Hydrological properties of bark of selected
forest tree species. Part I: the coefficient of
development of the interception surface of
bark
Ilek Anna & Kucza Jarosław
Trees
Structure and Function
ISSN 0931-1890
Volume 28
Number 3
Trees (2014) 28:831-839
DOI 10.1007/s00468-014-0995-0
1 23
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1 23
Trees (2014) 28:831–839
DOI 10.1007/s00468-014-0995-0
ORIGINAL PAPER
Hydrological properties of bark of selected forest tree species.
Part I: the coefficient of development of the interception surface
of bark
Ilek Anna • Kucza Jarosław
Received: 8 August 2013 / Revised: 3 February 2014 / Accepted: 12 February 2014 / Published online: 5 March 2014
Ó The Author(s) 2014. This article is published with open access at Springerlink.com
Abstract
Key message The coefficient of development of the
interception surface of bark allows for objective
assessment of the degree of bark surface differentiation
between different species.
Abstract Inter-species differentiation of bark morphology
and its variability progressing with tree age suggest that the
hydrological properties of the bark of particular species
depend on the degree of development of the outer bark
surface of trees. The aim of the present research was to
develop a method of calculating the actual bark surface
with the use of the coefficient of development of the
interception surface of bark, describing the degree of
development of the outer bark surface of trees. The primary
aim was to show inter-species differentiation of the coefficient of development of the interception surface of bark at
breast height, as well as its variability within a single
species, progressing with tree age. The present study shows
the results obtained for 77 bark samples collected at the
breast height of the following tree species: Pinus sylvestris
L., Larix decidua Mill., Abies alba Mill., Picea abies L.,
Quercus robur L., Fagus sylvatica L., Acer pseudoplatanus
L. and Betula pendula Ehrh. In all of the examined species,
the coefficient of development of the interception surface
of bark shows a distinct relation to the breast-height
Communicated by H. Pfanz.
I. Anna (&) K. Jarosław
Department of Forest Engineering, Faculty of Forestry,
University of Agriculture in Cracow, Al. 29 Listopada 46,
31425 Cracow, Poland
e-mail: a.ilek@wp.pl
K. Jarosław
e-mail: j.kucza@ur.krakow.pl
diameter. The highest values of coefficient of development
of the interception surface of bark among the thickest trees
are reached by: L. decidua—2.56, Pinus sylvestris—2.28
and B. pendula—2.44, whereas the lowest values are
reached by the bark of European beech F. sylvatica—1.07.
The coefficient of development of the interception surface
of bark describes the morphological differentiation of the
outer bark surface of trees in an objective way. Owing to its
mathematical form, the coefficient of development of the
interception surface of bark may be useful in the modelling
of hydrological processes occurring in forest ecosystems.
Keywords Forest hydrology Plant interception Bark of
forest trees Bark surface Coefficient of development of
the interception surface of bark
Introduction
The bark of forest trees has a number of various functions.
From the point of view of the formation of water balance in
forest ecosystems, what is focused on is the role of bark in
rainfall retention (Herwitz 1985; Levia and Herwitz 2005;
Levia and Wubbena 2006; Valovà and Bieleszovà 2008) as
well as the influence of the differences in bark roughness
and water capacity in different tree species on the size of
stemflow production (Návar 1993; Aboal et al. 1999; Levia
et al. 2010; Van Stan and Levia 2010). Bark constitutes the
environment for the life of numerous organisms, such as
bryophytes and lichens, whose species composition and
distribution over the bark surface largely depend on differences in the texture and acidity of the bark of different
forest tree species (Bates and Brown 1981; Stephenson
1989; Kuusinen 1996; Everhart et al. 2009; Öztürk and
Güvenç 2010; Öztürk and Oran 2011). In the literature, it is
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832
stated that bark may be used in the biomonitoring of air
pollution (Schulz et al. 1999) and that it is important in the
protection of the vascular cambium during the occurrence
of heat stress caused by forest fires. Among important
factors that are frequently decisive in the survival of a tree
during a fire are bark thickness (Harmon 1984; Hengst and
Dawson 1994; Pinard and Huffman 1997; Barlow et al.
2003) and its volume density (Bauer et al. 2010).
