Abstract

An inverse algorithm is developed to retrieve hyperspectral absorption and backscattering coefficients from measurements of hyperspectral upwelling radiance and downwelling irradiance in vertically homogeneous waters. The forward model is the azimuthally averaged radiative transfer equation, efficiently solved by the EcoLight radiative transfer model, which includes the effects of inelastic scattering. Although this inversion problem is ill posed (the solution is ambiguous for retrieval of total scattering coefficients), unique and stable solutions can be found for absorption and backscattering coefficients. The inversion uses the attenuation coefficient at one wavelength to constrain the inversion, increasing the algorithm’s stability and accuracy. Two complementary methods, Monte Carlo simulation and first-order error propagation, are used to develop uncertainty estimates for the retrieved absorption and backscattering coefficients. The algorithm is tested using both simulated light fields from a chlorophyll-based case I bio-optical model and radiometric field data from the 2008 North Atlantic Bloom Experiment. The influence of uncertainty in the radiometric quantities and additional model parameters on the inverse solution for absorption and backscattering is studied using a Monte Carlo approach, and an uncertainty budget is developed for retrievals. All of the required radiometric and inherent optical property measurements can be made from power-limited autonomous platforms. We conclude that hyperspectral measurements of downwelling irradiance and upwelling radiance, with a single-wavelength measurement of attenuation, can be used to estimate hyperspectral absorption to an accuracy of ±0.01m1 and hyperspectral backscattering to an accuracy of ±0.0005m1 from 350 to 575 nm.

© 2013 Optical Society of America

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2012 (6)

M. Alkire, E. D’Asaro, C. Lee, M. Jane Perry, A. Gray, I. Cetinić, N. Briggs, E. Rehm, E. Kallin, J. Kaiser, and A. González-Posada, “Estimates of net community production and export using high-resolution, Lagrangian measurements of O2, NO3−, and POC through the evolution of a spring diatom bloom in the North Atlantic,” Deep Sea Res. I 64, 157–174 (2012).
[CrossRef]

X. Xing, A. Morel, H. Claustre, F. D’Ortenzio, and A. Poteau, “Combined processing and mutual interpretation of radiometry and fluorometry from autonomous profiling Bio-Argo floats: 2. Colored dissolved organic matter absorption retrieval,” J. Geophys. Res. 117, C04022 (2012).
[CrossRef]

H. Lavigne, F. D’Ortenzio, H. Claustre, and A. Poteau, “Towards a merged satellite and in situ fluorescence ocean chlorophyll product,” Biogeosciences 9, 2111–2125 (2012).
[CrossRef]

I. Cetinić, M. J. Perry, N. T. Briggs, E. Kallin, E. A. D’Asaro, and C. M. Lee, “Particulate organic carbon and inherent optical properties during 2008 North Atlantic Bloom Experiment,” J. Geophys. Res. 117, C06028 (2012).
[CrossRef]

W. Zhou, G. Wang, Z. Sun, W. Cao, Z. Xu, S. Hu, and J. Zhao, “Variations in the optical scattering properties of phytoplankton cultures,” Opt. Express 20, 11189–11206 (2012).
[CrossRef]

A. Mahadevan, E. D’Asaro, C. Lee, and M. J. Perry, “Eddy-driven stratification initiates North Atlantic spring phytoplankton blooms,” Science 337, 54–58 (2012).
[CrossRef]

2011 (4)

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

X. Xing, A. Morel, H. Claustre, D. Antoine, F. D’Ortenzio, A. Poteau, and A. Mignot, “Combined processing and mutual interpretation of radiometry and fluorimetry from autonomous profiling Bio-Argo floats: chlorophyll a retrieval,” J. Geophys. Res. 116, C06020 (2011).
[CrossRef]

W. J. Bagniewski, K. Fennel, M. J. Perry, and E. A. D’Asaro, “Optimizing models of the North Atlantic spring bloom using physical, chemical and bio-optical observations from a Lagrangian float,” Biogeosciences 8, 1291–1307 (2011).
[CrossRef]

E. Rehm, and N. J. McCormick, “Inherent optical property estimation in deep waters,” Opt. Express 19, 24986–25005(2011).
[CrossRef]

2010 (7)

Z. Lee, R. Arnone, C. Hu, P. J. Werdell, and B. Lubac, “Uncertainties of optical parameters and their propagations in an analytical ocean color inversion algorithm,” Appl. Opt. 49, 369–381 (2010).
[CrossRef]

V. Garg and I. Chaubey, “A computationally efficient inverse modelling approach of inherent optical properties for a remote sensing model,” Int. J. Remote Sens. 31, 4349–4371(2010).
[CrossRef]

S. Maritorena, O. H. F. d’Andon, A. Mangin, and D. A. Siegel, “Merged satellite ocean color data products using a bio-optical model: characteristics, benefits and issues,” Remote Sens. Environ. 114, 1791–1804 (2010).
[CrossRef]

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]

K. J. Voss, S. McLean, M. Lewis, C. Johnson, S. Flora, M. Feinholz, M. Yarbrough, C. Trees, M. Twardowski, and D. Clark, “An example crossover experiment for testing new vicarious calibration techniques for satellite ocean color radiometry,” J. Atmos. Oceanic Technol. 27, 1747–1759 (2010).
[CrossRef]

D. Creanor and A. Cunningham, “Origins of ambiguity in the inversion of remote sensing reflectance signals by spectral matching in optically complex shelf seas,” JEOS RP 5, 10081S (2010).
[CrossRef]

M. Williams and M. Eaton, “A probabilistic study of the influence of parameter uncertainty on solutions of the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 111, 696–707 (2010).
[CrossRef]

2009 (2)

H. R. Gordon, M. R. Lewis, S. D. McLean, M. S. Twardowski, S. A. Freeman, K. J. Voss, and G. C. Boynton, “Spectra of particulate backscattering in natural waters,” Opt. Express 17, 16192–16208 (2009).
[CrossRef]

K. S. Johnson, W. M. Berelson, E. S. Boss, Z. Chase, H. Claustre, S. R. Emerson, N. Gruber, A. Kortzinger, M. J. Perry, and S. C. Riser, “Observing biogeochemical cycles at global scales with profiling floats and gliders: prospects for a global array,” Oceanography 22, 216–225 (2009).
[CrossRef]

2008 (2)

E. Boss, D. Swift, L. Taylor, P. Brickley, R. Zaneveld, S. Riser, M. Perry, and P. Strutton, “Observations of pigment and particle distributions in the western North Atlantic from an autonomous float and ocean color satellite,” Limnol. Oceanogr. 53, 2112–2122 (2008).
[CrossRef]

W. Li, K. Stamnes, R. Spurr, and J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29, 5689–5698 (2008).
[CrossRef]

2007 (4)

R. Spurr, K. Stamnes, H. Eide, W. Li, K. Zhang, and J. Stamnes, “Simultaneous retrieval of aerosols and ocean properties: a classic inverse modeling approach. I. Analytic Jacobians from the linearized CAO-DISORT model,” J. Quant. Spectrosc. Radiat. Transfer 104, 428–449 (2007).
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S. W. Brown, S. J. Flora, M. E. Feinholz, M. A. Yarbrough, T. Houlihan, D. Peters, Y. S. Kim, J. L. Mueller, B. C. Johnson, and D. K. Clark, “The marine optical buoy (MOBY) radiometric calibration and uncertainty budget for ocean color satellite sensor vicarious calibration,” Proc. SPIE 6744, 67441M (2007).
[CrossRef]

M. Defoin-Platel and M. Chami, “How ambiguous is the inverse problem of ocean color in coastal waters?,” J. Geophys. Res. 112, C03004 (2007).
[CrossRef]

A. Morel, H. Claustre, D. Antoine, and B. Gentili, “Natural variability of bio-optical properties in Case 1 waters: attenuation and reflectance within the visible and near-UV spectral domains, as observed in South Pacific and Mediterranean waters,” Biogeosciences 4, 913–925 (2007).
[CrossRef]

2005 (4)

S. Maritorena and D. A. Siegel, “Consistent merging of satellite ocean color data sets using a bio-optical model,” Remote Sens. Environ. 94, 429–440 (2005).
[CrossRef]

C. D. Mobley, L. K. Sundman, C. O. Davis, J. H. Bowles, T. V. Downes, R. A. Leathers, M. J. Montes, W. P. Bissett, D. D. R. Kohler, and R. P. Reid, “Interpretation of hyperspectral remote-sensing imagery by spectrum matching and look-up tables,” Appl. Opt. 44, 3576–3592 (2005).
[CrossRef]

P. Wang, E. S. Boss, and C. Roesler, “Uncertainties of inherent optical properties obtained from semianalytical inversions of ocean color,” Appl. Opt. 44, 4074–4085 (2005).
[CrossRef]

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

2004 (5)

J. Worden, S. S. Kulawik, M. W. Shephard, S. A. Clough, H. Worden, K. Bowman, and A. Goldman, “Predicted errors of tropospheric emission spectrometer nadir retrievals from spectral window selection,” J. Geophys. Res. 109, D09308 (2004).
[CrossRef]

G. Chang, K. Mahoney, A. Briggs-Whitmire, D. Kohler, C. Mobley, M. Lewis, M. A. Moline, E. Boss, M. Kim, and W. Philpot, “The new age of hyperspectral oceanography,” Oceanography 17, 22–29 (2004).
[CrossRef]

M. Sydor, R. W. Gould, R. A. Arnone, V. I. Haltrin, and W. Goode, “Uniqueness in remote sensing of the inherent optical properties of ocean water,” Appl. Opt. 43, 2156–2162 (2004).
[CrossRef]

C. A. Brown, Y. Huot, M. J. Purcell, J. J. Cullen, and M. R. Lewis, “Mapping coastal optical and biogeochemical variability using an autonomous underwater vehicle and a new bio-optical inversion algorithm,” Limnol. Oceanogr. Methods 2, 262–281 (2004).
[CrossRef]

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

2003 (1)

D. McKee, A. Cunningham, and S. Craig, “Estimation of absorption and backscattering coefficients from in situ radiometric measurements: theory and validation in case II waters,” Appl. Opt. 42, 2804–2810 (2003).
[CrossRef]

2002 (4)

Z. 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).
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H. R. Gordon, “Inverse methods in hydrologic optics,” Oceanologia 44, 9–58 (2002).

