Physically Based Canopy Interception Model for a Beech Forest Using Remote Sensing Data

Abstract

Precipitation retained by tree canopies (~25%) is a key part of the forest water cycle, making our understanding of it vital for ecohydrological studies. Canopy interception varies seasonally with changes in canopy storage capacity. While remote sensing for rainfall partitioning is still developing, there is a strong demand for the calibration of canopy interception models based on ground measurements. In addition, most studies cover no longer than a few years, limiting long-term insights. Therefore, the main objective of this study is to upgrade a Merriam-type canopy interception model (derived partly from physical parameters) for European beech (Fagus sylvatica L.), which takes into account the dynamically changing reservoir capacity of the canopy (based on remotely sensed LAI data). The model was tested with annual precipitation totals for the period of 2017–2022. The results indicate that interception has a significant partitional effect on rainfall, which is notable in terms of its proportions, especially for small precipitation events (0–5 mm). The value of yearly interception was 20% (13% in dormancy and 24% in the growing season). The calibrated model can provide beech interception values in areas with similar climatic parameters to those of the study area.

1. Introduction

The process of precipitation interception plays a fundamental role in the hydrological cycle and land–atmosphere interactions, leading to a net ‘loss’ of water for ecosystems, while providing a net ‘gain’ of moisture for the atmosphere [1].

Incident precipitation on vegetation canopies is partitioned into three components. Interception loss $\left(Esu\right)$ is the portion directly evaporated from leaf and wood surfaces back into the atmosphere without reaching the ground. The next component is throughfall $\left(TF\right)$ as diffuse input, which passes directly through gaps or drips from the canopy to the ground. Finally, the stemflow $\left(SF\right)$ acts as point input, as it is funneled to the base of the plant via the branch structure and trunk [2,3,4].

Forest cover significantly influences the hydrological cycle across different regions worldwide [5]. For example, forests generally mitigate the negative impacts of floods by facilitating water drainage in undisturbed forested areas [6]. Forests affect water dynamics at various stages, including via transfers to the atmosphere and rivers [4,7]. In the forests, the portion of precipitation that reaches the floor is unevenly distributed in space [8]. Litter cover greatly influences the water balance of the root zone by retaining precipitation, thus preventing it from entering the soil below and potentially reducing the amount of water available for absorption by the roots. Simultaneously, the drying of the soil is also influenced by the litter [9]. However, the remaining water infiltrates into the forest soil and replenishes subsurface water reservoirs. The amount of precipitation that does not infiltrate into the soil evaporates to the atmosphere or generates surface runoff. Accordingly, intercepted precipitation by its definition is unavailable for soil infiltration or surface or subsurface runoff.

The amount of rainfall intercepted by plant canopies of the forest depends on its species composition [10,11,12] and typically constitutes 10%–30% of the gross rainfall $\left(P\right)$ (in temperate climates it is between 20% and 30%) [8,13]. Consequently, accurate monitoring of interception is essential not only for water and forest management but also for climatic and meteorological applications [1], as well as for our understanding of forest ecohydrology [14].

Rainfall partitioning effects in any forest stand depend on rainfall characteristics, meteorological conditions, vegetation structure, and the interactions among these factors [15,16,17]. Precipitation distribution within a year largely influences the amount of rainfall interception. Thus, years with a given annual precipitation but more frequent large precipitation events will experience the smallest percentage of rainfall interception [9]. Therefore, the smaller the rain events, the higher the amount of interception becomes [18,19,20]. It can even approximate 100%, when the amount of precipitation is less than 1 mm, it is windy and the tree canopy is dry [21].

Interception, nevertheless, is highly variable in time, since canopy storage capacity may greatly vary between summer and winter (seasonal pattern) [22]. Klamerus-Iwan and Błońska [23] pointed out the significant difference in intercepted values between dormancy and the growing season: 6% by bare trees but 22% for a fully leaved forest. According to Führer [24], the value of interception loss in the winter is about half of the summer values. Additionally, Zabret et al. [25] observed that the amount of intercepted rainfall is similar for wet years and leafless periods, as well as for dry years and leafed periods. Consequently, interception is largely a function of the leaf area index or $LAI$ [26].

