ORIGINAL ARTICLE

Lars Hakanson

The relationship between salinity, suspended particulate matter andwater clarity in aquatic systems

Received: 19 January 2005 / Accepted: 22 June 2005 / Published online: 11 August 2005� The Ecological Society of Japan 2005

Abstract This work presents and recommends 1) anempirically based new model quantifying the relation-ship between salinity, suspended particulate matter(SPM) and water clarity (as given by the Secchi depth)and (2) an empirical model for oxygen saturation in thedeep-water zone for coastal areas (O2Sat in %). Thispaper also discusses the many and important roles thatSPM plays in aquatic ecosystems and presents compar-isons between SPM concentrations in lakes, rivers andcoastal areas. Such comparative studies are very infor-mative but not so common. The empirical O2Sat modelexplains (statistically) 80% of the variability in meanO2Sat values among 23 Baltic coastal areas. The modelis based on data on sedimentation of SPM, the per-centage of ET areas (areas where erosion and trans-portation of fine sediments occur), the theoretical deep-water retention time and the mean coastal depth. Thesetwo new models have been incorporated into an existingdynamic model for SPM in coastal areas that quantifiesall important fluxes of SPM into, within and fromcoastal areas, such as river inflow, primary production,resuspension, sedimentation, mixing, mineralisation andthe SPM exchange between the given coastal area andthe sea (or adjacent coastal areas). The modified dy-namic SPM model with these two new sub-models hasbeen validated (blind tested) with very good results; themodel predictions for Secchi depth, O2Sat and sedi-mentation are within the uncertainty bands of theempirical data.

Keywords Aquatic systems Æ Coastal ecosystems ÆSalinity Æ SPM Æ Water clarity Æ Secchi depth ÆEmpirical models Æ Dynamic model

Introduction

This work presents compilations and statistical analysesof data on salinity, suspended particulate matter (SPM)and Secchi depth (a standard measure of water clarity,see Wetzel 2001) from aquatic systems (lakes, rivers andmarine systems). The results of the statistical analyseswill be put into a dynamic coastal model for SPM (fromHakanson et al. 2004a), which also calculates sedimen-tation and oxygen saturation in the deep-water zone.

There are many reasons to focus on salinity, SPMand water clarity. Salinity is of paramount importanceto the number of species, as shown in Fig. 1. It alsoinfluences the aggregation of suspended particles (whichwill be discussed in this paper). This is of particularinterest in modelling and understanding how SPM varieswithin and among systems, and the many roles thatSPM plays in influencing important structural andfunctional aspects of aquatic ecosystems (Hakanson2005). The SPM regulates the partition coefficient, andhence also the two major transport routes, the dissolvedtransport in the water (the pelagic route) and the par-ticulate sedimentation (or benthic) route, of all types ofmaterials and contaminants. The SPM in the watercolumn is also a metabolically active component ofaquatic ecosystems. The carbon content of SPM is cru-cial at low trophic levels as a source of energy for bac-teria, phytoplankton and zooplankton (see Jørgensenand Johnsen 1989; Wetzel 2001; Kalff 2002). The SPM isalso directly related to many variables of general use inwater management as indicators of water clarity (e.g.,Secchi depth, water colour and the depth of the photiczone; see Hakanson 1999). Suspended particles willsettle out on the bottom and the organic fraction will besubject to bacterial decomposition. This will influencethe oxygen concentration and hence also the survival ofzoobenthos, an important food source for fish (Hakan-son and Boulion 2002). The SPM influences primaryproduction of phytoplankton, benthic algae and mac-rophytes, the production and biomass of bacterio-

L. HakansonDepartment of Earth Sciences, Uppsala University,Villav 16, 752 36 Uppsala, SwedenE-mail: Lars.Hakanson@geo.uu.seFax: +46-18-4712737

Ecol Res (2006) 21:75–90DOI 10.1007/s11284-005-0098-x

plankton, and hence also the secondary production of,e.g., zooplankton, zoobenthos and fish. The effects ofSPM on recycling processes of organic matter, majornutrients and pollutants determine the ecological sig-nificance of SPM in any given aquatic environment.Understanding the mechanisms that control the distri-bution of SPM in rivers, lakes and marine systems andthe role played by salinity in this respect is an issue ofboth theoretical and applied concern, as physical,chemical and biological processes ultimately shapeaquatic ecosystems. Many sources are known to regulatethe SPM concentration in aquatic systems (Vollenweider1958, 1960; Carlson 1977, 1980; Brezonik 1978; OECD1982; Ostapenia et al. 1985; Preisendorfer 1986; Boulion1994, 1997). The most important sources/factors are asfollows:

1. Autochthonous production (i.e., the amount ofplankton, faeces, etc. in the water—more plankton,etc. means a higher SPM)

2. Allochthonous materials, such as the amount ofcoloured matter (e.g., humic and fulvic substances)

3. The amount of resuspended material

This is easy to state qualitatively, but more difficultto express quantitatively because these three factors arenot independent: high sedimentation leads to highamounts of resuspendable materials; high resuspension

leads to high internal loading of nutrients and in-creased production; a high amount of coloured sub-stances means a smaller photic zone and a lowerproduction; a high input of coloured substances and ahigh production mean a high sedimentation, etc. Theresults presented by Wallin et al. (1992) show that thewater clarity should be much greater than that ob-served if only plankton cells were responsible for thelight extinction. This means that particles other thanplankton cells are perhaps the most important factorsfor determining water clarity.

