Remineralization rate of terrestrial DOC as inferred from CO2 supersaturated coastal waters

Coastal seas receive large amounts of terrestrially derived organic carbon (OC). The fate of this carbon, and its impact on the marine environment, is however poorly understood. Here we combine underway CO2 partial pressure (pCO2) measurements with coupled 3-D hydrodynamical– biogeochemical modelling to investigate whether remineralization of terrestrial dissolved organic carbon (tDOC) can explain CO2 supersaturated surface waters in the Gulf of Bothnia, a subarctic estuary. We find that a substantial remineralization of tDOC and a strong tDOC-induced light attenuation dampening the primary production are required to reproduce the observed CO2 supersaturated waters in the nearshore areas. A removal rate of tDOC of the order of 1 year, estimated in a previous modelling study in the same area, gives a good agreement between modelled and observed pCO2. The remineralization rate is on the same order as bacterial degradation rates calculated from published incubation experiments, suggesting that bacteria has the potential to cause this degradation. Furthermore, the observed high pCO2 values during the ice-covered season argue against photochemical degradation as the main removal mechanism. All of the remineralized tDOC is outgassed to the atmosphere in the model, turning the northernmost part of the Gulf of Bothnia into a source of CO2 to the atmosphere.


Answers to reviewer 1 I am generally satisfied by the way the authors addressed my comments. I only have a few additional points which the authors could consider before publication:
We want to thank reviewer 1 for rereading our manuscript and for these additional comments. Please find below our answers and a description of the modifications we have done in the text.

1) While eq 1 is now better described, the meaning (and the units) of the factor 10-3 are still not described in the text
We added a description on page 5, line 18 in the new manuscript.

2) Page 5, Lines 8-10: "in All experiments the terrestrial derived organic nutrients are subject to a degradation..". Is this really the case for all the experiments (I guess not) or only for the TP, 1Y and 10Y? I think it would be better to specify to avoid confusion
This is the case for all experiments. We have clarified this on lines page 5, 8-10 in the revised manuscript.

3) I would suggest to introduce a bit better the function f(sal) reported in table 1
We have specified the number of the equation in Fransner et al. 2018, where it can be found and introduced it better in the table caption. (page 5, line 12 and Table 1 in the new manuscript).

