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 Accurate rates of primary productivity (PP) in the ocean are critical to understanding the ocean's carbon cycle and potential impact of climate change on atmospheric CO2 levels. Yet, methods to measure PP cannot be calibrated absolutely and thus need to be evaluated for accuracy. Concurrent measurements of PP at the time series station ALOHA by three methods, i.e., 14C bottle incubations (14C-PP), 18O bottle incubations (18O-GOP) and triple oxygen isotope budget approach (17Δ-GOP), where GOP is gross oxygen productivity, provided a rare and useful opportunity to compare incubation and non-incubation PP methods. The results of this PP comparison lead Quay et al.  to question the accuracy of incubation-based PP methods based on the consistently higher GOP rates estimated from the budget-based 17Δ-GOP method (by 25–60%) compared to the incubation-based 18O-GOP method. The observed discrepancies in these two independent measures of GOP were attributed to several possible factors (e.g., bottle effects, different integration times of methods, stochastic PP events, to name a few).
Marra  in his response to Quay et al.  raises questions about the accuracy of the 17Δ-GOP method based on PP limits imposed by photochemical reaction rates within the phytoplankton cell. Potentially, this may provide a useful constraint on PP that was not considered by Quay et al. Marra concludes that the 17Δ-GOP estimates often exceeded maximum GOP limits and raises the question of whether the 17Δ-GOP method overestimates GOP.
 Although we present evidence that challenges Marra's  conclusions, as discussed below, this reply to Marra's comments is not meant to discourage critical evaluation of the 17Δ-GOP method. Quite the opposite, as continued evaluation of all PP methods (whether based on incubations, budgets or satellites) is exactly what is needed by the oceanographic community. As initially stated by Quay et al.  and reiterated by Marra, there is a clear need to resolve discrepancies between PP methodologies in order to improve our understanding of PP in the ocean.
Marra  uses three physiological attributes of phytoplankton to evaluate 17Δ-GOP rates, that is, quantum yield, assimilation number and growth rate. Marra assumes GOP decreases linearly with depth (to a zero value at 120 m) in order to convert the depth integrated 17Δ-GOP rates reported by Quay et al.  to a volumetric rate and assumes the production rate of O2/C equals 1.
Marra  calculates quantum yield (φ) as equal to PP/[Ez*aph*chl], where φ is in mol C (or O2) per mol of photons, PP is in mol C (or O) m−3 d−1, Ez is photosynthetically active radiation (PAR) at depth (mol photon m−2 d−1), aph is mean pigment adsorption per unit chlorophyll (m2 per mg chlorophyll a) and chl is the chlorophyll a concentration (mg m−3). Marra uses values for Ez and chlorophyll concentration measured on the day and at the depths of the 14C-PP incubations for each HOT cruise, PP rates obtained from either 17Δ-GOP or 14C-PP and assumes a constant value for aph of 0.023 m2 mg chl−1 measured previously at HOT. Marra finds that a significant number of volumetric 17Δ-GOP rates exceed by up to 2–3× the quantum yield limit of 0.125 implied by needing 8 photons to produce 1 molecule of O2 from 2 molecules of H2O. In contrast, the quantum yield based on measured 14C-PP rates are always significantly less than this theoretical upper limit.
Marra  calculates an assimilation number (AN), which he expresses as the volumetric PP rate divided by chlorophyll a concentration, and compares the calculated AN to a maximum rate of 25 mg C h−1 mg chl−1 estimated by Falkowski . He finds that on some HOT cruises the surface 17Δ-GOP chl−1 exceeds the imposed AN limit.
Marra  calculates a growth rate by dividing PP by autotrophic biomass and finds that growth rates calculated using 14C-PP are approximately at the growth rate limit of ∼0.7 d−1 based on Eppley  for surface layer temperatures at ALOHA whereas some 17Δ-GOP estimates exceed this imposed growth rate limit by 3–5×.
