LETTERSPUBLISHED ONLINE: 23 MAY 2016 | DOI: 10.1038/NGEO2720

Organic carbon decomposition rates controlled bywater retention time across inland watersNúria Catalán1*, Rafael Marcé2, Dolly N. Kothawala3 and Lars. J. Tranvik1

The loss of organic carbon during passage through thecontinuum of inland waters from soils to the sea is acritical component of the global carbon cycle1–3. Yet, theamount of organic carbon mineralized and released to theatmosphere during its transport remains an open question2,4–6,hampered by the absence of a common predictor of organiccarbon decay rates1,7. Here we analyse a compilation ofexisting field and laboratory measurements of organic carbondecay rates and water residence times across a wide rangeof aquatic ecosystems and climates. We find a negativerelationship between the rate of organic carbon decay andwater retention time across systems, entailing a decrease inorganic carbon reactivity along the continuumof inlandwaters.We find that the half-life of organic carbon is short in inlandwaters (2.5 ± 4.7 yr) compared to terrestrial soils and marineecosystems, highlighting that freshwaters are hotspots oforganic carbon degradation. Finally, we evaluate the responseof organic carbon decay rates to projected changes in runo�8.We calculate that regions projected to become drier or wetteras the global climate warms will experience changes in organiccarbon decay rates of up to about 10%, which illustratesthe influence of hydrological variability on the inland waterscarbon cycle.

Each year, around 2 Pg of carbon originating from terrestrialecosystems are lost during transport through inland waters1–3.Emission to the atmosphere as carbon dioxide (CO2)5 and methane(CH4)9, due to photo- and biodegradation processes acting onorganic carbon (OC), account for most of these losses, but theyalso include sedimentation and burial within freshwater systems1.Despite the global relevance of OC losses in inland waters10 andnumerous studies on the kinetics of OC decay11,12, the controlof decay rates along the continuum of inland waters is poorlydefined. Consequently, determining the factors that define changesin OC loss rates remains a major obstacle to predicting thefate of OC and, consequently, to the development of globalbiogeochemical models13.

Time has been identified as an important constraint onthe decomposition and preservation of OC stored in marinesediments14,15, where OC loss rates have been found to decrease asa function of time after settling onto the sediment (congruent withsediment depth14). Accordingly, the mineralization of OC inmarinewaters slows down as it descends through the water column16,17,but a global empirical relationship between time of downwardtransport and decay rates has yet to be proposed13. In inlandwaters, attempts have been made to assess the variability of OC lossthrough the aquatic continuum18,19. Previous studies assessing the

log[water retention time (yr)]

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Figure 1 | Regression between the log-transformed water retention time(WRT) and decay rates of organic carbon (OC). The data set spans acrossa multitude of freshwater systems, including bioassays, field studies andseveral biomes. Open symbols correspond to ocean (WRT over centuries)and artificial substrates (WRT of hours) that are excluded from the analysis.Blue dashed lines represent the 95% confidence interval in the regressionparameters, and red dotted lines represent the 95% prediction interval.

relationship between decay rates and water retention time (WRT)20have found encouraging patterns within regional catchments21 andgroups of lakes22. Building on this, we postulate that OC decayrates are dependent onWRT, and that this relationship holds acrosslaboratory and field methods, ecosystems and geographical regions.

The kinetics of OC degradation have been studied using severalempirical models23–25. Here we examine a continuous and directdependence of the OC degradation rate on WRT. We hypothesizethat the OC pool will gradually lose the most-reactive componentsas it passes through the aquatic continuum, in accordance withwhat has been observed in marine environments17,25. Conceptually,different segments of the aquatic continuum can be regarded asa series of interconnected water bodies existing in steady state,and therefore an OC decay rate (k) unique to each segment canbe determined. In this way, we can apply a single exponential

1Limnology/Department of Ecology and Genetics, Uppsala University, 75236 Uppsala, Sweden. 2Catalan Institute for Water Research (ICRA), Emili Grahit101, 17003 Girona, Spain. 3Department of Aquatic Sciences and Assessment, Swedish University of Agricultural Sciences, 75007 Uppsala, Sweden.*e-mail: nuria.catalan@ebc.uu.se, ncatalangarcia@gmail.com

