The University of Victoria Earth System Climate Model (UVic ESCM) version 2.9 is an intermediate-complexity Earth system model with a resolution of 3.6° by 1.8° and 19 vertical ocean depth levels. It contains an ocean model, land and vegetation components, a dynamic-thermodynamic sea ice model, and sediments. The atmosphere is represented by a two-dimensional energy-moisture balance model. Winds are prescribed from monthly NCAR/NCEP reanalysis data . Continental ice sheets are fixed. The biogeochemical module (UVOK) is a nutrients-phytoplankton-zooplankton-detritus (NPZD) model that contains two classes of phytoplankton (ordinary phytoplankton and nitrogen-fixing diazotrophs), a single zooplankton class, and inorganic tracer representation of nitrate, phosphate, oxygen, dissolved inorganic carbon (DIC), and alkalinity. Water column denitrification is simulated but benthic denitrification is not. updated the parametrisation of grazing and added iron limitation to the phytoplankton growth equations based upon the seasonal model outputs of the global biogeochemistry model BLING . separated the UVic ESCM version 2.9 biogeochemistry into the stand-alone UVOK module and introduced a Transport Matrix Method (TMM) interface.

The TMM is an efficient, matrix-based simulation scheme for ocean biogeochemical tracers . It allows the offline computation of seasonally cycling, steady-state solutions by applying the biogeochemical equations to a sparse matrix of physical tracer tendencies which encapsulate the model steady-state circulation. Furthermore, it is massively parallel (the online UVic ESCM is serial code), which reduces equilibration times from weeks to hours when integrated on sufficiently large high performance computing machines . The TMM's computational efficiency enables the systematic testing of biogeochemical model parameter space, including model calibration and parameter optimisation against various metrics.

introduced an estimation of distribution algorithm (the covariance matrix adaptation evolution strategy; CMA-ES, ) to the TMM framework. The CMA-ES framework defines for each iteration (that is, “generation”) a population of 10 individual parameter value combinations that are selected from within a prescribed parameter value probability distribution. These 10 parameter combinations are integrated in the TMM for 3000 years to achieve approximate model steady-state, at the end of which a misfit function (the root-mean-square-error, RMSE) is evaluated against annual-mean gridded observations of modern ocean phosphate (j=1), nitrate (j=2), and oxygen (j=3) . The misfit is weighted by the volume Vi of each individual grid cell and is expressed as a fraction of total ocean volume VT. Each individual component (j) is normalised by the global mean concentration of the observed tracer (oj¯) for summation. The misfit function (J) is thus: 1J=∑j=131oj¯∑i=1N(mi,j-oi,j)2ViVT. Here, N is the number of model grid cells (87 307 in the UVic ESCM) and mi,j and oi,j are modelled and observed tracer concentrations, respectively. Results of the evaluation, as well as those of the previous generations, inform a revision of the parameter value probability distribution for the next generation. Thus, the algorithm reduces misfit until an optimal parameter combination that minimizes the misfit is achieved (typically, 70–150 generations in our particular framework and model). Testing suggests the framework is limited to calibration of about 6 parameters simultaneously; more than that prevents the misfit from converging to a minimum solution.

