Abstract

The estimation of the bathymetry and the detection of targets located on the seabed of shallow waters using remote sensing techniques is of great interest for many environmental applications in coastal areas such as benthic habitat mapping, monitoring of seabed aquatic plants and the subsequent management of littoral zones. For that purpose, knowledge of the optical effects induced by the neighborhood of a given seabed target and by the water column itself is required to better interpret the subsurface upward radiance measured by satellite or shipborne radiometers. In this paper, the various sources of photons that contribute to the subsurface upward radiance are analyzed. In particular, the adjacency effects caused by the neighborhood of a given seabed target are quantified for three water turbidity conditions, namely clear, moderately turbid and turbid waters. Firstly, an analytical expression of the subsurface radiance is proposed in order to make explicit the radiance terms corresponding to these effects. Secondly, a sensitivity study is performed using radiative transfer modeling to determine the influence of the seabed adjacency effects on the upward signal with respect to various parameters such as the bathymetry or the bottom brightness. The results show that the highest contributions of the adjacency effects induced by the neighborhood of a seabed target to the subsurface radiance could reach 26%, 18% and 9% for clear, moderately turbid and turbid water conditions respectively. Therefore, the detection of a seabed target could be significantly biased if the seabed adjacency effects are ignored in the analysis of remote sensing measurements. Our results could be further used to improve the performance of inverse algorithms dedicated to the retrieval of bottom composition, water optical properties and/or bathymetry.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. Z. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S. Patch, “Hyperspectral remote sensing for shallow waters. I. A semianalytical model,” Appl. Opt. 37(27), 6329–6338 (1998).
    [Crossref] [PubMed]
  2. Z. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S. Patch, “Hyperspectral remote sensing for shallow waters. 2. Deriving bottom depths and water properties by optimization,” Appl. Opt. 38(18), 3831–3843 (1999).
    [Crossref] [PubMed]
  3. S. Maritorena, A. Morel, and B. Gentili, “Diffuse reflectance of oceanic shallow waters: influence of water depth and bottom albedo,” Limnol. Oceanogr. 39(7), 1689–1703 (1994).
    [Crossref]
  4. V. E. Brando, J. M. Anstee, M. Wettle, A. G. Dekker, S. R. Phinn, and C. Roelfsema, “A physics based retrieval and quality assessment of bathymetry from suboptimal hyperspectral data,” Remote Sens. Environ. 113(4), 755–770 (2009).
    [Crossref]
  5. A. G. Dekker, S. R. Phinn, J. Anstee, P. Bissett, V. E. Brando, B. Casey, P. Fearns, J. Hedley, W. Klonowski, Z. P. Lee, M. Lynch, M. Lyons, C. D. Mobley, and C. Roelfsema, “Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments,” Limnol. Oceanogr. Methods 9(9), 396–425 (2011).
    [Crossref]
  6. J. Hedley, C. Roelfsema, and S. R. Phinn, “Efficient radiative transfer model inversion for remote sensing applications,” Remote Sens. Environ. 113(11), 2527–2532 (2009).
    [Crossref]
  7. S. Jay and M. Guillaume, “A novel maximum likelihood based method for mapping depth and water quality from hyperspectral remote-sensing data,” Remote Sens. Environ. 147, 121–132 (2014).
    [Crossref]
  8. S. Jay and M. Guillaume, “Regularized estimation of bathymetry and water quality using hyperspectral remote sensing,” Int. J. Remote Sens. 37(2), 263–289 (2016).
    [Crossref]
  9. S. Jay, M. Guillaume, A. Minghelli, Y. Deville, M. Chami, B. Lafrance, and V. Serfaty, “Hyperspectral remote sensing of shallow waters: considering environmental noise and bottom intra-class variability for modeling and inversion of water reflectance,” Remote Sens. Environ. 200, 352–367 (2017).
    [Crossref]
  10. B. Bulgarelli, G. Zibordi, and F. Mélin, “On the minimization of adjacency effects in SeaWiFS primary data products from coastal areas,” Opt. Express 26(18), A709–A728 (2018).
    [Crossref] [PubMed]
  11. B. Bulgarelli and G. Zibordi, “On the detectability of adjacency effects in ocean color remote sensing of mid-latitude coastal environments by SeaWiFS, MODIS-A, MERIS, OLCI, OLI and MSI,” Remote Sens. Environ. 209, 423–438 (2018).
    [Crossref] [PubMed]
  12. B. Bulgarelli, V. Kiselev, and G. Zibordi, “Adjacency effects in satellite radiometric products from coastal waters: a theoretical analysis for the northern Adriatic Sea,” Appl. Opt. 56(4), 854–869 (2017).
    [Crossref] [PubMed]
  13. L. Feng and C. Hu, “Cloud adjacency effects on top-of-atmosphere radiance and ocean color data products: a statistical assessment,” Remote Sens. Environ. 174, 301–313 (2016).
    [Crossref]
  14. V. Kiselev, B. Bulgarelli, and T. Heege, “Sensor independent adjacency correction algorithm for coastal and inland water systems,” Remote Sens. Environ. 157, 85–95 (2015).
    [Crossref]
  15. B. Bulgarelli, V. Kiselev, and G. Zibordi, “Simulation and analysis of adjacency effects in coastal waters: a case study,” Appl. Opt. 53(8), 1523–1545 (2014).
    [Crossref] [PubMed]
  16. S. Belanger, 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(1), 51–68 (2007).
    [Crossref]
  17. A. Sei, “Analysis of adjacency effects for two Lambertian half-spaces,” Int. J. Remote Sens. 28(8), 1873–1890 (2007).
    [Crossref]
  18. R. Santer and C. Schmechtig, “Adjacency effects on water surfaces: primary scattering approximation and sensitivity study,” Appl. Opt. 39(3), 361–375 (2000).
    [Crossref] [PubMed]
  19. 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(21), 4453–4471 (1995).
    [Crossref] [PubMed]
  20. J. Otterman and R. S. Fraser, “Adjacency effects on imaging by surface reflection and atmospheric scattering: cross radiance to zenith,” Appl. Opt. 18(16), 2852–2860 (1979).
    [Crossref] [PubMed]
  21. M. Guillaume, Y. Michels, and S. Jay, Joint estimation of water column parameters and seabed reflectance combining maximum likelihood and unmixing algorithm, in 7th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), (IEEE, 2015, pp.1–4)
    [Crossref]
  22. D. Tanré, M. Herman, P. Y. Deschamps, and A. Leffe, “Atmospheric modeling for space measurements of ground reflectances, including bidirectional properties,” Appl. Opt. 18(21), 3587–3594 (1979).
    [Crossref] [PubMed]
  23. E. Vermote and A. Vermeulen, “Atmospheric correction algorithm: spectral reflectances (MOD09)”, NASA MODIS Algorithm Theoretical Basis Document, version 4.0 (1999).
  24. M. Chami, B. Lafrance, B. Fougnie, J. Chowdhary, T. Harmel, and F. Waquet, “OSOAA: a vector radiative transfer model of coupled atmosphere-ocean system for a rough sea surface application to the estimates of the directional variations of the water leaving reflectance to better process multi-angular satellite sensors data over the ocean,” Opt. Express 23(21), 27829–27852 (2015), doi:.
    [Crossref] [PubMed]
  25. T. Sagawa, E. Boisnier, T. Komatsu, K. B. Mustapha, A. Hattour, N. Kosaka, and S. Miyazaki, “Using bottom surface reflectance to map coastal marine areas: a new application method for Lyzenga’s model,” Int. J. Remote Sens. 31(12), 3051–3064 (2010).
    [Crossref]
  26. J. M. Jaubert, J. R. M. Chisholm, A. Minghelli-Roman, M. Marchioretti, J. H. Morrow, and H. T. Ripley, “Re-evaluation of the extent of Caulerpa taxifolia development in the northern Mediterranean using airborne spectrographic sensing,” Mar. Ecol. Prog. Ser. 263, 75–82 (2003).
    [Crossref]
  27. C. Mobley and L. K. Sundman, “Effects of optically shallow bottoms on upwelling radiances: Inhomogeneous and sloping bottoms,” Limnol. Oceanogr. 48(1), 329–336 (2003).
    [Crossref]
  28. K. Z. Doctor, C. M. Bachmann, D. J. Gray, M. J. Montes, and R. A. Fusina, “Wavelength dependence of the bidirectional reflectance distribution function (BRDF) of beach sands,” Appl. Opt. 54(31), F243–F255 (2015).
    [Crossref] [PubMed]