The SPM is generally a complex mix of substancesof different origins with different properties (size,form, density, specific surface area, capacity to bindpollutants, etc.). The SPM may be divided into par-ticulate organic matter (POM) and particulate inor-ganic matter (PIM). Total organic matter (TOM) isgenerally divided into POM and dissolved organicmatter (DOM). Normally, POM is about 20% ofTOM, but this certainly varies among and withinsystems (Ostapenia 1987, 1989; Velimorov 1991; Bou-lion 1994). Normally, about 4% of POM is livingmatter and the rest is dead organic matter (detritus).About 80% of TOM is generally in the dissolvedphase, and of this, about 70% is conservative in thesense that it does not change due to chemical andbiological reactions in the water mass.

This work will address the following relationships: (1)the empirical relationship between salinity, SPM andSecchi depth by making use of data available to theauthor to develop an algorithm that can be used in dy-namic modelling of SPM in coastal areas and (2) theempirical relationship between the oxygen saturation inthe deep-water zone and sedimentation of SPM. Thesetwo empirical models will be put into an existing dy-namic model for SPM (from Hakanson et al. 2004a andHakanson 2005). The idea is to test how the sub-modelswork by comparing the predictions from the dynamicmodel with empirical data. There are three target vari-ables for the model predictions: sedimentation of SPM,mean coastal Secchi depth and the mean oxygen satu-ration in the deep-water zone. Measured data on thesetarget variables are available from 17 coastal areas andwill be used in the model validations.

The basic perspective or scale underlying these studiesis the ecosystem scale, i.e., the interest is focused ondefined coastal areas (and not sampling sites) and meanmonthly conditions in coastal areas. This is also a targetscale in water management when questions are askedabout the status of a given ecosystem and what can bedone to improve its condition. It should be stressed thatthere is no contradiction between work at the largerecosystem scale and sampling and work at a smallerscale, since the mean values characterising ecosystemconditions and the standard deviations characterisingthe variability around such mean values must emanatefrom sampling at individual sites.

During the last 10 years, there has been something ofa ‘‘revolution’’ in aquatic ecosystem modelling. The

Fig. 1 Relationship between salinity and number of species.Redrawn from Remane (1934)

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major reason for this development is the Chernobylaccident. Following the pulse of radionuclides throughecosystem pathways has meant that important transportroutes have been revealed and the algorithms to quantifythem have been developed and tested (Hakanson 2000).It is important to stress that many of those structuresand equations are valid not just for radionuclides, butfor most types of contaminants, e.g., for metals, nutri-ents and organics—and for SPM—in most types ofaquatic environments (coastal areas, rivers and lakes).

In lake studies, it is easy to define the ecosystem, sincethis is often the entire lake. The ‘‘Data and methods’’section will discuss a method to also define coastalecosystems. 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 sub-stances in the water is often separated into a particulatephase, subject to gravitational sedimentation, and adissolved phase, generally the most important phase fordirect bio-uptake. Operationally, the limit between theparticulate phase and the dissolved phase is generallydetermined by means of filtration using a pore size of0.45 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 sedimento-logical, ecological and mass-balance modelling perspec-tives.

Data

A data set for lakes (see Table 1) from several investi-gations has been compiled by Lindstrom et al. (1999)and used in this work. The river database has beencompiled and described by Hakanson et al. (2005). Itconsists of three parts: the European database (the datacome mainly from the United Nations EnvironmentalProgramme, GEMS/Water); the UK database (Fosteret al. 1996, 1997, 1998), which provides a range of datafor 79 monitoring sites in UK rivers; and a Swedishdatabase for lakes (Hakanson and Peters 1995). Themarine database concerns SPM and co-variables inBaltic coastal areas (from Wallin et al. 1992 andHakanson et al. 2004a). The 17 coastal areas (see Ta-ble 2) are located in the Baltic Sea. Five of the areas arein the St. Anna archipelago off the Swedish east coast,seven areas are located in the Blekinge archipelago, inthe south of Sweden, and the remaining five areas are inthe Abolands archipelago of Finland. The Baltic Sea isbrackish with a salinity ranging from 5–10& in a north-south gradient (see Fig. 2). The Baltic Sea is shallow(mean depth 56 m) and is almost entirely surrounded byland. The tidal variation is small (<20 cm; see Voipio1981). The Abolands archipelago is the largest archi-pelago in the Baltic Sea. It reaches from Aland to theFinnish main land. The St. Anna archipelago has manyislands and deep, long bays, often with thresholds to-wards the sea. The Blekinge archipelago in southernSweden is narrow and the water circulation is generallygood (Persson et al. 1994).

Table 1 Data for the 17 studied Baltic coastal areas

Area Code Latitude(�N)

Landuplift(mm/year)

Area(km2)

Dmax

(m)Dm

(m)At(km2)

Chl(lg/l)

Salinity(&)

Fishprod.(times/year)

SedDW SedSW Secsea(m)

(g dw/m2 day)