4) It would be nice to see how the simulation BIO performs with respect to 1Y and 1YS when compared with observations (nutrients and chlorophyll).. This comparison could provide additional support to the idea that the inclusion of riverine DOM is crucial to properly simulate the investigated ecosystem
We see your point, and it could have been interesting if the experiments would have been designed in another way. However, our experiments are designed to focus on the carbon in the DOM, and only difference between BIO and 1Y experiment is the inclusion of terrestrial organic carbon. The input and degradation of organic nutrients is constant over the experiments (to avoid changes in the primary production). Therefore, the only difference between BIO and 1Y will be in the carbonate system, and there is no effect on the nutrients and chlorophyll. by bacteria and photochemical processes, is however poorly constrained (Blair and Aller, 2012). Whereas conservative mixing of tDOC with salinity (Mantoura and Woodward, 1983;Dittmar and Kattner, 2003) points towards an inert behaviour, other studies suggest that there is a large removal, mainly by bacterial and photochemical degradation (Benner and Kaiser, 2011;Fichot and Benner, 2014). The high pCO 2 measured in many inner estuaries (Frankignoulle et al., 1998;Borges et al., 2005;Anderson et al., 2009) further indicates that a substantial remineralization of tDOC could take place, but it is not clear how 5 much of this signal is caused by lateral transport of CO 2 oversaturated waters from rivers and wetlands (Raymond et al., 2000;Cai, 2011).
The Gulf of Bothnia, in the Northern Baltic Sea (Figure 1), is a subarctic estuary that receives large amounts of allochthonous organic carbon (Sandberg et al., 2004;Alling et al., 2008;Deutsch et al., 2012;Hoikkala et al., 2015) originating from surrounding coniferous forests and peatlands. Recent isotope and modelling studies have shown that a majority of this terrestrially 10 derived organic carbon is removed in the transit from estuarine to more oceanic waters (Alling et al., 2008;Deutsch et al., 2012;Gustafsson et al., 2014;Fransner et al., 2016;Seidel et al., 2017), but no direct evidence of the responsible processe(s) exists, and the time scales of the removal are unclear (Fransner et al., 2016). Upscaling of small scale experiments in the Baltic Sea suggests that photochemical remineralization could account for a major removal (Aarnos et al., 2012), while only a small fraction is available for bacterial degradation (Wikner et al., 1999;Asmala et al., 2013Asmala et al., , 2014aHerlemann et al., 2014;15 Figueroa et al., 2016;Kuliński et al., 2016) and flocculation processes (Asmala et al., 2014b). Other studies, showing that phytoplankton production of organic carbon is not large enough to support the secondary production, suggest on the other hand that the bacterial production to a large degree is supported by tDOC (Zweifel et al., 1995;Kuparinen et al., 1996;Sandberg et al., 2004). Based on observed pCO 2 values, mainly from offshore waters, Löffler et al. (2012) calculated that the Bothnian Bay is a slightly heterotrophic system. Whether this net heterotrophy is due to discharge of river waters supersaturated in 20 CO 2 , or remineralization of tDOC into dissolved inorganic carbon (DIC), remains to be investigated. To better understand the dynamics of tDOC, observations are needed in the nearshore areas, where the largest tDOC concentrations and likely also the largest tDOC removal takes place (Deutsch et al., 2012).
Here we explore the remineralization dynamics of terrestrial dissolved organic carbon in the Gulf of Bothnia by combining high resolution underway pCO 2 measurements with numerical simulations from a 3D coupled hydrodynamic-biogeochemical 25 model. The underway pCO 2 measurements cover CO 2 supersaturated nearshore waters next to some of the larger rivers draining into the Gulf of Bothnia as well as offshore waters. A 3D hydrodynamic model makes it possible to take water movements into account, which cannot be neglected on longer time scales. A suite of modelling experiments is performed to describe the underlying processes behind the observed pCO 2 . The objectives of this study are to investigate if, and in that case on what time scale, remineralization of tDOC into DIC is needed to explain the observed high pCO 2 values in the coastal waters, or 30 if input of CO 2 supersaturated river water is enough to explain this pattern. Because there is no clear consensus on which is the dominating remineralization process in the Baltic Sea, it is parameterized as a simple linear decay (after Fransner et al. (2016)) that is assumed to include the effects of both bacterial and photochemical remineralization. We further investigate the potentially damping effect the tDOC can have on the primary production and the pCO 2 drawdown by increasing the light attenuation in nearshore waters. We conclude by looking at the impact of the tDOC on the air-sea CO 2 exchange in the Gulf of Bothnia and weather it turns it to a net heterotrophic system.

Model setup
The model setup used for this study (BFM-NEMO-GoB) consists of a 3D coupled hydrodynamical-biogeochemical model 5 applied to the Gulf of Bothnia (GoB, Figure 1), (Fransner et al., 2018). It has approximately two nautical miles (3704 m) horizontal resolution and 36 vertical levels with increased resolution towards the ocean surface. An open boundary towards the Baltic Proper is located in the Southern part of the domain at 59.9 • N ( Figure 1). The hydrodynamical part is based on the NEMO-Nordic model (Hordoir et al., 2013(Hordoir et al., , 2015(Hordoir et al., , 2018, which is a NEMO 3.6 (http://www.nemo-ocean.eu, Madec and the NEMO team (2016)) configuration for the Baltic and the North Seas with the LIM3 sea ice model (Vancoppenolle et al., 2009).

