Quantification of vegetation and meteorological variables influencing the kinetic energy of raindrops

Quantification of vegetation and meteorological variables influencing the kinetic energy of raindrops Lana Radulovi´ c, Katarina Zabret, Mojca ˇ Sraj * University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova 2, SI-1000 Ljubljana, Slovenia ARTICLE INFO Keywords: Rainfall interception Throughfall Kinetic energy Urban trees Machine learning ABSTRACT The process of interception, whereby vegetation partitions rainfall, largely influences natural processes such as soil erosion. The kinetic energy of rainfall plays a crucial role in evaluating this impact. In this study, we measured rainfall characteristics using three disdrometers placed above and below vegetation, specifically under two distinct tree species (birch and pine) in an urban area in Ljubljana, Slovenia. The study period extends over two years, subdivided into a dry and a wet sub-period. The investigation encompasses the effects of vegetation characteristics, raindrops characteristics and meteorological variables on the kinetic energy of throughfall. Two methods, namely boosted regression trees and random forest, were used to evaluate the influence of vegetation and meteorological variables on raindrop characteristics and their kinetic energy. The results indicate that, in general, pine reduces the kinetic energy of raindrops to a much greater extent than birch, and that birch exerts a positive effect on the reduction of kinetic energy only during the leafed period. Both applied machine learning models confirmed that the amount of throughfall has the greatest influence on kinetic energy, regardless of vegetation type. Furthermore, rainfall intensity and median-volume drop diameter exhibited a greater influence in the case of pine compared to the birch tree. Additionally, the findings indicate that the influence of the event duration on kinetic energy of throughfall differs depending on the presence of foliage on the tree canopy. 1. Introduction During rainfall events, a portion of the rainfall never reaches the ground because it remains on the vegetation and evaporates during or after the event. This process is called rainfall interception. Rainfall reaching the vegetation canopy is divided into intercepted rainfall, throughfall - the portion of rainfall that reaches the ground by dripping from the leaves and branches or falling directly through the gaps in the canopy - and stemflow, which is the portion of the rainfall that flows down branches and stems (Levia et al., 2017; Yue et al., 2021; Zabret and ˇ Sraj, 2019, 2021). Thus, vegetation has a major influence on the hydrological cycle (e.g., Radulovi´ c et al., 2023; ˇ Sraj et al., 2008; Van Stan et al., 2011; Zabret et al., 2018), as it significantly alters the distribution of precipitation. In addition to changing the amount of precipitation reaching the ground, rainfall interception by vegetation also significantly changes the properties of raindrops (raindrop microstructure) (Lüpke et al., 2019; Zabret et al., 2016). Changes in the microstructure of raindrops have a significant impact on changes in their kinetic energy (KE) (Zabret et al., 2016; Zore et al., 2022). The KE of rainfall is often used as an indicator of the erosive potential of rainfall events (Meshesha et al., 2019). It has been demonstrated that raindrops with higher KE possess greater erosive power (Lv et al., 2023). Brasil et al. (2024) demonstrated that in semiarid regions, vegetation can reduce the KE of rainfall by up to 30 %, suggesting that vegetation can partially regulate the impact of events with high KE of precipitation and mitigate their effects on soil erosion. Moreover, in light of climate change, there will be an expectation of increased frequency and intensity of extreme rainfall events, exhibiting higher erosive power and loss of soil (Burt et al., 2016). More specifically, Panagos et al. (2017) found that by 2050 rainfall erosivity in Europe could increase by 18 %. Consequently, there is a growing need for a more profound understanding of rainfall interception to ensure the effective management of water resources and soil in the future. The process of soil erosion by precipitation consists of the separation of individual soil particles and their transport (Carollo et al., 2015). This process is predominantly determined by antecedent hydrological conditions, such as prolonged periods without rain, which have been observed to enhance the water repellency of soils, potentially * Corresponding author. E-mail address: [email protected] (M. ˇ Sraj). Contents lists available at ScienceDirect Agricultural and Forest Meteorology journal homepage: www.elsevier.com/locate/agrformet https://doi.org/10.1016/j.agrformet.2025.110835 Received 15 May 2025; Received in revised form 28 August 2025; Accepted 3 September 2025 Agricultural and Forest Meteorology 375 (2025) 110835 Available online 8 September 2025 0168-1923/© 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC license ( http://creativecommons.org/licenses/bync/4.0/ ). contributing to erosion (de Jonge et al., 1999; Radinja et al., 2019). Dekker & Ritsema (1994) found that dry soils are the most water repellent, while wet soils may not repel water at all. While wet soils have better infiltration capacity compared to dry soils, similar issues arise in urban environments, where surface runoff can lead to the displacement of soil particles (Svetina et al., 2023). Due to the climate change, dry and wet periods have become more pronounced (Almazroui and S ¸en, 2020; Bl¨ oschl et al., 2019). Consequently, there is an increasing need to study the influence of these