2.1 Satellite data

Our analysis focuses on the period 1998–2007. Monthly SeaWiFS data become inconsistent beginning in 2008. For study of interannual trends, avoiding the need to fill gaps in the record is desirable. For additional comparison and extension of the record, biomass estimated from MODIS for 2003–2015 is also presented, again selecting years for which all months are available. For both SeaWiFS and MODIS, biomass is estimated using the updated CbPM algorithm (Westberry et al., 2008). Additionally, we compare trends of modeled net primary productivity (NPP) to NPP from SeaWiFS estimated with both CbPM and the VGPM algorithms (Behrenfeld and Falkowski, 1997). All data were provided by the Ocean Productivity Group at Oregon State University (http://www.science.oregonstate.edu/ocean.productivity/index.php, SeaWiFS biomass downloaded 28 November 2016; MODIS biomass downloaded 24 January 2018; NPP downloaded 29 May 2018).

2.2 Regional hindcast model

The Massachusetts Institute of Technology General Circulation Model configured for the North Atlantic (MITgcm.NA) (Marshall et al., 1997a, b) is used. The model domain extends from 20^∘ S to 81.5^∘ N, with a horizontal resolution of $\mathrm{0.5}{}^{\circ }\times \mathrm{0.5}{}^{\circ }$ and a vertical resolution of 23 levels that have a thickness of 10 m at the surface and gradually become coarser to 500 m thickness intervals for depth levels deeper than 2200 m. NCEP/NCAR Reanalysis I daily wind, heat, freshwater and radiation fields from 1948 to 2009 force the model (Kalnay et al., 1996). To correct for uncertainties in air–sea fluxes, SST and SSS (sea surface salinity) are relaxed to monthly historical SST (Had1SSTv1.0, Rayner et al., 2003) and climatological SSS (Antonov et al., 2006) observations, on the timescale of 2 and 4 weeks, respectively (Ullman et al., 2009). To characterize subgrid-scale processes, the Gent–McWilliams (Gent and McWilliams, 1990) eddy parameterization, the K-profile parameterization boundary layer mixing schemes (Large et al., 1994), and Fox-Kemper et al. (2008) submesoscale physical parameterization are used. The phosphorus-based ecosystem is parameterized following Dutkiewicz et al. (2005), and with modest revisions by Bennington et al. (2009). This ecosystem has one zooplankton class and two phytoplankton classes (“large” diatoms and “small” phytoplankton). The biogeochemical model explicitly cycles phosphorus, silica and iron, and complete carbon chemistry is also included. This model is identical to the one presented in Breeden and McKinley (2016) and uses the same biogeochemical code as Bennington et al. (2009), Ullman et al. (2009) and Koch et al. (2009).

The coupled model has previously been shown to capture the timing and magnitude of the subpolar spring bloom chlorophyll and its variability, as observed by SeaWiFS (Bennington et al., 2009). Mixed layer depths, carbon system variables and nutrients are well simulated at Bermuda and in the northwest subpolar gyre (Ullman et al., 2009; Koch et al., 2009). As is common in this type of moderate-resolution model, productivity in the subtropics is too low (Bennington et al., 2009). Physical variability since 1948 is consistent with observations (Breeden and McKinley, 2016).

As in Breeden and McKinley (2016), the physical model was spun up for a 100-year period, with 1948–1987 repeated twice and then followed again by 1948–1967, for a total physical spin-up of 120 years. The biogeochemical model was then initialized using World Ocean Atlas phosphate concentrations and spun up for 10 years using 1948–1957 daily forcing. To avoid initialization shock, the model was then forced for 5 years with repeating 1948 fields before the 1948–2009 experiment started. Due to Had1SSTv1.0 fields only being available through 2009, this model integration ends in 2009. Future studies using Had1SSTv1.1, which extends beyond 2009, will require re-initialization and new spin-up integrations.

2.3 Phosphate diagnostics

To assess the processes modifying phosphate concentration, we employ phosphate diagnostics that quantify flux convergences (in mmol m⁻³ yr⁻¹) for net biological processes, vertical advection and diffusion, and horizontal advection and diffusion. These terms describe the tendency of each process at every time step during the model simulation, averaged to monthly for output (Ullman et al., 2009; Breeden and McKinley, 2016). For conciseness, the biological uptake term presented here is the sum of separate diagnostic terms for phosphate utilization by primary producers and remineralization that returns phosphate to the water column.