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LETTERS NATURE GEOSCIENCE DOI: 10.1038/NGEO2720

log[retention time (yr)]

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OC

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r−1)]

10 yr 100 yr1 yr1 d 1 m

−6 −4 −2

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Figure 2 | Comparison of the relationship for inland waters and marinesediments. The relationship between retention time and OC decay rate kfollows the same pattern for field data in Middleburg (1989; open squares:marine sediments), and for this study (grey circles: inland waters).

decay model for each compartment of the aquatic continuum,k= ln (OCt/OC0)/t , where OCt and OC0 are the organic carbonconcentrations at time t and at initial time, respectively. From thevalues of k, we obtain the half-life of OC using t1/2= ln(2)/k.

We compiled 315measurements of OC decay rates, derived from208 bioassay and 107 field studies (Supplementary Information 1.1).The data set spans eight orders of magnitude for both k and WRT,from hours to centuries. Different aquatic systems are considered,including streams, rivers, lakes, reservoirs, catchments, wetlandsand estuaries covering ten climatic regions of the Köppen–Geigerclassification26, mainly centred in temperate and boreal biomes(Supplementary Excel Table).

Our results show that the decay rate of OC in inland waters issignificantly and negatively related with WRT (r 2=0.41; p<0.001;n = 315, Fig. 1 and Supplementary Information 2). In systemswith longer WRT, decay rates are slower. This relationship fits theequation: log k=−0.45 (±0.08) log WRT −0.96 (±0.03), wherethe number in brackets corresponds to the standard deviation(s.d.) of the slope and intercept derived from uncertainty analysis(Supplementary Information 2.1). The mean WRT across inlandwaters was 1.5 yr (s.d. ± 3.7 yr) and the mean decay rate k was2.37 yr−1 (s.d. ± 4.4 yr−1) (Supplementary Information 1). Thisempirical relationship suggests that an increasing time of OCexposure to mineralization across the continuum of inland waters,measured as WRT, results in a decreasing decay rate. Accordingto the reactivity continuum models of OC decay12,14, changesin OC during mineralization affect the decay rate. Therefore,the composition of OC becomes skewed towards compoundsthat are degraded more slowly with increasing WRT, resultingin a downstream continuum of overall OC reactivity alonginland waters. This continuum of reactivity has been related tocompositional changes in OC, as illustrated by the links foundbetween OC molecular composition and WRT27 in lakes, or thepredicted distribution of organic compound diversity along theRiver Continuum Concept28. Moreover, the relationship presentedhere is in agreement with previous studies linking OC loss withretention time in the boreal region20,21, and is especially close tothe correlation found by Curtis and Schindler22 for 12 Canadian

Inlandwaters Litter Soil OC

OceanDOC

Oceansediment OC∗

Oceansediment OC+

Hal

f-lif

e (y

r)

n = 315a

n = 17d

n = 87bc

n = 20cn = 44

b

n = 75a

100

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102

104

106

108

Figure 3 | Half-lives of organic carbon in di�erent systems. Box plots showmedian (line), interquartile range (box) and data extremes (whiskers).Significant di�erences between groups (p<0.05, post hoc tests) aremarked with di�erent letters. The horizontal line represents one year.∗, data from Middleburg (1989); +, data from other studies, includingsediments from abyssal ocean areas (see Supplementary Information 1.2).Open circles represent potential outliers. DOC, dissolved organic carbon.

Precambrian Shield lakes (log k=−0.41 log WRT). The currentstudy greatly expands on these site-specific findings to broadergeographical gradients, suggesting a global role of WRT in OCdegradation across inland waters.

