Comprehensive Summaries of Uppsala Dissertations from theFaculty of Science and Technology 584

Predictive Modelling of HeavyMetals in Urban Lakes

BY

MARTIN LINDSTRÖM

ACTA UNIVERSITATIS UPSALIENSISUPPSALA 2000

Dissertation for the Degree of Doctor of Philosophy in Sedimentologypresented at Uppsala University in 2000

ABSTRACT

Lindström, M. 2000. Predictive Modelling of Heavy Metals in Urban Lakes. ActaUniversitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations fromthe Faculty of Science and Technology 584. 28 pp. Uppsala. ISBN 91-554-4854-2.

Heavy metals are well-known environmental pollutants. In this thesis predictivemodels for heavy metals in urban lakes are discussed and new models presented. Thebase of predictive modelling is empirical data from field investigations of manyecosystems covering a wide range of ecosystem characteristics. Predictive modelsfocus on the variabilities among lakes and processes controlling the major metalfluxes.

Sediment and water data for this study were collected from ten small lakes in theStockholm area, the Eastern parts of Lake Mälaren, the innermost areas of theStockholm archipelago and from literature studies. By correlating calculated metalloads to the land use of the catchment area (describing urban and natural land use),the influences of the local urban status on the metal load could be evaluated. Copperwas most influenced by the urban status and less by the regional background. Theopposite pattern was shown for cadmium, nickel and zinc (and mercury). Lead andchromium were in-between these groups.

It was shown that the metal load from the City of Stockholm is considerable. There isa 5-fold increase in sediment deposition of cadmium, copper, mercury and lead in thecentral areas of Stockholm compared to surrounding areas.

The results also include a model for the lake characteristic concentration ofsuspended particulate matter (SPM), and new methods for empirical model testing.The results indicate that the traditional distribution (or partition) coefficient Kd(L kg-1) is unsuitable to use in modelling of the particle association of metals. Insteadthe particulate fraction, PF (-), defined as the ratio of the particulate associatedconcentration to the total concentration, is recommended. Kd is affected by spuriouscorrelations due to the definition of Kd as a ratio including SPM and also secondaryspurious correlations with many variables correlated to SPM. It was also shown thatKd has a larger inherent within-system variability than PF. This is important inmodelling.

Key words: Predictive modelling, heavy metals, lakes, urban influences.

Martin Lindström, Department of Earth Sciences, Uppsala University, Villavägen 16,SE-752 36 Uppsala, Sweden

© Martin Lindström 2000

ISSN 1104-232XISBN 91-554-4854-2

Printed in Sweden by Kopieringshuset, Uppsala 2000

Preface

This thesis is based on the following papers, which in the comprehensivesummary will be referred to by their Roman numerals:

I. Lindström, M., 2000. A compilation of sub-models for predictive lakeheavy metal modelling. Submitted.

II. Lindström, M., Håkanson, L., Abrahamsson, O. and Johansson, H., 1999.An empirical model for prediction of lake water suspended particulatematter. Ecological Modelling 121: 185-198.

III. Johansson, H., Lindström, M. and Håkanson, L., 2000. On the modellingof the particulate and dissolved fractions of substances in aquaticecosystems - sedimentological and ecological interactions. Submitted.

IV. Lindström, M., 2000. Distribution of particulate and reactive mercury insurface water of Swedish forest lakes - An empirically based predictivemodel. Accepted for publication in Ecological Modelling.

V. Lindström, M. and Håkanson, L., 2000. A model to calculate heavy metalload to lakes dominated by urban runoff and diffuse inflow. Submitted.

VI. Lindström, M., 2000. Urban land use influences on heavy metal fluxesand surface sediment concentrations of small lakes. Water, Air, & SoilPollution (in press).

VII. Lindström, M., Jonsson, A., Brolin, A. and Håkanson, L., 2000. Heavymetal sediment load from the City of Stockholm. Accepted forpublication in Water, Air, & Soil Pollution.

The papers are reproduced with kind permissions from Kluwer AcademicPublishers, Wiley-VCH and Elsevier.

Description of my part of the work in the papers with more than one author:In paper II, the idea originated from the second author, additional ideas anddata were added by the last two authors while I did most of the analyses andwriting. In paper III, the first two authors shared most of the work equally. Inpaper V, I did most of the work. In paper VII the sampling was done by thethree first authors, the chemical analyses mostly by the second author and allauthors contributed with ideas, I did most of the calculations and writing.

Contents

1. Background and introduction ____________________________ 52. Aims______________________________________________ 93. Study areas, material and methods _______________________ 10

3.1.Study areas _____________________________________ 103.2.Material and methods______________________________ 10

4. A model for the characteristic suspended particulatematter (SPM) concentration in lakes______________________ 12

5. Predictive modelling of the distribution of metalsbetween particulate associated and dissolvedfractions __________________________________________ 13

6. Stability tests of predictive models _______________________ 167. A lake heavy metal mass-balance model___________________ 168. Influence of the City of Stockholm on the transport

of metals _________________________________________ 188.1.Urban land use effects on metal transport _______________ 188.2.Modelling the Stockholm influences on the

sediment loads___________________________________ 208.3.Metal fluxes in Stockholm __________________________ 21

9. Conclusions________________________________________ 2210. Acknowledgements __________________________________ 2311. References ________________________________________ 23

5

1. Background and introduction

Ecological sciences have been criticised for not providing appropriate tools todeal with practical environmental problems (Peters, 1991). They do generallynot provide good enough quantitative methods, and are too focused onecosystem descriptions. One answer to this criticism is predictive modelling,which in this thesis is the activity of structuring empirical data and knowledgeand to derive models which will enable predictions in other situations thanthose used in the model calibrations. The basic objectives for modelling could,e.g., be related to scientific or lake management questions. For example, for atarget variable that is difficult (and/or expensive) to determine, it would bevaluable to be able to use a model to predict the variable. Models could also beused to simulate target variable responses to changes in very complex systems.For such systems, models could also be used as tools for quantifying andranking the importance of influencing factors, and to estimate fluxes. Toachieve these overall goals, models should be designed, tested and usedaccording to a certain procedure that will be discussed.

