Environmental control of phytoplankton productivity in turbulent turbid systems

Factors affecting phytoplankton productivity are analysed in turbid systems, such as shallow lakes and rivers. When resuspension from the sediment or loading from the catchment significantly increases inorganic (non-algal) turbidity and hence light attenuation potentials for high production are not realised. Energy available for phytoplankton growth is strongly regulated by underwater light availability which depends on the critical mixing depth, fluctuating light intensities and algal circulation patterns. Higher production rates in shallow waters are often compensated by greater algal respiration due to higher water temperatures when compared to deeper lakes.Total daily integral production of turbulent, turbid environments can be predicted from a combination of easily measured variables such as maximum photosynthetic rates, algal biomass, surface irradiance and some measure of underwater light attenuation.     

ABSORPTION AND UTILIZATION OF IRRADIANCE BY CYANOBACTERIAL MATS IN TWO ICE-COVERED ANTARCTIC LAKES WITH CONTRASTING LIGHT CLIMATES

We investigated the under-ice light climate and the efficiency with which light was absorbed and utilized by benthic algal mats in Lakes Hoare and Vanda, two perennially ice-covered lakes in the McMurdo Dry Valleys area of Southern Victoria Land, Antarctica. The ice cover and water column of Lake Vanda were much more transparent than those of Lake Hoare (18% vs. 2% transmission though ice and attenuation coefficients for downwelling irradiance of 0.05 vs. 0.12 m ^{− 1}, respectively). In both lakes the under-ice spectra were dominated by blue-green wavelengths. The benthic flora under perennial ice covers of both lakes comprised thick mucilaginous mats, dominated by cyanobacteria. The mats were well suited to absorb the dominant blue-green wavelengths of the under-ice light, with phycoerythrin being present at high concentrations. The pigment systems of the benthic mats absorbed 30%–50% of the light that reached them, varying with depth and lake. There was a tendency for the percentage of absorption to increase as ambient irradiance decreased. The efficiency of utilization of absorbed irradiance was examined by constructing absorbed irradiance/oxygen evolution curves to estimate community quantum yield. Mats from 13 m in Lake Hoare showed the highest quantum yields, approaching 1 mol of carbon fixed for every 8 mol quanta absorbed under light-limiting conditions. Lake Vanda mats had lower quantum yields, but these increased with depth. Calculated in situ irradiance occasionally exceeded the measured saturating irradiance for oxygen evolution in both lakes, thus efficiency in situ was below the maximum at times. As in other environments, optimization strategies allowed efficient capture and utilization of the lower and middle ranges of experienced irradiance but led to a compromised capacity to use the highest irradiances encountered at each depth.     

Effects of suspensoids (turbidity) on penetration of solar radiation in aquatic ecosystems

In mainland Australia and in southern Africa, the aridity of the climate and sparse vegetative cover increase the susceptibility of the soils to erosion, and as a consequence surface waters are usually turbid. The inanimate suspensoids in such waters, the tripton fraction of the limnologist, are responsible for virtually all the light scattering, and also, by virtue of the yellow-brown humic materials adsorbed on their surface, for a substantial part of the light absorption. Spectral absorption data for suspensoids in terms of theirin situ absorption coefficient values, and the contribution of suspensoids to absorption of photosynthetically available radiation (PAR) are given for certain Australian water bodies.To understand the effect of suspensoids on attenuation of the solar flux with depth, the scattering coefficient must also be known, and this can be determined from the nephelometric turbidity or from up- and down-welling irradiance measurements. The effect of particle size on scattering efficiency is discussed.An equation expressing the vertical attenuation coefficient for downward irradiance as a function of absorption coefficient, scattering coefficient and solar altitude is presented, and is used to explore the effects of absorption due to dissolved colour and suspensoids, and the effects of scattering by suspensoids, on the penetration of PAR.Suspensoids, by increasing the rate of attenuation of the solar flux with depth, can greatly diminish the euphotic depth of a water body, with a consequent decrease in the ratio of the euphotic to the mixed depth: thus turbidity can reduce productivity of a water body substantially below that which might be expected on the basis of nutrient availability. Shallow turbid waters of low intrinsic colour can, however, be highly productive. By diminishing the depth of the layer within which solar energy is dissipated as heat, suspensoids can greatly modify the hydrodynamic behaviour of water bodies, and this also has far-reaching ecological consequences.Suspensoids drastically impair the visual clarity of water, a fact of major significance for the aquatic fauna, as well of aesthetic significance for humanity. The reciprocal of the Secchi depth is more correctly thought of as a guide to the vertical contrast attenuation coefficient rather than to the vertical attenuation coefficient for irradiance. The reflectivity of a water body, being at any wavelength proportional to the backscattering coefficient divided by the absorption coefficient, is highly dependent on the concentration, and optical character, of the suspensoids present. This has implications not only for the appearance (colour, muddiness) of the water to an observer, but also for the remote sensing of water composition by air- or satellite-borne radiometric sensors.     

