Subtropical Gyre Nutrient Cycling in the Upper Ocean: Insights From a Nutrient‐Ratio Budget Method

We use a nutrient‐ratio budget method to investigate the relative importance of different nutrient source and sink terms at time‐series Station ALOHA and Bermuda Atlantic Time‐series Study (BATS) in the North Pacific and North Atlantic subtropical gyres, respectively. At mean state conditions over annual and multi‐year time scales, vertical phosphate ( PO43– ${\mathrm{P}\mathrm{O}}_{4}^{3\mbox{--}}$ ) supply from the subsurface accounts for ∼60% of the total phosphorus supply at both sites. Dissolved organic matter transport and zooplankton excretion are more important phosphorous export pathways than sinking particles at Station ALOHA and BATS. The nutrient‐ratio budget approach provides quantitative, observation‐based constraints on nutrient sources and sinks in the surface ocean, which helps improve our understanding of the biological carbon pump in oligotrophic oceans.

nutrients has been proposed as another important supply mechanism in the oligotrophic subtropical gyres (e.g., Abell et al., 2000;Letscher et al., 2016;Lomas et al., 2010;Mahaffey et al., 2004;Reynolds et al., 2014). The relative importance of each nutrient supply mechanism and the associated impact on exported matter N/P has been difficult to quantify observationally, however.
A budget method, based on ratios of inorganic nutrient  , NO − 3 and dissolved inorganic carbon) supply, has been used to estimate the C/N/P ratio of organic matter exported from the surface ocean in the Pacific Ocean (Quay, 2021). We expand on this work by including the input and output of dissolved organic nutrients (e.g., Abell et al., 2000;Hopkinson & Vallino, 2005) and the export of dissolved nutrients (inorganic and organic) through zooplankton excretion (Hannides et al., 2009;Steinberg et al., 2002). The steady state framework of our budget method dictates that the N/P ratio of all dissolved nutrient sources to the mixed layer (ΔNO 3 /ΔPO 4 , ΔDON/ΔDOP), supplied either vertically or laterally, should equal the N/P ratio of all nutrient sinks (sinking particles, dissolved organic matter (DOM) transport, zooplankton excretion) from the mixed layer. In the subtropical gyres, nitrogen fixation is an important source of nitrogen (Böttjer et al., 2017;Karl et al., 1997) and needs to be incorporated into the budget method. The advantage of a "ratio" budget is that it does not require nutrient flux estimates, which typically carry large uncertainties. The nutrient-ratio budget method provides quantitative constraint on the relative importance of nutrient sources and sinks when the source or sink terms are characterized by a distinct N/P ratio.

Nutrient Data
Nutrient observations (dissolved, particulate, and sediment trap) used in this study come from time-series Station ALOHA (22.8°N, 158.0°W) and the Bermuda Atlantic Time-series Study (BATS; 31.6°N, 64.2°W) (Figure 1) (Karl et al., 2021;Lomas et al., 2013). The annual mean N/P ratio of sinking particles (excluding N/P ≥ 100) from the shallowest sediment trap (150 m) at Station ALOHA and BATS is calculated as an integrated N/P ratio over the course of each year, weighted by the particulate P flux. The multi-year mean N/P ratio of sinking particles (Sinking N/P) is computed as the mean of all annual mean N/P ratios, weighted by the number of sediment trap flux observations in each year. Likewise, the multi-year mean surface N/P ratio of suspended particles (Suspended N/P) is calculated as the mean of all annual mean N/P ratios (0-150 m), weighted by the number of suspended particle observations in each year. Additional data sources include NO − 3 and PO 3-4 data from World Ocean Atlas (WOA18) monthly climatology (Garcia et al., 2018), and DON and DOP observations from cruises near Station ALOHA and BATS (Abell et al., 2000;Cavender-Bares et al., 2001;Church et al., 2008;Torres-Valdés et al., 2009) (Figure 1). Figure 1. Location of Station ALOHA and BATS (cyan pentagrams) and cruise tracks of dissolved organic nutrients measurements superimposed on surface nitrate concentrations from the WOA18 annual climatology (Garcia et al., 2018). Coordinates in the North Pacific are from Abell et al. (2000) (diamonds) and COOK-BOOK cruises (Church et al., 2008) (squares). North Atlantic data are from Cavender- Bares et al. (2001) (CB;circles) and Torres-Valdés et al. (2009) (36N;triangles). Regions of WOA18 nutrient data used to calculate surface lateral supply ratios are highlighted with four green boxes that are 30° × 5° and twenty 1-degree latitude or longitude bands.

