Introduction

Nitrous oxide (N2O) is the leading ozone-depleting agent of the 21st century1,2,3 and a potent greenhouse gas, with a global warming potential 273 times that of carbon dioxide (CO2) on a 100-year timescale1. The ocean, a net source, plays a critical role in the global N2O budget, yet the magnitude of marine N2O emissions remains highly uncertain, particularly in dynamic, historically undersampled regions such as the Southern Ocean4,5,6. This uncertainty limits our ability to assess the impact of marine N2O emissions on climate, because even trace amounts of N2O emitted from the ocean may play a major role in offsetting marine CO2 uptake in terms of radiative forcing7,8. Furthermore, this counteracting effect may be directly stimulated by enhanced biological activity, such as that triggered by natural or intentional ocean iron fertilization7,8.

The Southern Ocean is a major contributor to global marine N2O emissions, yet estimates of its contribution have varied widely. Initial studies suggested that the Southern Ocean accounted for 24–43% of total marine N2O emissions4,5,9, but recent work revised the Southern Ocean flux down to only 19% of global emissions6. These inconsistencies leave a wide range of estimates of the Southern Ocean N2O source (0.8–1.6 Tg N/year; Table 1), making it difficult to assess its significance as a greenhouse gas source to the atmosphere. Furthermore, previous estimates relied on sparse sampling, spatial averaging, and/or climatological monthly means of air-sea N2O disequilibrium, and are thus unlikely to capture the sub-seasonal scales of variability that are important to Southern Ocean biogeochemistry and air-sea gas exchange10,11,12.

Table 1 Annual Net Southern Ocean nitrous oxide (N2O) flux
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Here, we apply machine learning models to high space- and time-resolution Biogeochemical Argo (BGC-Argo) in situ sensor data to investigate a key driver of sub-seasonal variability: the passage of strong storms through latitudes 50–65°S every 4–8 days13,14,15. The barometric pressure in the centers of extratropical cyclones can drop to as much as 8% below 1 atm (Fig. S1–S12; S2,4), creating conditions favorable for N2O outgassing. Recent work on storm-driven CO2 fluxes demonstrated that storms significantly enhance air-sea gas exchange, driving high CO2 fluxes through turbulent entrainment of the deeper inorganic carbon reservoir16,17,18. Under-sampling storm-driven CO2 fluxes, which occur on timescales of days, can distort seasonal and annual air-sea CO2 flux estimates11,12. Previously impossible due to the lack of observational coverage, we can now quantify the effect of storms on Southern Ocean N2O fluxes using BGC-Argo data, and thus better constrain the role of the Southern Ocean in greenhouse gas exchange with the atmosphere.

Results and discussion

Float-based observations of N2O flux

To project sparse N2O measurements onto distributed sensor data, we trained machine learning models on the Global Ocean Ship-based Hydrographic Investigations Program (GO-SHIP) N2O dataset (n = 1968 profiles; Fig. S13), then applied these models to predict N2O concentrations from parameters measured by profiling BGC-Argo floats (n = 28,112 profiles; Fig. S14). BGC-Argo floats provide year-round, distributed measurements of ocean biogeochemistry, and, along with gliders, have transformed our understanding of Southern Ocean CO2 emissions16,17,19. Because BGC-Argo floats cannot measure N2O directly, we turned to supervised learning algorithms, which have been used to map chemical distributions of iodide20, methane21, pCO222, and surface N2O saturation6. Supervised learning algorithms are a natural framework for modeling the sharp gradients in marine N2O concentrations because, unlike multiple linear regression, they are robust to non-linearity and perform well on the smaller datasets inherent to labor-intensive ocean sampling23. We found that dissolved N2O is highly predictable from dissolved oxygen, conservative temperature, absolute salinity, and nitrate concentration (Fig. S15). Based on a test dataset comprised of profiles withheld from model training, our models predicted the seawater partial pressure of N2O (\(p{N}_{2}{O}_{{sw}}\)) with R² ≥ 0.91, and root mean squared error ≤ 21 natm in the Southern Ocean (Fig. S15).

Storms drive hotspots of N2O flux

Applying these models to BGC-Argo float profile data revealed that high sea-to-air N2O fluxes tend to be collocated with coherent low-pressure centers with high wind speeds (Fig. S1–S12). The air-sea partial pressure disequilibrium of N2O is defined as:

$$\triangle p{N}_{2}O=p{N}_{2}{O}_{{sw}}-p{N}_{2}{O}_{{atm}} , $$
(1)
$$p{N}_{2}{O}_{{atm}}\approx P\cdot \chi {N}_{2}{O}_{{atm}}$$

where \(p{N}_{2}{O}_{{sw}}\) is the partial pressure of N2O dissolved in surface seawater, \(p{N}_{2}{O}_{{atm}}\) is the atmospheric partial pressure of N2O, P is the barometric pressure, and \(\chi {N}_{2}{O}_{{atm}}\) is the dry mixing ratio of N2O in air. Low barometric pressures in the centers of storms reduce \(p{N}_{2}{O}_{{atm}}\), widening \(\triangle p{N}_{2}O\) (Fig. 1b) and driving greater flux out of the water (Fig. 1c). In other words, the low barometric pressure in storms acts to suck gas out of the water; we term this “the Hoover Effect.”

Fig. 1: Distribution of gas exchange-relevant parameters in the Southern Ocean.
Fig. 1: Distribution of gas exchange-relevant parameters in the Southern Ocean.
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a Barometric pressure in atmospheres (atm) corresponding to each of 28,112 float profiles. The barometric pressures displayed are the mean of ERA5 and NCEP reanalysis products that have been interpolated to the location and time of float profiles. b Air-sea nitrous oxide (N2O) pressure disequilibrium, \(\Delta p{N}_{2}O\), defined as the partial pressure of N2O in seawater (\(p{N}_{2}{O}_{{sw}}\)) minus the partial pressure N2O in the atmosphere (\(p{N}_{2}{O}_{{atm}}\)), such that positive values indicate \(p{N}_{2}{O}_{{sw}} > p{N}_{2}{O}_{{atm}}\). c Air-sea N2O flux in micromoles/meter squared/day (µmol/m2/day). Positive values indicate flux out of the water. In all subplots, points are scaled by the magnitude of air-sea N2O flux (a–c).