 A useful evaluation of the 17Δ-GOP method should present the rates accurately and account for the uncertainties in the method. The significant uncertainty in individual cruise estimates of 17Δ-GOP was clearly stated in Quay et al.  and the reason why they concluded “the uncertainty in an individual 17Δ-GOP determination precludes detection of monthly variations in GOP.” Despite the uncertainty in 17Δ-GOP estimated for individual HOT cruises, seasonally averaged rates of 17Δ-GOP during summer and winter were estimated by Quay et al. using a depth-integrated modification of the 17Δ-GOP method that accounted for time rate of change and corrected for entrainment biases (equation (5) in Quay et al.). During the winter, when the mixed layer is deepening, the depth-integrated 17Δ-GOP estimates indicated a substantial overestimation (by 75%) of the GOP rate for the mixed layer if the 17Δ-GOP method was applied in the usual manner (i.e., assuming steady state and negligible mixing effects) due to entrainment of subsurface waters with high 17Δ values.
 It is important to emphasize that the 17Δ-GOP method integrates productivity over the residence time of O2 in the mixed layer (typically 1–3 weeks at ALOHA) that is significantly longer than single day productivity rates measured by bottle incubations methods (14C-PP and 18O-GOP) and is not necessarily represented by the biological conditions measured during a HOT cruise (chlorophyll, PAR, biomass, etc.). Additionally, it is worth reiterating that 17Δ and 18O methods measure the gross PP rate, whereas 14C method measures something close to net PP [Marra, 2009].
 With these conditions in mind, we evaluate the evidence presented by Marra .
3.1. Quantum Yield
 All the occurrences when quantum yield based on 17Δ-GOP exceeded the limit of 0.125 happen during the winter when the mixed layer 17Δ-GOP is overestimated due to entrainment of subsurface water, as mentioned above (Figure 1). During the summers of 2006 and 2007, φ values at all depths for all summertime HOT cruises are ≤0.125. Using mean 17Δ-GOP rates corrected for time rate of change and entrainment (123 ± 44 mmol O2 m−2 d−1 during summer and 82 ± 42 mmol O2/m−2 d−1 during winter) reported by Quay et al.  (see their Table 2) and average depth profiles of PAR and chlorophyll yields a depth range in φ (5 to 100 m) from 0.03 to 0.08 in summer and 0.02 to 0.125 in winter (Figure 1).
 Two points about the φ calculation are relevant. First, the φ calculation uses PAR measured during the single day 14C-PP incubation on a HOT cruise and does not represent PAR over the integration time represented by 17Δ-GOP. Second, using only downwelling irradiance likely overestimates φ at depth where scattering can contribute significantly (up to ∼40%) to the photon flux available to phytoplankton.
 In conclusion, the mean summer and winter 17Δ-GOP rates yield φ values less than the maximum of 0.125 (except at 75 m during winter where φ equals 0.125). Thus 17Δ-GOP rates do not exceed the imposed φ limit. Quantum yields based on 14C-PP should always be substantially less than the limit, as Marra  determined at ALOHA, because 14C-PP represents close to net PP that will be substantially lower (∼50%) than gross PP.
3.2. Assimilation Number
 A maximum photosynthetic O2 production rate per unit chlorophyll has been estimated at 2 mmol O2 h−1 (mg chlorophyll)−1 based on an assumed chlorophyll/O2 (Emerson-Arnold number) of 2000, density of O2 evolving centers of 3.3 × 1011 per ug chlorophyll and an O2 turnover time of 1 ms [Falkowski and Raven, 2007], which corresponds to ∼25 mg C (mg chlorophyll)−1 hr−1, i.e., the maximum AN value used by Marra , assuming a molar equivalence of O2 production and carbon fixation. The uncertainty in this AN limit is not reported by Marra.
