Emergence of anthropogenic signals in the ocean carbon cycle


The attribution of anthropogenically forced trends in the climate system requires an understanding of when and how such signals emerge from natural variability. We applied time-of-emergence diagnostics to a large ensemble of an Earth system model, which provides both a conceptual framework for interpreting the detectability of anthropogenic impacts in the ocean carbon cycle and observational sampling strategies required to achieve detection. We found emergence timescales that ranged from less than a decade to more than a century, a consequence of the time lag between the chemical and radiative impacts of rising atmospheric CO2 on the ocean. Processes sensitive to carbonate chemical changes emerge rapidly, such as the impacts of acidification on the calcium carbonate pump (10 years for the globally integrated signal and 9–18 years for regionally integrated signals) and the invasion flux of anthropogenic CO2 into the ocean (14 years globally and 13–26 years regionally). Processes sensitive to the ocean’s physical state, such as the soft-tissue pump, which depends on nutrients supplied through circulation, emerge decades later (23 years globally and 27–85 years regionally).


The invasion of anthropogenic carbon and heat into the global ocean occurs through a cascade of biogeochemical and physical changes that are coupled to the ocean’s carbon cycle1. The ocean carbon cycle, and in particular the ocean carbon pumps, redistribute not only carbon, but also nutrients, oxygen and organic matter between the ocean’s surface and the ocean’s interior, an important role in determining the concentration of atmospheric CO2 and the functioning of marine ecosystems2,3. As such, anthropogenic changes in the ocean carbon pumps and the ecosystem parameters and processes to which the pumps are coupled are critical for both future climate sensitivity and marine health1,4,5,6.

The characterization of ocean carbon pumps arises from a conceptual framework, originally proposed by Volk and Hoffert2, that distinguishes three pumps: a solubility pump, operating via the increased solubility of CO2 in cold (deep) waters, and two biologically operated pumps that export organic carbon (the soft-tissue pump) and inorganic carbon (the calcium carbonate (CaCO3) pump) from the surface to the deep. In the contemporary ocean, the sequestration or invasion of anthropogenic carbon is predominantly driven by rising atmospheric CO2 concentrations (for example, Arora et al.7), which constitutes a subset of the solubility pump that can be denoted the invasion flux8.

Given the importance of the ocean carbon pumps for marine life and of the invasion flux for the strength of the ocean carbon sink and climate, there have been substantial efforts to quantify and detect changes in global carbon budgets9,10,11,12,13,14,15 and project changes in the pumps3,16,17,18. However, both model projections and observational records of the coupled carbon–climate system are subject to uncertainties (Fig. 1). Natural variability uncertainty, the uncertainty that stems from natural variability inherent in the climate system, is a shared uncertainty among modelling and observational efforts and has been shown to be a significant source of uncertainty in assessing anthropogenic changes in the ocean carbon sink17,19,20.

Fig. 1: Venn diagram schematic of the sources of uncertainty in simulating (using an ESM approach) and observing changes in the Earth system.

For the emergence, detection or attribution of an observed or simulated signal, the signal must overcome the sources of uncertainty in their respective brackets.

Emergence denotes when a simulated anthropogenic trend ‘emerges’, in a statistical sense, above either natural variability17,19,21,22,23,24,25,26 (this work) and/or model uncertainty27 (Fig. 1). Detection denotes when an observed trend exceeds the uncertainty posed by both the natural variability and the measurement capability of the observing system (for example, Carter et al. 28). For a perfectly resolved observing system, the emergence and detection times are equivalent. However, for an imperfectly resolved observing system, detection times exceed emergence times due to the additional uncertainty of mapping and/or measurement error, which must be overcome for detection to be achieved. Therefore, emergence timescales set a lower bound or minimum for timescales required for detection and attribution.