2018 (2)

B. Bulgarelli, G. Zibordi, and F. Mélin, “On the minimization of adjacency effects in SeaWiFS primary data products from coastal areas,” Opt. Express 26(18), A709–A728 (2018).
[Crossref] [PubMed]

B. Bulgarelli and G. Zibordi, “On the detectability of adjacency effects in ocean color remote sensing of mid-latitude coastal environments by SeaWiFS, MODIS-A, MERIS, OLCI, OLI and MSI,” Remote Sens. Environ. 209, 423–438 (2018).
[Crossref] [PubMed]

2017 (2)

B. Bulgarelli, V. Kiselev, and G. Zibordi, “Adjacency effects in satellite radiometric products from coastal waters: a theoretical analysis for the northern Adriatic Sea,” Appl. Opt. 56(4), 854–869 (2017).
[Crossref] [PubMed]

S. Jay, M. Guillaume, A. Minghelli, Y. Deville, M. Chami, B. Lafrance, and V. Serfaty, “Hyperspectral remote sensing of shallow waters: considering environmental noise and bottom intra-class variability for modeling and inversion of water reflectance,” Remote Sens. Environ. 200, 352–367 (2017).
[Crossref]

2016 (2)

L. Feng and C. Hu, “Cloud adjacency effects on top-of-atmosphere radiance and ocean color data products: a statistical assessment,” Remote Sens. Environ. 174, 301–313 (2016).
[Crossref]

S. Jay and M. Guillaume, “Regularized estimation of bathymetry and water quality using hyperspectral remote sensing,” Int. J. Remote Sens. 37(2), 263–289 (2016).
[Crossref]

2015 (3)

2014 (2)

B. Bulgarelli, V. Kiselev, and G. Zibordi, “Simulation and analysis of adjacency effects in coastal waters: a case study,” Appl. Opt. 53(8), 1523–1545 (2014).
[Crossref] [PubMed]

S. Jay and M. Guillaume, “A novel maximum likelihood based method for mapping depth and water quality from hyperspectral remote-sensing data,” Remote Sens. Environ. 147, 121–132 (2014).
[Crossref]

2011 (1)

A. G. Dekker, S. R. Phinn, J. Anstee, P. Bissett, V. E. Brando, B. Casey, P. Fearns, J. Hedley, W. Klonowski, Z. P. Lee, M. Lynch, M. Lyons, C. D. Mobley, and C. Roelfsema, “Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments,” Limnol. Oceanogr. Methods 9(9), 396–425 (2011).
[Crossref]

2010 (1)

T. Sagawa, E. Boisnier, T. Komatsu, K. B. Mustapha, A. Hattour, N. Kosaka, and S. Miyazaki, “Using bottom surface reflectance to map coastal marine areas: a new application method for Lyzenga’s model,” Int. J. Remote Sens. 31(12), 3051–3064 (2010).
[Crossref]

2009 (2)

J. Hedley, C. Roelfsema, and S. R. Phinn, “Efficient radiative transfer model inversion for remote sensing applications,” Remote Sens. Environ. 113(11), 2527–2532 (2009).
[Crossref]

V. E. Brando, J. M. Anstee, M. Wettle, A. G. Dekker, S. R. Phinn, and C. Roelfsema, “A physics based retrieval and quality assessment of bathymetry from suboptimal hyperspectral data,” Remote Sens. Environ. 113(4), 755–770 (2009).
[Crossref]

