Seasonal Dynamics of Rainfall Erosivity in Switzerland

One major controlling factor of water erosion is rainfall erosivity, which is quantified by the kinetic energy of a rainfall event and its maximum 30-min intensity. Rainfall erosivity is often expressed as R-factor in soil erosion risk models like the Universal Soil Loss Equation (USLE) and its revised version (RUSLE). As rainfall erosivity is closely correlated 10 with dynamic rainfall amount and intensity, the rainfall erosivity of Switzerland can be expected to have a characteristic regional and seasonal dynamic throughout the year. This intra-annual variability was mapped by a monthly modelling approach to assess simultaneously spatial and monthly pattern of rainfall erosivity. So far only national seasonal means and regional annual means exist for Switzerland. We used a network of 87 precipitation gauging stations with a 10-minute temporal resolution to calculate long-term monthly mean R-factors. Stepwise regression and Leave-one-out cross-validation 15 (LOOCV) were used to select spatial covariates which explain the spatial and temporal pattern of the R-factor for each month across Switzerland. The monthly R-factor is mapped by its specific regression equation and the ordinary kriging interpolation of its residuals (Regression-Kriging). As covariates, a variety of precipitation indicator data has been included like snow depths, a combination product of hourly precipitation measurements and radar observations (CombiPrecip), daily alpine precipitation (EURO4M-APGD) and monthly precipitation sums (RhiresM). Topographic parameters (elevation, 20 slope) were also significant explanatory variables for single months. The comparison of the 12 monthly rainfall erosivity maps showed a distinct seasonality with highest rainfall erosivity in summer (June, July, and August) influenced by intense rainfall events. Winter months have lowest rainfall erosivity. A proportion of 62% of the total annual rainfall erosivity is identified within four months only (June to September). Highest erosion risk can be expected for July where not only rainfall erosivity but also erosivity density is high. Additionally to the intra-annual temporal regime, a spatial variability of this 25 seasonality was detectable between different regions of Switzerland. The assessment of the dynamic behavior of the R-factor is valuable for the identification of susceptible seasons and regions.


Introduction
Soil erosion by water is a major environmental issue in Switzerland which has been measured (Konz et al., 2012, Alewell et al., 2014, mapped (Mosiman, 1990;Prasuhn, 2011;Prasuhn, 2012), and modelled (Gisler et al., 2011;Prasuhn et al., 2013) extensively. Since the 1950s, soil erosion by water is increasing in Switzerland on land under arable land (Weisshaidinger & Leser, 2006) as well as in mountain grasslands (Meusburger & Alewell, 2008). Mosimann et al. (1991) assessed a quantity 5 of up to 20% of all cultivated land in Switzerland to be affected by soil erosion. The costs of soil erosion for Switzerland's arable land were estimated to be about 53 million CHF yr-1 (US $55.2 million yr-1; Ledermann, 2012). Increasing trends of water erosion are predicted for Switzerland under future climate change due to more frequent and heavy precipitation during winter month (Fuhrer et al., 2006). Trends towards increasing rainfall erosivity are already observable in the months May to October (Meusburger et al., 2012). 10 Rainfall has direct impacts on soil mobilization by processes like rapid wetting or splash and runoff effects and is, therefore, one of the main driving forces of water erosion. The R-factor, one of the five soil erosion risk factors (rainfall erosivity, soil erodibility, slope steepness and length, cover management, and support practices) of the Revised Universal Soil Loss Equation (RUSLE) (Renard et al., 1997;Foster et al., 2008) expresses the impact of rainfall on soils as rainfall erosivity. The RUSLE is widely used for calculating soil loss, but each of the five factor maps also has an essential message on its own. 15 Besides being an important driving factor of soil erosion, the R-factor can also be used to conclude on soil vulnerability, flood hazard, and natural hazards or probability of droughts 2015a).
