Abstract

We propose a modeling of the aggregation processes of optical properties and temperature over the heterogeneous landscape in the infrared domain (314μm). The main objectives of the modeling are to understand how these parameters aggregate and to study their links at different spatial scales. As the landscape is described at each scale by its radiative parameters, general equations linking the radiative parameters at a given high spatial scale to those at a rough scale are proposed. Then these equations are applied to several synthetic landscapes. An analysis based on a design of experiments is conducted to point out the influence of each of the input factors. The results show the importance of the intrinsic parameters (reflectance, emissivity, and surface temperature) of each surface element and also the directional and spectral behaviors of the aggregated parameters.

© 2010 Optical Society of America

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2008 (1)

2006 (2)

Z. Jiang, A. R. Huete, J. Chen, Y. Chen, J. Li, G. Yan, and X. Zhang, “Analysis of NDVI and scaled difference vegetation index retrievals of vegetation fraction,” Remote Sens. Environ. 101, 366–378 (2006).
[CrossRef]

B. Coudert, C. Ottlé, and B. Boudevillain, “Contribution of thermal infrared remote sensing data in multiobjective calibration of a dual-source SVAT model,” J. Hydrometeorology 7, 404–420 (2006).
[CrossRef]

2004 (2)

L. Coret, X. Briottet, Y. Kerr, and A. Chehbouni, “Simulation study of view angle effects on thermal infrared measurements over heterogeneous surfaces,” IEEE Trans. Geosci. Remote Sensing 42, 664–672 (2004).
[CrossRef]

L. Chen, Z.-L. Li, Q. Liu, S. Chen, Y. Tang, and B. Zhong, “Definition of component effective emissivity for heterogeneous and non-isothermal surfaces and its approximate calculation,” Int. J. Remote Sensing 25, 231–244 (2004).
[CrossRef]

2003 (1)

L. Su, X. Li, S. Liang, and A. H. Strahler, “Simulation of scaling effects of thermal emission from nonisothermal pixels with the typical three-dimensional structure,” Int. J. Remote Sensing 24, 3743–3753 (2003).
[CrossRef]

2001 (1)

G. Yan, M. Friedl, X. Li, J. Wang, C. Zhu, and A. H. Strahler, “Modeling directional effects from nonisothermal land surfaces in wideband thermal infrared measurements,” IEEE Trans. Geosci. Remote Sensing 39, 1095–1099 (2001).
[CrossRef]

2000 (1)

Z.-L. Li, J. Wang, and A. H. Strahler, “Scale effects and scaling-up by geometric-optical model,” Science in China (Series E) 43, 17–22 (2000).
[CrossRef]

1999 (1)

Z.-L. Li, A. H. Strahler, and M. Friedl, “A conceptual model for effective directional emissivity from nonisothermal surface,” IEEE Trans. Geosci. Remote Sensing 37, 2508–2517 (1999).
[CrossRef]

1997 (2)

J. A. Voogt and T. R. Oke, “Complete urban surface temperatures,” J. Appl. Meteorol. 36, 1117–1132 (1997).
[CrossRef]

R. B. Myneni, R. R. Nemani, and S. W. Running, “Estimation of global leaf area index and absorbed par using radiative transfer models,” IEEE Trans. Geosci. Remote Sensing 35, 1380–1393 (1997).
[CrossRef]

1996 (1)

Z. Wan and J. Dozier, “A generalized slipt-window algorithm for retrieving land surface temperature from space,” IEEE Trans. Geosci. Remote Sensing 34, 892–905 (1996).
[CrossRef]

1995 (4)

F. Becker and Z.-L. Li, “Surface temperature and emissivity at various scales: definition, measurement and related problems,” Remote Sens. Rev. 12, 225–253 (1995).
[CrossRef]

A. Chehbouni, E. Njoku, J.-P. Lhomme, and Y. Kerr, “Approaches for averaging surface parameters and fluxes over heterogeneous terrain,” J. Clim. 8, 1386–1393 (1995).
[CrossRef]

J. M. Norman and F. Becker, “Terminology in thermal infrared remote sensing of natural surfaces,” Agri. For. Meteorol. 77, 153–166 (1995).
[CrossRef]

J. Norman and F. Becker, “Terminology in thermal infrared remote sensing of natural surfaces,” Remote Sens. Rev. 12, 159–173 (1995).
[CrossRef]

Acharya, P. K.

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, and S. M. Adler-Golden, “Modtran 4” (1999).

Adler-Golden, S. M.

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, and S. M. Adler-Golden, “Modtran 4” (1999).

Anderson, G. P.

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, and S. M. Adler-Golden, “Modtran 4” (1999).

Becker, F.

J. Norman and F. Becker, “Terminology in thermal infrared remote sensing of natural surfaces,” Remote Sens. Rev. 12, 159–173 (1995).
[CrossRef]

J. M. Norman and F. Becker, “Terminology in thermal infrared remote sensing of natural surfaces,” Agri. For. Meteorol. 77, 153–166 (1995).
[CrossRef]

F. Becker and Z.-L. Li, “Surface temperature and emissivity at various scales: definition, measurement and related problems,” Remote Sens. Rev. 12, 225–253 (1995).
[CrossRef]

B. Seguin, F. Becker, and T. Phulpin, “Irsute: un concept de minisatellite pour l’estimation des flux de surface échangés par la biopshère continentale à l’échelle locale de la parcelle,” in Symposium International de Courchevel (France) (1997), Vol. 2, pp. 861–870.

F. Becker, M. Meneti, and M. Raffy, “Surface heterogeneity at various scales: concepts, measurement & impact on modeling,” presented at the 8th International Symposium of Physical Measurements & Signatures in Remote Sensing, Aussois, France 2001.

Berk, A.

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, and S. M. Adler-Golden, “Modtran 4” (1999).

