The standard version of HAMOCC represents sinking fluxes of POC, FPOC, at depth z>z0, according to the concept of the Martin curve : 1FPOC(z)=F0zz0-β, where F0 is the POC flux out of the euphotic zone at export depth z0. For simplicity, the export depth is globally defined as being z0=100 m in HAMOCC. Above z0, a constant sinking speed of 3.5 m d-1 is assumed. Below z0, we assume a linearly increasing mass concentration-weighted mean sinking velocity with depth. The ratio between the remineralization rate of POC, RPOC,remin, and the vertical gradient of the sinking velocity, ∂zws‾, determines the POC flux slope, β=RPOC,remin/∂zws‾ . In the standard version of HAMOCC, remineralization of POC is temperature-independent and comprehends oxygen-concentration-dependent aerobic remineralization as well as sulfate reduction and denitrification under sub-anoxic and anoxic conditions.

The sinking tracers, opal and CaCO3, are treated separately from POC and sink with their own, constant sinking velocity. Aeolian dust is, apart from the release of bioavailable iron in surface waters, inert and sinks slowly through the water column. The opal dissolution rate in the standard model is linearly temperature-dependent. HAMOCC accounts for dissolution in carbonate ion undersaturated conditions below the dynamically emerging lysocline. In the following, we refer to this version of HAMOCC as “standard”.

Natural waters exhibit a size spectrum of aggregates whose diameter, d, composition and microstructure determine their terminal sinking velocity. In the M4AGO approach, we explicitly represent microstructure and heterogeneous composition of aggregates. For the aggregate size spectrum, we limit the representation to a variable power law number distribution, n(d), with slope b and power law factor a following e.g.,: 2n(d)=ad-b. This way, we avoid the computational costs of size-class-based model approaches .

The local concentration-weighted mean sinking velocity, 〈ws〉, in M4AGO is eventually computed from the number distribution (Eq. ) that is truncated at the minimum and maximum aggregate sizes, dmin and dmax, respectively, and expressions for the aggregate mass, m(d), and the sinking velocity of aggregates, ws(d), of a particular diameter, d. Integration over the aggregate size spectrum yields 〈ws〉 3〈ws〉=∫dmindmaxn(d)m(d)ws(d)dd∫dmindmaxn(d)m(d)dd. We only implicitly account for aggregation and fragmentation and explicitly represent the temporally and spatially variable heterogeneity and microstructure of aggregates and their effect on the mean sinking velocity. We refrain from representing the potential heterogeneity of aggregate composition within the local size spectrum see, e.g.,. Consequently, and in contrast to the standard configuration, the settling tracers in HAMOCC, opal, CaCO3, detritus and dust sink in M4AGO at the same mean sinking velocity of aggregates (Eq. ). In contrast to , and , we explicitly incorporate both variable aggregate size and ballasting through heterogeneous composition. Under the above assumptions, we derive the terms for b, m(d), ws(d), dmin and dmax in the following sections.

Marine aggregates tie heterogeneous components together that are disparately remineralized or dissolved. By contrast, in the standard model, detritus, opal and CaCO3 were sinking separately from each other, and the global remineralization and dissolution rates are tuned independently because the processes are artificially decoupled. In M4AGO, remineralization of detritus and dissolution of, in particular, opal is tightly linked through the same sinking velocity which let us re-evaluate and revise the formulations for opal dissolution and remineralization.

Opal dissolution is temperature-dependent and is microbially mediated . Intact diatom frustules are protected from dissolution by an organic matrix . Once the organic protection surrounding the silicate frustule becomes utilized by temperature-dependent microbes, they initiate and mediate the dissolution of opal . Hence, opal dissolution follows a sequential process: (i) an initial temperature-dependent remineralization of the organic coating of the silicate frustule and (ii) the microbially mediated dissolution of opal with a temperature dependency of Q10≈2.3 . We here focus on the temperature-dependent microbially mediated dissolution and introduce a Q10 temperature-dependent opal dissolution: 30∂∂t[opal]|dissolution=-ropalQ10,opalT-Tref,opal10[opal], where ropal is the opal dissolution rate at the reference water temperature Tref,opal and T is the ambient water temperature. In the standard version, we remain with the former linearly temperature-dependent opal dissolution ∂t[opal]=-ropal(0.1(T+3))[opal];.

Analogously to opal, we incorporate a temperature-dependent Q10 factor to aerobic POC remineralization which depends on oxygen concentration, [O2] , where KO2 is the half-saturation constant in Michaelis–Menten kinetics, and rPOC is the remineralization rate at reference temperature Tref,POC: 31RPOC,remin=-rPOC[O2]KO2+[O2]Q10,POCT-Tref,POC10. We keep the anaerobic remineralization temperature-independent, since we do not expect temperature shifts in ocean depths, where oxygen minimum zones appear in HAMOCC. In the standard run, the remineralization rates are temperature-independent (Q10,POC=1).

The global pattern of the depth-integrated primary production is dominated by global circulation and thus nutrient transport. The global pattern of annual mean integrated primary production therefore remains similar between the standard and the M4AGO run (Fig. ). Globally integrated, the annual net primary production is ≈55.3 Gt C yr-1 in M4AGO compared to ≈44.7  Gt C yr-1 in the standard run.

The ratio between carbon export out of the euphotic zone at depth z0=100 m and the net primary production, NPP, 32p ratio(z)=POCfluxatdepthz=z0NPP, provides an estimate of how efficient the export is with respect to the net primary production. Globally, about 5.56 and 6.28 Gt C yr-1 is exported out of the euphotic zone in M4AGO and the standard run, respectively. In the standard run, the subtropical gyres exhibit p ratios of more than 0.2, and the high latitudes feature lower export efficiency (Fig. c). In the M4AGO run, the equatorial Pacific exhibits the lowest export efficiencies, the subtropical gyres feature maximum values of about 0.14–0.16 and the Arctic region maximum value is about 0.20 (Fig. d). The M4AGO run thus possesses smaller latitudinal variability in the p ratio compared to the standard run.

