Modelling Dissolved Organic Carbon Turnover in Humic Lake Örträsket, Sweden

Environmental Modeling and Assessment 6: 159–172, 2001. 2001 Kluwer Academic Publishers. Printed in the Netherlands.

Modelling dissolved organic carbon turnover in humic LakeÖrträsket, Sweden

Charlotta Pers a, Lars Rahm b, Anders Jonsson c,d, Ann-Kristin Bergström d and Mats Jansson d

a Swedish Meteorological and Hydrological Institute, SE-601 76 Norrköping, SwedenE-mail: [email protected]

b Dept. of Water and Environmental Studies, Linköping University, SE-581 83 Linköping, SwedenE-mail: [email protected]

c Climate Impacts Research Centre, Box 62, SE-981 07 Abisko, Swedend Dept. of Ecology and Environmental Science, Umeå University, SE-901 87 Umeå, Sweden

E-mail: {Anders.Jonsson, Ann-Kristin.Bergstrom, Mats.Jansson}@eg.umu.se

The organic carbon balance of a lake with high input of allochthonous organic carbon is modelled integrating physical, chemical andbiological processes. The physical model captures the behaviour of real thermal stratification in the lake for different flow situations duringthe period 1993–1997. The dissolved organic carbon model is based on simulated trajectories of water parcels. By tracking parcels, accountis kept of environmental factors such as temperature and radiation as well as DOC quality for each parcel. The DOC concentration showsseasonal variations primarily dependent on inflow. The organic matter degradation (bacterial- and photodegradation) in the lake amounts to1.5−2.5 mg C l−1 yr−1, where photooxidation is responsible for approximately 10%. The estimated DIC production in the lake is largecompared to sediment mineralisation and primary production. The main conclusion is that the model with the selected parameterisations ofthe degradation processes reasonably well describes the DOC dynamics in a forest lake.

Keywords: DOC model, fluid particle model, lake, organic matter

1. Introduction

A fraction of the terrestrial primary production is lost toaquatic ecosystems [1]. The dissolved part of this organicmatter plays important roles in many lakes. One is to serveas a source of energy and nutrients for heterotrophic bacte-ria, resulting in a build-up of bacterial biomass and produc-tion of CO2 from bacterial respiration [2,3]. Lakes which re-ceive moderate to high amounts of allochthonous dissolvedorganic carbon (ADOC) are net heterotrophic in the sensethat more CO2 is produced than is fixed by primary produc-tion [4]. Consequently, these lakes are net sources of CO2 tothe atmosphere.

Net heterotrophic lakes are frequent in boreal regionswhere large pools of soil organic carbon serve as sourcesof ADOC to streams and lakes. The high percentage of landarea covered by lakes in these previously glaciated regionscould make the export of carbon dioxide from lakes an im-portant component in the global carbon balance.

In addition to bacterial degradation and sedimentation,photooxidation of organic matter with CO2 as an end prod-uct affects the carbon balance of lakes. Photodegradation isimportant only in the upper regions of the water mass sincethe effective wavelengths (mainly UV-A and UV-B) are ef-ficiently absorbed [5]. In addition to direct production ofCO2, photooxidation may also alter the structure of organicmatter making it more sensitive to bacterial degradation [6].

Most of the knowledge on degradation and degradationrates of dissolved organic carbon (DOC) derives from labo-ratory studies (e.g., [7–9]). The turnover of DOC in whole

lake environments is of another scale. Obviously this lack ofcoupling between controlled laboratory conditions and thenet result of a manifold of processes in natural environmentsis unsatisfactory. A model simulation may be used to up-scale those small-scale process studies.

In the present study we modelled the organic carbonbalance in a boreal forest lake, Lake Örträsket, where thecarbon turnover is dominated by a relatively high input ofADOC. DOC input as well as physical, chemical and bi-ological processes in the lake are integrated in the model.Still, a model is always an idealisation. The objective wasto model the DOC concentration and the CO2 productionover a five-year period. The hypothesis was that variationsin these variables could be predicted from discharge, lakemorphometry, thermal stratification, DOC supply throughinflow and primary production, and degradation of organiccarbon due to bacterial activity and photooxidation. A sec-ond objective was to test our present knowledge, thereforea sensitivity analysis of the different processes is valuable.A few model tests were done regarding different model as-sumptions and are included in the discussion. Detailed un-certainty and sensitivity analyses are not presented here butin Pers [10], where the sensitivity to parameters in the DOCmodel is investigated.

2. Lake Örträsket

Lake Örträsket was chosen as the model lake because es-sential input data for the model could be obtained from alarge number of field studies carried out in this lake during

160 C. Pers et al. / Modelling lake dissolved organic carbon turnover

Figure 1. Location of the River Öre and Lake Örträsket.

the second half of the 1990s (e.g., [11–17]). Lake Örträsketis a long narrow lake located at 64◦6′N and 19◦1′E in thenorthern part of Sweden (figure 1). It is situated in a deepvalley surrounded by forest-covered hills. It is the only largelake in the main stream of the River Öre. This river drains3000 km2 and discharges into the Gulf of Bothnia. Thedrainage area mainly consists of coniferous forest (∼75%)and mires (∼20%). These conditions make Lake Örträsketa dystrophic lake rich in humic substances (DOC is foundin the range 8−13 mg C l−1) with a short hydraulic resi-dence time of three months. The surface area of the lake is7.3 km2 at mean water level. The mean depth is 23 m andthe maximum depth is 62 m. The water level rises about2 m during spring flood. Most of the organic matter in thelake is of allochthonous origin and arrives through two mainfeeder streams, River Örån and River Vargån. River Vargån,draining 341 km2, is more colored (8–40 mg DOC l−1; 1–60 m3 s−1) than the larger River Örån (5−30 mg DOC l−1;1-250 m3 s−1), which drains 1741 km2 [12]. The lake alsoreceives water from diffuse inlets draining 84 km2 [12]. Sup-ply of water and DOC through groundwater is unknown, butprobably small, and is therefore ignored.

2.1. Data and pre-processing

The morphometry of the lake is described by the model’shypsographic curve. A piecewise linear function was es-timated from interpolated depth measurements (figure 2).The mean surface area of the model lake was estimated to8.2 km2. This is 12% larger than the 7.3 km2 given in mostreferences and caused by uncertainties in interpolation.

The physical model is forced by meteorological data;wind velocity (at 10 m above ground), air temperature, rela-tive humidity and cloud coverage. Data with a sampling fre-quency of 3 hours from the weather stations of the SwedishMeteorological and Hydrological Institute (SMHI) at UmeåAirport (75 km SE of the lake) and Vindeln (40 km NE of

Figure 2. The size of lake boxes and the hypsography for the physicalmodel.

the lake) were used. The simulation period was from 1 May1993 to 31 December 1997. This period was chosen bothfor the existence of field data for validation and because itcovers a variety of runoff situations.

