The calculation of 17Δocean relies on the isotopic composition of dissolved oxygen (32O2, 33O2, 34O2), which is controlled by three main processes: photosynthesis, respiration, and air–sea gas exchange. Consequently, all these processes must be considered to accurately represent the 17Δocean (Fig.  – Green part).

To validate the implementation of the 17Δocean, a total of 2482 measurements were compiled (Fig. ). These data were primarily obtained during oceanographic campaigns, where oxygen concentrations were measured either using sensors mounted on a CTD-rosette or by collecting water samples in bottles. The data were processed by averaging replicate measurements and recording their standard deviation. When it was necessary, 17Δocean value was recalculated using the logarithmic definition (Eq. ), with a reference slope (λ) of 0.518.

To validate the modelled distribution of total dissolved oxygen, we used annual climatological data from the World Ocean Atlas 2023 (WOA23), provided at 1°×1° horizontal resolution . The dataset includes 32 506 unique locations with vertical profiles of dissolved oxygen at various depth. To produce spatial maps from this large dataset, the data points were interpolated using linear interpolation.

It should be noted that the observational datasets used in this study were collected under modern oceanic conditions and represent measurements at specific locations, depths, seasons, and times; whereas the simulations were performed at equilibrium under pre-industrial forcing. Given these differences in temporal representation and the simplified ocean circulation of iLOVECLIM, a point-by-point agreement between model and observations is not expected. Therefore, the geographical comparison is intended to evaluate the large-scale consistency of the simulated oxygen and isotope distributions. As a complementary assessment, the model–data comparison was also examined in temperature–salinity space to evaluate the potential influence of differences in the representation of water masses (Fig. ).

First, we evaluate the modelled distribution of total dissolved oxygen, which serves as the basis for interpreting oxygen isotope tracers. Since total dissolved oxygen reflects both biogeochemical processes and gas exchanges between the air and the sea, a realistic representation is essential to ensure the robustness of the proxy representation. Overall, the distribution of total dissolved oxygen in the photic zone is generally consistent with the interpolated WOA23 data (Fig. ). In polar regions, the model exhibits a slight depletion of approximatively 30 µmolkg-1 relative to observations. Conversely, some equatorial upwelling areas appear slightly enriched in dissolved oxygen in the model.

Similarly, in the subsurface ocean, the large-scale patterns of dissolved oxygen are generally well captured by the model (Fig. ). In the Atlantic Ocean, below 2000 m, the model tends to underestimate total dissolved oxygen concentrations (Fig. b and c). In both the Pacific and Atlantic Oceans, Oxygen Minimum Zones (OMZ) are overestimated, with simulated low-oxygen regions extending beyond those observed in the data (Fig. a and c). In general, the spatial distribution of total dissolved oxygen is reasonably well reproduced by the model, both in the photic zone and at depth, despite some regional discrepancies.

In the iLOVECLIM model, the total phytoplankton production is controlled by three parameters: the maximum daily growth rate, which is influenced by sunlight and temperature; the nutrients availability; and the phytoplankton mass . Since GPPO2 is defined as twice the PP in iLOVECLIM, its spatial distribution is governed by these same processes. After evaluating the model's performance in simulating total dissolved oxygen, we next assess GPPO2, which directly contributes to the isotopic signature observed in surface waters.

Owing to high temperature and maximum solar irradiance, optimum GPPO2 occurs at the equator, reaching 150 mol O2m-2d-1 (Fig. ). Upwelling regions, where nutrient supply is enhanced, are also areas of elevated GPPO2. At high latitudes, annual mean GPPO2 remains elevated because intense spring blooms compensate for low winter production. In contrast, at the center of subtropical gyres, GPPO2 is low due to the limited availability of nutrients.

