Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 1028

Predictive Modeling ofLake Eutrophication

BY

JAN MIKAEL MALMAEUS

ACTA UNIVERSITATIS UPSALIENSISUPPSALA 2004

Get behind the mule In the morning and plow

Tom Waits

List of Papers

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

I Malmaeus J.M. and Håkanson L., 2004. Development of a Lake Eutrophication Model. Ecol. Model. 171, 35-63.

II Malmaeus J.M. and Håkanson L., 2003. A dynamic model to predict suspended particulate matter in lakes. Ecol. Model. 167, 247-262.

III Malmaeus J.M., 2004. Variation in the Settling Velocity of Suspended Particulate Matter in Shallow Lakes, with Special Implications for Mass Balance Modelling. Int. Rev. Hydro-biol. 89, 426-438.

IV Malmaeus J.M. and Rydin E., 2004. A dynamic phosphorus model for the profundal sediments of Lake Erken, Sweden. Manuscript.

V Malmaeus J.M., Blenckner T., Markensten H. and Persson I., 2004. Lake phosphorus dynamics and climate warming: A mechanistic model approach. Submitted.

Contents

1 Introduction ...........................................................................................91.1 Background and aim.....................................................................91.2 Predictive (mass-balance) modeling.............................................91.3 Lake eutrophication ....................................................................121.4 Climatic change..........................................................................13

2 Study areas...........................................................................................152.1 Lake Erken .................................................................................162.2 Lake Mälaren..............................................................................162.3 Belarusian lakes..........................................................................172.4 Lake Balaton...............................................................................172.5 Lake Kinneret .............................................................................17

3 Lake models.........................................................................................193.1 The LEEDS-model .....................................................................193.2 The SPM-model .........................................................................203.3 Sedimentation.............................................................................223.4 Diffusion.....................................................................................23

4 Model application: Climatic change ....................................................25

5 Main findings.......................................................................................28

6 Conclusions .........................................................................................29

7 Acknowledgements..............................................................................31

8 Summary in Swedish ...........................................................................32

9 References ...........................................................................................34

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Introduction

1.1 Background and aim Ecological modeling may be used to structure different types of informa-tion about complex natural systems, to test hypotheses about the function of these systems and to make predictions about the system’s response to natural or anthropogenic perturbations. There are many types of models and modeling approaches, and there is no clear definition of what actually constitutes a scientific model. Generally, models complement field stud-ies and laboratory experiments in the pursuit of scientific knowledge. Without empirical data to drive and test models, they are useless. In com-plex systems, however, empirical data may be of limited use if there are no models to structure and interpret the data.

This work deals with one specific environmental problem (eutrophica-tion) in one type of ecosystem (lakes) using one modeling approach. The starting point is a lake eutrophication model with certain specifications and limitations, and the basic aim of this thesis is to test and develop this model in order to obtain a practically useful tool in water research and management. Paper I and II define and develop the model and its sub-models. In Paper III and IV, internal lake processes are studied using exclusive data sets in order to improve the description of these processes within the framework of predictive mass-balance models. Paper V is an application of the lake eutrophication model where the impact of climate change on lake eutrophication is explored in three Swedish lakes.

1.2 Predictive (mass-balance) modeling Since modeling is a wide concept, this section will try to clarify the inten-tions and methods of the modeling contained within this thesis. Basically, a predictive model is defined by its intention to predict masses or fluxes of specified target variables in a given type of system at a given frame of time. Models for predicting mass balances of substances in aquatic sys-tems have been widely used since Vollenweider proposed his famous phosphorus model in 1968 (Vollenweider, 1968). In contrast to most

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stochastic models and regression models, mass balance models try to capture the most important processes in a system using differential equa-tions. The principal idea is to treat the system as one or several mixed reactors where mass is conserved. In its simplest form, a mass balance model for a substance in a lake may be defined as:

dM/dt = Inflow – Outflow – Sedimentation (1)

where dM/dt is the rate of mass change of the substance. This model may be expanded with more internal processes or divisions of the system into a number of subsystems, such as surface water, deep water and sedi-ments. The optimal level of complexity depends on a number of factors including uncertainty in and access to driving variables and the purpose of the model. Modeling a complex reality sometimes requires complex models, but if the complexity cannot be supported by empirical data and solid mechanistic understanding, model parameterization becomes unsta-ble and calibration and validation may become problematical (see, e.g., Håkanson and Peters, 1995; Monte, 1996; Canham et al., 2003).