The discharge of the two major inlets were measureddaily during the ice-free period in 1993, 1994, 1995 and ir-regularly during 1997. The diffuse inflow to the lake wascalculated as the drainage area of diffuse inlets times the spe-cific runoff of River Örån. The discharge of the lake outlet(River Öre) was measured daily during the ice-free periodin 1993 and 1994. For days without discharge registration,outflow were estimated from the flow at the SMHI stationTorrböle (continuous measurements), 60 km downstreamfrom Lake Örträsket. A relation (Qout = 0.667∗QTorrböle,R2

adj = 0.96, n = 432) was established by comparing mea-sured outflow during 1993 and 1994 with the discharge at

C. Pers et al. / Modelling lake dissolved organic carbon turnover 161

Figure 3. Modelled inflow, 1 May 1993–31 December 1997.

Torrböle. For days lacking inflow measurement the inflowwere assumed equal to the outflow. Figure 3 shows the mod-elled inflow (River Vargån + River Örån + diffuse inflow).

The daily temperature of River Örån water was measuredduring parts of the year 1994 (A. Jonsson unpubl. data).These observations were compared with measured air tem-perature (mean of the twelve preceding days provided bestfit) resulting in different relations for spring flood (with flowsabove 100 m3 s−1) and the rest of the year. These relationswere used to estimate the temperature of the inflow water.During spring flood this relation was used:

Twater = 1.7Tair − 6.4, R2adj = 0.94, n = 15

while:

Twater ={

1.2Tair + 1.5, Tair � −1.7,−0.5 Tair < −1.7,

R2adj = 0.97, n = 143

was used for the rest of the year. The river water was prob-ably not supercooled during winter, but the observed and re-ported value (−0.5) was used anyway. This should not affectthe model, since the inflow level is not changed and the lowdischarge makes the error in heat content small. All vari-ables mentioned in the text are given in table 1. The DOCconcentration of the inflowing water (measured in mg C l−1)was estimated in a similar way:

DOCin =

2.58(log10(Qin)

)2 + 6.02 June − Sept.R2

adj = 0.78, n = 32,

3.28 log10(Qin) + 4.64 Oct. − MayR2

adj = 0.67, n = 21,

(1)

where Qin (measured in m3 s−1) is inflow. The relations inequation (1) were derived from concurrent measurements of

DOC and discharge in River Örån during 1993–1995 and1997. Use of a relation combining measurements from RiverÖre and River Vargån did not improve the modelled DOCconcentration of the lake and the relation explained less ofthe DOC variations in inflow. A separation of the two maininflows were not considered because of the complexity itwould give to the model and their lower R2

adj. The result-ing DOC concentration of the inflow varies between 5 and20 mg C l−1.

Net bacterioplankton production (BPP) in Lake Örträsket(1–40 µg C l−1 d−1; n = 44) has been reported for 1994by Jonsson et al. [18], for 1995 by Isaksson et al. [16] andJansson et al. [17], for 1996 by A.-K. Bergström (unpubl.data) and for 1997 by Bergström and Jansson [14]. In thesestudies bacterial production was determined immediately af-ter sampling by the 3H-leucine uptake method [17]. Thesedata were used to parameterise the biotic degradation in themodel assumed only to be bacterial degradation.

Radiation experiments performed on DOC from LakeÖrträsket and surrounding waters [15] were used for para-meterisation of the abiotic degradation (photooxidation). Inthe experiment, DOC loss was measured during 24 h expo-sure of DOC sample to light from an UV-A lamp (UV-B= 0.3 W m−2, UV-A = 20 W m−2, PAR = 5 W m−2) fivetimes during the summer of 1998. Photosynthetically ac-tive radiation (PAR) was measured at the lake surface dur-ing the period 1995–1997 (Bergström unpubl. data). Theextinction coefficient for short-wave radiation (β, table 1)was estimated from insolation observations in the lake, ofwhich the natural logarithms were taken (ln(light) = β ∗ zs,R2

adj = 0.53, n = 254). The relatively low adjusted coeffi-cient of determination is partly due to four non-zero obser-vations of light at depths larger than 6 m.

Planktonic primary production (PP) was measured (14Cuptake, see [17]) during the summers 1995–1997 [17,19].A mean value (53 mg C m−2 d−1) for the summer period(June–September) was used in the model.

In addition temperature profiles and DOC observations inepilimnion, metalimnion and hypolimnion were available tovalidate the model. Unfortunately, for DOC only spring andsummer observations were available.

3. Mathematical descriptions of models

The physical lake model is a one-dimensional transientboundary layer model. This model simulates the verticalvariation of water temperature, turbulent mixing and hori-zontal velocity. It is chosen because it captures the effectof turbulence reasonably well [20,21]. The DOC model, onthe other hand, is based on a Lagrangian dispersion modelbut linked to the physical model by the turbulence variables(figure 4). The dispersion model has the merit of allowingfor time-dependent changes in, e.g., the quality of DOC. Inthis model, the trajectories of fluid particles are simulatedwith the vertical velocity represented by a Markov sequence.Each fluid particle represents a small water parcel that con-


Table 1Notation list.

DICPRODexp DIC production during UV-A experiment, mg C l−1 s−1

DICPRODUVA DIC production due to UV-A, mg C l−1 s−1

DOC DOC concentration of a water parcel, mg C l−1

DOCin DOC concentration of inflow, mg C l−1

DOClake mean DOC concentration in epilimnion (during stratification) or in the whole lake, mg C l−1

k turbulent kinetic energy, m2 s−2

n number of observationsN number of boxesNlake number of parcels in the lakeNnpa number of parcels added through inflowPAR photosynthetically active radiation, 400–700 nm, W m−2

Pout probability that a particle is removed from lakeP0 probability of not adding a new particle to the simulation due to inflowP1 probability of adding a new particle to the simulation due to inflowq the quality of the DOC in a parcelqinitial the initial quality of the DOC in a parcelQin inflow, m3 s−1

Qout outflow, m3 s−1

QTorrböle flow in River Öre at Torrböle, m3 s−1

R2adj adjusted coefficient of determination

SR net short-wave radiation, W m−2

t time, stin lake time a parcel spent in lake, sTair mean air temperature during the preceding 12 days, ◦CTwater temperature of the inflow, ◦CUVA ultraviolet-A radiation, 320–400 nm, W m−2

Vlake volume of the lake, m3

Vz>60.5 volume of the lake above 60.5 m, m3

w (Lagrangian) vertical velocity of fluid particle, m s−1

z vertical co-ordinate (positive upward), mzs depth below water surface, mαbact bacterial degradation parameter, non-event material, s−1

αbact,e bacterial degradation rate parameter in epilimnion, event material, s−1

αbact,h bacterial degradation rate parameter in hypolimnion, event material, s−1

βUVA extinction coefficient for UV-A radiation, m−1

ε dissipation of turbulent kinetic energy, m2 s−3

σ 2wL variance of Lagrangian vertical velocity, m2 s−2

τl Lagrangian integral time scale, s

tains DOC. By tracking each parcel, account is kept of envi-ronmental factors such as temperature and radiation. Thesefactors, among others, control the DOC concentration in theparcel. By studying an ensemble of parcels, their mean ef-fect was determined and used to represent the DOC turnoverin the lake.

