Field measurement of wind characteristics and induced tree response during strong storms

Haixin Jiang·Hongfu Zhang·Dabo Xin·Yagebai Zhao·Junliang Cao·Baichao Wu·Yikun Su

Abstract Typhoons have caused considerable damage to individual tree and forest ecosystems.To reduce windinduced tree damage and better predict the risk of damage，improving our understanding of wind-tree interactions during strong wind conditions is important.To this purpose，wind characteristics and movements of an individual Betula platyphylla Suk.in a forest stand were monitored during three typhoons (Bavi，Maysak and Haishen).Results revealed that the average wind twists with increasing height，with a large twist gradient within the canopy and a small twist gradient outside the canopy.The maximum wind twist angle was approximately 110°.The disturbance of trees increases the turbulence intensity of the wind field in the canopy.The maximum power of the wind spectra and the turbulence anisotropy of the three turbulence components decrease with increasing height.B.platyphylla did not resonate with the wind in any of the typhoons but responded strongly to gusts near its free vibration peak frequencies.The peak frequency of the mechanical transfer function of B.platyphylla is essentially the same as the peak frequency of the response power spectra.The mechanical transfer function of the wind-induced response of the tree is almost the same as the transfer function of the damped harmonic oscillator which has similar characteristics to coniferous trees.

Keywords Betula platyphylla ·Spectral analysis·Tree motion·Typhoon·Wind-tree interaction

Introduction

Wind is a major factor that causes damage to individual trees and forest ecosystems (Everham and Brokaw 1996;Sellier et al.2006).When typhoons with enormously strong wind energy strike，they cause significant damage，not only affecting the stability of forest ecosystems (Mitchell 2012) but also leading to severe losses in the economic value of forest production (Schelhaas et al.2003;Gardiner et al.2010;Fischer et al.2013;Hanewinkel et al.2013).The key to reducing wind-induced tree damage and better predicting the risk of damage is to improve our understanding of wind-tree interactions during strong wind conditions.In particular，the dynamic loading effects of wind have been found to be of considerable importance to tree damage.

In previous studies，there has been given particular emphasis on the importance of the dynamic effects of wind when determining stem movement and stress in conifers(Schindler et al.2013;Dupont et al.2018).When the excitation frequencies of wind gusts and the frequency of tree sway are similar or identical (i.e.，resonance effects occur in trees)，the dynamic effects of gusts increase the bending of the tree stem，and the wind speed at which the tree is broken or blown down will be considerably lower than that predicted in the pulling tests under calm wind conditions(Schindler et al.2013).Dupont et al.(2018) identified a frequency peak on wind velocity fluctuations related to the fundamental vibration modes of trees in the edge flow based on field measurements.

It is difficult to obtain measurement results during severe weather events such as typhoons.Most previous investigations on wind-tree interactions have primarily been based on field measurements during low wind conditions (Schindler 2008;Sellier et al.2008;Dupont et al.2018).Moreover，data from field measurements have mostly focused on windinduced vibration behaviour of conifers (Flesch and Wilson 1999;Dupont et al.2018).Spectral methods such as Fourier analysis are commonly used to analyse the response behaviour data of measured conifers from wind-tree interaction studies (Baker 1997;James et al.2006;Rudnicki et al.2008;Schindler et al.2010).

To date，less is known about characteristics of wind fields in forest areas during typhoons.Further，research on wind-induced dynamic responses of deciduous broadleaved trees during typhoon conditions is unknown.In fact，deciduous broadleaved trees，which often have more complex architecture than conifers，and are also at risk during severe windy days.Moreover，in numerous forests，such as in Europe，conifers are gradually being replaced by deciduous broadleaved trees (Schelhaas et al.2003).In many cities in Europe，most urban trees are deciduous broadleaved species (Zhu et al.2003).However，there are only a few studies that have performed tree winching experiments (Roodbaraky et al.1994;Bartens et al.2010) and numerical simulations (Rodriguez et al.2008)，providing some clues about the response of deciduous broadleaved tree species under non-destructive wind conditions.Thus，there are three key questions remaining unanswered:(1) Under the influence of trees，what are the changing rules of the average and fluctuating wind characteristics in a forest area? (2) What is the dynamic behaviour of deciduous broadleaved species during typhoons and does it resonate with fluctuating winds in high wind environments (such as typhoon)? And，(3) What is the mechanism of the transfer of wind energy into deciduous broadleaved tree movement?

