We assess 36 ESMs from 13 different climate modelling centres (CCCma, CMCC, CNRM-CERFACS, CSIRO, HAMMOZ-Consortium, IPSL, MIROC, MOHC, MPI-M, MRI, NCAR, NCC, and NOAA-GFDL), which took part in the fifth and/or sixth phases of the Climate Model Intercomparison Project (CMIP5, Taylor et al., 2012; CMIP6, Eyring et al., 2016). We only consider ESMs for which Alk is not prescribed but determined by physical and biogeochemical processes represented in the models (e.g. calcification and dissolution, or also primary production and remineralization). This leads us to include 17 ESMs for CMIP5 and 19 for CMIP6 (Table 1). In this study, we use “[ESM_name] (CMIP[number])” to refer to a given ESM, indicating whether it was used for CMIP5 or CMIP6, but we also refer to modelling centres or to the specificities of the marine biogeochemical components of the given ESMs.

In total, this ESM intercomparison encompasses 15 marine biogeochemical models (CMOC, CanOE, BFM, PISCES, WOMBAT, OECO, diat-HadOCC, MEDUSA, HAMOCC, NPZD-MRI, BEC, MARBL, TOPAZ, BLING, COBALT) with different versions and/or configurations depending on the CMIP and the modelling group. All the ESMs considered in this study represent the carbonate pump, with the exception of CMCC-CESM (CMIP5), which we include in our analysis to highlight the effect of implementing such a pump. NASA-GISS ESMs were not included as they prescribe Alk.

We review the key properties of marine biogeochemical models simulating Alk, seeking to share an in-depth overview of the representation of the Alk tracer in these models as well as its main interior driver, the carbonate pump. Specifically, we have collected a wide range of information from the different groups, both for CMIP5 and CMIP6, regarding the protocols followed (e.g. spin-up, initialization), the model boundary conditions (e.g. river discharge, Alk restoration), and the biological complexity and representation of explicit or implicit mechanisms (e.g. CaCO3 production, dissolution, sedimentation). In addition, we also report the nitrogen reactions taken into account by the different models, but we do not explore their effects on the Alk distribution, which can be complex under low-oxygen conditions (e.g. Stock et al., 2020). Finally, it should be noted that we were unable to collect comparable information for all models, notably the HAMMOZ-Consortium group, which is assumed to be identical to MPI-M for CMIP6 in terms of marine biogeochemistry modelling (Table 1).

For the different ESMs, we systematically processed the CMIP piControl (pre-industrial control) and Historical (covering the recent past) experiments. For CMIP5, where the historical simulation covers only the time period up to 2005, we concatenated the Historical experiments with RCP4.5 (or RCP8.5 if not available) from 2005 to 2014 to allow for data averaging over 1992–2012, for consistency with observations (see Sect. 2.3). Finally, we analyse only one ensemble member per ESM (Table 1), such that we do not address the role of internal variability in the emergence of climate-related changes in the key marine biogeochemistry variables we consider in this analysis.

The following variables were processed when available: (i) two-dimensional (2D) variables: “epc100” (sinking flux of organic matter at 100 m, mol m-2 s-1), “epcalc100” (sinking flux of calcite at 100 m, mol m-2 s-1), “eparag100” (sinking flux of aragonite at 100 m, mol m-2 s-1); (ii) three-dimensional (3D) variables: “talk” (total alkalinity, mol m-3), “dissic” (dissolved inorganic carbon, mol m-3), “no3” (nitrate concentration, mol m-3), “po4” (phosphate concentration, mol m-3), “so” (salinity, g kg-1), “thetao” (potential temperature, K for CMIP5 and ∘C for CMIP6). Export values at 100 m were extracted from 3D export fields when 2D exports at 100 m were not provided using “expc” (sinking flux of organic matter, mol m-2 s-1), “expcalc” (sinking flux of calcite, mol m-2 s-1), and “exparag” (sinking flux of aragonite, mol m-2 s-1). Although modelled, export data were not available for MIROC-ESM and MIROC-ESM-CHEM (CMIP5).

To facilitate the ESM intercomparison, we used Climate Data Operator (CDO) functions to regrid ESM outputs and observations. Specifically, we used distance-weighted average remapping “remapdis” to regrid the data on a regular 1∘×1∘ grid and linear-level interpolation with extrapolation “intlevelx” to regrid to the World Ocean Atlas (WOA) vertical grid with 33 depth levels up to 5500 m (even though 5500 m is not accessible for some of the CMIP5 ESMs). The mid-point of the uppermost level, which we refer to as the surface hereafter, was set to 5 m, given this is the deepest upper-ocean level among the ESMs considered. The analysis was performed in Python with the use of the Gibbs SeaWater (gsw) oceanographic toolbox for ocean property conversions. We also used mocsy 2.0 (Orr and Epitalon, 2015) to compute the ocean carbonate system over our averaging period (1992–2012) with the use of (i) Alk, DIC, phosphate (or nitrate divided by a Redfield ratio, rN:P=16, if not available), salinity and temperature from ESM outputs, (ii) silicate from GLODAPv2 observations (Olsen et al., 2020) as it is not included in many ESMs, and (iii) the seawater equilibrium constants recommended for best practices (Dickson et al., 2007; Orr and Epitalon, 2015). Quality control of ESM outputs led us to (i) exclude “po4” for CMCC-CESM (CMIP5) due to anomalously high values and long-term drift, and to (ii) exclude certain values at high latitudes given at 5500 m for MIROC ESMs in CMIP5 because they were not plausible and were likely affected by an error in model output processing before outputs were shared. Finally, each model is weighted in the calculation of CMIP5 and CMIP6 statistical values (mean, standard deviation, quartiles, and linear regressions) such that each modelling group has the same total contribution. Further 3D assessment of simulated variables by basin was performed through profiles, sections, and maps. Although beyond the scope of this study, these figures are provided online: 10.5281/zenodo.7637538.

We did not correct for potential drift in the ESM outputs in order to maintain consistency between the internal mechanisms of the ESMs. However, the piControl simulations were assessed for drift and are discussed in Sect. 4.2.1. Using the piControl data coincident with the Historical simulation and the RCP (Representative Concentration Pathway) for CMIP5 simulations or SSP for CMIP6 simulations (250-year-long piControl simulations), we were able to assess whether the ESMs had reached a quasi steady state prior to the Historical simulation. We assessed the drift of the vertical gradients of Alk, DIC, nitrate, and phosphate between the surface and deep ocean, considering the difference between the first and last 20 years of the piControl simulations. Similarly, we also estimated the drift in surface salinity and temperature as well as the spatially integrated exports of PIC and POC at 100 m. Drift assessment was not possible for MRI-ESM1 (CMIP5) due to a lack of piControl outputs and was only carried out for DIC and Alk for CanESM2 (CMIP5) as nitrate data were unavailable.

