4.1. Impacting Factors of Tree’s Sway and Tilt Analysis
The ambient environment poses a great influence on trees. When exposed to natural hazards, aerial parts of trees may bend and break. Trees become less stable when exposed to strong wind events such as windstorms, hurricanes, and tropical cyclones frequently. External forces such as rockfall, debris flow, and avalanches [
35] could also affect the stability of trees. The capacity of a tree to withstand under wind loading varies with physical status, inherent tree features, and different botanical groups, in addition to the external forces on trees.
Thus, an in-depth investigation of tree responses to wind can help better understand wind-induced damage to trees, and prevent the occurrence of potential root hazards. To investigate tree responses under wind loading, considerations on tree attributes and physical attributes are first introduced, followed by the summary of internal and external factors of tree movement.
4.1.1. The Specialty of Inherent Tree Features—Internal Factors
Young’s modulus of elasticity (E) [
72] is a numerical constant named after the British physicist Thomas Young. It describes the resistance of a solid structure in only one direction when under lengthwise tension or compression. Young’s modulus can be described mathematically using the following equation:
where
stress is the force that could cause deformation and
strain is the ratio of the change.
Wood has independent mechanical properties in three perpendicular axes—longitudinal (
L), radial (
R), and tangential (
T) [
73]. Accordingly, the three moduli of elasticity are denoted by
,
and
, respectively. The modulus of elasticity, which is determined from bending, is usually species-specific [
31], and used to measure the bending moment and the natural frequency of trees. For an open-grown sugar maple (
Acer saccharum), the elasticity of trees was considered with three other parameters (i.e., tree slenderness, DBH, and the damping ratio) as major factors that could affect tree sway [
48]. For eight different deciduous broadleaf tree species [
31], tree elasticity is speculated to be negatively correlated with fundamental vibrational frequency (FVF) significantly, but not the leaf-off-above-freezing condition.
Some of the previous studies [
28,
51,
60] focused on the measurement of the natural swaying frequency of some tree species, e.g., Lime tree, Sitka spruce, and Scots pine. The periodic motion of trees can be described by amplitude, frequency, and time. Frequency (
f) is the reciprocal of period (
t), the amplitude is defined as the maximum displacement. At nature swaying frequency, trees oscillate under free vibration with occasionally very high amplitude. The swaying of trees increases with heightening wind speed and can be used as an important indicator of tree stability under windy conditions.
An early study measured the natural swaying frequency of Red pine (
Pinus resinosa) and White pine (
Pinus strobus) trees by using a stopwatch [
74]. The bole and mass of the crown of diameter/height (D/H) ratios were considered as two main factors leading to the sway period of trees. In Baker’s study, natural swaying frequencies of the lime trees were measured using a laser Doppler interferometer [
28]. Baker found that tree geometry and seasonality could produce notable changes in natural swaying frequency with the findings, which had recorded higher magnitude in winter and lower in summer from the measurement at Nottingham University, UK. The major cause leading to the significant difference in natural tree frequency could be attributed to the fully in-leaf condition of trees in summer with dry ground, and leafless condition in winter with the rather moist ground. According to one review study [
36], the natural swaying frequency of conifer trees can be reliably estimated from tree height (H) and diameter at breast height (DBH).
Compared to studies on conifer trees, the study of the natural frequency of broadleaf trees is limited. Free vibrations of Bradford pear and Chestnut oak were measured [
32] using pull-and-release tests in Massachusetts and Virginia, USA. For both species, they found that the pulling direction would not affect the natural swaying frequency, yet the sway frequency could increase through the pruning exercises and reduce the likelihood of tree failure. The findings of this dynamic property can help to refine models to predict tree failure with the continuous measurements of tree tilt.
Frequency is a significant index of tree stability regarding the natural vibrational nature of trees. By measuring the resonant frequency of 10 Sitka spruces [
60] in the static pulling test, the maximum frequency is 0.37 Hz, and the minimum frequency is 0.26 Hz for each whole tree. For the stem of Sitka spruce, the maximum frequency is 0.70 Hz and the minimum frequency is 0.43 Hz. For broadleaf trees, the fundamental frequency of one Flame of the Forest [
57] was measured, showing a range from 0.47 Hz to 0.59 Hz. According to one study [
28], the natural frequency of lime trees was recorded higher in winter (0.62 Hz) and lower in summer (0.25 Hz). Nevertheless, the accuracy of the natural frequency measurement depending upon the sensing method and sensor configuration.
