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1 DO BIO-OPTICAL PARAMETERS AND RELATIONSHIPS APPLY TO EXTREME ALGAL BLOOMS? Stacey M. Etheridge 1,2 , Collin S. Roesler 2 , Heidi M. Franklin 2 , and Emmanuel Boss 3 1 Dept. of Marine Sciences, Univ. of Connecticut, 1080 Shennecossett Rd., Groton, CT 06340; 2 Bigelow Laboratory for Ocean Sciences, P.O. Box 475, West Boothbay Harbor, ME 04575; 3 School of Marine Sciences, Univ. of Maine, Libby Hall,Orono, ME 04469 Abstract Recently there has been increased interest in the remote detection of harmful algal blooms (HABs), given that they are often associated with significant changes in water color. Questions have arisen, however, regarding the applicability of established optical methods and algorithms to extreme blooms. During two intense blooms of the non-toxic dinoflagellate Prorocentrum micans, we investigated: 1) the range of chlorophyll-specific absorption (a*) and the use of chlorophyll alone to estimate spectral absorption, 2) the application of an inherent optical property (IOP) model (particulate beam attenuation inversion), and 3) the application of an apparent optical property (AOP) model (reflectance inversion). In situ conditions were characterized by extraordinarily high chlorophyll concentrations (nearly 500 µg L -1 ) and particle size ranges that did not display the Junge-like distributions typically encountered in the ocean. Particle area and volume distributions exhibited a modal diameter of 23 µm, consistent with dominance by P. micans cells. Even with extremely high chlorophyll, a* coefficients accurately represented algal photoacclimation, yet measurements of chlorophyll alone were not sufficient to model spectral phytoplankton absorption. The IOP and AOP models evaluated were robust despite violation of key assumptions. Limitations to some optical techniques were a function of how sensitive each optical measurement was to the cells causing the bloom, relative to other constituents. The P. micans cells were dominant contributors to absorption, but not to attenuation thereby allowing for the optical separation of bloom and non-bloom particles. Success of certain optical parameters and relationships during blooms suggests that some existing optical techniques may be used to detect blooms and potentially develop early warning systems for HABs. Introduction Optical methods provide rapid, noninvasive ways to examine aquatic ecosystems; thus to improve our understanding of oceanography, optical relationships are continually being derived and tested. Developing rapid, reliable detection methods for algal blooms is of primary concern because they are responsible for much of the oceanic carbon fixation, have a high potential for exporting carbon (Legendre 1990), and may be harmful and/or toxic. Since blooms are often associated with distinct variations in water color, it is feasible that they can be assessed using established bio-optical techniques (e.g. Carder and Steward 1985; Johnsen and Sakshaug 1993; Cullen et al. 1997; Kahru and Mitchell 1998). However, is there a point at which blooms become too extreme and bio-optical relationships fail to provide accurate information?

Do bio-optical parameters and relationships apply to extreme algal blooms

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DO BIO-OPTICAL PARAMETERS AND RELATIONSHIPS APPLY TO EXTREME ALGAL BLOOMS?

Stacey M. Etheridge1,2, Collin S. Roesler2, Heidi M. Franklin2, and Emmanuel Boss3

1Dept. of Marine Sciences, Univ. of Connecticut, 1080 Shennecossett Rd., Groton, CT 06340; 2Bigelow Laboratory for Ocean Sciences, P.O. Box 475, West Boothbay Harbor, ME 04575; 3School of Marine Sciences, Univ. of Maine, Libby Hall,Orono, ME 04469

