

Since biases in RPs are likely to be variant throughout the diurnal cycle, the bias correction was independently applied for each hour timestep in a day using a 3 h moving window pooling of all hourly values following a diurnal bias correction scheme [52]. The bias correction also accounted for the seasonal variation in the rainfall and was therefore applied separately for different quarters in the year: December to February (DJF), March to May (MAM), June to August (JJA) and September to November (SON) [52].

2.3.3. Impact of Bias Correction on Rainfall Estimation across the RPs

The impact of bias correction of rainfall data is evaluated following four levels of assessments, including visual and statistical metrics, and considering various timescales and distribution aspects.

The first step of the evaluation is a quantitative assessment. In this stage, statistical metrics, such as Pearson’s coefficient of correlation (r, Equation (1)), mean absolute error (MAE, Equation (2)), root mean square error (RMSE, Equation (3)), percentage of bias (PBIAS, Equation (4)) and Kling–Gupta efficiency (KGE, Equation (5)), were evaluated between gauge observations and raw/bias-corrected RPs using the hydroGOF R package [86].

$$r={\displaystyle \frac{\left(n{\sum }_{i=1}^n{P}_i\widehat{P_i}-{\sum }_{i=1}^n{P}_i\times {\sum }_{i=1}^n\widehat{P_i}\right)}{\sqrt{\left[n{\sum }_{i=1}^n{P}_i^2-{\left({\sum }_{i=1}^n{P}_i\right)}^2\right]\left[n{\sum }_{i=1}^n{\widehat{P_i}}^2-{\left({\sum }_{i=1}^n\widehat{P_i}\right)}^2\right]}}}$$

(1)

$$MAE={\displaystyle \frac{1}{n}}\sum _{i=1}^n|P_i-\widehat{P_i}|$$

(2)

$$RMSE=\sqrt{\sum _{i=1}^n{\displaystyle \frac{{\left(P_i-\widehat{P_i}\right)}^2}{n}}}$$

(3)

$$PBIAS={\displaystyle \frac{{\sum }_{i=1}^n(P_i-\widehat{P_i})}{{\sum }_{i=1}^n{P}_i}}\times 100$$

(4)

$$KGE=1-\sqrt{{\left(r-1\right)}^2+{\left(\overline{P_s}/\overline{P}-1\right)}^2+{\left(C{V}_s/CV-1\right)}^2}$$

(5)

where $P_i$ is the observed rainfall (rain gauge measurement); $\widehat{P_i}$ is the corresponding estimate from a given RP; $\overline{P}$ and ${\overline{P}}_s$ are, respectively, the averages of observed rainfall and RP estimates; $n$ is the total number of observations; $r$ is the Pearson’s product moment correlation coefficient between observed rainfall and RP estimates; $C{V}_s$ and $CV$ are, respectively, the coefficients of variation of observed rainfall and RP estimates. The optimal values are 1 for r and KGE and 0 for MAE, RMSE, and PBIAS.

A second level of assessment was conducted at the daily timescale using categorical metrics to evaluate how bias correction impacts the ability of RPs to detect rainfall events of various levels. Three (03) categorical metrics are used, presented in

Table 3. Categorical metrics used to evaluate RPs in this study.

Metric	Description	Formula 1	Range
Probability of detection (POD)	Fraction of events correctly identified to the total rainfall events occurrences	$POD={\displaystyle \frac{h}{h+m}}$	0 (no skill)–1 (perfect score)
False alarm ratio (FAR)	Fraction of predicted rainfall events which did not occur in gauge measurements	$FAR={\displaystyle \frac{f}{h+f}}$	0 (perfect score)–1 (no skill)
Threat score (TS) or critical success index (CSI)	Fraction of observed and/or predicted events that were correctly predicted	$TS=CSI={\displaystyle \frac{h}{h+m+f}}$	0 (no skill)–1 (perfect score)

¹ h: hit, event predicted in the RP to occur, and did occur in gauge measurements; m: miss, event not predicted in the RP to occur, but did occur in gauge measurements; f: false alarm, event predicted in the RP to occur, but did not occur in gauge measurements.

, namely, the probability of detection (POD), the false alarm ratio (FAR) and the threat score (TS) or critical success index (CSI). These metrics were evaluated against pooled daily rainfall observations at synoptic stations for various rainfall thresholds in the range of 12.7 mm to 25 mm by increments of 2.5 mm. The categorical metrics were evaluated using the verification R package [87] and were evaluated on RPs before and after the application of the bias correction procedure.

A third level of assessment included a specific look at single rainfall events’ duration and average intensity, which are key aspects in the rainfall distribution that further determine rainfall erosivity [12,13]. In this stage, the probability density functions of rainfall event duration and average rainfall intensity across the RPs are compared to that of the reference IMERG product before and after the application of bias correction to assess the specific adjustments brought by the statistical treatment.

The fourth level of assessment focused on the evaluation of spatial rainfall patterns. In this stage, the average annual rainfall is estimated over the period 2001–2020 at the 10 synoptic stations and is further used to map spatial patterns in average annual rainfall across the entire country through the ordinary kriging spatial interpolation technique. The resulting maps are compared to that derived from the reference IMERG before and after the application of bias correction processing to further assess its impacts on the representation and consistency of spatial rainfall patterns across these RPs.

2.3.4. Calculation of Rainfall Erosivity

Rainfall erosivity (RE) is expressed through the R-factor, which accounts for the combined effect of the rainfall event’s duration, magnitude, and intensity, as well as the frequency of so-called erosive events over a continuous and long-term period of, typically, 20 years. The definition from the Revised Universal Soil Loss Equation (RUSLE), version 2 [12,13] was used in this study to estimate the R-factor, which is dependent on the EI₃₀ index, calculated in Equation (6):

$$E{I}_{30}=\left(\sum _{r=1}^k{e}_r{v}_r\right)I_{30}$$

(6)

where $e_r$ is the unit rainfall energy (MJ ha⁻¹ mm⁻¹), $v_r$ is the rainfall volume (mm) accumulated during a given timestep, $k$ is the total number of timesteps within the rainfall event duration, and $I_{30}$ is the maximum 30 min rainfall intensity (mm h⁻¹). The unit rainfall energy term ($e_r$) is calculated according to Equation (7), developed as part of RUSLE2 [88]:

$$e_r=0.29[1-0.72\exp (-0.082i_r)]$$

(7)

where $i_r$ is the rainfall intensity during a given timestep (in mm h⁻¹). The average annual R-factor is then calculated as in Equation (8) [17,18,20,27]:

$$R={\displaystyle \frac{1}{n}}\left(\sum _{j=1}^n\sum _{k=1}^{m_j}{\left(E{I}_{30}\right)}_k\right)$$

(8)

where $R$ is the average annual rainfall erosivity R-factor (in MJ mm ha⁻¹ h⁻¹ year⁻¹), $n$ is the number of years of rainfall data processed, $m_j$ is the number of rainfall erosive events in the year $j$, and $k$ is the index of a single rainfall event and its corresponding erosivity index $E{I}_{30}$.

