Ecol Res (2006) 21:75–90
DOI 10.1007/s11284-005-0098-x
O R I GI N A L A R T IC L E
Lars Håkanson
The relationship between salinity, suspended particulate matter and
water clarity in aquatic systems
Received: 19 January 2005 / Accepted: 22 June 2005 / Published online: 11 August 2005
Ó The Ecological Society of Japan 2005
Abstract This work presents and recommends 1) an
empirically based new model quantifying the relationship between salinity, suspended particulate matter
(SPM) and water clarity (as given by the Secchi depth)
and (2) an empirical model for oxygen saturation in the
deep-water zone for coastal areas (O2Sat in %). This
paper also discusses the many and important roles that
SPM plays in aquatic ecosystems and presents comparisons between SPM concentrations in lakes, rivers and
coastal areas. Such comparative studies are very informative but not so common. The empirical O2Sat model
explains (statistically) 80% of the variability in mean
O2Sat values among 23 Baltic coastal areas. The model
is based on data on sedimentation of SPM, the percentage of ET areas (areas where erosion and transportation of fine sediments occur), the theoretical deepwater retention time and the mean coastal depth. These
two new models have been incorporated into an existing
dynamic model for SPM in coastal areas that quantifies
all important fluxes of SPM into, within and from
coastal areas, such as river inflow, primary production,
resuspension, sedimentation, mixing, mineralisation and
the SPM exchange between the given coastal area and
the sea (or adjacent coastal areas). The modified dynamic SPM model with these two new sub-models has
been validated (blind tested) with very good results; the
model predictions for Secchi depth, O2Sat and sedimentation are within the uncertainty bands of the
empirical data.
Keywords Aquatic systems Æ Coastal ecosystems Æ
Salinity Æ SPM Æ Water clarity Æ Secchi depth Æ
Empirical models Æ Dynamic model
L. Håkanson
Department of Earth Sciences, Uppsala University,
Villav 16, 752 36 Uppsala, Sweden
E-mail: [email protected]
Fax: +46-18-4712737
Introduction
This work presents compilations and statistical analyses
of data on salinity, suspended particulate matter (SPM)
and Secchi depth (a standard measure of water clarity,
see Wetzel 2001) from aquatic systems (lakes, rivers and
marine systems). The results of the statistical analyses
will be put into a dynamic coastal model for SPM (from
Håkanson et al. 2004a), which also calculates sedimentation and oxygen saturation in the deep-water zone.
There are many reasons to focus on salinity, SPM
and water clarity. Salinity is of paramount importance
to the number of species, as shown in Fig. 1. It also
influences the aggregation of suspended particles (which
will be discussed in this paper). This is of particular
interest in modelling and understanding how SPM varies
within and among systems, and the many roles that
SPM plays in influencing important structural and
functional aspects of aquatic ecosystems (Håkanson
2005). The SPM regulates the partition coefficient, and
hence also the two major transport routes, the dissolved
transport in the water (the pelagic route) and the particulate sedimentation (or benthic) route, of all types of
materials and contaminants. The SPM in the water
column is also a metabolically active component of
aquatic ecosystems. The carbon content of SPM is crucial at low trophic levels as a source of energy for bacteria, phytoplankton and zooplankton (see Jørgensen
and Johnsen 1989; Wetzel 2001; Kalff 2002). The SPM is
also directly related to many variables of general use in
water management as indicators of water clarity (e.g.,
Secchi depth, water colour and the depth of the photic
zone; see Håkanson 1999). Suspended particles will
settle out on the bottom and the organic fraction will be
subject to bacterial decomposition. This will influence
the oxygen concentration and hence also the survival of
zoobenthos, an important food source for fish (Håkanson and Boulion 2002). The SPM influences primary
production of phytoplankton, benthic algae and macrophytes, the production and biomass of bacterio-
76
Fig. 1 Relationship between salinity and number of species.
Redrawn from Remane (1934)
plankton, and hence also the secondary production of,
e.g., zooplankton, zoobenthos and fish. The effects of
SPM on recycling processes of organic matter, major
nutrients and pollutants determine the ecological significance of SPM in any given aquatic environment.
Understanding the mechanisms that control the distribution of SPM in rivers, lakes and marine systems and
the role played by salinity in this respect is an issue of
both theoretical and applied concern, as physical,
chemical and biological processes ultimately shape
aquatic ecosystems. Many sources are known to regulate
the SPM concentration in aquatic systems (Vollenweider
1958, 1960; Carlson 1977, 1980; Brezonik 1978; OECD
1982; Ostapenia et al. 1985; Preisendorfer 1986; Boulion
1994, 1997). The most important sources/factors are as
follows:
1. Autochthonous production (i.e., the amount of
plankton, faeces, etc. in the water—more plankton,
etc. means a higher SPM)
2. Allochthonous materials, such as the amount of
coloured matter (e.g., humic and fulvic substances)
3. The amount of resuspended material
This is easy to state qualitatively, but more difficult
to express quantitatively because these three factors are
not independent: high sedimentation leads to high
amounts of resuspendable materials; high resuspension
leads to high internal loading of nutrients and increased production; a high amount of coloured substances means a smaller photic zone and a lower
production; a high input of coloured substances and a
high production mean a high sedimentation, etc. The
results presented by Wallin et al. (1992) show that the
water clarity should be much greater than that observed if only plankton cells were responsible for the
light extinction. This means that particles other than
plankton cells are perhaps the most important factors
for determining water clarity.
The SPM is generally a complex mix of substances
of different origins with different properties (size,
form, density, specific surface area, capacity to bind
pollutants, etc.). The SPM may be divided into particulate organic matter (POM) and particulate inorganic matter (PIM). Total organic matter (TOM) is
generally divided into POM and dissolved organic
matter (DOM). Normally, POM is about 20% of
TOM, but this certainly varies among and within
systems (Ostapenia 1987, 1989; Velimorov 1991; Boulion 1994). Normally, about 4% of POM is living
matter and the rest is dead organic matter (detritus).
About 80% of TOM is generally in the dissolved
phase, and of this, about 70% is conservative in the
sense that it does not change due to chemical and
biological reactions in the water mass.