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The performance of the sea ice dynamics in NEMO-Nordic is validated in Pemberton et al. (2017). A comparison between modelled and observed sea ice concentration climatologies can also be found in Figure S1 in the supplementary material. BFM-NEMO-GoB is driven by hourly downscaled ERA40 data (Samuelsson et al., 2011), and river runoff from the EHYPE model (Donnelly et al., 2016). The biogeochemical part consists of the Biogeochemical Flux Model (BFM; http://bfm-community.eu) (Vichi et al., 2007a(Vichi et al., , 2015a. BFM is a stoichiometric model that simulates the biogeochemical cycles of carbon (C), nitrogen 15 (N), phosphorus (P) and silica (Si). It has four phytoplankton groups, four zooplankton groups (partitioned into micro and meso-zooplankton), one group of bacteria, particulate organic matter, and two groups of dissolved organic matter of different lability. A separate functional group representing terrestrial dissolved organic matter has been added to the BFM-NEMO-GoB setup (Fransner et al., 2018). While the organic matter that is a built in feature in BFM is degraded by bacteria, the terrestrial dissolved organic matter is subject to a linear decay, which will be further described in section 2.3. The forcing data for the 20 biogeochemical part consists of river inputs of inorganic and organic C,N,P, Si, and total alkalinity, as well as atmospheric depositions of DOC, phosphate and inorganic and organic nitrogen. The riverine loads have been calculated by multiplying measured concentrations of the chemical species with the volume flow in EHYPE Fransner et al. (2016. The riverine input of organic carbon is supposed to consist of 10% particulate organic carbon (POC) and 90% DOC (Fransner et al., 2016(Fransner et al., , 2018. As in Fransner et al. (2016), the DOC of atmospheric origin is considered as tDOC. A complete description and 25 evaluation of the BFM-NEMO-GoB setup, including the mean seasonal pCO 2 cycle, can be found in Fransner et al. (2018).

pCO 2 data
The pCO 2 was measured during 25 cruises, spanning January to October 2012, with the TransPaper cargo (Fransson et al., in preparation). The TransPaper cargo sails from Gothenburg on the Swedish west coast, through the Baltic proper and northwards through the Bothnian Sea and the Bothnian Bay to the ports of Oulu and Kemi in Finland. The pCO 2 data were gained by 30 infrared analysis of equilibrator headspace samples. The specific instrument was supplied by General Oceanics ® and designed 3 following the principles presented by Pierrot et al. (2009) using two-stage showerhead equilibration and a LICOR ® 7000 nondispersive infrared detector. The system was calibrated using four high-qualitative reference gases with approximate values of 250, 350, 450 and 550 ppm, traceable to reference standards (National Oceanic and Atmospheric Administration -Earth System Research and Laboratory), see Pierrot et al. (2009) for a more detailed description of the system. The seawater was supplied from an intake located mid-ships, at approximately 7 m water depth. Temperature was recorded in the surface-water 5 intake using a Seabird CTD and in the equilibrator using 1521 temperature probes from Hart Scientific, with an accuracy of 0.01 • C. The mole fraction of CO 2 (xCO 2 ) in the atmosphere was measured in air samples, pumped from an air intake located at approximately 50 m above sea level, where contaminated samples were removed. Air pressure was recorded by a high precision Druck barometer mounted at the air intake.
The measured pCO 2 and the cargo route for every month are displayed in Figure 2.