Mass balance models may be used as engineering tools in, e.g., lake management and/or as tools for water research. This work is mainly fo-cused on scientific understanding about processes, but the ultimate aim is to strengthen the mechanistic foundation in predictive lake eutrophication models, hoping to improve the ability to make quantitative predictions. Here, this means that the lake models are rather complex and that each included process should correspond to one well defined (and measurable) process in the natural system. In several cases, the processes may be more readily accessed by mass balance calculations than by empirical studies. For instance, this is often true for processes of outflow, water mixing and phosphorus release from accumulation sediments.

Choosing appropriate spatial and temporal scales is crucial for suc-cessful modeling. To obtain time and area compatibility between mod-eled and measured information about the system requires a sound struc-turing of empirical data into appropriate time and spatial units.

To exemplify the issue of time resolution, a data base for chlorophyll concentration from the River Danube (a site close to Regensburg) will be used (see Håkanson et al., 2003a). Figure 1 gives a compilation of CV-values calculated for empirical mean values from weekly, two types of monthly values (individual monthly data and monthly data based on val-ues from several years) and yearly values, as well as the CV-value for the 459 individual data of chlorophyll concentration (CV = coefficient of variation = SD/MV; SD = standard deviation, MV = mean value; CV is a

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Figure 1. Compilation of CV-values based on mean values from different time intervals; daily, weekly, monthly (from individual months and monthly data from several years), yearly and all data from 1995-1999 for chlorophyll from the River Danube (Regensburg station). The box-and-whisker plot to the right gives for comparative purposes CV-values based on all data from several years from 19 UK rivers. The results for the UK river sites should be compared to the CV-value of 0.96 calculated using all data from the Regensburg station (from Håkanson et al., 2003a).

standard measure of variability in any given variable). It is clear that when a longer time period is considered, higher variation in any variable may be expected than for a shorter period of time. Theoretically, this would imply that a high time resolution should be preferred. On the other hand, it is nearly impossible or very laborious to access reliable data on a long term basis at short time scales, which means that there is a practical lower limit on the time resolution. There should be an optimal time scale where the combined shortcomings of uncertainty and accessibility have a minimum. This is illustrated in figure 2. In practical applications in con-texts of lake studies, this optimum is often found between one week and one month.

CV

CV for Chl

0

.2

.4

.6

.8

1

1.2

1.4

1.6

1.8

2

Days Weeks Individual months

Bymonthseveralyears

Years All data 5 years

All data severalyears,among 19 UK river sites

MV: 0.35 0.55 0.80 0.95 0.96 1.22

N=5

N=12

N=47

N=62�n 3

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Figure 2. Illustration of factors regulating the optimal size of practically useful predictive models in aquatic ecology. From Håkanson (2004).

The same argument for modeling at a time scale would be relevant for spatial resolution. The lake models used in this thesis separate surface water from deep water, but assume complete mixing within these two compartments. In addition to technical reasons, there is a user perspective on time and space resolution. What model output does a lake manager need to make decisions about a given system? Mass balance models giv-ing monthly predictions of average concentrations of nutrients in lakes may be preferred for several reasons.

There exists an abundance of different lake eutrophication models, us-ing different scales, target variables, modeling structures and driving variables (see, e.g., Imboden and Gächter, 1978; Jørgensen et al., 1986; Chapra and Canale, 1991; Del Furia et al., 1995). It is generally hard to make meaningful comparisons of model performance since the intentions and circumstances are very different. Interesting attempts have been done by, e.g., Straškraba (1994), Seo and Canale (1995), Canale and Seo (1995) and Jørgensen (1999).

1.3 Lake eutrophication The term ‘eutrophic’ refers to a system rich in nutrients, and hence eutro-phication means nutrient enrichment, particularly by increasing levels of nitrogen and phosphorus (e.g., Vollenweider, 1990; Wetzel, 2001; Kalff, 2002). In lakes, phosphorus is generally regarded as the limiting nutrient for primary production (see, e.g., Dillon and Rigler, 1974; Schindler, 1977; Guildford and Hecky, 2000), implying that increasing phosphorus

Day Week Month Year

CV

Accessibilityof data (Ac =1/d)

Criteria of usefulness

Optimal curve for predictive models (Op = 10·(1–CV^2)·Ac)

0

0,2

0,4

0,6

0,8

1

Val

ue (C

V, A

c, O

p)

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concentrations will result in increasing production of phytoplankton and benthic algae. Excessive amounts of phytoplankton cause low Secchi depths and may consequently wipe out the benthic flora by shading the light (e.g., Scheffer et al., 1993; Egertson et al., 2004). Toxic cyanobacte-ria tend to bloom when nutrient levels are high (e.g., Paerl and Ustach, 1982; Paerl, 1988; Bowling, 1994). Apart from being a nuisance in their own right, settling phytoplankton may cause anoxia in hypolimnetic wa-ters as their decomposition consumes oxygen (e.g., Seto et al., 1982), and this may result in extinction of the benthic fauna (e.g., Jónasson, 1984) and fish feeding on such animals. Altogether, these eutrophication effects threaten the foundations of aquatic ecosystems. The low oxygen levels in hypolimnetic waters associated with eutrophication may also cause mobi-lization of phosphorus in the sediments, thus inducing a feedback mecha-nism where already high nutrient levels increase even more.