Before calculating the R-factor, the rainfall data is processed to identify erosive events. According to the RUSLE handbook definition, such erosive rainfall events are defined based on the following three criteria: (1) the cumulative rainfall of the event is greater than 12.7 mm; (2) the rainfall event has at least one peak greater than 6.35 mm in 15 min or 12.7 mm in 30 min; (3) a rainfall accumulation of less than 1.27 mm in 6 h splits a longer storm period into two [12,13,28]. It should be noted that the threshold value of 12.7 mm defining an erosive event is based on observations of over 10,000 plot-years of data [10,88]. Moreover, Lu and Yu [89] showed that using a threshold of 0 mm (instead of 12.7 mm) only increases the annual rainfall erosivity estimate by ~3.5%, which is regarded as not significant. Therefore, applying the three criteria defined above helps filter out light rainfall events that would not bring significant change to the average annual R-factor, allowing for a faster processing time [28].

Equations (6)–(8) were used to derive rainfall erosivity from IMERG rainfall data in this study because of their half-hourly (30 min) temporal resolution. For the other RPs, which provide hourly rainfall data, an adjustment of the $E{I}_{30}$ index through the use of a calibration factor is needed to avoid an underestimation of the $E{I}_{30}$ index [21,90]. The R-factor therefore calculates as in Equation (9):

$$E{I}_{30}=a\times E{I}_{60}$$

(9)

where the ${EI}_{60}$ index is based on the maximum 60 min rainfall intensity during a rainfall event and $a$ is a conversion factor. Some values for the calibration factor have been reported in the literature. For instance, Yin et al. [21] estimated a calibration factor of 1.811 in China, while Panagos et al. [90] suggested a calibration factor of 1.5597 in Europe, which suggests that the calibration factor from hourly to half-hourly rainfall intensity is site-specific. In this study, we used IMERG rainfall data, which were aggregated from their original half-hourly to hourly temporal resolution, to further calculate site-specific calibration factors from a linear regression between $I_{30}$ and $I_{60}$ rainfall intensities [21,90,91]_.

2.3.5. Comparison of Rainfall Erosivity with Reference Values

The rainfall erosivity estimates calculated from the RPs using both raw and bias-corrected rainfall data were compared to the Global Rainfall Erosivity Database (GloREDa) estimates, which was selected as a reference in this study for the evaluation of the accuracy of rainfall erosivity estimates from the RPs. GloREDa is the first open-access database of rainfall erosivity data based on the combination of hourly and sub-hourly rainfall records at the global scale [28]. GloREDa was compiled through a global collaboration between a network of researchers, meteorological services, and environmental organisations from 65 countries. In terms of coverage, the database contains erosivity values provided as R-factors from 3625 stations across 10 countries, including countries in Europe, North America, South America, Africa, Asia, and the Middle East [17,28]. The database is accessible to download from the European Soil Data Centre (ESDAC) repository (https://esdac.jrc.ec.europa.eu/content/global-rainfall-erosivity (accessed on 5 April 2024)) and provides raster data at a 1 km spatial resolution. GloREDa is the result of extensive data collection of high-temporal resolution rainfall data, with a total of 59,380 observational years, averaging 16.8 years of data per station [17,20,28].

In this study, the global GloREDa R-factor maps were downloaded (in TIFF format) and processed within ESRI ArcGIS (version 10.3.1) [92] to retrieve annual R-factor estimates at the 10 synoptic gauge stations in Burkina Faso. These values served as a reference for comparison against rainfall erosivity estimates from RPs. The metrics used to assess the biases between GloREDa estimates and the erosivity estimates from the RPs were the RMSE, the MAE, and PBIAS, which were calculated in the R programming language [73]. Additionally, a visual comparison of the boxplot distributions between the reference and estimate values was performed using the ggpubr R package [93]. Finally, a spatial assessment was also carried out to further highlight the contribution of bias correction to improving the representation of spatial patterns of rainfall erosivity.

2.3.6. Trend Analysis of Rainfall Erosivity over the Period 2001–2020

Rainfall erosivity is typically evaluated as an average value over a long-term period (20 years). However, another important aspect lies in the annual trend over the considered period, which can unveil a gradual increase or decrease in rainfall erosivity. In this study, to evaluate the impact of bias correction on rainfall erosivity trends over the period 2001–2020, the rainfall erosivity time series, calculated from raw and bias-corrected RPs at the 10 synoptic stations, were used as inputs to the non-parametric Mann-Kendall (M-K) trend test with a 5% significance level [94,95]. The application of the M-K test in this study includes a trend-free serial prewhitening [96] correction to account for autocorrelation. The procedure is applied using the tfpwmk function in the modifiedmk R package [97]. The magnitude of trend slopes is evaluated using the non-parametric Theil–Sen [98,99] slope estimator, as given in Equation (10):

$$\beta =Median\left({\displaystyle \frac{x_j-x_i}{j-i}}\right),\forall i<j$$

(10)

where $x_i$ and $x_j$ are sequential values in the time series at times $i$ and $j,$ respectively, and $\beta$ is the robust unbiased estimate of the trend slope magnitude [98,99].

3. Results

3.1. Sub-Daily Bias Correction of RPs

Using IMERG as the reference dataset, the diurnal bias correction procedure is applied to adjust the rainfall distribution in the remaining 6 gridded RPs. Figure 3 shows the average diurnal rainfall pattern over the period 2001–2020 according to the 7 RPs before (Figure 3a–d) and after (Figure 3e–h) the bias correction. It clearly outlines the improved adjustment in the mean of the distribution of IMERG values, especially for May to November, which covers the rainy season in Burkina Faso. It can also be observed that the bias correction procedure is less effective on PDIR-Now rainfall, especially in the months of June to August and in the months of September to November to a lesser extent.

