Dissolved organic carbon (DOC) in the ocean represents one of the largest reservoirs of organic matter on the Earth's surface, containing a similar amount of carbon as atmospheric carbon dioxide (CO₂) (Hedges, 2002). The main processes responsible for the removal of DOC from the ocean water column are: (1) photochemistry, where DOC is degraded directly to CO₂, carbon monoxide (CO) or low molecular weight organic compounds readily available for prokaryote uptake (Moran and Zepp, 1997; Mopper et al., 2015); (2) abiotic aggregation into microparticles (Kerner et al., 2003) or sorption to particles (Chin et al., 1998); (3) abiotic degradation via free radical reactions with oxygen (Rontani et al., 2014); and (4) degradation by marine heterotrophic prokaryotes (Lønborg and Álvarez-Salgado, 2012), with the latter representing the major DOC sink in the ocean (Carlson and Hansell, 2015).

Although the DOC pool comprises a myriad of compounds covering a widespread molecular size-reactivity continuum (Amon and Benner, 1996; Benner and Amon, 2015), it is operationally divided into a biologically labile fraction (DOC_L) that is degraded over hours to days, a semi-labile fraction (DOC_SL) with turnover times from weeks to months, a semi-refractory fraction (DOC_SR) that can be stored for decades, a refractory fraction (DOC_R) with lifetimes of thousands of years, and an ultra-refractory fraction (DOC_UR) resistant to removal for tens of thousands of years (Hansell, 2013). Bioavailability has traditionally been linked to the chemical composition and structure of DOC, but more recently it has been shown to also vary depending on a range of other external factors (Raymond and Spencer, 2015). These factors include nutrient status, redox state, mineral-particle associations, terrestrial inputs, sun-light, biological production of recalcitrant compounds, changing microbial community composition, and the effect of priming or the extreme dilution of individual molecules (e.g., Amon and Benner, 1996; Thingstad et al., 1999; Del-Giorgio and Davies, 2003; Bianchi, 2011; Keil and Mayer, 2014; Arrieta et al., 2015; Letscher et al., 2015). About 4% of the ocean's net primary production escapes degradation in the surface layer to be exported as DOC to the ocean interior at a rate of about 2 Pg C year⁻¹ (Hansell et al., 2012), roughly equalling the annual net ocean uptake of CO₂ (Sarmiento and Gruber, 2006). Therefore, climate induced changes in DOC production, degradation, and/or export to deeper waters could potentially impact the atmospheric CO₂ concentration and the Earth climate system. Previous studies have proposed that changes in the degradation of ocean DOC over global scales could have an important role in regulating the long-term climate, with the rate and magnitude of degradation impacting atmospheric CO₂ levels, which in turn influences the cooling and warming of the Earth surface (Peltier et al., 2007; Swanson-Hysell et al., 2010; Sexton et al., 2011).

The temperature sensitivity of natural organic matter degradation has been studied extensively in soils (Davidson et al., 2000; Davidson and Janssens, 2006), demonstrating that increasing ambient temperature preferentially stimulates the microbial degradation of the more recalcitrant organic matter fractions. These studies suggest that the lability of a substrate can be defined by the change in the activation energy (E_a) needed in order for the degradation to take place; the more recalcitrant the compound, the higher its E_a and, following the Arrhenius law, the higher its temperature sensitivity to microbial degradation (Davidson et al., 2000; Davidson and Janssens, 2006; Sierra, 2012). In the marine environment, studies of the microbial activity response to temperature in sediments have shown that the E_a varies as a function of compound class and the organisms degrading the organic matter (Westrich and Berner, 1988; Middelburg et al., 1996). More recently, the Arrhenius law has been used for calculating the E_a of plankton community metabolism, suggesting that marine autotrophs and heterotrophs might react differently to ocean warming (Yvon-Durocher et al., 2012; Chen and Laws, 2017). It has also been shown that the temperature dependence of heterotrophic prokaryote production is fundamentally different between the upper and deeper layers of the ocean (Lønborg et al., 2016). Dissolved oxygen utilization rates in the ocean, computed from dissolved oxygen concentrations and apparent water age estimates, have also revealed a noteworthy temperature sensitivity of microbial respiration (Brewer and Peltzer, 2016, 2017).

