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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 9 — Aug. 28, 2012
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Particle backscattering as a function of chlorophyll and phytoplankton size structure in the open-ocean

Robert J.W. Brewin, Giorgio Dall’Olmo, Shubha Sathyendranath, and Nick J. Hardman-Mountford  »View Author Affiliations


Optics Express, Vol. 20, Issue 16, pp. 17632-17652 (2012)
http://dx.doi.org/10.1364/OE.20.017632


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Abstract

Using an extensive database of in situ observations we present a model that estimates the particle backscattering coefficient as a function of the total chlorophyll concentration in the open-ocean (Case-1 waters). The parameters of the model include a constant background component and the chlorophyll-specific backscattering coefficients associated with small (<20μm) and large (>20μm) phytoplankton. The new model performed with similar accuracy when compared with a traditional power-law function, with the additional benefit of providing information on the role of phytoplankton size. The observed spectral-dependency (γ) of model parameters was consistent with past observations, such that γ associated with the small phytoplankton population was higher than that of large phytoplankton. Furthermore, γ associated with the constant background component suggests this component is likely attributed to submicron particles. We envisage that the model would be useful for improving Case-1 ocean-colour models, assimilating light into multi-phytoplankton ecosystem models and improving estimates of phytoplankton size structure from remote sensing.

© 2012 OSA

1. Introduction

Spectral variations in visible sea-surface reflectance (R) form the basis of ocean colour radiometry. By analysing these variations, concentrations of optically-distinct water constituents such as phytoplankton, detritus and coloured dissolved organic matter may be estimated. In Case-1 waters [1

1. A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977). [CrossRef]

], typically encountered in the open ocean, and comprising ∼60% of the world ocean [2

2. Z. P. Lee and C. Hu, “Global distribution of Case-1 waters: An analysis from SeaWiFS measurements,” Remote Sens. Environ. 101, 270–276 (2006). [CrossRef]

], spectral variations in R are mainly driven by the abundance of phytoplankton, with a co-varying influence from detritus and coloured dissolved organic matter.

Whereas phytoplankton influence aph directly, the influence of phytoplankton on bbp in Case-1 water is thought to be indirect, caused by factors that covary with phytoplankton. Phytoplankton are thought to contribute only a small fraction of bbp as they have a refractive index close to that of seawater, and lower than inorganic particles [4

4. D. Stramski and D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991). [CrossRef]

], and are large with respect to visible wavelengths. However, recent evidence has suggested that phytoplankton-sized particles may contribute more to bbp than previously believed [5

5. R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26(2), 191–212 (2004). [CrossRef]

8

8. A. L. Whitmire, W. S. Pegau, L. Karp-Boss, E. Boss, and T. J. Cowles, “Spectral backscattering properties of marine phytoplankton cultures,” Opt. Express 18, 15073–15093 (2010). [CrossRef] [PubMed]

]. Our understanding of the relationship between phytoplankton and bbp has to be improved, to enhance further development of ocean-colour models in Case-1 waters.

Phytoplankton are the primary component responsible for changes in the ocean colour detected by satellites over Case-1 waters [9

9. H. R. Gordon and A. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A review (Springer-Verlag, New York, 1983). [CrossRef]

], and are recognised as an Essential Climate Variable by the Global Climate Observing System. Thus, a better understanding of the relationship between chlorophyll (a common measure of phytoplankton concentration) and bbp is required to improve satellite-based chlorophyll estimates [10

10. H. Loisel, B. Lubac, D. Dessailly, L. Duforet-Gaurier, and V. Vantrepotte, “Effect of inherent optical properties variability on the chlorophyll retrieved from ocean color remote sensing: an in situ approach,” Opt. Express 18(20), 20949–20959 (2010). [CrossRef]

].

Typically, in many Case-1 ocean-colour models, the non-water components of a and bb are parameterised as functions of chlorophyll (e.g. [9

9. H. R. Gordon and A. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A review (Springer-Verlag, New York, 1983). [CrossRef]

, 11

11. H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and S. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. [Atmospheres] 93, 10909–10924 (1988). [PubMed]

16

16. S. Sathyendranath, V. Stuart, G. Cota, H. Mass, and T. Platt, “Remote sensing of phytoplankton pigments: a comparison of empirical and theoretical approaches,” Int. J. Remote. Sens. 22, 249–273 (2001). [CrossRef]

]). Power-law functions have proven to be useful predictors of aph (e.g. [17

17. L. Prieur and S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter and other particulate materials,” Limnol. Oceanogr. 26, 617–689 (1981). [CrossRef]

22

22. A. Bricaud, H. Claustre, J. Ras, and K. Oubelkheir, “Natural variability of phytoplanktonic absorption in oceanic waters: Influence of the size structure of algal populations,” J. Geophys. Res. [Oceans] 109, C11010 (2004), [CrossRef] [PubMed]

]) and bbp (e.g. [15

15. R. A. Reynolds, D. Stramski, and G. Mitchell, “A chlorophyll-dependent semianalytical reflectance model derived from field measurements of absorption and backscattering coefficients within the Southern Ocean,” J. Geophys. Res. [Oceans] 106, 7125–7138 (2001). [CrossRef] [PubMed]

, 23

23. M. Stramska, D. Stramski, R. Hapter, S. Kaczmarek, and J. Stoń, “Bio-optical relationships and ocean color algorithms for the north polar region of the Atlantic,” J. Geophys. Res. [Oceans] 108, C53143 (2003), [CrossRef] [PubMed]

, 24

24. Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosci. 5, 495–507 (2008). [CrossRef]

]). However, the interpretation of the parameters of a power-law is difficult from an analytical perspective [25

25. E. Devred, S. Sathyendranath, V. Stuart, H. Mass, O. Ulloa, and T. Platt, “A two-component model of phytoplankton absorption in the open ocean: Theory and applications,” J. Geophys. Res. [Oceans] 111, C03011 (2006), [CrossRef] [PubMed]

, 26

26. V. A. Lutz, S. Sathyendranath, and E. J. H. Head, “Absorption coefficient of phytoplankton: Regional variations in the North Atlantic,” Mar. Ecol. Prog. Ser. 135, 197–213 (1996). [CrossRef]

]. Recently, aph has been expressed as the sum of contributions of phytoplankton populations that are optically-distinct, typically linked with size structure [16

16. S. Sathyendranath, V. Stuart, G. Cota, H. Mass, and T. Platt, “Remote sensing of phytoplankton pigments: a comparison of empirical and theoretical approaches,” Int. J. Remote. Sens. 22, 249–273 (2001). [CrossRef]

,25

25. E. Devred, S. Sathyendranath, V. Stuart, H. Mass, O. Ulloa, and T. Platt, “A two-component model of phytoplankton absorption in the open ocean: Theory and applications,” J. Geophys. Res. [Oceans] 111, C03011 (2006), [CrossRef] [PubMed]

,27

27. A. M. Ciotti, M. R. Lewis, and J. J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47(2), 404–417 (2002). [CrossRef]

,28

28. R. J. W. Brewin, E. Devred, S. Sathyendranath, S. J. Lavender, and N. J. Hardman-Mountford, “Model of phytoplankton absorption based on three size classes,” Appl. Opt. 50(22), 4535–4549 (2011). [CrossRef] [PubMed]

]. Such an approach ensures biological and bio-optical interpretation of model parameters and has allowed for the extraction of additional information, such as phytoplankton community composition, from ocean-colour observations [29

29. S. Sathyendranath, L. Watts, E. Devred, T. Platt, C. Caverhill, and H. Mass, “Discrimination of diatoms from other phytoplankton using ocean-colour data,” Mar. Ecol. Prog. Ser. 272, 59–68 (2004). [CrossRef]

31

31. E. Devred, S. Sathyendranath, V. Stuart, and T. Platt, “A three component classification of phytoplankton absorption spectra: Applications to ocean-colour data,” Remote Sens. Environ. 115(9), 2255–2266 (2011). [CrossRef]

].

In this paper, we develop a simple model that captures the relationship between chlorophyll and bbp, with a similar performance when compared with a traditional power-law model, but offering model parameters that are readily explained and the capability of estimating size-fractionated bbp. The model is parameterised using a large dataset of chlorophyll and bbp observations in the open ocean at two wavelengths (470 nm and 526 nm), validated using independent data, compared with current satellite models, and fitted to a multi-spectral database of chlorophyll and bbp to investigate spectral-dependency in model parameters beyond the two wavelengths used in model development.

1.1. Statistical tests

Model performance was quantified using the Pearson linear correlation coefficient (r) and the centre-patterned (or unbiased) root mean square error (Δ) between the modelled and measured values, the latter expressed as
Δ=[1Ni=1N([Xi,E(1Nj=1NXj,E)][Xi,M(1Nk=1NXk,M)])2]1/2,
(4)
where, X is the variable (bbp(λ)) and N is the number of samples. The subscript E denotes the estimated variable and the subscript M denotes the measured variable. The bias (δ) between the modelled and measured values was also used, expressed as
δ=1Ni=1N(Xi,EXi,M).
(5)
All statistical tests were performed in log10 space, considering bbp(λ) is approximately log-normally distributed.

1.2. Data

In this study, data sampled in surface waters were used, after partitioning into four separate databases for model development (database A), validation (database B), comparison with satellite models (database C) and analysis of spectral-dependency in model parameters (database D).

1.2.1. Database A: model development

For model development, in situ particle backscattering coefficients at two wavelengths (bbp(470) and bbp(526)) and chlorophyll concentrations were downloaded from the NASA SeaBASS website (http://seabass.gsfc.nasa.gov/, [44

44. P. J. Werdell and S. W. Bailey, “The SeaWiFS Bio-optical Archive and Storage System (SeaBASS): Current architecture and implementation,” Tech. Rep., NASA Goddard Space Flight Center, Greenbelt, Maryland, 45.

]) inclusive of a variety of geographic locations and trophic conditions in the open ocean (Case-1 waters, [1

1. A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977). [CrossRef]

]).

