In order to evaluate spatial and temporal variability in rainfall erosivity, six meteorological stations located in the northern part of Slovenia were selected (Figure 1), belonging to the national observational meteorological network developed and maintained by the Slovenian Environment Agency (ARSO). Kneške Ravne station is located on the hillslopes of the Julian Alps, just below a major orographic barrier, positioned perpendicular to the dominant direction (from SW toward NE) of the wet air masses flow (Krklec et al., 2018; Rusjan et al., 2019). A few kilometers northwards, the Vogel station is situated on a windy plateau. Korensko sedlo station is located in the far NW corner of Slovenia, on a mountain pass close to the Slovenian-Austrian border. Downstream the Sava River, a large urban area is found in the valley where Kranj station is located among buildings. Pohorje is a mountain range in NE Slovenia where Rogla station is positioned on one of its domed summits, while Hočko Pohorje station is found on its eastern hillslopes. Table 1 shows the main characteristics of the selected stations.

The stations can be geographically grouped into two subgroups: Korensko sedlo, Vogel, Kneške Ravne, and Kranj are part of group 1 (Figure 2) and Rogla and Hočko Pohorje are part of group 2 (Figure 3). The distance between Rogla and Hočko Pohorje stations is around 20 km, while the other four stations cover an area of around 750 km². Korensko sedlo, Vogel, Kneške Ravne, and Rogla stations are positioned in Alpine climate (Dolšak et al., 2016) and are also located at a higher elevation. On the other hand, Kranj and Hočko Pohorje stations are located at a lower elevation and are impacted by a mix of Alpine and temperate continental climates. In Slovenia, three climate types are present: Alpine, temperate continental, and Mediterranean (Dolšak et al., 2016).

In this study, the data from July 2018 until August 2020 were used. All six stations are equipped with Thies Clima optical disdrometers (Thies Clima: Laser Precipitation Monitor, 2020) and OTT pluviographs (OTT Pluvio, 2020). This means that 1 min DSD data measured using disdrometers and 5 min rainfall data measured using pluviographs were available for all locations. Missing DSD data are indicated in Table 1. It should be noted that pluviographs also had some missing data (i.e., less than 2%); however, these periods were of shorter duration and are therefore not indicated in Table 1. The measuring area of the disdrometers is 45.6 cm². The Thies Clima disdrometer has 22 drop size classes (from 0.16 to 8 mm) and 20 velocity classes (from 0.2 to 20 m/s) and it measures rainfall intensities from 0.005 to above 250 mm/h (Thies Clima: Laser Precipitation Monitor, 2020). The measurement quality is in the range of 15% for intensities between 0.5 and 20 mm/h (Thies Clima: Laser Precipitation Monitor, 2020). Some past studies already evaluated the performance of the Thies Clima disdrometers (Frasson et al., 2011; Angulo-Martínez et al., 2018; Johannsen et al., 2020b). The pluviograph measuring area is 200 cm², and it has a resolution of 0.01 mm/h and an accuracy of 1% (OTT Pluvio, 2020). Vogel and Rogla stations also have wind speed measurements available. Therefore, for these two stations, we also used 10 min wind speed measurements for the investigated period with the aim of investigating the possible wind effects on the DSD data and rainfall erosivity.

Figure 4 shows the relationship between erosivity, altitude, and long-term mean annual precipitation. Linear trend lines are also shown. One can notice that R ² (i.e., coefficient of determination) between erosivity and long-term mean annual precipitation is higher than the coefficient of determination between erosivity and altitude (Figure 4). This means that altitude is not a very good predictor of erosivity in the case of Slovenia. The main reason is probably the relatively complex topography and rainfall generation mechanisms that often lead to flash floods or rainfall-induced landslide triggering (Mikoš et al., 2006; Rusjan et al., 2009; Bezak et al., 2015a; Jemec Auflič et al., 2017; Mikoš, 2020b, 2020a, 2021).

