Estuarine, Coastal and Shelf Science (1999) 48, 293–305
Article No. ecss.1998.0420, available online at http://www.idealibrary.com on
The Geometric Features, Shape Factors and Fractal
Dimensions of Suspended Particulate Matter in the
Scheldt Estuary (Belgium)
R. G. Billiones, M. L. Tackx and M. H. Daro
Ecology Laboratory, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium
Received 14 April 1998 and accepted in revised form 15 September 1998
Water samples from the Scheldt estuary were collected in three fractions: (a) unfiltered water, (b) water filtered
through a 50 ìm net and (c) water filtered through a 300 ìm net. Particles easily recognisable from the majority of
the amorphous particles were isolated and their geometric dimensions measured. From the measurements, shape
factors were calculated. Measurement of fractal dimensions was attempted. From the first fraction, the particles
isolated and measured were circular and chained diatoms. In the second fraction, zooplankters were easily
distinguishable and representatives of the three dominant groups (cladocerans, cyclopoids and calanoids) were
measured. In the third fraction, detrital pieces from monocotyledon and dicotyledon plants were recognised,
isolated and measured. Fractal dimensions were only measurable in particles from fraction 3. The geometric
features, shape factors and fractal dimensions of the particles were tested and proven to be effective ‘ fingerprints ’ to
distinguish these particles from the majority of the unidentifiable amorphous particles in the samples.
1999 Academic Press
Keywords: suspended particulate matter; geometry; fractals; fingerprints; Scheldt estuary
Introduction
SPM in estuaries
Suspended particulate matter (SPM)
The complexity and heterogeneity of SPM are most
evident in estuaries. Inputs from river, land and sea,
turbulence and limited depth result in the characteristic high SPM load of the estuarine ecosystem. SPM has
diverse ecological roles and it is necessary to look at the
individual components of this assemblage to fully
understand these roles. A 20–80% quantity of suspended particles in estuarine and riverine environments consist of detritus (Poulet, 1983) which are
mostly allochthonous. Due to the above-described
characteristic of estuarine SPM, it was believed that
zooplankters in estuaries were unselective detritivores
(Hummel et al., 1988). In recent years, evidence of
selective feeding by estuarine copepods has arisen
(Vanderploeg et al., 1988; Tackx et al., 1995a,b;
Gasparini & Castel, 1997). These latest findings indicate that though the living components (e.g. planktonic
organisms) form a very small fraction of the carbon
mass in the system, they play a very crucial role in the
trophic dynamics of the system, particularly in the link
between primary producers and the higher trophic
levels. Thus, the quantification of the different components and the differentiation of the living from the
non-living components becomes even more important.
Suspended in all natural waters, from the smallest
mountain stream to the deepest ocean, are assemblages of small particles of different sizes and shapes
which make up what we call seston or suspended
particulate matter (SPM). No single definition in the
literature ever satisfactorily describes the real nature of
this mixed confusion of particles. They may occur as
single particles, as aggregates (Mel’nikov, 1976) or in
flocs (Eisma and Cadeé, 1991). Yet among this confusion is the very source of life, since very small
particles comprising SPM, such as bacteria, plankton
and detritus are the main actors in the carbon cycling
of the aquatic ecosystem.
Studies on the nature of SPM indicate a very
heterogeneous nature (Mel’nikov, 1976; Kranck,
1980; Billones et al., in press). This heterogeneity
presents problems in the characterisation and
classification of the particles. Yet, the physical
characterisation of SPM can give important
insights into the structure and functioning of an
ecosystem which can not be obtained from other
analysis.
0272–7714/99/030293+13 $30.00/0
1999 Academic Press
294 R. G. Billiones et al.
Another characteristic of estuarine systems is the
high degree of interaction with bordering terrestrial
ecosystems, which provide an important source of
detritus (Pomeroy, 1980; Schleyer, 1986). The
amount of detritus coming into the estuary and the
ecological fate of these detrital materials depends, to a
substantial degree, on the type of litter. The recognition of various types of litter is, however, difficult.
Once in the water, the litter rapidly undergoes fragmentation and decomposition, and is transformed
into smaller particles which form the unrecognisable
part of SPM. Chemical analyses of SPM measure the
chemical characteristics of the totality of all particles.
However, to study the interaction between the
terrestrial and aquatic system, the differentiation
between the different SPM components is necessary.
Morita, 1976; Ammerman et al., 1984). Shapes can
affect predation and vice versa. Algal cells with spines
and appendages or in colonies (and chains) are not
readily swallowed by zooplankton (Vanderploeg et al.,
1988; Hansson & Tranvik, 1996). Some phytoplankton species can even alter their cell or colony
morphology in the presence of grazers (Lurling &
Vandonk, 1996).
For non-living particles, shape is important in
determining sedimentation and transport, as well as
decomposition rates. Flake-like particles (e.g. clay,
detrital pieces) tend to be more buoyant than other
bulkier shapes (Chamley, 1989). In larger forms (e.g.
leaves) more surface area is exposed to decomposers.