3.1. Basic physical model

The lake is assumed to be horizontally homogeneous,why a one-dimensional model is applied. The physicalmodel treats the vertical distribution of horizontal momen-tum, heat, turbulence and density. It is based on Reynoldsaveraging of the Navier–Stokes equations and the conceptof turbulent viscosity [22]. To close the system and estimatethe turbulent viscosity, the turbulent kinetic energy (k) andits dissipation rate (ε) are modelled parallel to momentumand heat by the classic k–ε model [23,24].

Conservation equations describe the rate of change inhorizontal momentum. By adding the turbulent viscosity tothe molecular viscosity in the diffusion term, the turbulent

momentum exchange is included in these equations. Theheat equation includes heat diffusion and absorption of heatwithin the water body in the form of solar radiation. Ab-sorption is assumed to follow an exponential decay law withthe extinction coefficient β for incoming short-wave radia-tion except for the infrared part (40%). This part is assumedto be absorbed in the uppermost surface layer. Net solar ra-diation depends on the cloud coverage in addition to severalother constants (e.g., F0 – solar constant) and variables (e.g.,day and hour of the day) [25]. Ice cover will, in addition,strongly influence the amount of solar radiation reaching thewater body [21]. Density is quadratically dependent on tem-perature around the temperature of maximum density (Tref).The values of parameters are given in table 2.

The turbulence model is described thoroughly by Rodi[24,26]. The two turbulence variables (k, ε) are used to cal-culate the turbulent viscosity by the Prandtl–Kolmogorovrelation [26,27]. For a detailed derivation of the physicalmodel see Svensson [20], and for a broader backgroundon models of turbulent flows see Rodi [24] or ASCE TaskComittee on Turbulence Models in Hydraulic Computa-


Table 2Parameter symbols and values.

Symbol Value Parameter Equation(s)

β 1.6 m−1 extinction coefficient for short-wave radiation –F0 1360 W m−2 solar constant –Tref 3.89◦C temperature of maximum density –�t 100 s time step of Lagrangian model (2), (3)X 2 number of PP particles per day –PP 13.2 µg C l−1 d−1 primary production in upper 4 m –α1 2.3 ∗ 10−8 s−1 bacterial degradation rate constant (4c), (4d)α2 3.0 bacterial degradation rate decrease due to quality parameter, epilimnion (4b)α3 1.6 bacterial degradation rate decrease due to quality parameter, hypolimnion (4b)αq 9.3∗10−8 s−1 quality decrease rate (4d)Qub 175 m3 s−1 upper bound of inflow with event DOC (4e)Qlb 8.75 m3 s−1 lower bound of inflow with event DOC (4e)bDIC 1.6*10−6 s−1 regression coefficient (5)UVAexp 20 W m−2 UV-A radiation during photooxidation experiment (6)bPAR 0.487 PAR fraction of solar radiation (7)

Figure 4. Partial models and their flow of information.

tion [27]. In Svensson [20] an extended verification is re-ported of this type of model by laboratory experiments andfield studies in a lake.

In the present model, inflow is introduced at a level with adensity corresponding to the temperature of the inflow, whileoutflow is assumed uniform in the layers above the down-stream sill. (No attempt is made to simulate the selectivewithdrawal.) Inflows and outflows control the surface levelof the lake.

The model is numerically simulated by finite differencesin PROBE, which uses an implicit scheme and a standardtridiagonal matrix algorithm [22]. In this article the lake hasbeen partitioned vertically into N = 90 boxes (figure 2),

with thicknesses varying between 2.5 m at the bottom to0.2 m at the top. Normal water level (62 m) corresponds to70 boxes, more are used for high water levels during spring.The physical model was simulated with a time step of 600 s,which was tested and found adequate. The initial values arezero for all dependent variables except heat for which a con-stant temperature of 4◦C is assumed.

3.1.1. Boundary conditionsThe wind stress gives the upper boundary condition of

momentum [22,28]. Presence of an ice cover blocks thewind, which is why a no velocity condition due to fric-tion is used in this case. This condition is always used atthe lower boundary. Ice is formed when the top layer ofthe lake (<0.2 m) has a mean temperature less than 0◦C.The modelling of ice growth and ice melt follows that bySahlberg [21]. It is based on a simple day-degree calcula-tion.

The top boundary condition for the heat equation is basedon observed meteorological conditions. The total heat flux isthe sum of net long-wave radiation, latent heat flux and sen-sible heat flux during ice-free conditions, otherwise there isno heat flux at the upper boundary. Net long-wave radiationis the difference between the long-wave radiation from thewater body, which depends on water surface temperature,and the net air-emitted long-wave radiation [25]. The air-emitted long-wave radiation depends on the meteorologicalforcing; air temperature and cloud coverage, but it is partlyreflected at the surface.

Latent heat flux is due to evaporation, condensation andsublimation [25] and depends on wind velocity, relative hu-midity and the temperature of water/air. Sensible heat fluxdepends on wind velocity in addition to the temperature dif-ferences between air and water [25,29]. The heat flux bound-ary condition at the bottom is zero flux, ignoring the heatflux from sediment, though this flux can be influential dur-ing winter [21] at least in shallow lakes.

The boundary conditions for turbulence are based onshear stress and boundary heat flux [20,22].


3.2. Lagrangian fluid particle model

The motions of fluid particles were simulated in a La-grangian dispersion model [30]. Only the vertical displace-ment is considered, since the lake model is one-dimensional.Langevin’s equation describes the Lagrangian velocity of afluid particle which is subjected to a random acceleration, alinear retarding force and a correction term due to weak in-homogeneous vertical velocity variance [30,31]. Langevin’sequation simulates a turbulent process with an exponentialautocorrelation function. The correlation time scale is calledthe Lagrangian integral time scale (τl) and it is a measureof how long the velocity of the particle is correlated to itspast [30].

In discrete time, a corresponding Markov sequence de-scribes the vertical velocity w based on the state of the pre-ceding time step. To derive the coefficients of the Markovsequence we used the solution to Langevin’s equation [30].The coefficients depend on the time scale (τl) and the vari-ance of the velocity (σ 2

wL), and on a random number froma Gaussian distribution with zero mean and unit variance.The parameters and thus the Lagrangian velocity w are de-pendent on the turbulence variables k and ε, the equivalenceof velocity variance [32] and the effective exchange coeffi-cient [33].

Integrating the Lagrangian velocity simulates the verti-cal position of a fluid particle. The fluid particles reflect ifthey reach a boundary. Downward moving particles can bein such a part of the lake that its bottom is deeper than thepresent layer and then they continue downwards, or they canbe close to the bottom in which case they reflect. The prob-ability of reflection depends on the proportion of the bottomarea of the actual depth. If reflected, a fluid particle stays atthe same level as it is, but with reversed velocity.