To quantify the integrated effect of low barometric pressure in storms on air-sea N2O fluxes, we calculated air-sea N2O fluxes with the global mean barometric pressure (1 atm) in place of the observed barometric pressures (with wind and all other inputs being equal). We compare against fluxes calculated with 1 atm, as opposed to the mean Southern Ocean barometric pressure, because the characteristically low mean Southern Ocean pressure is itself a product of frequent storm activity13. In particular, storms tend to converge at 60° S18,24, creating the upward motion that dynamically maintains the mean low pressure of the Subpolar Low25,26,27.

The difference between the fluxes based on true barometric pressure and 1 atm is of a similar order of magnitude to the flux itself (Fig. S16), indicating that barometric pressure is a primary driver of high fluxes in the centers of these storms. This result implies that low-pressure storms create conditions that promote hotspots of N2O flux, and conversely, that estimates based on smoothed barometric pressure fields or 1 atm barometric pressure may be missing a substantial proportion of the net annual Southern Ocean N2O flux. When we take these low barometric pressures, or the Hoover Effect, into account, we find that the net annual Southern Ocean N2O source is 1.6 ± 0.3 Tg N2O-N/year (Fig. 2). In contrast, when we calculate the net annual Southern Ocean N2O source with 1 atm barometric pressure, the net annual flux drops to 0.9 ± 0.3 Tg N/year, or by a margin of 50 ± 20% (Fig. 2). This observation suggests that roughly half of the total flux is driven by deviations in barometric pressure from the global mean.

Fig. 2: Cumulative Southern Ocean nitrous oxide (N2O) flux, ordered by barometric pressure.
Fig. 2: Cumulative Southern Ocean nitrous oxide (N2O) flux, ordered by barometric pressure.
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Cumulative curves of the area- and time-integrated air-sea N2O fluxes associated with each BGC-Argo data point in teragrams of nitrogen per year (Tg N yr−1), sorted by barometric pressure in atmospheres (atm), and calculated with: a the observed barometric pressure (blue) and b 1 atmosphere barometric pressure (black). Cumulative curves are the average of fluxes calculated from four different combinations of wind product and gas exchange parameterization (shades of green). Small envelopes of uncertainty around each wind product-parameterization pairing (green) reflect uncertainties propagated from \(p{N}_{2}{O}_{{sw}}\), atmospheric \(\chi {N}_{2}{O}_{{atm}}\) with a Monte Carlo simulation; the overall uncertainty (light blue, gray) reflects the combined Monte Carlo uncertainties, standard deviation of the four pairings, and uncertainty from the bootstrap analysis. The histogram of barometric pressures is shown at the top of the figure.

Furthermore, low barometric pressures and high wind speeds act synergistically in storms, creating a nonlinear response. The mixed partial derivative term of the Taylor expansion of \({F}_{W14}\) (equation S4) with respect to wind speed and barometric pressure, centered on the median wind speed \({U}_{{med}}\) and 1 atm barometric pressure \({P}_{1{atm}}\), has the form:

$${\left.\frac{{\partial }^{2}{F}_{W14}}{\partial P\partial {U}_{10}}\right|}_{{U}_{{med}} , {P}_{1{atm}}}\left({U}_{10}-{U}_{{med}}\right)\left(P-{P}_{1{atm}}\right)$$
$$=2{\cdot U}_{{med}}\cdot 0.251$$
$$\cdot s{\left(\frac{{Sc}}{660}\right)}^{-1/2}(-\chi {N}_{2}{O}_{{atm}})\left({U}_{10}-{U}_{{med}}\right)\left(P-{P}_{1{atm}}\right)$$
(2)

Where U10 is the wind speed at 10 meters, \({U}_{{med}}\) is the median Southern Ocean wind speed, \({P}_{1{atm}}\) is a barometric pressure of 1 atm, \(s\) is the Henry’s Law constant, and Sc is the Schmidt number. Given that, in storms \(\left({U}_{10}-{U}_{{med}}\right) > 0\) and \(\left(P-{P}_{1{atm}}\right) < 0\), the sign of this second-order mixed partial derivative is positive, indicating that the combination of high winds and low pressure in storms produces more flux than would be expected from their individual effects alone. The Taylor expansion of \({F}_{L13}\) (eqns. S21–S23) is more complex but yields a similar result (Supplementary Text S2).

To obtain a discrete approximation of the interaction effect, we can compare the observed flux to 1) a “baseline” case calculated with 1 atm barometric pressure and median piston velocities (k); 2) a “wind effect” case calculated with 1 atm barometric pressure and observed piston velocities; and 3) a “pressure effect” case calculated with observed barometric pressures and median piston velocities (Supplementary Text S2). This empirically calculated interaction effect accounts for a significant proportion of the overall flux (Fig. 3). This result implies that the interaction of low barometric pressures and high wind speeds in storms could lead to a nonlinear response of air-sea N2O flux to increasing storm frequency28.

Fig. 3: Interaction effect between low pressure and high wind speeds in storms.
Fig. 3: Interaction effect between low pressure and high wind speeds in storms.
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Cumulative curves of the area- and time-integrated air-sea N2O fluxes associated with each BGC-Argo data point in teragrams of nitrogen per year (Tg N yr−1), sorted by barometric pressure in atmospheres (atm). Fluxes are calculated with median piston velocities and 1 atm (“baseline”, dark purple) and the observed piston velocities and barometric pressures (black line). The pure pressure effect corresponds to \({F}_{{median\; k}}-{F}_{{baseline}}\) (medium purple); the pure wind effect corresponds to \({F}_{1{atm}}-{F}_{{baseline}}\) (light purple); and the interaction (palest purple) is the remainder.