Lilla Rimmo SE1 58 2 2.59 17.6 8.3 0.0172 2.3 6.4 41 20.2 4.2 3Eknon SE2 58 2 14.04 19.5 8.5 0.0168 3.5 5.4 32 5.3 2.0 2.5Lagnostrommar SE3 58 2 5.41 20.1 3.8 0.0032 4.6 6.4 125 22.7 11.1 2Grasmaro SE4 58 2 14.15 46.9 13.8 0.0825 2.6 6.6 200 18.3 1.1 3Alon SE5 58 2 6.54 35.2 8.0 0.0162 2.1 6.6 300 9.5 3.7 3Matvik SS1 56 0 3.12 14.3 5.2 0.0067 1.4 6.5 135 12.7 4.2 4.5Bokofjard SS2 56 0 7.05 21.6 7.1 0.0141 1.4 7.2 70 6.7 1.6 5Tarno SS3 56 0 1.54 11.1 5.1 0.0062 1.6 7.2 50 7.6 3.1 5Guavik SS4 56 0 2.86 22.8 5.2 0.0074 2.0 7.3 50 6.4 1.9 5Jarnavik SS5 56 0 3.49 18.6 5.7 0.0081 1.3 7.3 10 8.1 1.5 5Spjutso SS6 56 0 3.49 15.6 5.8 0.0188 0.9 7.4 50 8.7 4.4 5Ronneby SS7 56 0 11.94 17.6 4.3 0.0176 2.1 6.5 100 20.2 4.1 4Kaldo F1 61 5 3.14 16.7 7.6 0.0040 2.7 6.5 50 20.0 11.0 2Havero F2 61 5 2.54 22.5 8.6 0.0172 2.1 6.5 22 38.7 9.2 2Hammarosalmi F3 61 5 2.21 19.3 7.9 0.0114 2.2 6.5 381 13.4 9.1 3Laitsalmi F4 61 5 4.28 18.5 7.6 0.0080 2.7 6.5 85 37.0 17.6 1.5Kaukolanlahti F5 61 5 1.38 13.3 4.8 0.0006 9.6 6.5 35 26.3 15.3 1Min. 56 0 1.4 11.1 3.8 0.0006 0.9 5.4 10 5.3 1.1 1Max 61 5 14.2 46.9 13.8 0.0825 9.6 7.4 381 56.4 17.6 5.0Mean (MV) 58 2.1 5.3 20.7 6.9 0.0151 2.65 6.6 102 17.7 6.2 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 Hakanson (2000)

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Definition of coastal areas

The question is where to place the boundaries betweenthe sea and/or adjacent coastal areas. It is crucial to usea technique that provides an ecologically meaningfuland practically useful definition of the coastal ecosys-tem. How should one define this area so that parameters,like mean depth (Dm in metres), can be relevant as modelvariables (x) to predict target y variables? The problemis shown in Fig. 3a using data on Secchi depth (the yvariable in this example) and mean depth (Dm, the xvariable that reflects, e.g., resuspension processes).

For lakes, there exists a significant (r2 =0.38,P=0.0001 for 88 Swedish lakes) positive relationshipbetween Dm and Secchi depth: the deeper the lake, thelarger the bottom areas beneath the wave base, the lessresuspension, the less suspended materials in the lakewater, the clearer the water and the greater the Secchidepth. This is logical. The mean depth has a significantmeaning for an important ecosystem variable, Secchidepth. 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 establishcoastal ecosystems where morphometric parameters likethe mean depth have meaning in predictive ecosystemmodels? This is illustrated in Fig. 3b. In this example,there are three boundary lines, A, B and C, definingthree coastal areas. The mean depths of the enclosedareas are 4.5, 3.5 and 2.5 m, respectively. The exposureof the coastal area (Ex) is a morphometric parameter

defined by the ratio between the section area and theenclosed coastal area (Ex=100ÆAt/Area, whereAt=section area or the opening area towards the sea inkm2 and Area=coastal area in km2). The Ex values arequite different for the coastal area given by lines A(0.05), B (0.1) and C (0.2), but the Secchi depth is thesame in all three cases (2 m). Arbitrary borderlines (suchas A, B and C) can be drawn in many ways and the meandepths of the corresponding enclosed coastal areaswould be devoid of meaning in models for target eco-system variables, such as Secchi depth.

The approach in this work (from Hakanson et al.1986 and Pilesjo et al. 1991) assumes that the borderlinesare drawn at the topographical bottlenecks so that theexposure (Ex) of the coast from winds and waves fromthe open sea is minimised. It is easy to use the Ex valueas a tool to test different alternative borderlines anddefine the coastal ecosystem where the Ex value isminimal. If the coastal ecosystem is defined in this way,there exists, as shown in Fig. 3b, a weak but statisticallysignificant (r2 =0.14, P=0.08 for 23 Baltic coastalareas) negative relationship between Secchi depth andmean depth: the greater Dm, the more suspended mate-rials will be retained in the coastal water, the more tur-bid the water will be and the smaller the Secchi depthwill be. This is also logical because coastal areas are bydefinition 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 significantpart of the fine materials suspended in the water can‘‘escape’’ from the coastal area to the open water area orto surrounding coastal areas. This is not the case in thesame way for lakes. Open, exposed coastal areas withsmall mean depths will generally, therefore, have coarsebottom sediments (sand, gravel, etc.) and small amountsof fine materials, which cause a high turbidity whenresuspended.

Results

Background

Comparative studies in aquatic sciences often aim tofind general factors regulating and explaining whysystems differ in fundamental properties. Figure 4 gives

Table 2 Results of the stepwise multiple regression for the oxygen saturation in the deep-water zone (mean O2Sat in the deep-water zoneduring the growing season in %) using the coastal database

Step r2 Model variable Model

1 0.43 x1=log(SedDW) y=0.925Æx1+0.1322 0.64 x2=�ET y=0.974Æx1�0.185Æ x2+1.723 0.74 x3=log(1+TDW) y=0.866Æx1�0.151Æx2+0.244Æx3 +1.394 0.80 x3=�Dm y=0.643Æx1�0.118Æx2+0.301Æx3+0.323Æx4+0.470

n=23 Baltic coastal areas, F>4. y = log(101�O2Sat). SedDW Sedimentation in sediment traps placed in the deep-water zone of thecoastal 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 fromSkagerrak (in the North Sea) to the Bothnian Bay in the northernpart of the Baltic Sea (from Hakanson 1991)

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a comparison between SPM values from marinesystems, lakes and rivers. Many factors (x-variables)could potentially influence the variability in SPMamong and within systems. The statistical analysisbased on empirical data can be used to rank theimportance of how the different x-variables influence y.In these contexts, one must clearly differentiate betweenstatistical and causal analyses. Statistical treatments cannever mechanistically ‘‘explain’’ why certain x-variablesend up with a high correlation towards y, but resultsfrom correlations and regressions can provide impor-tant information for further mechanistic interpretationsand modelling.

