The achievement of even 48.3 Pg across some 360 x 106 km2 of ocean (note, areal average ~133gC fixed m-2a-1) should be viewed against the typically small active photosynthetic standing-crop biomass (on average, perhaps just 1-2gCm-2, Pn/B ~ 100). The supportive potential of this conversion is certainly impressive but it represents poor productive yield against the potential yield were every photon of the solar flux captured and its energy successfully transferred to carbon reduction. It is possible that the rate is constrained; or that the rate is rapid but the producer biomass is constrained; or, again, that other processes impinge and the productive yield is constrained.

These are problems of capacity - how rapidly can production proceed before the metabolic losses might balance the productive gains or before the assembly of biomass might become, subject only to the supply of the material components. The problem will not be addressed fully before the physiology of resource gathering and growth have been addressed (Chapters 4 and 5). For the present, we will examine the constraints of insolation and carbon flux on the biomass of phtoplankton that may be present.

Commencing with the productive capacity of the solar quantum flux to the top of the atmosphere (see Fig. 2.2), the income of 25-45 MJm-2d-1 provides the basis for a theoretical annual income of 12-13 GJ m-2 annually. Taking only the PAR (46%) and subjecting the flux to absorption in the air by water vapour, reflec tion by cloud and backscattering by dust, it is unrealistic to expect much more than 30% of this to be available to photosynthetic organisms (say 3.6 GJm-2 PAR). Using the relationships considered in Section 3.2.3, the potential maximum yield of fixed carbon is 3.6GJm-2/470kJ(molC fixed)-1, i.e. in the order of 7 kmol m-2 a-1, or about 85 kg C m-2 a-1. This is about 100 times greater than measured or inferred optima. Even if we start with something a little less optimistic, such as the PAR radiation measured at the temperate latitude of the North Sea (annual PAR flux ~1.7GJm-2), we still find that no more than about 1.5% of the energy available is trapped into the carbon harvest of primary production.

Looking at the issue in the opposite direction, the minimum energy investment in the carbon that is harvested (Table 3.3) by planktic primary producers is usually a small proportion of that which is available. To produce 50-800 g C m-2 a-1 requires the capture of a minimum of 9-144 mol photons m-2 a-1, equivalent to 2-32 MJm-2 a-1, or less than 2% of the available light energy.

There are many reasons for this apparent inefficiency. The first consideration is the areal density of the LHCs needed to intercept every photon. This can be approximated from the area of the individual centre, the (temperature-dependent) length of time that the centres are closed following the preceding photon capture and, of course, the photon flux density. It was argued, in Section 3.2.1, that the area of a PSII LHC (aX) covers about 10 nm2. Thus, in theory, it requires a minimum of 1017 LHCs to cover 1 m2. It was also shown that 1 g chlorophyll could support between 2.2 and 3.4 x1018 LHCs and, so, might project an area of ~22 m2 and harvest photons over its entire area. At very low flux densities, the intact LHC network (0.045 g chla m-2) has some prospect - again, in theory - of intercepting all the bombarding photons but, as the flux density is increased, it is increasingly likely that photons will fall on closed centres and be lost. Saturation of the network (Ik) is, in fact predicted by:

where tc is the limiting reaction time (in s photon-1). At 20 °C, when tc ~ 4 x10-3 s (see Section 3.2.1), Ik is solved from Eq. (3.24) as (10 x

With supersaturation, more of the photons pass the network or bounce back. Increasing the areal density of LHCs increases the proportion of the total flux intercepted but, in the opposite way, the increasing overlap of LHC projection means that individual LHCs are activated less frequently.

There is no light constraint on the upper limit of light-intercepting biomass surface per se, but the cost of maintaining underemployed photo-synthetic apparatus and associated organelles is significant. Ultimately, the productive capacity is set not by the maximum rate of photosynthesis but by the excess over respiration. Reynolds (1997b) developed a simple model of the capacity of the maximum photon flux to support the freshwater unicellular chlorophyte Chlorella. The alga was chosen for its well-characterised growth and photosynthetic properties. The 'maximum' set was 12.6 MJ m-2 d-1, based upon the flux at the summer solstice at a latitude of 52 °N and supposing a dry, cloudless atmosphere throughout (equivalent daily photon flux, 57.6 mol). Higher daily incomes occur in lower latitudes but the small shortfall in the adopted value need not concern us here).

The available light energy is represented by the vertical axis in Fig. 3.18. The temperature is assumed to be invariable at 20 °C. A relatively small numbers of cells of Chlorella (diameter 4 | m, cross-sectional area 12.6 | m2, carbon content 7.3 pg C or 0.61 x 10-12 mol C cell-1, carbon specific projection 20.7 m2 (mol cell C)-1) are now introduced into the light field. They begin to harvest a small fraction of the flux of photons. At low concentrations, the cells have no difficulty in intercepting the light. At higher concentrations, cells near the surface will partly shade out those beneath them. Even if the whole population is gently mixed, the probability is that cells will experience increasingly suboptimal illumination and approach a condition where a larger aggregate portion of each day is passed by each cell in effective darkness. The onset of suboptimal absorption begins when there is a probabilistic occlusion by the Chlorella canopy, i.e. at

an areal concentration of 1/(20.7 m2 (mol cell C)-1) = 0.0483 mol cell C m-2 (or ~0.58gC, or about 11 mg chla m-2). Above this threshold, the cell-specific carbon yield decreases while the cell-specific maintenance remains constant. Thus, for increasingly large populations, total maintenance costs increase absolutely and directly with crop size; total C fixation also increases but with exponentially decreasing efficiency. While the daily photon flux to the lake surface remains unaltered, the asymptote is the standing crop which dissipates the entire 12.6 MJ m-2 d-1 without any increase in standing biomass (somewhere to the right in Fig. 3.18).