The time step needs to be small compared to τl for cor-relation of velocity to be present [30,31], otherwise one getsan ordinary random walk model. The correlation time scalevaries typically between 1 and 1000 s in the model. The timestep should also be so large that the dependence is not longerthan one time step, otherwise the velocity depends on veloci-ties further back in time, which is not modelled [30,31]. Thetime step cannot be chosen so that it always fulfils both thesedemands for this model, therefore a time step (�t) of 100 swas chosen, trying to fulfil the τl demand but also giving areasonable calculation time.

3.3. Dissolved organic carbon model

Each simulated fluid particle symbolises a DOC contain-ing water parcel. As the parcel moves up and down by theturbulent motion, it is subject to different conditions and theDOC of the parcel decreases due to organic matter degrada-tion. Degradation can be performed by bacteria and, if it isin the upper parts of the lake, by photooxidation.

Each modelled water parcel is assigned a specific DOCconcentration when entering the lake. The simulation startswith 1000 parcels equally distributed in the lake. The initial

DOC concentration on 1 May 1993 was chosen to be 9 mgC l−1 in the whole lake, since this is a typical value of theconcentration in spring before the spring flood. Throughoutthe simulation, parcels are added due to inflow and primaryproduction, and removed due to outflow. The addition ofparcels by inflow or removal through outflow maintains therelative proportion between inflow/outflow and the volumeof the lake. Primary production, on the other hand, increasesthe DOC concentration in the euphotic zone by adding PPparcels.

A parcel added to the lake, simulating inflow, is assignedthe DOC concentration of the inflow (equation (1)). Theparcels are created in proportion to inflow volume and thedensity of parcels in the lake:

Nnpa = int

[Qin�t

Nlake

Vlake

]+

{1 with probability P1,0 with probability P0,

(2a)

P1 = mod

[Qin�t

Nlake

Vlake

], P0 = 1 − P1. (2b)

Nnpa is the number of water parcels added during a time step(�t), Nlake is the number of parcels in the lake, and Vlakeis the lake volume. int denotes the integer part and modthe remainder of the bracketed expression. An extra parcelis added with probability P1 equal to the remainder of theexpression (equation (2b)).

Primary production is mimicked by adding X waterparcels per day during the production season representingthe integrated production in the euphotic zone, the upper 4 mof the lake. We assumed that 100% of the material producedwas transformed to DOC, which is supported by the lack ofsettling algae in the hypolimnion [18]. The DOC concentra-tion of the new parcels is determined by the requirement thatmean DOC concentration in the upper 4 m (euphotic zone)after adding the parcels should be equal to the mean DOCconcentration in the same layer before adding the parcelsplus the primary production (PP, table 2).

Outflow causes water parcels to be removed from simu-lation. The number of water parcels leaving the lake is pro-portional to the outflow (Qout) and the density of parcels inthe volume of water above the outflow sill at z = 60.5 m(Vz>60.5; see figure 2 for definition of z). Each parcel in thisvolume is removed with the probability Pout:

Pout = Qout�t

Vz>60.5(3)

The DOC concentration of the outflow is calculated as themean concentration of the parcels leaving the lake duringone day, if any.

The degradation is modelled separately for each parcel.Both biological and photochemical degradation are assumedto result in dissolved inorganic carbon (DIC). The bioticdegradation performed by bacteria has different rates de-pending on the circumstances under which DOC enters thelake and where it resides. The bacterial degradation in a wa-ter parcel is modelled from measurements of the bacterialproduction in Lake Örträsket at in situ temperature in the


dark [14], using a bacterial growth efficiency of 30% [34].Bergström and Jansson [14] found an exponentially decreas-ing relationship between the BPP/DOC ratio observed sev-eral times during summer and time after the spring floodepisode. The decline in the ratio after an episode reflects thedecrease of bioavailability of the organic matter due to bacte-rial degradation and photodegradation during the time spentin the lake [14]. Bergström and Jansson [14] also demon-strated how the production and the BPP/DOC ratio differedbetween epilimnion and hypolimnion. Other factors, such asthe temperature dependence and the effect of UV-radiationon the bacterial growth are not considered explicitly in thepresent model. We have assumed that the quality of the DOC(as reflected by the time spent in lake) is sufficient at thisstage to describe the bacterial degradation rate:

dDOC

dt= −αbactDOC (4a)

event

{αbact,e = 2α1e

−α2(1−q),

αbact,h = 1α1e−α3(1−q),

0 < q � 1, (4b)

non-event αbact = 0.1α1, q = 0, (4c)

q ={

qinitial − αq tin lake, qinitial � αq tin lake,0, qinitial < αqtin lake, (4d)

qinitial =

1, PP parcel or parcel with Qin > Qub,0, parcel with Qin < Qlb,ln

(QinQlb

)−α2

, parcel with Qlb < Qin < Qub.(4e)

The rate parameter αbact is decreasing with quality (q) of theorganic material (equation (4b), which in turn decreases withtime (equation (4d)). This is in line with the size-reactivitycontinuum model [35] which describes that more recent,high molecular weight components have higher bioreactiv-ity than older, low molecular weight compounds. For highquality material (called event material) the rate decreases ex-ponentially with quality (equation (4b)). The degradationrate for event material (q = 1) in epilimnion, αbact,e, istwice that in the rest of the lake, αbact,h. The thermoclinedepth separating epilimnion from hypolimnion was definedas the level with a maximum temperature gradient largerthan 0.2◦C m−1. The degradation rate for non-event mate-rial (q = 0) is derived from BPP/DOC observations duringlate autumn [14]. α1 transforms αbact to relevant units (ta-ble 2).

Primary produced DOC is initially considered to be ofhigh quality (q = 1), as is allochthonous carbon comingwith flows above Qub (spring flood). Allochthonous mater-ial coming with a lower inflow gets an initial quality propor-tional to the natural logarithm of the flow (equation (4e)).This because an exponentially declining bioavailability de-pendent on the time spent in the river is assumed like thatin epilimnion. For flows below Qlb the organic material isconsidered of non-event quality (q = 0).

Abiotic degradation of organic matter was modelled asfollows. The photooxidation rate, estimated from experi-ments with UV-A radiation, was correlated to the DOC con-

centration of the sample by linear regression. The loss ofDOC due to radiation was assumed to result in a productionof dissolved inorganic carbon according to:

DICPRODexp = bDICDOC, R2adj = 0.55, n = 32.

