Assessment of Effective Wind Loads on Individual Plantation-Grown Forest Trees

Abstract

Quantifying wind loads acting on forest trees remains a major challenge of wind-tree-interaction research. Under wind loading, trees respond with a complex motion pattern to the external forces that displace them from their rest position. To minimize the transfer of kinetic wind energy, crowns streamline to reduce the area oriented toward the flow. At the same time, the kinetic energy transferred to the trees is dissipated by vibrations of all aerial parts to a different degree. This study proposes a method to estimate the effective wind load acting on plantation-grown Scots pine trees. It evaluates the hypothesis that the effective wind load acting on the sample trees can be estimated using static, non-destructive pulling tests, using measurements of stem tilt under natural wind conditions and static, non-destructive pulling tests. While the analysis of wind-induced stem displacement reconstructs the temporal tree response dynamics to the effective wind load, results from the pulling tests enable the effective wind load quantification. Since wind-induced stem displacement correlates strongly with the sample trees’ diameter at breast height, the effective wind load estimation can be applied to all other trees in the studied stand for which diameter data is available. We think the method is suitable for estimating the effective wind load acting on trees whose wind-induced response is dominated by sway in the fundamental mode.

1. Introduction

An essential factor of the atmospheric environment that affects the growth, development, and survival of trees and forests is the endemic wind load regime [1,2,3,4]. Turbulent and non-turbulent parts of local airflow cause a dynamic response in trees resulting from the tree-specific conversion of kinetic airflow energy to elastic energy [5,6].

The energy transfer into trees occurs on several different temporal and spatial scales on all aerial tree parts—from individual leaves to entire canopies [7,8]. Depending on their intensity, wind loads can be classified as recurrent or critical. Recurrent wind loads are an inherent part of the endemic wind climate. Critical wind loads occur infrequently and cause damage to trees and forests [9].

Maximum gust speed is an effective indicator of critical wind loads [3,10,11,12] used in statistical [13,14] and hybrid-mechanistic modeling of storm damage to forests [15,16,17,18].

Because storms frequently damage enormous numbers of trees and forests worldwide, there is a fundamental interest in a comprehensive understanding of the processes that contribute to storm damage. Considerable efforts have been made to better understand the origin [19,20], the patterns [21,22], and the impacts of storm damage in forests [23,24,25] and urban trees [26] as well as the growth reaction of trees to storm and wind stimulus [27,28].

The first step in analyzing wind-forest tree interactions is a comprehensive assessment of the excitation of the above-ground tree parts exposed to the wind. Because of the broad spectrum of spatial and temporal scales at which full-scale tree excitation can occur under natural wind conditions, analysis of the components involved in inducing tree response is inherently complex [29].

A simple assumption, which cannot represent the whole complexity, is based on the decomposition of wind loads into turbulent and non-turbulent or mean wind loads. The turbulent wind loads, which are associated with the occurrence of gusts, act on shorter time scales (<1 min) and more minor space scales (maximum a few hundred meters) than the mean wind loads (typically 10 to 60 min averaging intervals). Under high natural winds, the mean loads can also be called quasi-static because they have lower spatiotemporal variability than turbulent scales. Hybrid-mechanistic storm damage models combine turbulent and quasi-static wind loading to calculate the critical wind speed. The critical wind speed is the minimum wind speed required to break or overturn forest trees [9].

Trees do not respond equally to the whole wind load spectrum. A key finding is that the frequencies where the wind excites forest tree motion and the frequencies of the trees’ dominant damped sway modes occur do not coincide [6]. The primary response to wind loads occurs at frequencies below the frequency range associated with the fundamental sway mode.

Earlier studies [30,31] found that in plantation-grown Scots pine (Pinus sylvestris L.) trees, sway in the fundamental mode is an indirect reaction to displacement from the rest position mainly caused by organized turbulence in the canopy airflow. The median duration of the organized turbulence elements at their measurement site was in the range of 20 s. They characterized the organized wind loads as quasi-static because they act on trees significantly longer than the fundamental sway period and cause non-oscillatory motion. There was no evidence that wind loading in the frequency range of the fundamental sway mode significantly contributed to the wind-induced tree motion pattern. They suggested that oscillatory tree sway in the fundamental mode results from the elastic energy stored in the aerial parts and roots and the damping that returns the trees to their rest position.

