AN INCUBATOR DESIGNED FOR EXTENSIVE
AND SENSITIVE MEASUREMENTS OF
PHYTOPLANKTON PHOTOSYNTHETIC
PARAMETERS

M Babin, A Morel, R Gagnon

► To cite this version:

M Babin, A Morel, R Gagnon. AN INCUBATOR DESIGNED FOR EXTENSIVE AND SENSITIVE MEASUREMENTS OF PHYTOPLANKTON PHOTOSYNTHETIC PARAMETERS. Limnology and Oceanography, 1994, 39 (3), pp.694-702. 10.4319/lo.1994.39.3.0694. hal-03504906

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Distributed under a Creative Commons Attribution 4.0 International License
of sediment inclusions in deep-sea deposition: Arctic-Antarctic comparisons, p. 187-211. *In* U. Bleil and J. Thiede [eds.], Geological history of the Polar Oceans: Arctic versus Antarctic. Kluwer.

SCHWARZACHER, W. 1959. Pack-ice studies in the Arctic Ocean. J. Geophys. Res. **64**: 2357-2367.

SPINDLER, M. 1990. A comparison of Arctic and Antarctic sea ice and the effects of different properties on sea ice biota, p. 173-186. *In* U. Bleil and J. Thiede [eds.], Geological history of the Polar Oceans: Arctic versus Antarctic. Kluwer.

UNTERSTEINER, N. 1968. Natural desalination and equilibrium salinity profile of perennial sea ice. J. Geophys. Res. **73**: 1251-1257.

—. 1990. Structure and dynamics of the Arctic Ocean

ice cover, p. 37-51. *In* A. Grantz et al. [eds.], The Arctic Ocean region. Geol. Soc. Am.

WADHAMS, P. 1988. The underside of Arctic sea ice imaged by sidescan sonar. Nature **333**: 161-164.

—, AND S. MARTIN. 1990. Processes determining the bottom topography of multiyear Arctic sea ice, p. 136-141. *In* W. F. Weeks and S. F. Ackley [eds.], Sea ice properties and processes. CRREL Monogr. 90-1.

ZUBOV, N. N. 1945. Arctic ice [English transl.]. U.S. Navy Electron. Lab.

Submitted: 24 May 1993

Accepted: 23 September 1993

Amended: 2 November 1993

## An incubator designed for extensive and sensitive measurements of phytoplankton photosynthetic parameters

*Abstract*—An improved incubator for the determination of the photosynthesis rate-irradiance curve is described. It allows measurements of carbon fixation in waters with low chlorophyll *a* concentration by using rather large seawater volume. The irradiance gradient inside the incubation chambers is reproducible and can be accurately determined. With the capability of simultaneous measurements on 10 water samples, extensive determination of vertical profiles of photosynthetic parameters is achievable. Examples of photosynthetic parameters are given for waters collected in eutrophic, mesotrophic, and oligotrophic sites of the tropical Atlantic Ocean.

The curve describing the rate of photosynthesis as a function of irradiance has provided basic elements for understanding photosynthetic mechanisms (e.g. *see* Rabinowitch and

### Acknowledgments

M.B. received postdoctoral scholarships from the Fonds pour la Formation de Chercheurs et l'Aide à la Recherche (FCAR) of the Quebec Government, and from the Université des Réseaux d'Expression Française/Association des Universités Partiellement ou Entièrement de Langue Française (UREF/AUPELF). The original prototype of the radial incubator was designed by R.G. within the programs of the Maurice Lamontagne Institute (Dept. Fisheries and Oceans, Biological Oceanography Division).

We are grateful to H. Claustre, J. Cullen, M. Gosselin, M.-J. Perry, and P. Raimbault who provided their data. We express particular appreciation to A. Bricaud, A. Post, and P. G. Falkowski for criticisms, and to R. A. Anderson for comments on polystyrene culture flasks.

Govindjee 1969). In plant physiology, the *gross* photosynthetic rate is determined with high resolution and reproducibility by measuring oxygen evolution or variable fluorescence. In the mid-1970s, the determination of photosynthesis rate-irradiance curves, based on radiolabeled carbon assimilation (*P* vs. *E* curves), progressively became a classical tool in biological oceanography (*see* Steemann Nielsen 1975); *P* represents the carbon fixation rate expressed as mg C m⁻³ h⁻¹ and *E* the incident irradiance, in terms of photosynthetic available radiation (PAR, e.g. Tyler 1966), generally expressed as µmol quanta m⁻² s⁻¹.

