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  • Vol. 9, Iss. 5 — Apr. 29, 2014
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Simulation and analysis of adjacency effects in coastal waters: a case study

Barbara Bulgarelli, Viatcheslav Kiselev, and Giuseppe Zibordi  »View Author Affiliations


Applied Optics, Vol. 53, Issue 8, pp. 1523-1545 (2014)
http://dx.doi.org/10.1364/AO.53.001523


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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

1. Introduction

While satellite ocean color can rely on consolidated knowledge of the optical properties of the oceanic waters, intense investigations are still needed to correctly interpret the more complex optical properties of coastal regions. The higher level of complexity derives from the simultaneous presence of not-covarying in-water optically significant components (i.e., pigments, colored dissolved organic matter, and suspended sediments), eventual sea bottom reflectance, and adjacency effects induced by the reflectance of the nearby mainland.

Adjacency effects always occur in the presence of a scattering atmosphere over a nonuniform reflecting surface, which causes the radiance from high-reflectivity areas to spill over neighboring low-reflectivity regions, thus modifying their apparent brightness [1

1. J. Otterman and R. S. Fraser, “Adjacency effects on imaging by surface reflection and atmospheric scattering: cross radiance to zenith,” Appl. Opt. 18, 2852–2860 (1979). [CrossRef]

].

The problem of adjacency effects for satellite land observations has been extensively investigated for decades (see [2

2. D. Tanré, M. Herman, P. Y. Deschamps, and A. de Leffe, “Atmospheric modeling for space measurements of ground reflectances, including bidirectional properties,” Appl. Opt. 18, 3587–3594 (1979). [CrossRef]

5

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

] and references therein), and has led to the implementation of atmospheric correction codes that take into account adjacency perturbations (e.g., [6

6. E. Vermote and A. Vermeulen, “Atmospheric correction algorithm: spectral reflectances (MOD09),” NASA MODIS ATBD version 4.0 (1999).

]). Conversely, fewer studies specifically addressed adjacency effects in coastal waters [7

7. 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]

12

12. 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]

], and most of the operational ocean color atmospheric correction codes assume a uniform underlying reflecting surface [13

13. H. W. Gordon and M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 33, 443–452 (1994). [CrossRef]

,14

14. 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]

]. Processors for the correction of adjacency effects in coastal regions are only available at a prototypal stage, such as the Improve Contrast between Ocean and Land (ICOL) processor [9

9. R. Santer and C. Schmechtig, “Adjacency effects on water surfaces: primary scattering approximation and sensitivity study,” Appl. Opt. 39, 361–375 (2000). [CrossRef]

,15

15. R. Santer and F. Zagolski, “ICOL—improve contrast between ocean and land,” ATBD-MERIS Level 1-C, version 1.1 (2009).

].

When neglected, adjacency effects become a source of spectral perturbations in satellite data. Considering that the determination of ocean color products is very sensitive to even small sources of noise [16

16. 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]

], accurate evaluation of adjacency effects is of the greatest relevance in ocean color remote sensing of coastal waters.

Within such a frame, the main objective of this work is an extensive and highly accurate theoretical evaluation of the adjacency effects in coastal regions for realistic and representative conditions, accounting for the actual sensor radiometric resolution. Indeed, a true knowledge of the actual amount of adjacency effects and a deep understanding of their physical dependences is a fundamental and necessary prerequisite for any successive quantification of adjacency-induced perturbations in satellite-retrieved products and for any further development of simplified approaches for the operational correction of adjacency effects.

On the basis of the above considerations, this work attempts the simulation of adjacency effects with an improved level of accuracy, properly accounting for the involved uncertainties. This is achieved by previously solving the radiative transfer equation (RTE) for representative test cases taking into consideration off-nadir views, the Fresnel reflectance of a wind-roughed sea surface, the actual coastal morphology, and the average radiometric resolution of ocean color sensors. The accurate evaluation of uncertainties in simulated results is performed accounting for uncertainties both in the simulation procedure and on a number of input parameters.

The selected test cases correspond to the observation conditions encountered in a littoral area of the northern Adriatic Sea hosting the Aqua Alta Oceanographic Tower (AAOT, 45.31N, 12.51E) site. Since 1995 the AAOT site has been used to validate satellite ocean color products [17

17. 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.

], and it is the first site included in the Ocean Color component of the Aerosol Robotic Network (AERONET-OC) [18

18. 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]

], a subnetwork established in 2006 to support the validation of satellite ocean color products through highly accurate, cross-site consistent, and globally distributed measurements performed in coastal regions at distances from the land varying from a few up to several tens of kilometers. The comprehensive multiannual record of in situ measurements performed at the AAOT [17

17. 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.

,18

18. 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]

] allows a precise and complete characterization of the optical properties of atmosphere and seawater, enabling the definition of realistic and seasonally dependent test cases for the analysis of the adjacency effects. Furthermore, the selected region, characterized by mid-latitude atmospheric conditions and a cropland ecosystem, is well representative of mid-latitude coastal areas covered by a deciduous vegetation type (the most diffuse in Europe) in the absence of snow. Additionally, the selected optical aerosol properties correspond to those mostly encountered at different AERONET-OC sites [19

19. 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]

]. Results are hence expected to provide general conclusions applicable to a variety of measurement conditions and coastal regions. Finally, the extremely complex coastal pattern of the Venice Lagoon makes it optimally suitable to analyze the influence on adjacency effects of the actual coastal morphology.

The accurate simulation of adjacency effects in the selected coastal region should provide a theoretical quantification of the adjacency contributions to TOA radiances, and allow and analysis of their dependence on different geophysical parameters, and an evaluation of the physical impact of commonly adopted approximations. Specifically, it should help in evaluating the relevance of sea surface anisotropy, actual coastal morphology, off-nadir views, and atmospheric multiple scattering within the limits established by the sensor radiometric resolution. Finally, it should provide an estimate of the horizontal range of adjacency effects taking into account the actual radiometric resolution of the measuring sensors.

The quantification of the adjacency effects is performed in terms of the adjacency radiance Ladj. By identifying the target element as the sensor effective footprint given by the intersection of the sensor instantaneous field of view (IFOV) with the ground for the whole sensor integration time [21

21. I. S. Robinson, Measuring the Oceans from Space (Springer-Verlag, 2004).

], and the background radiance Lb [22

22. 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]

] (also called environmental radiance [11

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

]) as the radiance reflected by the background surface of such a target element and then scattered by the atmosphere in the sensor IFOV, the adjacency radiance is defined as the difference in the background radiance between the case accounting for the nonuniformity of the underlying reflecting surface and the case assuming a uniform surface.

Adjacency radiance and its contribution to the signal at the TOA are simulated here making use of (i) the newly developed Novel Adjacency Perturbation Simulator for Coastal Areas (NAUSICAA) full three-dimensional (3D) backward Monte Carlo (MC) code, whose precision is set to meet actual ocean color sensors’ radiometric resolutions, and (ii) a highly accurate plane-parallel code based on the finite element method (the FEM code) [23

23. V. B. Kisselev, L. Roberti, and G. Perona, “Finite-element algorithm for radiative transfer in vertically inhomogeneous media: numerical scheme and applications,” Appl. Opt. 34, 8460–8471 (1995). [CrossRef]

,24

24. 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]

].

To reduce computing time, the adjacency radiance is modeled assuming isotropic and homogeneous land and water reflectances, allowing the decoupling of land and water optical properties from the atmospheric scattering. The anisotropic reflectance of the sea surface is instead fully accounted for. This approach, while allowing a detailed and accurate (although computer-time expensive) description of the radiance propagation through the medium properly accounting for the sea surface roughness, also offers the capability to easily vary land and water input parameters.

The simulation exercise is carried out at relevant ocean color center wavelengths along a transect crossing the Venice Lagoon and intersecting the AAOT. The study includes viewing geometries typical of ocean color sensors such as the sea-viewing wide field-of-view sensor (SeaWiFS), the moderate resolution imaging spectroradiometer (MODIS), and the medium resolution imaging spectrometer (MERIS). Simulated results are analyzed along the whole transect with specific focus on results at the AAOT site.

The applied methodology is introduced in Sections 24. Specifically, Section 2 presents the modeling of the adjacency radiance, Section 3 the simulation procedure, and Section 4 the selected case studies. An accurate assessment of the simulation results is given in Section 5, while results are presented and discussed in Section 6. Conclusions are drawn in Section 7.

2. Modeling of the Adjacency Radiance

In general terms, the image of an object is the sum of the convolution of the original signal f(x,y) with the point-spread function h(x,y) (i.e., the function describing the transmission of the original signal through the propagating system), plus the noise n(x,y):
g(x,y)=n(x,y)+f(x,y)h(x,y).
(1)

According to this formulation, the radiance received by a space sensor observing a target element located at (x0,y0) with observation direction ξ^v can be modeled as
Lt(x0,y0;ξ^v)=Latm(x0,y0;ξ^v)+Lsfc(x,y;ξ^)h(x,y;x0,y0;ξ^,ξ^v).
(2)
The unit vector ξ^ is defined as ξ^=(θ,ϕ), where θ is the zenith angle measured from the nadir direction, and ϕ is the azimuth angle measured positive clockwise with respect to the north. The dependence on the sunbeam direction ξ^0, the optical thickness τ, the single scattering albedo ω0, the wavelength λ, and the reflectance properties of the surface is omitted for simplicity. With reference to Eq. (2), Latm(x0,y0;ξ^v) is the atmospheric radiance, i.e., the radiance that the sensor would receive if the underlying surface were completely absorbing; Lsfc(x,y;ξ^v) is the upgoing radiance distribution at the surface level; and h(x,y;x0,y0;ξ^,ξ^v) is the atmospheric point-spread function (APSF). The APSF is here assumed to include the singular additive term describing radiance propagation through the atmosphere without undergoing any scattering event.