conditions on the environment (Peng et al., 2021; Zabret and ˇ Sraj, 2021). Processes related to precipitation interception are strongly influenced by multiple factors, including meteorological conditions and vegetation characteristics (Nanko et al., 2013; Nooraei Beidokhti and Moore, 2021; Zabret and ˇ Sraj, 2021; Zore et al., 2022). Meteorological variables that affect the interception process are the characteristics of rainfall events (total amount of precipitation, duration and intensity of the event, size and velocity of raindrops) and the climatic conditions during the events (e.g., air temperature, wind speed and direction, humidity) (Zabret et al., 2018). The impact of vegetation characteristics that affect interception is predominantly associated with the tree canopy encompassing factors such as projected canopy area, canopy openess and leaf characteristics. Different types of vegetation have different characteristics, affecting the rainfall distribution (Crockford and Richardson, 2000; Yue et al., 2021; Zabret, 2013). Multiple studies have demonstrated that the phenological phase plays an important role in rainfall distribution (e.g., Radulovi´ c et al., 2023; Zabret et al., 2018; Zore et al., 2022), which is part of the reason why conifers intercept more rainfall over a year compared to deciduous trees (Pflug et al., 2021; Xiao et al., 1998). A study on rainfall interception under a birch tree conducted by Zore et al. (2022) found that deciduous trees reduce the KE of rainfall by 3 % in the leafless period and by 30 % in the leafed period (Zore et al., 2022), indicating that the phenological phase also plays an important role in KE mitigation. The rainfall interception process is part of the hydrological cycle, influenced by vegetation. Therefore, it is expected that extremely dry or wet periods will also impact this process and related ones, such as changes in the kinetic energy of throughfall and its rainfall erosivity. Many studies have investigated the influence of vegetation (e.g., Nanko et al., 2016; Radulovi´ c et al., 2023; Zabret, 2013) and meteorological conditions (Zabret et al., 2018; Zabret and ˇ Sraj, 2021) on the characteristics and distribution of precipitation, but only a few include a sufficiently extensive study period to cover both dry and wet sub-periods and thus examine their influence on rainfall interception process in more detail (Zabret and ˇ Sraj, 2021).The main aim of this study is therefore to investigate how wet and dry conditions impact the influence of the vegetation and precipitation characteristics on the changes in KE, using two different machine learning methods. In addition, the impact of two distinct types of trees on KE of raindrops in dry and wet conditions and two phenological phases will be investigated. 2. Data and methods 2.1. Study site and data The research plot is located at Hajdrihova 28, in Ljubljana, Slovenia (Fig 1). The surface area of the plot is approximately 600 m 2 . The region’s climatic classification is subalpine, with marine and subcontinental influences (Ogrin et al., 2023). Average long-term (1991–2020) annual rainfall of the area is 1368 ±191 mm (ARSO, 2025b). As the research plot does not include a meteorological station, the meteorological variables used in this study, were obtained from the meteorological station at the roof of the near building, located approximately 800 m from the research plot (Fig 1). This study includes measurements of precipitation above and below the canopy of two distinct tree types, namely the common birch (Betula pendula Roth.) and the black pine (Pinus nigra Arnold). The measurements were obtained using three optical OTT Parsivel disdrometers (OTT Hydromet, 2016). One disdrometer is positioned on the roof of the building approximately 45 m from the trees at a height of 14.5 m (similar to the height of the tree canopies). It was used to measure rainfall characteristics above the tree canopy. Two additional disdrometers were placed under the canopies of the two individual trees (i. e., birch and pine) at the height of 2 m above the ground to measure throughfall characteristics (Fig. 1). The considered measurements were Slovenia Ljubljana Research plot Meteorological station Disdrometer under pine Disdrometer under birch Disdrometer on the roof Fig. 1. Location of the research plot, meteorological station and the arrangement of disdrometers on the research plot. L. Radulovi´ c et al. Agricultural and Forest Meteorology 375 (2025) 110835 2 divided into individual phenological phases, namely the leafless and leafed periods, which were defined according to the leaf area index (LAI) measurements using the LAI-2200 plant canopy analyzer (Li-Cor Inc.). The following dates delineate the boundary between the two phenological phases within the considered data period: November 21, 2022; April 21, 2023, and October 20, 2023, respectively. The period from July 2022 to June 2024 is investigated in the study. This period is further divided into two sub-periods, namely the dry subperiod from July 2022 to June 2023 and the wet sub-period from July 2023 to June 2024. According to the Slovenian Environment Agency (ARSO), the year 2022 was below average in terms of precipitation, with a total rainfall amount of 1264.3 mm, which is less than two-thirds of the annual values recorded at the Ljubljana-Beˇ zigrad meteorological station over the 30-year reference period. More specifically, summer 2022 was exceptionally dry in terms of precipitation (ARSO, 2023). As a result, Slovenia experienced several months of extreme drought in 2022, which was the third most extreme drought in terms of precipitation deviation and the second most severe