Simulations
The experiments have been performed in three sets (Table 1). In the first set, containing two experiments, all terrestrial organic carbon (both particulate and dissolved) is excluded. The first experiment (CHEM) investigates whether river water oversaturated in CO 2 can explain the high pCO 2 in the low-salinity region. It is done by excluding all biological processes in the water column and in the sediments. The model is thus only computing the carbonate chemistry. The only processes affecting 15 the state of the carbonate chemistry in this experiment are river discharge of total alkalinity and DIC, air-sea exchange, and changes in temperature and salinity (due to riverine and atmospheric forcing). In the second experiment, BIO, the biological processes are activated, to see whether remineralization of autochthonous organic carbon, both in the sediments and in the water column, can explain the waters oversaturated in CO 2 .
In the second set, the remineralization experiments (Table 1), the remineralization kinetics of riverine POC and DOC are 20 examined by running three experiments, TP, 1Y and 10Y. The aim of these experiments are to investigate whether remineralization of tPOC is enough to explain the high pCO 2 in the low-salinity region, or if a remineralization of tDOC (and in that case on what times scale) is needed. The TP experiment is the same as the BIO experiment, with the addition of the supply of terrestrially derived POC. For simplicity we haven't added a separate group for terrestrial POC and it is therefore subject to the same dynamics as the autochthonous POC, meaning that it is degraded by bacteria with a time scale of 10 days. As be obtained with two different parameterizations of tDOC removal. In the first parameterization, a decay rate on of the time scale of ten years was applied to 100% of the tDOC entering the Baltic Sea. In the second one, 20% of the tDOC was assumed to be refractory (resistant to removal), and 80% was assumed to be labile subject to a decay rate on the time scale of 1 year.
Here we apply the same experiments in a biogeochemical model. Because tDOC can be remineralized by both bacteria and solar radiation, and there is no clear consensus on which of these are the dominating process in the Baltic Sea, we use the same linear decay as in Fransner et al. (2016) that is assumed to include the effect of both of these processes, instead of letting it be degraded by the bacteria in the model. In the 1Y experiment (similar to the REF experiment in Fransner et al. (2018)) a decay constant of 1 y −1 is applied to 80% of the tDOC (the labile pool) entering the Gulf of Bothnia, and the remaining 20% is assumed to be refractory. The refractory part of the tDOC is not modelled explicitly, and is removed from the river load. In 5 the 10Y experiment a decay constant on the time scale of 10 years is applied to the whole pool of tDOC. The remineralized tDOC goes directly to the DIC pool. Terrestrially derived organic nutrients have been shown to be important nutrient sources for phytoplankton in the Baltic Sea (Stepanauskas et al., 2002). In all experiments the terrestrially derived organic nutrients are subjected to ::: The ::::: input ::: and :::::::::: degradation ::::: (with a degradation rate of 1 y −1 (Fransner et al., 2018) , :: on ::: the :::: time ::::: scale :: of ::: one ::::: year) :: of :::::::: terrestrial :::::: organic :::::::: nutrients ::::::::::::::::::::: (Fransner et al., 2018) are ::::::: constant :::: over ::: all :::::::::: experiments ::: and ::: all ::::: three ::: sets : to make sure that any 10 differences in pCO 2 is not caused by changes in primary production.
The aim of 1YS is to investigate the potential indirect effect tDOC could have on the pCO 2 by dampening phytoplankton growth and carbon fixation. Unfortunately, there are little data available of simultaneously measured DOC concentration and 15 photosynthetic available radiation. We have therefore created a simple parameterization where we let the tDOC-induced light extinction coefficient (k d tDOC ) vary as a linear function of the labile tDOC according to: where tDOC l is the concentration of the labile tDOC in µ : mg C m −3 the simulations are compared to the observed pCO 2 . The comparison between modelled and observed pCO 2 will be done in salinity space as the influence of river discharge on the pCO 2 becomes more apparent with these coordinates. Maps of modelled salinities are shown in Figure S2 in the supplementary material.

