Global-scale variations of the ratios of carbon to phosphorus in exported marine organic matter

inmarinephytoplank-tonisthoughttobeconstantthroughouttheworlds’oceans

explicit parameter that varies across 11 surface regions chosen to separate the nutrient-depleted subtropical gyres from the nutrientrich upwelling and high-latitude regions (Fig. 1).The resulting model allows us to infer the C:P ratio of exported organic matter using a Bayesian inversion procedure combined with a numerical optimization technique that finds the most probable (C:P) exp parameters conditioned on the PO 4 and DIC tracer observations (Methods and Supplementary Methods).
The inferred globally integrated (C:P) exp is equal to 105:1, and thus in close agreement with the canonical Redfield value of 106:1.However, we also see regional variation, whereby (C:P) exp ranges from a minimum of 63:1 in the sub-polar North Atlantic to a maximum of 355:1 in the subtropical North Atlantic (Fig. 1).The model with variable (C:P) exp improves the agreement between the simulated and observed DIC concentrations compared to the model with constant (C:P) exp set to the mean value of 105:1 (Fig. 2).The layer-averaged root mean squared (r.m.s.) error in the model with variable (C:P) exp is decreased by as much as 75% at ∼3,800 m and by 40% on average.This decrease in r.m.s.error over the whole water column implies that (C:P) exp is best represented by values unique to each region.
Our inverse model reveals elevated (C:P) exp values in the subtropical gyres and lower (C:P) exp values in the equatorial and high-latitude regions.If we assume that the low C:N ratio observed in high-latitude suspended particles 17 is also present in exported organic matter, the low (C:P) exp in high-latitude regions is consistent with the high-latitude dominance of diatoms, which have been shown to contribute export with low N:P ratios 18 .We also find extensive regional variation in (C:P) exp between the subtropical gyres.For example, the North Atlantic (C:P) exp is approximately twice that of the North Pacific subtropical gyre.A large difference is also observed in the C:P ratio of sinking particulate matter measured using sediment traps at the Bermuda Atlantic Time-series Study (BATS) and the Hawaii Ocean Time-series (HOT; Supplementary Fig. 1).We suggest that this difference is driven by the more extreme phosphorus limitation of the North Atlantic 19,20 .We also see an elevated ratio in the subtropical gyres of the Northern Hemisphere versus the Southern Hemisphere.We speculate that differences in (C:P) exp among subtropical gyres are linked to the degree of P stress, which is influenced by multiple factors-including basinscale inputs of N, P and Fe, and basin-scale rates of nitrogen fixation and denitrification [21][22][23] .The strongest evidence for P-limitation is in the North Atlantic subtropical gyre 19 , where we find the largest (C:P) exp and a maximum C:P in the bulk surface POM (ref.5).
We next compared our inferred (C:P) exp to the ratio measured in suspended particles, (C:P) particles (ref.5) and find that they show a remarkable degree of consistency (Fig. 3).Although the particulate  3.
measurements show considerable scatter, the available data suggest that (C:P) particles is elevated in the subtropical gyres compared to the tropical upwelling and sub-polar regions, in agreement with our inverse-model estimates.It has been hypothesized that the variability observed in plankton elemental ratios might be averaged out by the seasonal succession of phytoplankton, or possibly by trophic interactions 18 .The general agreement between the largescale variability in (C:P) exp and (C:P) particles is inconsistent with the ecosystem-averaging hypothesis and suggests that the spatial variations in the C:P ratio of exported organic material reflect the C:P variability of phytoplankton.Furthermore, the high (C:P) exp values in the gyres indicate that oligotrophic ecosystems can make an appreciable contribution to carbon export fluxes by more efficiently using the limited P resource 24 .
The spatial variability of (C:P) exp has important implications for the spatial pattern of annual net community production (ANCP).At present, satellite-derived estimates of ANCP are fairly uncertain, but tend to show values that are at least a factor of two lower in the subtropics compared to high latitudes 25,26 .In contrast to the satellitebased estimates and those of most global ocean biogeochemical models, the limited number of sites with experimental determinations of ANCP indicate less variation 10 .We compare these experimentally determined ANCP values against the export production computed with either a constant (C:P) exp or the optimal spatially varying (C:P) exp (Fig. 4).Both models have the same globally integrated export production, but the model with a constant (C:P) exp underestimates carbon fluxes in the subtropical gyre sites (BATS and HOT) by ∼60% and overestimates carbon fluxes in the highlatitude North Pacific site (OSP) by more than 40%.In contrast, the carbon export fluxes estimated from the model with the variable (C:P) exp are in agreement with the experimentally determined fluxes at all locations.Particularly notable is the increase in the fraction of the globally integrated carbon export for the subtropical North Atlantic Ocean from ∼3% for the fixed C:P = 105:1 model to 9% for the variable stoichiometry model (Supplementary Fig. 4e,f).The agreement of our estimates with the experimental determinations points towards the need for continued evaluation of the satellitebased NCP estimation algorithms and for the need to implement variable stoichiometry in marine biogeochemical models.If we use our model to extrapolate the limited number of experimentally determined ANCP values to the global ocean, the resulting spatial pattern of export flux implies a more efficient biological carbon pump in the subtropical gyres because the residence time of carbon exported from subtropical gyres tends to be longer than that of carbon exported from upwelling regions 27 .
In this study we developed a new method for inferring (C:P) exp from PO 4 and DIC tracer data that uses a Bayesian inverse method with a numerical optimization technique applied to a global biogeochemical model coupled to a data-assimilated ocean circulation model.The use of a three-dimensional model to explicitly account for the dominant physical and biogeochemical processes that maintain the climatological PO 4 and DIC gradients greatly reduces the unexplained fraction of data variance.In comparison to simple endmember mixing models, this new method provides a more powerful technique for detecting the regional (C:P) exp signal in the tracer data.However, it is important to consider possible limitations of the model.In particular, the analysis assumes that organic carbon and phosphorus remineralize at the same rate.In support of this simplifying assumption, we find that the results from this simpler model are qualitatively robust, when compared to a model with element-and region-specific rates (Supplementary Methods and Supplementary Figs 5-7).The inferred (C:P) exp from both the complex and simpler models agree within two standard deviations in all regions and within one standard deviation in 8 of the 11 regions.For the model with element-and regionspecific rates the remineralization C:P ratio tends to increase with depth in most regions, but the general pattern of a higher C:P ratio for material exported from nutrient-poor surface regions persists with depth (Supplementary Fig. 6).Our model also assumes that, apart from the invasion of anthropogenic carbon into the ocean, the marine carbon and phosphorus cycles are in steady state.This assumption is made because of the lack of data to the contrary, but the possibility that global marine biogeochemical cycles may not be stationary is something that needs to be explored with prognostic biogeochemical models that allow for variable elemental stoichiometry.
The general correspondence between patterns of C:P variability in phytoplankton and in C:P variability of remineralization fluxes implies that shifts in plankton community or in resource allocation within species driven by climate change might result in changes in (C:P) exp that would produce potentially important feedbacks on the Earth's carbon cycle and climate.Present Earth System Models (which assume fixed Redfield stoichiometry) suggest declines in carbon productivity and export over the twenty-first century, due in part to expanding oligotrophic regions 3,4,28 .Our results suggest that the more efficient carbon export in these regions would partially offset these expected declines in production and export.