Our analysis focuses on the representation of Alk and the carbonate pump in the open ocean. Thus, most of the analysis and the associated figures consider the open ocean (defined in Appendix A) rather than the entire ocean. Indeed, our aim was to exclude coastal regions due to the coarse ESM resolution, but particularly to avoid inclusion of river discharge effects on Alk (see Sect. 2.4). The entire ocean was considered when values were integrated to compare with observationally based estimates (e.g. PIC and POC exports at 100 m). Unless otherwise specified, differences between consideration of the open ocean and the entire ocean were negligible.

All biogeochemical models that consider the carbonate pump represent pelagic calcification implicitly in both CMIP5 and CMIP6. No model explicitly incorporates a representation of a calcifying planktonic functional type (PFT). For most of the models, biogenic CaCO3 is in the form of calcite, although aragonite is also considered by NOAA-GFDL in TOPAZ2 and COBALTv2. Certain groups represent a generic biogenic CaCO3 (CSIRO with WOMBAT for CMIP6, MIROC with OECO1/2 for CMIP5/6, and MOHC with diat-HadOCC for CMIP5) but attribute it either to calcite or aragonite based on their outputs and consistency with these two forms of CaCO3 (e.g. export distribution) to conform to CMIP output requirements. Finally, we note that no model represents benthic production of CaCO3. This reinforces the decision to focus our analysis on the open ocean and to exclude the coastal ocean when possible.

The parameterizations used to represent implicit pelagic calcification are various and show dependence on a variable number of drivers. Most of the models determine implicit calcification rates as a function of the fate of phytoplankton (through mortality and excretion by zooplankton after grazing), with certain models additionally considering the fate of zooplankton (through mortality and excretion by other zooplankton after consumption). In contrast, in CMIP5, diat-HadOCC for MOHC, OECO1 for MIROC, and TOPAZ2 for NOAA-GFDL are the only models for which calcification is directly related to phytoplankton growth. In addition, model calcification exhibits various dependencies on nutrient concentrations (phosphate, nitrate, iron, and silica), temperature, light, depth, and the calcium carbonate saturation state (Ω): 10Ω=CO32-⋅Ca2+Ksp≈CO32-CO3sat2-, where CO32- is the carbonate ion concentration, Ca2+ is the calcium ion concentration – which is considered proportional to salinity – and Ksp is the apparent solubility product of CaCO3. Ω is approximated in some models to the ratio between the carbonate ion concentration and that at saturation, CO3sat2-. NOAA-GFDL with TOPAZ2, BLINGv2, and COBALTv2 and MOHC with MEDUSA-2.0 all consider CaCO3 production to be dependent on the saturation state, with no calcification in undersaturated waters (Ω<1). The implicit calcification parameterizations adopted by ESMs directly relate net CaCO3 production to the export of PIC, as opposed to gross CaCO3 production, of which only a fraction is exported. By not explicitly resolving the grazing of calcifying plankton and partial egestion of CaCO3 by zooplankton (e.g. due to gut dissolution), it is expected that simulated CaCO3 production will generally be less than observational estimates of the total production of biogenic calcium carbonate.

The sinking of PIC is model-dependent, with both explicit and implicit representations in the CMIP5 and CMIP6 ensembles. When represented explicitly, a sinking speed is considered for PIC. This speed is constant in the models with the exception of PISCESv1/2(-gas), where it is depth-dependent. PIC dissolution is computed using a dissolution rate and/or a dependence on the calcium carbonate saturation state. This dependence on the saturation state is variously represented in the models. Generally, PIC dissolution in the water column occurs in undersaturated waters (Ω<1), with a linear dependence on the saturation state (BFM5.2, PISCESv2(-gas), HAMOCC5.2/6, HAMOCC5.1/iHAMOCC, TOPAZ2, and COBALTv2), although its representation is more complex in PISCESv1 and BLINGv2.

When PIC sinking and dissolution are represented implicitly, a dissolution length scale and an exponential decay of the downward flux divergence of CaCO3 represent the combination of instantaneous sinking and dissolution in the water column. diat-HadOCC is unique in representing PIC dissolution homogeneously through the water column below a globally uniform lysocline depth – the upper limit of the transition zone, where sinking CaCO3 starts to substantially dissolve.

In the water column, PIC can be considered both as a ballast for organic matter, increasing the sinking speed of POC, but also as a protector of organic matter reducing the rate at which it is remineralized. It is relevant to distinguishing both processes, as their feedback on the soft-tissue pump are often exclusively treated. However, what modelling groups typically consider a ballast effect is generally better described as a protection effect, as it reduces organic matter remineralization during the sinking of POC. The formulation of this process is typically based on the model proposed by Armstrong et al. (2001) in which a component of the sinking POC flux is associated with sinking CaCO3 and experiences reduced remineralization. It is generally parameterized using the data collated by MEDUSA-2.0, BEC, MARBL, TOPAZ2, BLINGv2, and COBALTv2. PISCESv1/2(-gas) and BEC are the only models which parameterize a ballast effect. In PISCESv1/2(-gas) half of the POC produced by nanophytoplankton is associated with calcifiers and is routed to quickly sinking particles, while in BEC and MARBL a fraction of the POC is associated with the higher-dissolution length scale for “hard” particles.

The fate of PIC reaching the seafloor is one of the determinants of the ocean Alk inventory and closure of the CaCO3 budget. There is a high diversity among models in their representation of sedimentation processes associated with calcium carbonate. For some models, all of the PIC reaching the seafloor is considered permanently buried and lost from the ocean (e.g. CMOC and OECO2). Other models dissolve all of the PIC reaching the seafloor, closing the calcium carbonate cycle and avoiding its processing in the seabed (e.g. WOMBAT and NPZD-MRI). A final sub-set of models represents sediment processes. Some of these distinguish a dissolved and buried PIC fraction (e.g. CanOE, BFM5.2, and PISCES), while others represent diagenesis with a sediment module (e.g. HAMOCC, BLINGv2, and COBALTv2).

