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Radiative Transfer

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Computational Intelligence Applied to Inverse Problems in Radiative Transfer

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Abstract

In this chapter, the formulation and solution of the radiative transfer problem in one-dimensional homogeneous participating media and two-layer heterogeneous participating media are presented. The phenomenon of radiative transfer in participating media, i.e., absorbers, scatterers, and emitters, is modeled with the Boltzmann Equation. The solution of this equation, with the respective boundary conditions, is obtained with the Discrete Ordinates Method and the Finite Difference Method. Possible effects on the boundary or inside (interface) of the medium due to refractive index are not considered. To the two-layer one-dimensional heterogeneous participating media, both reflection and transmission in the interface are considered to be diffuse.

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References

  1. M. Abramowitz and I. A. Stegun (Ed.). Handbook of Mathematical Functions. New York: Dover Publications, 1970.

    Google Scholar 

  2. Z. Altaç and M. Tekkalmaz. “Radiative Transfer in Absorbing, Emitting and Isotropically Scattering Segregated Two Layered, 3D Rectangular Enclosures”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2014, 133, pp. 570–578.

    Article  Google Scholar 

  3. N. I. Alvarez Acevedo, N. C. Roberty and A. J. Silva Neto. “An Explicit Formulation for the Inverse Transport Problem Using Only External Detectors - Part I: Computational Modeling”. Computational & Applied Mathematics, 2010, 29, pp. 343–358.

    Article  MathSciNet  MATH  Google Scholar 

  4. N. I. Alvarez Acevedo, N. C. Roberty and A. J. Silva Neto. “An Explicit Formulation for the Inverse Transport Problem Using Only External Detectors - Part II: Application to One - Dimensional Homogeneous and Heterogeneous Participating Media”. Computational & Applied Mathematics, 2010, 29, pp. 359–374.

    Article  MathSciNet  MATH  Google Scholar 

  5. W. An, Q. Zhu, T. Zhu and N. Gao. “Radiative Properties of Gold Nanorod Solutions and Its Temperature Distribution Under Laser Irradiation: Experimental Investigation”. Experimental Thermal and Fluid Science, 2013, 44, pp. 409–418.

    Article  Google Scholar 

  6. D. A. Anderson, J. C. Tannehill and R. H, Pletcher. Computational Fluid Mechanics and Heat Transfer. New York: Hemisphere Publishing Corporation, 1984.

    Google Scholar 

  7. A. Bablet, P. V. H. Vu, S. Jacquemoud, F. Viallefont-Robinet, S. Fabre, X. Briottet, M. Sadeghi, M. L. Whiting, F. Baret and J. Tian. “MARMIT: A Multilayer Radiative Transfer Model of Soil Reflectance to Estimate Surface Soil Moisture Content in the Solar Domain (400–2500 nm)”. Remote Sensing of Environment, 2018, 217, pp. 1–17.

    Article  Google Scholar 

  8. L. B. Barichello and M. T. Vilhena. “General Approach to One Group One Dimensional Transport Equation”. Kerntechnik, 1993, 58, pp. 182–184.

    Article  Google Scholar 

  9. A. Battaglia and S. Mantovani. “Forward Monte Carlo Computations of Fully Polarized Microwave Radiation in Non-Isotropic Media”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2005, 95, pp. 285–308.

    Article  Google Scholar 

  10. R. Bennartz and R. Preusker. “Representation of the Photon Pathlength Distribution in a Cloudy Atmosphere using Finite Elements”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2006, 58, pp. 202–219.

    Article  Google Scholar 

  11. T. E. Booth. “An Alternative Monte Carlo Approach to the Thermal Radiative Transfer Problem”. Journal of Computational Physics, 2011, 230, pp. 1516–1527.

    Article  MATH  Google Scholar 

  12. R. Brittes and F. H. R. França. “A Hybrid Inverse Method for the Thermal Design of Radiative Heating Systems”. International Journal of Heat and Mass Transfer, 2013, 57, pp. 48–57.

    Article  Google Scholar 

  13. B. Bulgarelli and J. P. Doyle. “Comparison Between Numerical Models for Radiative Transfer Simulation in the Atmosphere-Ocean System”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2004, 86, pp. 315–334.

    Article  Google Scholar 

  14. R. F. Carita Montero, N. C. Roberty and A. J. Silva Neto. “Reconstruction of a Combination of the Absorption and Scattering Coefficients with a Discrete Ordinates Method Consistent with the Source-Detector System”. Inverse Problems in Engineering, 2004, 12, pp. 81–101.