3.1 Description of observed pCO 2
There is a strong seasonal as well as spatial variability in the observed pCO 2 (Figure 2). In January to March rather high pCO 2 values of 400-500 µatm are observed in the offshore areas. In the North-Eastern parts of the Bothnian Bay, supersaturated waters of up to 1500 µatm are observed. In April the spring bloom begins in the Bothnian Sea and patches of undersaturated 5 waters can be observed. The waters in the Bothnian Bay stay oversaturated. In May, the waters are undersaturated in pCO 2 in the Bothnian Sea, and oversaturated in the Bothnian Bay. The waters in the North-Eastern parts of the Bothnian Bay stay highly oversaturated (>1000 µatm) in the observations also in April and May. During June and July the waters in almost the entire domain are undersaturated. The waters in the North-Eastern parts are however slightly oversaturated. In August the pCO 2 starts rising due to a combination of lower productivity and mixing/entrainment of CO 2 rich deep water, and in October it returns to 10 to 400-500 µatm. In the North-Eastern Bothnian Bay no CO 2 supersaturated (pCO 2 >1000) waters are found during September and October. During November and December no observational data exists.
The influence of river water on the pCO 2 becomes clearer in salinity coordinates (i.e. if plotting the pCO 2 against salinity instead of in lat-lon coordinates, Figure 4). A distinct decrease of pCO 2 with increasing salinity is observed especially from January to May. High pCO 2 values well above 1000 µatm are observed at salinities below 3. The pCO 2 values in this low-15 salinity region (0-3) are scattered, but there seems to be a general pattern with two branches, one with higher pCO 2 and one with lower. They might correspond to whether the ship was breaking through compact sea ice or going in an already open channel, respectively. Also in June and July there is a clear decrease of pCO 2 with salinity, although the pCO 2 in the lowsalinity region is not as high as during the first five months of the year. In August the pCO 2 values in the low-salinity region are rather scattered. In September and October no pCO 2 measurements exist in the waters with the lowest salinity. 3.2 High pCO 2 river water and marine OC When comparing modelled pCO 2 in the CHEM experiment with the observations it becomes clear that discharge of river water oversaturated in CO 2 cannot explain the observed high pCO 2 values in the low-salinity region ( Figure 4). The influence of river water on pCO 2 is overall negligible for the pCO 2 dynamics in the Gulf of Bothnia, and the modelled pCO 2 in the CHEM experiment is close to atmospheric equilibrium, with the exception of temperature effects that causes a seasonal variation in 25 the pCO 2 of up to 100 µatm.
When activating the biology and the autochtonous production of organic carbon (the BIO experiment), as well as the watersediment interaction, the model simulates a slight oversaturation of CO 2 in the low-salinity region during January-April ( Figure   4). It is, however, not high enough to explain the observed pCO 2 values. During summer the model draws down the pCO 2 too much in the low-salinity area, which could either be a result of too little remineralization, or a too high primary production. When adding river discharge of highly degradable terrestrial POC (tPOC) to the BIO setup (TP experiment), the model simulates the lower branch of the observed pCO 2 in the low-salinity region from January to March ( Figure 5). It is however not enough to explain the observed high pCO 2 values, indicating that there is not enough remineralization in this area.
Subjecting tDOC to a decay, as in the 1Y and 10Y experiments, results in higher remineralization per volume unit where 5 the highest concentrations of tDOC occur. Consequently, in the North-Eastern Bothnian Bay, where the highest tDOC concentrations are found (not shown here, but in Fransner et al. (2016)), the remineralization rates are also the highest ( Figure   6). It is in the areas with the highest remineralization that the largest impacts on the pCO 2 are seen (Figure 2 and 6). Adding remineralization of tDOC results in an increase in pCO 2 by up to 350 in the coastal waters in the 1Y experiment, while the increase is only 80 in the 10Y experiment, on annual average ( Figure 6).

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As seen in Figure 5, the 1Y experiment reproduces the observed CO 2 supersaturated (>1000 µatm) waters in spring, although it does not capture the highest observed values. The 10Y experiment results in higher pCO 2 than the TP experiment in the lowsalinity region, but the differences are small, and it barely simulates a pCO 2 above 1000 ppm, except at the lowest salinities.
Interestingly, the high pCO 2 values above 1000 µatm only exist during periods when there is sea ice, both in the 1Y experiment and in the observations. When removing the damping effect of sea ice on the air-sea CO 2 exchange, the 1Y experiment no 15 longer simulates the higher pCO 2 values, and the simulated pCO 2 values in the low-salinity region approach the ones in the TP and 10Y experiments ( Figure S3 in Supplementary Material). This is an additional indication that the two observed branches in the pCO 2 during the ice-covered months could be a result of whether the ship has travelled through open or ice-covered water.
During the productive season, none of the remineralization experiments, not even the one with a higher degradation of tDOC, is capable of reproducing the higher pCO 2 values in the low-salinity region ( Figure 5 e-h). This is probably due to a too high 20 productivity, which will be discussed in Section 3.4.

Terrestrial DOC and light extinction
Adding a linear dependency of the light extinction coefficient on the tDOC concentration, as in experiment 1YS, gives a steeper gradient in the light availability between coastal and offshore waters (Figure 3). The reduced light availability decreases the primary production and nutrient consumption in coastal areas (Figure 7), which results in a larger transport of nutrients offshore, 25 partly explaining the increased primary production in the middle of the basins. The parameterization of the light extinction coefficient in the 1YS also results in slightly clearer waters in the middle of the basins, which also increases the primary production. The tDOC dependent light extinction has the largest effect in the Bothnian Bay, where the primary production is reduced by 25% (Table 3). In the Northern Quark and the Bothnian Sea, as well for the whole domain, there is barely any change in the total primary production.