For analysis of mean and linear trends for 1998–2007, we use biological, vertical and horizontal diagnostic terms. Unfortunately, the biological diagnostics prior to 1998 were lost after simulations were completed. Thus, for correlations for 1949–2009, we use biomass in place of the biological diagnostics. This choice is supported by strong correlations ($R=-\mathrm{0.87}$ to −0.98) between biomass and the biological diagnostics in our three focus regions (defined below) for 1998–2007. Biomass and biological diagnostics have an opposite sign because phosphate is removed as biomass accumulates.

2.4 Light and nutrient limitation

As detailed in Dutkiewicz et al. (2005), model phytoplankton growth is limited by light and the most limiting nutrient. Limiting nutrients are phosphate (PO₄) and iron (Fe) for small phytoplankton and PO₄, Fe and silicate (SiOH₄) for large phytoplankton. There is no nitrogen cycle in the model, consistent with other ecological models of comparable complexity (Galbraith et al., 2010). The parameterization uses Michaelis–Menton ratios that tend to 0 as the resource becomes severely limiting to growth, and approach 1 when replete. A lower value indicates a greater stress, and thus the phytoplankton group with the larger half- saturation constant will be more limited for the same ambient nutrient or light concentration.

Specifically, maximum growth rates (${\mathit{\mu }}_{\max ,\mathrm{small}}=$ 1/1.3 d⁻¹, ${\mathit{\mu }}_{\max ,\mathrm{large}}=$ 1/1.1 d⁻¹) are reduced through multiplication by limitation terms. T_func modifies maximum growth based on temperature following Eppley (1972).

With half-saturation constants $I_{o,\mathrm{small}}=$ 15 W m⁻², $I_{o,\mathrm{large}}=$ 12 W m⁻², light limitation is

and for nutrients

For phosphate, X= PO₄, $K_{o,{\mathrm{PO}}_{\mathrm{4}},\mathrm{small}}=$ 0.05 mmol m⁻³ and $K_{o,{\mathrm{PO}}_{\mathrm{4}},\mathrm{large}}=$ 0.1 mmol m⁻³. For iron, X= Fe, $K_{o,\mathrm{Fe},\mathrm{small}}=$ 0.01 µmol m⁻³ and $K_{o,\mathrm{Fe},\mathrm{large}}=$ 0.05 µmol m⁻³. For large phytoplankton only, silicate limitation also applies, with $K_{o,{\mathrm{SiOH}}_{\mathrm{4}},\mathrm{large}}=$ 2 mmol m⁻³. Because of their higher half-saturation constant for phosphate, modeled large phytoplankton are more phosphate stressed than small phytoplankton. In contrast, the higher light half-saturation makes small phytoplankton experience greater light stress. Due to high levels of aeolian dust deposition in the North Atlantic, parameterized here with the imposition of climatological fields from Mahowald et al. (2003), iron is never limiting in our study area and is not further discussed.

For this analysis, monthly mean light and nutrient fields are used to calculate limitation terms for light and nutrients for each phytoplankton type.

2.5 Analysis

Throughout the study, annual averages over the top 100 m are used. This depth is selected because it is a reasonable approximation for both the euphotic zone and the Ekman layer, and is a computationally efficient choice consistent with previous work (Williams et al., 2000, 2014; Long et al., 2013). For analysis of light limitation, however, it is important to consider that deep mixing will move mixed layer phytoplankton to substantially below 100 m (Sverdrup, 1953). This effect would be poorly captured if light limitation terms were averaged only over the surface 100 m. The more appropriate choice, used here, is to use either the depth of the monthly mixed layer or 100 m, whichever is deeper. Light limitation is calculated monthly in this way and then annually averaged. For consistency, we apply the same averaging approach for nutrient limitation. However, since nutrients are homogenized by deep mixing, results for nutrient limitation are not substantially different from this calculation using a strict 100 m average. Limitation terms are not biomass-weighted.