Sedimentation is one way to balance broader inputs, and especially riverine discharge that many models either ignore or represent in only simplified ways (freshwater, Alk, DIC, and nutrient discharge). At the global scale, the sedimentation of PIC at the seafloor corresponds to a net biological sink of Alk, while sediment mobilization – essentially through the dissolution of CaCO3 present in sediments – and river discharge are a net source. Although Alk sinks and sources are ideally balanced in steady state to avoid drift in the global Alk inventory, this is difficult to achieve in certain models and is forced in others through the use of a fixed Alk inventory and a restoring term. As a result, sedimentation processes appear to be key to closing the CaCO3 budget and are further discussed in Sect. 4.4.2.

The representation of surface Alk has evolved from CMIP5 to CMIP6 with a convergence of the global average value within the model ensembles, while regional disparities remain but to a lesser extent (Fig. 3). In CMIP5, the open-ocean mean surface Alk is higher than the observations (+0.022 mol m-3; +0.9 %), and in CMIP6 it is lower (-0.030 mol m-3; -1.3 %). This reflects a global decrease in surface Alk between CMIP5 and CMIP6, with an inversion of the bias relative to GLODAPv2 observations (Fig. 3 and Fig. 4a). In addition, from CMIP5 to CMIP6, the variability among the ESMs with regards to surface Alk was reduced, with a decrease in the ensemble standard deviation of surface Alk globally (from 0.057 to 0.047 mol m-3), and particularly in the Arctic Ocean (Fig. 3). However, in both CMIP5 and CMIP6, global-mean surface biases relative to the observations cannot be attributed to a specific and consistent regional bias among the ESMs (see Fig. D1).

Normalizing Alk by salinity (sAlk) to remove the impact of freshwater fluxes has little impact on CMIP ensemble biases (Fig. 4). Indeed, the open-ocean mean surface sAlk bias compared to observations is reversed and reduced in CMIP6 (-0.019 mol m-3; -0.8 %) compared to CMIP5 (+0.034 mol m-3; +1.4 %), and the ensemble standard deviation of surface Alk has slightly decreased (from 0.044 to 0.039 mol m-3; Fig. 4a). We can therefore infer that these changes are mainly driven by biogeochemical processes rather than changes in surface salinity driven by freshwater fluxes. In particular, the zonally averaged sAlk for CMIP6 is closer to observations, with an enhancement in meridional variability (Fig. 4a). This improvement between CMIP5 and CMIP6 seems to be mainly due to the elimination of some poorly performing models in CMIP6. The CNRM-CERFACS, MOHC, MIROC, and NCC ESMs in particular have a more consistent representation of the standard deviation of the sAlk surface distribution compared to observations, alongside improved correlation (Fig. 4b). However, the standard deviation of sAlk in MRI ESMs has slightly decreased from CMIP5 to CMIP6, moving away from observations, although the correlation is similar. Furthermore, there is only improvement in the correlation of sAlk in CMCC, while for IPSL the sAlk correlation is improved, but this is accompanied by an excessive increase in the surface standard deviation.

Associated with the global improvement in the representation of the surface sAlk is a significant increase in the sAlk vertical gradient (Fig. 5). The groups for which the ESMs show an improvement in the correlation and a considerable change from CMIP5 to CMIP6 in the surface sAlk standard deviation – corresponding either to an improvement (CNRM-CERFACS, MOHC, MIROC, and NCC) or a large bias (IPSL) – are the groups that reveal major improvement in the vertical profile of sAlk (Fig. 5). Indeed, from a relatively uniform sAlk profile, they now exhibit a profile with increased Alk at depth, more consistent with observations, albeit with concentrations too high. For instance, the magnitude of the sAlk vertical gradient (the concentration anomaly at 5000 m with respect to the surface) has increased from 0.02 mol m-3 in CMIP5 to 0.17 mol m-3 in CMIP6 for the IPSL ESMs, and from 0 mol m-3 in CMIP5 to 0.17 mol m-3 in CMIP6 for MOHC ESMs. The ESMs of these groups are predominantly responsible for the strengthened sAlk vertical gradient in CMIP6, which has increased from 0.05 ± 0.05 to 0.12 ± 0.05 mol m-3 (2.6-fold). The magnitude of the CMIP6 sAlk vertical gradient is now closer to that of the observations (0.16 mol m-3).

The global improvement in the representation of surface sAlk and the increase in the sAlk vertical gradient in CMIP6 is accompanied by an enhancement of the carbonate pump. This is illustrated by a global increase of 11 % in the PIC export at 100 m between CMIP5 (49 Tmol yr-1) and CMIP6 (55 Tmol yr-1; Fig. 6). Additionally, we report a decoupling in the trends from CMIP5 to CMIP6 for the PIC and POC exports, with an increase for the former and a decrease for the latter by 7 % between CMIP5 (712 Tmol yr-1) and CMIP6 (659 Tmol yr-1; Fig. 6). The combination of the two results in a 20 % increase in the rain ratio (RR) – defined as the ratio between PIC and POC export at 100 m (from 0.070 in CMIP5 to 0.083 in CMIP6; Fig. 6). Overall, CMIP6 ESMs tend to better match observational estimates of the exports and the RR compared to CMIP5 ESMs. While the CMIP6 average is 18 ± 27 % higher (+100 ± 151 Tmol yr-1) for the POC export compared to the observationally informed estimates from DeVries and Weber (2017), it is 28 ± 26 % lower (-21 ± 20 Tmol yr-1) than the estimate from Sulpis et al. (2021) for the PIC export, highlighting inter-ESM variability (Fig. 6). Although there is a global increase in the RR from CMIP5 to CMIP6, this shift is strongly associated with certain ESMs, specifically, CNRM-CERFACS and IPSL, where the increase is principally due to enhanced PIC export, and NCC, where it is due to reduced POC export (Fig. 6). While our focus is on the open ocean, when the global ocean is considered, the integrated CMIP6 mean POC and PIC exports both increase by 31 % (+155 and +13 Tmol yr-1 respectively), reflecting the importance of coastal ocean export.