    Article  Google Scholar 

  15. F. Cassol, P. S. Schneider, F. H. R. França and A. J. Silva Neto. “Multi-Objective Optimization as a New Approach to Illumination Design of Interior Spaces”. Building and Environment, 2011, 46, pp. 331–338.

    Article  Google Scholar 

  16. F. N. Çayan and N. Selçuk. “The Method of Lines Solution of Discrete Ordinates Method for Non-Grey Media”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2007, 104, pp. 228–237.

    Article  Google Scholar 

  17. E. S. Chalhoub. “Discrete-Ordinates Solution for Radiative Transfer Problems”, Journal of Quantitative Spectroscopy & Radiative Transfer, 2003, 76, pp. 193–206.

    Article  Google Scholar 

  18. E. S. Chalhoub. “Discrete-Ordinates Solution for Uncoupled Multi-Wavelength Radiative Transfer Problems”, Journal of Quantitative Spectroscopy & Radiative Transfer, 2005, 92, pp. 335–349.

    Article  Google Scholar 

  19. E. S. Chalhoub, H. F. de Campos Velho, R. D. M. Garcia and M. T. Vilhena. “A Comparison of Radiances Generated by Selected Methods of Solving the Radiative-Transfer Equation”. Transport Theory and Statistical Physics, 2003, 32, pp. 473–503.

    Article  MathSciNet  MATH  Google Scholar 

  20. E. S. Chalhoub, H. F. de Campos Velho and A. J. Silva Neto. “Evaluation of Radiances Generated by Solving the Radiative Transfer Equation with Different Approaches”. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2012, 34, pp. 184–192.

    Article  Google Scholar 

  21. E. S. Chalhoub and R. D. M. Garcia. “The Equivalence Between Two Techniques of Angular Interpolation for the Discrete - Ordinates Method”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2000, 64, pp. 517–535.

    Article  Google Scholar 

  22. S. Chandrasekhar. “On the Radiative Equilibrium of a Stellar Atmosphere II”. Astrophysical Journal, 1944, 100, pp. 76–86.

    Article  MathSciNet  MATH  Google Scholar 

  23. S. Chandrasekhar. Radiative Transfer. London: Oxford University Press, 1950.

    MATH  Google Scholar 

  24. N. Chen, W. Li, C. Gatebe, T. Tanikawa, M. Hori, R. Shimada, T. Aoki and K. Stamnes. “New Neural Network Cloud Mask Algorithm Based on Radiative Transfer Simulations”. Remote Sensing of Environment, 2018, 219, pp. 62–71.

    Article  Google Scholar 

  25. Y. Chen and K. N. Liou. “A Monte Carlo Method for 3D Thermal Infrared Radiative Transfer”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2006, 101, pp. 166–178.

    Article  Google Scholar 

  26. M. I. Disney, P. Lewis, J. Gomes-Dans, D. Roy, M. J. Wooster and D. Lajas. “3D Radiative Transfer Modeling of Fire Impacts on a Two-Layer Savanna System”. Remote Sensing of Environment, 2011, 115, pp. 1866–1881.

    Article  Google Scholar 

  27. M. A. Eleveld, D. van der Wal and T. van Kessel. “Estuarine Suspended Particulate Matter Concentrations from Sun - Synchronous Satellite Remote Sensing: Tidal and Meteorological Effects and Biases”. Remote Sensing of Environment, 2014, 143, pp. 204–215.

    Article  Google Scholar 

  28. T. Fause, H. Isaka and B. Guillemet. “Neural Network Retrieval of Cloud Parameters of Inhomogeneous and Fractional Clouds”. Remote Sensing of Environment, 2001, 77, pp. 123–128.

    Article  Google Scholar 

  29. E. L. Gaggioli, O. P. Bruno and D. M. Mitnik. “Light Transport with the Equation of Radiative Transfer: The Fourier Continuation - Discrete Ordinates (FC-DOM) Method”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2019, 236, pp. 106589. 1–11.

    Google Scholar 

  30. R. L. Galski, F. L. de Sousa, F. M. Ramos and A. J. Silva Neto. “Application of a GEO+SA Hydrid Optimization Algorithm to the Solution of an Inverse Radiative Transfer Problem”. Inverse Problems in Science and Engineering, 2009, 17, pp. 321–334.