The damping ratio describes the decay of oscillation after a disturbance, e.g., gusty winds, water waves, or earthquakes [
50]. Damping is of great importance for trees to withstand heavy wind loading over time. During the windstorm, only the mechanism of passive damping can reduce the effect of the wind on the trunk and roots [
50]. Generally, the damping ratio of trees can be divided into two types, i.e., internal and external [
75]. Internal damping is caused by the internal friction of tree stems [
76]. External damping is mainly due to the aerodynamic drag on the foliage and contact between the crowns of adjacent trees [
36].
For open-grown deciduous trees, the natural frequency and the damping ratio of trees have been considered as two important parameters that may lead to tree failure [
32]. For conifer trees, experimental results of 24 Norway spruces show that velocity proportional damping (viscous damping) could be used to model tree–wind interactions [
43].
Diameter at breast height (DBH) is a standard measurement of expressing the diameter of the trunk of a standing tree. Despite different definitions of DBH in previous studies, the convention now is the diameter at 1.3 m above the ground level [
77]. DBH is always considered as a direct parameter to represent tree sway and has been used in most tree–wind studies [
31,
65,
78].
As a function of tree height (H) and DBH, DBH × H
−2 [
31,
36] is often used to calculate tree slenderness. At the same time, DBH × H
−1 is another definition of slenderness and that was used in some studies. Tree slenderness is a coefficient of trees [
79], which is a significant indicator of sway frequency measurement. DBH × H
−2 is expected to be positively correlated with frequency [
32] and is considered correlating with three other measures (tree slenderness, the elasticity of trees, the presence of foliage, and temperature) [
31,
78]. This expression is an important parameter to measure the tree sway frequency of all sites and species.
4.1.2. Impact of External Forces on Trees
The tree–wind interaction is dynamic and determined by the degree of wind loading and the natural frequency of trees. As a natural force, wind can affect the physical condition of trees, leading to the distortion of the tree root anchorage, the tilt of tree stems, or even falling. There are many approaches to calculate the wind load imposed on a tree, among which the most significant parameter is wind speed. To measure wind speed, the anemometer is the major instrument. In several studies [
51,
57], wind speed is a significant factor in tree tilt because the swaying of trees increases with the wind speed. The wind speed over a tree canopy can be defined using the following equation [
80]:
where z is the height above the surface,
is friction velocity,
is von Karman’s constant (around 0.4),
is the zero-plane displacement, and
is the aerodynamic roughness.
By exploring the relationship between wind speed and stem displacement of four Scots pines in the southern Upper Rhine Valley, time-series decomposition was used. The results showed that wind-induced excitation caused minor effects on the overall tree movement on the sample trees [
78]. Yet, according to one study on the Flame tree [
57], the wind speed in terms of four corresponding measurements, which are the mean wind magnitude (WM
MEAN), maximum wind magnitude (WM
MAX), mean wind amplitude (WA
MEAN) and maximum wind amplitude (WA
MAX) tested on a single broadleaf Flame tree in Hong Kong, the results showed that mean sway amplitude (SA
MEAN) was the preferred parameter that can reflect the association of branch sway and wind speed.
Although there are manifold effects of wind on trees, some common features can be utilized to estimate tree responses under wind loading, e.g., wind speed, wind direction, and decomposed wind vectors.
The mass of the root–soil plate and the shear strength of the soil are considered by Jonsson et al. [
35], which indicates two soil-related components that may contribute to the rotational moment of trees. A root anchorage model for Sitka spruce was developed, regarding the tree and soil as a simple mechanical system [
44]. The soil resistance [
81] and the weight of the root–soil plate were considered contributing to the overturning forces of trees [
35,
82], while conversely the root–soil system of 66 mature Norway spruce trees was studied to investigate the turning moment (
M) at three different locations in Switzerland, where the function of tree size and weight are more significant rather than that of the soil resistance [
42].
Overall, the mechanism of tree tilt associated with tree displacement and tree decay are sophisticated systems and are affected by a combination of internal and external factors in which only one single parameter alone cannot explain the mechanism of tree tilt thoroughly. The combination of multiple indicators and measures could be more convincing to examine the tree status under windy conditions, measure the rotational angles of tree root tilt, and predict the stability of trees in high wind events.
4.2. Four Major Measures for Tree Tilt and Sway Analysis
The rotational angle of the root is a direct measure of the tree tilt. Considering the in-situ studies, the angular sway data is usually obtained from the inclinometer. Although numerous studies have focused on tree sway behavior analysis [
19,
49,
83], the exact vertical deflection of tree roots has not been clarified. The main concern, however, is that angular sway data of trees cannot efficiently reflect the tree architecture and help understand tree sway behavior. Therefore, different measurements have been used to analyze the vertical displacement of trees. Here, four commonly used measurements (
Table 1) are summarized as (1) the angular sway data, (2) the vertical displacement, (3) the sway frequency of trees, and 4) the critical wind speed that would trigger a tree to sway, tilt, and even collapse.