Sources of phosphorus in lakes include anthropogenic sewage, fertiliz-ers used in agriculture and emissions from industries in addition to natu-ral sources. In the 1970’s, effluent water treatment was introduced in many places and water quality improved (e.g., SNV, 1993; Wilander and Persson, 2001). Expected recovery was, however, delayed in some lakes where phosphorus accumulated in the sediments continued to release significant amounts even after the external emissions were reduced (Ahl-gren, 1977; Marsden, 1989). Today eutrophication remains a problem in a relatively small number of lakes, but these lakes tend to be situated close to populated areas where they play an important role for fishing and rec-reation. Less than 800 out of 60000 Swedish lakes larger than 4 ha may be regarded as eutrophicated, with total phosphorus concentrations ex-ceeding 25µg·l-1 (SNV, 2004).

1.4 Climatic change Climatic change and fluctuations in temperature and precipitation is natu-ral both on long and short time scales (Petit et al., 1999; Santer et al., 2000; Seppä and Birks, 2001). However, emissions of greenhouse gases (especially carbon dioxide, CO2) from the burning of fossil fuel since the beginning of the industrial revolution is now generally accepted to be the cause of the observed climate warming in the last decades (e.g., Stott et al., 2000; IPCC, 2001b). Observations of the Earth's near-surface tem-perature show a global mean temperature increase of approximately 0.6 ºC since 1900 (Tett et al., 1999).

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To prevent this climatic change seems very difficult since the sources of carbon dioxide – e.g., oil and carbon power plants and petrol driven cars – are deeply built into society, and in most parts of the world emis-sions tend to increase rather than decrease. The Intergovernmental Panel on Climate Change (IPCC), established by the UN in 1988, has proposed a number of scenarios of greenhouse gas emissions for the next hundred years, and these scenarios are used by scientists to make predictions about the effect on the earth’s climate. Although there are many uncer-tainties involved, model projections indicate that the mean temperature of the earth will increase between 1.4 and 5.8 ºC until year 2100 relative to 1990 (IPCC, 2001a). Timing and distribution of precipitation is also ex-pected to change, even though these predictions remain even more uncer-tain than the temperature predictions.

Obviously, these changes provide great challenges for both man and nature, also in aquatic ecosystems. Climatic change is not a major theme in this thesis but is considered because it may affect the nutrient status of lakes. The warming of the earth may also be seen as a very large scale experiment. Just as the Chernobyl accident in 1986 provided environ-mental scientists with an opportunity to test and develop their models of transport processes in nature, the climate changes may be used by re-searchers to study and calibrate the temperature dependence of their models.

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2 Study areas

In this thesis, seven lakes from Europe and the Mediterranean area are included for data collection and model developments. These lakes are Lake Erken (Sweden), Lake Mälaren (Sweden), Lake Batorino (Belarus), Lake Miastro (Belarus), Lake Naroch (Belarus), Lake Balaton (Hungary)

Figure 3. Geographic locations of the lakes included in this thesis.

Lake Naroch Lake Miastro Lake Batorino

Lake Erken

Lake Mälaren

Lake Balaton

Lake Kinneret

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Table 1. Lake characteristics. Lake

area(km2)

Meandepth(m)

Waterretention

time (years)

Meanannualepilim-netic

tempera-ture(ºC)

Meantotal

phospho-rus

concen-tration(µg·l-1)

Meansummerchloro-phyll

concen-tration (µg·l-1)

L. Erken 24 9 7.4 8.6 27 4.2 L. Mälaren 1096 12.8 2.8 7.4 20-55 4-22 L. Batorino 6.3 3 0.65 8.9 60 27.1 L. Miastro 13 5.4 1.7 8.9 40 12.1 L. Naroch 80 9 8.1 8.9 22 4.0 L. Balaton 596 3.2 1.3 13 55-90 8-25 L. Kinneret 160 24 7.3 22 27 14.5

and Lake Kinneret (Israel and Syria). The locations of the lakes are shown in figure 3. Lake characteristics are summarized in table 1.

