The pCO2 in boreal lakes: Organic carbon as a universalpredictor?

Søren Larsen,1 Tom Andersen,1 and Dag O. Hessen1

Received 12 May 2010; revised 8 December 2010; accepted 15 February 2011; published 24 May 2011.

[1] During the past two decades, it has become evident that a majority of lakes arenet conduits of CO2 to the atmosphere. This insight has implications both for lakemetabolism per se and for assessing the role of lakes in the global C cycle. Theconcentration of dissolved organic carbon (DOC), which constitutes >90% of the totalorganic carbon (TOC), has been identified as a key driver of partial pressure of CO2 (pCO2).A crucial question is whether one may identify global relationships in the DOC‐pCO2

relationship in lakes or whether this has to be determined regionally or locally. Asecond major aspect is how to best predict CO2 as a function of DOC. Based on asurvey of pCO2 and a range of lake and catchment variables in 112 lakes, we supportthe view that DOC is by far the most important determinant of pCO2 while groundwaterinflux has a minor contribution. Contrary to expectations, total phosphorus (P) alsoapparently contributed positively to pCO2, owing to the fact that most P in these lakes ison the form of allochthonously organic P, and thus correlates strongly with DOC.Physical principles dictate that even a lake completely devoid of DOC should have anonzero pCO2. This is not reflected in power models, which imply that the pCO2

approaches zero with zero DOC. Based on this study as well as published data onDOC‐pCO2 relationships, we argue that identity link gamma–generalized linear modelsare appropriate for predicting pCO2 in lakes and that their application makes it possible toreach reasonably accurate global models for how pCO2 relates to DOC and otherenvironmental factors.

Citation: Larsen, S., T. Andersen, and D. O. Hessen (2011), The pCO2 in boreal lakes: Organic carbon as a universal predictor?,Global Biogeochem. Cycles, 25, GB2012, doi:10.1029/2010GB003864.

1. Introduction

[2] Freshwater systems constitute a comparatively smallproportion of our planet’s surface. The impact of freshwatersystems has therefore until recently, and still not infrequently,been considered marginal in the context of ecosystem feed-backs in the global carbon (C) cycle. Beginning in the early1990s it became clear, however, that freshwater ecosystemswere not only important conduits of CH4 [Kelly et al., 1997;Bastviken et al., 2004], but they were also commonly netheterotrophic, serving as sources of CO2 due to bacterialmineralization of terrestrially derived organic C [Hessenet al., 1990; Kling et al., 1991; Cole et al., 1994]. Build-ing on an increasing amount of evidence, the consensus isnow that CO2 supersaturation in circumboreal lakes is thenorm rather than the exception, and not only a property ofheavily colored humic lakes. Several reports suggest thatlakes, in disproportion to their relative area, are significantcomponents in the carbon budget of terrestrial ecosystemsand vent a considerable amount of CO2 to the atmosphere

[Dean and Gorham, 1998; Cole et al., 2007; Tranvik et al.,2009]. Hence, the conversion of organic to dissolved inor-ganic C (DIC), and the fate and flux of DIC has become amajor issue in the context of the global C cycle as well as forthe understanding of lake metabolism and C budget.[3] The literature offers a wide range of factors which

potentially regulate the degree of supersaturation of CO2 infreshwaters. The physical and morphometric propertiesof lakes (e.g., lake area, depth and temperature) influencethe net atmospheric gas exchange in several ways. Largeamounts of organic carbon are stored in lake sediments[Dean and Gorham, 1998; Tranvik et al., 2009], which,depending on redox conditions and mixing processes, mayserve as a source of CH4 or CO2 to the water column. Amajor fraction of produced CH4 may subsequently be con-verted to CO2 by water column methanotrophs [cf. Ruddand Hamilton, 1978; Hessen and Nygaard, 1992]. Thebathymetric properties of a lake determine the ratio of sed-iment surface to lake volume and thus, the impact of thesediment. Likewise, the ratio of lake area to lake volumemight determine the efficiency of gas exchange over thesurface. Lake area per se could also affect gas exchange asincreased fetch facilitates the wind induced mixing of thetop layer. Finally, solar irradiation may generate high levelsof photo‐oxidation of dissolved organic carbon (DOC) in

1Department of Biology, University of Oslo, Oslo, Norway.

Copyright 2011 by the American Geophysical Union.0886‐6236/11/2010GB003864

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surface layers [Granéli et al., 1998], while the solar heatingof the upper water column will in itself play a key role forCO2 exchange via the negative relationship between gassaturation and temperature.[4] Since the net CO2 exchange in ecosystems is primarily

governed by the balance between photosynthesis and res-piration, biotic processes have been the focus of moststudies on CO2 saturation in lakes. The concentration ofallochthonous DOC has been suggested as the main driver forthe flux of CO2 from lakes to the atmosphere [del Giorgio et al.,1997; Prairie et al., 2002;McCallister and del Giorgio, 2008],and in humic, or brown water lakes, the production of hetero-trophic bacteria is high and “subsidized” by allochthonous C[Hessen et al., 1990; Tranvik, 1990; Jansson et al., 2008].The veryC rich nature of both dissolved and particulatematterin many freshwater localities may further induce high respi-ratory disposal of “excess C” [cf. Hessen and Anderson,2008]. In‐lake processes are not the only source of lakeCO2 however. Some studies suggest that weathering pro-cesses as well as soil and root respiration may generate highlevels of CO2 in the catchment, which have been subse-quently transported to the lakes via groundwater or surface

flow. Such processes serve as another route of allochtho-nously generated CO2 in lakes [Rantakari and Kortelainen,2008], which have been reported to be of similar magnitudeas in‐lake DOC mineralization [Stets et al., 2009; Humborget al., 2009].[5] There seems to be a general consensus that, among

