Abstract

This work intercompared two Bi-directional Reflectance Distribution Function (BRDF) models, the modified Minnaert’s model and the RossThick-LiSparse-R model, in the estimation of the directional emissivity in Middle Infra-Red (MIR) channel from the data acquired by the Spinning Enhanced Visible and Infra-Red Imager (SEVIRI) onboard the first Meteosat Second Generation (MSG1). The bi-directional reflectances in SEVIRI channel 4 (3.9 µm) were estimated from the combined MIR and Thermal Infra-Red (TIR) data and then were used to estimate the directional emissivity in this channel with aid of the BRDF models. The results show that: (1) Both models can relatively well describe the non-Lambertian reflective behavior of land surfaces in SEVIRI channel 4; (2) The RossThick-LiSparse-R model is better than the modified Minnaert’s model in modeling the bi-directional reflectances, and the directional emissivities modeled by the modified Minnaert’s model are always lower than the ones obtained by the RossThick-LiSparse-R model with averaged emissivity differences of ~0.01 and ~0.04 over the vegetated and bare areas, respectively. The use of the RossThick-LiSparse-R model in the estimation of the directional emissivity in MIR channel is recommended.

© 2008 Optical Society of America

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  1. T. Y. Lee and Y. J. Kaufman, "Non-Lambertian effects in remote sensing of surface reflectance and vegetation index," IEEE Trans. Geosci. Remote Sens. 24, 699-708 (1986).
    [CrossRef]
  2. M. Minnaert, "The reciprocity principle of linear photometry," Astrophys. J. 93, 403-410 (1941).
    [CrossRef]
  3. C. L. Walthall, J. M. Norman, J. M. Welles, G. Gampbell, and B. L. Blad, "Simple eqution to approximate the bidirectional reflectance from vegetation canopies and bare soil surfaces," Appl. Opt. 24, 383-387 (1985).
    [CrossRef] [PubMed]
  4. T. Nilson and A. Kuusk, "A reflectance model for the homogeneous plant canopy and its inversion," Remote Sens. Environ. 27, 157-167 (1989).
    [CrossRef]
  5. J. L. Roujean, M. Leroy, and P. Y. Deschamps, "A bidirectional reflectance model of the Earth’s surface for the correction of remote sensing data," J. Geophys. Res. 97, 20,455-20,468 (1992).
    [CrossRef]
  6. W. Wanner, X. Li, and A. H. Strahler, "On the derivation of kernels for kernel-driven models of bidirectional reflectance," J. Geophys. Res. 100, D10: 21,077-21,089 (1995).
  7. X. Li and A. H. Strahler, "Geometric-optical bidirectional reflectance modeling of the discrete crown vegetation canopy: Effect of crown shape and mutual shadowing," IEEE Trans. Geosci. Remote Sens. 30, 276-292 (1992).
    [CrossRef]
  8. G. M. Jiang, Z.-L. Li, and F. Nerry, "Land surface emissivity retrieval from combined mid-infrared and thermal infrared data of MSG-SEVIRI," Remote Sens. Environ. 105, 326-340 (2006).
    [CrossRef]
  9. F. Becker and Z.-L. Li, "Temperature independent spectral indices in thermal infrared bands," Remote Sens. Environ. 32, 17-33 (1990).
    [CrossRef]
  10. Z.-L. Li, F. Petitcolin, and R. H. Zhang, "A physically based algorithm for land surface emissivity retrieval from combined mid-infrared and thermal infrared data," Sci. China Ser E 43 Supp. 22-33 (2000).
    [CrossRef]
  11. F. Petitcolin, F. Nerry, and M. P. Stoll, "Mapping directional emissivity at 3.7 ?m using a simple model of bi-directional reflectivity," Int. J. Remote Sens. 23, 3443-3472 (2002).
    [CrossRef]
  12. Z.-L. Li and F. Becker, "Feasibility of land surface temperature and emissivity determination from AVHRR data," Remote Sens. Environ. 43, 67-85 (1993).
    [CrossRef]
  13. F. E. Nicodemus, "Directional reflectance and emissivity of an opaque surface," Appl. Opt. 4, 767-773 (1965).
    [CrossRef]
  14. M. C. Saint-Pé, and F. Rigaut, "Ceres surface properties by high-resolution imaging from Earth," Icarus 105, 271-281 (1993).
    [CrossRef]
  15. J. W. Parker, S. A. Stern, P. C. Thoms, M. C. Festou, W. J. Merline, E. F. Young, R. P. Binzel, and L. A. Lebofsky, "Analysis of the first disk-resolved images of Ceres from ultraviolet observations with the Hubble Space Telescope," Astron 123, 549-557 (2002).
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  17. W. Lucht, "Expected retrieval accuracies of bidirectional reflectance and albedo from EOS-MODIS and MISR angular sampling," J. Geophys. Res. 103, 8763-8778 (1998).
    [CrossRef]
  18. W. Lucht and P. Louis, "Theoretical noise sensitivity of BRDF and albedo retrieval from EOS-MODIS and MISR sensors with respect to angular sampling," Int. J. Remote Sens. 21(1), 81-98 (2000).
    [CrossRef]
  19. B. Hu, W. Lucht, X. Li, and A. H. Strahler, "Validation of kernel-driven models for the BRDF of land surfaces," Remote Sens. Environ. 62, 201-214 (1997).
    [CrossRef]
  20. J. L. Privette, T. F. Eck, and D. W. Deering, "Estimating spectral albedo and nadir reflectance through inversion of simple BRDF models with AVHRR/MODIS-like data," J. Geophys. Res. 102(D24), 29,529-29,542 (1997).
    [CrossRef]
  21. I. Pokrovsky, O. Pokrovsky, and J. L. Roujean, "Development of an operational procedure to estimate surface albedo from the SEVIRI/MSG observing system by using POLDER BRDF measurements II: Comparison of several inversion techniques and ncertainty in albedo estimates," Remote Sens. Environ. 87, 215-242 (2003).
    [CrossRef]
  22. J. Susaki, K. Hara, J. G. Park, Y. Yasuda, K. Kajiwara, and Y. Honda, "Validation of temporal BRDFs of paddy fields estimated from MODIS reflectance data," IEEE Trans. Geosci. Remote Sens. 42, 1262-1270 (2004).
    [CrossRef]

