A new methodology for estimating rainfall aggressiveness risk based on daily rainfall records for multi-decennial periods

A NEW METHODOLOGY FOR ESTIMATING RAINFALL AGGRESSIVENESS RISK BASED ON DAILY RAINFALL RECORDS FOR MULTI-DECENNIAL PERIODS Leoncio García-Barrón1, Julia Morales2, Arturo Sousa2* 1 Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, España 2 Departamento de Biología Vegetal y Ecología, Universidad de Sevilla, E-41012 Sevilla, España ABSTRACT The temporal irregularity of rainfall, characteristic of a Mediterranean climate, corresponds to the irregularity of the environmental effects on soil. We used aggressiveness as an indicator to quantify the potential environmental impact of rainfall. However, quantifying rainfall aggressiveness is conditioned by the lack of sub-hourly frequency records on which intensity models are based. On the other hand, volume models are characterized by a lack of precision in the treatment of heavy rainfall events because they are based on monthly series. Therefore, in this study, we propose a new methodology for estimating rainfall aggressiveness risk. A new synthesis parameter based on reformulation using daily data of the Modified Fournier and Oliver´s Precipitation Concentration indices is defined. The weighting of both indices for calculating the aggressiveness risk is established by multiple regression with respect to the local erosion R factor estimated in the last decades. We concluded that the proposed methodology overcomes the previously mentioned limitations of the traditional intensity *Correspondence to: A. Sousa, Departamento de Biología Vegetal y Ecología, Universidad de Sevilla, E-41012 Sevilla, Spain. Email: [email protected] *Revised manuscript with no changes marked Click here to view linked References and volume models and provides accurate information; therefore, it is appropriate for determining potential rainfall impact over long time periods. Specifically, we applied this methodology to the daily rainfall time series from the San Fernando Observatory (1870-2010) in southwest Europe. An interannual aggressiveness risk series was generated, which allowed analysis of its evolution and determination of the temporal variability. The results imply that environmental management can use data from longterm historical series as a reference for decision making. KEY WORDS: Aggressiveness; Rainfall erosivity; Land use; Environmental risk; Southwest Europe 1. Introduction One of the features of the rainfall regime in a Mediterranean climate is the interand intra-annual irregularity (García-Barrón et al., 2013). Inter-decadal climate studies help to explain the causes of terrain alteration over time (Diodato et al., 2008). Rainfall erosivity causes a loss of fertile soil, damage to agriculture and infrastructure and water pollution and is influenced by changes in rainfall patterns (Martín-Fernández & Martínez-Nuñez, 2011; Sánchez-Moreno et al., 2014) and by predictable effects of climate change (Diodato et al., 2011). In this study, we consider aggressiveness risk as a potential estimate of the physical effects of rainfall on soil dynamics sensu Fournier (1960). Our view is that aggressiveness risk is an appropriate environmental indicator and directly related to erosion and associated with the incidence of torrents, floods, landslides, displacement, etc. (Gregori et al., 2006). Therefore, knowledge of this variable over long periods is particularly useful for the management of water resources, soil conservation, agricultural planning and the development of environmental policy. Moreover, annual estimates of aggressiveness risk enable the comparison of orders of magnitude among different observation sites at different times. This environmental indicator is based on daily rainfall records and does not include other aspects related to erosion such as slope length, soil types, wind activity, land use, etc. For the direct calculation of soil erosion, the universal soil loss equation (USLE) has been frequently used (Wischmeier & Smith, 1978). Specifically, the rainfall erosivity, or R factor, depends on the energy of every rainfall episode (Panagos et al., 2015). The R factor is an accepted instrument for local erosion measurement, successively updated and empirically endorsed by means of field measurements (Renard et al., 1997). Models such as the USLE and RUSLE were originally developed for detailed scale application in the farming sector, so their application on a regional scale presents some limitations (Terranova et al., 2009). Although USLE is one of the most widely used erosivity models worldwide, it has some limitations because the estimations of soil erosion do not fit the empirical measures of sedimentation, and the R erosivity factor does not explicitly incorporate direct runoff of water, which affects the accuracy of the model (Kinnell, 2010). Additionally, the spatial distribution tends to overestimate the R factor at regional or river basin levels (Hernando & Romana, 2016), and its is not recommended in areas different from those in which it was developed without an