This included surface flow-through measurements taken in the Equatorial Pacific (April–May 2007, R/V Ka’imi Moana, [7

7. G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosci. 6(6), 947–967 (2009). [CrossRef]

, 45

45. T. Westberry, G. Dall’Olmo, M. J. Behrenfeld, and T. Moutin, “Coherence of particulate beam attenuation and backscattering coefficients in diverse open ocean environments,” Opt. Express 18(15), 15419–15425 (2010). [CrossRef]

]) and the North Atlantic (May 2008, R/V Knorr, [45

45. T. Westberry, G. Dall’Olmo, M. J. Behrenfeld, and T. Moutin, “Coherence of particulate beam attenuation and backscattering coefficients in diverse open ocean environments,” Opt. Express 18(15), 15419–15425 (2010). [CrossRef]

]), representing 1 minute averages sub-sampled at 10 minute intervals. Optical measurements were collected and processed with the same experimental set-up on both the Equatorial Pacific and the North Atlantic cruises. Periodic comparisons were made between optical flow-through data and optical data measured from surface seawater collected with a traditional CTD rosette [45

45. T. Westberry, G. Dall’Olmo, M. J. Behrenfeld, and T. Moutin, “Coherence of particulate beam attenuation and backscattering coefficients in diverse open ocean environments,” Opt. Express 18(15), 15419–15425 (2010). [CrossRef]

]. Flow-through absorption measurements were made with a hyperspectral absorption-attenuation meter (WET Labs ACs) and backscattering measurements with a multispectral backscattering sensor (WET Labs ECO-BB3). Every 10 minutes seawater was diverted through a 0.2 μm nylon cartridge filter providing a baseline for dissolved substances, calibration uncertainties and short-term bio-fouling. Calibration independent particulate optical quantities, with an uncertainty close to instrument precision [7

7. G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosci. 6(6), 947–967 (2009). [CrossRef]

,45

45. T. Westberry, G. Dall’Olmo, M. J. Behrenfeld, and T. Moutin, “Coherence of particulate beam attenuation and backscattering coefficients in diverse open ocean environments,” Opt. Express 18(15), 15419–15425 (2010). [CrossRef]

], were computed by subtracting the baseline from the bulk measurements. For additional details of the flow-through set-up, the reader is referred to Dall’Olmo et al. [7

7. G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosci. 6(6), 947–967 (2009). [CrossRef]

] and Westberry et al. [45

45. T. Westberry, G. Dall’Olmo, M. J. Behrenfeld, and T. Moutin, “Coherence of particulate beam attenuation and backscattering coefficients in diverse open ocean environments,” Opt. Express 18(15), 15419–15425 (2010). [CrossRef]

].

Each through-flow dataset provided measurements of bbp(470), bbp(526) and absorption coefficient of particulate matter (ap) at 650 nm, 676 nm and 714 nm. Any measurements less than or equal to zero were removed and the chlorophyll concentration was estimated from absorption using the approach of Boss et al. [46

46. E. S. Boss, R. Collier, G. Larson, K. Fennel, and S. W. Pegau, “Measurements of spectral optical properties and their relation to biogeochemical variables and processes in Crater Lake, Crater Lake National Park, OR,” Hydrobiologia 574(1), 149–159 (2007). [CrossRef]

], such that chlorophyll = (ap(676) − (0.6ap(650) + 0.4ap(714)))/0.014. This approach uses the line-height of the chlorophyll absorption peak at red wavelengths and it was selected as it performed with high accuracy when compared with discrete in situ High Performance Liquid Chromatography (HPLC) chlorophyll data for both the Equatorial Pacific and North Atlantic datasets (see Fig. 3 of Westberry et al. [45

45. T. Westberry, G. Dall’Olmo, M. J. Behrenfeld, and T. Moutin, “Coherence of particulate beam attenuation and backscattering coefficients in diverse open ocean environments,” Opt. Express 18(15), 15419–15425 (2010). [CrossRef]

]). This resulted in 633 and 217 samples from the Equatorial Pacific and North Atlantic respectively. HPLC data taken during the North Atlantic cruise were also downloaded from the NASA SeaBASS website, and an additional HPLC dataset from the Equatorial Pacific, taken as part of the Tropical Atmosphere Ocean project in 2006.

In addition to Equatorial Pacific and North Atlantic samples, data were downloaded from the NASA NOMAD database (Version 2.0, 18/07/2008, [47

47. P. J. Werdell and S. W. Bailey, “An improved in situ bio-optical data set for ocean colour algorithm development and satellite data production validation,” Remote Sens. Environ. 98, 122–140 (2005). [CrossRef]

, 48

48. P. J. Werdell, “Global bio-optical algorithms for ocean color satellite applications,” EOS Trans. AGU 90(1), (2009), [CrossRef]

]), which provided point in situ samples of remote-sensing reflectances, backscattering coefficients (bb(λ)), chlorophyll concentrations and HPLC data. To remove all Case-2 samples from the NOMAD data, we used the method of Lee and Hu [2

2. Z. P. Lee and C. Hu, “Global distribution of Case-1 waters: An analysis from SeaWiFS measurements,” Remote Sens. Environ. 101, 270–276 (2006). [CrossRef]

] which partitioned Case-1 and 2 waters using remote-sensing reflectances. Only Case-1 NOMAD samples with original bb(470) were used in database A, to be consistent with the flow-through measurements. As original bb(526) data were unavailable in NOMAD, bb(526) values were estimated by application of a power-law spectral fit to nearby wavelengths [49

49. P. J. Werdell, “An evaluation of Inherent Optical Property data for inclusion in the NASA bio-Optical Marine Algorithm Data set,” NASA Ocean Biology Processing Group Science Systems and Applications, Inc. Document Version 1.1, corresponding to NOMAD Version 1.3 19th September 2005: Online http://seabass.gsfc.nasa.gov/seabass/data/werdell_nomad_iop_qc.pdf (2005).

, 50

50. D. Stramski, R. A. Reynolds, M. Babin, S. Kaczmarek, M. R. Lewis, R. Röttgers, A. Sciandra, M. Stramska, M. S. Twardowski, B. A. Franz, and H. Claustre, “Relationships between the surface concentration of particulate organic carbon and optical properties in the eastern South Pacific and eastern Atlantic Oceans,” Biogeosci. 5, 171–201 (2008). [CrossRef]

], fitted individually for each sample. This approach was validated by comparing original bb at available green wavelengths (514, 532 and 589 nm) with estimated bb at corresponding wavelengths assuming a power-law spectral fit. The average difference was ∼2.7 %. Note also that for these 163 measurements, the difference in spectral slopes between 470 and 526 nm using original bb(470) and estimated bb(526) and the slopes using original bb(470) and original bb at green wavelengths (514, 532 or 589 nm) was <9%.

This resulted in 163 NOMAD samples that could be used in database A. For these samples, where available, chlorophyll concentrations were taken from HPLC, and where not available, from fluorometric measurements or estimated from remote-sensing reflectances using the OC4v6 algorithm [51

51. J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. [Oceans] 103, 24937–24953 (1998). [PubMed]

]. Corresponding measurements of HPLC and OC4v6 estimated chlorophyll in NOMAD (Case-1 waters [2

2. Z. P. Lee and C. Hu, “Global distribution of Case-1 waters: An analysis from SeaWiFS measurements,” Remote Sens. Environ. 101, 270–276 (2006). [CrossRef]

]) are in good agreement (r = 0.937, Δ = 0.197, δ = −0.059, 544 log10-transformed samples), as are corresponding measurements of HPLC and fluorometry estimated chlorophyll (r = 0.967, Δ = 0.118, δ = 0.037, 235 log10-transformed samples), supporting our combining of chlorophyll measured using these different methods. The bbp values were estimated from the NOMAD data according to bbp = bbbbw, and the backscattering coefficient of pure sea-water (bbw) was computed from Zhang and Hu [52

52. X. Zhang and L. Hu, “Estimating scattering of pure water from density fluctuation of the refractive index,” Opt. Express 17, 1671–1678 (2009). [CrossRef] [PubMed]

] and Zhang et al. [53

53. X. Zhang, L. Hu, and M.-X. He, “Scattering by pure seawater: Effect of salinity,” Opt. Express 17, 5698–5710 (2009). [CrossRef] [PubMed]

], consistent with the analysis on flow-through measurements. Figure 1 shows the geographical distribution of database A.

Fig. 1 The geographic distribution of the bbp(λ) and chlorophyll data used in this study. Light grey pixels represent cloud or high sun-zenith angles for the May 2006 SeaWiFS composite and dark grey pixels represent Case-2 waters as classified according to Lee and Hu [2].

1.2.2. Database B: independent validation

For model validation, a large dataset of surface flow-through measurements, representing 1 minute averages, were taken from the Atlantic Meridional Transect (AMT) cruise 19 (35,961 samples, October–November 2009, RRS James Cook), from the Mediterranean Sea (5618 samples, June–July 2008, R/V L’Atalante [45

45. T. Westberry, G. Dall’Olmo, M. J. Behrenfeld, and T. Moutin, “Coherence of particulate beam attenuation and backscattering coefficients in diverse open ocean environments,” Opt. Express 18(15), 15419–15425 (2010). [CrossRef]

, 54

54. G. Dall’Olmo, E. Boss, M. J. Behrenfeld, T. K. Westberry, C. Courties, L. Prieur, M. Pujo-Pay, N. J. Hardman-Mountford, and T. Moutin, “Inferring phytoplankton carbon and eco-physiological rates from diel cycles of spectral particulate beam-attenuation coefficient,” Biogeosci. 8, 3423–3439 (2011). [CrossRef]

]) and from the North East Pacific (4760 samples, August 2009, CCGS John P. Tully [45

45. T. Westberry, G. Dall’Olmo, M. J. Behrenfeld, and T. Moutin, “Coherence of particulate beam attenuation and backscattering coefficients in diverse open ocean environments,” Opt. Express 18(15), 15419–15425 (2010). [CrossRef]

]). Data from these cruises were collected and processed using the same methods as flow-through data used in database A. Only data after the 26th of August 2009 from the North East Pacific were used, as prior to this date conditions were very rough and flow-through measurements may have been contaminated by bubbles [55

55. Toby Westberry, Department of Botany and Plant Pathology, Oregon State University, Corvallis, OR, 97331, USA (personal communication, 2011).

]. Database B included bbp taken at two wavelengths (470 and 526 nm) and corresponding hyperspectral measurements of particle absorption (see [7

7. G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosci. 6(6), 947–967 (2009). [CrossRef]

] for methodological details). The AMT continuous flow-through measurements of bbp were verified against discrete overlapping in situ bbp sampled using an optical profiler, and found to be in good agreement (Δ = 0.028, δ = −0.042 at 470 nm, and Δ = 0.025, δ = −0.022 at 526 nm) consistent with the flow-through measurements from the Equatorial Pacific, the Mediterranean and the North Atlantic [7

7. G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosci. 6(6), 947–967 (2009). [CrossRef]

,45

45. T. Westberry, G. Dall’Olmo, M. J. Behrenfeld, and T. Moutin, “Coherence of particulate beam attenuation and backscattering coefficients in diverse open ocean environments,” Opt. Express 18(15), 15419–15425 (2010). [CrossRef]

]. For each sample, the chlorophyll concentration was estimated from absorption [45

45. T. Westberry, G. Dall’Olmo, M. J. Behrenfeld, and T. Moutin, “Coherence of particulate beam attenuation and backscattering coefficients in diverse open ocean environments,” Opt. Express 18(15), 15419–15425 (2010). [CrossRef]

, 46

46. E. S. Boss, R. Collier, G. Larson, K. Fennel, and S. W. Pegau, “Measurements of spectral optical properties and their relation to biogeochemical variables and processes in Crater Lake, Crater Lake National Park, OR,” Hydrobiologia 574(1), 149–159 (2007). [CrossRef]

] and found to be in good agreement with discrete HPLC estimated chlorophyll sampled from the flow-through system (Δ = 0.163 and δ = −0.030 in log10 units). Of the AMT samples, only those with chlorophyll concentrations >0.02 mg m−3 were used, which corresponded to the minimum values of the discrete HPLC extracted measurements. Database B was used for independent model validation, and its geographical distribution is shown in Fig. 1.

