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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, C09015, doi:10.1029/2009JC005303, 2009

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Retrieval of the particle size distribution from satellite ocean color observations T. S. Kostadinov,1,2 D. A. Siegel,1,3 and S. Maritorena1 Received 23 January 2009; revised 4 June 2009; accepted 12 June 2009; published 18 September 2009.

[1] The particle size distribution (PSD) provides important information about pelagic

ocean ecosystem structure and function. Knowledge of the PSD and its changes in time can be used to assess the contributions made by phytoplankton functional groups to primary production, particle sinking, and carbon sequestration by the ocean. However, few field measurements of the PSD have been made in the pelagic ocean, and little is known about its space-time variation. Here, a novel bio-optical algorithm is introduced to retrieve the parameters of a power law particle size spectrum from satellite ocean color observations. First, the particle backscattering coefficient spectrum, bbp(l), is retrieved from monthly Sea-viewing Wide Field-of-view Sensor (SeaWiFS) normalized water-leaving radiance observations following Loisel et al. (2006). Mie modeling is then used to estimate the parameters of a power law PSD (the PSD slope and the particle differential number concentration for a given reference diameter) as a function of the particulate backscattering spectrum. Algorithm uncertainties are greater when bbp(l) slopes are low, which occurs in high-productivity areas. Satellite-based retrievals of PSD parameters are reasonably consistent with available field observations. As an example, the algorithm was applied to monthly SeaWiFS global imagery from August 2007. Global spatial distributions show subtropical oligotrophic gyres characterized by higher PSD slopes and smaller particle number concentrations, as compared with coastal and other high-productivity areas. Partitioning particle number and volume concentrations into picophytoplankton-, nanophytoplankton-, and microphytoplankton-sized classes indicates that the abundance of picoplankton-sized particles is roughly constant spatially and that they dominate the particle volume concentrations in oligotrophic regions. On the other hand, abundances of microplankton-sized particles vary over many orders of magnitude, and they contribute to volume concentration only in the highest-productivity areas. These results are consistent with current understanding of particle dynamics of pelagic ecosystems and provide new tools for biogeochemical modeling and assessment of the global ocean ecosystem. Citation: Kostadinov, T. S., D. A. Siegel, and S. Maritorena (2009), Retrieval of the particle size distribution from satellite ocean color observations, J. Geophys. Res., 114, C09015, doi:10.1029/2009JC005303.

1. Introduction [2] Understanding and predicting natural and anthropogenic changes to Earth’s global systems has emerged in recent decades as an overarching goal of Earth System science, including ocean biogeochemistry. The world’s oceans and their biota are an integral part of the planetary carbon cycle. Photosynthetic productivity in the oceans’

1 Institute for Computational Earth System Science, University of California, Santa Barbara, California, USA. 2 Interdepartmental Graduate Program in Marine Science, University of California, Santa Barbara, California, USA. 3 Department of Geography, University of California, Santa Barbara, California, USA.

Copyright 2009 by the American Geophysical Union. 0148-0227/09/2009JC005303$09.00

euphotic zone leads to accumulation of biomass, the fate of which on different spatial and temporal scales determines the biological pump’s role in the global carbon cycle. An important way of characterizing pelagic ecosystems is the size distribution for the plankton community and suspended particles [Chisholm, 1992]. The particle size distribution (PSD) provides important information of the dominant phytoplankton functional types (PFTs) present [Falkowski et al., 1998; Vidussi et al., 2001; Falkowski et al., 2003; Le Que´re´ et al., 2005; Hood et al., 2006]. The distribution of particle sizes also influences particle sinking and carbon export [e.g., McCave, 1975; Eppley and Peterson, 1979; Falkowski et al., 1998; Buesseler et al., 2007]. Hence, observation of the size structure of the particles associated with global pelagic ecosystems is of great interest to a variety of applications. [3] Surface ocean particle size distributions (PSDs) have been found to most often follow the Junge-type [Junge,

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KOSTADINOV ET AL.: PSD PARAMETERS FROM OCEAN COLOR

1963] power law size distribution [e. g. Bader, 1970; Sheldon et al., 1972; Stramski and Kiefer, 1991; Twardowski et al., 2001; Boss et al., 2001a, 2001b]. The differential number concentration as a function of particle diameter of such a PSD spectrum has the form N ð DÞ ¼ No

D Do

x ð1Þ

where N(D) is the number of particles per volume of seawater normalized by the size bin width (units of m4), D is the particle diameter [m], Do is a reference diameter (2 mm is used here), No is the particle differential number concentration at Do (units of m4), and x is the Junge slope of the PSD. The Junge slope, x, and the reference abundance, No, are the two parameters of the Junge-type size distribution. The total number of particles per unit volume of seawater in a given size range can be found by integrating equation (1) from a minimum size, Dmin, to a maximum size, Dmax, enabling the PSD to be partitioned into distinct classes (compare picoplankton, etc.). The limits of integration can be thought of as two additional parameters, fully describing this idealized PSD [Boss et al., 2001a]. Alternative representations of equation (1), such as normalized biomass spectra, are common [Vidondo et al., 1997]. The properties of a power law PSD are also thought to have ecological significance [Chisholm, 1992]; certain slopes of such a size distribution are linked to a steady state ecosystem [Platt and Denman, 1977]. Alternative explanations, such as sizeselective predation, have also been proposed [Kiefer and Berwald, 1992]. [4] Little is known about the spatial and temporal variations in the parameters of the PSD due to the paucity of appropriate observations. This is in spite of the advent of several particle sizing techniques in the recent decades, such as the Coulter counter [Sheldon and Parsons, 1967; Sheldon et al., 1972; Milligan and Kranck, 1991], laser scatter particle sizers [Agrawal and Pottsmith, 2000; Slade and Boss, 2006; Karp-Boss et al., 2007] and flow cytometry [e.g., Yentsch et al., 1983; Chisholm, 1992]. Further, in situ measurements cannot provide the necessary global synoptic coverage that would allow for PSD measurements to be used in global ecosystem and biogeochemical models. Satelliteborne platforms of observation are therefore needed in order to provide the necessary spatiotemporal coverage. [5] Bio-optics has the potential to provide the link between optical properties measurable from satellite ocean color sensors and the underlying PSD. Scattering properties of particle assemblages when suspended in seawater are strongly dependent on the particle composition as well as the PSD and can be predicted using Mie theory [Mie, 1908]. Mie theory assumes the scatterers are homogenous spheres and requires the particle complex index of refraction relative to the medium and the particle size distribution, as well as incident light wavelength as input parameters. On the other hand, the backscattering coefficient is both analytically and empirically related to the spectrum of satellite-observed normalized water-leaving radiance, LwN(l) [e.g., Gordon et al., 1988; Reynolds et al., 2001; Kostadinov et al., 2007]. Semianalytical algorithms have been developed that retrieve the total backscattering coefficient from the satellite derived