The interception of rainfall by forest trees is a complex
process, dependent on many factors, such as rainfall
intensity, duration, and raindrop size (Calder 1996, 1999;
Suliński et al. 2001). The interception ability is closely
connected with the total surface of the overground parts of
a plant, which is largely determined by the plant species, its
height, weight, and morphological features (Cebulska and
Osuch 1998; Keim et al. 2006). Research on plant interception, understood as a process of rainfall detention by the
whole surface of a plant (Suliński et al. 2001), do not allow
for distinguishing the extent to which the amount of
intercepted water is affected by the surface of leaves,
branches or the stem. Research focused only on the rainwater interception by leaves may understate the actual
water capacity of the tree crowns, and consequently lead to
an underestimation of the role of bark in rainwater retention (Klaassen et al. 1998). Given the heterogeneity of the
various parts of the plant, its surfaces with different
retention properties must be considered separately. Therefore, there is a need to divide the plant into the surface of
leaves, shoots and bark, whose water retention properties
vary depending on the age (Osuch 1998; Osuch et al.
2005a, b).
The bark of forest trees is a structure which undergoes
constant changes due to the dying of some tissues and the
growth of new ones (Grochowski 1990). The water
capacity of bark depends on the properties of the bark
tissue, such as its thickness and texture, which change with
the tree age and thickness (Hengst and Dawson 1994; Pinard and Huffman 1997; Pypker et al. 2011). The bark of
different species is very diversified with respect to its
thickness and texture—from extremely rough to completely smooth (Jackson 1979; West 2009). For example,
the surface of bark of Scots pine Pinus sylvestris L. and
beech Fagus sylvatica L., of the same thickness and height,
will differ due to their different structure. Pine bark has
numerous cracks and fissures, while beech bark is relatively smooth over the entire length of the stem. Thus, the
active area of the bark taking part in the interception of
rainwater will differ greatly between these two species.
Differences in the degree of development of the bark surface between these species may suggest that the potential
interception capacities of the pine bark surface will be
larger than the potential interception capacities of the
beech bark surface.
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Trees (2014) 28:831–839
Morphological differentiation of bark occurs also within
a single species. For example, Pawłowski (1956) described
three types of outer bark of Norway spruce Picea abies L.:
numularis with round flakes, squamata with slightly elongated flakes and corticata with quite thick flakes. Similarly,
Eremin (1977) classified the three types of outer bark in
spruce as four categories by including anatomical characteristics. Etverk (1972) attempted to analyse the succession
of features of outer bark in spruce by distinguishing the
following forms: rimescocarta, globocarta and an intermediate form. According to research by Hoffmann (1958),
the features of bark in Norway spruce are also related to the
conditions of tree growth. The richer and more abundant
the habitat, the thicker the bark formed by this species.
The differentiation of the bark surface is relatively hard
to parametrize and there is little information on the methods of its measurement. An attempt to determine the
allometry of bark thickness was made by Harmon (1984) as
well as by Adams and Jackson (1995). MacFarlane and
Luo (2009) described the bark structure of 15 tree species
using the bark-fissure index (BFI) while Van Stan et al.
(2010) constructed a device which measures the bark
microrelief.
Owing to inter-species differentiation in the bark morphology and its variability progressing with tree age,
research on interception and water capacity of bark should
take into consideration its actual surface. Therefore, the
object of this study is the actual surface of the bark of the
stem of selected forest tree species, including its morphological properties. The aim of the study was (1) to develop
and propose a method of calculating the actual surface of
the bark Ad by means of the coefficient of development of
the interception surface Csd. describing the degree of
development of the outer bark layer in trees; and (2) to
demonstrate the interspecies differences in the shaping of
the coefficient of development of the interception surface
Csd at breast height and its variability within a single
species, progressing with the age of trees.
The coefficient of development of the interception surface Csd can be defined as the ratio of the actual surface Ad
of a bark sample to the surface of a section of the cylinder
corresponding to the smooth surface of the examined
sample. Assuming that the surface of the bark of the stem
was perfectly smooth, the coefficient of development of the
interception surface Csd would have the minimum value of
1.0. The greater the coefficient of development of the
interception surface Csd, the more developed the actual
surface of the stem bark Ad and the greater the theoretical
possibility of retaining the rainwater which is in direct
contact with the bark and which flows down the stem.
The inspiration for the present study was experiments on
the water capacity of the bark of different tree species; their
results are presented in Part II of this study.