The simulation was performed under pre-industrial boundary conditions, whereas the estimates of are representative of the modern ocean. Therefore, the following comparison focuses on the large-scale patterns and order of magnitude of simulated productivity. Compared with the global GPPO2 derived from O2 measurements during incubation and 17Δ measurements of seawater sample Table 2, the GPPO2 is relatively well represented in the model. Consistent with the two calculation methods presented by , global GPPO2 is estimated at 9.68×1015molO2yr-1 for the pre-industrial simulation (Table 2). However, regional discrepancies are observed: GPPO2 in the Indian Ocean is underestimated, whereas values in the Arctic and the Southern Ocean are overestimated. The underestimation in the Indian Ocean may reflect limitations in the model's representation of regional processes, such as nutrient supply and monsoon-driven dynamics. Conversely, the overestimation at high latitudes may be due to the absence of iron limitation in the model. Iron is a limiting nutrient for phytoplankton growth, especially in high-nutrient low-chlorophyll regions (HNLC), such as the Southern Ocean and parts of the Pacific Ocean.

With both total dissolved oxygen and GPPO2 reasonably well reproduced by the iLOVECLIM model, we now examine its capacity to simulate oxygen isotope tracers. As mentioned above, the distribution of these tracers is influenced by various processes, including respiration, photosynthesis and air–sea exchange . Hence, isotopic tracers are related to the distribution of total dissolved oxygen: when total dissolved oxygen decreases, isotopic tracers increase (Fig. ). The choice of isotopic fractionation values also affects tracers distributions. Rayleigh curves were plotted using different fractionation values to illustrate the impact of fractionation during respiration (Figs.  and ). Model-data comparison indicates that isotopic tracers are well captured by iLOVECLIM, although some discrepancies appear for 17Δocean. These deviations reflect differences in the relative influence of the governing processes.

δ18O–O2 is primarily affected by respiration (Figs. a and a). In surface waters, where O2 is relatively abundant, the combined processes produce a comparatively stable δ18O–O2 signal. In the subsurface waters, where respiration dominates, δ18O–O2 follows a Rayleigh-type fractionation trajectory with prescribed fractionation factor. Meanwhile, 17Δocean reflects the integrated influence of the three processes (Figs. b and b). When photosynthesis prevails, both 17Δocean and O2 concentration increase. In both tracers, air–sea gas exchange exerts a restoring effect, driving δ18O–O2 and 17Δocean toward their respective equilibrium values (Fig. ).

The simulated annual mean δ18O–O2 distribution reveals clear spatial gradients, both at the surface and at depth (Fig. ). At the surface, δ18O–O2 is about -0.5 ‰ at the equator, while it is about 1 ‰ at the poles (Fig. a). Zones of high productivity (equator, upwelling and Southern Ocean) are marked by a depleted δ18O–O2, whereas enhanced respiration leads to enrichment. At depth (Fig. b and c), δ18O–O2 increases relative to the surface, by an average of 7 ‰ in the Atlantic Ocean and 10 ‰ in the Pacific Ocean. The enriched δ18O–O2 in the subsurface water masses, in particular around the OMZ, is primarily due to respiration. This is particularly evident within OMZ, where the highest δ18O–O2 values are observed, reaching ∼16 ‰ in the Atlantic OMZ and up to ∼22 ‰ in the Pacific OMZ. The stronger enrichment in the North Pacific compared to the Atlantic reflects the older age of water masses, allowing for greater fractionation along the Rayleigh curve. Deep-ocean δ18O–O2 values are further modulated by circulation: waters formed in the North Atlantic and around Antarctica begin with relatively high δ18O–O2, and their progressive aging along circulation pathways enhances enrichment through cumulative respiration.

The simulated annual mean 17Δocean distribution reveals different spatial gradients as δ18O–O2 (Fig. ). At the surface, elevated 17Δocean values indicate regions of high productivity, highlighting the dominant role of GPPO2. At the Equator, the 17Δocean is ∼50ppm, compared with -5 to 20 ppm at the center of the ocean gyres (Fig. a). In upwelling regions, nutrient input leads to high phytoplankton productivity, with a 17Δocean of around 40 ppm. In polar regions, elevated 17Δocean can be explained by various processes, including the presence of sea ice, or model limitation related to the absence of iron representation. Near Antarctica, values reaching up to 100 ppm are consistent with the seasonal extent of sea ice, which inhibits ocean–atmosphere exchange and leads to the accumulation of 17Δocean beneath the ice. At the end of the Antarctic winter, the maximum extent of sea ice can reach 55° S latitude, emphasizing the vast area where seasonal air–sea fluxes are blocked. At depth, similarly to δ18O–O2, an increase of 17Δocean values is observed (Fig. b and c). This vertical distribution can partly be explained by the sinking of water masses, which transports high values to the deep ocean. Additionally, at depth, signals may reflect both the accumulation of respiration and the presence of old water masses.