Methods
Ocean circulation model.The circulation is based on the model of refs 6,7, which assimilates climatological observations of temperature, salinity, phosphate, natural radiocarbon, mean sea surface height, and air-sea heat and freshwater fluxes, as well as transient CFC-11 observations.Biogeochemistry model.The biological uptake of phosphorus is modelled using where [PO 4 ] is the model phosphate concentration and γ is a rate coefficient estimated empirically from satellite-derived net primary production (NPP; ref. 29) and surface PO 4 observations 9 with two adjustable coefficients, as described in the Supplementary Methods.The spatial dependence of γ , inherited from NPP and [PO 4 ] obs , accounts for growth-limiting factors other than phosphate availability.Carbon uptake is modelled using J C = (C : P) exp • J P with a separate (C:P) exp parameter for each region shown in Fig. 1.A fraction δ of the production is routed to dissolved pools of organic phosphorus and carbon, which is regenerated with timescale κ −1 .The remaining fraction is exported by sinking particles with a flux profile J (z) ∝ (z/z c ) −b , where z c = −73.4m.In addition to organic carbon fluxes due to the formation and remineralization of particulate and dissolved organic carbon, the carbon model also includes air-sea fluxes of natural and anthropogenic CO 2 , fluxes due to sinking CaCO 3 shells, and the concentrating and diluting effect of evaporation and precipitation.The fluxes of carbon due to sinking CaCO 3 shells introduces two further nuisance parameters in the model, the particulate inorganic to organic carbon ratio (R) and the e-folding remineralization length scale (d) for particulate inorganic carbon.The equilibrium model solutions are obtained efficiently by applying Newton's method to the steady-state equations 30 .A Bayesian inverse procedure is used to infer the most probable (C:P) exp values, taking into account the uncertainty in the nuisance parameters α, β, δ, b, κ, R and d (see Supplementary Methods for complete details).

Figure 1 |
Figure 1 | Map of (C:P) exp values inferred from the inverse model.The values correspond to the location of the maximum of the posterior probability density function (pdf).The error bars correspond to ± 1 standard deviation of the posterior pdf.Nutrient-depleted subtropical regions are indicated in dark green and nutrient-rich regions are indicated in light green.The boundary separating the regions is based on the (0.3 mmol/m −3 )-contour of the annually averaged PO 4 concentration.The sensitivity of the inversion results to the choice of boundary threshold is explored in Supplementary Methods and Supplementary Table3.

Figure 2 |
Figure 2 | Layer-averaged root mean squared (r.m.s.) DIC misfit (µmol C kg −1 ).The red circles correspond to the spatially varying (C:P) exp model and the blue squares correspond to the constant (C:P) exp model.Data for only the upper 2,000 m (shaded region) were used to optimize the (C:P) exp parameters, but the improvement in the fit extends to the bottom of the ocean.Further figures showing the model-data misfits are available in Supplementary Figs 2 and 3.

896Figure 3 |Figure 4 |
Figure 3 | Comparison of the C:P ratio of suspended particulate organic matter (POM) to that of exported organic matter.The C:P ratio of suspended POM data is from ref. 4 and comprises data for the upper 300 m of the water column binned into our 11 regions.The box plots show the 25, 50 and 75 percentiles, while the whiskers cover 99.3% of the data, with the remaining data points shown with '+' symbols.Values of (C:P) exp inferred from our geochemical inverse model are shown with error bars corresponding to the errors shown in Fig. 1.