Nutrient-Ratio Budget Method
The relative importance of external N sources (N src ) to the N export flux (N exp ) can be estimated by combining the N and P budgets for the surface ocean (Quay, 2021) where N src /N exp is the fraction of exported organic nitrogen supported by external N sources to the surface ocean, (N/P) sup is the dissolved N and P nutrient supply ratio to the surface ocean, and (N/P) exp is the N/P ratio of exported organic matter from the surface ocean.
The dissolved nutrient supply term is further decomposed into vertical (v) and lateral (l) components. As in Quay (2021), the vertical nutrient supply (flux) ratio from the subsurface, (ΔNO 3 /ΔPO 4 ) v , is estimated from the slope of NO − 3 to PO 3-4 data between the mean mixed layer depth (MLD) and 300 m for each year of observations at Station ALOHA and BATS. Robust regression is used to minimize the influence of outliers (robustfit in MATLAB). The vertical nutrient supply ratio incorporates the influence of preferential P remineralization in the subsurface. The multi-year mean (ΔNO 3 /ΔPO 4 ) v between 1988 and 2020 is averaged from the annual vertical inorganic supply ratios ( Figure S1 in Supporting Information S1). The sensitivity of (ΔNO 3 /ΔPO 4 ) v to the depth interval used for the regression is discussed in Text S1 in Supporting Information S1. The steady-state assumption is supported by the lack of significant changes in the N/P of annual vertical supply and sinking particles with time using all data available in the past 30 years at Station ALOHA and BATS (p > 0.05; Figure S1 in Supporting Information S1). The mean lateral nutrient supply ratio, (ΔNO 3 /ΔPO 4 ) l , is calculated from the slope of NO − 3 to PO 3-4 within the annual mean MLD using WOA18 monthly climatology data (Garcia et al., 2018) across specified meridional (30° latitude × 5° longitude) and zonal (5° latitude × 30° longitude) transects centered at Station ALOHA and BATS ( Figure S2 in Supporting Information S1). Each transect is divided into five 1-degree longitude or latitude bands to estimate the variability of lateral supply ratios meridionally or zonally, respectively. Concurrent DON and DOP measurements near the time-series stations are limited (Hansell et al., 2021;Knapp et al., 2021). In the North Atlantic, we use observations from individual cruises (N = 5) to calculate the slope of the DON to DOP within the annual mean MLD across meridional (26-41°N and 62-71°W; Cavender- Bares et al., 2001) and zonal (35-38°N and 8-75°W; Torres-Valdés et al., 2009) transects to estimate lateral supply ratios, (ΔDON/ΔDOP) l , at BATS ( Figure 1). In the North Pacific, we use DON and DOP observations from three cruises between 10 and 45°N along 152-158°W (Abell et al., 2000), and between 24-55°N along 152-157°W (Church et al., 2008) to estimate the meridional lateral organic nutrient supply ratio at Station ALOHA ( Figure 1). We were unable to find cruise data appropriate for determining the zonal (ΔDON/ΔDOP) l ratio for Station ALOHA. The vertical supply of semilabile DON and DOP from the subsurface is minimal Mahaffey et al., 2004) and not considered in our budgets. Surface ocean N and P budgets. Nutrient supply (sup) and external N source (src) terms: vertical and lateral supply of dissolved inorganic and organic N and P; nitrogen fixation and atmospheric (atm.) deposition. Nutrient export (exp) terms: sinking (Sinking) and suspended (Suspended) particles; exported dissolved organic matter (DOM); and zooplankton (Zoo.) excretion.