these factors, the concentration of DOC primarily sets thestage for the net exchange of inorganic C, but that there isalso a major variability in the DOC‐CO2 relationshipsowing to abiotic and biotic properties of the lakes and theircatchments. Furthermore, there may be interregional incon-sistencies in the slopes and intercepts of regression modelsrelating CO2 (actually, the partial pressure of CO2 − pCO2)to DOC [Roehm et al., 2009]. A crucial question is whetherone may identify global relationships in the DOC‐pCO2

relationship in lakes, or whether this has to be determinedregionally or locally. A second major aspect is how to bestpredict CO2 as a function of DOC. The general approach hasbeen to log transform both variables (to attain homosce-dasticity in the data set) and fit the data to a linear model(i.e., log(y) = log(a) + b log(x)), which is equivalent to apower function model when back‐transformed to a linearscale (i.e., y = axb). This approach implies that the pCO2

approaches zero with zero DOC. However, physical prin-ciples dictate that even a lake completely devoid of DOCshould have a nonzero pCO2 close to that of the air. Thus,it is reasonable to assume that a power function is not themost appropriate model for describing the relationshipbetween pCO2 and DOC. In this study, we have modeledpCO2 in lakes under the assumption that the relationbetween DOC and pCO2 is linear with a nonzero intercept.[6] Thus, while it is widely recognized that the vast

majority of boreal lakes are supersaturated with CO2, therole of DOC relative to other parameters still remains to besettled, and so do the issues of global versus local relation-ships, as well the statistical model chosen to represent thisrelationship. To assess these issues and explore the impactof a wider range of ambient parameters on lake pCO2, wesurveyed 112 lakes with respect to pCO2 and a range ofparameters related to lake water chemistry (total phosphorus,total nitrogen, chlorophyll, pH and sulfate), physical lakeproperties (surface area, altitude, depth and drainage arearatio), and watershed characteristics (runoff, annual air tem-perature, vegetation density (NDVI, Normalized DifferenceVegetation Index), slope and the catchment proportions ofbog, forest and farmland). The wide span of parameters andlake properties allowed us to examine the relative contributionof in‐lake processes, lake physical properties and watershedcharacteristics on the pCO2 in lakes. We also compare ourresults with various published models relating pCO2 in lakesto physical, chemical and catchment properties.

2. Methods

[7] This study was based on a regional lake surveycomprising 112 lakes in southern and central Norway(Figure 1). The lakes were chosen to ensure that all geo-graphical regions and a wide span in lake properties wererepresented. Each lake was sampled once during the day-time in October 2004. Most lakes were reached by hydro-plane that also was used as a platform for the sampling.

Figure 1. Map of southern Norway with the 112 localitiesrepresented as yellow disks with areas proportional to themeasured pCO2 (matm). The color code of the map repre-sents the fraction of land covered with bog. The rectanglein the map insert shows the global location.

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Samples for water quality parameters and pCO2 were takenat 0.7–1.0 m depth at the deepest part of the lake.[8] Analyses of pCO2 were done according to Sobek et al.

[2003] in duplicate 1.125 L bottles, flushed by at least twiceits volume by gently lowering the water sampler tube to thebottom of the bottle while ensuring that no bubbles weregenerated. Each bottle was sealed with a rubber stopperand inserted into separate thermoinsulated containers. Watertemperature at the time of sampling was measured with athermometer fitted inside the water sampler, which couldthen be compared to the water temperature at the time ofanalysis. The partial pressure of CO2 was analyzed in the fieldby infrared gas analysis of a 50 mL head space. The headspace was generated by gently injecting ambient air into thebottles with a plastic syringe while simultaneously with-drawing water. The bottles were shaken vigorously for twominutes to ensure gas equilibrium before gas was extractedand analyzed in an EGM‐4 high‐precision gas analyzer (PPSystems). Each replicate was analyzed twice to quantifymeasurement errors (mean coefficient of variation = 0.23%).Atmospheric CO2 partial pressure was recorded and thepCO2 in the water sample calculated by applying Henry’slaw to the partial pressure of CO2 in the head space and usingcorrection factors for temperature, atmospheric pressure, andCO2 introduced by injecting ambient air into the bottles. Themean coefficient of variation for duplicate samples was 0.96%.[9] Two separate 200 mL samples for chlorophyll quan-

tification were vacuum filtered on 25 mm Whatman GF/Ffilters on the day of sampling. The filtered volume wasreduced to 100 mL for samples with a visible high contentof chlorophyll. After filtration, the filters were placed in zip‐locked plastic bags and frozen in liquid nitrogen for laterchlorophyll extraction in acetone and fluorometric analysis.All other water chemistry parameters were analyzed by theaccredited laboratory at the Norwegian Institute for WaterResearch (NIVA) using standard methodology. In brief, totalphosphorus (TotP) was measured as PO4 by manual spec-trophotometry after wet oxidation with peroxodisulfate. Totalorganic carbon (TOC) was measured as CO2 after catalytichigh‐temperature combustion and detected by infrared gasanalysis. In general, the dissolved fraction of TOC (DOC)makes up >90% of TOC. Total nitrogen (TotN) was analyzedcolorimetrically in a segmented flow autoanalyzer afterconversion to NO3 by wet oxidation. The base cations Na, K,Mg and Ca, as proxies of groundwater influence, wereanalyzed by atomic absorption spectrophotometry. Cationconcentrations were corrected for seawater influence by sub-tracting the product of the Cl concentration and the respectiveCl to cation seawater ratios.[10] Key catchment properties (slope, area, altitude, NDVI,

runoff, temperature and the proportion of forest, bog andfarmland) were analyzed from digital maps with ESRIArcGis 9.3 geographic information system (GIS) using theextension of Hawth’s Analysis Tools (H. L. Beyer, Hawth’sanalysis tools for ArcGIS: Version 3.08, 2004; available athttp://www.spatialecology.com/htools). Runoff was repre-sented by averages over the period 1960–1990 obtainedfrom the Norwegian Water Resources and Energy Director-ate (NVE). Mean catchment slope and altitude were calcu-lated from a 1x1 km digital elevation model of Norwayfrom the Norwegian Mapping Authority (Statkart). Landarea use was extracted from 1:50k vector maps from Statkart.