They are therefore more easily shredded compared to
more solid detrital particles, such as twigs and
branches.
The role of sizes and shapes in aquatic ecology
Sizing is a convenient and common way of characterising SPM in aquatic systems. Most biological processes are size related, including metabolic rate,
lifespan, reproductive age and embryonic development (Fenchel, 1974; Malone, 1980; Williams,
1997). Size plays an important role in the trophic
placement of aquatic organisms, and predator-prey
relationships in the pelagic aquatic ecosystem are
size-dependent (Sheldon et al., 1977). Size generally
increases as one goes up the trophic levels and
predators can only feed on prey which are 1–10% of
their size (Kiørboe, 1993). Size is also an important
factor in sinking and floating processes in aquatic
systems (Hughes, 1980; Walsby & Reynolds, 1980).
Size distribution of particles in a system can
provide information about the dynamics of that system. Sheldon et al. (1972) have found that particle
size distribution patterns of surface oceanic waters
vary geographically. Size spectra analysis of particles
enabled researchers to effectively study the trophic
dynamics of pelagic ecosystems such as those of lakes
(Sprules et al., 1983; Minns et al., 1987; Sprules et al.,
1991) and estuaries (Tackx et al. 1991, 1994, 1995a).
After size, shape is a very important feature of SPM.
There is less variation in the shapes of pelagic organisms than in those on land, due to structural limits
imposed by a medium, water being 800 times denser
than air (Sheldon et al., 1977). However, the shape of
a planktonic cell can be a determinate factor in
nutrient dynamics and in predation. A spherical object
has a much higher surface to volume ratio, thus
spherical cells are much more adapted to nutrientlimited environments (Taylor, 1980; Kiørboe, 1993).
Bacteria are known to shift their morphology from
rods to cocci in response to starvation (Novitsky &
Geometric and fractal characteristics of particles
The use of Euclidean geometry in biology is not new.
Systematics describe and classify biota in terms of
their size, symmetry and shape. The concept of
geometrical similarity of organisms has gained
popularity in biophysics (Pennycuick, 1992). The
geometric terms, biovolume and diameter, have been
used to describe bacterial and algal cell sizes.
Mathematicians employ certain mathematical conventions to define what constitutes ‘ size ’. In general,
it is taken as the average distance between two points
in the outline of a particle, the so-called statistical
diameter (Herdan, 1953). Another expression of size
takes the diameter of a circle having the same area as
the projected image of the particle, when viewed in
the direction perpendicular to the plane of greatest
stability, the so-called circular (or spheric) equivalent
diameter (SED; Herdan, 1953).
Shape factors are size-independent features calculated from geometric dimensions. These factors are
very important in characterising the shapes of particles, regardless of their sizes. The use of shape
factors as classifiers has been applied to differentiate
rock particles (Schäfer & Teyssen, 1987) and plant
leaves (Yonekawa et al., 1996). Examples of shape
factors are: (a) elongation, which is the ratio of the
length and the width; (b) circularity, which provides
an indication of how closely the particle resembles a
circle relative to its perimeter (Joyce Loebl, 1988); (c)
roundness, which is indicative of roundness or compactness relating to area (Yonekawa et al., 1996)
and (d) fractal dimension, which is a measure of
‘ ruggedness ’ (Kaye, 1989).
The introduction of the concept of fractals has
substantially influenced the present view of biomath-
Characterisation of estuarine suspended matter 295
Materials and methods
To cover a wide range of particle sizes, three different
size fractions of suspended particulate matter were
collected from different sampling points in the Scheldt
estuary in 1996. Particles were all measured using the
Magiscan Image Analysis system of Joyce Loebl, as
described in detail by Billiones et al. (in press). To
convert grey images to binary form, thresholding was
interactively chosen for the maximum separation of
particles. In cases where automated separation was
not possible, the particles where separated manually.
During all of the measurements, the illumination
and focus were kept as constant as possible to
avoid inconsistencies between measurements. In all
measurements, only two-dimensional characteristics
of the particles are considered. Conversion to
three-dimensional volumes is dealt with separately
(Billiones et al., in press).
The different features measured under the image
analysis as shown in Figure 1 are, according to Joyce
Loebl, 1988:
(a) length l, the maximum distance between two
points on the boundary
(b) width w, diameter normal to the length
(c) Feret length lf, the Feret diameter parallel to the y
axis
a
ad
wf
w
ematics. First introduced by Mandelbrot (1977),
fractal geometry has become an important tool in
most of natural sciences including chemistry (Avnir,
1989), biology (Kaandorp, 1994; Williams, 1997),
medicine (Peiss et al., 1996) and geology (Goryainov
et al., 1997). Conventional mathematics easily
describes objects using straight lines and angles. However, when faced with ‘ irregular ’ shapes, such as
those found in nature, finding a tractable formula
is almost impossible. Traditional geometry is said to
be best suited to describe man-made objects while
fractals provide an excellent description of natural
shapes (Voss, 1988).
