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

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1 SUPPLEMENTARY INFORMATION DOI: /NGEO2303 Global-scale variations of the ratios of carbon to phosphorus in exported marine organic matter Yi-Cheng Teng 1, Francois W. Primeau 1, J. Keith Moore 1, Michael W. Lomas 3, and Adam C. Martiny 1,2 Data sources used to constrain the biogeochemical model Tracer data: Hydrographic and inorganic nutrient datasets used in this study include the following: (i) Annual average alkalinity (TA), DIC, CFC-11, natural radiocarbon from Global Ocean Data Analysis Project (GLODAP) data 8 ( ); (ii) temperature, salinity, and PO 4 from World Ocean Atlas 2009 (WOA 2009) 9, ( ) Satellite-derived net primary production: Ten years (2002 to 2012) of monthly satellite-derived net primary production (NPP) (fields (MODIS CbPM, carbon-based primary production model 29, were averaged and interpolated horizontally on our model grid. Other data sources used in the analysis Suspended particulate organic matter: The databases of suspended particulate matter are compiled from 18 previously published and publically available cruises or time series and collected data during seven further cruises (see Ref. 5 Methods and Supplementary 1 NATURE GEOSCIENCE 1

2 Table S1 for more details). We excluded all observations with <5 nm POP, as that was set as our practical detection. Sinking particulate organic matter: The data of sinking particle fluxes are collected by sediment trap at BATS ( ) and HOT ( ), respectively. ( ( Global ocean biogeochemistry model Phosphorus-Cycling Model The phosphorus-cycling model is based on the linear formulation described in [Ref. 6], which we briefly review along with a description of the improvements to the biological production formulation. The horizontal resolution is 2 2 with 24 vertical layers ranging in thickness from ~36 m at the surface to ~633 m at depth. In total the model has N = wet grid boxes. The model considers two pools of phosphorus: an inorganic pool (PO 4 ), and a semi-labile organic pool (DOP). The model does not carry an explicit pool of particulate organic matter (POP) but does parameterize the vertical transport of organic matter by sinking particle using a power-law function for the vertical attenuation of the vertical flux 31. The divergence of the sinking flux of POP implies a solubilization flux from the POP pool to the semi-labile DOP pool before remineralization to PO 4. The governing equation for the phosphorous-cycling model written in matrix form is d dt PO! DOP T + diag(γ) κi + S! T + κi PO! DOP = γ!( PO! PO! ) 0 S1 where T U K is a sparse N N matrix advection-diffusion operator subject to no flux boundary conditions at the surface and on the bottom boundaries; diag γ is a 2

3 diagonal matrix formed from the spatially dependent biological P assimilation rate; κ is the DOP remineralization rate constant, I is the N N identify matrix; and S p is a linear operator that combines the biological production of organic phosphorus and the vertical transport by sinking particles, i.e. S! PO! = 1 δ δγ PO! z Θ(z z z!) z!!!! γ PO! dz!! if z z! if z < z! S2 where z! = 73.4 m is the base of the euphotic layer, i.e. the vertical coordinate of the bottom of the model's second layer; Θ(z z! ) is a Heaviside step function that ensures conservation of phosphorus by forcing the particle flux reaching the ocean bottom at z = z! to be solubilized into DOP; δ is the fraction of organic matter production directly allocated to DOP in the euphotic zone; (1 δ) is the fraction of the organic matter production that is first exported to depth following a power law particle-flux profile with exponent b. Once discretized S! becomes a sparse N N matrix. The source term on the right hand side is a weak (γ! = [10! years]!! ) phosphate restoring term to the observed global mean concentration. This small geological source term is needed to set the total number of moles of P in the model ocean because our steady state model is independent of any initial condition, which is the usual way in which models impose the total inventory of a conserved tracer (see Ref. 5 for more details). The biological production of organic phosphorus is parameterized as being proportional to the modeled PO 4 concentration with a spatially varying rate constant, γ α NPP/(1 mg C m!! day!! )! PO!!"# /(1 mmol P m!! ), S3 3