Predictive models for nutrients (in lakes mainly phosphorous) dealing witheutrophication have been developed and used for more than three decades. Thisthesis focuses not on nutrients but on heavy metal modelling, which is a morerecent area of predictive modelling. Predictive modelling of processesimportant for the fluxes of heavy metals in lakes will be discussed. Heavymetals are well-known environmental pollutants. They are non-degradable,commonly used and widely dispersed. Concentrations higher than normal,background, values are often recorded (see, e.g., Monitor, 1982; Salomons andFörstner, 1984; Monitor, 1987; Vernet, 1991; Foster and Charlesworth, 1996).A review of predictive models for heavy metals in lakes is presented in paper I.From the summary in table 1, one can note that there exists only few metalmodels (compared to the great number of phosphorous models available). Inaddition to the models in table 1, there are also models available for processesthat are not metal-specific. These models may be used to model the generalprocesses in lakes, i.e., a framework in which the metal modelling may beincorporated. For example, models for sedimentation of particulate matter(e.g., Håkanson, 1994a; Håkanson, 1995a; Tartari and Biasci, 1997),

Table 1. Summary of sub-models for predictive lake heavy metal modelling. For further information,see paper I.Lake sub-model for:

Description Reference

Lake heavymetal load

Multiple regression models for metal transport in ruralstreams. Mainly based on water runoff and concentrationsuspended particulate matter (SPM).

Cuthbert and Kalff,1993

Sediment metalconcentration

Multiple regression models for sediment metal concentrationin lakes without point sources. Mainly based on sedimentwater content and site depth.

Rowan and Kalff,1993

Distributioncoefficient (Kd)

Kd for estuary waters. Based on two empirical constants, pH,particulate matter and iron concentrations and concentrationof dissolved solids.

Sung, 1995

Distributioncoefficient (Kd)

Multiple regression models for Kd for lakes. Based on thesame water chemical driving variables used for a chemicalpartitioning model.

Koelmans andRadovanovic, 1998

6

percentage accumulation area (Håkanson, 1982), boundary depth for sedimentaccumulation (Håkanson, 1977; Rowan et al., 1992) and sediment resuspensionand focusing (Hamilton and Mitchell, 1996; Weyhenmeyer et al., 1997). Theconclusion is that there is a need for more predictive models for metals.Predictive models for processes influencing the metal distribution in lakes, e.g.,metal sedimentation, diffusion, particulate fraction and redox effects would beuseful.

For this thesis, it was assumed that it should be possible to design generalmodels for fluxes of heavy metals in lakes. General models should becalibrated with empirical data from many lake ecosystems of differentlimnological characteristics. Generality means that the same fundamentalprocesses (such as inflow, outflow, sedimentation, mixing and diffusion) couldbe assumed to control pools and transport paths of all substances in all lakes(within the model domain). The goal is to find general methods to determinehow important each process is for a specific case and to assign values ofspecific model variables. Examples of factors and processes that could beconsidered for specific data are:

1. Lake-specific:– Morphometric parameters describing size and form of lakes and

catchment areas.– Co-ordinates giving the position of the lakes and catchment areas

(longitude, latitude and altitude).2. Metal-specific:

– Diffusion.– Distribution between particulate associated and dissolved phases.– pH influences.– Volatilisation.– Redox influences.

Measured field data should primarily be used for the necessary drivingvariables. In the absence of such data, sub-models might be used, predictingtarget variables from readily accessible variables. Therefore, this thesis willdiscuss such sub-models for lake heavy metal models. Some generalrequirements regarding the driving variables could be noted. Driving variablesshould preferably:

• Be simple to calculate and readily available (e.g., from maps, so called mapvariables, or from standard lake monitoring programs).

• Have a low variability (in both analytical precision and natural variation).

A well-balanced model structure minimises the influence of data uncertaintyand maximises the predictive power. The number of driving variables shouldneither be too many, nor too few. A practically useful predictive model shouldnot be built on too many driving variables since each driving variable influencesnot only the predictive power but also the model uncertainty.Uncertainty accumulates and model uncertainty generally increases with modelcomplexity (Håkanson, 1995b; Jørgensen, 1995). When practically usefulpredictions are in focus, one should aim for simple models and include only themost important components. This is easier to state than to actually do. It meansthat detailed descriptions (with many variables and processes) might have to besacrificed for the purpose of increased predictive power and practical utility.

7

The accuracy of predictions depends on the uncertainty and variability of thedriving variables, the structure of the model and the size and representativity ofthe data set available for calibrations.

UrbanisationUrban areas could be labelled ecological hotspots (Bergbäck, 1992; Anon.,1995) in the meaning that they cause a high level of stress on mostenvironments. It seems, however, that ecosystem effects of environmentalstress in urban areas are not as well studied and understood as are effects inspatially larger areas such as forests or agricultural areas. Table 2 gives aselection of ecosystems effects related to heavy metals in urban aquaticenvironments.

Table 2. A selection of published literature on environmental effects of urbanisation on heavy metals inaquatic ecosystems.Effect Area (site) ReferenceA. Increased abiotic concentrationsRiver water and sediments Linggi River (Malaysia) Sarmani et al., 1992

Rouge River, Michigan (US) Murray, 1996Gomati River (India) Singh et al., 1997River Alb (Germany) Fuchs et al., 1997Sullivan’s creek (Australia) Liston and Maher, 1986River Seine (France) Estèbe et al., 1998

Lake sediments Central Park Lake NYC (US) Chillrud et al., 1999Lake Ellyn, Ill. (US) Striegl, 1987

Lake water Lakes Superior, Erie and Ontario (US,Canada)

Nriagu et al., 1996

Archipelago sediments Töölönlahti Bay, Helsinki (Finland) Virkanen, 1998Stockholm archipelago (Sweden) Broman et al., 1994;

Blomqvist and Larsson,1996

Estuary sediments Hudson River (US) Feng et al., 1998Avon-Heathcote Estuary (New Zeeland) Deely and Fergusson,