The physiological response of photosynthesizing microalgae to environmental conditions was examined through variations in the initial slope (α) and the saturation plateau (Pmax) of the P vs. E curve. This method has been widely used following the development by Lewis and Smith (1983) of the now conventional "photosynthetron." Besides the fact that carbon fixation is the relevant process in most marine biological or biogeochemical studies, the use of the ¹⁴C method was motivated by the sensitivity required in aquatic environments where relatively low abundances of autotrophic organisms are common. Nevertheless, and in spite of the sensitivity of the ¹⁴C technique, the level of resolution and the achievable reproducibility do not allow unequivocal expla-
<figure><img src="image_2.png" /><figcaption>Fig. 1. Schematic view of (A) an incubation chamber and of (B) the whole radial photosynthetron.</figcaption></figure>

nations of phenomena. For instance, when one tries to discriminate between the different sources of variability in the maximum quantum yield of photosynthesis at sea, it is necessary to decrease instrumental random error.

In oligotrophic waters, for which there is a growing interest (Cleveland et al. 1989; Kolber et al. 1990; Platt et al. 1992), it is hard to address the problem of quantum yield variability with a conventional photosynthetron. Here we present a method that satisfies the needs for high reproducibility and resolution in measurements of *P* vs. *E* curves. This device also allows extensive samplings and fast handling, as is often necessary in oceanographic studies.

Figure 1A shows a schematic view of one of the 10 elements of the “radial” photosynthetron (Fig. 1B). This watertight incubation chamber is made of Plexiglas and designed to contain a stack of twelve 50-ml culture flasks (Falcon, Corning, Nunc, or Costar). All walls (including the cover) are black, but the one facing the light source is made of white-difusing Plexiglas. The chamber has a false bottom and an overflow outlet that maintains the

water level in such a way that the samples in the flasks are always completely immersed. Temperature-controlled water enters through the false bottom to emerge near the front face, then flows around the flasks and finally exits the chamber through the overflow outlet.

The radial photosynthetron (Fig. 1B) consists of 10 such incubation chambers, supported by a 1-m square aluminum plate, arranged radially around a 250-W arc lamp (OSRAM, HQI-T 250 W/D) that provides a maximum irradiance of ~2,000 µmol quanta m⁻² s⁻¹. Other sources can be used.

The dimensions and optical characteristics of the flasks are highly reproducible and fit perfectly with each other. They are made of perfectly transparent polystyrene with a refractive index close to that of water, so that there is no significant reflection along and between the 12-flask stack. This arrangement provides a regular light gradient, essentially a function of the distance from the diffusing front face (see below). The range of irradiance typically spans >1.5 orders of magnitude (a ratio of 33 between the front and the rear of the chamber). The volume of the flasks is larger
than the typical one used in the photosynthetron (50 ml instead of 1 to 20 ml). The filtration of 50 ml improves the sampling reliability—important in waters where phytoplankton abundance is low.

Such polystyrene flasks are widely used for phytoplankton cultures (e.g. at the Provasoli-Guillard Center for Culture of Marine Phytoplankton). There is no evidence of polystyrene toxicity (Blankley 1973; R.A. Andersen pers. comm.), even for sensitive phytoplankton strains (F. Partensky and D. Vaulot pers. comm.). Therefore, we assume that polystyrene does not affect the rate of carbon fixation of phytoplankton during a short incubation (max. 2 h).

The initial light intensity is adjusted with a sheet of neutral supple plastic filter (LEE Filters Ltd.) shaped as a cylinder fitted around the lamp. When individual adjustments are needed, filters of different densities can also be shaped to fit the individual front face of the incubation chambers. If colored filters are used, the radial photosynthetron can also measure the action spectra.

