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European Journal of Forest Research ISSN 1612-4669Volume 131Number 1 Eur J Forest Res (2011) 131:203-217DOI 10.1007/s10342-010-0448-2

Wind loading of trees: influence of tree sizeand competition

Sophie E. Hale, Barry A. Gardiner,Axel Wellpott, Bruce C. Nicoll & AlexisAchim

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ORIGINAL PAPER

Wind loading of trees: influence of tree size and competition

Sophie E. Hale • Barry A. Gardiner •

Axel Wellpott • Bruce C. Nicoll • Alexis Achim

Received: 25 February 2010 / Revised: 31 August 2010 / Accepted: 20 October 2010 / Published online: 23 November 2010

� UK Crown 2010

Abstract Wind damage to forests is an important eco-

logical disturbance factor. At the same time, it can have

serious economic consequences due to a reduction in tim-

ber production. Current models for predicting the risk of

wind damage are useful, but generally only focus on the

‘‘mean’’ tree within uniform stands. This paper presents

measurements made of wind loading on trees of different

sizes within four forest stands of different structure and

management history, but all well-acclimated to current

wind conditions. Each tree demonstrated a linear relation-

ship between the maximum hourly turning moment and the

square of the average hourly wind speed at the canopy top;

we defined this ratio (the gradient of the line Mmax vs. u2)

as the turning moment coefficient (TC). TC was correlated

with tree size, in a relationship that differed little between

the four forest sites despite the differences between the

stands. The relationship between TC and individual tree

competition within each stand was investigated, using both

distance-independent and distance-dependent competition

indices. All sites showed decreasing TC with increasing

competition. However, the relationships differed between

sites and would also be expected to change through time

for a single site. The distance-dependent indices offered no

improvement over the simpler, non-spatial indices that

required only a diameter distribution. We suggest how,

subject to further work, the results presented could be

applied to calculate the risk of wind damage to trees of

different sizes within a forest stand, and how the risk of

wind damage to individual trees might change in response

to thinning.

Keywords Wind damage � Risk � Competition indices �Wind loading � Picea sitchensis (Bong.) Carr. �Larix decidua Mill

Introduction

Wind is a major natural disturbance factor throughout

many forested parts of the world (Putz et al. 1983; Schaetzl

et al. 1989; Ennos 1997). From an ecological perspective,

wind is an important agent for creating environments for

natural regeneration, and for increasing diversity in forest

stands (Quine 2001; Ruel and Pineau 2002). For the forest

industry, however, wind throw (wind-induced damage e.g.

stem breakage or uprooting) reduces profitability of timber

production, through reduced economic value of wind

blown timber (Savill 1983; Nieuwenhuis and Fitzpatrick

2002) and increased costs of harvesting (Quine et al. 1995).

Harvesting stands before the age of optimum economic

return to reduce the risk of wind throw also reduces the

economic return (Gardiner and Quine 2000).

Access to tools that predict the risk of wind damage

would enable forest managers to plan fellings or thinnings

This article belongs to the special issue ‘Wind Effects on Trees’.

Communicated by J. Bauhus.

S. E. Hale (&) � B. A. Gardiner � A. Wellpott �B. C. Nicoll � A. Achim

Forest Research, Northern Research Station, Roslin,

Midlothian EH25 9SY, UK

e-mail: sophie.hale@forestry.gsi.gov.uk

A. Wellpott

Facility for Airborne Atmospheric Measurements,

Cranfield University, Cranfield, Bedford MK43 0AL, UK

A. Achim

Faculte de foresterie et de geomatique, Universite Laval,

Quebec G1V 0A6, Canada

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DOI 10.1007/s10342-010-0448-2

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in order to avoid or minimise wind damage to a stand.

Gardiner et al. (2008) synthesised the current status of

mechanistic modelling tools for the prediction of wind

damage risk. The modelling effort to date has generally

been at stand level, predicting risk of damage to the mean

tree in a stand (for example HWIND; Peltola et al. 1999,

and ForestGALES; Gardiner et al. 2000; 2004). Some

attempts have been made to model wind risk to individual

trees within stands (Ancelin et al. 2004; Cucchi et al. 2005;

Schelhaas et al. 2007), but in reality, these are stand-level

models applied to individual trees, rather than true indi-

vidual tree risk models. In Britain, where the predominant

silvicultural system has been clear-fell and replant, For-

estGALES was developed as a tool to enable forest man-

agers to assess and manage the risk of wind damage in

uniform even-aged stands (Gardiner et al. 2000; 2004).

However, even in ‘‘uniform’’ even-aged stands, there is a

distribution of tree sizes. Furthermore, in Britain, there has

been a policy shift at a national level (Anonymous 2004)

and at a country level in both Scotland (Anonymous 2006)

and Wales (Anonymous 2009) towards alternative methods

of forest management, broadly termed continuous cover

forestry, which involve maintaining the forest canopy at

one or more levels while regenerating the stand (Mason

et al. 1999; Mason and Kerr 2004). This will result in an

increased number of forest stands in Britain with a wide

range of tree sizes, in either a simple (one or two layer) or

complex (three or more layers) structure (Mason and Kerr

2004). Such forest types are much more common in central

European forestry (Hart 1985) and are regarded as being

closer to natural forest stands. Therefore, increasingly,

there is a requirement for wind risk models that can predict

the risk of wind damage to all trees in any structure of

stand, whether for forest management or for understanding

ecological processes in natural forests.

All of the models described by Gardiner et al. (2008)

contain some empirical relationships. A key empiricism is

the method used to relate the maximum turning moment to

the mean turning moment that occurs in response to the

mean wind speed. This relationship is poorly parameter-

ised, yet model output is very sensitive to it (Gardiner et al.

2000). If it was possible to quantify the relationship

between maximum turning moment (or bending moment)

and mean wind speed for individual trees, there would be

no need to convert between mean and extreme wind

loading.1 The critical turning moment required to break or

overturn a tree can be calculated from the physical prop-

erties of the tree and site (Gardiner et al. 2000; Nicoll et al.

