Vertical fluxes of particulate organic carbon (POC) from the euphotic zone to the deep sea are an important part of the carbon cycle in the oceans. In this study, oceanic fluxes of POC below the euphotic zone were simulated with the Hamburg ocean carbon cycle model (HAMOCC5.1) by using different POC-flux parameterizations and compared with sediment trap data. Overall, the geochemical distributions in the deep sea showed a high sensitivity to the selection of POC flux parameterization. Below 2000 m in the oceans, differences between simulated and observed carbon tracers (PO4, Alk*) and model-data differences of POC fluxes are lowest when a regionally variable POC flux parameterization is used. Specifically, model-data differences are lowest in the subtropics when simulated vertical POC flux considers mineral ballasting, while they are lowest in the Arabian Sea and west coast of Africa when a mineral dust parameterization is used for the vertical POC flux.
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 Particulate organic carbon (POC) and the ratio of particulate inorganic carbon (PIC) to POC that sinks below the euphotic zone down to ocean sediments plays a significant role in the partitioning of carbon between the ocean and atmosphere [Archer et al., 2000]. Therefore proper quantification of the export and remineralization of POC in ocean carbon cycle models and corresponding changes in POC/PIC ratios is important. Earlier studies [Suess, 1980; Betzer et al., 1984; Berger et al., 1987; Martin et al., 1987, Pace et al., 1987] have attempted to predict POC export from the euphotic zone as well as the depth dependence of POC fluxes by relating POC fluxes at depth to primary production or export production (defined as the POC flux at the base of the euphotic zone). The interdependence among primary production, export production and the depth dependence of POC fluxes has been reevaluated using more recent and widespread data sets [Antia et al., 2001; Lutz et al., 2002]. The studies of Antia et al.  and Lutz et al.  have revealed high geographical variability in the relationship between export production and primary production. Furthermore, the depth dependence of POC penetration profiles was shown to vary independently of export production. Several studies [e.g., Honjo, 1982; Ittekkot, 1993; Hedges et al., 2001; Armstrong et al., 2002; Francois et al., 2002; Passow, 2004] have investigated the dependence of the vertical POC flux on mineral particle aggregation in the ocean, but mechanisms of this aggregation are not well known. For example, an increase in dust deposition may influence the penetration depth of POC [Ittekkot, 1993]. Recently, Armstrong et al.  showed that despite high variability in POC fluxes in sediment traps, the ratios of POC flux to mineral fluxes tend to be almost constant in the deep ocean. Armstrong et al.  proposed a partition of POC fluxes into different fractions: a free fraction remineralizing at a length scale similar to that proposed by Martin et al.  and a mineral-associated fraction that remineralizes at length scales similar to that of the minerals. The mineral-associated fraction could be further partitioned between mineral opal, CaCO3 and lithogenic material [Klaas and Archer, 2002]. Hence the distribution and geographical variability of POC fluxes in the deep ocean could determine the flux and composition of minerals. Conversely, the flux and composition of minerals can have an impact on POC fluxes. Because the fraction of POC associated with CaCO3 is substantially higher than the fraction associated with opal, such a parameterization might preclude large variation in the PIC:POC rain ratios into the sediments. Francois et al.  have also shown that the variability in POC fluxes at depth is related to the composition of mineral fluxes with higher POC to mineral flux ratios associated with CaCO3 fluxes.
 The purpose of this study is therefore to test the sensitivity of the carbon cycle and PIC:POC rain ratios below the mixed layer to the different formulations of the depth dependence of POC fluxes. Specifically, the response of a 3D model of the marine carbon cycle that includes a detailed description of nutrient co-limitation (including iron) and an ecosystem dynamics parameterization that resolves the seasonal cycle is investigated. In addition we test the sensitivity of the model to the following parameters: remineralization rates, penetration depths (or the so-called e-folding depths) of POC, CaCO3, and opal, and the PIC:POC ratio (rain ratio) of export production. The rain ratio is of considerable interest for transfer of carbon into the deep sea and has been controversially discussed [e.g., Koeve, 2002; Mekik et al., 2002; Sarmiento et al., 2002; Balch et al., 2005].