2007 (2)

S. Belanger, 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(1), 51–68 (2007).
[Crossref]

A. Sei, “Analysis of adjacency effects for two Lambertian half-spaces,” Int. J. Remote Sens. 28(8), 1873–1890 (2007).
[Crossref]

2003 (2)

J. M. Jaubert, J. R. M. Chisholm, A. Minghelli-Roman, M. Marchioretti, J. H. Morrow, and H. T. Ripley, “Re-evaluation of the extent of Caulerpa taxifolia development in the northern Mediterranean using airborne spectrographic sensing,” Mar. Ecol. Prog. Ser. 263, 75–82 (2003).
[Crossref]

C. Mobley and L. K. Sundman, “Effects of optically shallow bottoms on upwelling radiances: Inhomogeneous and sloping bottoms,” Limnol. Oceanogr. 48(1), 329–336 (2003).
[Crossref]

2000 (1)

1999 (1)

1998 (1)

1995 (1)

1994 (1)

S. Maritorena, A. Morel, and B. Gentili, “Diffuse reflectance of oceanic shallow waters: influence of water depth and bottom albedo,” Limnol. Oceanogr. 39(7), 1689–1703 (1994).
[Crossref]

1979 (2)

Anstee, J.

A. G. Dekker, S. R. Phinn, J. Anstee, P. Bissett, V. E. Brando, B. Casey, P. Fearns, J. Hedley, W. Klonowski, Z. P. Lee, M. Lynch, M. Lyons, C. D. Mobley, and C. Roelfsema, “Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments,” Limnol. Oceanogr. Methods 9(9), 396–425 (2011).
[Crossref]

Anstee, J. M.

V. E. Brando, J. M. Anstee, M. Wettle, A. G. Dekker, S. R. Phinn, and C. Roelfsema, “A physics based retrieval and quality assessment of bathymetry from suboptimal hyperspectral data,” Remote Sens. Environ. 113(4), 755–770 (2009).
[Crossref]

Babin, M.

S. Belanger, 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(1), 51–68 (2007).
[Crossref]

Bachmann, C. M.

Belanger, S.

S. Belanger, 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(1), 51–68 (2007).
[Crossref]

Bissett, P.

A. G. Dekker, S. R. Phinn, J. Anstee, P. Bissett, V. E. Brando, B. Casey, P. Fearns, J. Hedley, W. Klonowski, Z. P. Lee, M. Lynch, M. Lyons, C. D. Mobley, and C. Roelfsema, “Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments,” Limnol. Oceanogr. Methods 9(9), 396–425 (2011).
[Crossref]

Boisnier, E.

T. Sagawa, E. Boisnier, T. Komatsu, K. B. Mustapha, A. Hattour, N. Kosaka, and S. Miyazaki, “Using bottom surface reflectance to map coastal marine areas: a new application method for Lyzenga’s model,” Int. J. Remote Sens. 31(12), 3051–3064 (2010).
[Crossref]

Brando, V. E.

A. G. Dekker, S. R. Phinn, J. Anstee, P. Bissett, V. E. Brando, B. Casey, P. Fearns, J. Hedley, W. Klonowski, Z. P. Lee, M. Lynch, M. Lyons, C. D. Mobley, and C. Roelfsema, “Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments,” Limnol. Oceanogr. Methods 9(9), 396–425 (2011).
[Crossref]

V. E. Brando, J. M. Anstee, M. Wettle, A. G. Dekker, S. R. Phinn, and C. Roelfsema, “A physics based retrieval and quality assessment of bathymetry from suboptimal hyperspectral data,” Remote Sens. Environ. 113(4), 755–770 (2009).
[Crossref]

Bulgarelli, B.

Carder, K. L.

Casey, B.

A. G. Dekker, S. R. Phinn, J. Anstee, P. Bissett, V. E. Brando, B. Casey, P. Fearns, J. Hedley, W. Klonowski, Z. P. Lee, M. Lynch, M. Lyons, C. D. Mobley, and C. Roelfsema, “Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments,” Limnol. Oceanogr. Methods 9(9), 396–425 (2011).
[Crossref]

Chami, M.

S. Jay, M. Guillaume, A. Minghelli, Y. Deville, M. Chami, B. Lafrance, and V. Serfaty, “Hyperspectral remote sensing of shallow waters: considering environmental noise and bottom intra-class variability for modeling and inversion of water reflectance,” Remote Sens. Environ. 200, 352–367 (2017).
[Crossref]

M. Chami, B. Lafrance, B. Fougnie, J. Chowdhary, T. Harmel, and F. Waquet, “OSOAA: a vector radiative transfer model of coupled atmosphere-ocean system for a rough sea surface application to the estimates of the directional variations of the water leaving reflectance to better process multi-angular satellite sensors data over the ocean,” Opt. Express 23(21), 27829–27852 (2015), doi:.
[Crossref] [PubMed]

Chisholm, J. R. M.

J. M. Jaubert, J. R. M. Chisholm, A. Minghelli-Roman, M. Marchioretti, J. H. Morrow, and H. T. Ripley, “Re-evaluation of the extent of Caulerpa taxifolia development in the northern Mediterranean using airborne spectrographic sensing,” Mar. Ecol. Prog. Ser. 263, 75–82 (2003).
[Crossref]

Chowdhary, J.

Dekker, A. G.

A. G. Dekker, S. R. Phinn, J. Anstee, P. Bissett, V. E. Brando, B. Casey, P. Fearns, J. Hedley, W. Klonowski, Z. P. Lee, M. Lynch, M. Lyons, C. D. Mobley, and C. Roelfsema, “Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments,” Limnol. Oceanogr. Methods 9(9), 396–425 (2011).
[Crossref]

V. E. Brando, J. M. Anstee, M. Wettle, A. G. Dekker, S. R. Phinn, and C. Roelfsema, “A physics based retrieval and quality assessment of bathymetry from suboptimal hyperspectral data,” Remote Sens. Environ. 113(4), 755–770 (2009).
[Crossref]

Deschamps, P. Y.

