Comparison and Bias-Correction of Satellite-Derived Precipitation Datasets at Local Level in Northern Kenya

: Understanding ongoing trends at local level is fundamental in research on climate change. However, in the Global South it is hampered by a lack of data. The scarcity of land-based observed data can be overcome through satellite-derived datasets, although performance varies according to the region. The purpose of this study is to compute the normal monthly values of precipitation for the eight main inhabited areas of North Horr Sub-County, in northern Kenya. The o ﬃ cial decadal precipitation dataset from the Kenyan Meteorological Department (KMD), the Global Precipitation Climatology Centre (GPCC) monthly dataset and the Climate Hazards Group Infrared Precipitation with Stations (CHIRPS) monthly dataset are compared with the historical observed data by means of the most common statistical indices. The GPCC showed the best ﬁt for the study area. The Quantile Mapping correction is applied to combine the high resolution of the KMD dataset with the high performance of the GPCC set. A new and more reliable bias-corrected monthly precipitation time series for 1983–2014 results for each location. This dataset allows a detailed description of the precipitation distribution through the year, which can be applied in the climate change adaptation and tailored territorial planning.


Introduction
Over the past decades, research on climate change has become of primary concern for different disciplines at a global level. However, the understanding of the climate at a local level is key to interpreting undergoing changes. Although there is an abundance of data in the Global North, the countries of the Global South are struggling to fill the gap. More specifically, land-based meteorological stations in African countries are still around half the optimal number required, unevenly distributed and poorly equipped [1][2][3].
In Kenya, there are thirty-two land-based meteorological stations, distributed mainly in the south and on the coast, which are the most developed and geared towards tourism [4]. To improve the livelihoods of communities, enhance and protect property [5], the Kenyan government is promoting the country's research and development in climate information.
In North Horr Sub-County, situated in Marsabit County in northern Kenya, there are no land-based meteorological stations to provide past climate observations. At a distance of 250 km, there are three weather stations, two located in the highlands and one near lake Turkana. However, they are not close enough to describe the peculiarities of the local climate of North Horr.
The area investigated is mainly inhabited by semi-nomadic pastoral communities which rely on livestock production. They move around the area during the year looking for pasture and water
The most commonly used statistical indices were calculated: Bias, Mean Absolute Error, Mean Squared Deviation, Root Mean Squared Deviation, Correlation Coefficient and standard deviation [26][27][28]39,40]. The Taylor diagram was used as a graphical evaluation instrument [41].
The comparative analysis highlighted the relatively high performance of the GPCC dataset and the low performance of the KMD dataset. The GPCC gauge-based dataset selected was used to rectify the KMD dataset at local level on sampled reference points-the main inhabited areas, usually cited in policy planning [42,43]-using the Quantile Mapping [44] bias correction algorithm. Specific normal monthly precipitation values were identified for the reference points.
The new normal monthly precipitation values can be used in future studies for local purposes while the experimented methodology can be applied in other scant data contexts.
In Section 2, the study area is described along with the precipitation datasets that were analyzed. The steps of the methodology adopted are also detailed. In Section 3, the main results are presented. Finally, in Section 4 the conclusions are discussed with particular attention to the limits and to the possible future perspectives of the research.

Study Area
The study aims to define the best-fit precipitation dataset for North Horr Sub-County, which is situated in Marsabit County, northern Kenya ( Figure 1). The area is considered to be part of the ASALs, with an evaporation rate that exceeds rainfall by more than ten times. However, there are some peculiarities due to the influence of the altitude on the precipitation, which makes Mt. Marsabit (1865 m above sea level), Mt. Kulal (2235 m above sea level), Hurry Hills (1685 m above sea level) and the Moyale-Sololo escarpment (up to 1400 m above sea level) quite wet areas. By contrast, the Chalbi Desert, a large salted depression lying between 435 m and 500 m above sea level, is the dryer feature of the area [45].
There are no land-based meteorological stations in the Sub-County. Therefore, an area within a 250 km radius from North Horr, the main village, has been defined and the meteorological stations located inside this area have been selected. These land-based meteorological stations are situated in Lodwar, Moyale and Marsabit.
The main inhabited areas-i.e., reference points-besides North Horr are Balesa, Dukana, El Gadhe, El-Hadi, Gus, Kalacha and Malabot. There are no land-based meteorological stations in the Sub-County. Therefore, an area within a 250 km radius from North Horr, the main village, has been defined and the meteorological stations located inside this area have been selected. These land-based meteorological stations are situated in Lodwar, Moyale and Marsabit.