NDVI was acquired as monthly composites from the U.SGeological Survey Eurasia Land Cover Characteristic data-base (http://edc2.usgs.gov/glcc/). Data on mean annual airtemperature were downloaded as a 1 × 1 km raster mapfrom the BioClim database [Hijmans et al., 2005] (http://www.worldclim.org/). Total catchment specific yearly runoffwas calculated as the product of area specific yearly runoff(mm yr−1) and catchment area (km2). Lake volumes were esti-mated from a power function of lake surface area, explain-ing 88% of the lake volume variation in an independent dataset from 490 Norwegian lakes (S. Larsen et al., manuscriptin preparation).[11] The pCO2 and TOC data exhibited a large degree of

heteroscedasticity such that a logarithmic transformationwould be the common remedy called for to reduce skew-ness. Since we consider a nonzero intercept be an importantfeature of the pCO2‐DOC relationship, we used generalizedlinear models (GLMs) [McCullagh and Nelder, 1989] basedon the gamma distribution with an identity link functioninstead of the canonical inverse link. The link function ina GLM is a transformation linking the expectation of theresponse variable to a linear predictor of the explanatoryvariables. Identity link means that it is the expectation of theuntransformed response variable which is predicted by theexplanatory variable(s). Modern statistics [e.g., Venablesand Ripley, 1999] uses the linear model as the commonterm for statistical models where the dependent variable ispredicted by a linear combination of the independent vari-ables, such as in multiple regression, analysis of variance andcombinations of these. The unexplained variation in thedependent variable of a linear model is assumed to beequivalent to that of the independent variable, normally dis-tributed noise with constant variance. Generalized linearmodels [McCullagh and Nelder, 1989] extend this concept tosituations where the dependent variable belongs to any dis-tribution of the exponential family, which includes binomial,Poisson, and gamma distributions as well as the normal dis-tribution. The linear predictor of a GLM is functionallyrelated to the expectation of the dependent variable by a linkfunction, which can be nonlinear.[12] The gamma distribution can be used to model contin-

uous, positive variables where the standard deviation is pro-portional to the mean, i.e., that have a constant coefficient ofvariation. This heteroscedasticity property is characteristicfor many types of chemical analysis, including measurementsof the partial pressure of CO2 in water. A gamma‐GLM withan identity link function is particularly suitable for modelingpCO2 because it both captures the heteroscedasticity of themeasurement errors and allows the predicted relationshipto have a nonzero intercept with the y axis.[13] In statistics tools like R, S+, or SAS, GLM models

are fitted by maximizing the likelihood of the observationsgiven the model parameters by iteratively reweighted leastsquares. The negative logarithm of the likelihood at the bestparameter fit can be partitioned into so‐called deviancecomponents, representing the contributions from the inde-pendent variables and the unexplained error to the totalvariation in the dependent variable. Deviance componentscan be compared by analysis of deviance, in direct analogywith the classical analysis of variance for normally distrib-uted variables. The negative log likelihood of a model isalso a key component of the Akaike information criterion

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(AIC) and other parsimony indicators, used for selecting thebest balance between goodness of fit and model complexity(number of model parameters or independent variables) instatistical modeling [Johnson and Omland, 2004].[14] Initially, we also tested generalized additive models

(GAMs) [Hastie and Tibshirani, 1997] which are able tocapture nonlinear relationships between dependent andindependent variables, but they failed to improve the pre-dictions beyond those of the GLM models.[15] Measured pCO2 in lakes was first fitted to univariate

gamma‐GLMs with an identity link to assess the predictivepowers of each of the independent variables. As this step,established TOC was by far the best predictor of pCO2, anda second set of GLMs using the same distribution andlink function were fitted to groups of covariate variables ininteraction with TOC to identify factors influencing thepCO2‐TOC relationship. The covariate groups were chosento reflect aspects of the origin and fate of TOC (lake physicalproperties, in‐lake processes and water chemistry, catchmentproperties and parameters related to groundwater influ-ence; see Table 1 for further details), Regression modelswere simplified by stepwise backward elimination usingmodel selection by the Bayesian information criterion (BIC)[Johnson and Omland, 2004]. All statistical analyses wereperformed with the R statistical programming environmentversion 2.6.1 [R Development Core Team, 2008].

