To check the significance and robustness of the associations between phytoplankton abundance and the physical-biogeochemical variables of interest (the bottom-up controls) discussed in Sect. 3.1, we use regression and correlation analysis to study these associations in greater detail within three individual models with well-established, complex ocean biogeochemical modules (GFDL-ESM2G, HadGEM2-ES and IPSL-CM5A-MR). An important point to note is that multi-model mean changes in a given variable may be dominated by models with the biggest changes in some cases, so the analysis of individual models here is helpful in better illuminating particular relationships between variables.

In Fig. 2, we show scatter plots of PB versus our variables of interest on multiple timescales, across the four chosen zonally banded biomes (as defined in Sect. 3.1). We use only the grid points within each of the four zonal bands in a given model where the 100-year change in PB is predicted to go in the same direction as the entire band in the all-model average. As an example, in Fig. 1a, we see that PB is expected to increase with future warming in the Antarctic band (south of 65∘ S) in the all-model average; accordingly, we mask the grid points south of 65∘ S within each individual model where PB increases and study those grid points alone to understand what is driving PB increases within the south-of-65∘ S band as a whole. By this same procedure, we mask and investigate only the areas where PB decreases between 30–40∘ S, where it increases between 40–50∘ S, where it decreases between 50–65∘ S, and where it increases south of 65∘ S. We undertake this masking procedure because we would like to tease out the dominant driver of the net phytoplankton response within the zonal band of interest and masking helps to further amplify the signal we are looking for by focusing on what the majority of points we are interested in are doing, thus effectively diluting the confounding effects of natural background variability. To confirm that masking does not significantly alter our results besides by potentially enhancing the signal-to-noise ratio of our correlations, we repeat any analyses (namely, Figs. 2–4) involving masking with all (both masked and unmasked) grid points. Results from these all-inclusive analyses agree with those presented here for masked points only, but with slightly weaker correlation coefficients between phytoplankton biomass or productivity and a given driving variable of interest in some cases, as expected (see discussion below).

After spatially averaging PB and our variables of interest over the masked grid points within each zonal band, we then created different time series representing multiple timescales. To remove the effects of climate change and isolate interannual variability, we subtracted a 25-year running mean from every spatially averaged yearly data point within each scenario's raw yearly time series (historical from 1911–2005, rcp8.5 from 2006–2100). To capture variability and mechanisms which act on a longer than interannual but shorter than decadal timescale in the absence of confounding climate change effects, we took the 5-year running mean of the raw yearly time series data and then subtracted a 25-year running mean from each 5-year running mean-smoothed annual value. Here we purposely chose to use detrended historical scenario time series rather than preindustrial control scenario time series (forced with constant preindustrial CO2 concentrations) for practical reasons (not all the models provided all the necessary variables in the preindustrial control experiment). We did, however, prove that in at least model GFDL-ESM2G, the interannual drivers affect phytoplankton biomass in the same direction and with a similar magnitude in the preindustrial control case and the detrended historical and rcp8.5 cases, as expected. Finally, to investigate and emphasize the effects of climate change, we created a set of historical and rcp8.5 “climate change” time series by taking 10-year averages (not running means, but rather averages of non-overlapping 10-year intervals) of the same raw yearly spatially averaged time series as before.

A quick summary of the making of Fig. 2 is as follows: we spatially averaged PB and our driving variables of interest over each masked zonally banded biome and temporally correlated them across three distinct timescales of variability. Only those variables of interest which were significantly correlated with PB over at least two of the three (interannual, 5-year and decadal) studied timescales are shown (see Fig. S12 for examples of how correlations between PB and variables which were not chosen looked in comparison to the correlations between PB and the variable which was chosen). The driving variables shown are thus the ones whose relationships with PB hold on interannual, five-year, as well as longer-term climate change timescales in both the historical and rcp8.5 scenarios. Significantly, this implies that changes in these particular variables are the likely drivers of changes in phytoplankton biomass on an interannual as well as a longer-term timescale associated with future warming. It is important to note here that these inferred linkages are based only on correlations, but in all cases are also supported by model equations and previous studies.