In this study, we use an Earth system model (ESM) as an observing system simulation experiment (OSSE) to quantify the minimum detection timescales (that is, time of emergence (ToE)) for changes in the ocean carbon cycle. To estimate the emergence timescales, we unravelled natural variability from the anthropogenic trends in the ocean carbon cycle using a 30-member Large Ensemble (LE) experiment conducted with the ESM2M model from the Geophysical Fluid Dynamics Laboratory (GFDL)29,30 (Methods). We referenced all the ToE calculations to the year 1990, as this is the approximate beginning of the biogeochemical ocean-observing era (for example, Woods31) and therefore the start of the reference period from which contemporary anthropogenic trends can emerge.

The analysis centres around the three ocean carbon pumps, with complimentary tracers and processes to which the pumps are coupled, such as acidification, warming, oxygen, nutrients and ocean colour, which provided for a mechanistic insight and connection to the observational record and observing system optimization. Additional model experiments that separate the rapid carbonate-chemical versus slow climate impacts of rising atmospheric CO2 provide an attributive insight into the anthropogenic drivers of change in the ocean (Supplementary Fig. 1). The chronology of emergence below provides a roadmap as to when and why the underway and imminent changes in important ocean biogeochemical processes and tracers might be detectable.

Overview of emergence chronology

Variables that reflect the accumulated or integrated invasion of anthropogenic CO2 into the ocean, such as surface pH and partial pressure of CO2 (\(p_{{\rm{CO}}_2}\)), emerge most rapidly, with ~100% of the ocean area emerging within 15 years (Fig. 2), and the majority of regional signals emerging in less than a decade (Fig. 3). The impact of acidification on the CaCO3 pump follows closely behind, with timescales of local emergence between 20–30 years (Fig. 2), and regional emergence between 9 years (the Southern Ocean) and 18 years (the Arctic) (Fig. 3).

Fig. 2: Percentage of ocean with emergent anthropogenic trends in ocean biogeochemical and physical variables.

A time series of the percentage of the global ocean area with locally emergent anthropogenic trends illustrates the disparity of emergence timescales for anthropogenic changes in the ocean carbon cycle. Emergence is defined as the point in time when the LE’s signal-to-noise ratio for a linear trend referenced to the year 1990 first exceeds a magnitude of two, which represents a 95% confidence in the identification of an anthropogenic trend in the LE. Ω applies to the saturation of both the aragonite and calcite forms of CaCO3, for which the emergence times are approximately equivalent. The CaCO3 and soft-tissue pump were calculated as the export flux at a 100 m depth of CaCO3 and particulate organic carbon, respectively. The heat content was calculated as an integral over 0–700 m, whereas the O2 inventories consider the integral 200–600 m, and chlorophyll inventories were considered over 0–500 m. NPP represents an integral over 0–100 m. All the other variables represent sea surface properties.

Fig. 3: Global and regional ToE for globally and regionally integrated anthropogenic signals and 50% of the local anthropogenic signals for the given biogeochemical variables.

Globally and regionally integrated signals emerge considerably sooner than local trends for most of the variables considered. For each domain a single domain-averaged or domain-integrated time series for each variable was used to compute the ToE. The three ocean carbon pumps are shown by dashed boxes. Variables are defined as in the caption for Fig. 2.

Next to emerge, with local ToEs between 30 and 50 years and regional ToEs between 10 and 30 years, are the sea surface temperature (SST), upper ocean heat content (integration between 0 and 700 m depth) and carbon variables that are sensitive to both the physical and carbonate-chemical state of the ocean—\(\Delta{p_{\rm{CO}_2}}\) and air–sea CO2 fluxes (Figs. 2 and 3). The upper ocean heat content emerges rapidly (four years) on a global scale, consistent with a detection–attribution study for which data-based estimates of global upper ocean temperature increases emerged within a decade32. Southern Ocean SST presents an outlier, with ToEs that extend beyond year 210023. Non-emergence results from weak anthropogenic trends in SST (Supplementary Fig. 4) are attributed to the dynamic effects of surface freshening that stabilizes the water column and to decreasing convective heating from warmer subsurface waters, and thereby offset the surface invasion of anthropogenic heat33.