2006 (1)

G. M. Jiang, Z.-L. Li, and F. Nerry, "Land surface emissivity retrieval from combined mid-infrared and thermal infrared data of MSG-SEVIRI," Remote Sens. Environ. 105, 326-340 (2006).
[CrossRef]

2004 (1)

J. Susaki, K. Hara, J. G. Park, Y. Yasuda, K. Kajiwara, and Y. Honda, "Validation of temporal BRDFs of paddy fields estimated from MODIS reflectance data," IEEE Trans. Geosci. Remote Sens. 42, 1262-1270 (2004).
[CrossRef]

2003 (1)

I. Pokrovsky, O. Pokrovsky, and J. L. Roujean, "Development of an operational procedure to estimate surface albedo from the SEVIRI/MSG observing system by using POLDER BRDF measurements II: Comparison of several inversion techniques and ncertainty in albedo estimates," Remote Sens. Environ. 87, 215-242 (2003).
[CrossRef]

2002 (2)

J. W. Parker, S. A. Stern, P. C. Thoms, M. C. Festou, W. J. Merline, E. F. Young, R. P. Binzel, and L. A. Lebofsky, "Analysis of the first disk-resolved images of Ceres from ultraviolet observations with the Hubble Space Telescope," Astron 123, 549-557 (2002).
[CrossRef]

F. Petitcolin, F. Nerry, and M. P. Stoll, "Mapping directional emissivity at 3.7 ?m using a simple model of bi-directional reflectivity," Int. J. Remote Sens. 23, 3443-3472 (2002).
[CrossRef]

2000 (1)