Bernstein, L. S.

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, and S. M. Adler-Golden, “Modtran 4” (1999).

Binder, K.

K. Binder and D. W. Heermann, Monte Carlo Simulation in Statistical Physics: An Introduction (Springer, 2002).

Boudevillain, B.

B. Coudert, C. Ottlé, and B. Boudevillain, “Contribution of thermal infrared remote sensing data in multiobjective calibration of a dual-source SVAT model,” J. Hydrometeorology 7, 404–420 (2006).
[CrossRef]

Briottet, X.

G. Fontanilles, X. Briottet, S. Fabre, and T. Trémas, “Thermal infrared radiance simulation with aggregation modeling (TITAN): an infrared radiative transfer model for heterogeneous 3-D surface—application over urban areas,” Appl. Opt. 47, 5799–5810 (2008).
[CrossRef]

L. Coret, X. Briottet, Y. Kerr, and A. Chehbouni, “Simulation study of view angle effects on thermal infrared measurements over heterogeneous surfaces,” IEEE Trans. Geosci. Remote Sensing 42, 664–672 (2004).
[CrossRef]

X. Briottet, J.-P. Lagouarde, G. Fontanilles, A. Hénon, G. Pigeon, J.-P. Gastellu Etchegorry, P. Mestayer, I. Calmet, V. Masson, and A. Brut, “Intercomparison exercise of infrared radiative transfer models in the urban canopy,” submitted to Remote Sens. Environ.

Brut, A.

X. Briottet, J.-P. Lagouarde, G. Fontanilles, A. Hénon, G. Pigeon, J.-P. Gastellu Etchegorry, P. Mestayer, I. Calmet, V. Masson, and A. Brut, “Intercomparison exercise of infrared radiative transfer models in the urban canopy,” submitted to Remote Sens. Environ.

Calmet, I.

X. Briottet, J.-P. Lagouarde, G. Fontanilles, A. Hénon, G. Pigeon, J.-P. Gastellu Etchegorry, P. Mestayer, I. Calmet, V. Masson, and A. Brut, “Intercomparison exercise of infrared radiative transfer models in the urban canopy,” submitted to Remote Sens. Environ.

Chehbouni, A.

L. Coret, X. Briottet, Y. Kerr, and A. Chehbouni, “Simulation study of view angle effects on thermal infrared measurements over heterogeneous surfaces,” IEEE Trans. Geosci. Remote Sensing 42, 664–672 (2004).
[CrossRef]

A. Chehbouni, E. Njoku, J.-P. Lhomme, and Y. Kerr, “Approaches for averaging surface parameters and fluxes over heterogeneous terrain,” J. Clim. 8, 1386–1393 (1995).
[CrossRef]

Chen, J.

Z. Jiang, A. R. Huete, J. Chen, Y. Chen, J. Li, G. Yan, and X. Zhang, “Analysis of NDVI and scaled difference vegetation index retrievals of vegetation fraction,” Remote Sens. Environ. 101, 366–378 (2006).
[CrossRef]

Chen, L.

L. Chen, Z.-L. Li, Q. Liu, S. Chen, Y. Tang, and B. Zhong, “Definition of component effective emissivity for heterogeneous and non-isothermal surfaces and its approximate calculation,” Int. J. Remote Sensing 25, 231–244 (2004).
[CrossRef]

Chen, S.

L. Chen, Z.-L. Li, Q. Liu, S. Chen, Y. Tang, and B. Zhong, “Definition of component effective emissivity for heterogeneous and non-isothermal surfaces and its approximate calculation,” Int. J. Remote Sensing 25, 231–244 (2004).
[CrossRef]

Chen, Y.

Z. Jiang, A. R. Huete, J. Chen, Y. Chen, J. Li, G. Yan, and X. Zhang, “Analysis of NDVI and scaled difference vegetation index retrievals of vegetation fraction,” Remote Sens. Environ. 101, 366–378 (2006).
[CrossRef]

Chetwynd, J. H.

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, and S. M. Adler-Golden, “Modtran 4” (1999).

Coret, L.

L. Coret, X. Briottet, Y. Kerr, and A. Chehbouni, “Simulation study of view angle effects on thermal infrared measurements over heterogeneous surfaces,” IEEE Trans. Geosci. Remote Sensing 42, 664–672 (2004).
[CrossRef]

Coudert, B.

B. Coudert, C. Ottlé, and B. Boudevillain, “Contribution of thermal infrared remote sensing data in multiobjective calibration of a dual-source SVAT model,” J. Hydrometeorology 7, 404–420 (2006).
[CrossRef]

Dozier, J.

Z. Wan and J. Dozier, “A generalized slipt-window algorithm for retrieving land surface temperature from space,” IEEE Trans. Geosci. Remote Sensing 34, 892–905 (1996).
[CrossRef]

Durand, P.

V. Masson, G. Pigeon, P. Durand, L. Gomes, L. Salmond, J.-P. Lagouarde, J. Voogt, T. Oke, C. Lac, C. Liousse, and D. Maro, “The Canopy and Aerosol Particles I Toulouse Urban Layer (CAPITOUL) experiments: first results,” in Proceedings of the Fifth Symposium on the Urban Environment (AMS, 2004).

Etchegorry, J.-P. Gastellu

X. Briottet, J.-P. Lagouarde, G. Fontanilles, A. Hénon, G. Pigeon, J.-P. Gastellu Etchegorry, P. Mestayer, I. Calmet, V. Masson, and A. Brut, “Intercomparison exercise of infrared radiative transfer models in the urban canopy,” submitted to Remote Sens. Environ.

Fabre, S.

Fan, W.

X. Xu, W. Fan, and Y. Zhang, “The component temperature of mixed pixel retrieved by multi-angle combined multi-time thermal infrared remotely sensed data,” presented at the International Symposium, Valence, Spain 2002.