Exactly 850 ml of the seawater samples are poured into 1-liter amber bottles. The tracer ($NaH_{14}CO_3$) is added with a positive displacement pipette (Labsystems Finnpipette or Ependorf), ensuring sample-to-sample reproducibility of the volume of tracer added. After a few minutes of magnetic stirring, a 12-flask set held in a specially designed rack is filled using an automatic 50-ml Socorex digital dispenser, which fits directly onto the amber bottles. The 12 flasks are then quickly placed into an incubation chamber. Aliquots for initial activity determination are taken and put into 20-ml scintillation vials containing an organic base (ethanolamine or phenethylamine) and the scintillation cocktail (e.g. 50 µl of the sample with 50 µl of ethanolamine, 0.5 ml of water, and 10 ml of Aquasol-2). Two technicians need 30 min to perform all the preceding steps, preferably in the dark or green-dim light.

The 12 flasks are squeezed together and pushed in front of the incubation chamber. The temperature of each chamber is individually adjusted according to the vertical profile of in situ temperature, using thermoregulated baths. As all volumes are carefully controlled (seawater sample, tracer, flasks, and activity aliquots), two independent estimations of the

initial activity can be obtained by relying on the dilutions and by measuring radioactivity of the aliquots. The dark carbon fixation is estimated by adding a constant ($P_0$) to the photosynthesis model used to fit the data (Cullen et al. 1992).

After a 20-120-min incubation, the samples are gently filtered onto GF/F Whatman filters (note that the flasks fit firmly upside down onto 15-ml Millipore funnels). The filters are rinsed with filtered seawater, placed into 20-ml scintillation vials, wetted with 1.0 N HCl, and placed under a fuming hood for 1 h, after which 10 ml of scintillation cocktail is added. Two technicians need 45 min to perform the latter steps. Three hours are sufficient to complete a set of 10 simultaneous *P* vs. *E* curves.

A precise knowledge of PAR is critical to obtain accurate, non-noisy, *P* vs. *E* curves. This measurement is generally performed with a quantum meter equipped with a $4\pi$ collector when dealing with unicellular algae in suspension (e.g. see Kirk 1983). The flasks used here (as well as the incubation chambers) are geometrically identical. Therefore, the light gradients inside each of the 10 incubation chambers (PAR as a function of the position) do not vary in relative units, as repeatedly verified, and they are identical. This relative gradient is obtained by normalizing all values to the irradiance measured at a single position (the third one is the best compromise). In order to derive the absolute irradiances for all flask positions, a single PAR measurement in absolute units is carried out only at the third position in each individual chamber.

The angular response of a $4\pi$ collector is never perfect (i.e. equal over the $4\pi$ sr), as it should ideally be; care must be taken that the collector is always oriented in the same way. In addition, the sensor never completely fills the space occupied by the liquid sample, so that the reliability of PAR measurements with such collectors remains questionable. In principle they can provide reliable relative measurements under the proviso that the angular distribution of light is constant from one position to the other inside the incubation chamber. In the case of the radial photosynthetron, the structure of the light field varies significantly from the front diffusing face to the end of the chamber. Even if the light gradient determined with a scalar quantum irradiance
meter (Biospherical QSL-100) is regular and free from noise (Fig. 2), there may be a bias in its shape.

To check this point, we used a chemical actinometric technique (modified from Hatchard and Parker 1956) which behaves strictly as a perfect $4\pi$ collector. This method is based on the photocatalyzed reduction of ferric to ferrous potassium ferrioxalate, for which the quantum yield is known and constant over a wide range of temperatures and light intensities. After exposure to light, the product of this reaction is simply quantified by spectrophotometry with phenanthroline. Although Hatchard and Parker (1956) used an optically thick actinometer, we used an optically thin solution to obtain a measurement not for the entrance wall of the flask, but a representative value for whole flask volume. The actinometric measurements were done sequentially at each position in the incubation chambers by exposing 50 ml of potassium ferrioxalate for 1 h in a given culture flask; the 11 other flasks were filled with pure water.

The results of the actinometric method, also expressed as a mean (over three chambers) and normalized (third position) distribution, are shown in Fig. 2 together with the distribution derived from the Biospherical instrument. The Biospherical collector overestimates PAR for the first positions. We believe this is because near the diffusing plate, light varies quickly with distance. It follows that the $4\pi$ collector, with a dimension nearly equal to the thickness of the flask, harvests light mostly in the first half of the flask where irradiance is higher than that prevailing in the whole volume. Therefore, a relative light gradient determined via the actinometric calibration is certainly more accurate than that obtained with a standard $4\pi$ collector.

