Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 687

_____________________________ _____________________________

On Distribution Coefficients inAquatic Systems

BY

HÅKAN JOHANSSON

ACTA UNIVERSITATIS UPSALIENSISUPPSALA 2002

Dissertation for the Degree of Doctor of Philosophy in Earth Sciences withspecialization Environmental Analysis presented at Uppsala University in 2002

ABSTRACT

Johansson, H. 2002. On Distribution Coefficients in Aquatic Systems. ActaUniversitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations fromthe Faculty of Science and Technology 687. 20 pp. Uppsala. ISBN 91-554-5245-0.

In this thesis, different types of chemical and physical distribution coefficients areidentified, examined and used to describe the fate and transport pathways ofsubstances in aquatic systems. Observations from field experiments in streams with non-reactive and reactive tracersconstituted the basis for development of an advection-dispersion model. Differencesin the concentrations in both the water and sediment data for the tracers were due tothe particle affinity of the reactive tracer. This difference in behaviour could bedescribed by including an instantanous and a kinetically controlled sorption, whichincluded distribution coefficients, in the water column (Kd) and in the streambedsediment (KB), respectively.The results presented in this thesis also include a model for the lake characteristicconcentration of suspended particulate matter (SPM). The SPM-model can be used todescribe mass flows of particles in lakes. The traditional distribution (or partition)coefficient Kd has been found to be unsuitable for interpretations of the particleassociation of solutes and also for distributing solute mass flows. Instead, theparticulate or the dissolved fraction, PF and DF, defined as ratios of the particulate ordissolved concentration to the total concentration respectively, is recommended formass-balance calculations. A new PF-model for phosphorus has meant that this partis no longer the most sensitive part of predicting concentrations of phosphorus inlakes using a more extensive dynamic model. New methods have also been developed to describe the shape of lakes. Together withthe mixing depth of lakes, the shape of a lake can be transformed into a distributioncoefficient that physically determines the portion of a lake that is exposed, bothareally and vertically, to continuously mixing.

Key words: Distribution coefficient, lake, modelling, morphometry, stream.

Håkan Johansson, Department of Earth Sciences, Uppsala University, Villavägen 16,SE-752 36 Uppsala, Sweden

© Håkan Johansson 2002

ISSN 1104-232XISBN 91-554-5245-0

Printed in Sweden by Akademitryck AB, Edsbruk 2002

Preface

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

I. Johansson, H. and Håkanson, L., 1993. Partitioning coefficients inaquatic systems: Metals partitioning between water and particulatematter; impact on ecosystem modelling. In: Pettersson, K. and L. Forsell(Eds.) 21st Nordic Sediment Symposium, LIU 1993 B:7, Department ofLimnology, Uppsala University, p. 23-36.

II. Wörman, A., Forsman, J. and Johansson, H., 1998. Modelling retentionof sorbing solutes in streams based on tracer experiment using 51Cr,Journal of Environmental Engineering, 124: 122-130.

III. Johansson, H., Jonsson, K., Forsman, K.J. and Wörman, A., 2001.Retention of conservative and sorptive solutes in streams - simultaneoustracer experiments. The Science of the Total Environment, 266: 229-238.

IV. Jonsson, K., Johansson, H. and Wörman, A., 2001. Hyporheic exchangeof reactive and conservative solutes in streams - tracer methodology andmodel interpretation. Manuscript.

V. 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.

VI. Johansson, H., Brolin, A.A. and Håkanson, L., 2001. New morphometricapproaches to the modelling of lake basin shape influenced processes andproperties in lakes. Manuscript.

VII. Johansson, H., Lindström, M. and Håkanson, L., 2001. On the modellingof the particulate and dissolved fractions of substances in aquaticecosystems - sedimentological and ecological interactions. EcologicalModelling 137: 225-240.

VIII. Johansson, H., and Håkanson, L., 2002. Models to predict the particulateand dissolved fraction of phosphorus in lakes. Manuscript.

The publishers kindly gave their permission for reproduction of the papers.

The contribution to the papers by the authors is as follows:

I) In this paper I was responsible for most of the writing, whereas the original ideaoriginated from the second author. II) In this paper I was responsible for a significantpart of scientific planning, evaluation and writing. III) In this paper I was responsiblefor most of the writing, and additionally made major contributions to scientificplaning and evaluation. IV) In this paper I made major contributions to scientificplaning, evaluation and writing. V) In this paper I contributed with ideas andcompilation of lake data while most of the writing was done by the first author. VI) Inthis paper writing was mostly done on a collaborative basis by the first and the secondauthor, although the main part was done by the first author. VII) In this paper writingwas mostly done on a collaborative basis by the first and the second author. VIII) Inthis paper I was responsible for the compilation of lake data and made most of theevaluation of lake data and most of the writing.

Table of contents

AbstractPrefaceTable of contents1. Introduction.....................................................................................................12. Background.....................................................................................................1

2.1. General .....................................................................................................12.2. Streams.....................................................................................................32.3. Lakes ........................................................................................................5

3. Objectives of the thesis ...................................................................................64. Study areas, material and methods .................................................................7

4.1. Study areas ...............................................................................................74.1.1. Streams ..............................................................................................74.1.2. Lakes .................................................................................................7

4.2. Material and methods...............................................................................84.1.1. Streams ..............................................................................................84.2.2. Lakes .................................................................................................8

5. Results.............................................................................................................85.1. Streams - transport parameters and processes (papers II - IV) ................85.2. Lakes - transport parameters and processes (papers V-VIII).................11

6. Conclusions...................................................................................................16Acknowledgements...........................................................................................17References.........................................................................................................19

1

1. Introduction

In an aquatic ecosystem, there exist many different processes that control thefate and transport pathways, and also ecological effects of substancesintroduced into the ecosystem. The governing processes are many and theinteractions between them can be very complex. It is therefore very importantto structure the studied systems and the regulating processes so that the keyprocesses or the result of these processes can be parameterised and described ina simple manner. One way to partly achieve this is through the usage ofdistribution coefficients.

