The Invisible Carbon Footprint as a hidden impact of peatland degradation inducing marine carbonate dissolution in Sumatra, Indonesia

In Indonesia, land use change (LUC) in the form of peatland degradation induces carbon loss through direct CO2 emissions, but also via soil leaching of which circa 50% is decomposed and emitted as CO2 from the rivers. However, the fate of the remaining exported leached carbon is uncertain. Here, we show that the majority of this carbon is respired in the estuaries and emitted to the atmosphere. However, a portion is adsorbed into the marine carbon pool where it favors CaCO3 dissolution and can therefore be seen as the invisible carbon footprint. We conclude that the effects of LUC stretch beyond the terrestrial realm and are not limited to CO2 emissions, but also affect marine ecosystems. Considering the ecological and economical importance of these ecosystems, it is important that this so far invisible carbon footprint, as well as the aquatic and marine CO2 emissions, are included in climate mitigation strategies.

Peatland degradation in Southeast Asia is recognized as an important carbon source to the atmosphere 1 albeit so far not yet considered in all global estimates of CO 2 emissions. It would increase the LUC emissions from 1100 Tg C yr −1 (ref. 2 ) to 1389 ± 938 Tg C yr −1 (26%) only by considering CO 2 emissions caused by peat oxidation and forest fires (289 ± 138 Tg C yr −1 ) (ref. 3 ). In Indonesia, regrowth of secondary vegetation could reduce this CO 2 emission to 105 Tg C yr −1 (ref. 4 ). However, this estimate would again enhance by 42% to 149 Tg C yr −1 , as a recent study 5 revealed that degradation of peatlands has increased carbon leaching from soils by 200% with a leaching rate of 183 g C m −2 yr −1 , as opposed to 62 g C m −2 yr −1 from pristine peatlands 6 . This increase results partly from changes in the hydrological cycle due to drainage (38%), but is primarily due to regrowth of secondary vegetation (62%) with leaves consisting of relatively labile organic carbon. Despite the carbon-enriched peat soils and enhanced leaching rate, the location of the peatlands near the coast limits the decomposition of leached carbon in the rivers by reducing its residence time in the river, which leads to a relatively modest river outgassing rate of 21-25 Tg C yr −1 (87-109 g C m −2 yr −1 ) in Indonesian disturbed peatlands 5,7 . With roughly half of the carbon that enters the freshwater system being decomposed and emitted into the atmosphere, it remains unclear what the fate of the exported riverine carbon is once it has reached the estuaries and coastal ocean. In general, tropical estuaries and coastal oceans are heterotrophic systems emitting CO 2 8-10 . In contrast, a recent study 11 shows that coastal oceans in west Southeast Asia are considered to be a carbon sink, which would imply that the carbon that is leached from peat soils and exported via the rivers to the coastal ocean is absorbed in the water column.
In this study, we aim to resolve these knowledge gaps in Sumatra, Indonesia, by quantifying the riverine carbon export and investigate the estuarine and marine processes to better understand the fate of terrestrial carbon in the coastal ocean.

Results and Discussion
Riverine carbon processes and exports. Tropical peatlands in Sumatra cover approximately 15.6% 12 or 72,431 km 2 of the land area with a thickness between 2 and 10 m 13 and are mostly located on the coastal plains. The large majority of these peatlands is disturbed as a consequence of deforestation and drainage to make way for agricultural cropland and in particular palm oil plantations 12 , with only a small portion (6%) of pristine tropical peatlands remaining in Southeast Asia 14 . A total of three expeditions were carried out along the north and east coast of Sumatra in October 2009, October 2012 and April 2013, with 72, 32 and 57 sampling stations, respectively. Six rivers were investigated, namely the Musi, Batanghari, Indragiri, Kampar, Siak and Rokan (Fig. 1), of which the river catchments contain various amounts of peatland coverage, ranging from 3.5% in the Musi up to 30.2% in the Rokan catchment (Table 1). Through leaching, carbon is mobilized from the peat soils into the rivers, which is further enhanced through disturbance 6 and the labile content of the leaves of secondary vegetation 5 . The export ratio between total organic carbon and total inorganic carbon (TOC:TIC) increases with increasing peat coverage as the overlying peat soils leach organic carbon and simultaneously reduce the contribution of dissolved (inorganic) carbonate derived from weathering of underlying mineral soils to the rivers 15,16 . The relative importance of dissolved inorganic