Abstract

A methodology has been developed and applied to accurately quantify and analyze adjacency effects in satellite ocean color data for a set of realistic and representative observation conditions in the northern Adriatic Sea. The procedure properly accounts for sea surface reflectance anisotropy, off-nadir views, coastal morphology, and atmospheric multiple scattering. The study further includes a sensitivity analysis on commonly applied approximations. Results indicate that, within the accuracy limits defined by the radiometric resolution of ocean color sensors, adjacency effects in coastal waters might be significant at both visible and near-infrared wavelengths up to several kilometers off the coast. These results additionally highlight a significant dependence on the angle of observation, on the directional reflectance properties of the sea surface, and on the atmospheric multiple scattering.

© 2014 Optical Society of America

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2013 (1)

F. Mélin, G. Zibordi, and B. N. Holben, “Assessment of the aerosol products from the SeaWiFS and MODIS ocean-color missions,” IEEE Geosci. Remote Sens. Lett. 10, 1185–1189 (2013).
[CrossRef]

2012 (1)

2010 (1)

2009 (2)

G. Zibordi, J. F. Berthon, F. Mélin, D. D’Alimonte, and S. Kaitala, “Validation of satellite ocean color primary products at optically complex coastal sites: Northern Adriatic Sea, Northern Baltic Proper and Gulf of Finland,” Remote Sens. Environ. 113, 2574–2591 (2009).
[CrossRef]

G. Zibordi, F. Mélin, J. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, and G. Schuster, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26, 1634–1651 (2009).
[CrossRef]

2008 (2)

E. G. Moody, M. D. King, C. B. Schaaf, and S. Platnick, “MODIS-derived spatially complete surface albedo products: spatial and temporal pixel distribution and zonal averages,” J. Appl. Meteorol. Climatol. 47, 2879–2894 (2008).

H. R. Gordon and B. A. Franz, “Remote sensing of ocean color: assessment of the water-leaving radiance bidirectional effects on the atmospheric diffuse transmittance for SeaWiFS and MODIS intercomparisons,” Remote Sens. Environ. 112, 2677–2685 (2008).
[CrossRef]

2007 (3)

A. Sei, “Analysis of adjacency effects for two Lambertian half-spaces,” Int. J. Remote Sens. 28, 1873–1890 (2007).
[CrossRef]

S. Bélanger, J. K. Ehn, and M. Babin, “Impact of sea ice on the retrieval of water-leaving reflectance, chlorophyll a concentration and inherent optical properties from satellite ocean color data,” Remote Sens. Environ. 111, 51–68 (2007).
[CrossRef]

G. Zibordi and B. Bulgarelli, “Effects of cosine error in irradiance measurements from field ocean color radiometers,” Appl. Opt. 46, 5529–5538 (2007).
[CrossRef]

2006 (1)

H. Iwabuchi, “Efficient Monte Carlo methods for radiative transfer modeling,” J. Atmos. Sci. 63, 2324–2339 (2006).
[CrossRef]

2005 (2)

B. Pinty, A. Lattanzio, J. V. Martonchik, M. M. Verstraete, N. Gobron, M. Taberner, J.-L. Widlowski, R. E. Dickinson, and Y. Govaerts, “Coupling diffuse sky radiation and surface albedo,” J. Atmos. Sci. 62, 2580–2591 (2005).
[CrossRef]

S. B. Hooker and G. Zibordi, “Platform perturbations in above-water radiometry,” Appl. Opt. 44, 553–567 (2005).
[CrossRef]

2004 (2)

B. Bulgarelli and J. Doyle, “Comparison between numerical models for radiative transfer simulation in the atmosphere-ocean system,” J. Quant. Spectrosc. Radiat. Transfer 86, 315–334 (2004).
[CrossRef]

V. Kisselev and B. Bulgarelli, “Reflection of light from a rough water surface in numerical methods for solving the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 85, 419–435 (2004).
[CrossRef]

2003 (4)

G. Thuillier, M. Hersé, D. Labs, T. Foujols, W. Peetermans, D. Gillotay, P. C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400  nm as measured by the SOLSPEC spectrometer from the ATLAS and EURECA missions,” Sol. Phys. 214, 1–22 (2003).
[CrossRef]

B. Bulgarelli and G. Zibordi, “Remote sensing of ocean colour: accuracy assessment of an approximate atmospheric correction method,” Int. J. Remote Sens. 24, 491–509 (2003).
[CrossRef]

B. Bulgarelli and F. Mélin, “SeaWiFS-derived products in the Baltic Sea: performance analysis of a simple atmospheric correction algorithm,” Oceanologia 45, 655–677 (2003).