The term Lsfc in a coastal area may be distinguished in Lland and Lsea for land and sea elements, respectively. Indicating with the term sea the ensemble of water (designating the sole water volume) and sea surface, the term Lsea may be further separated into the radiance reflected by the sea surface, Lss, and the radiance emerging from the water, Lw (the so-called water-leaving radiance), so that Eq. (2) becomes
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),
(3)
where M(x,y) is the land–water matrix:
M(x,y)={1for land elements0otherwise.
(4)
In the open sea, Eq. (3) takes the simple form
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).
(5)
It is worthwhile to underline that Eq. (5) is equivalent to the expression traditionally used in ocean color remote sensing to model TOA radiances [13

13. H. W. Gordon and M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 33, 443–452 (1994). [CrossRef]

,14

14. 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]

]:
Lt(x0,y0;ξ^v)=Lpath(x0,y0;ξ^v)+Lg(x0,y0;ξ^v)+t(ξ^v)·Lw(x0,y0;ξ^v),
(6)
where Lpath (following the terminology applied in [14

14. 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]

]) represents the radiance due to atmospheric scattering along the optical path and to specular reflection by the sea surface of atmospherically scattered light (in ocean color remote sensing this term is often indicated tout court as Latm [13

13. H. W. Gordon and M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 33, 443–452 (1994). [CrossRef]

]); Lg is the radiance contribution due to specular reflection of direct sunlight by the sea surface; t(ξ^v) is the diffuse atmospheric transmittance (according to the definition given by Gordon and Franz [25

25. 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]

]); and Lw is the water-leaving radiance assumed to be spatially uniform and isotropic [13

13. H. W. Gordon and M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 33, 443–452 (1994). [CrossRef]

]. Indeed,
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)
(7)
and
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)
(8)
with Lw(x,y;ξ^)Lw(x0,y0;ξ^v).

The adjacency radiance Ladj, quantified as the difference ΔLb in background radiance between the coastal and the open-sea cases, is obtained by subtracting Eq. (5) from Eq. (3). As such, its value can range from negative to positive:
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).
(9)

Each land element may be further characterized by a spectral bihemispherical reflectance (BHR), defined as the ratio between the irradiance reflected by the surface and the irradiance impinging at the surface [26

26. 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]

], often simply termed albedo. So defined, the surface albedo is not an intrinsic property of the surface but is rather determined by both the surface and the overlying atmosphere [26

26. 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]

]. The decoupling between surface and atmospheric scattering properties can be obtained by assuming an isotropic surface reflectance. By further assuming a spatially homogeneous albedo ρl, Lland can be modeled as
Lland=ρlEdρ=ρlπ=ρlEdρ=0π(1ρlS),
(10)
where S is the atmospheric spherical albedo of the bottom of the atmosphere. The term (1ρlS) accounts for multiple reflections at the surface, so that the total downward irradiance at surface level Edρ=ρl can be computed from Edρ=0 for a completely absorbing surface. Although this formalism is exact only for horizontally homogeneous surfaces, it represents a good approximation of the total downward irradiance at the surface even near the land/water boundary.

Analogously, by assuming that the reflectance of the water volume is isotropic and exhibits small spatial variations, Lw can be modeled as
Lw=RrsEdρ=ρsea=RrsEdρ=01ρseaS,
(11)
where Rrs is the remote sensing reflectance and ρsea is the sea albedo, i.e., the BHR of both water and sea surface (see Ref. [27

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

], p. 193).

Inserting Eqs. (10) and (11), Eq. (9) finally becomes
Ladj(x0,y0;ξ^v)={ρlπ(1ρlS)Rrs1ρseaS}C(x0,y0;ξ^v)W(x0,y0;ξ^v),
(12)
where
C(x0,y0;ξ^v)=Edρ=0(x,y)·M(x,y)h(x,y;x0,y0;ξ^,ξ^v)
(13a)
and
W(x0,y0;ξ^v)=Lss(x,y;ξ^)·M(x,y)h(x,y;x0,y0;ξ^,ξ^v).
(13b)
It is recalled that the functions C and W also depend on ξ0, τ, ω0, λ, and on the scattering phase function.

Expression (12) allows separating the dependence of Ladj on land and water reflectance properties, decoupling these from the scattering properties of the atmosphere.

The simulation of terms C(x0,y0;ξ^v) and W(x0,y0;ξ^v) requires a full 3D description of the propagating system. Differently, the simulation of term S can be performed with a plane-parallel radiative transfer code. The input parameters ρl and Rrs can be extrapolated from satellite-derived and in situ measured data, respectively. An approximation is applied to calculate the parameter ρsea, which indeed appears in Eq. (12) only to account for multiple reflections at the sea surface:
ρsea=ρss+ρw0.04+πRrs,
(14)
where the term ρss0.04 in Eq. (14) indicates a typical irradiance reflectance of the sea surface for the propagation from air to water (Ref. [27

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

], p. 494), and ρw is the water reflectance, which simply equals πRrs when assuming an isotropic angular distribution of the water-leaving radiance.

The proposed modeling additionally allows distinguishing the different contributions to the adjacency radiance. Indeed, Eq. (12) may be symbolically written as
Ladj=LlandTOAL˜wTOAL˜ssTOA,
(15)
where LlandTOA={ρl/[π(1ρlS)]}C represents the land contribution, i.e., the radiance at the sensor originating from the area covered by the land, while
L˜wTOA=Rrs(1ρseaS)C
and L˜ssTOA=W represent the masked water and the masked sea surface contributions, respectively, i.e., the water-leaving radiance and the sea surface radiance that would reach the sensor from the same area if still covered by the sea. The latter term is sometimes called the Fresnel mask [9

9. R. Santer and C. Schmechtig, “Adjacency effects on water surfaces: primary scattering approximation and sensitivity study,” Appl. Opt. 39, 361–375 (2000). [CrossRef]

].

3. Simulation Procedure

Functions C and W [Eq. (13)] have been computed with the NAUSICAA backward MC code, while the plane-parallel FEM numerical algorithm [23

23. V. B. Kisselev, L. Roberti, and G. Perona, “Finite-element algorithm for radiative transfer in vertically inhomogeneous media: numerical scheme and applications,” Appl. Opt. 34, 8460–8471 (1995). [CrossRef]

,24

24. 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]

] has been used to simulate atmospheric optical quantities such as atmospheric spherical albedo S, diffuse transmittance t, atmospheric radiance Latm, and downward irradiance at the surface Ed.

A. NAUSICAA Monte Carlo Code

The NAUSICAA MC code has been specifically developed to quantify adjacency effects in satellite ocean color data acquired in coastal regions. The code simulates fully 3D optical photon transport in a nonhomogeneous and physically realistic atmosphere bounded by a nonuniform reflecting surface. The medium is modeled on a 3D grid delimiting the largest macroscopic volumes or cells of uniform optical properties. The 3D grid is then surrounded by a background plane-parallel atmosphere bounded by a uniform reflecting surface.

In each cell of the grid, the characteristics of the optically active components (air molecules and aerosols) are specified through their optical thickness τ, single scattering albedo ω0, and scattering phase function p. The latter can be either analytical [Rayleigh for air molecules and two-terms Henyey–Greenstain (TTHG) for aerosol] or given in a tabulated form. In the first case the distribution function P is also expressed in analytical terms.

Each element of the underlying reflecting surface can be characterized either by a Fresnel specular reflectance (suitable for a flat sea surface) or by a bidirectional reflectance distribution function (BRDF [sr1]). The BRDF defines the directional reflectance properties of the surface element, describing the reflection of a parallel beam of incident light from one direction into another direction in the same hemisphere [33

33. 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).

]. The accurate expression of the BRDF for a wind-generated rough sea surface is taken from Kisselev and Bulgarelli [34

34. 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]

]. This is preferred to the well-known BRDF expression from Cox and Munk [35

35. C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. 44, 838–850 (1954). [CrossRef]

] because, although based on the same two-dimensional Gaussian sea surface wave slope distribution [35

35. C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. 44, 838–850 (1954). [CrossRef]

], it does not tend to infinity for angles of reflection close to the horizontal direction. The approach to model the reflectance of a wind-roughed sea surface through a BRDF is applied here to ensure an equivalent sampling of photons interacting with the land and photons interacting with the sea surface, thus avoiding the eventual occurrence of artificial biases induced by oversampling one type of photons with respect to the other.

