Abstract

The making of atmospheric corrections is a critical task in the interpretation of ocean color imagery. In coastal areas, a fraction of the light reflected by the land reaches a sensor. Modeling the reduction of image contrast when the atmospheric turbidity increases, the so-called adjacency effect, requires large amounts of computing time. To model this effect we developed a simple approach based on the primary scattering approximation for both nadir and off-nadir views. A sensitivity study indicates that the decisive criterion for measurement accuracy for aerosols is their vertical distribution. As this distribution cannot generally be determined from space, it is not possible to include a suitable correction of the adjacency effects on satellite imagery. Conversely, we propose a simple correction for molecular scattering based on the isotropic approximation. We also address the problem of reduction of the coupling between the Fresnel reflection and the atmosphere for observations of coastal water. We study the influence of the adjacency effects on determination of the abundance of chlorophyll in water by combining use of the red and the infrared bands for aerosol remote sensing and the blue/green-ratio technique for retrieval of these data.

© 2000 Optical Society of America

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References

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  1. D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: 5S code,” Int. J. Remote Sens. 11, 659–668 (1990).
    [CrossRef]
  2. D. Tanré, M. Herman, P. Y. Deschamps, “Influence of the background contribution upon space measurements of ground reflectance,” Appl. Opt. 20, 3676–3684 (1981).
    [CrossRef] [PubMed]
  3. D. Tanré, P. Y. Deschamps, C. Devaux, M. Herman, “Estimation of Saharan aerosol optical thickness from blurring effects in Thematic Mapper data,” J. Geophys. Res. 93, 15,955–15,964 (1988).
    [CrossRef]
  4. D. Tanré, M. Legrand, “On the satellite retrieval of Saharan dust optical thickness over land: two different approaches,” J. Geophys. Res. 9, 5221–5227 (1991).
    [CrossRef]
  5. E. F. Vermote, N. El Saleous, C. O. Justice, Y. J. Kaufman, J. L. Privette, L. Remer, J. C. Roger, D. Tanré, “Atmospheric correction of visible to middle-infrared EOS–MODIS data over land surfaces: background, operational algorithm and validation,” J. Geophys. Res. 102, 17,131–17,141 (1997).
    [CrossRef]
  6. P. N. Reinersman, 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] [PubMed]
  7. J. V. Martonchik, D. J. Diner, R. A. Kahn, T. P. Ackerman, M. Verstraete, B. Pinty, H. R. Gordon, “Techniques for the retrieval of aerosol properties over land and ocean using multi-angle imaging,” IEEE Trans. Geosci. Remote Sens. 36, 1212–1227 (1998).
    [CrossRef]
  8. D. J. Diner, J. V. Martonchick, “Influence of the aerosol scattering on atmospheric blurring of surface features,” IEEE Trans. Geosci. Remote Sens. 23, 618–624 (1985).
    [CrossRef]
  9. E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effect of humidity variations on their optical properties,” (Optical Physics Division, U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).
  10. R. Santer, V. Carrère, P. Dubuisson, J. C. Roger, “Atmospheric correction over land for MERIS,” Int. J. Remote Sens. 20, 1819–1840 (1999).
    [CrossRef]
  11. A. Morel, “Optical modeling of the upper ocean in relation to its biogeneous matter content (case I waters),” J. Geophys. Res. 93-C9, 10,749–10,768 (1988).
    [CrossRef]

1999

R. Santer, V. Carrère, P. Dubuisson, J. C. Roger, “Atmospheric correction over land for MERIS,” Int. J. Remote Sens. 20, 1819–1840 (1999).
[CrossRef]

1998

J. V. Martonchik, D. J. Diner, R. A. Kahn, T. P. Ackerman, M. Verstraete, B. Pinty, H. R. Gordon, “Techniques for the retrieval of aerosol properties over land and ocean using multi-angle imaging,” IEEE Trans. Geosci. Remote Sens. 36, 1212–1227 (1998).
[CrossRef]

1997

E. F. Vermote, N. El Saleous, C. O. Justice, Y. J. Kaufman, J. L. Privette, L. Remer, J. C. Roger, D. Tanré, “Atmospheric correction of visible to middle-infrared EOS–MODIS data over land surfaces: background, operational algorithm and validation,” J. Geophys. Res. 102, 17,131–17,141 (1997).
[CrossRef]