Here, we quantify the E_a associated with the microbial degradation of DOC _L, DOC_SL, and DOC_SR, which partly controls the ocean prokaryotic production and oxygen consumption. To achieve this goal, we combine data from laboratory microbial cultures and latitudinal DOC concentration and water mass age gradients collected during oceanographic cruises, with the outputs from a global ocean DOC cycling model. This analysis allows us to also assess the impact of future ocean warming on the microbial degradation and size of the DOC fractions and the potential implications for the ocean carbon cycle.

Sensitivity of the DOC_L and DOC_SL decay constants to temperature, on the order of days to months, can be tested with microbial incubation experiments. However, this approach is not feasible for DOC_SR, which turns over in years to decades. In this case, calculating rates using latitudinal gradients of DOC concentrations and water ventilation times obtained during oceanographic cruises are more suitable (Carlson et al., 2010). Furthermore, models that combine ocean circulation with DOC biogeochemical cycling provide insights into the global implications of temperature dependence of DOC_SL and DOC_SR degradation.

Apparent E_a values, temperature coefficients (Q₁₀), and average decay constants (k_C) of DOC degradation estimated from microbial incubation experiments conducted with phytoplankton-derived DOC, marine humic substances, and natural DOC from a coastal embayment are summarized in Table 1. Applying the Arrhenius law, we estimated apparent E_a, values varying from (average ± standard error) 35 ± 10 kJ mol⁻¹ for the DOC_L to 67 ± 11 kJ mol⁻¹ for the DOC_SL pool, while the Q₁₀ increased from 1.7 to 2.7 (Table 1). The corresponding average DOC decay constants ranged from 110 ± 0.1 × 10⁻³ day⁻¹ (half-life, ln2/k_C, 6.3 ± 0.6 days) for the DOC_L to 5 ± 1 × 10⁻³ day⁻¹ (half-life, 152 ± 18 days) for the DOC_SL (Table 1).

The Arrhenius plot of the DOC_SR decay constants, obtained from the DOC concentrations and CFC apparent water ages collected during the CLIVAR A16N cruise, clearly show two distinct data clusters for the bathy- and mesopelagic North Atlantic Ocean (Figure 1) with significantly different (t-test, p < 0.05) apparent E_a (average ± standard error) of 87 ± 9 and 146 ± 21 kJ mol⁻¹, which translate into Q₁₀ values of 3.8 ± 0.5 and 8 ± 3, respectively (Table 1). The most likely reason for this difference is that the bathypelagic North Atlantic is filled with fresher DOC during the massive water mass formation that occurs in the Arctic seas, which constitutes the engine of the meridional overturning circulation. Uncertainties in this analysis of the temperature response of DOC_SR primarily stem from the fact that the surface ocean waters ultimately ventilating the meso- and bathypelagic zones do not have identical initial DOC content; while both waters contain DOC_SR and DOC_R, they are at different concentrations and likely partially different chemical compositions. Note that for the bathypelagic ocean, b₁ (degraded pool) and b₂ (resistant pool) in Equation (1) remained constant at 5.6 ± 0.4 and 40.6 ± 0.7 μmol kg⁻¹ for all temperatures, but for the mesopelagic ocean b₁ decreased and b₂ increased with increasing temperature (Table S1). These changes are most likely explained by an increasing proportion of recalcitrant DOC in subtropical compared with subpolar mode waters, although the influence of decreasing age range with increasing temperature cannot be disregarded (Table S1). In any case, to avoid this effect, we restricted our analysis of the temperature response of the mesopelagic layer to the 8 to 11°C isotherms, where b₁ and b₂ remained constant at 11 ± 2 and 42 ± 2 μmol kg⁻¹ for all temperatures. When extrapolating this analysis, it should be remembered that our dataset is restricted to one CLIVAR section (A16N). Other cruises have not been included as they contained too few data points (2–3) and it was therefore not possible to obtain k_C over a wide temperature range, which is a prerequisite for calculating reliable E_a and Q₁₀ values.