Photic Volume in Photobioreactors Supporting Ultrahigh Population Densities of the Photoautotroph Spirulina platensis

Characterization of the photic zone and light penetration depth in cultures with ultrahigh cell densities represents a major issue in mass cultures of phytoautotrophic microorganisms grown in enclosed photobioreactors. In a study of the effect of underwater optical properties on the penetration depth of photosynthetically active radiation, the inherent optical properties of algal suspensions, i.e., absorption and scattering coefficients, as well as their apparent optical properties, i.e., the reflectance and the vertical attenuation coefficient of downwelling irradiance, were determined by using high-spectral-resolution radiometric measurements. The vertical attenuation coefficient was used to estimate quantitatively the depth of light penetration into a reactor containing an ultrahigh cell density (chlorophyll concentration, up to 300,000 mg m(sup-3)). For such a high cell density, the photic volume in the reactor was found to be extremely small; nevertheless, it differed between the blue and red light (less than 0.06 mm) and the green light (about 0.5 mm). This suggests a singular role for green light under the unique circumstances existing in ultrahigh-cell-density cultures of photoautotrophs.     

Stratification by cyanobacteria in lakes: a dynamic buoyancy model indicates size limitations met by Planktothrix rubescens filaments

The ability of the Planktothrix rubescens to stratify in Lake Zürich is related to the size and shape of the cyanobacterial filaments. Detailed measurements made in the lake are used in a dynamic computer model of buoyancy regulation to investigate the vertical movements of filaments tracking the depth at which the irradiance would support neutral buoyancy. The movement of the filament lags behind the constantly changing target depth owing to (a) the time taken for the filament to respond to the irradiance by changing its density and (b) the time it takes to move by sinking down or floating up through the water column. The model simulates the stratification depth over a 5-month period of the summer from the continuous measurements of irradiance and weekly measurements of light attenuation and temperature, without any further adjustment over the period. Models using filaments of the size observed in Lake Zürich explain several details of the observed depth changes: smaller planktonic cyanobacteria (e.g. Limnothrix sp.) are unable to migrate fast enough and larger ones (e.g. Anabaena spp.) will overshoot and become entrained in the epilimnion. The model can be used to simulate recruitment of Planktothrix filaments from different depths after vernal stratification. Recruitment of filaments from depths down to 45 m will contribute to the metalimnetic population increase in early July.     

The Burgundy-blood phenomenon: a model of buoyancy change explains autumnal waterblooms by Planktothrix rubescens in Lake Zürich

Buoyancy changes of the cyanobacterium Planktothrix rubescens- the Burgundy-blood alga - were modelled from its buoyancy response to light and irradiance changes in Lake Zürich during autumnal mixing. The daily insolation received by filaments at fixed depths and circulating to different depths was calculated from the measured light attenuation and surface irradiance. The active mixing depth, za5, was determined from the vertical turbulent diffusion coefficient, Kz, calculated from the wind speed, heat flux and temperature gradients. The fixed depth resulting in filament buoyancy, zn, decreased from 13 to 2 m between August and December 1998; the critical depth for buoyancy, zq, to which filaments must be circulated to become buoyant, decreased from >60 m in the summer to <10 m in winter. When za5 first exceeded zn, in September, P. rubescens was mixed into the epilimnion. In October, zq > za5: circulating filaments would have lost buoyancy in the high insolation. Often in November and December, after deeper mixing and lower insolation, za5 > zq: filaments would have become buoyant but would have floated to the lake surface (the Burgundy-blood phenomenon) only under subsequent calm conditions, when Kz was low. The model explains the Burgundy-blood phenomenon in deeper lakes; waterblooms near shallow leeward shores arise from populations floating up in deeper regions of the lake.     