For physical comparisons, mixed layer depth is calculated using monthly density fields and a criteria of 0.03 kg m⁻³ increase above the surface density. The barotropic streamfunction is calculated using a north-to-south integration of the full depth zonal velocity fields (Breeden and McKinley, 2016). To find the minimum barotropic streamfunction of the subpolar gyre, the minimum within a region 50–65^∘ N, 60–30^∘ W is used. A preliminary comparison of nutrient flux variability to climate indices uses the winter (DJFM) East Atlantic pattern (http://www.cpc.ncep.noaa.gov/data/teledoc/ea.shtml, downloaded 15 December 2017) and the winter North Atlantic Oscillation (Hurrell and NCAR, 2017).

This analysis is based on annual mean fields for both the observations and the model. A 3-month lag of the biology diagnostics and biomass fields after physical diagnostics and other physical fields is employed to account for the maximum physical forcing occurring in the winter prior to the spring bloom. Thus, annual mean physical fields are averaged from October of the prior year to September of the year in question. The use of 0, 1, 2 or 4 month lags leads to lower correlations, but does not substantially modify results. Biological fields are January to December averages.

To compare directly to the 10-year period of prime SeaWiFS observations, our primary focus is on linear trends over 1998–2007, with significance bounds set at p<0.05 (95 %). To complement this analysis with a consideration of interannual variability across the full model experiment (1948–2009), we also consider correlations of physical and biogeochemical time series calculated as area-weighted averages over three selected regions (defined below), and then linearly detrended prior to correlation analysis. Because of the aforementioned biological lag, the time frame for correlations becomes 1949–2009.

3.1 Model comparison to observations

The simulation captures the magnitude of mean 1998–2007 subpolar biomass reasonably in comparison to the satellite-based observations (Fig. 1a, b). The detailed spatial pattern of biomass is impacted by the North Atlantic Current extension being too diffuse and too directly east–west (i.e., not turning to the northeast as it should at about 25^∘ W), as is common in models of this resolution (Williams et al., 2014). The maximum of biomass is displaced to the east. Also, subtropical biomass is too high in the Gulf Stream extension, but otherwise too low in the remainder of the basin, and thus the gradient from south to north in the model from 35 to 50^∘ N is too sharp (Bennington et al., 2009).

Despite these imperfections, the model captures well the pattern and magnitude of statistically significant biomass trends north of 40^∘ N over 1998–2007 (Fig. 1c, d). In both observations and the model, biomass declines to the east of 30^∘ W from 40 to 50^∘ N and 35^∘ W from 50 to 60^∘ N, while it increases to the west. For simplicity, we refer to this boundary as 30–35^∘ W in our discussion. Model trends are slightly weaker than the observed trends, but the coherent regions of statistically significant change are of similar size. Declines to the east occur in two regions in both model and observations, one in the northeast and one in the southeast. Consistent with the mean biomass structure, simulated biomass trends are not in exactly the same locations as observed, but are displaced about 5^∘ to the south in the southeast and northwest, and 5^∘ to the south and 5^∘ west for the northeast region. Comparison to net primary productivity (NPP) from SeaWiFS estimated with both the CbPM algorithm and older VGPM algorithm indicate comparable changes to in biomass, though trends in the northeast are not significant for NPP (Fig. S1 in the Supplement).

In both observations and models, the magnitudes of these changes are large in comparison to the mean. In the declining regions where mean biomass is 15–25 mgC m⁻³ (Figs. 1, 2, S2), trends of −0.5 to −1.5 mgC m⁻³ yr⁻¹ over 10 years lead to changes of 30 %–50 %. In the increasing region to the west, changes are of similar magnitude. To focus our analysis, we select three regions in the model that capture these significant biomass changes (Fig. 1d). We will use these regions for discussion and for averaging of biogeochemical and physical terms. In the northeastern subtropical gyre, or intergyre (Follows and Dutkiewicz, 2002), lies our southeast (SE) region, just south of the physical separation between the subpolar and subtropical gyre based on the barotropic streamfunction (Sect. 3.4). The SE region is bounded between 30–15^∘ W and 40–50^∘ N. The northeast (NE) region lies in the eastern subpolar gyre to the southeast of Iceland, 35–20^∘ W and 55–60^∘ N. The northwest (NW) region is south of Greenland at 35–20^∘ W and 50–60^∘ N. Regional mean changes in biomass from SeaWiFS (in the model) are −19 % (−17 %) in the SE region and −15 % (−10 %) in the NE. To the west of 30–35^∘ W in the NW region, regional mean changes are +6 % (+9 %).