2006). If we know how the maximum turning moment

changes with mean wind speed, it enables the critical wind

speed (the mean hourly wind speed at which damaging

gusts occur, i.e. the wind speed at which the critical turning

moment is reached) to be calculated.

In general, the turning moment experienced by large

trees at a given wind speed will be higher than for a smaller

tree because of the larger crown (increased ‘‘sail’’ area) and

increased moment arm (wind loading is at a higher effec-

tive height). However, two identical trees might be

expected to respond differently to the same wind speed

depending on how much shelter they receive from neigh-

bouring trees in the stand. A tree of height H, surrounded

by trees taller than H, might be expected to experience a

lower turning moment than the same tree surrounded by

trees smaller than H. Similarly, if neighbours are removed

from around a particular tree during a thinning, the tree will

become more exposed to the wind and would be expected

to bend more at a given wind speed than prior to thinning.

Wind throw is common at a newly created windward-

facing edge, or in an excessively thinned stand, as the trees

are not yet acclimated to their new wind environment

(Gardiner et al. 2005; Lanquaye-Opoku and Mitchell 2005;

Scott and Mitchell 2005). Trees may take several years to

acclimate to an altered wind environment (Urban et al.

1994) and regain their mechanical stability. This process

requires an altered allocation of assimilates within the tree

to strengthen parts that now experience the largest

mechanical stress, such as the lower stem and structural

roots (Stokes et al. 1997; Nicoll and Gardiner 2006).

The concept of local shelter as an influence on wind

environment has parallels with forest growth modelling,

where competition indices are widely used to determine the

growth of individual trees (e.g. Courbaud et al. 2001;

Pretzsch et al. 2002; Stadt et al. 2007; Kiernan et al. 2008).

There are many approaches of varying complexity,

including stand-level indices; individual-tree non-spatial

indices that essentially use the size rank of each tree in the

stand; and individual-tree spatial indices, based on the

proximity and relative size of each tree and its neighbours.

Several papers exist reviewing and comparing different

indices (e.g. Biging and Dobbertin 1992, 1995). In practice,

the competition index chosen for a given application will

largely be influenced by the data available. In this paper,

we investigate the idea that the competition experienced by

a tree, as well as influencing tree growth, is likely to reflect

how much that tree is sheltered from the effects of the

wind. Studying the turning moment of different trees in

response to wind loading will allow us to improve the

existing approach to wind risk modelling, by quantifying

the risk to all trees within a forest stand of any structure.

1 The assumption in all wind damage risk modelling to date is that

the extreme (maximum) wind loading in any particular storm is the

key factor in determining whether damage occurs. However, this has

never been verified in field experiments due to the lack of

measurements during damaging storms, and it is possible that root

fatiguing (Rogers et al. 1995) from a number of storms could actually

be more important.

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Linking this to local competition has the potential to enable

us to model the immediate effects of thinning on the risk of

wind damage and will also facilitate the integration of wind

risk modelling within forest growth models.

In summary, the aims of the work reported were to

investigate: (i) if individual trees within a stand showed a

systematic change in maximum turning moment in

response to wind loading at different wind speeds; (ii) if

this response varied systematically for trees of different

sizes within a stand, and specifically in relation to their

local competition; and (iii) if the response varied system-

atically for different forest stands; and finally, (iv) to

suggest a method for modelling risk of wind damage to

trees of different sizes within a stand, including changes

that might occur as a stand is thinned.

Materials and methods

Extensive measurements of wind speed and tree turning

moment were taken at three sites, and a small additional

data set was available for comparison from a fourth site.

The experimental sites and forest stands are described

below and summarised in Table 1. Instrumentation, data

processing and the competition indices used are reported in

subsequent sections.

Study sites and sample trees

Clocaenog (North Wales, UK, 53� 080 N, 3� 430 W) was an

exposed, even-aged, widely spaced Sitka spruce (Picea

sitchensis (Bong.) Carr) plantation on an intergrade brown

earth-ironpan soil (Table 1). The overstorey was aged

54 years at the time of measurements in 2005. It had a

history of thinning, most recently in 1999. The assessment

plot was 1 ha, but due to cable-length restrictions, the

sample trees were clustered together within an area of

approximately 25 9 25 m. A relatively wide range of tree

heights was present in the stand (from 20 to 34 m), and an

understorey of naturally regenerated Sitka spruce was

present (height generally less than 0.5 m, although some up

to 1 m). Nine sample trees were selected, covering a range

of tree sizes (Table 2). Measurements of tree turning

moment and wind speed were taken between May and

November 2005. Data logging was started manually during

periods of moderate to strong winds, and almost 400 h of

data were collected, with average hourly wind speeds up to

8 m s-1 (see Wellpott 2008 for further details).

Kyloe (Northumbria, UK, 55� 320 N, 1� 990 W) was a

relatively sheltered, well-thinned and widely spaced plan-

tation stand of European larch (Larix decidua Mill.) on a

brown earth soil (Table 1). There was a dense understorey,

beneath part of the stand, of naturally regenerated Sitka

spruce. The overstorey larch was 59 years old at the time

of measurements in 2006. The assessment plot was

0.24 ha. Tree height of the overstorey trees ranged from 20

to 28 m. The understorey was up to 15 m high. Nine

sample trees were selected: four were larch in the area with

an understorey; two were larch in the area with no under-

storey; three were understorey Sitka spruce (Table 2).

Measurements of tree turning moment and wind speed

were taken between March and November 2006, and

between approximately 1,000 and 5,000 h of data were

collected for each sample tree. Average hourly wind speeds

up to 11 m s-1 were recorded, although most were below

9 m s-1 (see Wellpott 2008 for further details).