Deville, Y.

S. Jay, M. Guillaume, A. Minghelli, Y. Deville, M. Chami, B. Lafrance, and V. Serfaty, “Hyperspectral remote sensing of shallow waters: considering environmental noise and bottom intra-class variability for modeling and inversion of water reflectance,” Remote Sens. Environ. 200, 352–367 (2017).
[Crossref]

Doctor, K. Z.

Ehn, J. K.

S. Belanger, 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(1), 51–68 (2007).
[Crossref]

Fearns, P.

A. G. Dekker, S. R. Phinn, J. Anstee, P. Bissett, V. E. Brando, B. Casey, P. Fearns, J. Hedley, W. Klonowski, Z. P. Lee, M. Lynch, M. Lyons, C. D. Mobley, and C. Roelfsema, “Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments,” Limnol. Oceanogr. Methods 9(9), 396–425 (2011).
[Crossref]

Feng, L.

L. Feng and C. Hu, “Cloud adjacency effects on top-of-atmosphere radiance and ocean color data products: a statistical assessment,” Remote Sens. Environ. 174, 301–313 (2016).
[Crossref]

Fougnie, B.

Fraser, R. S.

Fusina, R. A.

Gentili, B.

S. Maritorena, A. Morel, and B. Gentili, “Diffuse reflectance of oceanic shallow waters: influence of water depth and bottom albedo,” Limnol. Oceanogr. 39(7), 1689–1703 (1994).
[Crossref]

Gray, D. J.

Guillaume, M.

S. Jay, M. Guillaume, A. Minghelli, Y. Deville, M. Chami, B. Lafrance, and V. Serfaty, “Hyperspectral remote sensing of shallow waters: considering environmental noise and bottom intra-class variability for modeling and inversion of water reflectance,” Remote Sens. Environ. 200, 352–367 (2017).
[Crossref]

S. Jay and M. Guillaume, “Regularized estimation of bathymetry and water quality using hyperspectral remote sensing,” Int. J. Remote Sens. 37(2), 263–289 (2016).
[Crossref]

S. Jay and M. Guillaume, “A novel maximum likelihood based method for mapping depth and water quality from hyperspectral remote-sensing data,” Remote Sens. Environ. 147, 121–132 (2014).
[Crossref]

M. Guillaume, Y. Michels, and S. Jay, Joint estimation of water column parameters and seabed reflectance combining maximum likelihood and unmixing algorithm, in 7th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), (IEEE, 2015, pp.1–4)
[Crossref]

Harmel, T.

Hattour, A.

T. Sagawa, E. Boisnier, T. Komatsu, K. B. Mustapha, A. Hattour, N. Kosaka, and S. Miyazaki, “Using bottom surface reflectance to map coastal marine areas: a new application method for Lyzenga’s model,” Int. J. Remote Sens. 31(12), 3051–3064 (2010).
[Crossref]

Hedley, J.

A. G. Dekker, S. R. Phinn, J. Anstee, P. Bissett, V. E. Brando, B. Casey, P. Fearns, J. Hedley, W. Klonowski, Z. P. Lee, M. Lynch, M. Lyons, C. D. Mobley, and C. Roelfsema, “Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments,” Limnol. Oceanogr. Methods 9(9), 396–425 (2011).
[Crossref]

J. Hedley, C. Roelfsema, and S. R. Phinn, “Efficient radiative transfer model inversion for remote sensing applications,” Remote Sens. Environ. 113(11), 2527–2532 (2009).
[Crossref]

Heege, T.

V. Kiselev, B. Bulgarelli, and T. Heege, “Sensor independent adjacency correction algorithm for coastal and inland water systems,” Remote Sens. Environ. 157, 85–95 (2015).
[Crossref]

Herman, M.

Hu, C.

L. Feng and C. Hu, “Cloud adjacency effects on top-of-atmosphere radiance and ocean color data products: a statistical assessment,” Remote Sens. Environ. 174, 301–313 (2016).
[Crossref]

Jaubert, J. M.

J. M. Jaubert, J. R. M. Chisholm, A. Minghelli-Roman, M. Marchioretti, J. H. Morrow, and H. T. Ripley, “Re-evaluation of the extent of Caulerpa taxifolia development in the northern Mediterranean using airborne spectrographic sensing,” Mar. Ecol. Prog. Ser. 263, 75–82 (2003).
[Crossref]

Jay, S.

S. Jay, M. Guillaume, A. Minghelli, Y. Deville, M. Chami, B. Lafrance, and V. Serfaty, “Hyperspectral remote sensing of shallow waters: considering environmental noise and bottom intra-class variability for modeling and inversion of water reflectance,” Remote Sens. Environ. 200, 352–367 (2017).
[Crossref]

S. Jay and M. Guillaume, “Regularized estimation of bathymetry and water quality using hyperspectral remote sensing,” Int. J. Remote Sens. 37(2), 263–289 (2016).
[Crossref]

S. Jay and M. Guillaume, “A novel maximum likelihood based method for mapping depth and water quality from hyperspectral remote-sensing data,” Remote Sens. Environ. 147, 121–132 (2014).
[Crossref]

M. Guillaume, Y. Michels, and S. Jay, Joint estimation of water column parameters and seabed reflectance combining maximum likelihood and unmixing algorithm, in 7th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), (IEEE, 2015, pp.1–4)
[Crossref]

Kiselev, V.

Klonowski, W.

A. G. Dekker, S. R. Phinn, J. Anstee, P. Bissett, V. E. Brando, B. Casey, P. Fearns, J. Hedley, W. Klonowski, Z. P. Lee, M. Lynch, M. Lyons, C. D. Mobley, and C. Roelfsema, “Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments,” Limnol. Oceanogr. Methods 9(9), 396–425 (2011).
[Crossref]

Komatsu, T.