Recognising this possibility, the aim of this thesis concerns the examination,development and usage of different types of distribution coefficients in aquaticsystems.

2. Background

2.1. General

Plants, animals and humans are all dependent on the supply of water. Tohumans, a secure supply of healthy freshwater is of outermost importance forour existence. With the population density literally exploding during the 20th

century, it has been a necessity to allocate more and more land as well as waterresources for providing humans with food and products/activities associatedwith the structure of modern society.

The extensive exploitation of natural resources has lead to increased pressureon land and water systems. The result has been an increased load anddispersion of metals (e.g., copper, cadmium, mercury, lead, etc.), fertilisers(phosphorus and nitrogen) and other substances (e.g., polychlorated biphenyls,dioxins, etc.) into the biogeosphere.

The main pathways of these substances to the biogeosphere are atmosphericdeposition, surface runoff, groundwater and waste outlets. The fact that manyof these substances degrade slowly or even accumulate in the biogeosphere hasmade them to possible threats to life on land and in streams, lakes and oceans.Elevated concentrations of pollutants in these systems have for instance lead tothe problems of eutrophication and bioaccumulation of toxic metals.

As these substances constitute a potential threat to the structure of ecosystemsin streams, lakes and oceans, it is very important to gain an increased generalunderstanding of the mechanisms that govern and alter (1) the fate andtransport routes, and (2) the ecological impact of pollutants in these systems.Assessing the ecological impacts at the ecosystem level and the construction ofecosystem models are multi-disciplinary scientific problems.

2

In any study of ecological impact, fate and transport routes, the key variablesand processes need to be identified. Then they can be mathematically describedand implemented into models assessing the ecological impact. This isimportant for development of remedial strategies.

All substances introduced into the environment are not equally harmful.Generally, the most toxic substances appear naturally with low concentrationsin water, sediments and biota, whereas the opposite is true for the less harmfulsubstances (Håkanson and Jansson, 1983). The total concentration of asubstance is, however, not the only or the most important measure thatdetermines the toxicity. A key factor that regulates the toxicity of a substance isits bioavailability. The toxicity also depends on the substance’s transformationsand interference with enzymatic systems and metabolites (Förstner andWittmann, 1981).

From an ecosystem perspective, also the degree of particle association iscrucial for a substance’s biological uptake, and further also for its ecologicalimpact and transport routes. Fig. 1. illustrates schematically a solute’sassociation to particles. The occurrence of fine particulate matter, especially inform of organic particles (e.g., humus), are known to alter the degree ofparticle association, due to their strong sorption capacities (Håkanson andJansson, 1983; Meili, 1992).

--

- ---++

-

--

--

-+

+

Adsorption

Desorption

Mez+ (aq)--

- ---+

+

-

--

--

-++Mez+ (aq)

Mez+ (aq)

Me

Mez+ (aq)Me

Me

Fig. 1. Illustration of one of the key processes that regulates the fate, transport routesand to a large extent also ecological impact of substances in aquatic environments: thedegree of association to particles (modified from paper VII).

Precipitation, dissolution, complex formation with organic and inorganicligands, and sorption are some of the reactions that regulate the particleassociation of solutes. In general, it is much more difficult for biota to take upsolutes associated to particles (Luoma, 1983). Exceptions exist. It is forinstance known that particle-associated solutes can be uptaken by, e.g., filter-feeders (Turner and Whitfield, 1980). However, solutes existing withinparticles (e.g., in the crystal lattice of minerals) are generally regarded notavailable for biological uptake.

3

From a mass-balance perspective, concentration of particulate matter anddegree of particle association regulate transport routes and distribute massflows. Varying physio-chemical conditions (e.g., pH, conductivity, alkalinity,etc.) may further change a substance’s degree of particle association. Differenttypes of distribution coefficients (papers I-V, VII-VIII) can usually be used todescribe the degree of particle association. Particles larger than approximately0.45 µm can, accordingly to Stoke’s law, be subjected to gravitationalsedimentation (Håkanson and Jansson, 1983). Operationally, these particlesand solutes associated to these particles constitute suspended particulate matter(SPM) and the particulate fraction of solutes, respectively.

Fig. 2. illustrates how the degree of particle association may impact thebiouptake. Also the hydrodynamic conditions in streams and lakes play animportant role for fate and transport routes of particles and substances (seesections 2.2. and 2.3.).

0.2

0.1

0.05 0.025

Month

240 60 180 120 0

20000

10000

0Conc

entra

tion

in p

reda

tor (

Bq/kg

ww)

Kd

(for pH 6)

Kd =

WhereKd = partition or distribution coefficient (-)Ca = concentration of particulate cesium (µg/L)Cd = concentration of dissolved cesium (µg/L)

Cd + Cd Ca

Fig. 2. Sensitivity test for the ecological effect parameter, Cs-137 in predatory fish(Bq/kg wet weight), for different cases when the degree of particle association (Kd)for cesium in lakes is varied and other model variables are kept constant. Thesesensitivity tests are related to a peak fallout of 25 Bq/m2 during month 24 (modifiedfrom paper I). Note that Kd in this figure equals the dissolved fraction (DF) in papersV, VII and VIII and not the expression for Kd given in those papers.

2.2. Streams

Streams constitute highly important transport systems for transport ofsubstances from watersheds to lakes and oceans. The main hydraulicmechanisms for the transport and spreading of solutes in the main channel ofstreaming waters are advection and dispersion, see Fig. 3. Streambeds can alsoretain extensive quantities of solutes (attached to particles and/or dissolved inthe pore water) for shorter or longer times (see, e.g., Berndtsson, 1990; HeliosRybicka, 1996). A net transport of solutes from the sediment to the stream

4

water column can, however, occur if the concentration of solutes is higher inthe pore water of the sediments than in the water column or by erosion.