W. Lucht and P. Louis, "Theoretical noise sensitivity of BRDF and albedo retrieval from EOS-MODIS and MISR sensors with respect to angular sampling," Int. J. Remote Sens. 21(1), 81-98 (2000).
[CrossRef]

1998 (1)

W. Lucht, "Expected retrieval accuracies of bidirectional reflectance and albedo from EOS-MODIS and MISR angular sampling," J. Geophys. Res. 103, 8763-8778 (1998).
[CrossRef]

1997 (2)

B. Hu, W. Lucht, X. Li, and A. H. Strahler, "Validation of kernel-driven models for the BRDF of land surfaces," Remote Sens. Environ. 62, 201-214 (1997).
[CrossRef]

J. L. Privette, T. F. Eck, and D. W. Deering, "Estimating spectral albedo and nadir reflectance through inversion of simple BRDF models with AVHRR/MODIS-like data," J. Geophys. Res. 102(D24), 29,529-29,542 (1997).
[CrossRef]

1995 (1)

W. Wanner, X. Li, and A. H. Strahler, "On the derivation of kernels for kernel-driven models of bidirectional reflectance," J. Geophys. Res. 100, D10: 21,077-21,089 (1995).

1993 (2)

Z.-L. Li and F. Becker, "Feasibility of land surface temperature and emissivity determination from AVHRR data," Remote Sens. Environ. 43, 67-85 (1993).
[CrossRef]

M. C. Saint-Pé, and F. Rigaut, "Ceres surface properties by high-resolution imaging from Earth," Icarus 105, 271-281 (1993).
[CrossRef]

1992 (2)

X. Li and A. H. Strahler, "Geometric-optical bidirectional reflectance modeling of the discrete crown vegetation canopy: Effect of crown shape and mutual shadowing," IEEE Trans. Geosci. Remote Sens. 30, 276-292 (1992).
[CrossRef]

J. L. Roujean, M. Leroy, and P. Y. Deschamps, "A bidirectional reflectance model of the Earth’s surface for the correction of remote sensing data," J. Geophys. Res. 97, 20,455-20,468 (1992).
[CrossRef]

1990 (1)

F. Becker and Z.-L. Li, "Temperature independent spectral indices in thermal infrared bands," Remote Sens. Environ. 32, 17-33 (1990).
[CrossRef]

1989 (1)

T. Nilson and A. Kuusk, "A reflectance model for the homogeneous plant canopy and its inversion," Remote Sens. Environ. 27, 157-167 (1989).
[CrossRef]

1986 (1)

T. Y. Lee and Y. J. Kaufman, "Non-Lambertian effects in remote sensing of surface reflectance and vegetation index," IEEE Trans. Geosci. Remote Sens. 24, 699-708 (1986).
[CrossRef]

1985 (1)

1965 (1)

1941 (1)

M. Minnaert, "The reciprocity principle of linear photometry," Astrophys. J. 93, 403-410 (1941).
[CrossRef]

Becker, F.

Z.-L. Li and F. Becker, "Feasibility of land surface temperature and emissivity determination from AVHRR data," Remote Sens. Environ. 43, 67-85 (1993).
[CrossRef]

F. Becker and Z.-L. Li, "Temperature independent spectral indices in thermal infrared bands," Remote Sens. Environ. 32, 17-33 (1990).
[CrossRef]

Binzel, R. P.

J. W. Parker, S. A. Stern, P. C. Thoms, M. C. Festou, W. J. Merline, E. F. Young, R. P. Binzel, and L. A. Lebofsky, "Analysis of the first disk-resolved images of Ceres from ultraviolet observations with the Hubble Space Telescope," Astron 123, 549-557 (2002).
[CrossRef]

Blad, B. L.

Deering, D. W.

J. L. Privette, T. F. Eck, and D. W. Deering, "Estimating spectral albedo and nadir reflectance through inversion of simple BRDF models with AVHRR/MODIS-like data," J. Geophys. Res. 102(D24), 29,529-29,542 (1997).
[CrossRef]

Deschamps, P. Y.