B. Bulgarelli, G. Zibordi, and J. Berthon, “Measured and modeled radiometric quantities in coastal waters: toward a closure,” Appl. Opt. 42, 5365–5381 (2003).
[CrossRef]

2002 (3)

J. P. Doyle and G. Zibordi, “Optical propagation within a three-dimensional shadowed atmosphere-ocean field: application to large deployment structures,” Appl. Opt. 41, 4283–4306 (2002).
[CrossRef]

B. Pinty, J. L. Widlowski, N. Gobron, M. M. Verstraete, and D. J. Diner, “Uniqueness of multiangular measurements. I. An indicator of subpixel surface heterogeneity from MISR,” IEEE Trans. Geosci. Remote Sens. 40, 1560–1573 (2002).
[CrossRef]

B. Sturm and G. Zibordi, “SeaWiFS atmospheric correction by an approximate model and vicarious calibration,” Int. J. Remote Sens. 23, 489–501 (2002).
[CrossRef]

2001 (1)

C. Hu, K. L. Carder, and F. E. Muller-Karger, “How precise are SeaWiFS ocean color estimates? Implications of digitization-noise errors,” Remote Sens. Environ. 76, 239–249 (2001).
[CrossRef]

2000 (3)

1999 (2)

B. Bulgarelli, V. Kisselev, and L. Roberti, “Radiative transfer in the atmosphere-ocean system: the finite-element method,” Appl. Opt. 38, 1530–1542 (1999).
[CrossRef]

D. Antoine and A. Morel, “A multiple scattering algorithm for atmospheric correction of remotely sensed ocean colour (MERIS instrument): principle and implementation for atmospheres carrying various aerosols including absorbing ones,” Int. J. Remote Sens. 20, 1875–1916 (1999).
[CrossRef]

1997 (2)

E. Vermote, D. Tanrè, J. L. Deuzè, M. Herman, and J. J. Morcrette, “Second simulation of the satellite signal in the solar spectrum (6S): an Overview,” IEEE Trans. Geosci. Remote Sens. 35, 675–686 (1997).

L. Roberti, “Monte Carlo radiative transfer in the microwave and in the visible: biasing techniques,” Appl. Opt. 36, 7929–7938 (1997).
[CrossRef]

1995 (3)

1994 (1)

1993 (1)

H. Rahman, B. Pinty, and M. M. Verstraete, “Coupled surface-atmosphere reflectance (CSAR) model: 2. Semiempirical surface model usable with NOAA advanced very high resolution radiometer data,” J. Geophys. Res. 98, 20791–20801 (1993).
[CrossRef]

1986 (2)

E. C. Monahan and I. G. O’Muircheartaigh, “Whitecaps and the passive remote sensing of the ocean surface,” Int. J. Remote Sens. 7, 627–642 (1986).
[CrossRef]

W. A. Pearce, “Monte Carlo study of the atmospheric spread function,” Appl. Opt. 25, 438–447 (1986).
[CrossRef]

1984 (1)

1983 (1)

P. Y. Deschamps, M. Herman, and D. Tanré, “Definitions of atmospheric radiance and transmittances in remote sensing,” Remote Sens. Environ. 13, 89–92 (1983).
[CrossRef]

1981 (1)

1980 (2)

1979 (3)

1974 (1)

A. A. Lacis and J. Hansen, “A parameterization for the absorption of solar radiation in the Earth’s atmosphere,” J. Atmos. Sci. 31, 118–133 (1974).
[CrossRef]

1969 (1)

W. A. Marggraf and M. Griggs, “Aircraft measurements and calculations of the total downward flux of solar radiation as a function of altitude,” J. Atmos. Sci. 26, 469–477 (1969).
[CrossRef]

1961 (1)

A. Ångström, “Techniques of determining the turbidity of the atmosphere,” Tellus 13, 214–223 (1961).
[CrossRef]

1954 (1)

1953 (1)

E. Vigroux, “Contribution à l’étude expérimentale de l’absorption de l’ozone,” Ann. Phys. 8, 709–762 (1953).

Alberotanza, L.