From Fig. 4, one can note that SPM seems to vary ina systematic way among and within marine/brackishsystems, rivers and lakes. A key objective of this work isto try to explain the role of salinity in the variations inSPM shown in Fig. 4.

SPM and water clarity

Water clarity is a fundamental variable in aquaticstudies since it regulates primary production of phyto-plankton, benthic algae and macrophytes (see Hakansonand Boulion 2002). Secchi depth is a standard variablefor water clarity in lake management, but not in marinestudies. Values of Secchi depth are easy to understand

by the general public—clear waters with large Secchidepths seem more attractive than turbid waters. Manyfactors are known to influence the Secchi depth (Vol-lenweider 1958, 1960; Carlson 1977, 1980; Brezonik1978; OECD 1982; Ostapenia et al. 1985; Preisendorfer1986; Boulion 1994, 1997).

Fig. 4 Comparison of SPM data from marine/brackish systems,lakes and UK and European rivers. The box-and-whisker plotsprovide the medians, quartiles, 90th and 10th percentiles andoutliers

Fig. 3 Illustration and rationale for thedefinition of ecosystem boundaries fora lakes and b coastal areas. The coastalecosystem in this work is defined by theborderline marked A, which gives aminimum value for the exposure (Ex; the‘‘topographical bottleneck method’’)

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Figure 5a shows the very strong and logical rela-tionship between lake Secchi depth and the concentra-tion of SPM (in mg/l) based on 573 individual samplesfrom 23 lakes (covering a wide limnological domainfrom oligotrophic to highly eutrophic conditions; datafrom Hakanson and Boulion 2002). Figure 5b shows asimilar regression using data for Baltic coastal areas.One can note some interesting differences:

– As shown in Fig. 4, marine/brackish waters generallyhave a higher clarity than lakes and rivers, and thevariability in SPM values is generally significantlysmaller in marine/brackish systems. Figure 5 alsoindicates that the slope of the regression line is smallerfor marine systems than for lakes (�0.59 compared to�1.12), which indicates that a given change in Secchidepth would correspond to a smaller change in SPMvalues for marine systems than for lakes. The range inthe coastal data used here is relatively small since thedata in Fig. 5b come from the Baltic, but the corre-lation is highly significant (r2=0.80) even in thisnarrow range.

– One mechanistic reason for this difference betweenlakes and marine systems is related to the fact that thesalinity of the system will influence the flocculation/aggregation, and hence also the settling velocity, ofthe suspended particles (SPM): the higher the salinity,the greater the aggregation of suspended particles, thebigger the flocs and the faster the settling velocity(Kranck 1973, 1979; Lick et al. 1992). This will bediscussed further in the following sections.

SPM versus Secchi depth and salinity

The information in Fig. 5 is shown again in anotherway in Fig. 6. In this case, the figure does not giveregressions but empirically based deterministic rela-tionships related to defined boundary requirements.Based on the available empirical data shown in Fig. 6,

one can assume that the maximum average SPM con-centration in surface waters (SPMSW) in lakes andmarine coastal areas (but not in rivers; see Hakansonet al. 2005) should generally be lower than 50 mg/l. Onecan 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 depthin coastal areas with a salinity of 6.5& should be about50 m; and the Secchi depth should approach 200 m ifthe salinity approaches 30&. There are many data inFig. 6 supporting the relationship between SPM, Secchidepths and salinity for lakes, fewer data for Balticcoastal areas and no data for coastal areas with highersalinities. The relationships outlined in Fig. 6 should,therefore, be regarded as a working hypothesis. Fromthe 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 behigher than 200 m because even distilled water willscatter light and set a limit to the Secchi depth. Figure 7shows the relationship between z and the surface-water(SW) salinity (salSW in &). One can see that:

w ¼ 0:15uþ 0:3 ð1Þ

where w=log(1+z) and u=log(1+salSW); and hencefrom Fig. 6:

ðy � zÞ ¼ ðzþ 0:5Þ=ð�0:3� 1:7Þðxþ 0:3Þ ð2Þ

or

y ¼ ðzþ 0:5Þðxþ 0:3Þ=ð�2Þ þ z ð3Þ

Fig. 5 a The relationshipbetween Secchi depth (in m) asa standard measure of waterclarity and the SPMconcentration (mg/l) based on573 data from 23 lakes coveringa wide limnological domain(from highly eutrophic tooligotrophic conditions). b Thecorresponding regression for 26Baltic coastal areas and acomparison between the tworegression lines for lakes andcoastal areas. The figure givesthe regression line, r2 coefficientof determination and n numberof data

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where y = log(Sec) and x = log(SPMSW)

z ¼ 10 0:15 log 1þ salSWð Þ þ 0:3ð Þ � 1ð Þ ð4Þ

This means that the desired algorithm to estimateSecchi depth (Sec) from SPMSW and salSW may be givenby:

Sec ¼ 10ð�ðð10ð0:15 logð1þ salSWÞ þ 0:3Þ � 1ÞÞþ 0:5ÞðlogðSPMswÞ þ 0:3Þ=2þ ð10ð0:15 logð1þ salSWÞ þ 0:3Þ � 1ÞÞÞ ð5Þ

where Sec is the Secchi depth in metres. SPMSW, as afunction of Secchi depth and salinity, may then be ex-pressed by:

