2.3.1 Temperature and salinity

The duplicate temperature (T) and salinity (S) sensors aboard the ship's profiler during the May process cruise agreed closely (median S difference ≤ 0.0018 and a median T difference ≤ 0.0006 ^∘C for each of 134 profiles). The ship TS sensors were therefore used as standards, after de-spiking and averaging (more details at http://data.bco-dmo.org/NAB08/Ship_TS_despiking-NAB08.pdf, last access: 23 July 2018). Duplicate T sensors aboard the float also agreed closely and were therefore combined into a single record without adjusting to match the ship. After reconciliation of duplicate S measurements on each platform, a small mismatch between float and ship salinity was identified from the calibration casts and corrected by subtracting 0.0075 from the float S (more details at http://data.bco-dmo.org/NAB08/CTD_float_Calibration-NAB08.pdf, last access: 23 July 2018).

2.3.2 Oxygen

Comparison between the SBE 43 and optode oxygen sensors aboard the float revealed differing sources of bias in each sensor. Bias in SBE 43 oxygen was introduced by changes in pumping rate during different modes of float operation and by wave action near the surface. Bias in optode oxygen arose from its factory calibration, T and pressure effects, and a slower time response. After reconciliation of the two sensors to reduce these biases, the SBE 43 oxygen was brought in line with the discrete oxygen samples on the best six calibration casts by subtracting a constant offset of 0.9 µMol kg⁻¹. We conclude that the accuracy of the corrected in situ oxygen estimates is better than 2 µMol kg⁻¹ based on agreement with discrete samples (Winkler titrations). More details on the float's oxygen calibration can be found at http://data.bco-dmo.org/NAB08/Oxygen_Calibration-NAB08.pdf, last access: 23 July 2018.

Figure 2POC ∕ c_p from the May cruise in the upper 30 m and the fit used to calculate POC_cp.

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2.3.3 POC from optical beam attenuation

Previous work has shown that measurements of light scattering by particles, including beam attenuation c_p and particulate backscattering b_bp, correlate strongly with POC in the open ocean (Cetinić et al., 2012, and references therein). Calibration of our c_p and b_bp measurements and conversion to POC estimates are described in the next two subsections. Raw output from the float optical beam transmissometer was aligned with raw ship transmissometer output using matchups from eight of the calibration casts. Agreement was very good (r²=0.99), showing no evidence of sensor drift. Intercalibrated raw transmissometer output was converted to particulate optical beam attenuation c_p using the mean of factory calibrations performed on the ship's transmissometer before and after deployment. More details can be found at http://data.bco-dmo.org/NAB08/C-Star_Calibration-NAB08.pdf, last access: 23 July 2018. We estimated c_p-derived POC (POC_cp) following Cetinić et al. (2012), but with a time-dependent adjustment in POC ∕ c_p ratio to account for community changes. After subtracting the POC ∕ c_p regression offset of 0.015 m⁻¹ (Cetinić et al., 2012) from our c_p measurements, we computed the POC ∕ c_p ratio for all ship POC and c_p samples for which c_p>0.2 m⁻¹ in the upper 30 m during the May process cruise (Fig. 2; gray points). Samples whose T, S, c_p, and b_bp matched the float ML measurements within 0.25 ^∘C, 0.01 m⁻¹, 0.1 m⁻¹, and 0.001 m⁻¹, respectively, are shown as black circles (Fig. 2). Three inflection points were fit by eye at 370, 310, and 450 mg m⁻² on 6, 11, and 15 May, respectively. A continuous estimate of POC ∕ c_p at the float patch was obtained by interpolating between these points and assuming constant POC ∕ c_p before 6 May and after 15 May (Fig. 2, red line). This continuous estimate of POC ∕ c_p was multiplied by float c_p (minus offset of 0.015 m⁻¹) to yield a c_p-based float POC estimate (POC_cp).