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, 404–417 (2002).
[CrossRef]

C. D. Mobley, L. K. Sundman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41, 1035–1050 (2002).
[CrossRef]

2001 (1)

E. Boss, M. S. Twardowski, and S. Herring, “Shape of the particulate beam attenuation spectrum and its inversion to obtain the shape of the particulate size distribution,” Appl. Opt. 40, 4885–4893 (2001).
[CrossRef]

2000 (4)

J. H. Smart, “World-Wide Ocean Optics Database (WOOD),” Oceanography 13, 70–74 (2000).
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M. Stramska, D. Stramski, B. G. Mitchell, and C. D. Mobley, “Estimation of the absorption and backscattering coefficients from in-water radiometric measurements,” Limnol. Oceanogr. 45, 628–641 (2000).
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H. Loisel and D. Stramski, “Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering,” Appl. Opt. 39, 3001–3011 (2000).
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G. C. Boynton and H. R. Gordon, “Irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: Raman-scattering effects,” Appl. Opt. 39, 3012–3022 (2000).
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1999 (1)

A. H. Barnard, J. R. V. Zaneveld, and W. S. Pegau, “In situ determination of the remotely sensed reflectance and the absorption coefficient: closure and inversion,” Appl. Opt. 38, 5108–5117 (1999).
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1998 (1)

H. R. Gordon and G. C. Boynton, “Radiance–irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: vertically stratified water bodies,” Appl. Opt. 37, 3886–3896 (1998).
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1997 (4)

S. A. Garver and D. A. Siegel, “Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation 1. Time series from the Sargasso Sea,” J. Geophys. Res. 102, 18607–18625 (1997).
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R. A. Leathers, and N. J. McCormick, “Ocean inherent optical property estimation from irradiances,” Appl. Opt. 36, 8685–8698 (1997).
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H. R. Gordon and G. C. Boynton, “Radiance-irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: homogeneous waters,” Appl. Opt. 36, 2636–2641 (1997).
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W. S. Pegau, D. Gray, and J. R. V. Zaneveld, “Absorption and attenuation of visible and near-infrared light in water: dependence on temperature and salinity,” Appl. Opt. 36, 6035–6046 (1997).
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1996 (1)

R. J. Geider, H. L. MacIntyre, and T. M. Kana, “A dynamic model of photoadaptation in phytoplankton,” Limnol. Oceanogr. 41, 1–15 (1996).
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1995 (1)

C. S. Roesler, and M. J. Perry, “In situ phytoplankton absorption, fluorescence emission, and particulate backscattering spectra determined from reflectance,” J. Geophys. Res. 100, 13279–13294 (1995).
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1994 (3)

Z. Tao, N. J. McCormick, and R. Sanchez, “Ocean source and optical property estimation from explicit and implicit algorithms,” Appl. Opt. 33, 3265–3275 (1994).
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J. R. V. Zaneveld, J. C. Kitchen, and C. C. Moore, “Scattering error correction of reflecting-tube absorption meters,” Proc. SPIE 2258, 44–55 (1994).
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G. R. Fournier, and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
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1993 (1)

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
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1992 (1)

N. J. McCormick, “Inverse radiative transfer problems: a review,” Nucl. Sci. Eng. 112, 185–198 (1992).

1990 (1)

W. W. Gregg and K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
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1980 (1)

P. Diehl, and H. Haardt, “Measurement of the spectral attenuation to support biological research in a ‘plankton tube’ experiment,” Oceanol. Acta 3, 89–96 (1980).

1975 (1)

H. R. Gordon, O. B. Brown, and M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14, 417–427 (1975).
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1902 (1)

J. Hadamard, “Sur les problemes aux dérivées partielles et leur signification physique,” Princeton Univ. Bull. 13, 49–52 (1902).

Alkire, M.

M. Alkire, E. D’Asaro, C. Lee, M. Jane Perry, A. Gray, I. Cetinić, N. Briggs, E. Rehm, E. Kallin, J. Kaiser, and A. González-Posada, “Estimates of net community production and export using high-resolution, Lagrangian measurements of O2, NO3−, and POC through the evolution of a spring diatom bloom in the North Atlantic,” Deep Sea Res. I 64, 157–174 (2012).
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Antoine, D.

X. Xing, A. Morel, H. Claustre, D. Antoine, F. D’Ortenzio, A. Poteau, and A. Mignot, “Combined processing and mutual interpretation of radiometry and fluorimetry from autonomous profiling Bio-Argo floats: chlorophyll a retrieval,” J. Geophys. Res. 116, C06020 (2011).
[CrossRef]

A. Morel, H. Claustre, D. Antoine, and B. Gentili, “Natural variability of bio-optical properties in Case 1 waters: attenuation and reflectance within the visible and near-UV spectral domains, as observed in South Pacific and Mediterranean waters,” Biogeosciences 4, 913–925 (2007).
[CrossRef]

Arnone, R.

Z. Lee, R. Arnone, C. Hu, P. J. Werdell, and B. Lubac, “Uncertainties of optical parameters and their propagations in an analytical ocean color inversion algorithm,” Appl. Opt. 49, 369–381 (2010).
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Arnone, R. A.

M. Sydor, R. W. Gould, R. A. Arnone, V. I. Haltrin, and W. Goode, “Uniqueness in remote sensing of the inherent optical properties of ocean water,” Appl. Opt. 43, 2156–2162 (2004).
[CrossRef]

Z. 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).
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Aster, R. C.

R. C. Aster, B. Borchers, and C. H. Thurber, Parameter Estimation and Inverse Problems, 2nd ed. (Academic, 2012).

Austin, R. W.

J. L. Mueller, C. Pietras, S. B. Hooker, R. W. Austin, M. Miller, K. D. Knobelspiesse, R. Frouin, B. Holben, and K. Voss, “Ocean optics protocols for satellite ocean color sensor validation, Revision 4, Volume II: instrument specifications, characterization and calibration,” NASA Tech. Memo. NASA/TM-2003-21621 (NASA, 2003).

Bagniewski, W. J.

W. J. Bagniewski, K. Fennel, M. J. Perry, and E. A. D’Asaro, “Optimizing models of the North Atlantic spring bloom using physical, chemical and bio-optical observations from a Lagrangian float,” Biogeosciences 8, 1291–1307 (2011).
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Bailey, S. W.

P. J. Werdell, and S. W. Bailey, “An improved in-situ bio-optical data set for ocean color algorithm development and satellite data product validation,” Remote Sens. Environ. 98, 122–140 (2005).
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P. J. Werdell, G. S. Fargion, C. R. McClain, and S. W. Bailey, “The SeaWiFS bio-optical archive and storage system (SeaBASS): current architecture and implementation,” NASA/TM-2002-211617 (NASA Goddard Space Flight Center, 2002).

Barnard, A. H.

A. H. Barnard, J. R. V. Zaneveld, and W. S. Pegau, “In situ determination of the remotely sensed reflectance and the absorption coefficient: closure and inversion,” Appl. Opt. 38, 5108–5117 (1999).
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Baum, B. A.

B. A. Baum and S. Platnick, “Introduction to MODIS cloud products,” in Earth Science Satellite Remote Sensing, J. J. Qu, W. Gao, M. Kafatos, R. E. Murphy, and V. Salomonson, eds. Vol. 1, Science and Instruments (Springer-Verlag, 2006), pp. 74–91.

Berelson, W. M.

K. S. Johnson, W. M. Berelson, E. S. Boss, Z. Chase, H. Claustre, S. R. Emerson, N. Gruber, A. Kortzinger, M. J. Perry, and S. C. Riser, “Observing biogeochemical cycles at global scales with profiling floats and gliders: prospects for a global array,” Oceanography 22, 216–225 (2009).
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Berthon, J.