SPMSW ¼ 10ð�0:3� 2ðlogðSecÞ� ð10ð0:15 logð1þ salSWÞ þ 0:3Þ � 1ÞÞ=ðð10ð0:15 logð1þ salSWÞ þ 0:3Þ � 1Þ þ 0:5ÞÞ ð6Þ

Figure 8 gives two nomograms illustrating the relation-ship between Secchi depth, salSW and SPMSW. FromFig. 8, one can note that a SPM value of 10 mg/l cor-responds to a Secchi depth of about 1.5 m in a lake anda Secchi depth of about 3.5 m if the salinity is 30&.Thisempirically based deterministic model linking SPM,Secchi depth and salinity will be tested in a followingsection, where SPM values will not come from mea-surements but from a dynamic SPM model (fromHakanson et al. 2004a). The dynamic SPM modelquantifies fluxes of SPM into, within and from coastalareas. Within this dynamic model there is also a newsub-model to predict the oxygen saturation in the

deep-water zone. This sub-model will be presented in thefollowing section.

SPM and oxygen in deep water

When the mean O2 concentration is lower than about2 mg/l, and the mean oxygen saturation (O2Sat in %) islower than about 20%, many key functional benthicgroups are extinct (see Fig. 9).

Empirical data on the amount of material depositedin deep-water sediment traps (1 m above the bottom;SedDW in g/m2 day) were used (see Table 1) in derivingthe empirical model (see Table 2) for O2Sat using sta-tistical methods discussed by Hakanson and Peters(1995). This empirical model for O2Sat will be put intothe dynamic SPM model, and then the empirical data onSedDW will be replaced by modelled values from thedynamic model. The values for O2Sat calculated in thismanner will be compared to mean empirical data onO2Sat from the growing season.

The sediment traps were placed at two to three sites ineach coastal area. They were out for about 7 days atleast two times during the period from July to Septemberin each coastal area (see Wallin et al. 1992, for furtherinformation). Many empirical data expressing size andform characteristics of the coastal areas and the waterquality (different forms of N, P, salinity, etc.) that mayaffect the values for O2Sat have been tested in the fol-lowing statistical analyses using methods described byHakanson and Peters (1995). The data come from 23Baltic coastal areas. Note that data from adjacentcoastal areas have been lumped together in the infor-mation given in Table 1. This is the reason why theempirical model for O2Sat discussed in this section is

Fig. 6 Illustration of the relationship between log(SPMSW) andlog(Secchi) using the data for freshwater systems (surface-watersalinity 0&) and Baltic areas (mean surface-water salinity 6.5&).Note that these are not regression lines but deterministically drawnlines from the end point (50 mg/l, 0.3 m) and the starting points onthe y-axis, where the values are given for the actual data for thesurface-water SPM and Secchi depth

Fig. 7 The relationship between log(1+z) and log(1+salSW)

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based on data from 23 areas and Table 1 gives data from17 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 thefollowing factors are most important:

1. Sedimentation in deep-water sediment traps (SedDW):the more oxygen-consuming matter in the deep-waterzone, the lower the O2Sat.

2. The prevailing bottom dynamic conditions in thecoastal area (ET areas): when variations in ET amongcoastal areas are accounted for, the r2 value increasesto 0.64. If ET is high (say 0.95), the oxygenation isalso likely high and O2Sat is high.

3. The theoretical deep-water retention time (TDW; seeHakanson 2000 for further information): variationsin mean O2Sat among coastal areas can also be sta-tistically explained by variations in TDW—the longerTDW, the lower O2Sat. This is logical and mechanis-tically understandable. If variations among coastalareas in TDW are accounted for, r2 increases to 0.74.

4. The mean depth (Dm): the mechanistic reason for thisis not so easy to describe since Dm influences differentfactors, e.g., (1) resuspension, (2) volume, and hence,all SPM concentrations, (3) stratification and mixingand (4) the depth of the photic zone and, hence,primary production. Nonetheless, coastal areas withsmall mean depths (contrary to lakes with small meandepths, see Fig. 3) generally have clear water, littleSPM, low sedimentation and high O2Sat. Fine sus-pended particles in open coastal areas will be trans-ported out of such areas and not be entrapped in thesame manner as in lakes. If variations among coastalareas in Dm are accounted for, the r2 value increasesto 0.80.

From the complex hydrodynamic and sedimentolog-ical conditions in coastal areas (Hakanson 2000), onemight get the impression that complexity preventsmodels 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 areaswith characteristics outside the limits given below, and itshould not be used for coastal areas dominated by tides.If the model is used for other coastal areas, then thecalculation must be regarded with due reservation, as ahypothesis rather than a prediction (see Table 2 fordefinitions of the abbreviations).

Dynamic modelling

Background

The dynamic coastal model has been described in detailelsewhere (Hakanson et al. 2004a; Hakanson 2005) andwill not be repeated here. This section will only give abrief outline of the dynamic model, which is illustratedin Fig. 10. There are three main compartments: (1)surface water, (2) deep water and (3) areas where pro-cesses of fine sediment erosion and transport dominatethe bottom dynamic conditions (the ET areas). Thevolumes of the surface and deep water are calculatedfrom the water depth separating transportation areas forfine particles from accumulation areas (see Hakansonet al. 2004b for definition). There are six SPM inflows:

1. Primary production (Fprod), which includes all typesof plankton (phytoplankton, bacterioplankton andzooplankton) 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 gdry weight per month in this model).

Fig. 8a, b Illustration of the relationship between Secchi depth,SPM in surface water and salinity in surface water. a Thenomogram using log-data and b using actual data

Dm (m) ET TDW (days) SedDW(g/m2 day)

Min. 3.8 0.19 1 5.3Max. 13.8 0.99 128 82.5

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3. Inflow of SPM to the deep water from the sea(FinDW).