To reduce the impact of seasonal variability, the model–data comparison focuses on deep-ocean values, where signals are more stable over time (Figs. b and c, b and c). For both δ18O–O2 and 17Δocean, the simulated values fall within the observed range in the Pacific and Atlantic basins. However, in the Atlantic Ocean, modeled values tend to be overestimated in the subsurface ocean. For example, at 20° S and 3 km depth, simulated δ18O–O2 reach 7 ‰, while observational data indicate a value closer to 3 ‰, corresponding to a relative error of approximatively 133 % (Fig. b). At the same location, simulated 17Δocean at 2 km depth shows a relative error of ∼30% compared to observations, with discrepancies increasing below 4 km. Several hypotheses could explain this overestimation, such as: excessive surface oxygen production exported to depth via Antarctic Bottom Water (AABW), or an inaccurate representation of the AABW dynamics in the model. The choice of values for 18α and 17/18θ during respiration are also factors that may induce an overestimation. In addition, part of the discrepancy may reflect the inherent uncertainties and sampling limitations of the observational datasets. suggest that observed data in this region may also be partly influenced by Labrador Sea Water, in particular the Iceland-Scotland Overflow Water (ISOW) and Denmark Strait Overflow Water (DSOW) masses. Such an influence could reduce the apparent discrepancy between simulated and observed 17Δocean values. By contrast, in the model this region is largely dominated by AABW, as illustrated in Fig. b.

These results demonstrate that the model provides a robust first-order representation of the δ18O–O2 and 17Δocean distributions. The discussion below addresses the origins of the remaining biases.

The deep ocean results suggest a slight overestimation of 17Δocean driven by AABW formation and water mass sinking. At the surface ocean, away from the equator, the distribution of 17Δocean is additionally modulated by seasonal effects. Therefore, to evaluate its distribution in the photic layer, it is crucial to compare observational data with simulated seasonal 17Δocean outputs. This is particularly relevant given that most of available observational data are measured from surface water samples collected at specific time, and reflect the state of surface water ecosystem over a few weeks. Year-round observations are only available at research stations (e.g. HOTS, BATS, etc).

For this purpose, monthly modelled 17Δocean values were extracted within the photic layer (0–100 m) at the exact locations of the available measurements to allow a direct comparison (Fig. ). In the Pacific Ocean, simulated 17Δocean values generally fall within the observed range. No clear seasonal pattern emerges from the comparison, although slightly larger deviations are observed for some locations during SON (September–October–November) and DJF (December–January–February). In the Southern Ocean, iLOVECLIM consistently overestimates 17Δocean, with all simulated points lying above the 1:1 line. Whereas observed values range from 0–80 ppm, the model estimates span from 20–160 ppm. Notably, neither the data nor the simulations exhibit a clear seasonal pattern. Due to the scarcity of measurements in the Atlantic Ocean, a robust assessment of 17Δocean representation in this basin is not possible.

As mentioned above, several hypotheses may explain the overestimation of 17Δocean in the Southern Ocean: (1) the absence of iron limitation in the iLOVECLIM model, which favors excessive phytoplankton growth and thus amplifies the photosynthetic 17Δocean signal; and/or (2) the accumulation of the 17Δocean under sea-ice. However, the second hypothesis is unlikely to play a major role here, as sea ice cover is minimal during the DJF season. Overall, this overestimation is most likely due to an overrepresentation of primary production in the model. Since PP depends on three key parameters, it seems possible to improve its representation by further refining the model and adjusting the parameters.

