Areal and volumetric efficiencies

We have seen that the efficiency of utilization of the light incident on the aquatic ecosystem for primary production is determined by two main factors: the extent to which the aquatic plants succeed in competing with the other components of the system for the quanta in the underwater light field, and the efficiency with which the absorbed light energy is converted to chemical energy. We shall now consider the overall efficiency that results from the simultaneous operation of these two factors.

The most common and generally useful way of expressing the overall efficiency is as the proportion of the light energy (400-700 nm) incident per m2 of water surface that is photosynthetically stored as chemical energy in plant biomass throughout the water column. This we shall refer to as the areal efficiency, eA: it is obtained by dividing the areal (integral) photosynthetic rate expressed in energy units (MJ equivalent of photo-synthetic assimilate) per m2 per unit of time (hour or day), by the total PAR (in MJ) incident per m2 of water surface in the same time eA = 0.472PA(C02)/Ed(on surface) (10.33)

For oceanic waters, eA values vary by a factor of 100 to 300 from the least to the most productive. Koblents-Mishke (1979) reviewing Russian and other work reported that marine eA values world-wide ranged from 0.02 to 5%. Morel (1978) reported eA values (calculated on a daily basis) of about 0.02% for the very oligotrophic Sargasso Sea, 0.02 to 0.07% for the Caribbean Sea (oligotrophic), 0.06 to 0.25% for the moderately productive eastern equatorial Pacific, and 0.4 to 1.66% for the eutrophic Mauri-tanian upwelling area in the eastern tropical Atlantic. Smith et al. (1987), studying primary productivity across a coastal front in the Southern California Bight, found eA to vary from 1.57% on the cold side of the front where phytoplankton concentration was high (~2.5mgchl a m-3), down to 0.11% on the warm side of the front where phytoplankton levels were much lower (0.1 to 0.5mgchl a m-3).

Brylinsky (1980) analysed the collected International Biological Programme data for lakes and reservoirs throughout the world. The calculated eA values for the whole growing season ranged from about 0.002 to 1.0%, most of the values being in the range 0.1 to 1.0%. Talling et al. (1973) found high efficiencies in two very productive Ethiopian soda lakes dominated by blue-green algae: eA based on half-hour incubations at high incident irradiances ranged from 0.5 to 1.6% in Lake Kilotes and from 1.2 to 3.3% in Lake Aranguadi. In the Sea of Galilee (Lake Kinneret), Dubinsky and Berman (1981) found eA (measured 09:00-12:00 h) to vary from 0.3% in August when the phytoplankton consisted mainly of small chlorophytes, to a maximum of 4% in April during the Peridinium (dinoflagellate) bloom.

From literature data for eight lakes covering a wide range of latitude and trophic status, Tilzer, Goldman and De Amezaga (1975) calculated values of eA ranging from 0.035% in the very oligotrophic, high-altitude Lake Tahoe (California, USA) up to 1.76% in the eutrophic Loch Leven (Scotland). Areal efficiency was strongly correlated with the concentration of algal biomass per unit volume: Tilzer et al. considered that the key factor responsible for the variation in eA in these lakes was the proportion of the total incident light captured by the phytoplankton. Areal efficiency tends to decrease with increasing surface irradiance.898,1087

In comparing the efficiency of primary production in different aquatic systems, it is interesting to compare not only the daily production per unit area, as expressed through eA, but also the relative performance of different phytoplankton populations, per unit phytoplankton biomass. As a measure of this Falkowski (1981) and Falkowski and Raven (2007) proposed the light utilization efficiency function, C, defined by

r-D

Pv (z, t) dz dt

J

0

where Pv (z, t) is the volumetric rate of photosynthesis at depth z and time t, in g Cm-3 h-1, zeu is the euphotic depth, D is the daylength in hours, [Chl](z) is the phytoplankton concentration in g chl a m-3 at depth z, and Ed (0+, t) is the downward irradiance of PAR on the surface at time t. In simple terms, C is the total amount of primary production carried out within a 1 m2 water column per day (g Cm-2 day-1) divided by the total phytoplankton biomass in that water column (gchl 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-2day-1): it thus has the units g C (g chl a)-1 (mol quanta)-1 m2. An early analysis of the data then available from various parts of the ocean, by Platt (1986) seemed to indicate a clustering of C values in the range 0.31 to 0.66 gC(g chl a)-1 (mol quanta)-1 m2. On the basis of an analysis of the much larger data set now available, Falkowski and Raven (2007), however, found a much greater variability to exist, with C values ranging from ^0.1 to ~1.5gC(gchl a)-1 (mol quanta)-1m2. They found that C increased as the average daily irradi-ance decreased, and that it was lower in low-nutrient regions of the ocean. It appears that the highest values in world oceans are those in the subarctic northwestern Pacific, at the times of phytoplankton blooms.1216

In an alternative version of the light utilization efficiency function, proposed by Morel (1991), the rate of photosynthesis and the incident radiant flux are both expressed in energy terms (kilojoules).