Harwood (Northumbria, UK, 55� 120 N, 2� 020 W) was a

moderately exposed, uniform even-aged Sitka spruce stand,

on a peaty-gley soil (Table 1). The stand was aged 36 years

at the time of measurements in 2008/2009. This stand was

younger than those at Clocaenog and Kyloe and had been

thinned approximately 10 years earlier. The assessment

Table 1 Characteristics of the four sample sites

Clocaenog Kyloeb Harwood Kershope

Altitude (m) 395 120 260 220

Slope (�) 2–5 5 2 5

Aspect S W SE NW

DAMSa 20 12 17 15

Species Sitka spruce European larch

(Sitka spruce)

Sitka

spruce

Sitka

spruce

Age (years) 54 59 (11) 36 22

Average spacing (m) 5.9 9.2 (*1) 2.4 1.8, 2.4, 2.8, 3.4, 4.9

Mean height (m) 27 25 20.4 12

a DAMS (Detailed Aspect Method of Scoring; Quine and White 1993) is a measure of exposure. DAMS of 12 represents a sheltered site; DAMS

of 20 represents an exposed siteb Values in brackets represent the understorey

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plot was 0.02 ha, although trees outside this were measured

if they were neighbours of a sample tree. Vertical differ-

entiation was less well-developed than at Clocaenog and

Kyloe. Sixteen sample trees were selected to cover the

range of tree heights within the study area (18–25 m;

Table 2). Measurements of tree turning moment and wind

speed were taken between September 2008 and October

2009, and over 8000 h of data were collected. Average

hourly wind speeds rarely exceeded 6 m s-1.

Kershope (Northumbria, UK, 55� 080 N, 2� 420 W) was a

moderately exposed, uniform even-aged Sitka spruce

plantation on a peaty-gley soil (Table 1). The stand was

aged 22 years at the time of measurements in 1989.

Originally planted at 1.8 9 1.7 m spacing, it was respaced

at canopy closure in 1975 to five different spacing treat-

ments (Table 1). Each assessment plot was approximately

0.06 ha. Eleven trees were sampled: two in each treatment,

plus an additional ‘‘reference’’ tree in the unthinned plot

(Table 2). For the reference tree, 13 h of data were

obtained; for the remaining trees, between 1 and 4 h of data

were obtained. This site and experiment are described in

detail in Gardiner et al. (1997). In the results, data from all

trees at Kershope are presented together, although unlike

data from the other forests, they are not representative of a

single stand because of the distinct treatment differences

(see Gardiner et al. 1997), which produced systematic

differences in terms of, e.g., stem taper and crown shape.

Tree characteristics measured and definition

of neighbours

At all sites, position and stem diameter at 1.3 m (D1.3 in

cm) of all trees in the assessment plot were recorded.

Additionally, height (H in m) was recorded for sample trees

(Table 2). At Clocaenog, crown width was also obtained

for all trees, calculated as the average crown width based

on measurement of maximum crown radius in eight

directions.

Voronoi polygons, which are commonly used in studies

of spatial distributions of forest canopies and competition

for resources (e.g. Goudie et al. 2009), were used as an

objective method for defining neighbours for each sample

tree for use in distance-dependent competition indices.

Using the Voronoi algorithm in the open-source statistical

package R (R Development Core Team 2008), a polygon

was drawn around each tree such that all points within that

polygon were closer to that tree than to any other tree. Two

trees with a common polygon side were designated as

neighbours. The sample trees in the sites studied here had

between four and nine neighbours. At Kyloe, the under-

storey trees were not included when defining the polygons

for the overstorey trees. Otherwise, a small understorey

Table 2 Tree dimensions, number of hours of measurement analysed

(N), turning moment coefficient (TC), and the correlation coefficient

(r2) of the linear relationship between hourly maximum turning

moment (Nm) and the square of the hourly average canopy-top wind

speed (m s-1)

Forest Tree

ID

D1.3

(cm)

Height

(m)

N TC

(kg)

r2

Clocaenog 4 59.8 29.6 392 1,324 0.962

Clocaenog 37 42.2 31.1 380 617 0.945

Clocaenog 38 38.9 27.3 383 421 0.962

Clocaenog 39 35.4 26.9 378 284 0.971

Clocaenog 40 37.6 28.0 306 391 0.945

Clocaenog 41 31.8 24.1 306 217 0.797

Clocaenog 42 28.5 22.8 389 103 0.905

Clocaenog 43 47.2 30.5 300 726 0.967

Clocaenog 80 54.5 31.9 361 906 0.938

Kyloe (EL)a 101 40.6 27.6 4,983 689 0.943

Kyloe (EL) 102 37.7 21.8 4,960 398 0.95

Kyloe (SS) 103 13.7 8.7 1,072 5.3 0.946

Kyloe (EL) 104 35.2 22.4 1,070 281 0.948

Kyloe (SS) 105 12.1 9.4 1,067 4.7 0.834

Kyloe (EL) 106 37.8 20.5 1,072 344 0.909

Kyloe (SS) 107 21.4 11.3 5,173 17 0.871

Kyloe (EL) 108 33.7 21.0 5,197 236 0.937

Kyloe (EL) 109 39.8 21.5 3,384 407 0.916

Harwood 1 15.1 20.1 8,753 35 0.885

Harwood 2 14.0 19.1 8,753 27 0.883

Harwood 3 29.2 20.9 8,753 262 0.905

Harwood 4 15.9 18.9 8,753 14 0.828

Harwood 5 22.9 20.2 8,753 87 0.855

Harwood 6 23.3 20.7 8,753 90 0.831

Harwood 7 18.8 19.0 8,753 31 0.846

Harwood 8 15.5 19.6 8,753 46 0.776

Harwood 9 13.7 17.6 8,752 18 0.821

Harwood 10 22.0 24.8 8,752 260 0.874

Harwood 11 22.3 20.1 8,752 25 0.773

Harwood 12 26.2 22.9 8,752 292 0.871

Harwood 14 19.9 20.7 7,925 119 0.864

Harwood 16 15.4 20.3 7,925 68 0.838

Harwood 17 20.0 22.0 7,925 105 0.856

Kershope (4.9)b 21 22.6 10.5 4 21 N/A

Kershope (1.8) 25 14.5 12.1 1 17 N/A

Kershope (3.4) 26 20.3 10.9 3 42 N/A

Kershope (2.4) 34 15.6 11.5 1 15 N/A

Kershope (4.9) 43 21.8 11.8 1 43 N/A

Kershope (3.4) 45 19.9 10.4 4 26 N/A

Kershope (2.8) 56 17.5 11.9 4 44 N/A

Kershope (2.8) 64 18.3 11.5 3 31 N/A

Kershope (2.4) 70 15.1 11.5 4 14 N/A

Kershope (1.8) 71 14.3 12.7 13 14 N/A

Kershope (1.8) 121 14.2 12.1 1 6.3 N/A

a Tree species. EL European larch SS Sitka spruceb Treatment spacing (m)

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tree (e.g. 12 m tall) could effectively block the inclusion of

an overstorey tree (e.g. 25 m tall) in the calculation of

competition index.

