1. Introduction

Eutrophication is a leading cause of impairment of aquatic ecosystems worldwide, and is accelerating in rate and extent due in large part to human activities [1]. Toxic algae, tainted freshwater supplies and fisheries-threatening hypoxia can all result in health risks and substantial economic losses. The need for improved water quality monitoring in vulnerable coastal regions and of inland freshwater resources is best addressed by a combined approach: increased monitoring of biogeophysical variables in these environments (both in situ and by remote sensing), coupled with the development of reliable bio-optical models in pursuit of better understanding of the biophysical relationships at play.

Existing optical modelling approaches [2–5] employ simple IOP models generally most suited to open-ocean (oligo- or meso-trophic) conditions and usually heavily dependent on Chlorophyll a (Chl a) specificity. Such models also typically decouple the phytoplankton absorption and backscattering terms, or use backscattering terms related only to the gross particulate: an approach that has served well in relatively low biomass oceanic waters, but is fundamentally restrictive for the analysis of the phytoplankton -specific ocean colour signal. This work has been undertaken, in part, to assess the suitability of a more holistic phytoplankton optical modelling approach for eutrophic environments, and ultimately to provide an enhanced capacity to analyse the ocean colour signal content related to the variability of phytoplankton functional types.

This EAP model represents a departure from existing modelling approaches in that it is population driven in terms of phytoplankton functional type (PFT). In other words, phytoplankton IOPs are formulated from population-specific refractive indices and so are not independent of each other. It has been established that at elevated biomass the spectral character of phytoplankton scattering becomes increasingly important [23,24]. Implementation of the EAP model allows investigation into when the resulting AOPs (including remote sensing reflectance, R_rs) may be sensitive to this variability, through the use of spectrally variant phase functions in the radiative transfer component of the model. Also, size- and assemblage-related influences are not well parameterised in the literature [7], and the EAP model additionally allows for investigation into these effects.

The very productive southern Benguela lends itself well to the development of optical modelling and validation activities. Inner shelf waters are typically dominated by 3 phytoplankton groups: potentially bloom-forming diatom and dinoflagellate assemblages, and nanophytes (small-celled assemblages, including some chlorophytes). These groups have distinctive optical characteristics and in any given natural assemblage there may be optically important components of all of them. For simplicity, modelling of only the dinoflagellate group is discussed here, as representative of frequently occurring high biomass blooms.

2. Biophysical modelling from first principles using two-layered spheres

2.1. Phytoplankton component

Assemblages are modelled using equivalent size distributions and a two-layered sphere cell geometry [6, 7], comprising a core sphere (representing the cytoplasm) and a shell sphere (chloroplast). Phytoplankton IOPs are generated from the real and imaginary parts of the cell refractive indices [7]. Where detailed refractive index data are not known at longer wavelengths (> 750 nm) and imaginary refractive indices are assumed to be very small, they are linearly interpolated from their values at 720 nm to 1e-5 at 750 nm, and then to 1e-9 at 900 nm, with subsequent quantified effect on the real part of the refractive index using established methods [7]. (This allows consistency between the RIs of different PFTs at long wavelengths).

The relative chloroplast volume is maintained at 20% while the effective diameter of the cell varies. The effective diameter of the modelled distribution is thus central to the IOP model, with the resulting IOPs depending heavily on particle size. The modelled IOPs have a constant Chl a density per cell (c_i), set at 2.5 kg.m⁻³ which was chosen as representative from the literature [7]. Recent experiments however indicate that covarying c_i with effective diameter may be more appropriate as the Chl a density of specific species becomes more important with the bloom’s monospecificity. However, this approach is not pursued further here.

For the forward modelling of example populations, a Standard normal particle size distribution (from 1 to 100 μm at 1 μm resolution) with effective variance of 0.6 is used as a reasonable approximation to the reduced species diversity typical of blooms of elevated biomass [6].

2.2. Other components

The primary intention here is to examine the modelled phytoplankton biomass and assemblage effects on ocean colour, so very simplistic scaling of other constituents is employed to demonstrate relative model performance.