in terms of temperature deviation in the period 1961–2022 (ARSO, 2023). In contrast, the years 2023 and 2024 were significantly above average in terms of precipitation, with total rainfall amounts of 1813.8 mm and 1552.5 mm, respectively (ARSO, 2023, 2024, 2025a). More specifically, year 2023 was the third wettest year since 1950 (ARSO, 2024). Moreover, in August 2023, Slovenia was hit by most extreme flood event in recent decades, caused by extreme rainfall amount in short time period (between 150 and 200 mm of rain fell in 6 to 12 h), which fell on previously wet soil (Bezak et al. 2023; ˇ Sraj and Bezak, 2025). Precipitation events were defined as continuous periods of rainfall during which there was no dry period of more than 6 h, where a dry period was defined as a time when rainfall did not exceed 1 mm. Preliminary analysis of the data measured with disdrometers was conducted to determine all the necessary information about each event, namely rainfall/throughfall amount, intensity, duration, velocity and droplet size, and to calculate the KE, using the R software (R Core Team, 2023). The data on rainfall events for both sub-periods and both phenological phases are shown in Fig. 2. Table 1 presents the number of events, the total rainfall amount, and the throughfall amount under both tree species according to the measured data during the considered period. For the droplet size analysis, D50 was used, instead of the average drop diameter. D50 is the median-volume drop diameter, meaning that half of the total precipitation volume has smaller diameter droplets, while the other half has larger diameter droplets. D50 is one of the key components in the calculation of the KE and was calculated for each event using the data measured with the disdrometers and the Eq. (1) (Nanko et al., 2016): D50 =bi +(0,5−cumi−1 proi)∗ (bi+1−bi)(1) In Eq. (1) D 50 [mm] represents the droplet diameter, b i [mm] represents the size class limits, pro i [-] represents the proportion of the water content spectrum in the class, cum i-1 [-] the cumulative proportion of the spectrum in the class, where the current class is denoted by i. KE was calculated from the drop size distribution (DSD), using data measured with the disdrometers and the Eq. (2) (Petan, 2010): KE(dsd) = π ∗ ρ 12 ∗103∗F∗Δt∗Σini∗1 Db,i−Da,i ∗∫ Db,i Da,i D3 idD ∗1 vb,i−va,i ∗∫ vb,i va,i v2 idv (2) In Eq. (2), ρ [kg/m 3 ] represents the density of water, F[mm] represents the measuring area of the disdrometer, Δt [1/60 h] represents the duration interval, ni [-] represents the number of droplets detected within the i th size range size class, Da,i[mm] represents the lower limit of the droplet diameter within the i th size class, Db,i[mm] represents the upper limit of the droplet diameter within the i th size class, Di[mm] represents the droplet diameter within the i th class, va,i[m/s] represents the lower limit of the drop velocity within the i th velocity class, vb,i[m/s] represents the upper limit of the droplet velocity within the i th velocity class, vi[m/s] represents the droplet velocity within the i th class. Meteorological data was recorded at 10-minute intervals, divided into events for further analysis. The data were split into events, taking into account the time period of the rainfall events previously determined. The meteorological variables obtained and used for the analysis encompassed maximum air temperature, average air temperature, maximum wind speed and average wind speed during the event. Gaps in the data were filled using the data from the Ljubljana Beˇ zigrad meteorological station, with no more than 10 % of the data being used to fill the gaps. Fig. 2. Data on rainfall events (duration, amount and intensity) for both sub-periods (overall), and for individual vegetation periods (leafed and leafless) of these two sub-periods. Box plots show the median line, as well as the upper and lower quartiles; the whiskers reach out to 1.5 times interquartile range. Violin plots show the distribution and density of the measured values. L. Radulovi´ c et al. Agricultural and Forest Meteorology 375 (2025) 110835 3 2.2. Data analysis Two machine learning methods, namely Boosted Regression Trees (BRT) and Random Forest (RF), were used to analyse the data. These algorithms require a large enough data set to ensure successful predictions. In this study, the number of events taken into account is sufficient for the selected models to be used (Luan et al., 2020). The BRT method integrates regression trees and boosting algorithm to improve the performance of the model. The boosting process is iterative, whereby the model recalibrates its predictions after each iteration, thereby progressively enhancing the precision of the predictions. The model consists of a large number of trees, and the final prediction is the result of the combination of these trees (Elith et al., 2008). In this study, the “gbm” package (Ridgeway, 2024) in R software (R Core Team, 2023) was used for the BRT method. The data set was divided into the data used for training (75 %) and the data used for testing (25 %) of the model. 