The emissions of carbon dioxide (CO2) from inland waters are substantial on a global scale. Yet the fundamental question remains open which proportion of these CO2 emissions is induced by sunlight via photochemical mineralization of dissolved organic carbon (DOC), rather than by microbial respiration during DOC decomposition. Also, it is unknown on larger spatial and temporal scales how photochemical mineralization compares to other C fluxes in the inland water C cycle. We combined field and laboratory data with atmospheric radiative transfer modeling to parameterize a photochemical rate model for each day of the year 2009, for 1086 lakes situated between latitudes from 55°N to 69°N in Sweden. The sunlight-induced production of dissolved inorganic carbon (DIC) averaged 3.8 ± 0.04 g C m−2 yr−1, which is a flux comparable in size to the organic carbon burial in the lake sediments. Countrywide, 151 ± 1 kt C yr−1 was produced by photochemical mineralization, corresponding to about 12% of total annual mean CO2 emissions from Swedish lakes. With a median depth of 3.2 m, the lakes were generally deep enough that incoming, photochemically active photons were absorbed in the water column. This resulted in a linear positive relationship between DIC photoproduction and the incoming photon flux, which corresponds to the absorbed photons. Therefore, the slope of the regression line represents the wavelength- and depth-integrated apparent quantum yield of DIC photoproduction. We used this relationship to obtain a first estimate of DIC photoproduction in lakes and reservoirs worldwide. Global DIC photoproduction amounted to 13 and 35 Mt C yr−1 under overcast and clear sky, respectively. Consequently, these directly sunlight-induced CO2 emissions contribute up to about one tenth to the global CO2 emissions from lakes and reservoirs, corroborating that microbial respiration contributes a substantially larger share than formerly thought, and generate annual C fluxes similar in magnitude to the C burial in natural lake sediments worldwide.
The emission of carbon dioxide (CO2) from inland waters to the atmosphere is substantial on a global scale [Cole et al., 2007; Tranvik et al., 2009; Raymond et al., 2013]. This finding led to a revision of the global carbon cycle in the most recent report of the Intergovernmental Panel on Climate Change, which now includes carbon flux estimates for inland waters [IPCC, 2013]. The CO2 which is emitted is largely produced during mineralization of organic matter which, in inland waters, is mostly in the form of dissolved organic carbon (DOC) and allochthonous, i.e., imported from the drainage area [Tranvik et al., 2009]. Allochthonous DOC is highly aromatic [Thurman, 1985] and its microbial mineralization is slow, with bulk half-lifes typically in the range of years [Dillon and Molot, 1997]. However, aromatic DOC absorbs light efficiently, in particular in the short wavelength range of the solar spectrum, and is photoreactive [Lindell et al., 1995; Wetzel et al., 1995]. Therefore, photochemical mineralization can partly explain why organic C that escapes microbial mineralization in soils is more reactive upon export into sunlight-exposed inland waters, which act as “windows” in an otherwise dark system [Cole, 1999].
Up to now, studies on photochemical DOC mineralization in inland waters focused on a limited set of lakes, and often on summer conditions. The resulting estimates of the relative contribution from photochemical mineralization to lake C cycling differ significantly. They range from contributions of less than 3% of water column DOC mineralization in May and July in a subtropical lagoon [Ziegler and Benner, 2000], to 12% of the total epilimnetic DOC mineralization during July in Swedish lakes [Granéli et al., 1996], to 64% of the total pelagic DOC mineralization during July in Lake Tuscaloosa, Alabama [Vähatalo and Wetzel, 2004]. Another study suggested that most of the annual DOC loss in Precambrian Shield lakes, Ontario, could be attributed to photochemical mineralization [Molot and Dillon, 1997]. Photochemical mineralization in inland waters has so far not been evaluated on larger spatial or temporal scales, since data required to model photochemical mineralization, including spectra of irradiance and of absorbance by chromophoric dissolved organic matter (CDOM), are scarce. Hence, we lack regional and global estimates of sunlight-induced CO2 emissions from inland waters, and the importance of photochemical mineralization for the total mineralization and for the inland water C balance remains enigmatic. While we still miss this fundamental information, sunlight-induced CO2 production in inland waters is already subjected to global change given, e.g., decreasing ice cover duration of inland waters in the Northern Hemisphere [Magnuson et al., 2000; Weyhenmeyer et al., 2011] and changes in atmospheric transmission and cloud properties [Wild et al., 2005].
This study is the first to quantify and analyze photochemical DOC mineralization in inland waters on a large scale. We address the questions which proportion of the total, annual CO2 emissions from inland waters is induced by sunlight, and how this flux compares to other C fluxes in the C balance. To this end, we combined field, laboratory, and literature data with atmospheric radiative transfer modeling to simulate the annual photochemical production of dissolved inorganic carbon (DIC) for 1086 lakes distributed across Sweden. Based on findings from this regional study, we were able to achieve a first estimation of the relevance of photochemical mineralization in inland waters on the global scale.
2 Materials and Methods
We used a unique data set of CDOM absorbance spectra from 1086 lakes distributed across Sweden, measured by the Swedish University of Agricultural Sciences during the 2009 Swedish National Lake Inventory. For each day of the year 2009 and for each of the 1086 lakes, we modeled the downwelling scalar irradiance across wavelengths using an atmospheric radiative transfer model and cloud cover data derived from satellite information. To parameterize the wavelength-specific DOC photoreactivity, we used a solar simulator and a set of cutoff filters to measure the apparent quantum yield (AQY) spectrum of DIC photoproduction from five Swedish lake waters of different DOC quality and quantity. To describe irradiance attenuation over water depth, we collected literature data and established regression relationships to estimate vertical attenuation coefficients from CDOM absorption coefficients. Finally, we used all the above measured and modeled data sets to simulate DIC photoproduction in Swedish lakes, and analyzed its regulation and sensitivity.
