## Comment

[1] A recently published article [*Behrenfeld et al*., 2013], hereinafter B2013, extends the work of *Behrenfeld* [2010] hereinafter B2010, to consider the annual cycles of primary production in the subarctic Atlantic Ocean.

[2] B2010 reevaluates the classic Critical Depth Theory, based on *Sverdrup* [1953], which suggests that the spring bloom can initiate when the shoaling mixed layer in the spring becomes shallower than the critical depth. B2010 uses satellite observations of surface colour in the North Atlantic and model-derived estimates of the mixed-layer depth to suggest that depth-integrated biomass actually peaks well before spring. B2010 introduces the Dilution-Recoupling Theory (DRT) to explain the bloom, where initiation of the early bloom is due to deepening of the mixed layer leading to dilution of phytoplankton concentrations and consequent lower total losses because grazing is reduced by lower prey concentrations.

[3] B2013 tests whether satellite-derived estimates of chlorophyll, carbon, and their annual cycles are reproduced in the 3-D primitive equation Biogeochemical Element Cycling-Community Climate System Model (BEC-CCSM). B2013 conclude that the model gives a similar early onset time for the bloom, and that this initiation is largely due to the physical disruption of grazing during winter mixed-layer deepening. They note that it is a “subtle disruption in the food web equilibrium that ultimately yields the spring bloom climax," and recast the DRT as a “disturbance-recovery” process.

[4] Both B2010 and B2013 rely heavily on the argument made in B2010 that mixed-layer deepening in autumn and winter can dilute biomass concentrations with the result that surface concentration does not represent the total biomass in the water column during that time of the year. As a result, B2010 and B2013 use two different formulae for estimating the specific biomass accumulation rates from satellite data, depending on season.

[5] In this comment, I show that the application of these formulae, fundamental to both B2010 and B2013, is flawed. As a result, many of the conclusions made in B2010 and B2013 are in potentially in error, especially during the spring.

[6] Using B2010's notation, the net specific biomass accumulation rate, *r*, is the time rate of change of biomass per unit of biomass.

where *C* is biomass concentration. This rate can be considered the difference between phytoplankton growth and loss rates

where *μ* is the plankton growth rate, and *l* represents all losses including cell respiration, grazing, sinking, and vertical mixing. The rates *r*, *μ* and *l* are specific (i.e., per unit of biomass concentration), have dimensions of inverse time and are usually measured in units of [day^{−1}]. The specific accumulation rate can be computed from the time rate of change of the natural log of biomass

[7] B2010 argues that when the mixed layer is shoaling, or is shallower than the euphotic zone, changes in surface concentration reflect the changes in total biomass in the mixed layer. However, he argues that during winter, the deepening mixed layer dilutes phytoplankton populations with phytoplankton-free water from below, so that changes in the surface concentration does not reflect the changes in total biomass. Indeed, the surface concentration may decrease even if the total biomass increases. B2010 thus argues that when the mixed layer is deepening, accumulation rates should be calculated from the depth-integrated biomass.

[8] As a result, when the seasonal thermocline is shoaling or is shallower than the euphotic zone, i.e., in spring and summer, B2010 (his equation (4b)) and B2013, (their equation (4)), use a discrete form of equation ((3)) to estimate the specific biomass accumulation rate

where *C*_{p} is the surface concentration as determined from satellite, subscripts 1 and 0 indicate measurements at time *t*_{1} and *t*_{0}, respectively, and Δ*t* = *t*_{1} − *t*_{0}.

[9] But, when the seasonal thermocline is deepening i.e., in autumn and winter, B2010 (his equation (4a)) and B2013, (their equation (3)) estimate the accumulation rate from

where Σ*C* is the depth-integrated biomass and can be computed from

where *M* is the mixed-layer depth.

[10] Both B2010 and B2013 present annual cycles in *r* (e.g., B2013 Figure 2b) and use these values to derive their conclusions. In particular, they base much of their argument on ecosystem functioning by analysing loss rates inferred by subtracting *r* as measured by equations ((4)) or ((5)) from depth-integrated growth determined by the Vertically Generalized Production Model [*Behrenfeld and Falkowski*, 1997].