This work will address the following relationships: (1)
the empirical relationship between salinity, SPM and
Secchi depth by making use of data available to the
author to develop an algorithm that can be used in dynamic modelling of SPM in coastal areas and (2) the
empirical relationship between the oxygen saturation in
the deep-water zone and sedimentation of SPM. These
two empirical models will be put into an existing dynamic model for SPM (from Håkanson et al. 2004a and
Håkanson 2005). The idea is to test how the sub-models
work by comparing the predictions from the dynamic
model with empirical data. There are three target variables for the model predictions: sedimentation of SPM,
mean coastal Secchi depth and the mean oxygen saturation in the deep-water zone. Measured data on these
target variables are available from 17 coastal areas and
will be used in the model validations.
The basic perspective or scale underlying these studies
is the ecosystem scale, i.e., the interest is focused on
defined coastal areas (and not sampling sites) and mean
monthly conditions in coastal areas. This is also a target
scale in water management when questions are asked
about the status of a given ecosystem and what can be
done to improve its condition. It should be stressed that
there is no contradiction between work at the larger
ecosystem scale and sampling and work at a smaller
scale, since the mean values characterising ecosystem
conditions and the standard deviations characterising
the variability around such mean values must emanate
from sampling at individual sites.
During the last 10 years, there has been something of
a ‘‘revolution’’ in aquatic ecosystem modelling. The
77
major reason for this development is the Chernobyl
accident. Following the pulse of radionuclides through
ecosystem pathways has meant that important transport
routes have been revealed and the algorithms to quantify
them have been developed and tested (Håkanson 2000).
It is important to stress that many of those structures
and equations are valid not just for radionuclides, but
for most types of contaminants, e.g., for metals, nutrients and organics—and for SPM—in most types of
aquatic environments (coastal areas, rivers and lakes).
In lake studies, it is easy to define the ecosystem, since
this is often the entire lake. The ‘‘Data and methods’’
section will discuss a method to also define coastal
ecosystems. Data from several databases will be used,
and the next section will present those databases.
Data and methods
The total amount of a substance or a group of substances in the water is often separated into a particulate
phase, subject to gravitational sedimentation, and a
dissolved phase, generally the most important phase for
direct bio-uptake. Operationally, the limit between the
particulate phase and the dissolved phase is generally
determined by means of filtration using a pore size of
0.45 lm. The SPM is sometimes also referred to as SSC,
the suspended sediment concentration (Gray et al. 2000).
Filtration is often a justifiable method from sedimentological, ecological and mass-balance modelling perspectives.
Data
A data set for lakes (see Table 1) from several investigations has been compiled by Lindström et al. (1999)
and used in this work. The river database has been
compiled and described by Håkanson et al. (2005). It
consists of three parts: the European database (the data
come mainly from the United Nations Environmental
Programme, GEMS/Water); the UK database (Foster
et al. 1996, 1997, 1998), which provides a range of data
for 79 monitoring sites in UK rivers; and a Swedish
database for lakes (Håkanson and Peters 1995). The
marine database concerns SPM and co-variables in
Baltic coastal areas (from Wallin et al. 1992 and
Håkanson et al. 2004a). The 17 coastal areas (see Table 2) are located in the Baltic Sea. Five of the areas are
in the St. Anna archipelago off the Swedish east coast,
seven areas are located in the Blekinge archipelago, in
the south of Sweden, and the remaining five areas are in
the Åbolands archipelago of Finland. The Baltic Sea is
brackish with a salinity ranging from 5–10& in a northsouth gradient (see Fig. 2). The Baltic Sea is shallow
(mean depth 56 m) and is almost entirely surrounded by
land. The tidal variation is small (<20 cm; see Voipio
1981). The Åbolands archipelago is the largest archipelago in the Baltic Sea. It reaches from Åland to the
Finnish main land. The St. Anna archipelago has many
islands and deep, long bays, often with thresholds towards the sea. The Blekinge archipelago in southern
Sweden is narrow and the water circulation is generally
good (Persson et al. 1994).
Table 1 Data for the 17 studied Baltic coastal areas
Area
Lilla Rimmö
Eknön
Lagnöströmmar
Gräsmarö
Ålön
Matvik
Boköfjärd
Tärnö
Guavik
Järnavik
Spjutsö
Ronneby
Käldö
Haverö
Hämmärösalmi
Laitsalmi
Kaukolanlahti
Min.
Max
Mean (MV)
Code
SE1
SE2
SE3
SE4
SE5
SS1
SS2
SS3
SS4
SS5
SS6
SS7
F1
F2
F3
F4
F5
Latitude
(°N)
58
58
58
58
58
56
56
56
56
56
56
56
61
61
61
61
61
56
61
58
Land
uplift
(mm/year)
2
2
2
2
2
0
0
0
0
0
0
0
5
5
5
5
5
0
5
2.1
Area
(km2)
Dmax
(m)
Dm
(m)
At
(km2)
Chl
(lg/l)
2.59
14.04
5.41
14.15
6.54
3.12
7.05
1.54
2.86
3.49
3.49
11.94
3.14
2.54
2.21
4.28
1.38
1.4
14.2
5.3
17.6
19.5
20.1
46.9
35.2
14.3
21.6
11.1
22.8
18.6
15.6
17.6
16.7
22.5
19.3
18.5
13.3
11.1
46.9
20.7
8.3
8.5
3.8
13.8
8.0
5.2
7.1
5.1
5.2
5.7
5.8
4.3
7.6
8.6
7.9
7.6
4.8
3.8
13.8
6.9
0.0172
0.0168
0.0032
0.0825
0.0162
0.0067
0.0141
0.0062
0.0074
0.0081
0.0188
0.0176
0.0040
0.0172
0.0114
0.0080
0.0006
0.0006
0.0825
0.0151
2.3
3.5
4.6
2.6
2.1
1.4
1.4
1.6
2.0
1.3
0.9
2.1
2.7
2.1
2.2
2.7
9.6
0.9
9.6
2.65
Salinity
(&)
6.4
5.4
6.4
6.6
6.6
6.5
7.2
7.2
7.3
7.3
7.4
6.5
6.5
6.5
6.5
6.5
6.5
5.4
7.4
6.6
Fish
prod.