Precipitation Datasets
Previous studies have assessed the performance of different gridded precipitation products over East Africa [32] and Kenya [34,35]. The comparison of GPCC, CHIRPS, TRMM 3B42 (Tropical Rainfall Measuring Mission) and MERRA Modern-Era Retrospective Analysis for Research and Application) based on eight major agro-ecological zones demonstrated that GPCC and CHIRPS achieved improved results in ASALs [35]. In fact, the GPCC dataset best estimates precipitation in tropical warm semiarid areas while CHIRPS best estimates precipitation in tropical warm arid areas. Similarly, the comparison of CHIRPS, TRMM 3B42, PERSIANN-CDR (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks Climate Data Record) and ARC2 (African Rainfall Climatology version 2.0) showed that CHIRPS have excellent performance in ASAL regions (high correlation, low RMSE, and low standard deviation) [34]. At regional level (East Africa), GPCC and CHIRPS have similar consistent results [32]. The other principal gridded precipitation products were evaluated. TRMM 3B42-as well as TRMM 3B43-has a reduced temporal (1998present) [46] coverage compared to the aim of this research . PERSIANN-CDR underestimates rainfall in different topographical features and climatic conditions [34,47]. MERRA has a coarse resolution (0.5°), best estimates rugged mountainous zones and inaccurately predicts the rainfall amounts in relatively low-lying areas [35]. Following these considerations, three precipitation datasets have been selected and compared ( Figure 2). The reference dataset is the KMD dataset provided by the National Meteorological Service. The other two datasets where selected on the base of previous studies results. They are highly reliable because they are provided by the World Meteorological Organization and the Climate Hazard Center funded by the U.S. Agency for

