The Optimality-based Plankton Ecosystem Model was originally implemented in UVic2.9 , which has since been updated to UVic2.10 for this study. In the current version, we also apply the temperature-independent mortality that has been used for ordinary phytoplankton to diazotrophs. This modification reduces nitrogen fixation in the Arctic region, where it was considered too high in , but it has only a marginal effect on the global nitrogen distribution and fluxes.

All steps of the experimental design are illustrated in the schematic Fig. , with the model calibration and selection of the best parameter sets described in the left hand column. We constructed 600 parameter sets, each representing a unique combination of values assigned to 19 model parameters, including detritus remineralisation rate, the linear increase of sinking velocity with depth, and 17 parameters related to plankton physiology (Table ). The leakage (implicit remineralisation of organic matter by bacteria) and mortality terms for non-N2-fixing ordinary phytoplankton and diazotrophs are assumed identical to reduce the number of possible parameter combinations.

The respective 600 simulations were restarted from a previously-calibrated simulation and spun up with a prescribed pre-industrial atmospheric pCO2 of 284.3 ppm for over 10 000 years.

We adopt a likelihood-based cost function for evaluating the biogeochemical model performance Eqs. 4–9 in. Our cost function considers mismatches in means, and spatial and temporal variabilities of PO43-, excess nitrate with respect to phosphate N*=NO3--16⋅PO43-+2.9mmolm-3,, and modified apparent oxygen utilisation (AOU*=AOU-2⋅PO43-), which eliminates the covariation between AOU and PO43-, in 17 biomes . Interestingly, most of the best-20 ranges cover about 80 % of the total ranges, except for the four grazing-related parameters ϕs, where the range is “only” about 40 %–60 %. This indicates that parameter values are relatively poorly constrained by currently available observations. Modern observations may include anthropogenic signals, which could bias parameter selection. Thus, we assume here that these effects are small relative to spatial variability and note this as a source of uncertainty we cannot quantify. The 20 best parameter sets (with the lowest cost function values) are employed for analysing model behaviour under pre-industrial (PI) and last-glacial-maximum (LGM) conditions.

We set-up a generic LGM configuration with LGM-specific orbital parameters of the Earth. Besides the different orbital parameters, LGM conditions, including the strength of the AMOC, likely also deviated from the pre-industrial era by a lower moisture diffusivity over the Southern Ocean and a different wind pattern . We adopt these forcings from and to investigate their influence on the marine biogeochemistry and carbon cycle. Specifically, meridional moisture diffusivity over the Southern Ocean was reduced by a factor of 2, and the wind stress patterns are from monthly averages of models which have participated in the PMIP3. Compared to pre-industrial conditions, the LGM wind field features an northward shift and intensification of the Southern Ocean westerlies, as well as enhanced trade winds in the tropics and pronounced wind stress anomalies in the North Atlantic (Fig. S1 in the Supplement).

In addition, we configure a 120 m lower sea level compared to PI conditions for the changes in biogeochemical fluxes. The lower sea level was not implemented through an explicit modification of model bathymetry. Instead, it was represented diagnostically in the parameterizations of benthic processes. Specifically, we excluded benthic denitrification and sedimentary Fe input in regions shallower than 120 m relative to the pre-industrial sea level, thereby mimicking the exposure of continental shelves under LGM conditions. This results in reduced benthic denitrification , reduced sedimentary input of Fe , and a 15 % increase in the PO43- inventory , which is conserved in the model. We also include a higher LGM Fe deposition, which was obtained from the LGM dust deposition estimate of their case C4fn-lgm. Applying a constant iron content of 3.5 % and 1 % solubility of deposited Fe yields an annual Fe deposition of 6.1 GmolFeyr-1, which is about four times the pre-industrial flux (Fig. ). All other physical and biogeochemical processes were computed using the same bathymetry as in the pre-industrial control simulation. This approach allows us to isolate the impact of shelf exposure on benthic fluxes without introducing additional changes to ocean circulation or ecosystem structure that would arise from a fully modified LGM bathymetry.