A simple exponential combined gelbstoff and detrital absorption term a_gd(λ) [8, 9] is used as representative of commonly occurring conditions in the Benguela:

An observed relationship of

Ecolight radiative transfer software (Sequoia Scientific, 2008) was used to generate R_rs from these IOPs (given total absorption, attenuation and backscattering data), using wavelength-specific Fournier Forand phase functions as b̃_b varies across the wavelength spectrum. Fluorescence quantum efficiency ϕ was approximated as follows by Chl a concentration: below 10 mg.m⁻³ = 1%, 10–50 mg.m⁻³ = 0.6%, 50–100 mg.m⁻³ = 0.2% and over 100 mg.m⁻³ = 0.1%.These values are based on MODIS ϕ_sat climatologies [14], and measurements [15] to characterise the reduction in ϕ as eutrophication increases. An annual average for solar irradiance and a solar zenith of 30 degrees was used in lieu of time and location.

3. A comparison of IOP models

EAP simulated R_rs were compared to a subset of those from models described by Alvain et al. [2] and Lee et al. [3], two prominent phytoplankton IOP models both well validated for their applications, designed for Chl a concentrations ranging from 0.02 – 3 mg.m⁻³ [2] and 0.03 – 30 mg.m⁻³ [3]. The IOP approaches of both models are abbreviated in Table 1. Abbreviations used are detailed in Table 2.

Table 1. IOP parameterisations of the models of Alvain [2] and Lee [3]

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The models of both Alvain and Lee use Chl a specific absorption spectra $a_{\varphi }^{*}(\lambda )$ as described by Bricaud [16]. The approaches taken to gelbstof absorption are similar to the EAP model. The Alvain model neglects a separate detrital absorption term (representing all non-algal particles) on the basis that the spectral shape is similar to that of a_gd(λ) and that absorption by non-algal particles represents just 10% of gelbstoff absorption (as determined by Siegel et al., 2002, in [2]). Neither model includes a fluorescence term.

A significant difference between these two approaches is the determination of the backscatter. The Alvain model uses a spectrally invariant Petzold phase function for the total particulate backscatter b̃_b. This results in a constant total backscatter fraction of 0.0189. The Lee model separates the backscatter into its two components, calculating b_bϕ from b_ϕ with a 1% Fournier Forand phase function, and b_bdet from b_bdet with a Petzold phase function.

Both models have included dynamic ranges of IOP values in order to account for the variability observed in natural waters. For clarity when making the comparison to the EAP model, IOP values were selected from within these dynamic ranges which most closely approximate those of the EAP model. For the a_g(λ) and a_gd(λ) contributions this selection was based on the EAP value of a_gd(400). Likewise, a constant detrital scattering function approximating that of the EAP was selected from the ranges offered by the Lee and Alvain models. This ensures that the comparison between models is made under consistent (i.e. Benguela-like) water type conditions. Furthermore, the Alvain and Lee models were constrained for the purposes of this comparison to use the same Chl a specific phytoplankton absorption spectra [16]. A subset of phytopankton scattering functions was selected by comparing the coefficients at 550 nm to those of the EAP model.

While these constraints inevitably reduce the range of resulting R_rs values, these subsets should be acceptable for the purpose of commenting primarily on the different approaches to modelling the backscattering and the significance of these approaches as phytoplankton biomass increases to eutrophic concentrations.

The Alvain IOPs were processed to R_rs using Ecolight’s two component model for Chl a concentrations of 1, 2, 5, 10, 15 and 30 mg.m⁻³, using total a and b and a Petzold phase function for all particulate matter. This results in a total particulate backscatter fraction of up to 1.9% which is considered too high for Chl a concentrations over about 1 mg.m⁻³ [17].

The Lee IOPs were also processed to R_rs using Ecolight’s two component model for Chl a concentrations of 1, 2, 5, 10, 15 and 30 mg.m⁻³ using the total absorption and scattering coefficients. A combined backscattering phase function was calculated for each wavelength using the 1% Fournier Forand phase function to retrieve the b_bϕ from the b_ϕ, and the Petzold to retrieve the b_bdet from the b_det. The sum of these, i.e. the total b_b, was then used as input for Ecolight’s wavelength-specific variable b̃_b Fournier Forand phase function selection option.