Long-term mean annual precipitation in Slovenia decreases from west to east where maximum values can exceed 3,000 mm and minimum values are around 900 mm (de Luis et al., 2014). The dominant direction of wet air masses in Slovenia is from southwest to northeast (Rusjan et al., 2019). However, relatively large variability in wet air masses direction in different seasons can be seen in Slovenia (Krklec et al., 2018), which also impacts the local rainfall erosivity rates. Therefore, one could argue that, in some cases, the impact of local orographic and climatological conditions on rainfall erosivity prevails over the air density-altitude relationship impact. Therefore, as one can see from Figure 4 that there are several meteorological stations that are located at similar altitudes (e.g., check stations around 900 m a.s.l.) but are characterized by annual rainfall erosivity ranging from 2,000 to 7,000 MJ mm ha⁻¹ h⁻¹. However, long-term mean annual precipitation shows a stronger dependence on erosivity (Figure 4). No dependence between station altitude and rainfall erosivity can be found if one considers all 1,675 stations included in the REDES, which cover almost entire Europe (Panagos et al., 2015a; Bezak et al., 2020). Thus, it seems that long-term mean annual precipitation is a better rainfall erosivity predictor than the meteorological station elevation.

Figure 5 shows the KE-I relationship between six analyzed stations calculated using Equations 1, 2 for the 1 min DSD data. One can notice that, for all six stations, the Bovec equation slightly overestimates KE for rainfall intensities larger than 5 mm/h (Figure 5). A similar phenomenon was observed by Wilken et al. (2018) who tested more than 30 different KE-I equations and observed different types of overestimation such as exponential (i.e., increasing) or constant. Other researchers have obtained similar results (Angulo-Martínez et al., 2016). Some equations in some cases also underestimated KE, while most of equations overestimated it; overestimation also occurred on the annual level (Wilken et al., 2018). Compared to Wilken et al. (2018), a larger percentage of data was needed to achieve 90% of the total KE. More specifically, 34, 33, 37, 34, 32, and 33% of the total rainfall minutes were needed to account for the 90% KE for the Kneške Ravne, Hočko Pohorje, Korensko sedlo, Kranj, Vogel, and Rogla stations, respectively. A similar pattern can also be seen for the KE-I relationship shown in Figure 5, where all stations show a similar structure of KE and I (a similar type of overestimation by the Bovec function). There are some differences in the maximum KE values found at different stations, whereas maximum values are obtained for the Vogel station. However, for all stations, only a few points exceed 3,000 J m⁻² h⁻¹. Thus, no clear effect of elevation can be seen based on the plots shown in Figure 5 and based on the percent of data needed to account for 90% of the total KE compared to some other studies (Montero-Martínez et al., 2020). It seems that local conditions prevail in the case of the analyzed stations (Figures 2, 3), at least when one investigates all KE-I values detected by the optical disdrometer. Furthermore, comparing seasonal characteristics under the Alpine climate, it can be seen that maximum 1 min values are usually observed in summer, followed by autumn and spring. On the other hand, the lowest KE values are observed in winter.

We also calculated the percentage of raindrops in different diameter classes (Figure 6). Only the first 11 diameter classes are shown, which corresponds to the raindrop diameter smaller than 3 mm (Thies Clima: Laser Precipitation Monitor, 2020). The data were divided into subgroups based on the rainfall intensity. The number of 1 min values in a specific intensity interval is also shown (i.e., n in top right corner). It should be noted that some stations have a larger percentage of missing data, which also affects the number of all 1 min values with a rainfall intensity larger than 0.1 mm/h (Table 1). Therefore, a direct comparison of the number of 1 min values in different classes is not straightforward but one can compare the percentage of 1 min values in different rainfall intensity classes. Vogel and Kneške Ravne stations that are characterized by large rainfall erosivity have around 70% of 1 min values in the lowest intensity class (I is between 1 and 5 mm/h). On the other hand, Kranj and Korensko sedlo stations that have a lower erosivity have around 83% of 1 min values in the lowest intensity class. These two stations have in the second class around 15% of 1 min values while Vogel and Kneške Ravne stations have in this class around 28% of 1 min values. Moreover, a slightly larger percentage of 1 min values was also obtained in the third class (i.e., I between 20 and 50 mm/h) for Vogel and Kneške Ravne stations compared to Kranj and Korensko sedlo stations. It should be noted that 5 mm/h can in some cases already trigger erosion processes (Mohr et al., 2013) while the duration of rainfall events could be important for the sediment yield and runoff rates (Almeida et al., 2021). A similar relationship can also be seen for the Rogla and Hočko Pohorje stations where Rogla has more 1 min values in classes 2, 3, and 4 compared to Hočko Pohorje, which is located at a lower elevation. If we observe the absolute number of 1 min values shown in Figure 6, then one can see that this is, as expected, related to the long-term mean annual precipitation (Table 1). Thus, the highest number of 1 min values is characteristic of Vogel and Kneške Ravne stations that also have larger long-term mean annual precipitation. Therefore, the main reason for higher erosivity values for Kneške Ravne, Vogel, and Rogla stations lies in the fact that these locations generally receive more rainfall and have a larger time-share with higher rainfall intensity. Moreover, lower intensity values for the Korensko sedlo station compared to the Kneške Ravne station can mainly be explained with its location and dominant direction of wet air masses (Krklec et al., 2018; Rusjan et al., 2019). Namely, the Kneške Ravne station is located at the foot of a high mountain range, while Korensko sedlo is positioned between high mountains and behind an orographic barrier.