1.2.3. Database C: satellite data

To compare models developed using database A with models that estimate bbp(470) and chlorophyll from satellite remote sensing reflectance (Rrs(λ)) data, we downloaded monthly, Level 3, mapped SeaWiFS composites of Rrs(λ) for May 2006 from the NASA website (http://oceancolor.gsfc.nasa.gov/). Using Rrs(λ), bbp(443) and aph(443) were estimated for each pixel using the model of Smyth et al. [56

56. T. J. Smyth, G. F. Moore, T. Hirata, and J. Aiken, “Semianalytical model for the derivation of ocean color inherent optical properties: description, implementation, and performance assessment,” Appl. Opt. 45(31), 8116–8131 (2006). [CrossRef] [PubMed]

] (hereafter denoted SMHA following the first initial of each author’s surname). In addition, monthly SeaWiFS composites of bbp(443) and chlorophyll for the GSM model [57

57. S. Maritorena, D. A. Siegel, and A. R. Peterson, “Optimization of a semianalytical ocean color model for global-scale applications,” Appl. Opt. 41(15), 2705–2714 (2002). [CrossRef] [PubMed]

] and the GIOP model [58

58. B. A. Franz and P. J. Werdell, “A generalized framework for modeling of inherent optical properties in ocean remote sensing applications,” Presented at Ocean Optics XX, Anchorage, Alaska, 27th Sept.–1st Oct. 2010.

, 59

59. P. J. Werdell, NASA Goddard Space Flight Center, Code 616, Greenbelt, MD 20771, USA, and B. A. Franz and colleagues are preparing a manuscript to be called “A generalized ocean color inversion model for retrieving marine inherent optical properties.”

] (default configuration), and bbp(443) and aph(443) for the QAA model [60

60. Z. P. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41, 5755–5772 (2002). [CrossRef] [PubMed]

], were downloaded from the NASA website. The GIOP model is designed as a test platform for algorithm development, offering freedom to specify various optimisation approaches and parameterisations. An initial default configuration for GIOP has been defined by a committee for the global ocean, this includes a fixed spectral slope for adg(λ) of 0.018, an assigned specific phytoplankton absorption coefficient following Bricaud et al. [20

20. A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. [Oceans] 100, 13321–13332 (1995). [CrossRef] [PubMed]

], a spectral backscattering dependency following the QAA and Levenburg-Marquardt optimisation. It is worth noting that this initial default configuration may be changed with time. For the QAA and SMHA models, chlorophyll was estimated using a power-law function of aph(443) with the coefficients presented in Bricaud et al. [20

20. A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. [Oceans] 100, 13321–13332 (1995). [CrossRef] [PubMed]

]. Values of bbp(470) for each pixel were estimated from bbp(443), according to the manner by which each model treats the spectral dependency of bbp. The GSM and SMHA models assume a fixed spectral backscattering dependency (γ) of 1.0337 and 0.5 respectively, and the QAA and GIOP treats the spectral backscattering as a function of a ratio of remote-sensing reflectance just below the sea-surface at two wavelengths (443/555 nm), estimated here using monthly Rrs(λ) for each pixel. Using the method of Lee and Hu [2

2. Z. P. Lee and C. Hu, “Global distribution of Case-1 waters: An analysis from SeaWiFS measurements,” Remote Sens. Environ. 101, 270–276 (2006). [CrossRef]

], all Case-2 pixels were removed. The geographical distribution of Database C is shown in Fig. 1.

1.2.4. Database D: spectral dependency in model parameters

For additional analysis of spectral-dependency in model parameters, the NOMAD dataset was again used. This included samples of remote-sensing reflectances, in situ backscattering coefficients at 20 wavelengths in the visible spectrum (bb(λ)), which were estimated by fitting a power-law spectral dependency to original data to remove moderate noise often resulting from instrument artifacts or calibration [49

49. P. J. Werdell, “An evaluation of Inherent Optical Property data for inclusion in the NASA bio-Optical Marine Algorithm Data set,” NASA Ocean Biology Processing Group Science Systems and Applications, Inc. Document Version 1.1, corresponding to NOMAD Version 1.3 19th September 2005: Online http://seabass.gsfc.nasa.gov/seabass/data/werdell_nomad_iop_qc.pdf (2005).

], and corresponding chlorophyll concentrations. Data were synthesized in the same manner as with the NOMAD samples used in database A to remove Case-2 samples. Some 210 concurrent spectra of bb(λ) at the 20 NOMAD wavelengths and chlorophyll concentrations (0.064 to 11.83 mg m−3, note only 12 samples <0.2 mg m−3 and therefore biased towards more eutrophic waters) were extracted. For these 210 concurrent spectra, when comparing original bb data at various wavelengths with estimated bb data at the corresponding wavelengths assuming a power-law spectral fit, we compute an average difference of <4%. The bbp values were computed from bb as described in database A. The geographical distribution of database D is shown in Fig. 1. Note that some of these measurements were not independent of the NOMAD samples used in database A. However, this dataset was not designed for validation, purely to investigate spectral variations in model parameters while fully acknowledging the limitations of the method by which such a multi-spectral database were developed [49

49. P. J. Werdell, “An evaluation of Inherent Optical Property data for inclusion in the NASA bio-Optical Marine Algorithm Data set,” NASA Ocean Biology Processing Group Science Systems and Applications, Inc. Document Version 1.1, corresponding to NOMAD Version 1.3 19th September 2005: Online http://seabass.gsfc.nasa.gov/seabass/data/werdell_nomad_iop_qc.pdf (2005).

]. A flow chart illustrating the procedures used to partition the data into the four databases (A–D) and develop and validate the model is provided in Fig. 2.

Fig. 2 Flow chart illustrating the procedures used to partition the data into the four databases (A–D) and develop and validate the model.

2. Model development and Results

2.1. Model development

As our study focuses on Case-1 waters, not inclusive of coastal waters, bbp(λ) can be tied to the chlorophyll concentration (C) using a power function (e.g. [24

24. Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosci. 5, 495–507 (2008). [CrossRef]

]), such that
Fig. 3 The particle backscattering coefficient (bbp) as a function of the chlorophyll concentration (C) for samples in database A and B. Database A is plotted at 470 nm (a) and 526 nm (b), with models parameterised to database A superimposed. Database B is plotted at 470 nm (c) and 526 nm (d) with models parameterised to the database A superimposed.
bbp(λ)=α(λ)Cβ(λ),
(6)
where α and β are wavelength-dependent empirical parameters. Equation (6) was fitted to database A using a standard least squares fit (Levenberg-Marquardt, IDL Routine MPFIT-FUN [61

61. C. B. Markwardt, “Non-Linear Least Squares Fitting in IDL with MPFIT,” Proc. ADASS XVIII, ASP Conf. Ser., D. Bohlender, P. Dowler, and D. Duran, ed. (Academic, 2009), 251–254.

]) with relative weighting to give equal weights to all measurements, and is superimposed onto database A in Fig. 3(a) and 3(b). Retrieved parameters are provided in Table 1 and are comparable to those obtained by Huot et al. [24

24. Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosci. 5, 495–507 (2008). [CrossRef]

] and by Antoine et al. [62

62. D. Antoine, D. A. Siegel, T. Kostadinov, S. Maritorena, N. B. Nelson, B. Gentili, V. Vellucci, and N. Guillocheau, “Variability in optical particle backscattering in contrasting bio-optical oceanic regimes,” Limnol. Oceanogr. 56(3), 955–973 (2011). [CrossRef]

]. Statistical results from fit are provided in Table 2. When fitting Eq. (6) to database A, as with subsequent models proposed in this study, we used the method of bootstrapping [63

63. B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap (Chapman and Hall, New York, 1993).

] to compute model parameters and their uncertainties. This involved randomly re-sampling (10,000 times) database A (1013 samples) and re-fitting equations for each iteration. From the resulting parameter distribution, mean values and 95% confidence intervals were computed.

Table 1. Parameter values obtained from fitting Eq. (8) and (9) to pigment data in Brewin et al. [28] and from fitting Eq. (6), (12), (13) and (14) to database A.

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Table 2. Results from the statistical tests between models and database A, B and C. All statistical tests were performed in log10 space.

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Using pigment data from Brewin et al. [28

28. R. J. W. Brewin, E. Devred, S. Sathyendranath, S. J. Lavender, and N. J. Hardman-Mountford, “Model of phytoplankton absorption based on three size classes,” Appl. Opt. 50(22), 4535–4549 (2011). [CrossRef] [PubMed]

] (NOMAD Version 1.3.h, 22/02/2007 HPLC evaluation dataset [47

47. P. J. Werdell and S. W. Bailey, “An improved in situ bio-optical data set for ocean colour algorithm development and satellite data production validation,” Remote Sens. Environ. 98, 122–140 (2005). [CrossRef]

]), the parameters of Eq. (8) and (9), as well as their uncertainties, were computed using bootstrapping (Table 1). The model was found to be in agreement with independent HPLC data from other cruises used in this study, as indexed by a low Δ and a δ close to zero, when comparing the fractional contribution of each size class to total chlorophyll estimated from the model and from independent HPLC data [36

36. J. Uitz, H. Claustre, A. Morel, and S. B. Hooker, “Vertical distribution of phytoplankton communities in open ocean: An assessment based on surface chlorophyll,” J. Geophys. Res. [Oceans] 111, CO8005 (2006), [CrossRef] [PubMed]

, 38

38. R. J. W. Brewin, S. Sathyendranath, T. Hirata, S. Lavender, R. M. Barciela, and N. J. Hardman-Mountford, “A three-component model of phytoplankton size class for the Atlantic Ocean,” Ecol. Model. 221, 1472–1483 (2010). [CrossRef]

, 64

64. F. Vidussi, H. Claustre, B. B. Manca, A. Luchetta, and J. C. Marty, “Phytoplankton pigment distribution in relation to upper thermocline circulation in the eastern Mediterranean Sea during winter,” J. Geophys. Res. [Oceans] 106, 19939–19956 (2001). [CrossRef] [PubMed]

] (Fig. 4). Expanding Eq. (7) by inserting the three-component pigment model (Eq. 8 to 11) leads to the following formulation
bbp(λ)=bbp,1*(λ){C1m[1exp(S1C)]}+bbp,2*(λ){C1,2m[1exp(S1,2C)]C1m[1exp(S1C)]}+bbp,3*(λ){CC1,2m[1exp(S1,2C)]}.
(12)
Using chlorophyll, bbp(λ) and the model parameters ( C1,2m, C1m, S1,2 and S1) as input, Eq. (12) was fitted to database A, to derive bbp,i*(λ) where i = 1 to 3 (Table 1), using the same fitting procedure as for Eq. (6). The fitted relationship is superimposed onto database A in Fig. 3(a) and 3(b) and statistical results from fit are provided in Table 2. Uncertainty in pigment parameters ( C1,2m, S1,2, C1m and S1) were accounted for when estimating bbp,i*(λ) using Monte-Carlo error propagation.