H. Claustre, J. Bishop, E. Boss, B. Stewart, J. Berthon, C. Coatanoan, K. Johnson, A. Lotiker, O. Ulloa, and M. Perry, “Bio-optical profiling floats as new observational tools for biogeochemical and ecosystem studies,” in Proceedings of the OceanObs ’09: Sustained Ocean Observations and Information for Society Conference, J. Hall, D. E. Harrison, and D. Stammer, eds. (ESA, 2010), ESA publication WPP-306, pp. 1–7.

Bishop, J.

H. Claustre, J. Bishop, E. Boss, B. Stewart, J. Berthon, C. Coatanoan, K. Johnson, A. Lotiker, O. Ulloa, and M. Perry, “Bio-optical profiling floats as new observational tools for biogeochemical and ecosystem studies,” in Proceedings of the OceanObs ’09: Sustained Ocean Observations and Information for Society Conference, J. Hall, D. E. Harrison, and D. Stammer, eds. (ESA, 2010), ESA publication WPP-306, pp. 1–7.

Bissett, W. P.

C. D. Mobley, L. K. Sundman, C. O. Davis, J. H. Bowles, T. V. Downes, R. A. Leathers, M. J. Montes, W. P. Bissett, D. D. R. Kohler, and R. P. Reid, “Interpretation of hyperspectral remote-sensing imagery by spectrum matching and look-up tables,” Appl. Opt. 44, 3576–3592 (2005).
[CrossRef]

Bogucki, D.

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
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Borchers, B.

R. C. Aster, B. Borchers, and C. H. Thurber, Parameter Estimation and Inverse Problems, 2nd ed. (Academic, 2012).

Boss, E.

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).
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E. Boss, D. Swift, L. Taylor, P. Brickley, R. Zaneveld, S. Riser, M. Perry, and P. Strutton, “Observations of pigment and particle distributions in the western North Atlantic from an autonomous float and ocean color satellite,” Limnol. Oceanogr. 53, 2112–2122 (2008).
[CrossRef]

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

G. Chang, K. Mahoney, A. Briggs-Whitmire, D. Kohler, C. Mobley, M. Lewis, M. A. Moline, E. Boss, M. Kim, and W. Philpot, “The new age of hyperspectral oceanography,” Oceanography 17, 22–29 (2004).
[CrossRef]

C. D. Mobley, L. K. Sundman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41, 1035–1050 (2002).
[CrossRef]

E. Boss, M. S. Twardowski, and S. Herring, “Shape of the particulate beam attenuation spectrum and its inversion to obtain the shape of the particulate size distribution,” Appl. Opt. 40, 4885–4893 (2001).
[CrossRef]

H. Claustre, J. Bishop, E. Boss, B. Stewart, J. Berthon, C. Coatanoan, K. Johnson, A. Lotiker, O. Ulloa, and M. Perry, “Bio-optical profiling floats as new observational tools for biogeochemical and ecosystem studies,” in Proceedings of the OceanObs ’09: Sustained Ocean Observations and Information for Society Conference, J. Hall, D. E. Harrison, and D. Stammer, eds. (ESA, 2010), ESA publication WPP-306, pp. 1–7.

Boss, E. S.

K. S. Johnson, W. M. Berelson, E. S. Boss, Z. Chase, H. Claustre, S. R. Emerson, N. Gruber, A. Kortzinger, M. J. Perry, and S. C. Riser, “Observing biogeochemical cycles at global scales with profiling floats and gliders: prospects for a global array,” Oceanography 22, 216–225 (2009).
[CrossRef]

P. Wang, E. S. Boss, and C. Roesler, “Uncertainties of inherent optical properties obtained from semianalytical inversions of ocean color,” Appl. Opt. 44, 4074–4085 (2005).
[CrossRef]

Bowles, J. H.

C. D. Mobley, L. K. Sundman, C. O. Davis, J. H. Bowles, T. V. Downes, R. A. Leathers, M. J. Montes, W. P. Bissett, D. D. R. Kohler, and R. P. Reid, “Interpretation of hyperspectral remote-sensing imagery by spectrum matching and look-up tables,” Appl. Opt. 44, 3576–3592 (2005).
[CrossRef]

Bowman, K.

J. Worden, S. S. Kulawik, M. W. Shephard, S. A. Clough, H. Worden, K. Bowman, and A. Goldman, “Predicted errors of tropospheric emission spectrometer nadir retrievals from spectral window selection,” J. Geophys. Res. 109, D09308 (2004).
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Boynton, G. C.

H. R. Gordon, M. R. Lewis, S. D. McLean, M. S. Twardowski, S. A. Freeman, K. J. Voss, and G. C. Boynton, “Spectra of particulate backscattering in natural waters,” Opt. Express 17, 16192–16208 (2009).
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G. C. Boynton and H. R. Gordon, “Irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: Raman-scattering effects,” Appl. Opt. 39, 3012–3022 (2000).
[CrossRef]

H. R. Gordon and G. C. Boynton, “Radiance–irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: vertically stratified water bodies,” Appl. Opt. 37, 3886–3896 (1998).
[CrossRef]

H. R. Gordon and G. C. Boynton, “Radiance-irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: homogeneous waters,” Appl. Opt. 36, 2636–2641 (1997).
[CrossRef]

Brickley, P.

E. Boss, D. Swift, L. Taylor, P. Brickley, R. Zaneveld, S. Riser, M. Perry, and P. Strutton, “Observations of pigment and particle distributions in the western North Atlantic from an autonomous float and ocean color satellite,” Limnol. Oceanogr. 53, 2112–2122 (2008).
[CrossRef]

Briggs, N.

M. Alkire, E. D’Asaro, C. Lee, M. Jane Perry, A. Gray, I. Cetinić, N. Briggs, E. Rehm, E. Kallin, J. Kaiser, and A. González-Posada, “Estimates of net community production and export using high-resolution, Lagrangian measurements of O2, NO3−, and POC through the evolution of a spring diatom bloom in the North Atlantic,” Deep Sea Res. I 64, 157–174 (2012).
[CrossRef]

E. A. D’Asaro, C. Lee, M. Perry, K. Fennel, E. Rehm, A. Gray, N. Briggs, and K. Gudmundsson, “The 2008 North Atlantic Spring Bloom Experiment I: overview and strategy,” EOS89(53), Fall Meeting Supplement, abstract OS24A-08 (2008).

N. Briggs, “The 2008 North Atlantic Bloom Experiment calibration report #7: intercalibration of the backscatter sensors,” (Biological and Chemical Oceanography Data Management Office, 2011), retrieved 21 July 2012, http://data.bco-dmo.org/NAB08/Backscatter_Calibration-NAB08.pdf .

Briggs, N. T.

I. Cetinić, M. J. Perry, N. T. Briggs, E. Kallin, E. A. D’Asaro, and C. M. Lee, “Particulate organic carbon and inherent optical properties during 2008 North Atlantic Bloom Experiment,” J. Geophys. Res. 117, C06028 (2012).
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Briggs-Whitmire, A.

G. Chang, K. Mahoney, A. Briggs-Whitmire, D. Kohler, C. Mobley, M. Lewis, M. A. Moline, E. Boss, M. Kim, and W. Philpot, “The new age of hyperspectral oceanography,” Oceanography 17, 22–29 (2004).
[CrossRef]

Brown, C. A.

C. A. Brown, Y. Huot, M. J. Purcell, J. J. Cullen, and M. R. Lewis, “Mapping coastal optical and biogeochemical variability using an autonomous underwater vehicle and a new bio-optical inversion algorithm,” Limnol. Oceanogr. Methods 2, 262–281 (2004).
[CrossRef]

Brown, O. B.

H. R. Gordon, O. B. Brown, and M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14, 417–427 (1975).
[CrossRef]

Brown, S. W.

S. W. Brown, S. J. Flora, M. E. Feinholz, M. A. Yarbrough, T. Houlihan, D. Peters, Y. S. Kim, J. L. Mueller, B. C. Johnson, and D. K. Clark, “The marine optical buoy (MOBY) radiometric calibration and uncertainty budget for ocean color satellite sensor vicarious calibration,” Proc. SPIE 6744, 67441M (2007).
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Cao, W.

W. Zhou, G. Wang, Z. Sun, W. Cao, Z. Xu, S. Hu, and J. Zhao, “Variations in the optical scattering properties of phytoplankton cultures,” Opt. Express 20, 11189–11206 (2012).
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Carder, K. L.

Z. 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]

W. W. Gregg and K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
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Center, G. S. F.

S. B. Hooker, C. R. McClain, A. Mannino, and G. S. F. Center, “NASA strategic planning document: a comprehensive plan for the long-term calibration and validation of oceanic biogeochemical satellite data” (NASA Goddard Space Flight Center, 2007).

Cetinic, I.