In comparison to previous estimates on global primary production, both model runs are well within the range of 30 to 70 Gt C yr-1 and show similar pattern of NPP . The higher NPP in M4AGO is due to the enhanced remineralization rates in surface waters, which also lead to the lower export efficiencies in the equatorial and subtropical regions. Estimates of the export efficiency from satellite data, in situ observations or models lead to partly contrasting patterns e.g.,. In contrast to our two model runs, the highest p ratios are suggested to be found in the North Pacific and Antarctic Ocean e.g.,. In the tropical and subtropical regions, the M4AGO run reduces the bias with respect to previously found low export efficiencies of about 1 % to 10 % .

The exported POC is accompanied by biogenic minerals and dust. The export flux ratios between opal and detritus exhibit a clear latitudinal pattern, with high values in the high latitudes and upwelling regions compared to the subtropical gyres (Fig. a, b). Both model simulations show a similar pattern of opal-to-detritus flux ratios. Higher CaCO3-to-detritus flux ratios are confined to equatorial and subtropical regions where silicate depletion favors calcification (Fig. c, d). M4AGO exhibits a higher CaCO3-to-detritus-mass flux ratio in the western tropical and subtropical Pacific than the standard run. The higher remineralization in the surface waters in this region reduces the amount of detritus that can coalesce with CaCO3. The spatial distributions of sinking tracers and their ratios prime the marine aggregate properties in M4AGO.

The spatial patterns of detritus and mineral fluxes are reflected in the distribution of aggregate properties (cf. pattern in Figs. b and d to a–f). The primed characteristics further evolve while aggregates descend through the water column and become remineralized. Hence, the information of the tracer distribution in the euphotic zone propagates into the mesopelagic zone. The mean primary-particle density, 〈ρp〉, ranges at export depth (100 m) from about 1100 kg m-3 in diatom-dominated regions to 1850 kg m-3 in the western Pacific, where CaCO3-to-detritus export ratios are high (Figs. b and d and a). In the Arctic, some regions harbor 〈ρp〉 of maximum 2600 kg m-3 where aggregates in our model are dominated by dust particles (Fig. a). Particularly in regions of high CaCO3-to-detritus export ratios, 〈ρp〉 increases with depth (Figs. a and g and a). Accordingly, the volume-weighted mean excess aggregate density, Δ〈ρf〉V, exhibits the same pattern as 〈ρp〉, while it ranges from about 2 kg m-3 in diatom-dominated regions to 35 kg m-3 in calcifier-dominated regions (Fig. d). Note that we chose Δ〈ρf〉V to account for the increasing porosity with size (Eq. ), thus decreasing aggregate excess density with size (Eq. ). As a mean value, Δ〈ρf〉V thus underestimates excess density for small aggregates, while it overestimates excess density for large aggregates. Generally both 〈ρp〉 and Δ〈ρf〉V tend to increase with depth (Fig. a, d). In the Pacific, CaCO3 as ballasting mineral becomes dissolved below the lysocline, and modeled 〈ρp〉 decreases again in the deep ocean (Fig. a, d). The mean primary-particle size, 〈dp〉, ranges between the attributed minimum and maximum primary-particle size of tracers, 2 to 20 µm, respectively. Mean primary-particle size shows an opposing pattern to 〈ρp〉 (Figs. a, b, g and h and a and b), since regions are either dominated by small, dense coccoliths or large, less dense diatom frustules. The global pattern of 〈dp〉, primed through export fluxes of detritus and minerals, varies only little throughout the water column (Fig. b), since we assumed invariance of primary-particle size to remineralization, dissolution and other processes.

Our simulated dmax is largest in the surface waters of the Southern Ocean and upwelling regions, where TEP-rich aggregates prevail. In calcifier-dominated regions, the maximum aggregate size is small. Generally, dmax tends to decrease with depth (Fig. e).

The microstructure of marine aggregates, modeled as fractal dimension, df, shows a pronounced spatial distribution. At 100 m depth, df ranges from about 1.7 in upwelling regions and the Southern Ocean to about 2.2 in the western equatorial Pacific and features maximum values of 2.38 in Arctic regions (Fig. c). With increasing depth in the mesopelagic zone, aggregates tend to experience a rapid compaction as df increases (Fig. c). Ongoing POM remineralization during aggregates' descent shifts the aggregate composition towards mineral components, which feature lower stickiness in our model. Thus the fractal dimension increases, which mimics compaction of aggregates. The global pattern tends to homogenize with depth at about 1000 m, where modeled aggregates feature df values of about 2.2 (Fig. i). Exceptions are upwelling regions, where df remains low, since detritus is slowly remineralized anaerobically in the associated oxygen minimum zones (OMZs). Below 1000 m, df only increases slowly with depth (Fig. c).