We define four sets of physical and six sets of biogeochemical model configurations, two of which represent pre-industrial climate conditions, PIctl (physical) and PIallbgc (biogeochemical), and the others are different combinations of our generic LGM configuration with PI and LGM boundary conditions (Table ): LGMatmctl and LGMallbgc refer to the full set of physical and biogeochemical LGM boundary conditions, LGMatmws has PI moisture diffusivity and LGM winds, LGMatmpi has PI moisture diffusivity and winds, and LGMFedep, LGMFesed, LGMPO₄ and LGMbdeni combine PI biogeochemical boundary conditions with one of LGM Fe deposition, Fe sedimentary release, PO43- inventory, and benthic denitrification, respectively. These result in a total of 24 (4 physical × 6 biogeochemical) combinations of different physical and biogeochemical boundary conditions. For example, PIctl_LGMallbgc stands for simulations with pre-industrial physics and full LGM biogeochemistry (Table ). The combination of LGM moisture diffusivity and PI wind stress resulted in a shut-down of the AMOC in the UVic_ESCM and hence is not discussed here. From the calibration stage, we selected the 20 parameter sets that best reproduce present-day observations, each corresponding to a fully spun-up pre-industrial simulation. These simulations serve as initial conditions for the 24 combinations of physical and biogeochemical boundary conditions.

For each of the 24 configurations, we restarted simulations using the 20 selected parameter sets, resulting in an ensemble of 480 simulations. During the spin-up, radiative forcing was prescribed according to a fixed pCO2 level (284.3 ppm for PI and 190 ppm for LGM), i.e., the feedback between atmospheric CO2 and radiative forcing was switched off, while atmospheric pCO2 was allowed to evolve freely in response to changes in the global carbon cycle.

This physically and biogeochemically coupled but radiatively uncoupled configuration allows us to isolate the effects of boundary conditions on pCO2, while also accounting for terrestrial carbon responses and ocean–atmosphere carbon exchange. All simulations in the ensemble were spun up for more than 10 000 years under their respective boundary conditions until the marine biogeochemistry approached a steady state. The interannual variability at steady state is negligible because the model simulates a repeating annual cycle (Fig. S2). Therefore, we use the results from the final year of the spin-up simulations for our analysis.

To evaluate whether different physical, biogeochemical, or both conditions result in ensembles that are significantly different from the 20 simulations in PIctl, PIallbgc, or PIctl_PIallbgc, we calculate their p values for each tracer evaluated with Student's t test in R package “Stats”. To understand if changes in individual parameters significantly influence the changes in atmospheric pCO2 from PIctl_PIallbgc to LGMatmctl_LGMallbgc, we obtain p values using the lm (Fitting Linear Models function) in R package “Stats”.

The 600 parameter sets yield a wide range of model-data misfit costs spanning 2 orders of magnitude (Fig. ). When the initial 600 pre-industrial simulations are ordered according to increasing cost, the 600 cost values overall show an approximately exponential increase from the low to the high end, with around 8 simulations on both ends deviating from the trend. The 20 simulations with the lowest costs comprise 3.3 % of all simulations, and the cost function values amongst these 20 best are no more than 1.3-fold higher than the overall lowest cost value.

Globally-averaged vertical profiles of NO3-, PO43-, O2, and dissolved inorganic carbon (DIC) in the 20 simulations of PIctl_PIallbgc are compared with observational data from the World Ocean Atlas 2013 WOA 2013, and GLODAPv2 , as well as the original UVic results in Fig. . Among the 20 best simulations, NO3- in the upper 500 m of the model is slightly lower than in WOA 2013 but higher than in the original UVic standard solution. In the deep ocean (below 2500 m), simulated NO3- concentrations are generally higher than WOA 2013. The globally-averaged concentrations are close to the WOA 2013 average. PO43- concentrations are slightly lower in the upper ocean but higher in the deep ocean than WOA 2013. Our 20 O2 profiles scatter around the WOA 2013 profile and are lower and closer to the observations than the original UVic simulation . The globally-averaged concentrations are about 1.7 % higher than WOA 2013. The DIC profiles are higher than in the original UVic and closer to the GLODAPv2 data. The global mean concentrations are 0.1 % higher than GLODAPv2 on average.

Simulated latitudinal patterns of carbon to nitrogen and carbon to phosphorus ratios in particulate organic matter (pC : N and pC : P, respectively) are also compared with observational data . Overall, the modeled ratios show good agreement with observations (Fig. ), although both the observational data and model results exhibit substantial variability. Modeled pC : N is slightly underestimated at high latitudes (>40°), and overestimated at low latitudes, while pC : P in general is well reproduced across latitudes.