50 iterations were performed for each combination of parameters and the Root Mean Squared Error (RMSE) was calculated for all iterations. During the tuning process, several values for learning rate (0.01, 0.1, 0.05), interaction depth (3, 5, 7), and number of trees (100, 150, 1000) were tested. The final BRT model was estimated using a Gaussian distribution and the optimal number of trees, interaction depth, and learning rate (Table 2). RF is a method that integrates regression trees and bagging to mitigate model overfitting and improve model performance. Bagging allows trees to grow on random subsets of the data set, reducing the correlation between trees and increasing the robustness of the model. RF uses a random selection of variables, which improves model’s ability to detect the most influential factors. The model repeats this process multiple times, with each tree contributing to the final prediction (Breiman, 2001). In this study, the “randomForest” package (Breiman, 2001) in R software (R Core Team, 2023) was utilized for the RF method. The dataset was divided into the data used for training (75 %) and the data used for testing (25 %) of the model. Several values for the number of trees (250, 1000, 5000), the maximum number of terminal nodes (10, 20, 30), and the number of variables randomly sampled at each split (1 to 9) were tested. For each combination, multiple iterations were performed, and the best performing parameters were selected according to the calculated Root Mean Squared Error (RMSE) (Table 2). The target variable was the KE of throughfall below birch and pine trees. The influencing variables tested were: amount of throughfall per event, average throughfall intensity per event, duration of events, D50, average droplet velocity per event, maximum air temperature, average air temperature, maximum wind speed and average wind speed. The results of both methods are presented as bar plots, illustrating the relative influence (RI) of each influencing variable on the KE of throughfall. To facilitate interpretation of the results, the RI values were normalized so that their sum is equal to 100. As influential variables we have considered those that together contribute at least 85 % of the impact. 3. Results 3.1. Kinetic energy 3.1.1. Whole period The maximum KE values of both rainfall and throughfall over the entire measurement period were reached during the leafed period of the dry sub-period 2022/23. These values were recorded as 87.2 MJ/ha for the open location, 64 MJ/ha for throughfall under the birch tree and 22.4 MJ/ha for throughfall under the pine tree. On the other hand, the maximum KE values for the leafless period were reached in the wet subperiod 2023/24, specifically 80 MJ/ha in the open and 5.6 MJ/ha under the pine tree. For throughfall under the birch tree, the maximum KE value in the leafless period was 32.3 MJ/ha, and it was reached in the dry sub-period 2022/23. Fig. 3 presents KE of rainfall and throughfall for the entire measurement period. The median KE was observed to be the greatest for the open location (2.09 MJ/ha), followed by the value under the birch tree (1.51 MJ/ha), while the value of the median KE of throughfall under the pine tree was the lowest (0.17 MJ/ha). Values of KE were significantly different between all three locations (p <0.001). Furthermore, the KE values were found to be greater during the leafed period compared to the leafless period for all three locations, however the differences were not statistically significant. The results indicate, that the KE values under the birch tree exhibited the most variations in KE between the two phenological phases, while KE values under the pine tree demonstrated comparatively minimal variation. The birch tree on average reduced the KE of precipitation by 32 % in the leafed period and by 18 % in the leafless period. On the other hand, the pine tree reduced the KE of Table 1 Data on rainfall and throughfall (TF) under the birch and pine trees according to the disdrometers measurements. Period Phenological phase No. of events P TF birch TF pine [/] [mm] [mm] [ %] [mm] [ %] Whole period Overall 171 3887.4 2621.5 67.4 % 1163 29.9 % Leafed period 98 2409.3 1622.3 67.3 % 739.9 30.7 % Leafless period 73 1478.1 999.2 67.6 % 423.1 28.6 % Dry sub-period (2022/23) Overall 80 1844.1 1313.7 71.2 % 594.1 32.2 % Leafed period 54 1252.9 862.8 68.9 % 416.8 33.3 % Leafless period 26 591.2 450.9 76.3 % 177.3 30.0 % Wet sub-period (2023/24) Overall 91 2043.3 1307.8 64.0 % 568.9 27.8 % Leafed period 44 1156.4 759.5 65.7 % 323.1 27.9 % Leafless period 47 886.9 548.3 61.8 % 245.8 27.7 % Table 2 Optimal parameters for the BRT and RF models. Period Tree BRT RF Learning rate Interaction depth Number of trees Number of terminal nodes Number of variables Number of trees Whole period (2022/24) Birch 0.01 5 150 10 9 250 Pine 0.01 3 150 20 9 5000 Dry sub-period (2022/23) Birch 0.05 3 150 20 8 250 Pine 0.01 7 150 30 9 250 Wet sub-period (2023/24) Birch 0.05 5 1000 30 8 250 Pine 0.1 5 100 20 8 250 L. Radulovi´ c et al. Agricultural and Forest Meteorology 375 (2025) 110835 4 precipitation by 92 % on average regardless the period. 3.1.2. Dry sub-period 2022/23 The results demonstrate that the KE of throughfall over the period of a year depends on the vegetation type and phenological phase (Fig. 4). Fig. 4 illustrates the variation in KE of rainfall in the open and throughfall under the birch and the pine trees varying according to the location of the disdrometer and the phenological phase during the dry sub-period. The maximum KE of rainfall and throughfall under the birch and the pine trees in the dry sub-period was reached in the leafed period. Conversely, during the leafless period, these values were lower. In the dry sub-period, the median KE of rainfall (2.09 MJ/ha) was the highest compared to the median KE of throughfall under vegetation, with median KE of 1.45 MJ/ha under birch and 0.23 MJ/ha under the pine tree. The differences were statistically significant between the three locations (p <0.001). The differences between the leafed and leafless periods were not pronounced, with the exception of the KE of throughfall under the birch tree, where the median value in the leafless period was for 32.1 % higher than the value in the leafed period, yet the differences were not statistically significant. The KE values under the pine tree remained low throughout the entire sub-period, with minimal variation between the two phenological phases (9.6 % on average). 