PA(C) is the areal photosynthetic rate, in gCm-2day-1. The factor, 39, converts g C to its energy equivalent in kilojoules. [Chl\totai is the total phytoplankton biomass in 1 m2 water column, and Ed(PAR, 0+) is the total light energy in the form of PAR incident upon the top of the water z

column in one day expressed in kilojoules. C* has the units, m2(gchl d)"1 and may be referred to as the chlorophyll-specific cross-section for photosynthesis. C and C are related by C = 6.174 C . At a coastal Antarctic region, studied over the period 1991 to 1994, Claustre et dl. (1997) found a six-fold variation in C* with time of year, the minimum occurring in the austral summer (Dec-Feb). They also found a taxonomic dependency of C*. For identical chlorophyll content and surface irradiance, the mean value of C* was 0.114 ± 0.051 m2(g chl d)"1 for diatom blooms, and 0.053 ± 0.011 m2(g chl d)"1 when cryptophytes dominated, emphasizing the desirability of having taxonomic information when estimating primary production from irradiance and chlorophyll data. In a region (500 km longitude by 750 km latitude, centred on 41.5° N, 19° W) of the northeast Atlantic, Claustre et dl. (2005) found C* to equal 0.088 m2 (gchl d)"1, which is about 25% higher than the average for the world's oceans. Looking more closely at how this production was distributed among the different size classes of phytoplankton, they found that carbon storage by the water column was more efficient (C = 0.135 m2 (g chl d)"1) with microphytoplankton (20-200 mm) than with nanophytoplankton (2-20 mm, C =0.089 m2(gchl d) 1) or picophytoplankton (<2 mm, C = 0.064 m2 (g chl d)"1). Their observations suggest that when large phytoplankton predominate at the expense of smaller ones, the specific absorption coefficient (dc) is, as expected, lower, while other photophysiological properties - a, Pm, fm - are higher. They conclude that large phytoplankton (essentially diatoms) are potentially more efficient in carbon storage than any other phytoplankton group, on a chlorophyll d or light basis.

A way of expressing the overall efficiency of light utilization, which can provide information about its variation with depth through the water column, is the volumetric efficiency, eV. We may define this as the proportion of the downwelling light energy (400-700 nm) incident upon the upper surface of any unit volume within a water body which is photosynthetically stored as chemical energy in plant biomass within that volume. A more all-embracing definition of eV should take into account the light incident upon the unit volume from all directions, i.e. scalar irradiance, E0, rather than downward irradiance, Ed. The definition based on Ed is, however, more convenient and serves the purpose well enough: eV is given by ev = °.472 [CM] nC02) (10.36)

P* (CO2) being expressed in moles CO2mg chl d"1h"1, and Ed(z) in MJ m _2h"1. Unlike ec and eA, ev is not dimensionless, since it has the units m-1. Platt (1969) pointed out that volumetric efficiency at a specific depth has the same dimensions, m-1, as the vertical attenuation coefficient for irradiance, and that it is in fact equivalent to that part of the total vertical attenuation coefficient for downward irradiance that is due to removal of light by photosynthetic conversion to chemical energy

Kd (total) = Kd (photosynthetic) + Kd (physical) Kd (physical) being that part of the total vertical attenuation coefficient which is due to removal of light by all processes other than photosynthetic conversion to chemical energy: it thus includes that part of the light absorption by phytoplankton which fails to result in photosynthesis.

Kd(photosynthetic) is equivalent to eV. Platt's data for St Margaret's Bay, Nova Scotia, Canada, indicate a general tendency for eV to increase with depth (average eV was 0.07%m-1 at 1m and 0.2l%m-1 at 10m). This is to be expected since, as we have already noted, conversion efficiency, ec, increases with depth, and eV = [Chl ]kcec.

Having noted the equivalence of eV with Kd(photosynthetic), we can now go on to define one more efficiency parameter, namely, the proportion of the total light energy absorbed within unit volume of medium that is photosynthetically stored as biomass chemical energy. This is equal to Kd(photosynthetic)/Kd(total) and, following Morel (1978), we shall refer to it as the radiation utilization efficiency, and give it the symbol, e e = KV (10-37)

From the definitions of ec and eV it follows that

Kd i.e. e is the (dimensionless) product of the fraction of the total absorbed light that is captured by phytoplankton and the energy conversion efficiency of the phytoplankton. Thus, e combines directly the two factors controlling the efficiency with which the aquatic ecosystem utilizes incident light energy for photosynthesis: e varies with depth and the integral of e(z) with respect to depth over the whole euphotic zone gives eA, the areal efficiency.

Given the tendency of the conversion efficiency, ec, to increase with depth we might expect e also to increase with depth, and this generally seems to be the case.940 However, variation in e with depth depends also on the variation of kc with depth resulting from changes in the spectral distribution. From one water body to another, e will increase as the phytoplankton biomass increases ([Chl] in eqn 10.38) but decrease as the background attenuation due to dissolved colour etc. (increasing Kd in eqn 10.38) rises. For the oligotrophic Sargasso Sea and Caribbean Sea, Morel (1978) found e to increase with depth from about 0.01 to 0.1%. In the somewhat more productive waters of the equatorial eastern Pacific the range was from about 0.01% near the surface to approaching 1% at low light levels. In the productive waters of the Mauritanian upwelling, e rose from 0.1 to 0.4% near the surface to 2 to 7% near the bottom of the euphotic zone. In Lake Kinneret (Sea of Galilee), Dubinsky and Berman (1981) found that during the Peridinium bloom (428 mg chl a m-2), e rose from just under 1% at the surface to 6.5% at 3 m. After the Peridinium bloom had collapsed, to be replaced with a much lower biomass (50 mg chl am-2, chlorophytes), e was ^0.3% at the surface, and rose to about 2% at 10 m.

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