    Article  MathSciNet  MATH  Google Scholar 

  31. B. D. Ganapol. “Radiative Transfer with Internal Reflection via the Converged Discrete Ordinates Method”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2011, 112, pp. 693–713.

    Article  Google Scholar 

  32. R. D. M. Garcia. “Radiative Transfer with Polarization in a Multi-Layer Medium Subject to Fresnel Boundary and Interface Conditions”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2013, 115, pp. 28–45.

    Article  Google Scholar 

  33. R. D. M. Garcia and C. E. Siewert. “A Simplified Implementation of the Discrete-Ordinates Method for a Class of Problems in Radiative Transfer with Polarization”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2011, 112, pp. 2801–2813.

    Article  Google Scholar 

  34. W. A. Ge, C. Y. Zhao and B. X. Wang. “Thermal Radiation and Conduction in Functionally Graded Thermal Barrier Coatings. Part I: Experimental Study on Radiative Properties”. International Journal of Heat and Mass Transfer, 2019, 134, pp. 101–113.

    Google Scholar 

  35. W. A. Ge, C. Y. Zhao and B. X. Wang. “Thermal Radiation and Conduction in Functionally Graded Thermal Barrier Coatings. Part II: Experimental Thermal Conductivities and Heat Transfer Modeling”. International Journal of Heat and Mass Transfer, 2019, 134, pp. 166–174.

    Google Scholar 

  36. P. Granate, P. J. Coelho and M. Roger. “Radiative Heat Transfer in Strongly Forward Scattering Media Using the Discrete Ordinates Method”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2016, 172, pp. 110–120.

    Article  Google Scholar 

  37. J. Guan, S. Fang and C. Guo. “Optical Tomography Reconstruction Algorithm based on the Radiative Transfer Equation Considering Refractive Index - Part 1: Forward Model”. Computerized Medical Imaging and Graphics, 2013, 37, pp. 245–255.

    Article  Google Scholar 

  38. J. Guan, S. Fang and C. Guo. “Optical Tomography Reconstruction Algorithm based on the Radiative Transfer Equation Considering Refractive Index - Part 2: Inverse Model”. Computerized Medical Imaging and Graphics, 2013, 37, pp. 256–262.

    Article  Google Scholar 

  39. K.-I. Han, J.-H. Choi and T.-K. Kim. “Comparison of Inverse Estimation Methods of Radiative Reflection Properties Using Temporal and Directional IR Radiances”. Journal of Mechanical Science and Technology, 2017, 31, pp. 4739–4745.

    Article  Google Scholar 

  40. N. P. Hanan. “Enhanced Two-Layer Radiative Transfer Scheme for a Land Surface Model with a Discontinuous Upper Canopy”. Agricultural and Forest Meteorology, 2001, 109, pp. 265–281.

    Article  Google Scholar 

  41. J. E. Hansen and L. D. Travis. “Light Scattering in Planetary Atmospheres”. Space Science Reviews, 1974, 16, pp. 527–610.

    Article  Google Scholar 

  42. B. He, X. Quan and M. Xing. “Retrieval of Leaf Area Index in Alpine Wetlands Using a Two-Layer Canopy Reflectance Model”. International Journal of Applied Earth Observation and Geoinformation, 2013, 21, pp. 78–91.

    Article  Google Scholar 

  43. R. S. Hoffmann, A. Seewald, P. S. Schneider and F. H. R. França. “Inverse Design of Thermal Systems with Spectrally Dependent Emissivities”. International Journal of Heat and Mass Transfer, 2010, 53, pp. 931–939.

    Article  MATH  Google Scholar 

  44. Z.-M. Hu, H. Tian, B.-W. Li, Y.-S. Yin, W. Zhang and M. Ruan. “The Performances of the Discrete Ordinates - Collocation Spectral Method for the Three - Dimensional Radiative Transfer Equation”. Numerical Heat Transfer, Part A, 2017, 71, pp. 867–880.

    Article  Google Scholar 

  45. G. Huang, Z. Li, X. Li, S. Liang, K. Yang, D. Wang and Y. Zhang. “Estimating Surface Solar Irradiance from Satellites: Past, Present, and Future Perspectives”. Remote Sensing of Environment, 2019, 233, pp. 111371.1–16.

    Article  Google Scholar 

  46. K. A. Jensen, J.-F. Ripoll, A. A. Wray, D. Joseph and M. El Hafi. “On Various Modeling Approaches to Radiative Heat Transfer in Pool Fires”. Combustion and Flame, 2007, 148, pp. 263–279.