Fig. 4 The pigment model of Brewin et al. [38] (parameters recomputed from [28], see Table 1) plotted alongside size-specific fractional contributions to total chlorophyll estimated from independent HPLC data (576 samples) used in this study [36, 38, 64]. F1, F2 and F3 denote the fractions of pico-, nano- and micro-phytoplankton in total chlorophyll. Note that for the fractions, δ and Δ are provided in linear space and all HPLC samples in cruises other than NOMAD are taken from the top 10 m of the water column. NOMAD samples are from version 2.0 in Case-1 waters [2] and all coincident data in NOMAD Version 1.3.h (used for the parameterisation of Eq. (8) and (9)) were removed.

Whereas Eq. (12) captures the relationship between bbp(λ) and chlorophyll at intermediate to high chlorophyll (Fig. 3(a) and 3(b)), it significantly underestimates both bbp(470) and bbp(526) at low chlorophyll (<0.1 mg m−3 chlorophyll, δ = −0.182 at 470 nm and δ = −0.174 at 526 nm). Therefore, an additional parameter was added to Eq. (12) leading to the following expression
bbp(λ)=bbp,1*(λ){C1m[1exp(S1C)]}+bbp,2*(λ){C1,2m[1exp(S1,2C)]C1m[1exp(S1C)]}+bbp,3*(λ){CC1,2m[1exp(S1,2C)]}+bbpk(λ),
(13)
where bbpk(λ) represents a constant background particle backscattering component. Equation (13) was fitted to database A using the same fitting procedure as with Eq. (12), and the results are shown in Fig. 3(a) and 3(b) and Table 2. By adding a constant background component, Eq. (13) captures the relationship between bbp and chlorophyll at low concentrations (<0.1 mg m−3 chlorophyll, δ = −0.012 at 470 nm and δ = −0.009 at 526 nm) and also performed with better accuracy than Eq. (12) at higher chlorophyll concentrations, as indexed by statistically lower Δ (t-test, p < 0.05) at both wavelengths for chlorophyll concentrations >0.1 mg m−3. Table 1 provides the retrieved chlorophyll-specific particulate backscattering coefficients ( bbp*(λ)) for the three size-classes of phytoplankton and the estimated bbpk(λ) at 470 and 526 nm, when fitting Eq. (13) to database A.

For both bbp(470) and bbp(526), the microphytoplankton chlorophyll-specific particle back-scattering coefficients ( bbp,3*) retrieved from fitting Eq. (13) were statistically lower than the corresponding values for both pico- ( bbp,1*) and nano-phytoplankton ( bbp,2*) (see Table 1). However, 95% confidence intervals in bbp,1* and bbp,2* overlapped at 470 nm (Table 1). Furthermore, when increasing confidence intervals to 99%, bbp,1* and bbp,2* overlapped at both 470 nm and 526 nm (99% confidence intervals: bbp,1*(470)=0.0011to0.0046, bbp,2*(470)=0.0040to0.0069, bbp,1*(526)=0.0008to0.0040 and bbp,2*(526)=0.0037to0.0065) suggesting these retrieved parameters were not significantly different for database A. Therefore, Eq. (13) was simplified by combining the pico- and nano-phytoplankton populations, such that
bbp(λ)=C1,2m[bbp,1,2*(λ)bbp,3*(λ)][1exp(S1,2C)]+bbp,3*(λ)C+bbpk(λ).
(14)
Equation (14) was fitted to database A (see Table 1 for parameters) and is plotted in Fig. 3(a) and 3(b). This simplified model (Eq. (14)) performed with the same accuracy as Eq. (13), as indexed by statistically similar r values (z-test, p > 0.05), Δ (t-test, p > 0.05) and δ (t-test, p > 0.05) for both wavelengths (Table 2), yet the number of model parameters at each wavelength was reduced from four to three ( bbp,1,2*(λ), bbp,3*(λ) and bbpk(λ)). Note that C1,2m and S1,2 were derived from independent HPLC data and held constant when fitting Eq. (14) to database A.

In Eq. (14), the parameters used to partition chlorophyll into the two size fractions ( C1,2m and S1,2) were derived using NOMAD HPLC Version 1.3.h data [28

28. R. J. W. Brewin, E. Devred, S. Sathyendranath, S. J. Lavender, and N. J. Hardman-Mountford, “Model of phytoplankton absorption based on three size classes,” Appl. Opt. 50(22), 4535–4549 (2011). [CrossRef] [PubMed]

, 36

36. J. Uitz, H. Claustre, A. Morel, and S. B. Hooker, “Vertical distribution of phytoplankton communities in open ocean: An assessment based on surface chlorophyll,” J. Geophys. Res. [Oceans] 111, CO8005 (2006), [CrossRef] [PubMed]

, 38

38. R. J. W. Brewin, S. Sathyendranath, T. Hirata, S. Lavender, R. M. Barciela, and N. J. Hardman-Mountford, “A three-component model of phytoplankton size class for the Atlantic Ocean,” Ecol. Model. 221, 1472–1483 (2010). [CrossRef]

, 47

47. P. J. Werdell and S. W. Bailey, “An improved in situ bio-optical data set for ocean colour algorithm development and satellite data production validation,” Remote Sens. Environ. 98, 122–140 (2005). [CrossRef]

, 64

64. F. Vidussi, H. Claustre, B. B. Manca, A. Luchetta, and J. C. Marty, “Phytoplankton pigment distribution in relation to upper thermocline circulation in the eastern Mediterranean Sea during winter,” J. Geophys. Res. [Oceans] 106, 19939–19956 (2001). [CrossRef] [PubMed]

]. Recently, modifications have been proposed to the pigment-based phytoplankton size classification to account for fucoxanthin associated with nano-phytoplankton [31

31. E. Devred, S. Sathyendranath, V. Stuart, and T. Platt, “A three component classification of phytoplankton absorption spectra: Applications to ocean-colour data,” Remote Sens. Environ. 115(9), 2255–2266 (2011). [CrossRef]

, 40

40. T. Hirata, N. J. Hardman-Mountford, R. J. W. Brewin, J. Aiken, R. Barlow, K. Suzuki, T. Isada, E. Howell, T. Hashioha, M. Noguchi-Aita, and Y. Yamanaka, “Synoptic relationships between surface Chlorophyll-a and diagnostic pigments specific to phytoplankton functional types,” Biogeosci. 8, 311–327 (2011). [CrossRef]

]. To investigate the effect this may have on the parameters obtained for Eq. (14), C1,2m and S1,2 were re-computed using the fucoxanthin modification of Devred et al. [31

31. E. Devred, S. Sathyendranath, V. Stuart, and T. Platt, “A three component classification of phytoplankton absorption spectra: Applications to ocean-colour data,” Remote Sens. Environ. 115(9), 2255–2266 (2011). [CrossRef]

], and then Eq. (14) was re-fitted to database A using the refined pigment parameters as input (see Table 1). Parameters for Eq. (14) that accounted for the fucoxanthin modification were found to be statistically similar to the original parameterisation (overlapping 95% confidence levels, Table 1) suggesting Eq. (14) is insensitive to the fucoxanthin refinement, at least for database A.

2.2. Model validation

Using chlorophyll from database B as input, bbp was estimated using Eq. (6) and Eq. (14). These values were then compared with bbp from database B (Fig. 3(c) and 3(d)). Both models are seen to perform reasonably, as indexed by high r values (>0.8), a low Δ and a δ close to zero for both wavelengths (470 nm and 526 nm, Table 2). Equation (14) obtained a δ closer to zero when compared with Eq. (6), for both wavelengths, whereas Eq. (6) obtained slightly higher r values and a slightly lower Δ for both wavelengths (Table 2).

Figure 3(c) and 3(d) shows higher bbp values in the NE Pacific data in comparison with the AMT and Mediterranean cruises at similar chlorophyll concentrations. Whereas all data prior to 26th August 2009 were removed from this cruise to reduce contamination from bubbles due to rough seas [55

55. Toby Westberry, Department of Botany and Plant Pathology, Oregon State University, Corvallis, OR, 97331, USA (personal communication, 2011).

], some measurements may still have been affected. Analysis of HPLC data from the NE Pacific indicated a dominance of nano-phytoplankton (see Fig. 4) with high concentrations of 19′-Hexanoyloxyfucoxanthin, a diagnostic pigment of prymnesiophytes, indicating presence of coccolithophores or Phaeocystis (also confirmed using additional HPLC data [65

65. Angelica PenaInstitute of Ocean Sciences, Fisheries and Oceans Canada (DFO), Sidney, B.C. V8L 4B2, Canada (personal communication, 2011).

]). During the cruise, samples for microscopy at two stations were taken at 5 m and both samples indicated presence of coccolithophores (∼10 and 250 cells ml−1 at station P26 and P4, respectively [65

65. Angelica PenaInstitute of Ocean Sciences, Fisheries and Oceans Canada (DFO), Sidney, B.C. V8L 4B2, Canada (personal communication, 2011).

]). It is important to note that the models developed are designed for Case-1 water exclusive of coccolithophore blooms. When removing NE Pacific data from database B, model performance significantly increased for both Eq. (6) and Eq. (14) (see Table 2), with Eq. (14) obtaining slightly higher r values, a lower Δ and a δ closer to zero for both wavelengths.

Fig. 5 Histograms showing log10 residuals between model estimates of bbp and database B below 0.05 mg m−3 chlorophyll for 470 nm and 526 nm (N refers to the number of samples).

2.3. Comparison with satellite models

Figure 6 show the results from the satellite retrieved bbp(470) plotted against satellite retrieved chlorophyll for the (a) GSM, (b) SMHA, (c) GIOP and (d) QAA models. Superimposed onto Fig. 6 are Eq. (6) and (14) for comparison. The QAA and the SMHA models display similar relationships between bbp(470) and chlorophyll which is expected to a certain degree, considering both models are conceptually similar whereby solutions are obtained through algebraic decomposition. The GIOP model also displays a similar relationship to that of the QAA, considering its preliminary configuration has some similar features to the QAA (such as the conversion of above to below reflectance and the spectral shape of the bbp), although the GIOP preliminary configuration uses Levenburg-Marquardt optimisation. Unlike the other satellite models, the GSM model shows more of a bilinear relationship between bbp(470) and chlorophyll [66

66. M. J. Behrenfeld, E. Boss, D. A. Siegel, and D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles 19, GB1006 (2005), [CrossRef]

].