Therefore，based on these questions，it was hypothesized that characteristics of wind field and wind-induced dynamic responses of deciduous broadleaved trees followed a specific pattern in a forest area during typhoon conditions.Based on this hypothesis，the deciduous broadleaved forest of the National Field Scientific Observation and Research Station of the Maoer Mountain Forest Ecosystem in Heilongjiang was considered the research site in this study.Wind field characteristics at five points within and above the forest were measured，and the wind-induced dynamic behaviour of an individualBetula platyphyllawas studied during three typhoon periods，the No.8 typhoon “Bavi”，the No.9 typhoon “Maysak” and the No.10 typhoon “Haishen”，all of which occurred in 2020.The aims of this study were to investigate the characteristics of the wind field and the dynamic behaviour of a single tree in a forest area during three typhoons.This study is important for understanding wind-induced tree damage and for better predicting the risk of damage.

Materials and methods

Site description

Beginning in the autumn of 2019，long-term measurements of wind velocity and tree response were carried out at a site located in a deciduous broadleaved forest at the Maoershan Forest Ecosystem Research Station of Northeast Forestry University，Heilongjiang Province，Northeast China (45°24′ N，127° 40′ E，400 m a.s.l.).The map of the site was drawn by BIGEMAP (Chengdu BIGEMAP Data Processing Co.，Ltd.，Chengdu，China) and ArcGIS10.5 software(Environmental Systems Research Institute，Inc.，Redlands，CA，USA)，as shown in Fig.1 a.The climate of the site is continental monsoon with a windy，dry spring，a warm and humid summer，and a dry and cold winter (Wang et al.2015).The mean (2006-2017) annual rainfall (March to November) was 591±152 mm (mean±SD)，of which～ 50%fell between June and August.The mean annual，January，and July air temperatures were 2.2±0.7°C，-19.7±2.8°C，and 20.2±0.7°C，respectively (Wang et al.2019).The study area is in a southwest-northeast valley.The mean slope around the tower was～ 9°，and the slope along the valley centre was～ 1° (Wang et al.2015).

Fig.1 a Study site and b sample tree

Forest inventory data and sample tree

The dominant tree species around the measurement site includeUlmus japonicaSarg.，F(xiàn)raxinus mandshuricaRupr.，B.platyphyllaSuk.，Populus davidianaDode.，Juglans mandshuricaMaxim.，etc.(Wang et al.2016).The mean height of the forest was 18-20 m (Wang et al.2016).Based on the inventory of 106 circular plots (with diameters of 20 m) within the fetch (1500 m×400 m)，the mean basal area and tree biomass density were 24.16 m2ha-1and 155.64 Mg ha-1，respectively (Liu et al.2016).From August to October of 2016 and 2018，the mean leaf area index (LAI，defined as a half of the total leaf area per unit horizontal ground surface area) in the canopy was approximately 6.95±0.65 m2m-2，varying from 5.95 to 7.96 m2m-2，based on the leaflitter collection method in eight permanent plots(Wang et al.2019).

AB.platyphyllalocated in the stand was selected as the sample tree for this field experiment (Fig.1 b).In the summer of 2020，its height (h) was approximately 23 m，the diameter at breast height (DBH，i.e.，diameter 1.3 m above ground level) was 28 cm，and the height of the crown centre was 16.8 m.

Wind velocity and tree response measurements

Wind velocity vector components in thex(u)，y(v)，andz(w) directions，wind direction and sound virtual air temperature within and above the forest at 5 m (z=0.22h，wherezis the height of the measurement point)，10 m(z=0.43h)，20 m (z=0.87h)，35 m (z=1.52h) and 50 m(z=2.17h) above ground level were simultaneously measured using five ultrasonic anemometers (Wind master，Gill，UK)，sampled at 10 Hz (Fig.2 a) and mounted on a 50 m high flux tower (Fig.2 b).The wind speed range that can be monitored was 0-45 m s-1，the resolution was 0.01 m s-1，and the accuracy less than 1.5% when the wind speed was less than 12 m s-1.The swaying of the sample tree was simultaneously measured in terms of wind measurements using a three-axis accelerometer (AIT2500，2 g;JingMing Technology Co.，Ltd.，Yangzhou，China)(Fig.2 c).The dimensions of the accelerometer were 45 mm×45 mm×50 mm，and the weight 200 g.The accelerometer was mounted horizontally at a height of 7.97 m(z=0.35h) above ground level northwest of the tree.