In addition to the inverse square root of the distance effect, some attenuation by water and a spectral change along the pathlength are expected. To estimate this change, we measured the spectral values of irradiance at each position with the flasks filled with pure water (Fig. 3A); in addition, we used the model of Morel (1988) to approximate the additional effect due to the presence of algae with varying chlorophyll *a* concentrations (Chl). The results are shown in Fig. 3B for Chl equal to 30 mg m⁻³. For both measured (water) and computed (wa-

<figure><img src="image_3.png" /><figcaption>Fig. 2. Photosynthetically available radiation (PAR) as a function of flask position in the incubation chamber, from the front face (1) to the end of the chamber (12). A comparison between the actinometer and the $4\pi$ collector was performed in the laboratory ($n=3$) and measurements were carried out at sea with the $4\pi$ collector ($n=10$) during EUMELI 4.</figcaption></figure>

ter + algae) attenuation, the spectral shift along the 0.3-m pathlength (0.22 m of water) is very weak and mostly located in the blue region, mainly because of absorption by the flasks themselves. At the last position, the error in the amount of absorbed light (convolution of a typical phytoplankton absorption spectrum and of the irradiance spectra) varies between 2 and 7% for Chl going from 0.03 to 30 mg m⁻³ (Fig. 3C). In conclusion, a constant spectrum can safely be used without significant error, particularly to determine the maximum quantum yield, for which absorbed quanta must be known.

The lamp was selected to mimic solar irradiance. The main failure, however, is the strong mercury emission band (at 546 nm) in the green part of the spectrum, fortunately where algae absorption is generally minimum (except for biliprotein-pigmented cells). Using mean in vivo phytoplankton absorption spectra measured at different sites (eutrophic, mesotrophic, and oligotrophic) during cruise EUMELI 4 (see below), we computed that 51–68%, 10–23%, and 21–31% of the lamp irradiance can be absorbed in the blue (400–525 nm), green (525–552 nm; mercury peak region), and red (552–700 nm) parts of the spectrum, respec-
<figure><img src="image_4.png" /><figcaption>Fig. 3. A. Relative spectral values of the scalar irradiance (normalized to the integral) measured at the 12 flask positions into an incubation chamber, with all flasks filled with pure water. B. Spectral values of the scalar irradiance predicted for the 12 flask positions into an incubation chamber, using the model of Morel (1988) for Chl equal to 30 mg m⁻³. Attenuation of the flask itself was added to attenuation of pure water and phytoplankton. C. Error made on the computation of the amount of light absorbed by phytoplankton at the last position (rear) into an incubation chamber, as a function of Chl, when assuming a constant irradiance spectrum. An in vivo absorption spectrum typical of dinoflagellates and diatoms was used. D. Convolution of the irradiance spectrum of the lamp and the mean absorption spectra of algae measured at the eutrophic, mesotrophic, and oligotrophic sites. The vertical bars delimit the spectral domain dominated by the mercury emission band (centered on 546 nm).</figcaption></figure>

tively (Fig. 3D). At worst, i.e. in the case where cyanobacteria dominated (the case at the mesotrophic site), enhanced absorption capabilities in the green part of the spectrum result in a situation where 23% of irradiance is ab-

sorbed in the mercury band region. So, in most cases the results obtained with such a lamp reflect the activity of all light-harvesting pigments.

To illustrate the performance of the radial
<figure><img src="image_5.png" /></figure>

Fig. 4. Typical examples of *P* vs. *E* curves obtained with the radial photosynthetron during EUMELI 4 at the eutrophic, mesotrophic, and oligotrophic sites. The water samples were collected at 3 × 10⁻⁵, 0.3, and 0.05% of surface PAR, respectively. Chl values were 1.1, 0.7, and 0.2 mg m⁻³, and the mean specific absorption coefficient weighted by the spectrum of E₀(λ) between 400 and 700 nm were 0.013, 0.028, and 0.020 m² (mg Chl)⁻¹, respectively.

photosynthetron method, we present some results obtained during a cruise of the French JGOFS program (EUMELI 4) that took place in June 1992 at 20°N between 17 and 32°W (off the Mauritanian coast). Seawater was collected at three fixed stations in a eutrophic, a mesotrophic, and an oligotrophic system. Additional results were obtained in the Liguro-Provençal basin of the Mediterranean Sea (March 1993).