3. Results

[16] All but three of the 112 lakes surveyed were super-saturated with pCO2, ranging from 351 matm (slightly

undersaturated) to 2512 matm (sevenfold supersaturation).Mean pCO2 was 774 matm and 74% of the lakes were morethan >150% supersaturated (Figure 1).[17] pCO2 had statistically significant relationships with

21 of the 26 tested variables in the single‐predictor models(Table 1), but TOC was by a good margin the best predictor.The identity link gamma‐GLM model with TOC as thepredictor (pCO2 = 426 (23.5) + 90.5 (7.7) TOC; numbers inparentheses are standard errors) explained 69% of the totaldeviance. The model intercept (426) was within the 95%confidence interval for air pCO2 (356–434). For comparisonwith the power function used in other studies, we alsofitted a linear model on log‐transformed pCO2 and TOC:log10(pCO2) = 2.72 (0.014) + 0.329 (0.023) log10(TOC).The power function model explained 65% of the variation inpCO2, but the model did not capture the asymptoticbehavior at low TOC in the data set. Furthermore, applyingthe two modeling approaches to subranges of the data sets(above and below the median TOC) revealed the powerfunction model to be less robust to the underlying range ofdata than the identity link gamma‐GLM model (Figure 2).The sample with the highest value for pCO2 (2512 matm)was identified as an influential outlier with high leverage.Omitting the outlier from the model resulted in an increasein the amount of variance explained to 73% for the GLMmodel and 67% for the power function model, while themodel coefficients remained within the original confidenceareas.[18] Having established TOC as the best predictor of

pCO2 in our data set, we proceeded to investigate how otherfactors may modify the effect of TOC on pCO2. We did this

Table 1. Single‐Predictor Gamma‐GLM Models With Identity Link for pCO2 Sorted by Goodness of Fita

Variable Unit Mean Median Range Transformation p Value R2

TOC mg L−1 3.9 3.1 0.250–24.6 None <2E‐16 0.73TotPb mg L−1 3.3 4.0 0.9–20 Log10 <2E‐16 0.55bogc % 3.63 2.32 0–17 Arcsin Sqrt <2E‐16 0.51Forestc % 41.4 36.8 0–88 Arcsin Sqrt <2E‐16 0.50TotNb mg L−1 265 255 42–645 None <2E‐16 0.49NDVIc Index 130 132 104–149 None 3.70E‐16 0.47Altituded M 464 392 10–1329 None 2.33E‐14 0.41Runoffc mm yr−1 1750 1411 341–6350 Log10 5.71E‐08 0.26Water temperature °C 7.55 7.60 2.3–12.2 None 6.45E‐08 0.25Ke mg L−1 0.23 0.18 0.04–0.84 Log10 6.04E‐07 0.24Air temperaturec °C 33.0 33.5 −2–7.5 None 2.69E‐07 0.23SO4

b mgS L−1 1.75 1.43 0.5–8.08 Log10 4.31E‐07 0.22Cae mg L−1 1.23 0.89 0.13–5.14 Log10 3.29E‐06 0.18Mge mg L−1 0.30 0.24 0.06–1.05 Log10 8.1E‐06 0.17Farmlandc % 0.508 0 0–0.5 Arcsin Sqrt 7.53E‐04 0.16Area ratioc ratio 0.096 0.074 0.004–0.470 Log10 3.49E‐04 0.13ANCe meq/L 48.9 33.3 −14.59–237 None 2.14E‐03 0.12Slopec degree 6.7 5.6 0.745–24.7 Log10 3.7E‐03 0.10Nae mg L−1 1.72 1.26 0.28–7.22 Log10 0.0124 0.08Depthd M 33.4 29 4–102 Log10 0.0234 0.06Catchment areac Km2 37.5 8.9 1.25–463 Log10 0.154 0.02N depositionc mg m−2 yr−1 0.68 0.70 0.251–1.08 None 0.343 0.01Lake aread Km2 1.7 0.7 0.02–21.7 Log10 0.316 0.01chlb mg L−1 0.79 0.60 0.07–3.7 Log10 0.923 0.00pHb 5.89 5.90 4.6–7.0 None 0.0612 0.4 × 10−3

Residence timec Years 1.05 0.56 0.004–9.27 Log10 0.913 0.9 × 10−4

aEach predictor variable is identified by name, unit, mean, median, range and transformation, as well as significance probability (p value) and fraction oftotal deviance explained by the corresponding regression model (R2).

bLake water chemistry.cCatchment properties.dLake physical properties.eGroundwater influence.

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by fitting gamma‐GLM models using three sets of variableschosen to represent different environmental factors (lake,water and catchment properties) either alone or in interac-tion with TOC (Table 2). Among the variables representingphysical properties of the lakes, only altitude and depthgave significant contributions and were thus included thefinal model, which explained 46% of the variation in pCO2

(Table 2). With TOC included in the model, 79% of thevariation in pCO2 was explained by TOC and its interac-tions with altitude and lake area. The effect of TOC onpCO2 decreased with increasing lake area and increasingaltitude.[19] The model based on parameters related to lake water

chemistry and in‐lake processes explained 62% of the var-iation. Unsurprisingly, Chla had a negative effect on pCO2,while the opposite was true for TotP and TotN. There

were no significant interactions with TOC in this subset ofvariables.[20] When catchment properties were considered alone,

five variables (Table 2) contributed significantly in a modelthat explained 69% of the variation in pCO2, while 86% wasexplained when TOC was also included in the model. Theinteractions in the latter model suggest that the effect ofTOC on pCO2 increases with N deposition and area ratiowhile it declines with the area‐specific runoff and residencetime. Air temperature, spanning 9.5°C across the data set,gave no significant contribution.[21] Parameters related to the influx of groundwater (Ca,

Mg, Na, K and ANC) explained 23% of the variation inpCO2 (Table 2). However, combining groundwater indicatorvariables together with TOC increased the amount of vari-ance explained to 83%.

Figure 2. Relationship between pCO2 and TOC fitted to the identity link gamma‐GLM model (solidlines) and the power function model (dashed lines). (left) The full data set and (middle and right) corre-sponding models fitted to subsets above or below the median TOC (represented by vertical solid lines).Horizontal lines indicate the mean and 95% confidence interval for ambient air pCO2.