3.1.3. Wet sub-period 2023/24 The values of the KE of rainfall in the open and throughfall in the wet sub-period are presented in Fig. 5. The maximum KE of rainfall for this sub-period was reached during the leafless period, while in the leafed period, the maximum value was more than two times lower. The KE of throughfall under the trees reached its maximum in the leafed period for both the birch tree and the pine tree. The median KE of rainfall and throughfall exhibited greater values during the leafed period (3.83 MJ/ha, 2.28 MJ/ha and 0.16 MJ/ha on the roof and under birch and pine tree, respectively) and lower values during the leafless period (1.04 MJ/ha, 1.22 MJ/ha and 0.10 MJ/ha on the roof and under birch and pine tree, respectively). The most pronounced differences between the two phenological phases were observed in the open location (72.9 %). Under the birch tree, KE values were also higher in the leafed period. Under the pine tree, KE values remained low throughout the whole period. As in the dry sub-period, differences in KE between locations were statistically significant (p < 0.001) in wetter conditions as well, but not between the phenological phases. 3.2. Influence of droplet characteristics and weather conditions on kinetic energy of throughfall 3.2.1. Whole period The results of the analysis for the entire measurement period, using two different methods, namely BRT and RF, are presented in Fig. 6. The BRT method identified a fewer number of influential variables on the KE of throughfall under both trees for the entire measurement period in comparison to the analysis of individual sub-periods separately. For the KE of throughfall under the birch tree, both methods assign the highest RI values to the throughfall amount (90 % BRT, 88.1 % RF) over the entire measurement period, making it the most influential variable. In the leafed period, the BRT method identifies throughfall amount (65.3 %), event duration (13.8 %) and intensity (11.1 %) as the most influential. In contrast, the RF method does not include precipitation intensity as one of the influential factors and assigns RI values of 72.2 % and 18.4 % to throughfall amount and event duration, respectively. In the leafless period, the BRT method recognizes throughfall amount as the single most influential factor with an RI value of 90.2 %. The RF method also assigns the highest value to throughfall amount (43.2 %), but also recognizes event duration (34.6 %), intensity (7.1 %) and maximum air temperature (6.6 %) as influential variables. The variables influencing the KE of throughfall under the pine tree during the entire measurement period are as follows. According to the BRT method the most influential variables are throughfall amount (80.8 %) and D50 (8.1 %). According to the RF method the most influential variables are throughfall amount (83.7 %) and intensity (12.2 %). In the leafed period, both methods identified throughfall amount (67.8 % BRT, 39.7 % RF), event duration (13.6 % BRT, 33.5 % RF) and intensity (9.2 Fig. 3. The observed KE values of rainfall in the open and throughfall under the birch and pine trees for the whole observation period. Box plots show the median line, the upper and lower quartiles, the whiskers reach out to 1.5 times interquartile range and the outliers are marked with dots. Fig. 4. The observed KE values of rainfall in the open and throughfall under the birch and pine trees for the dry sub-period. Box plots show the median line, the upper and lower quartiles, the whiskers reach out to 1.5 times interquartile range and outliers are marked with dots. Fig. 5. The observed KE values of rainfall in the open and throughfall under the birch and pine trees for the wet sub-period. Box plots show the median line, the upper and lower quartiles, the whiskers reach out to 1.5 times interquartile range and outliers are marked with dots. L. Radulovi´ c et al. Agricultural and Forest Meteorology 375 (2025) 110835 5 % BRT, 10.9 % RF) as the most influential, with the addition of maximum air temperature (6.4 %) according to the RF method. Also, during the leafless period, throughfall amount and event duration have the highest RI values according to both methods, while precipitation intensity was found to be influential only by the RF method with the RI value of 9.5 %. 3.2.2. Dry sub-period 2022/23 Fig. 7 presents the relative influence of various variables associated with throughfall characteristics and weather conditions on the KE of throughfall under the birch and the pine trees during the dry sub-period 2022/23. The results demonstrate the KE of throughfall under the birch tree in the dry sub-period was mostly influenced by throughfall amount (44.6 %), intensity (17.8 %), event duration (15.4 %), D50 (7.2 %) and maximum air temperature (4.7 %), according to the BRT method. Conversely, the RF method indicates that the KE of throughfall under the birch tree for that year is mostly influenced by throughfall amount (72.1 %) and duration (15.3 %). The BRT method indicates that the KE of throughfall under the pine tree in the dry sub-period was mostly influenced by throughfall amount (44.1 %), intensity (17.8 %), D50 (17.2 %) and duration of throughfall (12.5 %). Similarly, the RF method recognizes throughfall amount (63.1 %) and intensity (12.6 %) as the most influential variables. However, in contrast to the BRT method, the RF method assigned a greater RI to maximum wind speed (12 %) than to