Particle properties and molecular dynamic viscosity determine the concentration-weighted mean sinking velocity of aggregates, 〈ws〉 (Fig. f, l). For 〈ws〉, M4AGO considers particle sizes ranging from few micrometers to millimeters and thus the full size spectrum, where sinking velocities of O(1 m d-1) to O(>100 m d-1) are represented. 〈ws〉 thus can significantly differ from reported sinking velocities for large individual aggregates. At the export depth, 〈ws〉 ranges from about 10 m d-1 in the Southern Ocean and North Pacific region to about 35 m d-1 in the western equatorial Pacific and reaches maximum values of ∼48 m d-1 in dust-dominated Arctic regions (Fig. f, l). Upwelling-influenced surface waters tend to show smaller 〈ws〉 than the western equatorial Pacific. Generally, 〈ws〉 appears to increase rapidly with depth within the mesopelagic zone (Fig. f). At about 1000 m, the latitudinal pattern changes and the high latitudes, in the Southern Ocean at around 45∘ S, exhibit the highest 〈ws〉 of about 65 m d-1. Along the Equator, outside the OMZs, 〈ws〉 exhibits similarly high values of about 55 m d-1 (Fig. f). Inside the OMZs, where remineralization is slower than in oxygenated waters, the detritus residence time is longer and leads to lower 〈ws〉 (Fig. l). The subtropical regions, dominated by calcifiers, show a rather homogeneous mean sinking velocity (〈ws〉≈50 m d-1) throughout the water column apart from the first few hundred meters and near bottom regions. By contrast, diatom-dominated waters feature a significantly increasing 〈ws〉 with depth, which reaches values of up to approximately 80 m d-1 (Fig. f). Diatom-dominated aggregates in surface waters feature a high buoyancy through TEPs and a loose structure which diminishes with continuous remineralization during their descent.

The aggregate properties entering the M4AGO scheme are all directly or indirectly measurable. The comparison of simulated and measured aggregate properties is, however, difficult, as M4AGO depicts mean values of aggregate populations that in situ encompass heterogeneous composition among size spectra. In addition, measurements are often limited to particular aggregate characteristics, while others remain unconstrained within the same data set. We therefore compare M4AGO to field and laboratory measurements which examine subsets of the simulated aggregate characteristics.

The modeled aggregate excess densities in diatom-dominated regions compare well to former field and laboratory measurements, where marine aggregates showed excess densities of about 0 to ∼10 kg m-3 . In calcifier-dominated regions, aggregate excess densities are about ∼35 kg m-3, which is in the upper range of measured values of 2.1 to 41 kg m-3 . The increased excess density of CaCO3-dominated aggregates of about 100 to 150 kg m-3 in about 1000 m depth compares well with that of observed fecal pellets egested by coccolith-consuming zooplankton . These fecal pellets also show similar mean sinking velocities to our modeled 〈ws〉≈50 m d-1. The change of the excess density is linked to the increasing df of aggregates with depth that is in qualitative agreement with present conceptual understanding . The increasing df depicts the expected continuous repacking of aggregates and the zooplankton-mediated compaction in fecal pellets. The latter particularly takes place in the upper few hundred meters of the ocean and is a major pathway of coccolith transport .

The general difference in typical size between diatom-rich aggregates and CaCO3 shell-enriched aggregates compares well to observations that also showed smaller CaCO3-dominated aggregates . The decreasing dmax with depth is in qualitative agreement with observed vertically decreasing aggregate mean diameters . Decreasing maximum aggregate sizes with depth and reduced organic matter content also agree qualitatively well with experiments of and . Both studies showed a significant decrease in aggregate size with increasing mineral components. In their experimental setups, it remains elusive if a certain threshold of carrying capacity of POM was reached or if the balance between adhesive forces within the aggregates and the sinking-induced shear forces was shifted towards smaller aggregates. It is likely that both effects happen at the same time, since natural polymers possess stronger adhesive surface properties than biogenic minerals . In M4AGO, only the compaction towards higher fractal dimensions through lower internal binding forces, expressed as stickiness of the primary particles, is represented. Compaction can coincide with an increasing number of binding links in aggregates, which can lower the overall susceptibility of aggregates to shear stress. In M4AGO, we disregard this effect and keep Recrit globally constant.

In summary, the resulting mean sinking velocity in M4AGO is of same order of magnitude as that found in observations . We note, however, that mean sinking velocities estimated from observations potentially overestimate 〈ws〉, as they (i) are methodologically constrained to particles larger than a lower detection limit, which is typically much larger than primary-particle size, and (ii) depend on often uncertain size-to-mass relationships. We emphasize further that our modeled 〈ws〉 embraces numerous slowly sinking aggregates of primary-particle size (ws≈O(1 m d-1)) as well as rare, but large, fast sinking aggregates (ws≈O(1000 m d-1)). This range hence encompasses observations for single cells and coccoliths up to large marine snow aggregates and fecal pellets . Generally, the spatio-temporal variability in 〈ws〉 in M4AGO differs significantly from the simple underlying assumption of a linearly increasing sinking velocity with depth in the standard run. M4AGO resembles the strongly increasing sinking velocity found in the mesopelagic zone in observations e.g., and a modeling approach .

