2.1.1 Photoproduction

The photoproduction rate is driven by light, the quantity of organic matter bearing chromophoric function (CDOM) and the probability for excited CDOM to produce CO. It is a strongly wavelength-dependent process and, according to Fichot and Miller (2010), the relevant range for CO photoproduction is 290–490 nm with a maximum production around a wavelength (referred as λ in nm) of 325 nm. Hereafter, we describe our main hypotheses to compute the photoproduction.

Spectral solar irradiance

We first derive the spectral solar irradiance in the range 290–490 nm (E_CO(λ,0) in W m⁻²) reaching the surface of the ocean as a fraction f_CO(λ) of the total solar irradiance reaching the considered grid box (E_tot):

For each wavelength this fraction has been determined using the standard solar spectrum ASTM G173-03 (2012). The spectra are modeled using the ground-based solar spectral irradiance SMARTS2 (Simple Model for Atmospheric Transmission of Sunshine, version 2.9.2). Only the incident irradiance is considered to determine the quantity of photons affecting CDOM since the upwelling irradiance has been shown to be negligible even in the presence of reflective sediments (Kirk, 1994). This assumption widely simplifies the computation of photochemistry in the ocean. Irradiance then decreases with depth z (in m), with seawater attenuation coefficients k (in m⁻¹) depending on both λ and Chl a concentration according to the following relation:

The attenuation coefficients are computed from the coefficients for pure water K_w and biogenic compounds K_bio according to Morel and Maritorena (2001):

where the coefficients K_w, χ and e as published by Morel and Maritorena (2001) are known for wavelengths ranging between 350 and 800 nm. A linear extrapolation of the coefficients is performed to retrieve coefficients between 290 and 350 nm.

CDOM content

The CDOM content is usually characterized by the absorption coefficient (a_cdom(λ,z) in m⁻¹) at a given λ. For case 1 waters, i.e., far from terrestrial runoff and terrigenous influence, the CDOM is essentially composed of products released during the initial photosynthetic process (Morel, 2009), and hence a_cdom and Chl a co-vary (Morel and Gentili, 2009). We use here the Morel (2009) parameterization, which relates a_cdom (400 nm) to Chl a (in mg m⁻³):

The a_cdom (λ, z) values for each wavelength between 290 and 490 nm are then exponentially extrapolated from a_cdom (ref = 400 nm), with $S=-\mathrm{0.018}$ nm⁻¹ (Morel, 2009) (Fig. 1):

Figure 1CO apparent quantum yield (AQY in moles of CO per moles of photons) and CDOM absorption coefficient (a_cdom in m⁻¹) as a function of the wavelength (nm). For the AQY, the parameterizations of Ziolkowski and Miller (2007) and Zafiriou et al. (2003) are shown with dotted lines and the resulting mean relation used in PISCES is shown with a continuous line. For a_cdom, the relation is shown for a Chl a concentration of 1 mg m⁻³ and is calculated according to the parameterization of Morel (2009).

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Efficiency of the excited CDOM in producing CO

When the CDOM absorbs photons, only a small and variable fraction of the excited CDOM leads to a photochemical reaction. This fraction is called the apparent quantum yield (hereafter AQY in moles of CO produced per moles of photons absorbed by CDOM). We assume that CDOM is homogeneous in terms of composition and thus consider a unique spectral distribution of AQY. We compute the spectral variation in AQY by taking the average of two published parameterizations, Ziolkowski and Miller (2007) (Eq. 8) and Zafiriou et al. (2003) (Eq. 9a and b) (Fig. 1):

These empirical parameterizations were derived statistically from measurements of AQY spectra made on seawater samples collected in the Gulf of Maine, the Sargasso Sea and the northwestern Atlantic waters for Ziolkowski and Miller (2007), and during a transect carried out between 70^∘ S and 45^∘ N in the Pacific Ocean for Zafiriou et al. (2003).

Photoproduction

Finally, the resulting CO photoproduction term is computed by integrating over the spectrum of photochemically active solar radiation, the product of three terms (solar irradiance, CDOM absorption and AQY):

where λ∕hc converts moles of photons to W s (Joules) and h is Planck's constant ($\mathrm{6.6260755}\times {\mathrm{10}}^{-\mathrm{34}}$ J s) and c the speed of light in a vacuum (3.00×10⁸ m s⁻¹).