Precipitation Datasets
Previous studies have assessed the performance of different gridded precipitation products over East Africa [32] and Kenya [34,35]. The comparison of GPCC, CHIRPS, TRMM 3B42 (Tropical Rainfall Measuring Mission) and MERRA Modern-Era Retrospective Analysis for Research and Application) based on eight major agro-ecological zones demonstrated that GPCC and CHIRPS achieved improved results in ASALs [35]. In fact, the GPCC dataset best estimates precipitation in tropical warm semiarid areas while CHIRPS best estimates precipitation in tropical warm arid areas. Similarly, the comparison of CHIRPS, TRMM 3B42, PERSIANN-CDR (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks Climate Data Record) and ARC2 (African Rainfall Climatology version 2.0) showed that CHIRPS have excellent performance in ASAL regions (high correlation, low RMSE, and low standard deviation) [34]. At regional level (East Africa), GPCC and CHIRPS have similar consistent results [32]. The other principal gridded precipitation products were evaluated. TRMM 3B42-as well as TRMM 3B43-has a reduced temporal (1998-present) [46] coverage compared to the aim of this research (1983-2013). PERSIANN-CDR underestimates rainfall in different topographical features and climatic conditions [34,47]. MERRA has a coarse resolution (0.5 • ), best estimates rugged mountainous zones and inaccurately predicts the rainfall amounts in relatively low-lying areas [35]. Following these considerations, three precipitation datasets have been selected and compared ( Figure 2). The reference dataset is the KMD dataset provided by the National Meteorological Service. The other two datasets where selected on the base of previous studies results. They are highly reliable because they are provided by the World Meteorological Organization and the Climate Hazard Center funded by the U.S. Agency for International Development (USAID), the National Aeronautics and Space Administration (NASA) and the National Oceanic and Atmospheric Administration (NOAA).
International Development (USAID), the National Aeronautics and Space Administration (NASA) and the National Oceanic and Atmospheric Administration (NOAA). The KMD dataset is a decadal precipitation dataset, part of the Enhancing National Climate Services (ENACTS) project for development in Africa, which focuses on the creation of reliable climate data for national and local decision making. It has been produced by combining qualitycontrolled data from the national observation network with satellite estimates from the European Meteorological Satellites (METEOSAT). The data processing was performed using the Climate Data Tool software package developed by the International Research Institute (IRI) [36]. The dataset was directly furnished by the KMD but is also available at http://kmddl.meteo.go.ke:8081/SOURCES/.KMD/. It has a spatial resolution of 0.0375° and refers to the period 1983-2014.
The GPCC dataset, a monthly precipitation dataset, was developed by the Global Precipitation Climatology Project in support of the WMO World Climate Research Programme (WCRP) and the Global Energy and Water Cycle Experiment (GEWEX). It is a gauge-only product based on observations from rain gauge stations only available at a coarser resolution of 0.5° and a temporal coverage from 1901 to 2013 [37]. Version 7 (DOI: 10.5676/DWD_GPCC/FD_M_V7_050), available at NOAA/OAR/ESRL PSD website at https://www.esrl.noaa.gov/psd/, has been used for this study.
The CHIRPS dataset was developed to support the USAID Famine Early Warning Systems Network (FEWS NET). It builds on an high resolution and long recording period of precipitation estimates based on infrared Cold Cloud Duration (CCD) observations and on a station blending procedure based on a modified inverse distance weighting algorithm [48]. Several studies ascertain the effectiveness of this dataset in East Africa [26,27,38]. The monthly v2p0 version has been used, which is accessible through the IRI Data Library at https://iridl.ldeo.columbia.edu/SOURCES/.UCSB/.CHIRPS/. It has a spatial resolution of 0.05° and ranges from 1981 to near-present.
Finally, the monthly observed historical series from 1960 to 2016 from Marsabit, Moyale and Lodwar meteorological stations have been used as benchmark for the comparison analysis. They have been directly furnished by the KMD. Their characteristics are summarized in Table 1.  The KMD dataset is a decadal precipitation dataset, part of the Enhancing National Climate Services (ENACTS) project for development in Africa, which focuses on the creation of reliable climate data for national and local decision making. It has been produced by combining quality-controlled data from the national observation network with satellite estimates from the European Meteorological Satellites (METEOSAT). The data processing was performed using the Climate Data Tool software package developed by the International Research Institute (IRI) [36]. The dataset was directly furnished by the KMD but is also available at http://kmddl.meteo.go.ke:8081/SOURCES/.KMD/. It has a spatial resolution of 0.0375 • and refers to the period 1983-2014.
The GPCC dataset, a monthly precipitation dataset, was developed by the Global Precipitation Climatology Project in support of the WMO World Climate Research Programme (WCRP) and the Global Energy and Water Cycle Experiment (GEWEX). It is a gauge-only product based on observations from rain gauge stations only available at a coarser resolution of 0.5 • and a temporal coverage from 1901 to 2013 [37]. Version 7 (DOI: 10.5676/DWD_GPCC/FD_M_V7_050), available at NOAA/OAR/ESRL PSD website at https://www.esrl.noaa.gov/psd/, has been used for this study.
The CHIRPS dataset was developed to support the USAID Famine Early Warning Systems Network (FEWS NET). It builds on an high resolution and long recording period of precipitation estimates based on infrared Cold Cloud Duration (CCD) observations and on a station blending procedure based on a modified inverse distance weighting algorithm [48]. Several studies ascertain the effectiveness of this dataset in East Africa [26,27,38]. The monthly v2p0 version has been used, which is accessible through the IRI Data Library at https://iridl.ldeo.columbia.edu/SOURCES/.UCSB/.CHIRPS/. It has a spatial resolution of 0.05 • and ranges from 1981 to near-present.
Finally, the monthly observed historical series from 1960 to 2016 from Marsabit, Moyale and Lodwar meteorological stations have been used as benchmark for the comparison analysis. They have been directly furnished by the KMD. Their characteristics are summarized in Table 1.

Methodology
The methodology followed in this study was structured in three steps ( Figure 3): • Section 2.3.1 presents the comparison of the datasets with the observed historical series from the selected land-based meteorological stations. This step lead to the identification and selection of the "reference dataset" (D 1 ) and "dataset to correct" (D 2 ). • In Section 2.3.2, the correction method is detailed. The series from D 2 for each reference point are corrected with D 1 through the Quantile Mapping bias correction algorithm. This procedure leads to the definition of a group of five series for each reference point, each series resulting from a different correction method. The comparison of the five series with D 1 identifies the most appropriate correction method. Consequently, one series for each station and reference point has been selected. • Section 2.3.3 refers to the extraction and computation of the precipitation normals for each reference point.