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The lower primary production in the coastal areas in the 1YS experiment leads to elevated pCO 2 in these areas (Figure 7). In the low-salinity region, the pCO 2 stays oversaturated also during the summer period (Figure 8), and agrees better with observed pCO 2 than the 1Y experiment does. During the winter months the pCO 2 in the low-salinity region is slightly decreased. The decrease is caused by the lower primary productivity and consequently the reduced export of organic carbon to the sediments, which leads to a lower DIC (Dissolved Inorganic Carbon) efflux from the sediments. A comparison of the simulated pCO 2 in 1YS with observations in geographical space is shown in Figure 9. It shows an overall good agreement with the observations.
The largest discrepancies are found in the Bothnian Sea in March and September and are related to the onset of the spring bloom and the autumn mixing, respectively, which causes relatively large changes in pCO 2 over a short period of time. Both of 5 these discrepancies can be related to that the model results show a monthly mean, while the measurements have been taken in the first half of the month for March, and second half of the month of September, respectively. The measurements are therefore biased towards the period of high pCO 2 in both March and September. The tDOC dependent k d parameterization also results in a better agreement between modelled an observed seasonal cycles of nutrients in the North-Eastern Bothnian Bay ( Figure   S4 and S5 in supplementary material). In the middle of the basins (the stations in Figure 1) the difference between the 1Y and

Remineralization of terrestrial DOC
Our results clearly show that input of river water over-saturated in CO 2 is not enough to explain the high pCO 2 values observed in the Northern Gulf of Bothnia, and suggest that it is a result of a substantial remineralization of tDOC into DIC. Here we tried 15 two different rates of remineralization, one on the order of 1 year applied to 80% of the tDOC, and one on the order of 10 years applied to 100% of the tDOC. These removal rates were derived in a 3D model (Fransner et al., 2016) to simulate observed concentrations of tDOC in the Baltic Sea (Deutsch et al., 2012). We showed here that only the simulation with the faster rate was able to reproduce the CO 2 supersaturated waters, although it didn't capture the highest observed values. The reason for this could be that there are more labile pools (with faster degradation rates) of the tDOC that we do not resolve in our relatively 20 simple model. It is well known that organic matter consists of a continuum of pools with different lability that are subject to different remineralization rates (Hansell, 2013;Carlson et al., 2015). Pools with faster remineralization rates than the one we use would be remineralized closer to the river mouth, and therefore cause higher pCO 2 at lower salinities.
Considering that the removal rate of tDOC in the 1Y experiment not only results in a good agreement between observed and modelled concentrations of tDOC, as shown in Fransner et al. (2016), but also results in a good agreement with observed 25 pCO 2 values, it suggests that remineralization of tDOC into DIC is the main mechanism behind tDOC removal in the Gulf of Bothnia. In other words, flocculation into particulate organic carbon seems only to play a minor role in removal of tDOC from the water column, which also was suggested by Asmala et al. (2014b). The high pCO 2 values observed during the ice season, when there is little light reaching the surface water, would further argue against photochemical degradation as the main removal mechanism, in contrast to what was suggested by Aarnos et al. (2012). Incubation experiments do however suggest 30 that only 10-20% of the terrestrial DOC is available to bacterial degradation (Wikner et al., 1999;Asmala et al., 2013Asmala et al., , 2014aHerlemann et al., 2014;Hulatt et al., 2014;Figueroa et al., 2016). The time scale of these incubation experiments are on the other hand relatively short (on the order of weeks to a few months), and the availability could be larger if exposing the DOC to bacteria during a longer period of time, as discussed in Fransner et al. (2016).
Knowing the incubation length in time, and the relative change in DOC concentration, a average degradation rate of tDOC during the time of incubation can be calculated based on the the classical expression for exponential decay: where λ is the decay constant (degradation rate), t is the incubation length in years, C is the concentration of DOC at the end of the incubation and C 0 is the concentration of DOC at the start of the incubation. Rearranging Equation 2, an expression for λ is obtained: Interestingly, when calculating the degradation rates for various published incubation experiments from the Gulf of Bothnia, 10 many of them are on the time scale of the order of one year (  Kuparinen et al. (1996) and Sandberg et al. (2004) who, based on extrapolations of the carbon demand of secondary producers, suggested that a large part of the tDOC entering 15 the Gulf of Bothnia is degraded by bacteria. Table 2 gives furthermore an additional indication that the 1Y experiment is more realistic than the 10Y experiment.
Equation 3 is a very simple model of degradation; organic matter tends to consist of several pools subject to different degradation rates (Hansell, 2013;Carlson et al., 2015). Three of the incubation experiments in our comparison (Table 2) have several sampling points in time that indicate that the degradation rate decreases with time, and that the tDOC consists of more 20 than two pools of different lability in contrast to our experiment 1Y (Asmala et al., 2014a;Herlemann et al., 2014;Hulatt et al., 2014). Hulatt et al. (2014) for example, calculate the degradation rates with a continuum model at different times during the incubation and report degradation rates on the order of 3 months in the beginning and 5 years in the end of their experiments (after 55 days). When working on larger spatial scales such as our model and our in situ measurements cover, it is however difficult to go into these fine details of degradation dynamics. 9 constituents often are absent (depending on the experimental setup). It has been suggested, for example, that the lability of relatively refractory organic matter can increase in presence of more labile substrates (priming) (Bianchi, 2011;Blair and Aller, 2011) and solar radiation (Vähätalo et al., 2011), which would not occur in incubation experiments.