2.1 Lake Erken Lake Erken is a naturally mesotrophic, stratified (dimictic) lake with a small (141 km2) forest dominated catchment (Weyhenmeyer, 1999). There are no industrial activities or point sources in the catchment, and the external input of nutrients and matter is considered to have been con-stant over the last centuries (Rydin, 2000). Lake Erken has a long tradi-tion of limnological research, with regular measurements occurring since 1940. The lake is used for drinking water in a small community in the vicinity of the lake.

2.2 Lake Mälaren This is the third largest lake in Sweden, located within one of the most populated areas in the country. Stockholm is situated at the lake outflow to the Baltic Sea. The lake may be considered as a lobate system of smaller basins separated by narrow straits and morphological thresholds (Kvarnäs, 2001). Two of these basins, Galten and Ekoln, at two upstream ends of the larger lake (southwest and northeast, respectively) are in-cluded in this thesis for climate simulations. Due to the population pres-sure, Lake Mälaren is exposed to both sewage and industrial emissions and was rather eutrophicated in the 1960’s and 1970’s with phosphorus concentrations well over 100 µg·l-1 in some parts of the lake. During the

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1970’s sewage water treatment was introduced and improved around the lake and at present total phosphorus concentrations are around 50% lower than during the 1960’s (Wallin, 2000). The large catchment (22 603 km2)is mostly dominated by forest land, but also includes large agricultural areas.

2.3 Belarusian lakes The three lakes Batorino, Miastro and Naroch are located within the same catchment in the northern part of Belarus. Water flowing out from Lake Batorino goes into Lake Miastro, and the outgoing water of Lake Miastro enters into Lake Naroch. The catchment area (279 km2) is dominated by forest, and the lakes are famous for good fishing and recreation in Bela-rus. At the collapse of the Soviet Union in 1990 the supply of fertilizers terminated and the lakes experienced a period of oligotrophication (Håkanson et al., 2003b). Phosphorus concentrations were reduced by 25–40% (A. Ostapenia, personal communication).

2.4 Lake Balaton This large and shallow lake in the western part of Hungary is an impor-tant recreational lake with both sport and commercial fisheries. It has a history of rapid eutrophication during the 1970’s but the phosphorus load has been significantly reduced following a number of management meas-ures, including sediment dredging and construction of the Kis-Balaton reserve at the major inflow at the western shore (Istvánovics and Som-lyódy, 2001). The lake is rather elongated in its east-west direction and may be divided into four consequent basins, with basin 1 upstream of basin 2 and so on. The nutrient level decreases eastwards and the lake outflow is found in basin 4 (Somlyódy and van Straten, 1986).

2.5 Lake Kinneret This lake, well-known from the Bible, is utilized for drinking water and irrigation in a region where annual rainfall normally is not more than 400 mm. The main inflow is the Jordan River which drains an area of 1560 km2 supplying around 70% of the water. There is a constant risk of salini-zation as the water level (around 210 m below sea level) at times de-

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creases several meters when rainfall is scarce. The lake is rather deep and homothermy normally occurs between December and March (Hambright et al., 1994). Phosphorus concentration may be relatively low in the epilimnion, but at least one of the important phytoplankton species, Peridinium gatunense, may obtain phosphorus from the sediments during resting stages, thereby avoiding phosphorus limitation (Serruya, 1980). Tourism is well developed around the lake, and the lake supports a com-mercial fishery.

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3 Lake models

3.1 The LEEDS-model LEEDS (Lake Eutrophication, Effect, Dose, Sensitivity) is a dynamic mass balance model for phosphorus in lakes. An outline of the model is given in figure 4. The model gives monthly predictions of phosphorus in 9 different compartments in water and sediment. It contains compart-ments for dissolved, colloidal and particulate phosphorus in surface water and deep water, phosphorus in ET-sediments, A-sediments and phyto-plankton. Only phosphorus dissolved in surface water may be taken up by phytoplankton, and only particulate phosphorus is subject to gravitational settling. Colloidal particles are too small to settle due to gravity, but phosphorus bound to such particles are still not available to phytoplank-ton (cf. Gustafsson and Gschwend, 1997). Resuspension of particulate phosphorus may occur on shallow erosion and transport areas (ET-sediments) where wind and wave activity influence the hydraulics at the sediment-water interface. Importance and mechanisms of sediment resus-pension are discussed, e.g., in Bloesch (1994). In deeper areas of sedi-ment accumulation (A-sediments), phosphorus is only mobile through diffusive processes (Håkanson and Jansson, 1983). The extension of ET- and A-areas are calculated from the dynamic ratio (DR= Area/Mean depth). Mixing between deep water and surface water depends on the vertical temperature profile and is slow when the temperature difference between surface water and deep water is larger than 4ºC.