For \(\Delta{p_{\rm{CO}_2}}\) and air–sea CO2 fluxes, global signals emerge within 17 and 14 years, respectively, and all the regions emerge within the range of 13–29 years (Fig. 3). These emergence estimates are consistent with a detection–attribution study that found reconstructed, global and regional air–sea CO2 fluxes to be emergent sometime within the 46 year period considered34. We interpret these to reflect emergence timescales for changes in the invasion flux, as the impact of changes in the biological pumps on the surface ocean \(p_{{\rm{CO}}_2}\) is small (global average of 0.5 μatm) relative to that of rising atmospheric and surface ocean \(p_{{\rm{CO}}_2}\) (global average of 550 μatm) between 1990 and 2100 (Supplementary Figs. 1 and 2).

Last to emerge are variables tied indirectly to changes in the three-dimensional physical state of the ocean (that is, circulation, ventilation and stratification), with these changes also reflected in biological processes (Fig. 2). For these variables, the emergence of globally integrated signals is considerably shorter than the local emergence. The soft-tissue pump, for example, emerges globally in 23 years and for most regions in 50 years or less, but local emergence exceeds 76 years for 50% of the global ocean area (Fig. 3). The emergence of surface chlorophyll, the primary observable currently used to monitor biological productivity and export, follows closely behind, with the global signal emerging after 25 years; however, regional signals taking up to eight decades for emergence, which exceeds previously published, biome-scale ToE estimates by up to four decades26. If chlorophyll inventories over the upper 500 m, rather than the surface concentrations of chlorophyll, are considered, emergence times decrease by about ten years for the global signal and by multiple decades for many regions (Fig. 3).

The emergence of globally integrated O2 inventories requires only 17 years; however, the Arctic, the Indian Ocean and the Equatorial and South Pacific Ocean regions require more than 100 years to emerge (Fig. 3). The North Pacific stands out with only 20 years for the emergence of O2 inventories. The relatively early emergence of global and North Pacific O2 inventories is consistent with the findings of a detection–attribution study, in which observations of global and North Pacific O2 inventories over ~20 years were found to be anthropogenically forced, whereas inventory changes in all the other regions were indistinguishable from natural variability35. The thermally driven components of O2 trends (O2,SAT) emerge sooner than the full O2 signal, locally, globally and for most regions (Figs. 2 and 3). Regionally, the non-thermal component of O2 (the apparent oxygen utilization (AOU)) has ToEs comparable to those of O2, but the global signal for AOU is non-emergent over the twenty-first century, a consequence of compensating regional trends that diminish the globally integrated signal (Figs. 2 and 3 and Supplementary Fig. 4).

The local emergence of over half the ocean surface area occurs in the twenty-first century (Fig. 2 and the final column of Fig. 3), even for slowly emerging variables such as the net primary production (NPP) and mixed layer depth (MLD). This highlights the value of time-series observations in climate change monitoring efforts, particularly for the fields that are not directly observed remotely (for example, nutrients and O2). However, as a complement to time-series locations, globally or regionally resolved observations, which allow for integration over space, require less time for the detection to be achieved. This is a consequence of a noise reduction associated with averaging overcompensating features of natural variability (for example, the East and West Pacific SST anomalies during El Niño/Southern Oscillation events). Therefore, for nearly all the variables considered, the order of emergence is global, then regional and finally local, which demonstrates the utility of observing networks with large spatial footprints for the early detection of trends.

The CaCO3 pump

The contribution of changes in the CaCO3 export to the sequestration of anthropogenic carbon is small (Supplementary Fig. 2); however, changes in the CaCO3 pump still represent a change in the ocean carbon cycle and a biological impact of climate change. We present emergence timescales for the export of CaCO3 rather than the indirect chemical (buffering and/or alkalinity) contributions that impact surface \(p_{{\rm{CO}}_2}\) and air–sea CO2 gas exchange, as these are not explicit diagnostics in ESM2M.