1995

1991

D. Tanré, M. Legrand, “On the satellite retrieval of Saharan dust optical thickness over land: two different approaches,” J. Geophys. Res. 9, 5221–5227 (1991).
[CrossRef]

1990

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: 5S code,” Int. J. Remote Sens. 11, 659–668 (1990).
[CrossRef]

1988

D. Tanré, P. Y. Deschamps, C. Devaux, M. Herman, “Estimation of Saharan aerosol optical thickness from blurring effects in Thematic Mapper data,” J. Geophys. Res. 93, 15,955–15,964 (1988).
[CrossRef]

A. Morel, “Optical modeling of the upper ocean in relation to its biogeneous matter content (case I waters),” J. Geophys. Res. 93-C9, 10,749–10,768 (1988).
[CrossRef]

1985

D. J. Diner, J. V. Martonchick, “Influence of the aerosol scattering on atmospheric blurring of surface features,” IEEE Trans. Geosci. Remote Sens. 23, 618–624 (1985).
[CrossRef]

1981

Ackerman, T. P.

J. V. Martonchik, D. J. Diner, R. A. Kahn, T. P. Ackerman, M. Verstraete, B. Pinty, H. R. Gordon, “Techniques for the retrieval of aerosol properties over land and ocean using multi-angle imaging,” IEEE Trans. Geosci. Remote Sens. 36, 1212–1227 (1998).
[CrossRef]

Carder, K. L.

Carrère, V.

R. Santer, V. Carrère, P. Dubuisson, J. C. Roger, “Atmospheric correction over land for MERIS,” Int. J. Remote Sens. 20, 1819–1840 (1999).
[CrossRef]

Deroo, C.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: 5S code,” Int. J. Remote Sens. 11, 659–668 (1990).
[CrossRef]

Deschamps, P. Y.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: 5S code,” Int. J. Remote Sens. 11, 659–668 (1990).
[CrossRef]

D. Tanré, P. Y. Deschamps, C. Devaux, M. Herman, “Estimation of Saharan aerosol optical thickness from blurring effects in Thematic Mapper data,” J. Geophys. Res. 93, 15,955–15,964 (1988).
[CrossRef]

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

Devaux, C.

D. Tanré, P. Y. Deschamps, C. Devaux, M. Herman, “Estimation of Saharan aerosol optical thickness from blurring effects in Thematic Mapper data,” J. Geophys. Res. 93, 15,955–15,964 (1988).
[CrossRef]

Diner, D. J.

J. V. Martonchik, D. J. Diner, R. A. Kahn, T. P. Ackerman, M. Verstraete, B. Pinty, H. R. Gordon, “Techniques for the retrieval of aerosol properties over land and ocean using multi-angle imaging,” IEEE Trans. Geosci. Remote Sens. 36, 1212–1227 (1998).
[CrossRef]

D. J. Diner, J. V. Martonchick, “Influence of the aerosol scattering on atmospheric blurring of surface features,” IEEE Trans. Geosci. Remote Sens. 23, 618–624 (1985).
[CrossRef]

Dubuisson, P.

R. Santer, V. Carrère, P. Dubuisson, J. C. Roger, “Atmospheric correction over land for MERIS,” Int. J. Remote Sens. 20, 1819–1840 (1999).
[CrossRef]

Duhaut, P.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: 5S code,” Int. J. Remote Sens. 11, 659–668 (1990).
[CrossRef]

El Saleous, N.

E. F. Vermote, N. El Saleous, C. O. Justice, Y. J. Kaufman, J. L. Privette, L. Remer, J. C. Roger, D. Tanré, “Atmospheric correction of visible to middle-infrared EOS–MODIS data over land surfaces: background, operational algorithm and validation,” J. Geophys. Res. 102, 17,131–17,141 (1997).
[CrossRef]

Fenn, R. W.

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effect of humidity variations on their optical properties,” (Optical Physics Division, U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

Gordon, H. R.

J. V. Martonchik, D. J. Diner, R. A. Kahn, T. P. Ackerman, M. Verstraete, B. Pinty, H. R. Gordon, “Techniques for the retrieval of aerosol properties over land and ocean using multi-angle imaging,” IEEE Trans. Geosci. Remote Sens. 36, 1212–1227 (1998).
[CrossRef]

Herman, M.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: 5S code,” Int. J. Remote Sens. 11, 659–668 (1990).
[CrossRef]

D. Tanré, P. Y. Deschamps, C. Devaux, M. Herman, “Estimation of Saharan aerosol optical thickness from blurring effects in Thematic Mapper data,” J. Geophys. Res. 93, 15,955–15,964 (1988).
[CrossRef]

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

Justice, C. O.