Previously published studies on rainfall erosivity in Switzerland focused on national seasonal means (Panagos et al., 2015a) or regional annual means (Friedli, 2006;Gisler et al., 2011;Meusburger et al. 2012;Prasuhn et al., 2013;). Since Switzerland has large regional and altitudinal variety in climatic conditions (humid continental to oceanic climate; Köppen, 1936) 20 seasonal and temporal variations of the weather are consequential. As such, these spatio-temporal variations can be expected to influence patterns in the rainfall erosivity. Meusburger et al. (2012) already showed the presence of a strong seasonality of the rainfall erosivity for clustered stations at different altitudinal classes in Switzerland. However, simultaneously spatial and temporal pattern of the R-factors seasonality have not yet been established. These spatio-temporal patterns are decisive in combination with spatio-temporal patterns of vegetation cover in order to allow for an accurate soil erosion risk assessment 25 and relevant for a monthly and seasonal management of agriculture practices and hazard controls.
Here, we aim to assess the spatio-temporal seasonal variability of rainfall erosivity in Switzerland by (i) extending the network of gauging stations from Meusburger et al. (2012) to obtain rainfall erosivity events for Switzerland (ii) producing monthly R-factor maps based on high resolution spatial covariates using a regression-kriging 30 approach (iii) evaluate the spatio-temporal patterns of the seasonal R-factor dynamic in Switzerland Hydrol. Earth Syst. Sci. Discuss., doi:10.5194/hess-2016-208, 2016 Manuscript under review for journal Hydrol. Earth Syst. Sci. Published: 9 May 2016 c Author(s) 2016. CC-BY 3.0 License.

Rainfall erosivity (R-factor) calculation
The rainfall erosivity expressed as R-factor in RUSLE is a product of the kinetic rainfall energy (er) of an erosive rainfall event and its corresponding maximum intensity over a time span of 30 minutes (I30) (Brown & Forster, 1987). We used the erosive rainfall event thresholds defined by Renard et al. (1997) which were modified by Meusburger et al. (2012). The unit 5 rainfall energy (er) (MJ ha-1 mm-1) for each time interval is expressed as the intensity of rainfall (ir) (mm h-1) during that time interval. It is calculated by Brown and Forster (1987) as: The erosive rainfall event erosivity (EI30) (MJ mm ha-1¬ h-1¬) is a product of the unit rainfall energy (er) (Eq. (1)) and its maximum rainfall amount within a 30 minutes interval (according to Wischmeier & Smith, 1978): 10 EI 30 = (∑ e r v r k r=1 )I 30 ( 2) where vr is the rainfall volume (mm) during a time unit r and I30 is the maximum rainfall intensity within 30 minutes of the event (mm h-1).
The monthly rainfall erosivity (R) (MJ mm ha-1¬ h-1¬ month-1) is the mean of the accumulated event erosivity (EI30) (Eq. (2) within a month: 15 where n is the recorded number of years with the number of erosive events (mj) within a certain month j. k is the index of a single event with its corresponding event erosivity.
The event rainfall erosivity was calculated from the 10-min precipitation data for each station by applying the algorithm of Meusburger et al. (2012). The event rainfall erosivity was averaged by months to a long-term monthly mean R-factor (Rmo). 20 Usually, snow, snowmelt and rainfall on frozen soil are not assessed in the R-factor . Thus, a temperature threshold of 0°C was set to obtain only rainfall and exclude snow water equivalents which are subject to uncertainty in rainfall erosivity assessments (Leek & Olsen, 2000). Temperature data was measured simultaneous to precipitation (for 71 stations) or was directly derived (for 15 stations) from the closest stations (within a distance of less than 20 km) with similar elevation. We assumed only minor variation in temperature within that distance at a similar elevation 25 level.
Besides neglecting snow, we did not consider rainfall as hail which is mainly occurring during summer in Switzerland (Nisi et al., 2016;Punge & Kunz, 2016). Hurni (1978) investigated the impact of hail on rainfall erosivity in Switzerland and concluded that the erosivity of hail exceeds the one of rainfall.

Stations 30
We extended the gauging station network of Meusburger et al. (2012) (10 minutes measuring intervals) from 71 to an updated dataset of 87 stations (Fig. 1).