I. Cetinić, M. J. Perry, N. T. Briggs, E. Kallin, E. A. D’Asaro, and C. M. Lee, “Particulate organic carbon and inherent optical properties during 2008 North Atlantic Bloom Experiment,” J. Geophys. Res. 117, C06028 (2012).
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M. Alkire, E. D’Asaro, C. Lee, M. Jane Perry, A. Gray, I. Cetinić, N. Briggs, E. Rehm, E. Kallin, J. Kaiser, and A. González-Posada, “Estimates of net community production and export using high-resolution, Lagrangian measurements of O2, NO3−, and POC through the evolution of a spring diatom bloom in the North Atlantic,” Deep Sea Res. I 64, 157–174 (2012).
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E. Kallin, I. Cetinić, M. J. Perry, and M. Sauer, “Laboratory_analysis_report-NAB08,” (Biological and Chemical Oceanography Data Management Office, 2011), retrieved 21 July 2012, http://osprey.bcodmo.org/dataset.cfm?id=13820&flag=view .

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M. Defoin-Platel and M. Chami, “How ambiguous is the inverse problem of ocean color in coastal waters?,” J. Geophys. Res. 112, C03004 (2007).
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Z. Li, M. Cribb, F. Chang, and A. Trishchenko, “Validation of MODIS-retrieved cloud fractions using whole sky imager measurements at the three ARM sites,” presented at Proceedings of the 14th Atmospheric Radiation Measurement (ARM) Science Team Meeting, Albuquerque, New Mexico, 22–26 March 2004.

Chang, G.

G. Chang, K. Mahoney, A. Briggs-Whitmire, D. Kohler, C. Mobley, M. Lewis, M. A. Moline, E. Boss, M. Kim, and W. Philpot, “The new age of hyperspectral oceanography,” Oceanography 17, 22–29 (2004).
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Chase, Z.

K. S. Johnson, W. M. Berelson, E. S. Boss, Z. Chase, H. Claustre, S. R. Emerson, N. Gruber, A. Kortzinger, M. J. Perry, and S. C. Riser, “Observing biogeochemical cycles at global scales with profiling floats and gliders: prospects for a global array,” Oceanography 22, 216–225 (2009).
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V. Garg and I. Chaubey, “A computationally efficient inverse modelling approach of inherent optical properties for a remote sensing model,” Int. J. Remote Sens. 31, 4349–4371(2010).
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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, 404–417 (2002).
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Clark, D.

K. J. Voss, S. McLean, M. Lewis, C. Johnson, S. Flora, M. Feinholz, M. Yarbrough, C. Trees, M. Twardowski, and D. Clark, “An example crossover experiment for testing new vicarious calibration techniques for satellite ocean color radiometry,” J. Atmos. Oceanic Technol. 27, 1747–1759 (2010).
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S. W. Brown, S. J. Flora, M. E. Feinholz, M. A. Yarbrough, T. Houlihan, D. Peters, Y. S. Kim, J. L. Mueller, B. C. Johnson, and D. K. Clark, “The marine optical buoy (MOBY) radiometric calibration and uncertainty budget for ocean color satellite sensor vicarious calibration,” Proc. SPIE 6744, 67441M (2007).
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J. C. Clarke, “Modelling uncertainty: A primer,” Tech. Rep. 2161, (University of Oxford Department of Engineering Science, 1998), pp. 1–21.

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X. Xing, A. Morel, H. Claustre, F. D’Ortenzio, and A. Poteau, “Combined processing and mutual interpretation of radiometry and fluorometry from autonomous profiling Bio-Argo floats: 2. Colored dissolved organic matter absorption retrieval,” J. Geophys. Res. 117, C04022 (2012).
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H. Lavigne, F. D’Ortenzio, H. Claustre, and A. Poteau, “Towards a merged satellite and in situ fluorescence ocean chlorophyll product,” Biogeosciences 9, 2111–2125 (2012).
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R. J. Geider, H. L. MacIntyre, and T. M. Kana, “A dynamic model of photoadaptation in phytoplankton,” Limnol. Oceanogr. 41, 1–15 (1996).
[CrossRef]

Karp-Boss, L.

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]

Kattawar, G. W.

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
[CrossRef]

Kim, M.

G. Chang, K. Mahoney, A. Briggs-Whitmire, D. Kohler, C. Mobley, M. Lewis, M. A. Moline, E. Boss, M. Kim, and W. Philpot, “The new age of hyperspectral oceanography,” Oceanography 17, 22–29 (2004).
[CrossRef]

Kim, Y. S.

S. W. Brown, S. J. Flora, M. E. Feinholz, M. A. Yarbrough, T. Houlihan, D. Peters, Y. S. Kim, J. L. Mueller, B. C. Johnson, and D. K. Clark, “The marine optical buoy (MOBY) radiometric calibration and uncertainty budget for ocean color satellite sensor vicarious calibration,” Proc. SPIE 6744, 67441M (2007).
[CrossRef]

Kitchen, J. C.

J. R. V. Zaneveld, J. C. Kitchen, and C. C. Moore, “Scattering error correction of reflecting-tube absorption meters,” Proc. SPIE 2258, 44–55 (1994).
[CrossRef]

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J. L. Mueller, C. Pietras, S. B. Hooker, R. W. Austin, M. Miller, K. D. Knobelspiesse, R. Frouin, B. Holben, and K. Voss, “Ocean optics protocols for satellite ocean color sensor validation, Revision 4, Volume II: instrument specifications, characterization and calibration,” NASA Tech. Memo. NASA/TM-2003-21621 (NASA, 2003).

Kohler, D.

G. Chang, K. Mahoney, A. Briggs-Whitmire, D. Kohler, C. Mobley, M. Lewis, M. A. Moline, E. Boss, M. Kim, and W. Philpot, “The new age of hyperspectral oceanography,” Oceanography 17, 22–29 (2004).
[CrossRef]

Kohler, D. D. R.

C. D. Mobley, L. K. Sundman, C. O. Davis, J. H. Bowles, T. V. Downes, R. A. Leathers, M. J. Montes, W. P. Bissett, D. D. R. Kohler, and R. P. Reid, “Interpretation of hyperspectral remote-sensing imagery by spectrum matching and look-up tables,” Appl. Opt. 44, 3576–3592 (2005).
[CrossRef]

Kortzinger, A.

K. S. Johnson, W. M. Berelson, E. S. Boss, Z. Chase, H. Claustre, S. R. Emerson, N. Gruber, A. Kortzinger, M. J. Perry, and S. C. Riser, “Observing biogeochemical cycles at global scales with profiling floats and gliders: prospects for a global array,” Oceanography 22, 216–225 (2009).
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J. Worden, S. S. Kulawik, M. W. Shephard, S. A. Clough, H. Worden, K. Bowman, and A. Goldman, “Predicted errors of tropospheric emission spectrometer nadir retrievals from spectral window selection,” J. Geophys. Res. 109, D09308 (2004).
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H. Lavigne, F. D’Ortenzio, H. Claustre, and A. Poteau, “Towards a merged satellite and in situ fluorescence ocean chlorophyll product,” Biogeosciences 9, 2111–2125 (2012).
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Leathers, R. A.

C. D. Mobley, L. K. Sundman, C. O. Davis, J. H. Bowles, T. V. Downes, R. A. Leathers, M. J. Montes, W. P. Bissett, D. D. R. Kohler, and R. P. Reid, “Interpretation of hyperspectral remote-sensing imagery by spectrum matching and look-up tables,” Appl. Opt. 44, 3576–3592 (2005).
[CrossRef]

R. A. Leathers, and N. J. McCormick, “Ocean inherent optical property estimation from irradiances,” Appl. Opt. 36, 8685–8698 (1997).
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A. Mahadevan, E. D’Asaro, C. Lee, and M. J. Perry, “Eddy-driven stratification initiates North Atlantic spring phytoplankton blooms,” Science 337, 54–58 (2012).
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M. Alkire, E. D’Asaro, C. Lee, M. Jane Perry, A. Gray, I. Cetinić, N. Briggs, E. Rehm, E. Kallin, J. Kaiser, and A. González-Posada, “Estimates of net community production and export using high-resolution, Lagrangian measurements of O2, NO3−, and POC through the evolution of a spring diatom bloom in the North Atlantic,” Deep Sea Res. I 64, 157–174 (2012).
[CrossRef]

E. A. D’Asaro, C. Lee, M. Perry, K. Fennel, E. Rehm, A. Gray, N. Briggs, and K. Gudmundsson, “The 2008 North Atlantic Spring Bloom Experiment I: overview and strategy,” EOS89(53), Fall Meeting Supplement, abstract OS24A-08 (2008).

Lee, C. M.

I. Cetinić, M. J. Perry, N. T. Briggs, E. Kallin, E. A. D’Asaro, and C. M. Lee, “Particulate organic carbon and inherent optical properties during 2008 North Atlantic Bloom Experiment,” J. Geophys. Res. 117, C06028 (2012).
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Lee, Z.

Z. Lee, R. Arnone, C. Hu, P. J. Werdell, and B. Lubac, “Uncertainties of optical parameters and their propagations in an analytical ocean color inversion algorithm,” Appl. Opt. 49, 369–381 (2010).
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Z. 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).
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K. J. Voss, S. McLean, M. Lewis, C. Johnson, S. Flora, M. Feinholz, M. Yarbrough, C. Trees, M. Twardowski, and D. Clark, “An example crossover experiment for testing new vicarious calibration techniques for satellite ocean color radiometry,” J. Atmos. Oceanic Technol. 27, 1747–1759 (2010).
[CrossRef]

G. Chang, K. Mahoney, A. Briggs-Whitmire, D. Kohler, C. Mobley, M. Lewis, M. A. Moline, E. Boss, M. Kim, and W. Philpot, “The new age of hyperspectral oceanography,” Oceanography 17, 22–29 (2004).
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Lewis, M. R.