Laboratory scale enclosure: concept, construction and operation

A laboratory scale enclosure (LSE) was devised for studyingthe seston dynamics in shallow, wind-mixed lakes. The LSE isa continuous flow system suitable for mass balance studies oflake water columns, and for cultivation of phytoplankton speciesas a reference for potential growth at the lake's light andmixing regime. The construction of the LSE is described in detail.Results are given on the operation with water from Lake Loosdrecht(The Netherlands). The coefficient of vertical mixing in theLSE was variable from 7.6 to 25.6 cm² s^–1, i.e. similarto values reported for shallow, wind-exposed lakes. On average,the vertical light attenuation and the spectral changes withdepth in the LSE agreed well with the in situ underwater lightclimate. Mass balances for phosphorus and oxygen could be accuratelyestablished, while the loss of paniculate matter due to settlingand wall growth was insignificant. The LSE may also be appliedas an incubator for primary production measurements in a ‘natural’light gradient and allowed prolonged continuous cultivationof Prochlorothrix hollandica.     

Light limitations to algal growth in tropical ecosystems

1. Spatial and temporal variations in algal concentrations are controlled in many aquatic ecosystems by the availability of solar irradiance, rather that nutrients or grazing. In such light limiting conditions, changes in the optical or hydrological characteristics of the water column will directly impact biomass concentrations. Here we develop and test an approach based on the relationship between available solar irradiance within the mixed layer and algal biomass concentrations. 2. As with most nutrient/biomass relationships, an increase in available solar energy favours an increase in biomass when light limitation prevails. The ratio between light/biomass is then used to determine a critical light requirement that can be used to estimate critical depth and compensation irradiance and open the way to exploring how changes in mixing depth and vertical attenuation may influence algal biomass concentrations. 3. This approach is used to describe real conditions in two disparate algal communities; the phytoplankton community in Lake Victoria, East Africa and the microphytobenthos community in the lacustrine system of Esteros del Iberá (South America). 4. Differences in the critical light requirement were used to examine the relative efficiency of the algal communities in their use of available solar energy. The tropical phytoplankton community showed similar energetic requirements to theoretical estimates and were found to be less efficient when compared with the phytobenthos community.     

The role of phytoplankton in determining the underwater light climate in Lake Constance

At all seasons, the underwater light field of meso-eutrophic large (480 km²) deep (mean: 100 m) Lake Constance was studied in conjunction with the assessments of vertical distributions of phytoplankton chlorophyll concentrations. Vertical profiles of scalar, downwelling and upwelling fluxes of photosynthetically available radiation, as well as fluxes of spectral irradiance between 400 and 700 nm wavelength were measured.The overall transparency of the water for PAR is highly dependent on chlorophyll concentration. However, the spectral composition of underwater light is narrowing with water depth regardless of phytoplankton biomass.Green light is transmitted best, even at extremely low chlorophyll concentrations. This is explained by the selective absorption of blue light by dissolved organic substances and red light by the water molecules. Nevertheless, significant correlations were found between vertical attenuation coefficients of downwelling spectral irradiance and chlorophyll concentrations at all wavelengths. The slopes of the regression lines were used as estimates of chlorophyll-specific spectral vertical light attenuation coefficients (K _c()).The proportions of total upwelling relative to total downwelling irradiance (reflectance) increased with water depth, even when phytoplankton were homogeneously distributed over the water column. Under such conditions, reflectance of monochromatic light remained constant. Lower reflectance of PAR in shallow water is explained by smaller bandwidths of upwelling relative to downwelling light near the water surface. In deeper water, by contrast, the spectra of both upwelling and downwelling irradiance are narrowed to the most penetrating components in the green spectral range. Reflectance of PAR was significantly correlated with chlorophyll concentration and varied from 1% and 1-% at low and high phytoplankton biomass, respectively. Over the spectrum, reflectance exhibited a maximum in the green range. Moreover, in deeper layers, a red maximum was observed which is attributed to natural fluorescence by phytoplankton chlorophyll.     