Bioassays and field studies follow similar relationships withWRT (Fig. 1). This agreement between laboratory experimentsand field surveys suggests that the progression of OC decay overtime applies to both approaches, even beyond the initial stage ofincubation29. Still, bioassays are closed systems in which microbialheterotrophic degradation of OC is the dominating loss process,whereas field studies can be considered at steady state, integratingmultiple OC losses (for example, biodegradation, photodecay, andflocculation) along with new production and lateral inputs of OC.Thus, OC decay rates from field studies correspond to net ratesof OC loss, as they result from the combination of degradationand production processes, incorporating all the variability linked toin situ conditions. Indeed, the slope of decreasing k with increasingtime is more negative in field studies than in bioassays (p=0.0276;Supplementary Information 2.2). This implies that, for short WRT,processes resulting in a lower net k in field studies (that is, primaryproduction and lateral import of OC) may be overridden by decayprocesses that are typically not captured by bioassays (for example,photodecay and flocculation). It could also reflect that, in systemswith low WRT, OC sources are fresher, leading to more rapid OCmineralization. In contrast, for WRT above approximately 1 yr,the decay processes not captured in bioassays have only a minorinfluence on the decay rates of field studies (Supplementary Fig. 2.2).Therefore, the unexplained variance (59%) in the relationshipbetween k and WRT may be attributed to a host of processes,including differences in the internal production ofOC, lateral inputsof OC or hydrological exchange with groundwater. The effectsof these secondary predictors on the OC decay rates could bepartially addressed by analysis of combinations of variables suchas nutrients, gross primary production or OC loads. However,this requires a comprehensive carbon budget for each site that

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NATURE GEOSCIENCE DOI: 10.1038/NGEO2720 LETTERS

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s<−15 −13 −9 −5 −1 1 5 9 13 >15 (faster decay)(slower decay)

OC decay rate variation (%)

Figure 4 | Global distribution of percentage variation in OC decay rates based on the runo� changes scenario for a 2 ◦C increase in temperature.a, Global distribution of variation in OC decay rates. Areas with uncertain climate predictions are masked in grey. b,c, Distribution of variation in OC decayrates across lakes and reservoirs (b) and rivers (c) of di�erent biomes. Box plots show median (line), interquartile range (box) and 10th–90th percentile(whiskers), including the uncertainty associated with the predictions of runo� variation and the relationship between WRT and k (SupplementaryInformation 3). The freshwater area associated with each biome is indicated in the upper panels of b and c, and refers to the non-masked areas in a.

is not applicable at this scale (Supplementary information 2.3).Because the combined interactions of multiple processes actingsimultaneously (for example, lateral fluxes and primary production)are integrated in our approach, the net reported decay rate for aspecific system is probably conservative.

The empirical relationship between WRT and OC decay ratefor inland waters corresponds to the relationship between age ofOC and decay in marine sediment profiles14,15. When combined,these two independent data sets suggest a general relationship thatnow extents for two more orders of magnitude (Fig. 2). Thus,across timescales ranging from the rapid flushing of water throughlakes and rivers to sediment diagenesis, we find a continuous andprogressive decrease inOCdegradation rates. To further explore the

relevance of OC losses in inland waters, we compared the half-life ofOC in inland waters with that found in terrestrial soils and marinesystems (Fig. 3). We compiled a supplementary data set, comprising243 additional half-life measurements of OC in terrestrial (litterand soil organic carbon) and marine ecosystems (organic carbonin sediments and water column; Supplementary Information 1.2).OC in inland waters has a mean half-life of 2.5 (s.d. ± 4.7 yr),faster than previously estimated19 and analogous to that of soil litter(2.6 s.d. ± 3.6 yr), but significantly shorter than the composite ofsoil horizons (72.0 s.d. ± 297 yr). In comparison, the half-life ofOC in the marine water column can reach several hundred years(730 s.d. ± 1,600 yr), whereas OC in deep ocean sediments isextremely persistent, with half-lives of several thousand years. The

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LETTERS NATURE GEOSCIENCE DOI: 10.1038/NGEO2720

relevance of OC turnover in inland waters becomes apparent fromthis comparison. Even if freshwater systems constitute a smaller OCreservoir than terrestrial or marine systems10, the amount of OCthey process is disproportionately large, reinforcing that freshwaterecosystems are hot spots of OC loss1.

To provide an example of the implications of this relationshipin the inland waters carbon cycle, we performed a predictiveexercise aiming to evaluate the potential impact that projectedchanges in runoff could have on OC decay rates. We used theexpected changes in runoff in a 2 ◦C warmer world8 to calculateconcomitant changes in WRT across rivers, lakes and reservoirsglobally. Then, we applied our model relating k and WRT (Fig. 1)to estimate the changes in OC decay rates and their uncertainty inthemain biomes (Fig. 4 and Supplementary Information 3), with theassumption that the sources of OC in freshwaters remain constant(Supplementary Information 3). The projected redistribution of theOC decay rates shows a general decrease in the Mediterraneanbiome (around −13%) and a general increase in the boreal andtundra biomes (around 10%). The boreal and tundra are particularlyrelevant at a global scale, as these regions contain most of the globalfreshwater area (Fig. 4). This predicted variation in the decay ratesof OC illustrates the sensitivity of the freshwater carbon cycle toclimate change in general, and to shifts in the hydrological systemin particular.