(5)UV-A is considered to be the main source of energy to pho-todegradation and the DIC production modelled is due toUV-A only. Although Lindell [36] states that 40% of theDIC production during photooxidation at lake surface is dueto UV-A and that 45% and 15% is due to PAR and UV-Bradiation, respectively, their PAR fraction contained almosthalf of the UV-A spectrum. In addition, Granéli et al. [37]found that the vertical distribution of photooxidation wasmost similar to the depth distribution of UV-A radiation. As-suming a linear relation between intensity and degradationrate, the rate of change due to UV-A radiation can be calcu-lated as:

DICPRODUVA = DICPRODexpUVA

UVAexp, (6)

where UV-A radiation is assumed to be 10% of PAR withinthe atmosphere [36]. Modelled solar radiation (SR) wascompared to measured PAR at the lake surface resulting inthe linear relationship:

PAR = bPARSR, R2adj = 0.72, n = 332. (7)

The light intensity changes with depth as light is scattered orabsorbed in the water by organic molecules. The exponentialmodel:

UVA(zs) = UVA(0)e−βUVAzs (8)

was used for light at depth zs below surface. The extinctioncoefficient for UV-A (βUVA) is estimated from the relationgiven by Scully and Lean [38], where the extinction coef-ficient depends on DOC concentration in the lake. The es-timated mean DOC concentration in the epilimnion (duringstratification) or in the whole lake is used in the model. Theused relation was estimated for clear-water lakes (DOC < 8mg C l−1), but its extrapolation is not unreasonable (see datain [5]). Morris et al. [39] also fitted a power equation to UV-A data (DOC < 11 mg C l−1), but they conclude that themodels are comparable for moderate to high DOC concen-tration. Thus we feel confident to use this relation althoughour lake has sometimes DOC concentrations above 11 mgC l−1. The final expression for photooxidation in a waterparcel becomes:

dDOC

dt= −0.1bDICbPAR

UVAexpSR

× exp(−0.229(DOClake)

1.53zs)DOC

when combining the surface DIC production (equations (5),(6) and (7)) with the depth attenuation (equation (8)). Valen-tine and Zepp [40] found that the photoreactive fraction ofnatural organic matter behaved as a single pure compound,which supports our use of a photooxidation relationship forbulk DOC on small water parcels. In addition to production


of DIC, radiation may produce other organic compounds,which change the quality of the DOC [15]. This is onlyindirectly included in the bacterial degradation rate (equa-tion (4)).

The modelled DOC concentration of the lake was cal-culated from the DOC concentration of the parcels. Themean modelled DOC concentration in epilimnion and hy-polimnion was calculated as the mean of the parcels in thatvolume during a day. To calculate the mean of the wholelake, the lake was divided into six parts of approximatelyequal volume and the mean DOC of each compartment wascalculated separately. Then the six means were averagedto form the lake mean modelled DOC concentration. Thisweighted mean was used because the parcels do not repre-sent equal volumes. The mean DOC degradation (bacterialdegradation and photooxidation respectively) was calculatedby the same kind of weighted mean. The DOC distributionwas calculated from parcels in 16 equally spaced compart-ments. DOC concentration, DOC degradation and DOC pro-files were calculated for each day.

4. Results

The modelled discharge pattern varies between years (fig-ure 3). The years 1994 and 1995 were normal, with a springflood culminating in May. Heavy summer rains fell duringthe years 1993 and 1997, resulting in high discharges duringthese periods while the year 1996 showed an unusually smallspring flood. During the years with no flow measurement(1995–1996) no surface level variation could be modelled,since the Torrböle station downstream from Lake Örträsketwas used to estimate both inflow and outflow. This proce-dure can change the characteristics of the flow, i.e., flowpeaks may be smoothed and delayed and new peaks mayenter through heavy rains downstream from the lake. Apartfrom that, the model handles the different discharge patterns.

The physical model calculates the time-dependent ver-tical temperature distribution in the lake due to hydrolog-ical and meteorological forcing. The modelled tempera-ture development in the lake generally agrees with observeddata but there are deviations from the observed stratification.Generally the model forms a thermocline in May–June thatpersists until the autumn turnover in October. The depth ofthe modelled thermocline and the development of stratifica-tion vary between years; e.g., the summer maximum surfacetemperature varies between 15 and 21◦C. The summers of1994 and 1997 had the warmest surface waters and the shal-lowest thermoclines according to the model.

The temperature development in 1994 is described belowand illustrated in figure 5. It should be kept in mind thatthe model gives the horizontal mean temperature, while theobservations are taken at one location in the lake. In earlyspring (March–April) of 1994, the modelled surface temper-ature is between 2 and 4◦C, while the observed surface tem-perature is 0◦C (figure 5). Below 5 m, the observed and mod-elled profiles converge to about 3◦C. During spring turnover

Figure 5. Modelled and observed temperature profiles for four days in 1994.

both the modelled and the observed temperature are aboutfour degrees in the whole lake. In June the lake gets warmfaster in the upper 15 m than what the model predicts. Thedifference between the modelled and the observed surfacetemperature is largest on 15 June 1994, 8◦C and 11◦C re-spectively (figure 5), and thereafter the differences decrease.In the middle of July both the epilimnion temperature andthe depth of the thermocline (approx. 8 m) are similar. Themodelled hypolimnion is colder (up to 2◦C) than observedduring 1994 (figure 5). The modelled temperature of thehypolimnion is unchanged until autumn turnover. From theend of July the modelled thermocline deepens and sharp-ens, while the observed thermocline almost vanishes beforeit in August forms a new shallow thermocline (4 m), whichthen slowly deepens. In late September, the modelled ther-mocline has reached 20 m, while the observed is at about15 m depth. In addition, the observed temperature in epil-imnion decreases faster than the modelled one. After the au-tumn turnover (in the middle of October) the modelled lakeis rather homogeneous.

The outflowing water parcels often have spent less thantwo months in the lake. 30% of the water parcels removedspend more than 60 days in the model, while 40% spend lessthan 10 days. It is noteworthy that 30% of the water parcelsleaving are subject to less than 0.02 MJ m−2 of light (UV-A)and 60% to less than 0.06 MJ m−2.

The DOC model estimates the DOC concentration in thelake and in the outflow, as well as the loss of DOC. Generallythe modelled mean DOC concentration of the lake (figure 6)increases from 9 to 11 mg C l−1 during spring and earlysummer, whereupon it slowly decreases until next springflood unless there are high flows in the summer or autumn.The modelled outflow concentrations (figure 7) show a sim-ilar pattern. For all years except 1996, the modelled con-


Figure 6. Modelled mean DOC concentrations in the lake and observedDOC concentrations in epilimnion, metalimnion and hypolimnion.

centration increases rapidly in the whole lake during spring.A slow decrease during the rest of the year is evident for allperiods and layers (1994 is shown in figure 8). During sum-mers, stratification can be seen for the modelled DOC (fig-ure 8). The small spring flood in 1996 (figure 3) resulted in arelatively small peak in mean modelled DOC concentrationin the lake during that period. Concurrent peaks betweenmodelled water flow and modelled DOC concentration canalso be seen during years when heavy rains have fallen (com-pare figures 3 and 6).