2.1.2 Direct phytoplankton production

The direct production of CO by phytoplankton is not well understood. So far, only one study assesses the direct CO production rates from phytoplankton (Gros et al., 2009), by experimentally exposing different microalgal species to a diurnal cycle of 12 h of light and 12 h of dark conditions. The measured rates were highly variable from one species to another (from 19 to 374 µmol CO g Chl a⁻¹ d⁻¹ for diatoms and from 6 to 344 µmol CO g Chl a⁻¹ d⁻¹ for nondiatoms). Here, we used the median values of Gros et al. (2009) reported in Tran et al. (2013): 85.5 (k_nano) and 33.0 µmol CO g Chl a⁻¹ d⁻¹ (k_diat) respectively for the nanophytoplankton and the diatom types. The direct CO production by phytoplankton is thus computed using the following relation:

with Chl a_nano and Chl a_diat (in g Chl a L⁻¹) the respective Chl a concentrations for nanophytoplankton and diatoms. Note that we do not explicitly resolve the diurnal cycle in PISCES. Hence, to account for the variation in the daylight length, the production rates are divided by 12 h for conversion in µmol CO g Chl a⁻¹ h⁻¹ and then multiplied by the number of hours of light h, computed as a function of latitude and the period of the year.

2.1.3 Dark production

The mechanisms underlying dark production of CO are poorly understood. Here we use the parameterization of Zhang et al. (2008), in which dark production is considered as a thermal abiotic process depending on the quantity of CDOM substrate (represented by its absorption at 350 nm), temperature T (in ^∘ C), pH and salinity S by the following:

where the rate β_CO is in nmol m L⁻¹ h⁻¹. This parameterization was derived from dark incubations of water samples from the St. Lawrence estuary, with a_cdom (350) (0.23–15.32 m⁻¹) and salinity (0.1–34.7) ranges typical of coastal waters. This parameterization is the only one available in the literature. However, its extrapolation to the global ocean may lead to potentially large uncertainties (Zhang et al., 2008).

2.1.4 Bacterial consumption

The bacterial consumption of CO has been studied for the North Atlantic and for polar waters (Xie et al., 2005, 2009). According to these authors, it follows a first-order to zero-order chemical kinetic, or kinetics with a saturation threshold. The values of the parameters associated with these chemical kinetics are highly variable and depend on the environment and water masses characteristics. For a global application in PISCES, we chose a first-order chemical kinetic to reduce the number of uncertain parameters such as the following:

with k_CO the rate of bacterial consumption (0.2 d⁻¹) and CO the concentration of CO (mol L⁻¹).

2.1.5 Ocean–atmosphere CO exchanges

The CO flux at the ocean–atmosphere interface is described in a similar way to Fick's diffusion law. It depends on the concentration at the ocean surface and on the partial pressure in the atmosphere above the ocean (pCO_a in atm):

with p_atm the atmospheric pressure and f_CO the atmospheric dry mole fraction. In PISCES, the atmospheric CO concentration over the ocean is considered to be spatially constant and fixed to 90 ppbv, closed to its global surface average (Novelli et al., 2003 and ESRL NOAA-GMD, 2018). H is the Henry's constant, which relates the partial pressure of a gas with the equilibrium concentration in solution (CO_w^*):

It is calculated from Wiesenberg and Guinasso (1979) by the following:

with S‰ the salinity in parts per thousand. Finally, k_flx is the gas transfer velocity (in m s⁻¹), which depends on the Schmidt number Sc (Zafiriou et al., 2008), the temperature (T in ^∘C) and the wind speed at 10 m high (u in m s⁻¹) (Wanninkhoff, 1992):

Note that the global oceanic CO emissions have a low sensitivity to the atmospheric mole fraction. Hence, using a constant dry atmospheric mole fraction of 45 ppbv instead of 90 ppbv changes the global oceanic CO emissions by only 3 %.

CDOM parameterization

Regarding the CDOM absorption coefficient as a function of Chl a, two parameterizations were tested in addition to that of Morel (2009). The first one was initially developed for the photoproduction of carbonyl sulfide by Launois et al. (2015). It relates a_cdom at 350 nm to the log of Chl a (C in mg m⁻³):