4 parameterized in terms the satellite-derived net primary production (NPP) in units of mg C m!! day!!, the observed PO 4 concentration in units of mmol P m -3 and two adjustable constants, α with dimensions of inverse time and β a dimensionless parameter. For depths below z! the value of γ is set to zero. The advantages of using a spatially varying phosphate-uptake rate coefficient instead of using the more typical conditional nutrient restoring formulation (e.g. ref. 27) are that: (i) Unlike the nutrient restoring formulation, the parameterization given by equations (1) and (S3) is linear in the model PO 4 concentration, which allows the steady-state model solution to be obtained by direct matrix inversion without the need for a computationally more expensive iterative Newton solver; (ii) unlike the nutrient restoring formulation it does not artificially shut off biological production where modeled phosphate concentrations are slightly below the observed concentrations; and (ii) it better captures the observed spatial patterns of ocean productivity in a parsimonious way (only two adjustable parameters) by building in information from satellite-derived ocean productivity estimates and from the degree of phosphate depletion in surface waters. Because the model equations are linear, setting the time-derivative to zero and then solving the resulting linear system of algebraic equations by direct matrix inversion can be used to obtain the model s equilibrium state. Carbon-Cycling Model The carbon cycle model carries two explicit carbon tracers: DIC and semi-labile dissolved organic carbon (DOC). All the organic carbon production first cycles through the DOC pool before remineralizing to DIC with a constant decay rate coefficient, κ. The 4

5 source of organic carbon is proportional to the biological production of DOP, with proportionality constant (C:P) exp the primary parameter of interest in our study.. The governing equation for DOC is ddoc dt + TDOC = S! diag( PO! )Ωr κdoc, S4 where, r is an 11 1 vector whose i-th element is the (C:P) exp ratio for the i-th patch, and where Ω is an N 11 matrix whose i-th column is a vector whose elements are equal to 1 for grid boxes in the i-th patch and zero otherwise. Thus the product Ωr propagates the 11 region specific (C:P) exp values to the grid boxes where they apply, so that the export flux of POP can be converted to an export flux of POC. The governing equation for DIC is ddic dt + TDIC = J!"#$ + J!"#$ + J!"#$. S5 J!"#$ is the virtual flux of DIC due to the concentrating and diluting effects of evaporation and precipitation, J!"#$ represents the sea-surface flux of carbon due to airsea gas exchange. It is a function of both surface DIC, total alkalinity (TA), and atmospheric pco 2 as described in the Ocean Carbon Model Inter-comparison Project 2 (OCMIP-2) protocol 32,33. We do not model TA but instead use the observational estimate from GLODAP. In the OCMIP-2 protocol, the computation of the gas transfer velocity is based on the parameterization of [Ref 34]. J!"#$ is the source-sink term of DIC due to the biological production and remineralization of organic carbon and calcium carbonate (CaCO 3 ) carbon: J!!"# = Jb!"#$ + Jb!"!#!. S6 5

6 The first term on the right hand side is the sink-source term of DIC due to the production and remineralization of organic carbon and the second term is the sink-source term of DIC for the production and dissolution of CaCO 3. The Jb!"#$ term can be expressed as follows Jb!"#$ = κdoc diag γ diag( PO! )Ωr, S7 where the second term on the right hand side is the DIC drawdown due to biological production. Note that the dependence on Ωr imparts a distinct C:P ratio to each surface patch. In addition to exporting organic carbon, marine organisms can also export CaCO 3 hard shells. As in the OCMIP-2 protocol, this export flux is taken to be proportional to the export of particulate organic carbon. The rain ratio, R, is the proportionality constant at the base of the euphotic zone. The exported CaCO 3 is assumed to dissolve in the water column according to the divergence of a vertical-flux profile parameterized by an exponential curve. Above and below the base of the euphotic zone, Jb CaCO3 is given by Jb!"!#! = R diag(γ)diag( PO! )Ωr z z! R z Θ(z z!) exp z z!! diag(γ)diag( PO d! )Ωrdz z < z!!! S8 The parameter d is the length scale for the remineralization of CaCO 3. Notice that in this model, there is no sedimentary loss of C org and CaCO 3. The Heaviside step function, Θ(z z! ), ensures that all the sinking particulate flux of CaCO 3 that enters the bottom grid box is dissolved there. To compute the air-sea flux of CO 2, atmospheric pco2 is fixed at the preindustrial level of 278 ppm in our steady state DIC solver. The steady state solution is then used as the 6