H. R. Gordon, M. R. Lewis, S. D. McLean, M. S. Twardowski, S. A. Freeman, K. J. Voss, and G. C. Boynton, “Spectra of particulate backscattering in natural waters,” Opt. Express 17, 16192–16208 (2009).
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C. A. Brown, Y. Huot, M. J. Purcell, J. J. Cullen, and M. R. Lewis, “Mapping coastal optical and biogeochemical variability using an autonomous underwater vehicle and a new bio-optical inversion algorithm,” Limnol. Oceanogr. Methods 2, 262–281 (2004).
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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, 404–417 (2002).
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L. Li, H. Fukushima, R. Frouin, B. G. Mitchell, M.-X. He, I. Uno, T. Takamura, and S. Ohta, “Influence of submicron absorptive aerosol on Sea-Viewing Wide Field-of-View Sensor (SeaWiFS)-derived marine reflectance during Aerosol Characterization Experiment (ACE)-Asia,” J. Geophys. Res.108, 4472 (2003).
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W. Li, K. Stamnes, R. Spurr, and J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29, 5689–5698 (2008).
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R. Spurr, K. Stamnes, H. Eide, W. Li, K. Zhang, and J. Stamnes, “Simultaneous retrieval of aerosols and ocean properties: a classic inverse modeling approach. I. Analytic Jacobians from the linearized CAO-DISORT model,” J. Quant. Spectrosc. Radiat. Transfer 104, 428–449 (2007).
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R. Spurr, K. Stamnes, H. Eide, W. Li, K. Zhang, and J. Stamnes, “Error analysis for simultaneous retrieval of marine and aerosol properties from SeaWiFS,” presented at Proceedings of Ocean Optics XVIII, Montreal, Canada, 9–13 October 2006.

Li, Z.

Z. Li, M. Cribb, F. Chang, and A. Trishchenko, “Validation of MODIS-retrieved cloud fractions using whole sky imager measurements at the three ARM sites,” presented at Proceedings of the 14th Atmospheric Radiation Measurement (ARM) Science Team Meeting, Albuquerque, New Mexico, 22–26 March 2004.

Loisel, H.

H. Loisel and D. Stramski, “Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering,” Appl. Opt. 39, 3001–3011 (2000).
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H. Claustre, J. Bishop, E. Boss, B. Stewart, J. Berthon, C. Coatanoan, K. Johnson, A. Lotiker, O. Ulloa, and M. Perry, “Bio-optical profiling floats as new observational tools for biogeochemical and ecosystem studies,” in Proceedings of the OceanObs ’09: Sustained Ocean Observations and Information for Society Conference, J. Hall, D. E. Harrison, and D. Stammer, eds. (ESA, 2010), ESA publication WPP-306, pp. 1–7.

Lubac, B.

Z. Lee, R. Arnone, C. Hu, P. J. Werdell, and B. Lubac, “Uncertainties of optical parameters and their propagations in an analytical ocean color inversion algorithm,” Appl. Opt. 49, 369–381 (2010).
[CrossRef]

MacIntyre, H. L.

R. J. Geider, H. L. MacIntyre, and T. M. Kana, “A dynamic model of photoadaptation in phytoplankton,” Limnol. Oceanogr. 41, 1–15 (1996).
[CrossRef]

Mahadevan, A.

A. Mahadevan, E. D’Asaro, C. Lee, and M. J. Perry, “Eddy-driven stratification initiates North Atlantic spring phytoplankton blooms,” Science 337, 54–58 (2012).
[CrossRef]

Mahoney, K.

G. Chang, K. Mahoney, A. Briggs-Whitmire, D. Kohler, C. Mobley, M. Lewis, M. A. Moline, E. Boss, M. Kim, and W. Philpot, “The new age of hyperspectral oceanography,” Oceanography 17, 22–29 (2004).
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S. Maritorena, O. H. F. d’Andon, A. Mangin, and D. A. Siegel, “Merged satellite ocean color data products using a bio-optical model: characteristics, benefits and issues,” Remote Sens. Environ. 114, 1791–1804 (2010).
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Maritorena, S.

S. Maritorena, O. H. F. d’Andon, A. Mangin, and D. A. Siegel, “Merged satellite ocean color data products using a bio-optical model: characteristics, benefits and issues,” Remote Sens. Environ. 114, 1791–1804 (2010).
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S. Maritorena and D. A. Siegel, “Consistent merging of satellite ocean color data sets using a bio-optical model,” Remote Sens. Environ. 94, 429–440 (2005).
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P. J. Werdell, G. S. Fargion, C. R. McClain, and S. W. Bailey, “The SeaWiFS bio-optical archive and storage system (SeaBASS): current architecture and implementation,” NASA/TM-2002-211617 (NASA Goddard Space Flight Center, 2002).

S. B. Hooker, C. R. McClain, A. Mannino, and G. S. F. Center, “NASA strategic planning document: a comprehensive plan for the long-term calibration and validation of oceanic biogeochemical satellite data” (NASA Goddard Space Flight Center, 2007).

McCormick, N. J.

E. Rehm, and N. J. McCormick, “Inherent optical property estimation in deep waters,” Opt. Express 19, 24986–25005(2011).
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R. A. Leathers, and N. J. McCormick, “Ocean inherent optical property estimation from irradiances,” Appl. Opt. 36, 8685–8698 (1997).
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K. J. Voss, S. McLean, M. Lewis, C. Johnson, S. Flora, M. Feinholz, M. Yarbrough, C. Trees, M. Twardowski, and D. Clark, “An example crossover experiment for testing new vicarious calibration techniques for satellite ocean color radiometry,” J. Atmos. Oceanic Technol. 27, 1747–1759 (2010).
[CrossRef]

McLean, S. D.

H. R. Gordon, M. R. Lewis, S. D. McLean, M. S. Twardowski, S. A. Freeman, K. J. Voss, and G. C. Boynton, “Spectra of particulate backscattering in natural waters,” Opt. Express 17, 16192–16208 (2009).
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Mignot, A.

X. Xing, A. Morel, H. Claustre, D. Antoine, F. D’Ortenzio, A. Poteau, and A. Mignot, “Combined processing and mutual interpretation of radiometry and fluorimetry from autonomous profiling Bio-Argo floats: chlorophyll a retrieval,” J. Geophys. Res. 116, C06020 (2011).
[CrossRef]

Miller, M.

J. L. Mueller, C. Pietras, S. B. Hooker, R. W. Austin, M. Miller, K. D. Knobelspiesse, R. Frouin, B. Holben, and K. Voss, “Ocean optics protocols for satellite ocean color sensor validation, Revision 4, Volume II: instrument specifications, characterization and calibration,” NASA Tech. Memo. NASA/TM-2003-21621 (NASA, 2003).

Mitchell, B.

B. Mitchell, M. Kahru, and J. Sherman, “Autonomous temperature-irradiance profiler resolves the spring bloom in the Sea of Japan,” presented at Proceedings of Ocean Optics XV, Monaco, 16–20 October 2000.

Mitchell, B. G.

M. Stramska, D. Stramski, B. G. Mitchell, and C. D. Mobley, “Estimation of the absorption and backscattering coefficients from in-water radiometric measurements,” Limnol. Oceanogr. 45, 628–641 (2000).
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L. Li, H. Fukushima, R. Frouin, B. G. Mitchell, M.-X. He, I. Uno, T. Takamura, and S. Ohta, “Influence of submicron absorptive aerosol on Sea-Viewing Wide Field-of-View Sensor (SeaWiFS)-derived marine reflectance during Aerosol Characterization Experiment (ACE)-Asia,” J. Geophys. Res.108, 4472 (2003).
[CrossRef]

Mobley, C.

G. Chang, K. Mahoney, A. Briggs-Whitmire, D. Kohler, C. Mobley, M. Lewis, M. A. Moline, E. Boss, M. Kim, and W. Philpot, “The new age of hyperspectral oceanography,” Oceanography 17, 22–29 (2004).
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Mobley, C. D.

C. D. Mobley, “Fast light calculations for ocean ecosystem and inverse models,” Opt. Express 19, 18927–18944 (2011).
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C. D. Mobley, L. K. Sundman, C. O. Davis, J. H. Bowles, T. V. Downes, R. A. Leathers, M. J. Montes, W. P. Bissett, D. D. R. Kohler, and R. P. Reid, “Interpretation of hyperspectral remote-sensing imagery by spectrum matching and look-up tables,” Appl. Opt. 44, 3576–3592 (2005).
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C. D. Mobley, L. K. Sundman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41, 1035–1050 (2002).
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M. Stramska, D. Stramski, B. G. Mitchell, and C. D. Mobley, “Estimation of the absorption and backscattering coefficients from in-water radiometric measurements,” Limnol. Oceanogr. 45, 628–641 (2000).
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C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
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C. D. Mobley and L. K. Sundman, HydroLight 5.0, EcoLight 5.0 Technical Documentation (Sequoia Scientific, 2008).