The additional 16 stations were previously investigated for rainfall erosivity by Nogler (2012). On average, the network represents one station each 22 km x 22 km. The average distance of one station to all others is 113.6 km by a minimum distance to the closest station of 13.2 km. A majority of stations (63) have recorded data of at least 22yr. The mean length of observations is 19.5yr and thus, meet the proposed minimum time-scale requirements for rainfall erosivity calculations of a 15yr measuring period (Forster et al. 2008). The stations are well distributed and were subject to a quality control (Begert et 5 al., 2005;Nogler, 2012).

Data and Covariates
High temporal information on snow cover and snow water equivalents, high spatio-temporal information on rainfall and high spatial information on topography are acquired as covariates (Table 1) for the monthly erosivity maps since rainfall erosivity is mainly controlled by precipitation and relief parameters (Meusburger et al., 2012;Panagos et al., 2015a;Panagos et al., 10 2016b). All data have a much higher resolution than datasets used in previously R-factor studies for Europe (Panagos et al., 2015a;2016a) and Switzerland (Meusburger et al., 2012).
The long-term snow depth (derived from total snow depth monthly mean by MeteoSwiss) on a monthly resolution was used as an approximation for precipitation as snow. The monthly point data of snow depth was regionalized by Inverse Distance Weighting. Hourly Swiss CombiPrecip data (geostatistical combination of rain gauge measurements (150 automatic stations) 15 and three C-band radar observations; Sideris et al., 2014) was aggregated and averaged to a long-term monthly mean. Longterm mean daily precipitation per month was calculated based on the daily values of alpine precipitation in EURO4M-APGD (Isotta et al., 2014). Averaging the monthly spatial precipitation of RhiresM (MeteoSwiss, 2013) over the years leads to long-term monthly mean precipitation sums. The variables elevation, slope, and aspect are retrieved from a Digital Terrain Modell (SwissAlti3D) for Switzerland. 20

Mapping the seasonal variability of rainfall erosivity in Switzerland
We used regression-kriging (Hengl et al., 2004;Hengl, 2007;Hengl et al., 2007) to map the monthly variability of rainfall erosivity. The regression-kriging approach relies on the monthly mean rainfall erosivities for each of the 87 stations which are going to be explained by a generalized linear regression (GLM). Later, the GLM is used for interpolating R mo for Switzerland based on the spatial covariates. In an ordinary global kriging, the residuals of the regression are interpolated. 25 The combination of R mo with its residuals also enables the consideration of the standard error. Meusburger et al. (2012) discussed different interpolation methods for an annual mapping of rainfall erosivity in Switzerland. Their results show that regression-kriging is an adequate method for Switzerland if significant relations between rainfall erosivity and spatial covariates exist.
Leave-one-out cross-validation (LOOCV) (Efron & Tibishirani, 1997) was used to avoid a resampling-bias of the 87 R mo for 30 each month in the regression. Data-split is only valid for large n, otherwise it reduces the training observations, is random and limited in reproducibility (Steyerberg, 2009;Harrell, 2015). In consideration of the low number of n (n=87), LOOCV Hydrol. Earth Syst. Sci. Discuss., doi: 10.5194/hess-2016-208, 2016 Manuscript under review for journal Hydrol. Earth Syst. Sci. Published: 9 May 2016 c Author(s) 2016. CC-BY 3.0 License. omits only one observation from the dataset per run and estimates the model from the remaining n-1 observations. The process was repeated 100 times for a better accuracy.
A log-transformation of R mo resulted in a normal distribution of the data. The suitability of each covariate for the GLM was determined by an automated stepwise feature selection process according to the Akaike information criterion (AIC). The significance threshold for covariate selection was set to 0.1. We also tested Least Absolute Shrinkage and Selection Operator 5 (LASSO) as an alternative feature selection method to the stepwise GLM, but it was less transparent for evaluation and showed inappropriate residual diagnostics (systematic error). Both, the LOOCV stepwise regression, as well as LASSO, were performed in the R-package "caret" (v6.0-68). Outliers (Bonferroni-adjusted outlier test) and influential observations (Cook's Distance) were omitted in the stepwise GLM.