analysis of the validity of the equations. In the specific case of the study of rainfall aggressiveness effects, two complementary approaches are taken: intensity models are based on sub-hourly rainfall records, and volume models are based on monthly rainfall records. This model refers to the different partial accumulations of rainfall. That is, it does not take into account the number, the duration and the rainfall amount exclusively on the total monthly rainfall. Nevertheless for the direct calculation of the rainfall erosivity in large areas, it is desirable to make use of high frequency rainfall records collected by nearby weather stations during a period longer than twenty years (Angulo-Martinez et al., 2009). However, except for modern automatic weather stations, traditional observatories have no high-frequency series with sub-hourly records. On the other hand, volume models are based on monthly rainfall records that are extensively available in most countries. In this case, the regular use of the aggressiveness index in environmental studies (Fournier, 1960), subsequently modified by Arnoldus (1980) as the Modified Fournier Index (IFM) and complemented with the Precipitation Concentration Index (IPC) developed by Oliver (1980), is remarkable. Both estimations for calculating the intensity of rainfall aggressiveness present limitations. The drawback of the intensity models is the lack of adequate time series records, and that of the volume models is the imprecision in the treatment of heavy rain episodes because they are based on finer timescale resolutions. The amount of precipitation is not the only relevant parameter; its temporal distribution is also relevant, as studies on Mediterranean river basins in the NE Iberian Peninsula (Sánchez-Canales et al., 2015) and in the SW Iberian Peninsula (Sousa et al., 2009) have made evident. Various studies have compared the results obtained using intensity models (the R factor of USLE) to those obtained using volume models. In the Iberian Peninsula, the Institute for the Conservation of Nature (ICONA, 1988) under the Spanish Ministry of Agriculture proposed an empirical relationship that locally associates the R factor with the IFM index. Additionally, a high correlation between the R factor and the monthly and/or annual precipitation parameters, including the Fournier Index, has been obtained in various geographic areas, such as in the Mediterranean area (Diodato & Bellocchi, 2007; Taguas et al., 2013), East Asia (Lee &Heo, 2011; Yue et al., 2014) and the tropical zone (Sanchez-Moreno et al., 2014). In the USA, Renard & Freid (1994) proposed regression equations that calculate the R factor from IFM. Additionally, Loureiro & Couthino (2001) estimated the R factor based on the monthly rainfall aggressiveness in southern Portugal, and Da Silva (2004) estimated the same in Brazil. In this study, we propose to estimate the aggressiveness risk by means of a single annual parameter that improves the limitations of models based only on monthly records (volume models) and those based on sub-hourly records (intensity models). We used a method based on the daily scaled reformulation of the traditional indices of aggressiveness, IFM and IPC, that provides more accurate results. The method also allows numerous investigations because there are many weather stations that have large time series of daily data. This Estimated Annual Aggressiveness Risk (RA) is calibrated locally by means of regression equations with respect to the erosivity R factor for a period of simultaneity. Backwards extrapolation of the resulting function generates the corresponding time series of the aggressiveness risk. Recently, García-Barrón et al. (2015) have synthesized in this parameter the aggressiveness risk using IFM and IPC to study trends in river basins of the Iberian Peninsula. In this article, we propose two main objectives: a) To define and calculate a single annual parameter based on daily records that synthetically estimates the rainfall aggressiveness risk. b) To apply this methodology to a study area with a Mediterranean climate to analyse the temporal behaviour and deduce patterns in the evolution of the rainfall aggressiveness risk. 2. Study area and data We chose the South-Atlantic region of the Iberian Peninsula for the methodological application, which is based on a long period and can help to draw conclusions about the potential risks of rainfall on the land. Spain is one of the countries most severely affected by soil erosion in the European Mediterranean region due to extreme spatial and temporal variations in its physical environment, with frequent periods of drought and torrential rainfall (Solé, 2006). The importance of erosion in the Mediterranean is related to the long history of human activity in a region characterized by low annual precipitation, the occurrence of intense rainstorms and long-lasting droughts, high evapotranspiration, the presence of steep slopes and the occurrence of recent tectonic activity, together with the recurrent use of fire, overgrazing and farming (García-Ruiz et al., 