Trees (2014) 28:831–839
833
Materials and methods
Determination of the parameters needed to calculate the
actual bark surface Ad required the use of a number of
measurement and calculation procedures, details of which
are shown below.
The research area
Bark samples were collected in the Trzebunia Forest
Subdistrict (49°460 2800 N, 19°510 5100 E), which is part of the
Myślenice Forest District, located in the southern Beskid
Makowski in central Poland. The samples were obtained
from the bark of the trees growing on the mixed mountain
forest habitat, on an eastern slope within the altitudes from
650 to 700 m.
The scope of the research
The study included eight species of forest trees: Scots
pine (P. sylvestris L.), European larch (Larix decidua
Mill.), silver fir (Abies alba Mill.), Norway spruce (P.
abies L.), common oak (Quercus robur L.), European
beech (F. sylvatica L.), sycamore maple (Acer pseudoplatanus L.), and silver birch (Betula pendula Ehrh.). The
bark samples were obtained during the summer of 2011,
after the beginning of the growing season of the trees,
which made it possible to sample the study material
without mechanical damage to bark. The samples were
collected using a saw, a knife and a chisel from the stems
of living trees at breast height (1.3 m) by cutting, on the
tree side facing the top of the slope, possibly rectangular
pieces of bark with the size dependent on the thickness of
the tree. Because the bark samples were obtained from
trees growing under the same site conditions, the elaboration of the results was based on the assumption that tree
thickness is the measure of their age. To demonstrate
variation of the bark surface between the different species
as well as the coefficient of development of the interception surface Csd together with age, from 6 to 11 bark
samples were collected for each species from trees with
thickness ranging from 5 to 60 cm.
The actual bark surface
The actual surface of the bark in each sample was assumed
to be the surface with all irregularities, cracks and cavities.
According to the present authors, the actual surface can be
calculated according to the formula:
Ad ¼ A Csd
ð1Þ
where Ad is the actual surface of the bark sample (cm2);
A is the model surface of a bark sample (cm2), corresponding to the surface of the cylinder slice; Csd is the
coefficient of development of the interception surface,
describing the level of development of the outer bark layer
of the trees.
The model surface
The model surface for all tested samples of bark was calculated according to the formula:
A ¼ la ba
ð2Þ
where A is the model surface (cm2); la is the average length
of the side of the bark sample (cm), parallel to the core of a
tree stem; ba is the average value of the sample width
(curvature) (cm).
The length of the side parallel to the stem core la was
calculated from the arithmetic mean of several lengths li
measured with calipers. Measurements of lengths li were
taken at regular intervals (0.5–1.0 cm), and their number
was dependent on the width of the sample.
When calculating the average width (curvature) of the
bark samples ba, the researchers had to apply the geometrical relationships related to the circle. For this purpose, it
was assumed that the cross section of the examined tree
stems was round. This assumption allowed the calculation
of the average radius of the tree cross section R, based on
standard measurements of the tree diameter at breast height
(DBH), carried out in two directions perpendicular to each
other. The study sought to choose the trees in which the
values of the two diameters did not differ from each other
by more than 2 cm.
To calculate the length of the curvature ba, individual
bark samples were cut with a 0.6 mm thick saw into stripes
with the width s, dependent on the length of the sample
(Fig. 1). For each bark sample, the constant width s was
adopted, located in the range from 0.5 to 1.0 cm. The
division of the bark samples into strips was performed after
the completion of a series of experiments of simulated
rainfall, when the samples were in a state of maximum
filling with water.