N/P of Nutrient Supply
The mean vertical inorganic nutrient supply ratios (ΔNO 3 /ΔPO 4 ) v at Station ALOHA and BATS are 14.7 ± 0.6 and 19.6 ± 5.2, respectively ( Figure 3 and Figure S1 in Supporting Information S1). The lateral inorganic nutrient supply ratios (ΔNO 3 /ΔPO 4 ) l are much smaller than the vertical ratios ( Figure S2 in Supporting Information S1). Near Station ALOHA, the lateral surface transport comes mainly from the equatorial region to the north (Abell et al., 2000;Quay & Stutsman, 2003). A meridional (ΔNO 3 /ΔPO 4 ) l of 1.6 ± 0.6 is estimated using WOA18 nutrient data between 7-22.5°N and 155.5-160.5°W ( Figure S3 in Supporting Information S1). Near BATS, the largest lateral surface transport comes from the north (Palter et al., 2011;Siegel & Deuser, 1997;Williams & Follows, 1998). A meridional (ΔNO 3 /ΔPO 4 ) l of 5.3 ± 0.5 is estimated between 15-45°N and 62-67°W ( Figure  S2 in Supporting Information S1). We hereafter refer to the lateral supply ratio as that estimated from meridional (ΔNO 3 /ΔPO 4 ) l terms at both locations. These estimates are likely an upper limit of (ΔNO 3 /ΔPO 4 ) l since lateral gradients into the subtropics are generally largest near the coastal margins (McGillicuddy Jr. et al., 2003;Williams & Follows, 1998;Williams et al., 2011) and PO 3-4 concentrations in the subtropical gyre compiled by the World Ocean Atlas are higher compared to observations derived from high-sensitivity methods .
Semilabile DON and DOP transported from coastal regions into the interior ocean has been identified as a potential nutrient source for the oligotrophic gyres (e.g., Abell et al., 2000;Letscher et al., 2016;Lomas et al., 2010;Mahaffey et al., 2004;Reynolds et al., 2014). Abell et al. (2000) estimated the net supply flux of DON and DOP into the NPSTG to be 20 ± 2 mmol N and 4.4 ± 1.0 mmol P m −2 yr −1 , respectively, which yields a meridional (ΔDON/ΔDOP) l supply ratio of 4.5 ± 2.4 from the Equatorial region to Station ALOHA. The meridional ratio is 3.4 ± 1.6 estimated using DON and DOP data from the COOK-BOOK cruises (Church et al., 2008). We therefore use the average meridional ratio of 4.0 ± 2.9 for Station ALOHA. Near BATS, the lateral (ΔDON/ΔDOP) l supply ratio is 6.7 ± 4.4 meridionally (Cavender-Bares et al., 2001) and 6.9 ± 1.9 zonally (Torres-Valdés et al., 2009) ( Figure S4 in Supporting Information S1). All N/P supply (N/P) sup and export (N/P) exp terms in the surface ocean at Station ALOHA and BATS. Error bars represent ±1 standard deviations. "Supply" and "Export" boxes represent all nutrient supply and export terms, respectively.

N/P of Nutrient Export
Export of organic matter is categorized into three primary pathways, that is, the gravitational pump, mixing pump, and migrant pump (Siegel et al., 2023). The N/P representing the gravitational pump is determined from sinking particles collected in the 150-m sediment trap (Sinking N/P) which yield mean ± s.d. of 28.5 ± 7.8 and 40.5 ± 15.7 at Station ALOHA and BATS, respectively. Sinking N/P at both time-series stations are much higher than the Redfield ratio as well as the vertical and lateral supply ratios (Figure 3 and Tables S1 and S2 in Supporting Information S1).
The "mixing pump" represents the downward transport of both suspended particulate and DOM by various physical mechanisms (Dall'Olmo et al., 2016;Hansell et al., 2009;Levy et al., 2013;Omand et al., 2015;Roshan & DeVries, 2017;Resplandy et al., 2019). The multi-year weighted mean N/P ratios of suspended particles in the upper 150 m (Suspended N/P) are 23.1 ± 5.4 at Station ALOHA and 37.2 ± 5.8 at BATS, consistent with previous estimates Singh et al., 2015) and higher than the Redfield ratio. The lifetime of refractory DON and DOP (>4,000 years;  far exceeds the ventilation timescale of waters at 300 m (≥4-10 years; Bullister et al., 2006;Stanley et al., 2012), so we only consider the export of semilabile DON and DOP. The N/P ratio used to represent transport of semilabile DON and DOP export at both Station ALOHA and BATS (20 ± 3; (ΔDON/ΔDOP) exp ) comes from the mean of incubation experiments at Station ALOHA, Georges Bank, and the Mid-Atlantic Bight (Hopkinson & Vallino, 2005). This value aligns with the global mean N/P ratio of ∼20 for semilabile DON and DOP export in a modeling study . Depth gradients of suspended particle concentrations are on average ∼10%-20% of the depth DOM concentration gradients at Station ALOHA and BATS ( Figure S5 in Supporting Information S1) so we ignore the transport of suspended particles in this study.
The "migrant pump" represents dissolved (in)organic nutrients actively transported by migrating zooplankton. At Station ALOHA, Hannides et al. (2009) found that migrant excretions of dissolved nutrients (organic + inorganic) are characterized by a mean N/P ratio of 12. Steinberg et al. (2002) measured the dissolved inorganic N/P excretion ratios averaging 12.0 ± 4.9 for a few zooplankton species at BATS. The N/P ratios associated with migrant excretion (Zoo. N/P) in the NPSTG and NASTG are very similar, and are P-rich compared to sinking N/P.