2.3.4 POC from optical backscattering

An average of pre- and post-deployment calibrations was used to convert raw backscattering output from both the float and the ship to the volume-scattering function at the angle (140^∘) and wavelength (700 nm) of the sensors. The volume-scattering function of seawater was then calculated following Zhang et al. (2009) and subtracted to yield scattering due to particles. The result was multiplied by 2πχ to yield the particulate backscattering coefficient b_bp, where the angle-dependent scale factor χ is 1.132 for the FLNTU scattering sensors used in this study (Michael Twardowski, personal communication, 2010). Float b_bp was aligned with ship b_bp using matchups from eight calibration casts (r²=0.96). More details can be found at http://data.bco-dmo.org/NAB08/Backscatter_Calibration-NAB08.pdf, last access: 23 July 2018. Glider b_bp was calibrated against the ship FLNTU in a similar fashion to the float (Briggs et al., 2011). We estimated b_bp-derived POC (POC_bbp) following Cetinić et al. (2012) via the equation POC_bbp [mg C m⁻³] = 37 500 b_bp [m⁻¹] − 14, derived from a linear regression between colocated measurements of POC and b_bp within the mixed layer from the May process cruise.

2.3.5 Chlorophyll a

Raw chlorophyll fluorometer output from the ship was converted to an initial Chl a estimate Chl a_factory using the factory-calibrated scale factor and a dark offset derived from the minimum of all per-cast deep values (defined as the median between 550 and 580 m). An empirical fit between Chl a_factory, T, PAR, and ship discrete Chl a measurements was used to derive an in situ Chl a product

which was strongly correlated with discrete Chl a (r²=0.87). Float Chl a_factory was aligned with ship Chl a_factory, using the matchups from eight calibration casts (r²=0.95), allowing for the calculation of Chl a via Eq. (1) at the float as well. The FLNTU sensor was located at the bottom of the float, facing down, so Chl a data were removed whenever the float was moving upward at > 1.7 cm s⁻¹ due to the possible entrainment of deeper water. Chl a measurements in which PAR > 75 were also removed to eliminate non-photochemical quenching. In order to obtain a continuous, depth-resolved record of Chl a for the calculation of primary productivity, the remaining Chl a estimates, from both mixed-layer mode and profiles, were filtered using a 5-point running median, averaged in 1 h, 1 m bins, and then interpolated in depth and time via triangulation-based 2-D linear interpolation, with distance calculated as $\sqrt{\left(\mathrm{d}z\right[\mathrm{m}]/\mathrm{30}[\mathrm{m}]{)}^{\mathrm{2}}+\mathrm{d}t[\mathrm{days}{]}^{\mathrm{2}}}$ (i.e., a 30 m vertical interval and a 1-day time interval were considered equidistant).

2.3.6 Nitrate

A post-deployment laboratory calibration, including temperature and salinity corrections, was used to obtain initial NO₃ estimates from the float's ISUS NO₃ sensor. An additional scale factor of 1.15 and offset of +2.6 µM were required to bring these initial estimates in line with discrete samples taken during calibration casts. More details can be found in Alkire et al. (2012) and at http://data.bco-dmo.org/NAB08/ISUS_Nitrate_Calibration-NAB08.pdf, last access: 23 July 2018.

2.3.7 Silicate

SiO₄ was not measured by the float, but discrete shipboard SiO₄ measurements from the top 15 m were considered to represent mixed-layer SiO₄ at the float location if the corresponding temperature, salinity, and NO₃ measurements matched concurrent float ML measurements to within 0.25 ^∘C, 0.01, and 0.8 mmol m⁻³, respectively.

2.3.8 PAR

The factory calibration of the float PAR sensor was used “as is.”

2.5.1 Instantaneous K_PAR estimates

The diffuse attenuation coefficient of PAR K_PARwas calculated from each pair of consecutive PAR measurements made at times t₁ and t₂ via Eq. (2), where z is depth, $\overline{z}$ is the mean of z(t₂) and z(t₁), and $\overline{t}$ is the mean of t₂ and t₁.

2.5.2 K_PAR fit method

The uncertainty of individual K_{PAR(measured)} estimates was high and depended strongly on dz, which ranged from 0.2–30 m with a mean of 1.3 m. These 14 000 K_{PAR(measured)} estimates were therefore fit to Chl a and z using a nonlinear least squares multiple regression weighted by dz to obtain Eq. (3):

In order to evaluate the performance of this fit, K_{PAR(measured)} precision was increased by eliminating estimates with dz<2 m and combining the remaining estimates into 21-point medians, yielding a total of 118 independent in situ K_PAR estimates. A type-II linear regression of these estimates against 21-point medians of K_PAR estimated via Eq. (3) yielded an r² of 0.85, a root mean square error of 0.014 m⁻¹, and a mean bias of −0.004 m⁻¹. The residual error was not significantly correlated with depth, time, solar zenith angle, or the ratio of in situ Chl a to b_bp, a proxy for the plankton community in this system (Cetinić et al., 2015).