event duration and D50, indicating maximum wind speed as an influential variable. Fig. 6. Relative influence of variables on the KE of throughfall under pine and birch for the whole observation period. Fig. 7. Relative influence (RI) of variables on the KE of throughfall under pine and birch for the dry sub-period. L. Radulovi´ c et al. Agricultural and Forest Meteorology 375 (2025) 110835 6 3.2.3. Wet sub-period 2023/24 The results of the analysis for the wet sub-period using both methods (BRT and RF) are presented in Fig. 8. The BRT method identifies a greater number of variables that significantly influence the KE of throughfall under both the birch and the pine tree compared to the RF method. According to the BRT method, the KE of throughfall under the birch tree in the wet sub-period was most influenced by throughfall amount (39.6 %), intensity (13.8 %), event duration (10 %), average air temperature (8.5 %), maximum wind speed (8.5 %) and raindrop velocity (8 %). Conversely, the RF method assigned the highest RI to the throughfall amount (78 %) and event duration (8.9 %). The RF and BRT methods identified throughfall amount (50.2 % BRT, 84.4 % RF) and duration (10.8 % BRT, 8.1 % RF) as the variables with the highest RI values under the pine tree. According to the BRT method, other influential variables were throughfall intensity (9.8 %), D50 (7.6 %) and maximum air temperature (7.5 %). 4. Analysis and discussion The presented analysis refers to the differences in the KE of precipitation and throughfall under birch and pine trees during dry and wet periods. Additionally, differences in the variables influencing the KE of throughfall are expected, as these hydrologically distinct periods are assumed to influence both, vegetation and precipitation characteristics (Du et al., 2005; Zabret and ˇ Sraj, 2021). 4.1. Kinetic energy The maximum and median KE of throughfall are greater under the birch tree than under the pine tree for both sub-periods and both phenological phases (leafed and leafless) (Fig. 9). The pine tree is more efficient in reducing open rainfall KE than birch tree. This observation aligns with the fact, that pine tree as coniferous species is also more efficient at intercepting rainfall and reducing its intensity than the deciduous birch tree (Fischer et al., 2023; Pflug et al., 2021; Radulovi´ c et al., 2023; Zabret et al., 2017). During the study period, the throughfall under the birch tree accounted for 57.1 % of rainfall in the open on average per event, while under the pine tree it was equal to 17.9 %. Similarly, the birch tree reduced open rainfall intensity by an average of 0.5 mm/h, while the pine tree reduced it by 1.1 mm/h. Slight differences were observed between the wet and dry sub-periods. During the dry sub-period, TF under both trees was larger (5 % under the birch and 1 % under the pine tree, on average per event), while the reduction in throughfall intensity was lower (4 % under the birch and for 1 % under the pine tree, on average per event). The amount and percentage of TF are strongly related to the leaf area index (LAI), and studies have been shown that TF decreases with higher LAI values (Brasil et al., 2024; Crockford and Richardson, 2000; Zabret et al., 2018). At the study site, the LAI values for the birch tree were observed to vary between 0.8 in the leafless and 2.6 in the leafed period. For the pine tree, the average LAI was 3.9 (±0.7) (Alivio et al., 2023; Zabret et al., 2018; Zabret and ˇ Sraj, 2019). However, in the summer of 2022 (the dry sub-period), the LAI of the birch tree did not exceed 2.0, while the LAI of the pine tree was on average 3.4. In the leafed period of the wet sub-period, the average LAI was 2.6 for the birch tree and 3.5 for the pine tree. The lower LAI values during the dry-sub period can attribute to higher TF values, as well as higher KE of throughfall under both tree species (Fig 9). The influence of LAI values on difference in KE of throughfall is even more pronounced between the phenological phases. Notably, under the birch tree, during the leafless period, the median KE of throughfall under the tree was higher than the median KE of rainfall in the open location in both sub-periods (Fig. 9). Conversely, in the leafed period, the median KE of throughfall under the birch tree was significantly smaller than the median KE of rainfall. These findings are consistent with the results of previous studies, which demonstrated that the phenological state of the canopy exerts a substantial influence on the reduction of KE (Alivio et al., 2023; Geißler et al., 2013; Zore et al., 2022). In contrast, no significant difference in throughfall KE between phenological phases was observed under the pine tree, as would be expected for an evergreen species such as pine (Nanko et al., 2025). In the dry sub-period, the maximum KE of both rainfall and throughfall occurred during the same event (September 15, 2022), which had the highest rainfall amount (356 mm) and ranked second in both average (6 mm/h) and maximum 1-min (167.2 mm/h) intensity. Fig. 8. Relative influence (RI) of variables on the KE of throughfall under pine and birch for the wet sub-period. L. Radulovi´ c et al. Agricultural and Forest Meteorology 375 (2025) 110835 7 These findings are in accordance with findings of Brasil et al. (2024), who demonstrated that events with the highest KE coincide with events with the highest rainfall and throughfall amount. In the wet sub-period, the maximum value of KE of rainfall in the open and throughfall under the trees did not occur during the same event. The maximum KE of rainfall occurred during an event in the leafless period (January 18, 2024), which had