Fishman, G. S.

G. S. Fishman, Monte Carlo: Concepts, Algorithms, and Applications (Springer Verlag, 1996).

Fontanilles, G.

G. Fontanilles, X. Briottet, S. Fabre, and T. Trémas, “Thermal infrared radiance simulation with aggregation modeling (TITAN): an infrared radiative transfer model for heterogeneous 3-D surface—application over urban areas,” Appl. Opt. 47, 5799–5810 (2008).
[CrossRef]

X. Briottet, J.-P. Lagouarde, G. Fontanilles, A. Hénon, G. Pigeon, J.-P. Gastellu Etchegorry, P. Mestayer, I. Calmet, V. Masson, and A. Brut, “Intercomparison exercise of infrared radiative transfer models in the urban canopy,” submitted to Remote Sens. Environ.

Friedl, M.

G. Yan, M. Friedl, X. Li, J. Wang, C. Zhu, and A. H. Strahler, “Modeling directional effects from nonisothermal land surfaces in wideband thermal infrared measurements,” IEEE Trans. Geosci. Remote Sensing 39, 1095–1099 (2001).
[CrossRef]

Z.-L. Li, A. H. Strahler, and M. Friedl, “A conceptual model for effective directional emissivity from nonisothermal surface,” IEEE Trans. Geosci. Remote Sensing 37, 2508–2517 (1999).
[CrossRef]

Gomes, L.

V. Masson, G. Pigeon, P. Durand, L. Gomes, L. Salmond, J.-P. Lagouarde, J. Voogt, T. Oke, C. Lac, C. Liousse, and D. Maro, “The Canopy and Aerosol Particles I Toulouse Urban Layer (CAPITOUL) experiments: first results,” in Proceedings of the Fifth Symposium on the Urban Environment (AMS, 2004).

Heermann, D. W.

K. Binder and D. W. Heermann, Monte Carlo Simulation in Statistical Physics: An Introduction (Springer, 2002).

Hénon, A.

X. Briottet, J.-P. Lagouarde, G. Fontanilles, A. Hénon, G. Pigeon, J.-P. Gastellu Etchegorry, P. Mestayer, I. Calmet, V. Masson, and A. Brut, “Intercomparison exercise of infrared radiative transfer models in the urban canopy,” submitted to Remote Sens. Environ.

Hook, J. S.

J. S. Hook, ASTER, http://speclib.jpl.nasa.gov (1998).

Huete, A. R.

Z. Jiang, A. R. Huete, J. Chen, Y. Chen, J. Li, G. Yan, and X. Zhang, “Analysis of NDVI and scaled difference vegetation index retrievals of vegetation fraction,” Remote Sens. Environ. 101, 366–378 (2006).
[CrossRef]

Jiang, Z.

Z. Jiang, A. R. Huete, J. Chen, Y. Chen, J. Li, G. Yan, and X. Zhang, “Analysis of NDVI and scaled difference vegetation index retrievals of vegetation fraction,” Remote Sens. Environ. 101, 366–378 (2006).
[CrossRef]

Kerr, Y.

L. Coret, X. Briottet, Y. Kerr, and A. Chehbouni, “Simulation study of view angle effects on thermal infrared measurements over heterogeneous surfaces,” IEEE Trans. Geosci. Remote Sensing 42, 664–672 (2004).
[CrossRef]

A. Chehbouni, E. Njoku, J.-P. Lhomme, and Y. Kerr, “Approaches for averaging surface parameters and fluxes over heterogeneous terrain,” J. Clim. 8, 1386–1393 (1995).
[CrossRef]

Lac, C.

V. Masson, G. Pigeon, P. Durand, L. Gomes, L. Salmond, J.-P. Lagouarde, J. Voogt, T. Oke, C. Lac, C. Liousse, and D. Maro, “The Canopy and Aerosol Particles I Toulouse Urban Layer (CAPITOUL) experiments: first results,” in Proceedings of the Fifth Symposium on the Urban Environment (AMS, 2004).

Lagouarde, J.-P.

V. Masson, G. Pigeon, P. Durand, L. Gomes, L. Salmond, J.-P. Lagouarde, J. Voogt, T. Oke, C. Lac, C. Liousse, and D. Maro, “The Canopy and Aerosol Particles I Toulouse Urban Layer (CAPITOUL) experiments: first results,” in Proceedings of the Fifth Symposium on the Urban Environment (AMS, 2004).

X. Briottet, J.-P. Lagouarde, G. Fontanilles, A. Hénon, G. Pigeon, J.-P. Gastellu Etchegorry, P. Mestayer, I. Calmet, V. Masson, and A. Brut, “Intercomparison exercise of infrared radiative transfer models in the urban canopy,” submitted to Remote Sens. Environ.

Lhomme, J.-P.

A. Chehbouni, E. Njoku, J.-P. Lhomme, and Y. Kerr, “Approaches for averaging surface parameters and fluxes over heterogeneous terrain,” J. Clim. 8, 1386–1393 (1995).
[CrossRef]

Li, J.

Z. Jiang, A. R. Huete, J. Chen, Y. Chen, J. Li, G. Yan, and X. Zhang, “Analysis of NDVI and scaled difference vegetation index retrievals of vegetation fraction,” Remote Sens. Environ. 101, 366–378 (2006).
[CrossRef]

Li, X.

L. Su, X. Li, S. Liang, and A. H. Strahler, “Simulation of scaling effects of thermal emission from nonisothermal pixels with the typical three-dimensional structure,” Int. J. Remote Sensing 24, 3743–3753 (2003).
[CrossRef]

G. Yan, M. Friedl, X. Li, J. Wang, C. Zhu, and A. H. Strahler, “Modeling directional effects from nonisothermal land surfaces in wideband thermal infrared measurements,” IEEE Trans. Geosci. Remote Sensing 39, 1095–1099 (2001).
[CrossRef]

Li, Z.-L.