T. Sagawa, E. Boisnier, T. Komatsu, K. B. Mustapha, A. Hattour, N. Kosaka, and S. Miyazaki, “Using bottom surface reflectance to map coastal marine areas: a new application method for Lyzenga’s model,” Int. J. Remote Sens. 31(12), 3051–3064 (2010).
[Crossref]

Kosaka, N.

T. Sagawa, E. Boisnier, T. Komatsu, K. B. Mustapha, A. Hattour, N. Kosaka, and S. Miyazaki, “Using bottom surface reflectance to map coastal marine areas: a new application method for Lyzenga’s model,” Int. J. Remote Sens. 31(12), 3051–3064 (2010).
[Crossref]

Lafrance, B.

S. Jay, M. Guillaume, A. Minghelli, Y. Deville, M. Chami, B. Lafrance, and V. Serfaty, “Hyperspectral remote sensing of shallow waters: considering environmental noise and bottom intra-class variability for modeling and inversion of water reflectance,” Remote Sens. Environ. 200, 352–367 (2017).
[Crossref]

M. Chami, B. Lafrance, B. Fougnie, J. Chowdhary, T. Harmel, and F. Waquet, “OSOAA: a vector radiative transfer model of coupled atmosphere-ocean system for a rough sea surface application to the estimates of the directional variations of the water leaving reflectance to better process multi-angular satellite sensors data over the ocean,” Opt. Express 23(21), 27829–27852 (2015), doi:.
[Crossref] [PubMed]

Lee, Z.

Lee, Z. P.

A. G. Dekker, S. R. Phinn, J. Anstee, P. Bissett, V. E. Brando, B. Casey, P. Fearns, J. Hedley, W. Klonowski, Z. P. Lee, M. Lynch, M. Lyons, C. D. Mobley, and C. Roelfsema, “Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments,” Limnol. Oceanogr. Methods 9(9), 396–425 (2011).
[Crossref]

Leffe, A.

Lynch, M.

A. G. Dekker, S. R. Phinn, J. Anstee, P. Bissett, V. E. Brando, B. Casey, P. Fearns, J. Hedley, W. Klonowski, Z. P. Lee, M. Lynch, M. Lyons, C. D. Mobley, and C. Roelfsema, “Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments,” Limnol. Oceanogr. Methods 9(9), 396–425 (2011).
[Crossref]

Lyons, M.

A. G. Dekker, S. R. Phinn, J. Anstee, P. Bissett, V. E. Brando, B. Casey, P. Fearns, J. Hedley, W. Klonowski, Z. P. Lee, M. Lynch, M. Lyons, C. D. Mobley, and C. Roelfsema, “Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments,” Limnol. Oceanogr. Methods 9(9), 396–425 (2011).
[Crossref]

Marchioretti, M.

J. M. Jaubert, J. R. M. Chisholm, A. Minghelli-Roman, M. Marchioretti, J. H. Morrow, and H. T. Ripley, “Re-evaluation of the extent of Caulerpa taxifolia development in the northern Mediterranean using airborne spectrographic sensing,” Mar. Ecol. Prog. Ser. 263, 75–82 (2003).
[Crossref]

Maritorena, S.

S. Maritorena, A. Morel, and B. Gentili, “Diffuse reflectance of oceanic shallow waters: influence of water depth and bottom albedo,” Limnol. Oceanogr. 39(7), 1689–1703 (1994).
[Crossref]

Mélin, F.

Michels, Y.

M. Guillaume, Y. Michels, and S. Jay, Joint estimation of water column parameters and seabed reflectance combining maximum likelihood and unmixing algorithm, in 7th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), (IEEE, 2015, pp.1–4)
[Crossref]

Minghelli, A.

S. Jay, M. Guillaume, A. Minghelli, Y. Deville, M. Chami, B. Lafrance, and V. Serfaty, “Hyperspectral remote sensing of shallow waters: considering environmental noise and bottom intra-class variability for modeling and inversion of water reflectance,” Remote Sens. Environ. 200, 352–367 (2017).
[Crossref]

Minghelli-Roman, A.

J. M. Jaubert, J. R. M. Chisholm, A. Minghelli-Roman, M. Marchioretti, J. H. Morrow, and H. T. Ripley, “Re-evaluation of the extent of Caulerpa taxifolia development in the northern Mediterranean using airborne spectrographic sensing,” Mar. Ecol. Prog. Ser. 263, 75–82 (2003).
[Crossref]

Miyazaki, S.

T. Sagawa, E. Boisnier, T. Komatsu, K. B. Mustapha, A. Hattour, N. Kosaka, and S. Miyazaki, “Using bottom surface reflectance to map coastal marine areas: a new application method for Lyzenga’s model,” Int. J. Remote Sens. 31(12), 3051–3064 (2010).
[Crossref]

Mobley, C.

C. Mobley and L. K. Sundman, “Effects of optically shallow bottoms on upwelling radiances: Inhomogeneous and sloping bottoms,” Limnol. Oceanogr. 48(1), 329–336 (2003).
[Crossref]

Mobley, C. D.

A. G. Dekker, S. R. Phinn, J. Anstee, P. Bissett, V. E. Brando, B. Casey, P. Fearns, J. Hedley, W. Klonowski, Z. P. Lee, M. Lynch, M. Lyons, C. D. Mobley, and C. Roelfsema, “Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments,” Limnol. Oceanogr. Methods 9(9), 396–425 (2011).
[Crossref]

Z. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S. Patch, “Hyperspectral remote sensing for shallow waters. 2. Deriving bottom depths and water properties by optimization,” Appl. Opt. 38(18), 3831–3843 (1999).
[Crossref] [PubMed]

Z. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S. Patch, “Hyperspectral remote sensing for shallow waters. I. A semianalytical model,” Appl. Opt. 37(27), 6329–6338 (1998).
[Crossref] [PubMed]

Montes, M. J.

Morel, A.