[11] Unfortunately, equations ((4)) and ((5)) measure rates of change of quantities that have different units (*C*_{p} and Σ*C* have units [mg C m^{−3}] and [mg C m^{−2}], respectively). Thus, it is clear that B2010 and B2013 patch together two dimensionally inconsistent accumulation rates to construct an annual cycle to compare with depth-integrated growth rates. This is mathematically incorrect, and as a result, conclusions based on this rate are likely be erroneous. In addition, not only are *C*_{p} and Σ*C* dimensionally different, they have quite different annual cycles. Figure 1 shows annual cycles of *C*_{p} and Σ*C* reported by B2013 for the subarctic North Atlantic, together with their respective rates of change. During autumn and winter, *C*_{p} decreases, whereas Σ*C* increases. Conversely during spring, *C*_{p} increases, whereas Σ*C* decreases.

[12] However, it is not immediately clear what the implications of these potential errors are, and it is worth discussing them. B2013 are clear that their estimates of growth rates are depth-integrated and specific - “…NPP estimates per square meter, which were then divided by active phytoplankton biomass ….” Thus, the B2010 and B2013 estimates of losses appear to be valid for the period where they use equation ((5)) to compute *r* . Hence, one can accept the B2010 and B2013 conclusions about autumn and winter functioning. Their main conclusion here is that depth-integrated biomass increases during winter in the North Atlantic because growth exceeds losses. This alone is a significant conclusion, because it immediately voids the Critical Depth Theory (which requires a light-limited regime as initial winter conditions).

[13] The B2010 and B2013 spring-bloom arguments, however are erroneous because they compare surface concentration accumulation rates to depth-integrated growth rates. They also compare their calculations of *r* from before and after the time of deepest seasonal thermocline. Core to the DRT argument of ecosystem cycling in the spring is B2013's observation “…values of *r* are near maximum (at time of deepest MLD) but then **show little response** to the large spring-time increases in *μ* …” (my bold). As a result, B2010 suggests that the increase in *C*_{p} seen in the spring is a result of continued high depth-integrated growth, combined with the cessation of dilution once the seasonal thermocline stops deepening. Elaborating on this, B2013 attribute the spring bloom to a “subtle disruption in the food web equilibrium."

[14] Unfortunately, however, this apparent lack of response in *r* arises because of B2010's transition from equation ((5)) to equation ((4)) at the time of deepest MLD. In fact, based on their data (Figure 1), the depth-integrated accumulation rate rapidly decreases and becomes negative in the spring, indicating that depth-integrated losses exceed depth-integrated growth. At the same time, surface concentration increases. This suggests a decoupling between surface and deep processes. This decoupling supports the more traditional idea promoted by *Chiswell* [2011]; *Taylor and Ferrari* [2011] and others that the spring bloom is initiated by the emerging near-surface stratification in the spring when deep mixing turns off.

[15] There is one more point that needs to be made, in that B2010 and B2013 use equation ((6)) to estimate the depth-integrated biomass throughout the year from surface concentration and the mixed-layer depth, *M*. Implicit in B2010 and B2013 is that *M* is the depth of the seasonal thermocline, which has an annual cycle as shown in Figure 1. This use of equation ((6)) is based on the misconception that the water column above the thermocline remains well mixed in all tracers at all times, and that as the thermocline shoals in the spring, plankton below the thermocline are detrained and “lost” to the system. B2010 and B2013 fail to recognize that equation ((6)) is only valid when the seasonal thermocline is deepening. In the spring, once convective overturn ceases, increasing insolation creates shallow near-surface warm layers. These near-surface mixed layers do not extend as deep as the seasonal thermocline—in other words the correct value of *M* in the spring is many times shallower than the depth of the thermocline. In addition, there is likely to be growth in the euphotic zone below these near-surface mixed layers [*Chiswell*, 2011; *Taylor and Ferrari*, 2011]. The net result is that the vertical profile of biomass in the spring is likely to be maximum at the surface and decay with depth, but cannot be easily parameterized. As a result, depth-integrated biomass cannot be estimated from equation ((6)) in the spring. The direct implication of this for B2010 and B2013 is that their values of depth-integrated biomass after the time of deep mixing are likely to be significantly over estimated, with the result that the true value of *r* decreases even faster than shown in Figure 1.

[16] In summary then, the analyses of B2010 and B2013, which form the basis for the Dilution-Recoupling Theory, are potentially flawed by their use of a specific biomass accumulation rate that changes from using depth-integrated biomass to using surface concentration. Their formulation during autumn and winter is valid. As a consequence, the DRT provides a useful explanation of winter ecosystem functioning, and in particular, disputes the long-standing belief that winter production is light-limited in the North Atlantic. However, the formulation in the spring is invalid. Not only is their formulation mathematically incorrect but also their derived accumulation rate behaves in the opposite direction to the correct rate. As a consequence, the DRT does not provide an explanation for the evolution of the spring bloom.