During EUMELI 4, Chl ranged from 0.005 to 4.0 mg m⁻³ and a total of 228 *P* vs. *E* curves were determined. Initial ¹⁴C concentrations of 0.05–0.25 µCi ml⁻¹ were used and the incubations lasted between 60 and 120 min. The data points were fitted to the model of Jassby and Platt (1976) with the quasi-Newton algorithm of the Systat statistical package (Fletcher 1972). One representative example for each site is presented in Fig. 4. For all experiments, the data points fit the model of Jassby and Platt (1976) very well within the whole range of irradiances. Only one to three data points determine saturation. The dependence of *P*<sub>m</sub> on these points is examined

<figure><img src="image_6.png" /></figure>

Range of chlorophyll concentration (mg Chl a m⁻³)

Fig. 5. Average (1 - R²) as a function of different Chl ranges for the radial photosynthetron (N = 169) and the conventional photosynthetron (N = 44). The radial photosynthetron data were obtained during EUMELI 4; the conventional photosynthetron data are from Barlow et al. (1988), Cleveland et al. (1989), and Cullen et al. (1992).

above through the assessment of reproducibility. Also, if desired, the intensities can be expanded over higher values (up to 2,000 µmol quanta m⁻² s⁻¹) by changing the neutral filters. A discussion of the ecological features of these curves is beyond the scope of this paper.

To gain a first insight into the possible error, we analyzed the dispersion of the data points around the modeled curve at the level of each *P* vs. *E* curve. This dispersion is quantified via the coefficient of determination (R²) of the “predicted vs. observed *P*” relationship, as derived from each curve fitting. The results were compared to a pooled data set comprising 44 *P* vs. *E* curves obtained by Cleveland et al. (1989), Barlow et al. (1988), and Cullen et al. (1992), all of whom used a conventional photosynthetron. These data were processed with the same fitting procedure as for our data. The choice of the original *P* vs. *E* curve model was respected, but an intercept was added. The comparison in terms of (1 - R²) between the two sets of data is shown in Fig. 5, where the results are arranged according to the Chl *a* concentration. Dispersion is always smaller for the radial photosynthetron and, for this device, regularly decreases (from 0.03 to 0.003) when
<figure><img src="image_7.png" /><figcaption>Fig. 6. A typical vertical profile of nitrate concentration, Chl *a*+divinyl Chl *a* concentration, zeaxanthin: Chl *a*+divinyl Chl *a* ratio, fraction of incident PAR, αᵇ, Pᵇmax, and Iₖ as obtained at midday at the oligotrophic site during EUMELI 4 (21°02′N, 31°07′W; 23 June 1992).</figcaption></figure>

Chl increases. Likely because the conventional photosynthetron data set merges results from different campaigns, the (1 - R²) values are randomly distributed with regard to the pigment content.

The reproducibility of the method has also been studied. In addition to the dispersion originating from errors on individual determinations of *P* and *E*, the reproducibility involves all experimental errors associated with measurement (or estimation) of the total content of inorganic carbon, initial and dark activities, length of incubation, and quench correction. Reproducibility was tested with 12 *P* vs. *E* curves obtained in duplicate at the mesotrophic site during EUMELI 4. We computed the coefficient of variation (SD/σ̄) for the 12 couples and obtained an average equal

to 3.6% for P<sub>max</sub> and 4.8% for α. The reproducibility was again tested by simultaneously determining 10 *P* vs. *E* curves for the same sample (collected off Villefranche-sur-Mer, Chl = 0.31 mg m<sup>-3</sup>). An initial <sup>14</sup>C concentration of ~0.1 µCi ml<sup>-1</sup> was used and the incubations lasted ~120 min. For this experiment, the average (1 - R<sup>2</sup>) value was 0.0027, and the coefficients of variation with respect to P<sub>max</sub> and α were 8.0 and 7.1%.