2.8.1 Diel cycles of O₂ and POC

“Typical” diel cycles (minimum near dawn and maximum near dusk) were observed in mixed-layer records of O₂ (Fig. 4), consistent with previous studies (Caffrey, 2003; Hamme et al., 2012; Nicholson et al., 2015). We estimated mixed-layer gross oxygen productivity (GOP) at half-day intervals from these diel cycles. To estimate morning GOP, ML O₂ concentrations were smoothed with a 3-point running median, and a type-I linear regression (O₂ vs. time) was fit to data from dusk to dawn (Fig. 4a; solid black line). The regression fit was projected forward to provide an estimate of noontime mixed-layer O₂ in the absence of GOP. Measured noontime O₂ was calculated from a type-I linear regression of O₂ data taken within 1 h of local noon. Morning mixed-layer GOP was calculated as the difference between measured and projected concentration (Fig. 4; blue vertical bar) and divided by 0.5 days to convert to units of $\mathrm{mmol}{\mathrm{m}}^{-\mathrm{3}}{\mathrm{day}}^{-\mathrm{1}}$. Afternoon GOP was calculated in a similar fashion, by subtracting noontime mixed-layer O₂ from the noontime extrapolation of a linear fit of the following night's data. Similar diel cycles were observed in mixed-layer POC_cp, and the same method was used to calculate the mixed-layer gross primary productivity of POC (GPP_cp) from these cycles (Fig. 4b). Diel cycles in POC_bbp were less regular and usually out of phase with O₂ and POC_cp cycles, but GPP_bbp was calculated in the same way as GOP and GPP_cp for comparison. Note that this diel cycle method assumes homogeneous mixing to a constant depth and that any gain or loss terms other than GOP (or GPP) are constant day to night over the period of a single calculation (∼ 18 h). However, we find a clear diel cycle in MLD (Fig. 3), which amplifies the diel cycle in O₂ (and c_p and b_bp), causing PP calculated from diel cycles to exceed mean PP within the daily mean MLD. This is because nighttime ML deepening enhances the loss of ML concentration relative to daytime mixing losses. Analysis of the output of a coupled physical–biological model assimilating data from the Lagrangian float (Bagniewski et al., 2011), which accurately reproduced the diel cycle in mixing (Fig. 3, black line), shows that the mixing-amplified diel cycles of O₂ in the ML yield daily GOP estimates that correspond approximately to the mean GOP above the daily minimum MLD. Regression of diel GOP, calculated from ML O₂ time series output by the model as a function of “true” model GOP forced through zero, yields a slope ± 95 % confidence interval of 0.91 ± 0.12 and an RMSE of 0.12 $\mathrm{mmol}{\mathrm{m}}^{-\mathrm{3}}{\mathrm{day}}^{-\mathrm{1}}$. We therefore interpret our daily GOP and GPP_cp estimates as representing daily mean productivity between the surface and daily minimum MLD. Bias in GOP due to day–night differences in air–sea flux was also estimated using the difference between mean morning (or afternoon) dO₂∕dt due to air–sea flux and that of the previous (or next) nighttime. Mean bias was small (< 5 % of GOP) and linked primarily to the MLD diel cycle, so a separate correction was not deemed necessary. Other potential biases are discussed in Sect. 4.1.2 to 4.1.4.

Figure 5Example NPP vs. PAR relationship from ¹⁴C incubations, with best-fit “PvE” curve.

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Figure 6Photosynthetic parameters P_m (a), α (b), and R_Φ (c) vs. in situ Chl a with least squares power-law fits and 95 % confidence intervals. R_Φ estimates from April and June cruises are excluded from fit (panel c, open circles).