The solar source is described by a parallel beam of monochromatic photons that originates from a far field point and uniformly impinges on the TOA.

NAUSICAA implements ad hoc biasing techniques [36

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

,37

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

] to inhibit photon loss, thus reducing the computational time and keeping the statistical oscillations relatively small. Simulated results are provided with their statistical uncertainty, as determined by the selected number of initiated photons and by the threshold for photon survival [37

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

]. An extensive analysis of the uncertainties affecting NAUSICAA computations is presented in Section 5.

B. System Modeling

Simulations are performed at typical ocean color center wavelengths λ=412, 443, 490, 510, 555, 670, 765, and 865 nm.

The solar spectral extra-atmospheric irradiance E0 is taken from Thuillier et al. [38

38. 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]

], while an average Earth–Sun distance is adopted. The atmosphere is divided into 14 plane-parallel layers resolving the vertical distributions of aerosol, ozone, and other gas molecules. Each atmospheric layer contains a variable mixture of ozone (only absorbing), other gas molecules (only scattering), and aerosol (scattering and absorbing). The spectral vertical profile of the ozone optical thickness is computed in agreement with Lacis and Hansen [39

39. 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]

]. The ozone absorption coefficients are taken from Vigroux [40

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

], whereas an average ozone load of 300 DU is assumed. The spectral vertical profile of the Rayleigh optical thickness is computed according to Marggraf and Griggs [41

41. 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]

], Fröhlich and Shaw [42

42. C. Fröhlich and G. E. Shaw, “New determination of Rayleigh scattering in the terrestrial atmosphere,” Appl. Opt. 19, 1773–1775 (1980). [CrossRef]

], and Young [43

43. A. T. Young, “Revised depolarization corrections for atmospheric extinction,” Appl. Opt. 19, 3427–3428 (1980). [CrossRef]

] for an average atmospheric pressure. The spectral vertical profile of the aerosol optical thickness is modeled according to Ångström [44

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

] and Elterman [45

45. L. Elterman, “UV, visible, and IR attenuation for altitudes to 50  km,” Environmental Research Paper No. 285, AFCRL-68-0153 (Air Force Cambridge Research Laboratory, 1968).

], assuming a mean aerosol scale height of 1.2 km [45

45. L. Elterman, “UV, visible, and IR attenuation for altitudes to 50  km,” Environmental Research Paper No. 285, AFCRL-68-0153 (Air Force Cambridge Research Laboratory, 1968).

]. The molecular scattering is described by a Rayleigh phase function. The aerosol scattering phase function is approximated by a spectral TTHG analytical function whose asymmetry parameters g1, g2, and as were obtained from the analysis of experimental measurements performed at the AAOT [46

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

] as a function of λ [nm] and of the aerosol optical thickness τa at 865 nm:
g1=0.610+0.634τa(865),
(16a)
g2(g1,λ)=0.4537+1.5544g1+0.000358(λ440),
(16b)
as(g1,λ)=1.104(1.7097g1)(0.19018+g1)0.0001358(λ440).
(16c)

In the NAUSICAA simulations, the surface grid of nonuniform reflecting properties, centered on the AAOT and extending from 44.4° N to 46.2° N and from 11.3° E to 13.7° E, is divided into 101×101 squared elements, each 2×2km wide (Fig. 1). The corresponding matrix discriminating between land and sea elements [see Eq. (4)] is extracted from the operational land/sea mask used in the REMBRANDT code [47

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

] to process SeaWiFS data from the northern Mediterranean Sea. The width of the surface grid has been defined to minimize contributions from the background along the study transect, which, starting from the coast, crosses the Venice Lagoon and intersects the AAOT [Fig. 1(b)]. A wind-roughed sea surface in the absence of whitecaps is accounted for in the MC simulations. The latter assumption is reasonable for wind speeds lower than about 7ms1 [48

48. 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]

]. FEM simulations of atmospheric optical quantities do not require the presence of the sea surface.

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).

4. Case Studies

A. Geometrical Observation and Illumination Conditions

An analysis of the actual observation and illumination conditions encountered in the selected area for each considered sensor has been carried out using a comprehensive database extending over several years [49

49. F. Mélin, “Personal communication,” JRC-EC, Ispra (I).

]. On the basis of this analysis, typical illumination/observation conditions have been selected (Table 1). Solar and sensor zenith angles are determined with respect to the local vertical, while solar and sensor azimuth angles are counted clockwise from the north direction (as generally adopted in satellite geolocation). The solar zenith angle θ0 is allowed to range between 25° and 65°. In particular, it is set to 25° for the May–August test case, to 65° for the November–February test case, and to 45° in all other cases. The space sensor viewing angle θv varies from 5° to 50° and from 5° and 20° for MODIS and MERIS, respectively. It is limited to 20°–50° for SeaWiFS to account for the sensor tilt angle. The solar azimuth angle ϕ0 is set to ±160°, while ±100° and ±75° are the selected values for the satellite azimuth ϕv. A positive satellite azimuth indicates observations from over the sea, while a negative value indicates observations occurring from the land side. The specific illumination/observation geometries selected for the satellite sensors are indicated in Table 1.

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

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B. Atmospheric Features

The ranges of variability for the Ångström coefficient α and exponent ν have been defined in agreement with the average values observed during clear sky conditions in the northern Adriatic Sea [20

20. 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]

] (Table 2). The adopted aerosol single scattering albedo is approximately 0.99 at all wavelengths. Selected parameters correspond to an aerosol optical thickness at 555 nm ranging between 0.05 and 0.25, and equal to 0.14 for the standard case. In accordance with Eq. (16) parameter g1 of the aerosol scattering phase function ranges between 0.63 and 0.68, while parameter as ranges between 0.98 and 0.99 at 412 nm, and between 0.92 and 0.93 at 865 nm. A mean wind speed Ws=3.3ms1 is assumed as representative of the average conditions encountered at the AAOT [50

50. 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.

].

Table 2. Atmospheric Parameters Used for the Simulationsa

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C. Water Radiometric Features

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.

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

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D. Selected Land Reflectance Properties

Values of DHR and isotropic BHR (BHRiso) reflectances (reported as black-sky and white-sky albedos in the MODIS product suite) have been extracted from the MODIS multiyear climatological snow-free aggregate database [52

52. 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).

] at the MODIS land center wavelengths λ=470, 555, 659, and 858 nm and for each MODIS land pixel of a subset of the region of interest close to the coast (12.0° E to 13.1° E and 44.9° N to 45.8° N). These data are the sole providing quality climatological albedo products at high spectral and spatial resolution. DHR is the reflectance that would be measured if the atmospheric scattering effects were removed, thus leading to a purely monodirectional incident radiance field. Conversely, BHRiso is the reflectance that would be measured if the incident radiance field could be assumed isotropic [26

26. 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]

]. Both products are independent of the environmental conditions.

In accordance with the applied methodology, DHR and BHRiso data have been spatially averaged over the considered area, and the annual and intra-annual values have been computed (Fig. 3). The resulting products show their strongest seasonal dependence at 858 nm with a pronounced peak in summer. Mid-seasonal spectra look very similar in the NIR, but diverge in the visible spectral region. Annual mean spectra are very close to the September–October ones. Differences between corresponding values of time and spatially averaged DHR and BHRiso appear significant at 858 nm for the May–August and November–February periods. Therefore the “actual” average land BHR, hereafter simply termed land albedo ρl, has been computed for each annual and intra-annual period and at each wavelength, by weighting the two distinct surface reflectance products through the ratio SE between diffuse and direct irradiance at the surface [26

26. 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]

]:
ρl=(1SE)·DHR+SE·BHRiso.
(17)

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.

Land albedos at the ocean color wavelengths λ=490, 555, 670, and 865 nm have been taken equal to those of the closest MODIS land center wavelengths. Land albedos at the other ocean color wavelengths (i.e., 412, 443, 510, and 765 nm) have been obtained through inter/extrapolation, assuming a cropland ecosystem. Specifically, cropland spectral signatures from ASTER [53

53. ASTER Spectral Library [Online]. Available: http://speclib.jpl.nasa.gov/search-1/vegetation (Accessed: 21 April 2013].

] and USGS [54

54. USGS Digital Spectral Library [Online]. Available: http://speclab.cr.usgs.gov/spectral-lib.html (Accessed: 21 April 2013).

] spectral libraries have been used to define average spectral slopes at inter/extrapolation wavelengths. The slope variance, particularly high at 765 nm, has been taken into account in the uncertainty estimate of ρl. Indeed, the reflectance spectrum of cropland vegetation consistently varies with the cropland type, its phenological state, its moisture content, and the soil contribution. Particularly sensitive to these variations is the shape of the so-called red edge: the steep reflectance gradient around 700 nm. The assumption of a cropland ecosystem is justified by the similarity between the values of BHRiso displayed in Fig. 3(b) and the corresponding climatological values for the cropland ecosystem class over the 50°–40° N latitude belt provided by Moody et al. [52

52. 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).

]. The assumption is also supported by the classification of the area as a cropland ecosystem in the IGBP Land Ecosystem Classification Map Image [55

55. IGBP Land Ecosystem Classification Map Image [Online]. Available: http://modis-atmos.gsfc.nasa.gov/ECOSYSTEM/ (Accessed: 21 April 2013).