Having discussed the importance of sizes and
shapes of particles in aquatic ecology, we present here
an inventarisation of the geometric features, shape
factors and fractal dimensions of some different types
of suspended particles in an estuarine setting. Based
on the results, a technique to characterise particles will
be proposed, using the said characteristics as ‘ fingerprints ’ which can be used for automated classification
of suspended particles. In addition, this paper
explores how far the use of fractal dimensions can
contribute to the recognition of different types of plant
detritus suspended in the water.
l
p
lf
F 1. The different geometric features of a particle
which can be measured by image analysis: length l, width w,
Feret length lf, Feret width wf, perimeter p, total area a and
detected area ad. See text for explanations.
(d) Feret width wf, the Feret diameter parallel to the x
axis
(e) perimeter p, the sum of distances between midpoints of the vectors forming the boundary
(f) total area a, an integral from the boundary of a
particle not considering the enclosed holes
(g) detected area ad, the area taking account of the
holes
Two diameters of each particle were calculated.
The first one is d, which is the mean of the four
measured diameters l, w, lf and wf and the second is
dc, which is the diameter of a circle with an area
equivalent to the a value of that particle.
Shape factors were calculated as follows
(Joyce-Loebl, 1988; Yonekawa et al., 1996):
(a) Elongation.
(b) Circularity C.
(c) Roundness R.
(d) Porosity P.
(e) Fractal dimension D. The fractal character of an
object can be determined by measuring its perimeter,
p, repeatedly using different scales. By plotting the
logarithm of the different p measurements against the
logarithm of the corresponding scale length ë, a
dimensionless number called fractal dimension D is
derived from the slope of the regression line (Kaye,
1989):
296 R. G. Billiones et al.
determine the major features which differentiate the
particles from each other. Data were log transformed
prior to statistical analysis. It is hypothesized that
these characteristics could serve as ‘ fingerprints ’ that
would distinguish diatoms from the amorphous aggregates that make up the majority of the particles in
the sample. This was tested by twice measuring the
same viewing field of natural particulate matter. First,
all particles in the viewing field were automatically
counted and measured. From this dataset, particles
with characters within the range of those of the
diatoms as listed in Table 1 were extracted. In
the second measurement, only diatoms chosen
visually were measured. The numbers and areas of
these particles were then compared with the first
measurement.
Fraction 2
F 2. The circular diatoms (CD) and the long
(chained) diatoms (LD) in fraction 1. Calibration
bar=20 ìm.
E, C, and R are all equal to one when the particle is
a perfect circle. D values of two-dimensional objects
range between one and two. A shape of differentiable
curves has a D value of one and increases with
increasing convolutions (Bradbury & Reichelt, 1983).
Fraction 1
Water samples of 250 ml in volume were collected
directly from several stations in the Scheldt and fixed
in lugol’s iodine. Subsamples were sedimented in a
cuvette and viewed under the inverted microscope
(Sedival) connected to the image analyser. To obtain
a general overview of the range of particle size in the
sample, measurements were done in two microscopic
magnifications (400 and 25). In some of the
samples, a distinction was made between two types of
dominant diatoms: circular diatoms from the valvar
view and chained diatoms (Figure 2). The dimensions
of these particles were measured individually and their
shape factors calculated. The machine was found to
have difficulty in measuring p of very small particles
(<10 pixels), thus, the fractal dimensions D of the
particles could not be measured in this fraction.
Complete linkage cluster analysis was used to test
how effectively these characters differentiated the different particles measured. The data set was also
analysed using principal component analysis (PCA) to
Larger suspended particles were collected by filtering
50 litres of Scheldt water using a 50 ìm net. The
particles were measured in two magnifications, 25
(inverted microscope, Sedival) and 10 (binocular
microscope, Leica). In this fraction, zooplankters were
readily distinguishable from other materials. The
three most dominant zooplankton species, Eurytemora
affinis [Figure 3(a)], Acanthocyclops robustus
[Figure 3(b)] and Daphnia magna [Figure 3(c)], were
isolated and their body dimensions (excluding the
appendages) were measured using image analysis.
Cluster analysis and PCA were similarly performed, as
in fraction 1. The same measurements were conducted as in fraction 1 to test how effectively these
characters can be used as ‘ fingerprints ’ to differentiate zooplankters from the amorphous aggregates.
Though the measurement of p is possible in this
fraction, we were hindered by a limited number of
microscopic magnifications. Thus, we were not able to
measure the fractal dimensions of particles in this
fraction.