Fig. 6 The particle backscattering coefficient (bbp) as a function of the chlorophyll concentration (C) for samples in database C (satellite data). Models of Sathyendranath et al. [16] and Huot et al. [24] are also shown in (b) and (d) for comparison.

The SMHA model, and to a lesser degree the QAA and GIOP model, appear to overestimate bbp(470) at low chlorophyll when compared with Eq. (6) and (14). Note that the SMHA model has a flatter spectral dependency than the GSM model (γ of 0.5 in comparison with 1.0337, respectively) as it was developed using a Case-2 database [56

56. T. J. Smyth, G. F. Moore, T. Hirata, and J. Aiken, “Semianalytical model for the derivation of ocean color inherent optical properties: description, implementation, and performance assessment,” Appl. Opt. 45(31), 8116–8131 (2006). [CrossRef] [PubMed]

], which is likely to contribute to higher bbp(470) when extrapolating from bbp(443). The higher bbp(470) values at low chlorophyll for the satellite models may be partly explained by the fact that they are not accounting for Raman scattering. Lee et al. [67

67. Z. P. Lee, S. Shang, C. Hu, M. Lewis, R. Arnone, Y. Li, and B. Lubac, “Time series of bio-optical properties in a subtrophical gyre: Implications for the evaluation of interannual trends of biogeochemical properties,” J. Geophys. Res. [Oceans] 115, C09012, (2010) [CrossRef] [PubMed]

] found that derived bbp values from analytical algorithms can be elevated by as much as 60% for clear waters when not accounting for Raman effects. This possibility needs further investigation, but is beyond the scope of this paper.

Particle backscattering at 470 nm (bbp(470)) was computed from Eq. (6) and (14) using chlorophyll from the four satellite models as input. The retrieved bbp(470) values were then compared with the bbp(470) estimates from the four satellite models (Table 2). Higher r values were observed when comparing the results from Eq. (6) and (14) with bbp(470) estimated by the GIOP, QAA and SMHA models, in comparison with the GSM model (Table 2), indicating the relationship between bbp(470) and chlorophyll is less linear (in log10 space) for the GSM model. An δ value closer to zero was observed when comparing the results from Eq. (6) and (14) with the GSM model, in comparison with the GIOP, QAA and SMHA models (note that δ in Table 2 was computed assuming Xi,E = satellite bbp(470) and Xi,M = bbp(470) computed using Eq. (6) or (14), see Eq. (5)). Similar Δ values were observed for all four satellite models and are comparable with Δ values obtained using database B (Table 2). Equation (6) and (14) are in reasonable agreement with the models of Sathyendranath et al. [16

16. S. Sathyendranath, V. Stuart, G. Cota, H. Mass, and T. Platt, “Remote sensing of phytoplankton pigments: a comparison of empirical and theoretical approaches,” Int. J. Remote. Sens. 22, 249–273 (2001). [CrossRef]

] and Huot et al. [24

24. Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosci. 5, 495–507 (2008). [CrossRef]

] (Fig. 6(b) and 6(d)) at chlorophyll >0.1 mg m−3, but display higher estimates of bbp(470) at chlorophyll <0.1 mg m−3 and are in closer agreement with the satellite models.

2.4. Spectral dependency in model parameters

Assuming that the spectral shape of the particulate backscattering coefficient can be expressed using a power function (e.g. [31

31. E. Devred, S. Sathyendranath, V. Stuart, and T. Platt, “A three component classification of phytoplankton absorption spectra: Applications to ocean-colour data,” Remote Sens. Environ. 115(9), 2255–2266 (2011). [CrossRef]

,56

56. T. J. Smyth, G. F. Moore, T. Hirata, and J. Aiken, “Semianalytical model for the derivation of ocean color inherent optical properties: description, implementation, and performance assessment,” Appl. Opt. 45(31), 8116–8131 (2006). [CrossRef] [PubMed]

58

58. B. A. Franz and P. J. Werdell, “A generalized framework for modeling of inherent optical properties in ocean remote sensing applications,” Presented at Ocean Optics XX, Anchorage, Alaska, 27th Sept.–1st Oct. 2010.

,60

60. Z. P. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41, 5755–5772 (2002). [CrossRef] [PubMed]

]), the spectral dependency of the chlorophyll-specific particulate backscattering coefficients ( bbp,i*(λ)) associated with small and large phytoplankton, and the constant background particle backscattering component ( bbpk(λ)), may be expressed as
bbp,1,2*(λ)=bbp,1,2*(λ0)(λ/λ0)γ1,2,
(15)
bbp,3*(λ)=bbp,3*(λ0)(λ/λ0)γ3,
(16)
and
bbpk(λ)=bbpk(λ0)(λ/λ0)γk.
(17)
In the above equations, γ is the exponent of the power function describing the spectral shape of the particle backscattering coefficient for each component of the model, and λ0 is the reference wavelength, taken here to be 470 nm. The exponent for each model component can be estimated from database A according to
γ1,2=log[bbp,1,2*(λ1)/bbp,1,2*(λ2)]log[λ1/λ2],
(18)
γ3=log[bbp,3*(λ1)/bbp,3*(λ2)]log[λ1/λ2],
(19)
and
γk=log[bbpk(λ1)/bbpk(λ2)]log[λ1/λ2],
(20)
with λ1 = 470 nm and λ2 = 526 nm. Equations (18) to (20) were applied to database A to derive γ1,2, γ3 and γk (Table 3 and Fig. 7(a) and 7(b)) together with their 95% confidence levels using the bootstrap method. Expanding Eq. (14) by inserting Eq. (15) to (17) leads to the following expression:
bbp(λ)=bbp,1,2*(λ0)(λ/λ0)γ1,2{C1,2m[1exp(S1,2C)]}+bbp,3*(λ0)(λ/λ0)γ3{CC1,2m[1exp(S1,2C)]}+bbpk(λ0)(λ/λ0)γk.
(21)
Considering the limitations of determining γi from only two wavelengths [62

62. D. Antoine, D. A. Siegel, T. Kostadinov, S. Maritorena, N. B. Nelson, B. Gentili, V. Vellucci, and N. Guillocheau, “Variability in optical particle backscattering in contrasting bio-optical oceanic regimes,” Limnol. Oceanogr. 56(3), 955–973 (2011). [CrossRef]

], and therefore limitations of database A, we also estimated γi using database D. Equation (14) was first fitted to database D to compute bbp,1,2*(λ), bbp,3*(λ) and bbpk(λ) at each of the 20 wavelengths (Fig. 7), then Eq. (15) to (17) were fitted to the spectral data to compute γ1,2, γ3 and γk (Table 3).

Fig. 7 (a) and (b) show the spectral dependency in model parameters (Eq. (21)) for database A and D. (c) shows the fractional contribution of each component population to bbp(470) for a given chlorophyll concentration estimated using Eq. (22) for both database A and D, coloured shading represents a model ensemble calculated by varying model parameters between 95% confidence intervals (Table 3), in every possible permutation. (d) shows estimated γ using Eq. (21) as a function of chlorophyll, as well as the minimum and maximum of the model ensemble.

Table 3. Parameter values applicable to Eq. (21) and (22), obtained from fitting Eq. (14)(20) to database A and D.

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Estimated γ1,2 and γ3 using database D were similar to corresponding estimates from database A (overlapping confidence intervals in Table 3). However, γk derived from database D (∼3.4) was higher than γk from database A (∼1.9) and closer to that of pure water (e.g. ∼4.3 [68

68. A. Morel, “Optical properties of pure water and pure sea water,” in Optical Aspects of Oceanography, N. G. Jerlov and E. S. Nielsen, eds. (Academic, New York, 1974), pp. 1–24.

]). Considering only 12 samples in database D contained < 0.2 mg m−3 chlorophyll, with a minimum of 0.064 mg m−3, this may have been an artifact of uneven sample distribution. Nonetheless, γk estimates from both database A and D are consistent with satellite estimates in oligotrophic waters [32

32. H. Loisel, J. M. Nicolas, A. Sciandra, D. Stramski, and A. Poteau, “Spectral dependency of optical backscattering by marine particles from satellite remote sensing of the global ocean,” J. Geophys. Res. [Oceans] 111, C09024 (2006), [CrossRef] [PubMed]

, 33

33. T. S. Kostadinov, D. A. Siegel, and S. Maritorena, “Retrieval of the particle size distribution from satellite ocean color observations,” J. Geophys. Res. [Oceans] 114, CO9015 (2009), [CrossRef] [PubMed]

]. Unlike database A, database D has the advantage of being a multi-spectral database. However, it is difficult to determine the extent to which the power-law spectral dependency assumption of bb in database D influences the spectral dependency in model parameters.

Table 3 highlights that γ3 is not statistically different from zero (95% confidence intervals overlap with zero, also see Fig. 7(a)). Therefore, Eq. (21) can be further simplified by setting the spectral dependency of bbp,3*(λ) to equal zero, such that
bbp(λ)=bbp,1,2*(λ0)(λ/λ0)γ1,2C1,2m[1exp(S1,2C)]+bbp,3*(λ0){CC1,2m[1exp(S1,2C)]}+bbpk(λ0)(λ/λ0)γk.
(22)
Unlike an approach that estimates bbp(λ) as a power function of chlorophyll, the parameters of Eq. (22) are easy to interpret in relation to the composition of phytoplankton size and allow for estimates of size-fractionated bbp(λ). Power-law models, such as that of Huot et al. [24

24. Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosci. 5, 495–507 (2008). [CrossRef]

], typically requires four parameters to describe bbp(λ) as a function of chlorophyll (e.g. see Eq. 8 of Huot et al. [24

24. Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosci. 5, 495–507 (2008). [CrossRef]

]), whereas, considering C1,2m and S1,2 were derived independently from HPLC data, Eq. (22) requires five parameters ( bbp,1,2*(λ0), bbp,3*(λ0), bbpk(λ0), γ1,2 and γk). Yet the addition of another parameter appears justified with respect to the law of parsimony, given the increase in performance at low chlorophyll concentrations (Fig. 5).

Figure 7(c) shows the fractional contribution of each component population to bbp(470) for a given chlorophyll concentration estimated using Eq. (22). According to the model, the constant background component dominates bbp(470) when chlorophyll is low; as the chlorophyll increases beyond ∼0.2 mg m−3 the influence of small cells on bbp(470) increases, with its fractional contribution reaching a maximum of ∼0.7 at ∼1.0 mg m−3 chlorophyll; as the chlorophyll increases further, the influence from large cells to bbp(470) increases. The fractional contribution of each component to bbp varies with wavelength due to differences in the spectral dependency of each component population.