The spatial distribution of the RR has also evolved from CMIP5 to CMIP6, reflecting the variable trends of PIC and POC export. There is typically a greater increase in the RR at high latitudes, due to a higher increase in PIC export and a smaller decrease in POC export (see Fig. D2). There is also diversity among the ESMs with respect to the spatial distribution of PIC export at 100 m, with notable differences in the Pacific equatorial upwelling region, the great calcite belt in the Southern Ocean, and the coastal ocean (see Fig. D3 and Fig. D4). These points of disagreement between the ESMs are interestingly also found within the estimates proposed by Lee (2001), Jin et al. (2006), Sarmiento and Gruber (2006), and Battaglia et al. (2016).

Using the decomposition of the sAlk bias at depth expressed in Eq. (9), we can distinguish the roles of surface Alk, salinity, the carbonate pump, and the soft-tissue pump in driving biases between the ESMs and observations at depth. The carbonate pump and surface Alk are found to explain the large majority of sAlk biases at depth (Fig. 7). Surface Alk contributes 34 % of the ensemble-mean sAlk bias at 5000 m in CMIP5 and 41 % of the bias in CMIP6, while the carbonate pump contributes 51 % of the ensemble-mean bias in CMIP5 and 46 % of the bias in CMIP6. Their respective influence has nevertheless changed from CMIP5 to CMIP6, with a greater relative contribution of surface Alk to the sAlk bias and a reduced contribution of the carbonate pump, which is further analysed in Sect. 3.3. In contrast, we find that salinity and the soft-tissue pump have a minimal influence on the sAlk bias at 5000 m in both CMIP5 and CMIP6 ensembles, contributing less than 10 %.

The CMIP6 increase in PIC export at 100 m globally acts to decrease sAlk at the ocean surface and increase it at depth. This increase could be explained by enhanced upper-ocean production and/or enhanced sinking of PIC and/or dissolution at depth. Using all the ESMs, we find a significant relationship between the sAlk vertical gradient in the open ocean and the global PIC export at 100 m (R2=0.54, p<0.01; Fig. 8a). This reflects inter-ESM consistency between higher export of PIC at 100 m and an associated increase in the vertical gradient of sAlk – expressed as the difference between the mean sAlk between 4000 and 5000 m and the mean sAlk between 5 and 100 m. In particular, it highlights the shift towards higher values of PIC export and a strengthened sAlk vertical gradient in CMIP6. The relationship encompasses the wide variety of CMIP modelling schemes used to represent Alk and the CaCO3 cycle, despite differences in the representation of sinking, dissolution, and seabed processes. It should be noted, however, that some models clearly stand out, as is the case for UKESM1-0-LL (CMIP6) and CNRM-ESM2-1 (CMIP6). This discrepancy may be explained by the fact that for the biogeochemical scheme in UKESM1-0-LL (MEDUSA-2.1), the soft-tissue pump does not affect Alk and thus does not attenuate the sAlk vertical gradient. As for CNRM-ESM2-1 (CMIP6), very high values of the PIC export at 100 m in the Japan Sea may explain its excessive PIC export relative to the other ESMs.

The relationship established between the global sAlk vertical gradient and PIC export across the CMIP5/6 ESMs can be combined with the sAlk vertical gradient from the GLODAPv2 observations to infer PIC export at 100 m. This approach, similar to so-called “emergent constraint” methodologies (e.g. Eyring et al., 2019; Hall et al., 2019), provides a present-day PIC export estimate of 44–55 Tmol yr-1 at 100 m (see the black vertical line in Fig. 8a). This estimate is lower and out of the confidence interval of PIC export values independently assessed by Sulpis et al. (2021; 76 ± 12 Tmol y-1 at 300 m) and Battaglia et al. (2016; 75.0 [60.0; 87.5] Tmol yr-1). This reflects an apparent underestimation of the simulated PIC export at 100 m for a given sAlk vertical gradient in comparison with observational estimates.

The sAlk vertical gradient across the combined CMIP5/6 ESM ensemble is also consistently related to the surface meridional distribution of sAlk through the Meridional Overturning Circulation (MOC) with the upwelling of Alk-enriched deep waters in the Southern Ocean. In particular, models with a higher sAlk vertical gradient have higher meridional gradients of sAlk at the surface – expressed as the difference between surface sAlk in the Southern Ocean, [-90, -45]∘, and the low latitudes, [-45, 45]∘ – (R2=0.46, p<0.01; Fig. 8b). Here again, the shift towards higher values for the meridional sAlk gradient and the vertical sAlk gradient from CMIP5 to CMIP6 is noticeable. Despite known differences in the representation of Southern Ocean upwelling (Beadling et al., 2020) and the spatial distribution of PIC export within the CMIP5/6 ensemble, the relationship found for the ESMs agrees relatively well with the GLODAPv2 observations.

Differences in simulated ocean circulation do not appear to be a major driver of differences in Alk gradients across the CMIP ensemble. Other factors being equal, an overly sluggish ocean circulation for instance would lead to water masses at depth that are too old and thus amplify the sAlk vertical gradient. However, using Atlantic and Southern Meridional Overturning Circulation indices (AMOC and SMOC) as proxies of the ocean overturning circulation (Heuzé et al., 2015; Heuzé, 2021), we find no robust relationship between the intensity of the global-scale ocean circulation and the sAlk vertical gradient across the CMIP ensemble.

The drift that we assess in the ESMs is low enough to have minimal influence on our non-drift-corrected results centred on 2002 (see Sect. 2.2.1, Fig. 10, and also Figs. D7 and D8). For instance, the model drift per century of the sAlk and sDIC vertical gradients is less than 8 % of the observed vertical gradients. Similarly, model drift in surface-ocean salinity, temperature, and exports at 100 m is also limited and should have minimal influence on the results, in part due to salinity normalization. The largest drift was observed for CMCC-CESM (CMIP5) and CNRM-ESM1 (CMIP5); specifically, the global DIC inventory of CMCC-CESM (CMIP5) had not reached equilibrium prior to the Historical simulation. In CMIP6, these two groups have increased the spin-up duration, although the relative part of their online spin-up has decreased.