].

Table 4 summarizes the estimated land and sea spectral albedos for typical observation conditions (identified by the standard test case with θv=20°, ϕv=75°, and ϕ0=160°). It is recalled that the sea albedo ρsea, used to compute contributions from multiple reflections at the water surface [Eq. (12)], is obtained through an approximate relationship [Eq. (14)]. Acknowledging the qualitative relevance of ρsea, tabulated data indicate very similar sea and land albedos up to about 510 nm, while they significantly differ in the NIR.

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

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5. Evaluation of Uncertainties and Benchmark of Simulated Products

The quantification of the adjacency effects, the estimate of its horizontal range, as well the sensitivity analyses on selected geophysical parameters and the study of the impact of the commonly applied approximations, necessarily require an accurate evaluation of the involved uncertainties.

Uncertainties on simulated adjacency radiance σLadj comprise independent contributions from the simulation procedure and from the definition of the input parameters. Assuming exact the definition of the atmospheric system, uncertainties on quantities simulated with the highly accurate FEM numerical code are considered negligible, and σLadj can be simply expressed as
σLadj=[(σLadjMC)2+(σLadjref)2]1/2,
(18)
where σLadjMC and σLadjref represent the contributions from the MC simulation procedure and from the definition of the input reflectance properties of the surface, respectively.

A. Uncertainties Connected to the NAUSICAA Simulation Procedure

The MC method is intrinsically associated with random noise: its computations are inherently affected by statistical uncertainties strictly depending on the number N of initialized photons and on the selected threshold for photon survival. Computational products may additionally be affected by systematic uncertainties, so that σLadjMC can be expressed as
σLadjMC=[(σLadjrnd)2+(δLadjsys)2]1/2,
(19)
where σLadjrnd and δLadjsys represent the contribution from random and systematic uncertainties of MC computations, respectively.

In this study σLadjrnd is required to not exceed the average radiometric resolution of selected ocean color sensors expressed in terms of the noise equivalent radiance difference, NEΔL [21

21. I. S. Robinson, Measuring the Oceans from Space (Springer-Verlag, 2004).

]. At each wavelength, NEΔL is defined as the at-sensor incremental radiance that can still be discriminated from noise when observing a typical signal [21

21. I. S. Robinson, Measuring the Oceans from Space (Springer-Verlag, 2004).

]. Making reference to the signal-to-noise-ratio (SNR) and the typical ocean color at-sensor radiance values provided by Hu et al. [56

56. C. Hu, L. Feng, Z. Lee, C. O. Davis, A. Mannino, C. R. McClain, and B. A. Franz, “Dynamic range and sensitivity requirements of satellite ocean color sensors: learning from the past,” Appl. Opt. 51, 6045–6062 (2012). [CrossRef]

], NEΔL has been determined for each considered ocean color sensor and at each selected wavelength. In addition to these sensor specific values, an average ocean color sensor radiometric resolution has been defined as NEΔL¯=2E0×105Wm2μm1sr1. It is noted that for SeaWiFS, especially in the visible channels, NEΔL is considerably higher than NEΔL¯ [56

56. C. Hu, L. Feng, Z. Lee, C. O. Davis, A. Mannino, C. R. McClain, and B. A. Franz, “Dynamic range and sensitivity requirements of satellite ocean color sensors: learning from the past,” Appl. Opt. 51, 6045–6062 (2012). [CrossRef]

]. By initializing N=107 photons the requirement σLadjrnd<NEΔL¯ is fully satisfied. Table 5 lists the 0.95 quantiles of σLadjrnd for all test cases. The level of confidence on NAUSICAA computations is 99.7%, corresponding to the probability that the computed values fall within three standard deviations of the expected true value.

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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Contributions to σLadj due to systematic uncertainties (biases) affecting the NAUSICAA computations, δLadjsys, have been evaluated by comparing upwelling surface radiances at TOA, LsfcTOA, obtained with Eq. (12) for an infinite uniform reflecting surface, with the corresponding values from the totally converged solution of the plane-parallel highly accurate FEM numerical code [24

24. 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]

], assumed as the reference. The analysis has been performed for all test cases by initializing N=107 photons and assuming (i) an ideal (lossless) perfectly diffuse (Lambertian) surface and (ii) a Fresnel-reflecting surface. As illustrated by the distribution of δMCFEM/E0=(LsfcMCTOALsfcFEMTOA)/E0 [sr1] in Fig. 4, results indicate the absence of biases between FEM LsfcFEMTOA, and NAUSICAA, LsfcMCTOA results. Considering that the two codes rely on fundamentally different approaches to solve the RTE, the extremely good agreement between them provides a robust validation for the NAUSICAA code. Furthermore, δMCFEM is always lower than the statistical uncertainty of NAUSICAA simulations with a 99.7% level of confidence. The above findings allow us to assume that σLadjMC equals σLadjrnd in the presence of an infinite homogenous underlying reflecting surface. Because of the high agreement obtained for both Lambertian and Fresnel reflecting surfaces, analogous considerations are expected to also apply for a nonuniform underlying reflecting surface.

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.

B. Uncertainties Related to the Definition of the Surface Reflectance Properties

NAUSICAA simulations of adjacency effects require the assumption of a finite surface grid of nonuniform reflectance properties surrounded by an infinite uniform background surface (see Section 3).

It is worthwhile to mention that adjacency contributions from distant regions are likely due to photons that, once reflected by the surface itself, propagate until the upper atmospheric layers where they are eventually scattered by gas molecules in an almost horizontal direction. The very low optical thickness characterizing those atmospheric layers allows these photons to travel long distances before undergoing other scattering events and eventually propagating into the sensor field of view (FOV). This also suggests that volcanic aerosols, thin cirrus clouds, as well as any departure from the assumption of a plane-parallel atmosphere may affect the described phenomenon.

On the basis of the above considerations and assuming an exact knowledge of the sea surface BRDF, uncertainties on Ladj from input surface reflectances, σLadjref [see Eq. (18)], comprise contributions from the reflectance properties (i) of the land and water elements within the surface grid (σLadjρl and σLadjRrs, respectively) and (ii) of the uniform background surface (σLadjbg):
σLadjref=[(σLadjρl)2+(σLadjRrs)2+(σLadjbg)2]1/2.
(20)

The modeling presented in Section 2 allows a simple evaluation of the contributions σLadjρl and σLadjRrs from parameters ρl and Rrs via error propagation of their uncertainties σρl and σRrs (as given in Sections 4.D and 4.C, respectively). It is noted that uncertainties due to the nonuniformity of the land albedo are accounted for in the definition of σρl. Conversely, uncertainties induced by the nonuniformity of the water albedo are considered negligible here. An evaluation of the uncertainties induced by the assumption of isotropic reflectance of land and water would require a dedicated study, which is out of the scope of this paper. The estimate of the adjacency radiance contribution originating from the background surface has been performed assuming that the infinite background surface is composed of an unknown combination of land and sea with the same reflectance properties of the land and sea elements within the surface grid of nonuniform reflectance properties. The background contribution has been thus computed along the whole transect for the standard case considering two extreme situations: a homogenous land background and a homogenous sea background. The average between these two computations has been adopted as the background contribution Ladjbg for all NAUSICAA simulations, and a spectral uncertainty σLadjbg=±Ladjbg has been assumed.

C. Uncertainties of Simulated Adjacency Radiance

For typical observation conditions and at sample wavelengths, Table 6 lists the overall uncertainties σLadj affecting simulated Ladj at the AAOT, as well as individual contributions σLadjx to σLadj from various sources. Notably, contributions from uncertainties in the simulation procedure, σLadjMC, are by far the lowest. Towards the blue end of the spectrum the highest uncertainty contributions are from Rrs, while at larger wavelengths σLadjρl and σLadjbg predominate. Overall results indicate combined uncertainties lower than NEΔL¯.

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

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D. Benchmark with Literature Data

To further assess the NAUSICAA code in the presence of a nonhomogeneous reflecting surface, simulated results have been benchmarked with data obtained with the algorithm developed by Sei [11

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

]. Sei [11

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

] has proposed a closed-form error analysis of the coastal adjacency problem for nadir view. The analysis has been performed adopting three common exponential approximations of the environment weighting function (which describes the contribution of the surface surrounding the target element) heuristically inferred from different MC simulations: specifically, those proposed by Reinersman and Carder [7

7. 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]

], Vermote et al. [57

57. 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).

], and Tanré et al. [58

58. D. Tanré, M. Herman, and P. Y. Deschamps, “Influence of the background contribution upon space measurements of ground reflectance,” Appl. Opt. 20, 3676–3684 (1981). [CrossRef]

].

In order to perform the benchmark, equivalent observation conditions have been assumed, namely, two Lambertian half-planes in quasi-nadir observation. Additionally, the same surface albedos and the same total aerosol and Rayleigh optical thicknesses have been adopted. Values of ΔLsfcTOA=(Lsfc,NHTOA/Lsfc,HTOA1)×100 (where suffix NH indicates a nonhomogeneous underlying reflecting surface, and suffix H an homogenous one) at sample wavelengths are displayed in Fig. 5 as a function of the distance from the coast. Results from Sei [11

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

] refer to the approximation of the environment weighting function proposed by Reinersman and Carder [7

7. 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]

]. Analogous results are obtained when adopting the approximations proposed by Vermote et al. [57

57. 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).