The exchange of water between the main stream and zones with stagnant orslow circulating water (i.e., transient storage zones) adjacent to the mainstream, side pockets and bed sediment, changes transport routes, transporttimes and fate of solutes in flowing water. The exchange with these zonescauses a temporary detainment of a portion of the water relative the fastermoving waters in the main stream, see Fig. 3.

Dispers

ion

Advection

Side pockets

Impermeablesurface

Solutesin bed sediment

Solute exchangebetween main stream

and side pockets

Solute’s particle association

Solutes inside pocketstream area

Solute exchangebetween main stream

and bed sediment

Solutes inmain stream

area

--- --

-++

-

--

--

-+

+

Adsorption

Desorption

Mez+ (aq)

--- --

-++

---

--

-++

Mez+ (aq)

Mez+ (aq)

Me

Mez+ (aq)Me

Me

Fig. 3. A schematic illustration of how hydrodynamical and chemical processes affectexchange of solutes in streams, and thereby also the propagation velocity of solutes,transported from the watershed to lakes or oceans.

Physically, the relation between the cross sectional areas of these zones and ofthe main stream section may be treated with a distribution coefficient thatreflects the delay in the propagation velocity of stream water relative meanwater velocity of the stream (paper II).

The continuous “filtration” of stream water and dissolved solutes into and outof the bed sediment allow numerous different chemical reactions to occur inthe bed sediment. Depending on its particle affinity, the solute becomesattached or detached to particles. This has implications for the net exchange ofreactive solutes between the sediment and the overlaying stream water (papersII - IV). In a transport perspective, the distribution of (1) water between themain stream and adjacent zones and the distribution of (2) solutes to particlesin the water column and/or in the bed sediment dramatically alter the transport

5

time of solutes to lakes and oceans. This also has large implications for theecological effects of solutes both in streams and downstream aquatic systems.

2.3. Lakes

Lakes as streams constitute important watercourses for transport of solutesfrom watersheds to oceans. A lake is to a large extent a reflection of thewatershed’s size, topography, geology, land use and vegetation (see, e.g.,Nilsson and Håkanson, 1992; Müller et al., 1998; Thierfelder, 1998). When thestream water enters a lake, it is, however, the morphometry, the flushing rate,mixing regime and trophic status of the lake, and solutes’ particle affinity thatto large extent determine the fate, transport routes and also ecological impact ofsolutes within the lake, see Fig. 4.

E-area = Erosion areaT-area = Transportation areaA-area = Accumulation area

A-area

T-ar

eaT-area

E-area E-area

Sediment

Hypolimnion

EpilimnionMetalimnion

Inflow OutflowWind

Wav

e-in

duce

dwa

ter m

ass

circu

latio

n

Sedi

men

tatio

n

Photosynthesis

Mineralisation

Solute’s particle association

--- --

-++

-

--

--

-+

+

Adsorption

Desorption

Mez+ (aq)

--- --

-++

---

--

-++

Mez+ (aq)

Mez+ (aq)

Me

Mez+ (aq)Me

Me

Fig. 4. A schematic illustration of how some of the major hydrodynamical andchemical processes in lakes affect the fate and transport routes of solutes.

The concentration of SPM in lakes reflects both particulate matter enteringlakes with streams (i.e., allochtonous material) and produced within lakes (i.e.,authocthonous material) and resuspended bottom sediments (paperV).

Weyhenmeyer (1996) showed that resuspended particulate matter maycontribute significantly (47-92%) to the total sedimentation of particulatematter in lakes. According to Tartari and Biasci (1997) the settling flux ofparticulate material is proportional to nutrient status of lakes. In lakes withlonger flushing rates particles and particle-associated solutes have longer timeto settle down to the bottom (see, e.g., Vollenweider, 1968; 1975). Differentparticles have different settling velocities. Depending on degree of particleassociation, larger or smaller fraction of solutes may be transported to the lakebottom (papers V, VII-VIII). At certain specific lake conditions (e.g., wind-

6

induced resuspension of sediment bottom and redox-induced dissolution ofparticle-associated solutes) lake bottom sediment can cause internal loading ofparticles and solutes to the water column of lakes.

Particles do not settle down evenly distributed over the whole lake bottom. Thewind fetch at the lake surface determines the depth of the wave base and also,hence, the portion of the lake that are continuously mixed (paper VI). Duringstratified conditions, this portion of the lake is referred to as the epilimnion, seeFig. 4. Areas above the wave base are dominated by erosion and transportationprocesses/areas (see, e.g., Håkanson and Jansson, 1983). Accumulation areasare those areas below the wave base which receive a continuos settling flux offine-grained sediments (<63 µm). In comparison to erosion- and transportationareas, accumulation areas are often referred to as “end stations” of theseparticles.

Depending on the stability of the boundary between epilimnion and hypo-limnion, the thermocline (a density bar), exchange of water between theepilimnion (the active lake volume) and the hypolimnion is restricted (Cornettand Rigler, 1987; Cole and Pace, 1998). This changes the theoretical waterretention time of lakes (flushing rates), which, as pointed out by Vollenweider(1968; 1975) among others has a physical impact on retention rates and massflows of solutes.

Solutes’ particle affinity, usually described by a distribution coefficient,modifies and controls consequently the fate and transport routes of reactivesolutes in lakes, but also the shape of lake basins together with mixing depthsof lakes can be highly important. The shape of lake basins together with mixingdepths of lakes constitute lake specific distribution coefficients that regulatesvertical distribution patterns of physical, chemical and biological propertieswithin lakes.