The E_a values of DOC_SR obtained for the North Atlantic could be affected by water mass mixing because the latitudinal gradients of DOC and CFC apparent age were followed along isothermal rather than isopycnal surfaces. Note that although isopycnal surfaces are preferred to minimize the impact of mixing, it is compulsory to use isothermals when studying temperature sensitivities. Therefore, we used a global ocean DOC cycling model that accounts for ocean mixing of DOC to both constrain the validity of our approach (i.e., following gradients along isothermals) and provide estimates of the global impact. The most probable values for the apparent E_a conditioned on the global database of DOC observations were found to be 53.1 ± 1.3 kJ mol⁻¹ (average ± standard error) for DOC_SL and 101.3 ± 31.5 kJ mol⁻¹ for DOC_SR (Table 2). Corresponding Q₁₀ values using a reference temperature of 15°C yield a value of 2.2 ± 0.1 for the DOC_SL pool and 4.4 ± 2.1 for DOC_SR. These estimates are all within the ranges obtained from the incubation studies and the latitudinal gradients of DOC in the north Atlantic (Tables 1, 2). This good agreement between the model and experimental data, shows that the water mass mixing on the latitudinal DOC gradients did not significantly affect the estimate of DOC_SR decay constants, and secondly that our results are generally valid.

The most probable basin-specific apparent E_a values were also tested for the Atlantic and Pacific basin, yielding Atlantic values of 55.2 ± 2.1 kJ mol⁻¹ (Q₁₀ = 2.3 ± 0.1) and 86.2 ± 13.4 kJ mol⁻¹ (Q₁₀ = 3.1 ± 0.7) and Pacific values of 54.6 ± 1.8 kJ mol⁻¹ (Q₁₀ = 2.2 ± 0.1) and 92.7 ± 52.0 kJ mol⁻¹ (Q₁₀ = 3.9 ± 3.3) for the DOC_SL and DOC_SR pools, respectively (data not shown). Thus, apparent E_a (Q₁₀) values for the DOC_SL pool are statistically the same between the Atlantic and Pacific basins. More data are required to reduce the uncertainties in the inferred basin specific E_a for the DOC_SR pool in order to address the possibility of differing temperature sensitivities between ocean basins.

Using our estimates, we calculated the sensitivity of the size of the global ocean DOC reservoir per 1°C of equilibrium ocean warming, by comparing the modern ocean reservoir, computed with the most probable parameter values to the DOC cycling model, with that assessed by uniformly increasing the ocean temperature by 1°C. The modern ocean is found to hold 57.0 Pg C of DOC_SL + DOC_SR and 630.0 Pg C of DOC_R decreasing to 48.5 Pg C of DOC_SL + DOC_SR for a 1°C warming (Table 2; Model I, Redfield r_CP case). Therefore, in terms of size changes of the DOC reservoir for a 1°C warming scenario, our DOC cycling model predicts a decrease by 7 ± 1 Pg C (mean and SD of the four modeled DOC cycling sensitivity tests), i.e., ~15% of the DOC_SL + DOC_SR reservoirs (Table 2). In these calculations, we assume for simplicity a uniform warming throughout the ocean, which approximates the sensitivity of the ocean DOC reservoir to an equilibrium warming of the global ocean by 1°C. We ignore regional differences in warming and that most heat is absorbed by the surface and then slowly redistributed throughout the ocean interior that defines the transient response of the ocean to Earth surface warming (Drijfhout et al., 2014). The impact of changing ocean temperatures on DOC degradation will therefore vary, and would for the deep ocean be delayed relative to both the initial warming and the subsequent uptake of CO₂ and heat. Given the current observed rate of deep ocean (>1,000 m) warming of ~0.01°C per decade (Purkey and Johnson, 2010), the deep ocean would warm by 1°C from present in ~1 millennium, i.e., the 7 ± 1 Pg C reduction in the global ocean DOC reservoir would occur on a similar timescale as deep ocean ventilation. The temperature coefficients, Q₁₀, at a reference temperature of 15°C (see Equation 3 in methods) are 1.7–1.8 for DOC_L, 2–3 for DOC_SL, and 4–8 for DOC_SR, indicating that DOC compounds with higher activation energies have higher temperature dependence.