] and by Tanré et al. [58

58. D. Tanré, M. Herman, and P. Y. Deschamps, “Influence of the background contribution upon space measurements of ground reflectance,” Appl. Opt. 20, 3676–3684 (1981). [CrossRef]

]. Intercomparison results show optimal agreement. Still, a slight discrepancy with increasing distance from the coast indicates a slower convergence of NAUSICAA results. Differences are likely explained by an underestimate of adjacency effects with distance induced by the assumption of an exponential decay of the environment weighting functions. The applied exponential approximations were indeed acknowledged by the same authors “to account for the major part of the environment effect” [57

57. 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).

,58

58. D. Tanré, M. Herman, and P. Y. Deschamps, “Influence of the background contribution upon space measurements of ground reflectance,” Appl. Opt. 20, 3676–3684 (1981). [CrossRef]

], while Reinersman and Carder specifically stated that “the approximation was developed empirically [] and no claim is made that this method is optimal” [7

7. 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]

]. Results displayed in Fig. 5 are, moreover, in agreement with the slower convergence of MC simulations with respect to their exponential approximation as reported by Reinersman and Carder (see Fig. 27 of Ref. [7

7. 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]

]).

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.

6. Results and Discussion

Simulated results are presented and discussed through Ladj/E0 [sr1] and its percent contribution to the TOA signal, ξLtot=(Ladj/Ltot)×100, along the study transect with specific focus on the AAOT site.

A. Adjacency Effects along the Transect

The quantitative evaluation of the adjacency effects in the selected region is herein illustrated through a statistical analysis of ξLtot over all test cases and for each observed sea element along the considered transect. Results are illustrated in Fig. 6 at sample wavelengths as a function of the distance covered along the transect moving away from the coast. It is underlined that, due to the complex coastal pattern, the distance along the transect does not correspond to the minimum distance from the mainland. It is additionally noted that a different scale is applied to display data at 865 nm. It is finally pointed out that Lw is assumed spatially invariant.

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.

As expected, adjacency effects monotonically decrease when moving away from the coast. A minor non-monotonicity occurs in proximity of an isolated group of two land elements regarded as a small island in the applied surface grid [see Fig. 1(b)]. Values of mean adjacency contributions ξ¯Ltot lower than ±1% are observed throughout the transect up to 555 nm, where land and sea albedos are similar (see Table 4). At the other wavelengths, ξ¯Ltot always remains positive, exhibiting a steep decrease with distance. Values nearby the coast range from 2% at 670 nm up to 11% at 865 nm. As expected, the highest values occur at 865 nm, where the land is highly reflective and the water highly absorbing. All along the transect the sample variances are larger than the uncertainties on simulated results.

To further investigate the spectral and spatial trend of adjacency effects, Fig. 7 displays the average normalized adjacency radiance L¯adj/E0 for all test cases together with the separate average contributions originating from the nearby land, and from the masked water and sea surface [Eq. (15)]. It is noted that the two latter terms have negative sign. The mean land contribution L¯landTOA exhibits a correlation with both the atmospheric scattering intensity and the land spectral albedo. This is deduced by observing higher values where the land albedo is higher (in the NIR) and/or where the atmosphere is more scattering (toward the blue end of the spectrum). The same holds, with respect to the water-leaving radiance, for the masked water contribution L˜¯wTOA. The masked sea surface contribution L˜¯ssTOA is strongly correlated to the scattering properties of the atmosphere: it decreases moving from the blue to the NIR. It is noted here that the land contribution is not always the largest: Fig. 7 clearly shows that towards the blue end of the spectrum mean contributions from the masked sea are larger than those from the land.

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.

Figure 7 furthermore eases the interpretation of the negative peaks in correspondence of the small island (peaks are more evident in Fig. 6), which occur even at wavelengths where the land albedo exceeds the sea one (e.g., 670 nm; see Table 4). Plots distinctly indicate that such peaks are a consequence of the significant sea surface contribution masked by the island itself. This contribution is particularly strong due to the extreme forward peak of the sea surface BRDF and the location of the island in the solar half-plane, identified by Δϕ=|ϕvϕ0|<90°. To better illustrate the dependence of adjacency effects on the mutual position of land and Sun, Ladj/E0 is plotted along the study transect [Fig. 8(a)] and along a parallel transect positioned directly south of the small island [Fig. 8(b)]. The separate contributions originating from the nearby mainland, and the masked water and sea surface [Eq. (15)], are also indicated. Data are for typical observation conditions at 670 nm. The small island lays in the solar half-plane in the first case, and in the antisolar half-plane (for which Δϕ>90°) in the second case. Land and masked water contributions are clearly the same for sea elements located north or south of the island. Conversely, the masked sea surface contribution is much higher when the land is located in the solar half-plane, causing a global decrease in Ladj/E0.

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.

The masked sea surface contribution due to the mainland located in the solar half-plane is also the reason for negative adjacency contributions up to 1% at 490 nm (Fig. 6), where land and sea albedos are indeed very similar (Table 4).

While a constant Lw is assumed along the whole transect, the increasing water turbidity in approaching the coast may actually lead to an increase in Lw, particularly in the red spectral region [20

20. 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]

,50

50. 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.

]. Yet, an analysis performed at 670 nm assuming an exponential increase of Lw towards the coast up to values threefold those observed at the AAOT has not shown appreciable changes in Ladj and ξLtot.

To investigate the atmospheric, geometric, and seasonal dependencies of the adjacency effects in the study region, a sensitivity analysis has been performed accounting for the range of variation of the input parameters.

Adjacency effects show appreciable sensitivity to the aerosol load (see Fig. 9). As expected [11

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

], the lower the concentration, the slower the decrease of adjacency effects with distance. On the contrary, data do not show any appreciable dependence on the aerosol type. Results are only displayed in the NIR, where contributions are the largest.

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. 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.

To better explain the origin of the angular dependence of adjacency effects, Fig. 11 displays results obtained for analogous conditions, but assuming an isotropic sea surface reflectance with albedo ρss=0.04. Increasing the ground-to-sensor path, the probability for the radiance reflected by the surface to be scattered into the sensor FOV increases. At those wavelengths where land and sea albedos only slightly differ (e.g., 490 nm), if the BRDFs are also equivalent, the increase is the same for both contributions, and a compensation occurs (Fig. 11 left panel). The zenith angular dependence of Ladj observed in Fig. 10 (left panel) is hence primarily a consequence of the strong reflectance anisotropy of the sea surface. Conversely, when the land albedo is consistently larger than the sea one (e.g., 865 nm) and no compensation can occur anymore, the dependence on the zenith angle of observation is simply a consequence of the longer ground-to-sensor path (see Figs. 10 and 11 right panels).

Fig. 11. Same as in Fig. 10 but assuming an isotropic sea surface reflectance with albedo ρss=0.04.

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

Although not shown here, it is worthwhile to mention that adjacency effects are, as expected, slightly larger when the sensor is viewing the sea from over the land.

Finally, adjacency effects show a strong seasonal dependence (see Fig. 14). They increase in the summer, when the land is highly reflecting, the water is highly absorbing, and the Sun elevation is high. Conversely, they decrease in winter, when the land albedo is low, the water albedo is also at its maximum, and the Sun elevation is at its minimum. It is noted that ξ¯Ltot decreases with increasing solar zenith angle as a consequence of a corresponding decrease in the irradiance reaching the surface and an increase of the sea surface reflectance. In proximity of the coast, ξ¯Ltot at 865 nm seasonally varies from 4% to 17% from winter to summer, respectively.

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.

The results illustrated in this section are summarized in Table 7 for representative wavelengths and at given distances from the coast. These latter distances are computed as the minimum distance between the center of the target element and the center of the closest land element. Statistical values (i.e., mean and standard deviation) are given for the whole set of test cases, as well as for subsamples of specific geophysical quantities.

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

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B. Adjacency Effects at the AAOT

The AAOT, which is located at the 25th km along the selected transect and at 15 km from the closest mainland, is a recognized validation site for satellite ocean color data products. Consistent effort has been made over the years to investigate, quantify (and eventually correct) all possible sources of uncertainties affecting both in situ measurements and the satellite-retrieved products [18

18. 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]

,59

59. 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]

61

61. F. Mélin and G. Zibordi, “Vicarious calibration of satellite ocean color sensors at two coastal sites,” Appl. Opt. 49, 798–810 (2010). [CrossRef]

]. This sets the premises for an accurate theoretical quantification of adjacency perturbations in satellite ocean color data at the AAOT.

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. 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. 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. 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.

No significant differences are observed in the adjacency radiance contribution to the signal at the sensor when considering the geometries of observation of the selected sensors (Fig. 19). MERIS values, slightly below the average and with a smaller variance, are justified by the absence of very slanted observations (θv<40°). Consistently, the values slightly above the average and the larger variances observed for SeaWiFS are due to the absence of quasi-nadir observations (θv20°).