2. Model Description
 The Hamburg ocean carbon cycle model HAMOCC5.1, used in this study, is based on work by Maier-Reimer , Six and Maier-Reimer , Aumont et al. , Heinze et al. , and Gehlen et al. . Its components include an NPZD ecosystem model in which primary production is limited by macronutrients (N, P, Si) and micronutrients (Fe) and a 12-layer sediment model with pore water geochemistry (see also auxiliary Text S1). The model uses an Arakawa-type E-grid with approximate 3.5° × 3.5° resolution [Maier-Reimer et al., 1993] and 22 vertical layers varying in thickness from 25 m at the surface to 700 m in the deepest ocean areas. Geochemical tracers are advected like tracers in the corresponding physical model with a time step of 1 month, while a shorter time step of 3 days is used in the euphotic zone (the upper two layers of the model) for the quantities varying on short timescales that determine the ecosystem processes. The relatively coarse resolution of the model allows for long-term integrations and exploration of interaction between the water column and marine sediment. The model has been integrated for 10,000 years on an NEC supercomputer at the German Climate Modeling Center (DKRZ) in Hamburg.
 The biogenic CaCO3 (PIC) export production is parameterized as
with PCaCO3 the CaCO3 export production (expressed in units C per unit area and unit time), PorgC the export production of organic material, and PBsi the biogenic silica export production (for details, see Heinze ). The parameter A = 0.20, which results in a global mean PIC:POC ratio of 0.175, is used as a reference value in all model simulations. This formulation implies that as long as nutrients are available, diatoms constitute the export producers (assimilating silica and carbon at a ratio of 0.5). In areas with depleted silica concentration (with PBSi = 0), the PIC:POC increases according to (1) to 0.2. For equation (1), a reasonable assumption is made that most net primary production occurs in the euphotic zone. Export of POC from the euphotic zone in the reference experiment (REF) with exponentially declining uniform vertical POC is calculated according to Gieskes ,
where POC is the particulate organic carbon concentration, FOC the vertical POC flux, w the sinking speed of POC and r the POC remineralization rate. The quantity w/r = zp represents the e-folding length scale or “penetration depth” of POC. In the REF experiment, zp = 1033 m.
 The second category of experiments (REFD) utilizes the POC flux parameterization as described above, but includes a regionally variable dependence on the atmospheric dust input similar to that described by Ittekkot . In this approach the penetration depth is a function of the atmospheric dust deposition
where the regional distribution of dust is taken from an annual mean field from Mahowald et al. . A third category of experiments (MARTIN) uses the POC flux parameterization as described by Martin et al.  with
which can be obtained by setting r/w ∼ 0.858/z in (2).
 The fourth category of experiments (BAL) apply a particle flux parameterization using a mineral association approach based on work by Armstrong et al.  and Klaas and Archer . The total flux of organic carbon below the euphotic zone is given by
The vertical particle flux of organic carbon FOC includes a fraction of POC that sinks in association with mineral ballast and an “excess” fraction that sinks independently of mineral ballast. The ballast-mineral associated POC fraction is determined from the mineral fluxes (Fopal, FCaCO3 and Flith) and the carrying coefficients (kCaCO3 = 0.083, kopal = 0.026, klith = 0.068) [Klaas and Archer, 2002]. The vertical distribution of the excess POC fraction, FOCE, is parameterized by equations (1) and (2) as in the REF runs but with an e-folding depth of 770 m.
 The POC flux associated with the mineral ballast has an e-folding depth of 2000 m for CaCO3 and 4000 m for opal. Lithogenic material does not dissolve in the water column; hence all of the POC associated with lithogenic material directly sinks to the sediment.
3. Model Experiments
 Twelve experiments were conducted by varying parameter settings listed in Table 1 and auxiliary Table S2. Specific model-model and model-data comparisons of export production, POC fluxes, and carbon water mass tracers are given in the two following sections, 3.1. and 3.2. Focus on the data-model comparison is given for areas of high data coverage (Figure 1), i.e., the central equatorial Pacific, North Atlantic, North Pacific, Arabian Sea, and Southern Ocean.