The vertical displacement of a mixed stand (including coniferous trees and broadleaf trees) was calculated from angular tree sway data using the following equation [
49]:
where the vertical deflection of the tree (
V) measured from the center of the mass is a function of the center of mass measured from the top of the tree (
), the height of the tree
, and the stiffness coefficient (
. The vertical displacement was then converted to sway frequency data using the Fourier Transform, where the low-frequency peaks were characterized as the natural frequency of tree stems.
The tilt angle of
Eucalyptus tree root zones was measured using a tri-axial accelerometer for the static pulling test. The results [
61] demonstrated that the maximum structural root zone was tilted and the records during the static pulling tests were 0.6° among 10
Eucalyptus specimens, and 0.88° under wind loading conditions among 18
Eucalyptus trees (
Eucalyptus spp.). The numerical values of tree tilt from this study significantly represented a reference to the sway behavior analysis of
Eucalyptus and some broadleaf trees with similar kinds of features as
Eucalyptus.
Figure 4 shows the angular sway data measured from a fully leafed Norway maple tree branch. The values of vertical branch displacement (
Φ) increase against the installation height of biaxial inclinometers that was elevated from 0.5 m to 1.8 m. For the vertical displacement measured with a 0.5 m distance from the stem, the vibration range is within 5 degrees. The preliminary results of this sampled broadleaf tree denoted the swaying pattern of tree aerial parts is complicated and anisotropic, and the response characteristics of tree branches could be determined by the direction of the wind.
The critical wind speed (CWS) of 397 trees in a broadleaf forest in the UK was estimated based on a linear function of tree height, DBH, species, and tree architecture [
46]. The tree architecture, although complicated and species-specific, is measured by the cylinder models. Results obtained from this study showed that tree size and architecture are the main drivers to speculate CWS, and trees are at higher risk in summer if exposed to the same wind speed, despite the field data predicted lower CWS in summer than in winter, denoting that the presence of tree foliage is significantly affecting the imminent risk so the physical attributes are important for estimating CWS.
4.3. A Closer Look at Broadleaf Trees
One characteristic of the deciduous broadleaf trees differentiated from conifer trees is that some specimens usually shed leaves in autumn and turn into the status of leafless in winter. For deciduous broadleaf trees, the presence of foliage and the temperature are two major factors [
31] that may influence the sway frequency of tree trunk. A comparison between summer and winter denoted that Lime trees with the presence of foliage tend to have lower magnitudes of sway frequency in summer than that in winter [
28].
When it comes to the change of tree branches, pruning may increase the natural frequency of conifer trees [
83]. On the contrary to conifer trees, pruning broadleaf trees [
32] can reduce the likelihood of wind-induced tree failure, as measured from the free vibrations of two open-grown broadleaf trees, i.e., Bradford pear and Chestnut oak.
Empirical research has demonstrated that the natural frequency (
f) of conifer trees is highly correlated to DBH × H
−2 [
43,
83]. Similar to the results obtained from conifer trees, the DBH × H
−2, often defined as slenderness, is regarded as the dominant factor that may affect the sway frequency of tree trunk of several broadleaf species (e.g., Birch, Hickory, and Maple) [
31]. Baker stated that a lime tree, also a broadleaf tree, tends to have a lower natural frequency with a higher DBH [
28].
Overall, to investigate the tilt behavior of broadleaf trees under wind loads, parameters derived from conifer trees studies, e.g., DBH × H−2, are pertinent for analysis. Meanwhile, seasonality is considered an important factor, as the fully leafed and leafless condition could have a huge impact on the stability of broadleaf trees.
4.4. A Large-Scale Integrated Tree Monitoring System in Hong Kong
The overview of tree motion sensors and tree–wind interactions shows that the tree responses under wind loads have been widely investigated. In this point of view, the main challenges of current studies are three-fold. First, many previous and ongoing studies focused on boreal forests, in which coniferous trees are the main research targets. The number of studies carried out in urban and peri-urban areas along with existence of a mix of broadleaf and conifer in the tropical forest is relatively limited and short of available means. Second, a tree monitoring system that can examine, modulate the stability of trees, and estimate potential root hazards have not been provided so far in related studies. Third, tree management over a wide variety of trees planted in the urban area of Hong Kong lacks near-instant monitoring cases in which the tree failure could pose hazards with immediate adverse effects in case of strong wind events. Thus, a large-scale tree monitoring system in Hong Kong is presented to examine the instant status of the tree’s root motion and halt the associated hazards that might appear.