1994Ground water Stockholm (Sweden) Aastrup and Thunholm,

2000B. Other abiotic effectsIncreased concentration of Töölönlahti Bay, Helsinki (Finland) Virkanen, 1998more soluble metal forms Urban river sediments of Gothenburg

(Sweden)Wei and Morrison, 1992

C. Increased biotic concentrationsIncreased concentration in fish(especially bottom-feeder)compared to control sites

Stormwater treatment ponds, Orlando,Florida (US)

Campbell, 1994

Increased concentrations ininvertebrate tissue

River Roding (UK) Davis and George, 1987

D. Other biotic effectsLow species richness andbiomass of fish andinvertebrates

Three Piedmont streams, N. Carolina(US)

Lenat and Crawford,1994

Low bacterial enzyme activity Sediment from urban rivers ofGothenburg (Sweden)

Wei and Morrison, 1992

Reduced benthicmacroinvertebrate diversity

Green River, Mass. (US) Medeiros et al., 1983

8

The suggested causes for these effects are rarely very detailed. The listedeffects include increased abiotic and biotic heavy metal concentrations.Interestingly, there are also results suggesting that anthropogenic metalpollution may have a different solubility with increasing concentrations ofmore loosely bound forms, which means that aquatic ecosystems might besensitive to urban pollution. Biological effects such as changed speciescomposition in urbanised aquatic systems have been recorded, but it is difficultto tell whether it is the heavy metals or other factors that cause these effects.

During the last decades most point sources of heavy metals have beenregulated in Sweden and many other countries. The remaining diffuse sourcesare less well investigated. Several sources of diffuse contamination have beensuggested. Many would, however, be classified as industry-like sources, e.g.,waste incineration plants and waste water treatment effluents. Another possiblesource is the diffuse leaching of heavy metals due to corrosion and wear ofproducts from the pool of metals stored in the technosphere of urbanenvironments (e.g., Ayres and Ayres, 1994). This includes emissions fromtraffic which is often pointed out as a major source (e.g., Malmqvist, 1983).

Until present, ”land use influences” have most often concerned effects ofquantitatively large areas, such as forests, agriculture and the relations to lakequality (Nilsson and Håkanson, 1992; Håkanson, 1994b). If urban areas areincluded, they are generally represented as a single class (e.g., Meeuwig andPeters, 1996; Müller et al., 1998; Crosbie and Chow-Fraser, 1999). In thisthesis, a detailed classification of the land use in urban catchments will be usedto study the influences of urban status on lake heavy metals. Predictive modelsare going to be developed for the load and distribution of heavy metals inurban lakes.

9

2. Aims

From this background, the aims of the thesis were to:• Develop and test a model for the concentration of suspended particulate

matter (SPM). SPM is an important lake variable for many biotic and abioticprocesses. For heavy metals, SPM act as carrier particles and the fate ofmetals in lakes is strongly influenced by the SPM.

• Discuss the general possibilities and study methods to model the distributionof metals between the particulate associated and dissolved phases. Onemethod to distinguish between dissolved and particulate phases is filtration.From sedimentological, ecological and mass-balance modellingperspectives, it is important to differentiate between the filter-retained andfilter-passing fractions. This is rarely achieved by chemical models based onthermodynamics and there is a need for predictive models for the dissolvedand particulate fractions.

• Further develop methods to critically test empirical/statistical models.Causal explanations of predictive models have to be discussed and related tothe clusters of variables represented by the explanatory variables (or”independent” x-variables) in the models. It is therefore important to test thederived models critically and to assess the model stability.

• Develop and test a general heavy metal mass-balance model for small lakesdominated by diffuse sources and urban drainage. Heavy metal fluxes instorm water (as well as in streams and rivers) can vary a lot, which is notfavourable for modelling efforts. Lakes act as natural integrators, orreceiving basins (Müller et al., 1997), and the sediments further integrate theload over time (Håkanson and Peters, 1995). A lake also traps loads from alldifferent sources, point as well as diffuse sources. Therefore this thesis willsuggest a general mass-balance model for lakes based on existingknowledge of metal dynamics in lakes.

• Apply modelling methods to separate the local (urban) load from theregional background (natural) flux of metals, and to study how the relationbetween these depends on the variation in urban land use among a numberof lakes in Stockholm.

• Rank the investigated metals according to the influences of urban status ontheir dispersion into the Stockholm aquatic environments.

• Estimate the fluxes of metals to ten small lakes, Lake Mälaren and theinnermost Stockholm archipelago. These fluxes could be compared to otherfluxes in order to determine if and how much the Stockholm fluxes areenhanced compared to fluxes in surrounding areas.

10

3. Study areas, material and methods

3.1. Study areas

Stockholm, capital of Sweden with approximately 1.5 million inhabitants, issometimes called ‘Beauty on water’ and the inhabitants boasts of the easy-access to water. The main surface waters of Stockholm (see figure 1) are theEastern parts of Lake Mälaren, which in the central city passes one main outlet(Norrström) and enters the archipelago leading towards the brackish BalticSea. In this thesis 14 sub-areas along a transect through the City of Stockholmwas studied, A to G in Lake Mälaren and 1 to 7 in the archipelago. There arealso a number of small lakes in close vicinity of the city. Here ten lakes, withcatchment areas representing a gradient of urbanisation from virtually nourbanisation to almost complete urbanly developed, have been studied.

Figure 1. Location map of the study areas. Ten small lakes around the central parts of Stockholm (theirlocations are marked with a * 1 to 10), seven sub-areas of Lake Mälaren (A to G) and seven sub-areasof the Stockholm archipelago of the Baltic Sea (1 to 7).

3.2. Material and methods

Material and data for this thesis have been collected from the literature andduring several field studies. The thesis uses data on heavy metal concentrationsin lake and archipelago water and surface sediments. Map parameters,catchment area land use and lake morphometry are also used. The heavymetals examined are cadmium (Cd), chromium (Cr), copper (Cu), mercury(Hg), nickel (Ni), lead (Pb) and zinc (Zn). These metals are widely used in thetechnosphere and the pool of metals in urban areas can be large.