Table 2. Identity Link Gamma‐GLM Models Using Different Sets of Predictor Variables Representing Lake, Water, and CatchmentProperties as Well as Groundwater Indicators, Alone or in Interaction With TOCa

Model Single Variable Effects TOC Interactions R2 BIC

Lake properties altitude (−), depth (−), lake area (ns) Not included in model 0.46 1538.8Lake properties and TOC TOC (+), altitude (−), depth (ns), lake area (ns) TOC:altitude (−), TOC:lake area (−) 0.79 1430.8Water chemistry TotP (+), TotN (+), pH (ns), SO4 (ns), chl (−) Not included in model 0.62 1465.6Water chemistry and TOC TOC (+), TotP (+), TotN,(ns) pH(ns), SO4(ns), chl(−) No significant interactions 0.74 1424.4Catchment slope (ns), air temperature (ns), runoff (ns),

NDVI (ns), Ndep (ns), forest (+), bog (+),catchment area (−), farmland (+),area ratio (−), residence time (ns)

Not included in model 0.69 1474.7

Catchment and TOC TOC (+), slope (ns), air temperature (ns), runoff (+),NDVI (+), N deposition (−), forest (+),bog (ns), catchment area (−),arable (+), area ratio (−),residence time (+)

TOC:Ndep (+), TOC:runoff (−),TOC:area ratio (+),TOC:residence time (−)

0.85 1375.6

Groundwater indicator variables anc (ns), Ca (ns), Mg (ns), K (+), Na (ns) Not included in model 0.23 1481.6Groundwater indicators and TOC TOC (+), anc (ns), Ca (−),

Mg (−), K (+), Na (ns)None 0.83 1329.5

aSignificant single variable or interaction effects are marked with plus signs or minus signs for positive or negative regression coefficients, whilenonsignificant effects are marked with ns. R2 represents the fraction of total deviance explained in the models resulting from a backward eliminationprocess based on the Bayesian information criterion (BIC).

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4. Discussion

[22] By far, the best single predictor of pCO2 was TOC.The six next‐ranking predictors in Table 1 probably all owetheir positions to direct or indirect relationships with TOC.In these pristine catchments, both total N and P are mostly inorganic form and are closely correlated with TOC [Meili,1992; Hessen et al., 2009], and may thus act primarily asproxies for TOC. This confounding with TOC probablyoverruns the expected negative effect of total P on pCO2

through stimulating primary production [cf. del Giorgio andPeters, 1994; Hanson et al., 2004]. The positive effect ofN and P on pCO2 in high TOC lakes may also partly workthrough stimulating bacterial mineralization of organicmatter. The strong positive single‐predictor effects of catch-ment vegetation properties (forest, bog and NDVI) probablyreflect their role as TOC sources, while the negative effectof altitude is related to the general decrease in vegetationdensity with elevation. The five nonsignificant single‐predictor variables in Table 1 (catchment area, lake area, Ndeposition, chlorophyll and water residence time) all hadsignificant contributions as covariates with other explana-tory variables, or in interaction with TOC (Table 2).[23] The multiple‐predictor model using only the physical

properties of the lakes (altitude, lake depth and lake area)as covariates explained 46% of the pCO2 variation, whichincreased to 79%when interactions with TOCwere included.The negative interaction effect of altitude with TOC couldindicate qualitative changes in TOC related to its terrestrialsource. The negative interaction effect between TOC andlake area could be related to increased physical degassing ofCO2 with wind fetch, which would be positively related tolake surface area.[24] The multiple‐predictor model using only water

quality variables (total P, chlorophyll, pH and SO4) ascovariates explained 62% of the total deviance. The con-trasting effects of chlorophyll and total P is attributed tothe fact that total P correlates positively with TOC (r = 0.69,p < 2.2e−16), and probably acts as a proxy for it when TOCis absent from the model. By including TOC as a predictorvariable, the water chemistry related variables explained74% of the deviance, which was only slightly more thanthe model with TOC as a single predictor. While chloro-phyll, as a proxy for phytoplankton biomass, had no sig-nificant effect on pCO2 by itself (Table 1), it had negativecontributions both when combined with other water qualityvariables, and in interaction with TOC (Table 2). The appar-ently minor role of chlorophyll in this survey could also beaffected by the samples being taken late in the growing season.[25] The multipredictor model with catchment related

parameters alone explained 69% of the variation in pCO2,with significant positive contributions from fractional cov-erage of forest, bog and farmland and negative contributionsfrom catchment area and the lake to catchment area ratio.Although the degree of explanatory power of this modelwas somewhat less than the one with TOC as a singlepredictor (Table 1), it still had higher power for predictingpCO2 than what has been reported in many other studies[del Giorgio et al., 1999; Jonsson et al., 2003; Kelly et al.,2001; Prairie et al., 2002; Rantakari and Kortelainen, 2005;Roehm et al., 2009; Sobek et al., 2003]. The predictivepower is particularly notable when considering that this

model involves no variables that require actual water sam-pling; all the relevant catchment property parameters can beextracted from remote sensing products and digital land use,elevation and hydrology maps.[26] Including both catchment properties and their inter-

actions with TOC gave by far the best model for predictingpCO2, explaining 85% of the total deviance. While DOCderived from bogs is expected to be older and more recal-citrant than DOC from other sources, the absence of sig-nificant interaction effects between bog or forest cover andTOC indicates that such effects played a minor role in ourdata set. The significant positive interaction between TOCand N deposition may indicate that TOC mineralizationincreases with increased nitrogen deposition.[27] Inflow of CO2‐supersaturated groundwater could also