carbon (DIC) derived from respiration and silicate weathering can also be quantified by δ 13 C DIC . The riverine δ 13 C DIC is a mixture between low δ 13 C CO2 values from decomposed plant material, which amounts to an average of −28.0 ± 1.5‰ as derived from leached terrestrial dissolved organic carbon (DOC) measured in the Siak, Rokan and Kampar rivers in 2006, and HCO 3 − derived from weathering of mineral soils 17 , which have an isotopic signature of about 0‰ 18 . The Siak river has a δ 13 C DIC of −22.5‰ derived from decomposed terrestrial DOC and less from weathering and its DIC is composed primarily of CO 2 (Fig. 2a, Table 1 and Supplementary Fig. 1). In the Musi and Indragiri, which have smaller relative peat coverages, δ 13 C DIC values are higher with −16.8‰ and −9.0‰, respectively, which indicates that mineral soil weathering plays a more active role in these catchments. The dissolved and particulate organic and inorganic riverine carbon fluxes have been calculated based on measurements carried out between 2004 and 2013 (Supplementary Table 1) and were interpolated to encompass Sumatra. Exports were calculated by multiplying the average carbon end-member concentration with discharge, which was based on averaged monthly precipitation rates (Supplementary Table 1) and assuming an evapotranspiration rate of 37.9% 6 . DOC and DIC end-member concentrations per expedition were derived through correlating their concentrations with salinity, where the y-intercept at salinity 0 represents the end-member concentration. DIC concentrations (μmol kg −1 ) were calculated using the co2sys program with total alkalinity (TA) and pCO 2 measurements as input parameters, alongside other required inputs of salinity, temperature, pressure and nutrient measurements. Particulate organic carbon (POC) and particulate inorganic carbon (PIC) concentrations were derived from stations in a salinity range of 0-1, as it was not possible to obtain an end-member due to few data points. Exports normalized to catchment area represent the yield.
On average 72% of the exported carbon from Sumatra is organic with 10.72 ± 0.12 Tg C yr −1 of DOC and 4.87 ± 0.08 Tg C yr −1 of particulate organic carbon (POC), adding up to 15.59 ± 0.20 Tg C yr −1 of TOC ( Table 1). The export of TIC amounts to 6.05 ± 0.19 Tg C yr −1 , mostly consisting of DIC with 5.82 ± 0.19 Tg C yr −1 , whereas particulate inorganic carbon (PIC) contributes on a marginal level with 0.23 ± 0.00 Tg C yr −1 . As a whole, Indonesia, with a peat coverage of 11.9% or 2.3*10 5 km 2 (ref. 7 ), has a TOC export of 53.06 Tg C yr −1 and a TIC export of 25.65 Tg C yr −1 . In comparison, the Amazon river has riverine carbon exports of 36 Tg C yr −1 of TOC and 35 Tg C yr −1 of TIC 19 , which shows that Indonesia, regardless of its relatively small size of 1.9 million km 2 (ref. 7 ) compared to the Amazon catchment of 3.9 million km 2 (ref. 19 ), plays a crucial role with respect to carbon exports. Its relatively large riverine export of organic carbon shifts the attention to the fate of this organic carbon in the estuaries.
Carbon fluxes and processes in the estuaries and coastal ocean. As river waters reach the estuaries and coastal ocean of Sumatra, pCO 2 levels rapidly decrease. In order to investigate to which extent mixing with low pCO 2 ocean waters is responsible for this measured decrease, pCO 2 mixing lines were calculated. In the estuaries, TA and DIC concentrations increase in a linear fashion as low concentration river waters mix with high concentration coastal ocean waters. This linear relationship along a salinity gradient is referred to as a mixing line and represents the expected TA and DIC concentrations at a specific salinity as a consequence of mixing ( Supplementary Fig. 2). Based on these TA and DIC mixing lines calculated for the Musi, Indragiri and Siak estuaries, pCO 2 mixing lines were calculated using co2sys with the TA and DIC concentrations of the mixing lines as input parameters, in addition to temperature, salinity and air pressure. The pCO 2 (non-linear) mixing lines represent the expected decrease in pCO 2 concentrations along the salinity gradient caused by mixing and are visualized along with the measured pCO 2 concentrations for the Musi, Indragiri and Siak estuaries in Fig. 2b. The pCO 2 mixing lines are initially relatively high in accordance with the measurements, but quickly decrease exponentially. However, the higher pCO 2 measurements indicate that additional CO 2 is produced that increases the pCO 2 beyond the level expected during mixing. This confirms the general observation that especially the estuaries are heterotrophic systems, where respiration and decomposition of organic carbon are dominant processes.