The median percentage of raindrops in diameter classes 1 and 2 (i.e., mean diameter of drop size classes is 0.1875 and 0.3125 mm, respectively) is increasing with rainfall intensity, while for diameter classes larger than 4 (i.e., raindrops larger than 0.625 mm), this percentage is decreasing with increasing rainfall intensity (Figure 6). This kind of behavior can be seen for all six analyzed stations. Similar characteristics of raindrops were also reported by Wilken et al. (2018). However, optical disdrometers have several potential detection issues, such as splashing or uneven power distribution across the laser beam (Angulo-Martínez et al., 2018). Notably, the absolute number of detected raindrops in different diameter classes is increasing with intensity, which is an expected result (Raupach and Berne, 2015), but the increase is also large in case of small drops.

As an example, we present two rainfall events that occurred at Rogla and Hočko Pohorje stations (Figure 7). Basic information about the selected events is shown in Table 2. In the second event, maximum intensities were measured shortly after the start of the event, where also multiple raindrops were detected in the largest diameter classes. Thus, this means that some raindrops had a diameter up to almost 7 mm. Therefore, the July 12, 2019, event had more raindrops in all diameter classes, while the increase was also relatively big in the number of small drops (Figure 7). As an example of the elevation effect, Figure 7 also shows disdrometer measurements during the selected two events (Table 2). In both cases, the higher elevation station (i.e., Rogla) had more rainfall, higher intensities, more detected raindrops (Table 2), higher KE, and consequently higher rainfall erosivity. The July 12, 2019, event was a typical summer thunderstorm that was very localized (ARSO, 2019a) and where the elevation effect was very explicit. The June 22, 2019, event was of longer duration, less intense, and a consequence of a frontal system (ARSO, 2019b). Therefore, the elevation effect in case of this event was smaller. Furthermore, it should be noted that, at higher altitudes, different patterns can be observed and higher elevations can be characterized by more frequent light rain, while at a lower location, convective events can be more frequent as is the case of Andes (Orellana-Alvear et al., 2017). Moreover, a recent study that investigated the rainfall erosivity synchrony scale at the pan-European scale (Bezak et al., 2021a) indicated that the synchrony scale is the smallest in Alpine regions. Thus, in this area, the rainfall events are the most localized.