Year-round measurements at the BATS and HOTS allow for the seasonal assessment of the model's ability to represent 17Δocean across depth and basin at fixed coordinates. Overall, both measured and simulated 17Δocean display seasonal variability within the upper photic layer (Fig. ). At BATS, measured 17Δocean stabilizes below 250 m, while at HOTS, stabilization occurs around 300 m across all seasons. In contrast, the modelled 17Δocean stabilizes much shallower, around 100 m, limited by the prescribed photic layer depth. In both observational and simulated profiles, the most pronounced seasonal variation occurs between 50 and 100 m. While the model successfully captures the seasonal trend, it underestimates the amplitude. For instance, during SON, 17Δocean peaks at 120 ppm in the measurements, but only reaches  45 ppm in the model. Despite this underestimation, the seasonal cycle of 17Δocean in the photic layer is reasonably well reproduced.

Overall, the model captures the seasonal trend of 17Δocean reasonably well across different spatial scales, from ocean basins to fixed-point stations. However, it systematically over-estimates absolute 17Δocean values in the Pacific and Southern Oceans when compared point by point with observations. At station level, although the seasonal phase is reproduced, the amplitude remains underestimated and the vertical structure is too shallow, likely due to limitations in the photic layer depth and primary production representation. Indeed, limited variability in PP can reduce the production of oxygen, leading to an underestimation of 17Δocean at these stations. Other factors, such as local mixing processes or nutrient limitations, may also contribute, but the insufficient seasonal modulation of biological activity appears to be a primary driver (Appendix A). These discrepancies suggest that while the timing of seasonal variability is well represented, further refinement of the biological and vertical mixing processes in the model is necessary to improve the magnitude and spatial distribution of 17Δocean. Importantly, the implementation of 17Δocean revealed this bias, providing a direct diagnostic of the model's ability to reproduce seasonal cycles.

Beyond seasonal dynamics, the distribution of total dissolved oxygen is another factor that can indirectly influence 17Δocean. In iLOVECLIM, oxygen minimum zones tend to expand excessively, leading to unrealistic remineralization rates. To prevent such issues, an ad hoc lower oxygen threshold was introduced in the model. After testing, a minimum total oxygen concentration of 30µmolkg-1 was established, below which remineralization is halted to ensure numerical stability. However, this constraint also prevents the full development of OMZ. While it avoids unrealistic anoxia, it limits the emergence of strong subsurface oxygen gradients, which in turn may reduce the biogeochemical contrast necessary to simulate realistic isotopic composition around this region.

To further evaluate the representation of 17Δocean and δ18O–O2 in the model, we compare them against the OMZ using both theoretical estimates and available observations (Fig. ). The theoretical proxy is computed using a Rayleigh fractionation model, which isolates the effect of respiration while neglecting photosynthesis, water mass mixing and air–sea exchange. It provides a useful benchmark to assess the consistency between the simulated oxygen field (Fig. ) and the expected isotopic gradients, by isolating the influence of remineralization. This comparison serves as a diagnostic of the model's internal consistency.

In the eastern equatorial Pacific, both the model and theoretical calculations show an eastward increase in 17Δocean, near the American coast (Fig. a). However, sparse observational data in this region limit direct validation. The theoretical signal exhibits a more pronounced vertical gradient and higher values toward the east compared to the model. In contrast, the simulated 17Δocean is further diffuse, potentially due to excessive smoothing of primary production, limited vertical resolution, or inaccurately tuned remineralization rates. Additional contributions may arise from inaccurate isotopic fractionation values during both photosynthesis and respiration, which would directly affect the magnitude and vertical structure of 17Δocean. For δ18O–O2 (Fig. b), the model simulates strong enrichment along the eastern boundary, where OMZ are expected (Fig. c). However, observed values are lower, suggesting an overestimation of the isotopic signal associated with respiration. This bias may result from excessive remineralization just above the 30 µmolkg-1 threshold in iLOVECLIM, which suppresses anoxia while still allowing intense localized biogeochemical activity. Other potential biases include excessive remineralization rates, overestimation of isotopic fractionation during respiration, or mixing between different water masses. In addition, limited vertical mixing may amplify this signal. While remineralization under low oxygen conditions could occur, the behavior of isotopic fractionation under such conditions remains largely unknown. Diapycnal mixing may also contribute to the observed patterns. As a result, the model produces a truncated OMZ but an exaggerated isotopic response, complicating the interpretation of δ18O–O2 in these regions.