This study suggests a continuum of reactivity along inland watersand demonstrates the hydrological constraints on the decay rates ofOC.With OC decay rates much faster in inland waters than in othersystems, the need for an accurate quantification of the OC importedto inland waters from adjacent terrestrial systems2,5 is increasinglyapparent. The predicted global redistribution of OC decay ratesillustrates the connectedness of catchment hydrology and inlandwater carbon processing and allows the coupling of inland waterswith other Earth systems in global models, by identifying runoff asa common driver of carbon decay at regional scales30.

MethodsMethods, including statements of data availability and anyassociated accession codes and references, are available in theonline version of this paper.

Received 1 October 2015; accepted 22 April 2016;published online 23 May 2016; corrected online 2 June 2016

References1. Cole, J. J. et al . Plumbing the global carbon cycle: integrating inland waters into

the terrestrial carbon budget. Ecosystems 10, 171–184 (2007).2. Battin, T. J. et al . The boundless carbon cycle. Nature Geosci. 2, 598–600 (2009).3. Tranvik, L. J. et al . Lakes and reservoirs as regulators of carbon cycling and

climate. Limnol. Oceanogr. 54, 2298–2314 (2009).4. Raymond, P. A. et al . Global carbon dioxide emissions from inland waters.

Nature 503, 355–359 (2013).5. Aufdenkampe, A. K. et al . Riverine coupling of biogeochemical cycles between

land, oceans, and atmosphere. Front. Ecol. Environ. 9, 53–60 (2011).6. Lauerwald, R., Laruelle, G. G., Hartmann, J., Ciais, P. & Regnier, P. A. G. Spatial

patterns in CO2 evasion from the global river network. Glob. Biogeochem.Cycles 29, 534–554 (2015).

7. Sobek, S., Tranvik, L. J., Prairie, Y. T., Kortelainen, P. & Cole, J. J. Patterns andregulation of dissolved organic carbon: an analysis of 7,500 widely distributedlakes. Limnol. Oceanogr. 52, 1208–1219 (2007).

8. Schewe, J. et al . Multimodel assessment of water scarcity under climate change.Proc. Natl Acad. Sci. USA 111, 3245–3250 (2014).

9. Bastviken, D. et al . Freshwater methane emissions offset the continental carbonsink. Science 331, 50 (2011).

10. Ciais, P. et al . in Climate Change 2013: The Physical Science Basis(eds Stocker, T. F. et al .) 465–570 (IPCC, Cambridge Univ. Press, 2013).

11. Vähätalo, A. V., Aarnos, H. & Mäntyniemi, S. Biodegradability continuum andbiodegradation kinetics of natural organic matter described by the betadistribution. Biogeochemistry 100, 227–240 (2010).

12. Koehler, B., Von Wachenfeldt, E., Kothawala, D. N. & Tranvik, L. J. Reactivitycontinuum of dissolved organic carbon decomposition in lake water.J. Geophys. Res. 117, G01024 (2012).

13. Arndt, S. et al . Quantifying the degradation of organic matter in marinesediments: a review and synthesis. Earth Sci. Rev. 123, 53–86 (2013).

14. Middelburg, J. J. A simple rate model for organic matter decomposition inmarine sediments. Geochim. Cosmochim. Acta 53, 1577–1581 (1989).

15. Boudreau, B. P., Arnosti, C., Jørgensen, B. B. & Canfield, D. E. Comment on‘Physical model for the decay and preservation of marine organic carbon’.Science 319, 1616 (2008).

16. Hansell, D. A. Recalcitrant dissolved organic carbon fractions. Ann. Rev. Mar.Sci. 5, 421–445 (2011).

17. Middelburg, J. J. & Meysman, F. J. R. Burial at sea. Science 316,1294–1295 (2007).

18. Schindler, D. W. et al . Natural and man-caused factors affecting the abundanceand cycling of dissolved organic substances in precambrian shield lakes.Hydrobiologia 229, 1–21 (1992).