4. Results and Discussion

4.1. Comparison of the constrained Alvain, Lee and EAP models

The R_rs generated (Fig. 1) are beyond the expected performance of the Alvain model (i.e. Chl a concentrations up to 3 mg.m⁻³) and up to the very limit of the Lee model (up to 30 mg.m⁻³) in order to examine the impacts of the different approaches to the backscattering terms as biomass increases. R_rs from the 3 models agree well for the Chla = 1 and 2 mg.m⁻³ experiments. Divergence is observed after Chl a = 5 mg.m⁻³ (Fig. 1).

Most notable perhaps at first glance are the comparatively large differences in magnitude of R_rs between EAP Chl a = 1 and 2 mg.m⁻³ with respect to the other models’. It should be emphasised that the EAP model, in this its simplest implementation, describes a homogenous dinoflagellate population with an idealised size distribution. At these low phytoplankton concentrations, natural populations would likely be variable both in species and in particle size.

 

Fig. 1 Comparison of Ecolight modelled R_rs from 3 IOP models: EAP, Alvain [2] and Lee [3]. Chl a values are 1, 2, 5, 10, 15 and 30 mg.m⁻³ in each case.

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4.2. Preliminary validation of R_rs

A preliminary validation exercise was carried out using measured Tethered Surface Radiometer Buoy (TSRB) data from 2002–2008 in the Benguela, processed to R_rs using ProSoft proprietary software (Satlantic). Measurements were selected for each chosen Chl a class, and the mean spectrum is presented using one standard deviation as an indication of variability in the optical measurements of natural populations (Fig. 2).

In the lower biomass classes (up to 5 mg.m⁻³) the models all perform reasonably well considering the simplifications and constraints placed on them. As biomass increases past Chl a of 10 mg.m⁻³ however, the effect on the R_rs of the differences in the models’ approaches to back-scattering becomes evident. The notably reduced brightness of R_rs in the measurements is most accurately modelled using the EAP model’s spectrally variant total backscattering probability which varies in magnitude with both Chl a concentration and wavelength.

 

Fig. 2 Preliminary validation of the 3 models with measured R_rs, for Chl a classes of 1, 2, 5, 10, 15 and 30 mg.m⁻³. The mean measured spectrum in each class is presented with 1 standard deviation as an indication of natural variability. The mean measured Chl a for each set of measurements is presented at the top of each example with the standard deviation and the number of measurements, N.

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It should be noted here that the use of the Bricaud $a_{\varphi }^{*}$ by both Lee and Alvain implies a heavy dependence on size with increasing Chl a concentrations that make them unsuitable for use over very wide ranges of biomass. The Bricaud measurements were mostly performed in ocean basin areas with Chl a concentrations of around 0.05 to 8 mg.m⁻³ [18], with one sampling station going up to 24 mg.m⁻³ in the St. Lawrence estuary. These $a_{\varphi }^{*}$ are appropriate for oligo/mesotrophic waters where a relationship of increasing cell size effects with increasing Chl a is generally observed. In highly eutrophic waters this relationship does not necessarily hold [19]. Figure 3 shows how the EAP model is forced to choose implausibly large sizes at high Chl a concentrations to maintain consistency with the Bricaud absorption spectra. The absorption profiles modelled above fit EAP size classes with effective diameters of between 6 and 16 μm, which were chosen according to observed dominant phytoplankton species’ effective diameters rather than Bricaud-equivalent spectra (which would force the EAP model to go up to a D_eff of 45 μm at Chl a of 30 mg.m⁻³, representing an unusually large cell).

 

Fig. 3 Bricaud $a_{\varphi }^{*}$ for Chl a = 1, 2, 5, 10, 15 and 30 mg.m⁻³ matched to EAP $a_{\varphi }^{*}$ by effective diameter (D_eff), implying EAP assemblage D_eff of 6, 9, 16, 23, 26 and 45 μm respectively.

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4.3. Employing equivalent total absorption coefficients

To account for the differences in absorption, avoid the problem of an inherent dependency on large sizes at very high biomass, and in order to be able to comment more fully on the backscattering which is central to the EAP model and performing accurate IOP modelling in eutrophic waters, the comparative models were re-created, all using the EAP phytoplankton absorption spectra for each Chl a class (Fig. 4). Also, the EAP fluorescence term was neglected to match the other models. The Lee model’s detrital absorption term a_det (λ) was also neglected as it is not explicitly included in the other models, and as Lee a_g(λ) values were selected for this comparison to most closely match the EAP combined a_gd(λ), that term can be considered to include detrital absorption (Fig. 4).