The δ 13 C DIC data ( Fig. 2a) shows the influence of terrestrial carbon in the estuaries and coastal ocean. However, its increase with increasing salinity is in a linear fashion, thereby seemingly due to mixing. Decomposition of terrestrial organic carbon would result in more negative values, expressed in a curve below the observed linear correlation. On the other hand, outgassing of CO 2 at a pCO 2 twice or more that of the atmosphere raises the δ 13 C DIC values 20 , providing a curve above the observed correlation. Both processes occur in the estuaries and balance the resulting δ 13 C DIC values to appear linear. In order to quantify how much of the respired exported carbon is emitted as CO 2 to the atmosphere, the CO 2 yields of the estuaries and coastal ocean were calculated and amount to 670.7 ± 98.4 g C m −2 yr −1 and 49.4 ± 7.2 g C m −2 yr −1 , respectively (Table 2). Multiplied by their surface areas, this results in a CO 2 flux of 7.3 ± 1.1 Tg C yr −1 in the estuaries and 6.3 ± 0.9 Tg C yr −1 in the coastal ocean. This finding is contradictory to a recent study that predicts the coastal ocean of Southeast Asia to be a carbon sink 21 . Whereas this may be the case for the northern part of Southeast Asia from where this data point is extrapolated due to data scarcity, our data shows that the coastal ocean of Sumatra is instead a carbon source. Indeed, it appears that the short residence time of the rivers creates relatively modest CO 2 emissions in the rivers with 16.5 Tg C yr −1 in Sumatra 7 , but in fact shifts this process of CO 2 emission to the estuaries and coastal ocean where the exported organic carbon is To complement the figure with respect to pCO 2 measurements in the estuaries, the continuous pCO 2 measurements were used to calculate the average pCO 2 at each salinity point in the respective rivers (continuous). As the trip in the Siak river covered two days with a pause upstream, the pCO 2 data is divided between 'In' and 'Out' to highlight the difference in pCO 2 concentrations. During the way into the Siak the pCO 2 concentrations are slightly lower than during the way out. This is presumably due to a plankton bloom that occurred as relatively low DOC concentrations allowed for enhanced light availability, which absorbed CO 2 for photosynthesis 7  respired, thereby causing a combined CO 2 emission of 13.6 ± 2.0 Tg C yr −1 . In regard to the total carbon export of 21.6 Tg C yr −1 , this suggests that the excess of 8.0 Tg C yr −1 is either exported into the sediments or it is adsorbed by marine waters. Although actual sedimentation rates are uncertain, globally it is estimated that approximately 10% of the exported terrestrial organic carbon is sequestered in continental margin sediments 22 . Assuming a similar burial rate for Sumatra and its TOC export of 15.6 Tg C yr −1 , this results in a sedimentation rate of 1.6 Tg C yr −1 , which would reduce the excess of exported carbon from 8.0 to 6.4 Tg C yr −1 . The remaining excess of carbon may be partially exported to the open ocean 23 , but is most presumably further remineralized to form CO 2 (ref. 24 ). In addition to the exported DIC CO2 , this may be used for photosynthesis or alternatively is absorbed by marine waters through carbonate dissolution, which shifts the carbonate system towards lower CO 2 concentrations.