J. L. Roujean, M. Leroy, and P. Y. Deschamps, "A bidirectional reflectance model of the Earth’s surface for the correction of remote sensing data," J. Geophys. Res. 97, 20,455-20,468 (1992).
[CrossRef]

Eck, T. F.

J. L. Privette, T. F. Eck, and D. W. Deering, "Estimating spectral albedo and nadir reflectance through inversion of simple BRDF models with AVHRR/MODIS-like data," J. Geophys. Res. 102(D24), 29,529-29,542 (1997).
[CrossRef]

Festou, M. C.

J. W. Parker, S. A. Stern, P. C. Thoms, M. C. Festou, W. J. Merline, E. F. Young, R. P. Binzel, and L. A. Lebofsky, "Analysis of the first disk-resolved images of Ceres from ultraviolet observations with the Hubble Space Telescope," Astron 123, 549-557 (2002).
[CrossRef]

Gampbell, G.

Hara, K.

J. Susaki, K. Hara, J. G. Park, Y. Yasuda, K. Kajiwara, and Y. Honda, "Validation of temporal BRDFs of paddy fields estimated from MODIS reflectance data," IEEE Trans. Geosci. Remote Sens. 42, 1262-1270 (2004).
[CrossRef]

Honda, Y.

J. Susaki, K. Hara, J. G. Park, Y. Yasuda, K. Kajiwara, and Y. Honda, "Validation of temporal BRDFs of paddy fields estimated from MODIS reflectance data," IEEE Trans. Geosci. Remote Sens. 42, 1262-1270 (2004).
[CrossRef]

Hu, B.

B. Hu, W. Lucht, X. Li, and A. H. Strahler, "Validation of kernel-driven models for the BRDF of land surfaces," Remote Sens. Environ. 62, 201-214 (1997).
[CrossRef]

Jiang, G. M.

G. M. Jiang, Z.-L. Li, and F. Nerry, "Land surface emissivity retrieval from combined mid-infrared and thermal infrared data of MSG-SEVIRI," Remote Sens. Environ. 105, 326-340 (2006).
[CrossRef]

Kajiwara, K.

J. Susaki, K. Hara, J. G. Park, Y. Yasuda, K. Kajiwara, and Y. Honda, "Validation of temporal BRDFs of paddy fields estimated from MODIS reflectance data," IEEE Trans. Geosci. Remote Sens. 42, 1262-1270 (2004).
[CrossRef]

Kaufman, Y. J.

T. Y. Lee and Y. J. Kaufman, "Non-Lambertian effects in remote sensing of surface reflectance and vegetation index," IEEE Trans. Geosci. Remote Sens. 24, 699-708 (1986).
[CrossRef]

Kuusk, A.

T. Nilson and A. Kuusk, "A reflectance model for the homogeneous plant canopy and its inversion," Remote Sens. Environ. 27, 157-167 (1989).
[CrossRef]

Lebofsky, L. A.

J. W. Parker, S. A. Stern, P. C. Thoms, M. C. Festou, W. J. Merline, E. F. Young, R. P. Binzel, and L. A. Lebofsky, "Analysis of the first disk-resolved images of Ceres from ultraviolet observations with the Hubble Space Telescope," Astron 123, 549-557 (2002).
[CrossRef]

Lee, T. Y.

T. Y. Lee and Y. J. Kaufman, "Non-Lambertian effects in remote sensing of surface reflectance and vegetation index," IEEE Trans. Geosci. Remote Sens. 24, 699-708 (1986).
[CrossRef]

Leroy, M.

J. L. Roujean, M. Leroy, and P. Y. Deschamps, "A bidirectional reflectance model of the Earth’s surface for the correction of remote sensing data," J. Geophys. Res. 97, 20,455-20,468 (1992).
[CrossRef]

Li, X.