(times/year)
SedDW
41
32
125
200
300
135
70
50
50
10
50
100
50
22
381
85
35
10
381
102
20.2
5.3
22.7
18.3
9.5
12.7
6.7
7.6
6.4
8.1
8.7
20.2
20.0
38.7
13.4
37.0
26.3
5.3
56.4
17.7
SedSW
(g dw/m2 day)
4.2
2.0
11.1
1.1
3.7
4.2
1.6
3.1
1.9
1.5
4.4
4.1
11.0
9.2
9.1
17.6
15.3
1.1
17.6
6.2
Secsea
(m)
3
2.5
2
3
3
4.5
5
5
5
5
5
4
2
2
3
1.5
1
1
5.0
3.3
Dmax Maximum depth, Dm mean depth, At section area or opening area towards the sea, Chl chlorophyll-a concentration, SedDW
sedimentation in sediment traps placed in the deep-water zone, SedSW sedimentation in sediment traps placed in the surface-water zone,
Secsea Secchi depth in the sea just outside the coastal area. Data from Wallin et al. (1992) and Håkanson (2000)
78
Table 2 Results of the stepwise multiple regression for the oxygen saturation in the deep-water zone (mean O2Sat in the deep-water zone
during the growing season in %) using the coastal database
Step
r2
Model variable
Model
1
2
3
4
0.43
0.64
0.74
0.80
x1=log(SedDW)
x2=ÖET
x3=log(1+TDW)
x3=ÖDm
y=0.925Æx1+0.132
y=0.974Æx10.185Æ x2+1.72
y=0.866Æx10.151Æx2+0.244Æx3 +1.39
y=0.643Æx10.118Æx2+0.301Æx3+0.323Æx4+0.470
n=23 Baltic coastal areas, F>4. y = log(101O2Sat). SedDW Sedimentation in sediment traps placed in the deep-water zone of the
coastal area (g/m2 day), ET areas where erosion and transportation of fine sediments occur, TDW theoretical deep-water retention time
(days), Dm mean depth (m)
Fig. 2 Characteristic salinities in the Baltic Sea in a gradient from
Skagerrak (in the North Sea) to the Bothnian Bay in the northern
part of the Baltic Sea (from Håkanson 1991)
Definition of coastal areas
The question is where to place the boundaries between
the sea and/or adjacent coastal areas. It is crucial to use
a technique that provides an ecologically meaningful
and practically useful definition of the coastal ecosystem. How should one define this area so that parameters,
like mean depth (Dm in metres), can be relevant as model
variables (x) to predict target y variables? The problem
is shown in Fig. 3a using data on Secchi depth (the y
variable in this example) and mean depth (Dm, the x
variable that reflects, e.g., resuspension processes).
For lakes, there exists a significant (r2 =0.38,
P=0.0001 for 88 Swedish lakes) positive relationship
between Dm and Secchi depth: the deeper the lake, the
larger the bottom areas beneath the wave base, the less
resuspension, the less suspended materials in the lake
water, the clearer the water and the greater the Secchi
depth. This is logical. The mean depth has a significant
meaning for an important ecosystem variable, Secchi
depth. The entire lake is the defined ecosystem.
But how would this apply for a marine coastal area?
Is there a method to define the boundaries and establish
coastal ecosystems where morphometric parameters like
the mean depth have meaning in predictive ecosystem
models? This is illustrated in Fig. 3b. In this example,
there are three boundary lines, A, B and C, defining
three coastal areas. The mean depths of the enclosed
areas are 4.5, 3.5 and 2.5 m, respectively. The exposure
of the coastal area (Ex) is a morphometric parameter
defined by the ratio between the section area and the
enclosed coastal area (Ex=100ÆAt/Area, where
At=section area or the opening area towards the sea in
km2 and Area=coastal area in km2). The Ex values are
quite different for the coastal area given by lines A
(0.05), B (0.1) and C (0.2), but the Secchi depth is the
same in all three cases (2 m). Arbitrary borderlines (such
as A, B and C) can be drawn in many ways and the mean
depths of the corresponding enclosed coastal areas
would be devoid of meaning in models for target ecosystem variables, such as Secchi depth.
The approach in this work (from Håkanson et al.
1986 and Pilesjö et al. 1991) assumes that the borderlines
are drawn at the topographical bottlenecks so that the
exposure (Ex) of the coast from winds and waves from
the open sea is minimised. It is easy to use the Ex value
as a tool to test different alternative borderlines and
define the coastal ecosystem where the Ex value is
minimal. If the coastal ecosystem is defined in this way,
there exists, as shown in Fig. 3b, a weak but statistically
significant (r2 =0.14, P=0.08 for 23 Baltic coastal
areas) negative relationship between Secchi depth and
mean depth: the greater Dm, the more suspended materials will be retained in the coastal water, the more turbid the water will be and the smaller the Secchi depth
will be. This is also logical because coastal areas are by
definition open to the outside sea (i.e., At>0; if At=0,
then this is not a coastal area but a lake near the sea).
For open coastal areas with large Ex values, a significant
part of the fine materials suspended in the water can
‘‘escape’’ from the coastal area to the open water area or
to surrounding coastal areas. This is not the case in the
same way for lakes. Open, exposed coastal areas with
small mean depths will generally, therefore, have coarse
bottom sediments (sand, gravel, etc.) and small amounts
of fine materials, which cause a high turbidity when
resuspended.
Results
Background
Comparative studies in aquatic sciences often aim to
find general factors regulating and explaining why
systems differ in fundamental properties. Figure 4 gives
79
Fig. 3 Illustration and rationale for the
definition of ecosystem boundaries for
a lakes and b coastal areas. The coastal
ecosystem in this work is defined by the
borderline marked A, which gives a
minimum value for the exposure (Ex; the
‘‘topographical bottleneck method’’)
a comparison between SPM values from marine
systems, lakes and rivers. Many factors (x-variables)
could potentially influence the variability in SPM
among and within systems. The statistical analysis
based on empirical data can be used to rank the
importance of how the different x-variables influence y.
In these contexts, one must clearly differentiate between
statistical and causal analyses. Statistical treatments can
never mechanistically ‘‘explain’’ why certain x-variables
end up with a high correlation towards y, but results
from correlations and regressions can provide important information for further mechanistic interpretations
and modelling.