The present model version is discussed in Paper I, which gives exten-sive critical model testing and validation against empirical data from a wide limnological domain. Figure 5 shows the results from the model validation. It is evident that average phosphorus concentration is pre-dicted well in the five tested lakes, but there are seasonal dynamics that are not accurately predicted, such as the spring peak in the Belarusian lakes. It should be noted that the observed values in all lakes emanate from about 10 years of monthly measurements (single values) and that the uncertainty bands are relatively wide.

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Figure 4. An outline of the phosphorus fluxes handled by the LEEDS-model. The flow labels are explained in Paper I.

The driving variables for the LEEDS-model are all easily accessible climatic (e.g., annual precipitation) and morphometric variables (e.g., mean depth), plus the phosphorus concentration in tributary water. There is no need for calibration for individual lakes, since default model con-stants may be used.

3.2 The SPM-model Suspended particulate matter (SPM) is a very important variable in aquatic systems. It has a major impact on the light penetration and the Secchi depth in the water, thereby regulating the potential for primary production (e.g., Håkanson and Boulion, 2002). SPM also binds nutrients and metals, thus determining the fate of many important substances by its settling properties (e.g., Johansson et al., 2001). Furthermore, organic SPM may be used as an energy source by microorganisms in the water column (Jørgensen and Johnsen, 1989; Wetzel, 2001).

The SPM-model (Paper II) is included as a sub-model in LEEDS, but

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Figure 5. LEEDS-model results compared to empirical data on total phosphorus and chlorophyll-a concentrations. Empirical data represent monthly mean values for several years. The widths of the confidence limits are calculated with charac-teristic CV-values for TP (0.35) and Chl (0.25) as indicated. The CV-values represent 75% confidence intervals (MV±1·SD) using a characteristic CV for empirical lake data of 0.35 for TP and 0.25 for chlorophyll (data from Håkanson and Boulion, 2002).

it may also be used as a separate model giving monthly predictions of suspended particulate matter in two water compartments and one com-partment with SPM available for resuspension in ET-sediments. The model structure is presented in figure 6. The driving variables are basi-cally the same as in the LEEDS-model, so the inclusion of this model as a

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sub-model does not require any additional variables. The model generally shows good agreement with observed data on SPM concentration in 5 different lakes. Paper II demonstrates that the most important uncertain-ties in model predictions concern the tributary inflow of SPM and the autochthonous production of SPM. Autochthonous production is pre-dicted from total phosphorus and epilimnetic temperature. As the spring bloom of phytoplankton in Lake Kinneret is dominated by the dinoflagel-late Peridinium gatunense, which obtains its phosphorus from the sedi-ments, it is only natural that the spring peak in SPM concentration ema-nating from this bloom is not captured by the model, since this process is not accounted for.

Figure 6. Schematic outline of the SPM-model.

3.3 SedimentationSedimentation of SPM and particulate forms of pollutants is one of the most important internal processes in mass balance calculations for lakes. Gross sedimentation in a lake, e.g., measured as g DW·m2·d-1 (DW=dry weight), may be quantified in situ with sediment traps (Bloesch and Burns, 1980; Håkanson, 1994), whereas properties of settling material is difficult to study outside the laboratory (e.g., Burban et al., 1990). Set-tling velocity of particles (m·d-1) may be estimated by dividing gross sedimentation by the concentration of suspended particulate matter (g DW·m-3) above the traps. Since particles in a lake are carried by water currents and influenced by turbulence the settling velocity measured in the laboratory and settling velocity estimated from field observations often differ orders of magnitude. Both may give valuable information

MixingResuspension

Resuspension

Sedimentation

Sedimentation

Sedimentation

Mineralization

Primary production

Tributary inflow Precipitation

Outflow

Wave base

A-sediments

ET-sedimentsHypolimnion

Epilimnion

23

about the mechanisms determining the fate of particles and associated substances in aquatic systems. Large particles generally settle faster than smaller ones according to Stokes’ law, since the impact of drag resistance (viscosity) from the medium (water) decreases relative to the influence of gravity with increasing particle size (Håkanson and Jansson, 1983).

In Paper III, data from sediment traps and water samples were col-lected from Lake Erken and Lake Balaton in order to study the variation in settling velocity in these systems on short time scales (days to weeks) and possible regulating factors. It was found that the within site variabil-ity of settling velocity was substantial. The differences between 25th and 75th percentiles of estimated settling velocities were two- or three-fold. Regressions between settling velocity and possible regulating factors revealed that settling velocity tends to increase with SPM concentration in the water, which may be explained by particle flocculation at high SPM concentration, increasing the particle size and thereby the settling velocity. It was also implied that different types of material, e.g. ex-pressed by the organic content, had different settling properties. Based on the findings in Paper III, the following dimensionless moderator for set-tling velocity has been implemented in the LEEDS-model and in the SPM-model:

YSPM = 1 + 0.45·(CSPM/2 – 1) (2)

where CSPM is the concentration of SPM in g·m-3. This dimensionless moderator is multiplied with the default settling velocity in the models to get the actual settling velocity, resulting in an increased rate of sedimen-tation at higher concentrations of SPM.