3. Objectives of the thesis

An overall objective of the work has been to gain an increased understanding ofthe different processes and parameters in streams and lakes that controltransport routes of solutes and how this potentially can affect the ecologicalimpact of introduced solutes into these systems. More specifically, the intentionhas been to identify and describe important chemical and physical distributioncoefficients that regulate and distribute mass flow of solutes.

From this background, the specific aims of the thesis were:

● Streams (papers II - IV)

1) To quantitatively differentiate transport behaviour of conservative andreactive substances in streams by tracer experiments. Identify the key transport

7

processes and parameters and from this formulate a model framework so thatone acceptably, from observations in the water column and in the bed sediment,can describe solute transport in streams. Determine type of observations neededin a critical evaluation of the stream model concept.

● Lakes (papers I, V - VIII)

1) To develop a model that describes the concentration of suspended particulatematter (SPM) in lakes from readily available lake parameters. SPM is of crucialimportance for the fate and transport routes of solutes in lakes.

2) Examine and evaluate different possibilities to model the fraction of solutesassociated to SPM in lakes so that the degree of particle association could beincorporated in mass-balance models. The concentration of SPM and thedegree of particle association is of crucial importance for distributing massflows of solutes into pelagic pathways and to sedimentation onto areas oferosion, transport- and accumulation of lakes (benthic pathways).

3) The aim was also to develop a model for describing lake hypsographiccurves that allows development of lake sub-models differentiating lake bottomsinto erosion-, transport- and accumulation areas and lake volumes into activelake volumes, depending on differences in lake hypsographic curves.

4. Study areas, material and methods

4.1. Study areas

4.1.1. StreamsThe Lanna field tracer experiment was carried out in the Lanna Brook along a10200 m long reach on April 27, 1996, Skaraborg County, Sweden (paper II).In the upper part of the stream (0-5100 m), the stream was surrounded byconiferous forest, whereas the lower part (5100–11200 m) flowed througharable land.

The Säva field tracer experiment was conducted along a 30000 m long reach ofthe Säva Stream on May 19, 1998, Uppland county, Sweden (papers III - IV).The upper part of the stream (0-5400 m) was surrounded mainly by coniferousforest, whereas the lower part (5400–30000 m) was situated in arable land.

4.1.2. LakesThe empirical lake data used for papers V - VIII emanate mainly from Swedishlakes. In paper V, however, some European lakes also are included. They areall basically glacial lakes, the dominating lake type on earth. The lakes cover awide domain of limnological and morphometric characteristics.

8

4.2. Material and methods

4.2.1. StreamsRadioactive tracers were injected at a constant rate for ~5.5 and ~5 hours in thetwo experiments, respectively, to achieve pulses with approximately constantconcentrations. In the Lanna experiment, we injected the reactive radioactivetracer chromium (51Cr3+). In the Säva field tracer experiment, we injected tworadioactive tracers, reactive chromium (51Cr3+) and non-reactive tritiated water(3H20), simultaneously.

The possibility to estimate mass fluxes of solutes between the surface waterand the hyporheic zone (i.e. the streambed) were warranted by extensivemonitoring programs. The programs covered both brook water and streambedsediment at several stations along the two brooks.

4.2.2. LakesFor papers V - VIII, data (given in the papers) were compiled both fromliterature surveys and from Department of Limnology, Uppsala University,Uppsala, Sweden and Department of Environmental Assessment, SwedishUniversity of Agricultural Sciences, Uppsala, Sweden.

5. Results

5.1. Streams - transport parameters and processes (papers II - IV)

Evaluation of performed tracer experiments revealed that transient storage ofwater in stagnant or slow circulating water zones adjacent to the main stream(e.g., side pockets, streambed sediments) greatly affected the transport times ofsolutes (papers II - IV). The monitored breakthrough curves in the stream watershown in Fig. 5 indicated a significant retention of the reactive tracerchromium (51Cr) in comparison to the conservative tracer tritiated water (3H)(papers III - IV).

The bed sediment observations agreed with the water column observations.They showed that a 50% wash-out from the sediment of 51Cr and tritiated wateroccurred after ~500 and ~2 hours, respectively (papers III - IV). Besidesincreasing the uptake, the particle affinity also resulted in that chromium wasretained for a longer time. This demonstrated that the particle affinity of solutesacts as a distribution coefficient that controlled the mass flux of reactive solutesto the streambed sediment.

The particle affinity is, hence, crucial for modelling the fate and transportpathways of solutes. Advection-dispersion model formulations that included atransient storage as well as a particle affinity formulation were, hence, derivedto describe the transport of chromium (51Cr) in the two streams.

9

0 5 10 15 20 25 30 35 400

0.2

0.4

0.6

0.8

1

1.2

Time (h)

Norm

alise

d co

ncen

tratio

n (-)

A: + 125 m

B: + 2100 m

C: + 5400 m D: + 9600 m

51Cr3H

Fig. 5. Stream water breakthrough curves in the upper reaches (stations A-D) of theSäva stream. Differences in peak heights and tails arose due to differences inreactivity between the non-reactive tracer tritiated water (3H) and the reactive tracerchromium (51Cr) (modified from paper III).

Observations revealed that the loss of chromium in the water mainly was aresult of uptake into the bed sediment (papers II - IV). The Säva tracerexperiment with the non-reactive (3H) tracer also made it possible to quantifythe exchange of water with the sediment forced by hydrodynamical processesalone (papers III - IV).

In the model formulation, the exchange with the sediment, due tohydrodynamics alone, was assumed solely to occur in the dissolved phase andrepresented by a diffusive mass flux, see Fig. 6.

Mass flux = D∂ c∂ z z = 0

z

concentration (c)

Bed sediment

Main stream

Fig. 6. Illustration of the approximation of solute exchange between main stream waterand streambed sediment. The mass flux depends on the concentration gradient (∂c/∂z)at the water-sediment interface (z = 0) and diffusion coefficient D.