Role of Nitrogen Fixation in the Subtropical Nutrient Budget
At both Station ALOHA and BATS, the significantly greater N/P of exported organic matter than N/P of dissolved nutrient supply is due, in part, to external N supplied from nitrogen fixation. Given small atmospheric nitrogen deposition rates at Station ALOHA (Duce et al., 2008;Kim et al., 2014), the external N source must primarily be nitrogen fixation. Nitrogen fixation was previously estimated to supply about 30%-50% of exported organic N based on δ 15 N measurements at Station ALOHA (Böttjer et al., 2017;Karl et al., 1997). Using a simplified version of the nutrient-ratio budget method discussed here, Quay (2021) estimated that nitrogen fixation could support 33%-43% of the exported organic N (i.e., N src /N exp ).
At BATS, the difference in N/P between the dissolved nutrient supply and exported particles is even greater than at Station ALOHA (Figure 3 and Tables S1 and S2 in Supporting Information S1). Unlike at Station ALOHA, however, nitrogen fixation at BATS likely accounts for <10% of export flux based on δ 15 N measurements (Altabet, 1988;Knapp et al., 2005), N budgets (Helmke et al., 2010;Jenkins & Doney, 2003;Stanley et al., 2015;Tang et al., 2019), and models . Rate estimates of atmospheric nitrogen deposition are approximately half the nitrogen fixation at BATS (Knapp et al., 2010;Singh et al., 2013;Zamora et al., 2010). Thus N src /N exp is likely <15% at BATS, which is significantly lower than the >50% fraction needed to balance the N/P budget. Therefore, additional nutrient sources with higher N/P, and/or nutrient sinks with lower N/P ratios are needed to balance the N and P budgets at BATS.

Using N/P to Estimate the Relative Importance of Nutrient Sources and Sinks
We use the observed N/P of the nutrient sources and sinks coupled with observed constraints on N src /N exp at Station ALOHA and BATS to quantitatively estimate the relative importance of specific nutrient sources and sinks for the surface ocean. Using a Monte Carlo method, we randomly assign an N/P value for each of the three dissolved nutrient source terms ((ΔNO 3 /ΔPO 4 ) v , meridional (ΔNO 3 /ΔPO 4 ) l , and meridional (ΔDON/ΔDOP) l ) and the three nutrient sink terms (Sinking N/P, transported DOM N/P, and Zoo. N/P) based on their observed means and standard deviations assuming normal distributions (Tables S1 and S2 in Supporting Information S1). Input values for the fractional contributions of each nutrient source (supply) and sink (export) term are assumed to be independent and are randomly selected, but are forced to sum to 1 in each case. The N/P of total nutrient supply (N/P) sup and export (N/P) exp is determined and used to calculate N src /N exp based on Equation 1. The process is repeated 100,000 times. The subset of these scenarios that yield N src /N exp values within the observed ranges (0.3-0.5 at Station ALOHA and 0-0.15 at BATS, as discussed above) are used for interpretation. The mean, median, and interquartile range of each subset is used to determine the likely fraction of each nutrient source and sink term (Tables S1 and S2 in Supporting Information S1). Fractions of all nutrient terms are not normally distributed (Lilliefors test; p ≪ 0.05) and are better described by medians and interquartile ranges than means and standard deviations (Sainani, 2012). However, medians of the total nutrient source or sink do not sum to 100% whereas the means do. Therefore, we present both means and medians in the following discussion.
The vertical inorganic nutrient supply term that dominates the total supply in our Monte Carlo analysis represents all processes contributing to the vertical nutrient flux, such as turbulent diffusion below the base of the surface layer or episodic eddy events as observed by Johnson et al. (2010) at Station ALOHA. The skewness of histograms of fractional contributions is caused by the different N/P ratios of the individual nutrient sources and sinks, and the imposed range of N src /N exp (Figures S6 and S7 in Supporting Information S1). The N/P of nutrient sinks (Station ALOHA: 12.0-28.5; BATS: 12.0-40.5) differs greatly from the N/P of lateral (∆NO 3 /∆PO 4 ) l and (∆DON/∆DOP) l supply (1.6-6.7), while the N/P of vertical (∆NO 3 /∆PO 4 ) v supply (14.7-19.6) falls within the range of sink term N/P ratios (Figure 3 and Tables S1 and S2 in Supporting Information S1). The strong positive skewness for fractions of lateral inorganic and organic supply occurs because increasing the fraction of lateral supply decreases overall (N/P) sup ratio which severely diminishes the number of scenarios that can yield a balance N/P budget constrained by the upper bound of N src /N exp constraints (Station ALOHA: 0.5; BATS: 0.15). Likewise, most of the scenarios with a higher fraction of sinking particles (with highest N/P of ∼30-40) are filtered out because they require an external N source that exceed the imposed upper bound of N src /N exp .
To identify which N/P terms contribute the most uncertainty to the mean fractions of different nutrient sources and sinks, we repeated our Monte Carlo simulation while excluding the standard deviation on each N/P source or sink term, one at a time. Based on this sensitivity analysis (Table S3 in Supporting Information S1), the N/P terms that yield the most uncertainty in the estimated mean fractional contributions are lateral organic nutrient supply, sinking particles, and zooplankton excretion at both Station ALOHA and BATS, which suggests that better constraining N/P ratios of these terms should be a focus of future research efforts.
Note that the fractions of different N/P terms represent the relative contributions of different P sources and sinks to the surface P budget. The vertical supply of inorganic PO 4 3is the dominant dissolved P source and almost identical at Station ALOHA (mean: 58%) and BATS (55%). The combined export of semilabile DOP and zooplankton excretion far exceed (∼3 folds) the export by sinking particles at Station ALOHA (25 vs. 75%) and BATS (21 vs. 79%). The significant P fluxes from DOM export and zooplankton excretion may explain why oxygen and dissolved inorganic carbon budget based estimates of total organic matter export (Emerson, 2014;Quay, 2021;Stanley et al., 2015) consistently exceed sediment trap fluxes at 150 m at Station ALOHA and BATS (Church et al., 2013;Karl et al., 2021;Lomas et al., 2013Lomas et al., , 2022.