2.2 Study Lakes
The photochemical modeling study was conducted for 1086 lakes distributed between 11°2′ and 23°8′E and 55°5′ and 68°8′ N in Sweden (Figure 1). The lakes are predominantly small (median area: 0.13 km2) and shallow (median depth: 3.2 m), have a median ice cover duration of 4 months, and span a wide range in water color, total organic carbon concentration, nutrient content, and other physical and chemical characteristics (Table 1). Depending on lake morphology and position in the country, the ice-covered period begins between the end of October (day 296) and the beginning of January (day 5) and ends between the end of February (day 55) and the end of June (day 179).
Table 1. Physical, Chemical, and Optical Characteristics of the Modeling Study Lakesa
Mean ± SE
For lake area n = 1069, for mean depth n = 1022, for all other characteristics n = 1086; see http://www.slu.se/vatten-miljo/vattenanalyser for the methods of water chemical analyses; see section 2.3 for details on mean lake depth and ice cover duration. CDOM: chromophoric dissolved organic matter; SUVA305: specific UV absorption coefficient at 305 nm.
Absorption coefficient at 305 nm (m−1)
62.8 ± 1.6
1.5 ± 0.2
CDOM absorption coefficient (cm−1)
60.9 ± 1.6
Ice breakup (day of year)
122 ± 1
Ice duration (days per year)
133 ± 1
Mean depth (m)
3.9 ± 0.1
6.6 ± 0.02
SUVA305 (L mg C−1 m−1)
4.2 ± 0.04
Total nitrogen (mg N L−1)
0.5 ± 0.01
Total organic carbon (mg C L−1)
13.4 ± 0.2
Total phosphorus (µg P L−1)
16.9 ± 0.7
The five lakes for which we measured the AQY spectrum of DIC photoproduction are situated at around 60°N in Sweden and were selected to be representative for the range of DOC quantity and quality in the 1086 modeling study lakes (Tables 1 and 2). For comparison, DOC concentrations ranged between 1 and 20 mg L−1 in 87% of 7514 lakes distributed on six continents [Sobek et al., 2007].
Table 2. Chemical and Optical Water Characteristics of the Lakes From Which (1) the AQY spectrum of DIC Photoproduction Was Determined in This or Earlier Studies and (2) Measured DIC Photoproduction Profiles Were Used for Model Validationa
DIC (mg C L−1)
DOC (mg C L−1)
SUVA305 (L mg C−1 m−1)
AQY: apparent quantum yield; DOC: dissolved organic carbon; DIC: dissolved inorganic carbon; a305: absorption coefficient at 305 nm; SUVA305: specific UV absorption coefficient at 305 nm.
For the validation lakes, DOC concentrations as well as pH were taken from an earlier study [Granéli et al., 1996]. The absorbance data had been measured 1 year after that study in the same lakes during the same time of the year.
Photochemical DOC mineralization is equivalent to the photochemical production of DIC. Using the software R2.15.1 [R Development Core Team, 2012], we simulated depth- and wavelength-specific DIC photoproduction [Fichot and Miller, 2010] as
where is daily DIC photoproduction (mol C m−3 d−1), z is depth (m), λmin and λmax is the minimal and maximal wavelength (nm), is daily integrated downwelling scalar irradiation just below the water surface (mol photons m−2 d−1 nm−1), ag is the CDOM absorption coefficient (m−1), Kd is the vertical attenuation coefficient for downwelling irradiance (m−1), and Φ is the AQY of DIC photoproduction (mol C mol photons−1). The required input of spectra for irradiation, CDOM absorption, vertical attenuation, and apparent quantum yield (AQY) was modeled and/or measured as described in the below paragraphs. We simulated DIC photoproduction within a wavelength range from 280 to 600 nm (1 nm resolution) from the surface of each lake in 0.005 m increments down to 0.15 m, and in 0.05 m increments down to the mean lake depth. For the lakes >0.1 km2 area (n = 251), mean lake depth was available from the Swedish lake register of the Swedish Meteorological and Hydrological Institute (http://www.smhi.se/k-data/hydrologi/sjoar_vattendrag/sjoareal_SVAR_2009.pdf). For the lakes 0.01–0.1 km2 area (n = 771) we calculated 1) the volume based on lake area and the maximum slope in a 50 m zone around the lake shoreline [Sobek et al., 2011], and 2) the mean depth as the ratio of volume to area. For the remaining lakes <0.01 km2 (n = 64) we assigned the mean depth to the median depth of the lakes from 0.01 to 0.015 km2 area (2.3 m). Long-term average (1961–1990) ice breakup and ice duration for each lake was calculated based on an arc-cosine air temperature function [Weyhenmeyer et al., 2004, 2011] using air temperatures from the Swedish Meteorological and Hydrological Institute (http://www.smhi.se/klimatdata/meteorologi/temperatur/dataserier-med-normalvärden-1.7354). We assumed that irradiance is not transmitted into the underlying water during the ice-covered period, when snow usually covers the ice [Petrov et al., 2005]. The DIC photoproduction rates were converted from molar to C fluxes by multiplying with the molar mass of C, and areal DIC photoproduction was calculated by integrating across wavelength and depth using the trapezoid rule. All photoproduced DIC was assumed to be emitted as CO2 to the atmosphere, since boreal lakes generally have low alkalinity and are oversaturated with CO2 [Sobek et al., 2003]. Indirect effects of solar irradiance on DOC decomposition, such as the production of biologically labile compounds from recalcitrant DOC which may stimulate microbial mineralization [Geller, 1986; Miller and Moran, 1997], were not considered in the model.
Daily integrated downwelling scalar irradiation spectra just below the water surface were modeled using Matlab® 7.0.1 (The MathWorks, Natick, MA, USA, 2004) according to the following three main steps:
Clear-sky downwelling spectra of global and diffuse irradiance reaching the water-air interface.