serve as an important source of pCO2 in lakes. Based on astudy of more than 20,000 Swedish lakes, Humborg et al.[2009] claimed that the importance of groundwater was inthe same order of magnitude as DOC. Groundwater influxcould explain some 20–30% of the variation in pCO2, whichis consistent with the findings in our study (R2 = 0.27). Thereported contribution of TOC to pCO2 was no more than21%, however, in contrast to the 73% of variance explainedby TOC alone in our study. Humborg et al. did not measurepCO2 directly but estimated this from lake chemistry vari-ables. While this may have introduced some scatter in theirdata, it still does not explain why they arrived at such a lowimpact of DOC. The majority of the lakes in our study arelocated at relatively high altitude with a thin layer of topsoiland in areas dominated by bedrock which does not facilitatedeep water infiltration. It is also noteworthy that, in ourstudy, the best the best model according to the AIC valuewas based on TOC and K combined, which explained 83%of the observed variation in pCO2. Assuming that K servesas a good proxy of groundwater impact, it lends supportto the idea that groundwater has a significant contribution topCO2 in the studied lakes, albeit the contribution seems to berelatively minor compared to other studies [e.g., Humborget al., 2009].[28] Acknowledging DOC as the key predictor of pCO2, it

would be of major interest to assess the potential of thisparameter for global prediction of pCO2 in lakes. Roehmet al. [2009] claimed that the different sources and types ofDOC only allows for regional models, and support this by acomparison of empirical models of lake pCO2 as a functionDOC from different regions of the world. In their com-mentary to Figure 6 of Roehm et al. [2009], they point tothe regionally different intercepts and slopes, leading themto conclude that “This pattern would suggest that changesin DOC loading or input to lakes have very different con-sequences in terms of surface water pCO2 in lakes of differentregions, and this in turn could be related to fundamentaldifferences in the nature of the DOC among regions.” Asmentioned in our introduction, there is however no a priorireason to presume that a power function is the most ade-quate model for describing the relationship between pCO2

and DOC. In fact, elementary physical considerations speakagainst this, suggesting a nonzero intercept model such asthe identity link gamma‐GLM models which we have usedin this work.[29] Neither the gamma‐GLM model nor the power

function models managed to fully capture the relationship

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between pCO2 and TOC in Figure 2. The sensitivity of thepower function models to subsets of the data range resultedin very different models with overabundances of positiveresiduals at either the high or the low end of the TOC gradient.The gamma‐GLM model seemed to overestimate pCO2 atlow TOC values, but was less affected by the subsetting ofthe data set. Thus, the gamma‐GLM is more robust, with nodifference in slope over data ranges, while the slopes of thepower models depend on data range. Furthermore, a directcomparison of the fraction of deviance explained (R2) is infavor of the gamma‐GLM, which has the added advantageof producing physically plausible predictions when extrap-olated to zero TOC.[30] To further explore this, we gathered a wide range of

literature data sets (some transcribed from tables, but mostdigitized from published figures) for comparing the perfor-mances of the two modeling approaches (Figure 3). Theamount of variance explained by the GLM models were

equal to or larger than the amount of variance explained bythe power function models (Table 3). As expected fromRoehm et al. [2009], there is a wide span in the powerfunction model slopes and intercepts, which is not reflectedin the corresponding gamma‐GLM models. It should benoted that the while the power function approach does notcatch the asymptote at low TOC, the identity link gamma‐GLM models do. The intercepts in the gamma‐GLM modelscan be taken as estimates of pCO2 when no TOC is present.The gamma‐GLM model based on the entire data collectionhas an intercept at 361 ppm CO2. This value is consistentwith the range of literature values on the partial pressure ofCO2 in the ambient air, and with a priori considerations.This analysis suggests that the identity link gamma‐GLMapproach should be preferred over the power functionmodel. Furthermore, the apparent regional‐specific differ-ences in the correlation between DOC and pCO2 could be anartifact stemming from the power function model applied to

Figure 3. The relation between literature values of DOC and pCO2. (left) The power function approachgenerates models with highly variable intercepts and slopes, and (right) the identity link gamma‐GLMapproach reduces the apparent dissimilarity between models based on data from different regions. Greenlines, del Giorgio et al. [1999]; red lines, Sobek et al. [2003]; blue lines, Jonsson et al. [2003]; yellowlines, Roehm et al. [2009]; orange lines, Humborg et al. [2009]; black lines, this study; gray lines, all data.

Table 3. Power Function Model and Gamma‐GLM Model Summaries on pCO2 as a Function of DOCa

Reference

Power Function Model Gamma‐GLM Model

R2 Intercept Coefficient R2 Intercept Coefficient

del Giorgio et al. [1999] 0.06 2.52 (0.26) 0.39 (0.38)b 0.12 349 (166.6)b 64.3 (35.0)b

Sobek et al. [2003] 0.51 2.26 (0.09) 0.80 (0.09) 0.52 212 (110.8) 110.1 (11.9)Jonsson et al. [2003] 0.57 2.48 (0.04) 0.42 (0.05) 0.58 276 (34.34) 65.1 (8.6)Roehm et al. [2009] 0.39 2.26 (0.08) 0.61 (0.09) 0.43 238 (74.3) 53.5 (9.0)Humborg et al. [2009] 0.23 2.50 (0.10) 0.68 (0.11) 0.27 517 (163.6) 123.1 (19.8)This paper 0.65 2.7 (0.01) 0.33 (0.02) 0.69 426 (23.5) 100.5 (8.6)All data 0.46 2.59 (0.02) 0.46 (0.03) 0.48 360 (29.7) 95.4 (5.2)

aThe data originated from literature data sets; some transcribed from tables, but most digitized from published figures. In power function models, log‐transformed variables are fitted to a linear model (i.e., log10(pCO2) = log(a) + b log10(DOC), which is equal to pCO2 = a * DOCb), while gamma‐GLMmodels treat the relation between DOC and pCO2 as linear with a nonzero intercept (i.e., pCO2 = a + b*DOC). R2 under the power function modelsrepresents the fraction of total variance explained (i.e., the ratio of residual and total sum of squares). It is conceptually comparable to R2 under thegamma‐GLM model, which can also be generalized as the ratio of deviance explained by the model to the total deviance. Values in parentheses arestandard errors.

bNot significant.