The cross sections of the strips of each bark sample were
scanned at a scale of 1:1, in the resolution between 600 and
1,200 dpi. The choice of image resolution was dependent
on the degree of differentiation of the surface of the bark. It
should be noted that although the cross sectional line is
dimensionless, after cutting the bark with a saw with
0.6 mm thickness, the two sides of the cross section were
different from each other. Therefore, the surfaces of the
cross sections were scanned in two versions: first all of the
upper sections and then all bottom sections of the strips
which made up the sample (Fig. 1). Before scanning the
cross sections, it was necessary to check whether the
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Trees (2014) 28:831–839
Fig. 1 An example of the division of a bark sample into strips with corresponding cross sections, where s is the strip width in the range from 0.5
to 1.0 cm; 1, 20 –60 are the upper cross sectional scans of each strip; 2–7 are lower cross sectional scans of the strips
cross sections. Using the formula for the chord length ci,
which is
ci ¼ 2 R sin ui
ð3Þ
the value of the girth angle ui (°) was calculated between
the chord ci, and the tangent ti passing through the extreme
point of the arc on the surface of the bark (Fig. 2). On the
basis of the girth angle ui , for each cross section, the
central angle ai(°) of the arc segment was calculated using
the formula:
ai ¼ 2 ui
Fig. 2 A diagram showing the parameters measured and calculated
for each cross section of a bark strip, where R is the radius of the tree,
ci is the chord of a section of a bark arc, ti is the tangent passing
through the extreme point of the arc, ui is a girth angle, ai is the
central angle of a bark section, di is the length of the cross sectional
contour line, bi is the length of the arc cross section, calculated
according to geometrical relations, b0i is the length of the curvature of
the cross section, calculated in a subjective manner
curvature of the individual strips of bark corresponded to
the radius R of the tree from which it was collected. This
was done by means of previously prepared templates. In
the event, when non-compliance with the radius of the tree
was noted, the templates allow for giving the strips the
shape of the original curvature.
Measurements of all parameters needed for further calculations were made in the SigmaScan Pro.5 software on
the basis of scanned images.
To calculate the curvature ba of a given bark sample, for
each cross section the bark section chord ci was measured
(Fig. 2), which, together with the radius of the tree R, was
used to calculate the length of the curve bi of particular
123
ð4Þ
Knowledge of the central angle ai of a section of the
circle allowed for the calculation of the length of the arc bi
(cm) of individual strips of bark, using the formula:
bi ¼ ðai = 180 Þ p R
ð5Þ
On the basis of the calculated values bi of individual
sections, the length of the curvature of a sample ba was
calculated as the arithmetic mean of all values bi.
The presented procedure for calculating the length of the
average curvature ba of particular bark samples was aimed
to create a uniform and objective basis for these calculations for all examined samples. Figure 2 shows another
way of determining the average length of the curvature of a
bark sample b0a . The method consisted in measuring the
length of curves b0i for individual strips as a line following,
in a subjective manner, possibly the deepest depressions in
the cross section of a given strip. The average length of
curvature of a bark sample b0a was calculated as the arithmetic mean of the value b0i calculated for all cross sections
of a given bark sample. When using this method, formula 2
for the model surface takes the form:
Trees (2014) 28:831–839
A0 ¼ la b0a
835
ð6Þ
where A0 is the model surface of a sample (cm2); la is the
average length of a side of a bark sample, parallel to the
core of the tree stem (cm); b0a is the average width of a
sample, calculated with the subjective method (cm).
Analogously, formula 1 for the calculation of the actual
surface, described in the previous section, takes the form:
A0d
0
¼A
0
Csd
ð7Þ
where A0d is the actual surface of a bark sample (cm2); A0 is
0
is the
the model surface defined by formula 6 (cm2); Csd
coefficient of development of the interception surface of
bark, calculated as described further below.
differentiation of the outer bark layer of trees; it is determined by means of formulas:
Csd ¼
Pn
i¼1
Cski
n
ð10Þ
or
0
Csd ¼
Pn
0
i¼1
Cski
n
ð11Þ
where n is the number of cross sections of a given bark
sample.
The values of the coefficients of development of the
0
interception surface Csd or Csd obtained in this way were
0
used to calculate the actual surface Ad and Ad of bark
samples according to formulas 1 and 7.
The coefficient of development of the interception
surface
Results and discussion
The next stage, leading to the determination of the coefficient of development of the interception surface Csd and
0
Csd
, consists in measuring the length of the contour lines di
of particular cross sections of a given bark sample (Fig. 2).
The length of the contour line di allows for the calculation
of the degree of its distortion with respect to the length of
the curvature bi or b0i of a given cross section. As a measure
of this irregularity, one can regard the coefficient of
development of the contour line of the cross section Cski or
0
Cski
, calculated according to the formulas:
Cski ¼
di
bi
ð8Þ
di0
b0i
ð9Þ
or
0
Cski
¼
where di is the length of the contour line of a given cross
section of the bark (cm); bi and b0i are the lengths of the
curvatures calculated according to the methods described
above (cm).
