Content
Number of images - 3
Tables and charts - 2
Discrete Ordinate Radiative Transfer Model With the Neural Network Based Eigenvalue Solver: proof Of Concept Light & Engineering Vol. 29, No. 1

Light & Engineering 29 (1)

Volume 29
Date of publication 02/27/2021
Pages 56–62

Purchase PDF - $6

Discrete Ordinate Radiative Transfer Model With the Neural Network Based Eigenvalue Solver: proof Of Concept Light & Engineering Vol. 29, No. 1
Articles authors:
Dmitry S. Efremenko

Dmitry S. Efremenko received his Ph. D. degree from the Moscow State University in 2011 and the Habilitation degree from MPEI in 2017. Since 2011 he works as a research scientist at the German Aerospace Centre (DLR). He received the Elsevier/JQSRT Goody Award in 2017. In 2020, he obtained a title of Privatdozent from the Technical University of Munich. His scientific interests include radiative transfer, numerical methods and machine learning. He has over 70 scientific papers

Abstract:
Artificial neural networks are attracting increasing attention in various applications. They can be used as ‘universal approximations’, which substitute computationally expensive algorithms by relatively simple sequences of functions, which simulate a reaction of a set of neurons to the incoming signal. In particular, neural networks have proved to be efficient for parameterization of the computationally expensive radiative transfer models (RTMs) in atmospheric remote sensing. Although a direct substitution of RTMs by neural networks can lead to the multiple performance enhancements, such an approach has certain drawbacks, such as loss of generality, robustness issues, etc. In this regard, the neural network is usually trained for a specific application, predefined atmospheric scenarios and a given spectrometer. In this paper a new concept of neural-network based RTMs is examined, in which the neural network substitutes not the whole RTM but rather a part of it (the eigenvalue solver), thereby reducing the computational time while maintaining its generality. The explicit dependencies on geometry of observation and optical thickness of the medium are excluded from training. It is shown that although the speedup factor due to this approach is modest (around 3 times against 103 speed up factor of other approaches reported in recent papers), the resulting neural network is flexible and easy to train. It can be used for arbitrary number of atmospheric layers. Moreover, this approach can be used in conjunction with any RTMs based on the discrete ordinate method. The neural network is applied for simulations of the radiances at the top of the atmosphere in the Huggins band.
References:
1. Levit G. S., Krumbein W.E., and R. Grübel. Space and Time in the Works of V.I. Vernadsky // Environmental Ethics, 2000, Vol. 22, # 4, pp. 377–396.
2. Kataev M. Yu., Lukyanov A.K. Simulation of reflected solar radiation for atmosphere gas composition evaluation for optical remote sensing from space // Light & Engineering, 2018, Vol. 26, # 3, pp. 14–21.
3. TROPOMI on the ESA Sentinel‑5 Precursor: A GMES mission for global observations of the atmospheric composition for climate, air quality and ozone layer applications / J.P. Veefkind, I. Aben, K. McMullan et al. // Remote Sensing of Environment, 2012, Vol. 120, pp. 70–83.
4. Cybenko G. Approximation by superpositions of a sigmoidal function // Mathematics of Control, Signals, and Systems, 1989, Vol. 2, # 4, pp. 303–314.
5. Hornik K. Approximation capabilities of multilayer feed forward networks // Neural Networks, 1991. Vol. 4, # 2, pp. 251–257.