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LwN(l) spectrum, either at a reference wavelength [e.g., Maritorena et al., 2002] or for multiple wavelengths [Loisel and Stramski, 2000; Lee et al., 2002] without a priori assumptions about the spectral shape of the bbp(l) spectrum. [6] The particulate backscattering spectrum is often modeled as a power law function of wavelength, with two parameters describing its shape and magnitude [Morel, 1973; Garver and Siegel, 1997; Carder et al., 1999; Reynolds et al., 2001]. Recent in situ studies have shown that the spectral slope of bbp(l), h, is to first order related to the chlorophyll concentration, Chl [Twardowski et al., 2001; Sullivan et al., 2005; Stramska et al., 2006]. Since high Chl is positively correlated to relative dominance of large particles [Chisholm, 1992; Reynolds et al., 2001], it is reasonable to expect a relationship between the particle size spectrum and the spectral slope of backscattering. This relationship will depend on the wavelength range considered. Wozniak and Stramski [2004] report a positive correlation between the PSD slope and the bbp(l) spectral slope for minerogenic particles on the basis of Mie modeling results. Alternatively, the relationships of the spectral slope of the particle beam attenuation and of the backscattering probability ratio to the characteristics of the underlying particle assemblage have also been the focus of previous studies [Ulloa et al., 1994; Boss et al., 2004; Twardowski et al., 2001; Mobley et al., 2002]. [7] Loisel et al. [2006] used Sea-viewing Wide Fieldof-view Sensor (SeaWiFS) observations to calculate h from ocean color data using the spectrally retrieved bbp(l) [Loisel and Stramski, 2000; Loisel et al., 2001]. Their analysis demonstrated that (1) h can be retrieved from space and the range of values compare favorably to the few available in situ studies [e.g., Reynolds et al., 2001; Toole and Siegel, 2001; Kostadinov et al., 2007] and (2) there exist global spatial and temporal patterns of h that correlate to Chl distribution in the different ecological zones of the world ocean. Namely, high h values are found in the oligotrophic subtropical gyres where Chl is low, whereas low h values are found in coastal, Equatorial and high latitude waters where Chl is higher. Oligotrophic regions of the world ocean are associated with the predominance of small phytoplankton and regenerative production, whereas productive, highnutrient regions are associated with episodic blooms of large cells that sustain new production [e.g., Falkowski et al., 1998; Azam, 1998], and thus a relatively higher abundance of large particles is observed. Thus, Loisel et al. [2006] qualitatively interpret high h values to be associated with steep slopes of the PSD and vice versa, noting the need to quantitatively link parameters of the PSD to characteristics of the backscattering spectrum. [8] Here, a novel bio-optical model is presented that is capable of retrieving the parameters of a Junge-type particle size distribution using ocean color remotely sensed data. The algorithm builds on the results of Loisel et al. [2006] and uses Mie theory modeling in order to link the backscattering coefficient spectra to parameters describing the particle assemblage. This enables determinations of the PSD to be made over regional to global scales allowing a variety of data products to be computed such as partitioned particle number and volume concentrations in the size ranges corresponding to ecologically significant size classes of phytoplankton, namely, picophytoplankton, nanophyto-

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Table 1. A Summary of the Mie Model Parameters That Were Used in the Algorithm Developmenta Mie Parameter

Units

Default Value

Monte Carlo Simulation Variability

nm -

440, 490, 510, 550 1.05

n0(l)

-

x

-

[2.6; 1.65; 1.1; 0.75] 103 at the wavelengths above 2.5 – 6, step of 0.05

Picked from N (1.05, 0.05), n 2 [1.025, 1.2]. Half the values between 1.1 and 1.2 were then randomly removed, resulting in m(n) = 1.069. Dn0 picked from N(0,0.00075) was added to entire spectrum, keeping n0(l) 0 8 l. Retrieved parameter.

mm mm

0.002 30

l n

Dmin Dmax

Not varied. Here 75% was uniformly picked from the [20, 100] mm range, and 25% was uniformly picked from the [20, 200] mm range, resulting in m(Dmax) 63 mm.

References Morel [1973], Twardowski et al. [2001], Stramski [1999], Balch et al. [1996], and Wozniak and Stramski [2004] Babin et al. [2003] and Ahn et al. [1992] Risovic [1993], Boss et al. [2001a], and Loisel et al. [2006]; also see in situ data sets (Table 2) Stramski and Kiefer [1991] and Figure 13 Boss et al. [2001a], Vidussi et al. [2001], Le Que´re´ et al. [2005], and Clavano et al. [2007]

a The default values were used in the construction of the forward model illustrated in Figure 1. The range and distribution of the values as varied during the Monte Carlo simulations used for LUT construction and error assessment are indicated as well. N(m, s) stands for the normal distribution with a mean m and standard deviation s. The operational LUTs of Figure 2 were constructed by inverting each individual valid Monte Carlo – run LUTs for h between 1.5 and 3 and averaging the results. See section 2.2 for details.

plankton, and microphytoplankton. The PSD algorithm is applied to the August 2007 monthly SeaWiFS global image as an example. An analysis of uncertainty in the model indicates that the largest uncertainties are associated with low PSD slopes (associated with low h values), which are primarily found in coastal and productive oceanic areas. Analysis of the satellite-retrieved PSD parameters (x and No) and the derived products and their spatial distribution indicates that they are consistent with current understanding of oceanic ecosystems.

2. Data and Methods 2.1. PSD Parameterization and Mie Modeling [9] Mie theory is used to quantify the relationship between the Junge PSD parameters, x and No, and parameters describing the particulate backscattering spectrum. The PSD is assumed to follow a Junge-type power law form according to equation (1). Mie scattering theory provides an exact solution for the bulk inherent optical properties of a known particle suspension by solving Maxwell’s equations. All particles are assumed to be noninteracting, homogenous spheres. The backscattering efficiency of an individual particle, Qbb(D, l, m), is a function of the wavelength of light in vacuo, l, the diameter of the particle, D, and the particle’s complex index of refraction relative to the medium, m (= n i n0; where the real part, n, is the ratio of the speed of light in seawater relative to that in the particle and the imaginary part, n0, is proportional to the particle material’s bulk absorption coefficient [Morel and Bricaud, 1986; Mobley, 1994]). Note that the wavelength of light in the medium, lm = l/nm (where nm is the medium’s real index of refraction) needs to be used when calculating Mie’s size parameter [van de Hulst, 1981]. [10] Once the backscattering efficiency of a single particle is determined, the backscattering coefficient at the given wavelength is simply the sum of all particles’ efficiencies multiplied by the respective cross-sectional area of all particles of a given size. If a Junge-type PSD is assumed,

then the resulting bbp(l) spectrum due to the particle assemblage is [van de Hulst, 1981] Dmax Z

bbp ðlÞ ¼

x p 2 D dD D Qbb ð D; l; mÞNo 4 Do

ð2Þ

Dmin

with notation as above (see equation (1)). Equation (2) provides the path between satellite measurable optical properties, namely, the spectral particle backscattering coefficient, and the parameters of the assumed underlying power law PSD, x and No. Monte Carlo simulation is used to establish an operational relationship between bbp(l) and the PSD parameters. In addition, this allows assessment of the uncertainties due to expected open ocean variability of the rest of the input Mie parameters, namely, the complex index of refraction of the particles and the size limits of integration. Mie code [Bohren and Huffman, 1983; W. Slade and E. Boss, software, available at http://misclab.umeoce. maine.edu/software.php, 2007] was run in a forward mode for a range of PSD slopes, x, in the interval 2.5– 6 (parameter values are given in Table 1). Figure 1a illustrates an example output from the forward Mie run that uses the default parameters of Table 1. Each PSD slope results in a specific bbp(l) spectrum. The spectra were then fitted to the power law equation h l bbp ðlÞ ¼ bbp ðlo Þ lo

ð3Þ

in order to derive the spectral slope, h. Following Loisel et al. [2006], the three wavelength bands, 490, 510 and 550 nm (marked with a black arrow in Figure 1a) were used in the calculation of the slope h, which minimizes absorption effects on the shape of bbp(l); h was calculated by log transforming equation (3) and using ordinary least squares regression to estimate h, consistent with the results of Loisel et al. [2006]. [11] A single Mie calculation for x varying between 2.5 and 6 in the forward mode results in a given relationship

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Figure 1. Results of the forward Mie model run with the default parameters as in Table 1. (a) The resulting bbp(l) spectra are shown for different PSD slopes, as in the legend, from lowest (x = 2.5, black curve) to highest (x = 6, lightest shade of gray). The wavelengths at which Mie calculations were performed are marked with crosses. The particulate backscattering slope, h, was calculated using only the three wavelengths marked with arrows, both for modeled and SeaWiFS-retrieved spectra (see section 2.1 for details). (b) The resulting relationship between the power law slope of the PSD, x, and h (left y axis), as well as the relationship between x and the value of log10 (bbp(440)/No) (right y axis). These relationships are the basis of the look-up tables (LUTs) presented in the text. The determination coefficient, R2, of the linear regression used to calculate the bbp(l) slope is also shown (scale on left y axis). between the PSD slope x and the spectral bbp(l) slope, h, as well as the value of log10 (bbp(440)/No). These relationships are illustrated in Figure 1b for the example Mie run of Figure 1a, which uses the default parameters in Table 1. The coefficient of determination, R2, of the linear regression used to calculate h is also shown. Figure 1b demonstrates that a clear relationship exists between the PSD slope and log10 (bbp(440)/No) on the one hand, and the bbp(l) spectral slope, h, on the other hand. The value of log10 (bbp(440)/No) can be viewed as particle backscattering normalized to particle abundance, and since particle backscattering depends on size, a relationship is expected between log10 (bbp(440)/No) and the PSD slope (and thus also the bbp(l) slope, h); note that No can be taken out of the integral in equation (2). Additionally, the choice of Do (here 2 mm) does not influence the relationship between the PSD slope x and the bbp(l) slope h. The relationships in Figure 1b form the basis for the construction of the operational look-up tables (LUTs) for the PSD algorithm presented here.