the highest maximum 1-minute intensity (626.2 mm/h). This finding demonstrates the significance of maximum 1-minute intensity in reaching high values of the KE of rainfall, thus confirming the hypothesis that short but intense rainfall events strongly influence KE in open-field conditions (Brasil et al., 2024). Additionally, Yan et al. (2024) found that intense rainfall events directly correlate with increased KE of precipitation. The maximum KE of throughfall under the vegetation was observed during the event in the leafed period (August 3, 2023), which was the longest event (80.1 h) and had the highest amount of rainfall (151 mm). This observation aligns with the findings of Zore et al. (2022), who emphasized the primary influence of event duration and rainfall amount on throughfall. The maximum KE values were reached during events characterized by the highest precipitation amounts, the longest duration, and highest one-minute intensity. Analysis of these extreme events suggests that dry and wet sub-periods have a negligible influence. However, a comparison of other “normal” events shows otherwise. Two sets, each consisting of two events, one from dry and another from wet sub-period, were selected from the entire dataset (Table 3). Both sets occurred during the leafed period and had similar intensities. For set 1, the KE of open rainfall was higher during the event in the wet sub-period, while for set 2, the highest KE was observed during the rainfall event in the dry subperiod. Birch reduced open rainfall KE more during the event observed in the dry sub-period in both sets. However, pine tree reduced KE similarly regardless of sub-period. Due to the limited number of events, a direct relationship with vegetation conditions (i.e., LAI) cannot be established. Among the meteorological conditions, however, a significantly higher air temperatures were observed during both events in the dry sub-period. Higher air temperatures can lead to increased evapotranspiration, which is usually associated with lower TF (Staelens et al., 2008; ˇ Sraj et al., 2008; Xiao et al., 2000), and consequently lower KE. 4.2. Influence of droplet characteristics and weather conditions on kinetic energy of throughfall The fact that the BRT method distributes smaller values over a larger number of variables, while the RF method assigns larger values to a smaller number of key variables (Shinohara et al., 2018; Zabret and ˇ Sraj, 2021) is partly proven also in this study. This finding indicates that the BRT method detects a wider range of influencing factors, while the RF method highlights only those that have the strongest impact on KE. The throughfall amount is identified as the most influential variable for KE under both trees regardless the periods. This finding aligns with previous studies highlighting the dependence of the rainfall partitioning (Staelens et al., 2008; Su et al., 2019; Zabret et al., 2018; Zabret and ˇ Sraj, 2021) and of KE of throughfall (Brasil et al., 2022; Geißler et al., 2013) on the rainfall amount. The observed high RI value attributed to the throughfall amount was expected, as a higher amount of precipitation has been shown to increase the KE (Pflug et al., 2021). The duration of rainfall events over the entire measurement period, Fig. 9. Comparison of rainfall and throughfall KE between dry (2022/23) and wet (2023/24) sub-periods. The darker red represents the overlap of values between the two sub-periods. Table 3 A comparison of the characteristics of two sets of selected “normal” rainfall events, each consisting of two events, one from a dry and one from a wet sub-period. Subperiod Rainfall intensity [mm/h] Rainfall amount [mm] Rainfall duration [h] Rainfall KE [MJ/ha] TF KE Birch [MJ/ ha] TF KE Pine [MJ/ ha] Average air temperature [ ◦C] Max air temperature [ ◦C] SET 1 Dry 8.13 10.2 1.25 3.01 1.29 0.32 24.2 26.5 Wet 8.07 16.7 1.98 4.65 3.01 0.23 20.7 23.5 SET 2 Dry 0.45 14.6 32.1 4.46 1.15 0.16 22.5 30.0 wet 0.45 14.7 32.3 3.63 2.37 0.18 15.4 22.3 L. Radulovi´ c et al. Agricultural and Forest Meteorology 375 (2025) 110835 8 is not highlighted as an influential variable for any of the trees, although numerous studies (Muzylo et al., 2012; Nanko et al., 2025; Zabret et al., 2018) have determined that the duration significantly influences the partitioning of throughfall, which directly impacts KE of throughfall. However, within the individual sub-periods, duration is recognized as an influential variable for both vegetation types. A clear difference between the two tree species is observed when their phenological phases are compared. For the birch tree, both models identified duration as an influential variable only in the leafed period. In contrast, the influence of duration is observed in both phenological phases for the pine tree. This observation suggests that, in the presence of foliage on the canopy, the interaction between rainfall and the canopy makes event duration an important factor because of the time needed to saturate the canopy (Hadiwijaya et al., 2021; Keim et al., 2006). Conversely, when the foliage is absent and the canopy’s capacity to retain rainfall is significantly reduced, the duration loses its influence as raindrops directly fall to the ground. However, it seems that smaller changes in LAI between the wet and dry sub-periods have no such influence. This phenomenon aligns with the findings of Nanko et al. (2011), who found that saturated canopies generate more throughfall, characterized by larger drops. Consequently, higher KE is produced, meaning that the duration required to saturate the canopy can have a significant impact. In both sub-periods, D50 exerted a greater influence on the