The transfer efficiency of POC from z0=100 m to depth z in the ocean, 33Teff,POC,z=POCfluxatdepthzPOCfluxatdepth100m,forz>z0, provides an estimate on the fraction of exported POC that reaches a particular depth and is determined by sinking velocity and remineralization. In the Martin curve (Eq. ), the slope constant, β, prescribes the transfer efficiency, 34Teff,POC,z(Martin)=zz0-β, to a particular depth and leads to an almost homogeneous global transfer efficiency of Teff,POC,z(Martin)≈0.12 to about 1000 m depth in our standard run (Fig. a). The lower remineralization rates in sub-anoxic or even anoxic OMZs compared to oxygenated regions lead to higher transfer efficiencies, visible in the equatorial eastern Pacific Ocean, the northern Indian Ocean, and upwelling regions off the coast of Peru and Africa. Apart from these regions, the standard run features only little variability, as expected from the relationship between the Martin curve slope parameter and the transfer efficiency. The remaining variability is related to ocean currents and spatially variable turbulent mixing. By contrast, the transfer efficiency in M4AGO exhibits a distinct global pattern and possesses higher efficiency in high-latitude and upwelling regions compared to the subtropical gyres where low Teff,POC,z appears. Similar to the standard run, the OMZ regions feature high transfer efficiencies in M4AGO. Since local Martin curves provide meaningful information on the attenuation of POC fluxes with depth, we analyzed the effective slope parameter, β′, for both the standard and the M4AGO run. We fitted the Martin curve (Eq. ), to modeled POC fluxes below z0 to estimate β′. As expected, the standard run shows little spatial variability apart from the OMZs and features a global, area-weighted mean slope of 〈β′〉A,Martin≈0.82. In agreement with the transfer efficiency pattern, M4AGO possesses a strong latitudinal pattern of the effective slope β′ that varies between β′≈ 0.59 and 0.67 in high latitudes (Antarctic zone – AAZ; North Pacific – NP; subantarctic zone – SAZ) and ≈0.30 and 0.60 in OMZ regions and with a maximum β′≈1.31 in the subtropical Pacific gyres (Fig. ).

Recently, reconstructed the global transfer efficiency pattern by diagnosing particulate organic phosphate fluxes. Reconstructing the transfer efficiency via inverse modeling from phosphate concentrations circumnavigates the obstacle of sparse direct observations of fluxes and allows for a more reliable constrain on POC transfer efficiency . The comparison of the standard and M4AGO run reveals the inherent inability of the Martin approach to capture the latitudinal variability (Fig. a–c). M4AGO agrees qualitatively and quantitatively well with the reconstructed transfer efficiency pattern of . The overestimation of the transfer efficiency in the equatorial tropical Pacific (ETP) by both the standard and M4AGO run is due to the models overestimation of OMZs extensions . The large OMZ causes diminished remineralization and, hence, reduced attenuation of POC fluxes. In general, however, the increased transfer efficiency associated to OMZs is in agreement with observations that suggest lower flux attenuation and, hence, small β . Lower remineralization in OMZs keeps the POC-to-ballasting-minerals ratio higher when compared to oxygenated waters. Thus, the lower remineralization rates are potentially accompanied by lower sinking velocities, which provides a positive feedback loop on the OMZ evolution. The larger the vertical extent of the OMZ becomes, the longer the retention time becomes through higher POM aggregate content and lower sinking velocities. Eventually, OMZ evolution is balanced by the oxygen supply through mixing and transport processes. The global pattern of β′ in M4AGO agrees well with the geographical range and pattern found by and suggested by . However, M4AGO shows lower maximum values of β′≈1.31 compared to β′≈1.9 suggested by . Globally averaged, M4AGO exhibits an effective slope parameter of 〈β′〉A,M4AGO≈0.75, which is lower than the slope of β′=0.86, originally published by based on local observations. Noticeably, however, the trend of smaller to larger β′ values from the nearshore to open waters off the Pacific US coast is in agreement with the elusive trend found by . Overall, M4AGO clearly improves the representation of the POC transfer efficiency pattern compared to the standard Martin approach.

The attenuation of POC fluxes is primarily regulated by the sinking velocity and total remineralization rate of POC. Depth-dependent, sheared lateral transport and vertical water motion can additionally affect the vertical distribution of particulate matter and thus vertical fluxes. We neglect these processes in the following, since (i) the timescale of sinking from one layer to the next layer below is typically shorter than the lateral transport at grid resolutions used in our model runs, and (ii) sinking velocity is faster than typical vertical motions represented by models with this grid resolution. The remineralization length scale (RLS), zPOC*, is given by the local ratio of 〈ws〉 to remineralization (RPOC,remin), 35zPOC*=〈ws〉RPOC,remin, and defines the vertical distance in which POC would decay to 1/e (≈37 %) of its initial value, the POC e-folding depth . The RLS can be locally calculated and enables (i) exploring the local effects of remineralization and sinking velocity on the attenuation of POC fluxes and (ii) better understanding the depth-integrated information provided by the transfer efficiency or Martin's effective slope parameter, β′.

The RLSs in surface waters and the upper mesopelagic zone of subtropical and equatorial regions are shorter in the M4AGO run than in the standard run by more than a factor of 2 (Fig. a). This higher turnover causes the lower p ratio in M4AGO compared to the standard run in these regions (Fig. b). In the mesopelagic zone, the RLSs in M4AGO are similar or pronounced longer and decrease again in deeper regions compared to the standard run (Fig. a). The longer RLSs in the mesopelagic zone of the high-latitude ocean are the reason for the higher transfer efficiency of M4AGO compared to the standard run. In order to analyze which of the two processes, sinking or remineralization, is of primary importance for the change in the RLS and thus the transfer efficiency, we define their relative contributions to the difference between M4AGO and the standard run as 36RCPi,x[%]=∂PizPOC*⋅ΔPi,x∑i|∂PizPOC*⋅ΔPi,x|⋅100, where the processes, Pi={〈ws〉,RPOC,remin}, refer to Eq. (), ∂Pi is the partial derivative of zPOC* with respect to the process Pi (applying the standard run rates), and ΔPi,x is the difference between the value in the M4AGO run and the standard run at spatial point x. M4AGO possesses generally higher remineralization rates than the standard run, which would increase the flux attenuation compared to the standard run. The temperature-dependent remineralization in M4AGO shows lower rates in the cold waters of the high latitudes than in the equatorial and subtropical regions (Fig. a). Within M4AGO, this pattern enhances the RLSs, and thus transfer efficiency, in the high latitudes compared to the equatorial regions, which is in agreement with and . Compared to the standard run, higher 〈ws〉 overcompensates the effect of intensified remineralization below the thermocline and leads to a longer RLS (Fig. b) in the mesopelagic zone, which is particularly true in diatom-dominated regions. In CaCO3-dominated subtropical gyres, 〈ws〉 falls below the sinking velocity of the standard model in regions deeper than 3000 m and thus contributes further to the stronger flux attenuation compared to the standard run. The higher 〈ws〉 in M4AGO turns out to dominate over remineralization and increases the RLS, and hence the transfer efficiency, in the mesopelagic zone of the high latitudes. In summary, the temperature dependence of remineralization in M4AGO induces a latitudinal pattern of longer RLSs, and thus higher transfer efficiency, in high latitudes, which is further amplified by high sinking velocities of diatom-dominated aggregates in the mesopelagic zone.