3. Discussion

3.1. Model parameters

3.1.1. Phytoplankton size-specific backscattering coefficients

The chlorophyll-specific backscattering coefficients associated with small cells (Table 3) are consistent with recent observations. Martinez-Vicente et al. [72

72. V. Martinez-Vicente, G. Tilstone, S. Sathyendranath, P. I. Miller, and S. B. Groom, “Contributions of phytoplankton and bacteria to the optical backscattering coefficient over the Mid-Atlantic Ridge,” Mar. Ecol. Prog. Ser. 445, 37–51 (2012). [CrossRef]

] reported average bbp*(532) of ∼0.005 m2(mgC)−1 in mesotrophic regions of the North Atlantic with an associated chlorophyll of ∼1.0 mg m−3, consistent with our derived bbp,1,2*(526) (Table 1) and chlorophyll conditions where backscattering associated with small cells strongly influence total bbp (Fig. 7(c)). Lower bbp,3*(λ) obtained for large cells (Table 1 and 3) are consistent with Morel [73

73. A. Morel, “Chlorophyll-specific scattering coefficient of phytoplankton. A simplified theoretical approach,” Deep Sea Res. 34(7), 1093–1105 (1987). [CrossRef]

], who suggests larger cells with high intracellular pigment concentrations have a lower chlorophyll-specific scattering coefficient in comparison with small cells with lower intracellular pigment concentrations. However, it is important to note that the Morel [73

73. A. Morel, “Chlorophyll-specific scattering coefficient of phytoplankton. A simplified theoretical approach,” Deep Sea Res. 34(7), 1093–1105 (1987). [CrossRef]

] study focused on scattering and not backscattering. The observed spectral-dependency of bbp,1,2*(λ) and bbp,3*(λ) further support the interpretation and are in accordance with recent modelling studies [32

32. H. Loisel, J. M. Nicolas, A. Sciandra, D. Stramski, and A. Poteau, “Spectral dependency of optical backscattering by marine particles from satellite remote sensing of the global ocean,” J. Geophys. Res. [Oceans] 111, C09024 (2006), [CrossRef] [PubMed]

, 33

33. T. S. Kostadinov, D. A. Siegel, and S. Maritorena, “Retrieval of the particle size distribution from satellite ocean color observations,” J. Geophys. Res. [Oceans] 114, CO9015 (2009), [CrossRef] [PubMed]

], such that γ associated with the small phytoplankton population, γ1,2, is higher than that of large phytoplankton, γ3 (Table 3). This is consistent with the assumption that small phytoplankton have enhanced backscattering of blue photons, whereas larger phytoplankton tend to backscatter light similarly at all wavelengths [74

74. H. M. Dierssen, R. M. Kudela, J. P. Ryan, and R. C. Zimmerman, “Red and black tides: Quantitative analysis of water-leaving radiance and perceived color for phytoplankton, colored dissolved organic matter, and suspended sediments,” Limnol. Oceanogr. 51(6), 2646–2659 (2006). [CrossRef]

].

It is important to stress that these retrieved chlorophyll-specific backscattering coefficients are representative of not just the phytoplankton, but also their co-varying constituents (e.g. detrital matter, bacteria and viruses). It may be that the phytoplankton have a negligible direct influence on these coefficients [75

75. Y-H. Ahn, A. Bricaud, and A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep Sea Res. 39(11/12), 1835–1855 (1992). [CrossRef]

]. We also recognise that laboratory studies have highlighted large variability in chlorophyll-specific backscattering for different cultures [8

8. A. L. Whitmire, W. S. Pegau, L. Karp-Boss, E. Boss, and T. J. Cowles, “Spectral backscattering properties of marine phytoplankton cultures,” Opt. Express 18, 15073–15093 (2010). [CrossRef] [PubMed]

], which may explain some of the observed variability in bbp(λ) when plotted as a function of chlorophyll in Fig. 3, though it still remains to be revealed to what extent such laboratory studies are representative of the natural environment.

3.1.2. Constant background parameter

By introducing bbpk into Eq. (13), a significant model improvement was obtained by decoupling bbp from chlorophyll in clear waters (Fig. 5). The bbpk parameter may be interpreted in two ways: (i) bbpk is due to a constant background of non-algal particles (e.g. heterotrophic bacteria, detritus, viruses, minerogenic particles) [4

4. D. Stramski and D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991). [CrossRef]

, 76

76. A. Morel and Y-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates: A tentative assessment of their scattering role in oceanic waters compared to those of bacterial and algal cells,” J. Mar. Res. 49, 177–202 (1991). [CrossRef]

], or (ii) bbpk is partly influenced by very small phytoplankton (e.g. prochlorophytes), in addition to non-algal particles [66

66. M. J. Behrenfeld, E. Boss, D. A. Siegel, and D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles 19, GB1006 (2005), [CrossRef]

]. The high spectral dependency associated with bbpk is consistent with submicron particles [32

32. H. Loisel, J. M. Nicolas, A. Sciandra, D. Stramski, and A. Poteau, “Spectral dependency of optical backscattering by marine particles from satellite remote sensing of the global ocean,” J. Geophys. Res. [Oceans] 111, C09024 (2006), [CrossRef] [PubMed]

], regardless of their living or non-living status.

The decoupling between bbp and chlorophyll in the most oligotrophic waters (Fig. 3) is however, in disagreement with data from the South Pacific subtropical gyre, where bbp and chlorophyll were correlated down to chlorophyll values of ∼0.02 mg m−3 [24

24. Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosci. 5, 495–507 (2008). [CrossRef]

]. Whereas bbpk values are above instrument sensitivity, uncertainties in bbp and chlorophyll are expected to increase in oligotrophic waters [7

7. G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosci. 6(6), 947–967 (2009). [CrossRef]

]. These higher levels of uncertainty, coupled to errors in bbw [77

77. M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, “Optical backscattering properties of the “clearest” natural waters,” Biogeosci. 4, 1041–1068 (2007). [CrossRef]

], suggest that the parameter bbpk should be cautiously interpreted.

3.2. Model formulation and applications

The formulation of Eq. (22), as depicted in Fig. 7(c), may be interpreted in the following manner. In oligotrophic waters (low chlorophyll), bbp is controlled by the bbpk parameter. In mesotrophic waters (intermediate chlorophyll), bbp is controlled by bbp,1,2*, and therefore small phytoplankton together with their associated covarying constituents. In eutrophic waters (high chlorophyll), the backscattering coefficient is controlled by large phytoplankton cells displaying low chlorophyll-specific backscattering. The low chlorophyll-specific backscattering in eutrophic waters (Case-1) implies that the backscattering is primarily driven by the phytoplankton, and to a lesser degree the covarying detrital matter [73

73. A. Morel, “Chlorophyll-specific scattering coefficient of phytoplankton. A simplified theoretical approach,” Deep Sea Res. 34(7), 1093–1105 (1987). [CrossRef]

].

Recently, methods have been proposed to detect phytoplankton size structure from satellite observations. These methods typically use either information on the satellite-derived absorption coefficient of phytoplankton, such as its shape or magnitude [30

30. A. M. Ciotti and A. Bricaud, “Retrievals of a size parameter for phytoplankton and spectral light absorption by coloured detrital matter from water-leaving radiances at SeaWiFS channels in a continental shelf off Brazil,” Limnol. Oceanogr. Methods 4, 237–253 (2006). [CrossRef]

, 31

31. E. Devred, S. Sathyendranath, V. Stuart, and T. Platt, “A three component classification of phytoplankton absorption spectra: Applications to ocean-colour data,” Remote Sens. Environ. 115(9), 2255–2266 (2011). [CrossRef]

, 37

37. T. Hirata, J. Aiken, N. J. Hardman-Mountford, and T. J. Smyth, “An absorption model to derive phytoplankton size classes from satellite ocean colour,” Remote Sens. Environ. 112(6), 3153–3159 (2008). [CrossRef]

, 39

39. C. B. Mouw and J. Yoder, “Optical determination of phytoplankton size composition from global SeaWiFS imagery,” J. Geophys. Res. [Oceans] 115, C12018 (2010), [CrossRef] [PubMed]

], or information on the shape of the satellite-derived backscattering spectrum [32

32. H. Loisel, J. M. Nicolas, A. Sciandra, D. Stramski, and A. Poteau, “Spectral dependency of optical backscattering by marine particles from satellite remote sensing of the global ocean,” J. Geophys. Res. [Oceans] 111, C09024 (2006), [CrossRef] [PubMed]

34

34. T. S. Kostadinov, D. A. Siegel, and S. Maritorena, “Global variability of phytoplankton functional types from space: assessment via the particle size distribution,” Biogeosci. 7, 3239–3257 (2010). [CrossRef]

]. Recently, Fujiwara et al. [42

42. A. Fujiwara, T. Hirawake, K. Suzuki, and S-I. Saitoh, “Remote Sensing of size structure of phytoplankton communities using optical properties of the Chukchi and Bering Sea shelf region,” Biogeosci. 8, 3567–3580 (2011). [CrossRef]

] used information on both these variables empirically to derive satellite estimates of phytoplankton size-fractions in the Chukchi and Bering Sea shelf region. Considering that the reflectance observed by satellites is a function of both absorption and backscattering (Eq. (1)), accounting explicitly for information on size structure using both these variables may ultimately lead to better satellite retrievals of phytoplankton size. This may be achieved by combining Eq. (22) with a conceptually similar model of phytoplankton absorption (e.g. [16

16. S. Sathyendranath, V. Stuart, G. Cota, H. Mass, and T. Platt, “Remote sensing of phytoplankton pigments: a comparison of empirical and theoretical approaches,” Int. J. Remote. Sens. 22, 249–273 (2001). [CrossRef]

, 25

25. E. Devred, S. Sathyendranath, V. Stuart, H. Mass, O. Ulloa, and T. Platt, “A two-component model of phytoplankton absorption in the open ocean: Theory and applications,” J. Geophys. Res. [Oceans] 111, C03011 (2006), [CrossRef] [PubMed]

, 28

28. R. J. W. Brewin, E. Devred, S. Sathyendranath, S. J. Lavender, and N. J. Hardman-Mountford, “Model of phytoplankton absorption based on three size classes,” Appl. Opt. 50(22), 4535–4549 (2011). [CrossRef] [PubMed]

, 31

31. E. Devred, S. Sathyendranath, V. Stuart, and T. Platt, “A three component classification of phytoplankton absorption spectra: Applications to ocean-colour data,” Remote Sens. Environ. 115(9), 2255–2266 (2011). [CrossRef]

]).