These spectra were derived for 280 to 600 nm using the atmospheric radiative transfer model libRadtran version 1.6 [Mayer et al., 2011] at a 1 nm resolution and an altitude setting of 0 m (pressure of 1013 hPa). As solar spectrum file we used “Atlas plus Modtran.” The spectral albedo for water was parameterized according to the built-in library of the International Geosphere Biosphere Program [Belward and Loveland, 2006]. With these settings, we computed clear-sky spectra for a range of ozone columns and calculated solar zenith angles [Michalsky, 1988]. The resulting spectra were saved in a lookup table. The employed aerosol model assumed rural-type aerosols in the boundary layer, background aerosols above 2 km height, and a visibility of 50 km [Shettle, 1989]. The aerosol optical depth was scaled using the Ångström formula [Ångström, 1929] with α = 1.3 and β = 0.05. Subsequently, we calculated the actual solar zenith angle with an hourly time step for each lake and day of 2009, and extracted the actual ozone column fields for every sixth hour from the archived operational runs of the Integrated Forecasting System at the European Centre for Medium-Range Weather Forecasts available from the ECMWF (http://www.ecmwf.int/research/ifsdocs/CY33r1/index.html). The field closest in time to the actual hour was used together with bilinear interpolation in space to obtain the values at the coordinates of each lake. Finally, the clear-sky irradiance spectra for the given solar zenith angles and ozone columns were determined by interpolation in the previously created lookup table, and the clear-sky ratios between diffuse and global irradiances were calculated. We routinely used the atmosphere file “Subarctic Summer” since the standard atmosphere is only used to distribute the total ozone vertically and spring-summer aerosol conditions since we wanted to tune the settings to the summer when radiation is strongest. Hence, use of this parameterization throughout the year does not affect the resulting irradiance spectra considerably but allowed efficient computation across time and space via the lookup table approach. A linear regression of simulated versus observed clear-sky irradiance, i.e., all UV irradiance measurements from Norrköping in Southern Sweden in 2008 with a total cloud cover of <10% (continuation of measurements presented by Josefsson ), gave a R2 of 0.998 (n = 996, P < 0.0001).
Correction of the clear-sky irradiance spectra for attenuation by clouds.
We used a cloud effect function [Kasten and Czeplak, 1980]
where cc is total cloud cover (oktas), and τovercast = 0.37 and α = 2.1 are fit parameters which were estimated by nonlinear least squares regression based on all UV irradiance measurements from Norrköping in 2008 with >1% cloud cover and >5° solar height (n = 2400). The parameter τovercast represents the ratio between the measured overcast irradiances and the modeled clear-sky irradiances. We conducted a 100-fold cross validation in which, for each subvalidation, 2375 measured data points were used for regression and 25 data points were used for prediction. For cloudy conditions, i.e., >90% total cloud cover, the mean bias error was 1.2% and the relative root-mean-squared error was 29%. This comparison with broadband UV measurements motivated the use of the cloud effect function because more elaborate models based on vertical cloud profile information, either climatological or from numerical weather prediction models, performed worse than the simpler model based only on total cloud cover. Total cloud cover data were retrieved from the archive of the operational mesoscale analysis system MESAN at the Swedish Meteorological and Hydrological Institute [Hāggmark et al., 2000]. The cloud-corrected irradiance spectra were derived by multiplying the clear-sky irradiance spectra with τ(cc), assuming a constant cloud effect across wavelengths. The cloud correction for the ratio of diffuse to global irradiances was calculated as in Grant and Gao , using the UV-B parameters for wavelengths from 280 to 320 nm and the UV-A parameters for longer wavelengths.
Transmittance of the above water surface irradiance through the water-air interface.
Irradiance transmittance into the water body was calculated separately for the diffuse and the direct fraction. The transmittance of the diffuse fraction was set to 0.934 [Burt, 1954]. The transmittance of the direct fraction was calculated using Fresnel′s law [Kirk, 1994] in which the zenith angle of the irradiance below the water surface was calculated as asin(1/1.33 × sin(θ)), where θ is the solar zenith angle (degrees). Finally, the just below water surface hourly irradiance spectra were converted to scalar irradiance using a modified version of an empirical relationship [Prieur and Sathyendranath, 1981] between the average cosine of the underwater downwelling irradiance, which describes its angular distribution, the diffuse fraction of the above water surface irradiance, and the zenith angle of the underwater irradiance [Fichot and Miller, 2010]. These just below water surface downwelling scalar irradiance spectra of an hourly resolution were integrated to obtain daily integrated irradiation spectra.
2.5 CDOM Absorption
For the photochemical modeling study, we obtained absorbance spectra for 1086 lakes measured during the Swedish National Lake Inventory 2009 by the Swedish University of Agricultural Sciences. Lake water had been sampled between 6 September and 24 November 2009, in most cases in the middle of the lake at 0.5 m depth. UV-Vis absorbance spectra had been measured using a 1 cm or a 5 cm quartz cuvette in a Lambda 35 spectrophotometer (PerkinElmer Life and Analytical Sciences, Shelton, Connecticut, USA). For determination of apparent quantum yields of AQY spectra, absorbance spectra were measured using a 1 cm quartz cuvette in a Lambda 40 spectrophotometer (PerkinElmer Life and Analytical Sciences). Based on the Beer-Lambert law, absorption coefficients a (m−1) were calculated as
where A is absorbance (dimensionless) and L is optical path length (m) [Kirk, 1994]. We assumed that a is representative for all water depths. The ratio of the absorption coefficient at 305 nm (a305) and the DOC concentration is referred to as specific UV absorption coefficient (L mg C−1 m−1), denoted SUVA305. Total CDOM absorption coefficients were calculated by applying the trapezoid rule to a in the range 280 to 600 nm.