The total modelled DOC loss is 1.5–2.5 mg C l−1 yr−1

(40–60 g C m−2 yr−1) for the years 1993–1997 (table 3).The modelled annual bacterial degradation is about 45 g Cm−2 yr−1, and the modelled annual photooxidation 6 g Cm−2 yr−1. The modelled bacterial degradation rate variesfrom 0.002 mg C l−1 d−1 (50 mg C m−2 d−1) during win-ter to about 0.01 mg C l−1 d−1 (250 mg C m−2 d−1) duringthe summer season (figure 9). The modelled photooxidationproduces approx. 0.002 mg C l−1 d−1 (50 mg C m−2 d−1)during summer while it is insignificant during winter (fig-ure 9).

5. Discussion

5.1. Lake physics

The modelled weakly unstable surface layer in March(figure 5) is probably caused by solar radiation heating, andis retained by an underestimation of turbulence below theice cover. Also notice that the model does not handle thesnow cover, probably leading to an overestimation of the ra-diation to the lake. The quadratic density relation makesthe buoyancy differences small around temperature for max-imum density, differences that are presumed to force the

Figure 7. Modelled mean DOC concentrations in the lake, modelled DOCconcentrations of the outflow, and observed DOC concentrations of the out-

flow.

thermal convection in the lake. Furthermore, the lake modeldoes not take into account processes like internal waves anderosion due to turbulent inflow, which contribute to the mix-ing in a real lake.

Some of the discrepancies in the modelled lake temper-ature may be due to the primitive inflow routine used. Inthe model, the inflow level is determined by the inflow tem-perature, and the intrusion will be into one lake box. Inreality there is probably a continuous mixing of inflowingwater leading to intrusion into the lake at several differentdepths. This is problematic during autumn, when inlet wa-ter becomes colder. In the model, the inflowing water mayblend with hypolimnion water instead of epilimnion water,which is a possible explanation for the high modelled tem-perature in the epilimnion during autumn 1994 (figure 5).The model does not include supply of heat from sediment,but in a testrun of the model, the effects of this were toosmall for it to be the main cause of the cold hypolimnionwater.

The major shortcoming that arises due to the use of aone-dimensional model concerns the instant horizontal ho-mogenisation of the water in the lake. Since the circula-tion in the surface layer occurs on velocity scale an orderof magnitude larger than the net throughflow, our assump-tion of a well-mixed surface layer with insignificant hori-zontal gradients can still be justified. Another effect thatthe model cannot fully capture is when the spring and au-tumn turnover circulate the whole lake. When this happens,the model can only feature strong vertical turbulent mixing.A circulation in a vertically DOC stratified lake may causehorizontal variations in DOC concentration. Still, the modelshould minimize this problem since it calculates the inte-grated DOC concentration of each depth. Nevertheless, the


Figure 8. Modelled distribution of DOC concentrations, 1994.

Table 3Yearly modelled DOC loss due to degradation and DIC production.

Year DOC loss DIC production (mg C L−1 yr−1) Photooxidation

(mg C l−1 yr−1) (g C m−2 yr−1) bacterial photooxidation % of DOC degradation % of DIC production

1993 2.3 50 1.4 0.3 12 161994 2.2 50 1.4 0.3 12 161995 2.5 60 1.6 0.3 12 171996 1.5 40 0.9 0.3 19 251997 2.2 50 1.4 0.2 9 12

agreement between the modelled lake temperature and ob-servations is reasonably good. The modelled lake shows alikely stratification and thermocline development in spite ofits idealisation as a one-dimensional model. The discrepan-cies in lake temperature should not have too much influenceon DOC concentration since the DOC model do not dependon temperature, except for thermocline level separating epil-imnion and hypolimnion bacterial degradation rate expres-sions. The temperature stratification does influence the tur-bulence though and this is important for the mixing of thewater mass and thus the DOC.

5.2. Lagrangian fluid particle model

The Lagrangian fluid particle model lets us handle thevarying quality of DOC and avoid the numerical diffusionassociated with ordinary concentration models. The modelmakes it possible to follow a single water parcel, log its his-tory and adjust the degradation process for decreasing DOCquality. This is hard to do within an Eulerian context.

Since there is a continuous water flow through the lake,new parcels were introduced and others were removed. Thenumber of water parcels introduced (equation (2a)) dependson the density of parcels in the whole lake, while the re-moval of water parcels only depends on the density in theuppermost layer (equation (3)). In addition primary produc-tion parcels are added. Therefore the total number of parcelsin the lake increased. The model was limited to about 3500water parcels, since the calculation time and memory usewould otherwise increase to uncomfortable levels. To keepthis limit, the simulation was irregularly stopped and started

again with only a randomly selected number (about 1000)of the parcels in the lake still tracked. The amount of waterparcels followed has, of course, an effect on the model re-sult. The uncertainty of the model decreases with increasingnumber of water parcels since the result we are interestedin is their pooled values. In the lower layers of the lake thevolume is small (figure 2), and consequently contains so fewparticles that the results are unreliable in this region (see be-low). The residence time for the parcels may be too long,because their number increased more than motivated by theaddition of parcels due to primary production. This may leadto a smoothing of the seasonal variations of the water prop-erties (i.e., DOC concentration).

The short time leaving water parcels have spent in thelake is a reflection of the rapid flushing of the surface layerduring summer when most of the water exchange occur. Theresidence time of the water parcels is also dependent on theassumed homogeneous horizontal layers. As soon as an in-flowing water parcel is interleaved in the lake, it can re-side anywhere in that layer and it may follow the outflowin the next minute. Still, the lake mixing is larger than thedischarges transport time, so a fairly homogeneous surfacelayer should exist in the lake.

The amount of light the parcels are exposed to is cru-cial for the photodegradation process. The results obtainedare only approximate since the water parcels do not haveequal weight. The same parcel circulating in the water col-umn may represent different volumes at different times de-pending on where in the lake it resides. In addition onlyoutflowing water parcels are counted. The leaving parcelsare not representative for the parcels in the lake at a point of


Table 4Mean observed and modelled DOC concentrations, and mean of the differences between them.

Water mass DOC Year Number of samples,concentration “wet yrs”/“nrm

1993, 1997 “wet years” 1994, 1995 “normal years” 1996 “dry year” yrs”/“dry yrs”

epilimnion observed 12.6 9.7 9.1 7/18/5modelled 12.4 11.7 10.5difference 0.2 −2.0 −1.4

hypolimnion observed 11.8 10.3 – 5/8/0modelled 10.8 11.2 –difference 1.0 −0.9 –

outflow observed 11.9 9.8 – 8/16/0modelled (epilimnion) 12.2 11.7 –difference −0.3 −1.9 –

time. Still the majority of the leaving water parcels, and theirDOC, was subjected to a radiation less than 0.06 MJ m−2.This can be compared to the 1.8 MJ m−2 of UV-A that wasused in the photooxidation experiment or 3 h of UV-A insunlight (at surface) using typical values from Bertilssonand Allard [7]. During those experiments, DOC is exposedto radiation doses, which are much higher than most lakeDOC gets. This may introduce an error in the model if thedegradation rate changes over time due to i.e. change in ab-sorbance of the DOC.

