In interception, the canopy modifies raindrop size and velocity, and thus kinetic energy, while retaining part of the incoming rainfall. The Rutter model (Levia et al., 2011; Valente et al., 1997; Rutter et al., 1971; Gash and Morton, 1978) illustrates a traditional canopy interception process for rainfall, as depicted in Fig. 1. A segment of the rainfall is initially captured by the leaves, with drops dripping once leaf storage reaches saturation. Concurrently, another portion is retained by the stems, which, following interception and retention, is transported to the ground as stem flow. Throughout the rainy period, both stems and leaves are subject to evaporation.

Previous observations and research (Li and Tian, 2025; de Moraes Frasson and Krajewski, 2013) indicate that the canopy interception flow diagram proposed by Rutter et al. (1971) remains insufficient in capturing the comprehensive physical dynamics and kinetic energy of raindrops. Beyond the canopy drip phenomenon illustrated in Fig. 1a, raindrops are also subject to breakage and splashing upon collision with the canopy, which plays an important role in kinetic energy change of droplets. This splashing phenomenon is crucial for accurately depicting the canopy interception effect on rainfall (Murakami, 2021). Consequently, there is a need to refine the canopy interception process based on the Rutter flow diagram.

The revised canopy interception process is depicted in Fig. 1b. From a component perspective, raindrops penetrating the canopy can be classified into three types: free throughfall, splash throughfall, and canopy drip (Levia et al., 2017). In Fig. 1b, for the rainfall intercepted by leaves, the collision process results in two distinct forms of raindrops: splashed drops and canopy drips. Regarding the interception by stems, the impact of raindrops against the stem leads to some splashing or dripping, while another portion is retained by the stem, eventually contributing to stem flow once the stem is saturated. Given that the velocity of stem flow is significantly slower than that of raindrops falling directly from the sky, some water is retained during this process and the kinetic energy of stem flow is not taken into account. Moreover, evaporation occurs from the splashed drops on both leaves and stems, which, combined with surface evaporation, forms the total rainy season evaporation. Concurrently, water between leaves and stems may interchange during splashing and dripping. However, due to the minimal volume of this water, it is not accounted for in Fig. 2 nor in subsequent modeling analyses.

The model estimates under-canopy kinetic energy from the drop-size distribution and fall velocity implied by canopy structure. The derivation of this model is based on the work of Li et al. (2025) and Li and Tian (2025).

To evaluate model performance, we observed nine rainfall events on Aesculus chinensis Bunge, which had a height of 12.8 m, a diameter at breast height (DBH) of 23.3 cm and a clear bole height of 4.1 m, within the Tsinghua University campus. For raindrop spectrum observations, two OTT Parsivel² laser spectrometers were utilized, capable of dividing particle size and velocity into 32 bins, totaling 1024 combinations, with a size range of 0.0625 to 24.5 mm and a velocity range of 0.05 to 20.8 ms-1. It should be noted that both size and fall-velocity measurements are subject to uncertainties introduced by the instrument's non-uniform binning scheme, and subsequent analyses use the midpoint of each bin as the representative value. One of the laser spectrometers was situated under an Aesculus chinensis Bunge (116.3° E, 40.0° N), while the other was mounted on the roof of Tsinghua University sediment laboratory, approximately 150 m away, and we assumed similar above-canopy rainfall at the two locations.

As an effective means of observation, LiDAR has been widely used in the observation and analysis of vegetation structural parameters in recent years (Wang et al., 2023; Mostafa et al., 2022). In this study, a RIGEL VZ-600i terrestrial laser scanner (TLS) was used to observe and extract canopy parameters. Its ranging accuracy was 5 mm within 100 m and the scanning angle accuracy was 0.0028°. The FVC (Fraction of Vegetation Cover) is obtained from the voxel void statistics in the vertical direction. The leaf area density was calculated using the VCP algorithm based on contact frequency (Chen et al., 2024; Hosoi and Omasa, 2006), and then the LAI was obtained by integration along the vertical direction. The leaf inclination angle distribution was calculated using the principal component analysis method based on the leaf normal vector (Maćkiewicz and Ratajczak, 1993) shown in Fig. 3a. The stem area index and stem inclination angle parameters were extracted based on the branch reconstruction algorithm (Du et al., 2019), and the leaf area projection ratio G can be calculated according to the leaf inclination distribution.