2.2. Derivation of Mean Look-Up Tables and Uncertainty Estimation [12] Monte Carlo simulation was used to assess the uncertainty associated with Mie model parameters that were considered known in the assessment of the LUTs, namely, the limits of integration, as well as the complex index of refraction of the particles. These uncertainties are termed endogenous here. Rather than choosing a specific look-up table on the basis of a single set of model parameters, mean look-up tables were constructed on the basis of an ensemble of possible parameter combinations. The Dmin parameter was not varied during the simulation because it was found to not affect the results significantly, as long as it is sufficiently small (see section 4.2 and Figure 13). The complex index of refraction and Dmax were varied as shown in Table 1. Each individual Monte Carlo simulation yielded a unique random combination of input parameters. These resulting LUTs were then truncated (for the low h values) where the functional relationships h = f(x) and h = g(log10 (bbp(440)/No)) ceased

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Figure 2. The operational look-up tables for the PSD algorithm and the associated uncertainty due to variable input Mie model parameters, evaluated using Monte Carlo simulations. The LUTs are provided as auxiliary material. (a) The Junge slope LUT enveloped by one standard deviation. (b) The log10 (bbp(440)/No) LUT enveloped by one standard deviation. (c) A histogram of the bbp(l) slope h global observations for August 2007 (bars (see Figure 6)) and the number of valid Monte Carlo simulations available at each data point (solid black line), from the maximum N = 2995. Values of h below 1.5 and above 3 have been excluded from the histogram. to be injective (one-to-one), as this is necessary for inversion of f(x) and g(log10 (bbp(440)/No)) in order to construct the LUTs. The LUTs (in table form, linearly interpolated) were used to solve for x and log10 (bbp(440)/No) for h values between 1.5 and 3; all results at a given h value were averaged in order to derive the operational LUTs for both products and are available as auxiliary material.1 [13] The Monte Carlo derived LUTs have the benefit of determining uncertainty levels for the inversion. Figures 2a and 2b show the two LUTs graphically with an envelope of one standard deviation. The number of valid Monte Carlo runs for each h value is shown in Figure 2c, together with a histogram of h for global observations from August 2007 (see section 2.3.1). The distribution of h and Figure 2a indicate that relatively few pixels exhibit low h values for which uncertainty in the retrieved PSD slope will be highest (see section 4.2 for more details). Also note that this assessment is only for endogenous sources of uncertainty such as those associated with variability of the input Mie parameters used in the modeling. A detailed discussion of the uncertainties associated with the h estimation itself is given by Loisel et al. [2006]. [14] The relationship between the bbp(l) spectral slope, h, and the PSD slope x is very close to linear, with a + 3 offset (x = h + 3), for values of h > 1. Interestingly, this is the same as the well-known relationship between the spectral slope of the particle beam attenuation and the PSD slope for non1 Auxiliary materials are available at ftp://ftp.agu.org/apend/jc/ 2009jc005303.

absorbing spherical particles [e.g., Boss et al., 2001a, and references therein]. Boss et al. [2001a] introduce a correction for deviations from linearity for low beam attenuation slopes and finite limits of integration. Similarly, the relationship between x and h derived in the LUT here deviates significantly from linearity for low h values. Here, the relationship between h and x is better represented by a third-degree polynomial fit (relative RMS of only 0.0057) than by an exponential fit (relative RMS of 0.0233). So an analytical representation of the LUT for the PSD slope is x ¼ 0:00191h3 þ 0:127h2 þ 0:482h þ 3:52

ð4Þ

Equation (4) is merely a polynomial fit to the LUT and has no physical significance. 2.3. Ocean Color Satellite Data and Methods 2.3.1. Spectral Particulate Backscattering and Its Slope [15] Monthly Level 3 mapped SeaWiFS global images of normalized water-leaving radiance (LwN(l)) at 412, 443, 490, 510 and 555 nm (ftp://oceans.gsfc.nasa.gov/; reprocessing 5.2) for August 2007 are used to demonstrate the results of the bio-optical PSD algorithm. Corresponding chlorophyll-a imagery was also used in the analysis. Other month’s data as well as daily LAC matchup data are used when needed for validation (see section 4.4). In order to average out small-scale noise, the original 1/12° resolution mapped images were resampled at 1/4° resolution by taking the median in each 3 by 3 pixel box if more than 5 pixels in the original data were valid. All subsequent analyses were

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Figure 3. Flowchart of the PSD algorithm. (left) The process to create the necessary look-up tables and the associated uncertainties via Mie modeling and Monte Carlo simulation and (right) the flow of ocean color satellite data and calculations performed when the LUTs are used in the inverse mode in the operational algorithm. performed on the 1/4° resolution imagery unless otherwise noted. [16] The procedure detailed by Loisel et al. [2006] was used to retrieve spectral particulate backscattering coefficients at 410, 440, 490, 510, and 550 nm at every valid pixel and to calculate the spectral slope, h. Briefly, the Loisel and Stramski [2000] model was used to retrieve bbp(l) from the SeaWiFS estimates of LwN(l), using the methods given by Loisel et al. [2001] and Mueller [2000] to estimate the irradiance reflectance just below the surface, R(0, l), and the diffuse attenuation coefficients for downwelling irradiance, Kd(l). This model also requires the solar zenith angle, qs. The mean monthly pixel values for qs were computed from the daily values at each pixel’s latitude for solar noon, obtained from the equations of Meeus [1998] for 2007. In the case of LAC validation data, the actual qs was used. Values of bbp(l) outside the range [105 – 101] m1 were rejected ( 2.5% of the valid bbp(l) pixels for August 2007). The spectral slope of particulate backscattering, h, was calculated using the 490, 510 and 550 nm bands, consistent with the results of Loisel et al. [2006] and the Mie modeled spectral slope fit (section 2.1). 2.3.2. Retrieving the PSD Parameters and Derived Products [17] The look-up tables in Figure 2 were used to estimate the values of the PSD slope x and log10 (bbp(440)/No) at each valid pixel in the monthly images. Linear interpolation was used where values of h fell between tabulated values and values of h outside the range in the LUTs were not considered. Satellite estimates of bbp(440) were then used with the retrieved maps of log10 (bbp(440)/No) to calculate the values of No at each pixel. [18] A variety of relevant biogeochemical and ecological parameters can be derived once the PSD slope, x, and reference abundance, No, are known. Here, particle abundance and volume in the size ranges corresponding to picoplankton (0.5 – 2 mm), nanoplankton (2 – 20 mm), and microplankton (20 – 50 mm) [Sieburth et al., 1978; Vidussi et

al., 2001] were calculated. The total particle abundance N, [particles/m3], in a given size range Dmin to Dmax [m] was calculated as (for notation, see equations (1) and (2)),

Dmax Z

N¼

No

D Do

x dD ¼

1 1x D No Dxo D1x max min ð1 xÞ

ð5Þ

Dmin

and total particle volume in the same size class was calculated as Dmax Z

V ¼

x p 3 D 1 p 4x dD ¼ D No No Dxo D4x max Dmin 6 Do ð4 xÞ 6

Dmin

ð6aÞ

When x = 4, the integral above is not defined and V is instead calculated as Dmax Z

V¼

x p 3 D p Dmax dD ¼ No D4o ln D No Dmin 6 Do 6

ð6bÞ

Dmin

The ratio of the volume of particles in each size class to the volume of particles in the entire size range (0.5 – 50 mm) was also calculated. The implementation flowchart (Figure 3) summarizes the PSD bio-optical algorithm. Figure 3 (left) describes the Mie model runs that are used to create the two LUTs, and Figure 3 (right) describes the satellite data flow.