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2.8.2 ¹⁴C incubations

During the April and May cruises, daily 2 h ¹⁴C incubation experiments were conducted (n=28) to estimate photosynthetic parameters. Each day, a water sample was taken from the Chl a maximum, as determined by in situ fluorescence, and duplicate 2 h ¹⁴C incubations were carried out at seven different PAR levels ranging from 0–400 $\mathrm{\mu }\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{s}}^{-\mathrm{1}}$. The dark incubation ¹⁴C activities were weakly but significantly correlated with Chl a (type-II linear regression; r²=0.19; p<0.05; apparent NPP = Chl a⋅0.036 ± 0.026 $\mathrm{mg}\mathrm{C}\mathrm{mg}\mathrm{Chl}{a}^{-\mathrm{1}}{\mathrm{h}}^{-\mathrm{1}}$ + 0.049±0.035 $\mathrm{mg}\mathrm{C}{\mathrm{m}}^{-\mathrm{3}}{\mathrm{h}}^{-\mathrm{1}}$); dark activities were treated as sample-specific blanks and subtracted from the light incubation activities of the corresponding water sample. The resulting productivity estimates were interpreted as net primary productivity (NPP) based on findings that most phytoplankton do not respire old carbon when newly fixed carbon is available (Marra and Barber, 2004; Pei and Laws, 2013). Note that if, contrary to our assumptions, phytoplankton did respire old carbon at all light levels during these incubations, then our calculations below overestimate NPP and underestimate phytoplankton respiration (R_Φ), but GPP is unbiased. On the other hand, if old carbon is respired only in the low light incubations, then we underestimate R_Φ and GPP, but little bias is introduced in NPP. Seven of the 350 individual NPP estimates (all from the April cruise) were judged to be positive outliers and were manually removed before further analysis. In ∼ 60 % of the incubation experiments, NPP decreased with increasing PAR for PAR > 200 $\mathrm{\mu }\mathrm{mol}\mathrm{quanta}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{s}}^{-\mathrm{1}}$. We conclude that this apparent photoinhibition is likely not representative of most field conditions because in situ measurements of Chl a-normalized dO₂∕dt showed no consistent relationship with PAR between PAR values of 100 and 1000 $\mathrm{\mu }\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{s}}^{-\mathrm{1}}$. We therefore removed values of NPP in which PAR > 200 $\mathrm{\mu }\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{s}}^{-\mathrm{1}}$ if they were lower than the second-highest NPP observed in which PAR < 200 $\mathrm{\mu }\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{s}}^{-\mathrm{1}}$ (56 of 110 high light points removed). Remaining NPP vs. PAR data were fit to an empirical “PvE” model represented in Eqs. (6)–(8):

based on four parameters: maximum GPP (P_m), the initial slope of GPP ∕ PAR (α), R_Φ, and an efficiency factor (ε) representing the “sharpness” of the transition between light-limited and light-saturated photosynthesis. This parameterization is based on a conceptual model of photosynthesis in which there is a rate-limiting step that can receive and “store” up to ε “packets” of energy at once at above the limiting rate without wasting any of these packets. We used a single ε value of 6, which provided the best overall least-squared fit across all incubation experiments. This ε value yields an NPP vs. PAR relationship that is “sharper” than the commonly used “tanh” model (Harrison and Platt, 1986) and more linear at low PAR, leading to smaller y offset (smaller R_Φ estimate). See Fig. 5 for example fits. A power law was then fit between in situ Chl a estimates from the ship's profiling package (calculated via Eq. 1) and each of the three parameters obtained from each NPP vs. PAR fit (P_m: Fig. 6a; α: Fig. 6b; and R_Φ: Fig. 6c). Fits with P_m and α used data from all cruises, but the fit with R_Φ included only data from the process cruise (Fig. 6c; solid circles), as signals were too low to constrain R_Φ in April and R_Φ appeared consistently higher during the June cruise, possibly due to higher temperature.

2.8.3 Chl a-based GPP and NPP

The relationships in Fig. 6 were used to estimate photosynthetic parameters P_m(t,z), α(t,z), and R_Φ(t,z) and their uncertainty intervals at the float location from Chl a(t,z) (Sect. 2.3.5). We estimated gross primary productivity GPP_Chl a(t,z) and net primary productivity NPP_Chl a(t,z) via Eqs. (6)–(8) using the above photosynthetic parameters, PAR_extrapolated(t,z) (Sect. 2.6), and ε=6 as input. Uncertainties were propagated from P_m(t,z), α(t,z), and R_Φ(t,z) using the conservative assumption that they covary (i.e., upper bound of NPP_Chl a was derived from upper bounds of P_m and α and lower bound of R_Φ).