G. Zibordi, J. F. Berthon, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, and L. Alberotanza, “Coastal atmosphere and sea time series (CoASTS), Part 1: a tower-based, long-term measurement program,” NASA Technical Memorandum 206892, S. B. Hooker and E. R. Firestone, eds. (NASA Goddard Space Flight Center, 2002), Vol. 19, pp. 1–29.

Ångström, A.

A. Ångström, “Techniques of determining the turbidity of the atmosphere,” Tellus 13, 214–223 (1961).
[CrossRef]

Antoine, D.

D. Antoine and A. Morel, “A multiple scattering algorithm for atmospheric correction of remotely sensed ocean colour (MERIS instrument): principle and implementation for atmospheres carrying various aerosols including absorbing ones,” Int. J. Remote Sens. 20, 1875–1916 (1999).
[CrossRef]

Babin, M.

S. Bélanger, J. K. Ehn, and M. Babin, “Impact of sea ice on the retrieval of water-leaving reflectance, chlorophyll a concentration and inherent optical properties from satellite ocean color data,” Remote Sens. Environ. 111, 51–68 (2007).
[CrossRef]

Bélanger, S.

S. Bélanger, J. K. Ehn, and M. Babin, “Impact of sea ice on the retrieval of water-leaving reflectance, chlorophyll a concentration and inherent optical properties from satellite ocean color data,” Remote Sens. Environ. 111, 51–68 (2007).
[CrossRef]

Berthon, J.

G. Zibordi, F. Mélin, J. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, and G. Schuster, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26, 1634–1651 (2009).
[CrossRef]

B. Bulgarelli, G. Zibordi, and J. Berthon, “Measured and modeled radiometric quantities in coastal waters: toward a closure,” Appl. Opt. 42, 5365–5381 (2003).
[CrossRef]

J. Berthon, F. Mélin, and G. Zibordi, “Ocean colour remote sensing of the optically complex European seas,” in Remote Sensing of the European Seas (Springer, 2008), pp. 35–52.

Berthon, J. F.

G. Zibordi, J. F. Berthon, F. Mélin, D. D’Alimonte, and S. Kaitala, “Validation of satellite ocean color primary products at optically complex coastal sites: Northern Adriatic Sea, Northern Baltic Proper and Gulf of Finland,” Remote Sens. Environ. 113, 2574–2591 (2009).
[CrossRef]

G. Zibordi, J. F. Berthon, J. P. Doyle, S. Grossi, D. van der Linde, C. Targa, and L. Alberotanza, “Coastal atmosphere and sea time series (CoASTS), Part 1: a tower-based, long-term measurement program,” NASA Technical Memorandum 206892, S. B. Hooker and E. R. Firestone, eds. (NASA Goddard Space Flight Center, 2002), Vol. 19, pp. 1–29.

J. F. Berthon, G. Zibordi, J. P. Doyle, S. Grossi, D. van der Linde, and C. Targa, “Coastal Atmosphere and Sea Time Series Project (CoASTS), Part 2: Data Analysis,” NASA Technical Memorandum 206892, S. B. Hooker and E. R. Firestone, eds. (NASA Goddard Space Flight Center, 2002), Vol. 20, pp. 1–25.

Bruegge, C. J.

J. V. Martonchik, C. J. Bruegge, and A. H. Strahler, “A review of reflectance nomenclature used in remote sensing,” Remote Sens. Rev. 19, 9–20 (2000).

Bulgarelli, B.

G. Zibordi and B. Bulgarelli, “Effects of cosine error in irradiance measurements from field ocean color radiometers,” Appl. Opt. 46, 5529–5538 (2007).
[CrossRef]

B. Bulgarelli and J. Doyle, “Comparison between numerical models for radiative transfer simulation in the atmosphere-ocean system,” J. Quant. Spectrosc. Radiat. Transfer 86, 315–334 (2004).
[CrossRef]

V. Kisselev and B. Bulgarelli, “Reflection of light from a rough water surface in numerical methods for solving the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 85, 419–435 (2004).
[CrossRef]

B. Bulgarelli and G. Zibordi, “Remote sensing of ocean colour: accuracy assessment of an approximate atmospheric correction method,” Int. J. Remote Sens. 24, 491–509 (2003).
[CrossRef]

B. Bulgarelli and F. Mélin, “SeaWiFS-derived products in the Baltic Sea: performance analysis of a simple atmospheric correction algorithm,” Oceanologia 45, 655–677 (2003).