This relation has been derived from monthly climatologies of Chl a concentrations and surface reflectances obtained with the MODIS Aqua ocean color between July 2002 and July 2010 (Maritorena et al., 2010; Fanton d'Andon et al., 2009). Using these reflectances, the SeaUV algorithm developed by Fichot et al. (2008) allows the attenuation coefficients K_d at 320 nm to be calculated. Then a ratio $a_{\mathrm{cdom}}\left(\mathrm{320}\right)/K_{\mathrm{d}}\left(\mathrm{320}\right)=\mathrm{0.68}$ obtained from in situ measurements permits the calculation of a_cdom (320 nm) (Fichot and Miller, 2010). Finally, Eq. (7) has been used to estimate a_cdom at 350 nm. The second other parameterization tested is based on the calculation of a_cdom at 440 nm with the relation Garver and Siegel (1998). It has been obtained from computed organic matter absorption and observed Chl a concentration:

where per (a_cdom (440)) is the contribution of CDOM to the total absorbed radiation of colored organic compounds in sea water. It is calculated by the following:

with a_ph (440) the absorption of phytoplankton, proportional to the Chl a (Preiswerk and Najjar, 2000):

Equation (7) is then used to calculate a_cdom at each wavelength. The variations in the CDOM absorption with Chl a for all the parameterizations we tested, including the relation of Morel (2009), are shown in Fig. 2.

Figure 2CDOM absorption coefficient (m⁻¹) at 325 nm as a function of the Chl a concentration (mg m⁻³) for the parameterizations of Morel (2009), Preiswerk and Najjar (2000) and Launois et al. (2015). The continuous line indicates the chosen parameterization.

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Bacterial consumption rate

The rate of CO bacterial consumption is highly uncertain. According to experimental measurements, it seems to vary by several orders of magnitude. For example, Zafiriou et al. (2003) measured consumption rates of the order of 0.1 d⁻¹ in the Southern Ocean, while Day and Faloona (2009) measured rates of more than 19 d⁻¹. Hence, tests have been carried out on this rate. It is first considered constant with values ranging from 0.1 to 1.0 d⁻¹. Secondly, it is considered to vary with the intensity of phytoplanktonic activities (proportional to Chl a) and the water temperature, according to the study of Xie et al. (2005):

with Chl the Chl a concentration (in µg L⁻¹) and T the temperature (in ^∘C). A and Y are constant parameters (0.0029 and 0.16 respectively). This equation was derived from dark incubations of 44 water samples from the Delaware Bay, Beaufort Sea and northwestern Atlantic waters in summer and autumn. The study showed a positive correlation between k_CO, Chl a and temperature (R²=0.69 with μ=1). For its use in the global ocean and to reduce the mean resulting rate to 0.2 d⁻¹, we have reduced the calculated rate k_CO from the original equation of Xie et al. (2005) by multiplying by a constant μ, fitted to 0.05.

3.1.1 Global oceanic fluxes

At the scale of the global ocean, the CO inventory is 0.4 Tg C, with a residence time of 4.3 days. The global photoproduction term in the ocean is 19.1 Tg C yr⁻¹. It exceeds by a factor of 3 the direct phytoplankton production (6.2 Tg C yr⁻¹) and by a factor of 2 the dark production (8.5 Tg C yr⁻¹). The main CO sink is the bacterial consumption term (30.0 Tg C yr⁻¹). Indeed, the global CO emission to the atmosphere (4.0 Tg C yr⁻¹) is rather small compared to the biochemical source and sink processes. Figure 3 summarizes the values of the different terms of the CO budget in the oceanic surface layer. Only 0.1 Tg C of CO is contained in the surface layer (considered to be the first 10 m of the ocean). Almost one half of the CO photoproduction takes place in the surface layer of the ocean (9.3 Tg C yr⁻¹ in the first 10 m), whereas only 4.8 % (0.3 Tg C yr⁻¹) of the phytoplankton production and 5.9 % (0.5 Tg C yr⁻¹) of the dark production unfolds there. Most of the CO produced at the surface is either emitted to the atmosphere or transported vertically towards deeper layers. The mean downward flux from the surface layer (at 10 m depth) is estimated to be 2.1 Tg C yr⁻¹. It is therefore of the same order of magnitude as the estimated emissions to the atmosphere, which points out the importance of taking into account the effects of ocean circulation and mixing to estimate and map CO emissions.

3.1.2 Spatial patterns of the sources and sinks

Figure 4 presents the annual mean of oceanic CO concentrations and the different sources and sink terms, all vertically integrated on the first 1000 m. The integrated CO concentrations are highest at low latitudes and tend to decrease poleward. A strong CO maximum of more than 140 µmol m⁻² is reached along the Equator in the central western Pacific Ocean. The integrated CO concentrations pattern is close to the dark production one, which has a strong temperature dependence and hence higher values (exceeding 5 mmol m⁻² yr⁻¹) located at the western part of the pacific basins where warm waters penetrate deeper. Integrated concentrations are also influenced by photoproduction, whose integrated values are, however, highest (exceeding 8 mmol m⁻² yr⁻¹) at the middle and western part of the basin. On the contrary, the integrated direct biological production is stronger at midlatitudes, especially in the Southern Ocean where it reaches more than 3 mmol m⁻² yr⁻¹ and is weaker in the oligotrophic gyres (around 1 mmol m⁻² yr⁻¹). The bacterial consumption term (from 0 to 12 mmol m⁻² yr⁻¹) is linearly dependent on the CO concentration and is therefore following its spatial pattern.