Similar to , the UVic ESCM version 2.9 is equilibrated using pre-industrial (year 1776) atmospheric CO2 boundary conditions of 278 ppm, and 3 commonly used vertical mixing schemes: the default scheme, Bryan-Lewis (BL) , spatially constant (CON), and a tidally-driven mixing scheme (TID) . BL vertical mixing utilises a diffusivity parameter that increases with depth but is laterally constant . CON vertical mixing uses a scalar diffusivity parameter (both laterally and depth-independent). TID mixing adds topographically dissipated tidal energy to the constant diffusivity parametrisation in order to mimic lateral and depth variability in tidally-driven mixing, where a stability dependency permits the diffusivity to evolve with the model state (in a fully-coupled online implementation) . All are hand-tuned to an average Northern Hemisphere maximum meridional overturning strength of 17.5 Sverdrups (within the middle of the range provided in ); work flow step A in Fig. . The tuning was done by adjusting the scalar vertical diffusivity parameter (kv) in TID and CON, or parameter scaling (in the case of BL), until the desired overturning strength was achieved. The parameter scaling in BL preserves the slope of change between surface and seafloor vertical diffusivity, where the default configuration used a kv between 0.3 and 1.3 cm2s-1. Resulting vertical diffusivity values and a selection of biogeochemistry-relevant physical diagnostics used in our analysis are given in Table , and the vertical diffusivity is plotted by ocean basin in Fig. . Numerical ocean circulation models typically use observationally-informed kv values within a range of 0.01 to 0.5 cm2s-1 , so our model values are on the higher end of this range. All other physical parameters are the same across configurations. These three different models are produced to test the impact of vertical mixing parametrisation on biogeochemical parameter optimisation, while seeking to minimise the impact of variable meridional overturning. Models were integrated to steady-state over 10 000 years (work flow step B in Fig. ). Transport matrices were then extracted from the models using methods described by (work flow step C in Fig. ).

Note that a linear advection scheme is required for TMM matrix extraction, thus the three vertical mixing models were produced with a linear third-order advection scheme Quicker; as described in . demonstrated near equivalence in biogeochemical solutions using the transport matrices extracted with this approach, and those obtained with the non-linear Flux Corrected Transport advection scheme employed with the standard fully coupled UVic ESCM.

Biogeochemical parameter optimisation was conducted on each of the BL, CON, and TID matrices following the framework of , implemented for UVOK . This optimisation is represented in Fig.  as work flow step D. The model parameters were calibrated using annual mean global misfit to World Ocean Atlas (WOA) phosphate, nitrate, and oxygen data . The parameters selected for optimisation are:

the initial rate of detrital particle sinking (wD,0; Eq. )

The three optimal biogeochemical parameter sets determined by calibration within the offline TMM framework were then applied to the fully online coupled UVic ESCM, using the same physical configurations provided in BL, CON, and TID, and spun-up at least 10 000 years to physical and biogeochemical equilibrium at pre-industrial (year 1776) atmospheric boundary conditions. Atmospheric forcing encompasses CO2, sulphate aerosol and chlorofluorocarbon concentrations, volcanic and solar radiative forcing, land ice and agricultural cover . This is work flow step E (Fig. ). From year 1776, historical emissions forcing including fossil fuel and land use change CO2 emissions is applied to year 2005, in work flow step F (Fig. ). Solar insolation and wind forcing vary seasonally , but wind fields are fixed with respect to changing climate . After year 2005, the model is forced with CO2 emissions at a level consistent with the business-as-usual RCP8.5 atmospheric concentration scenario, to year 2100 . This scenario constitutes a rapid rise in emissions to year 2100, after which emissions stabilise and then linearly decrease to zero by 2250, and other forcings such as solar insolation and land use change remain at 2005 levels. This experimental set-up is designed to explore how the three equivalent models differ in their response to climate change.

Here we present a suite of physical circulation metrics to compare model differences that arise due to application of the different vertical mixing schemes (Bryan-Lewis; BL, tidal mixing; TID, and a constant vertical diffusivity; CON). AMOC is maximum Atlantic Meridional overturning, calculated between the depths of 300 and 5000 m within the latitude range of 15 to 60° N and including the eddy-induced residual circulation. ACC is the maximum value of the zonal Antarctic Circumpolar Current at 68° W, integrated between 50 and 70° S and 0 to 6000 m depth. AABW is the zonally integrated minimum (anti-clockwise) meridional flow at 35° S, between 1000–6000 m depth and including the eddy-induced residual circulation. CDW is minimum (anti-clockwise) meridional flow of Circumpolar Deep Water in the Indo-Pacific basin, reported at 35° S and integrated between 1000 and 6000 m depth. Ideal age is the amount of time since a water parcel last had contact with the atmosphere . These circulation metrics are selected for analysis due to their being previously demonstrated to exert control on ocean carbon storage, biogeochemistry, and primary production e.g., and because their responses to climate warming demonstrate strong variation across Earth System models e.g.,. Our definition of CDW effectively distinguishes the Indo-Pacific component of AABW in order to separately assess circulation-biogeochemistry correlations outside of the Atlantic. Globally averaged ideal age represents the integrated effect of the global overturning circulation on deep ocean water residence times.