pine tree than on the birch tree, which was showed by the BRT method only. For the pine tree, this influence was determined regardless of the period (whole, dry, wet), whereas for the birch tree, the influence was only evident in the dry sub-period. The needles of conifer trees have been shown to prevent the aggregation of droplets into larger ones (Levia et al., 2017), instead disperse them into smaller ones. This phenomenon, in turn, affects the characteristics of throughfall under the pine tree, leading to the reduction in KE of throughfall (Nanko et al., 2006; Zabret and ˇ Sraj, 2021). The RF method highlights throughfall intensity as one of the most influential variables for the pine tree during the whole observation period, regardless of the phenological phase. The strong influence of intensity is confirmed by both methods during the dry sub-period, but not during the wet one, indicating that the intensity exerts a greater impact during the dry sub-period. This phenomenon may be attributed to the lower amount of rainfall, which potentially resulted in a more pronounced effect on KE of throughfall from short but intense events, as was also found by Brasil et al. (2024). 5. Conclusions Rainfall interception by vegetation significantly affects the KE of precipitation, influencing soil erosion. This study examined the impact of meteorological factors, vegetation type, and seasonal conditions on KE under birch and pine trees. Machine learning models (BRT and RF) were used to evaluate the impact of meteorological factors on the KE of throughfall under both types of trees in wet and dry conditions. The results show that the KE of throughfall is higher under the birch than under the pine tree, which is expected as pine generally intercepts more precipitation than birch and therefore reduces the rainfall intensity and its KE. The fact that the KE of throughfall is highly dependent on the presence of leaves on the tree canopy is shown by the observation that the birch tree reduced the KE of throughfall to a much greater extent in the leafed period than in the leafless period. Additionally, during the dry sub-period LAI values were lower than in hydrologically normal year, resulting in higher TF values, as well as higher KE of throughfall under both tree species. The most pronounced KE events are consistent with the literature, which indicates that extreme precipitation conditions significantly contribute to the increased KE of rainfall. However, for the reduction of KE below the trees during the events with average amount and intensity of rainfall, other vegetation (e.g., LAI) and meteorological (e.g., air temperature) parameters seem to be more important than the intensity itself. This observation is also supported by the results of the BRT and RF models, which indicate that the KE of throughfall is significantly influenced by the amount of throughfall, the presence or absence of leaves, event duration, D50 and the maximum air temperature. The seasonal characteristics of the drop size distribution, as well as vegetation response during wet/leafless and dry/leafed periods, may be associated with this. However, a better understanding of this relationship requires measurements over a longer time period. With the presented analysis we aimed to evaluate the impact of extreme hydrological conditions on the process of rainfall interception, which is significantly related to the vegetation conditions and precipitation. We demonstrated that lower LAI values during the dry period, as well as different meteorological conditions (e.g., higher air temperature) and rainfall properties (e.g., more intense rainfall events) influence changes in throughfall KE. However, the evaluated differences were not as significant as expected. This may be because vegetation can adapt to extreme conditions for only a limited time, and the one-year period we considered may have been too short. Additionally, the groundwater level at the study site is quite high and can provide water for the trees’ extensive root systems during dry conditions. Therefore, to more comprehensively consider the effects of extreme hydrological conditions, it would be necessary to use a longer dataset, taking into account several longer dry and wet sub-periods, as well as comparing data from several locations. Funding The authors would like to acknowledge the financial support provided by the Slovenian Research and Innovation Agency (ARIS) within the scope of the projects J2–4489 and N2–0313, and the research program P2–0180. The study was also partially financed by the European Union’s Horizon Europe Research and Innovation Programme, within the scope of the project “SpongeScapes” (Grant agreement No. 101,112,738). CRediT authorship contribution statement Lana Radulovi´ c: Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation. Katarina Zabret: Writing – review & editing, Validation, Supervision, Methodology, Investigation, Data curation, Conceptualization. Mojca ˇ Sraj: Writing – review & editing, Validation, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Conceptualization. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments We thank two anonymous reviewers for their useful and critical comments, which greatly improved this work. Data availability The data can be obtained upon request from the corresponding author. References Alivio, M.B., Bezak, N., Mikoˇ s, M., 2023. The size distribution metrics and kinetic energy of raindrops above and below an isolated tree canopy in urban environment. Urban Forestry and Urban Greening 85, 127971. https://doi.org/10.1016/j. ufug.2023.127971. L. Radulovi´ c et al. Agricultural and Forest Meteorology 375 (2025) 110835 9