Because not all airflow components contribute to the excitation of wind-induced Scots pine tree motion, another study presented an approach for selecting the scales at which the Scots pine trees’ motion is coupled with wind loads [32]. It separates the effective turbulent scales from all scales that do not significantly contribute to the wind excitation of the trees. The components at the connected scales can be linearized and imitate the combined impact of effective turbulent and quasi-static wind loads. So far, the approach can only reproduce the dynamics of effective wind loading, and it is not yet helpful in approximating the absolute value of the effective wind load.

To apply the previously proposed approach, a parameterization via static pulling tests [33,34,35,36,37,38] has to be realized. Tree pulling tests are used for imitating quasi-static wind load components with a winch and cable system. The rationale behind static pulling tests is to approximate the mean force at a constant wind direction required to displace trees from their rest position or break or overturn the pulled trees [39]. We test the hypothesis that the effective wind load acting on trees can be estimated using static, non-destructive pulling tests.

This paper presents a novel approach to combine the temporal dynamics and the absolute values of effective wind loads on individual plantation-grown Scots pine trees. While the temporal dynamics were derived from tree motion measurements made with the Tree Motion Monitoring System TreeMMoSys [40], non-destructive pulling tests were applied to quantify the absolute values of the effective wind loads. The results show that this combination allows a tree-specific estimation of the dynamics and absolute values of effective wind loading on trees where the first sway mode dominates the wind-induced motion.

2. Material and Methods

2.1. Workflow

The main steps of data collection and analysis are summarized in Figure 1: (1) Collecting data from measurements of wind-induced stem tilt, airflow, and stem tilt and pulling force during non-destructive static pulling tests; (2) Splitting wind-induced stem displacement (D) time series into oscillatory (D_OC) and non-oscillatory (D_NOC) components using singular spectrum analysis; (3) Low-pass filtering of momentum flux data (M_NOC) to match the frequency range of D_NOC; (4) Applying regression analysis (significance level α = 0.05) for estimating the coefficients of D dependence on the force applied on the sample trees during non-destructive pulling tests; (5) Maximizing the local correlation between D_NOC and M_NOC using dynamic time warping; (6) Calculating of the effective force (F_eff) from dynamically time-warped D_NOC and M_NOC; (7) Determining of wind load coefficients (WLC) from F_eff and M_NOC values; (8) Calculating of the tree-specific, instantaneous effective wind load (WL_eff) using M_NOC and WLC values.

2.2. Research Site and Forest Characteristics

The study was carried out at the forest research site Hartheim operated by the University of Freiburg in Germany. The research site is located in the flat southern Upper Rhine Valley (47°56′04″ N, 7°36′02″ E, 201 m a.s.l.). During the measurement campaign, the Scots pine (Pinus sylvestris L.) forest at the research site had a mean density of 550 trees per hectare and a mean height of 18 m [41].

Detailed information on tree and stand characteristics at the site are available from terrestrial laser scans (TLS). The forest was scanned in March 2020 from 142 positions using a Rigel VZ-400i scanner (RIEGL Laser Measurement Systems GmbH, Horn, Austria). The device was placed at a tripod at 1.8 m height to scan the whole site in a 15 m × 15 m regular grid. An integrated RGB camera was recording pictures during the acquisition process. All scans were colorized using the RGB images, filtered for points with very low reflectance (brightness less than −15 dB), strongly deviated pulses (deviation more than 15), and scatter points (less than 5 points in 0.5 m radius) using the RiScan Software (Version 2.12.1, RIEGL Laser Measurement Systems GmbH, Horn, Austria). Afterward, the scans were combined into one-point clouds and duplicated points where merged within a search radius of 2 cm.

To validate whether crown area influences the wind-induced tree sway behavior, we extracted the crown points for each sample tree using a raster image created from the TLS point clouds. Located trees were manually segmented from the point clouds using the CloudCompare software version 2.12 [42]. To quantify the crown areas in x, y, and z directions, two-dimensional raster images at a 0.1 m × 0.1 m grid resolution were created.