3.2. Impact of Bias Correction on Rainfall

3.2.1. Comparison of Rainfall at Daily, Monthly, and Annual Timescales

The detailed metrics showing the quantitative evaluation of the accuracy of the RPs are presented in

Table 4. Effect of sub-daily bias correction on accuracy of the RPs over the period 2001–2020.

Timescale	Type	RP	R [-]	MAE [mm/timescale]	RMSE [mm/timescale]	PBIAS [%]	KGE [-]
Daily	reference	IMERG	0.85	6.49	8.58	6.20	0.83
	raw	CMORPH	0.50	13.56	18.06	0.70	0.40
	raw	ERA5	0.32	17.89	24.05	−18.70	0.07
	raw	MERRA-2	0.40	23.96	33.18	−38.80	0.01
	raw	PDIR-Now	0.26	24.34	33.80	−45.90	−0.07
	raw	PERSIANN	0.50	15.65	19.64	39.00	0.29
	raw	PERSIANN-CCS	0.46	16.17	20.61	42.10	0.27
	bc	CMORPH	0.81	6.38	8.42	8.60	0.78
	bc	ERA5	0.75	5.59	7.18	15.80	0.57
	bc	MERRA-2	0.81	5.42	6.75	16.10	0.69
	bc	PDIR-Now	0.78	5.67	7.48	18.10	0.57
	bc	PERSIANN	0.82	6.28	8.18	6.00	0.80
	bc	PERSIANN-CCS	0.84	6.35	8.40	4.50	0.83
Monthly	reference	IMERG	0.91	17.76	35.40	−5.50	0.88
	raw	CMORPH	0.88	21.64	38.96	14.90	0.77
	raw	ERA5	0.73	37.84	66.90	178.50	−1.03
	raw	MERRA-2	0.75	36.91	64.02	156.10	−0.75
	raw	PDIR-Now	0.64	42.78	76.03	262.70	−2.13
	raw	PERSIANN	0.79	56.07	92.16	−46.80	0.37
	raw	PERSIANN-CCS	0.65	84.19	137.29	−56.10	0.18
	bc	CMORPH	0.91	19.98	36.35	−7.10	0.85
	bc	ERA5	0.80	28.89	54.51	−2.50	0.76
	bc	MERRA-2	0.81	34.55	68.11	−18.40	0.60
	bc	PDIR-Now	0.86	65.54	123.90	−51.40	0.25
	bc	PERSIANN	0.89	22.15	41.05	−7.30	0.83
	bc	PERSIANN-CCS	0.85	25.62	47.88	−3.80	0.80
Annual	reference	IMERG	0.76	105.26	132.70	−7.50	0.78
	raw	CMORPH	0.69	132.35	166.36	14.90	0.64
	raw	ERA5	0.63	428.93	453.91	178.50	−0.96
	raw	MERRA-2	0.62	407.95	437.27	156.10	−0.62
	raw	PDIR-Now	0.67	485.18	505.83	262.70	−1.66
	raw	PERSIANN	0.48	589.38	625.33	−46.80	0.29
	raw	PERSIANN-CCS	0.40	969.96	1026.92	−56.10	−0.07
	bc	CMORPH	0.80	106.58	133.72	−7.10	0.78
	bc	ERA5	0.61	142.89	185.66	−2.50	0.58
	bc	MERRA-2	0.63	249.06	318.77	−18.40	0.37
	bc	PDIR-Now	0.41	718.46	768.25	−51.40	0.12
	bc	PERSIANN	0.73	124.00	152.57	−7.30	0.72
	bc	PERSIANN-CCS	0.58	179.99	244.99	−3.80	0.44

Raw: rainfall values from raw RPs-bc: rainfall values from gridded RPs.

for daily, monthly, and annual timescales and considering both raw and bias-corrected products.

In general, at all timescales, bias correction improves the accuracy of RPs. At the daily timescale, the bias correction significantly increased the correlation of each gridded RP, from the 0.26–0.50 range to the 0.75–0.84 range. CMORPH, PERSIANN, and PERSIANN-CCS showed the highest KGE, with values of 0.78, 0.80, and 0.83, respectively. However, IMERG still showed the optimal agreement with observations (KGE = 0.83).

At the monthly timescale, the correlation values in the raw products were initially important (with the 0.64–0.88 range), however, with large biases (PBIAS: −56.10% to 262.70%). Bias correction further improved the correlation (0.80–0.91), and significantly reduced biases (−51.40% to −2.50%), resulting in improved agreement (KGE in the 0.25–0.85 range), with optimal values for CMORPH (KGE = 0.85), PERSIANN (KGE = 0.83) and PERSIANN-CCS (KGE = 0.80). IMERG still showed the highest agreement at the monthly timescale (r = 0.91, PBIAS = −5.50% and KGE = 0.88).

At the annual timescale, it appears that bias correction caused an increase in correlation (from the 0.40–0.69 range to the 0.41–0.73 range) and a significant decrease in overall bias (PBIAS: from the −56.10–262.70% range to the (−51.40%)–(−2.50%) range). After bias correction CMORPH and PERSIANN showed the highest overall agreement, with KGE values of 0.78 and 0.72, respectively. IMERG still showed the highest agreement overall (r = 0.76, PBIAS = −7.50% and KGE = 0.78).

3.2.2. Categorical Metrics

Figure 4 shows the categorical metrics evaluated for all the RPs and daily rainfall thresholds between 12.7 and 25 mm before and after the bias correction. It appears that POD (Figure 4a,d) and TS (Figure 4c,f) generally decreased for increasing rainfall thresholds, while FAR (Figure 4b,e) increased with increasing rainfall thresholds.

Regarding POD, bias correction caused a general increase in the ability of RPs to detect rainfall events, especially for ERA5 and MERRA-2 products. It also appears that PERSIANN-CCS showed the highest POD values before bias correction (Figure 4a), which is quite lost after (Figure 4d). After bias correction, PERSIANN, IMERG, and CMORPH had the optimal POD values across the different thresholds analysed.

Regarding FAR, the bias correction procedure caused, in general, a slight likelihood of false alarms, as shown in Figure 4b,e. Before and after bias correction, IMERG and CMORPH emerged as the RPs with the least false alarms.