B. Hu, W. Lucht, X. Li, and A. H. Strahler, "Validation of kernel-driven models for the BRDF of land surfaces," Remote Sens. Environ. 62, 201-214 (1997).
[CrossRef]

W. Wanner, X. Li, and A. H. Strahler, "On the derivation of kernels for kernel-driven models of bidirectional reflectance," J. Geophys. Res. 100, D10: 21,077-21,089 (1995).

X. Li and A. H. Strahler, "Geometric-optical bidirectional reflectance modeling of the discrete crown vegetation canopy: Effect of crown shape and mutual shadowing," IEEE Trans. Geosci. Remote Sens. 30, 276-292 (1992).
[CrossRef]

Li, Z.-L.

G. M. Jiang, Z.-L. Li, and F. Nerry, "Land surface emissivity retrieval from combined mid-infrared and thermal infrared data of MSG-SEVIRI," Remote Sens. Environ. 105, 326-340 (2006).
[CrossRef]

Z.-L. Li and F. Becker, "Feasibility of land surface temperature and emissivity determination from AVHRR data," Remote Sens. Environ. 43, 67-85 (1993).
[CrossRef]

F. Becker and Z.-L. Li, "Temperature independent spectral indices in thermal infrared bands," Remote Sens. Environ. 32, 17-33 (1990).
[CrossRef]

Z.-L. Li, F. Petitcolin, and R. H. Zhang, "A physically based algorithm for land surface emissivity retrieval from combined mid-infrared and thermal infrared data," Sci. China Ser E 43 Supp. 22-33 (2000).
[CrossRef]

Louis, P.

W. Lucht and P. Louis, "Theoretical noise sensitivity of BRDF and albedo retrieval from EOS-MODIS and MISR sensors with respect to angular sampling," Int. J. Remote Sens. 21(1), 81-98 (2000).
[CrossRef]

Lucht, W.

W. Lucht and P. Louis, "Theoretical noise sensitivity of BRDF and albedo retrieval from EOS-MODIS and MISR sensors with respect to angular sampling," Int. J. Remote Sens. 21(1), 81-98 (2000).
[CrossRef]

W. Lucht, "Expected retrieval accuracies of bidirectional reflectance and albedo from EOS-MODIS and MISR angular sampling," J. Geophys. Res. 103, 8763-8778 (1998).
[CrossRef]

B. Hu, W. Lucht, X. Li, and A. H. Strahler, "Validation of kernel-driven models for the BRDF of land surfaces," Remote Sens. Environ. 62, 201-214 (1997).
[CrossRef]

Merline, W. J.

J. W. Parker, S. A. Stern, P. C. Thoms, M. C. Festou, W. J. Merline, E. F. Young, R. P. Binzel, and L. A. Lebofsky, "Analysis of the first disk-resolved images of Ceres from ultraviolet observations with the Hubble Space Telescope," Astron 123, 549-557 (2002).
[CrossRef]

Minnaert, M.

M. Minnaert, "The reciprocity principle of linear photometry," Astrophys. J. 93, 403-410 (1941).
[CrossRef]

Nerry, F.

G. M. Jiang, Z.-L. Li, and F. Nerry, "Land surface emissivity retrieval from combined mid-infrared and thermal infrared data of MSG-SEVIRI," Remote Sens. Environ. 105, 326-340 (2006).
[CrossRef]

F. Petitcolin, F. Nerry, and M. P. Stoll, "Mapping directional emissivity at 3.7 ?m using a simple model of bi-directional reflectivity," Int. J. Remote Sens. 23, 3443-3472 (2002).
[CrossRef]

Nicodemus, F. E.

Nilson, T.

T. Nilson and A. Kuusk, "A reflectance model for the homogeneous plant canopy and its inversion," Remote Sens. Environ. 27, 157-167 (1989).
[CrossRef]

Norman, J. M.

Park, J. G.

J. Susaki, K. Hara, J. G. Park, Y. Yasuda, K. Kajiwara, and Y. Honda, "Validation of temporal BRDFs of paddy fields estimated from MODIS reflectance data," IEEE Trans. Geosci. Remote Sens. 42, 1262-1270 (2004).
[CrossRef]

Parker, J. W.