There is great diversity with regards to the spin-up strategy employed by different groups (Séférian et al., 2016). Séférian et al. (2020) discussed this and pointed out that the spin-up duration has increased for all groups except IPSL and NOAA-GFDL. For these two groups, the considerable increase in resolution from CMIP5 to CMIP6 was balanced against a reduced spin-up duration as well as the completion of a fully online spin-up in the case of IPSL. Finally, we highlight two contrasting spin-up strategies with consequences for the mean ocean state of Alk and the CaCO3 cycle. In MPI-M ESMs for CMIP5, the model was initialized with the same Alk and DIC values in all ocean grid cells and, to reduce the spin-up duration, Alk was indirectly tuned to achieve a consistent representation of the ocean CO2 sink. This was achieved through increasing weathering fluxes and the CaCO3 content in sediments, leading to an increase in Alk and DIC to maintain the desired pCO2 field (Ilyina et al., 2013b). This explains the strong offset in both Alk and DIC content for MPI-M in CMIP5 (see Fig. C1). An alternative strategy was developed by NCAR for CMIP6 regarding the balancing of the global ocean budget of Alk. During the spin-up, the saturation-state threshold for the burial of CaCO3 was tuned to balance the loss of Alk from the burial of CaCO3 and the riverine input of Alk before starting the experimental simulations (Long et al., 2021). This resulted in the choice of an unusual threshold for the burial of CaCO3 (see MARBL in Appendix C). Similarly, NOAA-GFDL for CMIP6 in COBALTv2 set sediment calcite concentrations such that Alk lost through calcite burial balanced river Alk inputs at a certain year during the spin-up (Dunne et al., 2012). While it is probably advisable that model groups continue to work to balance the Alk budget at quasi steady state, observations suggest there may have been a slight net sink of Alk during the Holocene and therefore potentially an ocean carbon source to the atmosphere (Ciais et al., 2013; Cartapanis et al., 2018). The strategy of maintaining a degree of freedom at the seafloor during spin-up with the tuning of parameters associated with the CaCO3 sedimentation processes at the bottom of the ocean seems to be relevant to balancing the overall Alk budget at equilibrium. However, given the difficulty in running ESM simulations to equilibrium during the model development process, it is likely that drift correction of ocean CO2 system variables will continue to be a requisite of robust ESM intercomparisons.

As previously discussed, drift can depend not only on the spin-up strategy, but also on the initialization strategy. Indeed, it is interesting to examine the initialization of Alk and DIC in ESMs and to assess how this may influence model performance. Alk and DIC fields are recommended to be initialized using the second version of the GLODAP product (GLODAPv2, Lauvset et al., 2016) following the OMIP-BGC protocol for CMIP6 (Orr et al., 2017). For CMIP5, many groups were initialized with the first gridded version (GLODAPv1, Key et al., 2004), even though this was not specific to a protocol. GLODAPv2 surface fields are more heterogeneous than GLODAPv1, but it is mainly in the coastal ocean, and in particular in the Arctic, that the two datasets diverge due to the addition of new observations. At global scale, the difference between the GLODAP products does not appear to have a noteworthy impact on the representation of both present-day Alk and DIC (Fig. 11a, b and see also Appendix E). Thus, neither the change in the GLODAP mapping method nor the increase in the number of observations is responsible for the improvement in the Alk representation from CMIP5 to CMIP6. In fact, a number of groups did not follow the OMIP-BGC protocol and instead continued using GLODAPv1 to initialize their CMIP6 models (see Supplement Table S1).

Surprisingly, it is assumptions in the conversion of the GLODAP Alk field from gravimetric to volumetric units that contribute to differences between ocean Alk distributions across ESMs. The Alk field is provided in micromoles per kilogram in the GLODAP-mapped product and must, with the exception of the NOAA-GFDL models, be converted to volumetric units (e.g. mol m-3) to be used by the marine biogeochemical models. Multiple approaches are employed by the groups when performing this conversion. For most of the ESMs, the conversion was made using a constant seawater density, which itself varies between ESMs (from 1024 kg m-3 for ACCESS-ESM1-5 (CMIP6) to 1028 kg m-3 for CNRM-CERFACS, IPSL, and MIROC) with in situ density used by the other ESMs (see Fig. C1). Further investigation reveals that the method of volumetric conversion for the initial Alk field drives a surface Alk bias that influences both surface DIC concentrations and the global DIC content of the ocean. Although this bias in the initialization is confined to depth depending on the density used for the conversion (see in situ, potential, and 1026 kg m-3 in Fig. 11c), it results in a perturbed surface-ocean CO2 system once the ESM reaches a quasi steady state. Indeed, in an ocean with a conservative Alk inventory, the biological pump and in particular the carbonate pump only influence the distribution of Alk. Whatever the initialization of ocean DIC, the Alk content of the ocean is fixed at its initial value, and its gradient is determined through biogeochemical and physical processes. This means that surface Alk after spin-up can be inferred from the initialization field and the biogeochemical processes and ocean dynamics represented within a model. As a result, without taking into account salinity and temperature, the equilibrium between surface Alk, DIC, and atmospheric pCO2 tends to set the surface DIC concentration at the end of spin-up through air–sea carbon fluxes. The global content of DIC is therefore directly impacted by surface Alk after spin-up with an atmosphere considered an infinite carbon reservoir. Finally, although the NOAA-GFDL models avoid initialization issues by keeping tracers in gravimetric units, the use of a constant density of 1035 kg m-3 during post-processing to produce “talk” and “dissic” fields distorts the ocean CO2 system from the real ESM outputs, in particular with excessive surface values (see Fig. D1).

In addition to correct initialization of the global Alk inventory, initialization with a spatial Alk distribution consistent with observations is also required to allow accurate computation of the ocean CO2 system and likely air–sea carbon fluxes (see mocsy 2.0; Orr and Epitalon, 2015). Indeed, the ocean biogeochemical models are generally only able to directly affect the alkalinity components associated with carbonates, phosphates, and sometimes silicates, while the other components are computed from pH (water alkalinity), salinity (fluoride alkalinity), or both (borate; Uppström, 1974; Lee et al., 2010). Thus, an inaccurate initialization of the Alk distribution (e.g. for groups initializing with a constant density) could indirectly repartition Alk between its different components, including those not directly affected by biogeochemical processes in the models. The influence of even small biases in borate alkalinity has been shown to have non-negligible effects on the ocean CO2 system (Orr and Epitalon, 2015).

In summary, standardizing the Alk initialization protocol in CMIP exercises would reduce biases in the representation of ocean carbonate chemistry, especially at the surface. As ocean models typically apply an incompressibility assumption, it is meaningful to initialize the Alk field with the constant reference density of a given model. While a density of 1026 kg m-3 enables models to reproduce surface Alk values consistent with observations, the use of 1035 kg m-3 conserves the total alkalinity budget. However, the use of a constant density partly flattens the Alk spatial distribution, entailing potential biases. This could be partly counterbalanced by using potential density, which has a typical profile close to a constant value while maintaining spatial variability. As a consequence, we recommend initializing the Alk field with a weighted potential density in order to keep the density of reference considered within the ocean model as the mean density while being in agreement with the physical assumptions made in the models. We advise doing the same for DIC initialization.