7 initial condition for a transient DIC simulation that takes into account the increasing atmospheric pco 2. In this transient run the atmospheric CO 2 is prescribed to follow the observed record from 1765 to 1990 according to the OCMIP-2 protocol [Ref. 33]. The resulting modeled DIC distribution for the period of the 1990s can be compared to the DIC observations in the GLODAP database. Bayesian Inversion Procedure. The biogeochemical model described above predicts the anually averaged global concentrations of DIC and PO 4. These model-predicted concentrations are implicit functions of the eleven regional (C:P) exp parameters along with seven other model parameters (see Supplementary Table 1) that are not of direct interest. The inversion procedure, which we describe in greater detail below, consists essentially of finding the set of (C:P) exp values that makes the misfit between the model predicted concentrations and the observed concentrations as small as possible. This procedure leads to a nonlinear weighted least-squares problem that can be solved using standard minimization algorithm as implemented in Matlab s fminsearch routine. More formally, point estimates and uncertainties of the eleven regional (C:P) exp values are obtained from the following statistical model for the PO 4 and DIC tracer data d! d! = m! (θ) m! (θ) + e! e!, e! e! = R!! V!! 0 0 R!! V!! ε! ε!, S9 ε! ~N 0, σ! I, and ε! ~N 0, c! σ! I, 7

8 where d!, d!, m!, m!, e!, and e! are N 1 vectors representing the PO 4 and DIC data, model, and error discretized on the model grid (top 2000 m), and where θ is an 18 1 vector of model parameters including the logarithm of the 11 regional (C:P) exp parameters and the 7 nuisance parameters α, β, b, δ, κ, R, and d. The vectors m! (θ) and m! (θ) are obtained from the steady-state solutions of Equations (S1) and (S5), which are obtained by a direct matrix inversion in the case of the linear equation (S1) and by using Newton s method for nonlinear equation (S5) 30. The biological sink-source functions, J!!"#, in (S5) are obtained from the steady state solutions of (S1) and (S4), with the steady state solution of (S4) obtained by direct matrix inversion. Spatial correlations in the elements of the error vectors e! and e! are modeled by applying a diffusive process to independent and identically distributed normal error vectors ε! and ε!. The diffusion process is constructed by applying n implicit time-steps of a 3-d diffusion equation in which the diffusion operator is taken from the circulation model s diffusion operator, i.e. R = I τ K! and V is a diagonal matrix whose (i, i)-th element is the square root of the fractional volume of the i-th grid box. We experimented with different step sizes but settled on τ = 1 year because it produced, with a small value of n, noise with spatial correlations that were visually similar to those of the misfits when the model parameters were optimized with n=0. The results presented in the paper correspond to n = 1, but we also tested n = 2 and n = 3 and found that n = 0,1, or 2, produced qualitatively similar results for the estimated (C:P) exp values. The case of n = 3 greatly amplified the noise (or equivalently smoothed out the signal) in the DIC data making the model markedly worst. 8