Finally, for the TS, the effect of bias correction was quite marginal, with no significant changes observed on the RPs’ accuracy (Figure 4c,f). After bias correction, IMERG and CMORPH consistently provided the highest TS values, indicating that these products are optimal in terms of ratio of detection of rainfall events over misses and false alarms.

3.2.3. Distribution of Rainfall Events Intensity and Duration

Figure 5 highlights the effectiveness of the bias correction procedure on the distribution of rainfall intensities and rainfall events’ duration. It highlights the discrepancies in these distributions across the different raw RPs (Figure 5a,b), which are further harmonised after the bias correction procedure (Figure 5c,d). After bias correction, the average hourly rainfall intensity was in the range of 2.5–3.0 mm.h⁻¹, while the average rainfall duration was 2.3 h. Also, it appears that the bias correction was less effective on the distribution of rainfall events duration for PERSIANN-CCS, which could later affect the rainfall erosivity estimates derived from this product.

3.2.4. Spatial Patterns in Annual Rainfall

Figure 6 shows a comparison of average annual rainfall over the entire country for the period 2001–2020, as represented in the gridded raw RPs and the bias-corrected ones. IMERG reproduces well the observed spatial patterns (Figure 6b), albeit with a slight overestimation in the south and south-western locations. Before bias correction, CMORPH (Figure 6c), ERA5 (Figure 6d), MERRA-2 (Figure 6e), and PDIR-Now (Figure 6f) showed consistent agreement, in general, with observations, but underestimations in the northern and central regions. PERSIANN (Figure 6g) and PERSIAN-CCS (Figure 6h) clearly overestimated rainfall at all locations in space.

After bias correction, a general improvement was observed for all the gridded RPs except for PDIR-Now, which overestimated rainfall (Figure 6i). CMORPH (Figure 6i), ERA5 (Figure 6j), and MERRA-2 (Figure 6k) showed overestimation patterns in rainfall at southern and south-western locations similarly to IMERG (Figure 6b), although in more severe proportions. The same observation applies to both PERSIANN (Figure 6m) and PERSIAN-CCS (Figure 6n), albeit there were tremendous improvements observed for these RPs in comparison with their raw versions.

3.3. Impact of Bias Correction on Rainfall Erosivity Estimates from RPs

3.3.1. Estimation of Half-Hourly to Hourly Calibration Factors

The estimation of rainfall erosivity from hourly rainfall relies on the use of calibration factors to scale from half-hourly to hourly erosivity [21,90,91]. In this study, IMERG rainfall, initially provided at the half-hourly (30 min) temporal resolution, is further aggregated to hourly values, which are used to derive calibration factors through site-specific linear regression, presented in Figure 7. The results show that the linear adjustment between I₃₀ and I₆₀ is significant (R² = 0.93–0.94, p-values < 0.0001) for all locations, with calibration factors in the range of 1.597 (at Dori station) to 1.698 (at Ouahigouya station). The values of these conversion factors herein obtained suggest that calculating rainfall erosivity using hourly rainfall only is likely to result in an underestimation in the range of 60% to 70%, which can be alleviated using the estimated calibration factors.

3.3.2. Annual Rainfall Erosivity R-Factor

The annual rainfall erosivity R-factor in Burkina Faso over the period 2001–2020 at the 10 synoptic stations was derived from the 7 RPs and compared to GloREDa R-factors in Figure 8 using boxplot distributions.

Table 5. Statistical evaluation of RP-derived annual R-factors against GloREDa estimates.

Type	Product	Annual Mean (±sd) R-Factor (MJ mm ha−1 h−1 yr−1)	RMSE 1 (MJ mm ha−1 h−1 yr−1)	MAE 1 (MJ mm ha−1 h−1 yr−1)	PBIAS 1 (%)
	GloREDa	2964.9 ± 886.9
	IMERG	2929.7 ± 543.8	494.1	365.0	1.2
raw	CMORPH	2130.3 ± 312.5	1192.8	897.6	39.2
raw	ERA5	465.1 ± 142.6	2605.9	2499.7	537.4
raw	MERRA-2	410.0 ± 132.8	2682.9	2554.8	623.1
raw	PDIR-Now	372.5 ± 396.1	2638.6	2592.3	695.8
raw	PERSIANN	4583.3 ± 468.4	1951.9	1744.9	−35.3
raw	PERSIANN-CCS	12,344.3 ± 2014.2	9472.8	9379.4	−76.0
bc	CMORPH	3796.3 ± 678.4	934.6	862.0	−21.9
bc	ERA5	3704.6 ± 682.5	861.5	793.2	−20.0
bc	MERRA-2	4404.4 ± 782.5	1495.9	1439.5	−32.7
bc	PDIR-Now	7412.8 ± 955.9	4663.0	4447.9	−60.0
bc	PERSIANN	3846.8 ± 631.5	1004.0	930.9	−22.9
bc	PERSIANN-CCS	3777.0 ± 569.8	966.8	906.2	−21.5

¹ The RMSE, MAE, and PBIAS values are estimated from the comparison with GloREDa R-factor estimates at the 10 synoptic rainfall stations used in this study.

shows the quantitative accuracy assessment of RP-derived R-factors using statistical metrics.

The average annual R-factor in GloREDa is 2964.9 ± 886.9 MJ mm ha⁻¹ h⁻¹ yr⁻¹. The R-factors derived from raw RPs (Figure 8a) showed varying performance, with IMERG providing the closest estimates to GloREDa, though with a slight overestimation (RMSE = 494 MJ mm ha⁻¹ h⁻¹ yr⁻¹, PBIAS = 1.2%), followed by CMORPH (PBIAS = 39.2%). ERA5, MERRA-2, and PDIR-Now severely underestimated the annual R-factor (PBIAS = 537.4–695.8%), while PERSIANN (PBIAS = −35.3%) and PERSIANN-CCS (PBIAS = −76.0%) overestimated GloREDa reference values. It can also be seen that CMORPH, ERA5, and MERRA-2 showed flat distributions, which typically implies that the variability in derived rainfall erosivity is small, as represented in these RPs.