The previous paragraphs reveal that a sizeable fraction of uncertainty in forest water balance arises from the uncertainty of interception—potentially on the order of 10%–20% or even more—due to its variability across forest types and seasonal dynamics. On the other hand, challenges in measurement and modeling have also made a great contribution to the mentioned uncertainties. The major sources of uncertainty in land surface models are parameterization (such as storage capacity) and sub-grid heterogeneity related to canopy properties. In the case of remote sensing data, the scale mismatch, as they often provide information at different spatial and temporal scales than those required for accurate interception estimation, leads to uncertainties in capturing the heterogeneity of forest canopies and interception processes. Nevertheless, the satellite imagery and vegetation indices come with inherent errors and uncertainties due to sensor limitations, atmospheric conditions, and data processing steps [27].

European beech (Fagus sylvatica L.) is one of the most widespread broadleaved species in Central Europe [28]. In a monoculture European beech forest, the average annual percentages of throughfall, stemflow and crown interception were 63%, 6% and 31%, respectively, of the gross rainfall [29]. The beech forest distribution in its southern limit is restricted mainly by soil water availability [30]. The species is therefore particularly vulnerable to soil drought [31]. Consequently, interception is a crucial element of the water balance since it reduces water input for the root zone [9]. In Hungary, the total area of beech-climate-class sites have shrunk seriously in recent decades, primarily due to the radical increase in the summer mean temperature as a main consequence of the ongoing climate change [32].

Experiments at both the single-tree and plot levels have led to the development of various models, including empirical interception-precipitation regressions [33,34,35], stochastic models [36,37], and process-based formulations [3,16,38,39]. Recently, new approaches for estimating interception have emerged, such as a physically based model driven solely by precipitation [40,41] and an innovative soil moisture-based method that estimates storage capacity by assuming that infiltration begins only after interception storage is full [42]. Although there is great variation between modeling approaches, local case studies are important because they can reveal regional trends, helping to identify research gaps and guide future investigations [43].

Ground-based interception measurements are limited in space and time, but there is a great demand for canopy interception models that can be temporarily and spatially extended in water balance calculation studies [44]. Therefore, the main purpose of this work is to (i) upgrade the original Merriam canopy interception model, which is partly empirical (some parameters are physically based) for European beech (Fagus sylvatica L.) forests with consideration of the remote-sensing-based dynamic storage capacity of the plant canopy, and (ii) test this model with measured precipitation and interception data.

2. Materials and Methods

2.1. Study Area

A middle-aged beech (Fagus sylvatica L., 1753)-dominated forest ecosystem was selected for the present study (Figure 1). It is located in the Hidegvíz Valley Experimental Catchment (northern latitudes 47°35′08′′–47°39′06′′ and eastern longitudes 16°25′31′′–16°28′15′′ in WGS 84 datum) in the Sopron Hills in Hungary, at the eastern foothills of the Alps. The area is characterized by a sub-alpine climate with daily mean temperatures of 19 °C in July, and −2 °C in January, and with long-term annual average precipitation of 750 mm. Late spring and early summer are the wettest times, while autumn is the driest season [45,46].

The beech interception garden was established in a natural community of beech mixed with sessile oak (Quercus petraea) in the Farkas ditch. The forest stand is mixed, but the measurements were made in a patch where only beech is present. The interception garden is situated at an altitude of 510 m a.s.l., with a slope of 15% E to E, and is a free-draining site (no excess water effect). The soil group, conforming to the international soil classification system (World Reference Base for Soil Resources, WRB), is Cutanic Luvisol (Epidystric). The stand in the interception garden is 100% closed with a single canopy layer. Understory vegetation is sparse, with typical species such as coralroot bittercress (Dentaria bulbifera), wood sorrel (Oxalis acetosella), hairy sedge (Carex pilosa), male fern (Dryopteris filix-mas), and cordyalis (Coridalis spp.).

2.2. Measurements

For the purposes of model establishment, data from 2006 to 2010 on precipitation, throughfall and stemflow were used. From the daily precipitation data at the local weather station at Brennbergbánya, precipitation sums for the measuring days were calculated.