Fraction 3
Large detritus particles from the Scheldt were collected using a 300 ìm net. The size range of particles
in the sample (which has a range from 100 ìm up to
several centimetres) was too large to be covered by
the available microscopic magnification, thus a complete size range of particles cannot be measured. In
this fraction however, distinction could be made
between plant detritus originated from monocotyledon [Figure 4(a)] and dicotyledon plants
[Figure 4(b)]. Approximately similar-sized plant
detrital particles were isolated and measured in the
T 1. The geometric features, shape factors and fractal dimensions of different particles in three size fractions of water samples from the Scheldt
Length
l (ìm)
Area
a (ìm2)
Particles
Fraction 1
Centric diatoms
Chained diatoms
Fraction 2
E. affinis
A. robustus
D. magna
Fraction 3
Dicotyledon
Monocotyledon
Mean
Min
Max
82
112
5·2102
3·7102
1·2102
5·6101
8·5102
4·1103
87
70
112
2·0105
3·2105
1·5106
1·1105
1·5105
3·4105
89
91
6·9106
6·6106
7·2105
1·3106
n
Mean
Min
Max
Mean
27·3
70·8
13·4
53·0
35·9
451·3
4·3105
5·3105
6·1106
842·9
889·6
1818·1
662·8
583·1
868·2
2·0107
1·6107
4852·1
4391·7
2744·4
1221·2
Fraction 1
Circular diatoms
Chained diatoms
Fraction 2
E. affinis
A. robustus
D. magna
Fraction 3
Dicotyledon
Monocotyledon
Max
Mean
Min
Max
Mean
Min
Max
25·0
7·9
11·0
3·05
32·6
193·1
26·0
41·0
12·4
13·3
33·7
112·1
25·4
19·2
12·4
8·5
32·9
46·0
1240·5
1222·9
3556·0
309·4
488·1
1149·7
223·20
351·4
509·5
525·8
677·6
2359·0
604·5
703·5
1485·4
459·4
491·0
709·8
909·3
953·1
2965·3
499·4
634·3
1327·2
371·6
440·0
660·9
743·0
822·2
2779·7
8062·0
6824·8
2185·6
2915·5
696·3
386·8
4940·2
5382·8
nm
nm
nm
nm
nm
nm
mean
min
max
max
mean
min
82
112
0·94
0·23
0·82
0·07
1·01
0·53
1·09
8·62
0·99
3·44
1·25
19·69
0·87
0·10
0·75
0·03
87
70
112
0·56
0·67
0·78
0·45
0·49
0·62
0·66
0·80
0·90
2·75
1·83
1·50
2·21
1·30
1·15
3·16
2·37
2·06
0·35
0·51
0·54
89
91
0·29
0·47
0·04
14
0·63
0·80
1·54
2·50
1·02
1·01
2·89
5·22
0·44
0·36
nm
nm
Fractal
dimension
D
Roundness
R
n
nm=not measured; n=number of particles measured.
min
Diameter 2
dc (ìm)
Min
Elongation
E
mean
Diameter 1
d (ìm)
max
nm
nm
nm
nm
Porosity
P (%)
mean
min
max
0·96
0·24
nm
nm
nm
nm
nm
nm
<0·01
<0·01
0·00
0·00
<0·01
<0·01
0·28
0·40
0·37
0·43
0·69
0·77
nm
nm
nm
nm
nm
nm
nm
nm
nm
<0·01
<0·01
<0·01
0·00
0·00
0·00
<0·01
<0·01
<0·01
0·17
0·18
0·71
0·70
12·32
<0·01
<0·01
<0·01
31·56
0·19
1·46
1·17
1·25
1·04
1·86
1·37
mean
min
max
Characterisation of estuarine suspended matter 297
Circularity
C
Particles
Width
w (ìm)
298 R. G. Billiones et al.
F 3(a). Eurytemora
bar=100 ìm.
affinis
(EA).
Calibration
F 3(c). Daphnia
bar=200 ìm.
magna
(DM).
Calibration
the object, in place of a measuring scale. At each
magnification, the pixel size is calibrated by a microscope stage micrometer. In changing from one magnification to another, the dimensions of a pixel do not
change relative to the video screen but do change
relative to the calibration scale units. Thus, the pixel
length is considered to be the scale length ë. The ë
values used in this measurement were 10·7, 16·2 and
23·4 ìm in the magnifications 16, 10 and 6·5,
respectively. Cluster analysis and PCA were performed as in fraction 1, but only shape factors were
considered in the tests, due to the size-based isolation
of particles.
Results
Fraction 1
F 3(b). Acanthocyclops robustus (AR). Calibration
bar=100 ìm.
image analysis. This non-random isolation of
particles is due to the fact that only particles of a
certain size-range can be effectively measured by
the available microscopic magnifications. Individual
fractal dimensions of pieces of detritus were determined by measuring the p of each particle at three
magnifications (16, 10 and 6·5) under the
binocular microscope (Leica). Pixels are overlaid over
Figure 5 shows the typical size distribution of the
particles measured in this fraction. The 400 magnification measured particles up to the size range (dc) of
0·5–30 ìm and the 25 measured up to 130 ìm. d
values, however, go up to 250 ìm. Further measurements at a magnification lower than 25 (binocular
microscope) occasionally showed particles larger than
130 ìm, but these occurrences were very few and were
thus not considered. Thus, a 250 ml sample from the
Scheldt was found to contain particles of maximally
d=250 ìm and dc =130 ìm.