The retrieval of satellite-derived chlorophyll using empirical algorithms is highly dependent upon specific IOP values [10

10. H. Loisel, B. Lubac, D. Dessailly, L. Duforet-Gaurier, and V. Vantrepotte, “Effect of inherent optical properties variability on the chlorophyll retrieved from ocean color remote sensing: an in situ approach,” Opt. Express 18(20), 20949–20959 (2010). [CrossRef]

, 78

78. C. A. Brown, Y. Huot, P. J. Werdell, B. Gentili, and H. Claustre, “The origin and global distribution of second order variability in satellite ocean color and its potential applications to algorithm development,” Remote Sens. Environ. 112, 4186–4203 (2008). [CrossRef]

] and phytoplankton community structure [29

29. S. Sathyendranath, L. Watts, E. Devred, T. Platt, C. Caverhill, and H. Mass, “Discrimination of diatoms from other phytoplankton using ocean-colour data,” Mar. Ecol. Prog. Ser. 272, 59–68 (2004). [CrossRef]

, 79

79. S. Alvain, C. Moulin, Y. Dandonneau, H. Loisel, and F. M. Bréon, “A species-dependent bio-optical model of case 1 water for the global ocean color processing,” Deep Sea Res. Part I 53, 917–925 (2006). [CrossRef]

]. Loisel et al. [10

10. H. Loisel, B. Lubac, D. Dessailly, L. Duforet-Gaurier, and V. Vantrepotte, “Effect of inherent optical properties variability on the chlorophyll retrieved from ocean color remote sensing: an in situ approach,” Opt. Express 18(20), 20949–20959 (2010). [CrossRef]

] highlighted that empirical chlorophyll algorithms are sensitive to bbp*(λ), with higher-than-average bbp*(λ) values resulting in an overestimation of chlorophyll. The model presented here may be useful for incorporation into ocean-colour models, to constrain better the influence of bbp*(λ) and phytoplankton community structure on satellite chlorophyll estimates.

To advance our understanding of marine biogeochemical cycling, marine ecosystem models have developed more sophisticated representations of the phytoplankton community, typically partitioned according to size (e.g. [80

80. O. Aumont, E. Maier-Reimer, S. Blain, and P. Monfray, “An ecosystem model of the global ocean including Fe, Si, P colimitations,” Global Biogeochem. Cycles 17(2), 1060 (2003), [CrossRef]

82

82. I. Marinov, S. C. Doney, and I. D. Lima, “Response of ocean phytoplankton community structure to climate change over the 21st century: partitioning the effects of nutrients, temperature and light,” Biogeosci. 7, 3941–3959 (2010). [CrossRef]

]). There are clear benefits of coupling bio-optical models to ecosystems models [43

43. M. Fujii, E. Boss, and F. Chai “The value of adding optics to ecosystem models: a case study,” Biogeosci. 4, 817–835 (2011). [CrossRef]

, 83

83. C. D. Mobley, “Fast calculations for ocean ecosystem and inverse models,” Opt. Express 19(20), 18927–18944 (2011). [CrossRef] [PubMed]

], such as a better representation of the underwater light field required for photosynthesis and photochemistry computations. Coupling bio-optical models to ecosystems models requires specifying IOPs for state variables that modify the light field, such as the phytoplankton communities. Our backscattering model may be useful in such studies, considering the parameters are specific to the phytoplankton size structure.

In comparison with the relationship between chlorophyll and phytoplankton absorption, the relationship between bbp and chlorophyll is likely to be more variable considering phytoplankton absorption and chlorophyll are influenced by both abundance and physiology, whereas bbp is influenced by non-algal particles as well as phytoplankton abundance. Equation (22) was fitted to data representative of the global ocean (Fig. 1), but we acknowledge that a global parameterisation is not likely to capture fully the spatio-temporal variability in the relationship between bbp and chlorophyll. Nonetheless, with adequate regional datasets, the model may be used as a tool to investigate such spatio-temporal variations (e.g. [25

25. E. Devred, S. Sathyendranath, V. Stuart, H. Mass, O. Ulloa, and T. Platt, “A two-component model of phytoplankton absorption in the open ocean: Theory and applications,” J. Geophys. Res. [Oceans] 111, C03011 (2006), [CrossRef] [PubMed]

]).

4. Summary

A model has been presented that infers total and size-dependent particle backscattering as a function of chlorophyll in Case-1 waters. The model was parameterised using a database of chlorophyll and particle backscattering coefficients collected in various oceans and representative of oligotrophic to eutrophic waters (Case-1 water only). When compared with a large independent dataset, the model was found to perform with similar accuracy to a traditional power-law model, but with the added advantages of providing better performance at very low chlorophyll (<0.05 mg m−3), greater interpretation in model parameters and estimating size-fractionated particle backscattering. Spectral dependency in model parameters supports their interpretation and a simplified equation was presented to estimate backscattering as a function of chlorophyll over the entire spectral range. Model applications include: refining forward and inverse Case-1 ocean-colour models, ecosystem modelling and estimating phytoplankton size structure from remote sensing.

Acknowledgments

The authors thank SeaBASS, contributors to NOMAD and all principle investigators, scientists and crew involved with flow-through and pigment data. We thank Toby Westberry and Angelica Pena for comments on the NE Pacific data and Jeremy Werdell for comments on GIOP. We thank two anonymous reviewers for their comments on the paper. SeaWiFS data used in this publication were produced by the SeaWiFS project at the Goddard Space Flight Center. Use of this data is in accord with the SeaWiFS Research Data Use Terms and Agreements. This is a contribution to the Ocean Colour Climate Change Initiative of the European Space Agency. This study was supported by the NCEO, the UK Natural Environment Research Council and Oceans 2025. This is contribution number 219 of the AMT programme.

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P. J. Werdell and S. W. Bailey, “The SeaWiFS Bio-optical Archive and Storage System (SeaBASS): Current architecture and implementation,” Tech. Rep., NASA Goddard Space Flight Center, Greenbelt, Maryland, 45.

45.

T. Westberry, G. Dall’Olmo, M. J. Behrenfeld, and T. Moutin, “Coherence of particulate beam attenuation and backscattering coefficients in diverse open ocean environments,” Opt. Express 18(15), 15419–15425 (2010). [CrossRef]

46.

E. S. Boss, R. Collier, G. Larson, K. Fennel, and S. W. Pegau, “Measurements of spectral optical properties and their relation to biogeochemical variables and processes in Crater Lake, Crater Lake National Park, OR,” Hydrobiologia 574(1), 149–159 (2007). [CrossRef]

47.

P. J. Werdell and S. W. Bailey, “An improved in situ bio-optical data set for ocean colour algorithm development and satellite data production validation,” Remote Sens. Environ. 98, 122–140 (2005). [CrossRef]

48.

P. J. Werdell, “Global bio-optical algorithms for ocean color satellite applications,” EOS Trans. AGU 90(1), (2009), [CrossRef]

49.

P. J. Werdell, “An evaluation of Inherent Optical Property data for inclusion in the NASA bio-Optical Marine Algorithm Data set,” NASA Ocean Biology Processing Group Science Systems and Applications, Inc. Document Version 1.1, corresponding to NOMAD Version 1.3 19th September 2005: Online http://seabass.gsfc.nasa.gov/seabass/data/werdell_nomad_iop_qc.pdf (2005).

50.

D. Stramski, R. A. Reynolds, M. Babin, S. Kaczmarek, M. R. Lewis, R. Röttgers, A. Sciandra, M. Stramska, M. S. Twardowski, B. A. Franz, and H. Claustre, “Relationships between the surface concentration of particulate organic carbon and optical properties in the eastern South Pacific and eastern Atlantic Oceans,” Biogeosci. 5, 171–201 (2008). [CrossRef]

51.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. [Oceans] 103, 24937–24953 (1998). [PubMed]

52.

X. Zhang and L. Hu, “Estimating scattering of pure water from density fluctuation of the refractive index,” Opt. Express 17, 1671–1678 (2009). [CrossRef] [PubMed]

53.

X. Zhang, L. Hu, and M.-X. He, “Scattering by pure seawater: Effect of salinity,” Opt. Express 17, 5698–5710 (2009). [CrossRef] [PubMed]

54.

G. Dall’Olmo, E. Boss, M. J. Behrenfeld, T. K. Westberry, C. Courties, L. Prieur, M. Pujo-Pay, N. J. Hardman-Mountford, and T. Moutin, “Inferring phytoplankton carbon and eco-physiological rates from diel cycles of spectral particulate beam-attenuation coefficient,” Biogeosci. 8, 3423–3439 (2011). [CrossRef]

55.

Toby Westberry, Department of Botany and Plant Pathology, Oregon State University, Corvallis, OR, 97331, USA (personal communication, 2011).

56.

T. J. Smyth, G. F. Moore, T. Hirata, and J. Aiken, “Semianalytical model for the derivation of ocean color inherent optical properties: description, implementation, and performance assessment,” Appl. Opt. 45(31), 8116–8131 (2006). [CrossRef] [PubMed]

57.

S. Maritorena, D. A. Siegel, and A. R. Peterson, “Optimization of a semianalytical ocean color model for global-scale applications,” Appl. Opt. 41(15), 2705–2714 (2002). [CrossRef] [PubMed]

58.

B. A. Franz and P. J. Werdell, “A generalized framework for modeling of inherent optical properties in ocean remote sensing applications,” Presented at Ocean Optics XX, Anchorage, Alaska, 27th Sept.–1st Oct. 2010.

59.

P. J. Werdell, NASA Goddard Space Flight Center, Code 616, Greenbelt, MD 20771, USA, and B. A. Franz and colleagues are preparing a manuscript to be called “A generalized ocean color inversion model for retrieving marine inherent optical properties.”

60.

Z. P. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41, 5755–5772 (2002). [CrossRef] [PubMed]

61.

C. B. Markwardt, “Non-Linear Least Squares Fitting in IDL with MPFIT,” Proc. ADASS XVIII, ASP Conf. Ser., D. Bohlender, P. Dowler, and D. Duran, ed. (Academic, 2009), 251–254.

62.

D. Antoine, D. A. Siegel, T. Kostadinov, S. Maritorena, N. B. Nelson, B. Gentili, V. Vellucci, and N. Guillocheau, “Variability in optical particle backscattering in contrasting bio-optical oceanic regimes,” Limnol. Oceanogr. 56(3), 955–973 (2011). [CrossRef]

63.

B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap (Chapman and Hall, New York, 1993).

64.

F. Vidussi, H. Claustre, B. B. Manca, A. Luchetta, and J. C. Marty, “Phytoplankton pigment distribution in relation to upper thermocline circulation in the eastern Mediterranean Sea during winter,” J. Geophys. Res. [Oceans] 106, 19939–19956 (2001). [CrossRef] [PubMed]

65.

Angelica PenaInstitute of Ocean Sciences, Fisheries and Oceans Canada (DFO), Sidney, B.C. V8L 4B2, Canada (personal communication, 2011).

66.

M. J. Behrenfeld, E. Boss, D. A. Siegel, and D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles 19, GB1006 (2005), [CrossRef]

67.