The goodness-of-fit of the model was described by the coefficient of determination (R²), the root mean square error (E RMS ) 10 and the deviance. Regression diagnostics to evaluate the model included normality, non-constant error variance (homoscedasticity), multicollinearity (variance inflation factor; vif) and autocorrelation.
Twelve monthly maps of the long-term mean R mo were derived by applying the regression equation with the covariates and Each monthly map is subject to an individual GLM. Therefore, a subset of individual covariates explains rainfall erosivity for each month separately. A combination of three monthly maps leads to long-term seasonal mean R-factor (R seas ) maps for Switzerland with high spatial resolution. In addition, the sum of all twelve maps results in an updated (compared to Meusburger et al., 2012) long-term annual mean R-factor (R year ) map. Improvements of the new map are the extended 20 network of gauging stations, the cross-validation of the regression-kriging approach, and the inclusion of new high spatiotemporal covariates in order to increase the spatial resolution of the maps.

Cumulative daily R-factors
The cumulative percentage of R-factor is obtained and grouped by Swiss biogeographic regions to obtain the share of the total annual rainfall erosivity for Switzerland by seasons. These regions show distinct differences in climate, soils, elevation, 25 steepness, and geographic location. The cumulative curve of rainfall erosivity events enables the extraction of the annual share of rainfall erosivity on a daily scale. Therefore, all recorded rainfall events measured at stations within an individual biogeographic unit are averaged on a daily level.
Smaller values of ED mo indicate that the influence of monthly precipitation on the monthly rainfall erosivity is mainly driven by its amount. On the other hand, high values of ED mo show that relative to the absolute rainfall amount a high kinetic energy of rainfall was observed (e.g., strong storm events; Panagos et al., 2016b). Highest soil erosion risk is expected for areas where rainfall erosivity is high but related to a few intense rainfall events (small P mo ) instead of a high monthly 5 precipitation amount. As such, ED mo can reflect the temporal variability of rainfall intensity (Dabny et al., 2011) and can indicate how precipitation (short duration events with high intensities or high amounts of rainfall) controls the seasonality of rainfall. For the calculation of ED mo , we used RhiresM as the monthly precipitation dataset. According to Dabny et al.
Most of the monthly R-factors (96%) of the lowest 10% of all monthly values are part of the period between November and April whereas 97% of the highest 10% are monthly rainfall erosivities from May to October.
The recently published "Monthly Rainfall Erosivity" for Europe by Panagos et al. (2016a) and the national observations of 20 Mosimann et al. (1990) for a single station in Switzerland (Bern, Swiss Midland) fit the present calculations with highest rainfall erosivity for the season from June/July to August. The Swiss monthly rainfall erosivities in the European assessment (Panagos et al., 2016a) are smaller on average by 3 MJ mm ha -1 h -1 month -1 (after rescaling with the calibration factors from 30 to 10 minutes). That discrepancy by 5% mainly arises due to the different numbers and time series of gauging stations (87 vs. 71). 25 Seasonality of R mo is also observed for Italy (Borrelli et al., 2016), Greece (Panagos et al., 2016b), Iran (Sadeghi et al.,  month -1 , respectively, compared to 272 MJ mm ha -1 h -1 month -1 in Switzerland), and the peak of the R-factor is shifted from July to September for Italy and November for Greece respectively.

Mapping of monthly rainfall erosivity and related uncertainties
All covariatesaspect excludedwere significant (p-value < 0.1) within the stepwise regressions for at least one month to explain R mo (Table 2). For each month, an individual selection of covariates was achieved by the stepwise GLM. 5 Model efficiency averaged over all twelve months has a mean R² of 0.51 and a mean E RMS of 0.61 MJ mm ha -1 h -1 month -1 .