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.

C. Sensitivity Analysis on Commonly Applied Approximations

The need to provide easy-to-implement formulations of the adjacency effects in coastal waters has been commonly accomplished by applying one or more of the following assumptions: i) isotropic surface reflectance [7

7. 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]

,11

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

], ii) nadir observation [11

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

], iii) straight coastline [11

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

], and iv) single scattering approximation [9

9. R. Santer and C. Schmechtig, “Adjacency effects on water surfaces: primary scattering approximation and sensitivity study,” Appl. Opt. 39, 361–375 (2000). [CrossRef]

]. Nevertheless, the physical impact of most of these approximations has never been thoroughly assessed. Their effects are individually analyzed here for the considered study region.

The need to take into account the Fresnel reflectance of the masked sea surface contribution was already underlined in [9

9. R. Santer and C. Schmechtig, “Adjacency effects on water surfaces: primary scattering approximation and sensitivity study,” Appl. Opt. 39, 361–375 (2000). [CrossRef]

] and as well identified in Section 6.A. Yet, most studies assume an isotropic reflectance for both land and sea [7

7. 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]

,11

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

]. Figure 20 presents at sample wavelengths the average normalized adjacency radiance over all test cases, L¯adj/E0, along the considered transect. Computations have been performed assuming an isotropic sea surface with albedo ρss=0.04 and accounting for the BRDF of a rough sea surface (defined by Ws=3.3ms1). It is noted that latter results, significantly sensitive to the Sun azimuth, may appreciably vary for different land locations with respect to the Sun. For all considered cases, neglecting the anisotropy of the sea surface reflectance leads to misestimates of L¯adj particularly significant at the lower wavelengths (e.g., at 490 nm L¯adj is underestimated by approximately 40% throughout the transect). Moving towards the NIR, misestimates become appreciable only in the right vicinity of the coast. Actually, in correspondence of the AAOT (Fig. 21) differences are only appreciable up to 510 nm. Misestimates are expected to increase with the sensor and Sun zeniths. Indeed, the specular reflectance of the sea surface sharply increases for incident angles larger than 60° [27

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

]. Overall results indicate the need to take into account the anisotropy of the sea surface reflectance, particularly towards the blue end of the spectrum.

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. 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.

The results additionally suggest enquiring the need to consider the intrinsic directional reflectance properties of the land, here assumed isotropic (conversely, the water reflectance can be assumed with good approximation as isotropic). Even though a detailed investigation fully addressing the topic is out of the scope of this paper, some general considerations may be drawn from examples of land BRDF. The majority of terrestrial surfaces exhibit a bowl-shaped anisotropy, although surface heterogeneity may also lead to a bell-shaped pattern [62

62. 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]

]. Realistic land BRDF can be obtained through the parametric semi-empirical model developed by Rahman et al. (the so-called RPV model [63

63. 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]

]). The overall shape of the angular distribution is there defined through three parameters: ρ0, representing the reflectance of the surface for illumination and viewing at the zenith; k, controlling the slope of the reflectance with respect to illumination and viewing angles [it is close to 1.0 for a quasi-Lambertian surface, lower (higher) than 1.0 when a bowl-shaped (bell-shaped) pattern dominates]; and Θ, which establishes the degree of forward (positive Θ) or backward (negative Θ) scattering. As an example, Fig. 22 reproduces the land BRDF obtained assuming k=0.6, 1.0, and 1.2 [62

62. 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]

,63

63. 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]

], Θ=0, accounting for the default relative increase in reflectance in the direction of illumination (the so-called hotspot), and selecting ρ0 to obtain albedo values ρl=0.04 and 0.26 (corresponding to the values applied in the present work at 412 and 865 nm for typical observation conditions; see Table 4). The BRDFs of a sea surface roughed by wind speeds Ws=2.3, 3.3, and 4.3ms1 [34

34. 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]

] are also shown. Data are plotted for an incident direction defined by θi=45° and ϕi=0°, and for observations performed in the principal solar plane (the vertical plane identified by the incoming direct solar radiation). In the plane normal to the principal solar plane, the sea surface BRDF is close to zero. The considered sample data suggest that accounting for the anisotropy in the land reflectance might affect simulations of adjacency effects towards the NIR, but not in the blue end of the spectrum. They additionally suggest the need to investigate the influence of wind speed on adjacency effects.

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. 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.

The influence of assuming a straight coastline clearly depends on the actual coastal morphology. Additionally, due to the strong anisotropy of the sea surface reflectance in the forward direction, it also depends on the orientation of the coast with respect to Sun and sensor (as already evidenced in Section 6.A). The sensitivity analysis has been performed separately for each sea element along the transect by assuming a straight coastline located at the minimum distance from the land and oriented along the south–north direction. By assuming typical observation conditions, the results summarized in Fig. 24 indicate significant differences only in the Venice Lagoon, where the coastal morphology highly differs from a straight coastline. Differences at the AAOT are negligible throughout the spectral region. Misestimates might be more appreciable when the land contribution is larger, as in summer and for slanted observations.

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.

Finally, Fig. 25 displays results obtained by solving the RTE accounting or not for atmospheric multiple scattering. Values are given at representative wavelengths and for typical observation conditions. All separate contributions to the adjacency radiance [LlandTOA originating from the land and L˜wTOA and L˜ssTOA originating from the masked sea; see Eq. (15)] are largely underestimated in single scattering approximation. Their underestimation consistently increases towards the blue end of the spectrum (where the atmosphere is more scattering) and moving away from the coast (where the multiple scattering contribution is larger due to the longer path the radiance reflected by the land has to cover before entering the sensor IFOV). However, the underestimation of the sea mask contribution is more pronounced as a consequence of the strong anisotropy of the sea surface reflectance: Fig. 26 clearly illustrates how the misestimates induced at 490 nm by the single scattering approximation drastically decrease under the assumption of an isotropic sea surface reflectance (ρss=0.04). This is explained by acknowledging that in single scattering approximation L˜ssTOA originates only from reflection of the direct solar irradiance. This generates an even stronger anisotropic angular distribution of L˜ss, which becomes non-null only in a narrow cone centered on the direction specular to that of the direct Sun beam. As a consequence, the masked sea surface contribution practically disappears throughout the spectrum, except in the right vicinity of the land. Misestimates induced on the adjacency radiance clearly depend on the relative importance of the different contributions. Where the masked sea contribution is more important (e.g., at 490 nm), the misestimate of the adjacency radiance is particularly large. Compensations may eventually occur at some wavelengths (e.g., at 555 and 670 nm for typical observation conditions). In the NIR the underestimate of the adjacency radiance reflects the underestimate of LlandTOA, which is the only relevant contribution. In conclusion, the single scattering approximation would not allow appreciating any adjacency contribution up to 510 nm, except in the right vicinity of the land, and it would induce an appreciable underestimate of adjacency effects even in the NIR. Some compensation may arise at certain wavelengths, depending on the specific observation conditions. Results for the AAOT are summarized in Fig. 27.

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

Overall results indicate that, out of the Venice Lagoon, simulations could be performed for a straight coastline, opportunely oriented, without a significant loss in accuracy. Conversely, they highlight the need to properly take into account the anisotropy of the sea surface reflectance, particularly at the visible wavelengths, the actual zenith angle of observation, and the atmospheric multiple scattering.

The above considerations have been drawn accounting for an average radiometric resolution of the sensor. Clearly, for a less sensitive sensor such as SeaWiFS, the misestimates induced by the approximations may become less significant.

D. On the Horizontal Range of Adjacency Effects

For typical observation conditions and a straight coastline along the south–north direction, adjacency effects have been analyzed as a function of the distance from the coast by accounting for the radiometric resolutions of different ocean color sensors [56

56. C. Hu, L. Feng, Z. Lee, C. O. Davis, A. Mannino, C. R. McClain, and B. A. Franz, “Dynamic range and sensitivity requirements of satellite ocean color sensors: learning from the past,” Appl. Opt. 51, 6045–6062 (2012). [CrossRef]

]. Figure 28 illustrates Ladj/E0 at representative wavelengths along a transect perpendicular to the coast. The radiometric noise thresholds for SeaWiFS and MODIS sensors are also indicated [56

56. C. Hu, L. Feng, Z. Lee, C. O. Davis, A. Mannino, C. R. McClain, and B. A. Franz, “Dynamic range and sensitivity requirements of satellite ocean color sensors: learning from the past,” Appl. Opt. 51, 6045–6062 (2012). [CrossRef]

]. The horizontal scale of Ladj is 10km. Considering that the selected observation conditions correspond to a clear atmosphere, results are consistent with those from Tanré et al. [58

58. D. Tanré, M. Herman, and P. Y. Deschamps, “Influence of the background contribution upon space measurements of ground reflectance,” Appl. Opt. 20, 3676–3684 (1981). [CrossRef]

] and Vermote et al. [57

57. 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).

], indicating a horizontal scale for the environment weighting function of 1km for the aerosol scattering and 10km for the Rayleigh scattering.

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.