4.1.1 GPP_Chl a

GPP_Chl a and GPP_cp are estimates of the same quantity obtained independently. GPP_Chl a is derived from PAR and Chl a estimates using robust local parameterizations obtained from ¹⁴C incubations. GPP_cp is derived entirely from c_p measurements converted to POC using another robust, local empirical relationship. The averaging depth (daily minimum MLD) for GPP_Chl a was chosen to match the diel cycle method based on the results of a model tuned to match local conditions (Bagniewski et al., 2011). In this context, the combination of strong correlation and absolute agreement between GPP_Chl a and GPP_cp (Fig. 9c; within 19 %) provides confidence in both methods during the bloom growth and post-bloom periods. The GOP ∕ GPP_Chl a slope of 2.1 (Fig. 9b) is at the upper end of the expected range, providing additional first-order support for GPP_Chl a accuracy. Neither GPP method includes DOC production, so the range of expected photosynthetic quotients (∼ 1–1.45; Laws, 1991; Robertson et al., 1993), combined with the fraction of GPP released as DOC in marine and estuarine environments (2–50 %; Baines and Pace, 1991), implies a possible GOP ∕ GPP range of 1–2.9. During the main bloom observed by the float in this study, Alkire et al. (2012) estimate that DOC accounts for 22–40 % of NCP in the mixed layer. If these estimates apply to GPP as well, our expected GOP ∕ GPP range narrows to 1.3–2.4 (Fig. 9a, b; gray dashed lines). Thus, our GOP estimates suggest either that both the photosynthetic quotient and phytoplankton DOC production are high during bloom growth (and GPP is accurate) or that both GPP estimates are biased low. As mentioned in Sect. 2.8.2, a negative bias in GPP_model could be explained if phytoplankton respired substantial old, unlabeled carbon in our low light incubations, but not in the high light incubations. In this case a separate explanation (see next section) is needed for the high GOP ∕ GPP_cp slope of 2.6 (Fig. 9a).

During bloom peak and decline, the strong discrepancies between GPP_cp and GPP_Chl a imply either an underestimate by GPP_cp (discussed in the next section) or an overestimate by GPP_Chl a. If diatoms reduce GPP in response to sustained SiO₄ limitation, then we expect GPP_Chl a overestimation at peak biomass given that GPP_Chl a is only a function of Chl a and PAR, without any nutrient limitation term. Twelve mixed-layer SiO₄ samples were collected in the vicinity of the float on 11–13 May, and the mean and maximum measured concentrations were 0.3 and 0.6 mmol m⁻³, respectively, suggesting that diatom growth was most likely severely limited (Fig. 7a). This does not necessarily imply that diatom carbon fixation rates were reduced, but previous studies have indeed observed a large and reversible reduction in apparent diatom photosynthetic efficiency under multi-day SiO₄ limitation (Lippemeier et al., 1999, 2001). Both FlowCAM microscopy and HPLC pigments indicate that diatoms accounted for ≥ 50 % of phytoplankton biomass at bloom peak (Cetinić et al., 2015), so we expect a substantial reduction in bulk phytoplankton growth (and likely GPP) under these conditions. This expectation, combined with the observed reduction in both GPP_cp and GOP at bloom peak, leads us to conclude that GPP_Chl a is most likely overestimated at bloom peak. This conclusion agrees with the coupled physical–biological model of Bagniewski et al. (2011), which assimilated float biogeochemical measurements and achieved optimal fit when diatom GPP was limited by SiO₄ with a half-saturation constant of 1 µmol m⁻³. GPP inferred from this model closely matches our observed GPP_cp during SiO₄ limitation (Fig. 8, gray line vs. black circles), even though Bagniewski et al. (2011) assimilated daily binned data, removing any diel cycle information. On the other hand, three ¹⁴C incubations were conducted between 10 and 14 May using water with SiO₄ < 0.5 mmol m⁻³, although not at the float location, and there was not a substantial reduction in measured P_m. These samples may not be representative of the water sampled by the float, despite similar Chl a and SiO₄ concentrations, or it is possible that a bottle effect enhanced GPP. But we cannot rule out the alternative hypothesis that the Si-limited community continued to fix carbon at a constant rate and that GPP_cp and GOP estimates were reduced for another reason (discussed in next sections).