Figure 2Annual anomalies of surface ocean biomass for SeaWiFS (1998–2007, red), MODIS (2003–2015, blue) and our model (1998–2009, 0–100 m, black): (a) SE region, (b) NE region and (c) NW region. The corresponding monthly time series is shown in Fig. S2.

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In these three regions, annual anomalies of simulated biomass are compared to estimates from the SeaWiFS (1998–2007) and MODIS (2003–2015) satellites (Fig. 2). Monthly biomass time series are presented in Fig. S2. In all regions, simulated biomass anomalies are quantitatively different from the observations to a similar degree that the observations differ from each other. In the SE region, the shift from positive biomass anomalies before 2004 to negative anomalies after 2004 is found in SeaWiFS and the model, and MODIS indicates a return to positive anomalies after 2010 (Fig. 2a). Of the three regions, this is the one where annual changes in the model are significantly correlated to those in SeaWiFS (R=0.79, p<0.05), despite the small sample size (n=10). Linear trends for 1998–2017 in SeaWiFS and the model are the same, −0.41 mgC m⁻³ yr⁻¹; however, the observations are better explained by this trend (R²= 0.76 for SeaWiFS, R²= 0.35 for model). In the NE region, higher frequency variability is suggested, with mostly positive anomalies over 1998–2003 and negative anomalies from 2005 to 2009 (Fig. 2b). In this region, the linear trend for 1998–2007 in SeaWiFS is −0.26 mgC m⁻³ yr⁻¹ (R²=0.15) and −0.34 mgC m⁻³ yr⁻¹ (R²=0.50) in the model. The spatial displacement between the modeled and observed anomalies (Fig. 1c, d) is not accounted for with the regions used for Fig. 2b, but these comparisons do not substantially change if the averaging region for the observations in the NE is shifted 5^∘ north and 5^∘ east (not shown). In the NW region, positive anomalies of comparable magnitude dominate in 2003–2008, the time frame over which the three records coincide (Fig. 2c). Negative anomalies are largely found both before and after. In the last 3 MODIS years, positive anomalies return to the NW region. For 1998–2007, the linear trend in SeaWiFS is +0.22 mgC m⁻³ yr⁻¹ (R²=0.22) and for the model +0.23 mgC m⁻³ yr⁻¹ (R²=0.55). Having demonstrated that this model reasonably captures the patterns and magnitudes of biomass change, we now use the model to explain the mechanistic drivers in all three regions over the SeaWiFS period, 1998–2007.

Figure 3Phosphate: (a) World Ocean Atlas (Garcia et al., 2006), (b) 0–100 m modeled phosphate, (c) 0–100 m modeled phosphate trend 1998–2007. In (c), significant trends are marked with a black contour and the three focus regions are outlined in red.

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3.2 Nutrient changes

Modeled anomalies are not due to zooplankton top-down pressure on biomass, as evidenced by zooplankton trends that are positively correlated with biomass trends (Fig. S3). Thus nutrient and light, the bottom-up drivers in this model that change in a manner that drives biomass changes consistent with observations (Fig. 1), are the focus of this analysis. The model captures the large-scale pattern of the phosphate field well, but mean values are 10 %–20 % too low across most of the subpolar gyre (Fig. 3a, b). Changes in the nutrient field could drive these observed and modeled changes, and as temporally resolved large-scale nutrient datasets are not available, the model alone allows us to evaluate nutrient trends (Fig. 3c). Modeled nutrient concentrations decline significantly over 1998–2007 across most of the region north of 50^∘ N. The pattern suggests these changes are important to the declines of biomass in the SE and NE regions. However, there is no increase in phosphate in the NW region where biomass was observed to increase.

Figure 4Surface ocean small and large phytoplankton biomass: (a) 0–100 m modeled large phytoplankton biomass, (b) 0–100 m modeled small phytoplankton biomass, (c) large phytoplankton trend 1998–2007 and (d) small phytoplankton trend 1998–2007. In (c) and (d), significant trends are marked with a black contour and the three focus regions are outlined in red.