We first compare the simulations with LGM and PI physics, each combined with PI biogeochemistry (PIallbgc) to assess the glacial-interglacial changes in global temperature and the Atlantic Meridional Overturning Circulation (AMOC). We then evaluate the effects of different biogeochemical conditions across physical conditions, and vice versa, on marine biogeochemical inventories and atmospheric pCO2.

The UVic-ESCM responds to the transition from pre-industrial to LGM wind stress with an increased northward salt transport in the North Atlantic, which enhances surface salinity and density, thereby strengthening North Atlantic Deep Water formation while intensifying and deepening the AMOC. In contrast, reduced atmospheric moisture diffusivity decreases meridional freshwater transport to the Southern Ocean, leading to changes in surface buoyancy and enhanced vertical stratification. This suppresses deep water formation, particularly of Antarctic Bottom Water, which weakens the deep return flow, resulting in a weaker and shallower global overturning circulation, including the AMOC (Sigman et al., 2007; Somes et al., 2017). When all LGM physical boundary conditions are applied simultaneously (LGMatmctl_PIallbgc), the maximum AMOC strength at 26.5° N shows a 29 % reduction, and the depth remains similar to pre-industrial conditions (PIctl_PIallbgc).

The model results show only small changes in the MOC of the Indian and Pacific Oceans, with close agreement between LGMatmctl_PIallbgc and PIctl_PIallbgc. This indicates that the effect of the LGM lower surface temperature is almost compensated by the LGM winds and atmospheric moisture diffusivity. As a consequence of the virtual insensitivity of the Indo-Pacific MOC to a switch from pre-industrial to LGM boundary conditions, changes in the global MOC essentially mirror the changes in the AMOC (Fig. ).

Among the four interglacial-glacial changes in biogeochemical boundary conditions investigated, iron supply has the strongest impact on the inventories and fluxes. Clearly, it is the changes in Fe availability within the surface layer that alter iron limitation and affect NPP and POC export (Fig. ). The lower dFe inventory during the LGM seems in conflict with the general understanding of Fe fertilisation during the LGM . Interestingly, although NPP and POC export are lower in the *_LGMallbgc relative to the *_PIallbgc simulations, the corresponding atmospheric pCO2 in general is lower as well (Fig.  and Table S1). The atmospheric pCO2 in the *_LGMallbgc simulations is lower compared to *_PIallbgc, and is primarily driven by a spatial redistribution of surface DIC and the associated changes in global air–sea CO2 fluxes (Fig. S8).

Glacial-interglacial changes in sedimentary Fe input were not considered in several earlier studies . Nevertheless, the strong sensitivity of the biogeochemical inventories and fluxes to changes in sedimentary influx of Fe demonstrates its importance. In our model, the lower glacial sea level leads to a proportional reduction in sedimentary Fe supply from *_PIallbgc to *_LGMFesed (≈80 %, corresponding to a drop of 10.3 GmolFeyr-1). This reduction is larger than the increase in atmospheric Fe deposition from *_PIallbgc to *_LGMFedep (4.7 GmolFeyr-1), resulting in smaller dFe inventories in *_LGMallbgc.

At first glance, one might expect that the magnitude of sedimentary Fe input in the model is relatively large and that its reduction could therefore be overestimated. However, the simulated sedimentary Fe flux in PIctl_PIallbgc (12.6 GmolFeyr-1) falls close to the lower end of estimates from other models 0.6–194 GmolFeyr-1,. A recent sensitivity study also shows that a much higher present-day sedimentary Fe release (117 GmolFeyr-1) yields a better model-data fit in global and surface dFe distributions . Assuming that the glacial loss of sedimentary Fe input scales proportionally with the PI baseline due to shelf exposure, our low PI baseline implies that the absolute drop in sedimentary Fe supply (10.3 GmolFeyr-1) is a conservative estimate; a higher PI baseline would yield an even larger net Fe deficit relative to the atmospheric supply. On the other hand, a higher PI baseline would also leave a larger absolute amount of sedimentary Fe available during the LGM, which would mitigate the severe ocean-wide iron limitation observed in our simulations. This highlights the critical need to better constrain both the baseline magnitude and bathymetric scaling of sedimentary Fe release when evaluating glacial-interglacial biogeochemical cycles.