B. Bulgarelli, G. Zibordi, and J. Berthon, “Measured and modeled radiometric quantities in coastal waters: toward a closure,” Appl. Opt. 42, 5365–5381 (2003).
[CrossRef]

B. Bulgarelli, V. Kisselev, and L. Roberti, “Radiative transfer in the atmosphere-ocean system: the finite-element method,” Appl. Opt. 38, 1530–1542 (1999).
[CrossRef]

B. Bulgarelli and F. Mélin, “SeaWiFS data processing code REMBRANDT,” Version 1.0 EUR 19154 EN (2000).

Carder, K. L.

C. Hu, K. L. Carder, and F. E. Muller-Karger, “How precise are SeaWiFS ocean color estimates? Implications of digitization-noise errors,” Remote Sens. Environ. 76, 239–249 (2001).
[CrossRef]

P. N. Reinersman and K. L. Carder, “Monte Carlo simulation of the atmospheric point-spread function with an application to correction for the adjacency effect,” Appl. Opt. 34, 4453–4471 (1995).
[CrossRef]

Cox, C.

D’Alimonte, D.

G. Zibordi, F. Mélin, J. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, and G. Schuster, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26, 1634–1651 (2009).
[CrossRef]

G. Zibordi, J. F. Berthon, F. Mélin, D. D’Alimonte, and S. Kaitala, “Validation of satellite ocean color primary products at optically complex coastal sites: Northern Adriatic Sea, Northern Baltic Proper and Gulf of Finland,” Remote Sens. Environ. 113, 2574–2591 (2009).
[CrossRef]

Davis, C. O.

de Leffe, A.

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[CrossRef]

G. Zibordi, J. F. Berthon, F. Mélin, D. D’Alimonte, and S. Kaitala, “Validation of satellite ocean color primary products at optically complex coastal sites: Northern Adriatic Sea, Northern Baltic Proper and Gulf of Finland,” Remote Sens. Environ. 113, 2574–2591 (2009).
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J. F. Berthon, G. Zibordi, J. P. Doyle, S. Grossi, D. van der Linde, and C. Targa, “Coastal Atmosphere and Sea Time Series Project (CoASTS), Part 2: Data Analysis,” NASA Technical Memorandum 206892, S. B. Hooker and E. R. Firestone, eds. (NASA Goddard Space Flight Center, 2002), Vol. 20, pp. 1–25.

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Figures (28)

Fig. 1.
Fig. 1.

(a) Map of the region represented by the surface grid in the NAUSICAA simulations; the AAOT (black circle, 45.31° N, 12.51° E) is also indicated. (b) Land/sea mask: land elements are indicated in dark gray, sea elements in light gray. The black line represents the transect intersecting the AAOT (black circle).

Fig. 2.
Fig. 2.

Spectral values of in situ L¯WN [Wm2μm1sr1] at the AAOT site: symbols represent different annual and intra-annual periods; error bars indicate the standard deviation σLWN.

Fig. 3.
Fig. 3.

Spectral values at MODIS land center wavelengths of time and spatially averaged (a) DHR and (b) BHRiso: symbols represent different annual and intra-annual periods; error bars indicate the standard deviations.

Fig. 4.
Fig. 4.

Normalized distributions of δMCFEM/E0=(LsfcMCTOALsfcFEMTOA)/E0 [sr1] for all considered test cases (Ncases) obtained by initializing N=107 photons and assuming (a) a uniform ideal Lambertian surface and (b) a uniform Fresnel-reflecting surface. The Gaussian fit of the distributions is displayed in black. Its mean δ/E0 and standard deviation σδ/E0 are also given. Note that the x scale for the Lambertian case is one order of magnitude higher than that of the Fresnel case.

Fig. 5.
Fig. 5.

Plot of ΔLsfcTOA=(Lsfc,NHTOA/Lsfc,HTOA1)×100 as a function of the distance from the coast and at sample wavelengths, obtained using the parameterization proposed by Sei [11] with the approximation of the environment weighting function proposed by Reinersman and Carder [7] (black line) and the NAUSICAA code (empty circles) for equivalent observation conditions: two Lambertian half-planes in quasi-nadir observation, with the same surface albedos and the same total aerosol and Rayleigh optical thicknesses. Error bars indicate the NAUSICAA statistical uncertainty with a 99.7% level of confidence.