Irradiance attenuation in lake water is usually governed by the absorption from CDOM [Morris et al., 1995], with particles and water making additional contributions [Kirk, 1994]. Particles also contribute to attenuation by scattering [Kirk, 1994]. To parameterize attenuation, we collected data from studies reporting both absorption coefficients a and vertical attenuation coefficients of downwelling irradiance Kd (wavelength-specific average values over the depths of measurement, see supporting information) from the same lakes or ponds. The data covered a range from clear alpine to turbid waters from lakes worldwide (n = 565; Table S1 in the supporting information). The use of Kd as approximation for the attenuation coefficient for scalar downwelling irradiance was justified since both coefficients are close in value for natural waters [Kirk, 1994]. The data were either extracted from tables or digitized from figures using Dagra (Blue Leaf Software, Hamilton, NZ). For nine wavelengths between 300 and 400 nm, we established linear least squares regressions with a as explanatory and Kd as response variable. The R2 of the regressions ranged from 0.90 to 0.99, with all P values <0.0003 (Table S1). Using these empirical relationships we calculated, based on the spectra of a available from each of the 1086 modeling study lakes, Kd at these nine wavelengths. With nonlinear least squares regression we then obtained continuous Kd spectra by fitting an exponential function to the discrete values, i.e., Kd = a exp(bλ) where a and b are fitting parameters.
2.7 Apparent Quantum Yield
In March/April 2012 we sampled surface water of five Swedish lakes (Table 2) and determined the AQY spectrum of DIC photoproduction in the laboratory [Johannessen and Miller, 2001]. Briefly, the water was filtered (Whatman GF/F filters, GE Healthcare, Buckinghamshire, UK) on the sampling day and stored at 4°C in the dark until further processing within maximally 2 weeks. On the day before irradiation, the water was filtered again, acidified using 10% hydrochloride acid (HCl) to a pH < 3, bubbled with CO2-free air for about half an hour to decrease the ambient DIC concentration, and readjusted to the original pH using 0.5 M sodium borate (Na2B4O7 · 10H2O). These reagents do not photochemically produce a measurable amount of DIC, and the procedure should not significantly affect the photochemical DOC reactivity [Miller and Zepp, 1995; Johannessen and Miller, 2001]. This generally inevitable DIC removal step caused an increase in UV-B absorbance of about 5% but did not affect absorbance at longer wavelengths, as previously reported [Johannessen and Miller, 2001]. PH was measured using a PW9420 pH meter with a BlueLine 11 electrode (Philips, Hamburg, Germany, and Schott Instruments, now SI Analytics GmbH, Mainz, Germany). In two lakes, Gäddtjärn and Hanelundssjön, no acidification prior to bubbling was needed to decrease the initial DIC concentrations sufficiently low. The preirradiance absorbance spectrum was determined, and the initial total organic carbon (TOC) concentration was measured using a Sievers 900 TOC Analyzer (General Electric Analytical Instruments, Manchester, UK) which operates in a range from 0.03 ppb to 50 ppm with a precision of <1% relative standard deviation and an accuracy of 2% or 0.5 ppb (whichever is greater) (General Electric Analytical Instruments, 2005). Since the bulk of TOC is dissolved [Tranvik et al., 2009] we use the term DOC throughout the text. The water sample was distributed into cylindric quartz vials (height 5 cm, illuminated area 12.56 cm2, volume 45 mL) which have planar tops and bottoms, and sides painted in black to avoid light to enter laterally. The vials were rinsed with diluted acid and pure water before each experiment. Initial DIC concentrations were measured with the Sievers 900 TOC Analyzer directly from each vessel, averaging over several minutes of stable measurements with DIC concentrations being recorded every 4 s. The vessels were filled completely with lake water again, and irradiation was conducted using a solar simulator (Q-Sun 1000 Xenon test chamber, Q-panel Lab Products Europe, Bolton, UK) with the vials standing inside a water bath connected to a cooling system to keep the samples at 18°C. We used five filters which cut off irradiances below 250, 310, 355, 385, and 420 nm, respectively (CVI Laser Corporation, obtained from former Gamma Optronik AB, Sweden and Oriel Instruments, Newport Corporation, Irvine, California). For each filter type and the dark controls we ran three subsample series. The water samples received an irradiance dose of about 600 W m−2 in the wavelength range up to 600 nm and were irradiated for 3 h or 6 h. This corresponds to about half of the global irradiation received in Southern Sweden during 1 day in July (Swedish Meteorological and Hydrological Institute, http://strang.smhi.se/data/117_o7m_1.png). The photochemical DIC production under each filter was calculated as the difference between the preirradiation and postirradiation DIC concentration minus microbial respiration (i.e., the mean DIC production in the dark controls). DIC production in the dark vessels averaged 1.3 ± 0.2 µg h−1, corresponding to 20 ± 3% and 42 ± 5% of the DIC production under the 250 nm and 380 nm cutoff filter, respectively. In three lakes (Gäddtjärn, Hålsjön, and Ramsjön; Table 2), the DIC photoproduction under the 420 nm cutoff filter did not differ from the DIC production in the dark controls (t test). For these three lakes, the data under this filter were therefore excluded from the AQY spectra calculation. The cutoff filters were always used in the same position in the solar simulator, and the respective irradiance spectra were measured using a concave grating spectrometer for UV-Vis applications with 1.5 nm resolution (Black Comet BLK-C, StellarNet, Tampa, Florida) equipped with a fiber optic cable (STE-F600-UVVis-SR, StellarNet) and a cosine receptor for UV-Vis near-infrared irradiance (STE-CR2, StellarNet). The number of absorbed photons was calculated accounting for the inner filter effect [Hu et al., 2002]. We then calculated the AQY spectrum using parameter optimization [Rundel, 1983] with the function optim in R2.15.1 [R Development Core Team, 2012] as
where Φ is the AQY of DIC photoproduction (mol DIC × mol photons−1), λ is wavelength (nm), and m1 and m2 are fit parameters [Johannessen and Miller, 2001].