Decreases in the export of CaCO3 emerge rapidly, with about 50% of the ocean being emergent within 30 years (Figs. 3 and Fig. 4a,d), lagging approximately a decade behind its principal driver of declining Ω, the saturation of CaCO3, which is critical for biological calcification. In ESM2M, the calcification rates are directly proportional to the degree of supersaturation of CaCO3, calcification immediately transforms into detritus and dissolution does not occur in the upper 100 m, where waters are supersaturated with respect to CaCO3. Therefore, it is changes in the production (and not dissolution) of CaCO3 that are responsible for changes in its export30. The decreased production and ultimately export are due entirely to the invasion of anthropogenic CO2, and not to changes in the physical climate (Supplementary Fig. 1), consistent with the emergence times for the CaCO3 pump, which mirror changes in carbonate chemistry (for example, Ω) rather than physics. The lag between the declines in Ω and the corresponding declines in the CaCO3 export is due to contributions from noisier co-drivers, such as temperature and nutrient concentrations, on CaCO3 production and ultimately export.

Fig. 4: ToE and signal maps for the three carbon pumps.

ac, The three pumps have local emergence times that span the twenty-first century, with a range in most grid cells of 2–3 decades for the CaCO3 pump (a), 3–5 decades for the air–sea CO2 flux (b) and more than a century for the soft-tissue pump (c). df, The underlying emerging signal or anthropogenic trend associated with each flux. Signals are defined as the mean of the 30 ensemble member’s linear trends between 1990 and the ToE for each grid cell. The corresponding maximum on the colour bar for df is an order of magnitude smaller for d than for e and f. The maximum for the CaCO3 pump (d) is 0.02 gC m−2 yr−1 yr−1 and that for the air–sea CO2 flux (e) and soft-tissue pump (f) is 0.2 gC m−2 yr−1 yr−1. [NO3] = 0.5 µmol kg−1 contours are imposed on f to show the concurrence of counter trends (anthropogenic increases in the soft-tissue pump) at the boundaries of surface NO3 limitation.

The emergence of CaCO3 export occurs earliest at the high latitudes (~20 years) rather than the mid and low latitudes (30–40 years) (Fig. 4a), despite the decline in export being strongest at low latitudes (Fig. 4d). This occurs because the spatial pattern of the ToE for CaCO3 export is strongly determined by the magnitude of decadal variability, which varies strongly by latitude (Supplementary Fig. 4a). In ESM2M, the decadal variability of CaCO3 export scales with the magnitude of export (that is, lowest at the high latitudes and greatest in the tropics (Supplementary Fig. 5)). As a consequence, the strongest signals and earliest emergence are anticorrelated (that is, areas with the most pronounced trend emerge the slowest).

Changes in CaCO3 cycling result in changes in the CO2 buffering capacity of seawater and salinity-normalized alkalinity (nALK (Supplementary Figs. 3 and 4)). Changes in nALK represent an accumulated or integrated effect of changes in the CaCO3 export, and therefore emerge prior to changes in this (for example, Figs. 2 and 3). In a previous study, the observational and interannual uncertainty for salinity and alkalinity normalized to organic matter cycling were combined to consider time of detection (ToD) of anthropogenic signals, and found a local ToD of 20–30 years for the low-to-mid latitudes and in excess of 40 years at the high latitudes28 (consistent with our ToE estimates presented in Supplementary Fig. 3). The longer ToE and ToD in the high latitudes results from the reduced exposure of upwelled waters to biogenic CaCO3 cycling28 and is consistent with the relatively weaker high-latitude anthropogenic trends in CaCO3 export shown in Fig. 4d. Estimates of ToD are only modestly longer than our estimates of ToE, as the contributions to uncertainty in the trend detection from measurement error are of the same order of magnitude as the contributions from natural variability on decadal timescales.