The data acquisition system used for wind speed measurement is CR6 data collector (Campbell，US) Fig.2 d.The accelerometer data were collected by a digital acquisition instrument (JM5981A，JingMing Technology Co.，Ltd.，Yangzhou，China) (Fig.2 e).Tree acceleration was recorded at 50 Hz using the same clock as for wind velocity.The layout of the experiment is shown in Fig.2 f.The instrumented sample tree was located 10 m northeast of the flux tower.

Fig.2 Test measurement system; a Gill Wind Master; b flux tower; c three-axis accelerometer; d data collector CR6; e JM5981A;and fschematic layout of the site

Typhoon events

Three typhoons，Bavi，Maysak and Haishen，occurred on August 27th，September 3rd，and September 7-8th 2020，respectively.The meteorological conditions of the three typhoons are summarized in Table 1.Maysak was the strongest，reaching the canopy top with a 10-min mean wind velocity of 6.82 m s-1and a maximum gust of 26.92 m s-1.The wind characteristics and tree response data measured on these three typhoon days were selected for subsequent analysis.

Table 1 Meteorological conditions for days analysed，including typhoon name，data，period，installation height of sensors (acceleration sensors in brackets and wind velocity sensors in others)，maximum 10-min average wind velocity，maximum wind gust velocity，average wind direction and number of 10-min periods for the statistics

Spectral analysis

Tree responses to turbulent wind load can be analysed using the time-course method and the spectral method.However，for practical purposes，it is nearly impossible to make use of the time-course method because the actual values for the response parameter of trees are unavailable (e.g.，the drag coefficientC Dand the frontal area of the crown perpendicular to airf olwA)under real wind conditions.Therefore，the spectral method is more useful (Haritos and James 2008).The general procedure of the spectral method for tree response to wind velocity is shown in Fig.3 (Mayer and Dr 1985;Mayer 1987).

The relationship in Fig.3 can be expressed by the following equation (Mayer 1987):

whereP l(f) is the power spectral density of the wind load，ρis the air density，Uis the mean wind velocity in the streamwise direction，T a(f) is the aerodynamic transfer function andP u(f) is the power spectral density of the streamwise wind velocity.

whereP t(f) is the power spectral density of the tree response，||Tm(if)||2is the imaginary mechanical transfer function and i is the imaginary unit.For practical purposes，generalizable descriptions of the variability ofC DandAunder real wind conditions are still unavailable (Schindler and Mohr 2018).Therefore，the power spectra of wind load cannot be obtained by Eq.(1).Therefore，Reynolds stressτis usually used as the measure of wind load in investigations on the response of trees under wind load.Reynolds stressτis the momentum transfer caused by turbulent velocity fluctuation and comprises turbulent normal stress and turbulent shear stress (Mayer 1987;Gardiner 1995).The mean value of Reynolds stress can be described by the following equation:

whereuandware wind velocity fluctuations in the streamwise and vertical directions，respectively.

The power spectra of the tree response are derived from the power spectra of the wind load using the mechanical transfer function (Fig.3).This function provides information on the response of trees to turbulence at various frequencies，and it is also a measure of the energy transfer efficiency from the turbulent wind field to tree movement(Gardiner 1994，1995;Hassinen et al.1998).The Reynolds stress power spectrum can be obtained by the average Reynolds stress expression of Eq.(3) and power spectrum estimation.Then，substitutingPˉτ(f) instead ofP t(f) into Eq.(2)，the mechanical transfer function ||Tm(if)||2can be calculated by the following equation:

Fig.3 Schematic of the spectral method

All of the estimations of power spectra were performed using the Pwelch function by MATLAB software (8.3 R2014a，Mathworks，Natick，MA，USA).By averaging 10-min power spectral densities (approximately 30) over approximately 5 h，the ensemble average results of tree acceleration atz=0.35hheight，wind velocity and Reynolds stress atz=2.17h，1.52h，0.87h，0.43hand 0.22hheight were obtained.The spectral estimations of the longitudinal(NE-SW direction，al) and lateral (SE-NW direction，a2)accelerations were calculated.The number of 10-min time periods used for the ensemble average calculation of each power spectrum is presented in Table 1.Power spectra were drawn using bi-logarithm coordinates，where the ordinate power spectral density was multiplied by the frequency (n)，normalized by the variance，i.e.，

wherei=u，v，wand plotted against Monin coordinates.i.e.，

Results

The time period during which the average wind velocity of 10 min at a height ofz=2.17his greater than 5 m s-1was selected during the three typhoons for all subsequent analyses.The selected time period for each typhoon day was approximately 5 h.

Wind speed and wind direction

Figure 4 a shows an average wind profile of streamwise velocity (u) measured during the three typhoons.The height and velocity were normalized to the height and velocity atz=0.87h(near the canopy top) as the reference height and the reference wind velocity.The three typhoons，Bavi，Maysak and Haishen，exhibited almost the same average wind profiles，which appeared approximately logarithmic above the canopy with a strong shear at the top and a rapid decrease in velocity within the canopy.The streamwise wind velocity increased fromz=0.43htoz=0.22hheight，indicating the presence of a secondary velocity maximum within the trunk layer.

For the different measurement points of the same typhoon，the wind twist angles varied greatly，and the maximum wind twist angle measured at the highest and lowest measurement points was approximately 110°，changing from the northeast to the south (Table 1)，which is different from the conventional wind profile.During the three typhoon events，the trend of the wind twist angle was similar as the increase in the height of the measurement point.When a gust enters the canopy from the upper part of the crown，the wind direction changes sharply (Fig.4 b)，because the disturbance effect on the tree has an impact on the wind characteristics.The larger wind twist angles may impose significant distortion effects on trees near the ground，which should be given attention in future research on the wind load of trees in a forest.

Fig.4 Wind profiles measured during three typhoons; a average wind profiles of streamwise velocity (u);height is normalized to z=0.87 h and velocity to z=0.87 h;and b average wind direction profiles;dashed line indicates the height of the tree

The time variations of the 10-min average wind velocity and wind direction during the three typhoon days are shown in Fig.5.

The three typhoons exhibited similar wind characteristics (Fig.5).The 10-min average wind velocity strongly decreased fromz=1.52hto 0.87hwhen reaching the canopy.This is because the leaves and branches extract momentum from the flow through drag (Fig.5 a).The wind velocity at two heights below the canopy (i.e.，z=0.43hand 0.22h)was almost the same，but the wind velocity atz=0.22hwas higher than that atz=0.43hin some periods，especially during typhoon Maysak.

For the same measurement point of the same typhoon during the period with high wind speeds，the 10-min average wind direction changed over a small range and basically remained stable.However，when the 10-min average wind speed atz=2.17h-1.52hwas less than 2.0 m s-1(atz=0.87hwas approximately less than 1.0 m s-1and atz=0.43h-0.22hless than 0.5 m s-1);the wind direction varies over a wide range (Fig.5 b).

Fig.5 Wind characteristics during the three typhoons:time variations of the a 10-min average wind velocity; b 10-min average wind direction measured at five heights within and above the forest (z=2.17 h，1.52 h，0.87 h，0.43 h and 0.22 h)，for Bavi，Maysak and Haishen;shaded areas highlight the analysis periods

Wind speed spectra

The power spectrum of wind velocity fluctuations reflects the distribution of fluctuating wind energy with frequency，and characterizes the contribution of various eddies of different frequencies in turbulent flow to turbulent kinetic energy.It is one of the important characteristics of wind fluctuation.When the frequency of wind fluctuation is close to or equal to the damped natural frequency of a high-rise structure，the turbulent fluctuation component significantly affects the response of the structure.The power spectra of velocity fluctuation comprise the horizontal longitudinal(streamwise)，horizontal transverse (spanwise) and vertical velocity fluctuation.In this study，the normalized ensembleaveraged 10-min power spectra at various heights are shown in Fig.6.