Terrestrial DOC and light extinction
The results from the 1YS experiment show that a strong extinction of light induced by terrestrially derived organic matter, 5 hampering the primary production, could explain why the waters stay oversaturated in pCO 2 in summer. It doesn't only improve the modelled pCO 2 , but also results in a better agreement between modelled an observed seasonal cycles of nutrients in the North-Eastern Bothnian Bay ( Figure S4 and S5  Although the tDOC-dependent light parameterization has an overall negligible effect on the primary production in the Gulf 15 of Bothnia (Table 3), it has quite large local effects. The primary production is reduced in coastal waters, leading to a larger offshore transport of nutrients. The filtering effect of coastal waters (Asmala et al., 2017) is thus decreased. Clearly, more measurements of the relationship between light and DOC are needed to better understand not only the carbon fixation in coastal waters, but also the exchange of nutrients between coastal and offshore waters.

4.3
The influence of terrestrial DOC on the air-sea CO 2 exchange 20 The remineralization of tDOC in the 1Y experiment reduces uptake of atmospheric CO 2 by in total 43% (Table 4), compared to the simulation with no terrestrial DOC (TP-simulation). The reduction in the atmospheric CO 2 uptake (17.5, 8.3, 6.7, 10.0 m −2 y −1 ) corresponds well to the amount of remineralized tDOC in each subbasin (18.2, 8.2, 6.6 and 10.1 mg m −2 y −1 for BB, NQ, BS and the whole domain, respectively), indicating that almost all of the remineralized tDOC is outgassed to the atmosphere, and that a negligible fraction of the remineralized DOC (1%) adds to the DIC pool. A surplus of remineralized 25 DIC is transported from the BB to the southern basins, which is why there is a slightly larger reduction in atmospheric uptake in these basins than calculated from the remineralized tDOC. The large amount of remineralized tDOC in the Bothnian Bay turns it to a source of atmospheric CO 2 (Figure 10), in agreement with estimations by Löffler et al. (2012). However, the modelled outflux of CO 2 to the atmosphere in the Bothnian Bay is larger than their estimations. The simulated air-sea exchange in the 1Y and 1YS experiment agrees overall better with the estimations by Löffler et al. (2012), than the simulation without any 30 remineralization of tDOC, strengthening our findings that a remineralization of tDOC into DIC takes place.
Adding a dependency of the light extinction on the tDOC increases the heterotrophy of the nearshore areas and the Bothnian Bay. Compared to the 1Y experiment (Table 4 and Figure 10), the outgassing of CO 2 is increased by 28% in the Bothnian Bay. In the central parts of the Bothnian Bay and the Bothnian Sea, on the other hand, the outgassing/uptake slightly decreases/increases due to the increased primary production in these areas. The overall effect on air-sea CO 2 exchange is minor with only a decrease of 4%.