In contrast to dark (or “thermal”) reactions, primary photochemical reaction rates are temperature independent since the required energy is gained through photon absorption rather than through collisions. However, a photochemically activated molecule usually initiates a series of “secondary” thermal reactions, explaining why photochemical reactions may appear temperature dependent [Chatwal, 2007]. Reactions of excited species in aqueous solutions, however, have relatively small activation energies of 10–30 kJ mol−1 [Schwarzenbach et al., 2003]. We, therefore, did not correct for potential small changes in reaction efficiencies due to variation between temperatures in situ and in our laboratory irradiations (i.e., 18°C).
To calculate the ratio of simulated DIC to carbon monoxide (CO) photoproduction, we also simulated photochemical CO production across the 1086 study lakes. For this purpose, we used all AQY measurements available for CO photoproduction in freshwater systems [Valentine and Zepp, 1993; Gao and Zepp, 1998] and fitted an exponential AQY function to this data set (equation (4)). The nonlinear least squares regression estimates were 8.1186 ± 0.0622 for the parameter m1 and 0.0427 ± 0.0051 for the parameter m2 (n = 33, P < 0.0001).
2.8 Model Validation
We compared simulated DIC photoproduction profiles with rates that had been observed at four depths in five Swedish lakes during July 1994 [Granéli et al., 1996] and in summer 2001 at the surface of three of these lakes [Anesio and Granéli, 2004]. From the first study, the data were digitized using Dagra (Blue Leaf Software), only using the observations in which significant DIC photoproduction was observed, and from the latter study the data were extracted from a table. Since reproducing the high observed rate at 0.65 m in lake Stråken would have required unrealistically small attenuation coefficients, we considered this observation an overestimate and excluded it from the validation. The lakes for which observations were available were representative for the range of DOC quantity and quality in the 1086 modeling study lakes (Tables 1 and 2). From the first measurement campaign only the absorbance at 30 nm was known (normalized to the cuvette path length of 1 cm) [Granéli et al., 1996]. However, in July one year later, absorbance was measured at eight wavelengths between 200 and 430 nm in the same lakes (L. J. Tranvik, unpublished data, 1995), and four absorbance spectra per lake measured during the years 2000 to 2001 were available as well (200–500 nm, 1 nm resolution; S. Sobek, unpublished data, 2000/2001). For parameterization of the validation model runs we used the spectral shape of the absorbance spectra from the years 2000 to 2001 and normalized it with the mean factor of the deviation from the absorbance known from 1995 at eight wavelengths. Irradiation spectra were modeled as described above, using cloud profiles from a weather station in Växjö about 30 km south of the study lakes and ozone data from a measurement site of the Swedish Meteorological and Hydrological Institute in Norrköping about 200 km northeast of the lakes.
Hence, the absorbance, attenuation, and irradiance spectra were measured or modeled specifically for each of the five lakes during the validation and for each of the 1086 lakes in the modeling study. AQY spectra were measured for five lakes representing a wide spectrum of DOC quality and quantity (Table 2). The AQY was therefore the model parameter with the greatest uncertainty. For that reason, we used the validation model simulations to investigate the sensitivity of the simulated DIC photoproduction rates to the AQY spectrum and to determine which AQY parameterization reproduced the observations most accurately (Table 3). That AQY parameterization was used to model DIC photoproduction across the 1086 modeling study lakes.
Table 3. Parameter Estimates for the Function Fitted to the AQY of DIC Photoproduction (Equation (4)) Per Lake, and Model Validation Dataa
Lake(s) From Which AQY was Obtained
Fit Parameter m1
Fit Parameter m2
Simulated DIC Photoproduction (mg C m−2 d−1)
Given are, for each AQY spectrum, the mean (±SE, n = 4) simulated DIC photoproduction rate for 0–2 m depth averaged across the five validation lakes (Table 2), R2 and slopes (±SE, n = 13) of linear regressions of the observed versus simulated DIC photoproduction rates, and normalized RMSEs. The intercepts of the regressions between observed and simulated values were nonsignificant in all cases. For comparison, the observed mean DIC photoproduction rate was 13.3 ± 1.7 [Anesio and Granéli, 2004] and 51.2 ± 2.8 mg C m−2 d−1 (excluding lake Stråken, see section 2.8, or 75.1 ± 24.1 mg C m−2 d−1 including lake Stråken) [Granéli et al., 1996]. To simulate DIC photoproduction for the 1086 modeling study lakes, we used the AQY spectrum based on the combined data of the five lakes for which we determined AQY in this study (Figure 2). AQY: apparent quantum yield; DIC: dissolved inorganic carbon; Norm. RMSE: normalized root-mean-squared error; SUVA305: specific UV absorption coefficient at 305 nm.