Methodology
The methodology followed in this study was structured in three steps ( Figure 3): • Section 2.3.1 presents the comparison of the datasets with the observed historical series from the selected land-based meteorological stations. This step lead to the identification and selection of the "reference dataset" (D1) and "dataset to correct" (D2). • In Section 2.3.2, the correction method is detailed. The series from D2 for each reference point are corrected with D1 through the Quantile Mapping bias correction algorithm. This procedure leads to the definition of a group of five series for each reference point, each series resulting from a different correction method. The comparison of the five series with D1 identifies the most appropriate correction method. Consequently, one series for each station and reference point has been selected. • Section 2.3.3 refers to the extraction and computation of the precipitation normals for each reference point.  [49]. A comparison of standard deviations (σ) was also performed in order to assess the dispersion of the values with regard to historical values.
A Taylor Diagram has also been created to provide an easier visual interpretation of the results. In the same graph, the CC, the RMSD, and the σ are shown for each series analyzed [41]. The MATLAB SkillMetrics toolbox developed by Peter Rochford has been used to create the diagram [50].

Correction through the Quantile Mapping Method
The KMD dataset, besides being provided by the official National Meteorological Service, has the higher resolution and therefore it was chosen as the dataset to be corrected (D2).  [49]. A comparison of standard deviations (σ) was also performed in order to assess the dispersion of the values with regard to historical values.
A Taylor Diagram has also been created to provide an easier visual interpretation of the results. In the same graph, the CC, the RMSD, and the σ are shown for each series analyzed [41]. The MATLAB SkillMetrics toolbox developed by Peter Rochford has been used to create the diagram [50].

Correction through the Quantile Mapping Method
The KMD dataset, besides being provided by the official National Meteorological Service, has the higher resolution and therefore it was chosen as the dataset to be corrected (D 2 ).
The GPCC dataset was preferred to the three land-based meteorological stations as reference dataset (D 1 ). The stations in a 250 km radius, in fact, are not representative of the ASALs, while the GPCC dataset offers reliable interpolated gauge-derived information. This approach, justified by the scarcity of observed data in the region, is in line with previous studies, which aimed to overcome this obstacle by resorting to gauge-derived datasets for the validation of satellite or reanalysis precipitation Sustainability 2020, 12, 2896 7 of 18 datasets [51,52]. The correction procedure aims at merging the information derived by the two datasets, namely integrating the satellite-derived data, which is found to have too low level performances, with the gauge-derived data [53,54]. Findings demonstrate that Quantile Mapping can cause inflation problems (same temporal structure and variability of the coarser grid) when applied to datasets of different resolution [55,56]. However, the procedure here used is opposite to the common downscaling procedure; in fact, it aims at correcting a high-resolution satellite-derived dataset with a coarser grid reference dataset.
The KMD dataset was therefore corrected using the Quantile Mapping bias correction algorithm technique, which has been widely used for correction of precipitation datasets [57][58][59] and has demonstrated high performances in arid and semi-arid areas [33,60]. In particular, the work of Ringard et al. demonstrated its usefulness for satellite-derived datasets correction in scarce observed data contexts [61]. Moreover, the Quantile Mapping correction method performs very well concerning the reproduction of the precipitation annual cycle and of the wet and dry periods length [62]. This characteristic is fundamental with reference to the monthly normal identification and for future climate analysis of the area.
The Quantile Mapping technique is based on statistical transformation which attempts to adjust the distribution of modelled data such that it closely resembles the observed climatology solved using a theoretical distribution The 'qmap' package developed by Lukas Gudmundsson for R software was used for the computation [63]. The procedure was carried out for all the reference locations using a pixel to pixel approach. The 'qmap' package supports five different analytical methods, both parametric and non-parametric transformations. These methods use different functions to transform the distribution of the modelled data to match the distribution of the observations. The five functions performed are parametric transformations (PTF), distribution derived transformations (DIST), non-parametric quantile mapping using empirical quantiles (QUANT), non-parametric quantile mapping using robust empirical quantiles (RQUANT) and quantile mapping using a smoothing spline (SSPLIN)(for further details see the documentation at the following link https://www.rdocumentation.org/packages/CSTools/ versions/2.0.0/topics/CST_QuantileMapping).
Five precipitation series were created for the three stations and for the eight reference locations. The results of the Quantile Mapping correction were compared with the GPCC series for each reference location through the statistical indices (Section 2.3.1). The most appropriate method was identified, leading to the selection of a best-fit precipitation series for each reference location.

Reference Values Computation
New reference values were computed on the new precipitation series by averaging the monthly precipitation amount for the entire period (1983-2013).