Table 1 shows the geometric features and shape
factors of the two diatom types from this fraction. The
Characterisation of estuarine suspended matter 299
4
40×
25×
2
× 10 µm ml
–1
3
6
2
1
0
0
30
60
90
120
150
µm
2
2
1
1
0
0
LD7
LD6
LD5
LD4
LD3
LD2
LD1
UN12
UN9
UN13
UN4
UN14
UN5
UN6
UN3
UN2
UN8
UN7
UN10
UN11
UN1
CD9
CD8
CD7
CD6
CD10
CD5
CD3
CD2
CD4
CD1
F 4(a). Pieces of detritus from a monocotyledon
(MON) plant. Calibration bar=500 ìm.
Linkage distance
F 5. Typical size distribution of area concentrations
(ìm2 ml 1) in a water sample from fraction 1 in two
magnifications, 400 ( ) and 25 ( ).
F 6. Cluster analysis of particles in fraction 1, the
circular diatoms (CD) and the chained (long) diatoms
(LD), and the unidentifiable amorphous particles (UN).
Data points are mean values of particles from a specific
sampling station.
F 4(b). A piece of detritus from a dicotyledon (DIC)
plant. Calibration bar=200 ìm.
two diameter measurements, d and dc, in the circular
diatoms are not significantly different (Wilcoxon,
P>0·05) though d is consistently bigger than dc in all
other particles (Wilcoxon, P<0·05). C and R values
(0·940·04, 0·870·04, respectively) are higher and
closer to the value of 1 in circular diatoms than in
chained diatoms (0·230·08, 0·100·04, respectively; Mann–Whitney, P<0·05). Conversely, the
chained algae have higher E values (8·623·22;
Mann–Whitney, P<0·05). The porosity P of particles
in this fraction is nearly zero.
In order to present the results graphically, not all
data points were used in the graph presented here.
Individual data points in Figures 6 and 7 represent the
mean values of particles from each station sampled.
Cluster analysis and PCA of the whole data set (total
number of data points n, listed in Table 1) showed
similar results to those presented here. The first step
in the cluster analysis produced two groups, the first
cluster consisting of long, chained diatoms (LD) and
the second group consisting of the circular diatoms
(CD) and the unidentified particles (UN). Further
steps resulted in a split between CD and UN. The
PCA results (Figure 7) showed that l, R, C, E and d
were the features with high factor loadings (solid lines)
in the first axis, while a and dc (broken lines) were
more associated with the second axis. The two factors
(first and second axes) accounted for 95% of the
variability in the data-set.
300 R. G. Billiones et al.
T 2. Comparison of two measurements of the same
viewing field, of total areas and numbers of the two diatoms.
Measurement one represents measurements of area and
number of particles which were visually identified as diatoms. Measurement two represents area and count data
selected automatically as ‘ diatom-like ’ from the total dataset of all particles in the viewing field, based on the ‘ fingerprint ’ characteristics of diatoms listed in Table 1. The
two different measurements of areas and numbers did not
significantly differ (P>0·05)
1.2
a
dc
w
UN9
UN4 UN13
0.8
UN1
UN5
Axis 2
LD*
CD*
UN2
0.4
R
d
C
0
–0.4
–0.8
–1.2
l
Viewing
field
E
–0.8
–0.4
0
Axis 1
0.4
0.8
1.2
F 7. Results of PCA tests on geometric features and
shape factors ( ) and particle types ( ) in fraction 1. Data
labels marked * indicate a group of data points of the same
acronym which are so close together that individual labels
cannot be shown on the graph. See text for explanation.
Table 2 shows results of the two measurements
of the two types of diatoms in ten viewing fields.
The second and third columns show counts and total
area measurements, respectively, of diatoms visually
chosen, while the fourth and fifth show those results
extracted from the total counts based on the ‘ fingerprint ’ characters. The two counts (Wilcoxon,
P>0·05) and the two measurements (Wilcoxon,
P>0·05) did not significantly differ.
Measurement one
Numbers
Measurement two
2
Area (ìm )
Numbers
Long (chained) diatoms
1
12
2959·2
2
8
4293·2
3
19
6938·2
4
8
3011·0
5
10
5046·7
6
10
4731·4
7
10
6320·6
8
12
6075·9
9
12
5621·7
10
7
2482·2
Circular diatoms
1
4
1639·2
2
5
3000·1
3
6
1962·4
4
6
2738·1
5
6
4367·8
6
7
5102·8
7
5
3373·3
8
7
3128·0
9
7
2568·2
10
4
1681·4
Area (ìm2)
13
8
17
66
11
10
99
11
12
7
3249·5
4526·2
6349·3
2696·7
5181·4
4744·0
6198·3
5483·8
5612·7
2287·3
4
5
7
6
5
9
5
8
7
4
1624·5
3035·2
2068·1
2693·0
4119·3
5524·8
3359·4
3389·9
2603·6
1690·2
Fraction 2
12
× 106 µm2 ml–1
Figure 8 shows the typical size distribution of the
particles measured in the fraction >50m. The 25
magnification measured particles up to the size range
(dc) of 9–280 ìm and the 10 up to 560 ìm. Thus, a
50 litre sample in this fraction from the Scheldt was
found to contain particles of maximally dc =560 ìm,
while d values can go up to 1000 ìm. Table 1 shows
the geometric dimensions and shape factors of the
three most dominant zooplankton species. E. affinis is
the most elongated of the three species with E values
ranging from 2·21–3·16. A. robustus ranks second,
with E values of 1·830·17. The cladoceran D.