During EUMELI 4, one to four 10-depth vertical profiles of the photosynthetic parameters were determined between dusk and dawn; each profile includes 10 samples from 10 different depths. Such a vertical profile is displayed in Fig. 6, together with the vertical distributions of PAR, Chl, NO₃, and the zeaxanthin: Chl ratio. The vertical profiles of
the various photosynthetic parameters are as well resolved as the other variables, especially $I_k (=P_{max}/\alpha)$ which is independent of the error on Chl measurement. As the vertical profiles of $\alpha^B$ ($\alpha$ normalized to Chl) are quite regular, the fraction of variance caused by technical random error is expectedly small. On that basis, relationships relating $\alpha^B$ or the quantum yield of photosynthesis, with nitrogen (Cleveland et al. 1989; Kolber et al. 1990) and the photoprotectant pigments (Demmig-Adams and Adams 1992) can be tested rigorously.

The photosynthetron introduced by Lewis and Smith (1983) has the advantage of consuming small volumes of seawater. In addition, because it involves no filtration, the results provided by this technique could reflect the gross photosynthesis more closely when incubation time is short enough. With larger volumes and an accurately known light field, the radial photosynthetron offers distinct improvements, especially significant in oligotrophic waters. In other more productive waters, larger volumes provide the possibility of reducing the incubation period (and the amount of ¹⁴C added). In addition, compared to the scintillation vials used in the conventional photosynthetron method, our flasks provide high reproducibility. The quality of the results obtained at sea with the radial photosynthetron becomes comparable to that attained in the laboratory with oxygen probes and fluorescence techniques; extensive sampling, and therefore detailed analyses of vertical profiles of the photosynthetic parameters, is possible.

Global scale models of primary production rest on a mechanistic understanding of the basic processes controlling photosynthesis at sea. The complexity of these models involves, for their definition and validation, obtaining large sets of photosynthetic parameters accurately determined over the world ocean. The incubator described above was developed for this purpose.

Marcel Babin

Laboratoire de Physique et Chimie Marines
Université Pierre et Marie Curie and CNRS
B.P. 8
F 06230 Villefranche-sur-Mer, France

André Morel

Laboratoire de Physique et Chimie Marines
Université Pierre et Marie Curie and CNRS

Réal Gagnon

Institut Maurice-Lamontagne
Ministère des Pêches et des Océans
B.P. 1000
Mont-Joli, Québec G5H 3Z4

References

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BLANKLEY, W. F. 1973. Toxic and inhibitory materials associated with culturing, p. 207-229. *In* J. R. Stein [ed.], Handbook of phycological methods. Cambridge.

CLEVELAND, J. S., M. J. PERRY, D. A. KIEFER, AND M. C. TALBOT. 1989. Maximal quantum yield of photosynthesis in the northwest Sargasso Sea. J. Mar. Res. 47: 869-886.

CULLEN, J. J., M. R. LEWIS, C. O. DAVIS, AND R. T. BARBER. 1992. Photosynthetic characteristics and estimated growth rates indicate grazing is the proximate control of primary production in the equatorial Pacific. J. Geophys. Res. 97: 639-654.

DEMMIG-ADAMS, B., AND W. W. ADAMS III. 1992. Photoprotection and other responses of plants to high light stress. Annu. Rev. Plant Physiol. Plant Biol. 43: 599-626.

FLETCHER, R. 1972. FORTRAN subroutines for minimization by quasi-Newton methods. AERE R. 7125.

HATCHARD, C., AND C. A. PARKER. 1956. A new sensitive chemical actinometer. 2. Potassium ferrioxalate as standard chemical actinometer. Proc. R. Soc. Lond. Ser. A 235: 518-536.

JASSBY, A. D., AND T. PLATT. 1976. The relationship between photosynthesis and light for natural assemblages of marine phytoplankton. J. Mar. Res. 12: 421-430.

KIRK, J. T. O. 1983. Light and photosynthesis in aquatic ecosystems. Cambridge.

KOLBER, Z., K. D. WYMAN, AND P. G. FALKOWSKI. 1990. Natural variability in photosynthesis energy conversion efficiency: A field study in the Gulf of Maine. Limnol. Oceanogr. 35: 72-79.