2.3. Airflow Measurements

We analyzed airflow data that was measured (sampling frequency 10 Hz) on seven windy days from 26 December 2020 to 1 January 2021 using four (S1 to S4) ultrasonic anemometers (type 81000VRE, R.M. Young Company, Traverse City, MI, USA). The ultrasonic anemometers were mounted to slender scaffold towers and measured the wind vector components in east-west (u), north-south (v), and vertical (w) directions at the heights 2 m, 9 m, 18 m, and 21 m above ground (Figure 2). The above-canopy momentum flux (M) at 21 m, which was used to approximate the temporal wind load dynamics [32], was calculated as [43]:

$$M=\sqrt{{\left(u\prime w\prime \right)}^2+{\left(v\prime w\prime \right)}^2}$$

(1)

where $u\prime$, $v\prime$ and $w\prime$ are the turbulent parts of u, v, and w after applying the Reynolds decomposition.

2.4. Stem Tilt Measurements

Previous studies show that the Scots pine trees at the research site start swaying in first mode under low wind speed conditions [29,40]. First-order mode vibration results from their monopodial branching pattern and small crowns and dissipates even small amounts of kinetic energy transferred to them quickly.

To continuously measure (sampling frequency 10 Hz) stem tilt (T, in degrees) in x (t_x, east-west) and y (t_y, north-south) directions, four Tree Response Sensors (TRS) [40] were mounted to the north facing side of the stems of five sample trees (B1 to B5) at the stem base (z_TRS,1 = 0.1 m), 1/7 H (z_TRS,2), 3/7 H (z_TRS,4), and 5/7 H (z_TRS,5), H is the tree height, and z is the measuring height (

Table 1. Height (H, m), stem diameter at breast height (DBH, 1.3 m a.g.l., cm), and crown area (CA, m²) of the sample trees B1 to B35. z_a is the height of pulling rope anchor point (m), RA is the pulling rope angle (°), and z_TRS,1 to z_TRS,5 are the Tree Response Sensor (TRS) stem tilt measurement heights.

Sample Tree	H	DBH	CA	za	RA	zTRS,1	zTRS,2	zTRS,3	zTRS,4	zTRS,5
B1	18.5	25.1	26.0	11.2	18.5	0.1	2.7	5.0	8.2	13.7
B2	20.4	28.6	31.2	13.4	17.9	0.1	2.9	5.0	8.6	14.3
B3	16.7	23.2	18.0	9.7	16.6	0.1	2.6	5.0	7.8	12.9
B4	19.4	28.6	15.9	11.2	18.4	0.1	2.8	5.0	8.4	13.9
B5	18.5	27.7	27.0	11.9	22.7	0.1	2.7	5.0	8.1	13.5
B6	17.7	26.8	27.3	11.7	26.8	0.1	2.5	5.0
B7	19.6	30.6	40.4	10.6	19.2	0.1	2.8	5.0
B8	17.7	21.9	26.6	9.7	22.5	0.1	2.5	5.0
B9	17.5	22.3	27.0	9.6	27.9	0.1	2.5	5.0
B10	16.5	20.7	17.9	9.5	22.3	0.1	2.4	5.0
B11	18.5	21.4	24.0	9.8	19.6	0.1	2.6	5.0
B12	18.7	25.2	33.3	11.5	23.4	0.1	2.7	5.0
B13	19.6	28.1	31.4	11.6	27.8	0.1	2.8	5.0
B14	18.8	21.3	21.3	10.8	26.2	0.1	2.7	5.0
B15	19.8	27.2	24.5	11.5	27.5	0.1	2.8	5.0
B16	17.6	22.2	24.9	11.6	27.8	0.1	2.5	5.0
B17	17.4	20.7	23.5	10.7	25.9	0.1	2.5	5.0
B18	18.3	25.3	19.8	11.1	32.4	0.1	2.6	5.0
B19	16.5	19.3	18.1	10.7	29.7	0.1	2.4	5.0
B20	17.5	24.8	22.8	10.4	30.5	0.1	2.5	5.0
B21	18.2	30.5	34.5	10.5	27.5	0.1	2.6	5.0
B22	20.6	34.8	53.8	12.8	32.6	0.1	2.9	5.0
B23	18.1	35.5	47.6	12.3	39.2	0.1	2.6	5.0
B24	16.8	20.6	14.0	10.7	25.5	0.1	2.4	5.0
B25	16.7	21.3	19.4	11.6	21.1	0.1	2.4	5.0
B26	15.5	17.0	11.1	11.8	30.5	0.1	2.2	5.0
B27	18.5	35.4	40.8	11.9	29.9	0.1	2.6	5.0
B28	16.8	20.5	14.3	10.7	39.9	0.1	2.4	5.0
B29	20.1	31.2	32.1	10.8	29.0	0.1	2.9	5.0
B30	16.0	19.4	13.1	11.2	39.9	0.1	2.3	5.0
B31	17.3	18.9	14.7	11.5	35.0	0.1	2.5	5.0
B32	16.6	18.2	13.1	10.0	25.8	0.1	2.4	5.0
B33	18.6	28.1	28.5	11.0	28.8	0.1	2.7	5.0
B34	18.6	28.7	37.6	12.2	29.7	0.1	2.7	5.0
B35	19.3	30.9	40.2	12.0	36.2	0.1	2.8	5.0

).