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Figure 5Terms for limitation: (a) phosphate, large phytoplankton (Eq. 3); (b) light, small phytoplankton (Eq. 2); (c) 1998–2007 trend in phosphate limitation; and (d) 1998–2007 trend in light limitation. All are unitless. In (c) and (d), significant trends are marked with a black contour and the three focus regions are outlined in red.

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3.3 Trends of light and nutrient limitation

To better understand drivers of simulated biomass trends, a next step is to decompose the biomass trends into those occurring in the small and the large phytoplankton (Fig. 4). With regard to the mean, in the open waters of the North Atlantic, simulated large phytoplankton have a greater contribution to the total biomass in the north and west (Fig. 4a), while small phytoplankton are dominant to biomass throughout the basin and particularly in the south and east (Fig. 4b). Trends in simulated small phytoplankton contribute most to total biomass change (Fig. 1d) in the SE and NW regions, while large phytoplankton trends are more important in the NE region (Fig. 4c, d).

Phosphate limitation for large phytoplankton has a strong gradient of being more limiting in the south and east to less limiting in the northwest (Fig. 5a), while light limitation for small phytoplankton has largely a south-to-north gradient from less to more limiting (Fig. 5b). Trends over 1998–2007 in the model limitation terms illustrate that the SE and NE declines in simulated biomass are spatially coherent with enhanced phosphate limitation (Fig. 5c), while the NW increase in biomass is spatially coherent with regions experiencing relief of light limitation (Fig. 5d). As shown in Fig. S2, the mean and trends for light limitation for large phytoplankton and phosphate limitation for small phytoplankton have nearly identical patterns.

Table 1Correlations of phosphate and light limitation for small phytoplankton to large and small biomass, 1949–2009. For conciseness, shown here are only small phytoplankton limitation terms, but since these are ratios calculated from identical fields, the correlations are very similar large phytoplankton (Table S1). Bold indicates statistical significance (p<0.05). Detrending is applied prior to correlation analysis.

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This distinction between the dominant limitations driving simulated biomass change in the east and west is borne out with detrended interannual correlations over the full model period, 1949–2009 (Table 1). In the SE region, phosphate limitation is strongly correlated with both small ($R_{\mathrm{SE}(\mathrm{small},{\mathrm{PO}}_{\mathrm{4}})}=\mathrm{0.68}$) and large phytoplankton ($R_{\mathrm{SE}(\mathrm{large},{\mathrm{PO}}_{\mathrm{4}})}=\mathrm{0.74}$), while light limitation is anti-correlated with biomass, i.e., less biomass occurs with more light, clearly illustrating that light is not the driving limitation. With respect to limitation terms in the NE region, the only significant correlation for large phytoplankton is to nutrient limitation ($R_{\mathrm{NE}(\mathrm{large},{\mathrm{PO}}_{\mathrm{4}})}=\mathrm{0.31}$). Thus, the large phytoplankton that quantitatively dominate the 1998–2007 biomass decline (Fig. 4d) due to nutrient limitation (Fig. 5c) also vary by a similar mechanism over the full model experiment.

Figure 6Barotropic streamfunction: (a) 1998–2000 mean and (b) 2005–2007 mean. The zero streamfunction contours between 55 and 15^∘ W for each period (bold black) and for the 1998–2007 mean (white) are marked. See Fig. S5 for map of 1998–2007 trend.

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In the NW region, the 1998–2007 biomass trend is dominated by small phytoplankton (Fig. 4d) via light limitation (Fig. 5d), and these relationships also hold for the full model experiment. Small phytoplankton light limitation is positively correlated with small phytoplankton biomass ($R_{\mathrm{NW}(\mathrm{small},\mathrm{light})}=\mathrm{0.61}$), while small phytoplankton biomass is reduced when more phosphate is available ($R_{\mathrm{NW}(\mathrm{small},{\mathrm{PO}}_{\mathrm{4}})}=-\mathrm{0.50}$, Table 1). Though large phytoplankton have the opposite sensitivities ($R_{\mathrm{NW}(\mathrm{large},\mathrm{light})}=-\mathrm{0.63}$, $R_{\mathrm{NW}(\mathrm{large},{\mathrm{PO}}_{\mathrm{4}})}=\mathrm{0.83}$), they are a smaller portion (40 %) of the total biomass (Fig. 4a, b) and have a lesser role in total biomass changes (Fig. 4c).