Evaluation of the model concept for the non-reactive tracer (tritated water)showed that the diffusive model formulation gave acceptable descriptions of thebreakthrough curves in the water column and in the bed sediment, see Fig. 7.Evaluation of the proposed model formulation describing the degree of particleassociation indicated that the sorption in the bed sediment not was instantaneous

10

but kinetically controlled, see Fig. 8. Instantaneous sorption lead to very highconcentrations in the tail of the breakthrough curve.

Fig. 7. Comparison of observed and simulated breakthrough curves for tritiated waterin (a) stream water at stations B-D and for (b) the inventory of tritium in the uppermost10 cm of the sediment at station A.

Fig. 8. Comparison of simulated chromium breakthrough curves in the stream waterwith observed at station D, with a kinetic sorption (KB = 20000 and k2 = 3×10-8 s-1)and an equilibrium concept with instantaneous sorption (KB = 15, k2 = ∞ ),respectively (modified from paper IV). KB is the bed sediment partitioning coefficientand k2 is the sorption rate coefficient.

The time scales for sorption processes could, however, not be captured fromthe breakthrough curves in the stream water alone. The number of differentcombinations of bed sediment partitioning coefficient (KB) and the sorption rate

11

coefficient (k2) that gave acceptable fits were large. The complementarysediment observations decreased the number of possible combinations.

5.2. Lakes - transport parameters and processes (papers V – VIII)

Evaluation of the role of SPM in lakes in papers V, VII and VIII concluded thatconcentration of SPM is of crucial importance for describing mass flows ofsolutes in lakes. Although the procedure to measure the concentration of SPMis relatively easy, it is not so often included in lake surveys. This is a veryregrettable fact.

To deal with the absence of SPM-measurements in monitoring programs apredictive model for lake characteristic concentration of SPM was derived inthis work (paper V), see Table 1.

Table 1. Model for prediction of SPM in lakes. TP is the total phosphorusconcentration, pH the hydrogen ion activity and DR is the dynamic ratio. All variablesare normal transformed. The coefficient of determination (r2) is 0.87, F-ratio >6 and nis the number of lakes.

Model r2 n

log(SPM) = 1.148·log(TP) + 0.137·pH - 0.286·log(D R ) - 1.985 0.87 26

Model variable range min max unit

TP 5 60 (µg P L-1)PH 5.1 8.5 (-)DR 0.07 7.88 (-)

In the model, the concentration of TP represents both production of biogenicparticles and resuspension of sediment particles containing phosphorus. Thesecond model parameter is pH. One of several explanations is that highproductivity lakes with production of biogenic particles generally reaches veryhigh pH during the summer bioproduction period (see, e.g., Håkanson andJansson, 1983). The dynamic ratio (DR, defined as a0.5/zm, where a is the lakearea in km2 and zm the lake mean depth in m) in the model represents resusp-ension of sediment particles by wind/wave action (Håkanson and Jansson,1983). The high correlation between TP and SPM is in agreement with findingsthat phosphorus associated to SPM constitutes on average ~59% of TP. (paperVIII).

In papers V, VII and VIII, it was concluded that the particle affinity of solutesto large extent controls transport routes and the distribution of mass flows inlakes. The dissolved fraction of solutes will remain in the water column(pelagic pathways) whereas the particle fraction can be subjected tosedimentation onto areas of erosion-, transport- and accumulation in lakes.

12

Traditionally, e.g., in contexts of metal pollution studies or in aquatic radio-ecology (see IAEA, 2000), the method to express the degree of particleassociation is the partition coefficient (Kd). Kd is generally defined as (L kg-1

dw-1):

diss

partd C

SPM/CK = (1)

where SPM is the concentration in mass dry weight (dw) per volume (mg dw L-1), Cdiss the dissolved (filter-passing) concentration (µg L-1) and Cpart isthe particulate concentration (µg L-1). If Kd is known, the particulate fraction(PF) (-) can be calculated from Kd and SPM:

DF-11SPMK

SPMKC

CPF

d

d

tot

part =+

== (2)

where Ctot is the total concentration per volume (µg L-1) and DF is thedissolved fraction (-). The Kd -value is often regarded as an equilibriumconstant between a substance in dissolved and particulate phases. This is achemical perspective.

In this work it has, however, been found that there exists several importantmotives to model PF or DF instead of Kd (papers VII - VIII).

1) The strongest motive is that PF or DF is the variable that directly and notindirectly as Kd distributes mass flows, see Fig. 9. If PF or DF is not known, ithas to be calculated from Kd and SPM. This would, however, be an extra stepthat would lead to a step-by-step prediction procedure, which probably is likelyto increase the uncertainty in the estimated PF or DF -values (see Håkanson,1999a).

Inflow of Mi = Q · Cin

Sedimentation of Mi = Mi · · KT

Outflow of Mi = Q · CMass of Miin

lake water

Particulate concentration of Xi in water column (µg/L)PF =

Total concentration of Xi in water column (µg/L)

PF

Fig. 9. Illustration of the basic (very simplified) dynamic lake model set-up for asubstance Mi. All fluxes are in mass per time unit (e.g., kg time-1), C and Cin areconcentrations (kg m-3), PF is the particulate fraction (-), Q is the water discharge (m3

time-1) and KT is the net settling rate of SPM (time-1) (modified from paper VII).

2) In modelling presented in the literature, a strong correlation between Kd andSPM has generally been found (see, e.g., Honeyman and Santschi, 1988). Anoften found result is a negative slope between log(Kd) and log(SPM) close to –

13

1. In the literature, the negative slope has mechanistically been attributed to theparticle concentration effect (see, e.g., O’Connor and Connelly, 1980; Moreland Gschwend, 1987; Benoit, and Rozan, 1999). This explanation is, however,not necessary a true one.