At the beech interception garden there are 10 ring collars (around tree trunks) in order to measure the stemflow (Figure 2). The amount of water flowing down a trunk, measured with the trunk ring collars, expressed in liters per canopy area, can be determined in two ways: (a) by diameter or (b) by circumference. For the present study, the circular area-based option was chosen, because it showed a better correlation between precipitation and stemflow. The measured stemflow for the interception garden as a whole (liters) had to be converted into per unit area (mm) using the diameter of breast height distribution of the beech plot. The estimation of the vertical projection of the tree canopy is based on the breast height area of the tree trunk (from the circumference diameter) of 10 trees with a trunk ring collar.

Throughfall is measured by eight tubs of 0.2 m² catchment area and 20 funnels of 0.0033 m² catchment area (Figure 2). The collected water volumes (liter) were subsequently converted to mm.

The measured values were reviewed and filtered before using them in this study. The throughfall values measured by the funnels may be uncertain (Figure 2), as they overflow more quickly due to their limited carrying capacity, and the data set has a larger spread. For the tubs, their clogging could become a problem. Therefore, if any of these issues were detected, the event was not considered in the study. Additionally, if the open area precipitation (mm) was less than the stemflow (mm) on the trunk, the data was considered erroneous and was filtered out as well. Therefore, the results of stemflow as well as throughfall do not represent whole years. Measurements were preferably carried out only during the growing season between March and October. Interception derived from these measurements can be obtained as follows:

$$I_{measured}=P-TF-SF$$

(1)

2.3. Modified Merriam Model

For the analysis of the precipitation–interception relationships, the so-called original Merriam model [33] was used as a basis:

$$E_{su}=S\ast \left(1-e^{-{\displaystyle \frac{P}{S}}}\right)+K\ast P$$

(2)

where

P—Precipitation amount [mm];

S—Forest canopy storage capacity [mm];

K—Parameter of the evaporation process during the rainfall event (-);

E_su—Interception [mm].

The first part of Equation (2) represents the refilling of the storage capacity, while the second part quantifies evaporation from the canopy during the precipitation event.

Canopy storage capacity $\left(S\right)$ is not a constant value, as it changes during the year, especially in the case of deciduous forests [47]. Consequently, static storage capacity value, determined by growing season measurements (because the data are generally collected during the growing season), gives an approximate maximum value ($S_{max}$). In order to overcome this aspect of the basic Merriam model, we introduced an additional element to the second part of the equation. This term describes the rate of evaporation during a precipitation event, which also depends on the size of the evaporating surface:

$$E_{su}=S\ast \left(1-e^{-{\displaystyle \frac{P}{S}}}\right)+K\ast {\displaystyle \frac{S}{S_{max}}}\ast P$$

(3)

The change in storage capacity during a year expresses strong correlation with the leaf area index $\left(LAI\right)$ and the projected surface of stems, branches and twigs $\left(SAI\right)$ [48]:

$$S=C_{int}·\left(LAI+SAI\right)$$

(4)

where

C_int—Maximum storage capacity per surface unit [mm/m²];

LAI—Projected leaf area surface [m²/m²];

SAI—Projected surface area of stems, branches, and twigs above a unit ground area [m²/m²].

Stem area index $\left(SAI\right)$ is the ratio of the total area of all woody stems on a plant to the area of ground covered by the plant. According to [49], $\left(SAI\right)$ can be calculated as follows:

$$SAI=C_s\ast HEIGHT\ast DENSEF$$

(5)

where

$C_s$—Ratio of projected stem area index (SAI) to $HEIGHT$, if $DENSEF$ = 1;

HEIGHT—Canopy height (m);

DENSEF—Canopy density multiplier (fixed parameter) between 0.05 and 1, dimensionless.

$DENSEF$ is typically 1. However, it should be reduced below 1 in the case of thinning simulations by cutting for an existing canopy.