magna is the least elongated (E=1·500·17) of the
three and with the highest C (0·780·06) and R
(0·540·08) values. All of the above mentioned
comparisons were statistically significant (Mann–
Whitney, P<0·05). The zooplankters were significantly bigger than the other particles found in this
fraction (Mann–Whitney, P<0·05). The porosity P of
zooplankters in this fraction is nearly zero.
25×
10×
8
4
0
0
300
150
450
600
µm
F 8. Typical size distribution of area concentrations
(ìm2 ml 1) in a water sample from fraction 2 in two
magnifications, 25 (Ä) and 10 ( ).
As in fraction 1, to present the results graphically,
not all data points were used in the graphs presented
here. All individual data points in Figures 9 and 10
represent the mean values of particles from each
4
4
2
2
0
0
UN7
UN6
UN5
UN3
UN2
UN4
UN1
DM5
DM6
DM4
DM3
DM2
DM1
AR4
AR3
AR2
AR1
EA5
EA3
EA2
EA4
EA1
Linkage distance
Characterisation of estuarine suspended matter 301
F 9. Cluster analysis of different particles in fraction
2, the zooplankters E. affinis (EA), A. robustus (AR), and D.
magna (DM) and the unidentifiable amorphous particles
(UN). Data points are mean values of particles from a
specific sampling station.
0.9
UN20
UN16
UN*
0.6
n
C
Axis 2
R
l
0.3
a
DM*
AR*
0
EA*
–0.3
–0.6
–1.2
E
–0.6
0
Axis 1
0.6
1.2
F 10. Results of PCA tests on geometric features and
shape factors ( ) and particle types ( ) in fraction 2. Data
labels marked * indicate a group of data points of the same
acronym which are so close together that individual labels
cannot be shown on the graph. See text for explanations.
station. Cluster analysis and PCA of the whole data
set (n values listed in Table 1) showed similar results
as presented here. The first step in the cluster analysis
resulted in two clusters, the first cluster consisting of
unidentifiable particles (UN) and the second cluster
consisting of zooplankters. In the next step, there was
clear grouping between the cladoceran D. magna
(DM) and the copepods E. affinis (EA) and A. robustus
(AR). The copepods in turn were split into two
distinct groups in the following step. The groupings
were reflected in PCA results in Figure 10. Furthermore, it showed that all features tested exhibited high
loadings (solid line) in relation to the first axis. The
top four highest factor loadings are on w, C, a and E.
The first factor (first axis) accounted for 90% of the
variability in the data set while the second factor
accounted for 9%.
Table 3 shows results of the two measurements of
the three types of zooplankters in ten viewing fields.
The second and third columns show counts and total
area measurements, respectively, of zooplankters visually chosen, while the fourth and fifth show those
results extracted from the total counts based on the
‘ fingerprint ’ characters. There were no significant
differences between the two counts (Wilcoxon,
P>0·05) and the two area measurements (Wilcoxon,
P>0·05).
Fraction 3
The geometric and fractal features of the two types of
detrital pieces (monocotyl and dicotyl) in this fraction
are shown in Table 1. Eighty-nine out of 100
measurements for the dicotyls and 91 out of 100 of
the monocotyls have regression coefficient values
(rd0·98) which were significant at the 5% level of
significance. Monocotyls had fractal dimensions
ranging from 1·04–1·37, with a mean value of
1·170·06. Higher D values (Mann–Whitney,
P<0·05) were observed in dicotyls with values ranging
from 1·25–1·86 with a mean of 1·460·11. Porosity
in dicotyls (P=12·38·6%) was significantly higher
(Mann–Whitney, P<0·05) than in monocotyls
(P<0·01%). Monocotyls were also more elongated
(E=2·50·95; Mann–Whitney, P<0·05) than the
dicotyls (E=1·540·04).
Cluster analysis showed a clear split between the
two groups of detrital particles, with 85 out 89 dicotyls
(DIC) in one cluster and with 91 out of 91 monocotyls (MON) plus four dicotyls in the second cluster.