The different strategies for initializing Alk and DIC highlight the importance of clear data sharing and precise protocols to enable robust ESM assessments and intercomparisons. In the following, we recommend increasing the priority of certain variables in CMIP exercises (Orr et al., 2017). First, we suggest that, in future intercomparisons, model groups share the three-dimensional export of POC and PIC (“expc”, “expcalc”, and “exparag”) and not only the exports at 100 m, as some groups have done for CMIP6. This would enable a more consistent estimate of POC and PIC export as well as the resulting rain ratio. Similarly, the potential inaccuracy of soft-tissue pump estimates based on fixed-depth POC export is well-known (e.g. Buesseler et al., 2020; Koeve et al., 2020). The simulated increase in sDIC in the upper 100 m of the water column, despite a relatively consistent sAlk, indicates that net remineralization of POC is occurring in much shallower waters than net dissolution of PIC in the ESMs. As such, POC export values should be used with caution when assessing rain ratios (see Figs. 6 and D2). Sharing of complete export fields would ideally be accompanied by three-dimensional fields of remineralization and dissolution (“remoc”, “dcalc”, and “darag”) to facilitate analysis of processes such as the biological pump throughout the water column. Finally, sharing of vertically integrated calcite and aragonite production (“intpcalcite” and “intparag”) and POC and PIC burial (“froc” and “fric”) would also improve assessments of the influence of the biological pump on vertical DIC and Alk profiles (see Fig. 9a, b).

Alongside the absence of certain model outputs, one issue that has presented itself throughout our analysis is a lack of model traceability between CMIP5 and CMIP6. In the absence of publications documenting model changes, it is typically not possible to trace ocean biogeochemical model developments without contacting individual developers and in certain instances asking for the model code. To address this, we propose that developers utilize a common online platform to share their code and provide an associated model guide. Such a platform would critically improve model traceability, enhancing ocean biogeochemical model transparency and accessibility (e.g. sharing river discharge values for both Alk and DIC). Within this context, the Earth System Documentation (ES-DOC, https://es-doc.org, last access: February 2022) project is highly relevant. However, in its current form, the tool is broadly insufficient for specific studies due to the paucity of ESMs participating and the level of model documentation provided.

In a CO2-concentration-driven simulation, the surface Alk and DIC are directly connected to each other through equilibration via air–sea CO2 fluxes. As a result, a modification of global-scale surface Alk has a direct effect on surface DIC (Fig. 12a). Indeed, neglecting the effect of temperature and salinity on the partial pressure of CO2 at the ocean surface, we can differentiate pCO2 as follows: 11dpCO2=∂pCO2∂AlkDIC,S,T⋅dAlk+∂pCO2∂DICAlk,S,T⋅dDIC, where pCO2, Alk, and DIC all refer to surface values and the partial differentials are both at fixed temperature and salinity. Rewriting the differentials “d” as the difference “Δ” between two ESMs gives 12ΔDIC=-∂pCO2‾∂Alk⋅∂DIC‾∂pCO2⋅ΔAlk+∂DIC‾∂pCO2⋅ΔpCO2, where the overbars correspond to the mean surface-ocean values for the partial differentials. At the global scale, we can assume that, for a surface ocean in balance with atmospheric pCO2, ΔpCO2=0. Consequently, surface differences in Alk and DIC between two ESMs are linearly related. Approximating the carbonate ion concentration to Alk–DIC and using the expression for pCO2 given in Sarmiento and Gruber (2006), this results at the ocean surface in 13ΔDIC≃Alk3⋅Alk-2⋅DIC⋅ΔAlk. Substituting the mean surface-ocean Alk and DIC of the combined CMIP5 and CMIP6 ensembles, ΔDIC≃0.81⋅ΔAlk, and indeed a very similar relationship between surface-ocean Alk and DIC anomalies for individual ESMs relative to CMIP5 ensemble-mean values is found (ΔDIC≃0.842(±0.009)⋅ΔAlk; R2=0.98, p<0.01; Fig. 12a).

This relationship between anomalies in surface Alk and DIC has implications for the wider surface-ocean CO2 system. As the slope associated with the linear regression is less than 1, an ESM with higher surface Alk will tend to have a higher Alk–DIC and therefore a higher surface concentration of CO32- and pH (Fig. 12a). The decrease in surface Alk from CMIP5 to CMIP6 therefore results in a slight decrease in pH and a generally lower calcite and aragonite saturation state, with the global surface-ocean carbonate ion concentration decreasing by 2.9 ± 2.7 % and up to 5 % in certain regions (Fig. 12b). As the timescale of air–sea CO2 exchange can be approximated as being proportional to the carbonate ion concentration (Sarmiento and Gruber, 2006), other factors being equal, CMIP6 mean surface-ocean pCO2 is likely to equilibrate faster with the atmosphere than that of CMIP5. An exception to this is the Southern Ocean, where upwelled deep waters are far from equilibrium with the atmosphere. In CMIP6, enhanced carbonate dissolution at depth results in upwelled Southern Ocean waters with a higher carbonate ion concentration, implying that Southern Ocean pCO2 has a longer equilibration timescale. While the change in the carbonate pump from CMIP5 to CMIP6 seems to have a slight effect on the representation of the present-day ocean CO2 system at the surface, it is likely to have negligible feedback on the projected ocean carbon sink, with an overall decrease in the Revelle factor (γDIC) of only 0.2 ± 1.3 % (Fig. 12b). The maximum potential influence of the carbonate pump and in turn surface Alk on the uptake of anthropogenic carbon over the historical era has previously been estimated as 5 % (Murnane et al., 1999). However, in the equatorial Pacific, where upwelling variability induced by the El Niño–Southern Oscillation (ENSO) strongly modulates surface concentrations of DIC and Alk, accurately reproducing the observed Alk vertical gradient in ESMs is important for correctly simulating the observed interannual variability of CO2 fluxes (i.e. anomalously outgassing during El Niño and ingassing during La Niña events; Feely et al., 2006). In a recent study, Vaittinada Ayar et al. (2022) showed that the mean state of the Alk vertical profile in the tropical Pacific influences both projections of ENSO-driven CO2 fluxes and long-term carbon uptake in the region.