Assuming that a bark sample was divided into the representative number of strips following the adopted rules,
according to the authors the average value of the coefficient
of development of the contour line of the cross section Csk
0
or Csk
calculated for all cross sections sufficiently illustrates the differentiation of this feature for the entire surface of a given bark sample. Therefore, it is the coefficient
0
of development of the interception surface Csd or Csd that
was regarded as the measure that describes the degree of
Measurements covered the total of 77 bark samples
obtained from the stems of 8 species of living coniferous
and deciduous trees at the height of DBH. The researchers
collected: 10 samples of the bark of Scots pine (P. sylvestris), 11 samples of the bark of European larch (L.
decidua), 10 samples of the bark of silver fir (Abies alba),
11 samples of the bark of Norway spruce (P. abies), 6
samples of the bark of sycamore maple (A. pseudoplatanus), 8 samples of the bark of silver birch (B. pendula), 10
samples of the bark of common oak (Q. robur), and 10
samples of the bark of European beech (F. sylvatica).
The lengths of the average curvatures ba and b0a of
particular bark samples, calculated using the methods
described in the research methodology, differ from one
another. Among the consequences of these differences are
also differences in the values of the parameters calculated
with their application, such as the model surface A and A0 ,
the coefficient of development of the interception surface
0
Csd or Csd
and the actual surface Ad and A0d . Examples of
these differences for selected bark samples are shown in
Table 1.
It should be noted that despite the differences in the
0
surfaces A and A , and in the coefficient of development of
0
the interception surface Csd or Csd
, the actual surfaces of
0
the samples Ad and Ad assume similar values. This is due to
the fact that a shorter length or curvature ba or b0a results in
a higher value of the coefficient of development of the
interception surface and vice versa: a higher length of the
curvature results in a smaller value of the coefficient Csd or
0
Csd
. Consequently, calculation of the actual surface Ad and
0
Ad using formulas 1 and 7 results in only a small difference
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Trees (2014) 28:831–839
Table 1 Comparison of the parameters of selected bark samples defined by the length of curvatures ba and b0a calculated with various methods
b0a
0
Csd
0
Csd
A
A
Ad
A0d
7.46
8.73
1.53
2.27
1.65
2.44
71.14
113.07
66.17
104.67
108.84
256.66
109.18
255.40
8.94
9.05
2.21
2.18
136.87
138.56
302.49
302.05
9.50
8.79
8.82
1.88
1.87
83.51
83.79
156.99
156.69
9.81
9.30
9.02
2.05
2.17
91.23
88.49
187.03
192.02
10.76
7.89
7.67
2.22
2.28
84.90
82.53
188.47
188.17
Number of sample
a
Pine 3
Pine 6
8.87
11.99
8.02
9.43
Pine 7
15.31
Larch 3
Larch 6
Larch 8
ba
Fir 4
9.35
7.52
7.43
1.01
1.01
70.31
69.47
71.02
70.17
Fir 8
13.46
6.25
6.28
1.29
1.29
84.13
84.53
108.52
109.04
Fir 10
14.51
9.33
9.41
1.45
1.43
135.38
136.54
196.30
195.25
Spruce 3
10.95
5.60
1.21
1.16
58.91
61.32
71.28
71.13
Spruce 4
8.62
6.63
6.95
1.49
1.42
57.15
59.91
85.15
85.07
Spruce 9
12.36
12.21
12.35
1.72
1.70
150.92
152.65
259.57
259.50
Birch 3
13.95
5.17
5.11
1.56
1.57
72.12
71.28
112.51
111.92
5,38
Birch 4
8.95
8.52
8.88
1.70
1.63
76.25
79.48
129.63
129.55
Birch 5
10.60
9.34
9.39
1.74
1.73
99.00
99.53
172.27
172.19
Oak 2
7.87
7.19
7.31
1.31
1.29
56.59
57.53
74.13
74.21
Oak 5
Oak 7
10.99
11.17
8.37
7.72
8.40
7.71
1.60
1.53
1.59
1.54
91.99
86.23
92.32
86.12
147.18
131.94
146.78
132.63
Beech 6
7.09
9.07
8.99
1.10
1.11
64.31
63.74
70.74
70.75
Beech 8
8.48
8.17
8.08
1.01
1.03
69.28
68.52
69.97
70.57
Beech 10
8.12
5.22
5.24
1.07
1.06
42.39
42.55
45.35
45.10
Maple 3
11.28
5.71
5.71
1.08
1.08
64.41
64.41
69.56
69.56
Maple 5
12.36
4.44
4.46
1.36
1.35
54.88
55.13
74.63
74.42
where a is the average length of the side of the sample parallel to the stem core (cm), ba is the average length of curvature of the sample
calculated from the geometrical relations (cm), b0a is the average length of curvature of the sample calculated in a subjective manner (cm), Csd
0
0
and Csd
are the coefficients of development of the interception surface of bark calculated using formulas 10 and 11, A and A are the model
2
0
surfaces of bark samples calculated using formulas 2 and 6 (cm ), Ad and Ad are the actual surfaces of bark samples calculated using formulas 1
and 7 (cm2)
Fig. 3 A diagram showing the course of the coefficient of development of the interception surface of bark Csd, in relation to the
diameter at breast height (DBH) of trees of coniferous species
Fig. 4 A diagram showing the course of the coefficient of development of the interception surface of bark Csd, in relation to the
diameter at breast height (DBH) of trees of deciduous species
while it is the actual surface that constitutes the ultimate
goal of the measurements (Table 1).