From Fig. 4, one can note that SPM seems to vary in
a systematic way among and within marine/brackish
systems, rivers and lakes. A key objective of this work is
to try to explain the role of salinity in the variations in
SPM shown in Fig. 4.
Fig. 4 Comparison of SPM data from marine/brackish systems,
lakes and UK and European rivers. The box-and-whisker plots
provide the medians, quartiles, 90th and 10th percentiles and
outliers
SPM and water clarity
Water clarity is a fundamental variable in aquatic
studies since it regulates primary production of phytoplankton, benthic algae and macrophytes (see Håkanson
and Boulion 2002). Secchi depth is a standard variable
for water clarity in lake management, but not in marine
studies. Values of Secchi depth are easy to understand
by the general public—clear waters with large Secchi
depths seem more attractive than turbid waters. Many
factors are known to influence the Secchi depth (Vollenweider 1958, 1960; Carlson 1977, 1980; Brezonik
1978; OECD 1982; Ostapenia et al. 1985; Preisendorfer
1986; Boulion 1994, 1997).
80
Fig. 5 a The relationship
between Secchi depth (in m) as
a standard measure of water
clarity and the SPM
concentration (mg/l) based on
573 data from 23 lakes covering
a wide limnological domain
(from highly eutrophic to
oligotrophic conditions). b The
corresponding regression for 26
Baltic coastal areas and a
comparison between the two
regression lines for lakes and
coastal areas. The figure gives
the regression line, r2 coefficient
of determination and n number
of data
Figure 5a shows the very strong and logical relationship between lake Secchi depth and the concentration of SPM (in mg/l) based on 573 individual samples
from 23 lakes (covering a wide limnological domain
from oligotrophic to highly eutrophic conditions; data
from Håkanson and Boulion 2002). Figure 5b shows a
similar regression using data for Baltic coastal areas.
One can note some interesting differences:
– As shown in Fig. 4, marine/brackish waters generally
have a higher clarity than lakes and rivers, and the
variability in SPM values is generally significantly
smaller in marine/brackish systems. Figure 5 also
indicates that the slope of the regression line is smaller
for marine systems than for lakes (0.59 compared to
1.12), which indicates that a given change in Secchi
depth would correspond to a smaller change in SPM
values for marine systems than for lakes. The range in
the coastal data used here is relatively small since the
data in Fig. 5b come from the Baltic, but the correlation is highly significant (r2=0.80) even in this
narrow range.
– One mechanistic reason for this difference between
lakes and marine systems is related to the fact that the
salinity of the system will influence the flocculation/
aggregation, and hence also the settling velocity, of
the suspended particles (SPM): the higher the salinity,
the greater the aggregation of suspended particles, the
bigger the flocs and the faster the settling velocity
(Kranck 1973, 1979; Lick et al. 1992). This will be
discussed further in the following sections.
SPM versus Secchi depth and salinity
The information in Fig. 5 is shown again in another
way in Fig. 6. In this case, the figure does not give
regressions but empirically based deterministic relationships related to defined boundary requirements.
Based on the available empirical data shown in Fig. 6,
one can assume that the maximum average SPM concentration in surface waters (SPMSW) in lakes and
marine coastal areas (but not in rivers; see Håkanson
et al. 2005) should generally be lower than 50 mg/l. One
can also assume that if the SPM value is very low
(0.5 mg/l), the Secchi depth in lakes (with salinity=0&)
should be about 10 m; the corresponding Secchi depth
in coastal areas with a salinity of 6.5& should be about
50 m; and the Secchi depth should approach 200 m if
the salinity approaches 30&. There are many data in
Fig. 6 supporting the relationship between SPM, Secchi
depths and salinity for lakes, fewer data for Baltic
coastal areas and no data for coastal areas with higher
salinities. The relationships outlined in Fig. 6 should,
therefore, be regarded as a working hypothesis. From
the boundary conditions defined for the lines in Fig. 6,
one can see that:
– For salinity 0&, log(Secchi)=1 for SPMSW=0.5 mg/
l; this y-coordinate defines z=1
– For salinity 6.5&, log(Secchi)=1.7 for SPMSW=
0.5 mg/l; this y-coordinate defines z=1.7
– For salinity 30&, log(Secchi)=2.3 for SPMSW=
0.5 mg/l; this y-coordinate defines z=2.3
It is assumed that the Secchi depth can never be
higher than 200 m because even distilled water will
scatter light and set a limit to the Secchi depth. Figure 7
shows the relationship between z and the surface-water
(SW) salinity (salSW in &). One can see that:
w ¼ 0:15u þ 0:3
ð1Þ
where w=log(1+z) and u=log(1+salSW); and hence
from Fig. 6:
ðy zÞ ¼ ðz þ 0:5Þ=ð0:3 1:7Þðx þ 0:3Þ
ð2Þ
or
y ¼ ðz þ 0:5Þðx þ 0:3Þ=ð2Þ þ z
ð3Þ
81
Fig. 6 Illustration of the relationship between log(SPMSW) and
log(Secchi) using the data for freshwater systems (surface-water
salinity 0&) and Baltic areas (mean surface-water salinity 6.5&).
Note that these are not regression lines but deterministically drawn
lines from the end point (50 mg/l, 0.3 m) and the starting points on
the y-axis, where the values are given for the actual data for the
surface-water SPM and Secchi depth
Fig. 7 The relationship between log(1+z) and log(1+salSW)
deep-water zone. This sub-model will be presented in the
following section.