Fig. 6.
Fig. 6.

Values of ξ¯Ltot at representative wavelengths as a function of the distance along the study transect. Error bars represent the standard deviation ±σ (black) and the sample variance (gray). Lw is assumed constant all along the transect. The vertical dotted line identifies the position of the AAOT site.

Fig. 7.
Fig. 7.

Values of L¯adj/E0 (black circles) at representative wavelengths as a function of the distance along the study transect. Contributions from land, L¯landTOA/E0 (gray circles), masked sea surface, L˜¯ssTOA/E0 (empty triangles), and masked water L˜¯wTOA/E0 (empty circles) are also displayed. Error bars represent the standard deviation ±σ. Lw is assumed constant all along the transect. The vertical dotted line identifies the position of the AAOT.

Fig. 8.
Fig. 8.

Values of Ladj/E0 (black circles) for typical observation conditions at 670 nm as a function of the distance (a) along the study transect and (b) along a parallel transect located just south of the small island. The land (gray circles), masked sea surface (empty triangles), and masked water (empty circles) contributions are also displayed. Error bars represent the standard deviation ±σ. Lw is assumed constant all along the transect.

Fig. 9.
Fig. 9.

Values of ξ¯Ltot at 865 nm as a function of the distance along the study transect. Plots on the left panel have been obtained for different values of the Ångstrom coefficient: α=0.02 (empty circles), α=0.05 (black circles), and α=0.08 (gray circles). Plots on the right panel have been obtained for different values of the Ångstrom exponent: ν=1.4 (empty circles), ν=1.7 (black circles), and ν=1.9 (gray circles). Error bars represent the standard deviation ±σ. Lw is assumed constant all along the transect.

Fig. 10.
Fig. 10.

Values of ξ¯Ltot at 490 nm (left panel) and at 865 nm (right panel) as a function of the distance along the study transect for different zenith angles of observation: θv=5° (empty circles), θv=20° (black circles), and θv=50° (gray circles). Bars solely represent the random uncertainties of simulated results ±σξLtotrnd.

Fig. 11.
Fig. 11.

Same as in Fig. 10 but assuming an isotropic sea surface reflectance with albedo ρss=0.04.

Fig. 12.
Fig. 12.

Values of ξ¯Ltot at 490 nm (left panel) and at 865 nm (right panel) as a function of the distance along the study transect for different Sun-sensor relative azimuths: black circles are for Δϕ=|ϕ0ϕ|=125°; empty circles for Δϕ=|ϕ0ϕ|=60°. Bars solely represent the random uncertainties of simulated results ±σξLtotrnd.

Fig. 13.
Fig. 13.

Same as in Fig. 12 but assuming an isotropic sea surface reflectance with albedo ρss=0.04.

Fig. 14.
Fig. 14.

Seasonal values of ξ¯Ltot at 865 nm for standard atmospheric conditions, as a function of the distance along the study transect. Bars represent the standard deviation ±σ. Black circles correspond to results obtained in November–February, empty circles in March–April (masked by empty diamonds), gray circles in May-August, and empty diamonds in September–October.

Fig. 15.
Fig. 15.

Spectral plot of ξ¯Ltot for all test cases (N=108) at the AAOT. Bars represent the standard deviation ±σ (black) and the sample variance (gray).

Fig. 16.
Fig. 16.

Seasonal values of ξ¯Ltot at representative wavelengths for standard atmospheric conditions. Bars represent the standard deviation ±σ (black) and the sample variance (gray). The dashed line indicates ξ¯Ltot determined from all test cases.

Fig. 17.
Fig. 17.

Values of ξ¯Ltot at 865 nm as a function (a) of the Ångstrom coefficient α and (b) of the Ångstrom exponent ν in selected ranges of variation (Table 2) for mean land and water parameters. Bars represent the standard deviation ±σ (black) and the sample variance (gray). The dashed line indicates ξ¯Ltot determined from all test cases.

Fig. 18.
Fig. 18.

Values of ξ¯Ltot at 865 nm as a function (a) of the zenith angle of observation θv and (b) of the Sun-sensor relative azimuth Δϕ=|ϕ0ϕ| in degrees in their selected ranges of variation (see Table 1). Bars represent the standard deviation ±σ (black) and the sample variance (gray). The dashed line indicates ξ¯Ltot determined from all test cases.