S. Maritorena, A. Morel, and B. Gentili, “Diffuse reflectance of oceanic shallow waters: influence of water depth and bottom albedo,” Limnol. Oceanogr. 39(7), 1689–1703 (1994).
[Crossref]

Morrow, J. H.

J. M. Jaubert, J. R. M. Chisholm, A. Minghelli-Roman, M. Marchioretti, J. H. Morrow, and H. T. Ripley, “Re-evaluation of the extent of Caulerpa taxifolia development in the northern Mediterranean using airborne spectrographic sensing,” Mar. Ecol. Prog. Ser. 263, 75–82 (2003).
[Crossref]

Mustapha, K. B.

T. Sagawa, E. Boisnier, T. Komatsu, K. B. Mustapha, A. Hattour, N. Kosaka, and S. Miyazaki, “Using bottom surface reflectance to map coastal marine areas: a new application method for Lyzenga’s model,” Int. J. Remote Sens. 31(12), 3051–3064 (2010).
[Crossref]

Otterman, J.

Patch, J. S.

Phinn, S. R.

A. G. Dekker, S. R. Phinn, J. Anstee, P. Bissett, V. E. Brando, B. Casey, P. Fearns, J. Hedley, W. Klonowski, Z. P. Lee, M. Lynch, M. Lyons, C. D. Mobley, and C. Roelfsema, “Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments,” Limnol. Oceanogr. Methods 9(9), 396–425 (2011).
[Crossref]

J. Hedley, C. Roelfsema, and S. R. Phinn, “Efficient radiative transfer model inversion for remote sensing applications,” Remote Sens. Environ. 113(11), 2527–2532 (2009).
[Crossref]

V. E. Brando, J. M. Anstee, M. Wettle, A. G. Dekker, S. R. Phinn, and C. Roelfsema, “A physics based retrieval and quality assessment of bathymetry from suboptimal hyperspectral data,” Remote Sens. Environ. 113(4), 755–770 (2009).
[Crossref]

Reinersman, P. N.

Ripley, H. T.

J. M. Jaubert, J. R. M. Chisholm, A. Minghelli-Roman, M. Marchioretti, J. H. Morrow, and H. T. Ripley, “Re-evaluation of the extent of Caulerpa taxifolia development in the northern Mediterranean using airborne spectrographic sensing,” Mar. Ecol. Prog. Ser. 263, 75–82 (2003).
[Crossref]

Roelfsema, C.

A. G. Dekker, S. R. Phinn, J. Anstee, P. Bissett, V. E. Brando, B. Casey, P. Fearns, J. Hedley, W. Klonowski, Z. P. Lee, M. Lynch, M. Lyons, C. D. Mobley, and C. Roelfsema, “Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments,” Limnol. Oceanogr. Methods 9(9), 396–425 (2011).
[Crossref]

V. E. Brando, J. M. Anstee, M. Wettle, A. G. Dekker, S. R. Phinn, and C. Roelfsema, “A physics based retrieval and quality assessment of bathymetry from suboptimal hyperspectral data,” Remote Sens. Environ. 113(4), 755–770 (2009).
[Crossref]

J. Hedley, C. Roelfsema, and S. R. Phinn, “Efficient radiative transfer model inversion for remote sensing applications,” Remote Sens. Environ. 113(11), 2527–2532 (2009).
[Crossref]

Sagawa, T.

T. Sagawa, E. Boisnier, T. Komatsu, K. B. Mustapha, A. Hattour, N. Kosaka, and S. Miyazaki, “Using bottom surface reflectance to map coastal marine areas: a new application method for Lyzenga’s model,” Int. J. Remote Sens. 31(12), 3051–3064 (2010).
[Crossref]

Santer, R.

Schmechtig, C.

Sei, A.

A. Sei, “Analysis of adjacency effects for two Lambertian half-spaces,” Int. J. Remote Sens. 28(8), 1873–1890 (2007).
[Crossref]

Serfaty, V.

S. Jay, M. Guillaume, A. Minghelli, Y. Deville, M. Chami, B. Lafrance, and V. Serfaty, “Hyperspectral remote sensing of shallow waters: considering environmental noise and bottom intra-class variability for modeling and inversion of water reflectance,” Remote Sens. Environ. 200, 352–367 (2017).
[Crossref]

Steward, R. G.

Sundman, L. K.

C. Mobley and L. K. Sundman, “Effects of optically shallow bottoms on upwelling radiances: Inhomogeneous and sloping bottoms,” Limnol. Oceanogr. 48(1), 329–336 (2003).
[Crossref]

Tanré, D.

Waquet, F.

Wettle, M.

V. E. Brando, J. M. Anstee, M. Wettle, A. G. Dekker, S. R. Phinn, and C. Roelfsema, “A physics based retrieval and quality assessment of bathymetry from suboptimal hyperspectral data,” Remote Sens. Environ. 113(4), 755–770 (2009).
[Crossref]

Zibordi, G.

Appl. Opt. (9)

Z. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S. Patch, “Hyperspectral remote sensing for shallow waters. I. A semianalytical model,” Appl. Opt. 37(27), 6329–6338 (1998).
[Crossref] [PubMed]

Z. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S. Patch, “Hyperspectral remote sensing for shallow waters. 2. Deriving bottom depths and water properties by optimization,” Appl. Opt. 38(18), 3831–3843 (1999).
[Crossref] [PubMed]

B. Bulgarelli, V. Kiselev, and G. Zibordi, “Adjacency effects in satellite radiometric products from coastal waters: a theoretical analysis for the northern Adriatic Sea,” Appl. Opt. 56(4), 854–869 (2017).
[Crossref] [PubMed]

R. Santer and C. Schmechtig, “Adjacency effects on water surfaces: primary scattering approximation and sensitivity study,” Appl. Opt. 39(3), 361–375 (2000).
[Crossref] [PubMed]

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(21), 4453–4471 (1995).
[Crossref] [PubMed]