L. Chen, Z.-L. Li, Q. Liu, S. Chen, Y. Tang, and B. Zhong, “Definition of component effective emissivity for heterogeneous and non-isothermal surfaces and its approximate calculation,” Int. J. Remote Sensing 25, 231–244 (2004).
[CrossRef]

Z.-L. Li, J. Wang, and A. H. Strahler, “Scale effects and scaling-up by geometric-optical model,” Science in China (Series E) 43, 17–22 (2000).
[CrossRef]

Z.-L. Li, A. H. Strahler, and M. Friedl, “A conceptual model for effective directional emissivity from nonisothermal surface,” IEEE Trans. Geosci. Remote Sensing 37, 2508–2517 (1999).
[CrossRef]

F. Becker and Z.-L. Li, “Surface temperature and emissivity at various scales: definition, measurement and related problems,” Remote Sens. Rev. 12, 225–253 (1995).
[CrossRef]

Liang, S.

L. Su, X. Li, S. Liang, and A. H. Strahler, “Simulation of scaling effects of thermal emission from nonisothermal pixels with the typical three-dimensional structure,” Int. J. Remote Sensing 24, 3743–3753 (2003).
[CrossRef]

Liousse, C.

V. Masson, G. Pigeon, P. Durand, L. Gomes, L. Salmond, J.-P. Lagouarde, J. Voogt, T. Oke, C. Lac, C. Liousse, and D. Maro, “The Canopy and Aerosol Particles I Toulouse Urban Layer (CAPITOUL) experiments: first results,” in Proceedings of the Fifth Symposium on the Urban Environment (AMS, 2004).

Liu, Q.

L. Chen, Z.-L. Li, Q. Liu, S. Chen, Y. Tang, and B. Zhong, “Definition of component effective emissivity for heterogeneous and non-isothermal surfaces and its approximate calculation,” Int. J. Remote Sensing 25, 231–244 (2004).
[CrossRef]

Maro, D.

V. Masson, G. Pigeon, P. Durand, L. Gomes, L. Salmond, J.-P. Lagouarde, J. Voogt, T. Oke, C. Lac, C. Liousse, and D. Maro, “The Canopy and Aerosol Particles I Toulouse Urban Layer (CAPITOUL) experiments: first results,” in Proceedings of the Fifth Symposium on the Urban Environment (AMS, 2004).

Masson, V.

V. Masson, G. Pigeon, P. Durand, L. Gomes, L. Salmond, J.-P. Lagouarde, J. Voogt, T. Oke, C. Lac, C. Liousse, and D. Maro, “The Canopy and Aerosol Particles I Toulouse Urban Layer (CAPITOUL) experiments: first results,” in Proceedings of the Fifth Symposium on the Urban Environment (AMS, 2004).

X. Briottet, J.-P. Lagouarde, G. Fontanilles, A. Hénon, G. Pigeon, J.-P. Gastellu Etchegorry, P. Mestayer, I. Calmet, V. Masson, and A. Brut, “Intercomparison exercise of infrared radiative transfer models in the urban canopy,” submitted to Remote Sens. Environ.

Matthew, M. W.

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, and S. M. Adler-Golden, “Modtran 4” (1999).

Meneti, M.

F. Becker, M. Meneti, and M. Raffy, “Surface heterogeneity at various scales: concepts, measurement & impact on modeling,” presented at the 8th International Symposium of Physical Measurements & Signatures in Remote Sensing, Aussois, France 2001.

Mestayer, P.

X. Briottet, J.-P. Lagouarde, G. Fontanilles, A. Hénon, G. Pigeon, J.-P. Gastellu Etchegorry, P. Mestayer, I. Calmet, V. Masson, and A. Brut, “Intercomparison exercise of infrared radiative transfer models in the urban canopy,” submitted to Remote Sens. Environ.

Montgomery, D. C.

R. H. Myers and D. C. Montgomery, Response Surface Methodology: Process and Product Optimization Using Designed Experiments (Wiley, 1995), Chap. 2.

Mukerjee, R.

R. Mukerjee and C. Wu, A Modern Theory of Factorial Designs, Springer Series I Statistics (Springer, 2006).

Myers, R. H.

R. H. Myers and D. C. Montgomery, Response Surface Methodology: Process and Product Optimization Using Designed Experiments (Wiley, 1995), Chap. 2.

Myneni, R. B.

R. B. Myneni, R. R. Nemani, and S. W. Running, “Estimation of global leaf area index and absorbed par using radiative transfer models,” IEEE Trans. Geosci. Remote Sensing 35, 1380–1393 (1997).
[CrossRef]

Nemani, R. R.

R. B. Myneni, R. R. Nemani, and S. W. Running, “Estimation of global leaf area index and absorbed par using radiative transfer models,” IEEE Trans. Geosci. Remote Sensing 35, 1380–1393 (1997).
[CrossRef]

Njoku, E.

A. Chehbouni, E. Njoku, J.-P. Lhomme, and Y. Kerr, “Approaches for averaging surface parameters and fluxes over heterogeneous terrain,” J. Clim. 8, 1386–1393 (1995).
[CrossRef]

Norman, J.

J. Norman and F. Becker, “Terminology in thermal infrared remote sensing of natural surfaces,” Remote Sens. Rev. 12, 159–173 (1995).
[CrossRef]

Norman, J. M.

J. M. Norman and F. Becker, “Terminology in thermal infrared remote sensing of natural surfaces,” Agri. For. Meteorol. 77, 153–166 (1995).
[CrossRef]

Oke, T.