AMOC is very similar across all three model configurations (Fig.  and Table ). It was hand-tuned by adjustment of the vertical diffusivity parameter value (or range of values in the case of the BL parametrisation) in each of the three vertical mixing configurations to obtain a maximum AMOC close to the middle of the range (17.5 Sv) of the observational estimate (15–20 Sv) of . Depth profiles of AMOC are also similar across configurations, with the cell reaching 2.7 km depth in BL and TID, and 2.6 km deep in CON on basin average, with the maximum strength reached at about 800 m depth and 30° N in all models.

Similarities in the AMOC strength and depth do not extend to other circulation metrics, with larger differences apparent in the unconstrained Southern Hemisphere (Fig. ). ACC strength is greater in TID and CON (133.5 and 133 Sv, respectively), and weakest in BL (125.9 Sv), Table ). The globally prescribed wind fields are identical across models, but surface atmospheric temperatures are slightly different (13.08, 13.00, and 12.99 °C for BL, TID, and CON, respectively), resulting in small variations in wind-driven transport due the addition and parametrisation of wind stress anomalies using thermal anomalies . AABW transport is strongest in BL (12.8 Sv) and weakest in CON (8.3 Sv), a factor 1.5 difference with respect to CON. More vigorous abyssal overturning circulation has been previously reported for higher values of diapycnal diffusivity (such as represented by the BL scheme) by , who also reported globally stronger upwelling in the BL model than found when using the TID or CON configurations in the UVic ESCM. CDW transport strength is 23 % larger in TID compared to BL. Mean ideal ages vary by 42 % with respect to the smallest value, with CON being the oldest (905 years) and TID being the youngest (639 years).

Connectivity between upper and lower global overturning cells via CDW clearly impacts mean ideal age. The oldest deep water ideal ages (Fig. ) in the CON simulation are consistent with this scheme having both weak CDW and the weakest AABW of the three parametrisations. The weak AABW, and strong and shallow AMOC in CON suggests a stronger isolation of deep water masses in this model configuration, with a rapidly-cycling upper ocean (including, a relatively strong ACC) and a relatively slowly circulating deep ocean. Likewise, the more “balanced” overturning in BL (estimated by AMOC-AABW yielding the smallest difference) suggests faster exchange of heat and carbon between the atmosphere and deep ocean, but the scheme does not have the youngest deep ocean on average because weaker CDW transport maintains a relatively older deep Pacific compared to TID. It is the TID scheme that has the youngest deep ocean, and mean ideal age, due to its vigorous CDW, which connects its upper and lower overturning cells of intermediate strength.

The optimal minimum misfit ranged from 0.57 (BL) to 0.62 (CON and TID). Nitrate fitness comprised the dominant fraction of the misfit, in an inverse relationship to phosphate (improvement to nitrate fitness resulted in reduction in phosphate fitness), a tradeoff that limited the total minimum misfit. Table  lists the optimal parameters from all three calibrations. Figure  examines whether the optimal misfit and optimal biogeochemical parameter values systematically vary with the models' physical circulation metrics using calculation of the square of the Pearson product moment correlation coefficient, R2. The sign of the correlation indicates the slope of the relationship. It is important to note that our small sample size of only three points increases the uncertainty in our analysis, and we furthermore do not account for covariance, nor do we attempt to identify causal links. These correlations are provided as a means to explore systematic relationships between optimal biogeochemical parameter sets and minimum misfit with the models' physical circulation metrics, which could suggest some physical-biogeochemical parameter compensation. Optimal minimum misfit and biogeochemical parameter values are also plotted against physical circulation metrics, with linear regression slopes in Fig. . Minimum misfit demonstrates strong correlation with AMOC and ACC strength (R2 values over 0.9, Fig. ), where weaker overturning is associated with a lower misfit. This association suggests a compensation between physical model uncertainty and biogeochemical parameter uncertainty.