3. Results 3.1. Chlorophyll-a, Particulate Backscattering Coefficient Spectrum, and Its Slope [19] The global distribution of chlorophyll-a concentration (Chl) for August 2007 follows typical patterns (Figure 4), namely, low values of Chl in the subtropical gyres, higher

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Figure 4. Map of the global chlorophyll-a concentration for August 2007 from monthly SeaWiFS observations. The data are from reprocessing 5.2; OC4v4 algorithm. The original 9 km per pixel data were down sampled to 1/4° resolution to match the PSD algorithm resolution. The color scale is logarithmic. values in coastal upwelling zones, Equatorial regions and higher latitudes. To first order, the high-Chl areas are associated with high productivity and vice versa. However, there are physiological confounding factors such as light acclimation that have to be taken into account [Behrenfeld et al., 2005; Siegel et al., 2005a].

[20] Values of the particulate backscattering coefficient at 440 nm (Figure 5a) and 550 nm (Figure 5b) for August of 2007 show similar patterns as Chl (Figure 4) but with reduced amplitudes. Higher values of the particulate backscattering coefficient are found for blue light (440 nm) rather than green (550 nm) for nearly all of the ocean

Figure 5. The particle backscattering coefficients at (a) 440 nm and (b) 550 nm for August 2007 as retrieved by the Loisel and Stramski [2000] algorithm. 7 of 22

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Figure 6. (a) Map of the global distribution of the spectral slope of bbp(l), h, for August 2007. (b) Map of the coefficient of determination, R2, of the type I linear regression used to calculate h. (compare Figures 5a and 5b). Regions characterized by high Chl (see Figure 4) and thus higher productivity have relatively high backscattering values, whereas regions with lower productivity have relatively low backscattering. For the August 2007 monthly mean image, values of bbp(440) and bbp(550) are correlated with values of Chl with linear correlation coefficients R = 0.81 and R = 0.94, respectively (correlation coefficients reported here were calculated in log10 space using only pixels with a valid PSD slope retrieval). This suggests that changes in particulate backscattering are associated with phytoplankton abundances and their covarying particle concentrations [Siegel et al., 2005a]. High-particulate backscattering levels are found for the Equatorial regions, upwelling zones associated with Eastern Boundary Currents and other coastal areas and marginal seas, as well as the high latitude regions, especially in the Northern Hemisphere (Figure 5). Comparatively low particle backscattering levels are associated with the subtropical gyres. [21] The distribution of the estimated slope of the particle backscattering spectrum, h, and the corresponding coefficient of determination of the linear fit used to calculate h are shown in Figures 6a and 6b, respectively. Consistent with the analysis of Loisel et al. [2006], high values of h are associated with the low Chl regions of the subtropical gyres, and low or even negative slopes are found in the more productive (high Chl) areas of the oceans (Figures 4 and 6a). The fit to a power law shape is particularly good for the

oligotrophic ocean, associated with high h values (Figure 6b). The fit deteriorates significantly in regions of higher Chl/ higher productivity. Accordingly, the linear correlation coefficient between h and log10 (Chl) is 0.76, and the coefficient of determination (R2) of the linear regression used to calculate h is low where Chl is high and vice versa. [22] Loisel et al. [2006] excluded negative PSD slopes in their analysis while these retrievals are kept here because negative h values appear in the theoretically modeled bbp(l) spectra (Figure 1a). Qualitatively consistent with these theoretical spectra, the observed bbp(l) spectra that are associated with low h values often do not have a shape that is consistent with a power law, resulting in a poor fit. 3.2. Algorithm Products (x and No) and Their Uncertainties [23] Maps of the retrieved Junge PSD slope, x, and the corresponding No parameter (in log10 space) for August 2007 are shown in Figures 7a and 7b, respectively. The oligotrophic subtropical gyres are characterized by relatively high PSD slopes and low No levels, as compared to the coastal, upwelling and high latitude regions, which tend to have lower PSD slopes and higher particle concentrations. This general pattern is consistent with the idea that low chlorophyll, low-productivity regions are characterized by smaller particles, whereas large particles are found more often in high-productivity areas [e.g., Falkowski et al.,

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Figure 7. Base products of the PSD algorithm for August 2007. (a) Map of the retrieved PSD Junge slope, x. (b) Map of the retrieved value of No in log10 space. The hyperbolic slope x and log10 (No) are strongly anticorrelated (R = 0.96). 1998]. Hence, a strong negative correlation is observed between x and log10 (No) (R = 0.97). Frequency distribution plots show that 78.4% of the x observations have values between 3.5 and 5, with a mean of 4.22, a median of 4.15 and a standard deviation of 0.59 (Figure 8a). Figure 8b shows the corresponding histogram for log10 (No). Its mean is 15.58, with a median of 15.71 and a standard deviation of 0.75. [24] The Monte Carlo simulations used in the development of the mean operational LUTs allow for the estimation of the endogenous sources of uncertainty due to variability in model parameters (Figure 2). All valid LUTs at the respective h value (Figure 2c) were used to retrieve an ensemble of PSD parameters x and No at each pixel with a valid h value (Figure 6a). Thus, standard deviations of the PSD parameter retrievals were mapped (Figures 9a and 9b). The highest uncertainty levels in the Junge slope retrieval are 0.2 and occur for the lowest (negative) h retrievals. This model based uncertainty then decreases rapidly with increasing h values and is only 0.04 for h = 1, which is the most common value (Figures 2a and 2c), and drops to 0.01 for h > 1.6. These endogenous uncertainties are driven primarily by a combination of the imaginary index of refraction and the maximum diameter of integration. For much of the ocean area (the subtropical oligotrophic gyres and their transition zones), the endogenous uncertainty in

the Junge slope retrieval is small (Figure 9a). Higher uncertainty tends to occur in higher productivity areas (Figure 9a) but overall uncertainty levels for x are considerably smaller than the retrieved values (Figure 8a). [25] In contrast to the Junge slope uncertainty pattern, the uncertainty levels for the No retrievals have a nearly uniform spatial pattern in terms of standard deviations in log10 space (Figure 9b; note the color scale). For most cases, log10 (No) uncertainty levels are about 0.4. The No uncertainty is driven primarily by the variability in the real index of refraction, which was allowed to vary widely in the Monte Carlo simulations (Table 1); thus this estimate of endogenous sources of uncertainty for log10 (No) should be interpreted as an upper bound. In all, the endogenous sources of uncertainty for retrievals of x and log10 (No) are small relative to the magnitude of typical retrievals (Figures 7 and 9). 3.3. Derived PSD Products and Their Uncertainties [26] Values of phytoplankton-sized (0.5 < D < 50 mm) particle abundance (particles/m3) span nearly 3 orders of magnitude for August 2007 (Figure 10a). As expected, higher total particle abundances are found corresponding to locations with higher Chl levels (Figure 4). Figures 10b– 10d show the partitioned number concentration among picophytoplankton-, nanophytoplankton-, and microphyto-

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Figure 8. Histograms and statistics of the retrieved (a) Junge slope and (b) log10 (No) for August 2007. Stdev, standard deviation. plankton-sized particles, respectively. The global, sizepartitioned abundance distributions exhibit several important characteristics. First, for all size classes, particle abundances are higher in the productive regions (at least by a couple of orders of magnitude) than they are in the oligotrophic subtropical gyres. Second, spatial variations in pico-sized particle abundances range over 3 orders of magnitude, nano-sized particle abundances vary 5 orders of magnitude, whereas micro-sized particles exhibit 7 orders of magnitude spatial variability (Figures 10b– 10d are on the same color scale). [27] Volume concentrations for phytoplankton-sized particles (shown in Figure 11a for August 2007) are useful because particle volume, rather than abundance, will be closely related to plankton biomass. This quantity is dimen-

sionless since it represents the total particle volume for a given size range per volume seawater. As expected, productive areas of the ocean exhibit relatively high particle volume, whereas the subtropical gyres exhibit the lowest particle volume concentrations. Figures 11b –11d are maps of the volume concentration contributions made by the three phytoplankton size classes, presented as percent of the total volume concentration of Figure 11a. These show that picoplankton-sized particles dominate total particle volume in the subtropical gyres where they contribute 60 to nearly 100% of the total particle volume (Figure 11b). Nano-sized particles are prevalent in transitional, upwelling, coastal and higher latitude regions and their maximum contribution is about 50%, which occurs over a significant fraction of the oceans (Figure 11c). Microplankton-sized particles contrib-