For the upscaling to Sweden we multiplied the mean annual DIC photoproduction rate (Table 4) with the total Swedish lake area of 39952.2 km2 (Swedish statistical central office, http://www.scb.se), i.e., assuming that the 1086 studied lakes are representative for all Swedish lakes. For the global estimate of annual DIC photoproduction we made use of the regression equation with annual photon flux obtained from the Sweden-wide photochemical rate model results (section 3.2). We based the global estimate on the lake and reservoir areas across latitudes presented by Downing and Duarte . Hence, we needed to simulate the latitudinal distribution of irradiance. For this purpose, we used the radiative transfer model libRadtran [Mayer et al., 2011] and step no. 3 described in section 2.4 to calculate clear-sky annual downwelling spectral irradiance just below the water surface from 60°S to 80°N with a 10° latitudinal resolution. The simulations were conducted from 280 to 600 nm with hourly time increments, using the default reference atmospheres and rural aerosol models (mode fall-winter between 23 September and 20 March and spring-summer otherwise). For the overcast-sky scenario we used a mean cloud modification factor of 0.365, calculated from the results of 14 studies based on visual observations (SE 0.038; excluding an Antarctic and a high-alpine site) [Calbó et al., 2005]. To estimate ice cover duration across latitudes, we used data from the years 2000 to 2009 of the Global Lake and River Ice Phenology Database, which contains freeze and ice-breakup dates for 212 lakes in the Northern Hemisphere for this time period [Benson and Magnuson, 2012]. The ice-on date showed no latitudinal dependency, with the median on 6 December. The ice-off date increased with increasing latitude according to ice-off date (day of year) = 30.89 (±4.21) + 1.55 (±0.08) × latitude (°N) (n = 1318, R2 = 0.51, and P < 0.0001). We assumed that, for 40°N to 80°N, no irradiance is transmitted between the median ice-on and ice-off date, when snow usually covers the ice [Petrov et al., 2005]. Since this approach does not consider the longitudinal dependency of ice cover, our irradiance estimate is conservative for Europe where the climate is milder due to the influence of the Gulf Stream, causing a shorter ice-covered period than calculated with the above relationship. Since we used the regression equation with irradiance for extrapolation, it is important to mention that its slope remained stable when we conducted simulations using the Swedish data set under a scenario of threefold increased irradiance, which covers the irradiance under a clear sky in the tropics (Figure S1). To assess the sensitivity of the global estimate to variation in the AQY, which we determined from a set of Swedish lakes, we conducted model simulations using the AQY spectra measured in this study or reported in the literature [Vähätalo et al., 2000; Vähatalo and Wetzel, 2004]. Note that attenuation was parameterized based on optical data from clear to turbid lakes worldwide (Table S1), making it appropriate for the area of extrapolation.
Table 4. Simulated Monthly and Annuala DIC Photoproduction in Swedish Lakesb
Mean ± SE (n = 1086); the upper row gives the simulated rate of DIC photoproduction per lake area, and the lower row gives the simulated DIC photoproduction for the total lake area in Sweden. Please see section 3.3 on the influence of central model assumptions. DIC: dissolved inorganic carbon.
mg C m−2 Month−1
g C m−2yr−1
5.5 ± 0.3
0.4 ± 0.2
3.0 ± 0.6
218.3 ± 7.7
601.4 ± 11.0
886.9 ± 5.4
775.6 ± 4.1
682.7 ± 4.2
398.9 ± 3.1
180.8 ± 1.7
40.0 ± 0.6
16.7 ± 0.5
3.8 ± 0.04 (3.9)
kt C Month−1
kt C yr−1
0.2 ± 0.01
0.02 ± 0.01
0.1 ± 0.02
8.7 ± 0.3
24.0 ± 0.4
35.4 ± 0.2
31.0 ± 0.2
27.3 ± 0.2
15.9 ± 0.1
7.2 ± 0.1
1.6 ± 0.03
0.7 ± 0.02
150.7 ± 1.4 (156.5)
2.10 Statistical Analyses
Linear least squares regressions were used to assess relationships between DIC photoproduction and explanatory variables (section 3.2), and the correlation between simulated and observed DIC photoproduction during model validation (section 2.8). Model significance was assessed by regression analysis of variance. Right-skewed data were logarithmically transformed before analysis. Differences were considered significant if P value < 0.05. Mean values in the text are given with ± 1 standard error and with ± 95% confidence intervals in regression equations. Analyses were conducted using R2.15.1 [R Development Core Team, 2012].
3.1 Model Validation
We validated the photochemical rate model by comparing simulated DIC photoproduction rates over water depth with observations in Swedish lakes. The simulations when using different AQY spectra (Figure 2) were assessed based on the slope for a regression between the simulated and observed values and on the root-mean-squared error (Table 3). We obtained the best validation when using the AQY spectrum for which we optimized the parameters simultaneously for the data of all five lakes combined (Figure 3). Using AQY spectra from single lakes generally worsened the performance in validation, with the exception of the AQY spectra from Lake Siggeforasjön which performed similarly good (Table 3). The simulated areal DIC photoproduction rate for the selected parameterization, i.e., using the AQY derived from all data simultaneously, amounted to 30.2 ± 2.5 mg C m−2 d−1 (Table 3), which was in the range of empirical estimates obtained in situ (13.3 ± 1.7 and 51.2 ± 2.8 mg C m−2 d−1) [Granéli et al., 1996; Anesio and Granéli, 2004].
Additionally, we assessed our model by simulating CO photoproduction to calculate the DIC:CO production ratio for the 1086 modeling study lakes. The simulated DIC:CO production ratio ranged from 24 to 50 with a mean of 38, which is in agreement with measurements in aquatic systems [e.g., Miller and Zepp, 1995; Gao and Zepp, 1998; Reader and Miller, 2012].
3.2 Patterns and Regulation of DIC Photoproduction in Lakes
At the surface of lakes, DIC photoproduction rate peaked at a wavelength of around 330 nm, being lower at the shorter wavelengths (Figure 4a) where the AQY is higher (Figure 2) but the incoming photon flux is small. Due to the wavelength-specific attenuation of irradiance, DIC photoproduction rates decreased and the peak shifted progressively toward longer wavelengths with increasing water depth. Because of the higher attenuation coefficients in lakes with high CDOM concentrations, peak photoproduction rates decreased quicker with increasing water depth than in lakes with low CDOM concentrations (Figure 4). Consequently, in high-CDOM lakes most of the DIC photoproduction occurred in a shallow water layer, whereas in low-CDOM lakes DIC photoproduction rates were lower but extended down to deeper depths. The depth-integrated, daily photoproduction rates followed the seasonal pattern of irradiance, with lowest rates during winter and largest rates during summer (Figure 5).