Conclusions
A nutrient budget method leveraging distinct elemental N/P ratios at Station ALOHA and BATS in the oligotrophic subtropical gyres was used to estimate the importance of different nutrient supply and export pathways in the surface layer at these two time-series stations. We found that vertically supplied PO 3-4 from below is the dominant nutrient source at both stations, accounting for ∼60% of the total phosphorus supply. At both stations, the combined export of organic matter via DOM transport and zooplankton migration and excretion is more important than export via sinking particles, which supports previously observed discrepancies between chemical tracer-budget estimates of export and sediment trap fluxes at these sites. 10.1029/2023GL103213 8 of 10 Elemental stoichiometry (e.g., N/P) is a powerful tool to study nutrient cycling in the ocean, because it avoids the need to estimate rates of nutrient supply and organic matter export which are difficult to make. To the best of our knowledge, these budgets provide the first observation-based constraints on the fractional contributions of multiple nutrient source and sink processes associated with organic matter export from the surface ocean. Contemporaneous measurements of the C/N/P elemental stoichiometry of particles, DOM, and zooplankton excretion across additional ocean biomes would improve characterization of nutrient cycling and the biological carbon pump at a global scale.

Data Availability Statement
The nutrient data used for estimating N/P ratios of vertical nutrient supply, sinking and suspended particles in the study are available at the home pages of the Hawaii Ocean Time-series (HOT) Project and Bermuda Atlantic Time-series Study. Station ALOHA data were obtained via the Hawaii Ocean Time-series HOT-DOGS application (https://hahana.soest.hawaii.edu/hot/hot-dogs/interface.html) from the University of Hawai'i at Mānoa under National Science Foundation Award # 1756517. The BATS data were obtained from the Bermuda Atlantic Time-series Study (http://bats.bios.edu/data/) supported by the NSF Chemical and Biological Oceanography Programs. The WOA18 nutrient data used to estimate horizontal nutrient supply ratios were obtained from the National Centers for Environmental Information website (https://www.ncei.noaa.gov/access/world-ocean-atlas-2018/). This study also uses data from the cruise RRS Charles Darwin CD171, provided by the British Oceanographic Data Centre and funded by the Natural Environment Research Council. DOP and DON data from the COOK-BOOK cruises can be found at https://hahana.soest.hawaii.edu/cookbook/cookbook.html. The code for the Monte Carlo approach used in this study can be found at https://doi.org/10.5281/zenodo.7568622.