2013). The southwestern Iberian Peninsula falls within the domain of the Mediterranean climate, although it is influenced by an oceanic effect because of its proximity to the Atlantic Ocean. The average annual rainfall is approximately 600 mm (average values are substantially higher in the mountain range separating the watersheds of the Guadiana and Guadalquivir rivers). Rainfall is subject to marked inter-annual irregularity, with great oscillations in annual totals that include multi-year periods of drought (Aguilar, 2007). In general, the profile of the intra-annual precipitation shows an asymmetric unimodal curve, ascending in autumn and descending smoothly from winter to summer, when it reaches its minimum. The Royal Observatory of the Spanish Navy (ROA) located in San Fernando (province of Cadiz, at the southern tip of the Iberian Peninsula) includes the oldest active weather station in Spain; rainfall records have been recorded since 1805 and accessible daily data since 1870. Because of these long-term and high-quality records, different studies have used ROA data as a reference to characterize the rainfall regime (Rodrigo, 2002; Martin-Vide & Lopez-Bustins, 2006) and the interand intra-annual behaviour (García-Barrón et al., 2013) of rainfall in the study area. The meteorological stations located in the province or district capitals of Spain and Portugal have been selected to quantify the level of regional representation of the ROA rainfall series (Figure 1). Data from the Spanish stations were provided by the Spanish Meteorological Agency (AEMET), and data from the Portuguese stations were provided by the Portuguese Sea and Atmosphere Institute (IPMA). The weather stations are distributed over different geographical areas as follows: Cadiz, Huelva and Faro in the coastal zone, Cordova and Seville in the Guadalquivir valley, and Badajoz and Beja in the Guadiana basin (Figure 1). Figure 1. Map showing the locations of the meteorological stations used in the study area. These series are homogeneous and have no missing data (Almarza et al., 1996; García-Barrón et al., 2013). We have chosen the period 1961-1990, recommended by the World Meteorological Organization, for comparing the ROA rainfall records to those of every selected regional station. Table 1 shows the representativeness of the ROA compared to every selected observatory in the area. To determine the representativeness, we calculated the proportionality of the average annual rainfall between the ROA and every selected station, the R-Pearson coefficient of the annual totals of the respective rainfall series and the R-Pearson coefficient of the monthly average of the intra-annual distribution. Table 1. Proportionality coefficient and annual and interannual correlation between the San Fernando Observatory (ROA) and the selected regional stations. Table 1 shows that although the total rainfall differs among neighbouring stations and in those within the same basin, the intraand inter-annual behaviour is similar. The high correlation of the results obtained in Table 1 shows that the region studied has the same climate and is subject to the same synoptic conditions. This corroborates the conclusions of previous studies on rainfall in the southwestern Iberian Peninsula (García-Barrón et al., 2011). Therefore, we assume that the general rainfall regime of the ROA sufficiently characterizes the Atlantic southern zone of the Iberian Peninsula for analysis of its temporal variability. Consequently, this study estimated the behaviour of the temporal evolution of the aggressiveness risk using daily rainfall records of the ROA from 1870 to 2010. Absolute homogeneity tests were applied to the annual series with AnClim software (Stepanek, 2007) and the Standard Normal Observatories Country Institution Latitude and Longitude Annual average rate R-Pearson Interannual R-Pearson Intra-annual San Fernando (ROA) Spain ROA - - - Cadiz Spain AEMET 1.04 0.96 1.00 Huelva Spain AEMET 1.03 0.94 0.98 Faro Portugal IPMA 37° 01' 00" N 7° 55' 59" W 1.04 0.76 0.97 Seville Spain AEMET 1.02 0.85 0.98 Cordova Spain AEMET 0.96 0.86 0.98 Badajoz Spain AEMET 38° 43 02 N 6° 49 45 W 1.02 0.72 0.94 Beja Portugal IPMA 38° 0.92 0.70 0.94 Applying equation 9 to the respective annual values of IFM* and IPC* for the entire study period allowed extrapolation and thus generation of the interannual estimated series of RA from 1870 to 2010. The units for RA are the same as those for R [(megajoules graphically represents the evolution of the annual risk estimated for the period 18702010 with the corresponding trend line. Figure 5. Temporal evolution of RA in the SW Iberian Peninsula. For the entire period, the average value, the coefficient of linear trend, the Vn coefficient of variation and the ID general disparity index of RA were calculated. The analysis results are shown in Table 2, which also includes the corresponding values of the indices IFM*and IPC* for comparison purposes. Table 2. Characterization of the RA and its comparison to the respective statistical components IFM* and IPC*: average, trend (linear