While dFe availability affects N2 fixation, simulations with higher dFe supply and concentrations do not necessarily result in higher NO3- inventories. For example, the average NO3- concentration for *_LGMFedep is 2.0 mmolm-3 lower than for *_PIallbgc. This is because changes in Fe supply in our simulations do not only affect N2 fixation, but can induce changes in denitrification, which in turn depends on the level and consumption of oxygen, in association with the attenuation of the exported particulate organic matter (POM). Two NO3- sinks can occur in the model solutions. One sink is due to the water-column (WC) denitrification, which is affected by WC O2 supply and consumption via POM remineralisation. The other is benthic denitrification, which is sensitive to the amount of POC reaching the sea floor. Thus, both water column and benthic denitrification are affected by the POM export. The higher Fe supply in the surface ocean increases not only N2 fixation but also NPP and POM export, thereby promoting both WC and benthic denitrification. The net effect on the NO3- inventory depends on the balance of these counteracting fluxes. Whenever NO3- concentrations are lower in a simulation in *_LGMFedep than in *_PIallbgc, the increase in denitrification is higher than the increase in N2 fixation at the beginning of the spin-up, because the increase in N2 fixation due to a higher Fe supply is hampered by the supply of the other limiting macronutrient, PO43-. Under such conditions, the model yields results with a lower NO3- inventory once the simulation reaches equilibrium despite an increase in N2 fixation. This explains that while global N2 fixation in *_LGMFedep simulations is higher than for *_PIallbgc (Fig. S5c and Table S2), the NO3- inventories in *_LGMFedep show a mixed response (Fig. S4c and Table S1).

Since the global PO43- inventory is fixed in the model, the higher PO43- levels in the LGMPO₄ configuration directly translate into higher surface concentrations. In the *_LGMPO₄ simulations, sPO43- on average is about 31 % higher than in *_PIallbgc, which is more than the 15 % increase in the inventory, indicating a non-linear relationship between sPO43- and its global distribution (Figs. , S4e and Table S1). Changes in ocean circulation also affect sPO43-. For example, for all the biogeochemical configurations, sPO43- for LGMatmws, LGMatmpi and particularly LGMatmctl are lower than for PIctl (Fig. S4m).

While earlier works have hypothesised that increased sPO43- and sNO3- during the LGM could have benefited NPP and decreased pCO2 , the changes of sPO43- in *_LGMPO₄ and sNO3- in *_LGMbdeni have only limited effects on the NPP and pCO2 in our simulations. The relatively weak effects of the increases in the two major nutrients can be ascribed to (1) co-limitation effects and (2) the variable stoichiometry in UVic-OPEM. PO43-, NO3-, and Fe are the three limiting nutrients for phytoplankton growth in the model, and nutrient co-limitation is observed in many regions of the ocean . An increase in PO43- or NO3- alone would trigger or aggravate limitation by the other two nutrients. The flexibility in the carbon to nitrogen (C : N) and carbon to phosphorous (C : P) ratios of phytoplankton in UVic-OPEM further complicates the relationship between NPP and nutrient limitation. When sPO43- or sNO3- increase, pC : P and pC : N decrease in response (Fig. S3 and Table S2), and this partly offsets the effect of increasing major nutrients on NPP, POC export, and pCO2 (Fig. ).

As a consequence, macronutrient availability alone exerts only a limited control on export production and associated oxygen consumption in our simulations. Instead, iron availability emerges as the more influential limiting factor, in particular in regions where Fe supply limits productivity. Changes in Fe supply therefore have a strong impact on POC export, remineralisation, and ultimately the O2 inventory.

A stronger Fe supply from atmospheric deposition, such as in the LGMFedep condition, could have enhanced the utilisation of PO43- and NO3-, leading to an expansion of ocean regions depleted in those major nutrients. This “nutrient robbing” effect, whereby stimulated productivity in one area depletes macronutrients in downstream regions, is a primary criticism of Ocean Iron Fertilisation as a marine CDR strategy, as it could limit long-term global net carbon sequestration . Nevertheless, our results suggest that the variable stoichiometry may partially mitigate this effect. By increasing pC : P and pC : N in response to nutrient stress, the variable stoichiometry formulation in our model sustains NPP even when macronutrient concentrations decline. This negative feedback mechanism does not exist in models that assume fixed stoichiometry, and warrants further investigation to determine its global significance in CDR scenarios.