V. Masson, G. Pigeon, P. Durand, L. Gomes, L. Salmond, J.-P. Lagouarde, J. Voogt, T. Oke, C. Lac, C. Liousse, and D. Maro, “The Canopy and Aerosol Particles I Toulouse Urban Layer (CAPITOUL) experiments: first results,” in Proceedings of the Fifth Symposium on the Urban Environment (AMS, 2004).

Oke, T. R.

J. A. Voogt and T. R. Oke, “Complete urban surface temperatures,” J. Appl. Meteorol. 36, 1117–1132 (1997).
[CrossRef]

Ottlé, C.

B. Coudert, C. Ottlé, and B. Boudevillain, “Contribution of thermal infrared remote sensing data in multiobjective calibration of a dual-source SVAT model,” J. Hydrometeorology 7, 404–420 (2006).
[CrossRef]

Pallotta, S.

S. Pallotta, “Compréhension du signal issu d’une surface hétérogène dans le domaine infrarouge en télédétection : analyse de l’agrégation des propriétés thermo-optiques de ses constituants,” Ph.D. dissertation (École Nationale Supérieure de l’Aéronautique et de l’Espace, ONERA, 2006).

Phan-Tan-Luu, R.

M. Sergent and R. Phan-Tan-Luu, “Méthodologie de la recherche expérimentale (Plans d’expériences), Vol. 1 et 2,” logiciel Nemrodw (2007).

Phulpin, T.

B. Seguin, F. Becker, and T. Phulpin, “Irsute: un concept de minisatellite pour l’estimation des flux de surface échangés par la biopshère continentale à l’échelle locale de la parcelle,” in Symposium International de Courchevel (France) (1997), Vol. 2, pp. 861–870.

Pigeon, G.

V. Masson, G. Pigeon, P. Durand, L. Gomes, L. Salmond, J.-P. Lagouarde, J. Voogt, T. Oke, C. Lac, C. Liousse, and D. Maro, “The Canopy and Aerosol Particles I Toulouse Urban Layer (CAPITOUL) experiments: first results,” in Proceedings of the Fifth Symposium on the Urban Environment (AMS, 2004).

X. Briottet, J.-P. Lagouarde, G. Fontanilles, A. Hénon, G. Pigeon, J.-P. Gastellu Etchegorry, P. Mestayer, I. Calmet, V. Masson, and A. Brut, “Intercomparison exercise of infrared radiative transfer models in the urban canopy,” submitted to Remote Sens. Environ.

Raffy, M.

F. Becker, M. Meneti, and M. Raffy, “Surface heterogeneity at various scales: concepts, measurement & impact on modeling,” presented at the 8th International Symposium of Physical Measurements & Signatures in Remote Sensing, Aussois, France 2001.

Running, S. W.

R. B. Myneni, R. R. Nemani, and S. W. Running, “Estimation of global leaf area index and absorbed par using radiative transfer models,” IEEE Trans. Geosci. Remote Sensing 35, 1380–1393 (1997).
[CrossRef]

Salmond, L.

V. Masson, G. Pigeon, P. Durand, L. Gomes, L. Salmond, J.-P. Lagouarde, J. Voogt, T. Oke, C. Lac, C. Liousse, and D. Maro, “The Canopy and Aerosol Particles I Toulouse Urban Layer (CAPITOUL) experiments: first results,” in Proceedings of the Fifth Symposium on the Urban Environment (AMS, 2004).

Seguin, B.

B. Seguin, F. Becker, and T. Phulpin, “Irsute: un concept de minisatellite pour l’estimation des flux de surface échangés par la biopshère continentale à l’échelle locale de la parcelle,” in Symposium International de Courchevel (France) (1997), Vol. 2, pp. 861–870.

Sergent, M.

M. Sergent and R. Phan-Tan-Luu, “Méthodologie de la recherche expérimentale (Plans d’expériences), Vol. 1 et 2,” logiciel Nemrodw (2007).

Shettle, E. P.

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, and S. M. Adler-Golden, “Modtran 4” (1999).

Strahler, A. H.

L. Su, X. Li, S. Liang, and A. H. Strahler, “Simulation of scaling effects of thermal emission from nonisothermal pixels with the typical three-dimensional structure,” Int. J. Remote Sensing 24, 3743–3753 (2003).
[CrossRef]

G. Yan, M. Friedl, X. Li, J. Wang, C. Zhu, and A. H. Strahler, “Modeling directional effects from nonisothermal land surfaces in wideband thermal infrared measurements,” IEEE Trans. Geosci. Remote Sensing 39, 1095–1099 (2001).
[CrossRef]

Z.-L. Li, J. Wang, and A. H. Strahler, “Scale effects and scaling-up by geometric-optical model,” Science in China (Series E) 43, 17–22 (2000).
[CrossRef]

Z.-L. Li, A. H. Strahler, and M. Friedl, “A conceptual model for effective directional emissivity from nonisothermal surface,” IEEE Trans. Geosci. Remote Sensing 37, 2508–2517 (1999).
[CrossRef]

Su, L.

L. Su, X. Li, S. Liang, and A. H. Strahler, “Simulation of scaling effects of thermal emission from nonisothermal pixels with the typical three-dimensional structure,” Int. J. Remote Sensing 24, 3743–3753 (2003).
[CrossRef]

Tang, Y.

L. Chen, Z.-L. Li, Q. Liu, S. Chen, Y. Tang, and B. Zhong, “Definition of component effective emissivity for heterogeneous and non-isothermal surfaces and its approximate calculation,” Int. J. Remote Sensing 25, 231–244 (2004).
[CrossRef]

Trémas, T.

Voogt, J.