Considering that most of the 662 ± 32 Pg C of DOC in the oceans has half-life times of decades to thousands of years (Hansell, 2013), knowledge on the impact of rising ocean temperatures on the decay constants of the less bioavailable DOC pools is relevant for predicting how climate change will affect the global carbon cycle.

Our combined modeling and experimental approaches indicate that DOC_SR has an apparent E_a of ~83–146 kJ mol⁻¹, which is comparable to values found for soil (67–120 kJ mol⁻¹; Leifeld and Von Lützow, 2013) and mesopelagic ocean dissolved oxygen consumption (86.5 mol⁻¹; Brewer and Peltzer, 2016). Comparatively, DOC_L and DOC_SL have lower apparent E_a of ~35–40 and ~50–70 kJ mol⁻¹, respectively, which are comparable to values estimated for the degradation of glucose (30 kJ mol⁻¹), tannin (70 kJ mol⁻¹), labile soil organic matter (~44 kJ mol⁻¹), and values recently predicted for marine respiration (~56 kJ mol⁻¹) and mesopelagic prokaryote production (~72 kJ mol⁻¹) (Knorr et al., 2005; Davidson and Janssens, 2006; Yvon-Durocher et al., 2012; Lønborg et al., 2016). Overall this suggests that the DOC_SR pool has higher activation energies and temperature dependence than the DOC_L and DOC_SL pools. A recent study demonstrated that in soils the Q₁₀ values scales inversely with temperature, with low temperature environments having a higher Q₁₀ than warmer ones (Koven et al., 2017). In a similar way we find that DOC_SR, mostly present in the deep ocean with lower temperatures, has a higher Q₁₀ of ~3–4, while DOC_SL, with higher concentrations in warmer mesopelagic waters, has a lower Q₁₀ of ~1.8–2. DOC decay in the future ocean will also vary depending on how factors other than temperature will be impacted by global change. These factors, amongst others, include changes in ocean circulation and the supply of inorganic nutrients, UV light exposure, dissolved oxygen levels, bacterial community composition, DOC chemical structure, and/or an extreme dilution of individual organic substrates (Lønborg et al., 2009; Kattner et al., 2011; Mopper et al., 2015; Repeta, 2015). Ocean models have predicted that warming may strengthen vertical stratification, thereby suppressing upward mixing of nutrients from the deep ocean and causing longer exposure to UV-light, with possible consequences for the DOC decay. Currently we do not have sufficient data to determine how this would impact our findings of the temperature sensitivity of DOC cycling. Over the last few years it has been demonstrated that global increases in ocean temperatures will reduce the overall O₂ content (i.e., “ocean deoxygenation”; Keeling et al., 2010) both directly (e.g., decreased solubility) and indirectly (e.g., increased respiration and decreased ocean ventilation). Studies in marine sediments have found that the degradation of organic matter under hypoxic and anoxic conditions is slower and less efficient than under oxic conditions (Zehnder and Stumm, 1988; Fenchel and Finlay, 1995), but due to the lack of data on DOC cycling under different O₂ levels we are not able to conclude how this might influence the relationships found in this study. The deep ocean bacterial community composition has been shown to vary over spatial and temporal scales, which could potentially affect DOC decay rates in the deep Ocean (Delong et al., 2006). However, a major influence seems unlikely as previous studies have suggested that DOC decay is generally independent of the bacterial community composition (Sjöstedt et al., 2013). The chemical composition of DOC in the deep ocean varies spatially (e.g., Martínez-Pérez et al., 2017 and our higher diagnosed activation energy for the DOC_SR than the DOC_SL pool point to a compositional control on the temperature sensitivity, i.e., the molecule types that make up the DOC_SR pool require more energy to be consumed than DOC_SL molecules. A similar conclusion was reached by Brewer and Peltzer (2017), who showed that the activation energy of ocean oxygen consumption varies widely (60.8 to 1662.9 kJ mol⁻¹) which they suggested was partly explained by some compounds being harder to oxidize than others.