Based on the results from a previous study [29], it was assumed that z_TRS,2, z_TRS,4, and z_TRS,5, represent the antinodal points of stem vibration. The time series of stem tilt components t_x and t_y were used to calculate the stem displacement vector (D):

$$D=z·\sin \left(\sqrt{t_x^2+t_y^2}\right)$$

(2)

To increase the number of continuously monitored trees for this study, the wind-induced motion of 15 other Scots pine trees (B6 to B20) was measured using a simpler set up with one TRS mounted at z_TRS,2. Earlier studies show that information on the Scots pine trees’ stem response measured at one point is sufficient for the following analysis [29,32]. All stem tilt data were collected wirelessly and stored on a ground receiver using the Tree Motion Monitoring System (TreeMMoSys) [40].

Continuously monitored B1 to B20 were subjected to static, non-destructive pulling tests described below. Another set of 15 trees (B21 to B35) was non-destructively pulled to enlarge the sample size and statistical certainty of the pulling test results. We selected the sample trees according to their accessibility, DBH, and based on their neighbors’ positions to enable undisturbed, non-destructive pulling tests without crown collisions.

2.5. Non-Destructive Tree Pulling

After completing the measurement campaign, B1 to B35 were subjected to static, non-destructive pulling tests to calibrate TRS measurements (Figure 3). A 3-fold pulley (CT-Climbing Technology, Torchio, Italia) combined with the PiCUS TreeQinetic system (Argus electronic, Rostock, Germany) was used for the pulling tests. The pulling rope (Dyneema, Dynamica Ropes ApS, Fredericia, Denmark) was attached to the sample trees’ stems below the crown base, corresponding to z_a = 0.6 H. This height was assumed to be a compromise between avoiding the effects of knots on the overall strength of the stems and being close enough to the crowns where the wind loading occurs [39].

The TreeQinetic forcemeter measured the applied force (F_a) along the rope into the pulling direction. Three TreeQinetic elastometers were mounted to the leeward side of the stems at 1 m (z_PTQ,2), 2 m (z_PTQ,3), and 3 m (z_PTQ,4) to measure strain in the marginal wood fibers. TRS (z_TRS,1, z_TRS,3) and TreeQinetic inclinometers were mounted to the stem base (0.1 m) and at 5 m height (z_PTQ,1, z_PTQ,5) to record t_x and t_y while B1 to B35 were pulled [44]. The pulling force was increased until a root plate inclination of 0.25° or 100 µm of strain in the marginal fibers were reached to prevent primary tree failure [45].

2.6. Processing and Analysis of Stem Displacement Data

To assess the coupling between wind loading and the wind-induced response of B1 to B20, a method proposed in a previous study was used [32]. The application of the method includes attenuating all variations of M shorter than 5 s by a fourth-order Butterworth low-pass filter yielding M_NOC and decomposing D into D_OC and D_NOC through the application of singular spectrum analysis (SSA) [46,47]. The D decomposition separates motion components responding to wind loading from components that dissipate elastic energy stored in the stem and roots, such as oscillatory sway in the fundamental mode [31].

Since the local correlation between instantaneous wind loading and tree response in the time domain is generally low [6,48,49], M_NOC and D_NOC were dynamically time-warped to synchronize their time series and maximize their correlation [50,51] as described in a previous study [32]. All further analyses were carried out with dynamically time-warped M_NOC and D_NOC. The oscillatory signal components were no longer considered.

2.7. Calculation of Effective Wind Load

Functional relationships between D and the wind load impact were approximated by the horizontal component of the pulling force (FP) at z_a using a modified approach proposed in a previous study [52]:

$$FP=F_a\times cos\left(RA\right)$$

(3)

with RA being the pulling rope angle between z_a and the rope anchorage point at the ground.