The distribution of drip-capable heights, shown in Fig. 3b, was derived from LiDAR point-cloud data by identifying the first leaf or stem surface encountered when searching upward from the ground. During model computation, the median value of each bin was used as the representative value for that range.

The model parameters under field experimental conditions need to be determined, as shown in Table 2. The observation dates, rainfall duration, accumulated rainfall, mean wind speed and mean rainfall intensity are shown in Table 3. The measured splashing and canopy-drip components were classified based on a droplet-diameter threshold: after excluding free throughfall, droplets smaller than 1.3 mm were categorized as splashing drops, whereas those larger than 1.3 mm were classified as canopy drip (Levia et al., 2019). It is worth noting that evaporation during rainfall is minimal (Li et al., 2025); therefore, evaporation of leaf and stem is neglected in the following analysis.

This section evaluates and analyzes the performance of the under-canopy kinetic energy estimation model by integrating raindrop spectrum observation data of Aesculus chinensis Bunge on nine field rainfall events.

The total R2 values were 0.769, 0.572, and 0.773, and the total RMSE values were 18.7, 2.0 and 18.7 Jm-2h-1, with measurement and uncertainty of 54.1 ± 12.4, 3.7 ± 0.1 and 50.4 ± 12.4 Jm-2h-1 respectively. For drip kinetic energy and total kinetic energy, the measurement uncertainty is already close to the RMSE, indicating that the model performance approaches the observational precision limit. The simulation of under-canopy dripping kinetic energy demonstrated higher accuracy than that of splashing kinetic energy, likely due to the greater complexity and higher uncertainty associated with the splashing phenomenon which is shown in Fig. 4. Table 4 also shows that the splash kinetic energy tends to be overestimated, while the drip kinetic energy is generally underestimated, likely because certain components such as stemflow drip points (Nanko et al., 2022) were not considered.

Taking the rainfall events on 20 and 26 August as examples, the raindrop spectrum data collected under the canopy reveals a trend of relative consistency between the measured and simulated raindrop sizes, which is shown in Fig. 4. Raindrops smaller than approximately 1.5 mm, which are primarily responsible for splashing (Levia et al., 2017), constitute approximately 10 %–30 % of the mass ratio. The proportion of measured raindrops within the splashing size range is relatively lower than that of the simulation. Over time, as canopy saturation increases, the relative frequency of splashing drops in both measured and simulated data decreases, while the proportion of dripping raindrops rises. This behavior is consistent across both datasets and aligns with the physical expectation that higher canopy saturation leads to greater canopy drip intensity. Figure 4 also suggests that the canopy exerts an aggregating effect on the kinetic energy of rainfall, indicating that for canopies with similar physical structures, the raindrop spectrum and distribution under the canopy remain relatively stable regardless of variations in the external raindrop spectrum. Based on the analysis in Sect. 2.2, this phenomenon occurs because the under-canopy raindrop spectrum (excluding direct throughfall) is primarily governed by canopy physical parameters such as leaf area index, leaf inclination angle, and leaf contact angle, through raindrop interactions including splashing, dripping, and coalescence within the canopy. This observation is consistent with the findings of Nanko et al. (2025).

Figure 5 shows a comparison between simulated and measured kinetic energy under the canopy during two rainfall events. The overall trends of both are generally consistent, and the variations in kinetic energy are also in agreement with those observed above the canopy. However, the simulated splash kinetic energy shows a slightly greater discrepancy compared to the measured values. The complexity of the splash phenomenon, including the presence of larger splash drops not accounted for in the simulation triangular distribution assumption, may explain the discrepancy. However, since splash droplet kinetic energy constitutes a small fraction of the total kinetic energy (about 3 %–10 %), its impact on the total under-canopy kinetic energy simulation is minimal.

Figure 6 compares measured and simulated cumulative kinetic energy per unit area for above-canopy and under-canopy rainfall during two rainfall events. Initially, under-canopy energy remains lower than open rainfall due to canopy interception. As the canopy approaches saturation, increased canopy dripping drives significant energy escalation under the canopy. In contrast, during the 26 August event, under-canopy energy surpasses above rainfall energy at t≈100 min, ultimately reaching nearly twice the open-environment value. Thus, assessing the canopy impact on rainfall kinetic energy requires a comprehensive analysis of canopy leaf inclination, contact angle, branch height, interception volume and the external raindrop spectrum to determine whether the kinetic energy under the canopy is greater or less than that above. Smaller branch heights and larger leaf inclination angles may result in smaller and slower canopy drip, potentially leading to lower kinetic energy under the canopy.