The vertical distribution of phytoplankton in stratified water columns

What determines the vertical distribution of phytoplankton in different aquatic environments remains an open question. To address this question, we develop a model to explore how phytoplankton respond through growth and movement to opposing resource gradients and different mixing conditions. We assume stratification creates a well-mixed surface layer on top of a poorly mixed deep layer and nutrients are supplied from multiple depth-dependent sources. Intraspecific competition leads to a unique strategic equilibrium for phytoplankton, which allows us to classify the distinct vertical distributions that can exist. Biomass can occur as a benthic layer (BL), a deep chlorophyll maximum (DCM), or in the mixed layer (ML), or as a combination of BL+ML or DCM+ML. The ML biomass can be limited by nutrients, light, or both. We predict how the vertical distribution, relative resource limitation, and biomass of phytoplankton will change across environmental gradients. We parameterized our model to represent potentially light and phosphorus limited freshwater lakes, but the model is applicable to a broad range of vertically stratified systems. Increasing nutrient input from the sediments or to the mixed layer increases light limitation, shifts phytoplankton towards the surface, and increases total biomass. Increasing background light attenuation increases light limitation, shifts the phytoplankton towards the surface, and generally decreases total biomass. Increasing mixed layer depth increases, decreases, or has no effect on light limitation and total biomass. Our model is able to replicate the diverse vertical distributions observed in nature and explain what underlying mechanisms drive these distributions.     

The responses of light interception,photosynthesis and fruit yield of cucumber to LED‐lighting within the canopy

Mathematical models of light attenuation and canopy photosynthesis suggest that crop photosynthesis increases by more uniform vertical irradiance within crops. This would result when a larger proportion of total irradiance is applied within canopies (interlighting) instead of from above (top lighting). These irradiance profiles can be generated by Light Emitting Diodes (LEDs). We investigated the effects of interlighting with LEDs on light interception, on vertical gradients of leaf photosynthetic characteristics and on crop production and development of a greenhouse‐grown Cucumis sativus‘Samona’ crop and analysed the interaction between them. Plants were grown in a greenhouse under low natural irradiance (winter) with supplemental irradiance of 221 µmol photosynthetic photon flux m^?2 s^?1 (20 h per day). In the interlighting treatment, LEDs (80% Red, 20% Blue) supplied 38% of the supplemental irradiance within the canopy with 62% as top lighting by High‐Pressure Sodium (HPS)‐lamps. The control was 100% top lighting (HPS lamps). We measured horizontal and vertical light extinction as well as leaf photosynthetic characteristics at different leaf layers, and determined total plant production. Leaf mass per area and dry mass allocation to leaves were significantly greater but leaf appearance rate and plant length were smaller in the interlighting treatment. Although leaf photosynthetic characteristics were significantly increased in the lower leaf layers, interlighting did not increase total biomass or fruit production, partly because of a significantly reduced vertical and horizontal light interception caused by extreme leaf curling, likely because of the LED‐light spectrum used, and partly because of the relatively low irradiances from above.     

The impact of phytoplankton on spectral water transparency in the Southern Ocean: implications for primary productivity

Spectral water transparency in the Northern Weddell Sea was studied during Austral spring. The depth of the 1-% surface irradiance level (euphotic depth) varied between 35 and 109 m and was strongly influenced by phytoplankton biomass. Secchi depths were non-linearly related to euphotic depth. In phytoplankton-poor water, the most penetrating spectral region was restricted to a relatively narrow waveband in the blue (488 nm), but the range was broader, between 488 and 525 nm when phytoplankton were abundant. Water transparency in the red spectral range was always low and only to a small extent affected by phytoplankton. Two independent procedures were used to quantify the impact of phytoplankton on spectral water transparency: (1) Regression analysis of spectral in situ vertical light attenuation coefficients in the sea, against coincident chlorophyll concentrations. This method gave chlorophyll-specific light attenuation coefficients; the y-intercept could be interpreted as a measure of light attenuation by pure water plus non-algal material. (2) Spectra of in vivo light absorption derived by spectroscopy, using phytoplankton enriched to varying degrees onto filters. Thus chlorophyll-specific absorption cross-sections were determined. Estimates obtained by both procedures were in close agreement. By integrating over the spectrum of underwater irradiance, in situ chlorophyll-specific absorption cross sections of phytoplankton suspensions, related to all photosynthetically active radiation, were calculated. Light absorption by phytoplankton for photosynthesis is accomplished mainly in the blue spectral range. Also dissolved and particulate organic matter contributed to the attenuation of blue light. Because in water poor in phytoplankton, underwater irradiance was progressively restricted to blue light, chlorophyll-specific absorption cross-sections of phytoplankton, averaged over the spectrum of photosynthetically active irradiance, increased with water depth. In water with elevated phytoplankton biomass, overall light attenuation was generally enhanced. However, because the spectral composition of underwater light changed relatively little with depth, except immediately below the water surface, light absorption cross-sections of phytoplankton changed little below 10 m depth. Vertical differences in the proportions of underwater light absorbed by the phytoplankton community here were mainly dependent on biomass variations. Because of the comparatively small attenuation of blue light by non-algal matter, the efficiency of light harvesting by phytoplankton at any given concentration of chlorophyll in Antractic waters is greater than in other marine regions. At the highest phytoplankton biomass observed by us, as much as 70% of underwater light was available for phytoplankton photosynthesis. When phytoplankton were scarce, <10% of underwater light was harvested by phytoplankton.Contribution within the European Polarstern Study (EPOS), supported by the Deutsche Forschungsgemeinschaft, Grant Ti 115/16-1 to MMT, the European Science Foundation, and by the Alfred Wegener Institut für Polar-und Meeresforschung, Bremerhaven     