All trees classified as neighbours were measured (D1.3)

and mapped with the exceptions detailed below, which

arose because only at Harwood was the experimental

design specifically set up to study competition indices. At

Kyloe, Tree 108 lay at the edge of the assessment area, and

its neighbours outside this area were not mapped or mea-

sured. At Kershope, Trees 25 and 56 lay at the edge of the

assessment areas within two plots. The very regular layout

of the trees within and around the assessment plots at

Kershope enabled the positions of the one unmapped

neighbour for each of these trees to be approximated. The

diameters of these two neighbours were estimated as the

average of the diameters of the remaining neighbours for

each of Tree 25 and 56. Finally, Tree 121 at Kershope was

missing a diameter measurement for one of its neighbours.

Again, this was estimated as the average of the diameters

of the remaining neighbours. There was no evidence of

inconsistency in the results from these trees compared with

other trees at this site.

Instrumentation

Wind speed and direction

Wind speed and direction were measured at or near the top

of the canopy at each site. Table 3 gives details of instru-

mentation and data loggers used for this. The cup ane-

mometer data were all recorded at 3 Hz and subsequently

processed to obtain average hourly wind speed. At Clo-

caenog, the upper anemometer was at the limit using the

tower available; it was slightly below the height of the

tallest trees. To be consistent across all sites for the height

of the wind speed measurement relative to the top of the

canopy, we used data from the anemometer at 27 m for

Kyloe; at Kershope, we interpolated to 13 m, and at

Harwood used the cup anemometer installed at 23 m. All

wind speeds used in the analysis were therefore for the

height as close as possible to that of the maximum tree

height.

Measurement of turning moment

Turning moment at Clocaenog, Kyloe and Harwood was

measured using strain transducers, which are described in

detail elsewhere (Blackburn 1997; Moore et al. 2005).

Each transducer is screwed into the tree at two points. Tree

bending causes this distance to increase or decrease and

causes a change in electrical resistance of the strain gauge

within the instrument. Strain (e) is defined as:

e ¼ DL=L

where DL is change in distance between attachment points,

and L is total distance. To enable the strain output to be

converted into turning moment, each sample tree was cali-

brated in two directions by applying a known load (measured

with a load cell) at a known height (generally 0.4–0.6 9 tree

height). The load was applied incrementally in four to six

stages and then released in stages. The load was converted to

turning moment, and a regression of turning moment against

output from the strain gauge provided a calibration coeffi-

cient for each strain transducer in situ. Further details of the

methodology can be found in Gardiner et al. (1997);

Blackburn (1997) and Wellpott (2008).

At Clocaenog, Kyloe and Harwood, two strain trans-

ducers were mounted orthogonally on the north and east

sides of each sample tree (to minimise the potential heating

effects of direct sunlight, which would cause differential

heating of the wood and metal), at approximately 1.3 m

above the ground. Output was logged at 4 Hz using three

CR10s at Clocaenog, a CR23X at Kyloe and four CR1000s

at Harwood (all loggers from Campbell Scientific, Logan,

USA). At Kyloe, a multiplexer (AM416, Campbell Scien-

tific, Logan, USA) was used for four of the sample trees;

Table 3 Instrumentation and data loggers used to measure wind speed and direction at the four sample sites

Forest Loggera Wind speed Wind direction

Height (m) Instrumentb Height (m) Instrumentb

Clocaenog 21X 30.8, 27 Cup anemometer 27 Wind vane

Kyloe CR23 30.8, 27 Cup anemometer 27 Wind vane

Harwood CR10 23 Cup anemometerc 29.7 Sonic anemometerd

Kershope see Gardiner et al. (1997) 14.8, 10.8 Sonic/Leda Not used

a All loggers were Campbell Scientific, Logan, USAb All cup anemometers were NRG#40, and wind vanes were NRG#200P (NRG Systems, VT, USA)c Installed after start of experiment. Data set was backfilled using data from the sonic anemometer at 29 m, based on a linear regression between

the two data sets for a 32-day period of overlapd Logged by University of Edinburgh

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these were activated only when wind speed above the

canopy exceeded 7 m s-1. At Kershope, LVDT (linear

variable differential transformer) transducers were used to

measure strain (Gardiner et al. 1997). The basic set-up and

calibration of these transducers on the individual trees was

the same as that used for the other three sites. Output was

recorded at 10 Hz, but data were extracted at 5 Hz for this

analysis to be more closely comparable with information

from the other three sites.

Data processing

Strain output from the two strain transducers (or LVDTs at

Kershope) on each sample tree was converted to turning

moment using the individual calibration coefficient for

each transducer derived from the pulling calibration. The

orthogonal turning moments were then combined to pro-

duce a single turning moment. The maximum turning

moment for each hour was obtained using the Gumbel

method (Cook 1985): each hour-long section of the time

series was divided into 20 periods of equal length (3 min),

and the maximum absolute turning moment for each period

was identified. The mode of these 20 values was taken as

the maximum turning moment for the hour. This is a robust

method that gives the most probable extreme value that

will be experienced during an hourly period. For each tree,

the relationship was investigated between the maximum

hourly turning moment and the average hourly wind speed.

All statistics were done using the open-source statistical

package R (R Development Core Team 2008) and Genstat

(Payne et al. 2008).