Of the optimal parameters, the phytoplankton growth parameter (a) shows the least variability (0.63–0.64 d⁻¹) between BL, TID, and CON. A value of 0.59 d⁻¹ is the original parameter value and this analysis demonstrates a similar value is robust for our model regardless of the vertical mixing parametrisation. The general high bias in our optimal parameter value could reflect a common bias in our model general circulation. Optimal values of a demonstrate a strong correlation with AABW strength, and strong anti-correlation with average ocean ideal age. Lower growth rates are associated with a shallower AMOC, a weaker AABW overturning, and older mean ocean ages.

Similarly, the R-O:N ratio also varies less than 4 % between BL, TID, and CON and is close to (but less than) the empirically-derived value of 10 . A robust R-O:N ratio is also broadly found in ocean observations . The R-O:N ratio also demonstrates a strong anti-correlation with average ocean ideal age, where the smallest values correspond to the oldest ages. Smaller oxygen consumption ratios are required to compensate for slower circulation in order to fit simulated oxygen to contemporary observations, and at the same time more nitrate must be converted to its inorganic form when a sluggish model bias encourages denitrification in low-oxygen midwaters. These dual pressures may both be affecting the R-O:N ratio, as well as the air-sea equilibration of oxygen but not nitrate, and which may be sensitive to the general circulation. That the calibrated ratio for all three vertical mixing models is less than 10 is not altogether surprising as it was earlier found that multiple versions of the UVic ESCM have a sluggish deep circulation, particularly in the deep Pacific .

The remaining parameters display greater variability between vertical mixing parametrisations, and reflect the competing influences of upper ocean mixing and deep ocean circulation. The nitrate uptake half saturation coefficient (kN) and initial detrital sinking rate (wD,0) “export production” parameters vary by a factor of 2 and 1.6 compared to the lowest values, respectively, and demonstrate strong correlation with both AMOC and ACC strength (R2 values above 0.9). Optimal wD,0 values are at the upper bound of the prescribed range for TID and CON configurations, which might partly explain the relatively poorer misfit of these two mixing configurations (a larger prescribed upper range might have improved the misfit, and assumptions regarding the parameter value bounds may need to be re-evaluated in the future). The optimal kN values in CON similarly approach the upper prescribed bound, but do not in TID. This might reflect the combined influence of AMOC (which is strong in both models) and upper-ocean diffusion gradients (stronger in TID). Light attenuation parameter kc varies by a factor of 1.7 relative to the lowest value, and is strongly anti-correlated with AMOC strength, where a stronger AMOC is associated with weaker optimal light attenuation, and correlated with AABW strength, where a stronger AABW is associated with stronger optimal light attenuation. These relationships reflect the sensitivity of organic particle fluxes to light attenuation parameter value, where weaker light attenuation increases organic particle fluxes into the deeper ocean, below the clockwise cells of AMOC and the ACC, with their relatively fast nutrient recycling.

The rate of increase of detrital sinking (wdd) varies by a factor of 1.6 relative to its lowest optimal value. It has the largest value in the BL calibration, which is surprising given this model is optimised with the lowest initial detrital sinking rates (wD,0). Optimal values of wdd strongly correlate with AABW strength, where larger rates of increase for particle sinking are associated with stronger AABW overturning, and are strongly anti-correlated with ideal age. We speculate the relatively low initial detrital sinking rates control export production into the relatively vigorous and long-pathway AABW, but a rapid increasing detrital sinking rate regulates (and encourages) deeper nutrient remineralisation, which removes nutrients from the upper ocean more effectively . This need in BL for upper ocean nutrient removal might relate to the relatively interactive upper and lower ocean water masses (recalling this configuration having very strong upwelling, as reported in , relatively high vertical diffusivity, as well as the weakest AMOC, which suggests more “balanced” upper and lower circulation cells). In contrast, the CON calibrated rate of increase (wdd) is only roughly 60 % of that found using TID and BL, because this configuration produces a much older, slower-circulating, and more isolated deep ocean (and hence, a longer timescale of deep nutrient sequestration).