The analysis of the RLS changes compared to the standard run emphasizes the role of sinking velocity for the longer RLS in the mesopelagic zone in high latitudes and thus for the enhanced transfer efficiency. We therefore aim to better understand the underlying factors that control the mean sinking velocity. We suggest in the following that the size of primary particles might be as important as the density of the ballasting material for defining the sinking velocity of aggregates.

M4AGO allows for assessing the contributions of aggregate properties and molecular viscosity to 〈ws〉. We define the relative contributions of the modeled particle properties and the molecular viscosity that control 〈ws〉 at particular depth z based on a first-order approach: 37RXi,z[%]=∂Xi〈ws(X‾i,z)〉⋅ΔXi,z∑i∂Xi〈ws(X‾i,z)〉⋅ΔXi,z⋅100, where Xi={〈ρp〉,〈dp〉,μ,dmax,b,df}, ΔXi,z=Xi,z-X‾i,z and ∑RXi,z≠100, but ∑RXi,z=100, and X‾i,z is the global mean of the contributing property at depth z. The relative contributions provide information about the main driving factors for the local 〈ws〉 when compared to 〈ws〉 of global average aggregates. For example, what is the percentage-wise contribution to the local sinking velocity by local primary-particle density compared to the global mean primary-particle density? By neglecting the higher-order terms, we provide only qualitative insights into the role of the different aggregate properties and molecular viscosity in 〈ws〉.

CaCO3 acts as a strong positive, 〈ws〉-increasing factor for sinking velocities in the equatorial and subtropical regions due to its high primary-particle density (Fig. a). As an exogenous factor, the low molecular viscosity in warm regions contributes positively to sinking velocity (Fig. d). Additionally, in our model, df increases particle excess density and thus 〈ws〉 in CaCO3-rich areas (Fig. c). In the Southern Ocean, North Pacific, North Atlantic and upwelling regions, particularly the large 〈dp〉 in diatom-dominated regions enhances 〈ws〉 (Fig. b). According to our model, dmax of aggregates and the number distribution slope, b, contribute positively to 〈ws〉 in the high latitudes, except for the Arctic Ocean, where mineral material strongly affects the aggregate properties. The pattern of highly variable endogenous and exogenous controls on 〈ws〉 emerges particularly in the upper ocean, while in deeper regions of about 1000 m depth, the aggregate properties become more and more homogeneous, except for 〈dp〉 and 〈ρp〉 and in OMZs (Fig. g–l). With homogenization of most aggregate properties with depth, the contrasting relative contributions of dense mean primary particles and large mean primary particles to 〈ws〉 become even more pronounced. Denser, small CaCO3 particles contribute to 〈ws〉 in the subtropical, oligotrophic regions of the oceans, while comparably less dense but larger opal frustules lead to high 〈ws〉 in nutrient-rich upwelling and high-latitude regions. Even though our formulation for 〈ws〉 is highly non-linear, we expect the qualitative pattern of the relative contributions to 〈ws〉, particularly through 〈dp〉 and 〈ρp〉, to be coherent. In sum, we therefore emphasize the potential role of primary-particle size, in particular that of diatom frustules, in determining 〈ws〉 and thus POC fluxes.

The effects of microstructure on in situ 〈ws〉 are not well studied, and df of aggregates is weakly constrained. It therefore warrants further investigation, especially if a spatially variable df effect occurs on in situ 〈ws〉 in the upper ocean. Vertically varying df has been suggested , and given the general importance of the microstructure for sinking velocity, a deeper understanding of the factors and processes influencing df is hence highly desirable.

Microstructure df directly prescribes the aggregate number distribution slope, b, in M4AGO (see Fig. c and f for a map of b). Observations show a higher variability in b≈2 to 5 than in M4AGO, where b varies between ≈ 3.19 and 3.76 and thus likely underestimates the spatial variability and relative contribution of b to 〈ws〉. At present, M4AGO is limited to the steady-state size distribution that represents the characteristic processes of aggregation and fragmentation in the system. Explicit modeling of the dynamics of the aggregate size spectrum would be required to cover the variability in measured b, which would further enhance the variability in 〈ws〉. We briefly discuss this current model limitation in Sect. .