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Figure 9. Algorithm uncertainty budgets for the base products (PSD slope, x, and No) for August 2007, obtained by using all valid Monte Carlo LUTs to perform the inversion and calculating the standard deviation of the products at each pixel. (a) Map of the standard deviation of the retrieved PSD Junge slope. (b) Map of the standard deviation of the retrieved value of No in log10 space. Figures 9a and 9b reflect just the endogenous uncertainty due to variability in the complex index of refraction and limits of integration (equation (2)). ute up to 50– 60% of the volume concentration only in regions known for their high productivity, such as coastal areas, the North Atlantic bloom region, the Equatorial and Eastern Boundary Current Upwelling zones, and higher latitude zones (Figure 11d). Abundances of microplankton-sized particles are extremely low in the subtropical gyres and much of their transition zones (Figure 10d). Thus their percent contribution to the volume concentration is virtually zero in these areas (Figure 11d). [28] The propagation of the endogenous uncertainty for selected derived products is shown in Figure 12. The uncertainty in total phytoplankton-sized particle abundance, s(log10 (Ntotal)), is driven largely by the No uncertainty and it has a similar magnitude and spatial distribution (Figure 12a), namely, the highest uncertainty levels are found in coastal and high-productivity regions; however values of s(log10 (Ntotal)) are relatively uniform spatially varying only between 0.37 and 0.47. In this context it is worth noting that log10 (No) has a really steep histogram, especially at the right tail (Figure 8b), indicating that particles of diameter about 2 mm are relatively conserved with respect to their absolute abundance throughout the ocean. The spatial variability of No and x for August 2007 (Figure 7) implies

that the variability of total number concentration of particles between 0.5 and 50 mm is driven both by No and by x. However, the volume concentration of particles in this diameter range is driven primarily by No. [29] The propagated endogenous uncertainty of the number concentration of microplankton-sized particles is shown in Figure 12b, where the color scale is slightly different and the uncertainty is slightly higher. The uncertainty maps for the other two size categories (picophytoplankton- and nanophytoplankton-sized particles) look similar and exhibit smaller values than Figure 12b (not shown). Figure 12c is a map of the endogenous uncertainty of the total volume of phytoplankton-sized particles. The values and the spatial distribution look similar to the microplankton-sized particle number concentration uncertainty, again indicating that No uncertainties are driving this derived product’s uncertainty. Finally, Figure 12d shows the endogenous uncertainty in the percent particle volume due to microplankton-sized particles. The oligotrophic gyres and their transition zones exhibit very low values of uncertainty, whereas the high productivity and coastal and high latitude areas uncertainty levels are 7%. This result of uncertainty propagation analysis is encouraging and is a reflection of the fact that

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Figure 10. Global maps of (a) number concentration of phytoplankton-sized particles (0.5 –50 mm), (b) number concentration of picoplankton-sized particles (0.5–2 mm), (c) number concentration of nanoplankton-sized particles (2–20 mm), and (d) number concentration of microplankton-sized particles (20 – 50 mm). Units are particles m3 of seawater (the pound signs in Figures 10a–10d stand for number of particles). Figures 10a– 10d are plotted in log10 space; note that Figure 10a has a different color scale from Figures 10b– 10d, which are on a common color scale.

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Figure 11. Global maps of (a) volume concentration of phytoplankton-sized (0.5 and 50 mm) particles, a dimensionless quantity, log10(volume of particles/volume of seawater); (b) percent volume due to picoplankton-sized particles (0.5– 2 mm); (c) percent volume due to nanoplankton-sized particles (2– 20 mm); and (d) percent volume due to microplankton-sized particles (20 – 50 mm).


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Figure 12. Global maps of propagated endogenous uncertainty for four select derived PSD algorithm products (obtained by using all valid Monte Carlo LUTs to perform the PSD algorithm inversion and calculate the derived products and the corresponding standard deviation at each pixel). (a) Standard deviation of number concentration of phytoplankton-sized (0.5 and 50 mm) particles, log10(N_total), (log10 (particles/m3)); (b) standard deviation of number concentration of microphytoplankton-sized (20 and 50 mm) particles, log10 (N_micro), (log10 (particles/m3)); (c) standard deviation of volume of phytoplankton-sized particles log10 (Phyto_Volume), (log10 (volume of particles/volume of seawater)); and (d) standard deviation of the percent biovolume due to microplankton-sized particles (PBv_micro).


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calculations of percent volume contributions do not require knowledge of No.

produced global maps of fractional contributions of picoplankton, nanoplankton, and microplankton to total Chl on the basis of a global data set of HPLC pigments analyses.

4. Discussion

4.2. Algorithm Parameters Choice and Endogenous Sources of Uncertainty [33] The uncertainty budget for the PSD algorithm can be partitioned into two categories: endogenous (from the parameters of the PSD algorithm itself) and exogenous (from the data used to drive the algorithm as well as the functional form of the model, section 4.3). Endogenous uncertainties are those due to model assumptions such as the Mie parameter ranges (see Table 1) and have already been quantified via Monte Carlo simulations (sections 2.2, 3.2, and 3.3 and Figures 9 and 12). The parameters varied during the simulations are the bulk particle assemblage complex index of refraction and the maximum particle diameter considered Dmax (equation (2)). Natural variability of the complex index of refraction is to be expected in the pelagic ocean. The real index of refraction of the particle assemblage could change as the phytoplankton species composition changes and/or as species at different physiological status could have varying cell carbon content [Stramski, 1999]. The imaginary index of refraction is also expected to vary with species and physiological adaptations, as the chlorophyll to cellular carbon ratio changes [Behrenfeld et al., 2005]. Additionally, as the living cell contribution to the particulate assemblage varies, the resultant imaginary index of refraction will vary. Variations are thus naturally expected in both magnitude and spectral shape. [34] The parameters’ probability distribution for the Monte Carlo simulation was chosen to be representative of the pelagic ocean variability (Table 1). The real index of refraction was allowed to vary between 1.025 and 1.2, spanning reported values for various materials that ocean particles could be composed of – from organic matter with high water content to mineral particles [Aas, 1996; Wozniak and Stramski, 2004]. The resulting mean of this distribution, 1.069, is slightly higher than the accepted value of 1.05 for organic matter in the ocean [e.g., Stramski, 1999]. This accounts for possible contribution by fine mineral dust particles, which have high indices of refraction as compared to organic particles. Additionally, Coccolithophores, which sometimes are quite prevalent and possess calcite plates, can also significantly influence the index of refraction of the particle assemblage, with calcite having an index of refraction of 1.19 [Balch et al., 1996; Wozniak and Stramski, 2004]. [35] The imaginary index of refraction relative to seawater, n0, was chosen to vary only by magnitude (Table 1). The values of Babin et al. [2003] were adopted as default, which are data for a large phytoplankton species (Prorocentrum micans) from Ahn et al. [1992]. These values are the lowest found among several species given by Ahn et al. [1992], as P. micans is large. This is consistent with our goal to represent the entire particle assemblage (rather than only living pigmented cells), including detritus, which should have low n0 values. [36] The choice of the limits of integration of equation (2) was driven by the need to capture most of the theoretical backscattering signal under most Junge slopes. The minimal value was chosen to be fixed at 0.002 mm after Stramksi and