LEWIS, M. R., AND J. C. SMITH. 1983. A small volume, short-incubation-time method for measurement of photosynthesis as a function of incident irradiance. Mar. Ecol. Prog. Ser. 13: 99-102.

MOREL, A. 1988. Optical modeling of upper ocean in relation to its biogenous matter content (case 1 waters). J. Geophys. Res. 93: 10,749-10,768.

PLATT, T., AND OTHERS. 1992. Nutrient control of phytoplankton photosynthesis in the western North Atlantic. Nature 356: 229-231.

RABINOWITCH, E., AND GOVINDJEE. 1969. Photosynthesis. Wiley.
STEEMANN NIELSEN, E. 1975. Marine photosynthesis with special emphasis on the ecological aspects. Elsevier.

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Submitted: 4 August 1993

Accepted: 24 November 1993

Amended: 3 January 1994

Limnol. Oceanogr., 39(3), 1994, 702-706

© 1994, by the American Society of Limnology and Oceanography, Inc.

# Characteristics of the light field in highly turbid waters: A Monte Carlo study

*Abstract*—The nature of the light field in waters with very high ratios of scattering coefficient to absorption coefficient (b:a) has been explored by Monte Carlo modeling. The progressive change in the angular structure of the field at a specified optical depth (z_m) as b:a increases up to an extreme value of 200 is illustrated in terms of the changes in average cosines $\bar{\mu}_d[z_m]$, $\bar{\mu}_u[z_m]$, $\bar{\mu}[z_m]$) and irradiance reflectance ($R[z_m]$).

The dependence of the vertical attenuation coefficient for downward irradiance on absorption and scattering is satisfactorily represented by

$$K_d(z_m) = (a^2 + 0.245ab)^{1/2}$$

A nomogram is presented, with the help of which the values of the absorption and scattering coefficients for highly turbid water bodies can be estimated from underwater irradiance data.

There are many interesting and important aquatic ecosystems in which the turbidity of the water is exceptionally high. Examples are areas of the open ocean where coccolithophores are blooming, many estuaries especially in the region of the turbidity maximum, shallow lakes with unconsolidated sediments, lakes and rivers receiving glacial meltwater, rivers in eroding catchments, and fjords. I describe here an investigation, by Monte Carlo modeling, of the nature of the light field that is established within such water bodies.

In a previous investigation (Kirk 1981a,b) waters with scattering: absorption (b:a) ratios up to 30 and irradiance reflectance ($E_u/E_d$) values up to 24% were studied, and relationships between reflectance, b:a, and average cosine ($\bar{\mu}$) were elucidated, partly because of their intrinsic

## Acknowledgments

This work received support from the Ocean Optics Program of the Office of Naval Research under grant N00014-91-7-1366.

interest, but also because they provide a simple method for estimating absorption and scattering coefficients from underwater irradiance measurements. It was thought at the time that this range of b:a and R values would cover the entire range of optical water types of significance. It has since become apparent, however, that waters with even higher reflectance values and scattering: absorption ratios, while not common, do occur. For example, in the turbid Rhode River estuary (Maryland), Gallegos et al. (1990) found in a series of 15 measurements (different sites, different dates) that in two cases b:a exceeded 30, being in one case as high as 79. In the Darling River, southeastern Australia, Oliver (1990) measured a b:a ratio of 33 on one occasion. In the glacier-fed Lake Tekapo, New Zealand, Vant and Davies-Colley (1984) observed an irradiance reflectance of 32%. In a coccolithophore bloom in the Gulf of Maine, Balch et al. (1991) observed reflectance values of 27-39% in the blue-green part of the spectrum.

So that the relationships between R, $\bar{\mu}$, and b:a could be understood and methods for estimating a and b from irradiance data be devised, even for exceptionally turbid water bodies such as these, additional Monte Carlo simulations of the light field have now been carried out for a range of optical water types up to a scattering: absorption ratio of 200.

Calculation of the light field established within water bodies having various values of the ratio of scattering to absorption coefficient was carried out by the Monte Carlo procedure as described previously (Kirk 1981a,b, 1984). As before, the water was assumed to have a scattering phase function identical to that measured by Petzold (1972) in San Diego harbor—the most turbid of the waters he studied. This