Figure 4Spatial distribution of the photoproduction (a), direct phytoplankton production (b), oceanic CO concentration (c), dark production (d) and bacterial sink (e), vertically integrated at 1000 m.

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In the surface layer (taken here as the first 10 m), the patterns of the annual mean CO concentrations and the related fluxes are slightly different from the vertically integrated patterns. Figure 5 presents the annual mean surface patterns of CO concentrations and of photoproduction (panels a and c). While integrated CO concentrations patterns are influenced by the different sources and in particular the dark production, the surface patterns are very close to the surface photoproduction patterns. Indeed, concentrations are higher at the Equator, but with a strong maximum (more than 4 nmol L⁻¹) found in the eastern equatorial Pacific Ocean. This CO maximum occurs in a highly productive area where surface waters are enriched in nutrients by the equatorial upwelling, which stretches from Galapagos Island to the South Equatorial Current and decreases westward (Wyrtki, 1981). CO is produced by an active photoproduction (up to 1.4 nmol L⁻¹ d⁻¹) there due to both high irradiance (more than 6 W m⁻²) and a high level of CDOM and is also easily concentrated in surface waters with the strong upward currents. Compared to the integrated patterns, the annual mean surface CO concentrations as well as the surface photoproduction present clear minima in the center of the subtropical gyres. Photoproduction there is around 0.5 nmol L⁻¹ d⁻¹ and CO concentration less than 1 nmol L⁻¹. In the oligotrophic gyres, Chl a and hence CDOM are low, which prevents high CO photoproduction. However, light penetrates deeper allowing photoproduction to occur, even at low rate, all along the irradiated water column. In an opposite way, photoproduction in highly productive areas occurs mainly in surface waters as organic materials absorb most of the available irradiance. Figure 5b and d also present the seasonal variability of the surface patterns with latitude. Both CO and photoproduction surface patterns present a strong seasonal cycle with maximums reached at the end of spring and summer in both hemispheres.

Figure 5Oceanic CO concentration (a, b) and photoproduction (c, d) between 0 and 10 m. Panels (a) and (c) present the surface spatial distribution of the annual mean. Panels (b) and (d) present the mean seasonal variation with latitude.

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3.2.1 Surface CO concentrations

Observed daily mean surface CO concentrations range from 0 to 13.9 nmol L⁻¹ with a mean value of 2.0 nmol L⁻¹. 75 % of the observed data are below 2.5 nmol L⁻¹. The simulated concentrations range from 0 to 4.4 nmol L⁻¹, with a mean of 1.6 nmol L⁻¹for the selected months and locations. The RMSE value resulting from the comparisons is 1.80 nmol L⁻¹.

Figure 6Comparison of in situ oceanic CO concentrations between 0 and 10 m simulated with PISCES with those measured in the surface ocean. (a) Position of the surface measurements collected in the literature. (b) Surface CO concentrations as a function of the latitude (Dots: observed concentrations; dotted line: longitudinal and monthly mean simulated CO concentration; green area: interval between maximum and minimum longitudinal mean concentrations; yellow area: interval between maximum and minimum CO concentrations at a given latitude). Note that a data point of 13.9 nmol L⁻¹ from the dataset of Tran et al. (2013) has been removed for better visibility. (c) Scatter plot the of the simulated CO surface concentrations vs. the observed concentrations. The solid line represents the 1–1 line and dotted lines the 2–1 and 2–1 lines.