11

For papers II, III and IV, data (given in the papers) were complied fromliterature surveys. For paper IV published data, originating from the SwedishEnvironmental Protection Agency’s research programme “Project Liming-Mercury“ (1985-1989) (see e.g., Håkanson, 1986a; 1986b; Lindqvist et al.,1991; Meili et al., 1991) were used together with predictions of lake waterSPM estimated by the model in paper II.

For papers V and VI primary data were collected during 1996. Ten lakes inStockholm, see figure 1, covering a wide range of lake and catchment areacharacteristics, including degree of urbanisation, were investigated. Surfacewater samples (approximately 1 m water depth) were collected and analysedfor standard water chemical variables by the Stockholm Water Companyweeks 9, 19, 33, 40 and 46. Filtered (0.45 µm) and unfiltered samples wereanalysed for heavy metal content by Svensk Grundämnesanalys AB, Luleå,Sweden. Surface sediments (0-2 cm) were sampled by using a Wilner gravitycorer. The samples were analysed for water content (W) and loss on ignition(IG) by standard methods (Håkanson and Jansson, 1983). Content of Cd, Cr,Cu, Ni, Pb and Zn were analysed by AAS and Hg by fluorescence (Hg byMeAna, Uppsala, Sweden). Measured sediment concentrations are within thesame range of values as other studies have reported (Lännergren, 1991;Östlund and Palm, 1998), except for Cr which might be explained by differentextraction methods. In 1996-1997 a detailed investigation of the land use of thecatchment areas was conducted in co-operation with the StockholmEnvironment and Health Protection Administration (Stockholmsmiljöförvaltning, 1998). The most important characteristics of the study lakesare summarised in table 3.

Table 3. Ranges of selected lake characteristics for the ten Stockholm lakes.Lake variable min mean max unitlake surface area 0.04 0.29 0.76 km2

mean water depth 1.3 2.9 7.2 mmaximum water depth 2.3 5.1 13.8 maccumulation area† 6 46 59 %theoretical water retention time 0.1 1.5 4.9 ytotal phosphorous of surface waters 13 58 117 mg L-1

Secchi depth 1.3 2.5 4.1 mpH of surface waters 6.6 7.6 8.0 -area of drainage area 0.58 1.96 4.75 km2

forests‡ 16 47 82 %wetlands‡ 0 3 8 %parks‡ 0 4 12 %housing area‡ 0 16 58 %roads‡ 0 5 10 %parking area‡ 0 1 5 %industries‡ 0 1 7 %† = percentage of lake surface area; ‡ = percentage of catchment area.

Sediment material for paper VII were sampled during two cruises by R/VSunbeam, August 1997 in the Stockholm archipelago, and June 1998 inEastern Lake Mälaren. Sediment cores were collected using a Gemini gravitycorer (Niemistö, 1974). Metal concentrations were determined by ICP-MS.Water content and loss on ignition were analysed by standard methods. Forfurther information, see paper VII.

12

Morphometric parameters have been calculated according to a digital method,see Pilesjö et al. (1991). To estimate the area of sediment accumulation (BA;see Håkanson and Jansson, 1983 for definition) of the small lakes, cores fromtransects from deep to shallow areas were studied. In Lake Mälaren and theStockholm archipelago sediment echosounder and side scan sonar were used toacoustically map the BA.

Further, more detailed information about study sites, material and methods canbe found in the papers.

4. A model for the characteristic suspended particulate matter (SPM)concentration in lakes

Suspended particulate matter (SPM) in lake water is an important variablerelated to a number of biotic and abiotic processes in lakes. Processes such as,e.g., sorption and precipitation result in a certain particle association of metals(Salomons and Förstner, 1984). This means that SPM acts as carrier particlesfor heavy metals. Settling of SPM through the water column causes heavymetal sedimentation (Sigg et al., 1987; Schindler, 1991; Lithner et al., 2000).Although SPM is relatively easy to measure, it is important, for general lakemodels, to access a simple predictive model for the SPM-concentration, e.g., tomodel effects of varying environmental conditions.

From a compilation of literature data from 26 European lakes, a regressionmodel was developed in paper II, see table 4. The model may be used topredict annual mean SPM as a function of total phosphorous concentration(TP), pH and the dynamic ratio (DR, see Håkanson, 1982). To obtainapproximately normal frequency distributions, included variables aretransformed according to recommendations given by Håkanson and Lindström(1997). TP is commonly used in empirical models and generally representsautochthonous lake production (e.g., Dillon and Rigler, 1974; Schindler, 1977;Peters, 1986). In this model, TP shows that bioproduction is important for theSPM-values in these lakes.

The second model parameter, pH, reflects both allochthonous andautochtonous influences on SPM. Lakes high in lake-systems generally havelow pH-values due to shallow soils and low neutralising capacity. Furtherdown the lake-system, lakes are usually surrounded by thicker soil layers andacidity has been neutralised. At the same time, low-order streams are generallysmall and do not carry much particulate matter. There exists a clearrelationship between river particle flux and water flow (e.g., Jansson, 1982;Cuthbert and Kalff, 1993; Shafer et al., 1997), i.e., the same streams/rivers thathave higher pH-values are also likely to have more SPM. It should, however,be noted that pH is a complex lake variable, involved in many lake processes.Particle aggregation is, e.g., influenced by pH (Gerritsen and Bradley, 1987)and pH is also related to the lake bioproduction (e.g., Håkanson and Jansson,1983).

13

The dynamic ratio (DR) in the model represents resuspension by wind/waveaction (Håkanson and Jansson, 1983). This is supported by the relationshipbetween sediment focusing and DR found by Weyhenmeyer et al. (1997).Resuspension is an important source of suspended particles in lakes (e.g.,Hilton, 1985; Weyhenmeyer, 1996).