4.1. Ecosystem and Biogeochemistry Interpretation and Potential Applications [30] The global distribution of size-fractionated abundance and particle volume contribution (Figures 10 and 11) pertain to the entire particle load that has contributed to optical backscattering, not just living or organic matter. In order to provide a valid ecosystem and biogeochemical interpretation for these PSD observations, it must be assumed that living particles and their covariates (such as detrital particles) are the first-order driver of the particle assemblage. We stress that the algorithm presented here is sensitive to the entire backscattering particle assemblage, not just to phytoplankton, and thus we term our size fractions phytoplankton-sized particles to avoid confusion. Essentially this is similar to making a case I bio-optical assumption, stating that the ocean’s backscattering is driven to first order by living cells and their covariates [e.g., Smith and Baker, 1978; Sathyendranath, 2000; Siegel et al., 2005a]. [31] The emerging global spatial patterns presented here are consistent with the current state-of-the-art understanding of ocean ecosystems [e.g., Chisholm, 1992; Falkowski et al., 1998; Uitz et al., 2006]. The high correlation of log10 (Chl) with the volume concentration values of Figure 11a (R = 0.82) suggests that the primary driver of the particle load variability is indeed biological activity and its documented global scale patterns [e.g., Falkowski et al., 1998]. The volume concentration ratios of Figures 11b– 11d are thus interpreted as a reasonable proxy of percent biovolume due to each size class. Oligotrophic areas (the five major subtropical gyres of the Pacific, Atlantic and Indian Oceans) are dominated by picoplankton-sized particles. Such ecosystems support regenerated production and these areas have minimal sinking/export. Mid-sized nanopankton particles are pretty ubiquitous in much of the ocean, especially high-productivity eutrophic and mesotrophic transition zones. Microplankton-sized particles are found in appreciable abundances only in high-productivity areas (coastal areas, the Equatorial Upwelling Zones, and high latitudes). Those areas can support new production and export, especially in times of episodic blooms. Indeed, the correlation coefficients of Chl with the percent volume contribution by picoplankton-sized particles (R = 0.72), and by microplankton-sized particles (R = 0.76) are consistent with the observations above. [32] Picoplankton-sized particles, which are thought to be associated with the microbial loop and regenerative production, are numerically dominant everywhere in the ocean (Figure 11b). The number concentrations for picoplanktonsized particles vary little spatially, as compared to nanoplankton- and especially microplankton-sized particles (see section 3.3). This supports the idea that small picoplankton are ubiquitous and constantly in the background, whereas episodic blooms and increases in Chl are caused by large, microplankton cells [Falkowski et al., 1998; Uitz et al., 2006]. These general results are also qualitatively consistent with the results and conclusions of Uitz et al. [2006], who

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Figure 13. Cumulative contribution to the bulk particulate backscattering coefficient due to particles smaller than a given diameter (on the x axis). Mie modeling was used to generate the curves; the different curves correspond to the different Junge slopes of the PSD, progressing from the darkest (x = 2.5) to the lightest (x = 6) shade of gray with a step of 0.25. Key values of x and the 95% cumulative bbp(510) line are indicated. Default Mie parameters were used (as in Table 1, where Dmin is 0.002 mm), except for Dmax which was set to 63 mm (the mean of the distribution used in the Monte Carlo simulation (see Table 1)). Kiefer [1991]. Figure 13 illustrates the cumulative percent of bbp(510) contributed by particles smaller than a given diameter, as solved for by Mie modeling with the default parameters (Table 1). The lower limit of 0.002 mm is sufficiently low to capture all optically significant sources of backscattering, even for the higher PSD slopes. In fact, significant contribution to backscattering at that wavelength does not begin until about 0.005 mm. The range and distribution chosen for Dmax (Table 1) encompasses most phytoplankton [Vidussi et al., 2001; Le Que´re´ et al., 2005; Clavano et al., 2007]. Figure 13 illustrates that when the average Dmax = 63 mm is considered, and for PSD slopes greater than 3.5 (which are most common in the open ocean (see Figure 8a)), about 77% of bbp(510) is due to particles less than 10 mm in diameter, and about 94%, to particles less than 30 mm in diameter. As expected, for higher PSD slopes the small particles contribute significantly more. Therefore, the choice of the distribution of Dmax is appropriate for representing most living organisms and other particles that are optically significant for the backscattering signal.

4.3. Algorithm Assumptions and Exogenous Sources of Uncertainty [37] Exogenous algorithm uncertainties are due to the assumptions of a Junge-type PSD and Mie theory as well as other factors, such as the input data, and cannot be quantified easily. Exogenous uncertainty will be associated with the algorithm’s input remote sensing products, namely, the retrievals of bbp(l) and its spectral slope, and will have many sources (SeaWiFS LwN(l) estimates and the algorithm of Loisel et al. [2006]). The Loisel et al. [2006] algorithm was shown to perform well with synthetic [Lee, 2006] and in situ [Lubac and Loisel, 2007] bbp(l) data. A complete error analysis for the h retrieval is given by Loisel et al. [2006]. In summary, they identify several major sources of uncertainty for the h retrieval: (1) atmospheric correction, (2) sensitivity to the ratio of molecular to total scattering, (3) errors in the estimation of Kd(l) from LwN(l), and (4) the assumption of a power law model for the bbp(l) spectrum. While a quantitative assessment of the combined effects of all these sources is nontrivial, they estimate that the effects of source 2 are minimal, while the effects of source 3 are linear and likely largest in coastal areas. Figure 6b indicates

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Table 2. Algorithm Validation Using Coulter Counter in Situ Measurements Matched up With Monthly PSD SeaWiFS Imagerya Cruise/Data Set

Region Code

N

TAO EqPac 2003 [Behrenfeld and Boss, 2006] TAO EqPac 2007 [Dall’Olmo et al., 2009] NABE 2008 California area Antarctic Peninsula Ross Sea area Open North Pacific Japan area Indian Ocean

1 2 3 4 5 6 7 8 9

62 81 17 58 20 49 13 38 25

In Situ x (m ± s) 3.93 3.64 3.96 4.08 3.53 3.53 3.96 3.83 4.25

± ± ± ± ± ± ± ± ±

0.17 0.20 0.71 0.53 0.47 0.54 0.27 0.64 0.29

SeaWiFS x (m ± s) 3.96 4.08 3.47 3.87 3.77 4.17 3.81 3.52 4.16

± ± ± ± ± ± ± ± ±

0.38 0.26 0.04 0.48 0.27 0.82 0.48 0.13 0.34

In Situ No (m ± s) 15.72 15.85 16.38 16.10 15.98 15.86 15.83 16.27 15.68

± ± ± ± ± ± ± ± ±

0.20 0.16 0.39 0.44 0.29 0.37 0.14 0.35 0.15

SeaWiFS No (m ± s) 15.93 15.81 16.53 16.01 16.09 15.79 15.96 16.39 15.67

± ± ± ± ± ± ± ± ±

0.35 0.32 0.01 0.54 0.26 1.00 0.59 0.19 0.40

a Algorithm validation statistics include mean m and standard deviation s. The statistics are calculated over all stations in each cruise/data set. Compare to Figure 14, where the LAC daily imagery was used for the validation. The region code data are used in Figure 14 to indicate the source region of each matchup point. See section 4.4 for details. Statistics shown in italics indicate that the satellite and in situ means are not significantly different from each other, as indicated by a paired two-tailed t test at the 5% significance level. N, number of sample points; TAO, Tropical Atmosphere-Ocean; EqPac, equatorial Pacific; NABE, North Atlantic Bloom Experiment.