Abstract Recently there has been increased interest in the remote detection of harmful algal blooms (HABs), given that they are often associated with significant changes in water color. Questions have arisen, however, regarding the applicability of established optical methods and algorithms to extreme blooms. During two intense blooms of the non-toxic dinoflagellate Prorocentrum micans, we investigated: 1) the range of chlorophyll-specific absorption (a*) and the use of chlorophyll alone to estimate spectral absorption, 2) the application of an inherent optical property (IOP) model (particulate beam attenuation inversion), and 3) the application of an apparent optical property (AOP) model (reflectance inversion). In situ conditions were characterized by extraordinarily high chlorophyll concentrations (nearly 500 µg L-1) and particle size ranges that did not display the Junge-like distributions typically encountered in the ocean. Particle area and volume distributions exhibited a modal diameter of 23 µm, consistent with dominance by P. micans cells. Even with extremely high chlorophyll, a* coefficients accurately represented algal photoacclimation, yet measurements of chlorophyll alone were not sufficient to model spectral phytoplankton absorption. The IOP and AOP models evaluated were robust despite violation of key assumptions. Limitations to some optical techniques were a function of how sensitive each optical measurement was to the cells causing the bloom, relative to other constituents. The P. micans cells were dominant contributors to absorption, but not to attenuation thereby allowing for the optical separation of bloom and non-bloom particles. Success of certain optical parameters and relationships during blooms suggests that some existing optical techniques may be used to detect blooms and potentially develop early warning systems for HABs. Introduction Optical methods provide rapid, noninvasive ways to examine aquatic ecosystems; thus to improve our understanding of oceanography, optical relationships are continually being derived and tested. Developing rapid, reliable detection methods for algal blooms is of primary concern because they are responsible for much of the oceanic carbon fixation, have a high potential for exporting carbon (Legendre 1990), and may be harmful and/or toxic. Since blooms are often associated with distinct variations in water color, it is feasible that they can be assessed using established bio-optical techniques (e.g. Carder and Steward 1985; Johnsen and Sakshaug 1993; Cullen et al. 1997; Kahru and Mitchell 1998). However, is there a point at which blooms become too extreme and bio-optical relationships fail to provide accurate information?

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Few assessments of optical techniques for blooms in the natural environment exist; therefore, the goal of this study was to determine if bio-optical parameters and relationships were robust during extreme algal blooms. Two intense blooms of the non-toxic dinoflagellate Prorocentrum micans formed in W. Boothbay Harbor, Maine in September 1999 and October 2001 and changed the water from green to a bright brownish-orange. During these blooms, we evaluated: 1) the range in chlorophyll-specific absorption (a*) and the use of chlorophyll values to estimate spectral absorption, 2) the application of an inverse IOP model (particulate beam attenuation inversion; Boss et al. 2001a, b), and 3) the application of an inverse AOP model (reflectance inversion; Roesler and Perry 1995).

Chlorophyll-Specific Absorption- Algal cells may experience considerable fluctuations in ambient light, especially over the course of bloom progression. Acclimation strategies include changing the size and number of photosynthetic units, both of which alter the amount of cellular light harvesting pigments (Perry et al. 1981; Prézelin 1981). Often a* coefficients are used to interpret photoacclimation (Bidigare et al. 1990; Hoepffner and Sathyendranath 1992) and reflect the degree of pigment packaging (Kirk 1975; Bricaud et al. 1995). Absorption in the blue is impacted by pigments other than chlorophyll a; thus, evaluating a* at 676 nm reduces the influence of accessory pigments. The theoretical maximum of a* (676) is 0.023 m2 mg-1. Values near this range indicate maximum chlorophyll absorption efficiency, expected for cells acclimated to high light. Lower a* values represent cells with more pigment and a decreased efficiency per molecule as would be expected for low-light acclimated cells. Algal size also plays a role in determining its capacity to become packaged (Morel 1991), whereby large cells may be more packaged due to a larger storage volume and a longer pathlength for absorption. Applicability of using a* to assess photoacclimation during blooms with extraordinarily high chlorophyll and high concentrations of large algal cells is evaluated. Additionally, chlorophyll concentrations alone are used in modeling to determine other optical parameters such as spectral absorption (e.g. Bricaud et al. 1995); thus, we assess how robust such models are during extreme blooms. Inverse IOP Model- Knowledge of particle size distributions (PSD) in the ocean is important, yet difficult to measure. Thus, a robust relationship between PSD and a parameter more easily determined could enhance our estimates of particle size ranges and concentrations. Recent papers (Boss et al. 2001a, b) test the theoretical relationship (Volz 1954; Morel 1973; Diehl and Haardt 1980) between the particulate beam attenuation spectrum and PSD shape. Briefly, the PSD in the ocean is typically polydispersed and can be approximated by a hyperbolic, Junge-like distribution:

N(D) = No(D/Do)-ξ (1)

where N(D) is the particle concentration per unit volume per unit bin width (number m-4), D is particle diameter (m), No is particle concentration (number m-4) at reference diameter Do (m), and ξ is the dimensionless, hyperbolic slope. Typical ranges for ξ in the ocean vary from -2.5 to -5, indicating there are more small particles than large ones (Morel 1973; Diehl and Haardt 1980; McCave 1983). Particulate attenuation, cp, is wavelength dependent and can be described by (van de Hulst 1957; Diehl and Haardt 1980):

cp(λ) = cp(λο)[(λ/λο)]-γ. (2) The variable cp(λο) is the particulate beam attenuation coefficient (m-1) at nominal wavelength λο (nm) and γ is the hyperbolic slope (dimensionless). Based on optical

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theory for an infinite distribution of polydispersed, non-absorbing spheres, ξ and γ are linearly related (Diehl and Haardt 1980):

ξ = γ + 3. (3) This model was modified by Boss et al. (2001b) for situations where the PSD is of finite size:

ξ = γ + 3 – 0.5 exp(-6γ). (4) Thus any change in the PSD slope is associated with changes in the spectral attenuation slope. This simple relationship provides a convenient means of assessing PSD in situ with a routine optical measurement; however, the full range of applicability in the field has not been tested. To date it has only been examined to a limited extent for oceanic particles (Kitchen et al. 1982) and in the bottom boundary layer where particles were expected to be polydispersed and relatively non-absorbing (Boss et al 2001a). Here we test the applicability of this approach to the other extreme: highly absorbing algal cells with a monodispersed PSD with respect to cross sectional area and volume, which may not be well described by Eq. 1. An additional challenge arises from sensitivity analyses showing that measurements of particulate attenuation are most sensitive to particles between 2-20 µm (Boss et al. 2001b); P. micans cells dominating these blooms were slightly larger.

Inverse AOP Model- Existing optical methods are available to discern the composition and contribution of the components in the water column (Bricaud et al. 1981; Kishino et al. 1985; Carder et al. 1989). It is the combination of the optical properties (absorption and backscattering) of all these components and water that determines the ultimate color of the water, described by the radiance reflectance:

CDOMCPMw

bCPMbbw

aaaa

bbbR

+++++≈

φ

φλ )( (5)

where bb is the backscattering coefficient (m-1) and a is the absorption coefficient (m-1) for water (w), phytoplankton (φ), colored non-phytoplankton particulate material (CPM), and colored dissolved organic material (CDOM). Based on this relationship, an inverse model was developed by Roesler and Perry (1995) to estimate aφ and bbp from R(λ). Originally, the model was tested in optically diverse regions with chlorophyll concentrations reaching 25.35 µg L-1. The model was also robust when applied to three published red tide reflectance data sets (Carder and Steward 1985; Clark and Kiefer 1990; Cullen et al. 1997; in Roesler and McLeroy-Etheridge 1998). In this paper we evaluate the ability of this model to predict aφ and bbp from R(λ) during blooms when chlorophyll reached 494.37 µg L-1.

Materials and Methods

Field/Laboratory Measurements- Surface water samples were collected in carboys on 23 September 1999 and 12 October 2001 in the afternoon near Bigelow Laboratory in W. Boothbay Harbor, Maine during the peak of each P. micans bloom when the water was intensely discolored. Concurrently, above water spectral downwelling irradiance (Ed) and subsurface (0.66 m) spectral upwelling radiance (Lu) were measured using a Satlantic HTSRB (hyperspectral tethered spectral radiometer buoy). Also, Lu was measured directly at the surface in 1999 by holding the HTSRB such that the Lu sensor was located just beneath the surface. Dark calibrations at in situ

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temperatures were applied, and R(λ) was calculated by Lu/Ed. Spectral particulate and dissolved absorption were measured in a Cary 3E UV-VIS spectrophotometer using the quantitative filter technique (Yentsch 1962; Mitchell 1990) and 10 cm cuvette measurements (Bricaud et al. 1981), respectively. Correction factors for pathlength amplification were applied (Roesler 1998). Filtration (Whatman GF/F) and pigment extraction (methanol) allowed for separation of dissolved, phytoplankton, and colored non-phytoplankton particulate absorption (Kishino et al. 1985; Roesler and Perry 1995). In 2001, IOPs (absorption and attenuation) were measured using a WETLabs ac9, which was set up in the lab for analysis of discrete water samples via gravity flow. Temperature (Pegau and Zaneveld 1993; Pegau et al. 1997) and scattering (Roesler and Zaneveld 1994; Bricaud et al. 1995) corrections were applied, and scattering was calculated by difference. The PSD was determined from 0.2 to 150 µm in 0.5 and 0.2 µm evenly spaced bins in 1999 and 2001, respectively, with a Galai CIS 100 laser particle analyzer (Roesler and Iturriaga 1994). Chlorophyll concentrations were determined using a Turner Designs fluorometer calibrated with purified standards from Sigma Chemical (Holm-Hansen et al. 1965).