E. F. Vermote, N. El Saleous, C. O. Justice, Y. J. Kaufman, J. L. Privette, L. Remer, J. C. Roger, D. Tanré, “Atmospheric correction of visible to middle-infrared EOS–MODIS data over land surfaces: background, operational algorithm and validation,” J. Geophys. Res. 102, 17,131–17,141 (1997).
[CrossRef]

Kahn, R. A.

J. V. Martonchik, D. J. Diner, R. A. Kahn, T. P. Ackerman, M. Verstraete, B. Pinty, H. R. Gordon, “Techniques for the retrieval of aerosol properties over land and ocean using multi-angle imaging,” IEEE Trans. Geosci. Remote Sens. 36, 1212–1227 (1998).
[CrossRef]

Kaufman, Y. J.

E. F. Vermote, N. El Saleous, C. O. Justice, Y. J. Kaufman, J. L. Privette, L. Remer, J. C. Roger, D. Tanré, “Atmospheric correction of visible to middle-infrared EOS–MODIS data over land surfaces: background, operational algorithm and validation,” J. Geophys. Res. 102, 17,131–17,141 (1997).
[CrossRef]

Legrand, M.

D. Tanré, M. Legrand, “On the satellite retrieval of Saharan dust optical thickness over land: two different approaches,” J. Geophys. Res. 9, 5221–5227 (1991).
[CrossRef]

Martonchick, J. V.

D. J. Diner, J. V. Martonchick, “Influence of the aerosol scattering on atmospheric blurring of surface features,” IEEE Trans. Geosci. Remote Sens. 23, 618–624 (1985).
[CrossRef]

Martonchik, J. V.

J. V. Martonchik, D. J. Diner, R. A. Kahn, T. P. Ackerman, M. Verstraete, B. Pinty, H. R. Gordon, “Techniques for the retrieval of aerosol properties over land and ocean using multi-angle imaging,” IEEE Trans. Geosci. Remote Sens. 36, 1212–1227 (1998).
[CrossRef]

Morcrette, J. J.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: 5S code,” Int. J. Remote Sens. 11, 659–668 (1990).
[CrossRef]

Morel, A.

A. Morel, “Optical modeling of the upper ocean in relation to its biogeneous matter content (case I waters),” J. Geophys. Res. 93-C9, 10,749–10,768 (1988).
[CrossRef]

Perbos, J.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: 5S code,” Int. J. Remote Sens. 11, 659–668 (1990).
[CrossRef]

Pinty, B.

J. V. Martonchik, D. J. Diner, R. A. Kahn, T. P. Ackerman, M. Verstraete, B. Pinty, H. R. Gordon, “Techniques for the retrieval of aerosol properties over land and ocean using multi-angle imaging,” IEEE Trans. Geosci. Remote Sens. 36, 1212–1227 (1998).
[CrossRef]

Privette, J. L.

E. F. Vermote, N. El Saleous, C. O. Justice, Y. J. Kaufman, J. L. Privette, L. Remer, J. C. Roger, D. Tanré, “Atmospheric correction of visible to middle-infrared EOS–MODIS data over land surfaces: background, operational algorithm and validation,” J. Geophys. Res. 102, 17,131–17,141 (1997).
[CrossRef]

Reinersman, P. N.

Remer, L.

E. F. Vermote, N. El Saleous, C. O. Justice, Y. J. Kaufman, J. L. Privette, L. Remer, J. C. Roger, D. Tanré, “Atmospheric correction of visible to middle-infrared EOS–MODIS data over land surfaces: background, operational algorithm and validation,” J. Geophys. Res. 102, 17,131–17,141 (1997).
[CrossRef]

Roger, J. C.

R. Santer, V. Carrère, P. Dubuisson, J. C. Roger, “Atmospheric correction over land for MERIS,” Int. J. Remote Sens. 20, 1819–1840 (1999).
[CrossRef]

E. F. Vermote, N. El Saleous, C. O. Justice, Y. J. Kaufman, J. L. Privette, L. Remer, J. C. Roger, D. Tanré, “Atmospheric correction of visible to middle-infrared EOS–MODIS data over land surfaces: background, operational algorithm and validation,” J. Geophys. Res. 102, 17,131–17,141 (1997).
[CrossRef]

Santer, R.