where y = log(Sec) and x = log(SPMSW)
z ¼ ð10^ð0:15 log ð1 þ salSW Þ þ 0:3Þ 1Þ
ð4Þ
This means that the desired algorithm to estimate
Secchi depth (Sec) from SPMSW and salSW may be given
by:
Sec ¼ 10^ððð10^ð0:15 logð1 þ salSW Þ þ 0:3Þ 1ÞÞ
þ 0:5ÞðlogðSPMsw Þ þ 0:3Þ=2
þ ð10^ð0:15 logð1 þ salSW Þ þ 0:3Þ 1ÞÞÞ
ð5Þ
where Sec is the Secchi depth in metres. SPMSW, as a
function of Secchi depth and salinity, may then be expressed by:
SPMSW ¼ 10^ð0:3 2ðlogðSecÞ
ð10^ð0:15 logð1 þ salSW Þ þ 0:3Þ 1ÞÞ=
ðð10^ð0:15 logð1 þ salSW Þ þ 0:3Þ 1Þ þ 0:5ÞÞ ð6Þ
Figure 8 gives two nomograms illustrating the relationship between Secchi depth, salSW and SPMSW. From
Fig. 8, one can note that a SPM value of 10 mg/l corresponds to a Secchi depth of about 1.5 m in a lake and
a Secchi depth of about 3.5 m if the salinity is 30&.This
empirically based deterministic model linking SPM,
Secchi depth and salinity will be tested in a following
section, where SPM values will not come from measurements but from a dynamic SPM model (from
Håkanson et al. 2004a). The dynamic SPM model
quantifies fluxes of SPM into, within and from coastal
areas. Within this dynamic model there is also a new
sub-model to predict the oxygen saturation in the
SPM and oxygen in deep water
When the mean O2 concentration is lower than about
2 mg/l, and the mean oxygen saturation (O2Sat in %) is
lower than about 20%, many key functional benthic
groups are extinct (see Fig. 9).
Empirical data on the amount of material deposited
in deep-water sediment traps (1 m above the bottom;
SedDW in g/m2 day) were used (see Table 1) in deriving
the empirical model (see Table 2) for O2Sat using statistical methods discussed by Håkanson and Peters
(1995). This empirical model for O2Sat will be put into
the dynamic SPM model, and then the empirical data on
SedDW will be replaced by modelled values from the
dynamic model. The values for O2Sat calculated in this
manner will be compared to mean empirical data on
O2Sat from the growing season.
The sediment traps were placed at two to three sites in
each coastal area. They were out for about 7 days at
least two times during the period from July to September
in each coastal area (see Wallin et al. 1992, for further
information). Many empirical data expressing size and
form characteristics of the coastal areas and the water
quality (different forms of N, P, salinity, etc.) that may
affect the values for O2Sat have been tested in the following statistical analyses using methods described by
Håkanson and Peters (1995). The data come from 23
Baltic coastal areas. Note that data from adjacent
coastal areas have been lumped together in the information given in Table 1. This is the reason why the
empirical model for O2Sat discussed in this section is
82
4. The mean depth (Dm): the mechanistic reason for this
is not so easy to describe since Dm influences different
factors, e.g., (1) resuspension, (2) volume, and hence,
all SPM concentrations, (3) stratification and mixing
and (4) the depth of the photic zone and, hence,
primary production. Nonetheless, coastal areas with
small mean depths (contrary to lakes with small mean
depths, see Fig. 3) generally have clear water, little
SPM, low sedimentation and high O2Sat. Fine suspended particles in open coastal areas will be transported out of such areas and not be entrapped in the
same manner as in lakes. If variations among coastal
areas in Dm are accounted for, the r2 value increases
to 0.80.
From the complex hydrodynamic and sedimentological conditions in coastal areas (Håkanson 2000), one
might get the impression that complexity prevents
models of high predictive power to be developed. It is,
therefore, interesting to conclude that this statistical/
empirical model can explain as much as 80% (r2=0.8;
see Table 2) of the variability in the target y-variable.
This O2Sat model should not be used for coastal areas
with characteristics outside the limits given below, and it
should not be used for coastal areas dominated by tides.
If the model is used for other coastal areas, then the
calculation must be regarded with due reservation, as a
hypothesis rather than a prediction (see Table 2 for
definitions of the abbreviations).
Fig. 8a, b Illustration of the relationship between Secchi depth,
SPM in surface water and salinity in surface water. a The
nomogram using log-data and b using actual data
Min.
Max.
Dm (m)
ET
TDW (days)
SedDW(g/m2 day)
3.8
13.8
0.19
0.99
1
128
5.3
82.5
Dynamic modelling
based on data from 23 areas and Table 1 gives data from
17 only areas.
Of all the many factors that could, potentially,
influence variations in O2Sat among these coastal areas,
this statistical analysis (see Table 2) has shown that the
following factors are most important:
1. Sedimentation in deep-water sediment traps (SedDW):
the more oxygen-consuming matter in the deep-water
zone, the lower the O2Sat.
2. The prevailing bottom dynamic conditions in the
coastal area (ET areas): when variations in ET among
coastal areas are accounted for, the r2 value increases
to 0.64. If ET is high (say 0.95), the oxygenation is
also likely high and O2Sat is high.
3. The theoretical deep-water retention time (TDW; see
Håkanson 2000 for further information): variations
in mean O2Sat among coastal areas can also be statistically explained by variations in TDW—the longer
TDW, the lower O2Sat. This is logical and mechanistically understandable. If variations among coastal
areas in TDW are accounted for, r2 increases to 0.74.
Background
The dynamic coastal model has been described in detail
elsewhere (Håkanson et al. 2004a; Håkanson 2005) and
will not be repeated here. This section will only give a
brief outline of the dynamic model, which is illustrated
in Fig. 10. There are three main compartments: (1)
surface water, (2) deep water and (3) areas where processes of fine sediment erosion and transport dominate
the bottom dynamic conditions (the ET areas). The
volumes of the surface and deep water are calculated
from the water depth separating transportation areas for
fine particles from accumulation areas (see Håkanson
et al. 2004b for definition). There are six SPM inflows:
1. Primary production (Fprod), which includes all types
of plankton (phytoplankton, bacterioplankton and
zooplankton) influencing SPM in the water.
2. Inflow of SPM to coastal surface water from the sea
(FinSW; all fluxes are abbreviated F and calculated in g
dry weight per month in this model).
83
Fig. 9 Bioturbation and laminated
sediments. Under aerobic (=oxic)
conditions zoobenthos may create a
biological mixing of sediments down to a
sediment depth of about 15 cm (the
bioturbation limit). If the deposition of
organic materials increases and hence also
the oxygen consumption from bacterial
degradation of organic materials, the
oxygen concentration may reach the
critical limit of 2 mg/l, when zoobenthos
die, bioturbation ceases and laminated
sediments appear (figure modified from
Pearson and Rosenberg 1976)
3. Inflow of SPM to the deep water from the sea
(FinDW).