3.4 DiffusionMolecular diffusion is the continuous redistribution of molecules result-ing from random movements, acting to level out concentration gradients. Although a slow process, molecular diffusion is the dominant transport process for many substances in calm waters, such as in deep water below the wave base in lakes. It is the most important process moving phosphate from sediment pore water to the overlying water column (Kamp-Nielsen, 1974; Hesslein, 1980). Phosphorus release from accumulation sediments also includes a number of chemical reactions and is affected by physical conditions and biological processes (e.g., Mortimer, 1941, 1942; Boström et al., 1982; Håkanson and Jansson, 1983). In this work, diffusion refers

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to release of molecular phosphate from accumulation sediments, as op-posed to phosphorus release from erosion- and transport sediments driven by resuspension.

It was concluded in Paper I that the LEEDS-model is sensitive to the rate of diffusion, and diffusive phosphorus release from the sediments is often one of the major internal phosphorus fluxes in lakes (Jensen and Andersen, 1992; Lijklema, 1994; Rydin and Brunberg, 1998). Paper IV is an attempt to formulate empirical findings in Lake Erken as a model de-scribing the phosphorus dynamics of profundal sediments, hoping to im-prove the understanding and ability to model processes of burial and dif-fusion in lake models.

Figure 7. Illustration of the sediment phosphorus model. IP = inert phosphorus; OP = organic phosphorus; DP = phosphorus dissolved in pore water; FeP = phosphorus sorbed to iron. Phosphorus fluxes include sedimentation (sed), burial (bur), mineralization (min), molecular diffusion (diff) and chemical equilibrium between dissolved and iron bound phosphorus (eq).

An outline of the model presented in Paper IV is given in figure 7. It divides phosphorus into four different operational fractions. These frac-tions are phosphate dissolved in pore water, organically bound phospho-rus, phosphorus sorbed to iron and an inert fraction. A chemical equilib-rium depending on the redox potential is assumed between the dissolved phosphate and the phosphorus sorbed to iron. Sediment redox potential is assumed to be proportional to hypolimnetic oxygen concentration. The modeled vertical profiles of the four phosphorus fractions in the sediment are similar to the observed profiles. In the model most of the phosphorus release occurs in August, and about 50% of the settling phosphorus is eventually buried.

IP

IP OP

OP

DP

DP

FeP

FeP

sed sed sed

bur bur bur bur

bur bur bur bur

diff

diff

diff

min

min

eq

eq

dz

WATER

SEDIMENT

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4 Model application: Climatic change

In Paper V the LEEDS-model is run with two climate scenarios (denoted A2 and B2; IPCC, 2000) for the years 2071–2100 and run for Lake Erken and two basins of Lake Mälaren – Galten and Ekoln. The climate scenar-ios are given by the IPCC and are based on different assumptions and predictions about the anthropogenic emissions of CO2 the coming one hundred years. Only temperature changes are considered here, since pre-dictions about water discharge and external nutrient load are yet very uncertain. Temperature is included in the LEEDS-model to calculate rates of mineralization, mixing and diffusion.

The scenarios predict mean annual epilimnetic temperature to increase by 1.2–1.9 ºC, and the most significant effect predicted by the model is an increased rate of diffusion resulting in increased total phosphorus concen-tration in the lakes. When hypolimnetic temperature increases, decompo-sition of organic material is intensified (e.g., Törnblom and Pettersson, 1998) resulting in increased oxygen consumption, which in turn reduces the capacity of the sediments to hold phosphorus (see, e.g., Paper IV). Furthermore, oxygen supply from the atmosphere to the profundal sedi-ments is low when the lake is stratified, and stratification is stronger in the climate scenarios. Increased phosphorus concentration in the water column resulting from higher diffusion rates may result in higher primary production which, in turn, results in increased sedimentation and hence higher oxygen consumption in the hypolimnion. All these processes are captured in LEEDS (see figure 4) and they all result in lake eutrophica-tion.