Comparison of Dataset Performance at Meteorological Station Level
The comparison of the precipitation datasets with the observed series led to an important first conclusion. The KMD dataset does not feature the best indices values for all the stations. Results from the first step of the analysis conducted indicated that the GPCC dataset was a better choice as the reference series.
According to the statistical indices (Tables 2 and 3) and to the Taylor diagrams (Figure 4), the GPCC dataset fits better for the stations of Marsabit and Moyale, while the KMD dataset fits better for Lodwar. However, for reasons of homogeneity and consistency, the GPCC dataset was also chosen as the reference dataset for Lodwar station since its statistical values are close to the values obtained for the KMD dataset. Table 2. Comparison based on statistical indices (BIAS, MAE, MSD, RMSD and CC) of the precipitation datasets with the observed historical series from the selected land-based meteorological stations (Lodwar, Marsabit and Moyale) for the period 1983-2013. For the CC index, "*" corresponds to a p-value < 0.01, "**" corresponds to a p-value < 0.001 and "***" corresponds to a p-value < 0.0001. Values in bold correspond to the best value of the index for each station.     Table 3) is proportional to the distance from the origin of the diagram. The Correlation Coefficient (in Table 2) between each series and the observed historical series is expressed by the azimuthal angle. Finally, the Root Mean Squared Deviation (in Table 2) between each series and the observed historical series is proportional to the distance from the point representing the observed historical series. Points closer to the historical series' marker, that is, with similar standard deviation, lower RMSD and higher Correlation Coefficient, correspond to the best-fit datasets.  Table 3) is proportional to the distance from the origin of the diagram. The Correlation Coefficient (in Table 2) between each series and the observed historical series is expressed by the azimuthal angle. Finally, the Root Mean Squared Deviation (in Table 2) between each series and the observed historical series is proportional to the distance from the point representing the observed historical series. Points closer to the historical series' marker, that is, with similar standard deviation, lower RMSD and higher Correlation Coefficient, correspond to the best-fit datasets.

Correction through the Quantile Mapping Method
As showed in the previous section, the GPCC dataset fits better than the other two datasets compared with the historical series. However, the GPCC dataset has a lower resolution (0.5 • ) compared to the KMD dataset and CHIRPS dataset (0.0375 • and 0.05 • , respectively), and the differences in local Sustainability 2020, 12, 2896 9 of 18 topography may be biased. Therefore, it was necessary to apply a bias correction method to overcome these two problems. The strategy adopted was to correct the KMD dataset (D 2 ), which is issued by the official National Meteorological Service and has the highest resolution, with the GPCC dataset (D 1 ) which performs better on ASALs.
The bias correction method is performed using the Quantile Mapping method from the 'qmap' R package. From comparison analysis, the Parametric Transformations method, which fits a parametric transformation to the quantile-quantile relation of observed and modelled values, provided the best results (see Appendices A and B). Hereinafter, the Bias-Corrected KMD dataset will be referred to as the BCKMD dataset (D 3 ).

Quantile Mapping Validation at Station Level
The performance of the new BCKMD dataset is assessed by means of the statistical indices mentioned previously (see Section 3.1). The indices have been calculated in relation to the historical series of the land-based meteorological stations, then compared with the same indices calculated for the KMD dataset.
As shown in Table 4, the BCKMD dataset fits the observed historical series better than the KMD dataset, apart from Lodwar station. This may be due to a higher performance of the KMD dataset-before correction-at Lodwar station compared to the GPCC concerning BIAS, MAE, MSD and RMSD. However, the errors obtained are still acceptably low. In fact, the standard deviation values and the relatively low values of the error's indices, even for Lodwar, justify the selection of the BCKMD dataset for the study area.

Quantile Mapping at Reference Point Level
The Quantile Mapping correction on the base of the GPCC dataset was also applied to the KMD dataset at the reference points. The Parametric Transformations method has been used in accordance with the validation carried out at the stations level. The result was a best-fit precipitation dataset for the eight locations.

Calculating Normal Values of Precipitation at Station Level
The normal values were calculated on the precipitation series obtained for the three stations, by averaging the monthly precipitation amount for the entire period (1983-2013) (reported in Table 5). Long rains amount, short rains amount and total annual amount were also calculated. Figure 5 compares the distribution of the precipitation through the year according to the observed series and to the new BCKMD dataset. with the validation carried out at the stations level. The result was a best-fit precipitation dataset for the eight locations.