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Between 50^∘ N and 50^∘ S, the model is able to represent most concentrations within a factor of 2 (Fig. 6c). For instance, the Atlantic Meridional Transect data (Stubbins et al., 2006b) from 45^∘ N to 30^∘ S present rather constant surface CO concentrations around 1.5 nmol L⁻¹ which are particularly well reproduced by the model. In the Pacific Ocean, the dataset of Bates et al. (1995) covers a broader range of latitudes and longitudes (Fig. 6a) and the model is consistent with the measured concentrations. A longitudinal gradient is observed with concentrations significantly higher in the east and central equatorial Pacific compared to the western part. Bates et al. (1995) attribute this gradient to increased biological productivity, Chl a and CDOM in the eastern upwelling region. Second, Bates et al. (1995) data show a clear latitudinal pattern, with higher concentrations from either side of the 15–30^∘ S oligotrophic band (Fig. 6b). This pattern has also been highlighted by Swinnerton and Lamontagne (1973), who sampled from 20^∘ N to more than 60^∘ S. However, their high values at the Equator (up to 6.3 nmol L⁻¹) are much higher than those of Bates et al. (3.0 nmol L⁻¹). Finally, the dataset of Bates et al., which covers different periods of the year, points out the seasonal variability of the concentrations at mid-latitudes, in agreement with the photochemical nature of the main CO source.

At latitudes higher than 50^∘ north or south, the model underestimates the reported high daily mean surface CO concentrations (Fig. 6b). In the Southern Ocean, simulated surface concentrations do not exceed 4.5 nmol L⁻¹, whereas the data of Swinnerton and Lamontagne (1973), sampled in December, can reach 8.9 nmol L⁻¹. The Southern Ocean is also the basin where Bates et al. (1995) reported their highest surface values (up to 4.7 nmol L⁻¹). In addition, their concentration is higher for December (3.5 nmol L⁻¹) than for March and April (0.8 nmol L⁻¹). Therefore, the underestimation seems to occur mainly during the phytoplankton bloom season, indicating a possible bias in the CO production processes. In the Arctic, we compared simulated concentrations with the datasets of Xie et al. (2009) and Tran et al. (2013). Xie et al. (2009) measured, in the open waters of the southeastern Beaufort Sea, a mean CO concentration of only 0.4 nmol L⁻¹ in autumn, which is particularly well represented by the model. However, their higher mean value of 4.7 nmol L⁻¹ during the spring season is highly underestimated, indicating once again a possible bias with the CO production processes. Tran et al. collected samples in July 2010 between Svalbard, Greenland and Iceland. Closer to the Norwegian basin, measurements have been performed in open-ocean water. It presents a high variability there (from 1.4 to 8.7 nmol L⁻¹), but most data points are under 4.0 nmol L⁻¹ and represented within a factor of 2 by the model. Closer to the Greenland shelf, measurements have been performed in polar waters where pack ice was present. In this area, measured surface concentrations are significantly higher (up to 13.9 nmol L⁻¹) and are clearly underestimated by the model. Other studies have measured high surface CO concentrations in polar regions (Xie and Gosselin, 2005; Valérie Gros, personal communication, 2018), which tends to strengthen the conclusion that major mismatches between our modeled and the observed CO concentrations occur in that region. Indeed, Valérie Gros (personal communication, 2018) measured, north of Svalbard, a mean concentration of 7.1 nmol L⁻¹ in May 2015. These high CO concentrations reported in polar regions could be due to the release of organic matter in the open ocean during ice melting due to algae growing in the ice (Belzile et al., 2000). It could also be due to the direct release of CO produced inside the ice. Indeed, Xie and Gosselin (2005) mentioned that sea ice is a suitable matrix for efficient photoreactions involving CDOM, and measured concentrations in May exceeding 100 nmol L⁻¹ in the bottom layer of a few first-year sea-ice cores sampled in the southeastern Beaufort Sea. However, according to Xie et al. (2009) and Zafiriou et al. (2003), the high CO concentrations reported at high latitudes may be mainly due to slower microbial CO uptake rates in cold waters. Indeed, Zafiriou et al. estimated rates as low as 0.09 d⁻¹ in the Southern Ocean.

It is the first time that such a dataset of in situ CO concentrations in the surface ocean have been gathered and that a 3-D global biogeochemical model is used to simulate the oceanic CO cycle. Despite the scarcity of measurements regarding space and time, PISCES reproduces the observed surface concentrations reasonably well, at least for the open ocean between 50^∘ N and 50^∘ S. While concentrations at low latitudes and midlatitudes are simulated within a factor of 2, photoproduction or consumption processes might not be well represented at high latitude.

3.2.2 Vertical CO profiles

In this section, we evaluate the vertical distribution of CO concentrations as simulated by PISCES against available observed vertical profiles. Only 10 available profiles out of 26 are shown hereafter (Fig. 7), covering different types of marine environments. Other profiles are available in the Supplement.

All simulated CO profiles exhibit a decrease with depth. They are mainly driven by the photoproduction source, which is a combination of the CDOM and irradiance levels. Indeed, no clear subsurface maximums, potentially associated with direct phytoplankton production, are seen. This is also the case for the observed profiles. At 100 m, simulated as well as observed concentrations reach values close to zero, explained by the negligible influence of light irradiance under these depths. However, the shapes of the decreases differ with time and location, which can be related both to differences in the light penetration and mixed layer depths.