In figure 8 the phosphorus concentration in the three study areas are shown as predicted by the model using the two climate scenarios (A2 and B2) and control simulations similar to present conditions (CTRL). It is notable that phosphorus concentration increases much more in Lake Erken than in the two basins of Lake Mälaren, and this is explained by the much longer water retention time (7 years) in Lake Erken compared to Ekoln (0.5 years) and Galten (0.07 years). Internal processes, such as those described above, are more significant when the water retention time is long, and this is reflected in the response to climate change. The results

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Figure 8. Mean, maximum and minimum values of predicted total phosphorus (TP) and epilimnetic dissolved phosphorus (EDP) concentrations (µg/l) for the three scenarios ( = CTRL; = A2; = B2 ).

Ekoln; EDP

j f m a m j j a s o n d0

20

40

60

80Ekoln; TP

j f m a m j j a s o n d0

20

40

60

80

Galten; TP

j f m a m j j a s o n d0

20

40

60

80Galten; EDP

j f m a m j j a s o n d0

20

40

60

80

Lake Erken; EDP

j f m a m j j a s o n d0

20

40

60

80Lake Erken; TP

j f m a m j j a s o n d0

20

40

60

80

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are supported by (unpublished) empirical observations in the three areas during the warm years at the end of the 1990’s and the beginning of the 2000’s.

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5 Main findings

The assumptions and structure of a phosphorus model for lakes are critically tested and the domain of the model is given. The values predicted by the model show good agreement against empirical data from the five tested lakes. A new version of this model is presented, including two new compartments for colloidal phosphorus, a sub-model for sus-pended particulate matter (SPM) and new algorithms for water content and organic content of accumulation sediments. New al-gorithms for lake outflow, mixing and diffusion are imple-mented.A dynamic model for SPM is validated and shown to provide satisfactory predictions of SPM concentration in the tested lakes. It was also found that uncertainties in allochthonous and autochthonous production of SPM are generally much more im-portant for predictions of SPM concentration than uncertainties in internal processes such as sedimentation and resuspension. The within-site variability of settling velocity of SPM was found to be large, implying that, if possible, this variability should be taken into account when predictions of particle sedi-mentation are made. A dimensionless moderator for the impact of SPM concentration on settling velocity is suggested. A mechanistic model for phosphorus dynamics in accumulation area sediments is defined and shown to provide accurate predic-tions of four different phosphorus forms at different sediment depths in Lake Erken sediments. Simulations with a lake model indicate that temperate lakes with long water retention time appear to be more sensitive to climate warming than lakes with short water retention time with respect to phosphorus concentration and eutrophication effects.

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6 Conclusions

All models are incomplete abstractions of more or less well-defined sys-tems, confined by their driving variables, mathematical formulations and empirical data. The models in this work are no exceptions. In this work, the LEEDS-model is defined and critically tested with respect to sensitiv-ity, uncertainty and accuracy in model predictions for a number of lakes. The effort to improve the model behavior will and should never be fin-ished, but may continue as long as more knowledge and more data can be obtained. However, with the existing foundation, it is possible to use the model for many scientific and practical purposes, as long as assumptions and limitations are recognized. Hopefully, this thesis has contributed to our knowledge of how lakes function and how this is expressed in the modeling approach used herein.

The LEEDS-model and the sub-model for SPM are shown to give rea-sonable predictions of their target variables at a monthly time-scale in the tested lakes (Paper I, II). Some special features of the lakes, such as the Peridinium bloom in Lake Kinneret, are not and should not be seen in the model validations, since the processes are not included in the model for-mulations. Some variability is not explained by the model for unknown reasons, but the uncertainty in the empirical data must also be kept in mind.

The dimensionless moderator for SPM concentration proposed in Pa-per III is now included in the SPM- and LEEDS-models to provide more accurate estimations of particle settling velocity. Phosphorus diffusion from accumulation sediments appears to be one of the most important model uncertainties, and a sediment model is developed in Paper IV as an effort to gain more quantitative knowledge about this important process. Conclusions from this paper may later be used to improve the diffusion algorithm in lake models. Ongoing climate change causing increased diffusion rates in many lakes may also be studied within this framework.

Model runs simulating possible future climate changes indicate that lakes with long water retention times, such as Lake Erken, may face in-creased phosphorus concentrations and hence also eutrophication effects in the future. It is found in Paper V that the phosphorus concentration

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may increase by more than 50% related to the assumed climatic changes alone, but it is also shown that there are large differences between differ-ent climate scenarios. This is important information concerning conflicts about climate change – the less warming of the climate, the less eutrophi-cation of temperate lakes. It should also be taken into account when man-agement planning is done for lakes with long water retention times.

The study of lake phosphorus dynamics and climate change shows the value of predictive models. If the models are well structured and used in the right way they may give valuable information about the system’s response to perturbations and possible remedial measures. It is also essen-tial to make the most of experience from past and contemporary variation in the systems to improve the models.