Competition indices

To investigate whether the bending response of trees to

wind loading was related to their position or status within

the stand, three distance-independent and five distance-

dependent competition indices were calculated for the

sample trees (Table 4). Distance-independent indices have

the advantage that individual tree positions are not

required, so they can be calculated from only a stand

diameter distribution, using all of the trees in each

assessment plot. These indices were scaled for differences

in plot size. The distance-dependent indices were calcu-

lated using the neighbours derived from the Voronoi

polygons.

The distance-independent indices were (i) sum of basal

area of trees larger than the subject tree (CBAL); (ii) sum of

diameter ratio of neighbour and subject trees (CDR); and

(iii) as for CDR but only for trees larger than the subject tree

(CDRL). These were calculated for all sample trees at all

sites. The first three distance-dependent indices (Table 4)

were calculated for all sites, using proximity in conjunction

with diameter ratios of neighbour and subject trees. The

first of these (CHegyi) was originally presented by Hegyi

(1974). C11 and C12 (numbered after Rouvinen and

Kuuluvainen 1997) are based on CHegyi, but place more

weight on proximity and diameter ratio, respectively.

These three indices were not calculated for Kyloe Tree

108, as its neighbours were not all mapped. At Clocaenog,

where crown information was available, two additional

distance-dependent indices, requiring crown characteris-

tics, were calculated for the sample trees (Table 4). The

first of these (CCWR) used proximity, and ratio of crown

width of competitor and subject trees (Bruchert 2003). The

most data-demanding index was developed by Schutz

(1989) to take into account differences in crown shape in

mixed-species stands. It uses tree height in addition to

crown radius and proximity (CSchutz).

Results

Turning moment coefficient

For each individual tree at Clocaenog, Kyloe and Harwood,

there was a linear relationship between the hourly maxi-

mum turning moment (Mmax) and the square of the hourly

mean wind speed at the canopy top; all regressions were

forced through zero (correlation coefficients are shown in

Table 4 Details of the competition indices calculated for the sample

trees

Distance-independent indices Source

CBAL ¼P

gc � y Biging and Dobbertin

1995

CDR ¼P dc

dsKiernan et al. 2008

CDRL ¼P dc

ds� y Kiernan et al. 2008

Distance-dependent indices using tree diameter

CHegyi ¼Pn

c¼1

dc=ds

Dcs

Hegyi 1974

C11 ¼Pn

c¼1

dc=ds

D2cs

Rouvinen and

Kuuluvainen 1997

C12 ¼Pn

c¼1

dc=dsð Þ2Dcs

Rouvinen and

Kuuluvainen 1997

Distance-dependent indices using crown and height measurements

CCWR ¼Pn

c¼1

Rc=Rsð Þ1:3D0:4

cs

Bruchert 2003

CSchutz ¼Pn

c¼1

0:5� Dcs� RcþRsð ÞRcþRsð Þ

þ 0:65 � Hc�Hs

Dcs

Schutz 1989

where g (m2) is basal area of competitor tree; y = 1 for trees with

diameter larger than that of the subject tree, otherwise y = 0; d is

D1.3, and subscripts s and c represent subject and competitor tree,

respectively; Dcs (m) is distance between subject and competitor tree;

R (m) is crown radius, and H (m) is tree height

208 Eur J Forest Res (2012) 131:203–217

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Table 2). For each site, the tree with the median correlation

coefficient was selected to illustrate this relationship

(Fig. 1). For Kyloe, no difference was found for leaf-on

and leaf-off periods; all data are presented together. These

results indicate that each tree has a consistent response to

increased wind loading, and in this paper, we define this

ratio (the gradient of the line Mmax vs. u2) as the turning

moment coefficient (TC). Residuals were normally dis-

tributed, with no trend to suggest non-linearity at higher

wind speeds. As there were insufficient data points for the

trees at Kershope to calculate a regression, TC for each tree

was calculated as the average of Mmax/u2 for the individual

hours of data available for that tree. Data from the refer-

ence tree, which had 13 h of measurement, are shown in

Fig. 1.

In some cases, the data showed a clear influence of wind

direction in the relationship between Mmax and u2. For

example, Tree 41 at Clocaenog had a value for TC (gradient

of relationship) over twice as high when the wind was from

the west and northwest (TC = 399) compared to when the

wind was from the southwest (TC = 167). The value pre-

sented in this paper was calculated for all wind directions

combined and lay between the two extreme values

(TC = 217) (Fig. 2). These differences correspond to the

positions of neighbouring trees: there was a canopy gap to

the west and northwest, and shelter from a neighbouring

crown to the southwest.

Larger trees had a higher TC than smaller trees at each

site (Fig. 3; note the difference scales on both axes).

0 10 20 30 40 50 60 70

010

000

3000

050

000

u2 (m2 s−2)

Mm

ax(N

m)

(a)

0 20 40 60 80 100 120 140

010

000

2000

030

000

u2 (m2 s−2)

Mm

ax(N

m)

(b)

0 10 20 30 40

010

0020

0030

0040

00

u2 (m2 s−2)

Mm

ax(N

m)

(c)

20 30 40 50

200

400

600

800

u2 (m2 s−2)

Mm

ax(N

m)

(d)

Fig. 1 Maximum hourly

turning moment (Mmax) plotted

against the square of the average

hourly wind speed measured at

the canopy top (u2) for one tree

from each forest. a Clocaenog

Tree 37, b Kyloe Tree 108

(overstorey larch), c Harwood

Tree 5, d Kershope Tree 71.

Note the differences in both the

x- and y-axes scales

0 10 20 30 40 50 60 70

050

0010

000

1500

0

u2 (m2 s−2)

Mm

ax(N

m)

Fig. 2 Maximum hourly turning moment (Mmax) plotted against the

square of the average hourly wind speed measured at the canopy top

(u2) for Tree 41 from Clocaenog, separated by wind direction. Filledcircles winds from west and northwest; open triangles winds from

southwest; open circles all other directions

Eur J Forest Res (2012) 131:203–217 209

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D1.32 H was chosen as an indicator of size as it showed a

more consistent relationship with TC across the sites than

either D1.3 or height alone. It has also been found in pre-

vious tree-pulling studies to be the parameter best corre-

lated with resistance to overturning (e.g. Peltola et al.