R² varies between 0.10 (Nov) and 0.66 (July). E RMS s ranges from 0.93 to 0.42 MJ mm ha -1 h -1 month -1 . Regression functions for November and December are the most uncertain ones with lowest R² and highest E RMS which need to be improved by additional covariates in the future, explaining rainfall erosivity in winter better. The low R²s are arising due to the lower rainfall erosivity mainly caused by the higher amount of snow (neglected in this study), which makes it more challenging 10 obtain better results. The same constrain was observed in a study for Greece with lowest rainfall erosivities and at the same time lowest R² (Panagos et al., 2016b). The higher the ratio of the null deviance to the residual deviance, the better the model fits by including the covariates. The residual deviance is lower than the null deviance in all twelve investigated months.
Monthly model efficiency and omitted influential outliers to increase the model's goodness of fit are summarized in Table 3.
The monthly observations of R mo at the 87 locations (exclusive outliers) as well as the residuals are normally distributed after 15 the log-transformation. A non-constant error (homoscedasticity), multicollinearity and non-autocorrelation were determined for all observations of the twelve months. H 0 was rejected by the Breusch-Pagan-test in all cases to confirm homoscedasticity. Regression diagnostics further show a vif<4 for each month. Therefore, we could not identify collinear data. According to a Durbin-Watson-test, the Swiss R mo -dataset is not autocorrelated.
The kriging of the residuals based on a stable variogram improved the interpolation in all months. The ranges of the 20 variograms exceed the mean distance (approx. 13.2 km) of neighboring stations in all months. The average prediction error of all 12 months is -0.0055 by an averaged root mean square standard error of 1.046 MJ mm ha -1 h -1 month -1 . The used stable semivariogram models are represented by 12 lag classes. The standard deviation maps of the monthly residual kriging show the usual pattern with lowest standard deviations close to the stations and higher standard deviations with increasing distance from the gauging stations. 25

Monthly rainfall erosivity maps for Switzerland
Temporal patterns of modelled R mo show a distinct seasonality with national means being lowest in January (10.5 MJ mm ha -1 h -1 month -1 ) and highest in August (263.5 MJ mm ha -1 h -1 month -1 ) (Table 4, Fig. 3).
Winter is the season with the lowest rainfall erosivity. The highest R mo peak in summer is consistent with the map of extreme point rainfall of 1h duration (100-year return period; Spreafico & Weingartner, 2005), where the strong influence of extreme 30 rainfall events on rainfall erosivity is indicated. Meusburger et al. (2012) already pointed to the relationship of thunderstorm activity to annual rainfall erosivity. The thunderstorm season in Switzerland lasts from late spring (May) to early fall Hydrol. Earth Syst. Sci. Discuss., doi:10.5194/hess-2016-208, 2016 Manuscript under review for journal Hydrol. Earth Syst. Sci. Published: 9 May 2016 c Author(s) 2016. CC-BY 3.0 License.
(September). Thunderstorms cause high amounts of rainfall within a short time-period (intense rainfall) and, therefore, are at least partly responsible for the high values of rainfall erosivity in summer. Starting from early fall (September), a decreasing trend of R mo is noticeable all over Switzerland.
Averaged months are aggregated to representative seasons (R seas ) to identify spatial differences (Fig. 4).
Mean winter rainfall erosivity shows highest values in the Jura Mountains, western and eastern parts of the Northern Alps 5 and the Southern Alps (canton Ticino). High winter rainfall erosivity can be explained by rainfall resulting from lowpressure areas in Northern Europe and weather fronts moved by north-westerly winds. These fronts are uplifted at the Jura Mountains what results in orographic rainfall. In spring, the Northern and the Southern Alps become more affected by high rainfall erosivity. The spatial variability of rainfall erosivity in spring in the Southern Alps (canton Ticino) corresponds to the air flow from the south and the onset of the thunderstorm season in that region which causes intense rainfall. High 10 rainfall erosivities are persisting from spring to fall in the Southern Alps. High summer R-factors in the Southern Alps, the Jura Mountains and the Northern alpine foothill are influenced by thunderstorms which have their main impacts in these regions (van Delden, 2001;Perroud & Barder, 2013;Nisi et al., 2016;Punge & Kunz, 2016). Furthermore, the high rainfall erosivity in summer in the Southern Alps can be explained by high intense rainfall originating from orographic uplifts (Schwarb et al. 2011;Perroud & Barder, 2013). The cantons of Valais and Grisons remain with relatively low rainfall 15 erosivity among all seasons. This is due to lower convection and thereby lower rainfall erosivity in summer.