9 The elements of the error vector ε! are assumed to be independent draws from a normal distribution with variance σ!, while those of the error vector ε! are assumed to be independent draws from a normal distribution with variance c! σ!. The variance σ! is an unknown parameter that we estimate as part of the inversion. The parameter c 1058 is a fixed parameter that scales the relative magnitude of the PO 4 and DIC errors. We obtained the value of c! as the ratio σ!!,! /σ!!,! where σ!!,! is the variance of the PO 4 misfit of a preliminary P-cycle model in which only the parameters α, β, b, δ, and κ were! optimized using only the PO 4 data and where σ!,! is the variance of the DIC misfit of a preliminary C-cycle model in which only the parameters R, d, and r were optimized using only the DIC data with the P-cycle parameters held fixed. With the likelihood function constructed from the statistical model given by equation (S9) and a uniform prior for θ and log (σ) Bayes theorem yields the posterior probability distribution for θ, σ whose logarithm is L θ, σ log det R! V! VR 2N + 1 log σ 1 2σ! d! m! θ! R! V! VR d! m! θ S10 1 2c! σ! d! m! θ! R! V! VR d! m! θ. The negative of the log-likelihood function for the P-cycle model is minimized with respect to θ using a numerical minimization algorithm to find θ = log α, β, δ, κ, b, R, d, r, the most probable parameter values. Parameter uncertainties are estimated by approximating the posterior pdf for θ with a multivariate Gaussian. This is done using Laplace s approximation, i.e. by expanding the log-posterior function, L θ, σ in a Taylor series about θ, σ = θ, σ and truncating the series at 2 nd order. 9

10 The required Hessian matrix, θθ L, is approximated using 2 nd order centered finite differences, which requires 1368 additional equilibrium solutions of (S1) and (S4,S5) for the computation of the 171 distinct elements of the posterior covariance matrix. In the Gaussian approximation, the Taylor expansions are taken about the most probable error variance, σ 2 which is obtained by maximizing (S10) with respect to σ so that σ = 1 2N + 1 d! m! θ! R! V! VR d! m! θ + 1 c! d! m! θ! R! V! VR d! m! θ. S11 The resulting most probable parameter values and their error bars are given in Supplementary Table 1. In Supplementary Figure 2 we compare the model and observed PO 4 concentrations and in Supplementary Figure 3 we compare the DIC misfit for the model with the optimal (C:P) exp that varies spatially to the model with a constant (C:P) exp = 105. Carbon export production To compute the export production from each region in our model we use the method described in [Ref. 6]. Conceptually, the method obtains the export rate by tracking separate organic-carbon tracers for production from each of the 11 patches defined in Figure 1 and integrating the remineralization rate of each tracer over the volume of the ocean below the euphotic zone. The modeled carbon export production for both constant C:P and varying C:P cases in each ocean region are shown in Supplementary Figure 4. The estimated total export productions for the two cases are close (9.13 Pg C/yr vs Pg C/yr), but the spatial variations and contribution from each patch are quite different. For example, the carbon 10

11 export in the constant C:P ratio case (Supplementary Figure 4e) shows that the subtropical gyre regions only account for 19.8% of the global export production. In contrast, the subtropical gyre regions account for 33.8% of the global export production in the varying C:P ratio case (Supplementary Figure 4f). Sensitivity to the boundary separating the regions To test the sensitivity of the inferred (C:P) exp to the criteria we used to separate the subtropical gyres from the rest of the ocean we tested the robustness of our inferred (C:P) exp by repeating the parameter estimation with different patch boundaries. We did two sensitivity tests in which the boundary was chosen to be the contour where the PO 4 concentration is 0.2 mmol/m -3 and 0.4 mmol/m -3. The relative change in our estimated (C:P) exp values are listed in Supplementary Table 3. Although we found that for different maps the values of inferred (C:P) exp were slightly changed at each patches (~7% on average), the inferred (C:P) exp from different regional maps revealed the same spatial patterns elevated (C:P) exp ratios in the nutrient-depleted subtropical gyres and depressed (C:P) exp ratios in the nutrient-rich high-latitude and upwelling regions. Preferential remineralization In our base model we assumed for simplicity that organic carbon and phosphorus remineralize at the same rate, but several studies have suggested that organic phosphorus can be preferentially reminearlized compared to carbon (e.g. Ref. 35 and 36). Such process would result in C:P remineralization ratios that increase with depth. We tested whether the large-scale patterns of our inferred (C:P) exp might be sensitive to this effect. In our model this possibility can be accommodated with independent length-scales for the attenuation of the vertical flux of particulate phosphorus and carbon (exponent b). In a 11