If the logarithms are taken of both sides of (Eq. 1), one gets:

log(Kd) = log(Cpart) - log(Cdiss) - log(SPM) (3)

which after division with log(SPM) gives:

1-)SPMlog()Clog(

-)SPMlog()Clog(

)SPMlog()Klog( disspartd = . (4)

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 (paper VII). This slope is a result of spurious correlation and amathematical inevitability due to the definition of Kd as a ratio including SPM(see, e.g., Kenney, 1982; Krambeck, 1995; Berges, 1997). This is to the best ofthe author’s knowledge, generally disregarded in Kd-models. Statisticalmethods such as multiple regressions would first identify the strong existinginherent mathematical coupling between Kd and SPM in Eq. (1).

3) Any statistical interpretation of Kd and how it varies relative to differentvariables would, moreover, be problematic due to the fact that the Kd -ratioconsists of more than two different variables (Cpart, Cdiss and SPM). Since thespurious correlation between Kd and SPM alone yields a slope of –1 betweenlog(Kd) and log(SPM), one would have to focus on slopes that do not equal –1.A pattern of data points between log(Kd) and log(SPM) with a slope close to 0(zero) could obscure any strong existing dependency between for instance Cpartand SPM. Statistical tests would reject such a pattern as statisticallyinsignificant scatter despite any existing real underlying relationships betweenCpart and Cdiss versus SPM.

4) The lower within-system variability as described by the coefficient ofvariation CVw (=SD/MV, where SD is the standard deviation and MV is themean value) for PF and DF compared to CVw for Kd motivates the usage of DFor PF rather than Kd in predictive models. Empirical data has shown that Kdgenerally has a larger inherent within-system variability than PF or DF. From aliterature compilation of 51 data-sets, it could be noted that CVw for Kd was~3.0 times larger than CVw for PF. Since predictive models should usevariables with as low variabilities as possible, it is better to use PF than Kd.More samples are also needed to determine a reliable Kd -value than a reliablePF or DF-value (as given by the sampling formula, see Håkanson and Peters,1995).

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For the derived PF-models for phosphorus in this work, describing the degreeof particle association, it was noted that CVw for Kd was ~2.8 times larger thanCVw for PF (paper VIII). Comparisons of empirical and modelled PF-value forthe median lake values revealed that PF-models described the empirical PF-values quite well, see Table 2.

The results are, however, based on data from only 10 lakes. They cover a widedomain of limnological characteristics: TP from 9 to ~900 µg P L-1, whichmeans that the entire range from oligotrophic to hypertrophic lakes areincluded. pH varies from 5.6 to 8.5, colour from very clear lakes (5 mg Pt L-1)to brown-water lakes (215 mg Pt L-1), area from 0.04 to about 23.7 km2 andmean depth from 0.5 to 21.9 m.. It is likely that, in the future, when more databecomes available from more lakes, a revision of these first results mayproduce somewhat different models.

Sensitivity analyses using the extensive LEEDS-model (Lake Eutrophication,Effect, Dose, Sensitivity; see Håkanson, 1999b, for further information)demonstrated that this approach to predict PF will lower the uncertainties inthe model predictions of mean monthly TP significantly. In absence of PF-measurements it is no longer necessary to guess PF. In fact, it was found thatthe uncertainty for lake PF is no longer the most crucial one for the modelpredictions of mean monthly TP. It is the uncertainty related to theconcentration of TP in the stream water entering lakes.

Table 2. Models for prediction of lake median PF in lakes (paper VIII). Coefficient ofdetermination (r2) gives the correlation between empirical and modelled lake medianPF. SRP is soluble reactive phosphorus, K the conductivity and n is the number oflakes. Empirical PF-range: 0.42-0.86.

Model r2 n

PF = 0.23·log(SPM) - 0.10·log(SRP + 0.1) - 0.085·log(D R ) + 0.66 0.847 10

PF = (-0.83· 0.1)/TP+(SRP + 0.048·pH + 0.69)2 0.785 10PF = (0.83·((TP - (SRP + 0.1))/TP) + 0.08·log(SPM) - 0.0052) 2 0.763 10PF = (1.25·((TP - (SRP + 0.1))/TP) + 0.047·pH - 0.68) 2 0.767 10PF = (0.26·log(TP) - 0.19·log(SRP + 0.1) + 0.46) 2 0.760 10

PF = (0.19·log(SPM) – 0.037· K + 0.83)2 0.691 9

In paper VI, it was revealed that the shape of the lake hypsographic curve andthe mixing depth can be transformed into a distribution coefficient thatregulates the portion of the lake area attributed to wave-induced resuspensionand the portion of the lake volume attributed to continuous mixing, see Fig. 10.

Although it is easy to estimate mixing depth of lakes (depends on the lake sizeand wind strength, see, e.g., Hanna, 1999) it is more difficult to estimate theportion of the lake attributed to “continuously” mixing. This is because ofdifferences in lake shape. In general, no information about the lakehypsographic curve is implemented in lake models due to the fact that it has

15

been rather problematic to incorporate mathematically the features of lakehypsographic curves in an easy and relevant way.

To address this problem (“shape and function” of lakes) two new models havebeen derived in this work to describe the shape of lake hypsographic curvemathematically. The models describe the hypsographic curve very well and areeasy to use since they are driven by readily available lake morphometricparameters (maximum depth, surface area and volume), see Figs. 11 and 12.

Wind

zmix1

A.

I

zmix2

WindB.

zmix2zmix1

III

II

Fig. 10. Conceptual figure showing how differences in lake basin shapes caninfluence to what extent lakes with identical surface areas and maximum depths willbe affected by different vertical processes such as wind-generated mixing (modifiedfrom paper VI). Cases I (zmix1) and II (zmix2) represent different wind conditions. A)Concave lake basin shape (Vd > 1). B) Convex lake basin shape (Vd < 1). Vd is thevolume development parameter (Vd = Vmax /(Amax zmax/3).