However, results clearly indicate that for a sensor such as SeaWiFS the adjacency radiance becomes lower than the radiometric noise threshold only at 25km off the coast in the NIR. Differently, for a more sensitive sensor such as MODIS, the adjacency radiance at 555 and 670 nm remains above the estimated sensor radiometric noise up to 20km, while in the NIR it may still be appreciable at distances larger than 30 km. At blue wavelengths the uncertainties on simulated results are much larger than at other wavelengths (particularly towards the coast), and most importantly, results at blue wavelengths may be particularly sensitive to the orientation of the coast with respect to the Sun and to a correct characterization of the sea surface roughness (see Section 6.C). Results from the analysis presented in this section are summarized in Table 8.

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

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The estimates presented for the horizontal range of adjacency effects have been determined for typical observation conditions. Recalling considerations drawn in Section 6.A, the spatial extent of adjacency effects is expected to be larger than the average in summer, for off-nadir views, for observations from over the land, and for a lower aerosol optical thickness. Conversely, it is predicted to be smaller in winter, for nadir viewing, for observations from over the sea, and for a higher aerosol optical thickness.

It is finally underlined that the above results were obtained with the assumption of a plane-parallel atmosphere. Any actual departure from this assumption (i.e., any horizontal inhomogeneity of the atmospheric properties) may consistently influence the horizontal range of adjacency effects.

7. Summary and Conclusions

A methodology to accurately quantify and analyze the adjacency effects in coastal waters accounting for the Fresnel reflectance of a wind-roughed sea surface, off-nadir views, the actual coastal morphology, and atmospheric multiple scattering has been illustrated. A modeling of the adjacency radiance has been proposed assuming isotropic and homogeneous land and water reflectances, allowing the decoupling of land and water optical properties from atmospheric scattering. The proposed model additionally allow distinguishing between the different contributions to the adjacency radiance, namely the land contribution (i.e., the radiance at the sensor originating from the area covered by the land) and the masked water and sea surface contributions (i.e., the water-leaving radiance and the reflected sea surface radiance that would reach the sensor from the same area if still covered by the sea).

Simulations requiring a full 3D description of the propagating system have been performed with the newly developed NAUSICAA backward MC code. Other simulations have been carried out with the highly accurate FEM plane-parallel numerical code.

Adjacency effects have been simulated for realistic and representative observation conditions along a transect crossing the Venice Lagoon and intercepting the AAOT site in the northern Adriatic Sea (utilized to support satellite ocean color validation activities). The description of the propagating system includes observation geometries representative for SeaWiFS, MODIS, and MERIS ocean color sensors; seasonal land and water optical properties and typical illumination conditions; the atmospheric variability observed for clear conditions in the northern Adriatic Sea; and a detailed picture of the complex coastal morphology.

An accurate evaluation of the uncertainties affecting simulated data has been performed accounting for an average ocean color sensor radiometric resolution. This included an assessment procedure of NAUSICAA simulated results through comparison with results from the FEM numerical plane-parallel code for all considered test cases, and a benchmark with respect to data from the literature.

The analysis of the average contribution ξ¯Ltot of adjacency radiance to the total signal at TOA indicates values lower than ±1% throughout the transect in the 412–555 nm spectral interval, where land and water spectral albedos are similar. At the other wavelengths, ξ¯Ltot always remains positive and shows a steep spatial gradient with values at the coast ranging from 2% at 670 nm to 11% at 865 nm. At the AAOT (about 15 km offshore) ξ¯Ltot never exceeds ±0.5% at the visible wavelengths, but becomes appreciably larger in the NIR where it reaches 2%. The highest values occur in the NIR, where the land is highly reflective and the water highly absorbing.

Adjacency effects exhibit sensitivity to the aerosol load and no appreciable dependence on the aerosol type. Furthermore, adjacency effects show a strong seasonal dependence, with increased values in summer when the land is highly reflecting, the water is highly absorbing, and the Sun elevation is high. Conversely, a decrease is observed in winter. At 865 nm and in proximity of the coast, ξ¯Ltot seasonally spans from 5% in winter to 18% in summer.

Adjacency effects are slightly larger for a sensor looking at the sea from over the land. Values display a significant increase with the zenith angle of observation, a slight variation with the Sun-sensor relative azimuth, and an appreciable dependence on the mutual position of land and Sun. The latter two are a consequence of the strong anisotropy of the sea surface reflectance, which induces a significant dependence of adjacency effects on the Sun azimuth. The sea surface reflectance anisotropy is also mostly responsible for adjacency effects at those wavelengths where land and sea albedos are similar (412–510 nm).

No significant differences have been found when distinguishing among the observation geometries of the considered satellite sensors.

The need to provide easy-to-implement formulations of the adjacency effects in coastal waters has been commonly accomplished by applying approximations, such as an exponential decay of the environment weighting function [7

7. 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]

,9

9. R. Santer and C. Schmechtig, “Adjacency effects on water surfaces: primary scattering approximation and sensitivity study,” Appl. Opt. 39, 361–375 (2000). [CrossRef]

,11

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

], Lambertian reflecting surfaces [7

7. 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]

,11

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

], a nadir geometry of observation [11

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

], a straight coastline [11

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

], and the single scattering approximation [9

9. R. Santer and C. Schmechtig, “Adjacency effects on water surfaces: primary scattering approximation and sensitivity study,” Appl. Opt. 39, 361–375 (2000). [CrossRef]

]. The separate impact of such approximations on the simulation of adjacency effects in the selected study region has been analyzed considering significant any misestimate larger than the average radiometric resolution of the selected sensor, which in turn has been assumed as the upper limit for random uncertainties on simulated data.

The analysis shows that the assumption of an exponential decay of the environment weighting functions leads to a slight underestimate of adjacency effects with distance. The impact of neglecting the anisotropy of the sea surface reflectance is particularly significant towards shorter wavelengths: the dependence of the adjacency effects on the angle of observation and on the mutual position of land and Sun disappears, while the average adjacency contributions are significantly reduced (e.g., by 40% throughout the transect at 490 nm). Moving towards the NIR, misestimates become appreciable only in the right vicinity of the coast. A quasi-nadir geometry of observation considerably underestimates off-nadir adjacency contributions throughout the transect. At 865 nm average adjacency contributions for θv=50° are 40% larger than those for θv=5°. The assumption of a straight coastline located for each sea element at the minimum distance from the land and oriented along the south–north direction indicates significant differences only for observations in the Venice Lagoon, where the coastal morphology decidedly differs from a straight coastline. Finally, solving the RTE in single scattering approximation induces misestimates that are particularly important at shorter wavelengths, but still appreciable in the NIR.

In conclusion, overall results point out that, within the accuracy limits defined by the radiometric resolution of the ocean color sensors, adjacency effects in coastal waters might be significant at both visible and NIR wavelengths up to several kilometers off the coast. The theoretical quantification of adjacency effects should rely on a proper description of the atmospheric aerosol concentration, account for the seasonal dependence of geophysical parameters, and include an appropriate description of multiple scattering events. It should definitely consider the actual angle of observation, allowing for off-nadir views. Additionally, and particularly at shorter wavelengths, it should take into account the radiance contributions from the masked sea region, include a proper description of the intrinsic directional properties of the sea surface, and take into consideration the land location with respect to the Sun and sensor position. Conversely, a straight coastline, opportunely oriented with respect to the Sun, can be assumed without a significant loss in accuracy, besides cases of complex coastal patterns such as the semi-enclosed basin of the Venice Lagoon.

The above considerations are relevant indications for the development of approximate algorithms for the actual quantification of adjacency effects in coastal waters. It is, however, remarked that the influence on retrieved products of the approximations applied in an operational algorithm for the correction of adjacency effects strictly depends on the overall correction procedure. Because of this, targeted analysis should be conducted for each specific data reduction scheme.

The conclusive remarks are valid for mid-latitude coastal regions characterized by a deciduous vegetation type in the absence of snow. In the presence of nondeciduous vegetation results would likely show a limited seasonal variation and higher average values. The presence of snow would exhibit radically different results, leading to consistent adjacency effects in the blue end part of the spectrum [12

12. 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]

].

Once the geometric and atmospheric inputs are defined, the proposed modeling of the adjacency radiance allows an easy evaluation of the adjacency effects for a wide variety of land and water spectral signatures. Thus, the possibility to assume a straight coastline without a significant loss in accuracy suggests that, widening the range of the selected geometric and atmospheric features, the proposed methodology could be easily applied to evaluate adjacency effects in the presence of a large variety of realistic conditions. Look-up tables or parameterizations of the modeling functions C and W could be the basis for the development of an operational scheme to correct adjacency effects in coastal waters.

The results from this study furthermore constitute an important reference frame for the assessment of any algorithm for the quantification and correction of adjacency effects. This is particularly relevant when considering the difficulties encountered in the experimental quantification of adjacency effects.

The dependence of adjacency effects on the intrinsic directional reflectance properties of the surface suggests the need to further investigate the sensitivity of results on land reflectance anisotropy and wind velocity. Finally, the influence of different aerosol profiles (including the presence of volcanic aerosols), thin cirrus clouds, as well as any departure from the adopted assumption of a plane-parallel atmosphere should also be investigated.