The invasion flux

The emergence of air–sea CO2 fluxes occurs within high and tropical latitudes between 20 and 30 years, but the subtropics remain non-emergent throughout the twenty-first century (Fig. 4b), consistent with the ToE and spatial patterns of LE simulations with an independent ESM of similar resolution19. The same pattern of emergence unsurprisingly holds for \(\Delta{p_{\rm{CO}_2}}\), the primary driver of changes in solubility and air–sea carbon fluxes (Fig. 5a). In the subtropics, the non-emergence is a consequence of the annual mean trends in air–sea fluxes and the sea–air \(\Delta{p_{{\rm{CO}}_2}}\) being weak (Figs. 4f and 5b). However, this weak annual mean trend results from and obscures significant increases in the amplitude of the seasonal cycle and diverging seasonal trends (Fig. 5d,f).

Fig. 5: Amplified seasonality of \(\Delta{p_{\rm{CO}_2}}\) ToE and signals.

af, ToE for annual (a), local summer (c) and local winter (e) trends in sea–air \(\Delta{p_{\rm{CO}_2}}\) and the corresponding trend (signals) in same order (b, d and f). July–September and January–March define summer and winter for their respective hemispheres. Signals are the linear trend between 1990 and the ToE for each grid cell. Summer and winter trends in \(\Delta{p_{\rm{CO}_2}}\) are stronger and emerge sooner than the annual mean trend. g, The ensemble mean seasonal cycle of SST and DIC at three locations along 160° W (marked in b.) for the year 1990 (solid) and the year 2100 (dashed). Isolines of \(p_{{\rm{CO}}_2}\) are superimposed under the assumption of constant salinity and alkalinity. The decreased spacing between the constant \(p_{{\rm{CO}}_2}\) isolines with increasing SST and DIC reflects the non-linearity in the buffering capacity of CO2 in seawater. The seasonal cycle over the subtropical gyres (for example, 35° N) amplifies (that is, crosses more \(p_{{\rm{CO}}_2}\) contours in a given year) between the years 1990 and 2100, which creates divergent anthropogenic trends in the summer and winter \(\Delta{p_{\rm{CO}_2}}\).

The seasonal cycle of surface ocean \(p_{{\rm{CO}}_2}\) is driven primarily through the seasonal cycles of dissolved inorganic carbon (DIC) and SST36, but it is not changes in the seasonality of the drivers that result in the seasonal amplification of \(p_{{\rm{CO}}_2}\) (that, is for the subtropics, DIC seasonality decreases by only 7% and SST seasonality increases by only 4% over the twenty-first century). Rather, amplification of the \(p_{{\rm{CO}}_2}\) seasonality is largely sustained through the cumulative effect of invading anthropogenic CO2 on the carbon dioxide buffering capacity of seawater, the Revelle factor (for example, Fassbender et al.37 and Gallego et al.38). The impacts of a reduced buffering capacity on the seasonal cycle of the air–sea CO2 fluxes and \(\Delta{p_{{\rm{CO}}_2}}\) finds a maximum expression in the summer over the subtropics (Fig. 5d), where the seasonal cycle is thermally dominated39,40. The trend towards summer outgassing (Fig. 5d) dominates the trend towards winter uptake (Fig. 5f) to produce the weak (and non-emergent) annual mean trend (Fig. 5a,b). The seasonal amplification at a subtropical location (35° N) is illustrated in the SST–DIC phase space (Fig. 5g), in which the seasonal cycles of SST and DIC remain relatively constant over time; however, the resulting \(p_{{\rm{CO}}_2}\) exhibits a strong amplification during the twenty-first century, as evidenced by the trajectory of the seasonal cycle crossing more \(p_{{\rm{CO}}_2}\) contours during the year 2100 than the year 1990.