When trying to compare simulated and observed profiles one by one, we observe quantitative differences. When the model is able to correctly simulate the concentration at the surface, the deeper concentration is also well simulated. On the contrary, when the model overestimate or underestimate the surface concentration, it is also the case below (see as an example the representation of the two profiles of Zafiriou et al., 2008 taken in the Sargasso Sea in March and August). Nevertheless, the model is always in good agreement with the nearly zero concentrations below 100 m. It is, however, particularly hard to bring out spatial or temporal trends for the observed underestimations or overestimations. As an example for the equatorial Pacific region, the model underestimates by a factor of 2 the concentrations of Johnson and Bates (1996), whereas in the same region in November the data of Ohta (1997) are well represented. Additionally, it is worth mentioning that high variability and uncertainty is associated with some measurements. For example, Yang et al. (2011) measured spring month concentrations of 0.0 to 7.5 nmol L⁻¹ between 25 and 50 m in the Coastal East China and Yellow seas. Also, when no standard deviation is available the data reflect one-time measures. In particular, this is the case for the 10 profiles of Swinnerton and Lamontagne (1973), taken during early afternoon. It is hence difficult to compare these profiles with monthly averaged model outputs.

Figure 7Comparison of simulated oceanic CO profiles with the measured profiles (simulated profiles for the same months and location as measurement). Only a few datasets are shown in this figure (others are available in the Supplement). Dotted lines represent the observed profiles and continuous lines the model output. The standard deviation of the observation, when available, is shown around each observed profile with the shaded area of the same color.

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3.3.1 CDOM parameterization

Surface CDOM absorption. Different parameterizations for the CDOM absorption coefficient have been tested, all using the same simulated Chl a concentrations. The latitudinal mean of these coefficients, taken at 443 nm and for the surface ocean, are shown in Fig. 8 and compared to the mean climatology of CDM (colored detrital matter) distributed within the GlobColour products (Maritorena et al., 2010; Fanton d'Andon et al., 2009), averaged over 2002–2012 (a). As all CDOM parameterizations depend on Chl a concentrations, Fig. 8 also shows the latitudinal mean of the Chl a (b), simulated by PISCES and distributed within the GlobColour products, in order to better separate the respective roles of the CDOM parameterization versus Chl a representation. Additional Chl a comparisons with satellite products are also available in the Supplement (Fig. S2). All CDOM parameterizations lead to similar distributions, with higher values at high latitudes, intermediate values near the Equator and the lowest values in the subtropical gyres, as is the case for Chl a surface concentrations. However, the magnitudes of these CDOM absorption coefficients are very different and vary within a factor of 3 across the different parameterizations. The magnitude from the parameterization of Morel (2009), chosen for our standard simulation, gives intermediate values (global mean is 0.014 m⁻¹) between Preiswerk and Najjar (mean 0.008 m⁻¹) and Launois et al. (mean 0.026 m⁻¹). The GlobColour CDM content can be considered as a proxy for CDOM as it has been postulated that the CDOM absorbance represents 90 % of the CDM absorbance (Siegel et al., 2002). Latitudinal variations are consistent between the satellite products and the tested parameterizations. Minima (less than 0.01 m⁻¹) are located in oligotrophic gyres. Quantitatively, those minima are best represented by the relation of Morel, since those of Launois et al. (2015) and of Preiswerk and Najjar (2000) give too high and too low values, respectively. The highest satellite-derived CDM absorptions are reached at high latitudes, especially in the Northern Hemisphere (latitudinal mean goes up to 0.060 m⁻¹ between 50 and 80^∘ N). These high CDM values correspond mainly to coastal areas, and none of the parameterizations tested here are able to reproduce them. Because the Chl a concentration is rather well represented in the Northern Hemisphere compared to satellite-derived Chl a (Figs. 8 and S2), this strong underestimation is attributable to the CDOM parameterization itself. Indeed, the different parameterizations are all depending on Chl a and are therefore probably better suited for Case-1 waters (Matsushita et al., 2012), for which most dissolved organic matter comes from local phytoplanktonic activities like cell lyses, exsudation or grazing (Para et al., 2010). Indeed, the CDOM concentration in coastal waters is also regulated by the interactions with the continent (Bricaud et al., 1981; Siegel et al., 2002), especially at river mouths where CDOM concentrations are generally higher than for the rest of the ocean (Para et al., 2010). This is the consequence of a local stimulation of primary production associated with nutrient supply (Carder et al., 1989), but also of a direct supply of continental CDOM (Nelson et al., 2007). This direct CDOM supply is not represented in the model, potentially leading to an underestimation of the CO photoproduction in coastal areas, and potentially also in open ocean waters under terrestrial influence. This is particularly the case for the Arctic Ocean as it is enriched in terrestrial dissolved organic matter due to high river supply (Dittmar and Kattner, 2003). Additionally, this could explain part of the CO underestimations in the Arctic, together with the aforesaid mechanism associated with the presence of sea ice. In the Southern Ocean, the CDOM content is slightly above the CDM content retrieved from space (except at the very close Antarctic coast). This could be due to the Chl a overestimation in that region (Figs. 8 and S2). However, whereas Chl a is overestimated, CO underestimations were observed. Hence, to explain CO underestimations, in this region it is better to opt for a link with the representation of the bacterial consumption term. Finally, among the three parameterizations, we chose the one of Morel (2009) for our representation of the CDOM absorption despite the underestimations in the Northern Hemisphere, because globally it fits the satellite-derived CDM better as the amplitude of the latitudinal gradient is the largest (standard deviation is 0.007 m⁻¹, compared to 0.005 m⁻¹ for Launois and 0.003 m⁻¹ for Preiswerk and Najjar relations). Nevertheless, it is important to mention that CDOM is very heterogeneous matter and therefore using Chl a as a proxy for CDOM is in any case obviously reductive, as CDOM has its own dynamic.