4. Land uplift (FLU). Land uplift is a special case for theBaltic Sea related to the latest glaciation.

5. Emissions of SPM from point sources (FPSSW), in thiscase from fish cage farms in the coastal areas.

6. Tributary inflow (FQ).

The amount of matter deposited on ET areas may beresuspended by wind/wave action. The resuspendedmatter can be transported either back to the surfacewater (FETSW) or to the deep water (FETDW). How muchthat will go in either direction is regulated by a distri-bution coefficient calculated from the form factor(Vd=3Dm/Dmax; Dm=mean depth; Dmax=maximumdepth) of the coastal area. Other internal processes aremineralisation, i.e., the bacterial decomposition of SPMin the surface water, the deep water and the ET com-partment (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 inTable 3. Compared to the model presented by Hakan-son et al. (2004a), there are two new parts:

1. The relationship among SPM, salinity and Secchidepth (and hence also the depth of the photic zone)described in the section ‘‘SPM versus Secchi depthand salinity’’

2. The empirical sub-model for O2Sat described in thesection ‘‘SPM and oxygen in deep water’’

It should also be mentioned that there exist othermodels for SPM in coastal areas. There are, e.g.,hydraulic coastal models for SPM, such as Threetox andCoasttox. Unlike the model discussed in this work, thoseare distributed two- or three-dimensional models based

on partial differential equations; the model POSEIDONis based on several interlinked boxes. These models areused 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 byonline meteorological data (winds, temperature andprecipitation) and hence cannot be used for predictivepurposes over time periods longer than 2–3 days since itis not possible to forecast weather conditions for longerperiods than that. Such models may be excellent tools inscience and may provide descriptive power rather thanlong-term predictive power.

There are also different types of ecosystem-orientedmodels and modelling approaches for sedimentationand variables influencing sedimentation in coastalareas (see, e.g., Wulff et al. 2001). However, there aremajor differences between the model discussed hereand other models, including differences in targetvariables (from conditions at individual sites to meanvalues over larger areas), modelling scales (daily toannual predictions), modelling structures (from usingempirical/regression models to the use of ordinary orpartial differential equations) and driving variables(whether accessed from standard monitoring pro-grams, climatological measurements or specific stud-ies). To make meaningful model comparisons is not asimple matter, and this is not the focus of this work.As far as the author is aware, there are no mass-balance models for SPM and coastal sedimentation ofthe type discussed here that account for total primaryproduction, point-source emissions, freshwater input,surface- and deep-water exchange processes, land up-lift, internal loading, mixing and mineralisation in ageneral manner designed to achieve practical utilityand predict monthly variations. Also the fundamentalunit, the defined coastal area, is determined in a waythat, to the best of the author’s knowledge, has not

Fig. 9 Bioturbation and laminatedsediments. Under aerobic (=oxic)conditions zoobenthos may create abiological mixing of sediments down to asediment depth of about 15 cm (thebioturbation limit). If the deposition oforganic materials increases and hence alsothe oxygen consumption from bacterialdegradation of organic materials, theoxygen concentration may reach thecritical limit of 2 mg/l, when zoobenthosdie, bioturbation ceases and laminatedsediments appear (figure modified fromPearson and Rosenberg 1976)

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been used before in dynamic modelling of sedimento-logical processes; no comparable models use thetopographical bottleneck approach to define thecoastal area. This modelling approach also makes itpossible to estimate the theoretical surface-water anddeep-water retention times (which are fundamentalcomponents in coastal mass-balance modelling) frombathymetric map data.

The accuracy of a model prediction is strongly influ-enced by the uncertainty in the empirical data used to runand validate the model (Hakanson 1999). Sedimentationis known to display considerable natural variation be-tween years, seasons and/or even between closely locatedstations (Blomqvist 1992; Matteucci and Frascari 1997;Heiskanen and Tallberg 1999). Douglas et al. (2003) haveshown that there are large variations in sedimentationeven during 36- to 48-h periods. The empirical sedimenttrap data used to validate this model have coefficients ofvariation (CV) of 0.58 for the surface-water and 0.50 forthe deep-water compartment (Wallin et al. 1992).

In models for lakes and/or coastal areas, the sur-face-water compartment is often separated from thedeep-water compartment by the thermocline (Carlssonet al. 1999), the pycnocline (Abdel-Moati 1997) or thehalocline (Andreev et al. 2002). However, the classiceffect-load-sensitivity model by Vollenweider (1968) forlakes does not separate surface and deep water at alland neither does De Schmedt et al. (1998) whenmodelling suspended sediments and heavy metals in theScheldt estuary. The thermocline, halocline and py-cnocline are all gradients, and they can be found overwide ranges of water depths (Hakanson et al. 2004b).This means that it is often difficult to find a relevantvalue to separate the surface-water compartment from

the deep-water compartment using, e.g., temperaturedata. In this modelling, the separation is not done inthe traditional way using temperature data, but by thewave base (the ‘‘critical water depth’’), i.e., the depthbelow which fine cohesive particles following Stokes’slaw are continuously being deposited. This gives adefined critical water depth for each coastal area. Fromthis water depth, it is easy to calculate requested watervolumes, sedimentation, resuspension, mixing, miner-alisation and outflow. This also leads to a relativelysimple model structure since the sedimentation of SPMfrom the deep water, and the deep water alone, ends upon areas of continuous sedimentation (the accumula-tion areas).

Table 4 gives the panel of driving variables. These arethe coastal-area-specific variables needed to run thedynamic SPM model. They are all easily accessed, e.g.,from standard monitoring programmes or maps. Noother part of the model should be changed unless thereare good reasons to do so.