In summary, while the phytoplankton growth parameter and R-O:N ratio were robust across model calibrations, their optimal values were strongly anti-correlated with average ocean age and correlated with AABW strength. This is also the case for wdd, which showed a larger sensitivity to circulation differences. “Export production” parameters kN and wD,0, and total misfit are more sensitive to ACC and AMOC overturning strength, while wdd and kc show strongest correlation with AABW strength. As was described in , faster overturning increases the resupply of nutrients to the upper ocean, which in turn requires stronger limitation on production parameters (which higher values of light attenuation and lower values of nitrate uptake half saturation achieve). Mean ideal age correlations with optimal parameters shows some (inverse) similarities with AABW strength, indicating the role of this transport pathway in regulating deep ocean age.

We next examine differences in model responses to the applied high-end CO2 emission scenario. Atmospheric CO2 concentrations increase uniformly until about year 2100 (Fig. ). Despite identical emissions, the models diverge in their atmospheric CO2 path after 2100, with a model ensemble spread of 62 ppm (ranging between 1425 and 1487 ppm) by the year 2300. The model with the greatest atmospheric CO2 increase is BL, which is in part due to it having the smallest pre-industrial surface ocean buffer (calculated from the surface DIC : alkalinity ratio, not shown). We find that models with higher atmospheric CO2 (and thus also temperature) have the smallest land carbon uptake over our simulations, reflecting a weakening of the land carbon sink with increasing global temperature (not shown).

With the exception of ACC circulation, global circulation metrics weaken, and ideal age increases, in all models (Fig. ). Dependencies on vertical mixing parametrisation become most apparent after about year 2100; in general, the largest changes in ocean circulation metrics occur in models with the fastest pre-industrial circulation, suggesting the importance of vertical mixing-induced differences in the uptake and communication of anthropogenic heat into the interior and its effect on ocean density gradients. The BL overturning (with its high interior diapycnal diffusivities producing a relatively slow pre-industrial AMOC and relatively strong AABW) slows the least in AMOC by year 2300 and slows the most in AABW (also seen in basin-averaged plots of change in ideal age, Fig. ). The CON model is less sensitive overall, with moderate responses in AMOC strength, ACC strengthening, AABW and CDW slow-down. The TID model (with its overall relatively strong pre-industrial circulation resulting in the youngest pre-industrial mean ideal age) shows the largest changes in circulation metrics for AMOC and CDW, and changes that are nearly equivalent to BL in AABW. In terms of absolute circulation strengths at the year 2300, we note convergence to smaller differences across the model range by year 2300 occurs in ACC, AABW, and CDW strengths, suggesting that the magnitude of the model responses are more sensitive to model forcing (which is identical across all simulations) than to choice of mixing parametrisation.

We find a range of ocean biogeochemical responses to increasing CO2 emissions and the associated global warming. The absolute range in NPP grows across models over the transient simulations (Fig. ), and there results an 11 PgCyr-1 spread in the increase in global NPP by year 2300 across the model ensemble (Fig. ). This is a smaller range in NPP response than found across the model ensemble for pre-industrial NPP. Similar to pre-industrial NPP, the strongest variation in change is in the low latitudes, where optimal model bias towards tropical NPP drives a stronger increase in NPP due to warming (Fig. ; R2=0.995, Fig. ). Increasing NPP with warming is a feature of the UVOK and other biogeochemical models, and is driven in part by an increase in upper-ocean nutrient recycling due to accelerating respiration, as well as warming of the high latitudes which both increases growth rates and reduces sea ice, increasing light availability e.g.. A high bias in tropical production increasing sensitivity to warming also results in strong correlations in pre-industrial OMZ volume and rates of nitrogen fixation with change in NPP (Fig. ). Pre-industrial biogeochemical and biogeochemical response metrics are plotted with linear regression slopes in Fig. .