The bias correction procedure further helped in improving annual rainfall erosivity estimates across the 6 RPs, which are now closer to GloREDa values (Figure 8b). The joint comparison with Figure 5 shows that ERA5, MERRA-2, and PDIR-Now probability–density curves are heavily left-skewed below IMERG, hence explaining the underestimation of R-factor in Figure 8a. The diurnal sub-daily bias correction carried out in this study effectively maps the rainfall distribution quantiles in the raw gridded RPs to the corresponding reference values, resulting in similar distributions in terms of median, skewness, and overall span of the data, both for rainfall event maximum intensity and rainfall event duration (Figure 5). These improvements are revealed to be critical to the improved estimation of average annual rainfall erosivity derived from the bias-corrected products (Figure 8b). CMORPH, ERA-5, MERRA-2, PERSIANN, and PERSIANN-CCS now provide closer annual R-factors to GloREDa values (PBIAS in the range of −32.7% to −20%), while PDIR-Now shows a larger overestimation bias (PBIAS = −60.0%).

3.3.3. Monthly Rainfall Erosivity R-Factors

The monthly R-factors derived from the bias-corrected RPs are compared in Figure 9, which shows similar patterns to seasonal rainfall. The months showing the largest monthly R-factors are the months of July, August, and September, corresponding to the rainy season period in Burkina Faso. The peak monthly R-factors in August are in the range of 95.4 to 2876.7 MJ mm ha⁻¹ h⁻¹ month⁻¹. It appears that IMERG consistently provides the closest monthly R-factor estimates to GloREDa reference values (Figure 9a), closely followed by CMORPH before bias correction (Figure 9b), which tends to underestimate monthly R-factors Also, the raw monthly rainfall erosivity values in ERA5, MERRA-2 and PDIR-Now (Figure 9c–e) severely underestimate GloREDa monthly R-factors, while PERSIANN (Figure 9f) and PERSIAN-CCS (Figure 9g) provide large overestimations, especially for the months of April to October.

After bias correction, CMORPH (Figure 9h), ERA5 (Figure 9i), MERRA-2 (Figure 9j), PERSIANN (Figure 9l) and PERSIAN-CCS (Figure 9m) show annual patterns more in line with GloREDa monthly R-factors, with, however, an overestimation for the months of July and August. PDIR-Now (Figure 9k) shows a global overestimation, with a quasi-bi-modal annual pattern with peaks in July and September, clearly not in line with the usual annual rainfall regime in the study area.

3.3.4. Spatial Patterns in Annual Rainfall Erosivity R-Factor

Figure 10 compares the spatial patterns in the average annual R-factor between GloREDa (Figure 10a) and the gridded RPs before and after bias correction. It shows that IMERG (Figure 10b) provides the highest level of spatial agreement with GloREDa. Among the raw products, CMORPH (Figure 10c) is also consistent, in general, with GloREDa, while the remaining products (Figure 10d–h) are less well-performing. After bias correction, for all the gridded RPs except PDIR-Now, the spatial patterns show a higher level of agreement with GloREDa, indicating that the bias correction was successful in improving the spatial distribution of the annual R-factor in each RP. PDIR-Now, however, (Figure 10l) is not in agreement with GloREDa’s spatial erosivity map, with a consistent overestimation of R-factors at all locations.

3.4. Impact of Bias Correction on Annual Trends in Rainfall and Rainfall Erosivity

Table 6. Impact of bias correction on rainfall and rainfall erosivity Theil–Sen slope trends over the period 2001–2020.