On average across the 1086 study lakes, 95% of the depth-integrated DIC photoproduction was reached within the upper 0.8 m of water. Consequently, there was no relationship between DIC photoproduction and mean lake depth (Figure 6a). The lakes were generally deep enough that all photochemically active photons were absorbed during penetration into the water column. Accordingly, the depth-integrated DIC photoproduction was only weakly related to the CDOM concentration (Figure 6b; R2 = 0.37 for all lakes, R2 = 0.29 for only lakes with total CDOM absorption coefficient >10 cm−1; note the logarithmic x axis scale). Here it needs to be considered that the lakes with the lowest CDOM concentrations in Sweden, in which DIC photoproduction was smaller, are mostly situated in the northern mountainous regions where annual irradiance is also smallest (Figure 1). While the CDOM absorption coefficient ranged more than 200-fold (Table 1), the frequency distribution of areal DIC photoproduction was constrained within an elevenfold range. The annual depth-integrated DIC photoproduction was tightly positively correlated with the cumulative incoming photon flux from 280 to 600 nm (mol DIC produced m−2 yr−1 = 7.2 × 10−5 (±5.5 × 10−7) mol photons m−2 yr−1; n = 1086, R2 = 0.984, and P < 0.0001; Figure 6c).
3.3 Simulated DIC Photoproduction in Swedish Lakes
DIC photoproduction across the 1086 Swedish study lakes averaged 3.82 ± 0.04 g C m−2 yr−1 (Table 1). Across entire Sweden, this results in an annual CO2 emission from Swedish lakes of 151 ± 1 kt C. These rates were calculated assuming no irradiance transmission during the ice-covered period, when snow usually covers the ice [Petrov et al., 2005]. If the irradiance would be fully transmitted into the water during the ice-covered period, the annual estimates would increase by 26%. If we had assumed that attenuation was governed by absorption from CDOM and water alone, i.e., neglecting absorption and scattering of photons by particles, the annual DIC photoproduction estimates would increase by 33%. The cloud cover observed in the year 2009 reduced the mean annual DIC photoproduction in Sweden under a clear sky by about one third.
3.4 Global Estimates of DIC Photoproduction
Using the predictive relationship with irradiance (Figure 6c) to upscale across the globe, the DIC photoproduction was highest in the northern temperate and boreal region, with a second smaller peak in the tropical region (Figure 7). Integrated across latitudes, global direct DIC photoproduction in lakes and reservoirs generated 13 Mt C yr−1 under continuously overcast sky and 35 Mt C yr−1 under continuously clear sky (Table 5). The actual DIC photoproduction lies within the range of DIC produced under these extreme sky conditions, depending on the cloud cover. If we had assumed full irradiance transmission through snow and ice in the winter, the annual estimates would increase by 33% in the boreal zone and by 23% in the temperate zone.
Table 5. Simulated Annual DIC Photoproduction in Lakes and Reservoirs Under an Overcast-Sky and a Clear-Sky Irradiance Scenarioa
To assess the sensitivity of the global estimates to the AQY parameterization, we ran simulations with the Swedish data set using all available lake-specific AQY spectra. The slopes of the relationship between incoming photon flux and DIC photoproduction ranged from 3.3 × 10−5 (lake Hålsjön) to 8.8 × 10−5 (lake Gäddtjärn), with a mean of 5.3 × 10−5 ± 0.9 (n = 7). Hence, if we had assumed that the least efficient AQY was representative for lakes and reservoirs worldwide, the global estimates would decrease to 6–16 Mt C yr−1. If we had assumed that the most efficient AQY was representative for lakes and reservoirs worldwide, the global estimates would increase to 16–43 Mt C yr−1.
Our study, which is the first to assess sunlight-induced CO2 emissions from inland waters on larger temporal and spatial scales, shows that annual photochemical DOC mineralization is a sizeable flux in the aquatic C cycle. Annual photochemical mineralization in Swedish lakes (Table 4) is comparable in size to the organic carbon burial in Swedish lake sediments of 4.1 ± 0.2 g C m−2 yr−1 [Algesten et al., 2004] or countrywide 0.1 Mt C yr−1 [Humborg et al., 2010]. Annual mean DIC photoproduction corresponds to about 12% of the total annual mean CO2 emission of 32.9 ± 2.9 g C m−2 yr−1 from Swedish lakes [Algesten et al., 2004] and to about 9% of the total loss of 1.7 Mt C yr−1 during transport through Swedish inland waters to the sea [Humborg et al., 2010; Weyhenmeyer et al., 2012]. Assuming that our simulated mean DIC photoproduction is representative for the entire boreal lake area comprising 142 Mha [Kortelainen et al., 2004], annual photochemical mineralization is extrapolated to 5.4 Mt C in boreal lakes, which corresponds to 9–12% of the annual lake CO2 emissions of 47–59 Mt C from this area [Kortelainen et al., 2006].
While the depth distribution of DIC photoproduction differed largely between low- and high-CDOM lakes, the wavelength- and depth-integrated production was only weakly related to CDOM concentration (Figure 6b). This pattern corroborates that the lakes were generally deep enough that all photons at wavelengths of significance for photochemical mineralization were absorbed within the water column. Since plant litter and suspended sediments are also photoreactive [Anesio et al., 1999; Estapa and Mayer, 2010], photons that might penetrate to the sediment in very transparent lakes will induce additional DIC photoproduction and counteract the reduced water-column DIC photoproduction. The model result is in accordance with measurements, which showed similar daily depth-integrated photochemical mineralization in four Swedish lakes despite very different depth distribution of DIC photoproduction and CDOM concentration [Granéli et al., 1996]. Therefore, we were justified in basing our annual simulations on just one absorption spectrum per lake. Changes in absorption over the seasons would not strongly influence the depth-integrated photochemical mineralization. Consistent with the above, there was a strong positive relationship between incoming photons and the DIC photoproduction, which was previously reported for a Finnish lake during summer conditions [Vähätalo et al., 2000]. Since the incoming photon flux represents the absorbed photons, the slope of the relationship represents the wavelength- and depth-integrated AQY of DIC photoproduction (Figure 6c). This regression equation is a simplification of the wavelength- and depth-specific photochemical rate model to obtain areal DIC photoproduction estimates from irradiance data alone, which is useful for the purpose of extrapolation when lake-specific data to parameterize a photochemical rate model is not available.