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data sets with different ranges of DOC. This concern shouldbe addressed in future studies before making conclusionsabout regional differences in the nature of DOC and howthis may influence the relationship between organic carbonand pCO2 in lakes.[31] TOC was by far the most significant predictor vari-

able for the partial pressure of carbon dioxide in Norwegiansurface waters, while a suite of catchment property para-meters also gave significant, but minor contributions. Thisstudy supports the hypothesis that the elevated pCO2 inlakes primarily stems from microbial mineralization ofallochthonous DOC. It also suggests that identity linkgamma‐GLM models are more appropriate for predictingpCO2 in lakes, and that their application makes it possibleto reach reasonably accurate global models for how pCO2

relates to DOC and other environmental factors.

[32] Acknowledgments. We acknowledge the Norwegian Institute ofWater Research for providing access to chemical data from the sampledlakes. This work was covered by grants from the Norwegian ResearchCouncil project 165139 “Biogeochemistry in Northern Watersheds, a Reactorin Global Change” to D.O.H. and project 196336 “Biodiversity, communitysaturation, and ecosystem function in lakes” to T.A.

ReferencesBastviken, D., J. Cole, M. Pace, and L. Tranvik (2004), Methane emissionsfrom lakes: Dependence of lake characteristics, two regional assessments,and a global estimate, Global Biogeochem. Cycles, 18, GB4009,doi:10.1029/2004GB002238.

Cole, J. J., N. F. Caraco, G. W. Kling, and T. K. Kratz (1994), Carbondioxide supersaturation in the surface waters of lakes, Science, 265,1568–1570, doi:10.1126/science.265.5178.1568.

Cole, J. J., Y. T. Prairie, N. F. Caraco, W. H. McDowell, L. J. Tranvik, R. G.Striegl, C. M. Duarte, P. Kortelainen, J. A. Downing, and J. J. Middelburg(2007), Plumbing the global carbon cycle: Integrating inland waters intothe terrestrial carbon budget, Ecosystems, 10, 172–185, doi:10.1007/s10021-006-9013-8.

Dean, W. E., and E. Gorham (1998), Magnitude and significance of carbonburial in lakes, reservoirs, and peatlands, Geology, 26, 535–538,doi:10.1130/0091-7613(1998)026<0535:MASOCB>2.3.CO;2.

del Giorgio, P. A., and R. H. Peters (1994), Patterns in planktonic P:Rratios in lakes: Influence of lake trophy and dissolved organic carbon,Limnol. Oceanogr., 39, 772–787, doi:10.4319/lo.1994.39.4.0772.

del Giorgio, P. A., J. J. Cole, and A. Cimbleris (1997), Respiration rates inbacteria exceed phytoplankton production in unproductive aquatic sys-tems, Nature, 385(6612), 148–151, doi:10.1038/385148a0.

del Giorgio, P. A, J. J. Cole, N. F. Caraco, and R. H. Peters (1999), Linkingplanktonic biomass and metabolism to net gas fluxes in northern temperatelakes, Ecology, 80, 1422–1431, doi:10.1890/0012-9658(1999)080[1422:LPBAMT]2.0.CO;2.

Granéli, W., M. Lindell, B. Marçal de Faria, and F. de Assis Esteves(1998), Photoproduction of dissolved inorganic carbon in temperateand tropical lakes—Dependence on wavelength band and dissolvedorganic carbon concentration, Biogeochemistry, 43, 175–195,doi:10.1023/A:1006042629565.

Hanson, P. C., A. I. Pollard, D. L. Bade, K. Predick, S. R. Carpenter, andJ. A. Foley (2004), A model of carbon evasion and sedimentation intemperate lakes, Global Change Biol., 10, 1285–1298, doi:10.1111/j.1529-8817.2003.00805.x.

Hastie, T. J., and R. J. Tibshirani (1997), Generalized Additive Models,Chapman and Hall, London.

Hessen, D. O., and T. R. Anderson (2008), Excess carbon in aquatic organismsand ecosystems: Physiological, ecological, and evolutionary implications,Limnol. Oceanogr., 53, 1685–1696, doi:10.4319/lo.2008.53.4.1685.

Hessen, D. O., and K. Nygaard (1992), Bacterial transfer of methane anddetritus: Implications for the pelagic carbon budget and gaseous release,Arch. Hydrobiol. Beih. Ergebn. Limnol., 37, 139–148.

Hessen, D. O., T. Andersen, and A. Lyche (1990), Carbon metabolism ina humic lake: Pool sizes and cycling through zooplankton, Limnol.Oceanogr., 35, 84–99, doi:10.4319/lo.1990.35.1.0084.

Hessen, D. O., T. Andersen, S. Larsen, B. L. Skjelkvåle, and H. A. de Wit(2009), Nitrogen deposition, catchment productivity, and climate as deter-

minants of lake stoichiometry, Limnol. Oceanogr., 54, 2520–2528,doi:10.4319/lo.2009.54.6_part_2.2520.