Finally, the trend in surface Alk and DIC from CMIP5 to CMIP6 also influences spatial heterogeneity, especially between the low latitudes ([-40, 40]∘) and the Southern Ocean ([-90, -40]∘), with enhanced meridional surface gradients of Alk and DIC in CMIP6 compared to CMIP5 (+0.024 and +0.013 mol m-3; Fig. 13). Neglecting model differences in ocean dynamics, we can estimate that differences in the amplitude of the soft tissue and carbonate pumps between CMIP6 and CMIP5 impact the meridional surface gradients of DIC and Alk. To estimate this effect, we define an attenuation coefficient (α) as the ratio between the meridional Alk gradient at the surface (δSouthern-midlatsAlksurf) and the vertical open-ocean Alk gradient (δ5000 m-surfsAlk): 14α=δSouthern-midlatsAlksurfCMIP6-δSouthern-midlatsAlksurfCMIP5δ5000 m-surfsAlkCMIP6-δ5000 m-surfsAlkCMIP5. We associate this coefficient with the upwelling that determines the vertical Alk gradient in the Southern Ocean. Hence, by multiplying the deviations of both the soft tissue and carbonate pumps at depth for CMIP6 relative to CMIP5 by this attenuation coefficient, we are able to trace the origin of the changes in the meridional gradients of Alk and DIC from CMIP5 to CMIP6 with a residual component (including the gas-exchange pump and anthropogenic carbon uptake; Fig. 13). This highlights that the increase in the carbonate pump from CMIP5 to CMIP6 is the main driver of the enhanced meridional surface gradients of Alk and DIC.

A quasi equilibrium of Alk on centennial timescales is commonly accepted, but observational data have only recently allowed the total global Alk budget to be closed (Middelburg et al., 2020). The riverine input of Alk is mainly balanced by the burial of PIC, but also to a lesser extent by the remobilization of sediments (essentially through submarine weathering and anaerobic remineralization of organic matter) and the burial of organic matter. Interplay between these fluxes makes Alk central to the understanding of the processes driving atmospheric CO2 over glacial and interglacial cycles (Archer and Maier-Reimer, 1994; Kerr et al., 2017; Boudreau et al., 2018). Although in modelling studies drift in the Alk inventory would impact the surface air–sea carbon flux, anthropogenic perturbation of the carbon cycle and the effect of climate change could cause transient changes in the ocean Alk inventory and its distribution. The timescales over which such perturbations may occur, and the potential consequences for projections of anthropogenic carbon uptake, are unclear.

Ocean Alk might increase through enhanced terrestrial rock weathering and an associated increase in riverine input in response to climatic drivers (e.g. enhanced precipitation, permafrost thaw; Raymond and Cole, 2003; Drake et al., 2018). In addition, shoaling of the saturation horizon due to ocean acidification is thought to explain recent observations of enhanced CaCO3 dissolution at the seafloor (Sulpis et al., 2018) initiating chemical carbonate compensation. This highlights the potential importance of representing sediment processes in models given that CaCO3 dissolution enriches waters in Alk and can therefore enhance ocean carbon uptake when these waters are recirculated to the surface ocean (Archer et al., 1998; Gehlen et al., 2008). Potential dissolution of coral reef CaCO3 in response to climate change (Cooley et al., 2022) may also increase Alk on centennial timescales – echoing the coral reef hypothesis and its potential effect on atmospheric CO2 during glacial–interglacial transitions (Berger, 1982; Opdyke and Walker, 1992).

Finally, the possibility of implementing large-scale ocean Alk enhancement (OAE, Renforth and Henderson, 2017; Bach et al., 2019) could increase the global Alk inventory on relatively short timescales. Representation of CaCO3 burial and sub-marine weathering is necessary in simulations of OAE, even on decadal to centennial timescales, since this could entail abrupt changes. To date, OAE model studies have typically directly enhanced surface-ocean Alk (Köhler et al., 2013; Ilyina et al., 2013a; Hauck et al., 2016; González and Ilyina, 2016; Lenton et al., 2018; González et al., 2018); however, in reality Alk is likely to be provided via the addition of a mineral such as olivine, of which only a fraction will dissolve in the surface ocean. The explicit simulation of alkaline mineral addition could enhance Alk at depth, deepening the carbonate saturation horizon, suppressing the dissolution of sediment carbonate that might otherwise occur, and increasing the burial of sinking CaCO3.

Strategies used to close the Alk budget in ESMs are questionable in simulations where the global Alk inventory may not be in quasi equilibrium (Keller et al., 2018). Indeed, in CMOC and CanOE, CaCO3 burial at the seafloor is redissolved at the ocean surface locally to close the Alk budget. This parameterization is intended to represent fluvial Alk sources (Christian et al., 2022) but does not impact the spatial distribution of surface Alk in the same manner. It also couples riverine discharge of Alk with the carbonate pump in projections. As previously discussed, in CMIP6, NCAR and NOAA-GFDL with COBALTv2 control the Alk balance at depth by tuning the calcite saturation-state threshold for burial and the sediment calcite concentration. Similarly, IPSL and CNRM in CMIP5 with PISCESv1 force this balance at depth, not explicitly taking into account the processes at the sediment interface. Other ESMs dissolve all the PIC that reaches the seafloor in the last ocean level, effectively avoiding the consideration of an Alk burial sink (WOMBAT, BEC, diat-HadOCC, and NPZD-MRI). For the models that include a sediment module, control of the global Alk budget under pre-industrial conditions might be complicated. However, the approach used by some groups (CNRM-CERFACS and IPSL in CMIP5 and CMIP6) to restore the global Alk inventory to ensure its conservation can mask Alk budget imbalances and potentially bias Alk vertical profiles. In particular, this could lead to drifts if Alk is no longer restored after spin-up (CNRM-CERFACS in CMIP6).

An ESM representation of the carbonate pump that includes ocean acidification and climate change sensitivities has the potential to produce climate feedbacks in centennial projections. Such a model would require a relatively high level of biological realism, taking into account the complexity of the response of the CaCO3 cycle to environmental stressors (Gattuso and Hansson, 2011; Schlunegger et al., 2019). Most studies suggest a negligible CaCO3 cycle climate feedback this century, although on longer timescales this feedback can be more important (e.g. Gehlen et al., 2007; Ridgwell et al., 2007; Schmittner et al., 2008; Hofmann and Schellnhuber, 2009; Gangstø et al., 2011; Pinsonneault et al., 2012; Krumhardt et al., 2019). However, uncertainties and diverse responses of calcifying organisms to environmental change (e.g. Kroeker et al., 2013) make it difficult to constrain model parameterizations with confidence. Furthermore, most studies only consider a sub-set of potential impacts on the CaCO3 cycle. Here we discuss current ESMs, highlighting developments that may affect the CaCO3 cycle climate feedback.