According to the authors, the method of calculating the
length of curvature ba using geometric patterns is
methodically more correct than the second method in
which the measurements are performed in a subjective
manner. Therefore, the study results were elaborated using
the values obtained from the measurements of the average
length of curvature ba using the first method. The second
method may find practical application in the calculation of
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Trees (2014) 28:831–839
837
the surface of the bark of trees with an irregular cross
section, in which the diameters measured at breast height in
two directions are substantially different from one another.
The results of the present study show differentiation the
coefficient of development of the interception surface of
bark Csd at the level of DBH not only between particular
species, but also its variation within a single species
(Figs. 3, 4). A feature that is common for most species is a
significant increase in the coefficient Csd with the age
(diameter at breast height) of trees, thereby increasing the
interception surface of the bark of the tree stem Ad.
European beech (F. sylvatica) is an exception as its coefficient of development of the interception surface of bark
Csd shows little variation in relation to the age of the trees.
Among all species, the largest values of the coefficient
Csd characterize the bark of the thickest trees (Figs. 3, 4).
Among the coniferous species, the highest values of the
coefficient Csd are reached by European larch L. decidua:
2.56 (DBH = 58 cm) and by Scots pine P. sylvestris: 2.28
(DBH = 56 cm), while among deciduous species—silver
birch B. pendula: 2.44 (DBH = 52 cm). For coniferous
species, the average values of the coefficient Csd are reached
by Norway spruce P. abies: 1.75 (DBH = 58 cm) while
among deciduous species by common oak Q. robur: 1.72
(DBH = 56 cm). Relatively low values of the coefficient
Csd among coniferous species are reached by silver fir A.
alba: 1.45 (DBH = 59 cm). The lowest values of the coefficient of development of the interception surface of bark Csd
are reached by European beech F. sylvatica: 1.07
(DBH = 59 cm). In the case of sycamore maple, the surface
of bark in the younger age classes does not show large
variation and its structure resembles the bark of European
beech (Fig. 4). The coefficient of development of the
interception surface of bark Csd in young sycamore trees has
values close to 1.00, while in thicker trees it can be seen that
the bark surface is highly differentiated, the bark is more
protruding and very fragile. The authors managed to capture
the moment when the coefficient of development of the
interception surface of bark Csd in sycamore maple begins to
differentiate. This moment coincides with the period when
the trees reach the diameter of about 37 cm at breast height.
The present study does not include data on the formation of
the coefficient of development of the interception surface of
bark Csd in sycamore maple trees which are more than 37 cm
thick because of the difficulty in collecting samples of the
bark with its structure left intact. However, based on field
observations, it can be concluded that the coefficient Csd for
old sycamore maple trees certainly assumes high values,
similar to larch and pine. Calculation of the surface of the
bark for older sycamore trees requires the development of
special methods for the sampling of the bark.
Within particular species, the highest variation of the
coefficient of development of the interception surface of
bark Csd characterizes B. pendula, L. deciduas, and P.
sylvestris, in which the coefficients of variation are,
respectively, 31.31, 25.12, and 23.47 % (Table 2). The
smallest variation of the coefficient Csd is shown by F.
sylvatica (3.41 %).
Therefore, the species presented in the present study can
be divided into three groups:
1.