Results

The quality of models is not governed by statements orarguments but by performance in blind tests. Note thatthe new sub-model has been motivated by empirical dataor results based on empirical data. There has been nocalibration of the dynamic SPM model. The results ofthe validations will be presented in the following way.To determine how well the model predicts, there will firstbe a comparison between empirical data, uncertainties inempirical data and model-predicted values for sedi-mentation, Secchi depth and oxygen saturation in one of

Fig. 10 A general outline of thestructure of the coastal model.Note that, for simplicity, point-source emissions to the deep-water compartment have beenomitted in this figure

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the 17 coastal areas. Then, the modelling results for all17 coastal areas will be directly compared to empiricaldata. This study asks the basic question: How well doesthe model predict using the new algorithm relatingsalinity to Secchi depth and SPM and the new empiricalsub-model for O2Sat?

The first results for a randomly selected coastal areaare given in Fig. 11 for coastal area Grasmaro, Swedisheast coast. Figure 11a gives the empirical values forsedimentation in surface-water sediment traps (calledempirical minimum values) and deep-water sedimenttraps (empirical maximum values). The modelled mini-mum values are calculated from sedimentation of SPMon accumulation areas (FDWA). Sedimentation on

accumulation areas should vary from zero at the wavebase to maximum values in the deepest part of thecoastal area (sediment focusing, see Hakanson andJansson 1983). In these calculations, a correction factorhas 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 valuesfrom deep-water sediment traps for U-shaped basinswith a form factor (Vd) of 3, and too low for V-shapedbasins with a form factor smaller than 3. Thus, the ratioVd/3 is used as a correction factor. This means that thevalues 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

Table 3 A compilation of the differential equations for the dynamic coastal SPM model

Equations

Surface water (SW)MSW(t)=MSW(t�d t)+(FinSW+FDWSWx+FETSW+Fprod+FPSSW+FLU–FoutSW�FSWDW�FSWET–FminSW�FSWDWx)Æd tMSW(t)=Mass (amount) in the SW compartment at time t (g)FinSW=Flow into the SW compartment from the sea (g/month); see textFDWSWx=Flow from deep water to surface water (upward mixing; g/month); see belowFETSW=Flow (resuspension) from ET areas to the SW compartment (g/month); see belowFprod=Flow into the SW compartment from primary production (g/month); see textFPSSW=Flow into the SW compartment from point-source emissions (g/month; see Hakanson et al. 2004a)FoutSW=Flow from the SW compartment and out of the coastal area (g/month); see textFSWDW=Flow (sedimentation) from the SW compartment to deep-water compartment (g/month); see belowFSWET=Flow (sedimentation) from the SW compartment to ET areas (g/month); see belowFminSW=Flow (mineralisation) from the SW compartment (g/month); see belowFDWSWx=Flow from surface water to deep water (downward mixing; g/month); see below

ET areas (ET)MET(t)=MET(t�d t)+(FLU+FSWET�FETDW�FETSW–FminET)Æd tMET(t)=Mass (amount) in the ET compartment at time t (g)FLU=Flow into the SW compartment from land uplift (g/month; see Hakanson et al. 2004a)FETDW=Flow (resuspension) from ET areas to the DW compartment (g/month); see belowFminET=Flow (mineralisation) from ET areas (g/month); see below

Deep water (DW)MDW(t)=MDW(t�d t)+(FSWDW+FETDW+FSWDWx+FinDW+FPSDW�FDWSWx�FDWA–FoutDW–FminDW)Æd tMDW(t)=Mass (amount) in the DW compartment at time t (g)FinDW=Flow into the DW compartment (g/month); see textFPSDW=Flow into the DW compartment from point-source emissions (g/month; see Hakanson et al. 2004a)FDWA= Flow (sedimentation) from the DW compartment to At areas (g/month); see belowFoutDW=Flow from the DW compartment and out of the coastal area (g/month); see textFminDW=Flow (mineralisation) from the DW compartment (g/month); see below

Other important algorithmsFDWSWx=MDWÆRmixÆ(VSW/VDW)FETSW=MET(1�Vd/3)Æ1/TET [TET=1 month]FSWDW=MSWÆ(1�ET)Æ(vdef/DSW)YZMTÆYSPMSWÆYsalSWÆYDRÆ((1�DCresSW)+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; calculatessedimentation effects related to the ‘‘zone of maximum turbidity’’]YSPMSW=(1+0.75Æ(CSW/50�1)) [calculates how changes in SPM (CSW) influence sedimentation]YSPMDW=(1+0.75Æ(CDW/50�1)) [calculates how changes in SPM (CDW) influence sedimentation]YsalSW=(1+1Æ(sal/1�1))=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((1�DCresSW)+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((1�DCresDW)+YresÆDCresDW)YDW: If TDW<7 (days) then YDW=1, else YDW=(TDW/7)0.5 [calculates how changes in T and turbulence influence deep-watersedimentation]

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traps (SedSW) should be compared to FDWA (afterdimensional adjustments so that the values are expressedin g/m2 day). From Fig. 11a, one can note the excellentcorrespondence between empirical and modelled valuesfor sedimentation in this coastal area.

Figure 11b gives similar results for Secchi depths.The empirical data in this figure are the mean measuredSecchi depth for the growing season and the mean valueminus two standard deviations (SD) as a measure of theuncertainty in the mean value for this coastal area. Onecan see that the modelled Secchi depth (using Eq. 5) islower than the measured mean value but within 2SD ofthe mean empirical value.

The results for the oxygen saturation in the deep-water zone in coastal area Grasmaro are given inFig. 11c. The figure gives the mean O2Sat value for thegrowing season and also the empirical mean value plus1SD. The modelled O2Sat value is slightly higher than

the mean empirical value, but well within the uncertaintyof the mean.