Previous studies support our finding that CaCO3 acts as a strong ballasting agent e.g.,. By contrast, opal density of the hollow silicate structures has a smaller effect on 〈ρp〉 (see Fig. a). Instead, silicate frustule size of diatoms significantly affects 〈ws〉 (see Figs. b and h and b). This contrasts the assumption of opal acting solely as ballasting material and is congruent with , who noticed that factors other than particle density likely play a role. As indicated by Eqs. () and (), primary-particle size affects the excess density and porosity of aggregates, which have decisive effects on sinking velocity . Deciphering the size effect of primary particles on in situ 〈ws〉 and fluxes might be particularly challenging in regions with a diverse size structure of the phytoplankton community. Oligotrophic regions typically harbor a narrower size distribution of phytoplankton see, e.g., size ranges and standing stocks in, which may produce more homogeneous aggregates and thus more predictable POC fluxes, as found by , who correlated POC fluxes to the oligotrophic phytoplankton community. In addition, interannual variability in the dominant size of primary producers has been suggested to drive the interannual change in export fluxes . In contrast to oligotrophic phytoplankton communities, diatom-dominated communities feature a higher size diversity and different morphologies, which both affect the sinking velocity of aggregates . Phytoplankton community size structure and morphology thus introduce higher variability to sinking velocity, which complicates attribution of cell size and morphology effects on POC fluxes. The higher size and morphology variability in diatom-dominated phytoplankton communities, together with variable cellular silicate-to-carbon ratios , likely explains the poor correlations of opal to POC fluxes e.g., found by. Similarly, the correlation between POC fluxes and, by number and size, more variable foraminiferal CaCO3 is weaker than for coccolith fluxes . We therefore suggest to factor in, or even focus on, frustule sizes and morphology as explanatory variables for POC fluxes when carrying out mineral ballasting and rain ratio studies in diatom-dominated regions.

Biogenic minerals, dust particles and detritus are tied together in M4AGO and define the composition, microstructure and thus sinking velocity of aggregates. In turn, the tracers are independently remineralized or dissolved. Both processes affect 〈ws〉 and thus the e-folding depth of tracers. For example, the remineralization of POC increases 〈ws〉 of diatom-dominated aggregates and thus increases the dissolution length scale of opal, which we refer to as the “opal RLS”. The combined sinking thus (i) affects the RLS of POC and opal (and CaCO3 when dissolution takes place) and (ii) couples the timing of mineral and POC fluxes at depth.

The Martin curve concept can be applied to represent the effective attenuation of opal fluxes. The effective Martin curve slope for opal, βopal′, exhibits similar regional variability in the M4AGO run compared to the standard run (Fig. ). However, the equatorial tropical Pacific (ETP) region shows higher spatial variability. The low POC remineralization in OMZs leads to small 〈ws〉 of aggregates and decreases the opal RLS and thus increases βopal′. Similar to POC fluxes, opal fluxes exhibit shorter opal RLSs in the surface waters, while they exceed the standard RLSs in the mesopelagic zone and below (not shown). Particularly in the deep waters of the high latitudes, the opal RLSs are longer than in the standard run. This is due to the aggregates' higher sinking velocity than the 25 m d-1 opal sinking speed in the standard run and partially to the reformulation of temperature-dependent opal dissolution. In the subtropical regions, opal is remineralized faster below 2000 m and fluxes are generally small (see Fig. a, b).

In sum, M4AGO estimates that globally ∼1.03 Gt Si yr-1 (∼1.04 Gt Si yr-1 in the standard run) reaches the seafloor, which is in good agreement with present estimates of about 1 Gt Si yr-1 . Generally, the modeled βopal′ is well within the range of observations with estimates of βopal′=0.22±0.53 . In M4AGO, dissolution of opal has the implication that ballasting mineral ratios between opal and CaCO3 shift towards higher importance of CaCO3 with depth. Since the dissolution of opal is temperature-dependent, the preservation efficiency for opal-to-CaCO3 ratios is thus lowest in regions with strong vertical temperature gradients.

The direct coupling of POC and biogenic mineral fluxes through marine aggregates potentially enhances the models' ability to represent rain ratios in space and time. We therefore aggregated the sediment trap data set of with 15 792 individual POC flux measurements at 673 unique locations to a monthly climatology of POC, particulate inorganic carbon (PIC) and silicate fluxes. We accounted for the time spans of sediment trap deployment ranging from hours to years by time-weighting with a minimum weight of 1 d per month in cases of few hours of measurement and for each covered month the full monthly weight in cases of a yearly measurement. We compared the climatologies to modeled monthly mean flux ratios at the stations at their respective depths. The M4AGO run represents the POC/PIC flux ratio equally as well as the standard run (not shown). For POC/Si fluxes, the scatter around the 1 : 1 line is reduced in M4AGO compared to the standard run (Fig. ).

However, M4AGO introduces a bias in regions deeper than ∼4000 m towards smaller POC/Si ratios. The RLSs in the deep ocean are hence too short in M4AGO. While the scatter of the POC/Si ratio reduces in M4AGO, the overall variability in the flux ratios becomes compressed compared to the measured variability. This compression might be caused by several factors. First, we assume a tight connection of aggregate components and ignore heterogeneous composition among local particle-size spectra which would potentially cause different sinking velocities among the different components. Second, HAMOCC ignores changing diatom silicification caused by temperature seeand references therein and by seasonal changes in nutrient availability . Generally, deficits exist in both the model runs and sediment trap data. The lack of resolving small-scale variability through eddies and their role in shaping the phytoplankton community, as well as general timing, internal variability, and spatial current shifts, limit the global models' ability to represent local features. Measurement limitations of sediment traps have the potential to additionally increase the mismatch see, e.g.,and references therein.

We evaluate the simulated spatial distribution of nutrients, oxygen and alkalinity by comparison to gridded observation climatologies. Silicate, phosphate, nitrate and oxygen are compared to the World Ocean Atlas WOA; . Alkalinity, AT, is compared to the Global Ocean Data Analysis Project (GLODAPv2) climatology . We present the results in Taylor diagrams , which aggregate correlation, root-mean-square deviation (RMSD), and standard deviation of simulated and observed variables into distances between model results and the reference observations (Fig. a–d). Here, we use spatial grid-cell-wise statistics derived from temporally averaged (100 year mean) fields for which we interpolated the observational data to the model grid. To be able to show all parameters in one plot, we derive normalized standard deviations and RMSDs. We evaluate the Atlantic and the Pacific Ocean separately to account for their different hydrographical features. For example, the Atlantic Ocean is characterized by ventilation through deep water formation in the high latitudes, a feature that does not exist in the Pacific. Furthermore, we select four depth levels: surface waters (6 m depth); the two depths that determine the transfer efficiency, 100 m and approximately 1000 m; and an intermediate depth in the mesopelagic zone, 362 m.