The importance of storms is also evident in the small number of profiles that contribute disproportionately to the net annual flux. For example, only 5% of the float profiles comprise 34 ± 9% of the net annual flux; 10 ± 3% of profiles make up 50% of the total flux (Fig. S17). Together, these results imply that brief, intense flux events in the middle of Southern Ocean storms account for a disproportionate amount of the net annual Southern Ocean N2O emissions. Previous estimates5,6 do not capture these brief, intense flux events in storms.

Biotic vs. abiotic drivers

It is a surprising result that a difference of only up to 8% in barometric pressure can drive an 88% increase in the net annual Southern Ocean N2O flux. Carbon studies show that air-sea CO2 flux is strongly mediated by the imprint of biology, with outgassing associated with upwelling/entrainment of remineralized carbon. In contrast, for N2O, we hypothesized that storms modulate sea-to-air flux primarily via lowering the barometric pressure, as opposed to entraining the deep N2O reservoir, due to the relatively low, uniform \(p{N}_{2}{O}_{{sw}}\) in the Southern Ocean (Fig. S18). To test this hypothesis, we performed a sensitivity test holding \(p{N}_{2}{O}_{{sw}}\) constant; this test produced a much smaller change than holding the barometric pressure constant at 1 atm (Fig. S19). The importance of barometric pressure in dominating flux also means that our results are somewhat agnostic to uncertainties in the machine learning prediction: because the effect is driven by low atmospheric pressure, not high surface \(p{N}_{2}{O}_{{sw}}\), the result doesn’t depend on perfectly capturing high \(p{N}_{2}{O}_{{sw}}\) in the centers of storms.

The large impact of variations in barometric pressure on N2O flux arises from the relatively small N2O partial pressure disequilibrium in much of the Southern Ocean (Fig. 1b): the median \(p{N}_{2}{O}_{{sw}}\) in the Southern Ocean is 334 natm, while the median partial pressure disequilibrium is only 11 natm. This means that small changes in barometric pressure represent a large percentage change in pressure disequilibrium, and thus large changes in air-sea flux. In the Antarctic Southern Zone, the surface water pN2O is close enough to equilibrium with the atmosphere that the pressure effect accounts for 100%—or even reverses the direction—of air-sea flux (Figs. 5, S20).

Seasonal cycles in N2O flux

While the magnitude of air-sea flux is driven by barometric pressure, the seasonality of flux is driven by the seasonal cycle in surface seawater dissolved N2O (\(p{N}_{2}{O}_{{sw}}\)), and, to a lesser extent, wind speed. The overall seasonal cycle suggests an autumnal peak in Southern Ocean integrated flux (Fig. 4), matched by April-June flux maxima in four out of five zones (Fig. 5). Drivers of this autumnal maximum are evident from sensitivity tests performed by calculating fluxes with 1 atm barometric pressure, median piston velocities (k), and median \(p{N}_{2}{O}_{{sw}}\) (Fig. 4). Fluxes calculated with 1 atm barometric pressure have a lower magnitude but the same seasonal cycle as the observed fluxes (Figs. 4a, 5); in contrast, fluxes calculated with median k values display a muted autumnal maximum (Fig. 4b), and fluxes calculated with median \(p{N}_{2}{O}_{{sw}}\) barely contain any seasonal cycle at all (Fig. 4c). This effect likely arises from the prominent seasonal cycles in wind speed and \(p{N}_{2}{O}_{{sw}}\) in each zone (Fig. S21). In the Subantarctic Zone and Polar Frontal Zone, there are particularly strong peaks in \(p{N}_{2}{O}_{{sw}}\) in April through June (Fig. S21f, i), which correspond to the autumnal entrainment maximum in these zones29. Future work should investigate the role of circulation in bringing N2O produced at depth to the surface.

Fig. 4: Annual cycle of nitrous oxide (N2O) flux in the Southern Ocean.
Fig. 4: Annual cycle of nitrous oxide (N2O) flux in the Southern Ocean.
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The seasonal cycle in observed net Southern Ocean N2O flux in teragrams of nitrogen per year (Tg N yr−1), integrated by month. The observed flux (solid pink line) is compared to the seasonal cycle in fluxes calculated with: a 1 atmosphere (atm) barometric pressure (dashed line in a), b median piston velocities k (dashed line in (b), c the median seawater partial pressure of N2O (\(p{N}_{2}{O}_{{sw}}\); dashed line in (c), and d without the capping effect of sea ice (dashed line in (d)). Shading around each curve indicates the uncertainty in the area- and time-weighted fluxes, which is driven primarily by the uncertainty in the choice of gas exchange parameterization. Vertical gray shading indicates winter months (March-November).

Fig. 5: Seasonal cycles of nitrous oxide (N2O) pressure disequilibrium (\(\Delta p{N}_{2}O\)) and area- and time-weighted N2O flux.
Fig. 5: Seasonal cycles of nitrous oxide (N2O) pressure disequilibrium ( $$\Delta p{N}_{2}O$$ Δ p N 2 O ) and area- and time-weighted N2O flux.
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\(\Delta p{N}_{2}O\) in nanoatmopheres (natm; a, c, e, g, i) and sea-to-air flux in teragrams of nitrogen per year (Tg N/yr; b, d, f, h, j) in the Subtropical Zone (green, STZ; a, b), Subantarctic Zone (red, SAZ; c, d), Polar Frontal Zone (blue, PFZ; e, f), Antarctic-Southern Zone (orange, ASZ; g, h), and Southern Ice Zone (purple, SIZ; i, j), calculated with the observed barometric pressure (bold solid line), 1 atmosphere (atm) barometric pressure (dashed line), and without the capping effect of sea ice (thin line; does not affect \(\Delta p{N}_{2}O\)). Shading indicates the standard error of the mean \(\Delta p{N}_{2}O\) in each zone and month (a, c, e, g, i) or the uncertainty in the area- and time-weighted fluxes, which is driven primarily by the uncertainty in the choice of gas exchange parameterization (b, d, f, h, j). Note varying y-axis scales to better visualize seasonal cycles.