Apart from Si limitation, possible explanations for GPP_Chl a overestimation include overestimation of Chl a due to increased fluorescence, underestimation of the MLD, or photoinhibition. Again, Chl a was calculated the same way for the floats and ship, so if the in situ fluorometric method overestimated Chl a at bloom peak, we would expect to see a deviation from the observed relationships between photosynthetic parameters and Chl a (Fig. 6). So this explanation, while plausible given the high Chl a ∕ b_bp ratio at bloom peak (Cetinić et al., 2015), also requires that none of our low SiO₄ bottle samples were representative of the bloom peak at the float location. The density-based MLD estimates appear quite robust during this period, consistently shallow and stable at 10–20 m and matched by the vertical motion of the float. And the daytime increases in O₂ (Fig. 4) and c_p on 11 and 12 May show no sign of photoinhibition, despite a peak hourly-averaged PAR of > 750 $\mathrm{\mu }\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{s}}^{-\mathrm{1}}$; increases are smooth throughout the morning and appear to continue at the same rate in the afternoon (Fig. 4). This result supports our decision to exclude photoinhibited bottle incubation data from our productivity vs. PAR fits, and we suggest that photoinhibition terms from bottle incubations should be applied with caution, if at all, in future studies. In this system, photoinhibition is likely reduced during deeper mixing events due to the shorter time phytoplankton is exposed to high light. During the stratified conditions, reduction in photoinhibition can be attributed to photoadaptation.

SiO₄ limitation may also explain some of the discrepancy between GPP_cp and GPP_Chl a during the bloom decline (13–16 May), at least when afternoon estimates are excluded (see Fig. 9b, c; open pink circles). Lower afternoon GPP_cp and GOP, combined with very shallow (< 5 m) MLDs at noon on 13 and 15 May, also raise the possibility of significant photodamage inhibiting afternoon productivity. Mean ML PAR exceeded 500 $\mathrm{\mu }\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{s}}^{-\mathrm{1}}$ for at least 2 h on both days. However, the negative afternoon GPP_cp estimates at this time suggest a bias in the diel cycle method as well (see next section).

4.1.2 GPP_cp

Potential sources of bias unique to GPP_cp include a diel cycle in grazing (e.g., due to diel migration of zooplankton), a diel cycle in export loss, or a diel cycle in the POC ∕ c_p ratio. The tight correlations between GPP_cp and GOP throughout the entire study period (r²=0.95; Fig. 9a) and between GPP_cp and GPP_Chl a during bloom growth (r²=0.96; Fig. 9b) provide encouraging support for GPP_cp as a measure of relative primary productivity at the very least. Furthermore, the quantitative agreement between GPP_cp and GPP_Chl a during both bloom growth and post-bloom (Fig. 9c; slope: 0.82 ± 0.06) is very close to our expected slope of 0.93 from model results (reanalysis of Bagniewski et al., 2011), suggesting that GPP_cp accuracy is comparable to other methods across most of the conditions encountered. These findings agree closely with those of White et al. (2017), who find a GPP_cp ∕ NPP ratio of 1.1 across a factor of 3 dynamic range of productivities in the subtropical North Pacific, suggesting that GPP_cp is either accurate or slightly underestimates true GPP. Taken together, our results are highly encouraging regarding the widespread applicability and accuracy of the GPP_cp method. However, it should be noted that our results still may not apply to certain other systems in which different phytoplankton size and/or timing of cell division could alter the diel POC ∕ c_p relationship (Dall'Olmo et al., 2011).