4. Land uplift (FLU). Land uplift is a special case for the
Baltic Sea related to the latest glaciation.
5. Emissions of SPM from point sources (FPSSW), in this
case from fish cage farms in the coastal areas.
6. Tributary inflow (FQ).
The amount of matter deposited on ET areas may be
resuspended by wind/wave action. The resuspended
matter can be transported either back to the surface
water (FETSW) or to the deep water (FETDW). How much
that will go in either direction is regulated by a distribution coefficient calculated from the form factor
(Vd=3Dm/Dmax; Dm=mean depth; Dmax=maximum
depth) of the coastal area. Other internal processes are
mineralisation, i.e., the bacterial decomposition of SPM
in the surface water, the deep water and the ET compartment (FminSW, FminDW and FminET) and mixing, i.e.,
the transport from deep water to surface water
(FDWSWx) or from surface water to deep water
(FSWDWx).
All basic equations of the model are compiled in
Table 3. Compared to the model presented by Håkanson et al. (2004a), there are two new parts:
1. The relationship among SPM, salinity and Secchi
depth (and hence also the depth of the photic zone)
described in the section ‘‘SPM versus Secchi depth
and salinity’’
2. The empirical sub-model for O2Sat described in the
section ‘‘SPM and oxygen in deep water’’
It should also be mentioned that there exist other
models for SPM in coastal areas. There are, e.g.,
hydraulic coastal models for SPM, such as Threetox and
Coasttox. Unlike the model discussed in this work, those
are distributed two- or three-dimensional models based
on partial differential equations; the model POSEIDON
is based on several interlinked boxes. These models are
used in the RODOS DSS (see http://www.rodos.fzk.de/),
and they are mainly designed to handle short-term
(hours to days) spatial variations. They are driven by
online meteorological data (winds, temperature and
precipitation) and hence cannot be used for predictive
purposes over time periods longer than 2–3 days since it
is not possible to forecast weather conditions for longer
periods than that. Such models may be excellent tools in
science and may provide descriptive power rather than
long-term predictive power.
There are also different types of ecosystem-oriented
models and modelling approaches for sedimentation
and variables influencing sedimentation in coastal
areas (see, e.g., Wulff et al. 2001). However, there are
major differences between the model discussed here
and other models, including differences in target
variables (from conditions at individual sites to mean
values over larger areas), modelling scales (daily to
annual predictions), modelling structures (from using
empirical/regression models to the use of ordinary or
partial differential equations) and driving variables
(whether accessed from standard monitoring programs, climatological measurements or specific studies). To make meaningful model comparisons is not a
simple matter, and this is not the focus of this work.
As far as the author is aware, there are no massbalance models for SPM and coastal sedimentation of
the type discussed here that account for total primary
production, point-source emissions, freshwater input,
surface- and deep-water exchange processes, land uplift, internal loading, mixing and mineralisation in a
general manner designed to achieve practical utility
and predict monthly variations. Also the fundamental
unit, the defined coastal area, is determined in a way
that, to the best of the author’s knowledge, has not
84
Fig. 10 A general outline of the
structure of the coastal model.
Note that, for simplicity, pointsource emissions to the deepwater compartment have been
omitted in this figure
been used before in dynamic modelling of sedimentological processes; no comparable models use the
topographical bottleneck approach to define the
coastal area. This modelling approach also makes it
possible to estimate the theoretical surface-water and
deep-water retention times (which are fundamental
components in coastal mass-balance modelling) from
bathymetric map data.
The accuracy of a model prediction is strongly influenced by the uncertainty in the empirical data used to run
and validate the model (Håkanson 1999). Sedimentation
is known to display considerable natural variation between years, seasons and/or even between closely located
stations (Blomqvist 1992; Matteucci and Frascari 1997;
Heiskanen and Tallberg 1999). Douglas et al. (2003) have
shown that there are large variations in sedimentation
even during 36- to 48-h periods. The empirical sediment
trap data used to validate this model have coefficients of
variation (CV) of 0.58 for the surface-water and 0.50 for
the deep-water compartment (Wallin et al. 1992).
In models for lakes and/or coastal areas, the surface-water compartment is often separated from the
deep-water compartment by the thermocline (Carlsson
et al. 1999), the pycnocline (Abdel-Moati 1997) or the
halocline (Andreev et al. 2002). However, the classic
effect-load-sensitivity model by Vollenweider (1968) for
lakes does not separate surface and deep water at all
and neither does De Schmedt et al. (1998) when
modelling suspended sediments and heavy metals in the
Scheldt estuary. The thermocline, halocline and pycnocline are all gradients, and they can be found over
wide ranges of water depths (Håkanson et al. 2004b).
This means that it is often difficult to find a relevant
value to separate the surface-water compartment from
the deep-water compartment using, e.g., temperature
data. In this modelling, the separation is not done in
the traditional way using temperature data, but by the
wave base (the ‘‘critical water depth’’), i.e., the depth
below which fine cohesive particles following Stokes’s
law are continuously being deposited. This gives a
defined critical water depth for each coastal area. From
this water depth, it is easy to calculate requested water
volumes, sedimentation, resuspension, mixing, mineralisation and outflow. This also leads to a relatively
simple model structure since the sedimentation of SPM
from the deep water, and the deep water alone, ends up
on areas of continuous sedimentation (the accumulation areas).
Table 4 gives the panel of driving variables. These are
the coastal-area-specific variables needed to run the
dynamic SPM model. They are all easily accessed, e.g.,
from standard monitoring programmes or maps. No
other part of the model should be changed unless there
are good reasons to do so.
Results
The quality of models is not governed by statements or
arguments but by performance in blind tests. Note that
the new sub-model has been motivated by empirical data
or results based on empirical data. There has been no
calibration of the dynamic SPM model. The results of
the validations will be presented in the following way.