3.1. Comparison of Simulated Export Production and POC Fluxes With Sediment Trap Data
 Export production is defined in this study as the amount of particulate organic carbon that sinks below the euphotic layers (the upper two model layers). Since nutrients are exported with POC in fixed Redfield ratios, different POC flux distributions with depth will affect the cycling of nutrients at depth and reinjection into the euphotic zone. This leads to changes in export production (Figure 2). A more effective downward POC export results in a decreased nutrient supply for the euphotic zone and thus weaker export production.
 The reference, experiment REF, generated an export production of 4.6 Pg C yr−1 and a net primary production of 27.0 Pg C yr−1 (Figure 2a). Highest export production rates are generated by experiment MARTIN followed by REFD, BAL and REF in decreasing order (Figure 2). In the North Atlantic, dust from the Sahara stimulates the export (Figure 2b), which yields a good match of experiment REFD to the sediment trap data (Figure 3a) (see also auxiliary Table S2). In subtropical gyres where CaCO3-producing organisms favor an enhanced mineral ballasting of POC, experiment BAL generally yields a reasonable fit. For example, at 14°N 54°W (Figure 3b), CaCO3-associated POC contributes significantly to the total POC flux below 2000 m (see also auxiliary Figure S3). Also in the subtropical South Atlantic (Figure 3d), there is a low model-data difference below 2000 m, with the best results obtained using the BAL formulation. In the equatorial Atlantic and Pacific, the use of a regionally variable POC flux parameterization also improves the prediction of POC fluxes (Figure 3c; see also auxiliary Table S2). In these regions, opal production dominates, but still results in lower POC fluxes above 3000 m than CaCO3-associated POC because of the low carrying coefficient of opal. In the Southern Ocean, REFD matches the data well. Experiment BAL (Figure 3c; see also auxiliary Table S2) has similar distributions of export production to experiment REF in the northern hemisphere, and slightly lower in the equatorial regions and Southern Ocean (Figure 3f). Strong currents and pulsed seasonal blooms in this region increase the uncertainty in sediment trap measurements, however, especially in the upper 1000 m [Gardner et al., 2000].
 In the Arabian Sea at 15°N 65°E (Figure 3e), annually averaged flux measurements from sediment traps show a high interannual variability, possibly due to the pulsed nature of blooms and seasonal to interannual variability of the monsoon [Kriest, 2002]. The different POC flux parameterization models reflect the complexity of this area for the upper 2000 m, but tend to be within the range of variability around 3000 m. Below 3000 m, trap fluxes tend to be higher than above, suggesting differences in trap efficiency or lateral transport of material. In this region, experiment REFD has the lowest model-data differences below 2000 m, possibly due to the importance of dust deposition in this region (see auxiliary Table S2).
 A sum of the cost function for each parameterization on sediment traps below 2000 m shows that in bathypelagic areas, the regionally varying parameterizations BAL and REFD have lower model-data differences than the regionally constant parameterizations REF and MARTIN. Experiment BAL has a 13.2% lower total cost function than REF and 12.8% lower than MARTIN, while experiment REFD has a 6.2% lower cost function than REF and a 5.7% lower cost function than MARTIN.
3.2. Effects of POC Flux Parameterization on Carbon Water Mass Tracers
 The simulated dissolved inorganic carbon (DIC) and phosphate distribution (Figures 4 and 5) is compared with data from the Global Ocean Data Analysis Project (GLODAP) [Key et al., 2004] and World Ocean Atlas 2001 [Conkright et al., 2002] (http:/www.nodc.noaa.gov OC5/WOA01F), respectively. Observed DIC is corrected by the ΔC* method of Gruber et al.  to remove the anthropogenic carbon perturbation (see http://cdiac.esd.ornl.gov/oceans/glodap/GlopDV.htm). The total error associated with the GLODAP data (measurement error plus the error from the anthropogenic correction) is generally between 4 and 12 μmol kg−1, with highest values located in the equatorial Pacific [Key et al., 2004] (see auxiliary Figure S1). The DIC difference at 3000 m between experiments and the GLODAP data is shown in Figure 4. Experiment REF (Figures 4b and 5a) has the lowest model-data difference, ranging for DIC from 30 μmol kg−1 in parts of the Southern Ocean to +30 μmol kg−1 in the central Atlantic, with near zero model-data difference in much of the central and northern Pacific. Experiments REFD (Figure 4c) and MARTIN (Figure 4d) with strong export production (Figure 3) have higher positive differences of DIC than BAL and REF as compared with GLODAP data. Experiment MARTIN has a model-data difference of up to +60 μmol kg−1 in the equatorial Pacific, and differences of up to +40 μmol kg−1 in the central Atlantic. In contrast to other experiments, simulated DIC in experiment REFD is much lower than GLODAP values (up to −40 μmol kg−1 in the central and North Pacific) suggesting a potential underestimate of POC fluxes using the dust parameterization. Experiment BAL (Figure 4d and 5d) is similar to REF, but with slightly higher values. Differences between BAL and GLODAP data range between −10 μmol kg−1 in the western Indian Ocean to around +40 μmol kg−1 in the North Atlantic, eastern equatorial Pacific, and parts of the Southern Ocean.