The total stem area index is roughly 2 for a 20 m closed canopy height [49], and for cylindrical “stems”, the $C_s$ value is estimated to be equal to 2/(20 π) = 0.035. In this study, these values were considered, i.e., $C_s$= 0.035, $HEIGHT$ = 20 m and $DENSEF$ = 1.

The maximum storage capacity for a unit surface is calculated as

$$c_{int}={\displaystyle \frac{S_{MAX}}{{LAI}_{MAX}+SAI}}$$

(6)

The value of $\left(SAI\right)$ is expected to be constant through the seasons, with a value of about 0.7 m²/m² calculated for the approx. 20 m height stand; however, the value of $LAI$ expresses significant variability in time [50]. $LAI$ quantifies forest coverage by considering the shadowing effects of stems, branches, and leaves. It is closely linked to the heterogeneity of canopy storage capacity, which reflects the canopy’s ability to intercept rainfall. This heterogeneity also influences gaps that allow direct throughfall and the formation of dripping points. These variations play a key role in shaping the canopy water balance across different climate and forest types, where a higher $LAI$ generally corresponds to greater canopy interception and reduced throughfall [13].

Based on the above, in this study, MODIS sensor-based $LAI$ time series [51] are used to estimate changes in the forest storage capacity. The MCD15A3H Version 6.1 MODIS Level 4, Combined Fraction of Photosynthetically Active Radiation (FPAR), and $LAI$ product 4-day composite data set with a 500 m pixel size were applied. The algorithm chooses the best pixel available from all the acquisitions of both MODIS sensors located on NASA’s Terra and Aqua satellites from within the 4-day period.

$LAI$ is defined as the one-sided green leaf area per unit ground area in broadleaf canopies and as one-half the total needle surface area per unit ground area in coniferous canopies. FPAR is defined as the fraction of incident photosynthetically active radiation (400–700 nm) absorbed by the green elements of a vegetation canopy. The exact coordinates on which we obtained the data series were the following: 47.656329, 16.45397, with 1 January 2017 as the starting date and 23 August 2023 as the ending.

Incorrect $LAI$ data (blank data due to cloudy weather) were filtered out, proper data were interpolated, and extra smoothing was performed (Figure 3). Winter values were approximated by zero.

A continuous time series curve was calculated from the smoothed MODIS $LAI$ data set of the research plot. The smoothed $LAI$ time series curve was used for the determination of a dynamic S.

The diameter classes were separated into four cm categories (Figure 4) (29 July 2006).

3. Results

3.1. Measured Interception Values

Based on the $LAI$ data and Equations (4)–(6), Figure 5 displays the dynamics of storage capacity data. The maximum value of $LAI$ is at around 6–7 June. The storage capacity follows the value of $LAI$ in the growing season, but in winter it is determined by the stem area index $\left(SAI\right)$.

The data of the filtered throughfall (Figure 6) expresses a highly skewed (asymmetric) distribution, due to a significant number of events with small precipitation. The average value is higher than the median. The variation between measurement points is due to the different crown structures.

The stemflow values for individual trees, based on their position within the stand, displays an even more varied (skewed) distribution (Figure 7) than the throughfall (Figure 6).

3.2. Modeled Interception Values

The parameters of the upgraded relationship (3) were determined by using the least-sum-of-squares method and the measured interception data (collected in the growing season) in the beech forest plot of the Hidegvíz valley experimental catchment during 2006–2010. The parametrized version of (3) contains a calibrated value of 1.9 for $S_{max}$ (Figure 8) while the value of $K$ was set to 0.1 according to [52]:

$$E_{su}=S\ast \left(1-e^{-{\displaystyle \frac{P}{S}}}\right)+0.1\ast {\displaystyle \frac{S}{1.9}}\ast P$$

(7)

As part of the calibration, the forest canopy storage capacity (S) had to be determined using the maximum storage capacity as

$$c_{int}={\displaystyle \frac{1.911}{7.1+0.7}} = 0.245$$

(8)

The proposed (upgraded) Merriam model, i.e., (7), was tested using the measured data set collected at the study site. The measurements were conducted in the growing seasons of 2006–2010.

