Integral photosynthetic rate

understand the role of oceanic photosynthesis in the global carbon cycle and therefore the greenhouse effect, and also by the wealth of data on the distribution of phytoplankton biomass through the world's oceans, which has come from remote sensing.

As pointed out by Behrenfeld and Falkowski (1997a) in their review of this topic, depth-integrated productivity models have been appearing in the literature on average once every two years for several decades. No attempt will be made here to describe all these: rather we shall outline just a few representative examples of the many different approaches that have been proposed for the determination of integral productivity. One useful generalization that can be made straight away is that expressions for areal production normally incorporate a ([Chl]Pm/Kd) term. Proportionality of production to the concentration, and to the photosynthetic capacity, of the phytoplankton in the water column is to be expected. Proportionality to 1/Kd is readily understood if we remember that the total amount of light instantaneously available in the water column is proportional to 1/wK0(av) (see §6.5).

Two of the earliest algorithms were those of Ryther (1956) and Talling (1957b); both of them for vertically homogeneous phytoplankton populations. Ryther arrived, on the basis of measurements of photosynthesis/ light intensity curves on cultures of 14 marine phytoplankton species, at a notional average relative light response curve (ratio of photosynthetic rate to maximum photosynthetic rate, as a function of irradiance) for marine phytoplankton populations. Using this curve he was then able to calculate a dimensionless parameter, Rs, which specified how the daily integral photosynthesis would vary with the daily insolation, and obtained the expression

Kd where Psat is the light-saturated photosynthetic rate of the population per unit volume of water (mg C m~3 hr_l), and Kd is the vertical attenuation coefficient for downward irradiance of PAR. Psat can be replaced by the product of phytoplankton concentration and the maximum specific photosynthetic rate.

If a plausible value for the maximum specific photosynthetic rate, or assimilation number (units mg C mg chl a-1 hr-1), P*m, can be assumed for the phytoplankton in a particular region, and if Kd can be estimated as a function of phytoplankton concentration ([Chl]), then daily integral production can be estimated simply from daily insolation (giving Rs, using the Ryther empirical curve) and phytoplankton concentration. Ryther and Yentsch (1957), on the basis of their own, and literature, data suggested that 3.7 mg C chl a-1 hr-1 was a good estimate of the assimilation number of oceanic phytoplankton, and found that when used in eqn 11.4 it gave estimates of integral production in good agreement with those from in situ measurement. Falkowski (1981), however, with the benefit of access to much more oceanographic productivity information than was available in 1957, concluded that phytoplankton assimilation numbers are affected by nutrient levels, temperature, cell size and light history, and in fact vary commonly between 2 and 10 mg C mg chl a-1 hr-1.

It will be noted that Ryther (1956), by adopting a standard relative light curve implicitly assumed a fixed value for the saturation onset parameter, Ek, of marine phytoplankton. In the Talling (1957b) algorithm for calculating areal production, by contrast, Ek is included as one of the parameters whose value is selected at each location. On the basis that phytoplankton photosynthesis varies with light intensity in accordance with the equation of Smith (1936) (eqn 10.8), and that irradiance of PAR diminishes exponentially with depth, and ignoring photoinhibition, Talling calculated a standard curve for the photosynthetic rate per unit volume, as a function of depth. By measurement of the area under the curve, and relating it to various parameters of the system, he was able to show that the following relationship approximately holds

A Kd

0.5Et

where Ed(0) is the downward irradiance of PAR just below the surface. Talling found that eqn 11.5 gave reasonably accurate estimates of PA over a wide range of values of Ed(0)/Ek, but significant discrepancies did arise for low surface light intensities (Ed(0) < Ek). To obtain the daily total of photosynthesis per unit area, Talling found the relationship

Areal photosynthesis per day — n

where Ed (0) is the mean value of subsurface downward irradiance during daylight hours, N is daylength in hours, and 0.9 is an empirical correction factor, to be satisfactory. The expression in square brackets corresponds to the Rs term in the Ryther equation (11.4). As with the Ryther equation, the Talling equation can be used to estimate daily integral production from daily insolation and phytoplankton concentration, with the additional requirement that an appropriate value be assigned to the saturation onset parameter, Ek. Platt et al. (1990) have, by a mathematically sophisticated approach, arrived at an exact but complex analytic solution for the daily integral of photosynthesis by phytoplankton in a vertically homogeneous water column.