Immediately noticeable in the resulting R_rs is the well constrained 600 to 650 nm region in the EAP model with respect to the Alvain model.

 

Fig. 4 Comparison of Ecolight modelled R_rs from the 3 IOP models: EAP, Alvain [2] and Lee [3]. Chl a values are 1, 2, 5, 10, 15 and 30 mg.m⁻³ in each case. This comparison uses identical (EAP) $a_{\varphi }^{*}(\lambda )$s in order to examine the effect of the different approaches to phytoplankton backscattering.

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The Alvain model’s total scattering compares well with EAP b(λ) in magnitude (Fig. 5, top left) but the choice of one spectrally invariant phase function for both phytoplankton and non-algal particles (Petzold) results in an unrealistically high backscatter fraction which is constant over varying biomass (Fig. 5, bottom left). In turn this results in greatly magnified backscattering at high Chl a concentrations.

 

Fig. 5 Scattering and backscattering characteristics of EAP, Alvain [2] and Lee [3] at Chl a concentrations 1, 2, 5, 10, 15 and 30 mg.m⁻³. Phytoplankton and detrital backscatter (bottom right) are shown for Chl a of 1 (lower line) and 30 mg.m⁻³ (upper line). The increased spectral detail of the EAP model’s phytoplankton scatter and backscatter becomes increasingly important with increasing biomass as is evident in the spectral variation in the resulting total backscattering probability (bottom left).

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The spectrally less variant total particulate scatter of the Lee model, and choice of spectrally flat phase functions (Fournier Forand 1% and Petzold) for both the phytoplankton and non-algal components results in total backscattering profiles with more or less indistinct spectral features, although the average magnitudes compare well to EAP in the mid biomass classes. The increased spectral variability of EAP backscattering is translated into the R_rs as a shift of the 680 nm peak towards 709 as biomass increases - a phenomena also caused by the increase in the red Chl a absorption band and the rapidly increasing water absorption with increasing wavelength. This is an important observed feature at the ”red edge” of eutrophic water reflectances [20].

Modelling backscattering as flattened spectra with reduced spectral variability may enable adequate R_rs modelling at low biomass but as Chl a concentration and the importance of non-algal scattering increases, such simple b_b models are unable to reproduce the spectral shape and magnitude variations in the R_rs successfully. The EAP model reflects an approach to backscatter derived from phytoplankton community optics rather than a calculation based on attenuation and/or the assumption of spectrally invariant particle scattering characteristics.

4.4. Characterising eutrophic water R_rs

Having shown the validity of the EAP model R_rs with respect to measurements made in the Benguela, the model can now be used to examine the characteristics of much more eutrophic water conditions. Figure 6 shows Ecolight modelled R_rs using IOPs generated using the EAP model, for biomass increasing from 1 to 200 mg.m⁻³. A Standard normal particle size distribution from 1 to 100 μm with effective diameter 16 μm is used here, representing a homogenous assemblage displaying the typical optical characteristics of a dinoflagellate population. This simulation (again using Ecolight) includes contributions from the combined gelbstoff/detrital absorption term a_gd(λ) and small particle backscattering b_bs(λ) as described earlier, and uses a choice of Fournier Forand phase function with a variable b̃_b at each output wavelength.

 

Fig. 6 Modelled EAP R_rs (above) for typical dinoflagellate assemblage with effective diameter of 16 μm. Chl a concentrations are 1, 2, 5, 10, 20, 30, 50, 100, 150, 200 mg.m⁻³. Below the shift from maximum peak reflectance height in the blue/green to the red is shown (dotted lines), for increasing Chl a. The first derivatives of these slopes (solid lines) cross at a Chl a of around 15 mg.m⁻³, the point at which the red features of high biomass reflectance spectra start to dominate.