The uncertainties and influences associated with external factors, the threshold values used for measured component partitioning, typical model parameters, the determination of falling height and canopy traits are analyzed in this section, which can be seen in Figs. 7–9 and Table 5. In the sensitivity analysis, only the parameter of interest was varied, while all other parameters were kept at the values listed in Table 2.

Since the RMSE metric is influenced by the total kinetic energy above the canopy, the R2 metric was adopted for the sensitivity analysis of external influencing factors of wind speed and rainfall intensity, as shown in Fig. 7. Figure 7a indicates that wind load has no significant effect on model performance, with p values consistently above 0.5. This likely occurs because the estimation of under-canopy raindrop size distribution accounts for wind load effects through the coefficient kw (see Eqs.  and  in Sect. 2.2, and Li et al., 2025), maintaining relatively stable model performance across varying wind speeds. As mean rainfall intensity increases, the performance for total kinetic energy and dripping kinetic energy shows a declining trend, while splashing kinetic energy exhibits an increasing trend. Notably, the simulation performance of splash kinetic energy increased significantly with increasing rainfall intensity (p<0.05). This phenomenon is consistent with the observations of Nanko et al. (2025), who concluded that splash is predominantly driven by rainfall. This may be attributed to: (1) splashing being less pronounced at low rainfall intensities, leading to biased splashing energy estimates; and (2) significant leaf vibration induced by high rainfall intensities, which is not currently considered in the model, resulting in slightly diminished performance in total and dripping energy with increasing rainfall intensity.

As shown in Fig. 8a, the experimentally measured component partitioning thresholds were relatively stable between 1.1 and 1.6 mm, with R2 fluctuating between 0.55 and 0.65. Thresholds below 1.1 mm or above 1.6 mm resulted in noticeable decreases. The drip kinetic energy and total kinetic energy were not sensitive to this threshold. Figure 4 also shows that the volume fraction of raindrops between 1 and 2 mm is relatively small, as most drip drops are larger than 2 mm and most splash drops are smaller than 1 mm; the contribution from 1–2 mm drops may mainly correspond to free throughfall. Therefore, selecting 1.3 mm as the experimentally measured threshold for analysis is appropriate.

As shown in Fig. 8b–d, the model is most sensitive to the parameter p, which is defined as the proportion of volume remaining on the leaf or stem after splashing. This is also evident from Eqs. () and (), where p, as an external multiplicative factor, has a direct and substantial impact, while the parameters β and rsd affect only specific terms. Physically, the value of p is related to factors such as rainfall intensity and leaf surface properties, and further investigation is needed to better understand its behavior.

Through sensitivity analysis in Table 5, it was found that using the height distribution shown in Fig. 3b for simulation versus using the average height resulted in very minor differences in this case. The mean deviation of splash kinetic energy was only 0.1 %, while deviations for drip kinetic energy and total kinetic energy were approximately 1.6 %, with correlation coefficients all exceeding 0.999, indicating no significant differences. The likely reason is that for this tree species, the branch height is relatively large (>4 m), so most raindrops reach over 90 % of their terminal velocity. In addition, due to the relatively high leaf area density of the species, the height distribution is concentrated, mostly between 4.7 and 5.1 m, resulting in a narrow distribution.

To further examine the influence of canopy traits on the model results, the percentage changes in the event-averaged kinetic energy across the nine rainfall events were plotted, using the parameters in Table 2 as the baseline.

Figure 9 indicates that the estimated kinetic energy decreases monotonically with increasing LAI; exhibits a decrease followed by an increase as θ increases; and increases with increasing αm. Sensitivity analysis further shows that the model is most responsive to variations in θ, followed by LAI and, to a lesser extent, αm. The observed increase in under-canopy kinetic energy corresponds to a reduction in canopy interception volume, reflecting concurrent decreases in splash and drip volumes with increasing LAI and decreasing leaf inclination angle. This concave-downward response to contact angle reflects the role of leaf surface hydrophobicity: lower hydrophobicity allows larger canopy drip size and higher kinetic energy, whereas stronger repellency limits water retention on leaves and increases drip and splash volume.