 Alkalinity* (Alk*) is defined to diagnose the biotic contributions to the modeled alkalinity by removing the effect of salinity,
where Alk is the modeled alkalinity, 2340 μeq kg−1 is the model-mean alkalinity, S is the modeled salinity in per mil, and 34.7 is the model-mean salinity. Changes in Alk* (Figure 6) in the deep ocean are driven by calcium carbonate dissolution (increase in alkalinity) and nutrient remineralization (decrease in alkalinity). Each of the plots in Figure 6 reflects the conveyor belt circulation of the deep ocean, with lowest values of Alk* found in the North Atlantic, ranging from −125 μeq kg−1 in experiment MARTIN to about −40 μeq kg−1 in experiment BAL. The highest values of Alk* are found in the North Pacific and Indian oceans, with maximum values ranging from 20 μeq kg−1 in experiment REF to around 135 μeq kg−1 in experiment MARTIN. Experiment BAL has the lowest model-data differences in the Pacific and Indian oceans, while experiment REFD has the lowest model-data differences in the Atlantic and Southern oceans. The very high values of Alk*, up to 135 μeq kg−1 in experiment MARTIN in the North Pacific (Figure 6b), are a result of the high export production generated in experiment MARTIN (Figure 2). We contend that the low model-data differences of Alk* in experiments BAL and REFD show that they are producing the most realistic fluxes of PIC as compared with data, related to a higher export of silica into the deep sea and thus according to equation (1) a preference of CaCO3 formation at the surface.
3.3. Sensitivity Experiments With Ballast Parameterization
 A series of sensitivity experiments were conducted with the ballast model (Table 1). They included (1) changing the remineralization rate of POC, (2) changing the penetration depth of CaCO3, opal, and unballasted (free) POC and (3) changing the PIC:POC rain ratio below the mixed layer.
Table 1. Experiment Names and Descriptions
reference run of model before implementation of ballast parameterization;
POC flux determined by constant penetration depth of 1033 m
reference run, POC flux determined by regionally variable dust input
reference run, utilizes Martin POC flux function of z−0.858
baseline run of model with ballast parameterization
remineralization rate increased to 0.03 month−1
remineralization rate increased to 0.20 month−1
e-folding penetration depth of opal increased to 10,000 m
e-folding penetration depth of calcite decreased to 500 m
e-folding penetration depth of opal decreased to 500 m
e-folding penetration depth of “free” POC increased to 1000 m
PIC:POC ratio decreased to 0.125 ± 0.011
PIC:POC ratio increased to 0.225 ± 0.011
 In experiment BALR1, the remineralization rate was increased from 0.02 (in experiment BAL) to 0.03 per month, an increase of 50%, but with no significant changes in the distributions of carbon tracers in the water column. In experiment BALR2, remineralization was increased to 0.20 per month, an increase of 500% from experiment BAL, with similar results to BALR1. These experiments identified a low sensitivity of major carbon tracer distributions to POC remineralization rates.