There is no seasonal cycle in barometric pressure in our dataset, but rather a large degree of spread throughout the year, reflecting the fact that floats encounter low-pressure centers associated with storms and intervening high-pressure ridges (Figs. S21, S22). The distribution shift towards lower pressures in the southernmost zones (Fig. S21) reflects the increasing storm density from north to south, which has been previously observed in the Southern Ocean18. Averaging over these points produces a general decline in barometric pressure moving from north to south, with the lowest barometric pressures in the Antarctic Southern Zone and Southern Ice Zone (Fig. S21j, m).

Sea ice causes fluxes to decrease over the course of austral winter in the southern ice zone; in the absence of sea ice limiting exchange, N2O fluxes in the southern ice zone could reach a September maximum of > 0.1 Tg N/year, more than twice as high as the peak flux in any other zone (Fig. 5j). Estimating the net annual flux based on peak months (April-June) vs. trough months (October-December) leads to statistically significant differences in each zone (Fig. S20), indicating the importance of sampling the full seasonal range of sea-to-air N2O fluxes in the Southern Ocean. Thus, extrapolating from summertime shipboard measurements may lead to an underestimate of the total annual flux, especially if those measurements take place during the early part of austral summer.

A higher estimate of the annual Southern Ocean N2O flux

Our float-based estimate of the net annual Southern Ocean N2O source (1.6 ± 0.3 Tg N/year) represents a significant upward revision from earlier work6 (0.8 ± 0.2 Tg N/year; Table 1). The discrepancy may be explained by the pressure effect: when using 1 atm barometric pressure, our estimate (0.9 ± 0.3 Tg N/year) is within error of previous work6 (Table 1). Previous work6 focused on predicting monthly mean N2O disequilibria (Δ\(\chi {N}_{2}O\)) with monthly mean World Ocean Atlas30 data, which may have smoothed over low-pressure centers in the centers of storms. In contrast, the BGC-Argo in situ observations used here allowed us to predict pN2O, and, thus, calculate fluxes on sub-daily timescales. Furthermore, our models were trained on both surface and subsurface data, which may have allowed them to better capture Southern Ocean winter conditions (i.e., source waters).

Our improved quantification of N2O flux suggests that the Southern Ocean is a more important component of the global N2O cycle than previously thought. Given a global N2O flux of 4.2 ± 1 Tg N/year6, our estimate indicates that the Southern Ocean represents 38 ± 12% of all marine N2O emissions, which represents a significant upward revision. An important caveat is that this estimate of the global source (4.2 ± 1 Tg N/year)6 is subject to the same uncertainties and potential aliasing as the corresponding earlier estimates of Southern Ocean N2O emissions. Our estimate also implies that N2O flux from the Southern Ocean offsets a greater proportion of CO2 uptake by the same region: using a N2O global warming potential of 2731, our updated flux predicts that Southern Ocean N2O outgassing offsets 218 ± 41 Tg CO2 uptake per year, twice the 109 ± 27 Tg CO2/year suggested previously6. Assuming an annual net Southern Ocean CO2 uptake of 0.87 Pg C/year31, this means that N2O outgassing from the Southern Ocean offsets 7% of the annual CO2 uptake by the same region.

Limitations of this analysis and avenues for future study

There are several key limitations of this analysis that could be improved with further work. Firstly, BGC-Argo oxygen measurements tend to be biased low32. A first-order correction for this bias resulted in a ~ 10% reduction in the net annual N2O flux, which is within our range of uncertainty (Supplementary Text S3). Correcting for float oxygen biases is still an area of active research32, however, so no correction was applied here. The observed reconstruction bias (“Methods”, vide infra) may have resulted in part from float oxygen bias, in addition to spatiotemporal sampling differences. Secondly, given typical ocean decorrelation length and time scales of ~160 km and ~60 days, respectively33,34, float profiles every 10 days may not be entirely independent, leading to an underestimate of the overall uncertainty.

Third, the parameterization of N2O air-sea gas exchange is still an active area of research, and the subjectivity in the choice of parameterization is one of the leading sources of uncertainty (Fig. 2). Since CO2 and N2O have similar solubilities, eddy covariance CO2 flux studies35,36,37,38 could help provide insight into N2O air-sea gas exchange, following previous work using eddy covariance to better constrain bubble fluxes of CO239,40. Future work should attempt to use the insights from these eddy covariance studies to help narrow the uncertainties due to the subjectivity of parameterization of air-sea gas exchange. Relatedly, the interactions between air-sea gas exchange and sea ice are more complex than the simple fractional correction applied here would suggest41,42,43. More work is needed on biogeochemical N2O cycling within and around sea ice itself, as well as a more nuanced treatment of how different types of sea ice (pancake ice, leads in sea ice) modulate air-sea gas exchange.

While BGC-Argo data improve spatial and temporal coverage compared to shipboard data, there are still locations where no float profiles exist, and additional data would likely improve our estimate. Although we perform a bootstrap analysis to assess uncertainty due to sparse coverage (Eq. 15), the estimated absolute flux values presented here apply only to the regions and seasons where float data are available. Missing coastal and shelf processes may be an especially important source of potential bias in our N2O fluxes. BGC-Argo provides good coverage of the open ocean but is missing coastal and shelf regions, where both emissions and uncertainties are high44; future work could take advantage of other autonomous technologies, such as gliders and moorings, to better constrain N2O emissions in the near-coastal regions of the Southern Ocean and elsewhere. There is also a need for more high-quality shipboard N2O measurements, especially in coastal regions, to improve the representativeness of the training dataset. Comparing artificially-seeded, autonomously-measured N2O fluxes to a model ground truth45 could help evaluate where additional N2O measurements would be most impactful.

