## Box 31 I The Secchi disk

Many variants of the Secchi disk have been employed in limnology and plankton science but the recommended standard is made of aluminium and painted white, is 300 mm in diameter and suspended by three cords attached to a single rope about 30 cm above. It is lowered carefully into the water until the observer just loses sight of it. It is often said to measure transparency or light penetration but these are not literally accurate. The image is lost to the observer through scattering of light rays. However it is a sufficiently useful and serviceable instrument for there to have been several attempts to relate measurements of Secchi-disk depth (zs) to more formal photometric light determinations (Vollenweider 1974; Preisendorfer; 1976; Stewart, 1976). The quest is not aided by differences between observers or; for a single observer; by differences between sun and cloud or between calm and waves. On the basis of simultaneous measurements, Poole and Atkins (1929) deduced that zs and e are in approximate inverse proportion and, thus, that the product zs x emin should be roughly constant. Their evaluation of this constant (1.44) is only just representative of the later estimates (1.4 to 3.0, with a mean of about 2.2: Vollenweider, 1974). Then the light intensity remaining at zs is between 5% and 24% of I0 (mean ~ 15%), whence the compensation depth is perhaps 1.2

(a) Typical depth profile of irradiance absorption; (b) 'random walk' of a phytoplankter entrained in the mixed layer of the same profile; (c) simultaneous plot of the photosynthetic rate that can be maintained at given depths (light-saturated above /k); (d) deduced instantaneous photosyntheyic rate that is maintained by the alga following the trajectory depicted in (b). Redrawn with permission from Reynolds (1997a).

photosynthesis is possible (hp), the more restrictive are the mixing conditions on the prospects of photosynthetic gain.

By extension of this argument, the smaller is hp in relation to hm, then the more difficult it is to sustain any net photosynthesis at all. It was long a tenet of biological oceanography that the major mechanism permitting phytoplankton recruitment through growth depended upon the depth of mechanical mixing relaxing sufficiently relative to light penetration for net photosynthesis to be sustainable. This relationship was considered by Sverdrup et al. (1942), although it is the eventual mathematical formulation of what is still known as Sverdrup's (1953) 'critical depth model' to which reference is most frequently made. In particular, the idea that the spring bloom in temperate waters, in lakes and rivers as well as open seas and continental shelves, is dependent upon the onset of thermal stratification, at least when it is compounded by a seasonal increase in the day length, remains a broadly plausible concept. However, it is lacking in precision, is open to too literal an interpretation and is not amenable to simulation in models. The problem is due partly to the perception of stratification (as pointed out previously, lack of a pronounced temperature or density gradient is not, by itself, evidence of active vertical mixing). Compounding this is the issue of short-term variability and the likelihood of incomplete mixing within a layer defined by a 'fossil structure' (as defined in Section 2.6.4).

These are important statements regarding an important paradigm, so care is needed to emphasise their essence. It is perfectly true, for instance, that mixing to depth does not only homogenise probable, time-averaged integrals of insolation but 'dilutes' it as well. I used an integral, I* (Reynolds, 1987c), to estimate light concentration in homogeneously mixed layers, based on the difference between the light availability at the surface and at the bottom, as extrapolated from the attenuation coefficient.

be shown to be profound. Supposing 10 is 800 |imolm-2s-1 and e is 1.0 m-1, then the light reaching the bottom of an 8-m mixed later would be 0.27 |imolm-2s-1 and I* for the whole 8-m layer is just under 15 |imol m-2 s-1. Doubling the mixed depth to 16 m, means that the light reach-

where Im is the extrapolated irradiance at the base of the contemporary mixed layer. Solved by Eq. (3.11), as Im = ¡0- e-ezm, deep mixing can ing the bottom would be 9 x 10-5 |imolm-2 s-1 and the integral for the 16-m layer would be <0.3 |mol m-2 s-1. A factor of two in the depth of mixing changes a light dose expected to sustain significant net photosynthetic gain to one which will not even satisfy respiration.

Furthermore, starting on the basis of areal integrations of measured photosynthesis and respiration rates versus depth (£NP and £NR), extrapolations of net photosynthesis over 24 h maybe approximated, as calculated as ££NP -££ NR. For short enough days (temperate winters!), high enough attenuation coefficients and verifiable mixing limits, it is probable that low or zero rates of observed phytoplank-ton increase are correctly attributed to inadequate energy income. To illustrate this, Reynolds (1997b) reworked some earlier data (Reynolds, 1978a; Reynolds and Bellinger, 1992) on the year-round observations on the phytoplankton dynamics in the turbid (e > 0.5 m), 30-m deep, eutrophic Rostherne Mere, UK. He showed that, in the period January-March, net photosynthetic gain would have been possible only when the mixed depth was <4 m and that the development of any significant spring diatom bloom was normally delayed until April. In a classical paper on the whole-column photosynthetic integrals in Windermere, Talling (1957c) showed that the observed population increase of Asterionella in Windermere in the first 3 to 4 months of the year would certainly account for a very high proportion (around 96%) of the extrapolated integral photosynthesis (and, hence, a simultaneously very low biomass-specific respiration rate) to be able to sustain it.

Later attempts to model the population growth from first principles underestimated the oft-observed growth performance in Winder-mere, unless some allowance was made for a diminishing Monin-Obukhov length (see Section 2.6.3) through the spring period (Reynolds, 1990; Neale et al., 1991a). In other words, the actual

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