J. W. Parker, S. A. Stern, P. C. Thoms, M. C. Festou, W. J. Merline, E. F. Young, R. P. Binzel, and L. A. Lebofsky, "Analysis of the first disk-resolved images of Ceres from ultraviolet observations with the Hubble Space Telescope," Astron 123, 549-557 (2002).
[CrossRef]

Petitcolin, F.

F. Petitcolin, F. Nerry, and M. P. Stoll, "Mapping directional emissivity at 3.7 ?m using a simple model of bi-directional reflectivity," Int. J. Remote Sens. 23, 3443-3472 (2002).
[CrossRef]

Z.-L. Li, F. Petitcolin, and R. H. Zhang, "A physically based algorithm for land surface emissivity retrieval from combined mid-infrared and thermal infrared data," Sci. China Ser E 43 Supp. 22-33 (2000).
[CrossRef]

Pokrovsky, I.

I. Pokrovsky, O. Pokrovsky, and J. L. Roujean, "Development of an operational procedure to estimate surface albedo from the SEVIRI/MSG observing system by using POLDER BRDF measurements II: Comparison of several inversion techniques and ncertainty in albedo estimates," Remote Sens. Environ. 87, 215-242 (2003).
[CrossRef]

Pokrovsky, O.

I. Pokrovsky, O. Pokrovsky, and J. L. Roujean, "Development of an operational procedure to estimate surface albedo from the SEVIRI/MSG observing system by using POLDER BRDF measurements II: Comparison of several inversion techniques and ncertainty in albedo estimates," Remote Sens. Environ. 87, 215-242 (2003).
[CrossRef]

Privette, J. L.

J. L. Privette, T. F. Eck, and D. W. Deering, "Estimating spectral albedo and nadir reflectance through inversion of simple BRDF models with AVHRR/MODIS-like data," J. Geophys. Res. 102(D24), 29,529-29,542 (1997).
[CrossRef]

Rigaut, F.

M. C. Saint-Pé, and F. Rigaut, "Ceres surface properties by high-resolution imaging from Earth," Icarus 105, 271-281 (1993).
[CrossRef]

Roujean, J. L.

I. Pokrovsky, O. Pokrovsky, and J. L. Roujean, "Development of an operational procedure to estimate surface albedo from the SEVIRI/MSG observing system by using POLDER BRDF measurements II: Comparison of several inversion techniques and ncertainty in albedo estimates," Remote Sens. Environ. 87, 215-242 (2003).
[CrossRef]

J. L. Roujean, M. Leroy, and P. Y. Deschamps, "A bidirectional reflectance model of the Earth’s surface for the correction of remote sensing data," J. Geophys. Res. 97, 20,455-20,468 (1992).
[CrossRef]

Saint-Pé, M. C.

M. C. Saint-Pé, and F. Rigaut, "Ceres surface properties by high-resolution imaging from Earth," Icarus 105, 271-281 (1993).
[CrossRef]

Stern, S. A.

J. W. Parker, S. A. Stern, P. C. Thoms, M. C. Festou, W. J. Merline, E. F. Young, R. P. Binzel, and L. A. Lebofsky, "Analysis of the first disk-resolved images of Ceres from ultraviolet observations with the Hubble Space Telescope," Astron 123, 549-557 (2002).
[CrossRef]

Stoll, M. P.

F. Petitcolin, F. Nerry, and M. P. Stoll, "Mapping directional emissivity at 3.7 ?m using a simple model of bi-directional reflectivity," Int. J. Remote Sens. 23, 3443-3472 (2002).
[CrossRef]

Strahler, A. H.

B. Hu, W. Lucht, X. Li, and A. H. Strahler, "Validation of kernel-driven models for the BRDF of land surfaces," Remote Sens. Environ. 62, 201-214 (1997).
[CrossRef]

W. Wanner, X. Li, and A. H. Strahler, "On the derivation of kernels for kernel-driven models of bidirectional reflectance," J. Geophys. Res. 100, D10: 21,077-21,089 (1995).