R. Santer, V. Carrère, P. Dubuisson, J. C. Roger, “Atmospheric correction over land for MERIS,” Int. J. Remote Sens. 20, 1819–1840 (1999).
[CrossRef]

Shettle, E. P.

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effect of humidity variations on their optical properties,” (Optical Physics Division, U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

Tanré, D.

E. F. Vermote, N. El Saleous, C. O. Justice, Y. J. Kaufman, J. L. Privette, L. Remer, J. C. Roger, D. Tanré, “Atmospheric correction of visible to middle-infrared EOS–MODIS data over land surfaces: background, operational algorithm and validation,” J. Geophys. Res. 102, 17,131–17,141 (1997).
[CrossRef]

D. Tanré, M. Legrand, “On the satellite retrieval of Saharan dust optical thickness over land: two different approaches,” J. Geophys. Res. 9, 5221–5227 (1991).
[CrossRef]

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: 5S code,” Int. J. Remote Sens. 11, 659–668 (1990).
[CrossRef]

D. Tanré, P. Y. Deschamps, C. Devaux, M. Herman, “Estimation of Saharan aerosol optical thickness from blurring effects in Thematic Mapper data,” J. Geophys. Res. 93, 15,955–15,964 (1988).
[CrossRef]

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

Vermote, E. F.

E. F. Vermote, N. El Saleous, C. O. Justice, Y. J. Kaufman, J. L. Privette, L. Remer, J. C. Roger, D. Tanré, “Atmospheric correction of visible to middle-infrared EOS–MODIS data over land surfaces: background, operational algorithm and validation,” J. Geophys. Res. 102, 17,131–17,141 (1997).
[CrossRef]

Verstraete, M.

J. V. Martonchik, D. J. Diner, R. A. Kahn, T. P. Ackerman, M. Verstraete, B. Pinty, H. R. Gordon, “Techniques for the retrieval of aerosol properties over land and ocean using multi-angle imaging,” IEEE Trans. Geosci. Remote Sens. 36, 1212–1227 (1998).
[CrossRef]

Appl. Opt.

IEEE Trans. Geosci. Remote Sens.

J. V. Martonchik, D. J. Diner, R. A. Kahn, T. P. Ackerman, M. Verstraete, B. Pinty, H. R. Gordon, “Techniques for the retrieval of aerosol properties over land and ocean using multi-angle imaging,” IEEE Trans. Geosci. Remote Sens. 36, 1212–1227 (1998).
[CrossRef]

D. J. Diner, J. V. Martonchick, “Influence of the aerosol scattering on atmospheric blurring of surface features,” IEEE Trans. Geosci. Remote Sens. 23, 618–624 (1985).
[CrossRef]

Int. J. Remote Sens.

R. Santer, V. Carrère, P. Dubuisson, J. C. Roger, “Atmospheric correction over land for MERIS,” Int. J. Remote Sens. 20, 1819–1840 (1999).
[CrossRef]

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: 5S code,” Int. J. Remote Sens. 11, 659–668 (1990).
[CrossRef]

J. Geophys. Res.

A. Morel, “Optical modeling of the upper ocean in relation to its biogeneous matter content (case I waters),” J. Geophys. Res. 93-C9, 10,749–10,768 (1988).
[CrossRef]

D. Tanré, P. Y. Deschamps, C. Devaux, M. Herman, “Estimation of Saharan aerosol optical thickness from blurring effects in Thematic Mapper data,” J. Geophys. Res. 93, 15,955–15,964 (1988).
[CrossRef]

D. Tanré, M. Legrand, “On the satellite retrieval of Saharan dust optical thickness over land: two different approaches,” J. Geophys. Res. 9, 5221–5227 (1991).
[CrossRef]

E. F. Vermote, N. El Saleous, C. O. Justice, Y. J. Kaufman, J. L. Privette, L. Remer, J. C. Roger, D. Tanré, “Atmospheric correction of visible to middle-infrared EOS–MODIS data over land surfaces: background, operational algorithm and validation,” J. Geophys. Res. 102, 17,131–17,141 (1997).
[CrossRef]

Other

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effect of humidity variations on their optical properties,” (Optical Physics Division, U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

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Figures (24)

Fig. 1
Fig. 1

Satellite sensor observes at nadir a pixel O of reflectance ρ t . By atmospheric scattering, a fraction of the incoming signal can originate from the neighborhood of this pixel. At a given point M, reflectance ρ e generally differs from the reflectance of the pixel that is directly observed by the sensor.