The higher DIC in the *_LGMFedep simulations can be attributed to increased primary production and carbon export driven by the Fe fertilisation effect, leading to greater uptake of CO2 from the atmosphere and increased carbon storage in the ocean. In contrast, the lower DIC in the *_LGMFesed simulations is likely linked to reduced primary production and carbon export, as Fe availability is a critical limiting factor for these processes. While global average DIC concentrations appear similar across the LGM physical configurations, the vertical distribution tells a more complex story (Fig. S9). Specifically, deep-water DIC concentrations vary with the circulation state; the LGMatmctl configuration, which exhibits the most sluggish AMOC in our ensemble, shows the highest deep-water DIC inventory. This suggests that the relationship between circulation strength and DIC storage is not straightforward and likely involves additional factors such as circulation geometry and deep ocean residence time.

Our results emphasise the importance of iron as a limiting nutrient, especially during the LGM, when changes in dust deposition and sea level had significant impacts on Fe availability. We also demonstrate that the lower temperatures during the LGM should have reduced NPP and POC export and thus the sedimentary flux of Fe, which also affects the oceanic dFe inventory.

Lower temperatures, different wind patterns, and reduced moisture diffusivity over the Southern Ocean in the three LGM physical configurations result in different general circulation patterns, which affect biogeochemical cycles, as demonstrated in previous modelling studies . The LGM boundary conditions affect inventories and fluxes differently. For example, DIC is higher for LGMatmpi_* than for PIctl_*, while the differences between LGMatmws_* and LGMatmpi_*, and between LGMatmctl_* and LGMatmpi_* are small (Fig. S4o). On the other hand, N2 fixation shows contrasting responses across the simulations. It decreases relative to PIctl_*, but increases in LGMatmws_* and LGMatmctl_*. This indicates that, in our experiments, the glacial-interglacial changes in the DIC inventory are dominated by the lower temperature, while N2 fixation is also sensitive to the changes in the physical conditions.

Across all biogeochemical conditions, our LGM configurations have lower pCO2 in LGMatmctl_*, LGMatmws_*, and LGMatmpi_*. The LGM wind pattern and moisture diffusivity over the Southern Ocean contribute about 16 ppm, similar to the 19 ppm drawdown of pCO2 owing to the lower temperature.

We also notice that the effects of the biogeochemical configurations depend on which physical configuration they are combined with and vice versa. For example, the NO3- deviations from PIctl_* are more strongly expressed in the *_LGMFedep simulations than in the other biogeochemical configurations (Fig. S4k and Table S1). This highlights how an increase in dFe supply enhances the sensitivity of N2 fixation and denitrification to changes in physical boundary conditions. The results underscore the importance of the interplay between the biogeochemical and physical boundary conditions in controlling the balance of NO3- gains and losses in the ocean. Furthermore, atmospheric pCO2 decreases to varying degrees depending on the specific combination of physical and biogeochemical boundary conditions applied. This non-linear interaction between physical circulation and biogeochemical processes is consistent with previous studies showing that the glacial pCO2 drawdown arises from the combined and often synergistic effects of ocean circulation changes and biological processes such as Fe fertilisation .

During the LGM, O2 and NO3- levels and distributions in the ocean were different from the pre-industrial era. According to paleo proxy data, O2 was lower during the LGM , and NO3- was higher . Globally-averaged O2 and NO3- in LGMatmctl_LGMallbgc simulations are 10 mmolm-3 lower and 1.8 mmolm-3 higher on average than in PIctl_PIallbgc (Table S1). In some of the *_LGMFedep simulations, O2 and NO3- levels both become lower than in PIctl_PIallbgc (Fig. ). In these simulations, high iron input from the atmosphere increases POM production and export, and the ensuing consumption of O2 causes more widespread oxygen deficient zones, where denitrification occurs.

Such a decrease in NO3- as simulated by some of the experiments is in conflict with the observational records. Thus, a low NO3- inventory indicates that a strong decrease in pCO2 might be due to the wrong reasons in the model, e.g., overestimation of the marine biological carbon pump. On the other hand, the strong Fe limitation in *_LGMFesed simulations results in a decrease in NO3- due to suppressed N2 fixation, an increase in pCO2 due to reduced primary production, and higher O2 concentrations as a result of lower O2 consumption from POM export (Fig. ). This increase in O2 is also inconsistent with proxy-based reconstructions. Those different NO3-, O2, and pCO2 values highlight the critical role of Fe supply for the LGM model experiments.