Future work could also situate the air-sea N2O fluxes calculated here in the context of storm geometry. A recent study found weaker storm activity in the Atlantic sector of the Southern Ocean18; the storm masks from that study could be used to quantify the percentage of high-N2O-flux profiles that occur within defined storms, and break this down by sector to quantify whether there are indeed fewer low-pressure points in the Atlantic sector. Visually, the highest N2O fluxes appear to occur on the northern edge of each low-pressure center (Fig. S1–S12); this aligns with the same recent study, which showed that the highest wind speeds tend to occur on the northern edge of the low-pressure center with respect to storm geometry18. An analysis of N2O fluxes with respect to storm geometry could be used to quantitatively evaluate this pattern.

Potential climate feedbacks

While changes in N2O flux under different warming scenarios are difficult to predict, we can perform sensitivity tests to demonstrate the potential response of N2O flux to different climate forcings such as increasing wind stress46,47,48, decreasing barometric pressure47,49, and increasing storm frequency28. The mean barometric pressure over the Southern Ocean is predicted to change by only 0.002 atm by 210026, not enough of a change to generate a significant increase in the annual net N2O flux, but a more drastic shift in the mean barometric pressure of 0.01 atm increased the annual net N2O flux by 31% to 2.1 ± 0.4 Tg N/year (Table 1). Models tend to disagree on both the amount and distribution of Southern Ocean sea ice loss50,51, so we performed a sensitivity test removing the capping effect of sea ice in its entirety. This increased the overall flux by 25% to 2.0 ± 0.4 Tg N/year (Table 1; Fig. S23), driven primarily by strong outgassing in the Southern Ice Zone (Fig. 5). Increasing wind speeds by 25%, which is the predicted increase in Southern Ocean wind stress under RCP8.525, increased N2O flux by 38% 2.2 ± 0.7 Tg N/year (Table 1; Fig. S23). The combined effects of increasing wind speeds by 25% and removing the sea ice barrier increased the net annual flux by 81% to 2.9 ± 0.8 Tg N/year (Table 1; Fig. S23). Finally, as shown above, low barometric pressures and high wind speeds have an interaction effect in storms, which could lead to a nonlinear response of flux to increasing storm frequency. While these sensitivity tests are not simulations of future climate scenarios with associated feedbacks, they demonstrate that the Southern Ocean N2O source is a dynamic system that is poised to experience a significant ramp-up in N2O emissions as the region changes.

Methods

Datasets

We compiled the Random Forest model training dataset from N2O measurements collected during CLIVAR (Climate and Ocean: Variability, Predictability and Change) and GO-SHIP (Global Ocean Ship-Based Hydrographic Investigations Program). The GO-SHIP dataset provides full water column, quality-controlled N2O data from 2005 to 2023 (Fig. S13; Supplementary Table 3). We restricted our training dataset to the GO-SHIP program due to the high level of quality control applied to the N2O measurements and accompanying hydrographic and nutrient measurements taken from the same Niskin bottle. GO-SHIP data were filtered to retain only samples for which the CTD pressure, temperature, salinity, and oxygen were flagged as good (flags 2, 6, and 7), the nitrate and N2O water samples were flagged as good (flags 2, 6, 7, and 8), and the Niskin bottle was flagged as good (2). This filtering left 35,664 data points from 1968 unique profiles from 24 cruises in the training dataset. GO-SHIP data from the full water column (as opposed to just the surface) were included in model training to better capture the conditions and water masses from which N2O in the Southern Ocean originates.

BGC-Argo is a global, autonomously drifting float array with in situ sensors for temperature, salinity, dissolved oxygen, nitrate, and other biogeochemically relevant parameters52. BGC-Argo floats sample for these parameters from 2000 m depth to the surface every 10 days, then transmit the data back to data assembly centers on land52. For this study, BGC-Argo float data were obtained from a snapshot of the BGC-Argo dataset from October 9th, 202453. The float dataset was limited to data points where [O2] and nitrate concentration ([NO3−]) were both available; excluding [NO3−] from the predictor features would increase the number of float profiles available for this analysis, which could be explored in further studies. Float data were filtered to retain only delayed-mode-adjusted pressure, temperature, salinity, [O2], and [NO3−] with quality flags 1 (“good”), 2 (“probably good”), 5 (“value changed”), and 8 (“interpolated, extrapolated, or other estimation”). Float data were further restricted to points south of 30°S. While the full water column was considered in model training, only surface points were retained in the BGC-Argo dataset because the parameter of interest was air-sea flux. To handle the ice avoidance algorithm, which prevents floats from rising shallower than 15–20 m when under ice, surface points were extracted by taking the shallowest point in each profile that was also shallower than 30 m. This left 28,112 surface data points from an equivalent number of unique profiles from 325 total floats in the Southern Ocean, starting in 2008 (Fig. S14). Floats were assigned to zones based on climatological mean locations of Southern Ocean fronts19,54 (Fig. S14a). The effective decorrelation length scales, calculated on a monthly mean basis, ranged from 160 to 240 km per float, with the best coverage in the Southern Ice Zone (Fig. S14b). Effective decorrelation time scales ranged from 0.04 to 0.06 days per float. While each float samples every 10 days, they sample at random intervals, providing much finer temporal resolution in aggregate55.

The atmospheric mixing ratio of N2O (\({{\rm{\chi }}}\)N2Oatm) was obtained from NOAA flask dataset measurements at the Palmer Station (64.6°S, 64°E) and South Pole (90°S, 0°E) monitoring stations56. Assuming that the atmosphere is zonally well-mixed, the Southern Ocean monthly mean was estimated by weighting each station by the cosine of its latitude (meaning that \({{\rm{\chi }}}\)N2Oatm was primarily driven by the Palmer Station). Monthly mean \({{\rm{\chi }}}\)N2Oatm were linearly interpolated in time to the date and time of each float profile.