J. Otterman and R. S. Fraser, “Adjacency effects on imaging by surface reflection and atmospheric scattering: cross radiance to zenith,” Appl. Opt. 18(16), 2852–2860 (1979).
[Crossref] [PubMed]

B. Bulgarelli, V. Kiselev, and G. Zibordi, “Simulation and analysis of adjacency effects in coastal waters: a case study,” Appl. Opt. 53(8), 1523–1545 (2014).
[Crossref] [PubMed]

D. Tanré, M. Herman, P. Y. Deschamps, and A. Leffe, “Atmospheric modeling for space measurements of ground reflectances, including bidirectional properties,” Appl. Opt. 18(21), 3587–3594 (1979).
[Crossref] [PubMed]

K. Z. Doctor, C. M. Bachmann, D. J. Gray, M. J. Montes, and R. A. Fusina, “Wavelength dependence of the bidirectional reflectance distribution function (BRDF) of beach sands,” Appl. Opt. 54(31), F243–F255 (2015).
[Crossref] [PubMed]

Int. J. Remote Sens. (3)

A. Sei, “Analysis of adjacency effects for two Lambertian half-spaces,” Int. J. Remote Sens. 28(8), 1873–1890 (2007).
[Crossref]

T. Sagawa, E. Boisnier, T. Komatsu, K. B. Mustapha, A. Hattour, N. Kosaka, and S. Miyazaki, “Using bottom surface reflectance to map coastal marine areas: a new application method for Lyzenga’s model,” Int. J. Remote Sens. 31(12), 3051–3064 (2010).
[Crossref]

S. Jay and M. Guillaume, “Regularized estimation of bathymetry and water quality using hyperspectral remote sensing,” Int. J. Remote Sens. 37(2), 263–289 (2016).
[Crossref]

Limnol. Oceanogr. (2)

S. Maritorena, A. Morel, and B. Gentili, “Diffuse reflectance of oceanic shallow waters: influence of water depth and bottom albedo,” Limnol. Oceanogr. 39(7), 1689–1703 (1994).
[Crossref]

C. Mobley and L. K. Sundman, “Effects of optically shallow bottoms on upwelling radiances: Inhomogeneous and sloping bottoms,” Limnol. Oceanogr. 48(1), 329–336 (2003).
[Crossref]

Limnol. Oceanogr. Methods (1)

A. G. Dekker, S. R. Phinn, J. Anstee, P. Bissett, V. E. Brando, B. Casey, P. Fearns, J. Hedley, W. Klonowski, Z. P. Lee, M. Lynch, M. Lyons, C. D. Mobley, and C. Roelfsema, “Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques in Australian and Caribbean coastal environments,” Limnol. Oceanogr. Methods 9(9), 396–425 (2011).
[Crossref]

Mar. Ecol. Prog. Ser. (1)

J. M. Jaubert, J. R. M. Chisholm, A. Minghelli-Roman, M. Marchioretti, J. H. Morrow, and H. T. Ripley, “Re-evaluation of the extent of Caulerpa taxifolia development in the northern Mediterranean using airborne spectrographic sensing,” Mar. Ecol. Prog. Ser. 263, 75–82 (2003).
[Crossref]

Opt. Express (2)

Remote Sens. Environ. (8)

B. Bulgarelli and G. Zibordi, “On the detectability of adjacency effects in ocean color remote sensing of mid-latitude coastal environments by SeaWiFS, MODIS-A, MERIS, OLCI, OLI and MSI,” Remote Sens. Environ. 209, 423–438 (2018).
[Crossref] [PubMed]

L. Feng and C. Hu, “Cloud adjacency effects on top-of-atmosphere radiance and ocean color data products: a statistical assessment,” Remote Sens. Environ. 174, 301–313 (2016).
[Crossref]

V. Kiselev, B. Bulgarelli, and T. Heege, “Sensor independent adjacency correction algorithm for coastal and inland water systems,” Remote Sens. Environ. 157, 85–95 (2015).
[Crossref]

J. Hedley, C. Roelfsema, and S. R. Phinn, “Efficient radiative transfer model inversion for remote sensing applications,” Remote Sens. Environ. 113(11), 2527–2532 (2009).
[Crossref]

S. Jay and M. Guillaume, “A novel maximum likelihood based method for mapping depth and water quality from hyperspectral remote-sensing data,” Remote Sens. Environ. 147, 121–132 (2014).
[Crossref]

S. Jay, M. Guillaume, A. Minghelli, Y. Deville, M. Chami, B. Lafrance, and V. Serfaty, “Hyperspectral remote sensing of shallow waters: considering environmental noise and bottom intra-class variability for modeling and inversion of water reflectance,” Remote Sens. Environ. 200, 352–367 (2017).
[Crossref]

V. E. Brando, J. M. Anstee, M. Wettle, A. G. Dekker, S. R. Phinn, and C. Roelfsema, “A physics based retrieval and quality assessment of bathymetry from suboptimal hyperspectral data,” Remote Sens. Environ. 113(4), 755–770 (2009).
[Crossref]

S. Belanger, 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(1), 51–68 (2007).
[Crossref]

Other (2)