2000). The relationships show more scatter for Harwood

and Kershope, where size differences between the sample

trees were less pronounced than in the more mature stands

at Clocaenog and Kyloe. The slope of the linear relation-

ship, with an origin of zero, between TC and tree size did

not differ statistically significantly between Clocaenog,

Kyloe and Harwood. A single fit can therefore be put

through all data from these sites (Fig. 4). The slope fit to

data from Kershope was also not significantly different, but

had a high standard error. Considering the paucity of data

on which the Kershope values are based, and the differ-

ences between the five respacing treatments at this site, the

general agreement is extremely encouraging. Note that the

three understorey Sitka spruce at Kyloe had very much

lower values of TC (range 5–17 kg) than the overstorey

trees (range 236–689 kg). The values were in fact similar

to TC values for the trees at Kershope, which were com-

parable in tree size. However, the wind loading was still

related to D1.32 H in the same manner.

Relationship between TC and competition indices

Figures 5 to 8 show the relationship between TC and each of

the six competition indices (eight for Clocaenog) for each

2 4 6 8 10

200

400

600

800

1200

D1.32 H (m3)

Tc

(kg)

(a)

0 1 2 3 4

010

030

050

070

0

D1.32 H (m3)

Tc

( kg)

(b)

0.5 1.0 1.5

5010

015

020

025

030

0

D1.32 H (m3)

Tc

( kg)

(c)

0.25 0.35 0.45 0.55

1020

3040

D1.32 H (m3)

Tc(k

g)

(d)

Fig. 3 Turning moment

coefficient (TC) plotted against

D1.32 H for a Clocaenog, b Kyloe,

c Harwood and d Kershope.

Note the differences in both the

x- and y-axes scales

0 2 4 6 8 10

020

060

010

00

D1.32 H (m3)

TC

( kg)

Fig. 4 Turning moment coefficient (TC) plotted against D1.32 H for all

four forests together. Closed circles Clocaenog; open squares Kyloe;

crosses Harwood; open triangles Kershope. The equation of the line,

fitted to all data points except Kershope, is y = 117.3�x

210 Eur J Forest Res (2012) 131:203–217

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site. Regardless of site, all indices show a decrease in TC

with increasing competition. It is important to note that for

each competition index, the relationship differs between

sites, e.g. if TC was plotted against CBAL for all sites toge-

ther, they would not lie on the same line. At Clocaenog,

almost all indices show a good relationship with TC (Fig. 5).

The two indices calculated using crown dimensions as well

as diameter and distance between neighbours (CCWR and

CSchutz) have a poorer relationship than the simpler indices.

The relationships are approximately linear, although Tree 4

(which had the largest D1.3 and D1.32 H) lies above the overall

trend for many of the indices. For Kyloe (Fig. 6), one of the

understorey Sitka spruce has a very much larger D1.3 than

the other two sampled understorey trees. The values of

CHegyi, C11 and C12 for this tree are closer to those of the

overstorey trees than the other understorey trees, despite its

low value of TC (17 kg). This difference is less pronounced

in the distance-independent indices. For the overstorey

trees, the distance-independent indices relate better to TC

than the distance-dependent indices. Similarly to the

0 5 10 15 20 25 30

200

400

600

800

1200

CBAL

Tc(k

g)

(a)

200 250 300 350 400

200

400

600

800

1200

CDR

Tc(k

g )(b)

0 100 200 300 400

200

400

600

800

1200

CDRL

Tc(k

g)

(c)

0.6 0.8 1.0 1.2 1.4

200

400

600

800

1200

CHegyi

Tc

(kg )

(d)

0.08 0.12 0.16 0.20

200

400

600

800

1200

C11

Tc(k

g )

(e)

0.05 0.10 0.15 0.20 0.25 0.30

200

400

600

800

1200

C12

Tc(k

g)

(f)

2 3 4 5

200

400

600

800

1200

CCWR

Tc

(kg)

(g)

0 1 2 3 4 5

200

400

600

800

1200

CSchütz

Tc(k

g)

(h)

Fig. 5 Turning moment coefficient (TC) plotted against each com-

petition index for Clocaenog. See text for detailed definition of the

indices. a, b and c are distance-independent; d, e and f are distance-

dependent derived from diameter ratios; g and h are distance-

dependent, utilising additional crown and height information

Eur J Forest Res (2012) 131:203–217 211

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relationship with size, the relationships between TC and

competition indices at Harwood (Fig. 7) show more scatter

than at Clocaenog or Kyloe. Again, the spatial indices offer

no improvement over the non-spatial indices. The data from

Kershope (Fig. 8), although showing scatter, corroborate

the trends found at the other sites.

For all of the sites, the distance-independent indices

perform at least as well as the distance-dependent ones. In

fact CBAL, the simplest distance-independent index asses-

sed, shows the most consistently good relationship with TC

for all sites, being significant at the 99.9% level for

Clocaenog, Kyloe and Harwood. This index is used below

to illustrate the potential application of these results in

modelling wind risk to trees of different sizes within a

forest following a thinning.

Discussion

This work shows the first quantification, as far as the

authors are aware, of the bending response of trees of

different sizes within a stand at a range of wind speeds.

Assuming that the relationship demonstrated between Mmax

and the square of the canopy-top wind speed is linear up to

critical turning moment, the wind speed associated with the

critical turning moment of a given tree can be estimated. At

these study sites, the conditions sampled at Clocaenog

came closest to critical conditions, with the calculated

critical turning moment of the trees being approximately

three times the maximum turning moment measured during

this experiment. This corresponds to an increase in wind

speed of about 70% above that which was measured during

the experiment.

The relationship between tree size and TC fitted well

across all four sites, despite substantial differences in tree

size, previous management, stand structure and two con-

trasting overstorey species (one of which was measured

both with and without needles).