that the fit to a power law is also poorest in coastal and highproductivity areas (low PSD slopes), which Loisel et al. [2006] relate to possible absorption effects (see next paragraph). Note that Mie-modeled bbp(l) spectra also deviate from power law shapes for low PSD slopes (Figure 1a). [38] The development of the PSD algorithm is based solely on backscattering in the green bands which minimizes dependence on Chl or CDOM absorption. Thus to the extent possible, the effects of photoadaptation and CDOM contribution are avoided [Behrenfeld et al., 2005; Siegel et al., 2005a, 2005b]. Additionally, variability in the blue-tored absorption ratio of phytoplankton as well as accessory pigment absorption is another source of exogenous uncertainty that is minimized by using just the green wavelength to calculate the bbp(l) slope. Sensitivity analysis run by Loisel et al. [2006] also indicates that using the green bands only minimizes absorption effects on the h retrieval. [39] Another significant assumption of the model is the power law parameterization of the particle size distribution (equation (1)). In most cases, oceanic particle size distributions follow this simple model closely, resulting in its widespread use [e.g., Bader, 1970; Sheldon et al., 1972; Morel, 1973; Rodriguez and Mullin, 1986; Gin et al., 1999; Cavender-Bares et al., 2001; Boss et al., 2001a]. However, real PSDs do not always conform to a power law model, and the size range of applicability of such a model can vary. For example, events such as phytoplankton blooms can create peaks in the PSD [e.g., Sheldon et al., 1972; Jonasz and Zalewski, 1978; Jonasz, 1983]. Indeed, in situ data from the North Atlantic spring bloom from May 2008 (see section 4.4 and Table 2) often exhibit peaks (D 5 mm) superimposed on the first-order power law fit. Temporal and spatial averaging performed in the analysis here (27 km pixels averaged over a month) is likely to obfuscate the effects of transient departures from a power law distribution associated with monospecific blooms in pelagic regions. Indeed, alternative models have been proposed [Risovic, 1993; Jonasz and Fournier, 1996] although there are few empirical observations that support their application compared with the power law PSD. This PSD remains a good first-order model on large spatiotemporal scales [Jonasz and Fournier, 1996], especially given its theoretical underpinnings [Platt and Denman, 1977; Kiefer and Berwald, 1992]. [40] The algorithm presented here makes the assumption that the Junge-type PSD is valid over the entire diameter

range of optically significant particles. It is not clear to what extent the Junge-type distribution would hold and/or the Junge PSD parameters would change depending on what size range is considered. Submicron particles likely play an important role in backscattering [Stramski et al., 2004] (Figure 13), especially at larger PSD slopes; however all previous PSD measurements and fits to a Junge slope do not include the submicron particles due to lack of measurement capability [Sheldon and Parsons, 1967; Boss et al., 2001b; Risovic, 2002]. There is lack of agreement in the literature as to whether small particles exhibit even steeper slopes [Loisel et al., 2006], or whether the smallest particles are not as abundant as a power law PSD would predict [Risovic, 2002]. The sources of particle backscattering in the ocean and their relative contribution remain an open issue [Stramski et al., 2004]. There is recent evidence that nanoplankton-sized particles contribute significantly to particle backscattering [Dall’Olmo et al., 2009]. This may be due to wrongly assuming a Junge-type PSD across the entire relevant size spectrum [Risovic, 2002], or to violations of Mie theory assumptions such as sphericity and homogeneity of the particles (see below). Clearly, there is a need for improvements in measurement capabilities for sampling the PSD over the optically relevant particle size range. [41] The assumptions inherent in Mie theory also provide an exogenous source of uncertainty for the retrieved PSD parameters. Mie theory assumes that all particles are (1) spherical and (2) homogeneous, although these assumptions do not often hold [e.g., Jonasz, 1987; Kitchen and Zaneveld, 1992; Quirantes and Bernard, 2004; Clavano et al., 2007]. There are theoretical reasons to believe that backscattering is more sensitive to particle shape than forward scattering [Bohren and Huffman, 1983; Bohren and Singham, 1991]. Furthermore, the degree of nonsphericity increases with size [e.g., Jonasz, 1987; Clavano et al., 2007]. The effects of nonsphericity on backscattering are difficult to generalize [Bohren and Huffman, 1983, p. 401] since no methods are available to compute the backward VSF for such particles for some of the size ranges of interest [Clavano et al., 2007]. Clavano et al. [2007] conclude that backscattering of polydispersions of spheroids is likely to be 10s of percent higher than equal volume spheres, which can help close the bulk backscattering coefficient budget for the ocean [Stramski et al., 2004]. Regarding particle inhomogeneity, Kitchen and Zaneveld [1992] and Quirantes and Bernard [2004, 2006]

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conclude that that the assumption of a homogeneous sphere can significantly underestimate the backscattering efficiency of particles in the relevant size range, up to an order of magnitude. Spectral changes are also reported [Quirantes and Bernard, 2004, and references therein], which is key, as the LUT for PSD slope retrieval (Figure 2) is based on the spectral shape of the bbp(l) and absolute values of bbp(l) are not important (although they are for retrieval of No). Thus, errors in modeled backscattering associated with particle shape or homogeneity would only affect the PSD slope and the percent biovolume estimates if the spectral shape is also affected. The authors are unaware of a comprehensive study of the effects of particle shape and composition on the spectral shape of backscattering. [42] Larger particles are expected to deviate more from sphericity [Jonasz, 1987] and are more likely to deviate from the homogeneity assumption (e.g., by having a large vacuole with chloroplasts and the cell wall in the periphery). Since large particles are dominant in coastal and highproductivity areas, the exogenous uncertainty of the PSD model presented here is likely to be largest in these zones, which coincides with larger endogenous uncertainties as well (Figure 9). Additionally, the particle assemblage may be influenced by substantial minerogenic contributions in coastal areas, which adds uncertainty in the biogeochemical interpretation of the PSD. Other exogenous sources of uncertainty, such as uncertainty in remotely retrieved model input variables (h and bbp(440)) (Figure 6b) are also likely to be highest in high-productivity and coastal zones. In these situations it may be advisable to combine the algorithm presented here with alternative approaches for assessing PFT spatiotemporal distributions [e.g., Alvain et al., 2005; Uitz et al., 2006; Raitsos et al., 2008; Nair et al., 2008]. 4.4. Validation of the PSD Algorithm Retrievals [43] We compiled a global data set of near-surface, Coulter counter PSD observations in order to independently validate the PSD algorithm satellite retrievals. Since ocean Coulter counter PSD observations are scarce, the data set is small (N = 363). 17 additional samples, mostly in the California Current, were of suspect quality (exhibiting unusually high No values at relatively low SeaWiFS Chl) and were rejected. All in situ data were processed using a type I linear regression fit to equation (1) on bin width normalized and log transformed data in the 2 – 20 mm range. [44] Two kinds of validation matchups were performed. First, daily SeaWiFS LAC data were used, imposing a 3 h maximum time difference between the in situ observation and the satellite overpass [Bailey and Werdell, 2006], only N = 22 valid matchups remain out of the quality controlled data set of N = 363. Matched up LwN(l) values were constructed by taking the mean of valid pixels from the corresponding daily SeaWiFS LwN(l) image in a 3 3 pixel box centered on the in situ sampling point [Bailey and Werdell, 2006]. The matched up LwN(l) values were then used as input to the PSD algorithm to calculate the satellite estimates for x and No for the daily LAC matchups. Figure 14 summarizes the resulting LAC validation regressions. Given the very few data points available, the performance of the PSD algorithm is reasonable, with R2 = 0.210 for x and R2 = 0.256 for log10 (No).

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[45] The second kind of validation uses monthly imagery for the entire validation data set (N = 363). Satellite estimates for x and No for the monthly GAC matchups were constructed by taking the median of valid pixels from the corresponding monthly SeaWiFS PSD image in a 1° box containing the in situ sampling point. The correspondence among individual matchup points for the monthly validation is generally poor (not shown). For all regions, means for SeaWiFS and in situ measurements fall within one standard deviation of each other (Table 2). Interregional differences in No correspond between satellite and in situ observations very well, whereas interregional changes in x correspond poorly. One-way ANOVA indicates that interregion variability for both x and No is generally greater than withinregion variability. This, although not obvious from Table 2, supports the conclusion that the SeaWiFS PSD parameter retrievals correctly ‘‘follow’’ large-scale trends in the in situ data, particularly for No. More rigorous statistical comparison of the satellite versus in situ means, using paired twotailed t tests at the 5% significance level (Table 2), indicate that (1) for x the SeaWiFS and in situ regional means are statistically the same for the TAO EqPac 2003, Antarctic Peninsula, Open North Pacific, and Indian Ocean data sets and (2) for No the means are statistically the same for all regions, except the TAO EqPac 2003 and the Japan Sea regions. [46] In conclusion, validation results indicate that (1) individual daily LAC matchups for x and No are satisfactory, (2) a regional-scale validation using monthly satellite data is satisfactory for both parameters, and (3) No interregional trends are well captured by the SeaWiFS monthly retrievals. Given the independence of the in situ data sets and the SeaWiFS retrievals, as well as the various validation issues (see below), the correspondence between available in situ Coulter counter PSD observations and the SeaWiFS retrievals is generally satisfactory. [47] Validation of the presented PSD algorithm is challenging not only because the open ocean data sets are scarce. First, the in situ validation data sets have a narrower diameter range (2 –20 mm) than the diameter range mostly contributing to backscattering by solid, homogeneous spheres (Figure 13) and the range used in the model (Table 1). This mismatch in size range has an unknown influence on the resulting validation statistics but underscores the importance of making appropriate measurements of the PSD in situ. Second, monthly satellite observations are averaged over a very large temporal scale, and both monthly and daily data are averaged spatially (3.3 km box for the LAC or 111 km box for the monthly validation (at nadir)). In contrast, in situ data are point samples with scales of meters and minutes. Thus, variability in the PSD parameters on short temporal and small spatial scales can affect the matchups, even though offshore waters exhibit relative spatial homogeneity at LAC scales. Indeed, the daily LAC validation results of Figure 14 are much better than the corresponding monthly validation of individual matchups, illustrating the influence of mismatching scales of comparison. The in situ sample is a discrete sample at a depth close to the surface, whereas 90% of the satellite LwN(l) signal is due to the first attenuation depth (z(l) = 1/Kd(l)) [Gordon and McCluney, 1975; Zaneveld et al., 2005]. Thus, vertical variability in the PSD parameters, which is certainly to be