The vertical distance of the blue points from the model curve in Figure 8 represents the deviation from the measured data, and the square of these deviations is summed. We tried to minimize that sum, relative to the measured data (blue points). Therefore, minimum RMSE was used as an objective function for determining the maximum storage capacity. We used iterative optimization to minimize the RMSE.

In order to derive and generalize interception losses, we used the calibrated Equation (7) from here onward.

Figure 9, Figure 10, Figure 11 and Figure 12 are based on measurements in the case of precipitation, while the interception data are derived from the fitted model.

A significant variation among years in precipitation was observed in the current study, whereas interannual variations in the interception values were smaller (Figure 9).

For the ratio of interception to precipitation, amongst the investigated years, 2022 had the highest rate of interception with 23%, while 2018 had the lowest with 17%.

Precipitation categories of Figure 10 and Figure 11 are as according to [53]. The year 2022 had the highest small precipitation sums (<2 mm) as well as the highest number of events, but also the lowest large precipitation sums (>20 mm). The years 2019 and 2020 had the lowest values and smallest number of light precipitation events, and the highest values for large events (>20 mm). Most of the difference between those two years can be found in the 5.01–10 mm and the 10–20 mm categories (

Table 1. Number of interception events in the different precipitation categories during the study period (2017–2022).

Precipitation Category	2017	2018	2019	2020	2021	2022
0–0.5 mm	54	43	22	21	44	55
0.51–1.0 mm	22	15	20	20	15	27
1.01–2.0 mm	24	19	22	21	18	22
2.01–5.0 mm	29	29	29	23	28	22
5.01–10.0 mm	25	30	16	24	17	20
10.01–20.0 mm	13	19	21	13	11	12
20.01< mm	5	5	7	7	7	5

).

We determined the ratios of the interception on the different precipitation categories (0–20mm) (

Table 2. Interception ratios in the different precipitation categories during the study period (2017–2022).

	Interception/Precipitation
Precipitation Category	2017	2018	2019	2020	2021	2022
0–0.5 mm	0.77	0.78	0.83	0.74	0.83	0.81
0.51–1.0 mm	0.72	0.47	0.61	0.59	0.56	0.60
1.01–2.0 mm	0.39	0.40	0.38	0.54	0.51	0.51
2.01–5.0 mm	0.27	0.23	0.30	0.33	0.29	0.31
5.01–10.0 mm	0.19	0.18	0.18	0.23	0.17	0.25
10.01–20.0 mm	0.14	0.12	0.16	0.17	0.12	0.17
20.01< mm	0.10	0.10	0.11	0.11	0.12	0.10

).

The relationship between interception and precipitation is linear (Figure 12).

The precipitation partitioning effects of forests can be significantly different between the growing season and dormancy. Therefore, we differentiated the data series of the six investigation years by vegetation status; growing season period from 10 May to 3 November, and dormancy from 4 November to 9 May (

Table 3. Six-year sums of interception and precipitation values (mm) in each precipitation category during dormancy and the growing season.

Precipitation Categories	I	P	I	P	I	P
	Dormancy (4 November–9 May)		Growing Season (10 May–3 November)		2017–2022
0–0.5 mm	17.50	25.68	22.22	23.36	39.72	49.04
0.51–1.0 mm	15.68	41.93	34.66	41.44	50.35	83.37
1.01–2.0 mm	27.74	97.40	54.95	84.66	82.70	182.05
2.01–5.0 mm	39.92	257.95	116.34	267.63	156.26	525.59
5.01–10.0 mm	39.99	388.44	150.78	530.71	190.77	919.15
10.01–20.0 mm	35.93	401.12	151.87	813.48	187.80	1214.60
20.01< mm	9.84	178.79	121.23	1002.65	131.07	1181.44
I sums [mm]	186.62		652.05		838.67
P sums [mm]		1391.31		2763.93		4155.24
I/P ratio (dynamic storage capacity)	0.13		0.24		0.20
I/P ratio (constant storage capacity)	0.42		0.30		0.34

).

The difference in the interception values between the growing and the dormant seasons is typically higher in the higher precipitation-sum categories (which is also true for the precipitation sums). In the growing season, the interception ratio is nearly double that of the dormant season (Table 3).