	Product	DORI	OUAHIGOUYA	BOGANDE	DEDOUGOU	OUAGADOUGOU	FADA	BOROMO	BOBO	PO	GAOUA
Rainfall	Observed	3.3 (0.263)	12.6 (0.069)	1.9 (0.675)	4.6 (0.294)	9.9 (0.014)	−3.8 (0.234)	8.1 (0.142)	18.5 (0.080)	−0.0 (1.000)	10.1 (0.294)
	IMERG	13.2 (0.208)	8.2 (0.401)	5.3 (0.576)	10.2 (0.234)	17.0 (0.030)	9.8 (0.401)	15.5 (0.069)	17.0 (0.042)	6.6 (0.401)	6.2 (0.401)
	CMORPH (raw)	10.1 (0.069)	19.3 (0.002)	9.2 (0.124)	14.8 (0.036)	9.4 (0.025)	11.3 (0.080)	11.1 (0.162)	20.4 (0.008)	7.3 (0.327)	8.1 (0.108)
	ERA5 (raw)	3.8 (0.263)	2.1 (0.484)	5.4 (0.080)	6.9 (0.080)	11.9 (0.021)	5.4 (0.142)	8.5 (0.162)	6.0 (0.363)	8.1 (0.069)	7.8 (0.142)
	MERRA-2 (raw)	10.4 (0.000)	8.1 (0.010)	11.1 (0.005)	11.4 (0.002)	17.7 (0.003)	7.2 (0.208)	17.8 (0.014)	13.5 (0.030)	9.7 (0.142)	13.4 (0.030)
	PDIR-Now (raw)	−1.0 (0.944)	2.3 (0.576)	−1.2 (0.889)	3.2 (0.726)	0.6 (0.944)	−1.4 (0.675)	2.6 (0.441)	−3.2 (0.726)	−4.5 (0.401)	−9.4 (0.184)
	PERSIANN (raw)	8.1 (0.294)	12.1 (0.069)	−0.3 (1.000)	9.4 (0.184)	−2.3 (0.675)	−3.8 (0.576)	4.8 (0.675)	4.5 (0.780)	−8.9 (0.675)	−11.6 (0.093)
	PERSIANN-CCS (raw)	49.0 (0.050)	16.1 (0.234)	35.4 (0.080)	18.4 (0.484)	2.8 (0.889)	−3.4 (0.834)	5.0 (0.780)	4.7 (0.726)	3.0 (0.889)	21.2 (0.363)
	CMORPH (bc)	13.5 (0.059)	7.7 (0.327)	10.8 (0.142)	10.7 (0.108)	13.0 (0.059)	4.1 (0.327)	14.0 (0.080)	12.6 (0.093)	6.9 (0.576)	5.7 (0.401)
	ERA5 (bc)	2.1 (0.780)	9.4 (0.025)	11.6 (0.184)	4.9 (0.441)	22.5 (0.030)	5.2 (0.263)	9.9 (0.234)	12.5 (0.184)	9.1 (0.108)	6.5 (0.441)
	MERRA-2 (bc)	26.9 (0.001)	30.9 (0.010)	36.2 (0.006)	38.7 (0.008)	42.2 (0.003)	30.2 (0.059)	44.6 (0.008)	60.7 (0.001)	49.1 (0.001)	32.5 (0.036)
	PDIR-Now (bc)	9.5 (0.401)	8.9 (0.624)	4.1 (0.675)	4.8 (0.675)	12.6 (0.327)	3.6 (0.726)	7.0 (0.780)	−1.1 (0.944)	8.0 (0.401)	0.0 (1.000)
	PERSIANN (bc)	3.2 (0.327)	2.5 (0.726)	5.6 (0.294)	4.7 (0.401)	−0.1 (1.000)	0.8 (0.944)	−3.5 (0.675)	1.7 (0.780)	−1.5 (0.889)	−0.4 (1.000)
	PERSIANN-CCS (bc)	16.9 (0.050)	5.9 (0.484)	9.5 (0.208)	15.0 (0.263)	10.0 (0.363)	0.2 (0.944)	13.1 (0.327)	12.6 (0.441)	8.4 (0.401)	3.8 (0.726)
R-factor	IMERG	50.9 (0.363)	6.1 (0.889)	31.6 (0.484)	42.8 (0.263)	88.7 (0.036)	−23.3 (0.726)	51.4 (0.363)	−0.0 (1.000)	−8.5 (0.889)	20.9 (0.363)
	CMORPH (raw)	37.7 (0.263)	78.5 (0.042)	15.3 (0.780)	30.9 (0.184)	61.7 (0.014)	−6.5 (1.000)	38.7 (0.184)	51.9 (0.108)	13.5 (0.484)	24.3 (0.484)
	ERA5 (raw)	5.2 (0.441)	4.2 (0.529)	−0.4 (0.944)	−1.7 (0.944)	11.0 (0.162)	−7.4 (0.484)	10.8 (0.441)	2.9 (0.726)	12.9 (0.184)	3.3 (0.624)
	MERRA-2 (raw)	24.1 (0.000)	26.6 (0.000)	14.1 (0.021)	49.3 (0.001)	29.5 (0.010)	11.4 (0.208)	33.9 (0.050)	25.3 (0.001)	14.5 (0.017)	24.3 (0.001)
	PDIR-Now (raw)	−0.2 (0.675)	4.4 (0.069)	2.4 (0.142)	1.7 (0.726)	5.3 (0.263)	3.8 (0.327)	6.2 (0.484)	−0.5 (1.000)	9.8 (0.576)	−7.1 (0.576)
	PERSIANN (raw)	172.3 (0.003)	175.7 (0.030)	77.9 (0.162)	120.8 (0.017)	123.2 (0.059)	97.0 (0.036)	112.1 (0.012)	124.5 (0.012)	51.0 (0.401)	94.8 (0.017)
	PERSIANN-CCS (raw)	526.1 (0.108)	286.9 (0.124)	529.9 (0.093)	371.6 (0.124)	200.8 (0.294)	99.7 (0.780)	219.4 (0.263)	167.4 (0.484)	92.9 (0.675)	431.5 (0.263)
	CMORPH (bc)	88.4 (0.208)	64.8 (0.363)	69.0 (0.025)	33.7 (0.529)	117.4 (0.030)	−53.6 (0.401)	95.9 (0.080)	−6.0 (0.944)	−1.3 (1.000)	35.9 (0.401)
	ERA5 (bc)	−74.0 (0.401)	74.9 (0.184)	59.5 (0.363)	3.8 (0.944)	133.6 (0.162)	22.4 (0.780)	70.9 (0.401)	105.1 (0.234)	21.6 (0.889)	−7.6 (0.944)
	MERRA-2 (bc)	155.2 (0.069)	189.4 (0.124)	146.9 (0.059)	229.8 (0.002)	167.8 (0.069)	129.7 (0.208)	188.5 (0.050)	383.0 (0.008)	318.3 (0.003)	114.0 (0.208)
	PDIR-Now (bc)	82.0 (0.441)	−28.6 (0.834)	−23.6 (0.780)	−16.5 (0.889)	1.3 (0.944)	−56.1 (0.441)	131.0 (0.162)	−151.7 (0.108)	41.4 (0.726)	18.4 (0.780)
	PERSIANN (bc)	5.8 (0.944)	38.9 (0.529)	66.4 (0.093)	43.9 (0.484)	50.7 (0.363)	−71.5 (0.263)	25.9 (0.944)	−25.0 (0.441)	19.6 (0.889)	−5.7 (1.000)
	PERSIANN-CCS (bc)	79.8 (0.234)	6.1 (0.780)	50.5 (0.363)	74.5 (0.484)	94.9 (0.184)	−35.1 (0.726)	86.3 (0.263)	36.4 (0.944)	110.9 (0.363)	94.6 (0.184)

Raw: values from raw gridded RPs; bc: values from bias-corrected products. Values in the tables are Theil–Sen slopes, while values in brackets are Mann-Kendall p-values. Bold values designate significant trends at $\alpha$ = 5% level.

analyses the significance of Theil–Sen slope trends in the time series of annual rainfall and annual rainfall erosivity values over the period 2001–2020 in Burkina Faso at all synoptic stations. According to gauge observation, a significant upward trend (p-value = 0.014; slope = 9.9 mm yr⁻¹) is detected at Ouagadougou (central region in Burkina Faso), which is reproduced by IMERG (p-value = 0.030; slope = 17.0 mm yr⁻¹) and ERA5 before bias correction (p-value = 0.021; slope = 11.9 mm yr⁻¹). IMERG also simulates a significant upward trend at Bobo, which does not appear in gauge observations. CMORPH and MERRA-2, before bias correction, simulate trends at most of the stations, while PDIR-Now, PERSIANN, and PERSIAN-CCS do not detect any significant trends. After bias correction, MERRA-2 and ERA5 (to a lesser extent) are now simulating trends at most of the stations, while the trend at Ouagadougou is still captured, albeit with a larger slope value (ERA5: 22.5 mm yr⁻¹; MERRA-2: 42.2 mm yr⁻¹). It is interesting to note that the bias correction is trend-preserving for MERRA-2, PDIR-Now, PERSIANN, and PERSIAN-CCS, and less skilful at preserving trends for CMORPH and ERA5.