Recent studies have also suggested that the dilute nature of individual compounds that constitute the DOC pool control its persistence in the oceans (Kattner et al., 2011; Arrieta et al., 2015). At very low concentrations, molecular diffusion could limit the utilization of DOC. Since molecular diffusion of organic matter is temperature sensitive, this could influence our findings. However, the E_a for molecular diffusion (~15 kJ mol⁻¹; Oelkers, 1991) is low compared with the E_a obtained in this study. The approaches combined here are also biased by different limitations; as an example, the incubation studies do not include the effects of some environmental factors (e.g., sunlight, pressure) and they could also be impacted by so called “bottle effects,” which could lead to different conditions compared with those found in the natural environment. On the other hand, both the DOC latitudinal gradients and modeling approach do not explicitly measure the microbial degradation but infer it indirectly from subsurface spatial gradients in DOC and temperature. However, it can be assumed that these approaches assess the temperature effects on microbial consumption of DOC, as long as abiotic particle-DOC scavenging or solubilization processes are minimal (Druffel et al., 1992, 2016).

Ocean warming varies spatially and over time, partly linked with the steady heat accumulation in the deep ocean, resulting in ~30% of the ocean warming occurring below 1,000 m (Whitney et al., 2007; Meehl et al., 2011; Balmaseda et al., 2013). As the ocean will most likely experience temperature increases of a few (1–4°C) degrees Celsius over the next decades (Meehl et al., 2011), we have estimated that the decay rates of the DOC_L, DOC_SL, and DOC_SR pools will increase by 4–6, 7–12, 15–18% for 1°C of warming. Note that for an increase of 2°C, which is possible for the surface ocean layer by the end of this century, the degradation rate of the DOC_SR pool will increase by 32–40% compared with the current situation. According to the microbial carbon pump (MCP) hypothesis, stimulation of microbial respiration will lead to an increase in the production of DOC_R relative to the production of the other DOC pools, with the magnitude and impact of this stimulation depend on the sensitivity of DOC_R degradation to changing temperature (Jiao et al., 2010; Legendre et al., 2015). In terms of size changes of the DOC reservoir for a 1°C warming scenario, our DOC cycling model predicts a decrease by 7 ± 1 Pg C (~15%) of the DOC_SL + DOC_SR reservoirs. Assuming a warming rate equal to the current sea surface increase of 0.01°C year⁻¹ (Rhein et al., 2013), the annual loss of DOC_SL + DOC_SR would be 0.07 Pg C year⁻¹, which represents about 3.5% of the annual net ocean uptake of CO₂ (Sarmiento and Gruber, 2006). Therefore, the overall loss of bioavailable DOC would significantly, but not massively, counteract the ocean CO₂ sink.

Our study found that, (1) the assumption of a constant Q₁₀ of ~2 is not universally applicable for the microbial degradation of DOC in the open ocean, (2) the empirically estimated Q₁₀ values indicate that increasing ocean temperature will enhance the microbial degradation of the more biologically resistant DOC with a high apparent E_a compared to the more labile DOC fractions with a low apparent E_a, and (3) increasing the equilibrium ocean temperature by just 1°C will result in a net loss of ~7 Pg C of bioavailable DOC. In this analysis we have not tested the temperature sensitivity for the DOC_R pool, since knowledge on the controls for removal of this pool is lacking, however abiotic processes are thought to contribute significantly (Hansell and Carlson, 2013). Further studies are therefore needed to determine the dominant loss processes for DOC_R before the possible temperature sensitivity can be assessed on this largest contributor to the global ocean carbon reservoir.

CL and XÁ-S conceived the study. CL, XÁ-S, and DH authors contributed equally to the data survey, analysis, and interpretation. RL performed the model simulation, developed new tracer transport diagnostics, and interpreted the model outputs. All authors wrote the paper.