Calculations and Modeling- Values of a* were calculated from measured chlorophyll and absorption coefficients. We also applied our chlorophyll concentrations to the empirical relationship of Bricaud et al. (1995), which estimates a* from chlorophyll concentrations alone. For the 2001 data set, R(λ) was only measured subsurface; therefore, we modeled reflectance directly at the surface by applying the vertical attenuation, k, to the measured subsurface R(λ). The k was estimated from measured absorption and scattering following Kirk (1981): k = (a2 + Gab)1/2 (6) where k is the vertically averaged value in the upper photic zone and G is a coefficient representing the relative contribution of scattering to vertical attenuation.

The standard Roesler and Perry (1995) model was used to estimate aφ and bbp. We also used a modified version of the model (Roesler and Boss, this volume), which does not place spectral shape limitations on bbp. For AOP inversions, we used R(λ) directly at the surface; these spectra differed in magnitude and shape from subsurface R(λ) (Fig. 1).

Results

Chlorophyll-Specific Absorption- Reasonable a* spectra were obtained for each P. micans bloom (Fig. 2a). Values of 0.0115 and 0.0075 m2 mg-1 at 676 nm were measured for 1999 and 2001, respectively. Both spectra indicate pigment packaging since the coefficients at 676 nm are lower than the theoretical maximum for non-packaged cells. Algae present in the 2001 bloom appear more packaged than in 1999 given the lower a* values and flatter peaks in the spectrum. The a* values modeled from the Bricaud et al. (1995) empirical relationship, however, did not agree well with those measured, in particular with regard to spectral shape (Fig. 2b,c). Modeled and measured spectra differed significantly near 480 and 550 nm, regions impacted by accessory pigments.

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Figure 1. Radiance reflectance magnitude (a and c) and spectral shape (b and d) at the surface (dark line) versus subsurface (thin line) in 1999 (a and b) and 2001 (c and d).

Figure 2. a) Measured spectral chlorophyll-specific absorption (a*) during the 1999 (dark line) and 2001 (thin line) P. micans blooms. Measured (dark line) versus modeled

(thin line) chlorophyll-specific absorption for b) 1999 and c) 2001. Inverse IOP Model- The model of Boss et al. (2001a,b) was evaluated for the

2001 data set, the only year for which we had attenuation measurements. The measured attenuation was spectrally flat with a hyperbolic slope, γ, of 0.027. When the measured γ was applied to Eq. 4, ξ was modeled to be –1.91, similar to the observed PSD slope of -1.96 (Table 1). The inverse IOP model estimated ξ, even though the key assumption of a Junge-like PSD was violated. The limitation, however, is that it is only possible to obtain the PSD slope rather than the PSD shape (Fig. 3) and the influence of the algal population was not significant.

Table 1. Measured spectral attenuation slope and PSD slope and the modeled PSD

slope based on Eq. 4. The 95% confidence intervals are given in parentheses.

γ ξ ξ̂

0.027 (6.922e-5, 0.054) -1.96 (-2.0965, -1.8309) -1.91

0

0.004

0.008

0.012

0.016

400 500 600 700

Wavelength (nm)

a*

(m2 m

g-1

)

0

0.004

0.008

0.012

0.016

400 500 600 700

Wavelength (nm)

a*

(m2 m

g-1

)0

0.004

0.008

0.012

0.016

400 500 600 700

Wavelength (nm)

a*

(m2 m

g-1

)

a b c

0

0.025

0.05

0.075

0.1

400 500 600 700 800

Wavelength (nm)

No

rma

lize

d R

()

0.00

0.01

0.02

0.03

400 500 600 700 800

Wavelength (nm)

R(

)

0.00

0.01

0.02

0.03

400 500 600 700 800

Wavelength (nm)R

()

0

0.025

0.05

0.075

0.1

400 500 600 700 800

Wavelength (nm)