Regarding trends in R-factors, the significant upward trend in rainfall appears in rainfall erosivity values at Ouagadougou according to IMERG R-factors (p-value = 0.036; slope = 88.7). This trend is also reported in CMORPH, either raw or bias-corrected. The trends in MERRA-2 R-factors before bias correction consistently follow the trends in annual rainfall from the same RP; however, these trends are mostly eliminated after bias correction, except for Boromo, Bobo, and Po stations, all of which are located in the south and south-western regions of the country. For the remaining RPs, no significant trends are detected in annual R-factors after bias correction.

4. Discussion

4.1. Key Findings in This Study

In this study, the impact of bias correction on gridded rainfall products’ representation of rainfall and rainfall erosivity is evaluated. In general, high-resolution gridded satellite rainfall products and rainfall reanalyses have been increasingly used in recent years in the literature to represent rainfall in West Africa, including Burkina Faso [31,37,38,39,40,42,44]. These products offer several advantages, such as improved spatial and temporal resolution, that alleviate the lack of gauge observations for monitoring rainfall-related risks and providing early warnings [31]. Moreover, since gauge observations are generally recorded at a daily timescale, such data are hardly appropriate for assessing the dynamics of specific processes such as soil erosion by rainfall [101,102,103].

This study revealed that at daily, monthly, and annual timescales, IMERG stands out as the optimal product in terms of accuracy in rainfall for all the stations in Burkina Faso. Also, its accuracy in detecting rainfall events of different cumulative values assessed in this study through categorical metrics further confirmed that IMERG is still the optimal product in capturing the timing of erosive rainfall events while generating less false alarms. High-resolution gridded satellite and reanalysis rainfall products have been evaluated in earlier studies for their representation of rainfall in Burkina Faso and, more largely, in West Africa. The performance of these products has been typically assessed at daily, dekadal, monthly, and annual timescales and across different climatic zones. Over West Africa, Houngnibo et al. [44] found that IMERG, MSWEP, RFE2, ARC2, and TAMSAT performed reasonably well, regardless of the West African climate zone and rainy season period. Specifically, for Burkina Faso, Dembélé and Zwart [38] and, more recently, Yonaba et al. [30] concluded that the RFE product provided an accurate representation of rainfall, followed by the TAMSAT rainfall product. Recently, Garba et al. [43] showed that TAMSAT also performed optimally across all climatic zones in Burkina Faso at the daily timescale, despite many biases. It should also be mentioned that the reasons why satellite and reanalysis RPs do not accurately represent observed rainfall in Burkina Faso and, more largely, West Africa are many: first, the complexity of precipitation processes that lead to rainfall, which vary greatly from one region to another [43]; second, the sensor limitations, which could explain why satellite-based retrievals of rainfall could not be accurate over specific surfaces or atmospheric conditions [43]; third, algorithm inaccuracies, which could introduce errors during the conversion of raw satellite data into rainfall estimates [74,75,78]; fourth, the sparsity of rain gauge networks, which are extremely low and often unreliable in West Africa, hindering the improvement of satellite and reanalysis RPs [38,43,44]. Also, temporal and spatial scales need extremely complex adjustments to accurately retrieve rainfall at sub-daily timescales, therefore limiting the potential applications of such RPs [74,75]. Finally, the climate variability context of West Africa—particularly the Sahel, where dramatic changes in precipitation patterns often occur—further complicates the task of accurately estimating rainfall from satellite and reanalysis products. Therefore, the selection of a given rainfall product should be carried out based on its intended application, and a careful and specific evaluation is recommended beforehand [31,43,44].

This study included a sub-daily bias correction of rainfall to reduce systematic biases in the representation of rainfall detected in RPs. Due to the non-availability of high-resolution rainfall observed, the optimal product in this study, which was IMERG, was selected as a reference to adjust the biases in the remaining RPs. The bias correction method used in this study accounted for adjusting the biases in the diurnal patterns of rainfall. In general, many studies agree upon the fact that bias correction improves the representation of hydrometeorological processes in satellite or reanalysis data through various mechanisms [52,53,85]. First, it addresses the prevalent issues of underestimation and overestimation of rainfall inherent in gridded rainfall datasets. By applying correction factors or distribution quantile adjustments, biases are mitigated, significantly improving the representation of rainfall patterns in terms of intensity and duration. Secondly, it fosters improved agreement between satellite or reanalysis data and ground-based measurements. Additionally, bias correction reduces seasonal biases present in satellite or reanalysis data. Lober et al. [83] carried out a bias correction of 20 years of IMERG satellite rainfall data in Canada and observed a significant improvement in the accuracy of the satellite precipitation data at daily and monthly scales. Specifically, for sub-daily rainfall, Faghih et al. [52] showed that following a diurnal bias correction technique is generally more effective than a standard bias correction since many hydrological processes, including rainfall, are generally affected by diurnal cycles, which are not typically captured through standard bias correction methods. Machine learning-based approaches have also been appraised for estimation or bias correction of rainfall erosivity [104,105,106] because of their ability to capture and model nonlinear patterns [107]. In this study, more insights on the impact of bias correction on rainfall have been highlighted, such as the reduction in biases in rainfall at the daily, monthly, and annual timescales; the increase in the probability of detection of erosive rainfall events; the adjustment in the distribution of rainfall event intensities and duration; and the improved representation of spatial annual patterns in rainfall.

The study also analysed the impact of bias correction of rainfall-on-rainfall erosivity estimates in Burkina Faso. It should be mentioned that rainfall erosivity is a multiannual factor averaged over a long-term period (i.e., 20 years); therefore, the timely detection of single rainfall events is not really needed, but rather, the cumulative amount and total duration of events plays a key role in the accuracy of R-factor estimation, which is typically the aspect of rainfall distribution treated by the bias correction procedure. IMERG rainfall produced an R-factor on the order of 2929.7 MJ mm ha⁻¹ h⁻¹ yr⁻¹, closest in agreement with the GloREDa R-factor (2964.9 MJ mm ha⁻¹ h⁻¹ yr⁻¹). In previous literature, Roose [8,9] carried out several plot-scale measurements and reported a simple relationship relating annual rainfall erosivity $R$ to annual rainfall $P$ over a 5–10 year period through the simple relationship $R=17.02\times [\left(0.5+0.05\right)\times P]$, which was found appropriate for the Ivory Coast, Burkina Faso, Senegal, Niger, and Chad in West Africa, with the exception of mountainous and coastal locations or areas at transition zones between unimodal and bimodal annual rainfall distributions [108]. However, this relationship cannot hold to the current climate conditions because of significant changes in soil surface conditions since the first Sahelian paradox (drought period in the 1970s and the 1980s), which also heavily affected surface runoff generation mechanisms [109,110]. Also, Yameogo et al. [111] estimated R-factor values of 362–493 MJ mm ha⁻¹ h⁻¹ yr⁻¹ in the Sissili watershed (southern region in Burkina Faso), while Ouedraogo et al. [112] provided estimates of 500–600 MJ mm ha⁻¹ h⁻¹ yr⁻¹ in the north-western region. These estimates are well below the reference estimates from GloREDa [28] and those reported in this study, probably because most of the previous studies used empirical relationships calibrated in different contexts, or which might no longer be applicable in the frame of the current climatic conditions in the West African Sahel. Also, such empirical equations were established using limited observations, while the estimates in this study use high temporal resolution rainfall data over a long-term period, which is deemed to be more appropriate according to the RUSLE2 handbook’s recommendations [13].