From the good results in Fig. 11, one can ask: Howwill the model predict in the other 16 coastal areas?

The data for all 17 coastal areas are compiled inFig. 12a1 for Secchi depth. The modelled values for thegrowing season are compared to empirical mean data.The r2 value is 0.84 and the slope 1.08. The error func-tion is shown in Fig. 12a1 and b1. The mean error isclose to zero (=0.086) and most modelled values arewithin the 95% uncertainty interval for the empiricaldata (±0.38). These are very good results for blind testsin aquatic ecology.

The results for oxygen saturation are compiled inFig. 12a2, where modelled values for the growing seasonare compared to empirical mean values. The r2 value is0.81 and the slope 0.89. The error function is given inFig. 12b2. The mean error is �0.19 and most modelledvalues are within the 95% uncertainty interval for theempirical data (±0.45).

For sedimentation, modelled mean values [((Vd/3)ÆFDW+FDWA)/2] are compared to empirical mean val-ues [(SedSW+SedDW)/2]. The r2 value is 0.89 and the slope1.17. 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 probablynot possible to obtain better results with these data.That is, the limiting factor for the predictive power isaccess to reliable empirical data rather than uncertain-ties in model structures. Clearly, it would be interestingto test this model for other coastal areas. One shouldalso note that this is a blind test in the sense that there

Table 4 Variables driving the dynamic SPM model

Variables

Morphometric parametersCoastal areaMean depthMaximum depthSection areaLatitude

Chemical variablesCharacteristic mean salinity in the coastal areaCharacteristic SPM concentration in the sea outside thegiven coastal area or adjacent coastal areas (here predictedfrom the corresponding Secchi depth values)Characteristic concentrations of chlorophyll for thegrowing season

Fig. 11 Validations in the Grasmarocoastal area (see Table 1) for aempirical and modelled minimum andmaximum values for sedimentation, bmodelled Secchi depths versusempirical data and uncertainty inempirical data (empirical mean minus2SD; SD standard deviation) and cmodelled values of the oxygensaturation in the deep-water zone andempirical data and uncertainty inempirical data (mean value plus 1SD)

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have been no changes in the model variables; only theobligatory coast-specific driving variables listed in Table4 have been changed.

The results are further elaborated in Fig. 13, whichgives information from the coastal area Ronneby, anestuary in southern Sweden. The salinity has been set

Fig. 12 Compilation of validation results for a1 Secchi depth, a2 oxygen saturation in the deep-water zone and a3 sedimentation, and thecorresponding error functions (b1, b2 and b3) and statistics for the 17 coastal areas

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to 0, 6.5 (the actual value for this coastal area) and30& while all other variables have been kept constant,including the SPM concentration in the sea outside thegiven coastal area (which is 5 mg/l). Under these con-ditions, one can see no major differences in the SPMconcentration in the water volume (Fig. 13a), but sed-imentation is much higher if the salinity is high(Fig. 13b) and the water clarity is also much higher athigher salinities (Fig. 13c). There are interesting com-pensatory effects in this example: a higher Secchi depthmeans a deeper photic zone and higher bioproduction;a higher salinity also means greater flocculation andaggregation, so sedimentation becomes higher, espe-cially during the summer months (Fig. 13b). The modelquantifies such dependencies and the net result isshown in Fig. 13.

Conclusion

The obligatory driving variables for the dynamic SPMmodel include four morphometric parameters (coastalarea, section area, mean and maximum depth), latitude(to predict surface-water and deep-water temperatures,stratification and mixing), salinity, chlorophyll andSecchi depth or SPM concentrations in the sea outsidethe given coastal area. The model is based on three

compartments: two water compartments (surface waterand deep water; the separation between these twocompartments is done not in the traditional mannerfrom water temperatures but from sedimentologicalcriteria, as the water depth that separates transportationareas from accumulation areas) and a sediment com-partment (ET areas, i.e., erosion and transportationareas where fine sediments are discontinuously beingdeposited). The processes accounted for include inflowand outflow via surface and deep water, input frompoint sources, SPM from primary production, landuplift, sedimentation, resuspension, mixing and miner-alisation.

The dynamic model with its new sub-models pre-sented in this work has been validated with good results.The predictions of sedimentation, Secchi depth andoxygen saturation are generally within the 95% uncer-tainty limits of the empirical data used to validate themodel predictions.

Many of the structures in the model are general andhave also been used with similar success for other typesof aquatic systems (lakes and rivers) and for other sub-stances than SPM (mainly phosphorus and radionuc-lides; see Hakanson 2005). Since the model is based ongeneral, mechanistic structures it could potentially beused for coastal areas other than those included in thisstudy, e.g., for open coasts, estuaries or areas influenced

Fig. 13 Sensitivity analyses illustratinghow different salinities (0, 6.5 and30&) would influence a total SPMconcentrations in water, bsedimentation on accumulation areasand c Secchi depths if every otherparameter is constant for coastal areaRonneby, southern Sweden, includingthe SPM concentration in the seaoutside the coastal area

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by tidal variations, but this testing requires data of thetype used in this work for Baltic coastal areas, and suchdata have not been available to the author. Hopefully,this work can encourage such data to be collected andused to critically test the dynamic model over a widerdomain of coastal areas than those used in this work.

Acknowledgements This work has been carried out within theframework of an INTAS project (no. 03-51-6541) coordinated byDr. Richard B. Kemp, University of Wales, and the author wouldlike to acknowledge the financial support from INTAS. I wouldalso like to thank two anonymous reviewers for very constructivecomments and suggestions.

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