19. Weyhenmeyer, G. A. et al . Selective decay of terrestrial organic carbon duringtransport from land to sea. Glob. Change Biol. 18, 349–355 (2012).

20. Hanson, P. C. et al . Fate of allochthonous dissolved organic carbon in lakes:a quantitative approach. PLoS ONE 6, e21884 (2011).

21. Algesten, G. et al . Role of lakes for organic carbon cycling in the boreal zone.Glob. Change Biol. 10, 141–147 (2003).

22. Curtis, P. J. & Schindler, D. W. Hydrologic control of dissolved organic matterin low-order Precambrian Shield lakes. Biogeochemistry 36, 125–138 (1997).

23. Westrich, J. T. & Berner, R. A. The role of sedimentary organic matter inbacterial sulfate reduction: the G model tested. Limnol. Oceanogr. 29,236–249 (1984).

24. Canfield, D. E. Factors influencing organic carbon preservation in marinesediments. Chem. Geol. 114, 315–329 (1994).

25. Boudreau, B. P. & Ruddick, B. R. On a reactive continuum representation oforganic matter diagenesis. Am. J. Sci. 291, 507–538 (1991).

26. Kottek, M., Grieser, J., Beck, C., Rudolf, B. & Rubel, F. World map ofKöppen–Geiger climate classification main climates (A4).Meteorol. Z. 15,259–263 (2006).

27. Kellerman, A. M., Dittmar, T., Kothawala, D. N. & Tranvik, L. J.Chemodiversity of dissolved organic matter in lakes driven by climate andhydrology. Nature Commun. 5, 3804 (2014).

28. Vannote, R. L., Minshall, G. W., Cummins, K. W., Sedell, J. R. & Cushing, C. E.The river continuum concept. Can. J. Fish. Aquat. Sci. 37, 130–137 (1980).

29. del Giorgio, P. A. & Davis, J. in Aquatic Ecosystems: Interactivity of DissolvedOrganic Matter (eds Findlay, S. E. G. & Sinsabaugh, R. L.) 400–420 (ElsevierScience, 2003).

30. Carvalhais, N. et al . Global covariation of carbon turnover times with climatein terrestrial ecosystems. Nature 514, 213–217 (2014).

AcknowledgementsDiscussions with M. Futter, B. Obrador and C. Gudasz improved the manuscript.A. M. Kellerman commented on an early version of the manuscript. We thank B. Koehlerfor the data set on litter decay. We thank J. Schewe for his assistance with theinterpretation of runoff change maps. The study was funded by grants from the SwedishResearch Council, the Swedish Research Council for Environment, Agricultural Sciencesand Spatial Planning (FORMAS) and the Knut and Alice Wallenberg Foundation to L.J.T.N.C. holds a Wenner-Gren foundation post-doctoral fellowship (2014–2016, Sweden).The participation of R.M. was supported by project REMEDIATION(CGL2014-57215-C4-2-R), funded by the Spanish Ministry of Economy andCompetitiveness.

Author contributionsN.C., D.N.K. and L.J.T conceived the study; N.C. performed the bibliographic review andthe statistical analysis, with comments and suggestions from D.N.K., R.M. and L.J.T.;R.M. provided data on global accumulated runoff and performed the global analysis;N.C. wrote the manuscript with significant contributions from D.N.K., R.M. and L.J.T.

Additional informationSupplementary information is available in the online version of the paper. Reprints andpermissions information is available online at www.nature.com/reprints.Correspondence and requests for materials should be addressed to N.C.

Competing financial interestsThe authors declare no competing financial interests.

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NATURE GEOSCIENCE DOI: 10.1038/NGEO2720 LETTERSMethodsDecay rates of organic carbon in inland waters. The full data set and references toliterature values included in this study are available in a Supplementary Excel File.When data on the decay rate of OC was not directly available in the reference, weapplied an exponential decay to the OC loss of each individual system usingOC(t)=OC0e−kt. For field studies, we used carbon balance data, in which theinitial OC concentration was considered the OC measured in the inlet of thesystem and the final OC was the OC measured concentration in the outlet of thesystem. The water retention time (WRT) for field studies was generally calculatedas WRT=V/Q, where V is the volume and Q the discharge of the system. Adetailed definition of water residence time is provided below. In the case ofbioassays, the initial and final OC was considered as the OC concentrationmeasured at the beginning and end of the incubation, respectively. The waterretention time considered in bioassays was the incubation period.