Calculating Normal Values of Precipitation at Station Level
The normal values were calculated on the precipitation series obtained for the three stations, by averaging the monthly precipitation amount for the entire period (1983-2013) (reported in Table 5). Long rains amount, short rains amount and total annual amount were also calculated. Figure 5 compares the distribution of the precipitation through the year according to the observed series and to the new BCKMD dataset.

Calculating Normal Values of Precipitation at Reference Point Level
The normal values were calculated on the precipitation series obtained for each reference point, by averaging the monthly precipitation amount for the entire period . Moreover, long rains amount, short rains amount and total amount were calculated.
The normal values for the eight reference points are shown in Table 6. A visual representation of the precipitation distribution at local scale is pictured in Figure 6.
The understanding of climate differences at local scale is crucial for an effective territorial planning against negative impact of climate change. This study succeeded in obtaining normal values of precipitation for each reference point despite the lack of land-based meteorological stations in the area and high-resolution and fitting satellite-derived precipitation time series. Differences in rainfall regime are evident in Figure 6, which shows higher precipitation amounts in the northern part of the Sub-County then in the southern reference points.
The new precipitation time series can be used for the evaluation of drought indices as well as for water security assessment. More specifically, the monthly normal values can be used as reference values for comparing measured or forecasted data in order to evaluate drought or wet periods. Moreover, it has been possible to calculate the normal values for the entire long rain season and short rain season, by cumulating monthly values for March, April and May and for October, November and December, respectively. Knowing the distribution of the precipitation throughout the year and the possible deviation from normal values is fundamental. This is at the base of the community organization for the local semi-nomadic pastoral population.

Conclusions
The aim of this study was to obtain the normal values of the monthly amount of precipitation for the main inhabited areas in North Horr Sub-County, in order to provide a benchmark for understanding the ongoing changes in the local climate. Therefore, it was necessary to identify an appropriate historical precipitation series. The comparison between the GPCC, KMD and CHIRPS datasets highlighted the lower performance of the KMD dataset compared to the others, despite it being the dataset officially issued and used by the Kenyan Meteorological Department for the whole country. Previous studies on East Africa indicated the CHIRPS dataset to be a reliable global dataset

Conclusions
The aim of this study was to obtain the normal values of the monthly amount of precipitation for the main inhabited areas in North Horr Sub-County, in order to provide a benchmark for understanding the ongoing changes in the local climate. Therefore, it was necessary to identify an appropriate historical precipitation series. The comparison between the GPCC, KMD and CHIRPS datasets highlighted the lower performance of the KMD dataset compared to the others, despite it being the dataset officially issued and used by the Kenyan Meteorological Department for the whole country. Previous studies on East Africa indicated the CHIRPS dataset to be a reliable global dataset for the region [26,27,32]. The relatively high performance of the GPCC dataset in northern arid Kenya is in line with the results of previous studies, which indicated it as a good fit for the ASALs [35], but with a low capacity in representing complex terrain [28]. However, the need to highlight local differences in the annual trend of precipitation led to the use of the KMD dataset after a correction procedure based on the GPCC dataset. This approach aimed to integrate the higher resolution of the KMD dataset-namely, its ability to detect differences in the precipitation trend at a local scale-with the higher ability of the GPCC dataset to represent the real historical values in the area. The methodology adopted created a new bias-corrected monthly precipitation time series for each reference point, from which the local normal values were extracted.
Since the need for high-resolution precipitation data covering the Global South is becoming urgent for any discipline that must consider the role of climate, this study represents an attempt to provide a solution to the scarcity of observed data. The absence of land-based meteorological stations in the area, however, cannot be ignored and constitutes a limit in the study. Future research should be directed to test the methodology proposed here in other contexts, where the availability of observed data could provide a yardstick for its usefulness and accuracy.  Table A1. Comparison based on statistical indices (BIAS, MAE, MSD, RMSD, CC and σ) of the GPCC dataset with the five bias-corrected series for the period 1983-2013. For the CC index, "*" corresponds to a p-value < 0.01, "**" corresponds to a p-value < 0.001 and "***" corresponds to a p-value < 0.0001. Values in bold correspond to the best value of the index for each reference point. Appendix B Table A2. Comparison based on statistical indices (BIAS, MAE, MSD, RMSD, CC and σ) of the historical values with the five bias-corrected series (PTf, DIST, RQUANT, QUANT, SSPLIN) for the period 1983-2013. For the CC index, "*" corresponds to a p-value < 0.01, "**" corresponds to a p-value < 0.001 and "***" corresponds to a p-value < 0.0001. Values in bold correspond to the best value of the index for each station.