The slope of the regression line between annual irradiance and DIC photoproduction, which we used for extrapolation, depends on the AQY parameterization in the model simulations for Sweden. In applying the relationship for lakes worldwide we therefore assumed that the AQY determined in this study from a range of Swedish lakes is representative for inland waters in general. The AQY spectra for DIC photoproduction reported from a lake in Finland [Vähätalo et al., 2000] and a lake in Alabama [Vähatalo and Wetzel, 2004] were similar to the AQYs determined in this study. DOC- and irradiance-normalized DIC photoproduction measured in tropical and temperate freshwaters did not differ, suggesting that their DOC is similarly photoreactive [Granéli et al., 1998]. Therefore, these studies support that we made a reasonable approximation.
Lake/reservoir area and irradiance are central factors explaining the latitudinal distribution of DIC photoproduction. The photoproduction peak in the northern temperate and boreal region (Figure 7) reflects that the lake and reservoir area is largest in this part of the world [Downing and Duarte, 2009]. Even though the tropical region experiences highest annual irradiances (Figure S1) a much smaller lake and reservoir area is found there [Downing and Duarte, 2009], explaining why DIC photoproduction is considerably smaller compared to the northern temperate and boreal region (Figure 7). We find direct DOC photomineralization to be a sizeable component of the global C balance, with 13–35 Mt C yr−1 (Table 5) generating annual C fluxes similar in magnitude to the most recent estimate of C burial in natural lake sediments of 22 Mt C yr−1 [Kastowski et al., 2011]. In addition to direct DOC-to-DIC photomineralization, irradiance also indirectly affects DOC decomposition via the production of biologically labile organic compounds from recalcitrant DOC [Geller, 1986; Miller and Moran, 1997]. The C loss due to enhanced microbial decomposition of photodegraded DOC can be similar to direct photomineralization [Miller and Moran, 1997].
Recent estimates of the global CO2 emission from lakes and reservoirs range from 0.32 to 0.53 Gt C yr−1 [Cole et al., 2007; Tranvik et al., 2009; Raymond et al., 2013]. The range in the flux estimates is largely due to differing underlying lake and reservoir areas, for which the values are still under debate [Downing et al., 2006; Downing and Duarte, 2009; Raymond et al., 2013]. This is a central factor which currently restricts the possibility for direct flux comparison. Yet our analysis implies that the directly sunlight-induced CO2 emissions contribute only a small fraction of up to about one tenth to the global CO2 emissions from lakes and reservoirs. This conclusion is valid no matter which of the available AQY spectra we apply (Figure 2), and which global CO2 flux estimate is used as a reference. Even under a continuously clear sky and assuming the most efficient AQY measured in lakes so far for all lakes worldwide, the contribution of direct photochemical mineralization to CO2 emissions would increase to maximal 13%. This conclusion is in accordance with recent findings that bacterial respiration in the epilimnion alone may contribute more than two thirds of the CO2 emissions from lakes, a substantially larger share than previously thought [Berggren et al., 2011], and that substantial microbial mineralization of allochthonous dissolved organic matter occurs on a multiannual scale under the absence of solar irradiation [Koehler et al., 2012].
A number of climate change processes can influence CO2 production in inland waters. Given that we find that more than 80% of the estimated global DIC photoproduction occurs during the ice-free period in the temperate and boreal zone (section 3.4, Table 5), the ongoing decrease in ice cover duration [Magnuson et al., 2000; Weyhenmeyer et al., 2011] will not substantially increase the sunlight-induced contribution to the total inland water CO2 emission. Owing to changes in stratospheric ozone concentrations and circulation, the clear-sky UV radiation index is projected to decrease somewhat within the coming decades at latitudes north of about 40° [Hegglin and Shepherd, 2009], where the bulk of the lake area is located [Downing and Duarte, 2009]. While this would translate into a small decrease in the sunlight-induced CO2 emission, it may also be affected by possible but yet uncertain changes in UV exposure caused by alterations of aerosols and cloudiness [IPCC, 2013]. In contrast, given the temperature sensitivity of microbial DOC respiration [Kosten et al., 2010], it is plausible that its relative importance for the total inland water CO2 emission may further increase under a warming climate.
Water chemical data from the Swedish National Lake Inventory 2009 is available at the “Data host for inland waters” from the Swedish University of Agricultural Sciences (http://info1.ma.slu.se/ri/www_ri.acgi$Project?ID=2009KS). The absorbance and irradiance spectra for each lake and the data to calculate the apparent quantum yield spectra (Figure 2), used for the photochemical rate modeling, are available upon request from the corresponding author. Further data sets used during the study are available online at the Swedish Meteorological and Hydrological Institute and the National Snow and Ice Data Center. This study was funded by the Swedish Research Council for Environment, Agricultural Sciences and Spatial Planning (FORMAS) as part of the research environment “The Color of Water” (grant 2009-1350-15339-81), by the Swedish Research Council (grant 2011-3475-88773-67) and by NordForsk within the Nordic Centre of Excellence “CRAICC-Cryosphere-atmosphere interactions in a changing arctic climate” (grant 26060). We acknowledge water sampling and analyses by the Swedish National Lake Inventory 2009, and the Swedish Environmental Protection Agency for funding it; A. Düker for the lake water absorption spectra; R. Müller for GIS data; J. Johansson for field and laboratory assistance; and G. Likens for comments on an earlier version of the manuscript. We also thank S. Bélanger, S. Johannessen, B. Lehner, W. Miller, C. Osburn, S. Sobek, E. von Wachenfeldt, and E. White for data sharing and/or advice.