    Article  Google Scholar 

  47. A. Kallel. “Extension of Virtual Flux Decomposition Model to the Case of Two Vegetation Layers: FDM-2”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2012, 113, pp. 440–460.

    Article  Google Scholar 

  48. S. Khayyam and S. M Hosseini Sarvari. “Inverse Estimation of Thermal Properties in a Semitransparent Graded Index Medium With Radiation - Conduction Heat Transfer”. Journal of Heat Transfer, 2018, 140, pp. 092701.1–10.

    Google Scholar 

  49. H. K. Kim and A. Charette. “A Sensitivity Function-Based Conjugate Gradient Method for Optical Tomography with the Frequency Domain Equation of Radiative Transfer”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2007, 104, pp. 24–39.

    Article  Google Scholar 

  50. A. D. Klose. “The Forward and Inverse Problem in Tissue Optics based on the Radiative Transfer Equation: A Brief Review”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2010, 111, pp. 1852–1853.

    Article  Google Scholar 

  51. D. C. Knupp and A. J. Silva Neto. “An Inverse Analysis of the Radiative Transfer in a Two-Layer Heterogeneous Medium”. Inverse Problems in Science and Engineering, 2012, 20, pp. 917–939.

    Article  MathSciNet  Google Scholar 

  52. D. C. Knupp, A. J. Silva Neto and W. F. Sacco. “Radiative Properties Estimation with the Particle Collision Algorithm Based on a Sensitivity Analysis”. High Temperatures-High Pressures, 2009, 38, pp. 137–151.

    MATH  Google Scholar 

  53. A. E. Kovtanyuk, A. Y. Cheboratev, N. D. Botkin and K.-H. Hoffmann. “Theoretical Analysis of an Optimal Control Problem of Conductive-Convective-Radiative Heat Transfer”. Journal of Mathematical Analysis and Applications, 2014, 412, pp. 520–528.

    Article  MathSciNet  MATH  Google Scholar 

  54. B. Le Corre, A. Collin, L. Soudre-Bau, Y. Meshaka and G. Jeandel. “Glass Sagging Simulation with Improved Calculation of Radiative Heat Transfer by the Optimized Reciprocity Monte Carlo Method”. International Journal of Heat and Mass Transfer, 2014, 70, pp. 215–223.

    Article  Google Scholar 

  55. J. Lenoble (org.). Standard Procedures to Compute Atmospheric Radiative Transfer in a Scattering Atmosphere. Boulder: National Center for Atmospheric Research, 1977.

    Google Scholar 

  56. K.-J. Lin, C.-Y. Wu and M.-F. Hou. “Discrete Ordinate Solutions Associated with the Finite Legendre Transform for Radiative Transfer in a Slab with Sinusoidal Refractive Index”. International Communications in Heat and Mass Transfer, 2012, 39, pp. 798–802.

    Article  Google Scholar 

  57. D. Liu. “Simultaneous Reconstruction of Temperature Field and Radiative Properties by Inverse Radiation Analysis Using Stochastic Particle Swarm Optimization”. Thermal Science, 2016, 20, pp. 493–504.

    Article  Google Scholar 

  58. F. S. Lobato, V. Steffen Jr. and A. J. Silva Neto. “Estimation of Space-Dependent Single Scattering Albedo in a Radiative Transfer Problem Using Differential Evolution”. Inverse Problems in Science and Engineering, 2012, 20, pp. 1043–1055.

    Article  MathSciNet  Google Scholar 

  59. M. Machida. “Numerical Algorithms of the Radiative Transport Equations Using Rotated Reference Frames for Optical Tomography with Structured Illumination”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2019, 234, pp. 124–138.

    Article  Google Scholar 

  60. M. Marin, F. Asllanaj and D. Maillet. “Sensitivity Analysis to Optical Properties of Biological Tissues Subjected to a Short - Pulsed Laser Using the Time - Dependent Radiative Transfer Equation”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2014, 133, pp. 117–127.

    Article  Google Scholar 

  61. A. Maurente, H. A. Vielmo and F. H. R. França. “A Monte Carlo Implementation to Solve Radiation Heat Transfer in Non-Uniform Media with Spectrally Dependent Properties”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2007, 108, pp. 295–307.