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).

Moline, M. A.

G. Chang, K. Mahoney, A. Briggs-Whitmire, D. Kohler, C. Mobley, M. Lewis, M. A. Moline, E. Boss, M. Kim, and W. Philpot, “The new age of hyperspectral oceanography,” Oceanography 17, 22–29 (2004).
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Montes, M. J.

C. D. Mobley, L. K. Sundman, C. O. Davis, J. H. Bowles, T. V. Downes, R. A. Leathers, M. J. Montes, W. P. Bissett, D. D. R. Kohler, and R. P. Reid, “Interpretation of hyperspectral remote-sensing imagery by spectrum matching and look-up tables,” Appl. Opt. 44, 3576–3592 (2005).
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Moore, C. C.

J. R. V. Zaneveld, J. C. Kitchen, and C. C. Moore, “Scattering error correction of reflecting-tube absorption meters,” Proc. SPIE 2258, 44–55 (1994).
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Morel, A.

X. Xing, A. Morel, H. Claustre, F. D’Ortenzio, and A. Poteau, “Combined processing and mutual interpretation of radiometry and fluorometry from autonomous profiling Bio-Argo floats: 2. Colored dissolved organic matter absorption retrieval,” J. Geophys. Res. 117, C04022 (2012).
[CrossRef]

X. Xing, A. Morel, H. Claustre, D. Antoine, F. D’Ortenzio, A. Poteau, and A. Mignot, “Combined processing and mutual interpretation of radiometry and fluorimetry from autonomous profiling Bio-Argo floats: chlorophyll a retrieval,” J. Geophys. Res. 116, C06020 (2011).
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A. Morel, H. Claustre, D. Antoine, and B. Gentili, “Natural variability of bio-optical properties in Case 1 waters: attenuation and reflectance within the visible and near-UV spectral domains, as observed in South Pacific and Mediterranean waters,” Biogeosciences 4, 913–925 (2007).
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C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
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Mueller, J. L.

S. W. Brown, S. J. Flora, M. E. Feinholz, M. A. Yarbrough, T. Houlihan, D. Peters, Y. S. Kim, J. L. Mueller, B. C. Johnson, and D. K. Clark, “The marine optical buoy (MOBY) radiometric calibration and uncertainty budget for ocean color satellite sensor vicarious calibration,” Proc. SPIE 6744, 67441M (2007).
[CrossRef]

J. L. Mueller, C. Pietras, S. B. Hooker, R. W. Austin, M. Miller, K. D. Knobelspiesse, R. Frouin, B. Holben, and K. Voss, “Ocean optics protocols for satellite ocean color sensor validation, Revision 4, Volume II: instrument specifications, characterization and calibration,” NASA Tech. Memo. NASA/TM-2003-21621 (NASA, 2003).

Ohta, S.

L. Li, H. Fukushima, R. Frouin, B. G. Mitchell, M.-X. He, I. Uno, T. Takamura, and S. Ohta, “Influence of submicron absorptive aerosol on Sea-Viewing Wide Field-of-View Sensor (SeaWiFS)-derived marine reflectance during Aerosol Characterization Experiment (ACE)-Asia,” J. Geophys. Res.108, 4472 (2003).
[CrossRef]

Pegau, W. S.

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).
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A. H. Barnard, J. R. V. Zaneveld, and W. S. Pegau, “In situ determination of the remotely sensed reflectance and the absorption coefficient: closure and inversion,” Appl. Opt. 38, 5108–5117 (1999).
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W. S. Pegau, D. Gray, and J. R. V. Zaneveld, “Absorption and attenuation of visible and near-infrared light in water: dependence on temperature and salinity,” Appl. Opt. 36, 6035–6046 (1997).
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Perry, M.

E. Boss, D. Swift, L. Taylor, P. Brickley, R. Zaneveld, S. Riser, M. Perry, and P. Strutton, “Observations of pigment and particle distributions in the western North Atlantic from an autonomous float and ocean color satellite,” Limnol. Oceanogr. 53, 2112–2122 (2008).
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H. Claustre, J. Bishop, E. Boss, B. Stewart, J. Berthon, C. Coatanoan, K. Johnson, A. Lotiker, O. Ulloa, and M. Perry, “Bio-optical profiling floats as new observational tools for biogeochemical and ecosystem studies,” in Proceedings of the OceanObs ’09: Sustained Ocean Observations and Information for Society Conference, J. Hall, D. E. Harrison, and D. Stammer, eds. (ESA, 2010), ESA publication WPP-306, pp. 1–7.

E. A. D’Asaro, C. Lee, M. Perry, K. Fennel, E. Rehm, A. Gray, N. Briggs, and K. Gudmundsson, “The 2008 North Atlantic Spring Bloom Experiment I: overview and strategy,” EOS89(53), Fall Meeting Supplement, abstract OS24A-08 (2008).

Perry, M. J.

A. Mahadevan, E. D’Asaro, C. Lee, and M. J. Perry, “Eddy-driven stratification initiates North Atlantic spring phytoplankton blooms,” Science 337, 54–58 (2012).
[CrossRef]

I. Cetinić, M. J. Perry, N. T. Briggs, E. Kallin, E. A. D’Asaro, and C. M. Lee, “Particulate organic carbon and inherent optical properties during 2008 North Atlantic Bloom Experiment,” J. Geophys. Res. 117, C06028 (2012).
[CrossRef]

W. J. Bagniewski, K. Fennel, M. J. Perry, and E. A. D’Asaro, “Optimizing models of the North Atlantic spring bloom using physical, chemical and bio-optical observations from a Lagrangian float,” Biogeosciences 8, 1291–1307 (2011).
[CrossRef]

K. S. Johnson, W. M. Berelson, E. S. Boss, Z. Chase, H. Claustre, S. R. Emerson, N. Gruber, A. Kortzinger, M. J. Perry, and S. C. Riser, “Observing biogeochemical cycles at global scales with profiling floats and gliders: prospects for a global array,” Oceanography 22, 216–225 (2009).
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E. Kallin, I. Cetinić, M. J. Perry, and M. Sauer, “Laboratory_analysis_report-NAB08,” (Biological and Chemical Oceanography Data Management Office, 2011), retrieved 21 July 2012, http://osprey.bcodmo.org/dataset.cfm?id=13820&flag=view .

Peters, D.

S. W. Brown, S. J. Flora, M. E. Feinholz, M. A. Yarbrough, T. Houlihan, D. Peters, Y. S. Kim, J. L. Mueller, B. C. Johnson, and D. K. Clark, “The marine optical buoy (MOBY) radiometric calibration and uncertainty budget for ocean color satellite sensor vicarious calibration,” Proc. SPIE 6744, 67441M (2007).
[CrossRef]

Philpot, W.

G. Chang, K. Mahoney, A. Briggs-Whitmire, D. Kohler, C. Mobley, M. Lewis, M. A. Moline, E. Boss, M. Kim, and W. Philpot, “The new age of hyperspectral oceanography,” Oceanography 17, 22–29 (2004).
[CrossRef]

Pietras, C.

J. L. Mueller, C. Pietras, S. B. Hooker, R. W. Austin, M. Miller, K. D. Knobelspiesse, R. Frouin, B. Holben, and K. Voss, “Ocean optics protocols for satellite ocean color sensor validation, Revision 4, Volume II: instrument specifications, characterization and calibration,” NASA Tech. Memo. NASA/TM-2003-21621 (NASA, 2003).

Platnick, S.

B. A. Baum and S. Platnick, “Introduction to MODIS cloud products,” in Earth Science Satellite Remote Sensing, J. J. Qu, W. Gao, M. Kafatos, R. E. Murphy, and V. Salomonson, eds. Vol. 1, Science and Instruments (Springer-Verlag, 2006), pp. 74–91.

Poteau, A.

H. Lavigne, F. D’Ortenzio, H. Claustre, and A. Poteau, “Towards a merged satellite and in situ fluorescence ocean chlorophyll product,” Biogeosciences 9, 2111–2125 (2012).
[CrossRef]

X. Xing, A. Morel, H. Claustre, F. D’Ortenzio, and A. Poteau, “Combined processing and mutual interpretation of radiometry and fluorometry from autonomous profiling Bio-Argo floats: 2. Colored dissolved organic matter absorption retrieval,” J. Geophys. Res. 117, C04022 (2012).
[CrossRef]

X. Xing, A. Morel, H. Claustre, D. Antoine, F. D’Ortenzio, A. Poteau, and A. Mignot, “Combined processing and mutual interpretation of radiometry and fluorimetry from autonomous profiling Bio-Argo floats: chlorophyll a retrieval,” J. Geophys. Res. 116, C06020 (2011).
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R. W. Preisendorfer, Hydrologic Optics, NTIS PB-259 793/8ST (NOAA Pacific Marine Environment Laboratories, 1976).

Purcell, M. J.