 The calculated AN values based on 17Δ-GOP for individual HOT cruises range from about 1 to 4 (mmol O2 h−1 mg Chl−1). The winter 17Δ-GOP are overestimated significantly (∼70%) due to entrainment effects, as discussed above. However, the summertime AN values at 5 m show a similar range of about 1 to 3.5. Assuming for now, that the AN limit of 2 is a firm maximum, then this limit implies that the 17Δ-GOP method overestimates GOP in surface waters during several summer cruises. This result is not surprising. As noted above, the ±40% uncertainty in an individual 17Δ-GOP estimate lead Quay et al.  to conclude the method could not detect monthly variations in GOP at ALOHA. The impact of the 17Δ-GOP uncertainty on AN is significant (e.g., assuming a mean surface AN = 2.0, then a ±40% uncertainty in individual AN estimates would imply that 95% of the individual estimates range from 0.4 to 3.6). To reduce the impact of 17Δ-GOP methodological uncertainties, Quay et al. based their comparison of PP methods on mean summer and winter 17Δ-GOP rates that corrected for entrainment biases and nonsteady state conditions, as discussed above. Using these mean summer and winter 17Δ-GOP rates (presented above and in Table 2 in Quay et al.) and converting to volumetric equivalents following Marra's  procedure yields a mean summer and winter surface AN values of 2.2 ± 0.8 and 1.0 ± 0.5 mmol O2 hr−1 mg Chl−1, respectively (Figure 2). The summer mean surface AN is 10% above the prescribed limit of 2 mmol O2 hr−1 mg Chl−1, although with significant uncertainty at ±0.8. It is useful in this context to compare to AN values estimated from 18O-GOP estimates as this incubation approach does not share the uncertainties associated with the 17Δ-GOP budget method. The range in surface 18O-GOP chl−1 was 1.0 to 1.9 (mean 1.5 ± 0.1) in summer and 0.5 to 1.3 (mean 0.9 ± 0.1) mmol O2 hr−1 mg Chl−1 in winter, with AN approaching the prescribed limit of 2 mmol O2 hr−1 mg Chl−1 during some summer cruises. The mean summer surface AN based on 17Δ-GOP was 50% higher than that based on 18O-GOP whereas the mean winter surface AN values for the two independent GOP estimates were the same.
 The key question is whether or not the imposed maximum AN of 2 mmol O2 hr−1 mg Chl−1 provides a meaningful constraint on mean summer 17Δ-GOP, which exceeds this limit by only 10% at the surface (with uncertainty of ±30%). Furthermore, what is the uncertainty in the imposed maximum AN? There is likely significant uncertainty in the three factors on which the AN limit is based. For example the assumed Emerson-Arnold number is chosen at 2000 but the range is from 1500 to 2500 [Falkowski and Raven, 2007]. What are the uncertainties in the assumed density of O2 evolving centers (3.3 × 1011 per ug chlorophyll) and O2 turnover time (1 ms) that yield the maximum AN of 2 mmol O2 hr−1 mg Chl−1? Thus it is not clear whether a mean surface AN of 2.2 ± 0.7 mmol O2 hr−1 mg Chl−1 in summer at ALOHA significantly exceeds the AN limit.
 It is not surprising that 14C-PP based AN rarely reach the maximum of 25 mg C hr−1 mg chl−1, as observed by Marra . 14C-PP measures closer to net than gross carbon fixation [Marra, 2009] and thus should substantially underestimate maximum AN. The 18O-GOP/14C-PP of 1.9 ± 0.5 observed by Quay et al.  at ALOHA indicate that the gross carbon fixation rate would be about twice the 14C-PP rate if the molar ratio of O2/C production during photosynthesis was 1. However, the O2/C production is likely significantly greater than 1 because of O2 production associated with Mehler and photorespiration that is measured by 17Δ-GOP and 18O-GOP but not represented by C fixation measured by 14C-PP. Supporting the observations at ALOHA, Halsey et al.  determined in chemostat cultures of model organisms that ∼25% of O2 evolution is not associated with C-fixation and net fixation is ∼40% of GOP.
 Thus the mean surface AN (at 5 m) in summer based on 14C-PP is only 30% of the prescribed maximum (7.4/25 mg C hr−1 mg Chl−1), whereas the AN based on 18O-GOP is at 75% of the maximum (1.5/2 mmol O2 hr−1 mg Chl−1) and 17Δ-GOP is 110% of maximum (2.2/2 mmol O2 hr−1 mg Chl−1).