    Article  Google Scholar 

  62. S. C. Mishra and C. H. Krishna. “Analysis of Radiative Transport in a Cylindrical Enclosure - An Application of the Modified Discrete Ordinate Method”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2011, 112, pp. 1065–1081.

    Article  Google Scholar 

  63. M. Mosavati, F. Kowsary and B. Mosavati. “A Novel, Noniterative Inverse Boundary Design Regularized Solution Technique Using the Backward Monte Carlo Method”. Journal of Heat Transfer, 2013, 135, pp. 042701.1–7.

    Article  Google Scholar 

  64. A. C. Mossi, H. A. Vielmo, F. H. R. França and J. R. Howell. “Inverse Design Involving Combined Radiative and Turbulent Convective Heat Transfer”. International Journal of Heat and Mass Transfer, 2008, 51, pp. 3217–3226.

    Article  MATH  Google Scholar 

  65. A. V. Nenarokomov, O. M. Alifanov, I. V. Krainova, D. M. Titov and A. V. Morzhukhina. “Estimation of Environmental Influence on Spacecraft Materials Radiative Properties by Inverse Problems Technique”. Acta Astronautica, 2019, 160, pp. 323–330.

    Article  Google Scholar 

  66. A. V. Nenarokomov, L. A. Dombrovsky, I. V. Krainova, O. M. Alifanov and S. A. Budnik. “Identification of Radiative Heat Transfer Parameters in Multilayer Thermal Insulation of Spacecraft”. International Journal of Numerical Methods for Heat & Fluid Flow, 2017, 27, pp. 598–614.

    Article  Google Scholar 

  67. U. M. Noebauer and S. A. Sim. “Monte Carlo Radiative Transfer”. Living Reviews in Computational Astrophysics, 2019.

    Google Scholar 

  68. P. Oliva Soares, A. J. Silva Neto, H. F. de Campos Velho and F. J. C. P. Soeiro. “A Two Steps Inverse Problem for Vertical Temperature Profile Retrieval in Cloudy Atmosphere Using Artificial Neural Networks”. \(22^{nd}\)International Congress of Mechanical Engineering, ABCM, Ribeirão Preto, Brazil, 2013, pp. 4364–4375.

    Google Scholar 

  69. A. K. Parwani, P. Talukdar and P. M. V. Subbarao. “Performance Evaluation of Hybrid Differential Evolution Approach for Estimation of the Strength of a Heat Source in a Radiatively Participating Medium”. International Journal of Heat and Mass Transfer, 2013, 56, pp. 552–560.

    Article  Google Scholar 

  70. M. R. Perrone, A. M. Tafuro and S. Kinne. “Dust Layer Effects on the Atmospheric Radiative Budget and Heating Rate Profiles”. Atmospheric Environment, 2012, 59, pp. 344–354.

    Article  Google Scholar 

  71. O. V. Postylyakov. “Radiative Transfer Model MCC\(++\) with Evaluation of Weighting Functions in Spherical Atmosphere for Use in Retrieval Algorithms”. Advances in Space Research, 2004, 34, pp. 721–726.

    Article  Google Scholar 

  72. Y. Qiao, H. Qi, Q. Chen, L. Ruan and H. Tan. “An Efficient and Robust Reconstruction Method for Optical Tomography with the Time-Domain Radiative Transfer Equation”. Optics and Lasers in Engineering, 2016, 78, pp. 155–164.

    Article  Google Scholar 

  73. A. Quirantes and S. Bernard. “Light Scattering by Marine Algae: Two-Layer Spherical and Nonspherical Models”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2009, 89, pp. 311–321.

    Article  Google Scholar 

  74. V. V. Rozanov, A. V. Rozanov, A. A. Kokhanovsky and J. P. Burrows. “Radiative Transfer through Terrestrial Atmosphere and Ocean: Software Package SCIATRAN”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2014, 133, pp. 13–71.

    Article  Google Scholar 

  75. C. F. Segatto and M. T. Vilhena. “Extension of the \(LTS_{N}\) Formulation for Discrete Ordinates Problem without Azimuthal Symmetry”. Annals of Nuclear Energy, 1994, 21, pp. 701–710.

    Article  Google Scholar 

  76. R. Siegel and C. M. Spuckler. “Refractive Index Effects on Radiation in an Absorbing, Emitting, and Scattering Laminated Layer”. Journal of Heat Transfer, 1993, 115, pp. 194–200.