With respect to the physical circulation, correlation patterns in global change in NPP are similar to those found for pre-industrial NPP, where the change in NPP is strongly anti-correlated with pre-industrial “upper-ocean metrics” AMOC and ACC strength (Fig. ). Pre-industrial circulation and biogeochemical response metrics are plotted with linear regression slopes in Fig. . Pre-industrial AMOC and ACC strength can both therefore indicate a global NPP response with warming, where weaker pre-industrial AMOC and ACC is associated with a larger change in NPP. Change in NPP is strongly correlated with the change in AMOC strength, the change in CDW strength, and the change in ideal age, with the smallest weakening of AMOC and CDW resulting in the largest increases in NPP. We speculate that enhanced biogeochemical sensitivity to warming in models with circulations that are less sensitive to warming reflects the continuing influence of upwelling returning nutrients to the upper ocean, where they can be utilized under warming environmental conditions. More dramatic stagnation of global circulation limits nutrient resupply, thus limiting the response of ocean ecosystems to warming. However, our biogeochemical parameter calibration also contributes to this pattern because we have tuned our parameters to have weaker limitation of primary production in models that have weaker pre-industrial circulations. In particular, the initial detrital sinking rate (wD,0) is slower in slower-circulation models, enhancing the availability of nutrients in the upper ocean. The weaker pre-industrial circulation contributes to lower sensitivity of the model physics to warming, but our tuning has enhanced the sensitivity of NPP to warming.

All models simulate a decline in both upper and deep ocean POC export fluxes before year 2100; Fig. ) Trends are within the range found in CMIP and other models to year 2100 (e.g., roughly between -1 % to -20 %) . The model ensemble response spread grows after year 2100, but the range in absolute values show little change, and a small convergence in deep POC fluxes (Fig. ). The BL mixing parametrisation produces a sustained long-term decline in deep and shallow POC fluxes, a result of the greater proportion of global NPP and export production occurring in the warm (and rapidly warming) low-latitudes, while the TID and CON parametrisations produce greater increases in POC fluxes in the cooler high latitudes (Fig. ), although spatial patterns are broadly similar across all model configurations. Examination of the biogeochemical parameter ranges in Table  suggests variability in trend magnitude might arise from the spread in kc, the light attenuation coefficient, which has previously been demonstrated to influence export production response to warming in the Southern Ocean . This model sensitivity arises because deeper primary production increases the amount of organic material exported to deeper levels. Indeed, Fig.  reveals the greatest increases in shallow and deep fluxes (calculated between years 2300 and 1765 at 130 m depth) occur in all models in the Southern Ocean, in contrast to the strongest increases in NPP which occur in the tropics. Increasing particle fluxes in the Southern Ocean is consistent with earlier findings using other models, e.g. , , . In our models, there are only two plankton functional types and their relative competitiveness is not calibrated, so ecosystem complexity is not a driver of POC flux differences e.g..

Correlations found in pre-industrial shallow and deep POC fluxes with circulation metrics largely do not hold for simulated change in fluxes under global warming (Fig. ). Circulation and biogeochemical response metrics are plotted with linear regression slopes in Fig. . The warming-induced changes in shallow and deep POC fluxes also do not demonstrate an inverse relationship with warming-induced circulation changes. There is closer agreement in the sign of the correlations of changes in deep and shallow fluxes with global warming against pre-industrial circulation metrics, where the change in shallow and deep fluxes with warming are correlated with pre-industrial AMOC and ACC strengths, and ideal age, and anti-correlated with AABW strength. Unlike NPP, pre-industrial bias in shallow and deep POC fluxes have lower correlation with shallow and deep POC flux responses to warming (Fig. ). Instead, the response of shallow POC fluxes to warming is best (anti-)correlated with pre-industrial NPP, of the metrics we explore. With respect to both shallow and deep POC fluxes, the better predictors of flux responses to warming are the changes in circulation metrics with warming, where both shallow and deep POC fluxes are strongly correlated with the change in ACC and AABW strengths, and anti-correlated with the change in ideal age (Fig. ). Thus it appears that with respect to POC fluxes, the largest changes occur in models with the largest changes in Southern Hemisphere-driven circulation metrics. We speculate that this is a product of model tuning, where models with Southern Hemisphere circulations that are more responsive to global warming were calibrated with faster rates of increase of particle sinking, therefore disproportionately exposing particle fluxes to deep ocean circulation slowdown (thereby reducing particle fluxes). These points highlight the difficulty in establishing simple, concrete relationships between physical and biogeochemical features that apply in both steady-state and transient environmental states.