The authors acknowledge Dr. Michel Verstraete, Dr. Frederic Mélin, Dr. Jean-Francois Berthon, Dr. Jean-Luc Widlowski, and Dr. Nadine Gobron for the fruitful discussions.

References

1.

J. Otterman and R. S. Fraser, “Adjacency effects on imaging by surface reflection and atmospheric scattering: cross radiance to zenith,” Appl. Opt. 18, 2852–2860 (1979). [CrossRef]

2.

D. Tanré, M. Herman, P. Y. Deschamps, and A. de Leffe, “Atmospheric modeling for space measurements of ground reflectances, including bidirectional properties,” Appl. Opt. 18, 3587–3594 (1979). [CrossRef]

3.

Y. J. Kaufman, “Effect of the Earth’s atmosphere on contrast for zenith observation,” J. Geophys. Res. 84, 3165–3172 (1979). [CrossRef]

4.

Y. J. Kaufman, “Atmospheric effect on spatial resolution of surface imagery,” Appl. Opt. 23, 3400–3408 (1984). [CrossRef]

5.

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

6.

E. Vermote and A. Vermeulen, “Atmospheric correction algorithm: spectral reflectances (MOD09),” NASA MODIS ATBD version 4.0 (1999).

7.

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]

8.

H. Yang, H. R. Gordon, and T. Zhang, “Island perturbation to the sky radiance over the ocean: simulations,” Appl. Opt. 34, 8354–8362 (1995). [CrossRef]

9.

R. Santer and C. Schmechtig, “Adjacency effects on water surfaces: primary scattering approximation and sensitivity study,” Appl. Opt. 39, 361–375 (2000). [CrossRef]

10.

K. G. Ruddick, F. Ovidio, and M. Rijkeboer, “Atmospheric correction of SeaWiFS imagery for turbid coastal and inland waters,” Appl. Opt. 39, 897–912 (2000). [CrossRef]

11.

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

12.

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]

13.

H. W. Gordon and M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 33, 443–452 (1994). [CrossRef]

14.

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]

15.

R. Santer and F. Zagolski, “ICOL—improve contrast between ocean and land,” ATBD-MERIS Level 1-C, version 1.1 (2009).

16.

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]

17.

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.

18.

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]

19.

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]

20.

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]

21.

I. S. Robinson, Measuring the Oceans from Space (Springer-Verlag, 2004).

22.

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]

23.

V. B. Kisselev, L. Roberti, and G. Perona, “Finite-element algorithm for radiative transfer in vertically inhomogeneous media: numerical scheme and applications,” Appl. Opt. 34, 8460–8471 (1995). [CrossRef]

24.

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]

25.

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]

26.

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]

27.

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

28.

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]

29.

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]

30.

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]

31.

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).

32.

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

33.

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).

34.

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]

35.

C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. 44, 838–850 (1954). [CrossRef]

36.

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

37.

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

38.

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]

39.

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]

40.

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

41.

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]

42.

C. Fröhlich and G. E. Shaw, “New determination of Rayleigh scattering in the terrestrial atmosphere,” Appl. Opt. 19, 1773–1775 (1980). [CrossRef]

43.

A. T. Young, “Revised depolarization corrections for atmospheric extinction,” Appl. Opt. 19, 3427–3428 (1980). [CrossRef]

44.

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

45.

L. Elterman, “UV, visible, and IR attenuation for altitudes to 50  km,” Environmental Research Paper No. 285, AFCRL-68-0153 (Air Force Cambridge Research Laboratory, 1968).

46.

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

47.

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

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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).

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56.

C. Hu, L. Feng, Z. Lee, C. O. Davis, A. Mannino, C. R. McClain, and B. A. Franz, “Dynamic range and sensitivity requirements of satellite ocean color sensors: learning from the past,” Appl. Opt. 51, 6045–6062 (2012). [CrossRef]

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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).

58.

D. Tanré, M. Herman, and P. Y. Deschamps, “Influence of the background contribution upon space measurements of ground reflectance,” Appl. Opt. 20, 3676–3684 (1981). [CrossRef]

59.

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]

60.

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

61.

F. Mélin and G. Zibordi, “Vicarious calibration of satellite ocean color sensors at two coastal sites,” Appl. Opt. 49, 798–810 (2010). [CrossRef]

62.

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]

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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]

OCIS Codes
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(010.5620) Atmospheric and oceanic optics : Radiative transfer
(010.0280) Atmospheric and oceanic optics : Remote sensing and sensors

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: August 12, 2013
Revised Manuscript: November 15, 2013
Manuscript Accepted: January 8, 2014
Published: March 5, 2014

Virtual Issues
Vol. 9, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Barbara Bulgarelli, Viatcheslav Kiselev, and Giuseppe Zibordi, "Simulation and analysis of adjacency effects in coastal waters: a case study," Appl. Opt. 53, 1523-1545 (2014)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=ao-53-8-1523


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References

  1. J. Otterman and R. S. Fraser, “Adjacency effects on imaging by surface reflection and atmospheric scattering: cross radiance to zenith,” Appl. Opt. 18, 2852–2860 (1979). [CrossRef]
  2. D. Tanré, M. Herman, P. Y. Deschamps, and A. de Leffe, “Atmospheric modeling for space measurements of ground reflectances, including bidirectional properties,” Appl. Opt. 18, 3587–3594 (1979). [CrossRef]
  3. Y. J. Kaufman, “Effect of the Earth’s atmosphere on contrast for zenith observation,” J. Geophys. Res. 84, 3165–3172 (1979). [CrossRef]
  4. Y. J. Kaufman, “Atmospheric effect on spatial resolution of surface imagery,” Appl. Opt. 23, 3400–3408 (1984). [CrossRef]
  5. W. A. Pearce, “Monte Carlo study of the atmospheric spread function,” Appl. Opt. 25, 438–447 (1986). [CrossRef]
  6. E. Vermote and A. Vermeulen, “Atmospheric correction algorithm: spectral reflectances (MOD09),” NASA MODIS ATBD version 4.0 (1999).
  7. 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]
  8. H. Yang, H. R. Gordon, and T. Zhang, “Island perturbation to the sky radiance over the ocean: simulations,” Appl. Opt. 34, 8354–8362 (1995). [CrossRef]
  9. R. Santer and C. Schmechtig, “Adjacency effects on water surfaces: primary scattering approximation and sensitivity study,” Appl. Opt. 39, 361–375 (2000). [CrossRef]
  10. K. G. Ruddick, F. Ovidio, and M. Rijkeboer, “Atmospheric correction of SeaWiFS imagery for turbid coastal and inland waters,” Appl. Opt. 39, 897–912 (2000). [CrossRef]
  11. A. Sei, “Analysis of adjacency effects for two Lambertian half-spaces,” Int. J. Remote Sens. 28, 1873–1890 (2007). [CrossRef]
  12. 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]
  13. H. W. Gordon and M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 33, 443–452 (1994). [CrossRef]
  14. 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]
  15. R. Santer and F. Zagolski, “ICOL—improve contrast between ocean and land,” ATBD-MERIS Level 1-C, version 1.1 (2009).
  16. 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]
  17. 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.
  18. 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]
  19. 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]
  20. 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]
  21. I. S. Robinson, Measuring the Oceans from Space (Springer-Verlag, 2004).
  22. 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]
  23. V. B. Kisselev, L. Roberti, and G. Perona, “Finite-element algorithm for radiative transfer in vertically inhomogeneous media: numerical scheme and applications,” Appl. Opt. 34, 8460–8471 (1995). [CrossRef]
  24. 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]
  25. 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]
  26. 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]
  27. C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).
  28. 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]
  29. 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]
  30. 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]
  31. 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).
  32. G. Zibordi and B. Bulgarelli, “Effects of cosine error in irradiance measurements from field ocean color radiometers,” Appl. Opt. 46, 5529–5538 (2007). [CrossRef]
  33. 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).
  34. 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]
  35. C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. 44, 838–850 (1954). [CrossRef]
  36. H. Iwabuchi, “Efficient Monte Carlo methods for radiative transfer modeling,” J. Atmos. Sci. 63, 2324–2339 (2006). [CrossRef]
  37. L. Roberti, “Monte Carlo radiative transfer in the microwave and in the visible: biasing techniques,” Appl. Opt. 36, 7929–7938 (1997). [CrossRef]
  38. 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]
  39. 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]
  40. E. Vigroux, “Contribution à l’étude expérimentale de l’absorption de l’ozone,” Ann. Phys. 8, 709–762 (1953).
  41. 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]
  42. C. Fröhlich and G. E. Shaw, “New determination of Rayleigh scattering in the terrestrial atmosphere,” Appl. Opt. 19, 1773–1775 (1980). [CrossRef]
  43. A. T. Young, “Revised depolarization corrections for atmospheric extinction,” Appl. Opt. 19, 3427–3428 (1980). [CrossRef]
  44. A. Ångström, “Techniques of determining the turbidity of the atmosphere,” Tellus 13, 214–223 (1961). [CrossRef]
  45. L. Elterman, “UV, visible, and IR attenuation for altitudes to 50  km,” (Air Force Cambridge Research Laboratory, 1968).
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