Future studies
In this study we have shown that remineralization is an important pathway for terrestrial DOC entering the Gulf of Bothnia.

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Considering that there is a large remineralization taking place under the sea ice (arguing against photochemical degradation), and that the rate we find is comparable to degradation rates calculated from bacterial incubation studies, we argue that bacteria has the potential to be responsible for this large removal. This needs to be investigated further, and an interesting next step from a modelling point of view would be to let the bacteria degrade the tDOC within the model, and compare modelled bacterial biomass/growth rates to measured ones. Interesting studies, that would be possible to perform with a stoichiometric flexible 10 model, could for example be done on the quality of terrestrial DOM (based on its nutrient content), and on the competition for inorganic nutrients between bacteria and phytoplankton, which has been shown to be dependent on the availability of organic carbon relative to nutrients (e.g. Bratbak and Thingstad (1985); Joint et al. (2002); Thingstad et al. (2008)).

Uncertainty analysis
In shallow areas such as the North-Eastern parts of the Bothnian Bay, sediment fluxes have a particularly large impact on the 15 carbon cycling and the air-sea CO 2 . The highest sediment-water DIC flux in the model is found next to the river mouths. The

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In this study the remineralization of terrestrial DOC, and its influence on the pCO 2 and the air-sea CO 2 exchange, is studied in the Gulf of Bothnia. It is done by combining results from a coupled physical-biogeochemical model together with high resolution underway measurements of pCO 2 data. Our conclusions are the following: 1. High pCO 2 values are explained by remineralization of terrestrial DOC, with a remineralization time scale of 1 year. 5 2. The remineralization rate agrees well with bacterial uptake rates of terrestrial DOC calculated from incubation experiments from the Northern Baltic Sea.
3. In addition to the terrestrial DOC remineralization, a high light attenuation induced by terrestrial DOC is needed to dampen the primary production and to reproduce the summer pCO 2 .
Code and data availability. The BFM and NEMO source codes can be obtained at http://bfm-community.eu and http://www.nemo-ocean.eu,

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respectively. The input files needed to reproduce the simulations can be obtained upon request to the corresponding author (filippa.fransner@hotmail.se).
The pCO2 is a part of a bigger pCO2 dataset of the Baltic Sea which will be presented (and made publicly available) in an article that is in preparation (Fransson et al., in preparation). Until then the data can be obtained upon request to Agneta Fransson (Agneta.Fransson@npolar.no).
The nutrient data used to produce Figure S4 in the supplementary material comes from the ICES data portal (http://ocean.ices.dk/Helcom/Helcom.aspx?Mode=1).
of Environment (Naturvårdsverket). The Baltic Nest Institute is supported by the Swedish Agency for Marine and Water Management through their grant 1:11 -Measures for marine and water environment. L.T. acknowledges support from the BONUS COCOA project (grant agreement 2112932-1), funded jointly by the European Union and the Academy of Finland. :: We ::::: wan't :: to :::: thank ::: the ::: two :::::::: anonymous :::::::: reviewers :: for :::: their ::::::::: suggestions ::: that ::: lead :: to :: an :::::::::: improvement :: of ::: our ::::: work.     The first column shows the site of the sampling, where BB= Bothnian Bay, NQ= Northern Quark, and GoB is the whole Gulf of Bothina (Figure 1). The second column shows the length of the incubation in days and the third column shows the percentage of tDOC that has been removed at the end of the incubation (if average values are available these values has been reported, otherwise ranges). The fourth column shows the calculated time scale of degradation based on Equation 3.
29 Table 3. Primary production  in g C m −2 y −1 in the 1Y and 1YS experiments (relative change with respect to 1Y).