Generally, the two model runs represent nutrients, silicate and oxygen distributions equally well at these depth (Fig. a–d); i.e., differences to observations are larger than among the two models. This is expected, as tracer distributions in the model are predominantly determined by the flow field and both simulations use identical physical model conditions. The Taylor diagram captures matches of spatial pattern such as location of fronts, extension of gyres and the location of water masses in an aggregated form. The ocean model represents such features realistically , but we cannot expect a perfect match of the circulation pattern with in situ conditions for multiple reasons. The climatological, simplistic atmospheric forcing damps in particular the interannual variability in ocean currents and can contribute to spatial shifts of, for example, frontal regions with respect to the observed climatology. In addition, the coarse horizontal resolution of the model and atmospheric forcing affects features such as upwelling strength and location. In turn, the spatio-temporal interpolation of data, necessary through scarcity of observations, limits the resolution of nutrient variability and introduces uncertainty, particularly in deeper regions, where the density of observations is lower than in surface waters. As a consequence, a mismatch between modeled biogeochemical tracers and the climatological mean of observations is expected.

Tracers undergoing less complex biogeochemical cycling, such as phosphate or silicate, reflect the quality of the flow field more directly than tracers such as nitrate, oxygen or alkalinity see also. The latter tracers are therefore generally more prone to biogeochemical model reformulation, and larger differences can be expected between M4AGO and the standard run. In addition, M4AGO links the cycles of phosphate and silicate closer to nitrate and oxygen through common sinking of particulate matter. Phosphate and silicate therefore experience an additional biogeochemical cycle imprint in M4AGO compared to the standard run. In surface waters of the Pacific, this led, for example, to a slight improvement of the phosphate correlation with WOA observations, while it increased the normalized standard deviation compared to the standard run (Fig. a). The improvement is related to the better representation of surface phosphate concentrations off the coast of Peru and the western coast of North America (see Fig. e–g).

In both simulations, biogeochemical tracer distributions in the Pacific are strongly influenced by the OMZ in the eastern boundary upwelling region. An exception is oxygen in surface waters, which is primarily determined by gas exchange processes. As a common feature of all state-of-the-art global ocean biogeochemistry models, OMZs are too large and result from nutrient trapping through a sluggish circulation and associated insufficient supply of oxygen . The sluggish circulation and mixing are likely associated with underrepresented equatorial currents, particularly the equatorial intermediate current system and equatorial deep jets . The OMZ shape in the eastern Pacific Ocean, though, changes between the runs. In M4AGO, the water column above 800 m is more oxygenated and below 800 m is less oxygenated than in the standard run. The change in OMZ shape imprints on AT, as anaerobic and aerobic remineralization processes change alkalinity in a different manner; i.e., denitrification and sulfate reduction increase alkalinity, whereas aerobic remineralization decreases alkalinity. While AT and silicate are generally worse than other tracers when compared to observations, M4AGO improves the representation of AT in the Pacific at 360 m compared to the standard run. This is visible through the higher correlation (∼0.45 compared to 0.4) and lower RMSD of ∼2.3 compared to ∼3.75 in the standard run (Fig. c; 362 m depth). The increased RMSD of silicate in surface waters and 100 m in M4AGO are associated to the eastern equatorial and upwelling regions in the Pacific. The lower remineralization in OMZs not only decreases the sinking velocity of detritus but also increases the retention time of the tightly coupled opal in M4AGO and thus enhances the opal dissolution and silicate concentration. In general, the tighter coupling of silicate to nutrients through common sinking in aggregates leads to a higher sensitivity of silicate to ocean circulation and temperature deficiencies in M4AGO than in the standard run. The high RMSD and low correlation for silicate compared to observations, particularly in the euphotic zone, can have additional implications for M4AGO, since the silicate distribution in the euphotic zone directly affects opal production and thus the sinking velocity of aggregates, transfer efficiency and nutrient distributions. The tighter coupling of silicate to other biogeochemical cycles in M4AGO therefore warrants further future investigation.

In a 100-year climatological steady state, both model runs show the Southern Hemisphere ocean acting as a net source of CO2 to the atmosphere, while the Northern Hemisphere acts as a net sink (Fig. a). Consequently, net oceanic CO2 transport across the Equator from the Northern to the Southern Hemisphere exists. In the simulation with M4AGO, a stronger CO2 uptake compared to the standard run occurs in the region between 60 and 45∘ S, which coincides with deeper transfer of POM reflected by an increased transfer efficiency (Fig. ). In both model runs, the tropical regions outgas CO2 to the atmosphere. As is visible from the decreasing difference between the cumulative zonal CO2 fluxes, M4AGO exhibits stronger outgassing in the tropical region, particularly in the Northern Hemisphere (Fig. a). Even though a small residual of zonally integrated fluxes of about 0.02 Gt C yr-1 between the two model runs remains, the small residual CO2 flux imbalance of 0.07 and 0.05 Gt C yr-1 in M4AGO and the standard run, respectively, indicate well-spun-up model runs. In general, the latitudinal zonal CO2 fluxes and the cross-equatorial southward oceanic CO2 transport agree qualitatively and quantitatively well with former forward-integrated models for preindustrial conditions e.g.,.