In the model, silicate is also limiting to large phytoplankton and its limitation also becomes more intense over 1998–2007 to the north of 50^∘ N (Fig. S4f). Yet, variability in silicate limitation is highly correlated to variability of phosphate limitation in the NW and NE areas for 1949–2009 ($R_{\mathrm{NE}\left({\mathrm{PO}}_{\mathrm{4}},{\mathrm{SiOH}}_{\mathrm{4}}\right)}=\mathrm{0.91}$, $R_{\mathrm{NW}\left({\mathrm{PO}}_{\mathrm{4}},{\mathrm{SiOH}}_{\mathrm{4}}\right)}=\mathrm{0.83}$, Table S1 in the Supplement). Due to these high correlations and the fact that large phytoplankton are only dominant to biomass trends in the NE region (Fig. 4c), the remaining analysis addresses only phosphate fluxes. For completeness, 1998–2007 light and silicate limitation trends for large phytoplankton and phosphate limitation for small phytoplankton are shown in Fig. S2, and 1949–2009 correlations in the three regions are given in Table S1.

Figure 7Maximum mixed layer depths for the (a) 1998–2000 mean and (b) 2005–2007 mean. Time series of monthly mixed layers for the (c) SE region, (d) NE region and (e) NW region.

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3.4 Physical changes and their impacts on light and nutrient limitation

Significant physical changes in the subpolar gyre influence the simulated nutrient and light fields. The model barotropic streamfunction experiences a positive change from a minimum value of −41 Sv for 1998–2000 to −28 Sv for 2005–2007 (Figs. 6, S5). With this anomaly, the zero line of the streamfunction shifts several degrees north at 45–40^∘ W and more modestly to the north in the east (bold black contours in Fig. 6a and b). The North Atlantic Current (NAC) flows along this contour, indicating a northward shift of the NAC.

Figure 8Phosphate diagnostics: (a) vertical, (b) horizontal, (c) net physical and (d) biological flux convergence (mmol m⁻³ yr⁻¹) averaged over 0–100 m. Biological is negative because biomass removes phosphate from the surface ocean. The three focus regions are outlined in red in each panel.

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Consistent with the weakening of the subpolar gyre, mixed layers shoal substantially, particularly to the west of 30–35^∘ W (Fig. 7a, b). A dramatic shoaling of maximum mixed layers is found in the NW region, going from almost 1200 m to less than 400 m (Fig. 7e, Våge et al., 2008). This shoaling explains the strong decline in light limitation in the NW region. There is modest shoaling of mixed layers in the NE region (Fig. 7d) and there is no significant trend in the SE region (Fig. 7c). Shoaling in the NE could contribute to the reduction in phosphate availability and reduced biomass. However, the lack of mixed layer depth change in the SE suggests that less vertical mixing is not the dominant driver of reduced biomass here.

Figure 9Phosphate diagnostics 1998–2007 annual time series: 0–100 m flux convergence (mmol m⁻³ yr⁻¹) for the (a) SE region, (b) NE region and (c) NW region.

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3.5 Phosphate diagnostic analysis

To fully assess the three-dimensional physical drivers of phosphate supply to the NE and SE regions, we employ the phosphate diagnostics that quantify flux convergences. With regard to the mean for 1998–2007 across the northern North Atlantic, vertical advection and diffusion supply phosphate to the euphotic zone (Fig. 8a), with the supply being much stronger in the region of the deepest mixed layers (Fig. 7). Horizontal advection and diffusion strongly diverges the converging vertical flux (Fig. 8b), leading to strong negative fluxes (divergence) coincident with strongly positive vertical fluxes. The horizontal flux divergence centered at about 30–35^∘ W leads to positive horizontal fluxes (convergence) to the east and west. As the sum of the vertical and horizontal components is net positive (Fig. 8c), the mean three-dimensional advection and diffusion supplies net phosphate to the subpolar gyre. The pattern of this supply is strongly influenced by both vertical and horizontal processes. Biological processes remove the physically supplied phosphate from the surface ocean (Fig. 8d).