Carbonate dissolution. Marine organisms primarily use two major forms of CaCO 3 , namely aragonite (corals and many mollusks) and calcite (coccolithophores, foraminifera and some mollusks) 25 . The saturation states of aragonite (Ω AR ) and calcite (Ω CA ), calculated using co2sys with TA and pCO 2 as input parameters, found in the Sumatran estuaries range between 0-1.1, which encourages carbonate dissolution 25 and hampers the growth of carbonate-producing organisms. In the coastal ocean, the values increase up to 3.5 for Ω AR and 5.5 for Ω CA (Fig. 3a and Supplementary Fig. 2, respectively). This gradient from the estuaries to the coastal ocean is notably reflected by the mollusk species richness and abundance, which is correlated to the sediment carbonate weight content 26 . Indeed, the minor sediment carbonate content in the river mouths (0-4%) and Malacca Strait (<1%) allow few mollusk species to thrive with very low abundance, whereas the increased carbonate content in East Sumatra (2-79%) and the Tuju Islands (27-92%) show increased species richness and mollusk abundance 26 . The sediment carbonate content is also correlated to the Ω, where the increase of carbonate content is translated in a relatively quick increase in Ω AR and stabilizes between 3 and 4 as the carbonate content reaches beyond 25% (Fig. 3b). Nonetheless, taking into account that calcification rates and cementation sharply decrease at Ω AR < 4 (ref. 27 ) and Ω AR < 3 (ref. 28 ), respectively, the findings indicate that calcification rates in the coastal ocean are not optimal. In order to visualize the balance between CaCO 3 dissolution and formation, the measured total alkalinity (TA) and DIC concentrations were compared to their respective mixing lines ( Supplementary Figs 3 and 4). The DIC and TA deviations were then plotted against each other to visualize their ratio, which sheds light on the occurring processes (Fig. 4). In accordance with their low Ω AR , most of the estuarine data points show the largest dissolution and are offset to the right due to additional DIC in  the form of respired CO 2 . This confirms our previous observation that, besides CaCO 3 dissolution as evident from this plot and the Ω AR /Ω CA , respiration is an active process in the estuaries. Whereas optimal Ω AR and Ω CA conditions in the coastal ocean would result in its data points along the CaCO 3 formation, the cluster is shifted toward dissolution instead, with an offset towards respiration. This indicates that ocean acidification as a consequence of oversaturation of respired CO 2 is taking its toll in the coastal ocean as well, through reduced calcification rates, but also carbonate dissolution. Although the carbonate source for dissolution in the estuaries consists of sediment and benthic calcifying organisms, such as mollusks, it may also affect coral reefs located a bit further out the coast as the situation persists or aggravates. Indeed, whereas a simultaneous study revealed global reefs situated in the open ocean to show net carbonate formation 29 , a patch at the northwestern tip of Sumatra was recently identified as 'dark spot' , distinguished by intensive fishing technologies, but also environmental shocks such as coral bleaching 30 . In addition, a recent survey in the coastal ocean of Sumatra has revealed that the status of coral reefs at 81% of 75 clustered survey stations ( Fig. 1) is fair to bad, meaning that less than 50% of the corals is alive 31 , although the precise cause for this status is uncertain. However, knowing that ocean acidification, which lowers the saturation states, may cause coral bleaching and productivity loss 32 , and seeing that the surveys were at the outskirts of the study area, coral reefs and other calcifying organisms closer to the coast may be in even worse condition and are at a higher risk to bleaching, reduced calcification rates and dissolution caused by lowered saturation states as a consequence of enhanced riverine carbon inputs, as already apparent in the mollusk assemblages 26 . The disappearance of carbonate-producing reef organisms would have vast ecological and economic impacts as the trophic system becomes disturbed, thereby affecting biodiversity, sediment production and sequestration, in addition to destabilization of the coast 33 .
The invisible carbon footprint. In Sumatra 62.7% of the exported total carbon (13.6 of 21.6 Tg yr −1 ) is emitted from the estuaries and coastal ocean and 10% of its organic carbon export is assumed to be sequestered in the sediments. Adopting similar emission and burial percentages for entire Indonesia with its total carbon export of 78.8 Tg C yr −1 and organic carbon export of 53.1 Tg C yr −1 , the CO 2 emissions from the estuaries and coastal ocean result in a total of 49.4 Tg C yr −1 with another 5.3 Tg C yr −1 buried in the sediments (Fig. 5). The remaining exported carbon of 24.1 Tg C yr −1 (30.6%) remains in the marine waters where it further respires and favors CaCO 3 dissolution by lowering the saturation states. As saturation states are lowered by inputs of Ca 2+ -poor and acidic freshwater, this situation is induced by the peatlands, which overlie mineral soils thereby reducing weathering, and moreover produce an acidic CO 2 -rich environment through decomposition of leached organic carbon in the rivers that extends into the estuaries and beyond. Having greatly increased DOC leaching from peat soils through degradation by 200% as compared to the natural situation 5 , anthropogenic disturbance may therefore be seen as a primary contributor to the low saturation states in the estuaries and, to a lesser extent, the coastal ocean. The respired carbon that remains in the ocean and favors carbonate dissolution can therefore be viewed as the invisible carbon footprint induced by LUC, which should be considered in terms of ocean acidification. UNESCO already recognizes ocean acidification as a serious threat and urges the UNFCCC to consider its negative effects on the ocean chemistry and marine ecosystem 34 . In addition, the UN Sustainable Development Goal 14 'Life below water' 35 aims to sustainably use marine resources and address the impact of ocean acidification. However, whereas this study shows that the effects of LUC stretch beyond the terrestrial realm, the invisible carbon footprint is currently overlooked in mitigation policies alongside the CO 2 emissions from the rivers, estuaries and coastal ocean, as the focus is on reducing direct terrestrial carbon emissions [36][37][38] . In Southeast Asia, approximately 6% of the peatlands remain pristine, whereas 11% is covered by disturbed (secondary) vegetation, 2% is (seasonal) water surface and 81% is degraded and converted peatland cover 14 . Assuming an even distribution, a peatland cover of 2.3 *10 5 km 2 and a yield of 433 g C m −2 yr −1 (ref. 4 ), the direct terrestrial CO 2 emission from secondary vegetation in Indonesia amounts to 10.9 Tg C yr −1 . Its direct terrestrial CO 2 emissions due to LUC via peat oxidation and fires from the degraded and converted peatland cover result in 109.9 Tg yr −1 (ref. 39 ) and 82.1 Tg C yr −1 (ref. 40 ), respectively, which amounts to a total direct terrestrial CO 2 emission of 202.9 Tg C yr −1 . Carbon loss due to indirect aquatic emissions from the rivers 53.9 Tg yr −1 , (ref. 7 ), estuaries and coastal ocean (49.4 Tg yr −1 ), as well as the invisible carbon footprint (24.1 Tg C yr −1 ), amounts to 127.4 Tg C yr −1 .