 The effect of changes in e-folding depth of opal and calcite are discussed in light of experiments BALEF1 and BALEF2. In both experiments, simulated DIC distribution changed significantly from experiment BAL. In experiment BALEF1, the sinking velocity w of opal was increased by a factor of 2.5 (equation (2)). In the deep North Pacific, the difference in DIC between experiments BALEF1 and BAL is up to 30 mmol m−3 because of the deeper remineralization of opal-associated POC (Figure 7a). In experiment BALEF2 the sinking velocity of CaCO3 (see Table 1) w was reduced by a factor of 8. The resulting DIC is increased up to 65 mmol m−3 relative to BAL in the deep North Pacific (Figure 7b). The changing sinking velocities of opal (BALEF1) and CaCO3 (BALEF2) affect the opal and carbonate deposition to the sediments, respectively. This can alter the CaCO3 deposition in the sediments and can feed back on the carbon cycle in the water column [Archer et al., 2000].
 The average value of the PIC:POC ratio in the world ocean is still widely disputed [Sarmiento et al., 2002], with estimates varying from 0.05 to 0.25. Here we test the response of the DIC and alkalinity distribution with respect to different PIC:POC ratios by changing coefficient A in equation (1) to 0.15 for experiment BALPP1 and to 0.25 for experiment BALPP2. The difference between experiment BALPP1 and BAL of Pacific alkalinity is shown in Figure 8. The alkalinity differences are up to 40 meq m−3 near the surface and down to −16 meq m−3 in areas of low oxygen concentration. The horizontal gradient of alkalinity differs significantly between these experiments through the supply of CO32− ion from calcite dissolution, affected by the different PIC:POC ratios.
 In Experiment BALPP2 (Figure 8b), the results are almost exactly the opposite of those from BALPP1. The largest difference in alkalinity occurs in the surface ocean and deep South Pacific, the same as where the largest difference in total alkalinity is predicted in experiment BALPP1. The result is a net increase in the alkalinity gradients.
 As shown in section 3, predicted POC fluxes and associated geochemical changes are sensitive to the different global and regional parameterizations of vertical carbon transport. The experiments which vary the PIC:POC ratio by varying the coefficient A in equation (1) have shown that the model generates a distribution of alkalinity with the lowest model-data difference when a coefficient of A = 0.2 is used, generating a global mean PIC:POC of 0.175. Koeve  suggested a global PIC:POC ratio between 0.20 and 0.25, but his findings differ substantially from the lower estimates of Sarmiento et al. , who suggested a global average PIC:POC ratio of 0.06 ± 0.03. Results from the comparison of modeled particle fluxes with data are in general agreement with the findings of Lutz et al. . A main point of agreement is the finding that a regionally varying particle flux parameterization (i.e., BAL, REFD) has lower model-data differences below 2000 m than a regionally constant parameterization (i.e., REF, MARTIN). Results of this study also support the study of Francois et al. , who suggested that a mineral ballasting parameterization should have better model-data agreement in subtropical regions; we found that experiment BAL had lower model-data differences than the other parameterizations in the subtropical North Pacific and the subtropical North Atlantic.
 The differences of the various simulations from the observations as discussed in section 3 are also related to physical and biogeochemical model uncertainties as well as errors related to the data and their distribution. Physical uncertainties of the model are for example associated with the model's limitation to the resolution and eddy parameterization. In the Southern Ocean, the coarse resolution of the model can lead to an overestimate of surface nutrient supply and productivity due to too vigorous vertical mixing. Nevertheless, the general structure of the deep-sea circulation is generally reproduced well as compared with, for example, radiocarbon data [Maier-Reimer et al., 1993] (see auxiliary Figure S2), CFC-11 [Dutay et al., 2002], and mantle Helium-3 [Dutay et al., 2004].