C. A. Brown, Y. Huot, M. J. Purcell, J. J. Cullen, and M. R. Lewis, “Mapping coastal optical and biogeochemical variability using an autonomous underwater vehicle and a new bio-optical inversion algorithm,” Limnol. Oceanogr. Methods 2, 262–281 (2004).
[CrossRef]

Rehm, E.

M. Alkire, E. D’Asaro, C. Lee, M. Jane Perry, A. Gray, I. Cetinić, N. Briggs, E. Rehm, E. Kallin, J. Kaiser, and A. González-Posada, “Estimates of net community production and export using high-resolution, Lagrangian measurements of O2, NO3−, and POC through the evolution of a spring diatom bloom in the North Atlantic,” Deep Sea Res. I 64, 157–174 (2012).
[CrossRef]

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Stamnes, J.

W. Li, K. Stamnes, R. Spurr, and J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29, 5689–5698 (2008).
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Stamnes, K.

W. Li, K. Stamnes, R. Spurr, and J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29, 5689–5698 (2008).
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C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
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K. J. Voss, S. McLean, M. Lewis, C. Johnson, S. Flora, M. Feinholz, M. Yarbrough, C. Trees, M. Twardowski, and D. Clark, “An example crossover experiment for testing new vicarious calibration techniques for satellite ocean color radiometry,” J. Atmos. Oceanic Technol. 27, 1747–1759 (2010).
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J. H. Zar, Biostatistical Analysis, 4th ed. (Prentice-Hall, 1999).

Zhang, K.

R. Spurr, K. Stamnes, H. Eide, W. Li, K. Zhang, and J. Stamnes, “Simultaneous retrieval of aerosols and ocean properties: a classic inverse modeling approach. I. Analytic Jacobians from the linearized CAO-DISORT model,” J. Quant. Spectrosc. Radiat. Transfer 104, 428–449 (2007).
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R. Spurr, K. Stamnes, H. Eide, W. Li, K. Zhang, and J. Stamnes, “Error analysis for simultaneous retrieval of marine and aerosol properties from SeaWiFS,” presented at Proceedings of Ocean Optics XVIII, Montreal, Canada, 9–13 October 2006.

Zhao, J.

W. Zhou, G. Wang, Z. Sun, W. Cao, Z. Xu, S. Hu, and J. Zhao, “Variations in the optical scattering properties of phytoplankton cultures,” Opt. Express 20, 11189–11206 (2012).
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Zhou, W.

W. Zhou, G. Wang, Z. Sun, W. Cao, Z. Xu, S. Hu, and J. Zhao, “Variations in the optical scattering properties of phytoplankton cultures,” Opt. Express 20, 11189–11206 (2012).
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Appl. Opt. (18)

H. Loisel and D. Stramski, “Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering,” Appl. Opt. 39, 3001–3011 (2000).
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Z. 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).
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D. McKee, A. Cunningham, and S. Craig, “Estimation of absorption and backscattering coefficients from in situ radiometric measurements: theory and validation in case II waters,” Appl. Opt. 42, 2804–2810 (2003).
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H. R. Gordon, O. B. Brown, and M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14, 417–427 (1975).
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Z. Lee, R. Arnone, C. Hu, P. J. Werdell, and B. Lubac, “Uncertainties of optical parameters and their propagations in an analytical ocean color inversion algorithm,” Appl. Opt. 49, 369–381 (2010).
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Z. Tao, N. J. McCormick, and R. Sanchez, “Ocean source and optical property estimation from explicit and implicit algorithms,” Appl. Opt. 33, 3265–3275 (1994).
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H. R. Gordon and G. C. Boynton, “Radiance-irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: homogeneous waters,” Appl. Opt. 36, 2636–2641 (1997).
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G. C. Boynton and H. R. Gordon, “Irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: Raman-scattering effects,” Appl. Opt. 39, 3012–3022 (2000).
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A. H. Barnard, J. R. V. Zaneveld, and W. S. Pegau, “In situ determination of the remotely sensed reflectance and the absorption coefficient: closure and inversion,” Appl. Opt. 38, 5108–5117 (1999).
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C. D. Mobley, L. K. Sundman, C. O. Davis, J. H. Bowles, T. V. Downes, R. A. Leathers, M. J. Montes, W. P. Bissett, D. D. R. Kohler, and R. P. Reid, “Interpretation of hyperspectral remote-sensing imagery by spectrum matching and look-up tables,” Appl. Opt. 44, 3576–3592 (2005).
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R. A. Leathers, and N. J. McCormick, “Ocean inherent optical property estimation from irradiances,” Appl. Opt. 36, 8685–8698 (1997).
[CrossRef]

P. Wang, E. S. Boss, and C. Roesler, “Uncertainties of inherent optical properties obtained from semianalytical inversions of ocean color,” Appl. Opt. 44, 4074–4085 (2005).
[CrossRef]

C. D. Mobley, L. K. Sundman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41, 1035–1050 (2002).
[CrossRef]

E. Boss, M. S. Twardowski, and S. Herring, “Shape of the particulate beam attenuation spectrum and its inversion to obtain the shape of the particulate size distribution,” Appl. Opt. 40, 4885–4893 (2001).
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C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
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W. S. Pegau, D. Gray, and J. R. V. Zaneveld, “Absorption and attenuation of visible and near-infrared light in water: dependence on temperature and salinity,” Appl. Opt. 36, 6035–6046 (1997).
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Biogeosciences (3)

A. Morel, H. Claustre, D. Antoine, and B. Gentili, “Natural variability of bio-optical properties in Case 1 waters: attenuation and reflectance within the visible and near-UV spectral domains, as observed in South Pacific and Mediterranean waters,” Biogeosciences 4, 913–925 (2007).
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W. J. Bagniewski, K. Fennel, M. J. Perry, and E. A. D’Asaro, “Optimizing models of the North Atlantic spring bloom using physical, chemical and bio-optical observations from a Lagrangian float,” Biogeosciences 8, 1291–1307 (2011).
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H. Lavigne, F. D’Ortenzio, H. Claustre, and A. Poteau, “Towards a merged satellite and in situ fluorescence ocean chlorophyll product,” Biogeosciences 9, 2111–2125 (2012).
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Deep Sea Res. I (1)

M. Alkire, E. D’Asaro, C. Lee, M. Jane Perry, A. Gray, I. Cetinić, N. Briggs, E. Rehm, E. Kallin, J. Kaiser, and A. González-Posada, “Estimates of net community production and export using high-resolution, Lagrangian measurements of O2, NO3−, and POC through the evolution of a spring diatom bloom in the North Atlantic,” Deep Sea Res. I 64, 157–174 (2012).
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Int. J. Remote Sens. (2)

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Supplementary Material (2)

» Media 1: MOV (594 KB)     
» Media 2: MOV (804 KB)     

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Figures (15)

Fig. 1.
Fig. 1.

Monte Carlo and first-order uncertainty analysis results for a single radiometric inversion. (Center) Color 2-D histogram of IOP inversion results for 10,000 samples of L u ( 490 ) and E d ( 490 ) with added Gaussian random noise (see text). Target IOPs for the mean L u and E d are shown as the black cross at a p g = 0.05 m 1 , b b = 0.00585 m 1 . The color bar indicates sample count in each 2-D color histogram bin. Uncertainty ellipses show good agreement between Monte Carlo (blue) and first-order (red) uncertainty ellipses. Gray 1-D histograms show projected univariate ( a p g , b b ) sample distributions, with fit of a normal distribution to the projected data (blue line) and projected 95% confidence intervals (dashed lines). The elliptical shape and orientation of the 2-D histogram and resulting uncertainty ellipses indicate positive correlation ρ a p g , b b = 0.86 between errors in the absorption and backscattering coefficients, even though errors in the input L u , E d data are uncorrelated.

Fig. 2.
Fig. 2.

Hyperspectral (3.3 nm) retrievals of (a) absorption a p g ( λ ) and (b) backscattering b b ( λ ) from simulated radiometric data for C h l = 0.01 , 0.1, 1, 3, 10 mg m 3 . Black dotted curves show true values, colored curves show retrievals. (c) Relative error ψ a p g in absorption retrievals. C h l = 0.01 shown as blue dotted curve. (d) Relative error ψ b b in backscattering retrievals.

Fig. 3.
Fig. 3.

Absolute average error for hyperspectral (3.3 nm) retrievals of (a) absorption | ψ ¯ a p g | and (b) backscattering | ψ ¯ b b | from simulated radiometric data.

Fig. 4.
Fig. 4.

Isosurfaces for L u (blue) and E d (red) at 490 and 650 nm, representing a subset of the domain of IOPs ( a p g , b b , b p g ) that can produce given values of L u or E d . The yellow cross identifies the true value of the IOP triplet for the given L u and E d . Notice how isosurfaces at 650 nm have folded closer together than at 490 nm. (a) Isosurface intersection (yellow lines) indicates the range of possible inverse solutions when given both L u and E d , indicating that b is completely ambiguous. (b) The projected dashed lines show the range of uncertainty in the estimated IOPs a p g and b b if no value of b is specified.

Fig. 5.
Fig. 5.