Table 4. Multiple regression model for SPM (from paper II) and ranges of the model variables.Included parameters are total phosphorous concentration (TP), pH and the dynamic ratio (DR, definedas √(area)/Dm, where area is the lake area in km2 and Dm the lake mean depth in m). All variables aresignificant at the 95 % level, r2 = 0.87, F > 6, n = 26.log(SPM) = - 1.985 + 1.148 × log(TP) + 0.137 × pH + 0.286 × log(DR)

Variable min max unitTP 5 60 (mg L-1)pH 5.10 8.50 (-)DR 0.07 7.88 (-)

5. Predictive modelling of the distribution of metals betweenparticulate associated and dissolved fractions

Settling of particulate associated metals is an important transport route forheavy metals in lakes. If different samples are analysed for the particulatefraction of metals, the values would probably vary among the samples. Thisvariability is important from a modelling perspective. The question is if thevariability could be explained and related to other environmental variables, andif a predictive model may be developed? The traditional method to express thedegree of particle association is with the so called distribution (or partition)coefficient, Kd (L kg-1), generally defined as:

Kd = (Cpart/SPM)/Cdiss (eq. 1)

where Cpart is the metal concentration of the solid (filter-retained) phase(mg L-1), Cdiss is the dissolved (filter-passing) concentration (mg L-1) and SPMis in (kg dw L-1). There are few examples of published (semi-) predictiveKd-models: (1) for Cd (Koelmans and Lijklema, 1992), (2) for Cd, Cu and Zn(Sung, 1995), and (3) for Cd, Cu, Pb, Ni and Zn (Koelmans and Radovanovic,1998). For these models, field data have been used to calibrate empiricalconstants (see also paper I).

In paper III, the variables included in eq. 1 have been studied. If the logarithmsare taken of both sides of eq. 1, we get:

log(Kd) = log(Cpart) - log(Cdiss) - log(SPM) (eq. 2)

which after division with log(SPM) gives:

log( Kd)

log( SPM)=

log(Cpart)

log(SPM )−

log(Cdiss

)log(SPM )

−1. (eq. 3)

14

If one would hypothetically assume, that the three distributions Cpart, Cdiss andSPM are independent, the relationship of log(Kd) versus log(SPM) will have aslope of -1. This slope is spurious and a mathematical inevitability due to thedefinition of Kd as a ratio including SPM (see, e.g., Kenney, 1982; Krambeck,1995; Berges, 1997). The spurious correlation makes it unsuitable to use Kd asa measure of the degree of particle association. This is, however, to the best ofthe author’s knowledge, generally disregarded in Kd-models.

In environmental investigations, negative slopes between log(Kd) andlog(SPM) are often found. For heavy metals the slopes are generally between-1.0 to -0.5 (see, e.g., Honeyman and Santschi, 1988). This is often attributedto the so called ”particle concentration effect” (see, e.g., O’Connor andConnelly, 1980; Honeyman and Santschi, 1988; Benoit et al., 1994; Benoit,1995; Benoit and Rozan, 1999). In environmental studies, Cpart versus SPMoften show a positive correlation, and Cdiss often show no correlation withSPM. According to eq. 3, this means that slopes between log(Kd) andlog(SPM) should be between -1 and 0, which is in agreement with literaturedata.

Instead of using Kd, it is suggested in paper III that the particulate fraction, PF(-), should be used in environmental investigations and modelling:

PF = Cpart/Ctot (eq. 4)

where Ctot is the total metal concentration (µg L-1). The factors in eq. 3 areillustrated in figure 2 for the mercury data in paper IV. Here reactive Hg isused instead of the dissolved concentration, and the corresponding modifieddistribution coefficient is denoted Kd*, and the modified particulate fraction isdenoted PF*. It is evident that Creact and Cnon-react (corresponding to Cdiss andCpart) versus SPM are the actual relationships and that the spurious correlationresults in an apparent strong relationship between Kd* and SPM. Note, that theslopes of the relations in figure 2 confirm eq. 3: - 0.80 = 0.19 - (- 0.01) - 1.

The spurious correlations thus give an opposite patterns for Kd versus SPMcompared to PF versus SPM. Both Kd and PF are meant to express the ”degreeof particle association”, and high values indicate high particle affinities. WhenPF is used, the ”degree of particle association” increases with increasing SPM,but for Kd, the ”degree of particle association” decreases with SPM. This is dueto the spurious correlations. In eqs. 5 and 6, multiple regressions for Kd* andPF* for the mercury data in paper IV are given:

log(Kd*) = 6.902 - 0.702 × log(SPM) - 0.225 × log(Fe)- 0.100 × log(area/ADA) (eq. 5)

r2 = 0.69, n = 25 lakes and F > 2 (see paper IV),

log(PF*) = 0.0075 + 0.094 × log(SPM) - 0.071 × log(Fe)- 0.031 × log(area/ADA) (eq. 6)

15

r2 = 0.33, n = 25 lakes and F > 3. These equations clearly illustrate the abovediscussion. In eq. 6, the correlation between log(PF*) and log(SPM) ispositive, and the r2-value decreases since this model does not include aspurious component. Using literature data, it is shown in paper III that thesame is true also for Kd- and PF-values based on filtration.

Empirical tests using randomly generated data are suggested and used inpapers III and IV to test the influences of the spurious correlations. It is shownthat random influences depends on the number of data cases (lakes).Environmental investigations do generally not include sufficient number ofdata to exclude random influences on the slope between log(Kd) and log(SPM).For the Kd*-model for Hg, it could be concluded that there are spuriousinfluences, but that they probably do not explain the whole effect. It shouldalso be noted that PF may also be influenced by spurious correlations.

Finally, two more arguments are given in paper III to use PF instead of Kd forpredictive models. (1) In dynamic models, PF is the variable that directly, andnot indirectly as Kd, partitions the fluxes. If PF is not known, it has to becalculated from Kd and SPM. (2) Empirical data show that Kd generally has alarger inherent within-system variability than PF. From a literature compilationof 51 data-sets, it could be noted that the coefficient of variation, CV (=standard deviation/mean value), for Kd was 3.0 times larger than CV for PF.Since predictive models should use variables with as low variabilities aspossible, it is better to use PF than Kd.

log(Cnon-react) = 0.19 × log(SPM) + 0.55, r2 = 0.05

log(Creact) = -0.01 × log(SPM) + 0.13, r2 = 0.00

log(PF*) = 0.10 × log(SPM) + 0.72, r2 = 0.09

log(Kd*) = -0.80 × log(SPM) + 6.42, r2 = 0.60

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

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log(SPM) (mg L-1)

log(

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, lo

g(C

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µg L

-1)

& P

F* (

-)

5.6

5.8

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7.0

log(

Kd*

) (L

kg

-1)

Cnon-reactCreactPF*Kd*Cnon-reactCreactPF*Kd*

Figure 2. Relationships between SPM and Creact, Cnon-react, Kd* and PF* for the Hg data in paper IV,n = 25.