As the objective of this study was to evaluate the decay rates of OCalong the continuum of inland waters, only systems with a net OC loss wereincluded. Therefore, systems with a negative k in which net production of OCoccurred within the system (a total of 12 data points) were discarded fromthe analysis.

We considered k to be sensitive to the effect of temperature. Therefore, tocompare the various observations of decay that we build this study on, we correctedthe k values of bioassay studies for the in situ water temperature of the study site atthe moment of sampling, using a form of the Arrhenius equation:

kT =k20

q(20−Temp)

1010

where k20 is the decay rate from laboratory incubations at 20 ◦C, Temp is the in situwater temperature at the sampling time, and q10 is the temperature coefficient(assumed to be 2.0). When not available in the publication, the in situ temperatureat the sampling time was obtained using the air mean monthly temperatures for theperiod 1961–9031,32 (http://www.cru.uea.ac.uk), from which the specifictemperature for the sampling month could be obtained from a 0.5◦ grid, usingQGIS33. These air temperatures were then corrected according to Morril et al.34 toobtain water temperatures.

Definition of water retention time.We consider water retention time (WRT) as‘the ratio of the mass of a scalar in a water body to the rate of renewal of thescalar’35,36. Thus, for lentic systems, WRT can be defined as the ratio between thevolume of a water body (V ; m3) and the volumetric flow rate through the system(Q; m3 s−1): WRT=V/Q. In the case of lotic systems, we used length of the riverreach (L; m) and velocity (u; m/s): WRT=L/u.

We chose this definition because we assume water bodies to act as closedsystems in steady state. In systems theory, a system in a steady state has numerousproperties that are constant over time37. This means that for those properties of thesystem, such as WRT, the partial derivative with respect to time is zero. Even iffluctuations occur in these ecosystems, considering a long enough period of time,these fluctuations are negligible, and we can concentrate on the overall stability ofthe system37, regarding WRT as a stationary ecosystem property. Therefore, wediscarded further definitions implying other physical processes and spatialvariability. This assumption of water bodies as closed systems in steady state alsofacilitates the comparison between water retention times with retention insediments, which is defined as depth in the sedimentary column.

Statistical analyses. Ordinary least squares correlation analysis was performed toexamine the relationship between WRT and k. The assumptions for general linearmodels were checked by inspection of diagnostic plots and tests, and met in all thecases. We used non-parametric bootstrapping resampling over the residuals of themodel and Monte Carlo simulations to evaluate the uncertainty of the modelparameters (Supplementary Information 2.1). The differences between the slopesof the regression lines of the two approaches, bioassays and field studies(Supplementary Information 2.2), were tested by bootstrapping the differencesbetween the parameters of the two models. Finally, differences between OChalf-lives of the different ecosystem types were examined using a non-parametricKruskal–Wallis test with a post hoc multiple comparison Dunn’s test. All analysiswere performed using R 3.1.338.

Predicted distribution changes in WRT and k. The global distribution ofpredicted changes in WRT and k was estimated from global geo-referenced datasets on present and predicted runoff, and is presented as a composite of the resultsfor the river network, lakes and reservoirs. In brief, we obtained the WRT for thecurrent runoff scenario and for the predicted runoff on a 2 ◦C increase in globalaverage temperature8, and then we estimated the changes in OC decay rates ininland waters using our empirical k–WRT relationship (Fig. 1).Current WRT and k in the global river network.We solved the water routing alongriver networks using the Dominant River Tracing (DRT), a global river networkdatabase designed to perform macroscale hydrologic calculations39. This database

merges the HydroSHEDS database40 with HYDRO1k (USGS,https://lta.cr.usgs.gov/HYDRO1K) to cover high-latitude regions not included inthe former. The streamflow (Q; m3 s−1) was obtained from an accumulated runofflayer (mmyr−1). Briefly, we combined the DRT flow direction and areaaccumulation rasters at 1/16th of a degree (approximately 7 km) with the localrunoff generation41 to calculate streamflow at each pixel, as in Marcé andcolleagues42. The working scale for this study is a compromise betweencomputing time needed for global calculations and the typical scale of fieldstudies of OC decay (in the range of kilometres), and it implies that we are missingat least the first two river orders. Therefore, headwaters are not considered inour analysis.