A.

y = 1.078x - 7.128r2 = 0.944

-30

-20

-10

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

Modelled relative area (%)

Empi

rical

rela

tive

area

(%)

95% prediction interval

B.

y = 0.982x - 6.467r2 = 0.958

-30

-20

-10

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

Modelled relative volume (%)

Empi

rical

rela

tive

volu

me

(%)

95% prediction interval

Fig. 11. Comparisons of values estimated from the volume development - approachand empirical values, including the resulting 95% prediction interval. A) Relativearea. B) Relative volume. Based on data from 105 area- and volume-depthdistribution curves.

Used together with models for estimating for instance mixing depths andcritical resuspension depth, these models can be used incorporated in

16

ecosystem models that are capable of describing the vertical extension ofphysical processes.

y = 0.968x + 1.173r2 = 0.988

0

10

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30

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50

60

70

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90

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0 10 20 30 40 50 60 70 80 90 100

Modelled relative area (%)

Empi

rical

rela

tive

area

(%)

A.

95% prediction interval

A.

y = 0.993x + 1.063r2 = 0.996

0

10

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60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

Modelled relative volume (%)

Empi

rical

rela

tive

volu

me

(%)

B.

95% prediction interval

B.

Fig. 12. A comparison between empirical area and volume and modelled valuesestimated by means of the hypsographic development - approach, including theresulting 95% prediction interval for individual estimations. A) Relative area. B)Relative volume. Based on data from 105 area- and volume-depth distribution curves.

6. Conclusions

Important findings from the thesis concern the identification of SPM as carrierparticle regulating solute mass flow in aquatic systems. Another importantfinding is that the morphology of streams and lakes together with lake andstream specific hydrodynamic conditions, additionally, modifies the exchangeand mass flows of solutes between different compartments within thesesystems.

A common feature of many of the processes and parameters that regulate thefate and transport pathways of solutes found in this thesis is that they can beparameterised so that mass flows of solutes between dissolved and particulateform and between different compartments in stream and lakes can be describedby different type of chemical and physical distribution coefficients.

More specifically new results are presented concerning:

1. Development of a model concept to describe the transport of solutes alonga stream due to differences in particle affinity and its impact on theexchange with streambed sediment.

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2. Development of a model for prediction of SPM suitable for incorporationin more comprehensive lake models aiming to describe mass flows of SPMand associated solutes in lakes.

3. It has been demonstrated that the partition coefficient, Kd, traditionallyused to describe the particle affinity of solutes in aqueous solutions, isunsuitable. Several reasons have been given why the particulate fraction orthe dissolved fraction, PF and DF, respectively, should be used instead.

4. Practically useful models to predict PF for phosphorus in lakes to be usedas sub-models within the framework of more extended lake eutrophicationmanagement models have been presented. It has been shown that theuncertainty for lake PF is no longer the most crucial factor for the modelpredictions of mean monthly TP. It is the uncertainty related to the tributaryconcentration of TP.

5. Development of two new methods that describe the shape of lake basins,allowing the development of sub-models that are capable of describing thevertical extension of physical processes and associated chemical, biologicaland physical properties important to lake ecosystems, have also beenpresented.

Acknowledgements

With the completion of this doctoral thesis, there are many people, directly andindirectly, to whom I owe many thanks.

First of all, I would like to express my gratitude to Prof. Lars Håkanson forguidance and encouragement and for many discussions and constructivesuggestions throughout the thesis work. I would also express the same gratitudeto Assoc. Prof. Anders Wörman for his support. Their collective support andconstructive comments contributed to improve this work.

My time at the department has been most enjoyable due to the excellentfellowship and co-operation of all my friends and colleagues at the Departmentof Earth Sciences. The fellow graduate students at the Department of EarthSciences and especially at LUVA and at the programme of sedimentology overthe years are acknowledged for this. We have shared a lot of relaxing momentsduring coffee breaks, discussing science as well as other things in life. Mydeepest and sincerest gratitude to them, and especially to the following persons:

…Karin Jonsson, for fruitful collaboration during a very time-demanding tracerexperiment, exchange of ideas and inspiring discussions, not only on scientificmatters but also on other issues such as different aspects of life. I have reallyenjoyed working with you! Many thanks for your friendship!

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…Jonas Forsman, for collaboration regarding performance of tracerexperiments, scientific writing, exchange of ideas and friendship. It was reallynice to work with you and also to attend all those different scientific meetingsabroad with you!…Shulan Xu, a former room mate of mine, for scientific discussions and helpwith mathematics. I remember the time when you translated my Swedish nameinto Chinese since I was going to attend a scientific meeting in China. I stillhave that visiting card with my Chinese name! Thanks for your friendship!…Angelica Brolin, for collaboration, scientific writing, scientific discussionsand discussions in general. Probably, only a few people, besides us, share thesame peculiar combination of interest in flowers and different shapes of lakes.Thanks for your friendship!…Martin Lindström, for collaboration, exchange of ideas, scientific writing,scientific discussions and friendship during the years of graduate studies. It isnice to know that at least some of the results in our papers were not spurious!…Mona Petersson, for participating in stream tracer experiments andfriendship. Many thanks!…Lennart Nordvarg and Torbjörn Johansson, for scientific stimulatingdiscussions, friendship and sharing my delight for popcorn. The only thing thatwas predictive about you was your mutual demand for popcorn!…Anna Lindahl, Mikael Malmeus, Andreas Gyllenhammar, Abdulaziz Kekli,Per Jonsson, Marcus Meili, Jan Eckhéll, Johan Persson and Pia Holmberg areacknowledged for different kinds help and discussions during these years aswell as being pleasant colleagues. Aziz thanks for checking I am in the sametime zone as you! …Sören Karlsson, our technician, for construction of the sampling equipment.Without your skill the tracer experiments could not have been performed.…Inger Påhlsson, for help at the Department’s laboratory so all the analysescould be done.…Bo Möller and all the other co-workers at the Earth Sciences Library, whopatiently assisted me in getting all the literature I needed throughout the years.