However, this value still includes the natural background indirect emissions from pristine peatland and non-peatlands. The natural indirect peatland emission can be deduced from the TOC leaching rate of pristine peatlands of 63 g C m −2 yr −1 (ref. 6 ) and amounts to 14.4 Tg C yr −1 . The indirect emission from non-peatland (1.7 *10 6 km 2 ) is deduced from the correlation with peat coverage and DOC, where a peat coverage of 0% results in a DOC leaching of 5.6 g C m −2 yr −1 or 9.5 Tg C yr −1 . POC values vary per river in a non-correlating fashion, but POC exports consist on average of 45% of the DOC export, resulting in an indirect POC leaching rate of 2.6 g C m −2 yr −1 or 4.4 Tg C yr −1 with a TOC emission from non-peatland of 13.9 Tg C yr −1 .
The total natural indirect TOC emission from peat (14.4 Tg C yr −1 ) and non-peatlands (13.9 Tg C yr −1 ) amounts to 28.3 Tg C yr −1 . Subtracting the natural indirect emission of 28.3 Tg C yr −1 from the current one of 127.4 Tg C yr −1 results in a total indirect LUC emission of 99.1 Tg C yr −1 . This indicates that LUC has not only increased soil DOC leaching by 200% 5 but also POC leaching, which leads to increased soil TOC leaching or indirect emissions by 350% as compared to the natural situation.
Including the direct terrestrial peatland emissions of 202.9 Tg C yr −1 , the total carbon loss due to LUC amounts to 302.0 Tg C yr −1 , which represents an increase of 49%.
Considering this large impact along with the environmental and economic effects on global climate and the marine ecosystem, it is of vital importance that LUC mitigation policies are not only limited to direct terrestrial greenhouse gas emissions, but also incorporate the aquatic and marine CO 2 emissions as well as the invisible carbon footprint.

Methods
Climate study area. Sumatra is subject to the Malaysian-Australian monsoon as a consequence of the meridional variation of the intertropical convergence zone. During the wet season, which lasts from October to April, the monsoon brings heavy rains from the north, whereas from May to September dry air currents from Australia induce a dry season 41 . Precipitation rates vary between 123 mm in July to 312 mm in November with an annual sum of 2,696 mm in Pekanbaru, Central Sumatra 42 . Sampling methods. Salinity, pCO 2 and temperature were measured continuously by means of underway instruments, which were connected via a through-flow system and supplied with surface water from an approx- In addition to continuous measurements, water samples were taken at each station using a Niskin bottle at circa 1.5 m depth. After a total storage (during and after expedition) of maximum three weeks, the samples were analyzed in the laboratory in Bremen, Germany. Samples for δ 13 C DIC were stored in amber-colored 20 ml bottles, deprived of air, intoxicated with mercuric chloride (HgCl 2 ) and analysed using the Finnigan GasBench II. In this instrument, organic compounds eluting from a GC column are converted into simple gases when traversing a capillary micro-reactor. Accordingly, all compound specific isotope ratios are analyzed in the IRMS. DOC samples were filtered (0.45 μm) into 60 ml high-density polyethylene (HDPC) bottles and acidified with phosphoric acid (20%) up to pH 2.0. By means of a Shimadzu TOC-VCPH Total Organic Carbon Analyzer, the samples were combusted at 680 °C within a quartz column and the released CO 2 was measured using the oxidative combustion-infrared analysis. The relative standard error for the method was ±1%. Alkalinity samples were collected in 250 ml glass bottles in 2009 and 2012 and in 125 ml LDPE flasks in 2013, deprived of air, intoxicated with HgCl 2 and analyzed using a VINDTA 3 S instrument. Known amounts of sampled seawater were titrated with constant increments of 0.15 ml of hydrochloric acid (HCl) until a total amount of 4.2 ml HCl was reached. The HCl in the device was calibrated with a sodium chloride solution to approximate the ionic strength of seawater. The process of the open cell titration allowed the assumption that the total amount of DIC was approximately zero in the pH