To attenuate small, short-term, and insignificant fluctuations in the time series of D and FP during the pulling tests, D and FP were low-pass filtered using SSA. Since the crucial step in the SSA application is the choice of the embedding dimension, which indicates the maximum lag up to which the D and FP time series were shifted against themselves, embedding dimensions were tested from 10 to 150 measurement values. The embedding dimensions that yielded the highest correlation coefficient values (r > 0.9) between FP and D at z_TRS,1 and z_TRS,2 were 80 and 40 for D at z_TRS,3 and z_TRS,5, respectively. On average, the first SSA component, which represents the low-pass filtered signal component of D (D_LP) and FP (FP_LP), explained 97% of the variance in the FP signals and 83% (z_TRS,1) to 96% (z_TRS,4) in the D signals.

The high values for the explained variance indicate that the SSA efficiently separated the signal components that are important for the analysis from the unimportant signal components. The remaining residual variance can be attributed to higher frequency signal components that have no influence on the pulling test results.

It was assumed that during the pulling tests, quasi-static D_NOC is represented by D_LP because from previous studies, it is known that at the research site, the Scots pine trees’ total wind-induced reactions are dominated by sway in the fundamental mode. Vibrations in higher modes are negligible [29,30,32].

Linear regression forced through zero was used to parameterize the functional relationships between D_LP and FP_LP:

$$s=\frac{F{P}_{\mathrm{LP}}}{D_{\mathrm{LP}}}$$

(4)

The variable s is the slope resulting from the pulling tests representing the change in force applied to z_a per meter of stem displacement, and has the same units as the spring constant (N/m). It is a measure of flexural tree stiffness.

The functional dependence of s on above-ground tree characteristics such as diameter at breast height (DBH, 1.3 m a.g.l.) and H and variables combined from them, was established with a power law. The power law provided better fits to the data than other simple regression models, especially at height z_TRS,1:

$$s=a_1\times c^{a_2}+a_3$$

(5)

here c is any above-ground tree characteristic, a₁, a₂, and a₃ are coefficients. The strength of the functional relationships was assessed with the coefficient of determination (r²).

Using D_LP and s, the effective pulling force applied at z_a (F_ZV) was calculated:

$$F_{ZV}=s\times D_{\mathrm{LP}}$$

(6)

To approximate the applied force at z_a under natural wind conditions, s and D_NOC were used to calculate the effective force (F_eff).

$$F_{\mathrm{eff}}=s\times D_{\mathrm{NOC}}$$

(7)

The effective force is assumed to be the base level of wind loading associated with the airflow components effectively involved in the excitation of the Scots pine tree motion.

To establish a relationship between M_NOC and F_eff, the wind load parameter (WLP) was calculated for 10 min intervals using a linear regression forced through zero:

$$WLP=\frac{F_{\mathrm{eff}}}{M_{\mathrm{NOC}}}$$

(8)

After the calculation of 10 min WLP values describing the effective tree-specific response to M_NOC, the wind load coefficient (WLC) was determined as the offset of the second phase (i.e., using all values greater than detected change points) of a two-phase regression of WLP on 10 min mean values of M_NOC (M_NOC,mean). WLC enables the calculation of the instantaneous, effective wind load (WL_eff):

$$W{L}_{\mathrm{eff}}=M_{\mathrm{NOC}}\times WLC$$

(9)

2.8. Change Point Analysis

An earlier study showed that the Scot pine tree response to the airflow systematically changes with increasing wind load [32]. This change in the response behavior can be associated with tree-specific M_NOC thresholds. We used a two-phase linear regression model for detecting these thresholds [53].

3. Results and Discussion

3.1. Non-Destructive Tree Pulling

With increasing D_LP, FP_LP calculated at height z_TRS,2 = 1/7 H increased during static pulling tests. The FP_LP maxima always occurred when 100 µm of strain was reached and the force application was aborted. After reaching the FP_LP maximum, F_a was steadily reduced, and the trees returned to their rest position. For B1 to B5, which were equipped with multiple sensors, s was calculated at heights z_TRS,1 to z_TRS,5 (Figure 4a). The vertical s profiles along the stem available are of similar shape, the highest values occurring at z_TRS,1, where stem diameters were always the biggest, resulting in the greatest flexural stiffness. From z_TRS,1 to z_TRS,2, the s values decrease by several orders of magnitude, which requires the results to be presented on a logarithmic scale. Due to the very small D_LP values, s needs to be considerably larger to reach the same FP_LP as at height z_a.