During the three typhoons，the 10-min ensemble-averaged power spectra of the three velocity vector components(u，vandw) atz=1.52hand 2.17h(above the canopy)displayed a shape similar to common atmospheric boundary layer spectra.Above the canopy，the slope of the wind spectra increases as a function off+1in the energy-containing range and decreases as a function off-2∕3in the inertial subrange (Fig.6).

Fig.6 Normalized ensemble-averaged 10-min power spectra of the a streamwise (u); b spanwise (v);and c vertical (w) wind-velocity components，measured at five heights within and above the forest(z=2.17 h，1.52 h，0.87 h，0.43 h and 0.22 h)，for Bavi，Maysak and Haishen typhoons;frequency fis normalized by the average wind velocity at z=0.87 h，u，and the height，z=0.87 h

The slope of theu-spectra for the three typhoons in the dissipation range becomes steeper and steeper with the decrease in height of the measurement point atz=2.17h，1.52h，0.87h，0.43hand 0.22h.This occurs because the development of the wake structure behind the canopy elements and the vegetation below the canopy accelerate turbulent dissipation (Dupont et al.2018).Specifically，for the three typhoons，the slope of the dissipation range ofu-spectra atz=0.43his slower than that atz=0.87h，which may be because the height of the measurement point atz=0.43his exactly at the trunk layer of the forest stand.The slope of theu-spectra of Maysak and Haishen in the dissipation range was slower than that of Bavi as a whole because the wind energy of Maysak and Haishen was obviously higher than that of Bavi.The maximum power of the power spectrum ofthe same velocity component of the same typhoon decreases with the increase in the heights of the measurement points.

The normalized peak frequency (i.e.，frequency with the maximum power) of the same velocity component power spectra of the same typhoon at different measurement points showed little difference.Relatively speaking，the peak frequency difference of thew-spectrum was slightly larger.For Typhoon Bavi，the normalized peak frequencies ofu，vandw-spectra weref=nz/u=0.54±0.04，0.60±0.08 and 0.92±0.15，respectively.For Typhoon Maysak，the normalized peak frequencies ofu，vandw-spectra weref=nz/u=0.47±0.03，0.48±0.05 and 0.91±0.17，respectively.For Typhoon Haishen，the normalized peak frequencies ofu，vandw-spectra weref=nz/u=0.52±0.02，0.51±0.05 and 0.86±0.15，respectively.

Based on the fluctuating wind speed spectra at the height of each measurement point and the normalized frequency formula，the peak frequency of the fluctuating wind can be obtained.The peak frequency of the streamwise and spanwise wind velocity components (uandv) were approximately 0.03 Hz，and the peak frequency of the vertical component (w) was approximately 0.06 Hz.There was a slight difference between the heights of various measurement points.

The power spectral density of three wind speed vector components (u，vandw) at the same height for each measurement point during the same typhoon is illustrated in Supplementary materials (Fig.S1).

For Typhoon Bavi，when the frequency was lower than the peak frequency，except forz=0.87h，theu-spectrum had a higher power spectral density than the other two wind speed component spectra.Thew-spectrum always has the lowest power spectral density value.Except for the height ofz=0.87h，the peak frequency of the three wind speed component spectra is always the highest in thew-spectrum and the lowest in theu-spectrum.For the stronger typhoons Maysak and Haishen，when the frequency was lower than the peak frequency，theu-spectrum may coincide with thev-spectrum or be greater than thev-spectrum，and thew-spectrum still had the lowest power spectral density.The different power spectral densities of the wind speed vector components indicate the anisotropic character of turbulence above the canopy，at the top of the canopy and within the canopy.Generally，for the same typhoon，the fluctuation intensity of wind speed in the horizontal direction was stronger than in the vertical direction，and the turbulence anisotropy decreased with increasing height of the measurement point.

Tree response and wind loading

The power spectra of the Reynolds stressτat five heights(z=2.17h，1.52h，0.87h，0.43hand 0.22h)，the power spectra of the tree longitudinal and lateral acceleration response atz=0.35h，and the mechanical transfer function are shown in Fig.7 a-c，respectively.