Unfortunately, results from such a large number of
sample points could not be presented graphically. The
result of cluster analysis on 20 randomly chosen
particles from the data set (ten particles from each
group) is shown in Figure 11. A clear split was
consistently observed in similar analysis. PCA results
in Figure 12 indicated two groupings in the classifying
features. D and P were closely associated with the
first axis (solid lines) while R and E were associated
with the second (broken lines). C seems to occupy
an intermediate position. The two factors (axes)
accounted for 94% of the variability in the data-set
(dotted lines).
Discussion
In aquatic ecosystems there is no exact size range
or average size of particles since there are no finite
limits to the population of particle sizes in the
302 R. G. Billiones et al.
T 3. Comparison of two measurements of the same viewing field of total areas and numbers of
the three types of zooplankters. Measurement one represents measurements of area and number of
particles which were visually identified as zooplankton. Measurement two represents area and count
data selected automatically as ‘ zooplankter-like ’ from the total data set of all particles in the viewing
field, based on the ‘ fingerprint ’ characteristics of zooplankters listed in Table 1. The two different
measurements of areas and numbers did not significantly differ (P>0·05)
Measurement one
Viewing field
D. magna
1
2
3
4
5
6
7
8
9
10
E. affinis
1
2
3
4
5
6
7
8
9
10
A. robustus
1
2
3
4
5
6
7
6·7105
8
9
10
Numbers
Measurement two
2
Area (ìm )
Numbers
Area (ìm2)
2
4
3
2
4
4
3
5
3
2
1·4106
1·8106
0·4106
0·3106
2·8106
3·7106
3·3106
3·7106
4·5106
1·9106
2
4
3
2
4
3
3
5
3
2
1·4106
1·9106
0·4106
0·3106
2·5106
2·2106
3·5106
3·5106
4·5106
1·9106
44
3
5
2
3
4
3
33
2
4
8·8105
5·0105
10·8105
3·6105
6·7105
8·4105
5·4105
6·1105
3·3105
6·9105
4
3
5
2
3
4
3
3
2
4
9·2105
4·9105
10·9105
3·6105
6·8105
8·5105
5·5105
6·3105
3·3105
7·0105
4
3
4
3
1
2
2
6·3105
7·0105
4·4105
6·3105
1·3105
3·6105
5·9105
3
3
4
3
1
2
33
5·2105
7·0105
4·4105
5·9105
1·2105
3·7105
3
2
4
6·1105
3·3105
7·1105
3
2
3
6·6105
3·3105
6·0105
system (Sheldon et al., 1972). Thus, one of the main
problems in studying the sizes of SPM is that the
range of observable sizes is highly dependent on
sample size and the system being studied. We have
tried to overcome this problem by analysing different
fractions at different microscopic magnifications. The
size distribution of particles in fractions 1 and 2 are
given, not to represent the entire size range of particles
in estuaries, but rather as a representation of what can
be measured in a certain fraction at certain magnifications in a specific estuary, the Scheldt. The particles
measured in the two fractions can be assumed to be
made up of microflocs (broken-up macroflocs) and
single particles as defined by Eisma and Cadee
(1991), with maximum particle size of approximately
560 ìm. Eisma (1991) has measured in situ
macroflocs in the Scheldt, of up to 800 ìm.
The results of cluster analysis (Figures 6, 9 & 11)
demonstrated that some of the features measured in
the three fractions were able to group particles of
similar types together. Cluster analysis in fraction 1
(Figure 6) revealed that these features can effectively
differentiate diatoms from unidentifiable amorphous
particles (UN). Furthermore, these features classified
these diatoms into their respective groups, the circular
type (CD) and the chained (long) type (LD). Cluster
6
4
4
2
2
0
0
DIC1
6
MON7
MON6
MON4
MON9
MON2
MON10
MON3
MON5
MON8
MON1
DIC5
DIC4
DIC10
DIC8
DIC7
DIC6
DIC9
DIC3
DIC2
Linkage distance
Characterisation of estuarine suspended matter 303
F 11. Cluster analysis of two types of detritus in
fraction 3, those which originated from monocotyledon
plants (MON) and those which come from dicotyledon
plants (DIC).
1.2
DIC*
DIC2
R
0.8
DIC*
DIC1
P
Axis 2
0.4
C
D
MON*
0
–0.4
–0.8
–1.2
–1.2
E
–0.8
–0.4
0
Axis 1
0.4
0.8
1.2
F 12. Results of PCA tests on shape factors ( ) and
particle types ( ) in fraction 2. Data labels marked *
indicate a group of data points of the same acronym which
are so close together that individual labels cannot be shown
on the graph. See text for explanations.
analysis in fraction 2 (Figure 9) also showed that
these features effectively differentiate the zooplankters
from unidentifiable particles (UN) in the sample, and
distinguish between the three species considered. This
supported our hypothesis that certain geometric
dimensions and shape factors are effective ‘ fingerprints ’ which distinguish certain particles from the
large number of amorphous aggregates composing
estuarine SPM. Results also showed that sizeindependent shape factors are as important as
size-related dimensions in characterising particles.