X. Li and A. H. Strahler, "Geometric-optical bidirectional reflectance modeling of the discrete crown vegetation canopy: Effect of crown shape and mutual shadowing," IEEE Trans. Geosci. Remote Sens. 30, 276-292 (1992).
[CrossRef]

Susaki, J.

J. Susaki, K. Hara, J. G. Park, Y. Yasuda, K. Kajiwara, and Y. Honda, "Validation of temporal BRDFs of paddy fields estimated from MODIS reflectance data," IEEE Trans. Geosci. Remote Sens. 42, 1262-1270 (2004).
[CrossRef]

Thoms, P. C.

J. W. Parker, S. A. Stern, P. C. Thoms, M. C. Festou, W. J. Merline, E. F. Young, R. P. Binzel, and L. A. Lebofsky, "Analysis of the first disk-resolved images of Ceres from ultraviolet observations with the Hubble Space Telescope," Astron 123, 549-557 (2002).
[CrossRef]

Walthall, C. L.

Wanner, W.

W. Wanner, X. Li, and A. H. Strahler, "On the derivation of kernels for kernel-driven models of bidirectional reflectance," J. Geophys. Res. 100, D10: 21,077-21,089 (1995).

Welles, J. M.

Yasuda, Y.

J. Susaki, K. Hara, J. G. Park, Y. Yasuda, K. Kajiwara, and Y. Honda, "Validation of temporal BRDFs of paddy fields estimated from MODIS reflectance data," IEEE Trans. Geosci. Remote Sens. 42, 1262-1270 (2004).
[CrossRef]

Young, E. F.

J. W. Parker, S. A. Stern, P. C. Thoms, M. C. Festou, W. J. Merline, E. F. Young, R. P. Binzel, and L. A. Lebofsky, "Analysis of the first disk-resolved images of Ceres from ultraviolet observations with the Hubble Space Telescope," Astron 123, 549-557 (2002).
[CrossRef]

Zhang, R. H.

Z.-L. Li, F. Petitcolin, and R. H. Zhang, "A physically based algorithm for land surface emissivity retrieval from combined mid-infrared and thermal infrared data," Sci. China Ser E 43 Supp. 22-33 (2000).
[CrossRef]

Appl. Opt. (2)

Astron (1)

J. W. Parker, S. A. Stern, P. C. Thoms, M. C. Festou, W. J. Merline, E. F. Young, R. P. Binzel, and L. A. Lebofsky, "Analysis of the first disk-resolved images of Ceres from ultraviolet observations with the Hubble Space Telescope," Astron 123, 549-557 (2002).
[CrossRef]

Astrophys. J. (1)

M. Minnaert, "The reciprocity principle of linear photometry," Astrophys. J. 93, 403-410 (1941).
[CrossRef]

Icarus (1)

M. C. Saint-Pé, and F. Rigaut, "Ceres surface properties by high-resolution imaging from Earth," Icarus 105, 271-281 (1993).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (3)

X. Li and A. H. Strahler, "Geometric-optical bidirectional reflectance modeling of the discrete crown vegetation canopy: Effect of crown shape and mutual shadowing," IEEE Trans. Geosci. Remote Sens. 30, 276-292 (1992).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Integrals and fitting results of the volumetric kernel (left) and the geometric kernel (right) of the RossThick-LiSparse-R model

Fig. 2.
Fig. 2.

Map of the study area generated from the Global Land Cover 2000

Fig. 3.
Fig. 3.

Polar representation of the solar zenith angle (0°-90°) and relative azimuth angle (0°-360°) at the four locations on July 17 and 19 of 2004

Fig. 4.
Fig. 4.

Normalized bi-directional reflectance versus solar zenith angle using the modified Minnaert’s model (left-hand column) and the RossThick-LiSparse-R model (right-hand column) at the four locations (φ=0° and θ s<0 for the backscattering, while φ=180° and θ s>0 for the forward scattering)

Fig. 5.
Fig. 5.