Conceptually, one of the simplest solutions to the problem of estimating oceanic primary production from remote sensing data makes use of the parameter, C, known as the the light utilization efficiency function,376,384 discussed earlier (§10.3), which is the total net integral daily primary production in a 1 m2 water column (g C m-2 day-1), divided by the total amount of phytoplankton chlorophyll a in the water column (g chl a m-2), and by the total light energy in the form of PAR incident upon the top of the water column in one day (mol quanta m-2 day-1). If it proved to be the case that C (units g C (g chl a)-1 (mol quanta)-1 m2) had, even if only very approximately, the same value everywhere in the ocean, then global marine primary production could be estimated from remotely sensed values of phytoplankton chlorophyll and surface-incident irradiance.

On the basis of a survey of literature data available up to that time, Platt (1986) arrived, as discussed earlier, at the encouraging conclusion that C varied only over the range 0.31 to 0.66 g C (g chl a)-1 (mol quanta)-1 m2. More recent data, however, indicate that C is in fact much more variable than this. Campbell and O'Reilly (1988) found, for example, in a wide-ranging study over the oceanographically diverse northwest Atlantic continental shelf, that C varied about 100-fold, from about 0.1 to 10, and furthermore that its average value was 1.47 g C(gchl a)-1 (mol quanta)-1 m2, much higher than the values reported by Platt.

Even though it does not seem to be quite the 'biogeochemical constant'944 that it was originally hoped to be, C is nevertheless a useful unifying concept, and consideration of why in fact it varies so much may be fruitful. Platt (1986) showed that in vertically homogeneous waters, C = a/4.6, where a is the initial slope of the photosynthesis versus light intensity curve (§10.1) of the phytoplankton population. Platt et al. (1992) found the value of a to vary about 12-fold with time and place in cruises in the western North Atlantic. Measurements within one water mass during the spring bloom indicated a marked decrease in a as nitrate levels declined.

Ways of increasing the accuracy with which the geographical distribution of integral primary productivity can be calculated from remote sensing data are under active study in a number of centres. In order to discuss what parameters need to be estimated, we can make use of a general formulation arrived at by Platt and Sathyendranath (1993) using dimensional analysis.

where D is daylength and f[Ed (0+)/Ek] is some function of the surface-incident solar irradiance and the saturation onset parameter of the phyto-plankton. An alternative, but essentially equivalent, general formulation is given by Behrenfeld and Falkowski (1997a)

where Csurf is the chlorophyll concentration in the surface layer (e.g. as determined by remote sensing), zeu is the euphotic depth (which is proportional to 1/Kd), Pbopt is the maximum chlorophyll-specific carbon fixation rate observed within a water column, DL is the daylength, and F is the relative fraction of potential photosynthesis lost within the euphotic zone due to light limitation (F being a function of Ed(0+)/Ek).

Values of [Chl ] can be obtained by remote sensing, but apply only to the surface layer: in the ocean, phytoplankton concentration can vary markedly with depth. Morel and Berthon (1989) and Uitz et al. (2006) found that the profile of chlorophyll as a function of optical depth varied in a systematic manner from quasi-uniformity in eutrophic waters to a clear-cut deep chlorophyll maximum in oligotrophic waters. On this basis, statistical relationships were derived by means of which the chlorophyll a content integrated over the euphotic zone could be estimated from the near-surface chlorophyll a concentration obtained by remote sensing. To characterize the actual depth distribution of chlorophyll where a DCM is present, Platt et al. (1988) proposed a generalized pigment profile consisting of a Gaussian curve (to represent the chlorophyll maximum) superimposed on a constant background level. Millan-Nunez et al. (1997) found the Platt et al. model to work satisfactorily for chlorophyll profiles in the California Current System between 28° and 37° N. Thus, once the trophic level of the water mass has been identified from the surface chlorophyll concentration, a plausible depth profile can be arrived at. Alternatively, total euphotic zone chlorophyll can be obtained from surface layer chlorophyll using empirically derived re1ationships946,1240 that have been found to apply, between these quantities. Balch et al. (1989a) used two standardized profiles, based on accumulated data, of relative chlorophyll concentration versus optical depth, one for nearshore and one for offshore waters.

Once the phytoplankton chlorophyll has been estimated, an approximate value of Kd(PAR) can be arrived using an empirical relationship.62 In the case of the very comprehensive Morel (1991) algorithm, however, the chlorophyll values are used, together with a standard phytoplankton absorption spectrum, to give the actual absorption coefficients in a series of 5 nm wavebands over the 400 to 700 nm interval.

The daily surface-incident solar irradiance, Ed(0+), is determined by the date, latitude and atmospheric conditions: the dependence of irradiance on the first two is readily calculable, but the third is the cause of enormous variation, particularly due to the influence of cloud cover. Kuring et al. (1990) have developed a procedure for estimating per cent cloud cover from remotely sensed satellite images and using these values to derive sea-surface irradiance.