Fig. 19.
Fig. 19.

Values of ξ¯Ltot at 865 nm for typical observation–illumination geometries at the AAOT for SeaWIFS (SWF), MODIS Aqua (MOD-A), MODIS Terra (MOD-T), and MERIS (MER). Bars represent the standard deviation ±σ (black) and the sample variance (gray). The dashed line indicates ξ¯Ltot determined from all test cases.

Fig. 20.
Fig. 20.

Values of L¯adj/E0 from all test cases (N=108) at representative wavelengths as a function of the distance along the study transect and obtained assuming i) the BRDF of a rough sea surface induced by Ws=3.3ms1 (full markers) and ii) an isotropic sea surface reflectance with albedo ρss=0.04 (empty markers). Both error bars and the dashed lines indicate ±NEΔL¯/E0. Lw is assumed constant all along the transect.

Fig. 21.
Fig. 21.

Spectral plot of L¯adj/E0 at the AAOT obtained assuming i) the BRDF of a rough sea surface induced by Ws=3.3ms1 (full markers) and ii) an isotropic sea surface reflectance with albedo ρss=0.04 (empty markers). Both error bars and the dashed lines indicate ±NEΔL¯/E0.

Fig. 22.
Fig. 22.

BRDF values in the principal plane for (i) a sea surface roughed by wind speeds Ws=2.3 (dashed line), 3.3ms1 (solid line), and 4.3ms1 (dotted line) and (ii) a land surface defined by ρl=0.04 (diamonds) and ρl=0.26 (circles), with Θ=0 and k=0.6 (gray markers), 1.0 (black markers), and 1.2 (empty markers). The sea surface BRDFs are obtained from [34], while the land BRDFs through the so-called RPV model [63].

Fig. 23.
Fig. 23.

Spectral values of L¯adj/E0 at the AAOT site for the test cases characterized by θv=50° (empty markers) and θv=5° (full markers) determined assuming (a) the BRDF of a rough sea surface induced by Ws=3.3ms1 and (b) an isotropic sea surface reflectance with albedo ρss=0.04. Both error bars and dashed lines indicate ±NEΔL¯/E0.

Fig. 24.
Fig. 24.

Values of Ladj/E0 for typical observation conditions at representative wavelengths as a function of the distance along the study transect. Full markers represent values obtained accounting for the actual coastal pattern. Empty markers indicate values obtained separately assuming for each observed sea element along the transect a straight coastline located at the minimum distance from the land and oriented along the south–north direction. Both error bars and the dashed lines indicate ±NEΔL¯/E0. Lw is assumed constant all along the transect.

Fig. 25.
Fig. 25.

Values of Ladj/E0 for typical observation conditions at representative wavelengths as a function of the distance along the study transect obtained accounting for multiple scattering (full markers) and adopting the single scattering approximation (empty markers). Both error bars and the dashed lines indicate ±NEΔL¯/E0. Lw is assumed constant all along the transect.

Fig. 26.
Fig. 26.

Same as in Fig. 25 at 490 nm but assuming an isotropic sea surface reflectance with albedo ρss=0.04.

Fig. 27.
Fig. 27.

Spectral plot of Ladj/E0 at the AAOT for typical observation conditions obtained in single scattering approximation (empty markers) and accounting for multiple scattering (full markers). Both error bars and dashed lines indicate ±NEΔL¯/E0.

Fig. 28.
Fig. 28.

Values of Ladj/E0 at representative wavelengths and for typical observation conditions as a function of the distance from a straight-line coast. Error bars represent the standard deviation. Lw is assumed constant all along the transect. The dashed and dotted lines correspond to ±NEΔL/E0 for the SeaWiFS and the MODIS sensors, respectively.