regression), explained variance, variability and Specific Disparity Index Average Trend r 2 VN ID IFM* 21.0 - 0.012 < 0.01 0.28 0.40 IPC* 3.8 < 0.001 < 0.001 0.27 0.35 RA 1742 - 4.63 < 0.1 0.47 0.64 The average value of RA was 1742 units. The linear trend (Figure 5) showed a slightly decreasing slope (-4.63 unit / year), statistically significant at the 95% level (T= -2.8 <-1.9) but climatically not relevant because the explained variance was lower than 1% (r2<0.1). Therefore, the central value was not a sufficient predictor for the temporal estimation of the RA; the high coefficient of variation (VN = 0.47) and the general disparity index (ID = 0.64) are proof of this state. This highlights the large temporary fluctuations of the RA series, even between consecutive years. Additionally, the coefficient of variation and the general disparity index for RA were higher than those for IFM* and IPC*. Despite the lack of a significant trend of RA, its accumulated relative deviations Ak allowed us to identify different multiannual sequences that characterized the interannual behaviour and, consequently, to identify sections of high and low risk of aggressiveness. Figure 6 represents the accumulated deviations with respect to the N average of the whole series of RA. An initial upstream line was observed until the end of the nineteenth century and involved a high frequency of years with an aggressiveness risk higher than the average of the series. This period of high frequency of the aggressiveness risk coincided with the end of the Little Ice Age in Andalusia, which led to an important clogging and reduction process in lagoons and small coastal brooks (Sousa et al., 2006) in the southwestern Iberian Peninsula. Diodato et al. (2011) noted that erosive forces increased towards the end of the Little Ice Age (~1850) over the western and central Mediterranean in general and have increased even more during the recent warming period in meridional Mediterranean regions because of a higher frequency of intense storms. On the other hand, Figure 6 shows a downward section at the first half of the 20th century, corresponding to years with aggressiveness risk below the average and that coincided with a slightly dry period with smooth annual rainfall fluctuations. Figure 6. Evolution of the accumulated deviations with respect to the average RA. Finally, a steep downward phase that we associate with a period of low rainfall aggressiveness stands out during the last thirty years of the 20th century (Figure 6). This phase coincided with a dry period in which there was a greater dispersion of the intraannual rainfall, a relative lack of rainfall in spring and a shift in rainfall towards the autumn months (García-Barrón et al., 2013). Data of the erosion and silting of the thalwegs of coastal brooks in the SW of Spain for this period show lower activity than that for both previously mentioned periods (the end of the 19th century and the 1960s of the 20th century), which showed high erosive activity (Figure 6). That is, phases of high rainfall aggressiveness during the 19th and 20th centuries in the SW of Europe caused wetland regression, especially in lagoons and coastal brooks (Sousa et al., 2013, 2015). 4.3 Temporal irregularity of the estimated risk of aggressiveness The irregularity of the environmental effects caused by rainfall originates in the annual and intra-annual rainfall irregularity itself. In the previous sections, we discussed the general variability of RA during the study period by means of VN and ID; consequently, it is necessary to analyse its interannual evolution. To do so, we calculated the mobile variation coefficients for periods of eleven years (V(11)n) for the n years of the series generated (obviously with a reduction of the first ten elements) during the observation period. The V(11)n variation coefficient associated with the time sequence of the RA annual value showed peaks of the estimated risk in the years 1887, 1922, 1961 and 2002 of approximately 0.5, separated by the corresponding periods of minimum values lower than 0.30 (Figure 7), which indicates higher temporal stability of the interannual RA values. This figure includes the representation of the values trend line. The last 25 years of the series is characterized by the greatest risk variability of the 140 years studied. Figure 7 shows a linear trend of the coefficient of variation values with a positive slope (y = 0.0009 x +0.387) significant for p = 0.05 (TC = 3.62> 1.98), with r2 equal to 0.09. The slope increases to 0.015 in the line that links the relative maximum values (1887, 1922, 1961 and 2002). Figure 7. Mobile variation of the RA coefficient for periods of eleven years with the trend line of the entire period analysed and that of the maximum relative values. Therefore, the temporal analysis of RA by means of the V(11)n variation coefficient shows an almost cyclical pattern with a pulsation of approximately 40 years (Figure 7). This cyclical component is unique, and we have no information indicating that it had been previously detected in the variability analysis of other climate variables in the Mediterranean environment. Equivalent results were obtained by analysing the Specific Disparity Index (Idj) are available in the Supporting Information section (S2). It is also noteworthy that the V(11)n variation coefficient of the RA presents a progressive increase of its relative extremes. 