PB between 30 and 40∘ S is strongly positively correlated with maximum annual surface nitrate concentration in all three models on all timescales (Fig. 2a). This suggests that predicted future decreases in PB between 30 and 40∘ S are largely driven by climate warming-induced decreases in macronutrient supply to the surface during winter. This decreased supply is in turn a consequence of increased water column stratification and decreased maximum annual wintertime MLD associated with future warming, as was suggested by the analysis of multi-model mean maps discussed in Sect. 3.1.

Between 40 and 50∘ S, projections of enhanced PB are driven by either increases in iron concentrations (GFDL-ESM2G and IPSL-CM5A-MR) or reduced light limitation associated with shoaling of the summertime mixed layer (HadGEM2-ES) (Fig. 2b), again in agreement with the analysis in Sect. 3.1.

Within the 50–65∘ S band, where PB is predicted to decrease across all three models, light and iron are the most important limiting factors (Fig. 2c). For GFDL-ESM2G, in regions within this band where PB decreases with climate change, cloud cover (which is negatively correlated with PB – plot not shown) increases, leading to a concomitant decrease in surface light availability, which is positively correlated with PB (Fig. 2c). Furthermore, in both GFDL-ESM2G and HadGEM2-ES, the summertime MLD is predicted to deepen with climate change, creating an even more light-limited environment for phytoplankton here (Fig. 2c), as was deduced using multi-model means in Sect. 3.1. In contrast to the first two models and missing from the analysis in Sect. 3.1, IPSL-CM5A-MR's wintertime surface iron concentrations appear to play the biggest role in determining PB between 50 and 65∘ S (wintertime MLD was also well correlated with PB on all studied timescales here, most likely because it drives the supply of iron from the deep ocean) (Fig. 2c).

South of 65∘ S, iron is significantly positively correlated with PB on all three timescales within the models GFDL-ESM2G and IPSL-CM5A-MR (Fig. 2d), as was expected from multi-model mean change analyses in Sect. 3.1. For HadGEM2-ES, both average annual sea ice fraction and maximum annual IPAR were significantly correlated with PP south of 65∘ S, such that available light at the ocean surface is likely the limiting factor within this model's Antarctic band. An increase in IPAR due to a decrease in sea ice fraction is thus the most probable cause of projected phytoplankton abundance increases here, again in agreement with the reasoning in Sect. 3.1.

In sum, these findings from Fig. 2 agree well with those deduced from Fig. 1, as discussed in Sect. 3.1. In particular, within each zonally banded biome, the proposed drivers of projected phytoplankton responses in the all-model means are the same ones driving phytoplankton responses within the individual models studied here (with the possible exception of the 50–65∘ S band, where iron appears to play a role within IPSL-CM5A-MR, but not in the all-model mean). Results for Fig. 2 were the same but with slightly smaller correlation coefficients when using all (both masked and unmasked) grid points (see Fig. S13).

To confirm that the bottom-up controls on PB proposed in Sects. 3.1 and 3.2.1 hold across the four SO biomes on even longer 100-year timescales, we undertake a spatial correlation analysis within the same three models as before. In Fig. 3, we show the results of this spatial correlation analysis in which we look at the relationship between 100-year changes in PB and the variables of interest at every grid point within each masked latitudinal band. Each dot in a scatter plot represents a masked grid point which undergoes a 100-year change in a variable of interest and an associated change in PB at that same grid point. By plotting only those variables with the largest magnitude correlation coefficients when correlated with PB, we are able to discover which variables affect PB most in each latitudinal band over 100-year timescales within each of the three models studied in detail (see Fig. S14 for an example of how correlations between PB and variables not chosen looked in comparison to correlations between PB and the variable chosen). For each chosen variable, scatter plots of either relative or absolute 100-year changes are shown, depending on which type of change generated the clearest relationship between PB and the variable of interest. Least squares best-fit lines are drawn for each scatter plot to help visualize the slopes and enable comparison with the corresponding slopes in Fig. 2. Because it is difficult to accurately test for significance in this type of spatial correlation (neighbouring grid points are likely highly correlated, leading to large significance overestimates), these regression lines may or may not be statistically significant. Thus, the lines are meant only to serve as a qualitative visual guide. As in Fig. 2, Fig. 3 showed the same results but with potentially slightly smaller correlation coefficients when using all (both masked and unmasked) grid points (see Fig. S15).