As a result of the amplification and diverging seasonal trends, ToE in the subtropical convergence regions is significantly earlier for \(\Delta{p_{{\rm{CO}}_2}}\) and fluxes considered separately for winter and summer (Fig. 5c,e) than for the annual mean (Fig. 5a). Observationally based products of the ocean surface \(p_{{\rm{CO}}_2}\) demonstrate an enhanced seasonality over the recent decades41, which is consistent with the ~30 year emergence timescales of seasonal trends in \(\Delta{p_{{\rm{CO}}_2}}\) (Fig. 5c,e).

The soft-tissue pump

As with the CaCO3 pump, the contribution of anthropogenic changes in the export of organic carbon to the sequestration of anthropogenic carbon is small (Supplementary Fig. 2), but represents a modification of important ecological processes. For most of the global ocean, reductions in the soft-tissue pump emerge by the mid-to-end of century (Fig. 4c,f). These reductions are ultimately a consequence of the reduced supply of nutrients to the surface ocean, which results from slowly emerging changes in the ocean circulation and stratification18 (Supplementary Figs. 3 and 4).

The soft-tissue pump and surface chlorophyll broadly agree in both the pattern and timing of emergence (Figs. 4 and 6). For the two fields, ToEs agree (within 20% of each other, that is |ToEsoft – ToEchlorophyll|/mean(ToEsoft, ToEchlorophyll) < 0.2) for 66% of the ocean area, and the underlying signal direction agrees for 87% of the ocean area (that is, decreased chlorophyll corresponds to decreased export). The agreement in timing and direction of the changes in surface chlorophyll concentrations and the soft-tissue pump in GFDL’s ESM2M supports the underlying assumption of field campaigns, such as NASA’s EXPORTS42, namely that anthropogenic signals in ocean colour correspond to the strength of biological pump on decadal-to-centennial timescales.

An exception to coupling between surface chlorophyll and the soft-tissue pump occurs over the Southern Ocean, where the export decreases despite increasing surface chlorophyll concentrations (Fig. 6). The disagreement between trends in surface chlorophyll and the soft-tissue pump arises from the increased iron limitation with depth, which produces divergent surface and subsurface trends in both productivity and chlorophyll concentration (Fig. 6 and Supplementary Fig. 6). Considering, instead, chlorophyll integrated over the upper 500 m (Fig. 6d), which decreases in the Southern Ocean, provides a better agreement with the reduction in upper-ocean NPP (Supplementary Figs. 3 and 4) and the soft-tissue pump (Fig. 4c,f).

Fig. 6: ToE and signal maps for surface versus depth-integrated chlorophyll.

a,c, The emergence of surface chlorophyll (a) is generally later than that of depth-integrated (0–500 m) chlorophyll (c) due to the noise reduction that occurs with depth integration. For the Southern Ocean, the signals for surface (b) and depth-integrated (d) chlorophyll are of opposite sign, with the depth-integrated signal being representative of upper-ocean declines in productivity and the soft-tissue pump. The corresponding maximum on the colour bar for b and d is two orders of magnitude larger for b than for d. The maximum is 2.3 × 10−3 mmol m−3 yr−1 for surface chlorophyll and 4 × 10−5 mmol m−3 yr−1 for depth-integrated chlorophyll.

Disagreement in the anthropogenic trends between the surface and subsurface chlorophyll increases the uncertainty for data-based estimates of NPP and the soft-tissue pump, which are derived primarily through observations of surface ocean colour. One solution to mitigate this uncertainty, and to reduce emergence times, is to increase the coverage by observing platforms that are not limited only to surface measurements, for example, biogeochemically equipped profiling floats43 and water-column-profiling satellite lidar44.

Emergence as a lower bound on detection

Our emergence timescales provide a lower bound for the detection timescales, for five reasons. First, overcoming the measurement and sampling error extends the duration of the observational time series needed for detection. Second, uncertainty in the methodology of emergence calculation, the indication that alternative methods can produce longer ToEs in the case of surface chlorophyll26 and ToEs that differ by >20% with the use pre-industrial rather than contemporary noise for a variety of ocean variables (Supplementary Fig. 7).