5. Discussion The proposed methodology for calculating RA was applied to the SW Iberian Peninsula. Temporal analysis of the generated RA series of San Fernando (ROA, 1870-2010) showed some sequences of consecutive years that, as a whole, show a frequency of annual values higher or lower than the mean value. There was a predominance of low aggressiveness during the first half of the 20th century, especially during the last thirty years; however, there were peaks of high aggressiveness in the late 19th and mid-20th centuries coinciding with periods of high soil erosion that resulted in siltation of lagoons (Sousa et al., 2013) and brooks (Sousa et al., 2015) in the southwestern Iberian Peninsula (Biosphere Reserve of Doñana). Although this study was developed in the Iberian Peninsula, the new parameter is based on IFM and IPC (indices used in different edaphic and meteorological conditions), and we consider that its application is valid for analysing the potential impacts of rainfall in different climatic and geographic areas. Thus, it is necessary to develop a weighting local equation of both indices, (IFM*, IPC*), determined by rainfall in each region. Several studies (Renard & Freid, 1994; Diodato y Bellocchi, 2007; Lee & Heo, 2011; Taguas et al., 2013; Yue et al., 2014) have shown a high correlation between the R factor and rainfall parameters such as the IFM. For their part, Michiels et al. (1992) used the IPC to analyse rainfall variability and considered that this index is appropriate for evaluating the erosivity, and Gabriels et al. (2003) used monthly precipitation data to analyse the interannual variability of erosivity. Apaydin et al. (2006), Elagib (2011), Elbasit et al. (2013) and Meshesha et al. (2015) used procedures based on these indices to analyse erosivity in arid regions. Based on the IFM, Sauerborn et al. (1999) and Nearing (2001) suggested the possibility of changes in the rainfall erosivity in Europe and the USA, respectively, during the 21st century. De Luis et al. (2010) separately applied IFM and IPC to study a possible increase in erosivity in the Spanish Mediterranean area. Additionally, both indices have been used to detect changes in the temporal trend of erosivity in southern Portugal (Nunes et al., 2016) and, in an integrated way, analyse the spatial and temporal variability of aggressiveness in the watersheds of the Iberian Peninsula (García-Barrón et al., 2015). The advantage of the proposed methodology is that it provides an accurate annual synthesis parameter of direct interpretation, potentially applicable to different geographical areas. RA overcomes the limitations of the intensity models because of the lack of sub-hourly records (R factor) and the imprecision of the traditional volume models (IFM and IPC) associated with the effects of heavy rainfall episodes. Therefore, the new RA parameter is an appropriate mechanism for estimating the potential environmental impact of rainfall aggressiveness and for performing spatial and temporal comparative analysis. To determine the equation FM, IPC) with sufficient accuracy, we needed minimum simultaneous daily and sub-hourly rainfall records in addition to local erosion data. An open research line for the future is to extend the application of this methodology to other study areas with different climatic conditions, particularly in the Mediterranean, semiarid environments and environments at risk of desertification, and to compare the results to the results obtained by other methods and at other time scales. Although the proposed methodology has theoretical foundations, it would be convenient to establish a direct empirical verification of RA to allow for the quantification of rainfall environmental impacts (runoff, siltation of wetlands, etc.). Another aspect to consider is that although RA estimates the rainfall potential energy, the erosive process is much more complex, and it is not always that rainfall amount and/or distribution the main factor affecting the erosive process. García-Ruiz et al. (2015) conducted a worldwide meta-analysis of soil erosion rates, based on data from more than 4000 sites, whose results show that there is extraordinarily high variability in erosion rates, with almost any rate apparently possible irrespective of land slope, climate, scale, land use/land cover and other environmental characteristics. Despite this variability, some general trends were found, including an increase in erosion rates with increasing land slope and annual precipitation, the association of agricultural practices with the highest erosion rates, and a correlation between shrub coverage and the lowest erosion rates. Even so, the worldwide meta-analysis of García-Ruiz et al. (2005) suggests that only order of magnitude approximations of erosion