No

rma

lize

d R

()a b

c d

6

Inverse AOP Model- The inverse model of Roesler and Perry (1995) was used to estimate spectral aφ (Fig. 4a), combined CDOM and CPM absorption (Fig. 4b), and bbp (Fig. 4c). Both the standard and modified model agreed well with measured aφ (Fig. 4a). Using the standard model there was only a 4.07 % and a 9.28% difference between modeled and measured spectra in 1999 and 2001, respectively. The modified model yielded a 22.38% and a 2.73% difference between modeled and measured spectra for 1999 and 2001, respectively. After adding the CDOM and CPM components together, both models performed fairly well at estimating the non-phytoplankton components for the 1999 data; however, the modeled CDOM and CPM for 2001 were much lower than measured (Fig. 4b). Unfortunately, backscattering measurements were not available during either bloom for comparison to the model. Nevertheless, the two versions of the model are in agreement as to the magnitude and general shape of spectral bbp (Fig. 4c).

Figure 3. Log of the measured particle size distribution (diamonds) and the slope (-1.96) of the particle size distribution (solid line) during the 2001 bloom. Dotted lines

represent modeled PSD slopes of –1 and –2.5 for comparison.

Discussion

Chlorophyll-Specific Absorption- Measured a* values were consistent with the given bloom conditions. Though the bloom was located directly at the surface in 1999, cells likely became packaged due to the high cell concentrations. In 2001, the bloom was well mixed in the upper 2-3 m, and it was expected that cells were more packaged in response to decreased light exposure. Measured a* coefficients were in the range of other reported values for P. micans in the laboratory (Ahn et al. 1992) and the natural environment (Ciotti et al. 2002). The empirical relationship of Bricaud et al. (1995), however, did not provide accurate estimates of spectral absorption. It is not surprising that this relationship was not robust under conditions with such high chlorophyll concentrations. The range of chlorophyll over which the empirical relationship was developed varied from 0.02 – 25 mg m-3, substantially lower than the values we encountered. The most significant deviation in the spectral shape of a* was around 550 nm. This was due to a signature associated with phycobilipigments, accessory pigments present in the observation used to derive the relationship, but not associated with P. micans. Our results suggest that measured a* values can be accurately obtained and may reflect algal photoacclimation during blooms. However, models for determining a*

1E+13

1E+14

1E+15

1E+16

1E+17

1E+18

0.000001 0.00001 0.0001

Diameter (m)

Co

nce

ntr

ati

on

(C

ell

s m

-4)

7

values, such as that by Bricaud et al. (1995), may not be robust in situations with extraordinarily high chlorophyll. Individual models would need to be evaluated under extreme blooms to assess their applicability.

Figure 4. Measured (bold lines) and modeled (standard – thin lines; modified – medium lines) results from reflectance inversion for a) phytoplankton absorption, b) combined CDOM and CPM absorption, and c) particulate backscattering. The left

panel is from the1999 bloom, and the right panel is from the 2001 bloom. Inverse IOP Model- The measured spectrally flat attenuation was either due to the

presence of the large P. micans cells or the polydispersed non-bloom particles. A monoculture of the 25-µm dinoflagellate Alexandrium tamarense exhibited spectrally decreasing attenuation. It is expected that P. micans cells alone would display a spectrally decreasing attenuation, similar to that of Alexandrium since both dinoflagellates are similar in size and pigment compositions (Fig. 5). Thus, it is likely that the flat attenuation observed during the bloom is the result of polydispersed non-bloom particles. Initially it was surprising that there was agreement between the measured and modeled PSD slope during the bloom since the overall PSD was non-Jungian; however, the non-bloom particles did display a Junge-like distribution. It is the non-bloom particles impacting attenuation, consistent with the idea that it is the non-bloom particles responsible for the observed spectrally flat attenuation. Thus, the PSD of the non-bloom particles is what is estimated using Eq. 4. Unfortunately, this inverse model did not

0

2

4

6

8

400 600 800

Wavelength (nm)

aφ (

m-1

)

0

0.5

1

1.5

2

400 600 800

Wavelength (nm)

aφ (

m-1

)01

23

4

400 600 800

Wavelength (nm)

aC

DO

M+C

PM (

m-1

)

00.5

11.5

2

400 600 800

Wavelength (nm)

aC

DO

M+C

PM (

m-1

)

0

0.2

0.4

0.6

400 600 800

Wavelength (nm)

bb

p (

m-1

)