V. Masson, G. Pigeon, P. Durand, L. Gomes, L. Salmond, J.-P. Lagouarde, J. Voogt, T. Oke, C. Lac, C. Liousse, and D. Maro, “The Canopy and Aerosol Particles I Toulouse Urban Layer (CAPITOUL) experiments: first results,” in Proceedings of the Fifth Symposium on the Urban Environment (AMS, 2004).

Voogt, J. A.

J. A. Voogt and T. R. Oke, “Complete urban surface temperatures,” J. Appl. Meteorol. 36, 1117–1132 (1997).
[CrossRef]

Wan, Z.

Z. Wan and J. Dozier, “A generalized slipt-window algorithm for retrieving land surface temperature from space,” IEEE Trans. Geosci. Remote Sensing 34, 892–905 (1996).
[CrossRef]

Wang, J.

G. Yan, M. Friedl, X. Li, J. Wang, C. Zhu, and A. H. Strahler, “Modeling directional effects from nonisothermal land surfaces in wideband thermal infrared measurements,” IEEE Trans. Geosci. Remote Sensing 39, 1095–1099 (2001).
[CrossRef]

Z.-L. Li, J. Wang, and A. H. Strahler, “Scale effects and scaling-up by geometric-optical model,” Science in China (Series E) 43, 17–22 (2000).
[CrossRef]

Wu, C.

R. Mukerjee and C. Wu, A Modern Theory of Factorial Designs, Springer Series I Statistics (Springer, 2006).

Xu, X.

X. Xu, W. Fan, and Y. Zhang, “The component temperature of mixed pixel retrieved by multi-angle combined multi-time thermal infrared remotely sensed data,” presented at the International Symposium, Valence, Spain 2002.

Yan, G.

Z. Jiang, A. R. Huete, J. Chen, Y. Chen, J. Li, G. Yan, and X. Zhang, “Analysis of NDVI and scaled difference vegetation index retrievals of vegetation fraction,” Remote Sens. Environ. 101, 366–378 (2006).
[CrossRef]

G. Yan, M. Friedl, X. Li, J. Wang, C. Zhu, and A. H. Strahler, “Modeling directional effects from nonisothermal land surfaces in wideband thermal infrared measurements,” IEEE Trans. Geosci. Remote Sensing 39, 1095–1099 (2001).
[CrossRef]

Zhang, X.

Z. Jiang, A. R. Huete, J. Chen, Y. Chen, J. Li, G. Yan, and X. Zhang, “Analysis of NDVI and scaled difference vegetation index retrievals of vegetation fraction,” Remote Sens. Environ. 101, 366–378 (2006).
[CrossRef]

Zhang, Y.

X. Xu, W. Fan, and Y. Zhang, “The component temperature of mixed pixel retrieved by multi-angle combined multi-time thermal infrared remotely sensed data,” presented at the International Symposium, Valence, Spain 2002.

Zhong, B.

L. Chen, Z.-L. Li, Q. Liu, S. Chen, Y. Tang, and B. Zhong, “Definition of component effective emissivity for heterogeneous and non-isothermal surfaces and its approximate calculation,” Int. J. Remote Sensing 25, 231–244 (2004).
[CrossRef]

Zhu, C.

G. Yan, M. Friedl, X. Li, J. Wang, C. Zhu, and A. H. Strahler, “Modeling directional effects from nonisothermal land surfaces in wideband thermal infrared measurements,” IEEE Trans. Geosci. Remote Sensing 39, 1095–1099 (2001).
[CrossRef]

Agri. For. Meteorol. (1)

J. M. Norman and F. Becker, “Terminology in thermal infrared remote sensing of natural surfaces,” Agri. For. Meteorol. 77, 153–166 (1995).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Geosci. Remote Sensing (5)

R. B. Myneni, R. R. Nemani, and S. W. Running, “Estimation of global leaf area index and absorbed par using radiative transfer models,” IEEE Trans. Geosci. Remote Sensing 35, 1380–1393 (1997).
[CrossRef]

L. Coret, X. Briottet, Y. Kerr, and A. Chehbouni, “Simulation study of view angle effects on thermal infrared measurements over heterogeneous surfaces,” IEEE Trans. Geosci. Remote Sensing 42, 664–672 (2004).
[CrossRef]

Z.-L. Li, A. H. Strahler, and M. Friedl, “A conceptual model for effective directional emissivity from nonisothermal surface,” IEEE Trans. Geosci. Remote Sensing 37, 2508–2517 (1999).
[CrossRef]

G. Yan, M. Friedl, X. Li, J. Wang, C. Zhu, and A. H. Strahler, “Modeling directional effects from nonisothermal land surfaces in wideband thermal infrared measurements,” IEEE Trans. Geosci. Remote Sensing 39, 1095–1099 (2001).
[CrossRef]

Z. Wan and J. Dozier, “A generalized slipt-window algorithm for retrieving land surface temperature from space,” IEEE Trans. Geosci. Remote Sensing 34, 892–905 (1996).
[CrossRef]

Int. J. Remote Sensing (2)

L. Chen, Z.-L. Li, Q. Liu, S. Chen, Y. Tang, and B. Zhong, “Definition of component effective emissivity for heterogeneous and non-isothermal surfaces and its approximate calculation,” Int. J. Remote Sensing 25, 231–244 (2004).
[CrossRef]

L. Su, X. Li, S. Liang, and A. H. Strahler, “Simulation of scaling effects of thermal emission from nonisothermal pixels with the typical three-dimensional structure,” Int. J. Remote Sensing 24, 3743–3753 (2003).
[CrossRef]

J. Appl. Meteorol. (1)

J. A. Voogt and T. R. Oke, “Complete urban surface temperatures,” J. Appl. Meteorol. 36, 1117–1132 (1997).
[CrossRef]

J. Clim. (1)

A. Chehbouni, E. Njoku, J.-P. Lhomme, and Y. Kerr, “Approaches for averaging surface parameters and fluxes over heterogeneous terrain,” J. Clim. 8, 1386–1393 (1995).
[CrossRef]