To study the effect of the changed transfer efficiency in M4AGO on the CO2 uptake without indirect climate effects, we perform model runs in which we linearly increase the atmospheric CO2 concentration with a yearly increment from ∼285 to 400 ppm within 150 years. The transient forcing does not feed back onto the physical climate state. We therefore emphasize that no climate feedback on, for example, ocean temperature, stratification, and thus primary production and remineralization occurs in these model runs.

During the atmospheric CO2 increase, both model runs show similar global annual oceanic CO2 uptake (Fig. b). About 181–185 Gt C is taken up by the global ocean throughout the 150-year period. The discrepancy of ≈4 Gt C between the two runs arises to a large extent from the residual imbalance of 0.02 Gt C yr-1 uptake, cumulated over 150 years.

The general trends in the regional cumulative fluxes remain the same between the two model runs (Fig. c–k), and most regions act as net sinks of CO2. Only the upwelling regions of the equatorial tropical Atlantic (ETA) and Pacific (ETP) are net sources of CO2 to the atmosphere at the end of the 150-year period. The magnitude of the regional cumulative fluxes, however, varies among the two model runs.

Since we can rule out temperature-driven effects on the differences in CO2 uptake when comparing the two climatologically forced runs, a different state and/or changes in AT and dissolved inorganic carbon (DIC) concentration determine the partial pressure of CO2, pCO2 and thus CO2 fluxes. In our runs, major changes in AT and DIC can locally occur due to a change in, first, the CaCO3-to-detritus rain ratio as a result of varying CaCO3 and POM production and remineralization, or, second, an increase in the POC transfer efficiency, for example, which reflects a transfer of carbon to deeper waters where CO2 is withdrawn from immediate exchange with the atmosphere. In addition, such different signals can be transported by the flow field, and remote effects can appear. Quantitatively, differences of regional cumulative CO2 fluxes larger than 5 Gt C appear in the Antarctic zone (AAZ), the subtropical Pacific (STP), the equatorial tropical Pacific (ETP) and the Indic Ocean (IO; Fig. c–k). In the upwelling and high-latitude regions, the pCO2 is lower in M4AGO than in the standard run, which translates to higher oceanic uptake (in AAZ and NP) or less outgassing (in ETP). Qualitatively, this coincides well with the primary production, respective export and the higher transfer efficiencies in these regions (cf. Figs.  and ). In regions of higher transfer efficiency but similar CO2 fluxes when compared to the standard run, either POC export fluxes are small (e.g., in the Arctic Ocean) or physical processes such as mixing or upwelling dominate over biologically induced CO2 fluxes (e.g., in the SAZ). In the STP region, where high CaCO3-to-detritus rain ratios occur (refer to Fig. ), AT is about 0.2 % lower in M4AGO than in the standard run, which enhances pCO2 by about 2 % and thus decreases the CO2 uptake.

In summary, under linearly increasing CO2 in a non-interactive mode, the global CO2 fluxes remain similar for the standard and the M4AGO run. However, regional CO2 fluxes change, which is potentially linked to the changing pattern of transfer efficiency and the CaCO3-to-detritus rain ratio. A detailed study on the feedbacks between the transfer efficiency, represented by M4AGO, and a transient climate on oceanic CO2 uptake is out of the scope of this paper and will be part of future investigations.

With M4AGO, the processes of temperature-dependent remineralization and a number of new model parameters to represent variable sinking velocity of marine aggregates were introduced to HAMOCC. We carried out three sensitivity experiments to provide insights into the response of HAMOCC to the uncertainty of selected parameters (see below for the criteria). As target variables, we chose (i) the transfer efficiency, (ii) phosphate as an essential nutrient for primary production, and (iii) silicate as a nutrient and circulation-reflecting agent.

Previously in Sect. , we suggested the size of primary particles, particularly that of opal frustules, to be an important factor for regulating 〈ws〉 and thus the transfer efficiency. We thus study the effect of primary-particle size in the sensitivity experiment S(dp,frustule) exemplarily for diatom frustules because (i) diatom size is highly variable, (ii) HAMOCC does not explicitly represent algae size classes and (iii) algae body size is expected to decrease with rising water temperatures . We decrease their size by 50 %, from dp,frustule=20 µm to dp,frustule=10 µm. In the second sensitivity experiment, S(df), the varying fractal dimension, ranging between 1.6 and 2.4 in the M4AGO run, is set to a constant, df=2, to eliminate its variable effect on b and 〈ws〉. In the third experiment, S(KP,diaz), we showcase the sensitivity of phosphate concentration in the subtropical gyres to diazotrophs' standing stock, which we noticed during the process of tuning the M4AGO run. Here, we increase the half-saturation constant for phosphate uptake by diazotrophs from 0.05 to 0.10 µmol L-1. All sensitivity runs are in a quasi-steady state, as reflected by surface properties that are in steady state.

Decreasing the opal frustule size by 50 % compared to the M4AGO run reduces 〈ws〉 and thus the RLS in diatom-dominated regions. As a consequence, the transfer efficiency in silicifier-dominated regions is lower in S(dp,frustule) than in M4AGO (Fig. g). Accordingly, opal dissolves closer to surface waters and the silicate concentration increases compared to the M4AGO run in silicifier-dominated regions, particularly in and downstream of coastal upwelling regions (Fig. d). In the subtropical gyres, where silicate is diminished, it further decreases in S(dp,frustule). The higher remineralization in the euphotic zone in upwelling regions increases the phosphate concentrations downstream in the subtropical gyres (Fig. a). In sum, the sensitivity to dp,frustule underpins the potential importance of primary-particle size for 〈ws〉 and thus for biogeochemical cycling.