For B1 to B35, s is available at heights z_TRS,1 to z_TRS,3. Generally, s values are orders of magnitude higher at the stem base than at the other measuring heights due to very small D_LP, ranging from 962 (B31) to 23606 (B23) kN/m at z_TRS,1 and 0.9 (B26) to 13.6 (B22) kN/m at z_TRS,3 (Figure 4b).

Regression analysis (α = 0.05) was performed to evaluate whether there is a functional relationship between s and the above-ground tree characteristics DBH [17,35,54], DBH³ [55], H [17,35,54], H/DBH [35], DBH/H² [56,57], DBH²/H [58], and DBH²H [17,58,59,60,61] that have been reported in previous studies to influence tree response on static pulling and wind loading. Crown and stem mass, which also influence tree response to external loading [56,57,58], were not included in this analysis since they were unavailable.

Figure 5 shows power law curves resulting from regressing s to tree characteristics (p < 0.001). The strongest relationships, as measured by r², were established between s and DBH, mean r² = 0.86 from z_TRS,1 to z_TRS,3. With increasing DBH, s also increases. The increase is more linear at z_TRS,2 = 1/7 H and z_TRS,3 = 5 m than at the stem base. We argue that the stronger nonlinear dependence at the stem base is due to the cable attachment height z_a = 0.6 H which is higher than in other studies [35,58]. The greater cable attachment height causes stronger bending of the upper stem parts [39], which mimics the stem bending of the sample trees under natural wind conditions better than the bending with cable attachment heights below 0.5 H. Regressing s against DBH³ as conducted in a previous study [58], did not raise the explained variance of DBH in s.

The functional dependencies of s on H/DBH² (mean r² = 0.83) and DBH²H (mean r² = 0.85) are only slightly weaker. As H/DBH² increases, s decreases. The decrease in s is most pronounced at z_TRS,1, but curvilinear at all displayed heights. With increasing DBH²H, which is used to represent stem volume, s increases. The strength of the presented functional relationships is in the range of previous studies [54,58]. Other tree characteristics such as H, H/DBH, DBH²/H, DBH/H², and TLS-measured CA available in different directions were tested, but their functional relationships were weaker (r² ≤ 0.75) at all studied heights.

3.2. Tree Response under Natural Wind Conditions

Figure 6 shows 10 min mean values of D_NOC (D_NOC,mean) of B1 to B5 along the stem at the heights z_TRS,5 to z_TRS,1 plotted against M_NOC,mean values. The D_NOC,mean values decrease by several orders of magnitude towards the stem base. At the same measurement heights, D_NOC,mean is mostly similar for B1 to B5. The greatest inter-tree differences occur at the stem base.

If 10 min mean values of F_eff (F_eff,mean) are plotted against M_NOC,mean, then large differences between the sample trees become apparent, although the tree-specific D_NOC,mean patterns are similar. This demonstrates that B1 to B5 were subjected to different wind loads, the wind load acting on B5 being the greatest at z_TRS,4 and z_TRS,5. The wind load acting on B3 is always the smallest. The inter-tree differences in F_eff,mean decrease from the crown space towards the stem base. There is a considerable spread of the data at the stem base resulting from the small D_NOC,mean values used in the F_eff,mean calculation.

In the near-origin area, where small D_NOC,mean values dominate, there are change points in the relationship of F_eff,mean and M_NOC,mean. Below the change points, D_NOC,mean was always close to zero, indicating minimal wind-induced stem displacement resulting from weak wind loading. Except for the nearest area around the coordinate origin, the dependence of F_eff,mean on M_NOC,mean is linear, as is demonstrated in detail for B2 (thickest tree with DBH = 28.6 cm) and B19 (thinnest tree with DBH = 19.3 cm) in Figure 7.

The points associated with the changes in the tree-specific response as expressed by F_eff,mean acting on B2 and B19 are at 0.20 (Figure 7a) and 0.60 m²/s² (Figure 7b). After passing these points, the dependence of the tree response on M_NOC,mean increases linearly.

The WLP values shown for B2 (Figure 7c) and B19 (Figure 7d) as a function of M_NOC,mean also show a two-phase pattern with a change point. After passing these points, the WLP distributions level off and are parallel to the x-axis. The small insets highlight the WLP development as a function of M_NOC,mean after the passage of the change points in a linearly scaled coordinate system.