5.3. DOC concentration

The model of DOC concentration in inflow (equation (1))is simple. Comparing the observed and estimated DOC ofthe inlet waters we overestimate DOC for most of the ob-servations during the summer of 1994; for one observationduring September 1994 the difference is as large as 3 mg l−1

(data not shown). The comparison also shows that DOCis underestimated in inflow during the late summer rains of1993, while early 1993 and whole 1997 estimates are con-sistent with observations.

The model shows the appropriate rise and fall in lakeDOC concentration, but the amplitude is too small (figure 6).During the high water flow in the summer of 1993, the mod-elled epilimnion DOC has a too low second peak comparedto observations in epilimnion, while during the low waterflow of the summers of 1994, 1995 and 1996 the modelledDOC of the lake is too high. This is probably caused by theunder/overestimated DOC concentration of the inlet waters(see above). The large epilimnion volume may also con-tribute, but the primary production’s contribution is small.A large modelled epilimnion volume is slower to decreaseits DOC concentration when the DOC concentration of theinflow becomes lower in summer. Test runs with less pri-mary production contribution to DOC (half and none, re-spectively) decrease the DOC concentration in the lake mar-ginally (2% and 5%, respectively) and mostly in autumn,winter and spring. Still the improvement is small, whichmeans that probably another factor is contributing to thesmall amplitude in mean lake DOC concentration. It is ev-ident that an underestimation of the degradation of DOCcould not have this strong effect on modelled DOC con-

centration. An investigation of the sensitivity of the DOCmodel also shows a clear influence from the DOC of inflowparameters, in addition to primary production and bacterialdegradation rate [10].

No simple statistical test of mean DOC concentration inthe lake (observed and modelled) could be done due to de-pendency of the samples, but the mean and differences arelisted in table 4. The observed DOC concentration showsthat lower values are found for dryer years. The modelshows the same tendency for epilimnion DOC concentra-tion but not so strongly. The difference is as much as 2 mgC l−1 during 1994–1995. In hypolimnion the model showshigher values for the “normal” years than for the “wet” yearsin contrast to the observed values. The model thus overes-timates the DOC concentration during “normal” and “dry”years. This is another example of the too low amplitude ofthe DOC concentration. The reason is probably a differenceof DOC concentration of inflow between dryer and wetteryears that is not captured by equation (1), i.e., DOC concen-tration does not depend solely on flow.

The modelled DOC concentration of the outflow waterfollows the pattern of the modelled mean DOC of the lakeand agrees reasonably well with observed values (figure 7).During summer the modelled outflow has a higher DOC con-centration than the modelled mean lake but during winter thereverse is true, mirroring the modelled surface water concen-trations (see below). Consequently, the over/underestimatesof modelled mean DOC concentration of the lake is visiblein modelled outflow DOC concentration too. In addition,the modelled outflow DOC concentration has large varia-tions between days because of the few parcels involved in thecalculation of the daily DOC concentration of the outflowand the large variation in DOC concentration of the waterparcels. When the water parcels pass through the lake theyare subjected to mineralisation processes of different inten-sity and thus receive different final concentrations. The dailyvariations in modelled outflow DOC concentration wouldtherefore be less if more water parcels were followed, re-sulting in a more representative mean of outflowing parcels.

The model gives a DOC stratification with higher con-centrations at the surface during summer. In 1994 the mod-elled stratification is relatively weak (figure 8). The strongestmodelled stratification is found during years with autumn


rains, indicating the importance of the DOC arriving withthese for the maintenance of DOC stratification. The lowmodelled DOC concentration of winter inflow causes lowmodelled concentrations in the upper layers. This controlsthe modelled DOC concentration of outflow, consisting ofwater from the surface layer of the lake, which makes itlower than the lake mean during winter as seen above (fig-ure 7). The reverse is true for the summers because of highermodelled DOC concentration in epilimnion compared to hy-polimnion. The modelled DOC concentration of the deep-est water is not significant, because of the small volumeand consequently few particles there. Note that due to thequadratic dependence of density on temperature, the surfacelayer will receive the modelled inflow water during a largepart of the year.

In spite of the deviations between modelled and observedDOC concentrations, it is obvious that the model is able topresent reasonably accurate estimates with regard to the ide-alisations of the model of the DOC concentration and itsspatial and temporal variations. Except for the input–outputDOC balance and primary production, which is small, thedegradation of DOC is the only process that is allowed toaffect the modelled DOC concentration. It is then possibleto discuss, in some detail, how the model predicts the mag-nitude and the temporal variation of different degradationprocesses.

5.4. Degradation

Seventy percent of the modelled bacterial degradation isassumed to result in DIC production, the rest is included inbacterial biomass [34,41]. The modelled DIC productionis between 1.2–1.9 mg C l−1 yr−1 (30–40 g C m−2 yr−1),of which 12–25% is due to photooxidation (table 3). Themodelled photooxidation agrees with the estimates for LakeÖrträsket by Jonsson et al. [18] who reported that 12%of the estimated DIC production by bacterial degradationand photooxidation during summer was due to photooxi-dation. Granéli et al. [37] found that the depth-integratedDIC production due to measured photooxidation was simi-lar for lakes with different DOC concentrations (44–56 mgC m−2 yr−1). Their estimates agree very well with our esti-mates of summer photooxidation rate (50 mg C m−2 yr−1).

Modelled microbial degradation was clearly dominantwhen compared to modelled photooxidation, except for afew days in spring, 1996 (figure 9). The import of highquality DOC failed and consequently the bacterial degrada-tion occurred at a slower rate in this year. Moreover, theamount of DOC supplied to the model was small in 1996due to the small spring flood, which was why the bacteriadid not have as much substrate as in other years. Modelledphotooxidation peaks in the beginning of May and stays highuntil the beginning of September. This is the period with suf-ficient solar radiation. Modelled microbial degradation, onthe other hand, varies more between years as it depends onthe modelled quality of DOC, although both processes de-pend on DOC concentration. Modelled bacterial degradation

generally peaks after the spring flood and decreases slowlyduring summer. This seasonal pattern reflects the fact thatthe modelled annual DIC production in the lake is quite de-pendent on the large input of modelled high quality DOCduring the spring flood. Most of the modelled summer DICproduction in the lake is from degradation of the spring floodDOC, which is retained in the lake because of the relativelylong modelled water renewal time during the summer. Ex-ceptions to this general pattern may occur, as in 1993 and1997, when large amounts of high quality DOC are suppliedto the lake in the middle of the summer in connection withmodelled high flow summer episodes (figure 3).

The deviations in modelled DOC concentration have con-sequences for the modelled degradation and DIC production,as both bacterial degradation and photooxidation depends onmodelled DOC concentration. A too high modelled DOCconcentration in the lake increases the bacterial degradation(equation (4a)). For photooxidation an increased DOC con-centration influences in both direction since the light pene-tration decreases while the DIC production also depend onDOC concentration. Deficiencies in the modelling of theDOC concentration therefore influence modelled degrada-tion, which in turn influences the DOC concentration, al-though to a lesser extent. We therefore consider this problemto be the single largest error in modelling the DOM degra-dation and DIC production in the lake.