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Figure 14. Validation regressions for (a) the PSD slope, x, and for (b) log10(No). Daily LAC SeaWiFS imagery was used to construct matchups, using a 3 3 pixel square containing the in situ sampling point and a 3 h time window. The data are plotted using the region code from Table 2 as symbols. Note the large reduction in available matchups when daily LAC data are used to construct the validation matchups, as opposed to monthly data (from N = 363 in Table 2 to N = 22 here). As both the in situ and satellite estimates are expected to have uncertainties, type II (reduced major axis) linear regression was used. The dashed lines are the one-to-one lines, whereas the solid lines are the resultant regression lines through the data. The R2 and bias statistics are independent of the type of regression used. Bias is normalized by N = 22 and carries the units of the respective variable; positive bias means SeaWiFS overestimation.

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expected, is likely to affect the comparison. Finally, the Coulter counter is sensitive to particle volume, whereas Mie theory and measured backscattering are sensitive to particle effective cross-sectional area. Deviations from sphericity will cause these two types of assessments to differ [Karp-Boss et al., 2007]. [48] Discrepancies in the PSD matchup validation are expected on theoretical grounds even with perfect in situ data, for the reasons stated above. However, Coulter counter measurements are imperfect, introducing an additional level of uncertainty in the validation. Coincidence problems at small particle diameters and statistical bias at large diameters are possible sources of counting uncertainty [Sheldon and Parsons, 1967; Milligan and Kranck, 1991]. Boyd and Johnson [1995] conclude that two additional sources of error, the edge effect and the shape effect, can cause an error in diameter estimation of up to 14%. Errors in bin counts can result, giving rise to PSD slope uncertainties. The number of acceptable Coulter counter size bin channels thus drops to around 17 for realistic marine conditions that include nonspherical particles, which is a lot less than the actual number of channels in the in situ data. Absolute concentrations over the entire size range will be estimated relatively accurately, but the resultant PSD slope may be associated with high uncertainty. Milligan and Kranck [1991] warn that caution should be used when interpreting plankton size spectra obtained from raw water with a Coulter counter. This reported Coulter counter uncertainty analysis is consistent with the monthly (large temporal and spatial scale) validation results, which are worse for the slope x and better for the No parameter (Table 2). 4.5. Suggestions for Improvement and Future Work [49] The PSD algorithm presented here is a proof-ofconcept approach for the remote assessment of the parameters of a Junge-type PSD from satellite ocean color imagery. As such it is aimed at understanding large-scale processes. The apparent success demonstrated here is encouraging and will hopefully inspire further research into the nature of particles in the ocean and their optical backscattering on regional to global scales. There are various pathways that could lead to improvements to the approach presented here. First, a better parameterization of the PSD parameters using backscattering coefficients at all wavelengths needs to be explored. Nonspherical and nonhomogeneous particles may need to be considered, as well as multiple populations of particles with different characteristics (the present model assumes the same complex index of refraction for all particles) and different PSD parameters (e.g., a phytoplankton fraction and a mineral fraction). Other more complex PSD parameterizations could be explored as well, such as two-component PSDs given by Risovic [2002]. However, many of these improvements would require more degrees of freedom that must be accounted for in the inversion scheme (Figure 3). Further, these ideas all require improvements in our ability to make appropriate determinations of the PSD (and associated characteristics) in the field (see below). [50] Future improvements in the remote sensing retrieval of bbp(l) itself will enable improvements in the PSD algorithm. This will come as observational capabilities to measure bbp(l) have improved dramatically over the past

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decade or so [e.g., Maffione and Dana, 1997; Kostadinov et al., 2007]. Improved data inventories of open ocean bbp(l) observations will provide validation for this elusive parameter which is not available presently [Dall’Olmo et al., 2009]. [51] Finally, making appropriate in situ measurements of oceanic PSDs is absolutely required. As of today, there are no operational approaches available to measure the PSD over the optically relevant range of particles needed to constrain models of the PSD and scattering as well as to provide validation data for satellite data products. Measurement tools are also needed to characterize nonspherical and nonhomogeneous particles as well as mixtures of simple particle classes. A subset of these determinations is required to be a standard part of ocean color sampling suite in order to ameliorate the scarcity of high-quality data for validating PSD and similar algorithms. [52] The ability to assess the total particle volume in any given size class presents an unprecedented opportunity to estimate particulate carbon biomass from space on global scales. Recent studies have relied on constant scaling from the values of backscattering coefficient at one wavelength [Behrenfeld et al., 2005; Westberry et al., 2008]. They demonstrated the ability to estimate phytoplankton physiology from independent retrievals of Chl and living carbon biomass. The algorithm presented here could improve upon the work of Behrenfeld et al. [2005] and allow quantitative estimation of phytoplankton carbon (e.g., through allometric relationships) independent of Chl retrievals and without a constant scaling to bbp(440). Challenges remain, not the least of which is the need (1) to assess the applicability of a given allometric relationship on global scales and (2) to estimate the amount of living cells among the measured total particle assemblage (which is also a limitation of present field measurements). [53] The ability to use global ocean color data in order to partition particle volume in the pelagic ocean into sizes relevant to phytoplankton functional types is also important for advancing ocean biogeochemical models and elucidating the ocean’s role in the global carbon cycle. The derived products of the PSD algorithm can thus be used as input to biogeochemical models that rely on PFT parameterizations [Le Que´re´ et al., 2005]. As mentioned previously, this may be most fruitful in combination with other alternative remote sensing approaches for characterizing PFT occurrence [e.g., Alvain et al., 2005; Uitz et al., 2006]. [54] Acknowledgments. The authors would like to acknowledge NASA Ocean Biology and Biogeochemistry Program for their support of this work (grants NNG06GE77G, NNX08AG82G, and NNX08AF99A). We acknowledge Hubert Loisel for use of his code for bbp(l) retrieval; Emmanuel Boss and Wayne Slade for their optimized Mie code; Giorgio Dall’Olmo, Mike Behrenfeld, Emmanuel Boss, Greg Mitchell, Haili Wang, Toby Westberry, and M. J. Perry for providing us with validation data; and Aslak Grinsted for his graphing script used in Figure 2. We thank Sean Bailey (NASA GSFC) for providing LAC SeaWiFS matchup observations. We acknowledge the NASA SeaWiFS Project and GeoEye, Inc. (formerly ORBIMAGE) for the SeaWiFS data products. The authors also acknowledge Emmanuel Boss and an anonymous reviewer for providing useful comments that significantly improved the paper.

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T. S. Kostadinov, S. Maritorena, and D. A. Siegel, Institute for Computational Earth System Science, University of California, Santa Barbara, CA 93106-3060, USA. ([email protected]; stephane@icess. ucsb.edu; [email protected])

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