In the LGMatmctl_LGMallbgc configuration, the average pCO2 is 43.5 ppm lower than in PIctl_PIallbgc (Fig. S4x and Table S1). The biogeochemical boundary conditions combined contribute less than the physical boundary conditions. The changes in pCO2 from *_PIallbgc to *_LGMallbgc (biogeochemical) with PIctl and LGMatmctl configurations are -0.8 and -9.3 ppm, respectively, while the changes from PIctl to LGMatmctl (physical) with *_PIallbgc and *_LGMallbgc conditions are -34.2 and -42.7 ppm, respectively (Table S1). The decreasing pCO2 due to the LGM physical configuration with *_PIallbgc (-34.2 ppm, PIctl_PIallbgc to LGMatmctl_PIallbgc) agrees with a 33 ppm decrease in a previous model experiment considering changes in physical boundary conditions . Nevertheless, the contribution from the LGM biogeochemical boundary conditions (*_PIallbgc to *_LGMallbgc) to the decrease in pCO2 is small, and the 43.5 ppm decrease from PIctl_PIallbgc to LGMatmctl_LGMallbgc are only about 50 % of the observed ≈90 ppm;. The main goal of our experiments is to evaluate changes in some biogeochemical and physical aspects that could affect pCO2, and not all processes, such as brine-induced stratification and air-sea disequilibrium , are considered. These missing processes might also contribute to the ocean receiving less carbon from terrestrial sources than suggested by observational estimates. In our simulations, terrestrial carbon input into the ocean-atmosphere system ranges from 177 ± 1 PgC in LGMatmctl to 198 ± 1 PgC in LGMatmpi simulations. These simulated values are slightly lower than the lower bound of the observational estimate of 511 ± 289 PgC, which is based on δ13C measurements from benthic foraminifera .

Some earlier experiments using Earth system models were able to generate a larger decline in the pCO2 -64 to -84 ppm;. However, these model experiments only consider the increase in atmospheric Fe deposition but not the decline in the supply from the sediment, which was included in our *_LGMallbgc conditions. When considering only the effects of Fe deposition, the average pCO2 in the LGMatmctl_LGMFedep simulations is 63 ppm lower than in PIctl_PIallbgc, i.e., 20 ppm more than for LGMatmctl_LGMallbgc. Further, different parameter combinations also affect the changes in pCO2, e.g., the maximum pCO2 drawdown in LGMatmctl_LGMFedep is 75 ppm (Fig. S4x), which is close to the observations. It is worthwhile to mention that increased Fe deposition alone reduces atmospheric pCO2 by 22.7 ppm from PIctl_PIallbgc to PIctl_LGMFedep, which is close to the changes in other model experiments considering only LGM dust deposition under pre-industrial climate conditions 14–22.8 ppm;.

The effects of variable stoichiometry on atmospheric pCO2 changes during the LGM have been examined in several previous studies. These include an empirical relationship between pC : P and ambient PO43-, and between pC : N and ambient NO3- , as well as a power law formulation for pC : P and pC : N that considers the influences of ambient PO43- and NO3-, temperature, and light intensity . For models that adopt the empirical relationship between pC : P and ambient PO43-, the magnitude of the pCO2 decline increases by 13–16 ppm . When the relationship between pC : N and ambient NO3- is also considered, the increase reaches 11 ppm . The power-law formulation of leads to an additional drawdown of 20 ppm compared to a fixed stoichiometry scheme using the Redfield ratio C:N:P=106:16:1.

To facilitate comparison with studies neglecting the changes in sedimentary Fe flux, benthic N-loss, and PO43- inventory, we calculate the changes in pC : N (26 %) and pC : P (28 %) from PIctl_PIallbgc to LGMatmctl_LGMFedep, which isolates the effect of enhanced atmospheric Fe deposition in our simulations. Multiplying the relative changes by the total pCO2 decline yields an estimated additional drawdown of approximately 16–17 ppm attributable to variable stoichiometry.

While this simple calculation neglects spatial variations, it provides a first-order estimate of the impact of stoichiometric flexibility on atmospheric pCO2 drawdown, showing that the effects of changes in elemental ratios on pCO2 in our simulations agree with previous studies considering the effects of Fe deposition.

In our experiments, pC : N and pC : P are lower under full LGM conditions (LGMatmctl_LGMallbgc) by 8 % and 10 %, respectively, than in PIctl_PIallbgc. In LGMatmctl_LGMallbgc, the higher surface nutrient concentrations, resulting from the weaker biological utilisation due to a lower global temperature and reduced Fe supply from the sediment, largely influence the elemental ratios of POM, as shown in the *_LGMFesed simulations. Nevertheless, the lower pC : N and pC : P could be simply linked to extra N and P incorporated into the POM, and do not necessarily indicate that the effects of variable stoichiometry of POM on atmospheric pCO2 are reversed in LGMatmctl_LGMallbgc. We note, however, that regional variations, particularly in regions such as the Southern Ocean, may differ from the global mean response and could play a more important role locally.