Modeled bi-directional reflectances versus retrieved bi-directional reflectances on July 17 and 19 of 2004 at the four locations using the Modified Minnaert’s model (left) and the RossThick-LiSparse-R model (right) (Δρ mean represents the mean of the differences between the retrieved reflectances and the modeled reflectances; Stdev is the standard deviation)

Fig. 6.
Fig. 6.

Directional emissivities modeled by the two models (left) and the emissivity differences (right) (RL and MM represent for the RossThick-LiSparse-R model and the modified Minnaert’s model, respectiveluy; ε 4,d,x represents the directional emissivity in SEVIRI channel 4 on date d modeled by model x, where x=RL or MM)

Fig. 7.
Fig. 7.

Maps of the directional emissivities in SEVIRI channel 4 modeled by the RossThick-LiSparse-R model and the differences between the directional emissivities modeled by the two models on July 17 and 19 of 2004 (Variables are the same as the ones in Fig. 6)

Tables (4)

Tables Icon

Table 1. Fitting parameters of Eqs. (15) and (16)

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Table 2. Description of the four specific locations

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Table 3. Fitting parameters and RMSEs at the four locations on July 17 and 19 of 2004

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Table 4. Averages and standard deviations of the emissivity differences over the entire study area

Equations (18)

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ε ( θ v ) = 1 ρ h ( θ v )
ρ h ( θ v ) = 0 2 π 0 π 2 ρ b ( θ v , θ s , φ ) sin ( θ s ) cos ( θ s ) d θ s d φ
ρ b ( θ v , θ s , φ ) = ρ 0 [ cos ( θ v ) cos ( θ s ) ] k 1 [ 1 + γ sin ( θ v ) sin ( θ s ) cos ( φ ) ]
ε 4 ( θ v ) = 1 2 π k + 1 ρ 0 cos k 1 ( θ v )
ρ b ( θ v , θ s , φ ) = k iso + k vol f vol ( θ v , θ s , φ ) + k geo f geo ( θ v , θ s , φ )
f vol ( θ v , θ s , φ ) = 4 3 π 1 cos θ v + cos θ s [ ( π 2 ξ ) cos ξ + sin ξ ] 1 3
cos ξ = cos θ v cos θ s + sin θ v sin θ s cos φ
f geo = O ( θ v , θ s , φ ) sec θ v sec θ s + 1 2 ( 1 + cos ξ ) sec θ v sec θ s
O ( θ v , θ s , φ ) = 1 π ( t sin t cos t ) ( sec θ v + sec θ s )
cos t = h b D 2 + ( tan θ v tan θ s sin φ ) 2 sec θ v + sec θ s )
D = tan 2 θ v + tan 2 θ s 2 tan θ v tan θ s cos φ
cos ξ = cos θ v cos θ s + sin θ v sin θ s cos φ
θ v = tan 1 ( b r tan θ v ) θ s = tan 1 ( b r tan θ s )
ε 4 ( θ v ) = 1 π k iso k vol I f vol ( θ v ) k geo I f geo ( θ v )
I f vol ( θ v ) = A 0 + A 1 exp ( θ v t 1 )
I f geo ( θ v ) = B 0 + B 1 ω π 2 exp [ 2 ( θ v θ c ω ) 2 ]
ρ b , 4 ( θ v , θ s , φ 0 ) = ρ b , 4 ( θ v , θ s , φ ) [ 1 + γ sin ( θ v ) sin ( θ s ) cos ( φ 0 ) ] 1 + γ sin ( θ v ) sin ( θ s ) cos ( φ )
ρ b , 4 ( θ v , θ s , φ 0 ) = ρ b , 4 ( θ v , θ s , φ ) [ K iso + K vol f vol ( θ v , θ s , φ 0 ) + K geo f geo ( θ v , θ s , φ 0 ) ] K iso + K vol f vol ( θ v , θ s , φ ) + K geo f geo ( θ v , θ s , φ )

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