If the SiO₄ limitation hypothesis is correct, then GPP_cp during the bloom peak and morning GPP_cp during the bloom decline may be accurate as well. On the other hand, if GPP_Chl a is accurate during this time, then GPP_cp is biased low by ∼ 50 % at this time. It is unclear what might cause such a low bias, especially at bloom peak. Between the afternoon of 11 May and the morning of 13 May, there is no anomaly in the diel cycles of POC_cp or O₂ (Fig. 10) indicative of daytime mixing, advection, or possible photoinhibition, and there is no change in the relationship between GPP_cp and GOP (Fig. 9a; rightmost pink symbol). Without grazing data, we cannot rule out enhanced daytime grazing as a possible explanation, although grazing is generally expected to be higher at night. Alternatively, particularly high photooxidation could potentially dampen O₂ diel cycles during this period and perhaps c_p diel cycles as well. This hypothesis is supported by laboratory measurements of diatom productivity under nutrient limitation (Spilling et al., 2015), although again we would need to explain why reduced P_m was not observed in our bottle incubations. On the other hand, the afternoon GPP_cp estimates during the bloom decline period show a clear example of negative bias in the diel cycle method. On 13, 14, and 15 May (bloom decline), the rates of net POC_cp (and O₂) accumulation are positive or near zero in the morning but negative each afternoon (e.g., Fig. 4; 13 May). One plausible explanation is horizontal advection of the float relative to the ML during its afternoon profile, causing it to resurface in water with lower biomass. During this period, comparison with ship, autonomous glider, and satellite measurements (Alkire et al., 2012) shows that the float was at the edge of a high biomass (and O₂) patch, so advection during this time would most likely cause a loss in POC_cp and O₂. Note that the afternoon reductions in GPP_cp during bloom decline are greater than the afternoon reductions in GOP (e.g., Fig. 4). This result is possible with the horizontal advection and mixing hypothesis alone, but high export combined with a shallow afternoon MLD may also play a role. Shallow MLD enhances the loss of ML concentration for a given export rate, and nighttime mixing can re-entrain some of this export, reducing the ML POC diel cycle relative to the O₂ diel cycle.

4.1.3 GOP

The tight fit between GOP and both GPP estimates over most of the study period provides important support for the O₂ diel cycle method as a measure of relative primary production in this region. Again, because all estimates were independent and taken at the same scale, and because the 2-month deployment allowed 14 independent matchups at a 3-day timescale spanning a wide range of productivities, this dataset represents the most extensive validation to date of the O₂ diel cycle method as a measure of relative primary productivity. Additionally, the overall accuracy of our GOP estimates may be assessed indirectly through comparison with independent ship-based GOP estimates made during the May process cruise (Quay et al., 2012) and through comparison of our GOP ∕ GPP and GOP ∕ NPP ratio estimates with previous estimates from this region. Quay et al. (2012) estimated ML-integrated GOP using measurements of three oxygen isotopes, ¹⁶O, ¹⁷O, and ¹⁸O, taken daily between 3 and 21 May during the process cruise. Mean GOP calculated by this method was 245 $\mathrm{mmol}{\mathrm{O}}_{\mathrm{2}}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{day}}^{-\mathrm{1}}$. This method integrates over several weeks, so we interpret their estimate to correspond roughly to mean ML depth-integrated GOP between 19 April (2 weeks before the first sample) and 21 May. For comparison, we multiply each half-day GOP estimate by MLD to obtain ML-integrated GOP and obtain an average from 19 April to 21 May of 149 $\mathrm{mmol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{day}}^{-\mathrm{1}}$, 40 % lower than the Quay et al. (2012) estimate. However, our estimate integrates to the daily minimum MLD, and while the triple O₂ isotope method assumes constant MLD, we expect it to more closely approximate daily maximum MLD in the presence of diel MLD fluctuations given its long integration time. Mean GPP_Chl a during this period, integrated to the bottom of the daily minimum MLD, is 30 % lower than mean GPP_Chl a integrated to the daily maximum MLD. If we assume the same relative difference for GOP, we obtain a revised ML-integrated GOP estimate of 213 $\mathrm{mmol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{day}}^{-\mathrm{1}}$, 13 % lower than the Quay et al. (2012) estimate. Given the uncertainties associated with the GOP methods and the differing spatiotemporal scales, this result provides first-order support for the accuracy of both methods. Our findings reinforce those of Hamme et al. (2012), who in the Southern Ocean in March–April found that mean ML-integrated GOP calculated via O₂ ∕ Ar diel cycles (similar to our method) was 18 % lower than GOP calculated via the triple oxygen isotope method (similar to Quay et al., 2012).