Single-frame excerpts from animations of two objective function surfaces over a range of scattering b from 0.1 to 1. 0 m 1 . (a) Objective function surface F ( L u , E d ) used in this work shows a single minimum (Media 1). (b) Objective function surface F ( R L ) = ( R L meas R L est ) / R L meas shows multiple local minima (Media 2).

Fig. 6.
Fig. 6.

Shape of normalized radiance distribution L ( θ v , λ ) in the plane of the sun as a function of viewing direction θ v and wavelength λ at six depths, as computed by HydroLight for vertically homogeneous waters, using a chlorophyll based model with C h l = 1 mg m 3 , θ s = 50 ° , U 10 = 5 m s 1 . Note broadening of shape at all wavelengths and nearly isotropic shape for 700 nm at 30 m.

Fig. 7.
Fig. 7.

Stability of optimization starting points m 0 = ( a p g , b b , b p g ) with b p g fixed at 0. 225 m 1 (50% error). (Left) Contours show influence of optimization starting point m 0 on absolute error in absorption retrieval | ψ ¯ a p g | at 480 nm. Starting points converge near the true value ( a p g , b b ) = ( 0.05 , 0.00585 ) m 1 (shown with black cross), with average absolute error shown by the contour region color bar. Dots indicate the computation grid, decimated by a factor of 4 for clarity. (Right) Contour plot of objective function F ( m 0 ) at the same grid points. Color indicates value of the objective function F ( m ) . Vectors illustrate magnitude and direction of objective function gradient F ( m 0 ) . Notice that starting points in the lower-left corner where both coordinates are smaller than the true value have the lowest absolute error (left plot) and largest gradients (right plot).

Fig. 8.
Fig. 8.

Sensitivity studies of retrieved IOPs to L u , E d , and E s . Dashed lines indicate true values for E d , L u , E s , and a p g , dotted lines for b b .

Fig. 9.
Fig. 9.

Sensitivity m / b of retrieved IOPs a p g ( 490 ) and b b ( 490 ) to forward model parameters. Retrieval sensitivity coefficients are derived from linear fits to indicated portions of data and (e) quadratic fit to all b p g data. Vertical scales are identical on each plot, so relative assessments of IOP retrieval sensitivity can be made.

Fig. 10.
Fig. 10.

IOP and radiometric profiles from Station 34 in the NAB08 data set. (Left) Typical IOPs were nearly homogeneous in the lit portion of the water column. (Right) Radiometric profiles of L u , E d , and E s at 488 nm on log scale. L u and E d show little curvature until 40 m, another indication of vertically homogeneous water.

Fig. 11.
Fig. 11.

Radiometric measurements d meas (solid), least-squares estimates d est (dashed), and relative error ψ ( λ ) at selected depths for (a)  E d ( λ ) and (b)  L u ( λ ) at NAB08 Station 34.

Fig. 12.
Fig. 12.

Retrieved absorption a p g ( λ ) at 3.3 nm increments from NAB08 stations (blue curves and dots) with 95% confidence intervals based on first-order uncertainty analysis (gray-shaded area). Retrieved quantities are averages over the mixed layer at each station. Measured AC-9 absorption (red diamonds). Spectrophotometric absorption replicates (fine colored curves, Stations 34, 94, 128).

Fig. 13.
Fig. 13.

Retrieved particulate backscattering b b p ( λ ) at 3.3 nm increments from NAB08 stations (blue curves and dots) with 95% confidence intervals based on first-order uncertainty analysis (gray-shaded area). Retrieved quantities are averages over the mixed layer for each station. Measured BB2F particulate backscattering (red diamonds).

Fig. 14.
Fig. 14.

Comparison of measured versus retrieved IOPs at NAB08 process cruise stations, identified by the symbols. (a) Comparison of retrieved absorption apg ( λ ) to AC-9 absorption (all stations) shown with red symbols. Comparison to spectrophotometric absorption (Stations 34, 94 and 128 only): violet, 350 λ < 400 ; blue, 400 λ 600 nm ; green, 600 < λ 700 nm . Note that most retrievals failed above 600 nm (green symbols). (b) Comparison of retrieved particulate backscattering bbp ( λ ) to that measured by the BB2F.

Fig. 15.
Fig. 15.

Absorption and backscattering error budgets for NAB08 Station 34. (a), (b) Retrieved absorption a p g ( λ ) and particulate backscattering b b p ( λ ) (blue), 95% confidence interval (gray-shaded area) and spectrophotometric absorption replicates [fine colored curves, (a) only]. (c), (d) 95% confidence ellipses at 15 nm spacing showing positive (e.g., 350–450 nm) and generally negative (e.g., 575 nm ) correlation between errors in a p g and b b . (e), (f) Estimated errors for NAB08 Station 34 retrieval of a p g ( λ ) and b b p ( λ ) . The final retrieval error (black) is composed of forward model parameter error (red), radiometric measurement error (green), and error from the inversion (optimization) process (blue).

Tables (5)

Tables Icon

Table 1. Optimization Stopping Criteria and Related Evaluation Parameters

Tables Icon

Table 2. Additional Model Parameters Supplied to EcoLight Forward Model G ( m , b )

Tables Icon

Table 3. Radiometric and IOP Data Points Used for Simulations

Tables Icon

Table 4. Summary Retrieval Statistics for Simulated Light Fields

Tables Icon

Table 5. Forward Model Parameters Used for NAB08 Stations

Equations (29)

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d = G ( m , b ) + ε ,
d = [ d 1 , , d 2 N ] T = [ L u ( z 1 ) , , L u ( z N ) , E d ( z 1 ) , , E d ( z N ) ] T .
m = [ m 1 , m 2 , m 3 ] T = [ a , b b , b ] T .
b = [ b 1 , , b 8 ] T = [ β ˜ ( θ , θ , λ ) , a w , b w , E s , θ s , cloud , U 10 , C h l ] T .
S ε = E [ ε ε ] ,
cos θ d L ( z , θ , λ ) d z = c ( λ ) L ( z , θ , λ ) + 0 π β ( θ , θ , λ ) L ( z , θ , λ ) sin θ d θ + S ( z , θ , λ ) ,
β ( θ , θ , λ ) = 0 2 π β ( θ , ϕ , θ , ϕ = 0 , λ ) d ϕ
min l m u log 10 ( d meas ) log 10 ( d est ) 2 2 = min l m u F ( m ) ,
f ( m ) = [ f 1 ( m ) f N ( m ) f N + 1 ( m ) f 2 N ( m ) ] = [ log 10 [ L u meas ( z 1 ) ] log 10 [ L u est ( z 1 ) ] log 10 [ L u meas ( z N ) ] log 10 [ L u est ( z N ) ] log 10 [ E d meas ( z 1 ) ] log 10 [ E d est ( z 1 ) ] log 10 [ E d meas ( z N ) ] log 10 [ E d est ( z N ) ] ] .
G ( m + Δ m , b ) G ( m , b ) + K m Δ m ,
K m = log ( 10 ) × diag [ L u est ( z 1 ) , , L u est ( z N ) , E d est ( z 1 ) , , E d est ( z N ) ] J ( m ) .
c p ( λ ) = c p ( 650 ) ( λ 650 ) γ ,
m ^ = m + G m ε + G m K b ( b b a ) + ε r ,
G m = m G = ( K m T S ε 1 K m ) 1 K m T S ε 1 ,
m ˜ = m ^ m = G m ε measurement error + G m K b ( b b a ) forward model parameter error + ε r retrieval noise .
S t = S m + S f + S r ,
δ 0.95 = t 0.975 ( 2 ) , N p × diag ( S t ) ,
N ( m ^ m ) T S t 1 ( m ^ m ) ( N 1 ) p ( N p ) F p , N p ( α ) ,
δ 0.95 = ( N 1 ) p N p F p , N p ( α ) × diag ( S t ) ,
res i ( z j ) = X i est ( λ i , z j ) X i meas ( λ i , z j ) ,
ψ i ( z j ) = 100 res i ( z j ) X i meas ( λ i , z j ) ,
δ L u , 0.95 = 1.96 × σ L u = Δ L u / 100 × L ¯ u , δ E d , 0.95 = 1.96 × σ E d = Δ E d / 100 × E ¯ d ,
σ ^ i 2 = 1 ν j = 1 N res i 2 ( z j ) ,
S m MC = 1 10 , 000 i = 1 10 , 000 ( m i m ¯ ) ( m i m ¯ ) T .
S b = diag ( σ θ s 2 , σ cloud 2 , σ U 10 2 , σ E s 2 , σ b 2 ) .
S r ( C h l , Δ λ i ) = [ ε RMS a p g ( C h l , Δ λ i ) 2 0 0 ε RMS b b ( C h l , Δ λ i ) 2 ] ,
f R ( m ) = [ log 10 [ R L meas ( z 1 ) ] log 10 [ R L est ( z 1 ) ] log 10 [ R L meas ( z N ) ] log 10 [ R L est ( z N ) ] ] ,
S IOP , R = σ IOP / IOP ¯ σ R / R ¯ ,
S IOP , b i = d IOP d b i b ¯ i IOP ¯ ,

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