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As biomass increases, the modelled R_rs show most distinctly a shift in the fluorescence peak at around 680 nm (in low biomass) towards 710 nm at Chl a concentrations of above 100 mg.m⁻³. This is caused by the combined effects of a decrease in the fluorescence quantum efficiency [20] and increased phytoplankton absorption as this region becomes the dominant identifier of high concentrations of Chl a. Water is also strongly absorbing in this region which magnifies this effect. The switch in dominance of the 443:555 to the 709:555 band ratio (Fig. 6, as per the SeaWiFs OC4 Chl a retrieval algorithm [21]) shows the importance of signal in the red for Chl a estimation in waters with concentrations over about 25 mg.m⁻³.

Other notable features of R_rs with increasing eutrophication are convergence at around 660 nm, as well as around 560 nm, and the well constrained region between these points. The decrease in R_rs in the blue is indicative of decreased influence of gelbstoff absorption with respect to Chl a absorption as the latter becomes more dominant spectrally.

4.5. EAP R_rs validation at very high biomass

Some very high biomass TSRB measured R_rs are presented here. The measurements (N=4, 6 and 5 respectively) represent a range of assemblage types and size distributions, which the EAP forward modelled R_rs do not consider here. This brief validation exercise shows that a chosen effective diameter of 12 μm most accurately matches all three high biomass blooms (for Chl a of 110, 150 and 180 mg.m⁻³ respectively). Most of the R_rs measurements were from a Prorocentrum triestinum-dominated bloom in 2005, with varying lesser proportions of Dinophysis acuminata, D. fortii and P. reticulatum [22]. P. triestinum is a small dinoflagellate approximately 18–22 μm in length and 6–11 μm in width. The variability in resulting R_rs from size effects is clearly seen.

As biomass increases, the need for the employment of wavelength-dependent phase functions for at very least the phytoplankton component is evident. Figure 7 (bottom right) shows the increasingly variable values of the backscatter fraction as Chl a increases (for consistent assemblage D_eff and phytoplankton type). These range from an essentially spectrally constant backscatter fraction at low Chl a (1 mg.m⁻³) to variability across the wavelength spectrum from 0.002 (i.e. 0.2%) to 0.024 (i.e. 2.4%) in eutrophic water conditions.

 

Fig. 7 High Biomass Validation of EAP R_rs, with EAP total backscatter probability shown for Chl a 1, 10, 50, 100, 150, 200 and 300 mg.m⁻³.

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Fig. 8 Contribution of Phytoplankton to total IOPs and R_rs signal, for Chl a values of 2 and 150 mg.m⁻³, for an idealised dinoflagellate assemblage with effective diameter of 16 μm.

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4.6. Proportional contribution of phytoplankton to total R_rs

From EAP modelled data, the proportional (percentage) contributions of Chl a to the total absorption, total scatter and backscatter are shown (Fig. 8) for Chl a = 2 mg.m⁻³ and 150 mg.m⁻³, keeping the effective diameter constant at 16 μm (representing a dinoflagellate assemblage). It can be concluded that at lower biomass, gelbstoff and detrital/small particles are optically significant, while at high biomass the signal is almost exclusively due to phytoplankton pigment. That being said, however, the relative contribution of detritus and small particles to backscatter remains important even at Chl a of 150 mg.m⁻³ and this is translated into the R_rs signal especially between 550 and 680 nm (Fig. 8).

[Note: These proportions include absorption and scatter of the medium itself (water). Phytoplankton R_rsp is calculated with only water + phytoplankton specific IOPs. Other contributions are total R_rs − R_rsp. Any optical interactions between phytoplankton and other components are therefore neglected here.]

5. Conclusion

The EAP model is shown to be appropriate for IOP and R_rs modelling in high biomass Case 1 waters. Here it is presented in its simplest, forward form but there is much scope for added complexity and sensitivity. The modelling of mixed assemblages (mixed phytoplankton types of varying c_i and pigment concentrations, and different population size distributions) can be replicated as required. Cells containing vacuoles and other anomalous scattering characteristics can be considered too. The importance of detailed spectral backscattering is emphasised here. A full investigation into the sensitivity of the model to the use of discretised phase functions is necessary to determine the extent of reliance on the detailed spectral backscattering component.

Table 2. Symbols and Abbreviations

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