There now remains the problem of finding a value for P*m, and it is here that the major uncertainty in the remote sensing of oceanic productivity lies. As we have seen, the photosynthetic characteristics of phytoplankton populations are highly variable both in space and in time, and the reasons are not well understood. One possible cause of variation is temperature. The light-saturated maximum photosynthetic rate, P*m, increases with temperature (Fig. 11.6). Balch et al. (1989a, b) obtained, using data from the Southern California Bight, an empirical expression for the dependence of P*m on water temperature, and another empirical expression for mixed-layer depth, and the rate of decline of temperature with depth below that, as a function of surface temperature. Their PTL algorithm (pigments, temperature, light) combines the calculated chlorophyll and P*m depth profiles to calculate photosynthesis as a function of depth through the euphotic zone.60,61,62 Behrenfeld and Falkowski (1997b), on the basis of a large amount of archived data from many oceanic locations, developed a polynomial expressing Pbopt as a function of surface temperature. The Morel (1991) algorithm also takes temperature into account. The significance of algorithms incorporating temperature in this manner is that sea-surface temperature can be mapped from space.

Pm is a linear function of maximum quantum yield, f m (since Pm = acEk fm) and fm appears to be strongly correlated with nitrogen flux151,512 (see §10.3). The decline of a as nitrate concentration decreased, in the western North Atlantic spring bloom referred to earlier, may be attributable to a decline in fm (since a = af* fm). Variation in fm due to variation in nitrogen availability is therefore another possible basis for variability in Pm, but unfortunately, nitrate concentration, or the depth of the nitracline, cannot be measured by remote sensing. Yet another major possible cause of variation in fm and hence of Pm, is community composition, which can vary either seasonally at a given location, or from one hydrographically distinct water mass to another along a transect in coastal waters.110,1252

Pm is also linearly related to af*, the chlorophyll-specific absorption coefficient of the phytoplankton, and this can not only vary for a given phytoplankton species in accordance with its nutritional status, but will vary even more markedly with the taxonomic composition of the phyto-plankton community, which as we have just seen is highly variable in both time and space.

All in all, therefore, there are good reasons why we must expect Pm to be a highly variable, and difficult-to-predict, quantity from one part of the ocean to another. The most feasible approach to the mapping of marine productivity may therefore be to divide the ocean up into regions, within each of which realistic estimates of the relevant physiological parameters can be made.1068 Platt et al. (2008) offer an approach by which this may be achieved. They define local algorithm to mean a procedure to convert pigment biomass into primary production, where it is understood that all information essential to implement the procedure is available for the particular space-time point concerned. The minimum information includes the pigment biomass and irradiance at the surface, an equation to describe the photosynthetic response to available light (the photosynthesis-light curve), the local magnitudes of the two parameters for this curve (the photosynthesis parameters), an equation to describe the vertical structure of the pigment biomass and the local magnitudes of the parameters of that equation. The values of the various parameters are assigned on a pixel-by-pixel basis, using archived data for the region in question, in accordance with the remotely sensed chlorophyll concentration and surface temperature. As an example, Platt et al. applied their approach to the Northwest Atlantic Ocean, and found it to work satisfactorily.

It will be noted that in all the above discussion of the areal productivity of different parts of the ocean, the light-absorbing biomass has been parameterized in terms of the concentration of phytoplankton chlorophyll a. An alternative approach is proposed by Marra, Trees and

O'Reilly (2007) who argue that over a range of trophic conditions in the ocean, variations in productivity are more closely related to variations in phytoplankton absorption than in chlorophyll a concentration. On the basis of data on primary productivity, phytoplankton pigments and absorption, and ocean optical properties, from the Equatorial Pacific, the Arabian Sea and the Antarctic Southern Ocean, they concluded that productivity normalized to absorption is relatively invariant in the world ocean. The authors acknowledge, however, that since they were unable to include data from the temperate ocean, or from the central ocean gyres, in their analysis, caution in the application of this approach is, for the time being, called for.

As an approach that is at the other extreme to the painstaking, pixel-by-pixel, assessment of biomass and photosynthetic parameters, Berthelot and Deschamps (1994) propose an algorithm that makes use only of the ratio of reflectance in two wavebands, together with incident PAR, using a purely empirical relationship derived by analysis of a large body of in situ data. The data consisted of measurements of chlorophyll, primary production, surface-incident solar irradiance, and spectral downward and upward underwater irradiance at stations (all case 1 type) in the West Atlantic (Sargasso Sea, Gulf of Mexico), East Atlantic (Mauritanian upwelling), tropical East Pacific and South Indian Antarctic Oceans. By statistical analysis of the data they arrived at the algorithm log10Pt = -4.286- 1.390log10(R44G/R55G)+0.621 log!0 (PAR) (11.9)

where Pt is daily production in g C m-2 day-1, R440 and R550 are the irradiance reflectances (subsurface upwelling/above-surface downward) at 440 and 550 nm, and PAR is in J m-2 day-1. Comparing predicted with observed values of primary production, their model had an r2 of 0.85 to 0.95. The rms accuracy of primary production estimation was 0.17 on a logarithmic scale, corresponding to a factor of 1.5. Berthelot and Deschamps suggest that their model should be applicable for the evaluation of primary production of those oligotrophic and mesotrophic waters that constitute most of the open ocean.