The group of species with the bark surface strongly
growing with age of the trees. It includes: P. sylvestris,
L. decidua, B. pendula, and A. pseudoplatanus.
The group of species with an average bark surface
development with age. It includes: P. abies, Q. robur,
and A. alba.
The group of species with the bark surface which
develops only slightly with age. It includes F.
sylvatica.
2.
3.
Analyzing the variability of the coefficient of development of the interception surface of bark Csd, with the age of
Table 2 Descriptive statistics of the coefficient of development of the interception surface of bark Csd for individual species
Sspecies
n
Mean
Median
Min
Max
SD
CV (%)
R2
P. sylvestris
10
1.83
1.90
1.23
2.28
0.43
23.47
0.92
L. decidua
11
1.96
2.02
1.07
2.56
0.49
25.12
0.91
P. abies
11
1.41
1.36
1.14
1.75
0.21
14.78
0.94
A. alba
11
1.20
1.22
1.01
1.45
0.17
14.05
0.90
Q. robur
B. pendula
10
8
1.45
1.74
1.44
1.72
1.23
1.02
1.72
2.44
0.15
0.55
10.15
31.31
0.84
0.96
–
–
–
–
–
1.03
1.01
1.10
0.04
3.41
0.30
A. pseudoplatanusa
F. sylvatica
6
10
–
1.05
where n is the sample size, SD is the standard deviation, CV is the coefficient of variation, R2 is the coefficient of determination describing the
dependence of the coefficient Csd on the breast height diameter of trees
a
Owing to the lack of data on the coefficient of development of the interception surface of bark Csd for thick trees, the calculation of descriptive
statistics was not performed
123
838
Scots pine, European larch, and silver birch (Figs. 3, 4), it
can be seen that there are two inflection points. The authors
put forward the hypothesis that one of them may occur
after the culmination of the growth of tree height, while the
other occurs after the culmination of the growth of tree
thickness. However, this hypothesis requires verification
during further studies.
The present research results constitute a proposal of
calculation of the bark surface of forest tree stems by
means of the coefficient of development of the interception
surface of bark Csd, describing the level of development of
the outer surface layer of the bark. The values of the
coefficients Csd in the present study concern only the bark
sections obtained at the breast height of trees and they
cannot be used for the calculation of the actual surface of
the bark of the whole stem. To determine actual surface of
the bark of the whole stem, one should calculate the variability of the coefficient of development of the interception
surface of bark Csd for each species over the entire length
of the tree stem, from its butt end to its top. These measurements may show large variations in the development of
the coefficient Csd within a single tree stem, and thus
variation in the water capacity of the bark along the stem.
This seems to be reasonable due to the variability of the
coefficient Csd with the age of trees within a single species
(Figs. 3, 4). Similarly to the age of the trees, the coefficient
Csd should vary along the tree stems.
Obtaining the average values of coefficients Csd
depending on the age and species of trees will be of great
cognitive and practical importance in the modeling of water
processes occurring in forest ecosystems. Based on the
average DBH and height of a stand, as well as the average
values of the coefficients Csd for the trees of particular
species, it will be easy to determine the entire interception
surface of the stem for whole stands. The application of this
methodology for the calculation of the actual surface of
twigs and branches along with the knowledge of the surface
of the assimilation apparatus will allow for determination of
the actual interception surface of stands.
Conclusions
The coefficient of development of the interception surface
of bark Csd allows for objective assessment of the degree of
bark surface differentiation between different species.
The coefficient Csd, is a measure to differentiate bark
morphology and indicates that each species has its own
properties in the shaping of the surface whose development
is dynamic and progresses with the age of trees.
Owing to the mathematical form of recording the degree
of differentiation of the bark surface, the coefficient Csd
may be useful for modelling the hydrological processes
123
Trees (2014) 28:831–839
occurring in forest ecosystems. As a measure of surface
differentiation, it allows for obtaining certain calculation
results when analysing water properties of the bark, thanks
to which one can better interpret the interception processes
of the bark of various species.
Acknowledgments We thank the two anonymous reviewers for
their valuable comments and suggestions on the manuscript.
Conflict of interest These investigations were supported by a grant
for young scientists from Polish Ministry of Science and Higher
Education (No. BM/4419/KIL/12, Determination of the water storage
capacity of bark of forest tree under laboratory conditions).
Open Access This article is distributed under the terms of the
Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original
author(s) and the source are credited.
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