rates are possible. This supposes a high degree of uncertainty and causes these authors to postulate the need to develop protocols that allow the comparison of the results of different sites. Human activity can also significantly affect the development and evolution of denudation hot spots, especially through changes in land use (Vergari et al., 2013). As these authors point out, this factor has a great importance associated with the croplands abandonment, and in general, in badlands of the Mediterranean area. The relationships among the various factors that influence the erosion intensity are very complex, and therefore new studies are needed to continue to deepen these aspects, with the support of real erosion measures taken directly from the field work. 6. Conclusions A new synthesis parameter RA was calculated by means of the combined use of the Fournier (IFM*) and Oliver concentration (IPC*) indices and reformulated with daily data. Weighting between both indices was obtained by multiple regression with the local erosivity. The historical extrapolation allowed the interannual series of the RA to be obtained. A comparative analysis of the temporal evolution of IFM* and IPC* showed that they were independent of each other and that their contributions to the calculation of RA were complementary. Obtaining the annual values of RA in the same units and scale as the USLE R function allowed for the generalization of the results, thus increasing their applicability and establishing a link among historical rainfall records and current values of the potential rainfall aggressiveness. In our opinion, the proposed methodology has the ability to provide consistent conclusions about historical erosive processes in each region linked to the potential rainfall aggressiveness. Therefore, it has a special relevance to the design of environmental measures and land management policies that prevent the direct and indirect impacts of rainfall. 7. Acknowledgements providing the rainfall records and the Environmental Information Network of the Ministry of Environment of the Junta de Andalucía for providing the data set to calculate the erosivity. We thank María Ángeles Garrido and Alicia Cebolla for their help in data processing. 8. References Aguilar M. 2007. Recent changes and tendencies in precipitation in Andalusia. In: Climate Change in Andalusia: trends and environmental consequences, Sousa A, García-Barrón L, Jurado V. (eds). Consejería de Medio Ambiente: Sevilla; 99116. https://idus.us.es/xmlui/handle/11441/30483 Alexandersson H. 1986. A homogeneity test applied to precipitation data. Journal of Climatology 6: 661675. DOI:10.1002/joc.3370060607. Almarza C, López A, Flores C. 1996. Homogeneidad y variabilidad de los registros históricos de precipitación en España. Instituto Nacional de Meteorología, Madrid. Angulo-Martínez M, López-Vicente M, Vicente-Serrano SM, Beguería S. 2009. 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Journal of Food, Agriculture & Environment 11: 1073-1077. http://world-food.net/download/journals/2013issue_2/2013-issue_2-environment/e55.pdf. Fournier F. 1960. Climat et érosion. Presse Universitaire de France, Paris. Gabriels D, Vermeulen A, Verbist K, Van Meirvenne M. 2003. Assessment of rain erosivity and precipitation concentration in Europe. In: Proceedings of the International Symposium, 25 Years of Assessment of Erosion, Gabriels D, Cornelis W (eds). Ghent; 87 92. Table 1. Proportionality coefficient and annual and interannual correlation between the San Fernando Observatory (ROA) and the selected regional stations Observatories Country Institution Latitude and Longitude Annual average rate R-Pearson Interannual R-Pearson Intra-annual San Fernando (ROA) Spain ROA - - - Cadiz Spain AEMET 1.04 0.96 1.00 Huelva Spain AEMET 1.03 0.94 0.98 Faro Portugal IPMA 37° 01' 00" N 7° 55' 59" W 1.04 0.76 0.97 Seville Spain AEMET 1.02 0.85 0.98 Cordova Spain AEMET 0.96 0.86 0.98 Badajoz Spain AEMET 38° 43 02 N 6° 49 45 W 1.02 0.72 0.94 Beja Portugal IPMA 0.92 0.70 0.94 Table 2. Characterization of the RA and its comparison to the respective statistical components IFM* and IPC*: average, trend (linear regression), explained variance, variability and Specific Disparity Index Average Trend r 2 VN ID IFM* 21.0 - 0.012 < 0.01 0.28 0.40 IPC* 3.8 < 0.001 < 0.001 0.27 0.35 RA 1742 - 4.63 < 0.1 0.47 0.64 FIGURE LEGEND Figure 1. Map showing the locations of the meteorological stations used in the study area. Figure 2.a) Temporal evolution of the IFM* and b) the IPC* showing the average value and mobile average for periods of eleven years. Figure 3. Pairwise scatterplot of the time series IFM* and IPC* for the period 1870-2010. Figure 4. Pairwise scatterplot of the USLE R factor and the RA time series for the period 1991-2010. Figure 5. Temporal evolution of RA in the SW Iberian Peninsula. Figure 6. Evolution of the accumulated deviations with respect to the average RA. Figure 7. Mobile variation of the RA coefficient for periods of eleven years with the trend line of the entire period analysed and that of the maximum relative values.