In the next step, we also computed rainfall erosivity of all erosive events using 1 min disdrometer data and also 5 min Pluvio data. Figure 8 shows the boxplots of rainfall erosivity for all erosive events that were determined using optical disdrometer data where KE was determined using DSD data. One can notice that Rogla, Vogel, and Kneške Ravne stations have larger erosivity values than the other three analyzed stations. The most extreme events had rainfall erosivity around 2,000 MJ mm ha⁻¹ h⁻¹. For the Korensko sedlo and Hočko Pohorje, the extreme values were up to 500 MJ mm ha⁻¹ h⁻¹. If one compares the median values of the erosive events shown in Figure 8, we can see that the highest value is characteristic of Vogel and Kneške Ravne stations, followed by the Rogla station. While the other three stations have similar median erosivity values of all erosive events (Figure 8). It seems that the large percentage of higher intensity 1 min values (i.e., above 5 mm/h) also leads to larger erosivity in the case of the aforementioned stations (i.e., Rogla, Vogel, and Kneške Ravne). Figure 9 shows a comparison between event-based rainfall erosivity using 1 min optical disdrometer data and 5 min pluviograph data. Comparison between event-based rainfall sum for both measuring sensors is also shown (Figure 9). Equations 4, 5 were used for calculating the KE in case of pluviograph data, while DSD data were used in case of disdrometer data. Generally, the optical disdrometer compared to the pluviographs can overestimate the total rainfall. Similar results were also obtained in some other studies (Lanza and Vuerich, 2009, 2012; Petan et al., 2010; Montero-Martínez et al., 2016). Lanza and Vuerich (2012) found that the optical disdrometer can overestimate rainfall intensities in the range of up to 50%. In our study, the optical disdrometer mostly overestimated the total rainfall, also in the range up to 30%, while the mean overestimation was approximately around 5% (Figure 9). Moreover, for the Rogla station, the overestimation was even more explicit (i.e., around 30%). Using the 10 min wind measurements available for the Rogla and Vogel stations, we also investigated the differences in the wind speed measurements. The comparison of the measured data shows that, in both cases, there are some dominant wind directions (not shown here). Based on the results presented in Figure 10, one can also notice that, for rainfall intensities up to 10 mm/h (i.e., 3–10 mm/h), the corresponding average wind speed for Rogla (i.e., 4.7 m/s) is larger than for the Vogel station (i.e., 2.3 m/s). Although it is true that the number of points on Figure 10 is around three times larger for Vogel station than for Rogla station, while for intensities, it is larger than 10 mm/h, this difference between stations is smaller, for Vogel and Rogla 2.8 and 3.9 m/s, respectively. Therefore, the reason for the previously mentioned overestimation could indeed be the microlocation of the Rogla station and the wind effect (Michaelides et al., 2009). In terms of overestimation, the Rogla station was followed by Kneške Ravne station where the overestimation of the total rainfall was around 17%, while for other stations, the overestimation was smaller than 10%. Furthermore, some studies also found that disdrometer measurements underestimate rainfall (Johannsen et al., 2020a). Similarly, in the majority of cases, the optical disdrometer yielded larger rainfall erosivity estimates compared to pluviograph values (Figure 9). This applies especially to the Brown and Foster KE-I equation. For the Bovec KE-I equation, higher values were obtained in case of Pluvio data for the Kneške Ravne, Hočko Pohorje, Kranj, Vogel, and also Korensko sedlo stations. Angulo-Martínez et al. (2016) pointed out that, on the event scale, there was a better agreement between observed and theoretical erosivity values as in the case of 1 min data. Similar conclusions can also be made based on the results presented in this study. Analysis of the event-based data confirms the findings made using 1 min data; i.e., there is no clear effect of altitude in case of selected stations and other local climatological conditions have an important impact on the rainfall erosivity.

There are several limitations related to this study under the Alpine climate in Slovenia that could affect the presented results. Firstly, two years of high-frequency data with a 1 min time step is not enough to obtain robust conclusions regarding the temporal variability as indeed year-by-year variability can be quite significant. Extreme events tend to occur less frequently compared to moderate or low magnitude erosive events. A recent study has indicated that the largest interannual inequality of rainfall erosive events in Europe was observed in the Alpine region (Bezak et al., 2021c) and this region was also associated with smaller synchrony scale values (Bezak et al., 2021a). Longer data series are needed to obtain additional insight into temporal variability. To this end, data collection at the selected stations in Slovenia will continue and similar investigations will be performed in the future. Secondly, if spatial data density was higher, with no orographic barriers positioned among the stations, probably a more significant altitude effect could be detected, particularly if additional stations would be positioned between Rogla and Hočko Pohorje stations. However, the network density is determined by the Slovenian Environment Agency, which is also the data provider, and it is very unlikely that density will increase in the future. Therefore, a specific experimental design has to be set up (e.g., Orellana-Alvear et al., 2017) in order to obtain better knowledge about the altitude effect. This could be done in the scope of the work performed at experimental catchments in Slovenia (Sapač et al., 2021). Thirdly, also local conditions (e.g., strong wind) can affect the accuracy of measurements conducted by the optical disdrometers. It should be noted that both Rogla station and Vogel station had a percentage of missing values above 10%, which could also affect the results.