The Gumbel method used to calculate Mmax from the

time series data was chosen to avoid an overemphasis on

single extreme values in a time period. Earlier analyses of

the data from Clocaenog (Achim et al. 2007; Wellpott

2008) and Kyloe (A. Wellpott, pers. comm.) used the

single highest turning moment in a 10-minute period to

quantify the relationship between maximum turning

moment and canopy-top wind speed. As expected, the

4 6 8 10 12 14 16 18

010

030

050

070

0

CBAL

Tc

(kg)

(a)

200 300 400 500

010

030

050

070

0

CDR

Tc(k

g )

(b)

100 200 300 400 500

010

030

050

070

0

CDRL

Tc(k

g)

(c)

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

010

030

050

070

0

CHegyi

Tc( k

g)

(d)

0.0 0.5 1.0 1.5 2.0

010

030

050

070

0

C11

Tc(k

g)(e)

2 4 6 8 10 12

010

030

050

070

0

C12

Tc(k

g)

(f)

Fig. 6 Turning moment coefficient (TC) plotted against each competition index for Kyloe. See text for detailed definition of the indices. a, b and

c are distance-independent; d, e and f are distance-dependent

212 Eur J Forest Res (2012) 131:203–217

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Gumbel method gave lower values of Mmax, being

approximately 70 and 80% of the single absolute Mmax

values for Clocaenog and Kyloe, respectively.

The relationships found between tree size and TC were

all measured in stands that had not been recently thinned.

All trees should therefore be well-acclimated to their

environment. If a stand was thinned, the response of a tree

to wind loading might be expected to be immediately

affected, whereas its size would not. The relationships with

competition indices indicate that within a stand, the trees

with higher local competition have a lower TC, i.e. expe-

rience a smaller turning moment for a given wind speed

than more exposed trees (with lower competition index).

This relationship is upheld to some extent for all sites, for

all indices in this study. The relationship itself is not sur-

prising, as competition influences tree size, and tree size

has been shown above to relate to TC; its value lies in its

potential to enable us to examine the impact of thinning on

the TC of individual stands.

The relationships between TC and competition indices

showed less scatter for the more differentiated widely

spaced stands (Clocaenog and Kyloe). At Harwood, scatter

leads us to suggest that acclimation to wind loading may

not be the major driving force and that competition for

light may be equally important. This could lead to those

trees that are struggling for light compromising their

mechanical stability in order to gain height and access to

light. At Kershope, the scatter shown in Fig. 8 is unsur-

prising, due to the extremely limited data set, and the

different spacing conditions in the five treatment plots. In

the more dense treatments, the same processes that are

operating at Harwood may also be at work.

These observations can be understood in terms of ac-

climative growth and the requirement of trees also to bal-

ance allocation of assimilates for various other functions

(see Niklas and Spatz 2006). Where wind movement is

limited, for example by the proximity of neighbours in a

close stand, little acclimative growth is required to provide

mechanical stability (Nicoll and Ray 1996). In this situa-

tion, allocation patterns within trees would be expected to

be driven more by other functional requirements such as

maximising growth for access to light. This non-mechan-

ical priority would only be a problem for the tree if

exposure to wind was suddenly altered, such as by forest

20 30 40 50 60

5010

015

020

025

030

0

CBAL

Tc(k

g)(a)

1400 1800 2200 2600

5010

015

020

025

030

0

CDR

Tc( k

g)

(b)

500 1000 1500 2000 2500

5010

015

020

025

030

0

CDRL

Tc(k

g)

(c)

1.5 2.0 2.5 3.0 3.5

5010

015

020

025

030

0

CHegyi

Tc

(kg )

(d)

1.0 1.5 2.0 2.5

5010

015

020

025

030

0

C11

Tc(k

g )(e)

1 2 3 4 5 6

5010

015

020

025

030

0

C12

Tc(k

g )

(f)

Fig. 7 Turning moment coefficient (TC) plotted against each competition index for Harwood. See text for detailed definition of the indices.

a, b and c are distance-independent; d, e and f are distance-dependent

Eur J Forest Res (2012) 131:203–217 213

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thinning operations, at which time acclimation to

mechanical stress would again become a priority.

Another surprising finding is that the relationship

between D1.32 H and TC was the same for the larch at Kyloe

and all of the Sitka spruce data (Fig. 4) despite differences

in the crown characteristics and wood properties of the two

species. This suggests that these two conifers may have

very similar allocation strategies for dealing with the threat

of wind damage in their balance between crown, stem and

root development. This is consistent with the statistically

similar resistance to overturning found by Nicoll et al.

(2006) for many of the combinations of conifer species and

soil types that they compared. There may also have been

changes to the wood properties of the trees in response to

differences in individual wind loading, such as found by

Bruchert and Gardiner (2006), but we were unable to test

this because no wood property measurements were taken in

any of the experiments.

At Clocaenog, the two more data-demanding indices

(CCWR and CSchutz) showed more scatter against TC than

the simpler indices. In fact for all the sites, the distance-

independent indices were as good as, or better than, those

indices using tree positions. This suggests that the stand as

a whole has an influence on the overall sheltering of a tree

and its consequent response to wind loading. This has an

advantage in modelling applications, as these indices are

computationally simpler, and it is easier to obtain data for

parameterisation and validation.

For a well-spaced stand with substantial canopy gaps

adjacent to some of the trees, a distance-dependent index

incorporating directionality of the wind might produce a

better relationship between TC and competition index.

Results from Tree 41 at Clocaenog showed a twofold dif-

ference in TC depending on wind direction. To incorporate

these effects into wind risk modelling would require both

distance-dependent stand representation, and knowledge of

the distribution of wind speed and direction for a given

forest.