Together, Figs. 2 and 3 show that the variables of interest within each zone that drive PB on decadal and shorter timescales also tend to be those that drive PB on an even longer 100-year climate change timescale. There are, however, a couple of important discrepancies. The first occurs in GFDL-ESM2G within the 50–65∘ S band, where light limitation is shown to be most important on decadal and shorter timescales (Fig. 2c) while iron limitation appears to take over on a 100-year timescale (Fig. 3c). This suggests the presence of iron–light co-limitation in this region within GFDL-ESM2G, in agreement with previous studies (e.g. Sunda and Huntsman, 1997; Boyd et al., 2001; Feng et al., 2010). The second discrepancy occurs in IPSL-CM5A-MR within the south-of-65∘ S band, where iron limitation is most important on decadal and shorter timescales (Fig. 2d) while increases in sea surface temperature (SST) become the dominant driver of PB increases on a 100-year timescale (Fig. 3d) (though iron is still somewhat important on the centennial timescale with R=0.703 when spatially correlated with PB change – plot not shown).

In sum, we find that for the most part, the mechanisms within each zonal band that determine PB on decadal and shorter timescales tend to be those that determine PB on longer, centennial climate change-driven timescales as well. The magnitude of each driver's effect on phytoplankton biomass (as seen from the slopes of best-fit lines in Figs. 2–3, summarized in Table 3) also remains the same across the relevant timescales, further supporting the notion that the same mechanisms act on the different timescales studied. Importantly, the magnitude of 100-year changes in the chosen variables of interest are also hypothetically large enough to drive most of the 100-year change in PB. We note, however, that in the real ocean, phytoplankton adaptation and evolution could alter the driver–response relationship observed at the interannual scale within these models.

Finally, we ask whether the mechanisms proposed in Sects. 3.1 and 3.2 hold across all 16 CMIP5 models with explicit phytoplankton biology. To answer this, we plot 100-year changes in PP versus 100-year changes in chosen variables of interest across all of the models and look for among-model agreement as to the effect of these variables on PP within each masked zonal band (Fig. 4). These variables were chosen by first plotting all of the potential drivers of interest (listed in Table 2) and then choosing the ones which showed the strongest correlations or most consistent directions of changes across the models, guided by the relationships found in Figs. 1–3. Here each point in a scatter plot represents a 100-year change in PP versus a 100-year change in the variable of interest spatially averaged over the given model's masked zonal band. We box only the points driven by processes which could be logically predicted from previously discussed mechanisms or model equations. For example, although almost all models undergo increases in cloud fraction and primary production south of 65∘ S, we do not box the orange points in the PP versus average annual cloud cover plot (Fig. 4e) because we know that an increase in cloud fraction would decrease light availability and consequently lead to decreases, not increases, in primary production. Thus, we can safely ignore changes in cloud cover as a driver of changes in primary production among the models south of 65∘ S and instead view these changes in cloud cover as merely a consequence of underlying dynamical changes already occurring in that region. Via this technique, we find a consistent set of mechanisms driving 100-year changes in productivity across the CMIP5 model suite (highlighted by coloured boxes in Fig. 4), in agreement with the mechanisms brought to light by the analyses in Sects. 3.1 and 3.2.