region of 3.0-3.5. The process was monitored using a pH glass electrode cell and the total alkalinity (TA) was calculated from the titrant volume and electromotoric force using a non-linear least-squares approach that corrected for the reactions with sulphate and fluoride ions. Measurements of temperature, salinity, pH, pCO 2 and TA at the stations are shown in Supplementary Table 3. CO 2 flux and piston velocity calculations for estuaries and coastal ocean. CO 2 fluxes (F) were calculated from the pCO 2 measurements of the continuous data using: where K CO2 is the CO 2 piston velocity, K 0 the solubility of CO 2 in seawater 43 and ΔpCO 2 is the sea-air pCO 2 difference with an average atmospheric CO 2 concentration of circa 390 ppm, as measured during the cruises. Although piston velocities are affected by many processes such as surface wave types, formation of air bubbles, humidity and temperature gradients and organic film coating, in the coastal systems and ocean piston velocities are primarily influenced by wind speed and the Schmidt number 44 . Therefore, piston velocity calculations related to wind speed have been chosen for this study. As calculations from Wanninkhof 45 and Nightingale et al. 46  Generally, the border between estuaries and coastal ocean is predetermined at a salinity equal to or more than 30 50 . However, in this study the correlation between salinity and the aragonite saturation state off the coast of Sumatra shows a clear distinction of this border, indicated by Ω AR values of ≤1 below salinity 25, and a rapid increase of Ω AR ≥ 1 at salinities ≥ 25 (Fig. 3a). Therefore, the border between estuaries and coastal ocean is here defined at a salinity equal to or higher than 25. By correlating the salinity and distance to shore, this border is found at an approximate distance of 3 km (Supplementary Fig. 5). Based on this distance, the surface area of the estuaries was estimated using ArcGIS 10.4 and, assuming that estuaries influence the entire coastline, amounts to 10,818 km 2 . The perimeter of the coastal ocean is based on the correlation between salinity and δ 13 C, where the terrestrial influence, characterized as δ 13 C values below the marine δ 13 C signature of circa +1‰ (ref. 51 ), reached up to a salinity of circa 32.8 (Fig. 2a). This salinity coincided with a distance of circa 67 km, which resulted in a surface area of 127,674 km 2 .
Calibration experiment. As pCO 2 was measured with different devices in 2009 and 2013, a CO 2 calibration experiment was conducted to validate the Contros measurements, during which different concentrations of CO 2 gas were delivered using a gas mixing system. The gas concentrations delivered by the gas mixing system were first monitored and compared by the mixing system regulator, the Li-Cor 7000, the Li-820 and the cavity ring-down spectrometer (Picarro G2201-i) in a range from circa 500 to 6000 ppm ( Supplementary Fig. 6a). The gas was then used to calibrate seawater in a range of 500-5000 ppm that was pumped into the Li-Cor 7000 equilibrator and the Contros sensor. The measured pCO 2 concentrations were highly correlated ( Supplementary Fig. 6b), especially in the lower concentration range common in the coast, which justified the Contros measurements.
Uncertainty estimates. The errors associated with the averaged parameters in the rivers, estuaries and coastal ocean are presented as the standard error (s.e.). The error range of the alkalinity is based on the standard error of the seawater standards measured during the sample analysis and applied to the respective samples. The error of DIC can be seen as best/worst case scenario, as the errors of TA and pCO 2 have been integrated throughout the co2sys calculations. The error range of the CO 2 yields and fluxes in the estuaries and coastal ocean are the result of the standard deviation of the piston velocities in turn as a consequence of the standard deviation of the wind speed (5.59 ± 0.41 m s −1 ), which was integrated in the CO 2 yield and flux calculations to give a best/worst case scenario.

Data Availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.