Figure 7 a shows that during the three typhoons，except for the height ofz=0.87h(near the canopy top)，the power spectral density of Reynolds stress (τ) in the low frequency region increased at other heights and then decreased gradually after reaching the maximum power spectral density.However，with the increase in typhoon intensity，the slope decreased more slowly.The power spectral density then increased again in the high-frequency region and showed an upward trend even greater than the peak frequency.There are few differences among different measurement points.However，with the increase in typhoon intensity，the consistency of the Reynolds stress spectrum at different heights became worse.At a height ofz=0.87h，when the power spectral density reached the maximum，there was a frequency range where the power spectral density was almost at the same level in a certain frequency range.The normalized peak frequencies of theτ-spectra of typhoons Bavi，Maysak and Haishen weref=nz/u=0.84±0.14，0.94±0.35 and 0.91±0.18，respectively.

The normalized wind-induced vibration peak frequencies of thea1anda2spectra during typhoons Bavi，Maysak and Haishen weref=nz/u=3.65 and 3.88，2.07 and 1.88，and 3.47 and 3.67，respectively (Fig.7 b).During the same typhoon，only small differences between the power spectra of the two acceleration vector components could be seen.

Fig.7 a Normalized ensemble-averaged 10-min power spectra of the Reynolds stress τ at five heights within and above the forest(z=2.17 h，1.52 h，0.87 h，0.43 h and 0.22 h); b power spectra of(left) longitudinal (NE-SW direction，a1) and (right) lateral (SE-NW direction，a2) acceleration of tree;and c mechanical transfer function based on power spectrum of τ at the height of z=0.87 h and power spectra of (left) longitudinal (NE-SW direction，a1) and (right) lateral (SE-NW direction，a2) acceleration of tree for Bavi，Maysak and Haishen typhoons

Based on the acceleration response spectra and normalized frequency formula，the wind-induced vibration peak frequencies of thea1anda2spectra of the tree in the three typhoons were 0.20 and 0.22 Hz，0.14 and 0.12 Hz，and 0.22 and 0.23 Hz，respectively.There were differences between different typhoon days.In addition，except for the strong Typhoon Maysak，two other notable peaks above the peak frequency were also observed in the acceleration response spectra of the other two typhoons，approximately 0.57 and 1.14 Hz，and 0.64 and 1.39 Hz，respectively，which may correspond to the second and third harmonic frequencies of the tree in multimodal behaviour.

To obtain the free vibration frequency of the tree，the hammer test was performed.The free vibration peak frequencies of the two acceleration components were 0.28 and 0.26 Hz，respectively，estimated from Fourier analysis，which were nearly consistent with the wind-induced vibration peak frequencies of the tree during typhoons.Amtmann (1986) and Stacey et al.(1994) studied conifers and obtained the similar results.

The comparison of the tree response power spectra during the three typhoons shows differences in the lowfrequency part of the spectra (Fig.7 b).There is less energy at low frequencies under lower wind conditions (Bavi and Haishen)，i.e.，the tree response is more sensitive to low frequencies on a strong typhoon day (Maysak).The reason for the difference may be the lower turbulence of the flow during typhoons with less storm intensity.And as a consequence，the first three vibration modes of trees were more obvious on weaker typhoon days.

By combining each Reynolds stress spectrum (S τ)and the acceleration response spectrum (S aa)of the tree，it can be seen that the wind-induced vibration peak frequencies obviously exist in the energy dissipation range of the Reynolds stress spectra.The tree did not resonate with the turbulent wind component in any typhoons but made the strongest response to gusts close to its free vibration peak frequency.Only by effectively absorbing the energy in the turbulence at the free vibration peak frequencies of the tree，is the normal energy dissipation process of turbulence short circuited (Gardiner1995).

The mechanical transfer function (||Tm(if)||2) showed an almost consistent trend as the acceleration response spectra (S aa)during the three typhoons，i.e.，the peak appeared at the free vibration peak frequencies of the tree，and then the spectral value decreased markedly (Fig.7 c).In addition，similar to the acceleration response spectra，there was only a small difference between the mechanical transfer functions of the two acceleration vector components.In addition，the mechanical transfer function showed differences in the low-frequency part under the three typhoons.There is less energy at low frequencies under lower wind conditions such as typhoons Bavi and Haishen.This means that the mechanical transfer function is a quantity related to wind intensity and is non-linear.