Nitrate emerges as the driver for changes in PP within the 30–40∘ S band across all models (i.e. all red points lie in the third quadrant and within the red box in Fig. 4b). Models with greater relative decreases in wintertime surface nitrate concentrations undergo significantly (p<0.05) greater decreases in average production within the 30–40∘ S band. It is worth noting that this is the only significant, highly linear intermodel relationship within any of the zonal bands. In the rest of the bands, we mostly interpret only the sign, rather than the linearity, of PP changes related to the driving variables of interest across models. Within the 40–50∘ S band, in general, models with increases in relative iron concentration and decreases in summertime MLD also experience relative increases in PP (Fig. 4a, c, purple boxes). Models NorESM1-ME and IPSL-CM5A-LR are exceptions to this, however, in that PP still increases while iron concentrations decrease (Fig. 4c, purple unboxed). In these models, increases in light availability due to shoaling of summertime MLDs (Fig. 4a) and decreases in cloud cover (Fig. 4e) are large enough to cancel out the PP-suppressing effects of iron concentration decreases (Fig. 4c) between 40 and 50∘ S. Further solidifying the importance of climate-driven changes in light availability within the 50–65∘ S band, models predicting relative increases in summertime MLD or average annual cloud cover, along with decreases in maximum annual IPAR, also predict relative decreases in PP in this region (Fig. 4a, d, e, green boxes). Iron also emerges as a potential driver of PP decreases within the 50–65∘ S band, but not across all of the models (Fig. 4c). In models which undergo PP decreases concurrent with iron concentration increases (GISS-E2-R-CC, GISS-E2-H-CC, HadGEM2-CC, HadGEM2-ES, IPSL-CM5A-LR, NorESM1-ME, and MPI-ESM-LR; see Fig. 4c, green unboxed), reductions in light availability tend to be relatively large such that they win out in determining overall PP change. For example, GISS-E2-R-CC exhibits the largest relative iron increase between 50 and 65∘ S out of all the models (Fig. 4c), but also the greatest relative summertime MLD deepening (Fig. 4a), leading to vast reductions in light supply to phytoplankton during the most productive time of year. An increase in both IPAR and iron supply across the models results in PP increases south of 65∘ S, as highlighted by the orange boxes in Fig. 4c and d. Models IPSL-CM5A-LR, IPSL-CM5A-MR, and GFDL-ESM2G deviate from this trend slightly in that they experience small relative decreases in IPAR south of 65∘ S, while still experiencing increases in PP. However, these three models also exhibit shoaling of the summertime MLD here, which would increase light availability, likely cancelling the effects of decreased IPAR at the surface. Note that for all models except for the three just mentioned, IPAR increases despite an increase in cloud cover (Fig. 4e, orange dots). This suggests that sea ice fraction, rather than cloud cover, is the most important factor in determining IPAR changes in this region within most models. As sea ice cover declines near the Antarctic continent within the models (Fig. S9), more light is able to reach the ocean surface, ultimately leading to increased IPAR and PP here.

While general agreement on the mechanisms driving 100-year phytoplankton changes among models is high, one noteworthy result is that there appear to be two distinct groups of models: one group with phytoplankton which are highly sensitive to changes in iron concentrations south of ∼ 40∘ S (consisting of GFDL-ESM2, CESM1-BGC, IPSL-CM5A, CMCC-CESM – see Fig. S16, for models where zonal PB or PP changes closely follow zonal iron changes) and a second group with phytoplankton which are less iron sensitive (NorESM1-ME, HadGEM2, GISS-E2, MPI-ESM) or do not include iron at all (CanESM2, MIROC-ESM, MRI-ESM1). Iron cycling within the ocean remains poorly characterized and is typically crudely parameterized (if at all) compared to the macronutrients. These models also differ considerably in many aspects of their treatment of iron including but not limited to the magnitude and location of sources (from both the atmosphere and the sediments), ligand dynamics, scavenging losses, and iron to carbon biomass ratios (J. K. Moore et al., 2013). It is out of the scope of this paper to assess all of these differences, but at first glance, it appears that the models with more complex iron cycling dynamics have phytoplankton that are more sensitive to iron changes. For example, the more iron-sensitive GFDL-ESM2, CESM1-BGC, and IPSL-CM5A models have variable iron to carbon ratios and include sedimentary sources of iron (however crudely parameterized) (Dunne et al., 2013; J. K. Moore et al., 2013; Aumont and Bopp, 2006), while the less iron-sensitive NorESM1-ME, HadGEM2, GISS-E2, MPI-ESM models do not (Assmann et al., 2010; Collins et al., 2011; Gregg, 2008). Models within the more iron-sensitive group tend to exhibit less well defined latitudinally banded 100-year phytoplankton changes, while the other models tend to exhibit a more obviously banded PB and PP change structure (see Figs. S1–2). These less iron-sensitive models also frequently display iron and phytoplankton changes of opposite signs south of 40∘ S (Fig. 4c, unboxed purple and green points; Fig. S16). In these cases, changes in light availability due to changes in MLD and IPAR are able to explain predicted phytoplankton trends (see Fig. S16, for models where zonal PB or PP changes closely follow zonal MLD and/or IPAR changes). Within the group of models with iron-sensitive phytoplankton, changes in physical variables altering light availability are also occurring, but their effects are much less pronounced because iron plays a more dominant role. As was discussed in Sect. 3.1, changes in MLD and IPAR in both groups of models are in turn driven by first-order changes in ocean–atmosphere dynamics associated with climate warming and an increasingly positive SAM index, such as westerly wind intensification, alterations to tropospheric stability and thermal structure (e.g. Ceppi et al., 2014; Kay et al., 2014), and poleward displacement of extratropical storm-tracks and associated clouds (e.g. Yin, 2005; Bender et al., 2012).