0

0.05

0.1

0.15

0.2

400 600 800

Wavelength (nm)

bb

p (

m-1

)

a

c

b

8

provide information regarding the cells causing the bloom. Nevertheless, the sensitivity of attenuation to small particles in this case allowed for the optical separation of non-bloom particles (e.g. detritus) from P. micans. During blooms dominated by large cells, attenuation could be used to provide the PSD of the non-bloom particles, whereas other methods for measuring the PSD of bloom cells would be necessary. In blooms of small cells (e.g. brown tides of the 2.5 µm Aureococcus anophagefferens), it is likely that attenuation will be sensitive to the algal cells as well as the non-bloom particles, affecting the estimation of the PSD slope. Measurements of attenuation and PSD during blooms of small cells would have to be made to assess the applicability of this inverse IOP model under those conditions.

Figure 5. Measured spectral particulate attenuation, cp, during the P. micans bloom (solid circles) in 2001 (chlorophyll concentration of 126.77 µg L-1) and for an A. tamarense (open circles) monoculture (chlorophyll concentration of 80.24 µg L-1).

Inverse AOP Model- During extreme blooms so much attenuation occurs in the

upper meter of water that standard HTSRB measurements at 0.66m depth are not sufficient to derive accurate reflectance spectra. When the Roesler and Perry (1995) and Roesler and Boss (this issue) models were applied to surface R(λ), they were very robust. Since the inversions have performed successfully for a variety of optically diverse conditions with chlorophyll ranging from 0.07 to 494.37 µg L-1, it is likely that they can be applied to most situations. The ability to estimate aφ and bbp from R(λ) alone is valuable for HAB detection. For certain algae the characteristics of these two IOPs will be enough to discern the bloom-forming alga. Spectral shape of aφ provides pigment compositions, an indicator of algal taxonomy, whereas the bbp spectra provides cell size information. In concert, these IOPs can be used to identify the species dominating the bloom, especially in regions where we have a priori knowledge about blooms. Though for some species, aφ spectra are not unique enough to distinguish between algal groups. Another challenge for detecting HABs optically is that some species do not contribute significantly to the algal community and do not become concentrated enough to impact ocean color. For example, blooms of the dinoflagellate Alexandrium spp. in the Gulf of Maine are not associated with changes in ocean color, though sufficient cells may be present to cause paralytic shellfish poisoning. In these situations it is unlikely that the inverse AOP model could detect Alexandrium per se. Still it is possible that optical detection may be useful for identifying Alexandrium blooms by targeting IOPs of other algae or constituents in the water column that co-exist with the bloom-forming cells.

0

1

2

3

4

5

400 500 600 700 800

Wavelength (nm)

c p (

m-1

)

9

Conclusions This investigation of extreme bloom bio-optical parameters and relationships provides evidence that certain optical techniques are applicable for evaluating blooms. Additional assessment of various optical techniques during blooms of other organisms is necessary to know the full extent to which these bio-optical parameters and relationships apply. From continued studies during blooms, regional-specific and/or species-specific sets of appropriate optical techniques can be determined thereby improving our capabilities for HAB optical detection and the development of early warning systems. Acknowledgments The authors thank J. Nicinski and A. Barnard for assisting with sample collection and Blake’s Boatyard for use of their dock. This research was funded by NASA Grants #NAG5-7872 and #NAG5-7654 awarded to C. Roesler through the ECOHAB Program. Notation ax absorption coefficient where subscript x represents colored dissolved organic

material (CDOM), phytoplankton (φ), non-phytoplankton particulate material (CPM), or water (w), m-1

a* chlorophyll-specific absorption, m2 mg-1 bbx backscattering coefficient where subscript x represents phytoplankton (φ), non-

phytoplankton particulate material (CPM), particulate material (p), or water (w), m-1

cp attenuation coefficient where subscript p represents particulate material, m-1 D particle diameter, m Do reference diameter, m Ed downwelling irradiance k vertical attenuation, m-1 Lu upwelling radiance N(D) number of particles per unit volume per unit bin width, number m-4

No number of particles per unit volume per unit bin width at reference diameter Do, number m-4

PSD particle size distribution R(λ) spectral radiance reflectance γ hyperbolic slope of spectral particulate attenuation, dimensionless ξ hyperbolic slope of the particle size distribution, dimensionless λ wavelength, nm λo reference wavelength, nm References Ahn, Y.-H., A. Bricaud, and A. Morel. 1992. Light backscattering efficiency and related

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