Taking the basal respiration rate of Chlorella at 20 °C to be ~1.1 x 10-6 mol C (mol cell C)-1 s-1 (Reynolds, 1990), the energy that would be consumed in the maintenance of the biomass present is supposed to be not to be less than 0.095 mol C (mol cell C)-1 d-1. To calculate the maximum biomass sustainable on a photon flux of 57.6 mol photon m-2 d-1, allowance must be made for the quantum requirement of at least 8 mol photons to yield 1 mol C and for the fraction of the visible light of wavelengths appropriate to chlorophyll excitation (~0.137: Reynolds, 1990,1997b). Then the daily photon flux required to replace the daily maintenance loss is equivalent to 0.095 x 8/0.137 = 5.55 mol photons (mol cell C)-1 d-1. This is the slope of the straight line inserted in Fig. 3.18. It follows that the maximum sustainable population is that which can harvest just enough energy to compensate its respiration losses under the proposed conditions, i.e. 57.6/5.55 = 10.4 mol cell C m-2 (~125gCm-2).

Not surprisingly, there is little evidence that quite such high levels of live biomass are achieved, much less maintained, in aquatic environments, although it is not unrepresentative of tropical rainforest. There the true producer biomass of up to 100gCm-2 is massively augmented by 10-20 kg C m-2 of biogenic necromass (wood, sclerenchyma, etc.: Margalef, 1997). In enriched shallow lakes, phytoplankton biomass is frequently found to attain areal concentrations equivalent to 600-700 mg chla m-2 (Reynolds, 1986b, 2001a), more rarely 800-1000 mg chla m-2 (Talling et al., 1973; i.e., 30-50gCm-2). This relative poverty is due, in part, to the markedly sub-ideal and fluctuating energy incomes that water bodies actualy experience. Moreover, frequent, weather-driven extensions of the mixed layer determine a lower carrying capacity for the entrained population (Section 3.3.3).

Light absorption by water is a powerful detraction from the potential areal carrying capacity that increases with the depth of entrainment. If we solve Eq. (3.17), for instance, against nominated values for I'0 = 1000 and for Im = 1.225 |imol photons m-2 s-1, the mixed-layer integral is I* = 35 |imol photons m-2 s-1, which is sufficient to impose a significant energy constraint on further increase in biomass. From Eq. (3.11), we can work out that the coefficient of attenuation equivalent to diminish 1000 down to 1.225

|imol photons m retical phytoplankton concentration that would generate these light conditions is demonstrably equivalent to 650 mg chla m-3 and that it would absorb some 97% of the incoming light. However, if the mixing extends to 10 m, Nea = 4.7, the chlorophyll a (470 mg m-2) can now have a maximum mean concentration of only 47 mg m-3, accounting for 70% of the light absorbed. If mixing extends 30 m, Nea = 0.7 and the chlorophyll a capacity (70 mg m-2) can have a concentration of no more than 2.3 mg chla m-3, which absorbs no more than 10% of the incoming light.

Finally, capacity may also be approximated from the integral equations for primary production and respiration. Taking the Vollenweider Eq. (3.20) for EENP, for instance, capacity is deemed to be filled when it is precisely compensated by respiration, i.e. when EENP = EENR, and EE NP /EE NR = 1. Given that EE NR is equivalent to the product, 24 h x H x NR, we may approximate that:

[0.75NPmax x r x ln (0.7010max/0.5Ik) x1/e]/[24h x H x NR] = 1

N = (1/ea)[0.75(Pmax/R) x (r/24) x ln(0.7010max/0.5Ik)

Now, supposing that this extinction occurs in a mixed layer extending through just the top metre (z = 1), we may deduce from Eq. (3.14) that s = 6.7 m-1 = (sw + sp) + Nsa. Putting (sw + sp) = 0.2 m-1 and sa = 0.01 m2 (mg chla)-1, the theo-

The general utility of this equation is realised in two ways. First, it can be used to gauge the annual variation in photosynthetic carrying capacity of a water body of known intrinsic light-absorbing properties (sw + sp) and known seasonal variation in mixed-layer depth (hm in substitution of H). In the application and spreadsheet solution of Reynolds and Maberly (2002), (Pmax/R) was set at 15 and sa at 0.01 m2 (mg chla)-1.

Second, the equation has been used by Reynolds (1997a, 1998a) to illustrate the impact of the depth of convective mixing on phytoplankton carrying capacity (reproduced here as Fig. 3.19). Against axes of mixed depth (hm) and background light extinction (sw + sp, with a minimum set, arbitrarily, for fresh waters at 0.2 m-1) and supposing r = 12 h, Fig. 3.19 shows graphically how the maximum chlorophyll-carrying capacity is diluted by mixing, from ~150mgchla m-3 in

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