More recent studies also provide R-factor estimates over West Africa. Using TMPA 3B43 monthly satellite data, Vrieling et al. [4] estimated an annual R-factor of 2000–6000 MJ mm ha⁻¹ h⁻¹ yr⁻¹ for the period 1998–2008 in Burkina Faso, further refined to 3000–6000 MJ mm ha⁻¹ h⁻¹ yr⁻¹ in Vrieling et al. [5] using TMPA 3B42 three-hourly rainfall for the period 1998–2012. Diodato et al. [29] used the African Rainfall Erosivity Subregional Empirical Downscaling (ARESED) model to estimate an annual R-factor of 2000–5000 MJ mm ha⁻¹ h⁻¹ yr⁻¹ in Burkina Faso over the 1998–2008 period. Recently, Emberson [35] estimated an annual R-factor of 2000–4000 MJ mm ha⁻¹ h⁻¹ yr⁻¹ over the period 2001–2021 using IMERG data, while Fenta et al. [20] and, further, Fenta et al. [113] estimated over the same period an annual R-factor in the range of 2050–4500 MJ mm ha⁻¹ h⁻¹ yr⁻¹ using a fusion of IMERG and GloREDa by following a residual-based merging approach. Bezak et al. [18] estimated a rainfall erosivity of 1150–3700 MJ mm ha⁻¹ h⁻¹ yr⁻¹ using CMORPH and ERA5 over the period 1998–2019 in Burkina Faso. The estimates in this study are in line with these previous studies conducted at the global or continental scale. However, our results provide a more nuanced and complete view of the spatial heterogeneities of rainfall erosivity in Burkina Faso.

Finally, the findings in this study suggest that bias correction is effective at improving the estimation of rainfall erosivity by treating the biases and uncertainties in rainfall events’ distributions, cumulative values, and durations. It also appears that although the R-factor estimates from all the bias-corrected RPs significantly improved in accuracy, none of them performed better than IMERG, which was selected as the reference product for bias correction. This further suggests that IMERG should be recommended for impact studies related to rainfall erosivity in Burkina Faso and, in general, in West Africa, given its accuracy in simulating rainfall. Also, since IMERG natively provides sub-daily rainfall at a 30 min resolution, it is effective for use in rainfall erosivity estimation without the need for half-hourly-to-hourly calibration factors.

4.2. Study Limitations and Future Work

A few limitations of the actual study should be acknowledged. First, the study uses high-resolution gridded rainfall products, which are typically prone to different types of biases, uncertainties, and inconsistencies arising from a variety of factors. In this regard, rainfall erosivity estimates are likely to be affected. A second point worth mentioning is that the study uses GloREDa values as a reference, which were developed from a database of gauge measurements collected from stations among which only a few were located in Africa (5% of the total) and none covered Burkina Faso [28]. Also, regarding trends in rainfall erosivity values, it should be acknowledged that stationary trend assumptions are generally hardly rejected on short timeseries (i.e., with small sample size of, typically, 10–20 values) [114]. Although these could call into question the truthfulness of the reference herein used, the annual average long-term rainfall erosivity estimates seem consistent with many other studies [4,5,18,20,28,29,35,113].

Building upon the findings in this study, future work could focus on IMERG rainfall products to establish rainfall erosivity estimation methods from daily, monthly, and annual rainfall while considering the variety of models already existing in the literature. Also, spatially consistent iso-erodent maps of rainfall erosivity in Burkina Faso for the current climatic conditions could be produced to shed light on the spatial patterns of soil erosion and land degradation. Finally, the recent iteration of CMIP6 global climate models [115] could be used to analyse the future evolution of rainfall erosivity under different warming scenarios to provide incentives for the development and promotion of sustainable soil and land management strategies.

5. Conclusions

This study carried out an assessment of the impact of bias correction of rainfall on rainfall erosivity estimations, with a focus on Burkina Faso in West Africa over the period 2001–2020 using high-resolution gridded satellite and reanalysis rainfall products. Firstly, the study showed that gridded rainfall products can be invaluable tools in poorly gauged environments like Burkina Faso, offering a viable solution for estimating rainfall erosivity in regions where the density of rain gauge observations is very sparse. The IMERG product, in particular, is identified as optimal among the studied rainfall products due to its superior accuracy in reproducing rainfall patterns across daily, monthly, and annual timescales. The diurnal sub-daily bias correction used in this study was revealed to be effective in improving the accuracy of all the gridded products at all timescales, their probability of detection of rainfall events, the spatial patterns in annual rainfall across the country, and the adjustment of bias in the distributions of rainfall events’ durations and intensities. These improvements were further paramount to improving the estimation of the long-term average annual rainfall erosivity in almost all the rainfall products, along with the seasonal average annual patterns in rainfall erosivity and spatial distribution of the average annual R-factor. The impact of bias correction on annual trends in rainfall and rainfall erosivity also revealed that bias correction was skilful in adjusting trends, most likely because of the trend-preserving nature of the bias correction method used in this study. The bias correction was further useful in aligning rainfall erosivity trends with rainfall trends.

This study underscores the broader importance of accurate rainfall observations, most likely at high spatial and temporal resolutions, which can serve in the bias adjustment of rainfall products. Further, this is critical for impact studies, such as rainfall erosivity estimation, especially in regions prone to soil erosion and land degradation.