 Uncertainties related to biogeochemical parameterizations are, for example, related to the use of a singular particle size class. A refinement of the ecosystem model by a more detailed consideration of different particle size classes based on observations may improve vertical particle fluxes significantly [Kriest, 2002]. Particle aggregation is an important process because large aggregates have a higher sinking velocity than smaller particles. However, several parameterizations in the ecosystem model like those associated with phytoplankton growth, grazing or exudation are not well constrained by the observational evidence, which may introduce additional error in the ecosystem modeling. Our model simulations, which include ecosystem dynamics and nutrient colimitation, confirm a high sensitivity to the POC flux parameterization identified in the study of Heinze et al. . For example, in the POC flux parameterization of Suess , a shallower recycling of POC is predicted by the function, leading to a strong increase in export production, which is comparable to the shallower penetration of POC and increased export production (Figure 2c) in experiment MARTIN. Overall, the consideration of a regionally varying parameterization (i.e., BAL and REFD) considerably reduces model-data differences below 2000 m (see auxiliary Table S2), but significant model-data discrepancies still exist, partially because the interannual-to-decadal variations are not considered in these simulations. In all experiments (REF, REFD, MARTIN, and BAL) the model predicts POC fluxes with the lowest model-data bias in the Atlantic ocean, subtropical North Pacific, and the Southern Ocean, but with significant differences among the different simulations (Figures 2 and 3). Differences in POC flux estimates between the model and data have a variety of causes. One important contributor to the model-data discrepancy in POC fluxes in many areas is probably the difference between modeled export production and observational estimates (Figure 2 and Table 2). In particular, POC fluxes in BAL are predicted as a function of simulated CaCO3 and opal flux and penetration depth and are therefore sensitive to production and export of POC, opal and CaCO3.
Table 2. Modeled Export Production (g C m−2 yr−1), Net Primary Production (NPP, g C m−2 yr−1), and f-Ratio From Experiment BAL Compared With Observational Estimates Compiled by Lutz et al. 
Greenland and Norwegian Seas
North Central Pacific gyre/HOT
South China Sea
Equatorial Pacific (±2 latitude)
Equatorial Pacific (±5 latitude)
Equatorial Pacific (±9 latitude)
Panama Basin, 82°W
Panama Basin, 86°W
Southern Ocean/Atlantic sector
 Observational uncertainties can be associated with significant errors in sediment trap measurement, which can result from horizontal advection of particles [Buesseler, 1991], “swimmers,” fish or other macroscopic marine organisms that can get caught in the trap [Hedges et al., 1993; Honjo, 1996]. Moreover, particles can degrade in traps, and differences in trapping efficiency may occur [Yu et al., 2001; Antia et al., 2001]. The temporal and spatial coverage of sediment trap data is still limited to a few areas, like the eastern equatorial Pacific, the North Atlantic, and the Arabian Sea, which have a significant coverage in observations (Figure 1). Usbeck et al.  estimated particle fluxes by assimilating hydrographic data into a carbon cycle model and noted that their model tended to overestimate the observed POC fluxes by 50%, consistent with flux calibration from radionuclides, but underestimated the POC fluxes for very deep sediment traps, which is in agreement with the results of this study (see auxiliary Table S2).
 From the results reported in this study and from other studies it is indicated that a use of a spatially varying parameterization for particulate organic carbon fluxes yields a better representation of the observations. Overall, the geochemical distributions in the deep sea showed a high sensitivity to the selection of POC flux parameterization. Agreement between modeled POC fluxes and sediment traps below 2000 m is highest when a regionally variable POC flux parameterization is used, but significant model-data differences still exist. Regionally, the mineral ballasting parameterization for POC results in the lowest model-data differences in subtropical areas of the Atlantic and the Pacific, while the parameterization dependent on regionally variable dust input results in lowest model-data differences in the Arabian Sea. We suggest further improvement to the model by a kind of hybrid approach to POC flux modeling, using a regional and temporal variable POC flux parameterization such as mineral ballasting below 2000 m, and a different formulation for fluxes above 2000 m. This would be particularly important in areas with high dust depositions. Inverse methods with a similar approach used in the study of Usbeck et al. , but a more detailed description of both the physical dynamics and biogeochemical cycles, would be an important future direction to provide a synthesis of the uncertainties of the models as well as the data. One example could be an improved parameterization of calcium carbonate producers. Quantifying the seasonal and spatial distribution of planktic foraminiferal fluxes reflected in sedimentary assemblages [Zaric et al., 2005] may lead to a better understanding of the PIC to POC fluxes on a global scale.
 This work was supported by NASA NAG5-11245, as well as the EU JGOFS program, grant 03F0321E. In addition, thanks go to Jerry Tjiputra and Rachel Howard for reading and commenting on the manuscript.