Potential of the approach for wind risk modelling

Although we are aware of limitations of our results (see

following section), the relationships found in this study

could potentially be applied to calculate the wind risk of

individual trees in any stand structure. Subject to valida-

tion in other forest stands, the relationship between tree

size (D1.32 H) and TC could be used to estimate TC for

different trees within a well-acclimated stand. The critical

10 15 20 25

1020

3040

CBAL

Tc(k

g)(a)

500 1000 1500 2000

1020

3040

CDR

Tc(k

g )

(b)

200 400 600 800 1200

1020

3040

CDRL

Tc(k

g)

(c)

1.0 1.5 2.0 2.5 3.0

1020

3040

CHegyi

Tc

( kg)

(d)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

1020

3040

C11

Tc(k

g)(e)

1.0 1.5 2.0 2.5 3.0 3.5 4.0

1020

3040

C12

Tc(k

g)

(f)

Fig. 8 Turning moment coefficient (TC) plotted against each competition index for Kershope. See text for detailed definition of the indices.

a, b and c are distance-independent; d, e and f are distance-dependent

214 Eur J Forest Res (2012) 131:203–217

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wind speed for each tree could then be calculated, based

on individual tree values of critical turning moment. All

else being equal, as the trees grow, D1.32 H will increase,

and TC of each tree will increase correspondingly. Cou-

pled with information about the wind climate at that site,

this will allow a distribution of risk within the stand to be

generated.

However, if the stand is thinned, the response of an

individual tree might be expected to change as its neigh-

bours are removed. Using D1.32 H will not account for this

immediate change in local sheltering effect, because tree

size will not change immediately but local shelter will.

Prior to thinning, it would be necessary to calculate a

competition index, e.g. CBAL, for each tree, which would

allow derivation of the TC versus CBAL relationship for that

stand. After a thinning, the trees will be the same size as

before, but generally have a lower CBAL. Assuming that the

individual trees remain on the line representing this rela-

tionship after thinning, the new CBAL values can be used to

estimate new TC values, and therefore a revised wind risk

distribution for the stand immediately after thinning.

If the relationship between size and TC remains the same

for acclimated trees as a stand grows, it follows that the

relationship between TC and competition index will change

with time. Tree size will increase with time, indicating an

increase in TC. If the relationship between TC and com-

petition index was to remain the same, then this increase in

TC would be met with a decrease in competition index.

However, assuming for illustrative purposes that all trees

experience the same percentage growth, then CBAL would

increase for each tree, and those indices based on diameter

ratios would remain the same. Crucially, in general, the

competition indices would not decrease. The relationship

between TC and competition index can therefore be used

only to indicate the immediate change in TC after a thin-

ning. It will not indicate how TC changes as the tree

acclimates to the new environment.

Limitations and future work

The values of TC for individual trees within a stand depend

on the wind speed at the canopy top. Wind speed can

change rapidly with height in this region, so small differ-

ences in height of the wind speed measurement potentially

have a large effect on the resulting TC values. Further, the

requirement for wind speed in parameterising the response

of individual trees to wind loading is onerous, as the

installation of a mast to raise an anemometer to canopy top

requires investment both in equipment and experimental

set-up time. Ideally, wind speed would have been measured

further above the forest canopy. However, at Clocaenog,

this was not possible with the equipment available.

In this study, measurements were taken on well-accli-

mated trees at four sites. The experiment needs to be

repeated in a range of different forest stands, including

stands with complex structure, to test the relationships

found, particularly the relationship between TC and tree

size and how it changes through time as a stand grows. TC

and competition indices need to be quantified before and

after a thinning, to confirm that individual trees within a

stand lie on the same TC versus competition index line

immediately after intervention. Instrumentation of trees

and monitoring them for a period of years following a

thinning or the creation of a new edge would provide

valuable information on the rate at which trees adapt to

changes in wind conditions, and on how the relationship

between TC and competition indices changes as the stand

grows.

The application of the relationship between Mmax and

wind speed at the canopy top to calculate critical wind

speed is based on the assumption that this relationship

remains linear at higher wind speeds than were recorded in

this study. Although there is no evidence from the residuals

for each tree that the form of the relationship changes at

high wind speeds, further measurements would be required

to validate this.

Conclusions

This study has quantified the relationship between hourly

maximum turning moment and hourly average canopy-top

wind speed for trees of different sizes in four forest stands.

At all sites, each tree showed a strong linear relationship

between maximum hourly turning moment and the square

of the average hourly wind speed measured at the canopy

top, characterising the turning response of an individual

tree at a given wind speed. This response (the gradient of

the line Mmax vs. u2), termed here TC, was found to be

correlated with tree size (D1.32 H), in a relationship that

differed little between the sites studied and indicated a

consistent acclimation to wind loading for trees of varying

size and social status within the stand. TC directly related

the maximum turning moment to the mean wind speed,

thereby offering a potential improvement on current

methods within wind risk models, which require an

adjustment from mean to extreme wind loading. At each

site studied, there was also a relationship between TC and

competition indices, with a decrease in TC with increasing

competition. Distance-independent indices performed bet-

ter than distance-dependent indices. The relationships dif-

fered for each site, and logically, they would also vary with

time for a given forest stand. Use of these relationships has

potential for modelling the immediate change in TC for

individual trees following a thinning. However, further

Eur J Forest Res (2012) 131:203–217 215

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work needs to be carried out to explore these relationships

before incorporating them into the next generation of forest

wind risk models, which will be able to calculate the wind

risk to individual trees, the distribution of risk within

stands, and how these risks change over time.

Acknowledgments All work presented in this paper was funded by

the G.B. Forestry Commission. We would also like to thank the

following people for assistance with this work: Dave Brooks, John

Strachan and Jim Nicholl for technical help with the logging systems;

Arne Pommerening and the Tyfiant Coed team (Bangor University)

for access to, and data from, Clocaenog; Peter Hale (Hale Associa-

tion) and Ian Robinson (Scottish Woodland), for allowing us to

conduct an experiment within Kyloe Wood; Sigrid Dengel (Univer-

sity of Edinburgh) for providing wind speed and direction data for

Harwood; Carl Foster, Brian Jones, Dai Evans, Shaun Mochan, Justin

Chappell, Sophie Bertin and Colin Gordon for assistance with field

work; Cynthia Moore for data processing and Tom Connolly for

statistical analysis. Thanks also Victoria Stokes and two anonymous

reviewers for helpful comments on this manuscript.

Conflict of interest The authors declare that they have no conflict

of interest

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