Third, we consider a high-emissions scenario, which would act to shorten the ToEs relative to a lower-emission scenario, but only for slowly emerging variables like the soft-tissue pump. In contrast, ToEs for more rapidly emerging variables, such as pH, CaCO3 export and SST, are scenario insensitive, as these variables generally emerge prior to the separation between future scenarios (year 2006 formally, but an additional 2–3 decades for the impact of differential emissions to be evident in upper-ocean temperature45), indicating a change induced from committed surface warming and acidification is sufficient for emergence.

Fourth, uncertainty in the model representation of natural variability could extend the detection times. Model intercomparison indicates that ESMs show significant differences in natural variability estimates (for example, Frölicher et al.27) and model–observation comparisons indicate that models such as ESM2M underpredict the natural decadal variability in the ocean’s physical state relative to the natural variability estimated from observational products (for example, McGregor et al.46 and England et al.47). Such insufficiencies in simulated variability have been shown to arise on interannual and shorter timescales due to insufficient resolution to permit eddies (for example, Penduff et al.48) and there continues to be open discussion in the literature as to why coupled ocean–atmosphere decadal variability is anaemic46. Under-represented natural variability in the models implies emergence calculations would be biased early.

Fifthly, uncertainty in the model response to anthropogenic forcing poses an additional scientific uncertainty for estimating ToE (that is, other ESMs have different forced responses, internal variability and potentially emergence timescales). For variables like O2 and NPP, the inclusion of model uncertainty in the framework for calculating emergence timescales extends emergence estimates by decades27 in comparison to the values presented here. Thus, for carbon pumps and drivers, its inclusion could also extend the ToEs presented here.


The three ocean carbon pumps considered have distinct spatial patterns of emergence, including the rapid emergence of CaCO3 export at high latitudes and the non-emergence of the annual mean invasion flux in the subtropics. The three pumps have disparate ToEs, which range from less than a decade to more than a century. This disparity reflects a slower emergence for the physical upper-ocean properties, which determine the emergence timescales for the soft-tissue pump, and a more rapid emergence for the invasion of anthropogenic CO2 and its biological impacts on calcification. The primary observables tied to each flux can emerge before (alkalinity preceding CaCO3 pump), in tandem (\(\Delta{p_{{\rm{CO}}_2}}\) and the invasion pump) or after (ocean colour lagging soft-tissue pump), which further widens the gap between detection timescales for changes in the ocean carbon pumps.

Our results highlight the considerable observing system requirements for trend detection, which include a high temporal and spatial resolution and multidecadal length sampling. For example, the analysis presented in this work shows that a full seasonal resolution of surface \(p_{{\rm{CO}}_2}\) and a depth resolution of ocean colour is critical to the optimal design of the OSSE. This LE OSSE is best understood as complementary to parallel OSSE efforts that consider the constraints of observing platforms and address optimal spatiotemporal sampling strategy (for example, Majkut et al.49 and Christian et al.50).

Another important challenge is to apply the results derived here to better constrain mechanistic controls on marine feedbacks to the climate system, an important source of uncertainty in climate projection over the coming decades to centuries51. We present the emergence times for changes in the ocean carbon cycle induced by the summation of direct anthropogenic forcings and climate–carbon feedbacks. Distinguishing between the two, within an emergence framework, could provide timescales over which the magnitude of the ocean’s climate–carbon feedback could be observationally constrained, and contribute to the mechanistically based framework for interpreting emergence timescales presented here.



All the simulations were conducted with the coupled GFDL-ESM2M model developed at the GFDL29,30, for which fidelity of the biogeochemical model (TOPAZ) has been documented for pre-industrial30, historical52 and future53 boundary conditions. We used a 30-member ensemble simulation over the period 1950–210023. Each simulation follows a historical (1950–2005) and RCP8.5 concentration pathway (2006–2100) boundary condition with prescribed atmospheric CO2 concentrations. The initial conditions of ensemble members 2–30 were modestly perturbed through using the climate state (ocean, atmosphere, land and sea-ice) from 2 January to 30 January of year 1950 from the first ensemble member as the 1 January 1950 condition for ensemble members 2–30. The initial condition perturbation results in a rapid (within ~5 years) randomization of the internal modes of variability across the ensemble members. Differences between the ensemble members are solely due to natural internal variability, and similarities in the evolution of ensemble members over time are due to anthropogenic forcing.