The spectrum of the UV-A lamps used in the photooxida-tion experiment is not equal to the sunlight UV-A spectrum(e.g., [15]). The intensity is lower for long wavelengths.The UV-B spectrum has satisfactory agreement, while PARis mostly lacking. A slightly higher (mostly 1.2–1.5 times)DIC production can be seen for sunlight compared to arti-ficial UV-A radiation [36,42]. This means that the presentmodelled photooxidation is underestimated. In addition, thelacking PAR and longer UV-A wavelengths can be expectedto reach deeper into the lake than the main UV-A wave-lengths.

Photooxidation provides labile high quality DOC for bac-teria but UV-light limits the bacterial activity in surface lay-ers [7,43,44]. In this model we have not separated the effectof photomodification of bacterial substrates. However, thebacterial degradation rates used in the model were based onin situ measurements integrating the possible effects of lightmodification and ageing of bacterial substrates. Therefore,the modelled bacterial degradation should account for pho-tochemical effects on bacterial degradation. This, however,does not include the effect the changed DOM characteristichas on continued photooxidation [5].

Similarly, temperature dependence of bacterial degrada-tion has not been modelled explicitly, since the quality vari-able together with the epilimnion/hypolimnion division cap-tured the temperature dependence for the seasonal variationof organic matter degradation [14]. This means that themodel accounts for temperature dependence but that it can-not be used for elucidating the effects of temperature.

Most of the modelled DIC production was from al-lochthonous DOC, since the modelled primary production


Table 5Yearly modelled DOC inflow, DIC production, primary production and estimated sediment mineralisation.

Year DOC inflow DIC production DIC production Primary production Sediment mineralisationa

(103 kg C yr−1) (103 kg C yr−1) (% of DOC inflow) (103 kg C yr−1) (103 kg C yr−1)

1993 11000 290 3 – 901994 7000 280 4 – 901995 8000 320 4 – 901996 3000 190 6 – 601997 8000 270 3 – 90mean 7000 270 4 42 90

a Gross sedimentation was calculated from [13]. Mineralisation was assumed to be 30% [13].

was only 15% of the modelled DIC production in the wa-ter (table 5). Lake Örträsket is thus a net DIC producer il-lustrating the importance of allochthonous organic carbonfor the net balance of CO2 flux across the lake surface (cf.[2,4]). The total DIC production in Lake Örträsket is greaterthan predicted by our model, since we only modelled degra-dation of organic matter in the water column. A compar-ison between the modelled DIC production and annual or-ganic matter mineralisation estimated for the sediments inLake Örträsket [13] demonstrates that the sediment mineral-isation adds another 30% to the modelled pelagic mineral-isation. The water column is thus the most important DICproducing environment. The modelled pelagic degradationof allochthonous matter is small when compared with themodelled input of DOC to the lake. The modelled DIC pro-duction corresponded to only 3–6% of the annual modelledinflow of DOC to Lake Örträsket (table 5). This share isreasonable in a lake with such a short water renewal timeas Lake Örträsket and agrees with experimental data onthe short-term availability of Lake Örträsket DOC to bac-terial degradation [41]. However, degradation should havea more pronounced effect on DOC concentrations in lakeswith longer residence times than in Lake Örträsket. The to-tal effect of lake degradation in a catchment is also depen-dent on the number and size of lakes. Lake Örträsket rep-resents less than 3% of the total catchment area, while theaverage lake area in Sweden is close to 10%. Lakes withhigh inputs of allochthonous DOC may therefore constitutean important site for DIC production and be a quantitativelyimportant link of carbon transfer from land to atmosphere innorthern environments.

6. Conclusions

The physical model captures the main features of the lakefor different flow situations during the test period 1993 to1997. It reproduces the thermocline behaviour and the effectof meteorological forcing, although with some discrepan-cies. The most important shortcoming of the physical modelmay be the inflow routine, where the modelled temperatureof the inflow rules its inflow depth without considering anyentrainment processes.

The DOC model describes the main features of the carbonsystem, but leaves out details like temperature dependence ofbacterial degradation and includes many idealisations. Still,

it gives reasonable estimates of the DOC concentration inthe lake, demonstrating the importance of the discharge andthe model of DOC input. The modelled DOC concentrationof the inflow determines the DOC concentration of the lake,modelled degradation has a minor influence. It is thereforeinteresting to test the model on a long residence time lakewhere this is not the case. This is planned for the future.

The quality of allochthonous DOC is important for mod-elled degradation, since the modelled bacterial degradationrate depends on the modelled quality of DOC. The mod-elled DIC production in the lake amounts to 1.2–1.9 mg Cl−1 yr−1, of which photooxidation is responsible for approx.15% (table 4). The estimated photooxidation rate is a lowerlimit because PAR is mostly ignored. The modelled DICproduction in the lake is large compared to both estimatedsediment mineralisation and modelled primary production(table 5). Still, only 5% of the organic carbon entering thelake by modelled inflow is mineralised in the lake. Thisraises the question of how uncertainties in these data influ-ence the model. The most uncertain parameters may be veryinfluential, causing unreliable results, or may have rather lit-tle influence on the results. An investigation of uncertaintyand sensitivity of the model is a logical next step and hasbeen done with Monte Carlo simulation by Pers [10].

Despite the comments made above, the conclusion is thatthe model describes the DOC dynamics in a forest lake rea-sonably well. This indicates that the model explains the lakebehaviour and combines the main processes modelled, DOCconcentration of inflow, bacterial and photochemical degra-dation, DOC generation by primary production and lakephysics, in a reasonable way. To conclude, we have beenable to model the DOC degradation and DIC production ina typical forest lake in the temperate region of the NorthernHemisphere.

This or similar models can be useful tools for investigat-ing large-scale carbon dynamics in boreal catchments andalso for determining their sensitivity to altered conditions inrunoff and terrestrial DOC export, for example due to cli-mate changes. This conclusion is supported by a sensitivityanalysis [10], which shows that differences between seasonsand annual inflow are important for the sensitivity of DOCto different parts of the model. In general, bacterial degrada-tion rate, primary production and DOC concentration of in-flow have the highest effect on the sensitivity of the modelled


DOC concentration. To conclude, the mean DOC concentra-tion has an uncertainty of 2–4% (coefficient of variation).

Acknowledgements

The Swedish Natural Sciences Research Council has fi-nancially supported this work and the authors are grateful toall participants of the project “Aquatic Transport and Trans-formation of Organic Carbon – Links in the Carbon Trans-fer from Land to Sea”. The authors also want to acknowl-edge Jörgen Sahlberg for valuable model discussions and formaking the equation solver PROBE available, Anders Stige-brandt for valuable criticism and SMHI for supplying mete-orological data.

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Documents

Modelling Dissolved Organic Carbon Turnover in Humic Lake Örträsket, Sweden