To determine how well the model predicts, there will first
be a comparison between empirical data, uncertainties in
empirical data and model-predicted values for sedimentation, Secchi depth and oxygen saturation in one of
85
Table 3 A compilation of the differential equations for the dynamic coastal SPM model
Equations
Surface water (SW)
MSW(t)=MSW(td t)+(FinSW+FDWSWx+FETSW+Fprod+FPSSW+FLU–FoutSWFSWDWFSWET–FminSWFSWDWx)Æd t
MSW(t)=Mass (amount) in the SW compartment at time t (g)
FinSW=Flow into the SW compartment from the sea (g/month); see text
FDWSWx=Flow from deep water to surface water (upward mixing; g/month); see below
FETSW=Flow (resuspension) from ET areas to the SW compartment (g/month); see below
Fprod=Flow into the SW compartment from primary production (g/month); see text
FPSSW=Flow into the SW compartment from point-source emissions (g/month; see Håkanson et al. 2004a)
FoutSW=Flow from the SW compartment and out of the coastal area (g/month); see text
FSWDW=Flow (sedimentation) from the SW compartment to deep-water compartment (g/month); see below
FSWET=Flow (sedimentation) from the SW compartment to ET areas (g/month); see below
FminSW=Flow (mineralisation) from the SW compartment (g/month); see below
FDWSWx=Flow from surface water to deep water (downward mixing; g/month); see below
ET areas (ET)
MET(t)=MET(td t)+(FLU+FSWETFETDWFETSW–FminET)Æd t
MET(t)=Mass (amount) in the ET compartment at time t (g)
FLU=Flow into the SW compartment from land uplift (g/month; see Håkanson et al. 2004a)
FETDW=Flow (resuspension) from ET areas to the DW compartment (g/month); see below
FminET=Flow (mineralisation) from ET areas (g/month); see below
Deep water (DW)
MDW(t)=MDW(td t)+(FSWDW+FETDW+FSWDWx+FinDW+FPSDWFDWSWxFDWA–FoutDW–FminDW)Æd t
MDW(t)=Mass (amount) in the DW compartment at time t (g)
FinDW=Flow into the DW compartment (g/month); see text
FPSDW=Flow into the DW compartment from point-source emissions (g/month; see Håkanson et al. 2004a)
FDWA= Flow (sedimentation) from the DW compartment to At areas (g/month); see below
FoutDW=Flow from the DW compartment and out of the coastal area (g/month); see text
FminDW=Flow (mineralisation) from the DW compartment (g/month); see below
Other important algorithms
FDWSWx=MDWÆRmixÆ(VSW/VDW)
FETSW=MET(1Vd/3)Æ1/TET [TET=1 month]
FSWDW=MSWÆ(1ET)Æ(vdef/DSW)YZMTÆYSPMSWÆYsalSWÆYDRÆ((1DCresSW)+YresÆDCresSW) [vdef=6 m/month]
YZMT: If Q>Qsea then YZMT=(salsea/salSW)Æ(Qsea+Q)/Q) else YZMT=(salsea/salSW)Æ(Qsea+Q)/Qsea) [Q values in m3/month; calculates
sedimentation effects related to the ‘‘zone of maximum turbidity’’]
YSPMSW=(1+0.75Æ(CSW/501)) [calculates how changes in SPM (CSW) influence sedimentation]
YSPMDW=(1+0.75Æ(CDW/501)) [calculates how changes in SPM (CDW) influence sedimentation]
YsalSW=(1+1Æ(sal/11))=1Æsal/1 [calculates how changes in salinities > 1& influence sedimentation]
YDR: If DR<0.26 then 1 else 0.26/DR [calculates how changes in DR and turbulence influence sedimentation]
DCresSW=FETSW/(FETSW+Fin+Fprod) [the resuspended fraction of SPM]
Yres=((TET/1)+1)0.5 [calculates how much faster resuspended sediments settle out]
FSWET=MSWÆETÆ(vdef/DSW)YSPMSWÆYsalSWÆYDRÆ((1DCresSW)+YresÆDCresSW) [vdef=6 m/month]
FminSW=MSWÆRminÆYETÆ(SWT/9)1.2 [Rmin=0.125]
YET=0.99/ET [calculates how changes in ET among systems influence mineralisation]
FminDW=MDWÆRminÆYETÆ(DWT/9)1.2 [Rmin=0.125]
FDWA=MDWÆRDW
RDW=vDW/DDW
vDW=(vdef/12)ÆYSPMDWÆYsalDWÆYDRÆYDWÆ((1DCresDW)+YresÆDCresDW)
YDW: If TDW<7 (days) then YDW=1, else YDW=(TDW/7)0.5 [calculates how changes in T and turbulence influence deep-water
sedimentation]
the 17 coastal areas. Then, the modelling results for all
17 coastal areas will be directly compared to empirical
data. This study asks the basic question: How well does
the model predict using the new algorithm relating
salinity to Secchi depth and SPM and the new empirical
sub-model for O2Sat?
The first results for a randomly selected coastal area
are given in Fig. 11 for coastal area Gräsmarö, Swedish
east coast. Figure 11a gives the empirical values for
sedimentation in surface-water sediment traps (called
empirical minimum values) and deep-water sediment
traps (empirical maximum values). The modelled minimum values are calculated from sedimentation of SPM
on accumulation areas (FDWA). Sedimentation on
accumulation areas should vary from zero at the wave
base to maximum values in the deepest part of the
coastal area (sediment focusing, see Håkanson and
Jansson 1983). In these calculations, a correction factor
has been applied to the model-predicted values of FDWA
based on this knowledge. The predicted values for FDWA
are assumed to be directly comparable to the values
from deep-water sediment traps for U-shaped basins
with a form factor (Vd) of 3, and too low for V-shaped
basins with a form factor smaller than 3. Thus, the ratio
Vd/3 is used as a correction factor. This means that the
values from the deep-water sediment traps (SedDW)
should be compared to modelled values given by (Vd/
3)ÆFDWA and values from the surface-water sediment
86
Table 4 Variables driving the dynamic SPM model
Variables
Morphometric parameters
Coastal area
Mean depth
Maximum depth
Section area
Latitude
Chemical variables
Characteristic mean salinity in the coastal area
Characteristic SPM concentration in the sea outside the
given coastal area or adjacent coastal areas (here predicted
from the corresponding Secchi depth values)
Characteristic concentrations of chlorophyll for the
growing season
traps (SedSW) should be compared to FDWA (after
dimensional adjustments so that the values are expressed
in g/m2 day). From Fig. 11a, one can note the excellent
correspondence between empirical and modelled values
for sedimentation in this coastal area.