The integral primary production we have discussed above is total primary production. A large part, usually most, of the plant biomass produced is eventually recycled within the euphotic zone as the result of grazing, fungal or viral infection etc., followed by microbial mineralization, but a proportion passes down through the thermocline, in the form of zooplankton faecal pellets and aggregated or dead phytoplankton cells at the end of a bloom, to the deep sea. This downward flux of organic matter from the euphotic zone is sometimes referred to as export production. It brings about a net transfer of carbon from the atmosphere to the deep sea, and is the reason why oceanic photosynthesis is of major importance in the global carbon cycle. In the context of global climate change, the transfer of carbon to the ocean depths by this mechanism is commonly referred to as the biological pump. Export production can take place in the much shallower seas of the continental shelf, as well as in the deep ocean, and can involve a mechanism other than passive downward sinking. Sharples etal. (2001) observed substantial rates of turbulent entrainment of carbon from the base of the deep chlorophyll maximum into the bottom mixed layer in a well-stratified region in the Western English Channel. They suggest that carbon export into the bottom mixed layer by this mechanism could account for as much as 25% of the gross primary production in stratifying shelf seas.

The downward transport of biomass removes not only carbon (which is continuously replenished by atmospheric CO2), but also essential mineral nutrients, especially nitrogen, and if the phytoplankton ecosystem of the euphotic zone is to remain productive, levels of these nutrients must be restored. Nutrients are in fact supplied from outside the euphotic zone in a number of ways: from deep water during seasonal, or temporary wind-induced, breakdown of stratification, from the atmosphere, from nitrogen fixation, and from rivers. Such considerations led Dugdale and Goering (1967) to introduce the concept of new production, which is that primary production associated with these nutrient inputs from outside the eupho-tic zone, as opposed to the primary production associated with the nutrients recycled within the euphotic zone. Clearly, continued export production is only made possible by the existence of new production, and quantitatively the two are approximately equivalent. Eppley and Peterson (1979) defined the f ratio as the ratio of new production to total primary production at any given location, and they showed that this varied regionally: f increases as total productivity increases, but levels off at about 0.5 for the most productive oceanic regions, such as the Peruvian upwelling. For the oceanic ecosystem as a whole they estimated an f ratio of 0.18 to 0.20. In the northeast basin of the Atlantic Ocean (16-22° W, 38-45° N) Fernandez et al. (2005) found the seasonal f ratio to be ^0.28 in winter, increasing to 0.34 in spring, then decreasing to 0.25 in late summer. In the equatorial Pacific, Le Bouteiller et al. (2003) found the f ratio to be 0.15 at 3° S, but as high as 0.37 at the equator. In the Southern Ocean, at stations along 141°30' to 143° E, Elskens et al. (2002) found low f ratios (0.08-0.14) in the Subtropical Convergence

Zone (STCZ, 42° S). South of the STCZ the f ratio increased to 0.43 to 0.51, and further south (47-55° S) oscillated between 0.22 and 0.44. For the summer-stratified North Sea, Weston et al. (2005) estimated that annual new production associated with the deep chlorophyll maximum, supported in part by nutrient flux from the nutrient-rich bottom mixed pool, accounted for 37% of the total new production.

Estimating total primary production by remote sensing, in the manner we have discussed, can provide indirect information about new, or export, production if plausible values of the f ratio can be assigned, and so is of great potential value for understanding the role of the oceans in the global carbon cycle. Clearly, however, it would be an advantage if some information on the prevailing value of the f ratio in the region under study could be obtained from remote sensing measurements. Sathyendranath et al. (1991) have taken advantage of the fact that nitrate concentration is often negatively correlated with temperature, and that the f ratio is positively correlated with the nitrate concentration. They combined CZCS-derived phytoplankton estimates with AVHRR sea-surface temperature measurements to estimate not only total primary production, but also the f ratio and hence new production in the sea over and around Georges Bank, east of Cape Cod (USA).1174 This method can, of course, only be applied where, as in this case, there is a substantial body of accumulated field data, relating nitrate concentration to temperature.

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