16

6. Stability tests of predictive models

A new procedure for predictive model testing has been developed and used forthe SPM and the Kd*-Hg models, see papers II and IV. It includes a new andfurther developed structured form of stability test. These tests address thefollowing questions (1) which model parameters should be included and (2)how should the model be interpreted if the data set had been different - howwould the model parameters, coefficients and r2-value change? In a stabilitytest, a number of lakes are randomly omitted and the model calibrated usingdata from the remaining lakes. (If half the data-set is omitted it is generallycalled a validation.) By doing this a number of times the model stability maybe evaluated (Håkanson and Peters, 1995).

Outliers should generally not be excluded from a data set without very goodreasons. To evaluate the effects of possible outliers and systematic data biases,a structured stability test was used to test the models in papers II and IV. Lakeswere here omitted according to a system. One to four of the lakes with thehighest/lowest values from several aspects (i.e., the most extreme lakes) wereomitted one after another and the model calibrated using the remaining lakes. Itcould, e.g., be argued that Lake IJsselmeer is an outlier, in paper II, due to anextremely high SPM-value. The test results show that this is not the case, andthe data from Lake IJsselmeer are included. The model has been tested, andgave an r2-value of 0.90 for 38 lakes with TP ranging up to 885 µg L-1, with pHand DR within the original model range (Johansson, H., personalcommunication).

These tests show the importance of model interpretations in the terms ofclusters of statistically and functionally related variables. The cluster variablesthat enter the model are suggested by a correlation matrix in combination withstability tests. Each cluster may be represented by several variables in the dataset, and any one of them may be used in the model. For the models in papers IIand IV, only the first variable clearly enters the models, the following variablesto enter the models varies with the selection of lakes. These results show that itis very difficult to give causal interpretations of a single variable included inmodels. The basis for the interpretations should instead be the clusters includedin the model. Concerning the models in papers II for SPM and IV for Kd*-Hg,allochthonous input and autochthonous production are the most importantprocesses, resuspension and possibly water chemistry are also of importance.

7. A lake heavy metal mass-balance model

There is a need to calculate the metal load to lakes affected by diffuse inflowand urban runoff. The dynamic mass-balance model developed in paper V aimsat describing annual fluxes. It is based on fundamental principles and usescomponents from other models. The lake model consists of tree compartmentsand the model handle fluxes to and from these, see figure 3 and furtherexplanations in paper V.

17

Lake water

A-areas

Burial

Diffusion

Inflow

Outflow

Sedimentation

Resuspension

ResuspensionET-areas

Figure 3. Illustration of the mass balance model structure used in paper V.

Since the model uses fluxes on an annual basis, several processes, related tothermal stratification in these dimictic lakes have been simplified. Stratificationis omitted. The active accumulation sediments (A-areas, with a continuoussettling of fine grained particles) are represented by one box. The 0-2 cmsediment depth is used since it represents the integrated recent load andmixing, during a time of approximately one to four years according datedsediment cores (Sternbeck, 1998 and Östlund and Palm, 1998). Erosion andtransportation areas (ET-areas, i.e., the areas above the wave base with adiscontinuous flux of settling fine material) are represented by another box.Flux-controlling rates are calculated from measured variables, calibratedempirical constants or estimated from empirical sub-models, see table 5.

The model is calibrated using measured metal concentrations in water andsediments. From five measurements of water and sediment concentrations, it ispossible to calculate CV as a measure of the within-lake variability. In figure 4,the CV-values are plotted against model deviations from empirical values,expressed as modelled/empirical concentrations. It can be noted that themodelled values of the sediment concentrations are more accurate than those ofthe water concentrations. The variability of metal concentrations in water werealso generally higher than the sediment concentrations.

Table 5. Driving variables for the mass-balance model (from paper V).Lake and metal specific data: Calibrated constants:Metal concentrations in sediments Settling velocity of particulate matter: 100-150 (m y-1)Metal concentrations in water Resuspension rate: 0.5 (y-1)Particulate fraction of metals†

Sedimentation of matter‡Diffusion constants: for Cd and Zn 0.35, for Cr, Cu,Hg, Ni and Pb 0.035#

Lake morphometry Outflow rates: f(T), see paper V† = For Hg, the model in paper IV has been used to get a best estimate of the particulate fractionalthough not all lakes were within the model range.‡ = For two lakes, values from a model were used (see paper V).# = The diffusion rate has been estimated by the diffusion constant/IG (y-1), where IG is the sedimentloss on ignition (%).

18

A: Water

CV

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

CdCrCuHgNiPbZn

Model deviation

CV

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

B: Sediment

CdCrCuHgNiPbZn

Figure 4. Plot of empirical CV-values versus the model deviations (= modelled/empiricalconcentrations) for water (A) and sediments (B).

The uncertainty in estimated values in mass-balance models is determined bythe major fluxes and, the uncertainty related to the major fluxes. To assess andrank the sources of uncertainty, paper V gives an uncertainty analysis. Itshowed that the key uncertainty was related to the value used for theparticulate fraction of the water metal concentrations (PF). The uncertaintiesrelated to the rates of diffusion and resuspension did not turn out to be veryimportant, which is interesting since the uncertainties (CV-values) of theserates were the highest.