    Article  Google Scholar 

  77. A. J. Silva Neto and J. C. Becceneri. Técnicas de Inteligência Computacional Inspiradas na Natureza - Aplicação em Problemas Inversos em Transferência Radiativa (Computational Intelligence Techniques Inspired by Nature - Application in Inverse Problems in Radiative Transfer), In Notas em Matemática Aplicada (Notes in Applied Mathematics), São Carlos: SBMAC, 2009, v. 41, 1 ed.

    Google Scholar 

  78. A. J. Silva Neto and J. C. Becceneri. Técnicas de Inteligência Computacional Inspiradas na Natureza - Aplicação em Problemas Inversos em Transferência Radiativa (Computational Intelligence Techniques Inspired by Nature - Application in Inverse Problems in Radiative Transfer), In Notas em Matemática Aplicada (Notes in Applied Mathematics), São Carlos: SBMAC, 2012, v. 41, 2 ed.

    Google Scholar 

  79. A. J. Silva Neto and M. N. Özisik. “An Inverse Problem of Simultaneous Estimation of Radiation Phase Function, Albedo and Optical Thickness”. Journal of Quantitative Spectroscopy & Radiative Transfer, 1995, 53, pp. 397–409.

    Article  Google Scholar 

  80. G. D. Smith. Numerical Solution of Partial Differential Equations - Finite Difference Methods. Oxford: Clarendon Press, 1985.

    Google Scholar 

  81. F. J. C. P. Soeiro and A. J. Silva Neto. “Inverse Radiative Transfer Problem in Two-Layer Participating Media”. III European Conference on Computational Mechanics: Solids, Structures and Coupled Problems in Engineering, Lisbon, Portugal, 2006.

    Google Scholar 

  82. E. R. Sommersten, J. K. Lotsberg, K. Stamnes and J. J. Stamnes. “Discrete Ordinate and Monte Carlo Simulations for Polarized Radiative Transfer in a Coupled System Consisting of Two Media with Different Refractive Indexes”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2010, 111, pp. 616–633.

    Article  Google Scholar 

  83. F. L. de Sousa, F. J. C. P Soeiro, A. J. Silva Neto and F. M. Ramos. “Application of the Generalized Extremal Optimization Algorithm to an Inverse Radiative Transfer Problem”. Inverse Problems in Science and Engineering, 2007, 15, pp. 699–714.

    Google Scholar 

  84. R. Spurr, K. Stamnes, H. Eide, W. Li, K. Zang and J. Stamnes. “Simultaneous Retrieval of Aerosols and Ocean Properties: A Classic Inverse Modeling Approach. I - Analytic Jacobians from the Linearized CAO-DISORT Models”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2007, 104, pp. 428–449.

    Google Scholar 

  85. K. Stamnes, B. Hamre, S. Stamnes, N. Chen, Y. Fan, W. Li, Z. Lin and J. Stamnes. “Progress in Forward-Inverse Modeling Based on Radiative Transfer Tools for Coupled Atmosphere-Snow/Ice-Ocean Systems: A Review and Description of the AccuRT Model”. Applied Sciences, 2018, 8, pp. 2682.1–52.

    Article  Google Scholar 

  86. J. Tang, B. Han, W. Han, B. Bi and L. Li. “Mixed Total Variation and \(L^{1}\) Regularization Method for Optical Tomography Based on Radiative Transfer Equation”. Computational and Mathematical Methods in Medicine, 2017, pp. 2953560.1–15.

    Google Scholar 

  87. W. Verhoef and H. Bach. “Simulation of Hyperspectral and Directional Radiance Images Using Coupled Biophysical and Atmospheric Radiative Transfer Models”. Remote Sensing of Environment, 2003, 87, pp. 23–41.

    Article  Google Scholar 

  88. J. Villadsen and M. L. Michelsen. Solution of Differential Equation Models by Polynomial Approximation. Englewood Cliffs: Prentice - Hall, 1978.

    MATH  Google Scholar 

  89. P.-Y. Wang, H.-E. Cheng and H.-P. Tan. “Transient Thermal Analysis of Semitransparent Composite Layer with an Opaque Boundary”. International Journal of Heat Mass Transfer, 2002, 45, pp. 425–440.

    Article  MATH  Google Scholar 

  90. L. Wang, J. I. Eldridge and S. M. Guo. “Comparison of Different Models for the Determination of the Absorption and Scattering Coefficients of Thermal Barrier Coatings”. Acta Materialia, 2014, 64, pp. 402–410.