Sensitivity of the oceanic CO budget to changes in the CDOM parameterization. Global fluxes have been calculated from the simulations using the different CDOM parameterization (Table 1, lines 1–3). The global photoproduction flux is more than doubled when using the parameterization of Launois et al. (49.1 Tg C yr⁻¹ compared to 19.1 Tg C yr⁻¹ when using that of Morel) and decreases with the one of Preiswerk and Najjar (14.2 Tg C yr⁻¹), in agreement with the quantitative tendencies of the CDOM surface values discussed above. In a similar way, the global dark production flux is more than tripled when using the parameterization of Launois et al. (29.5 Tg C yr⁻¹ compared to 8.5 Tg C yr⁻¹ when using that of Morel) and reduced with that of Preiswerk and Najjar (7.2 Tg C yr⁻¹). For these different tests, the bacterial consumption rates have been kept the same so that the changes in the CO budget and in other terms are solely due to changes in photoproduction and dark production. The CO flux to the atmosphere (3.0–10.2 Tg C yr⁻¹) and the bacterial sink (24.7–74.7 Tg C yr⁻¹) both vary accordingly with the changes in photoproduction and dark production. As a direct consequence, the oceanic CO total inventory is modified (0.3–1.0 Tg C), which also changes the values of the RMSE when comparing simulated surface CO concentrations with in situ measurements (it is 2.91 nmol L⁻¹ with Launois et al. and 1.91 nmol L⁻¹ with Preiswerk and Najjar, whereas it is 1.80 nmol L⁻¹ with Morel). Note that the direct phytoplankton production term remains the same as it does not depend on CO concentrations. Photoproduction has also been integrated in the mixed layer in order to be compared to the value of 39.3 Tg C yr⁻¹ computed by Fichot and Miller (2010) with a global model using ocean color data for the CDOM parameterization. With a budget of 45.4 Tg C yr⁻¹, the photoproduction of Launois et al. gives the closest estimation, those resulting from Morel and from Preiswerk and Najjar being much lower (17.7 and 13.1 Tg C yr⁻¹ respectively). Those two latter estimations are also lower than the most recent estimations based on extrapolations of in situ measurements. Indeed, Zafiriou et al. (2003) estimated the photoproduction between 30 and 70 Tg C yr⁻¹ based on a large dataset collected in the Pacific Ocean and Stubbins et al. (2006b) estimated it between 38 and 84 Tg C yr⁻¹ with Atlantic Ocean data. For the dark production, the use of the CDOM parameterizations of Morel on the one hand and Preiswerk and Najjar on the other hand give global values in the range of previous estimates (4.9–15.8 Tg C yr⁻¹; Zhang et al., 2008), whereas Launois et al.'s resulting estimate is much higher (29.5 Tg C yr⁻¹).