8. Influence of the City of Stockholm on the transport of metals

8.1. Urban land use effects on metal transport

The characteristics of the catchment areas influence the water and sedimentquality (see, e.g., Nilsson and Håkanson, 1992; Håkanson and Peters, 1995;Meeuwig and Peters, 1996; Müller et al., 1998; Thierfelder, 1998). As canbeen seen in table 1, many investigations show effects of urbanisation on the

19

metal status of aquatic environments. None, however, uses a detaileddescription of the catchment area land use as an indicator of urban status. Forpredictions of the water quality of urban runoff, Tasker and Driver (1988) usedindicator variables of residential, non-urban, commercial and industrial landuse. Based on percentage impervious areas, Klein (1979) recommendedallowable urban developments to maintain a high stream quality (speciesdiversity). In paper VI, urban land use influences on catchment transport ofheavy metals were studied for ten lakes with a varying degree of urbanisation.Metal loads (calculated using the model in paper V) and A-area sediment metalconcentrations were correlated to a set of parameters describing natural as wellas urban land use.

With ten study areas, and internal correlations among the land use descriptors,however, it was impossible to draw any detailed conclusions regarding therelations between land use and metal effect variables. The parameters weretherefore divided into two groups: (1) Those correlating to the size cluster(including closely correlated variables like lake and catchment areas and lakevolume, but also, some of the descriptors of urban land use), and (2) thosecorrelating to urban parameters (describing the urban status). The relationscould thus be expressed as:

‘lake load = intercept + a × size + b × urban status’ (eq. 7)

If the variables are normalised by subtraction of the mean and division with thestandard deviation (so called standard scoring) they are transformed to adimensionless scale on which the coefficients a and b could be compared. Thesize coefficient, a, reflects the influence of the size cluster on the lake load andcould be interpreted as a regional influence affecting all investigated lakes withthe same (size proportional) magnitude. The cause of such a load could be,e.g., a uniform atmospheric deposition or geological background load. Thenormalised regression coefficients are plotted in figure 5.

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

b ('urban status' coefficient)

a ('s

ize'

coe

ffic

ent)

Zn

Ni

Cu

Cr

Cd

HgPb

Figure 5. A plot of the size parameter coefficient, a, versus the urban status parameter coefficient, b,from the normalised lake load regression models.

Cd, Ni, Zn (and Hg) form one group of metals for which a is larger than b. ForCr and Pb a and b are approximately equal, and for Cu, finally, b is larger thana. This indicates that for the investigated Stockholm lakes, Cu is the metal thatis most influenced by the local urban land use, followed by Pb and Cr, whilethe load of the other metals mainly has regional background causes.

20

8.2. Modelling the Stockholm influences on the sediment loads

In papers V and VI the metal fluxes from small drainage areas were thesubjects. In Stockholm it is also possible to study the integrated sediment loadfrom more or less the whole city. Therefore the sediments were studied along atransect across the City of Stockholm (paper VII) from the Eastern parts ofLake Mälaren, through Norrström and the innermost archipelago areas.Investigations of the area of fine sediment accumulation, dated sediment coresand sediment metal concentrations made it possible to calculate the total metaldeposition. Figure 6 shows the focusing corrected deposition in each of the 14studied sub-areas. Sediment deposition increased approximately 5-fold for Cd,Cu, Hg and Pb and 3-fold for Zn in the most central areas of Stockholm.

0

0.1

0.2

0.3

0.4

0.5

0.6

A B G C E F D 1 2 3 5 4 6 7

100 Cd

Cr

Cu

100 Hg

Ni

Pb

Zn

Figure 6. Total sediment deposition in each of the Stockholm investigation sub-areas. A to G in theEastern parts of Lake Mälaren and 1 to 7 in the innermost archipelago (from paper VII).

To assess the Stockholm contribution of the total load, a backgroundconcentration/deposition which is not influenced by the city, has to beestimated. Since the sedimentation rates are high and Stockholm is an old cityit would be very difficult to estimate the background concentration by studyingdeep sediment layers. Therefore, in paper VII, normalisation with a tracerelement which is not influenced by the city and with the same sedimentologicalproperties as the element of interest, is used as a modelling approach to obtainbackground concentration values (see, e.g., Salomons and Förstner, 1984;Louma, 1990). Nickel was found to be possible to use as a tracer and bynormalising to this element it was found that of the total sediment deposition,more than half of the Hg may originate from the City of Stockholm; for Cd, Cuand Pb approximately half, and for Cr and Zn less than half.

At the main outlet of Lake Mälaren into to archipelago, there is a samplingstation of the national Swedish environmental monitoring programme. Thismeans that the fluxes of metals leaving Lake Mälaren are well known. Thesefluxes may be compared to the amounts of metals accumulating in each of thedefined sub-areas, as calculated in paper VII. For Hg and Pb the amountsleaving Lake Mälaren are trapped in the archipelago sediments of theinnermost two sub-areas. Cd, Cr, Cu, Ni and Zn on the other hand, are to ahigher degree transported towards the Baltic Sea.

21

8.3. Metal fluxes in Stockholm

A comparison of atmospheric deposition with catchment area outflow may beused to identify sources or sinks of metals in an area (see, e.g., Schut et al.,1986; Monitor, 1987; Dillon et al., 1988). As a way to assess the large scalemetal mobilisation, a metal budget for Stockholm will be discussed in thissection. In table 6, various metal fluxes are compiled into a large scaleStockholm budget. The data are:1) Metal fluxes from ten small Stockholm catchment areas from papers V and

VI.2) The sediment load from Stockholm (paper VII) divided with the total area

of Stockholm (including suburbs an area of 430 km2 have been used). Thisunderestimates the total Stockholm source since the transport to the BalticSea is not considered in the model (see paper VII).

3) Metal drainage from Swedish forest catchment areas (these data areincluded for comparison).

4) Atmospheric deposition at a site in central Stockholm (these values exceedthe background deposition estimated from remote areas by a factor 2 to 6).The representativity of this site is unknown, but spatial variation in metaldeposition in urban areas could be large (Simmons and Pocook, 1987).

5) Atmospheric deposition at Aspvreten, a remote site south of Stockholm.6) Atmospheric deposition at Fasterna-Mjölsta, a remote site north of

Stockholm.