3.3. Growth Rate
 Growth rate represents the time rate of change of phytoplankton biomass divided by the biomass, which Marra  approximates as PP (mg C m−3 d−1) divided by autotrophic biomass (mg C m−3). Using 14C-PP, which approximately represents net carbon fixation, yields a mean surface growth rate of ∼1.5 ± 0.7 d−1 in both summer and winter at ALOHA. This value is similar to the growth rate estimate of 1.3 ± 0.3 d−1 in the subtropical N. Pacific off Oahu by Laws et al. , which they compare to a maximum rate of 1.6 d−1 at 27°C based on Eppley . In contrast, estimating growth rate from gross PP rate (either 17Δ-GOP or 18O-GOP) seems inappropriate as it is net production, not gross production, which yields a time rate of change of phytoplankton biomass. As there is substantial autotrophic respiration, gross PP rates should substantially overestimate growth rate. This is demonstrated by calculating growth rates based on 18O-GOP measured at ALOHA which yield a mean surface growth rate of 3.8 ± 1.8 d−1 that is more than twice the growth rate estimated from 14C-PP. Thus growth rate limits do not constrain GOP measured either by 18O-GOP or 17Δ-GOP.
Marra  brings to the table additional tests of the 17Δ-GOP (and 18O-GOP) method that Quay et al.  had not considered, i.e., PP limits based on quantum yield and assimilation number. These are potentially useful constraints.
 Contrary to Marra's  conclusions that the 17Δ-GOP volumetric rates often exceed the maximum quantum yield, neither the summer nor winter 17Δ-GOP rates (corrected for time rate of change and entrainment) exceed quantum yield limits (Figure 1). This difference in conclusions emphasizes that comparisons of PP methods, although necessary and potentially informative, must be done with care.
 The mean summertime surface 17Δ-GOP at 2.2 ± 0.8 mmol O2 hr−1 mg Chl−1 barely exceeds the maximum assimilation number of 2 mmol O2 hr−1 mg Chl−1 prescribed by Marra . Given the significant uncertainties in both the 17Δ-GOP rate (±30%) and maximum AN (at least ±25%) it is not clear whether summertime surface 17Δ-GOP rates exceed AN limits. In winter, mean surface AN from 17Δ-GOP is at ∼50% of the AN limit. In contrast, AN estimates based on 14C-PP are not particularly useful because 14C-PP represents net rather than gross PP and would not be expected to reach a photosynthetic limit.
 Gross PP rates are not constrained by growth rate limitations as growth rate depends on net, rather than gross, PP.
 An important issue in any PP method comparison or evaluation is the one of PP currency. Currently employed PP methods measure gross O2 production (17Δ-GOP, 18O-GOP), fluorescence (FRRF) and carbon assimilation (14C-PP), yet comparison in a common currency of carbon productivity is not straightforward. Marra  assumes an O2:C production ratio of 1, yet photorespiration and Mehler reactions yield gross O2 production (as measured by 18O-GOP and 17Δ-GOP methods) that occurs without a corresponding net molar C fixation. Depending on the magnitude of these reactions, the O2:C production ratio may be significantly >1. For example, the ratio of photosynthetic O2 production to CO2 fixation has been observed to vary from 1 to 1.6 and depend on light and nutrient availability [Zehr and Kudela, 2009]. At ALOHA, the measured 18O-GOP/14C-PP decreased from 2.4 ± 0.3 at 5 m to 1.1 ± 0.1 at 100 m (Figure 1 in Quay et al. ) which in part could result from an O/C production ratio that increased with photon flux. Furthermore, a similar ratio of GOP/14C-PP of 2.9 ± 0.2 at ALOHA was estimated using GOP rates based on FRRF measurements [Corno et al., 2006].
 Clearly, more field and lab measurements are needed to unravel the reasons why the ratio of GOP (based on either 17Δ or FRRF) to 14C-PP vary so widely (3–8×) in the ocean [e.g., Sarma et al., 2005; Corno et al., 2006; Luz and Barkan, 2009; Robinson et al., 2009; Quay et al., 2010]. It is only because of the addition of non-incubation based PP estimates with which to compare to traditional incubation-based PP methods that these issues are being evaluated, discussed and argued about. This is a good thing.