The ranges of variation in the model’s parameter values, which generally reflect ranges of uncertainty, contribute significantly to the variability of the simulated carbon cycle responses during the Last Glacial Maximum (LGM) and form a central motivation for this study. This variability arises because the response of biogeochemical tracers and fluxes to changes in boundary conditions depends strongly on the choice of the combination of parameter values.

The changes in Fe supply greatly affect the mean changes in the tracers and fluxes when compared with the pre-industrial simulations, and also contribute to higher variability among the 20 simulations with different parameter settings for each model configuration (Figs. S4 and S5). It is not surprising that the variations among the 20 ensemble members are often stronger when the median values deviate more from the pre-industrial simulations, but that is not always the case. For example, NO3- shows a different behaviour. When compared with *_PIallbgc, the deviation of the median is highest in *_LGMFesed but the variation is much larger in *_LGMFedep (Fig. S4c). That is because the NO3- level is affected by N2 fixation, WC and benthic denitrification, and the shut-down of WC denitrification in *_LGMFesed subdues the variations in NO3-.

Compared to the pre-industrial reference condition (PIctl_PIallbgc), atmospheric pCO2 under full LGM conditions (LGMatmctl_LGMallbgc) decreases by 36 to 58 ppm among the 20 simulations. The difference between the minimum and maximum pCO2 changes amounts to 50 % of the 43.5 ppm average decrease. We apply the lm (fitting linear model) function in R package “stats” to calculate P values for the correlations between changes in pCO2 from PIctl_PIallbgc to LGMatmctl_LGMallbgc (ΔpCO2) and in the perturbed parameters to better understand how individual parameters contribute to the pCO2 variation (P<0.05, Fig. S10). Among the 19 parameters, the nitrogen subsistence quota (Q0,phyN), temperature-dependent mortality (λ0,phy), and zooplankton maximum specific ingestion rate (gmax⁡) are significantly associated with the ΔpCO2 (Fig. S10b, e, and m). Thus, not only phytoplankton- but also zooplankton (top-down)-related parameters affect the variations in pCO2 in our simulations.

Overall, the selected 20 parameter sets yield strongly different biogeochemical fluxes, inventories, and atmospheric pCO2 in our various LGM model configurations. The spread in simulated changes relative to pre-industrial conditions (PIctl, PIallbgc, and PIctl_PIallbgc) across the 20 ensemble members arises from differences in how the selected parameter sets control model sensitivity to LGM boundary conditions in each configuration. Interestingly, the ΔpCO2 appears unrelated to cost values based on the likelihood-based cost function we employed for the parameter selection (Fig. S10t). Indeed, the ΔpCO2 is not necessarily correlated with cost values, which may be explained by different correlations (a) among parameters within the best 20 parameter sets, (b) between parameters and cost values, and (c) between parameters and ΔpCO2. This is easiest to see when the best selection of values of a pair of parameters is highly correlated. It means that collinearities exist, with effects on the cost function that are strongly interconnected. For example, νdet and wdd are the strongest positively-correlated pair among the 19 parameters (Fig. S11), and because changes in νdet and wdd have opposite effects on ΔpCO2 (Fig. S10), they tend to compensate each other's effect on ΔpCO2 in the LGMatmctl_LGMallbgc simulations. Thus, the pairs in the best 20 parameter sets yield limited changes in the ΔpCO2, and a strong deviation in the ΔpCO2 can only occur when νdet and wdd change in opposite directions (Fig. a). The other case would be αdia and Q0,phyN, which is the strongest negatively-correlated pair among the 19 parameters (Fig. S11). Since changes in αdia and Q0,phyN also have opposite effects on the ΔpCO2, opposing changes in αdia and Q0,phyN could result in a larger deviation in the ΔpCO2 but the effects on the cost values remains limited (Fig. b), owing to a weak correlation of either parameter with the cost value among the best 20 simulations. The weak relationship between the ΔpCO2 and cost values demonstrates the complexity of LGM model simulations with respect to the parameter settings, and emphasises the importance of perturbed parameter ensemble simulations.