The map showing the range (Fig. 5) indicates the degree of maximal variation at a certain location along a year and is the difference between minamum and maximum monthly rainfall erosivity of all 12 months. The highest range (up to 6086 MJ mm ha -1 h -1 month -1 ) is apparent in the canton Ticino at the Southern Alps. Also the Northern Alps, Swiss Midland and Jura Mountains show a high variation within a year. The Eastern and Western Central Alps have lowest ranges in accordance 20 with their relatively low rainfall erosivity among the year.
Compared to the rainfall erosivity evaluation by Meusburger et al. (2012) on an annual scale, the range of the observed mean R year and spatial pattern did only change slightly due to the extended station network and high resolution spatial covariates (aggregated by all twelve monthly R-factor-maps).

Cumulative daily rainfall erosivity 25
Generally, steepest slopes of the cumulative rainfall erosivity curve for Switzerland is from June to September with a share of 62% of the total annual rainfall erosivity within these 4 months (Fig. 6). This proportion exceeds the average share of Europe of 53% during the same period (Panagos et al., 2016a). A much larger proportion (90%) of cumulative percentage of daily rainfall erosivity was observed by Schwertmann et al. (1987) for Bavaria. Mosimann et al. (1990) showed in a singlestation approach (Bern, Swiss Midland) that a proportion of 80% of the total annual erosivity occurs in the period from April 30 to September, which complies with the mean of 77% during the same period of a year resulting from the presented multistation (87) calculation.
All biogeographic units in Switzerland have similar trends of the cumulative daily rainfall erosivity. Highest proportions (from Jun to Sep) and, therefore, steepest slopes can be identified for the Southern Alps with a share of 70% of the total sum. This high percentage of rainfall erosivity within a short period of time (4 months) is likely to have a large impact on the soil erosion susceptibility since it may coincide with lowest (after harvesting of crops, carrots, etc.) and unstable vegetation cover (after late sowing) (Hartwig & Ammon, 2002;Wellinger et al., 2006;Torriani et al., 2007;Prasuhn 2011). Furthermore, 5 fully grown pre-harvest field crops (e.g. cereals, maize) might suffer by bend-over of corn stalks due to high intensity storms. In addition, water saturated conditions which are usual in May and September/October makes soils even more erodible. Highly susceptible soils may also be expected in areas cleared by forest fires in summer (which is the case especially for Ticino) (Marxer, 2003). The combination of the monthly rainfall erosivity maps with dynamic monthly Cfactors might enable a monthly soil erosion risk assessment for Switzerland. 10

Seasonal erosivity density
Erosivity density (expressed as monthly ratios of R mo to P mo ) can be used to distinguish between high rainfall erosivity which is mainly influenced by high rainfall amounts and those which is influenced by relatively low rainfall amounts but highly intense rainfalls. That distinction helps to evaluate the potential consequences of rainfall erosivity for each month. The combination of high rainfall erosivity and low precipitation amounts (high erosivity density value) is severe for soils since 15 extreme rainfalls might meet dry and thus unstable soil and vegetation systems. The maps (Fig. 7) show that the influence of rainfall intensity on rainfall erosivity also underlies seasonal and spatial variations.