Tables (8)

Tables Icon

Table 1. Parameters Defining the Illumination and Observation Geometriesa,b

Tables Icon

Table 2. Atmospheric Parameters Used for the Simulationsa

Tables Icon

Table 3. Spectral Values of in situ L¯WN [Wm2μm1sr1] at the AAOT Site and Related Standard Deviations σLWN

Tables Icon

Table 4. Land ρl and Sea ρsea Spectral Albedos, and Related Standard Deviations σ for Typical Observation Conditions

Tables Icon

Table 5. Values of the 0.95 Quantiles at Representative Wavelengths of σLadjrnd from Random Uncertainties of NAUSICAA MC Computations Performed by Initializing N=107 Photons and Assuming a Level of Confidence of 99.7%

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Table 6. Combined and Contributing Uncertainties Affecting Ladj Simulations (·E0×105 [sr1]) at the AAOT for Typical Observation Conditions

Tables Icon

Table 7. Values of ξ¯Ltot±σξ¯Ltot in Percent at Representative Wavelengths λ [nm] and at Several Distances from the Coast d [km] for all Test Cases (Global), for Typical Observational Conditions, and for Test Cases Characterized by the Ångström Exponent α=0.02 and 0.08, Viewing Zenith Angle θv=5° and 50°, and November–February and May–August Observation Conditions

Tables Icon

Table 8. Values of ξLtot±σξLtot in Percent at Representative Wavelengths λ [nm] and at Several Distances from the Coast d [km] Under Typical Observation Conditions for a Straight Coastline Oriented in the South–North Direction

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

g(x,y)=n(x,y)+f(x,y)h(x,y).
Lt(x0,y0;ξ^v)=Latm(x0,y0;ξ^v)+Lsfc(x,y;ξ^)h(x,y;x0,y0;ξ^,ξ^v).
Lt(x0,y0;ξ^v)=Latm(x0,y0;ξ^v)+{Lland(x,y;ξ^)·M(x,y)}h(x,y;x0,y0;ξ^,ξ^v)+{[Lss(x,y;ξ^)+Lw(x,y;ξ^)]·[1M(x,y)]}h(x,y;x0,y0;ξ^,ξ^v),
M(x,y)={1for land elements0otherwise.
Lt(x0,y0;ξ^v)=Latm(x0,y0;ξ^v)+Lw(x,y;ξ^)h(x,y;x0,y0;ξ^,ξ^v)+Lss(x,y;ξ^)h(x,y;x0,y0;ξ^,ξ^v).
Lt(x0,y0;ξ^v)=Lpath(x0,y0;ξ^v)+Lg(x0,y0;ξ^v)+t(ξ^v)·Lw(x0,y0;ξ^v),
Latm(x0,y0;ξ^v)+Lss(x,y;ξ^)h(x,y;x0,y0;ξ^,ξ^v)=Lpath(x0,y0;ξ^v)+Lg(x0,y0;ξ^v)
Lw(x,y;ξ^)h(x,y;x0,y0;ξ^,ξ^v)=Lw(x0,y0;ξ^v)·h(x,y;x0,y0;ξ^,ξ^v)dxdydξ^=t(ξ^v)·Lw(x0,y0;ξ^v)
Ladj(x0,y0;ξ^v)ΔLb(x0,y0;ξ^v)={Lland(x,y;ξ^)·M(x,y)}h(x,y;x0,y0;ξ^,ξ^v){[Lw(x,y;ξ^)+Lss(x,y;ξ^)]·M(x,y)}h(x,y;x0,y0;ξ^,ξ^v).
Lland=ρlEdρ=ρlπ=ρlEdρ=0π(1ρlS),
Lw=RrsEdρ=ρsea=RrsEdρ=01ρseaS,
Ladj(x0,y0;ξ^v)={ρlπ(1ρlS)Rrs1ρseaS}C(x0,y0;ξ^v)W(x0,y0;ξ^v),
C(x0,y0;ξ^v)=Edρ=0(x,y)·M(x,y)h(x,y;x0,y0;ξ^,ξ^v)
W(x0,y0;ξ^v)=Lss(x,y;ξ^)·M(x,y)h(x,y;x0,y0;ξ^,ξ^v).
ρsea=ρss+ρw0.04+πRrs,
Ladj=LlandTOAL˜wTOAL˜ssTOA,
L˜wTOA=Rrs(1ρseaS)C
g1=0.610+0.634τa(865),
g2(g1,λ)=0.4537+1.5544g1+0.000358(λ440),
as(g1,λ)=1.104(1.7097g1)(0.19018+g1)0.0001358(λ440).
ρl=(1SE)·DHR+SE·BHRiso.
σLadj=[(σLadjMC)2+(σLadjref)2]1/2,
σLadjMC=[(σLadjrnd)2+(δLadjsys)2]1/2,
σLadjref=[(σLadjρl)2+(σLadjRrs)2+(σLadjbg)2]1/2.

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