J. Hydrometeorology (1)

B. Coudert, C. Ottlé, and B. Boudevillain, “Contribution of thermal infrared remote sensing data in multiobjective calibration of a dual-source SVAT model,” J. Hydrometeorology 7, 404–420 (2006).
[CrossRef]

Remote Sens. Environ. (2)

Z. Jiang, A. R. Huete, J. Chen, Y. Chen, J. Li, G. Yan, and X. Zhang, “Analysis of NDVI and scaled difference vegetation index retrievals of vegetation fraction,” Remote Sens. Environ. 101, 366–378 (2006).
[CrossRef]

X. Briottet, J.-P. Lagouarde, G. Fontanilles, A. Hénon, G. Pigeon, J.-P. Gastellu Etchegorry, P. Mestayer, I. Calmet, V. Masson, and A. Brut, “Intercomparison exercise of infrared radiative transfer models in the urban canopy,” submitted to Remote Sens. Environ.

Remote Sens. Rev. (2)

J. Norman and F. Becker, “Terminology in thermal infrared remote sensing of natural surfaces,” Remote Sens. Rev. 12, 159–173 (1995).
[CrossRef]

F. Becker and Z.-L. Li, “Surface temperature and emissivity at various scales: definition, measurement and related problems,” Remote Sens. Rev. 12, 225–253 (1995).
[CrossRef]

Science in China (Series E) (1)

Z.-L. Li, J. Wang, and A. H. Strahler, “Scale effects and scaling-up by geometric-optical model,” Science in China (Series E) 43, 17–22 (2000).
[CrossRef]

Other (13)

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, and S. M. Adler-Golden, “Modtran 4” (1999).

F. Becker, M. Meneti, and M. Raffy, “Surface heterogeneity at various scales: concepts, measurement & impact on modeling,” presented at the 8th International Symposium of Physical Measurements & Signatures in Remote Sensing, Aussois, France 2001.

G. S. Fishman, Monte Carlo: Concepts, Algorithms, and Applications (Springer Verlag, 1996).

X. Xu, W. Fan, and Y. Zhang, “The component temperature of mixed pixel retrieved by multi-angle combined multi-time thermal infrared remotely sensed data,” presented at the International Symposium, Valence, Spain 2002.

B. Seguin, F. Becker, and T. Phulpin, “Irsute: un concept de minisatellite pour l’estimation des flux de surface échangés par la biopshère continentale à l’échelle locale de la parcelle,” in Symposium International de Courchevel (France) (1997), Vol. 2, pp. 861–870.

S. Pallotta, “Compréhension du signal issu d’une surface hétérogène dans le domaine infrarouge en télédétection : analyse de l’agrégation des propriétés thermo-optiques de ses constituants,” Ph.D. dissertation (École Nationale Supérieure de l’Aéronautique et de l’Espace, ONERA, 2006).

J. S. Hook, ASTER, http://speclib.jpl.nasa.gov (1998).

K. Binder and D. W. Heermann, Monte Carlo Simulation in Statistical Physics: An Introduction (Springer, 2002).

R. H. Myers and D. C. Montgomery, Response Surface Methodology: Process and Product Optimization Using Designed Experiments (Wiley, 1995), Chap. 2.

R. Mukerjee and C. Wu, A Modern Theory of Factorial Designs, Springer Series I Statistics (Springer, 2006).

M. Sergent and R. Phan-Tan-Luu, “Méthodologie de la recherche expérimentale (Plans d’expériences), Vol. 1 et 2,” logiciel Nemrodw (2007).

R free software, “Langage de programmation et environnement,” www.r-project.org.

V. Masson, G. Pigeon, P. Durand, L. Gomes, L. Salmond, J.-P. Lagouarde, J. Voogt, T. Oke, C. Lac, C. Liousse, and D. Maro, “The Canopy and Aerosol Particles I Toulouse Urban Layer (CAPITOUL) experiments: first results,” in Proceedings of the Fifth Symposium on the Urban Environment (AMS, 2004).

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Figures (24)

Fig. 1
Fig. 1

Aggregation principle.

Fig. 2
Fig. 2

Main radiative contributors at sensor level ( L S ): L D S is the at-sensor solar radiance, L A S is the at-sensor atmospheric radiance, L emis S is the at-sensor emitted radiance, and L env S is the at-sensor environment radiance.

Fig. 3
Fig. 3

Valley-shape landscape.

Fig. 4
Fig. 4

Spectral reflectances of tile and brick used on the full spectral domain ( 3 14 μm ).

Fig. 5
Fig. 5

(a) Equivalent emissivities and (b) sum of equivalent reflectances and equivalent emissivities.

Fig. 6
Fig. 6

Equivalent temperatures.

Fig. 7
Fig. 7

(a) Equivalent radiances and (b) differences between them.

Fig. 8
Fig. 8

Flat and heterogeneous surface.

Fig. 9
Fig. 9

Relative impact on the equivalent reflectance, depending on the input factors and interactions for a flat surface.

Fig. 10
Fig. 10

Spectral equivalent reflectance as a function of the proportion of material surface.

Fig. 11
Fig. 11

Relative impact on the equivalent temperature depending on the input factors and interactions in the MWIR band.

Fig. 12
Fig. 12

Spectral variation of T for several view angles θ s . For this simulation, the flat scene is divided into two parts: one is at 293 K (elements 1 and 2) and the other at 303 K (elements 3 and 4).

Fig. 13
Fig. 13

Rough and heterogeneous scene: valley shape.

Fig. 14
Fig. 14

Relative impact on the equivalent reflectance depending on the input factors and interactions for rough and heterogeneous surface.

Fig. 15
Fig. 15

Equivalent reflectance evolution according to slope angle θ k .