Barometric pressure and wind speed were obtained from surface-level ERA557 and NCEP38 reanalysis data, matching each float profile to the nearest 6-hourly ERA5 and NCEP values in space and time (Figs.1; S4b, S4c). Fractional sea ice cover was obtained from ERA5, because NCEP sea ice cover is only 0 or 138. NCEP winds tended to be higher than ERA5 winds (Fig. S24a), while the barometric pressures from the two datasets were more similar (Fig. S24b).

Derived variables

Absolute salinity (SA), potential temperature (PT), conservative temperature (θ), density (ρ), potential density anomaly (σθ), oxygen saturation, and spiciness were calculated with the Thermodynamic Equation of Seawater 2010 (TEOS-10) Python implementation58. Apparent oxygen utilization (AOU) was calculated from the dissolved oxygen concentration ([O2]) and solubility of oxygen at the in situ temperature and salinity59. The solubility of N2O in seawater was calculated based on ref. 60 using an updated version of a gas exchange toolbox61. The partial pressure of N2O, the target variable for the machine learning models, was calculated from:

$$p{N}_{2}{O}_{{sw}}=\frac{\left[{N}_{2}O\right]\cdot \rho }{{k}_{H}}\,$$
(3)

where \(p{N}_{2}{O}_{{sw}}\) represents the seawater partial pressure of N2O in natm, [N2O] is the concentration of N2O in nmol kg−1, \(\rho\) is the in-situ density in kg/m3, and \({k}_{H}\) is the Henry’s Law constant in mol m−3 atm−1. Additional derived variables included the day of the year, transformed as cos(2πDOY/365.25) to eliminate the discontinuity at the end of each calendar year, and longitude, transformed into two different predictors following refs. 62,63 as cos(π(LONGITUDE – 110°E)/180) (“LON1”) and cos(π(LONGITUDE – 20°E) /180) (“LON2”) to ensure that regions of maximum explanatory power occurred over the oceans.

Random forest model tuning and training

We trained random forest regressor models to predict \(p{N}_{2}{O}_{{sw}}\) from variables measured by BGC-Argo floats. Prior to random forest model training, a “test” dataset was generated by randomly withholding 20% of profiles from the full GO-SHIP dataset (Fig. S13). A random 20% of profiles, as opposed to 20% of data points, were withheld to ensure that inherent correlations among the data points from a single profile did not artificially boost the apparent effectiveness of the machine learning algorithm. The test dataset was completely withheld from the model selection, hyperparameter tuning, and training process (vide infra), to be used to evaluate each random forest model’s performance on unseen data after all training and validation steps.

The “validation” dataset was generated by withholding 20% of the data points from the remaining 80% of profiles. The validation dataset was used during the model selection and hyperparameter tuning process to fine-tune the model and prevent overfitting, helping to choose the best model parameters. This left 64% of the training dataset for model training during feature selection and hyperparameter tuning.

Six random forest regressor models, based on six candidate sets of predictor variables (Fig. S25), were tested as potential contributors to the final model ensemble. Instead of testing all possible combinations of predictor features, predictor features were chosen that were likely to provide information about water masses and N2O production mechanisms, and whose range in the training dataset covered the full dynamic range of values in the BGC-Argo dataset. Additionally, a model containing a larger number of predictor features was included in the model selection process as a point of comparison. To assess the uncertainty in each candidate model’s performance, a K-fold cross-validation was performed by training each model five times, withholding five distinct sets of data (folds) of validation data such that each point appeared in the validation dataset exactly once. Models were trained using the RandomForestRegressor from sci-kit-learn64, with 600 decision trees following ref. 62 and a minimum of one sample per leaf to maximize model performance. For each of the five folds, model R2, root mean square error (RMSE), and mean absolute error were obtained by applying the model to the validation dataset.

To quantify reconstruction bias45, candidate models were then applied to the BGC-Argo dataset to predict \(p{N}_{2}{O}_{{sw}}\), and the resulting median Southern Ocean surface \(p{N}_{2}{O}_{{sw}}\) was compared to the median Southern Ocean surface \(p{N}_{2}{O}_{{sw}}\) in the GO-SHIP dataset. Reconstruction bias was calculated as the difference between these two values:

$${bias}={{median}(p{N}_{2}O)}_{{BGC}}-{{median}(p{N}_{2}O)}_{{GO}-{SHIP}}$$
(4)

where \({{median}(p{N}_{2}O)}_{{BGC}}\) is the median Southern Ocean surface \(p{N}_{2}{O}_{{sw}}\) predicted from BGC-Argo float data in natm, and \({{median}(p{N}_{2}O)}_{{GO}-{SHIP}}\) is the median Southern Ocean surface pN2O in the GO-SHIP dataset. This procedure was repeated five times per candidate model, for each of the five folds, to obtain an uncertainty in that model’s bias.

The K-fold cross-validation revealed that adding more predictor features lowered RMSE but increased reconstruction bias (Fig. S25), suggesting that the models with a greater number of features were overfitting to spurious correlations within the training data, diluting the influence of core oceanographic features, and/or decreasing the effective sample size per feature65,66. Thus, to minimize overfitting and bias, we chose the simplest four models—including only absolute salinity, conservative temperature, either [O2] or AOU, and [NO3−]—to include in the final model ensemble. Because each Random Forest model consists of 600 decision trees, our approach is essentially an ensemble of ensembles.

The hyperparameters for each of the four chosen models were tuned by manually searching ranges of minimum samples per leaf, the number of decision trees, and minimum samples per split to find the combination of hyperparameters for each model that minimized that model’s RMSE in the Southern Ocean. The optimum values for minimum samples per leaf and minimum samples per split were one and two, respectively, so these were used for final model training. The number of estimators had minimal impact on model performance, so we used 600 estimators for final model training to minimize overfitting.