Hong Kong is situated in the sub-tropical zone, with a minimum temperature usually above 10 degrees Celsius in the urban area. The climate has cultivated a wide spectrum of tree species that are mostly discovered in a sub-tropical forest and some belong to temperate forest, yet in general, the broadleaf trees, whatsoever the evergreen and deciduous are deemed as more adaptable to grow in Hong Kong.
To study the wind-induced damages to broadleaf trees in Hong Kong, quantitative measures in other broadleaf trees studies can be regarded as reference stated in
Section 5. Meanwhile, many tree research studies on the resistance and resilience during storms such as hurricanes [
55,
56], tropical cyclones [
57], and windstorms [
24,
54] are of great importance to better understand the dynamics of tree–wind interactions.
Typhoon Mangkhut was an extremely powerful tropical cyclone affecting devastatingly to Hong Kong in 2018. On 16 September 2018, the Hong Kong Observatory issued Typhoon Signal No. 10, which is the highest level of tropical warning signals under the schematic framework of typhoon signal set out in Hong Kong. During the 10-h strong wind, we have simulated the wind speed (
Figure 5) and wind direction (
Figure 6) for the whole Hong Kong city using the Airflow Analyst. It is a 3D computed fluid dynamics (CFD) extension software [
84] running under ArcGIS. Through the direct and convenient use of GIS data, Airflow Analyst can create simulations and visualize the wind flow on the platform.
This system is the first-ever to build up a massive scale monitoring system to oversee 8,000 trees using geographic information systems (GIS) in Hong Kong, through the data collected from the communicating sensors with the platform and database instantly. Two pilot sites with high traffic and pedestrian density were selected—Kowloon East and Wan Chai—and another 10 districts are identified for test-bed sites. A variety of tree species are investigated, including Chinese hackberry (Celtis sinensis), Ironwood (Casuarina equisetifolia), Hong Kong orchid tree (Bauhinia spp.), Kassod tree (Senna siamea), Lemon-scented gum (Eucalyptus citriodora), Candlenut (Aleurites moluccana), Sea hibiscus (Hibiscus tiliaceus), Flame tree (Delonix regia), and Indian coral tree (Erythrina variegate), and many of other broadleaf species in Hong Kong. Measuring the displacement angles of these tree species can provide valuable information about tree responses under wind loads, thereby monitoring the anomalies of the physical status of these trees simultaneously on a massive scale.
In line with the monitoring system, the smart sensing technology (SST) sensor is developed to measure the tree tilt in urban areas of Hong Kong with an in-built systematic notification mechanism to send the alert to the registered correspondences once the tree tilt angle over the threshold values. The SST sensor integrates high precision accelerometers, geomagnetic sensors, and high-performance microprocessors. The SST sensor supports low-power operation mode, and the operation lifetime can be up to three years, subject to the mode frequency to be adjusted in the practical operation.
To transmit and record data, a low-power wide-area network (LPWAN) technology is used in this integrated monitoring system. LPWAN [
85] is designed to allow long-range communications at a lower bit rate. Comparing to the local area network (e.g., Bluetooth and Wi-Fi technology) and cellular network (see
Table 2), LPWAN is more efficient in low power consumption and low cost positioning. Therefore, it can be used to transmit data via sensors that operate on a long-lasting battery.
The time-space-based data collected from the SST sensors are converted to the time-frequency domain, and based on the threshold values of the tilt angle of root–plate that is determined by a collaborative consideration of several inherent tree features (e.g., DBH, wood elasticity, the damping ratio) and external forces acting on trees (e.g., wind speed and wind direction). Once the exceedance of the threshold values was recorded, the monitoring system will trigger a notification message from the SST sensor (
Figure 7), while the relevant information will be shown on a GIS-based platform for big data management.
As a significant part of the tree monitoring system, a dashboard with an easy-to-use user interface is developed for an application, displaying information such as temperature and wind, the location of individual trees, the number of activated and total sensors, influential factors under tree tilt and swaying conditions. With the fully equipped and informative dashboard (
Figure 8), the status of the respective tree tilt and the operation status of sensors can be viewed instantly. The sampling interval of each data is subject to change based on the weather and this will affect an up-to-date status being shown on the dashboard where the longest gap of duration of data taken is 12 h.
Big data create a paradigm shift to data-driven research [
86] and have enabled multiple functionalities of the GIS. A GIS platform is designed to store, compute, manipulate, analyze, manage and present geographic data. As a valuable tool, the GIS-based platform can manage different types of spatial data and display data in the way of thematic maps. Conventional GIS platforms were limited to low spatial data storage, spatial analysis, and spatiotemporal visualization performance [
87]. With the utilization of big data analytic techniques, large-scale data storage is optimized. Meanwhile, an integrated GIS-platform is provided for smart devices to process and analyze spatial-temporal data in real-time and display the results in all types of thematic maps.