My sincerest and deepest gratitude also to all the people who reminded me oflife outside the walls of the Department of Earth Sciences. Thanks to relativesand friends. I will mention only a few names:

…My parents, Alfhild and Birger, for supporting me. Thanks for all the help!Thanks also for supplying me, for numerous of times, with delicious bakeryproducts as well as with help with my ancient car.…My brother, Kjell, for always being there. Thanks also to his children, mynephew Niklas and my niece Camilla. It has been great to see you grow upduring these years of graduate studies! Love you!…Jop and Ann, for all delicious bakery products you have shared with meduring these years. Seeing you and your children always made me think aboutsomething else besides scientific matters! I do like to visit you!

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References

Benoit, G. and Rozan, T.F., 1999. The influence of size distribution on theparticle concentration effect and trace metal partitioning in rivers.Geochim. Cosmochim. Acta, 63:113-127.

Berges, J.A., 1997. Ratios, regression statistics, and “spurious“ correlations.Limnol. Oceanogr., 42:1006-1007.

Berndtsson, R., 1990. Transport and sedimentation of pollutants in a riverreach. A chemical mass balance approach. Wat. Resor. Res., 26:1549-1558.

Cole, J.J. and Pace, M.L., 1998. Hydrological variability of small northernMichigan lakes measured by the addition of tracers. Ecosystems, 1:310-320.

Cornett, R.J. and Rigler, F.H., 1987. Vertical transport of oxygen into thehypolimnion of lakes. Can. J. Fish. Aquat. Sci., 44:852-858.

Förstner, U. and Wittmann, G.T.W., 1981. Metal Pollution in the AquaticEnvironment. Springer-Verlag, Berlin Heidelberg, 486 pp.

Hanna, M., 1990. Evaluation of models predicting mixing depth. Can. J. Fish.Aquat. Sci., 47:940-947.

Helios Rybicka, E., 1996. Impact of mining and metallurgical industries on theenvironment in Poland. Appl. Geochem., 11:3-9.

Honeyman, B.D. and Santschi, P.H., 1988. Metals in aquatic systems. Environ.Sci. Technol., 22:862-871.

Håkanson, L., 1999a. Error propagations in step-by-step predictions: examplesfor environmental management using regression models for lakeecosystems. - Env. Modelling & Software, 14:49-58.

Håkanson, L., 1999b. Water pollution - methods and criteria to rank, model andremediate chemical threats to aquatic ecosystems. Backhuys Publishers,Leiden, 299 pp.

Håkanson, L. and Jansson, M., 1983. Principles of lake sedimentology.Springer-Verlag, Berlin, 316 pp.

Håkanson, L. and Peters, R.H., 1995. Predictive limnology. Methods forpredictive modelling. SPB Academic Publishing, Amsterdam, 464 pp.

IAEA, 2000. Modelling of the transfer of radiocaesium from deposition to lakeecosystems. Report of the VAMP Aquatic Working Group (chairman: LarsHåkanson). - International Atomic Energy Agency, Vienna, IAEA-TECDOC-1143, 343 pp.

Kenney, B.C., 1982. Beware of spurious self-correlations! Wat. Resour. Res.,18:1041-1048.

Krambeck, H.-J., 1995. Application and abuse of statistical methods inmathematical modelling in limnology. Ecol. Model., 78:7-15.

Luoma, S. N., 1983. Bioavailability of trace metals to aquatic organisms – areview. The Science of the Total Environment, 28:1-22.

Meili, M., 1992. Sources, concentrations and characteristics of organic matterin softwater lakes and streams of the Swedish forest region. Hydrobiologia,229:23-41.

20

Morel, F.M.M. and Gschwend, P.M., 1987. The role of colloids in thepartitioning of solutes in natural waters. In: W. Stumm (Editor), Aquaticsurface chemistry, Wiley-Interscience, New York, pp. 405-422.

Müller, B., Lotter, A.F., Sturm, M. and Ammann, A., 1998. Influence ofcatchment quality and altitude on the water and sediment composition of68 small lakes in Central Europe. Aquat. Sci., 60:316-337.

Nilsson, Å. and Håkanson, L., 1992. Relationships between drainage areacharacteristics and lake water quality. Environ. Geol. Wat. Sci., 19: 5-81.

O’Connor, D.J. and Connelly, J.P., 1980. The effect of concentration ofadsorbing solids on the partition coefficient. Wat. Res., 14:1517-1526.

Tartari, G. and Biasci, G., 1997. Trophic status and lake sedimentation fluxes.Wat. Air Soil Pollut., 99:523-531.

Thierfelder, T., 1998. An inductive approach to the modelling of lake waterquality in dimictic, glacial/boreal lakes. PhD Thesis, Uppsala University,Uppsala, Sweden.

Turner, D.R. and Whitfield, M., 1980. Chemical definition of the biologicalavailable fraction of trace metals in natural waters. Thalssia Jugosl.16:231-241.

Weyhenmeyer, G.A., 1996. The significance of lake resuspension in lakes. PhDThesis, Uppsala University, Sweden.

Vollenweider, R.A., 1968. The scientific basis of lake eutrophication, withparticular reference to phosphorus and nitrogen as eutrophication factors.Tech. Rep. DAS/DSI/68.27, OECD, Paris, 159 pp.

Vollenweider, R.A., 1975. Input-output models with special reference to thephosphorus loading concept in limnology. Schweiz. Z. Hydrol., 37:53-84.