Fig. 2
Fig. 2

Bias at 865 nm (the environment is neglected) at the center of a dark water disk of radius R surrounded by homogeneous and infinite land of 30% reflectance. Plots are labeled for the six atmospheric cases of Table 1.

Fig. 3
Fig. 3

Averaged reflectances (in percent) for Rayleigh scattering 〈ρ R 〉 and for aerosol scattering 〈ρ a 〉 plotted along a radius for circular lakes of (a) R = 5 km, (b) R = 10 km, and (c) R = 20 km. General conditions are those of Fig. 2.

Fig. 4
Fig. 4

Same as Fig. 3 but versus the distance at sea from a straight coastline. Reflectances given in percent.

Fig. 5
Fig. 5

Pixel O viewed at nadir. Let us consider, at an altitude z, an elementary layer of optical thickness dt. The light reflected by the surface at M, distant from O by r, can be scattered toward the sensor at scattering angle θ. If we consider, as in the 5S code, a disk of radius R, ξ is the maximum scattering angle.

Fig. 6
Fig. 6

Pixel O viewed by the sensor (θ v , φ v = 0 by convention). Let us consider the elementary layer dt at altitude z. We represent a beam reflected by the surface at M. M is located in polar coordinates (r = O z M, φ).

Fig. 7
Fig. 7

(a) Sea surface considered as a plane mirror. Curve one is the direct–direct path for Fresnel reflection. For curve two, the direct solar beam is reflected and then scattered toward the sensor. Curve three is the fraction of the diffuse downward irradiance reflected toward the sensor. (b) Pixel O is viewed at nadir. The elementary layer dt is again at altitude z with the direct solar beam as its source reflected by the sea at angle θ. The coastline is at a distance R from O, and z max represents the altitude maximum reached by the solar reflected beam. (c) Pixel O is viewed at nadir and again the elementary layer dt is at altitude z with the direct solar beam as its source reflected by the sea at angle θ. The coastline is at a distance R from O, and z min represents the altitude minimum reached by the solar reflected beam.

Fig. 8
Fig. 8

F versus r for a molecular atmosphere according to the 5S code and with the primary scattering approximation for molecular scale height H R = 7 km according to Eq. (20) or (21).

Fig. 9
Fig. 9

F versus r for the continental aerosol model as proposed in the 5S code. Comparisons with the primary scattering formulation for a Junge size distribution n(r) = r -4, m = 1.55, and H a = 2 km with Eq. (20) or (21).

Fig. 10
Fig. 10

Influence of the aerosol model on F(R). The vertical distribution corresponds to H a = 2 km with Junge size distribution r -v and refractive index m.

Fig. 11
Fig. 11

Influence on F(R) of the vertical distribution with H a = 1, 2, 4 km for n(r) = r -v and m = 1.55.

Fig. 12
Fig. 12

Viewing angles for off-nadir observations.

Fig. 13
Fig. 13

〈ρ R 〉 for the ocean–land system at 865 nm versus distance r at the coast. Solid curve, the nadir view. The scan plane is perpendicular to the coast, with θ v = 30°, 60°. The mean value of 0.15 is reached over the sea if the satellite is over land.

Fig. 14
Fig. 14

Same as Fig. 13 but for isotropic scattering.

Fig. 15
Fig. 15

For nadir observations, F(R) is computed for a molecular atmosphere and for an isotropic layer located at z = 4 km.

Fig. 16
Fig. 16

Same as Fig. 13 but for a unique isotropic layer located at z = 4 km.

Fig. 17
Fig. 17

Same as Fig. 13 but for the continental aerosol with H a = 2 km.

Fig. 18
Fig. 18

Additional reflectance owing to the adjacency effect at 865 nm for the conditions of Fig. 13.

Fig. 19
Fig. 19

Comparison of retrieval of angstrom coefficient values for 30 cases contaminated by (With) or not contaminated by (Without) the Rayleigh adjacency effect. Thirty cases were defined for which there were three visibilities, 50, 23, and 8 km; two solar angles, 30° and 60°; and give distances from the coastline, 1, 2, 5, 10, and 20 km. The first six cases in the order described in Table 1, correspond to a distance from the coast of 1 km. Then each set of six points corresponds to an increasing distance from the coast.