Hijmans, R. J., S. E. Cameron, J. L. Parra, P. G. Jones, and A. Jarvis(2005), Very high resolution interpolated climate surfaces for global landareas, Int. J. Climatol., 25, 1965–1978, doi:10.1002/joc.1276.

Humborg, C., C.‐M.Mörth,M. Sundbom, H. Borg, T. Blenckner, R. Giesler,and V. Ittekkot (2009), CO2 supersaturation along the aquatic conduitin Swedish watersheds as constrained by terrestrial respiration, aquaticrespiration and weathering, Global Change Biol., 16, 1966–1978.

Jansson, M., T. Hickler, A. Jonsson, and J. Karlsson (2008), Links betweenterrestrial primary production and bacterial production and respirationin lakes in a climate gradient in subarctic Sweden, Ecosystems, 11,367–376, doi:10.1007/s10021-008-9127-2.

Johnson, J. B., andK. S. Omland (2004),Model selection in ecology and evo-lution, Trends Ecol. Evol., 19, 101–108, doi:10.1016/j.tree.2003.10.013.

Jonsson, A., J. Karlsson, and M. Jansson (2003), Sources of carbondioxide supersaturation in clearwater and humic lakes in northern Sweden,Ecosystems, 6, 224–235, doi:10.1007/s10021-002-0200-y.

Kelly, C. A., J. W. M. Rudd, R. A. Bodaly, N. P. Roulet, V. L. St. Louis,A. Heyes, T. R. Moore, S. Schiff, R. Aravena, and K. J. Scott (1997),Increases in fluxes of greenhouse gases and methyl mercury followingflooding of an experimental reservoir, Environ. Sci. Technol., 31, 1334–1344, doi:10.1021/es9604931.

Kelly, C. A., E. Fee, P. S. Ramlal, J. W. M. Rudd, R. H. Hesslein, C. Anema,and E. U. Schindler (2001), Natural variability of carbon dioxide and netepilimnetic production in the surface waters of boreal lakes of differentsizes, Limnol. Oceanogr., 46, 1054–1064.

Kling, G. W., G. W. Kipphut, and M. C. Miller (1991), Arctic lakes andstreams as gas conduits to the atmosphere: Implications for tundra carbonbudgets, Science, 251, 298–301, doi:10.1126/science.251.4991.298.

McCallister, S. L., and P. A. del Giorgio (2008), Direct measurement of thed13C signature of carbon respired by bacteria in lakes: Linkages to poten-tial carbon sources, ecosystem baseline metabolism, and CO2 fluxes,Limnol. Oceanogr., 53, 1204–1216, doi:10.4319/lo.2008.53.4.1204.

McCullagh, P., and J. A. Nelder (1989), Generalized Linear Models,Chapman and Hall, London.

Meili, M. (1992), Sources, concentrations and characteristics of organicmatter in softwater lakes and streams of the Swedish forest region,Hydrobiologia, 229, 23–41, doi:10.1007/BF00006988.

Prairie, Y. T., D. F. Bird, and J. J. Cole (2002), The summer metabolic bal-ance in the epilimnion of southeastern Quebec lakes, Limnol. Oceanogr.,47, 316–321, doi:10.4319/lo.2002.47.1.0316.

Rantakari, M., and P. Kortelainen (2005), Interannual variation and climaticregulation of the CO2 emission from large boreal lakes, Global ChangeBiol., 11, 1368–1380, doi:10.1111/j.1365-2486.2005.00982.x.

Rantakari, M., and P. Kortelainen (2008), Controls of organic and inor-ganic carbon in randomly selected Boreal lakes in varied catchments,Biogeochemistry, 91, 151–162, doi:10.1007/s10533-008-9266-8.

R Development Core Team (2008), R: A Language and Environment forStatistical Computing, R Found. for Stat. Comput., Vienna. [Availableat http://www.R‐project.org.]

Roehm, C. L., Y. T. Prairie, and P. A. del Giorgio (2009), The pCO2dynamics in lakes in the boreal region of northern Québec, Canada,Global Biogeochem. Cycles, 23, GB3013, doi:10.1029/2008GB003297.

Rudd, J. W. M., and R. D. Hamilton (1978), Methane cycling in a eutrophicshield lake and its effects on whole lake metabolism, Limnol. Oceanogr.,23, 337–348, doi:10.4319/lo.1978.23.2.0337.

Sobek, S., G.Algesten, A.‐K.Bergstrom,M. Jansson, andL. J. Tranvik (2003),The catchment and climate regulation of pCO2 in boreal lakes, GlobalChange Biol., 9, 630–641, doi:10.1046/j.1365-2486.2003.00619.x.

Stets, E. G., R. G. Striegl, G. R. Aiken, D. O. Rosenberry, and T. C. Winter(2009), Hydrologic support of carbon dioxide flux revealed by whole‐lake carbon budgets, J. Geophys. Res., 114, G01008, doi:10.1029/2008JG000783.

Tranvik, L. J. (1990), Bacterioplankton growth on fractions of dissolvedorganic carbon of different molecular weights from humic and clearwaters, Appl. Environ. Microbiol., 56, 1672–1677.

Tranvik, L. J., et al. (2009), Lakes and reservoirs as regulators of carboncycling and climate, Limnol. Oceanogr., 54, 2298–2314, doi:10.4319/lo.2009.54.6_part_2.2298.

Venables, W. N., and B. D. Ripley (1999), Modern Applied Statistics WithS‐PLUS, 3rd ed., Springer, New York.

T. Andersen, D. O. Hessen, and S. Larsen, Department of Biology,University of Oslo, PO Box 1066 Blindern, N‐0316 Oslo, Norway.(soren.larsen@gmail.com)

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