    Article  Google Scholar 

  91. Z. Wang, S. Yang, Y. Qiao, S. Cui and Q. Zhao. “Multiple-Scaling Methods for Monte Carlo Simulations of Radiative Transfer in Cloudy Atmosphere”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2011, 112, pp. 2619–2629.

    Article  Google Scholar 

  92. L.-Y. Wei, H. Qi, X.-L. Zhang, S. Wen, M. A. Islam and L.-M. Ruan. “Reconstruction of Radiative Properties Fields in Participating Media by Using the Sequential Quadratic Programming Combined with Regularization Technique”. Journal of Heat Transfer, 2019, 141, pp. 022702.1–10.

    Article  Google Scholar 

  93. C.-Y. Wu. “Monte Carlo Simulation of Transient Radiative Transfer in a Medium with a Variable Refractive Index”. International Journal of Heat and Mass Transfer, 2009, 52, pp. 4151–4159.

    Article  MATH  Google Scholar 

  94. C.-Y. Wu and B.-T. Lu. “Radiative Transfer in a Two-Layer Slab with Fresnel Interfaces”. Journal of Quantitative Spectroscopy & Radiative Transfer, 1996, 56, pp. 573–589.

    Article  Google Scholar 

  95. C. R. Wylie and L. C. Barrett. Advanced Engineering Mathematics. 5 ed. Singapore: McGraw-Hill, 1985.

    Google Scholar 

  96. D. Y. Xu, A. Bilal, J. M. Zhao, L. H. Liu and Z. M. Zhang. “Near-field Radiative Heat Transfer Between Rough Surfaces Modeled Using Effective Media with Gradient Distribution of Dielectric Function”. International Journal of Heat and Mass Transfer, 2019, 142, pp. 118432.1–11.

    Article  Google Scholar 

  97. J. Xu, F. Schreier, A. Doicu and T. Trautmann. “Assessment of Tikhonov-type Regularization Methods for Solving Atmospheric Inverse Problems”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2016, 184, pp. 274–286.

    Article  Google Scholar 

  98. H.-C. Zhou, Y.-B. Hou, D.-L. Chen and C.-G. Zheng. “An Inverse Radiative Transfer Problem of Simultaneously Estimating Profiles of Temperature and Radiative Parameters from Boundary Intensity and Temperature Measurements”. Journal of Quantitative Spectroscopy & Radiative Transfer, 2002, 74, pp. 605–620.

    Article  Google Scholar 

  99. R.-R. Zhou and B.-W. Li. “The Modified Discrete Ordinates Method for Radiative Heat Transfer in Two-Dimensional Cylindrical Medium”. International Journal of Heat and Mass Transfer, 2019, 139, pp. 1018–1030.

    Article  Google Scholar 

  100. W. Zhu, Q. Yu, Y. Q. Tian, B. L. Becker, T. Zheng and H. J. Carrick. “An Assessment of Remote Sensing Algorithms for Colored Dissolved Organic Matter in Complex Freshwater Environments”. Remote Sensing of Environment, 2014, 140, pp. 766–778.

    Article  Google Scholar 

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Authors and Affiliations

  1. Rio de Janeiro State University, Nova Friburgo, Rio de Janeiro, Brazil

    Antônio José da Silva Neto

  2. National Institute for Space Research (INPE), São José dos Campos, Brazil

    Ezzat Selim Chalhoub & Haroldo Fraga de Campos Velho

Authors
  1. Antônio José da Silva Neto
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  2. Ezzat Selim Chalhoub
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  3. Haroldo Fraga de Campos Velho
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Correspondence to Antônio José da Silva Neto .

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  1. Rio de Janeiro State University, Nova Friburgo, Rio de Janeiro, Brazil

    Antônio José da Silva Neto

  2. National Institute for Space Research, São José dos Campos, São Paulo, Brazil

    José Carlos Becceneri

  3. National Institute for Space Research, São José dos Campos, São Paulo, Brazil

    Haroldo Fraga de Campos Velho

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da Silva Neto, A.J., Chalhoub, E.S., de Campos Velho, H.F. (2023). Radiative Transfer. In: Silva Neto, A.J.d., Becceneri, J.C., Campos Velho, H.F.d. (eds) Computational Intelligence Applied to Inverse Problems in Radiative Transfer. Springer, Cham. https://doi.org/10.1007/978-3-031-43544-7_2

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