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

M. Guillaume, Y. Michels, and S. Jay, Joint estimation of water column parameters and seabed reflectance combining maximum likelihood and unmixing algorithm, in 7th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), (IEEE, 2015, pp.1–4)
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Sources of the photons that contribute to the subsurface upward radiance Lu: Ludp is the radiance due to photons coming from the water column without having previously interacted with the bottom of the ocean, LBdir is the direct radiance that represents the photons which directly comes from a seabed target pixel P up to the sea surface without being scattered, LPdif is the diffuse radiance coming from the seabed target only, LMdif is the diffuse radiance of the neighborhood of the seabed target (excluding the seabed target), LBdif is the radiance that represents the photons coming from all pixels located in the seabed (i.e., target + neighborhood of the target M) and that are scattered towards the direction of observation at the subsurface level (LBdif is in fact the sum of LPdif and LMdif), ρt is the reflectance of the seabed target pixel P, ρn is the reflectance of a pixel in the neighborhood of the seabed target pixel P, ρenv(P) is the reflectance caused by all the pixels located at the seabed (i.e., the seabed target P and the neighborhood of the target M), Etot is the downward flux reaching the bottom.
Fig. 2
Fig. 2 Representation of the photons that contribute to the environment function γenv for the diffuse upward radiance.
Fig. 3
Fig. 3 Environment function Genv(R) (or δ) [Eq. (8)] at 550 nm, as a function of the radius R of a circular target P for bottom depth values of 1 m and 5 m and for the moderately turbid water condition.
Fig. 4
Fig. 4 Representation of the two configurations that are used to model the bottom albedo: (a) a bright seabed target of reflectance ρc surrounded by dark pixels having a low bottom albedo ρd (case 1), (b) a dark seabed target of bottom albedo ρd surrounded by bright pixels having an albedo ρc (case 2).
Fig. 5
Fig. 5 Relative variation of seabed contributions Δ (in %) at the subsurface level when accounting for or neglecting seabed heterogeneities (i.e., the weight of the seabed target is maximum when heterogeneities are neglected; δ = 1) for three water turbidity conditions (a) clear water, (b) moderately turbid water, (c) turbid water. The results are presented for the following conditions: target size radius of 0.2 m, three bottom depth values (1 m, 5 m, 10 m) and two bottom albedo configurations (bright and dark seabed target/neighboring pixels as illustrated in Fig. 4).
Fig. 6
Fig. 6 (a) Bottom reflectance spectra ρt of the seabed target (mix of the biogenic species Posidonia and Caulerpa Taxifolia) (red line) and its neighboring pixels (sand, blue line) ; Figs. 6(b)-6(d) show the terms δ × ρt (red dotted line) and ρn (blue dotted line) of the environment reflectance [Eq. (6)] for the clear water condition and for various bottom depth values: (b) 5 m, (c) 10 m, (d) 15 m.
Fig. 7
Fig. 7 Representation of the various radiances that contribute to the subsurface upward radiance, namely LBdir, LPdif, LMdif and Ludp, for (a) clear water, (b) moderately turbid water and (c) turbid water. Representation of the ratio ΔAE = [LBdif(δ)-LBdif(δ = 1)]/Lu, which quantifies the seabed adjacency effect, for (d) clear water, (e) moderately turbid water and (f) turbid water. The bottom depth value is 5 m.
Fig. 8
Fig. 8 Same as Fig. 7 but for a bottom depth value of 15 m and for the clear water case: (a) representation of the various radiances that contribute to the subsurface upward radiance, (b) ratio ΔAE.
Fig. 9
Fig. 9 (a) Variations of the environment function Genv with respect to the seabed target radius for different values of the Junge exponent of the size distribution of the hydrosols: 3.5, 4 and 4.5, for H = 1 m and 5 m and for moderately turbid water (same as Fig. 3), (b) ratio of Genv calculated for two couples of Junge exponents: (3.5 and 4) and (4.5 and 4) for H = 5 m.

Tables (6)

Tables Icon

Table 1 Parameters used as inputs in the OSOAA model: aCDOM (440 nm) is the absorption coefficient of CDOM at 440 nm, the CHL concentration is in mg m−3, the SED concentration is in mg L−1, τw is the water optical depth at 550 nm.

Tables Icon

Table 2 Bottom albedo values that are used for bright and dark pixels as inputs of the radiative transfer modeling at various wavelengths.

Tables Icon

Table 3 Mean value of the relative variation of seabed contributions Δmean (in %); the seabed target size radius R value is 0.2 m; the bottom depth values are 1, 5 and 10 m for three water turbidity conditions (clear, moderately turbid and turbid waters). σ is the standard deviation (in %).

Tables Icon

Table 4 Maximum values of the spectral ratio ΔAE for various bottom depths and for various water turbidity conditions.

Tables Icon

Table 5 Mean value of the relative variation of seabed contributions Δmean (in %) as a function of the seabed target radius R for various bottom depth values H (1, 5 and 10 m) and for the moderately turbid water condition. σ is the standard variation (in %).

Tables Icon

Table 6 Table 6. List of notations and abbreviations

Equations (10)

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

L u ( P, 0 , θ , θ ,λ )= L B dir ( P, 0 , θ , θ ,λ )+ L B dif ( P, 0 , θ , θ ,λ )+ L udp ( 0 , θ , θ ,λ )
L B dir ( P, 0 , θ , θ )= E tot (P,  θ ) π × ρ t ( P )× T dir ( 0 , θ )
L B dif ( P, 0 , θ , θ )= T dif ( 0 , θ )× MV(P) E tot (M,  θ ) π × γ env ( P,M )× ρ b ( M )  dS M
L B dif ( P, 0 , θ , θ )= T dif ( 0 , θ ) E tot (P, θ ) π × ρ env ( P )
ρ env = MV(P) γ env ( P,M )× ρ b ( M )  dS M
ρ env ( P )= δ × ρ t ( P )+ MP γ env ( P,M )× ρ b ( M )  dS M =  δ × ρ t ( P )+  ρ n ( P ) 
γ env ( M,P )= 1 S scene × dG env dR
G env ( R )= 0 τ wtot exp( τ w )  η 1 exp[ ( τ w tot τ w )/μ ]P( μ ) dμdτ w 0 τ w tot exp( τ w )  0 1 exp[ ( τ w tot τ w )/μ ]P( μ ) dμdτ w
L u ( P,  0 , θ )= E tot ( P ) π × ρ t ( P )× T dir ( 0 , θ )+ E tot ( P ) π × ρ t ( P )× δ × T dif ( 0 , θ ) + E tot ( P ) π × ρ n ( P )× T dif ( 0 , θ )+  L udp ( 0 , θ )
Δ= | [ L B dir + L B dif ]( δ )[ L B dir + L B dif ]( δ =1 ) | [ L B dir + L B dif ]( δ )

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