Additionally, we conducted two sensitivity experiments and a 1,600-year-long pre-industrial control run. The first sensitivity experiment excludes the radiative impacts of rising atmospheric CO2 on the climate system (that is, no warming) while maintaining the carbon chemistry impacts of rising atmospheric CO2 on the air–sea gas exchange (BGC-only in Supplementary Fig. 1). The second sensitivity experiment has precisely the opposite configuration, in which the radiative impacts of rising atmospheric CO2 are included (that is, warming), but the air–sea gas exchange is not affected by rising atmospheric CO2 (Rad-only in Supplementary Fig. 1).

ToE method

We refer to anthropogenically forced trends as ‘signals’ and natural trends as ‘noise’. The signal was computed by averaging across the 30 trends (linear, least squares) given by the LE. The noise was computed by taking the s.d. of these 30 trends. All the trend calculations were performed on annual means (unless otherwise stated) and started in the year 1990, as this is the approximate beginning of the ocean biogeochemical observing era31. Decadal trends in a stationary climate system (the noise) are approximately normally distributed about zero, and therefore we used the standard two-sided Student’s t test. The null hypothesis (signal is due to natural variability) is rejected with >95% confidence when the magnitude of the signal is twice the magnitude of the noise, that is, when the signal-to-noise equals or exceeds two. The ToE is the first year at which the signal-to-noise is ≥2.

ToE calculations were performed at the grid-cell level (1° × 1°), regionally and globally. At each grid cell, there were 30 individual time series. At each domain (either global or regional), first a single time series of the domain-averaged or domain-integrated quantity was computed to provide 30 individual time series. From these individual time series, the trends, signal, noise and ToE were computed.

The regional bounds from the Regional Carbon Cycle Assessment Project (RECCAP) protocol (http://www.globalcarbonproject.org/reccap/protocol.htm) were used. The Southern Ocean was defined as lying south of 44° S. The Arctic was defined as the region north of 65° N. For the Pacific and Atlantic basins, north was defined as 19–65° N, equatorial was defined as 18° N to 18° S and south was defined as 19–44° S. For the Indian basin, north is defined as lying north of 0° N, and south was defined as 44° S to 0°. The colour schemes for Figs. 26 and Supplementary Figs. 27 were created with tools available at davidjohnstone.net.

Data availability

The GFDL LE data that support the findings of this study are publicly available through Globus (http://poseidon.princeton.edu).


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This work was supported by NASA award no. NNX17AI75G. Support for K.B.R. was provided by the Institute for Basic Science project code IBS-R028-D1, with additional support through NOAA award nos NA17RJ2612 and NA08OAR4320752, including support through the NOAA Office for Climate Observations and NOAA award no. NA11OAR4310066. T.L.F. acknowledges support from the Swiss National Science Foundation under grant no. PP00P2_170687. The numerical simulations were performed with the computational resources of NOAA/GFDL.

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S.S. performed all the analysis and writing, with regular feedback from K.B.R., J.L.S, T.L.F., J.P.D., M.I. and R.S. The LE simulations were set up by K.B.R. and T.L.F. and performed and postprocessed by K.B.R. The sensitivity experiments and control runs were performed by R.S.

Correspondence to Sarah Schlunegger.

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Supplementary Notes 1–3, references and Figs. 1–7.

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Schlunegger, S., Rodgers, K.B., Sarmiento, J.L. et al. Emergence of anthropogenic signals in the ocean carbon cycle. Nat. Clim. Chang. 9, 719–725 (2019). https://doi.org/10.1038/s41558-019-0553-2

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