According to Table 3, the I/P ratio with constant storage capacity shows a much higher ratio of interception, especially in dormancy. The reason is because the basic model applies maximum storage capacity, which is preferably applicable for the growing season in the presence of the canopy of deciduous species.

4. Discussion

The European beech (Fagus sylvatica L.) is one of the most widespread broadleaved species in Central Europe [54], covering a large area (140–150,000 km²) [55], and thus transpiration and interception significantly affect the hydrological cycle and lower water availability [56]. On the southern limit of the beech’s distribution, where their occurrence is largely constrained by soil water availability, drought sensitivity has to be considered [30,31]. In the aftermath of the most recent severe heat waves in 2018–2020, the drought mortality rose by more than 5% per year in some Central European regions [57,58,59], especially in areas with shallow soils. In Hungary, the total area of beech-climate class sites has shrunk significantly in recent decades, primarily due to the drastic increase in the summer mean temperature. In the near future (2021–2050), the projected warming and decrease in available water, particularly in the growing season, may cause a complete disappearance of the beech-climate class from Hungary [32].

Recent advances in remote sensing technologies (including enhanced satellite sensor applications) have significantly improved the understanding of canopy interception [60]. However, the use of remote sensing to study interactions between forest canopies and the atmosphere—particularly in quantifying rainfall partitioning—remained in their early stage. This validates the continued importance of ground-based observations (as well as the utilization of them to accurately calibrate remote sensing systems). Nevertheless, remote sensing products often face limitations in spatial resolution, which may not be sufficient for detailed analyses of specific forest stands. Additionally, the temporal variability of canopy interception processes poses a challenge, as studies with less than two years of duration may fail to adequately capture the inherent complexity and variability of these systems [61]. Mello et al. [13] reviewed the scientific literature on canopy interception, noting that approximately 17% of research focuses on Fagus species in temperate climates, while Pinus species have garnered the most attention, accounting for about 27% of the studies. Most of the experiments span approximately over 15 months, with the number of collectors typically ranging from 2 to 4 or 14 to 27. Although ground-based studies are limited in time and space, they may provide essential information that can be expanded using models [44].

In this study, four years of measured throughfall and stemflow data were used to calculate rainfall interception for beech forest (Fagus sylvatica) in Hungary. During 2006–2010, throughfall of 68% and stemflow equal to 8% were measured, resulting in 24% rainfall interception. This value is similar to the rainfall interception values observed for beech in other studies. According to [62], precipitation interception by Fagus sylvatica in Europe is on average equal to 22% ± 5%. Lower interception values were observed in beech plantations at the forest edge, ranging on average between 14% and 16% [63]. Peck and Mayer [10] and Peck [64] reported a wider range of crown interception values for beech stands from 5% to 48% of precipitation, with an average of 20%. Staelens et al. [65] focused on a mature beech tree and estimated the interception value at the annual level as 21%. Slightly higher values of intercepted rainfall were found by Granier et al. [66], with 25%–27% in a young beech stand in Hesse Forest, France. Additionally, higher values were also observed by Tarazona et al. [67], who studied the water balance in two forest ecosystems dominated by beechwood in Spain and reported interception as 31.7%. Similarly, Novosadová et al. [29] reported that the annual crown interception was almost 31% in a beech monoculture forest, while in mixed beech–oak–linden forest, interception of 22% was observed.

This work used the measured values from the beech forest in Hungary in order to set up a modified Merriam model. Our results for the period 2017–2022 indicated monthly interception values of 20%. The original Merriam model [33] was previously applied to the same beech forest plot [52,53], resulting in an interception rate ranging from 28% to 40% (calculated with growing season storage capacity). However, using the modified Merriam model, rainfall interception was estimated to be between 13% in dormancy and 24% in the growing season, which corroborates the work of [25]. Higher values were observed in the previous study, which are the result of employing the original Merriam model, which only accounts for maximum storage capacity (S_MAX), throughout the entire year.