Bender et al. (1992) calculated a GOP ∕ NPP ratio of 2.5 during the spring bloom in the northeast Atlantic using in situ ¹⁸O incubations and 24 h ¹⁴C incubations. We calculate GOP ∕ NPP_Chl a as shown in Fig. 9b, but replace GPP_Chl a with NPP_Chl a and obtain a best-fit ratio and 95 % confidence interval of 2.4 ± 0.2 for the bloom growth period and 1.7 ± 0.4 for the entire deployment. These fits appear to support the accuracy of both our NPP_Chl a and GOP estimates during the bloom growth phase, consistent with our other findings. However, our GOP ∕ GPP ratio estimates of 2.6 ± 0.2 (Fig. 9a) and 2.1 ± 0.2 (Fig. 9b) are near or above the high end of our expected range of 1.3–2.4 (see Sect. 4.1.1). As discussed in previous sections, these ratios may be the result of a high photosynthetic quotient and high DOC production combined with a small negative bias in GPP_cp. Our GOP estimates may also be too high, but we cannot think of a plausible mechanism that would cause a substantial overestimate of diel-based GOP (but not of GPP_cp). Regardless of the source of our high GOP ∕ GPP ratios, they are also consistent with Hamme et al. (2012), who also estimated GPP from on-deck PvE incubations and GOP via O₂ ∕ Ar diel cycles, providing a very close methodological comparison in a different environment (autumn, Southern Ocean). They obtain an even higher GOP ∕ GPP ratio of 3.6. However, Hamme et al. (2012) assumed that 1–2 h ¹⁴C incubations represent GPP, while we assume that these same incubations represent NPP (when NPP > 0). If our assumption is correct, then their method provides a quantity closer to daytime NPP than GPP. However, even in this case, assuming moderate daytime phytoplankton respiration rates (≤ 30 % of GPP), GOP ∕ GPP during their study was > 2.5, which is in agreement with our estimates. It is also worth noting that related studies comparing diel cycles in O₂ and pCO₂ measurements (Johnson, 2010; Merlivat et al., 2015), both of which include the effects of DOC production, have found ratios of daytime oxygen production to carbon production that are within the expected range of 1–1.45. These results provide further support for diel-cycle-based O₂ production and the hypothesis that DOC production may drive the high GOP ∕ GPP observed in this and other studies (Bender et al., 1992; Hamme et al., 2012).

In total, the available evidence provides first-order support for the accuracy of our diel-cycle-based GOP estimates. Our findings build on important recent work in diverse environments showing that diel cycles in the O₂ ∕ Ar ratio yield ML GOP estimates that are consistent with independent GOP estimates (Hamme et al., 2012) and that diel cycles in O₂ measurements from autonomous gliders in the subtropical Pacific provide GOP estimates that are a reasonable multiple of independent NPP results (Nicholson et al., 2015). Our results add a third ocean region (springtime North Atlantic) and a third platform (Lagrangian mixed-layer float) in addition to new comparisons with c_p and b_bp diel cycles.

4.1.4 GPP_bbp

Because diurnal variability in b_bp can be estimated from geostationary satellites (Neukermans et al., 2012), the ability to accurately estimate GPP from b_bp diel cycles would be extremely valuable. While ship-based measurements from NAB08 show that b_bp and c_p were equally well correlated with POC over the May cruise (Cetinić et al., 2012), the poor matchups we find between GPP_Chl a and GPP_bbp suggest that diel changes are present in POC ∕ b_bp and can cause strong, consistent bias in GPP_bbp. Our results agree with previous findings that while beam attenuation and forward scattering by phytoplankton increase immediately after they begin to photosynthesize, b_bp and side scattering often do not, both in the lab (Ackleson et al., 1993; Poulin et al., 2018) and in the ocean (Kheireddine and Antoine, 2014). These results caution against the use of b_bp diel cycles to estimate GPP without further research. However, it is worth noting that our afternoon GPP_bbp estimates are reasonably well correlated with GPP_Chl a (r²=0.63, m=0.75 ± 0.23; data not shown) during the bloom growth period. If this result is found to be robust in other times and places, then a useful estimate of GPP from satellite (and other) b_bp time series may be possible. However, even if the b_bp diel cycle cannot be used to estimate GPP, it likely contains other useful information, especially in combination with c_p and/or O₂. If robust relationships between plankton communities and/or physiology and b_bp diel cycles can be established (and, ideally, understood mechanistically), then measurements of b_bp diel cycles may still provide valuable oceanographic information, whether from in situ platforms or satellites.