To get a wider sense of spatial agreement among models throughout the SO, we look at maps of intermodel consistency in projected SO phytoplankton trends and their proposed drivers across all 16 CMIP5 models with ocean biogeochemistry in Fig. 5 (complementary to Fig. 1). The maps in Fig. 5 detail the fraction of model realizations (via the bootstrap technique explained in Sect. 2.2) that predict a positive trend in the listed variable at each grid point. Thus, the closer the fraction to 1 at a given location, the greater the intermodel agreement on a positive trend at that point, and the closer the fraction to 0, the larger the intermodel agreement on a negative trend at that point (0.5 denotes the greatest amount of intermodel disagreement, where 50 % of model realizations predict an increasing trend and 50 % predict a decreasing trend). To also get a better idea of how well models agree with one another within each zonal band, Fig. 6 shows zonally averaged all-model mean projected trends (zonal averages of Fig. 1) and zonal band averaged intermodel agreement percentages (areal averages over each zonal band of Fig. 5, listed above each zonal band accompanied by an arrow indicating the direction of the trend agreed upon by the majority of model realizations). Only percentages for variables which are most important within each zonal band (as determined by Figs. 1–4) are listed and as such, represent a summary of the important drivers of projected phytoplankton change discussed here. Agreement among models is highest at the centre of each zonal band (Fig. 5), but decreases towards the edges due to offsets in the precise boundaries of water masses among the models. These slight offsets lower the zonal band-average agreement among models shown in Fig. 6, such that if one were able to perfectly compare water masses among models, consistency in predicted trends within each zonally banded biome would likely be even higher. Figure S17 complements Fig. 6 by showing zonally averaged all-model historical means and 100-year absolute changes in all variables of interest.

Within the subtropical (30 to 40∘ S) band, the majority of model realizations predict a decrease in both PB (64 %) and PP (62 %), accompanied by a highly consistent decrease in wintertime nitrate supply (77 %) (Figs. 5a–c, 6). This projected change agrees with the general expectation from previous theoretical and modelling studies that warming should stratify the water column, decrease macronutrient supply, and consequently lower biological productivity within the subtropics (e.g. Sarmiento et al., 2004b; Doney, 2006; Cabré et al., 2014). Within the transitional (40∘ S to 50∘ S) band, most of the model realizations predict an increase in PP (70 %) while only around half of the models predict an increase in PB (55 %) (Figs. 5a–b, 6). These predicted shifts are accompanied by a decrease in summertime MLD (71 %) and an increase in wintertime iron concentration (64 %) (Fig. 5c–d; Fig. 6). Because of a predicted poleward shift of the westerly winds in all of the models (Figs. 5h, S10), winds will weaken here, shoaling the MLD and prolonging the growing season by allowing phytoplankton to remain within the well-lit surface layers for longer. Thus, enhanced future phytoplankton populations within this transitional band are not unexpected. Within the subpolar (50 to 65∘ S) band, models are not as consistent in their predictions of phytoplankton changes compared with the other regions. The majority of model realizations predict an increase in PP (59 %), while 55 % predict a decrease in PB (Fig. 5a–b). Predicted changes in driving variables are somewhat more consistent within this region, however, with a decrease in summertime MLD predicted by 56 % of model realizations, a decrease in IPAR predicted by 71 %, and an increase in cloud cover predicted by 60 % (Figs. 5c, f, g, 6). With a projected poleward shift of the westerlies, cloud cover should increase (due to a concomitant shift in storm-track cloudiness and/or altered tropospheric stability with future warming) and MLDs should deepen as winds intensify within this band, both of which act to decrease phytoplankton populations, exactly as we see here. Within the Antarctic (south of 65∘ S) band, 76 % of model realizations predict an increase in PP, while 64 % predict an increase in PB, both of which are associated with projected increases in wintertime iron concentrations (72 %) and summertime light availability (59 %) (Figs. 5a–b, e–f, 6). This goes with our expectation that the melting of sea ice projected by the models will lead to higher amounts of light reaching the ocean surface and that intensified westerlies will bring a larger supply of upwelled iron to the surface in this region, both of which act to increase phytoplankton populations, just as we see here.