Figure 10Phosphate diagnostics 1998–2007 trends: 0–100 m flux convergence trend (mmol m⁻³ yr⁻²) for (a) vertical, (b) horizontal, (c) net physical, and (d) biological flux convergences. Positive biological trends are consistent with negative biomass trends because less phosphate is removed as less biomass is formed. Significant trends are marked with a black contour and the three focus regions are outlined in red in each panel.

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To east of 30–35^∘ W, horizontal and vertical phosphate flux convergences are comparable in magnitude and both supply nutrients to the surface (Fig. 8, 9). In the SE region, mean 1998–2007 vertical advection and diffusion supplies 0.13 mmol m⁻³ yr⁻¹ while horizontal advection and diffusion supplies 0.07 mmol m⁻³ yr⁻¹, together supporting biological utilization of −0.20 mmol m⁻³ yr⁻¹ (Fig. 9a). In the NE region, the mean vertical supply is 0.24 mmol m⁻³ yr⁻¹ while horizontal fluxes supply 0.08 mmol m⁻³ yr⁻¹, and thus a mean biological utilization of −0.32 mmol m⁻³ yr⁻¹is supported (Fig. 9b). The net convergence of vertical and horizontal fluxes in these regions can be contrasted with the NW region where the mean vertical flux converges 0.33 mmol m⁻³ yr⁻¹, and from this the horizontal flux diverges about 25 % (−0.08 mmol m⁻³ yr⁻¹) and biology diverges the remainder (−0.24 mmol m⁻³ yr⁻¹, Fig. 9c). In all three regions, note that the variability of both horizontal and vertical flux convergences are of magnitudes comparable to the biological flux variability (Fig. 9).

For 1998–2007, simulated trends in the supply and removal of phosphate indicate a large decrease in supply via vertical fluxes to the west of 30–35^∘ W (Fig. 10a) and a corresponding strong reduction in the horizontal divergence of phosphate, a positive anomaly (Figs. 9c, 10b). To the west of 30–35^∘ W, these opposing trends of the vertical and horizontal flux convergence largely negate each other. However, to the east of 30–35^∘ W there are weak and mostly negative tendencies in the vertical terms and significant negative trends in the horizontal terms. Thus, the net physical phosphate supply in the eastern subpolar gyre has an overall negative trend, albeit only large enough to be formally statistically significant in parts of the SE region (Fig. 10c). The pattern of reduced phosphate supply is consistent with the pattern of significant reduction in biomass (Fig. 1d) and significant positive tendencies in the biological diagnostic, indicating reduced phosphate utilization by phytoplankton (Fig. 10d). In summary, the model indicates that from 1997 to 2008, reduced vertical convergence of nutrients to the west of 30–35^∘ W led to less horizontal convergence of nutrients to the east of 30–35^∘ W, and thus less phosphate available for biological production. In this model, this mechanism is sufficient to explain biomass changes consistent with SeaWiFS-observed declines in biomass in the eastern subpolar gyre (NE region) and northeastern subtropical gyre (SE region).

Long-term (1949–2009) correlations between physical diagnostic terms and biomass support the conclusion that variability in horizontal flux convergence is important to modeled biomass interannual variability to the east of 30–35^∘ W (Table 2). In both the SE and NE regions, horizontal flux convergence is significantly correlated to biomass ($R_{\mathrm{SE}(\mathrm{Biomass},\mathrm{Horiz})}=\mathrm{0.44}$, $R_{\mathrm{NE}(\mathrm{Biomass},\mathrm{Horiz})}=\mathrm{0.48}$), suggesting that the 1998–2007 relationships are indicative of interannual behavior over the long-term, wherein reduced horizontal nutrient convergence leads to reduced biomass. For the SE region in the long term, vertical fluxes have also a significant correlation ($R_{\mathrm{SE}(\mathrm{Biomass},\mathrm{Vert})}=\mathrm{0.63}$), indicating that longer term interannual change in biomass in this region is determined by variability in both horizontal and vertical flux convergences. In the NW region, biomass and horizontal flux convergence is also positively correlated ($R_{\mathrm{NW}(\mathrm{Biomass},\mathrm{Horiz})}=\mathrm{0.69}$), but this appears to be an indirect relationship. As light limitation is relieved, biomass increases, and at the same time vertical convergence of phosphate is reduced (Fig. 10a) and there is a positive anomaly in the horizontal divergence (Fig. 10b). Consistent with this interpretation, vertical and horizontal convergence are strongly anti-correlated in the NW region ($R_{\mathrm{NW}(\mathrm{Horiz},\mathrm{Vert})}=-\mathrm{0.76}$).