Discussion

The phenomenon of a secondary velocity maximum within the trunk layer，which is often observed in canopies with an open trunk space，has been documented in previous studies(Baldocchi and Meyers 1988;Dupont et al.2011，2018).This phenomenon is still in this study but is not obvious，possibly because the measurement point ofz=0.22his located at the lower limit of the trunk space.

The values of the normalized peak frequencies ofu，vandw-spectra are somewhat different from the values obtained by Kaimal and Finnigan (1994) in which the peak frequencies ofuandw-spectra were 0.15±0.05 and 0.45±0.05，respectively，and the peak value ofv-spectra was between 0.10 and 0.35.This is inconsistent with the values reported by Dupont et al.(2018)，that “the peak positions of the spectra are similar above the canopy，at the canopy top，and in the upper trunk space aroundf=nz/u=0.18 foru，0.30 forv，and 0.45 forw″.On the one hand，the reason for this difference may be that the storm intensity in this study was relatively strong;on the other hand，it may be that the vegetation in the study area was different from those in previous studies.

During the same typhoon，only small differences between the power spectra of the two acceleration vector components could be seen，which is in agreement with Mayer and Dr(1985)，Mayer (1987) and Peltola (1996).Mayer (1989) indicated that these small differences may be due to the asymmetric distribution of canopy structure，the average wind direction and the development of root collars.

Except for the strong Typhoon Maysak，two other notable peaks above the peak frequency were observed in the acceleration response spectra of the other typhoons，which may correspond to the second and third harmonic frequencies of the tree in multimodal behaviour.Peltola (1996)proposed that，compared to Scots pine (Pinus sylvestrisL.)in a thinned forest，the smaller diameter Scots pine in an unthinned forest has relatively large flexibility，so the incident energy is divided into higher resonant modes.Scannell(1984) suggested that higher-order vibration modes may be caused by tree elements such as branches and leaves.During Typhoon Maysak，the peak values of the second-and thirdorder frequencies became less obvious，which may be due to the relatively strong storm intensity.

There was only a small difference between the mechanical transfer functions of the two acceleration vector components.These results are similar to those obtained by Holbo et al.(1980)，Amtmann (1986)，and Stacey et al.(1994).They demonstrated that the mechanical transfer function of a wind-induced conifer response was almost identical to that of a damped harmonic oscillator.That is，the tree acts as a filter converting the available energy in turbulence into its own motion (Mayer 1989).Moreover，forests can be regarded as arrays of harmonic oscillators that effectively absorb turbulent spectral energy at the free vibration peak frequencies of trees (Gardiner 1994).

Conclusions

Observations were made of the wind characteristics within and above a natural mixed forest，along with measurements of the motion of an individualB.platyphyllaclose to 23 m in height，during three typhoons.Using spectral analysis，the mechanical transfer function between the Reynolds stress power spectra and the tree response power spectra was calculated to obtain information about the response of the tree to turbulence at different frequencies.The conclusions drawn are as follows:

First，the disturbance effect of trees causes the average wind to twist with height，with a large twist gradient within the canopy height and a small twist gradient outside the canopy height.The maximum wind twist angle measured at the highest and lowest measurement points was approximately 110°，which is different from the conventional wind profile.

Second，during three strong typhoons，the maximum power of the wind spectra and the turbulence anisotropy of the three turbulence components decreased with increased height.The existence of trees breaks the large-scale flow structure into small-scale vortices.The higher the distance from the measurement point to the tree，the smaller the disturbance of the tree on the wind spectra，and the smaller the peak value of the spectra.

Third，B.platyphylladid not resonate with the turbulent wind component in any of the typhoons but responded strongly to gusts near its free vibration peak frequencies and shortened the normal energy dissipation process of gusts by effectively absorbing the turbulent energy at the free vibration peak frequency of the tree.

Fourth，the peak frequency of the mechanical transfer function ofB.platyphyllawas basically the same as the peak frequency of the response power spectra during the three typhoons.The mechanical transfer function of the wind-induced response of the tree was almost the same as that of the damped harmonic oscillator which has similar characteristics to coniferous trees.