Using these hyperparameters, each of the four chosen models was re-trained on the combined training and validation dataset (e.g., 80% of stations that were not withheld as test data). Model R2, RMSE, and MAE were then evaluated on the test data (e.g., the 20% of stations that were initially withheld). [O2] and AOU were the most important predictor variables; the exclusion of [NO3−] made little difference in the Southern Ocean, indicating that future work could exclude this variable to access a greater number of float profiles (Fig. S15). The models tended to underpredict extremely high values of \(p{N}_{2}{O}_{{sw}}\) (Fig. S15b, e, h, k), but this problem does not persist in the Southern Ocean data, which span a much smaller range of \(p{N}_{2}{O}_{{sw}}\) (Fig. S15c, f, i, l). To expand this analysis to global scales, more high-quality training data are needed from oxygen-poor upwelling regions where these high values of pN2O are found.

Application of random forest models to BGC-Argo data and associated uncertainties

Each of the four final trained models was applied to the surface BGC-Argo dataset in the Southern Ocean to predict \(p{N}_{2}{O}_{{sw}}\) from the temperature, salinity, dissolved oxygen, and nitrate measured by the BGC-Argo floats. This produced four datasets of predicted \(p{N}_{2}{O}_{{sw}}\) based on the four random forest models.

To generate a true prediction interval around model predictions for unseen points, it is necessary to consider uncertainty due to training dataset noise (aleatoric uncertainty) in addition to model uncertainty due to limited training data and/or model architecture (epistemic uncertainty). Based on tests with injected artificial noise (Supplementary Text S3), we approximate uncertainty due to training dataset noise with Mean Absolute Error, such that

$${\Delta }_{{residual}}^{2}={\left(\frac{1}{4}\right)}^{2}\sum _{i=1}^{4}{\left({{MAE}}_{i}\right)}^{2}$$
(5)

where \({\Delta }_{{residual}}\) is the residual variance of the training data, or the uncertainty due to the inherent “noise” or randomness of the data themselves, and \({{MAE}}_{i}\) is the mean absolute error of model i for the test dataset.

Because a Random Forest consists of an ensemble of decision trees, each of which excludes a certain number of training data points, it is designed to handle this sort of uncertainty. Techniques such as Quantile Regression Forests67 take advantage of the Random Forest model architecture by calculating not just the mean output of all the decision trees but also different quantiles. We take a simple version of this approach, taking the standard deviation of all of the decision tree predictions as the uncertainty around a given model’s output:

$${\Delta }_{{trees}}^{2}={\left(\frac{1}{4}\right)}^{2}\sum _{i=1}^{4}{\left({\sigma }_{{trees} , i}\right)}^{2}$$
(6)

where \({\sigma }_{{trees} , i}\) is the standard deviation of the 600 decision tree predictions for a given point by model i:

$${\sigma }_{{trees} , i}^{2}=\frac{1}{600-1}\sum _{j=1}^{600}{\left({p{N}_{2}O}_{j , i}-{\overline{p{N}_{2}O}}_{i}\,\right)}^{2}$$
(7)

where \({p{N}_{2}O}_{j , i}\) is the “leaf,” or prediction by tree j in model i. \({\overline{p{N}_{2}O}}_{i}\) is the mean predicted pN2O by model i for a given point, equal to the mean of all 600 decision trees:

$${\overline{p{N}_{2}O}}_{i}=\frac{1}{600}\sum _{j=1}^{600}{p{N}_{2}O}_{j , i}$$
(8)

We found that initializing the Random Forest model with a different set of predictor features produces different final results. Thus, in our analysis, we use four different Random Forest models initialized with four different sets of predictor variables. Because each Random Forest model consists of 600 decision trees, our approach is essentially an ensemble of ensembles. The disagreement between the mean predictions by the four models tends to exceed the disagreement between the decision trees for an individual model. So, as a final source of uncertainty, we include the uncertainty of the model ensemble:

$${\sigma }_{{ensemble}}^{2}=\frac{1}{4-1}\sum _{i=1}^{4}{\left({\overline{p{N}_{2}O}}_{i}-{\overline{p{N}_{2}O}}_{{ensemble}}\right)}^{2}$$
(9)

where \({\sigma }_{{ensemble}}^{2}\) is the disagreement between the four Random Forest models in the ensemble, and \({\overline{p{N}_{2}O}}_{{ensemble}}\) is the mean prediction of the four Random Forest models in the ensemble:

$${\overline{p{N}_{2}O}}_{{ensemble}}=\frac{1}{4}\sum _{i=1}^{4}{\overline{p{N}_{2}O}}_{i}$$

Together, the combined uncertainty in the predicted pN2O at a given point is calculated from:

$${\Delta }_{p{N}_{2}O}^{2}={\Delta }_{{residual}}^{2}+{\Delta }_{{trees}}^{2}+{\sigma }_{{ensemble}}^{2}$$
(10)

Where \({\Delta }_{{residual}}^{2}\) is the uncertainty due to noisiness in the training data, \({\Delta }_{{trees}}^{2}\) is the uncertainty due to each model’s architecture, and \({\sigma }_{{ensemble}}^{2}\) is the squared standard deviation of predictions by the four Random Forest models in the ensemble.

Air-sea flux

The air-sea flux of N2O was calculated according to two wind speed-based parameterizations of air-sea gas exchange (Supplementary Text S1). The first of these parameterizations68 has a quadratic dependence on wind speed that includes bubble-mediated exchange implicitly in the nonlinear component of the wind speed dependence. In the second parameterization69, diffusive and bubble-mediated gas exchange are modeled explicitly with linear and cubic dependences on wind speed, respectively.