To obtain WRT in the river reaches (that is, pixels in the river network), weestimated flow velocity (u; m s−1) and reach length (L; m) (see previous section onWRT). L was calculated in QGIS from the stream lines in the DRT. u was calculatedby solving the Manning equation at each pixel43:

u=n−1r 2/3s1/2

where n is the river bed roughness set to 0.04443, r the hydraulic radius (m) ands the river slope (m/m). R was calculated from river reach depth and widthassuming a rectangular section:

R=(DW )

2D+W

Depth (D) and width (W ) were obtained using power relationships withstreamflow (Q)44:

W=7.2Q0.5 and D=0.27Q0.39

The slope was calculated from the digital elevation models at approximately 1 kmresolution in HydroSHEDS41 (http://hydrosheds.cr.usgs.gov) and Hydro1k (USGS,https://lta.cr.usgs.gov/HYDRO1K) for regions above 60◦ N.

To obtain WRT in lentic water bodies we obtained volume (V ) and water flow(Q) values (see details in previous section). We used the GRanD45 for reservoirsand the GLWD46 database for lakes. For reservoirs, the GRanD database alreadycontains the volume and inflow of each system, so we exported maps in ASCIIformat and obtained the WRT from these variables. For lakes, volume is notavailable for all the systems. In those cases, we calculated volume (V ) asV = area×mean depth, using customary global relationships relating area andmean depth47,48. Similarly, inflow is not available for the whole WLGD database,and in those cases we used the runoff extracted from our river networkstreamflow map.

Finally, k was calculated in the river network pixels and lakes and reservoirsusing our empirical relationship with WRT (Fig. 1). We masked lakes andreservoirs from the river network layer to avoid double accounting.Predicted scenario of WRT and k for a 2 ◦C increase. To obtain WRT and k in theriver network of a 2 ◦C warmer world, we repeated the calculations detailed aboveusing spatially resolved scenarios of changes in annual runoff8 to modify the localrunoff generation. We considered the predicted changes included betweenquantiles 2.5 and 97.5% in ref. 8 to avoid extremely large values probably related toinconsistencies in the ensemble modelling approach. Once we had the modifiedstreamflow layer, we repeated the procedure detailed in the previous section toobtain the modified WRT and k.

For lakes and reservoirs, we used a similar approach, where the predictedinflow is the product of the current inflow and the predicted percentage ofstreamflow change of the region. We assume that the volume of the lentic systemswill remain constant.

The final composite of changes in k (Fig. 4) was obtained as the differencebetween the warming and current scenarios. To acknowledge the highuncertainty related to the predictions of runoff changes in response to climatechange, and to yield conservative results, we restricted the analysis to zones wherethere is strong consensus on the sign of the changes in runoff8. To do so, weidentified the zones where at least 75% of the 55 model simulations in Scheweet al.8 coincided in the sign of the predicted percentage of runoff change, andapplied them as a mask over the final composite. We further stratified the dataaccording to Olson biome zones49 using a simplified legend as in Carvalhais andcolleagues30. Finally, we reported the distribution of the changes in k across biomesincluding the uncertainty propagated from the predictions of change in runoff andfrom the empirical relationships used to derive WRT and k (SupplementaryInformation 3).

Code availability. The code is not available.

Data availability. The authors declare that all the data supporting the findings ofthis study are available within the Supplementary Information files, together with acomplete list of references included in the data set.

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LETTERS NATURE GEOSCIENCE DOI: 10.1038/NGEO2720

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In the version of the Letter originally published, in the ‘Predicted distribution changes in WRT and k’ section of the Methods, the equation describing ‘R’ was incorrect and the numerator should have been ‘DW’. This has been corrected in all versions of the Letter.

Corrigendum: Organic carbon decomposition rates controlled by water retention time across inland watersNúria Catalán, Rafael Marcé, Dolly N. Kothawala and Lars. J. Tranvik

Nature Geoscience http://dx.doi.org/10.1038/ngeo2720 (2016); published online 23 May 2016; corrected online 2 June 2016.

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