The precipitation category 0–2 mm produces the largest interception, because most of the light rain is retained by the canopy. Most of the rainwater from 2 to 5 mm events is also retained by foliage, but litter interception becomes important as well. Rainwater from 5 to 20 mm events infiltrates into the ground and becomes consumed by the forest stand through the roots. The majority of rainwater from precipitation events above 20 mm cannot be used by the plants, and therefore it will leave the area as runoff [53].

Using the modified Merriam model allows the analysis of intercepted precipitation not only for the growing season but also during dormancy, and so enables the estimation of seasonal difference. Rainfall interception in the growing season, when the canopies are fully leafed, is estimated to be significantly different than in dormancy (p < 0.01); on average, it is 11% higher. This modeled value corresponds well with observations by Gerrits et al. [22], who reported a 13% difference in interception efficiency during different vegetation periods, while a 15% difference was found by Aussenac and Boulangeat [68]. However, only an 8% difference between the vegetation periods was observed by Giacomin et al. [69] under pure beech coppice, and a 3.3% difference by Novosadová et al. [29] in a European beech monoculture forest, who in addition reported mainly different redistribution of rainfall per vegetation periods. Staelens et al. [65], on the other hand, reported a difference of as much as 20% in intercepted rainfall between growing and dormancy periods under a single beech tree (31% and 11%, respectively). The difference in interception ratio between dormancy and the growing period, calculated by the current model, is rather at the higher end. This is probably the consequence of smoothing the satellite-based $LAI$ data and assuming that $LAI$ equals zero during the winter time. However, it is still in the range of values observed during the measurements of rainfall interception by the beech tree.

The modeled interception values were also evaluated according to the precipitation classes. The highest interception of almost 80% was observed during the events with less than 0.5 mm of total rainfall amount. For every simulated year, a decreasing trend of interception ratio with increasing rainfall amount was observed. Similarly, Ahmadi et al. [70] reported that with the increase in the size of the rainfall events, intercepted gross precipitation by the oriental beech forest canopy decreased. Regardless of the class of rainfall amount, interception ratio was higher in the growing season than in dormancy, with the highest difference, observed for 0.5–1 mm rainfall class, being equal to 46%, and a 32% difference for the 1–10 mm rainfall class, which is larger than the 8% that was reported by Giacomin et al. [69] for the case of pure beech coppice. Rainfall interception per size class of rainfall was also studied by Giacomin et al. [69] in an 80-year-old beech stand (Fagus Sylvatica); they reported winter interception for events above 2 mm representing 10% of precipitation, while in summer it corresponded to 20% when precipitation exceeds 4 mm. These results are very close to the ones observed in this study, with 10.1% of interception in the dormancy period for events above 2 mm and 19.7% of intercepted rainfall in the growing season for events larger than 5 mm.

The calibrated model may be useful for measured local data of other beech stands with similar climatic parameters to those of the study area (i.e., the spatial extension of the model). Another possibility could be the development of an interception projection model using regional climate model (RCM) data. However, the RCM precipitation time series contains an unrealistically high amount of small precipitation events, which leads to excessive modeled interception sums. A further problem is the projection of canopy dynamics, due to the fact that climate warming is also associated with a lengthening of the growing season.

5. Conclusions

A Merriam-type canopy-interception model (derived partly from physical parameters), which considers the dynamically changing reservoir capacity of the canopy (based on remote-sensed LAI data), was upgraded for a European beech (Fagus sylvatica L.) forest. For the purpose of model establishment (as calibration), data from 2006 to 2010 on precipitation, throughfall and stemflow were utilized. The model was tested with annual precipitation totals for the period of 2017–2022.

The data of the filtered throughfall shows a highly skewed distribution, due to the significant number of events with small precipitation. The variation between measurement points is due to the different crown structures. The stemflow values for individual trees, due to their position in the stand, show an even more varied (skewed) distribution.

The results indicate that interception has a significant distributional effect on rainfall, which is notable in terms of its proportions, especially for small precipitation events (0–5 mm) (for example, almost 80% during the events with less than 0.5 mm). The average value of annual interception was 20% (19%–23%) of the total rainfall amount, with 13% in dormancy and 24% in the growing season.