3.3.2 CO consumption

Several simulations regarding the bacterial consumption have been performed. First, different values for a constant bacterial rate have been tested. Second, a variable rate as a function of Chl a and temperature according to the relation of Xie et al. (2005) has also been tested. Global budgets resulting from these different tests are shown in Table 1 (lines 4–8), using the same CDOM parameterization (Morel, 2009) so that the impact of the photo and dark productions terms on the oceanic CO concentration remains the same. When increasing the rate from 0.1 to 2.0 d⁻¹ (with a constant value), the bacterial sink increases from 27.5 to 33.9 Tg C yr⁻¹. This rise of consumption induces a strong decrease in the CO inventory (from 0.8 to 0.04 Tg C) and therefore also decreases the flux to the atmosphere (from 6.4 to 0.5 Tg C yr⁻¹). When changing the rate, the fit of the surface CO concentration with observations is also modified. Indeed, when it is 0.1 d⁻¹, the RMSE value is increased (= 1.97 nmol L⁻¹) compared to the control run (RMSE=1.80 nmol L⁻¹) because of an overall overestimation of CO concentrations. When the consumption rate exceeds 0.2 d⁻¹, the RMSE value is also increased but this time because of an overall underestimation. For the test using a spatiotemporally varying rate (Table 1, line 8), we slightly modified the initial equation of Xie et al. (2005) by adding a factor μ=0.05, so that the mean k_CO is 0.2 d⁻¹. Indeed, when using the original μ=1 with our model, bacterial rates vary from 3.8 to 7.0 d⁻¹ and thus lead to a strong underestimation of CO concentrations. When a varying rate is applied, the global bacterial sink, the CO inventory and the CO flux to the atmosphere are pretty much the same as using the standard run with a constant rate of 0.2 d⁻¹. Also, the RMSE value is almost identical (1.79 nmol L⁻¹). Thus, applying this varying rate did not help to improve the fit of CO concentrations against in situ measurements, which could be explained by the very low standard deviation of the resulting k_CO values (0.01 d⁻¹).

Being the main CO sink in the ocean, a more accurate parameterization of the bacterial CO consumption term is essential to quantify CO emissions to the atmosphere. However, little is known on the CO bacterial consumption, although it has been shown to be ubiquitous in diverse marine ecosystems, particularly in the northeastern Atlantic and Arctic waters (Xie et al., 2005, 2009). According to Xie et al. (2005), this process could follow different patterns from first- to zero-order kinetics or saturation, but most marine waters may be reasonably well approximated by the first-order kinetic, as CO concentrations rarely exceed the half-saturation constant value. It is nevertheless difficult to constrain the bacterial consumption rate based on experimental estimations, as they present a very high variability. The highest rates seem to be found for coastal waters, suggesting the presence of active CO oxidizing communities (Tolli et al., 2006; Tolli and Taylor, 2005). For example, Day and Faloona (2009) measured rates from 1.2 to 19.2 d⁻¹ along the Californian coasts and Jones and Amador (1993) rates from 0.2 to 12 d⁻¹ in the Caribbean Sea. In the remote ocean, measured rates are lower but the variability remains high. Zafiriou et al. (2003) measured a rate as low as 0.1 d⁻¹ in the Southern Ocean, whereas Conrad et al. (1982) retrieved values around 0.7 d⁻¹ in the equatorial Atlantic and Ohta (1997) more than 3.0 d⁻¹ in the equatorial Pacific. Part of this high variability might be explained by the fact that, as for other microbial processes, the CO consumption should also depend on a number of parameters like microbial species, productivity, temperature or ocean acidity (Xie et al., 2005). Using the only study proposing to compute the k_CO value with Chl a and temperature (Xie et al., 2005), we attempted to account for this variability. However, it seems that such an empirical equation, developed with data from the Delaware Bay, the northwestern Atlantic and the Beaufort Sea, is not suitable for a global application as it leads to very high k_CO values. Even when tuning with the factor μ, the remaining k_CO variability is too small to significantly improve the fit with the observed surface CO concentrations.

Based on these different tests, we show that the main terms controlling oceanic CO concentrations are still largely under-constrained, although available in situ CO concentrations, global budget estimates and the CDM concentrations retrieved from space are helping in the choice of standard, i.e., “best guess” simulation. Here, the best parameterization of CDOM absorption compared to satellite products is given by Morel (2009), which then dictates our choice for the standard simulation. However, it is worth mentioning that using the parameterization of Launois et al. (2015) with a higher bacterial consumption rate, or the one of Preiswerk and Najjar (2000) with lower consumption rate, would result in oceanic CO concentrations that give similar skill scores when compared to available CO concentration observations (tests not shown), but for which we have less confidence in the CDOM parameterization.