ED mo in winter is lower than 1 MJ ha -1 h -1 (Fig. 7) for Switzerland. Therefore, rainfall intensity is not the driving factor for rainfall erosivity in these months where low rainfall erosivity meets high rainfall amounts. The relative high R mo in the Jura Mountains is therefore mainly driven by large amounts of rainfall instead of high intensified rains. 20 ED mo has a maximum for Switzerland in July (1.8 MJ ha -1 h -1 ) which results from a relatively low rainfall amount indicating that rainfall erosivity is mainly controlled by high intensify events. Intense summer rainfall has its maximum in the regions of Jura, Swiss Midland, northern Alpine foothill, and Ticino. In these regions, R mo is high accompanied by relative low precipitation amounts. As such, the erosivity risk is the highest within the year especially when soils are dry during periods of rare but high rainfall intensities and therefore, infiltration is reduced due to crusts. 25 The distribution of the Swiss ED mo (Fig. 8) marks a bell-shaped curve as it also the case for investigated stations in the United States, Italy and Austria (Forster, 2008;Dabny et al., 2012;Borrelli et al., 2016;Panagos et al., 2016a). The monthly erosivity density of the neighboring country Austria complies with the Swiss values only with minor variability. Greece, Italy and the stations of the US are characterized by higher ED mo values than Switzerland. Nonetheless, the conclusion Panagos et al. (2016b) drew for Greece (Panagos et al., 2016b) that "rainfall erosivity is not solely dependent on the amount 30 of precipitation" is also generally valid for Switzerland.

Conclusion and Outlook
The main goal of the current study was to investigate the seasonal and regional variability of rainfall erosivity in Switzerland. A crucial advancement of the present research was to identify spatial and temporal windows of high erosivities.
Through the spatial-temporal mapping, it was possible to identify regions that are hardly affected by rainfall erosivity such as Grisons and Wallis and it was also possible to identify regions that are affected in a certain month, such as Jura 5 Mountains. The spatio-temporal variability of rainfall erosivity of Switzerland enables the controlled and time-dependent management of agriculture (like selective erosion measures, crop selection, time-dependent sowing) and droughts, ecosystem services evaluation, as well as the use for seasonal and regional hazard prediction (e.g. flood risk control, landslide susceptibility mapping). Rainfall erosivity based on high erosivity density has more severe impacts on soils, agriculture, droughts, and hazards in summer than in winter due the high impact of intense rainfalls. 10 In contrast to previous studies for Switzerland which were either limited spatially (to a few stations or a country) or temporally (to annual or seasonal R-factors) we were able to produce 12 monthly spatio-temporal maps. The maps are based on high resolution covariates in combination with an extended database of 87 automated gauging-stations recording in 10 min intervals, showing simultaneously spatial and temporal variations of R-factors. Regression-Kriging based on high spatio-temporal resolved covariates was successfully for most of the months (mean R²=0.51, E RMS =0.61 MJ mm ha -1 h -1 15 month -1 ). It was used to map the long-term monthly mean R-factors based on an extended database of rain-gauging stations.
The spatio-temporal mapping of rainfall erosivity and erosivity density revealed that intense rainfall events in August trigger the highest national mean value (263.5 MJ mm ha -1 h -1 month -1 ). Especially the regions of Jura, Swiss Midland, northern Alpine foothill, and Ticino on the Southern Alps show pronounced rainfall erosivity during that month. The months June to September have a total share of 62% of the total annual rainfall erosivity in Switzerland. 20 The current data highlight that rainfall erosivity has a very high variability within a year. These trends of seasonality vary between regions and consequently support that a dynamic soil erosion and natural hazard risk assessment is crucial. The combination of the dynamic RUSLE-factors (R-and C-factor) will lead to a more realistic and time-dependent estimation of soil erosion within a year which is valuable for the identification of more susceptible seasons and regions as well as for the application of selective erosion control measures. A mapping of the seasonality of the C-factor for a subsequent synthesis to 25 a dynamic soil erosion risk assessment for Switzerland is envisaged in a later study.
The findings of this study have a number of important implications for soil conservation planning. Based on the knowledge of the variability of rainfall erosivity, agronomists can introduce selective erosion control measures, a change in crop or crop rotation to weaken of the rainfalls impact on soils and vegetation by increasing soil cover or stabilizing topsoil during these susceptible months. As such, a targeted erosion control for Switzerland does not only reduce the direct costs of erosion by 30 mitigation but also shrinks the costs for the implementation of control measures to a requested minimum.