The impact of the physical drivers discussed earlier in this section on 1949–2009 biomass variability varies by study region. For the SE region, where biomass is positively driven by both horizontal and vertical nutrient flux convergence, biomass declines with positive anomalies of the minimum barotropic streamfunction of the subpolar gyre ($R_{\mathrm{SE}(\mathrm{Biomass},\mathrm{PsiMin})}=-\mathrm{0.37}$, Table 2), consistent with 1997–2008 relationships. However, the minimum barotropic streamfunction is not itself correlated to either horizontal or vertical flux convergence. Vertical supply is not a significant driver for 1997 to 2008 changes, but for the longer term, vertical nutrient fluxes decrease with shallower mixed layers (a negative anomaly) and warmer temperatures ($R_{\mathrm{SE}(\mathrm{MLD},\mathrm{Vert})}=\mathrm{0.66}$, $R_{\mathrm{SE}(\mathrm{SST},\mathrm{Vert})}=-\mathrm{0.64}$).

For both the NE and NW regions, correlations between changing minimum barotropic streamfunction (Fig. 6), shoaling mixed layers (Fig. 7), and horizontal and vertical nutrient convergences (Fig. 10) for 1949–2009 are generally weak and, in fact, opposite in sign to the relationships for the SeaWiFS period. For 1998–2007, the minimum barotropic streamfunction experienced a positive anomaly, mixed layers shoaled and horizontal fluxes declined in the NE region. For 1949–2009, positive anomalies of the minimum barotropic streamfunction are, instead, weakly associated with increased horizontal nutrient fluxes ($R_{\mathrm{NE}(\mathrm{PsiMin},\mathrm{Horiz})}=\mathrm{0.25}$). At the same time, shallower mixed layers (a negative anomaly) are associated with decreased vertical fluxes and increased horizontal fluxes ($R_{\mathrm{NE}(\mathrm{MLD},\mathrm{Vert})}=\mathrm{0.52}$, $R_{\mathrm{NE}(\mathrm{MLD},\mathrm{Horiz})}=-\mathrm{0.42}$). In the NW region, light limitation is clearly the driver of biomass changes on both timescales (Figs. 1, 4, Table 1), but large negative anomalies of vertical fluxes and positive anomalies of horizontal fluxes also occur as mixed layers shoal over 1997–2008 (Figs. 9, 10). However, for 1949–2009 in the NW, the reverse is found; vertical flux convergence increases and horizontal nutrient flux convergence decreases coincident with shallower mixed layers ($R_{\mathrm{NW}(\mathrm{MLD},\mathrm{Vert})}=-\mathrm{0.33}$, $R_{\mathrm{NW}(\mathrm{MLD},\mathrm{Horiz})}=\mathrm{0.46}$). Long-term correlations of physical changes to nutrient fluxes in the two subpolar regions differ from those occurring with 1998–2007 trends, consistent with the weak long-term correlations that explain no more than 30 % of the variance. The lack of consistent associations between biomass and physical variability over both timescales illustrates the complexity of the system and makes clear that relationships revealed by relatively short-lived observing systems are not necessarily representative of the long term.

Table 2Correlations of biomass to physical drivers and horizontal and vertical phosphate flux convergence, 1949–2009. The minimum barotropic streamfunction is found within 50–65^∘ N, 60–30^∘ W; maximum mixed layer depth (MLD) and sea surface temperature (SST) are area-weighted averages for each of the three averaging regions. Bold indicates statistical significance (p<0.05). Detrending is applied prior to correlation analysis.

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