Subject only to methodological shortcomings and the free availability of exploitable inorganic carbon, the most useful indicator of the potential primary production, Pg (or Pn, sensu Pg — Ra) (see Section 3.3.2) comes from the areal integration of the instantaneous measurements of pho-tosynthetic rate (ENP, in mgC fixed m—2h—1) (see Section 3.3.1). The productivity, sensu production per unit biomass, measured in mg C fixed (mg biomass C)—1 h—1, is a valuable comparator. However, for periods relating to the recruitment of new generations, it is helpful to measure (or to extrapolate) carbon uptake over longer periods, comparable, at least, with the generation time required for cell replication to occur. This generally means designing experimental exposures of 12 or 24 h. Such designs increase the risk of measurement error (through depletion of unre-plenished carbon, possible oxygen poisoning and the increasing recycling of 'old' carbon; see Section 3.3.2). These problems may be overcome by mounting contiguous shorter experiments (see the notable example of Stadelmann et al., 1974) but it is generally desirable to integrate results from a small number of short, representative field measurements (i.e. to extrapolate the values EE NP, EE NR). With alternative techniques for proxy estimates of biomass and production rates (remote variable chlorophyll fluorometry; Kolber and Falkowski (1993) and see Section 3.3.4), the usefulness of models to relate instantaneous estimates to water-column integrals over periods of hours to days is self-evident.
Integral solutions for calculating primary production over 24 h were devised some 50 years ago. Several, generically similar formulations are available, differing in the detail of the manner in which they overcome the difficult diurnal integration of the light field, especially the diel cycle of underwater irradiance in reponse to the day time variation in I0 and its relationship to Ik. For instance, Vollenweider (1965) chose an empirical integral to the diel shift in I0, employing the quotient, r[(0.70 ± 0.07) I0 max], where r is the length of the daylight period from sunrise to sunset. Extrapolation of EE NP, in respect of the measured NPmax (or, rather, an empirically fitted proportion, [(0.75 ± 0.08) NPmax], that compensates for the proportion of the day when I0 < Ik) invokes the coefficient of underwater light extinction (e). The Vollenweider solution is:
EE NP = (0.75 ± 0.08) NP max x r x ln([0.70 ± 0.07]I0max/0.5Ik) x 1/e
Talling (1957c) had earlier tackled the integration problem by treating the daily light income as a derivative of the daytime mean intensity, I0, applying over the whole day (r). He expressed I0 in units of light divisions (LD), where LD = ln(I0 max/0.5Ik) / ln2), having the dimensions of time. The daily integral (LDH) is the product of LD and r, approximating to:
The completed Talling solution, equivalent to Eq. (3.20) is:
Numerically, the two solutions are similar. Applied to the data shown in Fig. 3.3, for example, where N = 47.6 mg chla m-3, Pmax = 2.28 mg
, and suppos ing £ = 1.33 (£min) = 1.33 (£w + £p + N£a), where (£w + £p) = 0.422 m-1 and £a = 0.0158 m2 (mg chla)-1, EENP is solved by Eq. (3.20) to between 1531 and 2020 mg O2 m-2 d-1. For the Talling solution, the daily mean integral irradiance (406
|imol photons m is used to predict EENP
= 2119 mg O2 m-2 d-1. For comparison, interpolation of the profiles represented in Fig. 3.9 sum-mates to approximately 2057 mg O2 m-2 d-1.
Most of the variations in the other integra-tive approaches relate to the description of the light field. Steel's (1972, 1973) models used a proportional factor to separate light-saturated and sub-saturated sections of the P vs. I curve. Taking advantage of advances in automated serial measurements of the underwater light field, A. E. Walsby and his colleagues have devised a means of estimating column photosynthesis at each iteration and then summating these to gain a direct estimate of EE NP (Walsby, 2001) (see Section 3.3.3).
We may note, at this point, that all these estimates of gross production (Pg; on a daily basis, the equivalent of EE NP) need correction to yield a useful estimate of potential net production (Pn = Pg - Ra, as defined in Section 3.3.2). Again, taking the example from Fig. 3.3, we may approximate EENR as the product, 24 h x H x NR, where mean H = 4.8 m, R = 0.101 mgO2(mg chla)-1 h-1 and N = 47.6 mg chla m-3 to be EENR ~ 554mg O2 m-2 d-1. The difference with Pg gives the daily estimate of Pn (strictly, we should distinguish it as NP n):
Since many of these approaches were developed, it has become more common, and scarcely less convenient, to measure, or to estimate by analogy, photosynthetic production in terms of carbon. Supposing a photosynthetic quotient close to 1.0 (reasonable in view of the governing conditions - see Section 3.2.1), the net carbon fixation in the example considered might well have been about 0.564 g Cm-2 d-1. Relative to the producer population (4.8 m x 47.6 mg chla m-3) this represents some 2.47 mgC(mg chla)-1 d-1, or around 0.05mgC(mg cell C)-1 d-1.
Such estimates of local production are the basis of determining the production of given habitats (Pn), the potential biomass- (B-)specific productive yields (Pn/B) and the organic carbon made available to aquatic food webs. The productive yield may sometimes seem relatively trivial in some instances. Marra (2002), reviewing experimental production measurements, showed daily assimilation rates in the subtropical gyre of the North Pacific in the order of 6 mg C m-3 d-1. However, this rate was light saturated to a depth of 70 m. Positive light-limited photosyn-thetic rates were detected as deep as 120 m. Thus, area-integrated day rates of photosynthesis (~570mgCm-2d-1) could be approximated that are comparable to those of a eutrophic lake. However, the concentration of phytoplankton chlorophyll (~0.08mgchla m-3 through much of the upper water column reaching a 'maximum' of 0.25 mg chla m-3 near the depth of 0.5 Ik) indicates chlorophyll-specific fixation rates in the order of only 60mgC(mg chla)-1 d-1. Carbon-specific rates of ~1.2mgC(mg cell C)-1 d-1 are indicated. This is more than enough to sustain a doubling of the cell carbon and, in theory, of the population of cells in the photic layer. It is curious, not to say confusing, that eutrophic lakes are often referred to as being 'productive' when ultraoligotrophic oceans and lakes are described as 'unproductive'. This may be justified in terms of biomass supported but, taking (Pn/B) as the index of productivity, then the usage is diametrically opposite to what is actually the case.
In areal terms, reports of directly measured productive yields in lakes generally range between ~50mg and 2.5gCm-2d-1 (review of Jonasson, 1978). These would seem to embrace directly measured rates in the sea, according to the tabulations in Raymont (1980). Estimates of annual primary production run from some 30-90 g C fixed m-2 a-1 (in very oligotrophic, high-latitude lakes and the open oceans that support producer biomass in the order of 1-5 mg C m-3 through a depth of 50-100 m; or, say, <500mgCm-2), to some 100-200gC fixed
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