Table 6. Areal metal fluxes in Stockholm and Swedish forest areas (mg m-2 y-1).Cd Cr Cu Hg Ni Pb Zn

1. Stockholm drainage areasoutflow (from paper VI), min-(mean) max

0.01-(0.05)

0.17

0.13-(0.77)

2.06

0.43-(3.9)

18

0.00-(0.01)

0.03

0.30-(1.6)

2.6

0.42-(3.1)

12

1.5-(12)

492. Stockholm sediment load from

the city (paper VII)0.12 1.7 7.0 0.09 0 8.8 18

3. Drainage from Swedish forestareas (in the 1980-ties)1

0.02-0.11

- 0.2-0.5

0.0007-0.0061

- 0.2-0.5

0.1-1.8

4. Atm. dep. Central Stockholm,1995-962, †

0.065 0.42 - 0.013 0.89 2.5 31

5. Atm. dep. Aspvreten, 19933, † 0.041 0.14 1.9 0.006 0.27 1.6 4.56. Atm. dep. Fasterna-Mjölsta,

1993-944, †0.035 0.26 2.0 0.006 0.20 1.1 4.8

† = wet deposition, ‘open field’ values. - = no data. 1 = Borg and Johansson, 1989. 2 = SLB 1998.3 = approximately 65 km SSW of Stockholm, Kindbom et al., 1995. 4 = approximately 55 km N ofStockholm, Munthe and Kindbom, 1995.

From this table the following may be noted. The (mean to) maximum values ofthe range of the small drainage areas outflows (1) approximately match theStockholm sediment load (2), indicating that the upper part of this range maybe more representative of the whole Stockholm urban area than the meanvalues. The difference (between 1 and 2) may be due to a certainunrepresentativity of the small lakes. Most of the urban developments in thecatchment areas in paper VI are quite young (less then 100 years). For Hg inStockholm, Svidén and Jonsson (2000) showed that large amounts wereemitted before 1900. Large parts of these emissions may have beenaccumulated in the soil and may still affect the water and sediments of centralStockholm. In those days Stockholm mainly consisted of the most centralareas, which are not included in paper VI.

22

The metal load to the sediments from Stockholm (2) is the largest mean fluxfor all metals (except Ni). It is larger than the atmospheric deposition (5-6) anddrainage from forest areas (3) which indicates that there are sources of metalsin Stockholm, increasing the background flux by a factor of approximately 10for Hg and Pb and a factor 4 to 10 for Cd, Cr, Cu and Zn. This shows that thereare considerable sources of metals to the Stockholm aquatic environments.

For Ni, the central Stockholm atmospheric deposition (4) is three times higherthan the background (4-5) and the small catchment areas outflow (1) is higherthan the deposition. No nickel from Stockholm is however found in the LakeMälaren or archipelago sediments, indicating a dissolved transport out of thearea, towards the Baltic Sea.

There are many factors that influence metal budgets, and a simple comparisonis difficult. Due to vegetation, a certain degree of enrichment could beexpected in atmospheric deposition. In forest areas enrichment factors (totaldeposition in forests/wet deposition) larger than two could be expected for Cd,Cu and Hg (Grahn and Rosén, 1983; Bergkvist et al., 1989; Munthe et al.,1995). Even though these study areas are urbanised, they do have an average of47 % forests (table 3).

9. Conclusions

The most important findings from this thesis are:1. An empirical model for prediction of SPM has been calibrated using a

wide range of European lakes. It has a high r2-value and should be usefulfor lake predictive purposes.

2. It has been demonstrated that the traditional distribution coefficient, Kd,generally is unsuitable to use for interpretations of the degree of particleassociation of substances in aquatic environments. Several reasons havebeen given why the particulate fraction, PF, should be used instead.

3. For regression models, the stability tests have been further developed toinclude also a structured stability test, which may be used to assessinfluences of possible outliers in the data material.

4. A model has been proposed to calculate the annual load of metals to lakesmainly influenced by urban run-off and diffuse sources.

5. The role of the catchment area urbanisation for metal fluxes has beenstudied. The results suggest that Cu is the metal that is most influenced bylocal urban status, compared to the regional background. For Cr and Pb theinfluences are of the same order of magnitude, and Cd, Hg, Ni and Zn weremore influenced by the background than from the urban land use. The dataset was, however, small and it would be valuable to confirm these resultsagainst a larger data material.

6. Metal fluxes in Stockholm have been estimated from different aspects.They are generally enhanced in the city, compared to surrounding areas.

7. The results indicate that Hg and Pb are trapped in the sediments of theinnermost archipelago areas. The other investigated metals (Cd, Cr, Cu, Niand Zn) are to higher degrees transported towards the Baltic Sea.

23

10. Acknowledgements

I would like to acknowledge a number of persons that have contributed indifferent ways to make this thesis possible.

First of all, I would like to thank my supervisor Lars Håkanson for giving mefreedom and responsibility. Freedom to do things the way I wanted, and at thesame time the responsibility to fulfil our (or actually his) engagements in theprojects. It has been a rewarding way to work.

Six years ago I was a newcomer in this business and I am grateful to all thepeople that helped me find my way around, including the helpful staffs of thedepartments of Earth Sciences and Limnology. I also want to thank my fellowgraduate students and the senior researchers at the department, Arne Jonsson ofLinköping university and Anders Jönsson of Stockholm university. A numberof students have also helped to make sampling cruises successful.

The project group of the ”Metals in the urban and the forest environment” isacknowledged for providing an interesting project environment and thesystems-approach. The Stockholm project group is acknowledged for the localframework and perspective, thanks to the participants from: Stockholmenvironment and health protection administration, Stockholm Water Company,Stockholm streets and real estate administration, Stockholm City planningadministration, Huddinge and Nacka municipalities.

I would also like to thank my wife, family and friends for supporting my work,however, without really knowing too much what it concerns.

Financial support has been received from the Swedish environmentalprotection agency's research programme ”Metals in the urban and the forestenvironment” (Anon. 1995; Bergbäck and Johansson, 1996) and the Stockholmenvironment and health protection administration.

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