Z. P. Lee, S. Shang, C. Hu, M. Lewis, R. Arnone, Y. Li, and B. Lubac, “Time series of bio-optical properties in a subtrophical gyre: Implications for the evaluation of interannual trends of biogeochemical properties,” J. Geophys. Res. [Oceans] 115, C09012, (2010) [CrossRef] [PubMed]

68.

A. Morel, “Optical properties of pure water and pure sea water,” in Optical Aspects of Oceanography, N. G. Jerlov and E. S. Nielsen, eds. (Academic, New York, 1974), pp. 1–24.

69.

J. M. Sullivan, M. S. Twardowski, P. L. Donaghay, and S. A. Freeman, “Use of optical scattering to discriminate particle types in coastal waters,” Appl. Opt. 44, 1667–1680 (2005). [CrossRef] [PubMed]

70.

M. Stramska, D. Stramski, S. Kaczmarek, D. B. Allison, and J. Schwarz, “Seasonal and regional differentiation of bio-optical properties within the north polar Atlantic,” J. Geophys. Res. [Oceans] 111, C08003, (2006) [CrossRef] [PubMed]

71.

D. McKee, M. Chami, I. Brown, V. Sanjuan Calzado, D. Doxaran, and A. Cunningham, “Role of measurement uncertainties in observed variability in the spectral backscattering ratio: a case study in mineral-rich coastal waters,” Appl. Opt. 48(24), 4663–4675 (2009). [CrossRef] [PubMed]

72.

V. Martinez-Vicente, G. Tilstone, S. Sathyendranath, P. I. Miller, and S. B. Groom, “Contributions of phytoplankton and bacteria to the optical backscattering coefficient over the Mid-Atlantic Ridge,” Mar. Ecol. Prog. Ser. 445, 37–51 (2012). [CrossRef]

73.

A. Morel, “Chlorophyll-specific scattering coefficient of phytoplankton. A simplified theoretical approach,” Deep Sea Res. 34(7), 1093–1105 (1987). [CrossRef]

74.

H. M. Dierssen, R. M. Kudela, J. P. Ryan, and R. C. Zimmerman, “Red and black tides: Quantitative analysis of water-leaving radiance and perceived color for phytoplankton, colored dissolved organic matter, and suspended sediments,” Limnol. Oceanogr. 51(6), 2646–2659 (2006). [CrossRef]

75.

Y-H. Ahn, A. Bricaud, and A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep Sea Res. 39(11/12), 1835–1855 (1992). [CrossRef]

76.

A. Morel and Y-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates: A tentative assessment of their scattering role in oceanic waters compared to those of bacterial and algal cells,” J. Mar. Res. 49, 177–202 (1991). [CrossRef]

77.

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, “Optical backscattering properties of the “clearest” natural waters,” Biogeosci. 4, 1041–1068 (2007). [CrossRef]

78.

C. A. Brown, Y. Huot, P. J. Werdell, B. Gentili, and H. Claustre, “The origin and global distribution of second order variability in satellite ocean color and its potential applications to algorithm development,” Remote Sens. Environ. 112, 4186–4203 (2008). [CrossRef]

79.

S. Alvain, C. Moulin, Y. Dandonneau, H. Loisel, and F. M. Bréon, “A species-dependent bio-optical model of case 1 water for the global ocean color processing,” Deep Sea Res. Part I 53, 917–925 (2006). [CrossRef]

80.

O. Aumont, E. Maier-Reimer, S. Blain, and P. Monfray, “An ecosystem model of the global ocean including Fe, Si, P colimitations,” Global Biogeochem. Cycles 17(2), 1060 (2003), [CrossRef]

81.

J. C. Blackford, J. I. Allen, and F. J. Gilbert, “Ecosystem dynamics at six contrasting sites: a generic modelling study,” J. Marine Syst. 52, 191–215 (2004). [CrossRef]

82.

I. Marinov, S. C. Doney, and I. D. Lima, “Response of ocean phytoplankton community structure to climate change over the 21st century: partitioning the effects of nutrients, temperature and light,” Biogeosci. 7, 3941–3959 (2010). [CrossRef]

83.

C. D. Mobley, “Fast calculations for ocean ecosystem and inverse models,” Opt. Express 19(20), 18927–18944 (2011). [CrossRef] [PubMed]

OCIS Codes
(010.4450) Atmospheric and oceanic optics : Oceanic optics
(010.1350) Atmospheric and oceanic optics : Backscattering
(010.1690) Atmospheric and oceanic optics : Color

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: April 26, 2012
Revised Manuscript: June 28, 2012
Manuscript Accepted: June 30, 2012
Published: July 19, 2012

Virtual Issues
Vol. 7, Iss. 9 Virtual Journal for Biomedical Optics

Citation
Robert J.W. Brewin, Giorgio Dall’Olmo, Shubha Sathyendranath, and Nick J. Hardman-Mountford, "Particle backscattering as a function of chlorophyll and phytoplankton size structure in the open-ocean," Opt. Express 20, 17632-17652 (2012)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-16-17632


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References

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  38. R. J. W. Brewin, S. Sathyendranath, T. Hirata, S. Lavender, R. M. Barciela, and N. J. Hardman-Mountford, “A three-component model of phytoplankton size class for the Atlantic Ocean,” Ecol. Model.221, 1472–1483 (2010). [CrossRef]
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  45. T. Westberry, G. Dall’Olmo, M. J. Behrenfeld, and T. Moutin, “Coherence of particulate beam attenuation and backscattering coefficients in diverse open ocean environments,” Opt. Express18(15), 15419–15425 (2010). [CrossRef]
  46. E. S. Boss, R. Collier, G. Larson, K. Fennel, and S. W. Pegau, “Measurements of spectral optical properties and their relation to biogeochemical variables and processes in Crater Lake, Crater Lake National Park, OR,” Hydrobiologia574(1), 149–159 (2007). [CrossRef]
  47. P. J. Werdell and S. W. Bailey, “An improved in situ bio-optical data set for ocean colour algorithm development and satellite data production validation,” Remote Sens. Environ.98, 122–140 (2005). [CrossRef]
  48. P. J. Werdell, “Global bio-optical algorithms for ocean color satellite applications,” EOS Trans. AGU90(1), (2009), [CrossRef]
  49. P. J. Werdell, “An evaluation of Inherent Optical Property data for inclusion in the NASA bio-Optical Marine Algorithm Data set,” NASA Ocean Biology Processing Group Science Systems and Applications, Inc. Document Version 1.1, corresponding to NOMAD Version 1.3 19th September 2005: Online http://seabass.gsfc.nasa.gov/seabass/data/werdell_nomad_iop_qc.pdf (2005).
  50. D. Stramski, R. A. Reynolds, M. Babin, S. Kaczmarek, M. R. Lewis, R. Röttgers, A. Sciandra, M. Stramska, M. S. Twardowski, B. A. Franz, and H. Claustre, “Relationships between the surface concentration of particulate organic carbon and optical properties in the eastern South Pacific and eastern Atlantic Oceans,” Biogeosci.5, 171–201 (2008). [CrossRef]
  51. J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. [Oceans]103, 24937–24953 (1998). [PubMed]
  52. X. Zhang and L. Hu, “Estimating scattering of pure water from density fluctuation of the refractive index,” Opt. Express17, 1671–1678 (2009). [CrossRef] [PubMed]
  53. X. Zhang, L. Hu, and M.-X. He, “Scattering by pure seawater: Effect of salinity,” Opt. Express17, 5698–5710 (2009). [CrossRef] [PubMed]
  54. G. Dall’Olmo, E. Boss, M. J. Behrenfeld, T. K. Westberry, C. Courties, L. Prieur, M. Pujo-Pay, N. J. Hardman-Mountford, and T. Moutin, “Inferring phytoplankton carbon and eco-physiological rates from diel cycles of spectral particulate beam-attenuation coefficient,” Biogeosci.8, 3423–3439 (2011). [CrossRef]
  55. Toby Westberry, Department of Botany and Plant Pathology, Oregon State University, Corvallis, OR, 97331, USA (personal communication, 2011).
  56. T. J. Smyth, G. F. Moore, T. Hirata, and J. Aiken, “Semianalytical model for the derivation of ocean color inherent optical properties: description, implementation, and performance assessment,” Appl. Opt.45(31), 8116–8131 (2006). [CrossRef] [PubMed]
  57. S. Maritorena, D. A. Siegel, and A. R. Peterson, “Optimization of a semianalytical ocean color model for global-scale applications,” Appl. Opt.41(15), 2705–2714 (2002). [CrossRef] [PubMed]
  58. B. A. Franz and P. J. Werdell, “A generalized framework for modeling of inherent optical properties in ocean remote sensing applications,” Presented at Ocean Optics XX, Anchorage, Alaska, 27th Sept.–1st Oct. 2010.
  59. P. J. Werdell, NASA Goddard Space Flight Center, Code 616, Greenbelt, MD 20771, USA, and B. A. Franz and colleagues are preparing a manuscript to be called “A generalized ocean color inversion model for retrieving marine inherent optical properties.”
  60. Z. P. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt.41, 5755–5772 (2002). [CrossRef] [PubMed]
  61. C. B. Markwardt, “Non-Linear Least Squares Fitting in IDL with MPFIT,” Proc. ADASS XVIII, ASP Conf. Ser., D. Bohlender, P. Dowler, and D. Duran, ed. (Academic, 2009), 251–254.
  62. D. Antoine, D. A. Siegel, T. Kostadinov, S. Maritorena, N. B. Nelson, B. Gentili, V. Vellucci, and N. Guillocheau, “Variability in optical particle backscattering in contrasting bio-optical oceanic regimes,” Limnol. Oceanogr.56(3), 955–973 (2011). [CrossRef]
  63. B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap (Chapman and Hall, New York, 1993).
  64. F. Vidussi, H. Claustre, B. B. Manca, A. Luchetta, and J. C. Marty, “Phytoplankton pigment distribution in relation to upper thermocline circulation in the eastern Mediterranean Sea during winter,” J. Geophys. Res. [Oceans]106, 19939–19956 (2001). [CrossRef] [PubMed]
  65. Angelica PenaInstitute of Ocean Sciences, Fisheries and Oceans Canada (DFO), Sidney, B.C. V8L 4B2, Canada (personal communication, 2011).
  66. M. J. Behrenfeld, E. Boss, D. A. Siegel, and D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles19, GB1006 (2005), [CrossRef]
  67. Z. P. Lee, S. Shang, C. Hu, M. Lewis, R. Arnone, Y. Li, and B. Lubac, “Time series of bio-optical properties in a subtrophical gyre: Implications for the evaluation of interannual trends of biogeochemical properties,” J. Geophys. Res. [Oceans]115, C09012, (2010) [CrossRef] [PubMed]
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