12 separate optimization we included in the model a separate set of exponents for C and P for each of the 11 patches. This increased the number of adjustable parameters from 18 to 39. The resulting b exponents for POP and POC exported from each patch are shown in Supplementary Figure 5a,b respectively. Note that diagnosing the C:P ratio of exported organic matter for the model with element- and region-specific remineralization rates is not as straightforward as it was for our base model. For the more complex model the amount of C and P that remineralizes above and below the depth z c, that is the amount that gets exported, is no longer an explicit parameter in the model. For the base model where the C and P remineralization rates were equal the C:P ratio of newly produced organic matter was also the C:P ratio of the remineralization fluxes so that (C:P) prod = (C:P) exp. This is no longer the case for the more complex model because of the different remineralization parameters. In the more complex model only (C:P) prod appears as an explicit parameter and (C:P) exp must be diagnosed from the model solution by integrating the remineralization rate of C and P below the euphotic zone separately for the organic matter produced from each region. The results of the parameter optimization for the more complex model are summarized in Supplementary Figure 5. Panels (a) and (b) show the optimal b exponents for the POP and POC flux attenuation and panel (c) shows the optimal (C:P) prod parameter. The diagnosed (C:P) exp is shown in Supplementary Figure 5(d). For almost all the regions, the optimal (C:P) exp parameters are within the one standard deviation error bar of the simpler model (Figure 1) and none of the values are more than two standard deviations away. Importantly, the large-scale pattern is qualitatively similar to the one from the simpler 12

13 model the nutrient-poor subtropical gyres tend to have higher (C:P) exp values than the nutrient-rich equatorial and high latitude region. Supplementary Materials References: 31. Martin, J., Knauer, G., Karl, D. and Broenkow, W. VERTEX: Carbon cycling in the northeast Pacific. Deep Sea Res., Part I 34, (1987). 32. Najjar, R. G., et al. Impact of circulation on export production, dissolved organic matter, and dissolved oxygen in the ocean: Results from Phase II of the Ocean Carboncycle Model Intercomparison Project (OCMIP-2). Global Biogeochem. Cycles 21, GB3007, doi: / 2006GB (2007). 33. OCMIP-2 Protocol Wanninkhof, R. Relationship Between Wind Speed and Gas Exchange Over the Ocean. J. Geophys. Res., 97, , (1992). 35. Clark, L.L., Ingall, E.D., and Benner, R., Marine phosphorus is selectively remineralized. Nature, 393, 426 (1998). 36. Loh, A.N., and Bauer, J.E., Distribution, partitioning and fluxes of dissolved and particulate organic C, N and P in the eastern North Pacific and Southern Oceans. Deep Sea Res. Part I, 47(12), (2000). 13

14 Supplementary Tables: Supplementary Table 1: Point estimates and ±1 standard deviation posterior error bars for the model parameters. Parameters Value Units α 4.0!!.!!!.! 10!! yr -1!!.!"# β 0.62!!.!"# Dimensionless!!.!"# δ 0.39!!.!"" Dimensionless!!.!"# b 0.76!!.!"# Dimensionless!!.!! κ 1.0!!.!" yr -1 R!!.!"# 0.095!!.!"" Dimensionless!!"# d 1800!!"# m 14