Although projected ocean acidification and climate change impacts (e.g. warming and reduced upper-ocean nutrient concentrations) have diverse effects on calcification, meta-analyses generally support an expected decrease in calcification due to ocean acidification (Kroeker et al., 2013; Meyer and Riebesell, 2015; Seifert et al., 2020). This would lead to an increase in surface Alk and a decrease in Alk at depth, with possible effects on anthropogenic carbon uptake. The increased energetic cost of calcification could also impact the diversity of pelagic calcifiers and their niches (e.g. for coccolithophores; Monteiro et al., 2016). While the representation of saturation-state-dependent calcification was previously prioritized (Ridgwell et al., 2009; Gehlen et al., 2007; Gangstø et al., 2008, 2011; Hofmann and Schellnhuber, 2009; Pinsonneault et al., 2012), this is no longer the case. NOAA-GFDL and MOHC in CMIP6 are the only groups in this intercomparison to consider such a dependence. We recommend that the other groups follow their lead in improving the realism of the carbonate pump response to anthropogenic emissions.

The implicit representation of pelagic calcification in current ESMs depends on the fate of organic matter and therefore indirectly on net primary production (NPP). However, projected NPP changes this century are highly uncertain across the CMIP5/6 ensembles (Kwiatkowski et al., 2020). For all ESMs any environmental impact on planktonic calcifiers does not affect organic matter production. Moreover, changes in the growth rate of calcifiers do not impact CaCO3 production, with the exception of BEC and MARBL, in which an implicit calcite pool is considered in the phytoplankton group. The independence and potential influence of calcifiers on organic matter production (Gattuso and Hansson, 2011) would require their explicit representation through one or more PFTs. Explicit pelagic calcifiers have been implemented in MARBL (coccolithophores; Krumhardt et al., 2019) and PlankTOM (coccolithophores, foraminifers, and pteropods; Buitenhuis et al., 2019). However, the challenge in representing both organic carbon and carbonate biomasses simultaneously is complicated by scattered observational data products (see MARine Ecosystem Model Intercomparison Project (MAREMIP) papers; O'Brien, 2012; Bednaršek et al., 2012; Schiebel and Movellan, 2012). Finally, a comprehensive representation of the carbonate pump, and thus Alk, in coastal areas, even in ESMs, will probably require the representation of benthic calcifiers as they typically dominate coastal calcification (O'Mara and Dunne, 2019; Middelburg et al., 2020). This would also be valuable within the context of climate change and ocean acidification ecosystem impact projections. CSIRO recently included benthic carbonate production for regional applications addressing the Great Barrier Reef (Steven et al., 2019), and NOAA-GFDL developed neritic environments, such as coral reefs and carbonate-rich/carbonate-poor shelves (O'Mara and Dunne, 2019). However, no benthic calcification is currently represented in ESMs. Although CaCO3 dissolution is essentially abiotic, certain models explicitly represent the sinking of CaCO3 with dissolution dependent on the saturation state and therefore sensitive to ocean acidification. Specifically, models represent dissolution as linearly dependent on the saturation state in undersaturated waters (see Sect. 3.1.2 and Appendix C). This is despite laboratory studies indicating an exponent >1 in the water column (most likely around 3 to 4 for calcite) while maintaining a linear dependence at the seafloor (e.g. Subhas et al., 2015; Sulpis et al., 2017; Boudreau et al., 2020). Reconciling this mismatch between laboratory results and model parameterizations would increase simulated dissolution in less undersaturated waters and thus shallower waters. This could also partially compensate for the lack of pelagic aragonite production in most models – a carbonate mineral with a lower thermodynamic stability than calcite – while the absence of simulated aragonite could influence projections of how the distribution of Alk responds to acidification. The shoaling of the saturation horizon should increase Alk at depth with a reduction in CaCO3 burial (see Sect. 4.4.2) but also change the Alk vertical distribution with an increase in dissolution, and thus Alk, in sub-surface waters.

There is no consensus on the interaction between POC and PIC in the ocean interior with respect to a protection and/or ballast effect (see Sect. 3.1.3 and Fig. 2). Observational and laboratory data diverge (Klaas and Archer, 2002; Passow and De La Rocha, 2006; De La Rocha and Passow, 2007; Lee et al., 2009; Engel et al., 2009; Moriceau et al., 2009), highlighted by recent observations of dissolution in shallow supersaturated waters, supposedly due to POC remineralization influencing the PIC microenvironment (Subhas et al., 2022). Potential coupling between POC and PIC export may have side-effects in a transient climate change scenario with a decrease in CaCO3 production and export, modifying organic matter remineralization (Hofmann and Schellnhuber, 2009).

Additionally, implicit PIC production avoids the representation of gross PIC production and zooplankton gut dissolution (e.g. Jansen and Wolf-Gladrow, 2001), which can potentially occur deeper than 100 m. Simulating gross PIC production and zooplankton gut dissolution may permit the representation of a sub-surface dissolution peak in addition to the deep dissolution peak seen in models with explicit saturation-state-dependent dissolution. Such a double peak in dissolution would be consistent with observations (Feely et al., 2004; Sulpis et al., 2021; Subhas et al., 2022). The representation of these two dissolution peaks may be important in the context of transient simulations as they may have different sensitivities to climate perturbations.

In order to improve the representation of the carbonate pump and to account for the impacts and feedbacks associated with acidification and climate change, certain model developments are desirable. The main priority is the parameterization of CaCO3 production, particularly a consensus on its dependence on saturation state, temperature, and organic matter production, as this should influence the surface carbon cycle. Further desirable developments include (i) the representation of aragonite, which could partly redistribute Alk in the sub-surface and is more responsive to climate perturbations, (ii) the representation of benthic calcifiers, such as corals, which could respond on relatively short timescales, (iii) the explicit representation of saturation-state-dependent PIC dissolution, and (iv) the representation of dissolved and buried PIC fractions at the seafloor with or without the use of a diagenesis module.