Fig. 16
Fig. 16

Directional effects of the equivalent reflectance for several Sun locations (wavelength λ = 4 μm and slope angle θ k = 15 ° ). The Sun location is represented by a black diamond on the polar diagrams and a gray circle on the drawings.

Fig. 17
Fig. 17

Relative impact on the equivalent emissivity depending on the input factors and interactions for a rough and heterogeneous surface.

Fig. 18
Fig. 18

Equivalent emissivity evolution according to (a) several sensor locations and (b) different slope angles.

Fig. 19
Fig. 19

Relative impact on the equivalent temperature sensitivity depending on the input factors and interactions for a rough and heterogeneous surface.

Fig. 20
Fig. 20

Urban canyon profile with dimensions and surface materials (left) and shadow areas and surface temperatures (right).

Fig. 21
Fig. 21

Top view of an urban canyon pattern and the related aggregated area (thick black line square).

Fig. 22
Fig. 22

Spectral equivalent reflectance of our urban canyon at nadir with the spectral reflectances of used materials (left) and the spectral contribution Δ ρ of the neighborhood to the equivalent reflectance (right).

Fig. 23
Fig. 23

Spectral equivalent emissivity of our urban canyon at nadir with (a) spectral emissivity of used material and (b) spectral contribution Δ ε of the neighborhood to the equivalent emissivity.

Fig. 24
Fig. 24

Spectral equivalent temperature of our urban canyon at nadir (left) and the spectral contribution Δ T of the neighborhood to the equivalent temperature (right).

Tables (2)

Tables Icon

Table 1 Variation Range of Input Factors for Flat Surface (Factor L Corresponds to Surface Element Length)

Tables Icon

Table 2 Variation Range of Input Factors for Valley-Shaped Scene

Equations (30)

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

ε = ε BRDF + Δ ε GO ,
t k sensor = t k es × t es sensor , L k sensor atm , L k es atm , × t es sensor + L es sensor atm , ,
L S = L D S + L A S + L emis S + L env S + L S , atm ,
L D S = k S k ρ k d d ( u Sun , u s ) π E D , k × t k sensor ,
L A S = k S k × t k sensor Ω L atm , cos ( θ ) ρ k d d ( u , u s ) π d ω ,
L emis S = k S k ε k ( u s ) L BB ( T k ) × t k sensor ,
L env S = k S k × t k sensor m N ( k ) ρ k d d ( u k m , u s ) π g m ( k ) [ ρ m d d ( u Sun , u m k ) π E D , m ( k ) + ρ k h d ( u m k ) π E atm , m ( k ) + ε m ( u m k ) L BB ( T m ) ] d S m ( k ) ,
L S , atm = k S k L k sensor atm , .
L = ρ z d d π E D , z × t es sensor + t es sensor Ω L atm , cos ( θ z ) ρ z d d π d ω + ε z L BB ( T z ) × t es sensor + L es sensor atm , ,
ρ π E D = L D S + L D env S .
ρ = k S k × t k es [ ρ k d d ( u Sun , u s ) E D , k E D + m V ( k ) ρ k d d ( u k m , u s ) π g m ( k ) ρ m d d ( u Sun , u m k ) E D , m ( k ) E D d S m ( k ) ] .
k S k × t k es × ρ k d d ( u Sun , u s ) E D , k E D ,
k S k × t k es × m V ( k ) ρ k d d ( u k m , u s ) π g m ( k ) ρ m d d ( u Sun , u m k ) E D , m ( k ) E D d S m ( k ) ,
ε L BB ( T ) = k S k × t k es [ ε k L BB ( T k ) + m V ( k ) ρ k d d ( u k m , u s ) π g m ( k ) ε m L BB ( T m ) d S m ( k ) ] + k S k × L k es atm , .
ε = k S k [ ε k ( u c ) + m V ( k ) ρ k d d ( u k m , u c ) π g m ( k ) ε m ( u m k ) d S m ( k ) ] .
ε = ε + Δ ε GO ,
T = L BB 1 ( Σ k S k [ t k es × [ ε k ( u s ) L BB ( T k ) + m V ( k ) ρ k d d ( u k m , u s ) π g m ( k ) ε m ( u m k ) L BB ( T m ) d S m ( k ) ] + L k es atm , ] ε ) .
T = k = 1 N T k / N .
T = k = 1 N S k T k .
T = k S k T k 4 4 .
T = k S k ε k T k k S k ε k .
T = k S k ( ε k + Δ ε k ) T k k S k ( ε k + Δ ε k ) .
T = k S k ( ε k + Δ ε k ) T k + k S k ( ε atm , k ) T atm , k k S k ( ε k + Δ ε k + ε atm , k ) .
ε = k S k [ t k es × [ ε k ( u s ) L BB ( T k ) + m V ( k ) ρ k d d ( u k m , u s ) π g m ( k ) ε m ( u m k ) L BB ( T m ) d S m ( k ) ] + L k es a t m , ] L BB ( T ) .
ρ = k S k ρ k d d ( u Sun , u s ) .
ε = k S k ε k .
T = L BB 1 ( k S k ε k ( u s ) L BB ( T k ) ε ) .
ρ = k S k cos ( n es , u Sun ) [ ρ k d d ( u Sun , u s ) cos ( n k , u Sun ) + m m k ρ k d d ( u m k , u s ) ρ m d d ( u Sun , u m k ) π cos ( n m , u Sun ) g m k S m ] .
ε = k S k [ ε k ( u s ) + m m k ρ k d d ( u k m , u s ) π g m k ε m ( u m k ) S m ] .
T = b ln ( k S k ( ε k ( u s ) e b T k + m m k ρ k d d ( u k m , u s ) π ε m ( u m k ) e b T m g m k S m ) ε ) .

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