Fig. 20
Fig. 20

Comparison of retrieval of optical thickness values at 865 nm for the 30 cases of contamination (With) or no contamination (Without) by the Rayleigh adjacency effect.

Fig. 21
Fig. 21

Blue/green ratio versus chlorophyll content, reference, and contaminated ratio (two solar angles and three visibilities) for a distance to the shore d of 10 km.

Fig. 22
Fig. 22

Retrieval of chlorophyll values for three distances to the shore d. The six points of each chlorophyll content correspond to the two solar angles for each of the three visibilities.

Fig. 23
Fig. 23

Retrieval of chlorophyll values for three distances to the shore d, not contaminated by the Rayleigh adjacency effect. The six points of each chlorophyll content correspond to the two solar angles for each of the three visibilities.

Fig. 24
Fig. 24

Observed pixel O viewed at (θ v , φ v ). For the sublayer at altitude z the scattering element is in t. O z is the orthogonal projection of t. If O is at a distance d from the coast, O z is at dz. The integration in azimuth is done on a circle of center O z and of radius r z .

Tables (6)

Tables Icon

Table 1 Atmospheric Conditions To Simulate the Adjacency Effects According to 5S Computationsa

Tables Icon

Table 2 Additional Reflectance (in percent) Owing to Adjacency Effects Computed for the Cases of Fig. 2 for Disks of Radii R = 5, 10, 20 km at the Center of the Disk (upper value) and at the Edge (lower value)a

Tables Icon

Table 3 Additional Reflectance (in percent) Owing to Adjacency Effectsa

Tables Icon

Table 4 Contribution at 865 nm of Land to the Oceanic Signal for Points at Distance d from the Coasta

Tables Icon

Table 5 Reduction of the Fresnel Reflection (in percent) According to Eq. (28) versus Distance D from the Coast for Three Wavelengths, 440, 560, and 865 nma

Tables Icon

Table 6 Reduction of Fresnel Reflection (in percent) According to Eq. (30) versus Distance D from the Coast for Three Wavelengths, 440, 560, and 865 nma

Equations (36)

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

ρt*=TμsTμvρt/1-ρts,
ρt*=ρt exp-δ/μv+ρtdμvTμs/1-ρs,
ρ=0 ρrgrrdr,
ρr=1/2π02π ρr, φdφ
ρ=-- fx, yρx, ydxdy,
ρ=ρtFR+ρe1-FR.
FmR=am exp-αmR+bm exp-βmR,
Δρ*=tdμvρ-ρTμs/1-ρs.
d2L=dtdμPμρμ/4π,
μ=z/r2+z2.
LR=dt 02πη1Pμρμ/4πdμdφ= dt η1Pμρμ/2dμ,
LR  =dt 01Pμρμ/2dμ= dt0ηPμρe/2dμ+η1Pμρt/2dμ.
LR  =Tμsμs/1-ρsdt0ηPμρe/2dμ+η1Pμρt/2dμ,
LeTOA=ρtdμvTμsμs/1-ρs.
Lμ=Pμdt/μ4π.
ϕ=02π01 μLμdμdφ=dt/201 Pμdμ.
td=ϕ/μs=ϕ.
Fη=1-0η Pμdμ01 Pμdμ.
FR=0δη1 Pμdμdtδ 01 Pμdμ.
FR=1-1/δ0δ ηdt.
tt, μ=tz, μ=exp-δ-t/μexp-t,
FR=0δexp-tη1exp-δ-t/μPμdμdt0δexp-t01exp-δ-t/μPμdμdt.
d3L=ρμ, φPΘ/4πμvdμdφdt.
cos Θ=μvμ+sin θv sin θ cos φ.
dL=rμsPμsdt/4π.
L=rμsδPμs/4,
zmax=R/cos φs tan θs.
Δρ=rμsPμsδ-δmax/4μs.
Δρ=rμsPμsδ-δmin/4μs.
ρ=01 ρ0μdμ,
  Pμv, μ, φ=s=0S2-δ0,sPsμv, μcossφ,
ρμ, φ=r=0R2-δ0,rρrμcosrφ.
d2L=dt/2μvdμ s=0S2-δ0,sρsμPsμv, μ.
ρ=s=0S2-δ0,s0δ01 ρsμPsμv, μdμdt0δ01 P0μv, μdμdt.
ρsμ=1/2π02π ρμ, φcossφdφ.
ρ0=ρlφ1+π-φ1ρw/π, ρs=ρw-ρlsinsφ1/πs.

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