Figure 11b gives similar results for Secchi depths.
The empirical data in this figure are the mean measured
Secchi depth for the growing season and the mean value
minus two standard deviations (SD) as a measure of the
uncertainty in the mean value for this coastal area. One
can see that the modelled Secchi depth (using Eq. 5) is
lower than the measured mean value but within 2SD of
the mean empirical value.
The results for the oxygen saturation in the deepwater zone in coastal area Gräsmarö are given in
Fig. 11c. The figure gives the mean O2Sat value for the
growing season and also the empirical mean value plus
1SD. The modelled O2Sat value is slightly higher than
Fig. 11 Validations in the Gräsmarö
coastal area (see Table 1) for a
empirical and modelled minimum and
maximum values for sedimentation, b
modelled Secchi depths versus
empirical data and uncertainty in
empirical data (empirical mean minus
2SD; SD standard deviation) and c
modelled values of the oxygen
saturation in the deep-water zone and
empirical data and uncertainty in
empirical data (mean value plus 1SD)
the mean empirical value, but well within the uncertainty
of the mean.
From the good results in Fig. 11, one can ask: How
will the model predict in the other 16 coastal areas?
The data for all 17 coastal areas are compiled in
Fig. 12a1 for Secchi depth. The modelled values for the
growing season are compared to empirical mean data.
The r2 value is 0.84 and the slope 1.08. The error function is shown in Fig. 12a1 and b1. The mean error is
close to zero (=0.086) and most modelled values are
within the 95% uncertainty interval for the empirical
data (±0.38). These are very good results for blind tests
in aquatic ecology.
The results for oxygen saturation are compiled in
Fig. 12a2, where modelled values for the growing season
are compared to empirical mean values. The r2 value is
0.81 and the slope 0.89. The error function is given in
Fig. 12b2. The mean error is 0.19 and most modelled
values are within the 95% uncertainty interval for the
empirical data (±0.45).
For sedimentation, modelled mean values [((Vd/
3)ÆFDW+FDWA)/2] are compared to empirical mean values [(SedSW+SedDW)/2]. The r2 value is 0.89 and the slope
1.17. Figure 12b3 gives the corresponding error function.
One can see that the mean error is close to zero (=0.075)
and that the modelled values generally are within the 95%
uncertainty interval for the empirical data (±1).
These are good validation results and it is probably
not possible to obtain better results with these data.
That is, the limiting factor for the predictive power is
access to reliable empirical data rather than uncertainties in model structures. Clearly, it would be interesting
to test this model for other coastal areas. One should
also note that this is a blind test in the sense that there
87
Fig. 12 Compilation of validation results for a1 Secchi depth, a2 oxygen saturation in the deep-water zone and a3 sedimentation, and the
corresponding error functions (b1, b2 and b3) and statistics for the 17 coastal areas
have been no changes in the model variables; only the
obligatory coast-specific driving variables listed in Table
4 have been changed.
The results are further elaborated in Fig. 13, which
gives information from the coastal area Ronneby, an
estuary in southern Sweden. The salinity has been set
88
to 0, 6.5 (the actual value for this coastal area) and
30& while all other variables have been kept constant,
including the SPM concentration in the sea outside the
given coastal area (which is 5 mg/l). Under these conditions, one can see no major differences in the SPM
concentration in the water volume (Fig. 13a), but sedimentation is much higher if the salinity is high
(Fig. 13b) and the water clarity is also much higher at
higher salinities (Fig. 13c). There are interesting compensatory effects in this example: a higher Secchi depth
means a deeper photic zone and higher bioproduction;
a higher salinity also means greater flocculation and
aggregation, so sedimentation becomes higher, especially during the summer months (Fig. 13b). The model
quantifies such dependencies and the net result is
shown in Fig. 13.
Conclusion
The obligatory driving variables for the dynamic SPM
model include four morphometric parameters (coastal
area, section area, mean and maximum depth), latitude
(to predict surface-water and deep-water temperatures,
stratification and mixing), salinity, chlorophyll and
Secchi depth or SPM concentrations in the sea outside
the given coastal area. The model is based on three
Fig. 13 Sensitivity analyses illustrating
how different salinities (0, 6.5 and
30&) would influence a total SPM
concentrations in water, b
sedimentation on accumulation areas
and c Secchi depths if every other
parameter is constant for coastal area
Ronneby, southern Sweden, including
the SPM concentration in the sea
outside the coastal area
compartments: two water compartments (surface water
and deep water; the separation between these two
compartments is done not in the traditional manner
from water temperatures but from sedimentological
criteria, as the water depth that separates transportation
areas from accumulation areas) and a sediment compartment (ET areas, i.e., erosion and transportation
areas where fine sediments are discontinuously being
deposited). The processes accounted for include inflow
and outflow via surface and deep water, input from
point sources, SPM from primary production, land
uplift, sedimentation, resuspension, mixing and mineralisation.
The dynamic model with its new sub-models presented in this work has been validated with good results.
The predictions of sedimentation, Secchi depth and
oxygen saturation are generally within the 95% uncertainty limits of the empirical data used to validate the
model predictions.
Many of the structures in the model are general and
have also been used with similar success for other types
of aquatic systems (lakes and rivers) and for other substances than SPM (mainly phosphorus and radionuclides; see Håkanson 2005). Since the model is based on
general, mechanistic structures it could potentially be
used for coastal areas other than those included in this
study, e.g., for open coasts, estuaries or areas influenced
89
by tidal variations, but this testing requires data of the
type used in this work for Baltic coastal areas, and such
data have not been available to the author. Hopefully,
this work can encourage such data to be collected and
used to critically test the dynamic model over a wider
domain of coastal areas than those used in this work.
Acknowledgements This work has been carried out within the
framework of an INTAS project (no. 03-51-6541) coordinated by
Dr. Richard B. Kemp, University of Wales, and the author would
like to acknowledge the financial support from INTAS. I would
also like to thank two anonymous reviewers for very constructive
comments and suggestions.
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