PCA results (Figures 7, 10 & 12) showed that some
features were more important than others in the
clustering or grouping process. In the smallest
fraction, the size-independent shape factors (E, C and
R) seemed to be more important than size-related
geometric dimensions (a, dc and w) in particle classification (Figure 7). The high loadings of l and d were
due to the large differences in lengths between the two
major diatom groups LD and CD. d (but not dc) is
dependent on these l values, hence on the difference in
the loadings of the two diameter measurements. In
fraction 2, both size-related and size-independent
features seemed to be equally important classifiers
(Figure 10). We could not make this kind of observation in fraction 3 because only shape factors were
considered in this case. However, fractal dimension
D was shown to be an important classifying feature.
This was further indicated by very different factor
loadings of two closely related shape factors C and R
(Figure 12), mainly due to the fact that C is calculated
based on p (like D), while R is calculated based on l
values.
Recently, fractals have been very useful in describing and characterising aquatic particles. Kilps et al.
(1994) found that D values of marine snow differ
depending on particle composition of the aggregate.
Li and Logan (1995) were able to follow the different
stages of phytoplankton coagulation process as a function of time by measuring the changes in D values of
particles. From light scattering data, Risovic and
Martinis (1996) were able to calculate D values of
suspended particles of different sizes.
In this study, at the fraction of particles bigger
than 300 um, particle perimeters were successfully
measured and consequently the fractal dimensions
D were calculated. Higher D values in dicotyl
detrital particles indicate ruggedness or convolutions
on their perimeters. This difference in D values may
be due to the different venation patterns on the
leaves of the two groups of plants, the monocotyls
having parallel venation while the dicotyls having net
venation (Muller, 1979). It can be assumed that
during the fragmentation of the leaves into small
detrital pieces, the breaking up follows along the
lines of the venation pattern. Thus, a monocotyl
detritus will have the tendency to break up into
somewhat rectangular-shapes, following parallel lines
of venation [Figure 4(a)] while dicotyls will have
more irregular borders, like the fringes of a torn net
[Figure 4(b)]. This morphological difference is also
reflected in the differences in porosity between the
two types of detritus. This distinction between
detritus of different sources is especially relevant in
riverine and estuarine environments where a large
portion of the detritus is of terrestrial plant origin
(Pomeroy, 1980). Our results show that this distinction, based on D values, is possible even in particles
in the size range of a few millimeters.
304 R. G. Billiones et al.
The measurement of the p values (thus, their fractal
dimensions D) of the small particles in fraction 1 was
not possible because the scale (pixel) used is relatively
large in comparison to the size of particle. On the
other hand, fractal analysis of particles in fractions 2
and 3 was limited by the available microscopic magnifications. These problems can be remedied by the
use of smaller pixels and higher magnifications, using
the appropriate machinery. Thus, the measurement of
the fractal dimensions of microscopic particles by
image analysis is highly dependent on the capabilities
of the light microscope and that of the image analyser
system. The geometric dimensions, however, did not
seem to be not greatly affected by capabilities of the
system.
We can not make any statement at this point about
the fractal dimensions of diatoms and zooplankton,
since we were not successful in the measuring this
characteristic in fractions 1 and 2. Unlike the geometric dimensions, the measurement of D is not
so straightforward. However, it may be possible,
using more recent models of image analysers, to a
certain extent, to have an automated distinction between small-sized detritus of different sources as in
fraction 3.
The ‘ fingerprinting ’ described here has significant
consequences in the automation of SPM classification.
Jeffries et al. (1984) achieved a classification using
neural network and Zölder et al. (1996) classified
zooplankton from the Baltic Sea using very
sophisticated hardware and software. The ultimate
goal of such studies, however, is the taxonomic classification of zooplankters. Our study has demonstrated a
much simpler, yet effective way to distinguish
diatoms and zooplankters from other particles in
samples of high detrital content, typical of estuarine
waters. No special programming nor hardware is necessary for such classification, which can be done using
only the most basic capabilities of any image analysing
system. Although the technique could not be used to
characterize all plankters up to the species level, it can
be a useful tool for an automated inventarisation of the
living and non-living components of SPM in highly
turbid (estuarine) waters.
Recent developments in technology have produced
faster image analysis systems and software which can
also measure features such as fractal dimensions
(Kindratenko et al., 1996) and shape factors (Jandel,
1996) directly. A three-dimensional imaging analysis
has been developed for medical use (Elliot et al.,
1996). These new trends present many possibilities to
improve the method presented here and will promote
further the ecological application of the image analysis
technique.
Acknowledgements
This study was partly funded by the project Onderzoek
Milieu Effecten Sigmaplan in de Schelde (OMES). The
authors are grateful to R. Van Mieghem, C. du Rang
and R. Vanthomme for their help in the sampling and
to the Cytogenetics Laboratory (Vrije Universiteit
Brussel) for the use of its image analyser system. Prof.
N. Roggen provided some valuable information and
references on fractals.
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