15 Supplementary Table 2. Estimated carbon export (mol C m -2 yr -1 ) also known as Annual Net Community Production (ANCP) from 6 sites where experimental determinations. The Experimental values are from Table 2 from Ref. 9. The model estimated carbon export includes contributions from both DOC and POC and was calculated using on the Green-function diagnostics developed in Ref. 5. The model values were computed by averaging over a minimum box size of 6º 6º. Location Export Flux (mol C m -2 yr -1 ) Experimental C:P=105 VCP E. Subarctic N. Pac. (OSP) 50 N, 145 W 2.3 ± !!.!" 2.8!!.!" E. Subtropical N. Pac. (HOT) 23 N, 158 W !!.!" ± 2.4!!.!" E. Equatorial Pac W !!.!" ± 2.6!!.!" W. Equatorial Pac. 150 E-140 W !!.!" 1.9!!.!" Subarctic N. Atl. 40 N-65 N, 10 W-60 W !!.!! ± 3.2!!.!! W. Subtropical N. Atl. (BATS) 32 N, 64 W 3.8 ± !!.!" 3.8!!.!" 15

16 Supplementary Table 3. Influence of different regional maps on inferred (C:P) exp. Two cases: (1). relative differences (%) between (0.2 mmol/m -3 )-contour and (0.3 mmol/m -3 )- contour; and (2). Relative differences (%) between (0.4mmol/m -3 )-contour and (0.3 mmol/m -3 )-contour for each region. Relative errors (%) to original map (0.2 mmol/m -3 ) (0.4 mmol/m -3 ) N. Atlantic subtropical gyre +15% -17% Equatorial Atlantic and coastal regions +8% -4% S. Atlantic subtropical gyre -11% +1% Southern Ocean +1% -1% Southern Indian Ocean -8% +14% Northern Indian Ocean 0% -4% S. Pacific subtropical gyre +10% -9% Equatorial Pacific and coastal regions +6% -5% N. Pacific subtropical gyre +4% -8% Pacific subarctic regions +2% -1% Atlantic subarctic regions +14% -10% 16

17 Supplementary Figure Captions: Supplementary Figure 1: Depth profiles of the flux-weighted mean C:P ratio in sinking particulate organic matter collected in sediment traps at BATS (black sold line) and at HOT (red-dashed line). The plot shows that the C:P of sinking particulate organic matter is higher in the subtropical Atlantic Ocean compared to the subtropical Pacific Ocean, which is in agreement with the C:P ratios of exported organic matter estimated from the inverse model. Averages were computed from monthly resolution time-series The data from HOT covers the period from 01/ /2011 and the data from BATS covers the period from 10/ /2011. The error bars correspond to ±1 standard deviation of the posterior probability distribution for the flux-weight mean of the sinking particulate C:P ratio. Suppementary Figure 2: (a) and (b): Comparison between depth-averaged simulated and observed (World Ocean Atlas 2009) distributions of PO 4. (c): Relative difference between depth-averaged modeled and observed PO 4 (red colors indicate that the model concentration is higher than the observed concentration). Supplementary Figure 3: Relative difference between depth-averaged modeled and observed DIC: (a) C:P =105; (b) VCP case, (red colors indicate that the model concentration is higher than the observed concentration). 17

18 Supplementary Figure 4: Estimated export production for the constant C:P (C:P = 105) and the varying C:P cases. (a) and (b): average export production per unit area (mol C/m 2 /yr); (c) and (d): Integrated export production (Pg C/yr); (e) and (f): Proportion of the total export production exported from each patch (%). Supplementary Figure 5: (a). Map of the b exponent for POP flux atenuation; (b) Map of the b-exponent for the POC flux attenuation; (c) Map of the (C:P) prod ; (d) Map of the inferred (C:P) exp. Supplementary Figure 6: Map of the C:P ratio of the sinking particulate flux of organic matter through the 1005 m depth horizon. Supplementary Figure 7: Map of the integrated export flux of POC through the 1005 m depth horizon (Tmol C/yr). 18

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