Overall, this comparison highlights the value of combining isotopic proxies, theoretical simulations, and biogeochemical fields to diagnose internal model limitations. In particular, when the oxygen field reproduces expected structures but the associated isotopic signal does not, this may indicate a decoupling between biological processes and isotopic dynamics.

Air–sea gas exchange is one of the three fundamental processes controlling the isotopic composition of dissolved oxygen. The reference simulation (CTRL) uses the equilibrium and kinetic isotope fractionation factors described in Sect. 2.2.2. To evaluate the sensitivity of the isotopic tracers to recently revised air–sea isotope fractionation factors, we performed an additional simulation, hereafter referred to as the Exchange experiment, using the parameterization of . The corresponding fractionation factors are summarized in Table . Compared with the CTRL simulation, the equilibrium fractionation factor for 18O remains unchanged, whereas the kinetic fractionation factor for 18O and both the equilibrium and kinetic fractionation factors for 17O are updated.

Figure  shows the differences in simulated δ18O–O2 between the simulation using the updated air–sea exchange fractionation factors and the reference simulation (Exchange–CTRL). The impact of the revised parameterization on simulated δ18O–O2 remains relatively small at the ocean surface (Fig. a), with anomalies generally ranging between -0.5 and 0.5 ‰. Surface waters exhibit slightly higher δ18O–O2 values in the Exchange simulation, except in the Southern Ocean where lower values are observed. These negative anomalies propagate into the ocean interior, leading to decreases of up to 2.5 ‰ within oxygen minimum zones (Fig. b and c).

The impact is more pronounced for 17Δocean (Fig. ). At the ocean surface, differences range from approximately -10 to 10 ppm, with depleted values in the mid-to-high latitudes and equatorial regions, while enhanced values occur in the subtropical gyres (Fig. a). This spatial pattern highlights the regional influence of air–sea gas exchange on the isotopic composition of dissolved oxygen, especially in the regions of relatively weak biological productivity (e.g., subtropical gyres) or intense air–sea gas exchange (e.g., Southern Ocean). In the ocean interior, 17Δocean in the Exchange simulation decreases by up to approximately 16 ppm, with maximum differences reaching -24ppm within oxygen minimum zones (Fig. b and c). These pronounced anomalies indicate that changes in the isotopic signature acquired during air–sea gas exchange are subsequently transported into the ocean interior, where they amplify the differences between the two simulations.

These changes are consistent with the experimental results of , confirming that the revised air–sea gas-exchange isotope fractionation factors exert a non-negligible influence on the isotopic composition of dissolved O2. Despite these regional differences, the overall agreement between simulations and observations changes only marginally. The coefficient of determination remains unchanged for δ18O–O2 (R2=0.70 for both simulations), while it increases slightly for 17Δocean, from R2=0.02 in CTRL to R2=0.03 in the Exchange simulation. These relatively low coefficients mainly reflect the comparison of climatological model fields with sparse observations collected over different seasons, years, and spatial scales, rather than a point-by-point evaluation. Nevertheless, the updated coefficients noticeably improves the simulated isotope fields in oxygen minimum zones and in the Southern Ocean. Within oxygen minimum zones, the revised fractionation factors reduce δ18O–O2 by up to 2.5 ‰ and 17Δocean by up to 24 ppm, thereby reducing the model bias relative to the limited observations available in these regions (Fig. ). Similar improvements are found in the Southern Ocean, although significant discrepancies remain. These results suggest that the revised air–sea gas-exchange fractionation factors improve the regional distribution of the simulated isotope fields but cannot, by themselves, explain the remaining Southern Ocean model–data discrepancies. Additional physical and biogeochemical processes are therefore likely to contribute to the persistent biases.