Summer sedimentation in six shallow arctic lakes

The movement of sediment between the lake bottom and water column of shallow lakes can be sizeable due to the large potential for resuspension in these systems. Resuspended sediments have been shown to alter phytoplankton community composition and elevate water column production and nutrient concentrations. We measured the summer sedimentation rates of two lakes in 2003 and six lakes in 2004. All lakes were shallow and located in the Alaskan Arctic. In 2004, turbidity, light attenuation, total sediment:chlorophyll a mass in the sediment traps, and thermal stratification were also measured in each of the lakes. The sediment:chlorophyll a mass was much greater than if the sediment was derived from phytoplankton production in all of the lakes, indicating that the source of the sedimenting material was resuspension and allochthonous inputs. Consistent with these findings, the temporal variation in sedimentation rate was synchronous between most lakes, and sedimentation rate was positively related to wind speed and rainfall suggesting that sedimentation rate was strongly influenced by landscape-scale factors (e.g., wind and rain events). Two of the lakes are located on deposits of loess that accumulated during past glacial periods. These two lakes had sedimentation rates that were significantly greater and more variable than any of the other lakes in the study, as well as high turbidity and light attenuation. Our results indicate that sedimentation in these shallow arctic lakes is supported primarily by allochthonous inputs and resuspension and that landscape-scale factors (e.g., weather and geology) impact on the transport of materials between the lake bottom and water column. Handling editor: J. Saros     

Light availability as a possible regulator of cyanobacteria species composition in a shallow subtropical lake

1. Variations in the relative biovolumes of dominant cyanobacterial taxa were evaluated in the context of environmental conditions using canonical correlation analysis (CCorrA) and Redundancy Analysis (RDA). The objective was to test a conceptual model in which underwater irradiance determines dominance by bloom-forming (high light adapted) or non-blooming (low light adapted) taxa. 2. The data set consisted of 404 contiguous observations, collected over a 3-year period at eight pelagic sites, in shallow Lake Okeechobee, Florida, U.S.A. Data included species biovolumes, total phosphorus (TP), total nitrogen (TN), dissolved oxygen (DO) and chlorophyll a concentrations, as well as two indices: underwater irradiance (Secchi depth) and the ratio of Secchi:total depth. 3. The first environmental canonical variable was strongly correlated with the two light-related indices, and negatively correlated with TP. This reflects the predominant role of resuspended P-rich lake sediments in controlling underwater irradiance in the shallow lake. The first species canonical variable displayed a strong negative correlation with Lyngbya limnetica and L. contorta, and positive correlations with Anabaena circinalis, Aphanizomenon flos aquae and Microcystis spp. The results support the conceptual model; the first pair of canonical variables explained 55% of the variation in the species–environmental data set. RDA results provided further support for the hypothesis that irradiance was the major force controlling community structure. 4. One unexpected result was a positive association between Oscillatoria spp. dominance and indicators of high irradiance. This conflicts with past research indicating that Oscillatoria is a low light adapted taxon, and the finding that it is the most abundant taxon in Lake Okeechobee. This may reflect the fact that the two Lyngbya taxa were more strongly associated with low light conditions than Oscillatoria. CCorrA results indicated that Oscillatoria densities are strongly controlled by water temperature. There is a need for more detailed studies of cyanobacteria ecophysiology in order to explain fully the seasonality of phytoplankton in this and other shallow subtropical lakes.     