Uncertainty in air-sea flux

Uncertainties in individual air-sea fluxes were propagated from 1) uncertainties in wind speed; 2) uncertainties in \(\chi {N}_{2}{O}_{{atm}}\) and \(p{N}_{2}{O}_{{sw}}\):

$${\triangle F}_{i}^{2}={\Delta F}_{{winds} , i}^{2}+{\Delta F}_{{N}_{2}O , i}^{2}$$
(11)

where \({\triangle F}_{i}^{2}\) is the uncertainty in air-sea N2O flux associated with float profile i. To quantify uncertainties due to wind speed, fluxes were calculated with combinations of two gas exchange parameterizations (Supplementary Text S1) and two wind products (ERA557 and NCEP70). The uncertainty due to wind speed was estimated as the standard deviation of fluxes calculated from these four methods:

$${\Delta F}_{{winds} , i}={{\rm{\sigma }}}({F}_{i , W14 , {ERA}5} , {\,F}_{i , L13 ,, {ERA}5} , \,{F}_{i , W14 , {NCEP}} , \,{F}_{i , L13 , {NCEP}})$$
(12)

where \({F}_{i , W14 , {ERA}5}\) denotes the flux calculated from ref. 68 and ERA5 winds57 for individual float profile i.

The uncertainty \({\Delta F}_{{N}_{2}O , i}\) due to uncertainties in \(\chi {N}_{2}{O}_{{atm}}\) and predicted \(p{N}_{2}{O}_{{sw}}\) was calculated using a Monte Carlo simulation, accounting for covariances between different gas exchange parameterizations and wind speed products. For each profile i, 1000 realizations of \(p{N}_{2}{O}_{{sw}}\) were sampled from a normal distribution with µ = \(\overline{p{N}_{2}O}\) and σ = \({\Delta }_{p{N}_{2}O}^{2}\) and 1000 realizations of \(\chi {N}_{2}{O}_{{atm}}\) were sampled from a normal distribution with µ = the monthly mean atmospheric mixing ratio of N2O and a standard deviation derived from the errors published in the NOAA flask dataset35. Then, from these 1000 values, four flux estimates were calculated with different wind product-parameterization pairs. The combined uncertainty incorporates both the Monte Carlo uncertainties within each method (parameterization-wind product pair) and the covariance between methods:

$$\Delta {F}_{{N}_{2}O , i}^{2}=\frac{1}{{4}^{2}}\sum _{j=1}^{2}\sum _{k=1}^{2}{Cov}({F}_{j , i} , {F}_{k , i})$$
(13)

where \({Cov}({F}_{j , i} , {F}_{k , i})\) is the covariance between methods j and k for profile i. The summation is over all parameterization-wind product pairs. \({Cov}({F}_{j , i} , {F}_{k , i})\) is calculated from the 1000 Monte Carlo fluxes:

$${Cov}({F}_{j , i} , {F}_{k , i})=\frac{1}{1000-1}\sum _{{iter}=1}^{1000}\left({F}_{j , i , {iter}}-\overline{{F}_{j , i}}\right)\left({F}_{k , i , {iter}}-\overline{{F}_{k , i}}\right)$$
(14)

where \({F}_{j , i , m}\) is the flux for profile i, method j, Monte Carlo iteration iter, and \(\overline{{F}_{j , i}}\) is the mean flux for profile i, method j. It was assumed that the uncertainties in sea ice cover were negligible compared to the uncertainties in the other parameters.

The uncertainty in the net annual flux from the Southern Ocean \(({\Delta F}_{t})\) was calculated as the sum in quadrature of 1) the random uncertainties in individual fluxes; 2) the standard deviation of the net annual flux calculated from four different parameterization-wind product pairs; and 3) the uncertainty due to sparse sampling, calculated from bootstrapping:

$${\triangle F}_{t}^{2}=\Delta {F}_{t , {N}_{2}O}^{2}+\sigma {F}_{t , {winds}}^{2}+\Delta {F}_{t , {bootstrap}}^{2}$$
(15)

where \(\Delta {F}_{{t , N}_{2}O}^{2}\) is the cumulative sum of the individual uncertainties \({\Delta F}_{{N}_{2}O , i}\) from the Monte Carlo analysis:

$$\Delta {F}_{t , {N}_{2}O}^{2}=\sum _{i=1}^{28 , 112}{\left({\Delta F}_{{N}_{2}O , i}\cdot {A}_{{zone}}\cdot {D}_{{month}}\right)}^{2}$$
(16)

Where \({A}_{{zone}}\) is the area of the zone, and \({D}_{{month}}\) is the number of days in the month, in which a profile occurs.

The term \(\sigma {F}_{t , {winds}}\) is the standard deviation of the cumulative fluxes calculated from each parameterization-wind product pair:

$$\sigma {F}_{t , {winds}}=\sigma \left({F}_{t , W14 , {ERA}5} , {F}_{t , W14 , {NCEP}} , {F}_{t , L13 , {ERA}5} , {F}_{t , L13 , {NCEP}}\right)$$
(17)

where

$${F}_{t , W14 , {ERA}5}=\sum _{i=1}^{28 , 112}\left({F}_{i , W14 , {ERA}5}\cdot {A}_{{zone}}\cdot {D}_{{month}}\right)$$

where \({F}_{i , W14 , {ERA}5}\) denotes the flux calculated from ref. 68 and ERA5 winds57 for individual float profile i.

To evaluate the uncertainty associated with interpolating over locations where no float profiles exist, we performed a bootstrap analysis. Repeated this 1000 times, we randomly selected a subset of the floats, re-integrated the fluxes from those floats in space and time to account for fewer floats per zone and month, and summed the resulting integrated fluxes. We then obtained an uncertainty from the standard deviation of the 1000 bootstrap sums. As expected, this uncertainty increased with decreasing bootstrap sample size (Fig. S26); we chose a bootstrap sample size of 162 floats (50% of the dataset), which yielded \({\Delta F}_{t , {bootstrap}}\,\)= 0.06 Tg N/year.

In our estimate of the overall Southern Ocean N2O flux, \(\sigma {F}_{t , {winds}}\) or the subjectivity in the choice of gas exchange parameterization and wind product, are the leading sources of uncertainty, with much smaller contributions from \(\Delta {F}_{t , {N}_{2}O}^{2}\), and \({\Delta F}_{t , {bootstrap}}\) (Fig. 2).