The linear WLP dependence on M_NOC,mean after crossing the change points, allows the estimation of the wind-induced tree response as a function of M_NOC,mean. The WLP vs. M_NOC,mean change point values are very similar (r² = 0.89) to the F_eff,mean vs. M_NOC,mean change point value distribution, as is illustrated by boxplots for B1 to B20 in the inset in Figure 7b. The WLP-related change points range from M_NOC,mean = 0.18 m²/s² (B5) to M_NOC,mean = 0.67 m²/s² (B13), with the median WLP-related change point value being 0.32 m²/s². The medians of the F_eff- and WLP-related change points show no significant difference at the 95% confidence level as indicated by the boxplot notches.

Once the tree-specific WLC values have been identified, they can be used for calculating the instantaneous, tree-specific effective wind load (WL_eff) knowing M_NOC.

Figure 8a shows a short time series of 3000 WL_eff and F_eff 10 Hz values (300 s) as an example. The time series length is limited to highlight their similar behavior from small to some of the largest values that occurred during the study period. Calculated WL_eff is strongly correlated with measured F_eff (r² = 0.99). Over the entire study period, r² calculated from 2,263,673 WL_eff and F_eff values each per tree ranges between 0.45 (B6) and 0.94 (B5). The r² median is 0.89 (B11).

The relationship of the 3000 WL_eff and F_eff values is shown for B4 as red points in Figure 8b. The red points are plotted together with a binned (40 × 40 bins) scatter plot including the 2,263,673 WL_eff and F_eff values, exceeding the tree-specific M_NOC thresholds. The data from the interval shown in Figure 8a are in the range of the histogram bins that represent the total wind-induced response of B4 in the study period. The majority of all analyzed WL_eff and F_eff values (84%) are in the range smaller than WL_eff < 0.1 kN indicating the dominance of episodes with low wind loading.

The response of B1 to B20 to WL_eff in the study period is shown as bivariate histograms in Figure 9. The histogram bins of all trees group around the 1:1 line indicating a good approximation of F_eff. This figure shows the differences in tree-specific WL_eff. Lowest WL_eff acted on B10 and B19, the smallest of the presented trees. The largest effective wind load acted on B2, which is the tallest tree. Common to all trees is that high WL_eff values are rare. The highest share of WL_eff values of 90.4% can always be found close to the origin of the coordinate system for WL_eff < 0.1 kN. Due to measurement device failure, there are no data for B7 and B15.

4. Conclusions

This study demonstrates that for the investigated Scots pine trees, whose wind-induced sway behavior is dominated by first-order mode vibration, the effective wind load acting on them can be quantified using non-destructive pulling tests. It is assumed that the pulling test execution resembles the quasi-static stem displacement through the combination of organized turbulence and mean wind loading. Under dominant first-order mode vibration, wind loads acting on the Scots pines’ crown periphery are transferred through the needles and branches to the stem without much damping.

Based on the presented results, we propose that for trees whose stem sway behavior is dominated by first-order mode vibration, the method helps to bridge the gap between pure stem motion analysis and the assessment of acting wind loads at the individual tree level. Due to the strong correlation between the easily measurable tree characteristics DBH and DBH²H, the effective wind load can be estimated tree-specifically and used to determine the instantaneous effective wind load via the wind load coefficient WLC. The use of WLC will simplify future investigations into the Scots pine trees’ wind-induced motion behavior.

So far, the described approach cannot be applied to trees whose stem sway behavior is not dominated by first-order mode vibration. For example, in trees with large crowns, a substantial part of the kinetic energy transferred to them from the airflow is already dissipated by the foliage and branch motion. Foliage and branch motion then cause higher-order mode vibration in the stem, which static pulling tests cannot simulate. This relationship affects the execution and interpretation of results obtained from static pulling tests related to wind load estimation. Motion and bending moments measured at the stem, especially at the stem base, might not always be a good indicator for wind loading.

More investigations into the combination of pulling tests and effective wind loads could reinforce the importance of pulling tests for tree-specific wind load estimation. It can also provide an approach for reanalyzing the results of thousands of pulling tests conducted in Germany and elsewhere over the past decades. To further improve the understanding of loads acting on trees during pulling tests and under natural wind conditions, we propose to monitor root motion in addition to above-ground tree motion in future studies.