The increase in global ocean volume where oxygen concentrations fall below 5 mmolm-3 exhibits a factor 1.2 model ensemble spread at year 2300, with respect to the smallest change (Fig. ). However, the range in absolute suboxic volumes remains mostly unchanged (Fig. ). Figure  displays change in O₂ concentrations at 300 m depth between years 1765 and 2300 for each model. Strong declines occur in the North Atlantic, North Pacific, and in the Indian and Atlantic sectors of the Southern Ocean in all models. The magnitude of the decline in the central North Pacific is particularly variable. As with POC fluxes, relationships demonstrated against circulation metrics for pre-industrial values do not hold for transient responses. In our optimal models, changes in suboxic volume with warming have a strong correlation against pre-industrial ideal age, and strong anti-correlation against AABW strength (Fig. ). Like with POC, it is the response of the Southern-Hemisphere circulation metrics (ACC, AABW) that show the strongest correlations with change in suboxic volume with ocean warming. With respect to suboxic volume, the smallest changes occur in models with the largest declines in circulation metrics, i.e. the models that are the most physically sensitive to warming and had relatively strong pre-industrial deep circulations. This is likely due to compensating effects in the models, where the models showing the largest declines in deep circulation (which would increase suboxic volume) also show the largest declines in POC fluxes (which would act to decrease suboxic volume), to which the models with vigorous pre-industrial circulations use a R-O:N ratio calibrated to be particularly sensitive to changes in the POC flux in order to consume more oxygen in the pre-industrial deep ocean. This explains then why the pre-industrial suboxic volume is not useful in estimating the expansion of suboxic volume with warming, which is strongly anti-correlated with pre-industrial deep POC flux (Fig. ). The potential for compensation between biogeochemical parameter tuning and physical circulation responses furthermore suggests that model biases that might lead to an over- or under-estimate of suboxic volume in the pre-industrial ocean might not equivalently over- or under-estimate future expansion of suboxic volume with warming.

Changes in global nitrogen fixation rates similarly exhibit a 1.5 factor spread across the model ensemble response at year 2300, with respect to the smallest response (Fig. ). Nitrogen fixation increases across our model ensemble, and by year 2100 is within the range of CMIP models which do not agree on the sign of the trend,. The spread in absolute nitrogen fixation values grows within our model ensemble (Fig. ). We find the models that over-estimated the observed global nitrogen fixation rate (BL and CON) also show the strongest increases in nitrogen fixation rate with warming, although the correlation between pre-industrial nitrogen fixation rate and change in this rate is modest (R2=0.74) in optimal models (Fig. ). From our metrics, the strongest correlation that we found for the global increase in nitrogen fixation with warming is the pre-industrial POC flux at 130 m depth (Fig. ), reflecting calibration of wD,0 impacting remineralisation length scales, oxygen consumption and nutrient export. The pre-industrial shallow POC flux shows a modest (but weaker) correlation with the change in suboxic volume (the regions below 5 mmolm-3 support denitrification in our models), suggesting that trends in nitrogen fixation are regulated by more than trends in suboxic volume. Nitrogen fixation trends are strongly anti-correlated with pre-industrial CDW strength, which is similar to what we found for the pre-industrial values, suggesting that pre-industrial CDW is a useful predictor of nitrogen fixation response to warming.