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7 Acknowledgements

I would like to thank the following people for making my time as a PhD student a pleasant and rewarding experience:

- My supervisor Prof. Lars Håkanson for giving me the opportunity to work with an interesting topic, for sharing his joy for ecological modeling and for encouragement and support. - My senior colleague Emil Rydin, with whom I spent many hours in the car and in the boat into, within and out from Lake Erken. Thanks for many interesting and enlightening discussions and for nice company. - My senior colleague Toddy Blenckner, for nice cooperation and friend-ship. I learned a lot from working with you! - Kurt Pettersson for being around and organizing things. I appreciated the field work and the atmosphere at Lake Erken, and you have a great part in that! - Hampus Markensten, Irina Persson, Per Hyenstrand, Niklas Strömbeck and András Tálos at the Department of Limnology for cooperation at several occasions. - Helena Enderskog, Björn Mattsson, Per Odelström and Ulf Lindqvist at Erkenlab for technical assistance. - The research was partly financed by the EU-project “Phytoplankton on-line” (RTD Project EVK1-CT1999-00037). Thanks to all the partners in this project, especially Vera Istvánovics, Yosef Yacobi, Werner Eckert, Ute Bodemer and Volkmar Gerhardt for discussions and nice socializing. - Tomas Nord – If you were only half as helpful you would still have many friends. Not to mention all good music you brought… - Everyone at LUVA for providing a nice working environment. Espe-cially I would like to thank Aziz, Angelica, Andreas G, Andreas B, Sara-Sofia, Karin, Håkan, Niclas, Fredrik, Klas, Johan, Elin, Magnus, Fritjof, Hanna, Tony, Lotta, Sofia and Jenny for many memorable moments. - Magnus Karlsson for informing me about the position at the university and for letting me practice science in different situations. - Family and friends for support in many ways. Especially my parents Jan and Kerstin and my brother Fredrik for caring about me. I love you!

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8 Summary in Swedish

I denna avhandling presenteras prediktiva modeller för några viktiga pa-rametrar för eutrofiering i sjöar. Grunden är en dynamisk fosformodell baserad på ordinära differentialekvationer. Genom att beräkna fosforflö-den in och ut ur en sjö samt de mest betydelsefulla interna flödena kan koncentrationer av olika fosforformer uppskattas.

Den dynamiska modelleringsansatsen testas kritiskt och en ny modell-version presenteras. Två beräkningsboxar för kolloidalt fosfor, en sub-modell för suspenderat partikulärt material (SPM) och algoritmer för vattenutflöde, omblandning, diffusion, vattenhalt och organisk halt i ac-kumulationssediment introduceras. Värden från den nya modellversionen ger god överensstämmelse med empiriska data i fem testade sjöar.

Submodellen för SPM använder i stort sett samma drivvariabler som fosformodellen, så det krävs inga ytterligare variabler för att använda denna submodell. SPM-modellen kan även användas separat för månads-prediktioner av SPM i vatten och sediment. Även denna modell ger god överensstämmelse med empiriska data.

Empiriska data från sjöarna Erken (Sverige) och Balatonsjön (Ungern) används för att undersöka variation i fallhastighet för SPM. Det visade sig att variationen var betydande och en dimensionslös moderator för SPM-koncentration föreslås för att ta hänsyn till denna variation. Utifrån empiriska data från djupsediment i Erken tas en ny dynamisk modell för sedimentation, begravning och diffusion i sediment fram. Denna modell ger tillfredsställande månadsprediktioner av fyra fosforformer på olika sedimentdjup.

Simuleringar med den dynamiska fosformodellen för sjöar under två olika klimatscenarier indikerar att sjöar kan komma att påverkas mycket olika av klimatförändringar beroende på fysisk karaktär. Erken, som har en vattenomsättningstid på cirka sju år, verkar vara betydligt känsligare än två Mälarbassänger med avsevärt kortare vattenomsättningstid. Detta skulle kunna innebära allvarliga eutrofieringsproblem i framtiden i eutro-fa sjöar med lång vattenomsättningstid. Detta bör tas i beaktande i vat-tenplaneringen om vattenkvaliteten i dessa sjöar skall bibehållas.

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Studien av fosfordynamik och klimatförändringar visar värdet av pre-diktiva modeller. Om modellerna är välstrukturerade och vältestade kan de ge värdefull information om hur systemen påverkas av störningar och möjliga åtgärder. Förhoppningsvis har denna avhandling bidragit till kun-skap om hur sjöar fungerar och hur detta uttrycks i de modelleringsansat-ser som använts i detta arbete.

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