A Model to Predict Lake Water Colour

This study is an attempt to quantitatively determine variables of significance for predicting colour in small glacial lakes. Lake colour is an important variable in many lake ecological contexts. The data emanate from two extensive data-sets from Sweden, one of which concerns 1456 lakes, and the other 91 more well-suited lakes. Four year average values of lake colour were compared to catchment and morphometric parameters to help identify the processes which influence variability in colour between lakes. Various hypotheses concerning the factors regulating colour in lakes were formulated and tested. Various statistical tests were used to separate random influences from causal influences. Those “map parameters” with the most significant influence on colour were the theoretical lake water retention time, the percent of rocks, lakes and mires of the drainage area, the ratio between lake area and drainage area and the lake mean depth. Each model parameter provides only a limited explanation (statistical) of the variability in colour between lakes. The predictability of colour by these models can not be markedly improved by accounting for the distribution of the characteristics in the drainage area. The stability of the final model, which gives an r²-value of 0.74, has been tested with positive results. The model allows lake colour to be estimated from knowledge of “geological” characteristics of the lake and its drainage area. The variability between lakes from other factors, such as temperature, precipitation and/or contamination of acidifying substances and nutrients, may then be quantitatively differentiated from the impact of these “geological” factors.     

Seagrass depth limits

Examination of the depth limit of seagrass communities distributed worldwide showed that sea-grasses may extend from mean sea level down to a depth of 90 m, and that differences in seagrass depth limit (Z_c) are largely attributable to differences in light attenuation underwater (K). This relationship is best described by the equation

log Z_c (m) = 0.26 − 1.07 log K (m⁻)

that holds for a large number of marine angiosperm species, although differences in seagrass growth strategy and architecture also appear to contribute to explain differences in their depth limits. The equation relating seagrass depth limit and light attenuation coefficient is qualitatively similar to previous equations developed for freshwater angiosperms, but predicts that seagrasses will colonize greater depths than freshwater angiosperms in clear (transparency greater than 10 m) waters. Further, the reduction in seagrass biomass from the depth of maximum biomass towards the depth limit is also closely related to the light attenuation coefficient. The finding that seagrasses can extend to depths receiving, on average, about 11% of the irradiance at the surface, together with the use of the equation described, may prove useful in the identification of seagrass meadows that have not reached their potential extension.     

An analytical flat-plate photobioreactor with a spectrally attenuated light source for the incubation of phytoplankton under dynamic light regimes

An inexpensive and simple, analytical microalgal photobioreactor with a highly controllable, dynamic, spectrally attenuated light source is described. Spectral attenuation is achieved through the introduction of a variable thickness of CuSO₄ solution between the photobioreactor and a light source. The level of liquid is precisely determined via a computer-controlled peristaltic pump, which can be programmed to pump at a variety of rates. The resultant light fields consist of a wide range of irradiance intensities with concomitant spectral narrowing, which closely mimics modeled clear water attenuation patterns. Irradiance dynamics associated with virtually any mixing regime can be achieved. The culturing apparatus of the analytical photobioreactor is based on traditional flat-plate, photobioreactor design, but with several modifications: (1) The light path has been reduced to 1 cm to assure a uniform light field is experienced by all phytoplankton at relatively low cell densities; (2) carbon dioxide concentrations are kept constant through a negative feedback mechanism that pulses CO₂ into a constant air stream when culture media pH rises above a set point; (3) temperature is controlled in a similar manner, through the addition of cooling water to a water jacket in response to an increase in culture media temperature. This design is intended for use in photophysiological and bio- physical studies of microalgae under highly controlled culture conditions. It should prove easily adaptable to any number of more complex configurations.     

A model for light distribution and average solar irradiance inside outdoor tubular photobioreactors for the microalgal mass culture

A mathematical model to estimate the solar irradiance profile and average light intensity inside a tubular photobioreactor under outdoor conditions is proposed, requiring only geographic, geometric, and solar position parameters. First, the length of the path into the culture traveled by any direct or disperse ray of light was calculated as the function of three variables: day of year, solar hour, and geographic latitude. Then, the phenomenon of light attenuation by biomass was studied considering Lambert-Beer's law (only considering absorption) and the monodimensional model of Cornet et al. (1900) (considering absorption and scattering phenomena). Due to the existence of differential wavelength absorption, none of the literature models are useful for explaining light attenuation by the biomass. Therefore, an empirical hyperbolic expression is proposed. The equations to calculate light path length were substituted in the proposed hyperbolic expression, reproducing light intensity data obtained in the center of the loop tubes. The proposed model was also likely to estimate the irradiance accurately at any point inside the culture. Calculation of the local intensity was thus extended to the full culture volume in order to obtain the average irradiance, showing how the higher biomass productivities in a Phaeodactylum tricornutum UTEX 640 outdoor chemostat culture could be maintained by delaying light limitation. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 701-714, 1997.