6. Key J.R., Schweiger A.J. Tools for atmospheric radiative transfer: Streamer and FluxNet // Computers & Geosciences, 1998, Vol. 24, # 5, pp. 443–451.
7. Loyola D.G.R. Applications of neural network methods to the processing of earth observation satellite data // Neural Networks, 2006, Vol. 19, # 2, pp. 168–177.
8. The operational cloud retrieval algorithms from TROPOMI on board Sentinel‑5 Precursor / D.G. Loyola, S. Gimeno García, R. Lutz et al. // Atmospheric Measurement Techniques, 2018, Vol. 11, # 1, pp. 409–427.
9. Neural network radiative transfer for imaging spectroscopy / B.D. Bue, D.R. Thompson, S. Deshpande et al. // Atmospheric Measurement Techniques, 2019, Vol. 12, # 4, pp. 2567–2578.
10. Portable Remote Imaging Spectrometer coastal ocean sensor: design, characteristics, and first flight results / P. Mouroulis, B. Van Gorp, R.O. Green et al. // Applied Optics, 2014, Vol. 53, # 7, p. 1363.
11. Chandrasekhar S. Radiative Trasnfer/ Dover publications, inc. New York, 1950.
12. Budak V.P., Klyuykov D.A., Korkin S.V. Complete matrix solution of radiative transfer equation for PILE of horizontally homogeneous slabs // J. Quant Spectrosc. Radiation Transfer, 2011, Vol. 112, # 7, pp. 1141–1148.
13. V.P. Afanas’ev, A. Yu. Basov, V.P. Budak et al. Analysis of the Discrete Theory of Radiative Transferin the Coupled Ocean Atmosphere System: Current Status, Problems and Development Prospects // Journalof Marine Science and Engineering, 2020, Vol. 8, # 3, p. 202.
14. D.S. Efremenko, V. Molina Garcia, S. Gimeno Garcá, Doicu A. A review of the matrix-exponential formalism in radiative transfer // Journal of Quantitative Spectroscopy and Radiative Transfer, 2017, Vol. 196, pp. 17–45.
15. Plass G.N., Kattawar G.W., Catchings F.E. Matrix Operator Theory of Radiative Transfer 1: Rayleigh Scattering // Applied Optics, 1973, Vol. 12, # 2, p. 314.
16. Fischer J., Grassl H. Radiative transfer in an atmosphere-ocean system: an azimuthally dependent matrix-operator approach // Applied Optics, 1984, Vol. 23, # 7, p. 1032.
17. Budak V.P., Efremenko D.S., Shagalov O.V. Efficiency of algorithm for solution of vector radiative transfer equation in turbid medium slab // Journal of Physics: Conference Series, 2012, Vol. 369, p. 012021.
18. Natraj V., Spurr R.J.D. A fast linearized pseudospherical two orders of scattering model to account for polarization in vertically inhomogeneous scattering-absorbing media // Journal of Quantitative Spectroscopy and Radiative Transfer, 2007, Vol. 107, # 2, pp. 263–293.
19. A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols / J. Lenoble, M. Herman, J.L. Deuzé et al. // Journal of Quantitative Spectroscopy and Radiative Transfer, 2007, Vol. 107, # 3, pp. 479–507.
20. Waterman P.C. Matrix-exponential description of radiative transfer // J Opt Soc Am. 1981, Vol. 71, #. 4, pp. 410–22.
21. Nakajima T., Tanaka M. Matrix formulations for the transfer of solar radiation in a plane-parallel scattering atmosphere // J Quant Spectrosc Radiat Transfer, 1986, Vol. 35, # 1, pp. 13–21.
22. Budak V.P., Klyuykov D.A., Korkin S.V. Convergence acceleration of radiative transfer equation solution at strongly anisotropic scattering // Light Scattering Reviews 5, Springer Berlin Heidelberg, 2010, pp. 147–203.
23. Acceleration techniques for the discrete ordinate method / D. Efremenko, A. Doicu, D. Loyola, T. Trautmann // Journal of Quantitative Spectroscopy and Radiative Transfer, 2013, Vol. 114, pp. 73–81.
24. Multi-layer solar radiative transfer considering the vertical variation of inherent microphysical properties of clouds / Y.-N. Shi, F. Zhang, K.L. Chan et al. // Optics Express, 2019, Vol. 27, # 20, pp. A1569.
25. Spurr R., Natraj V. A linearized two-stream radiative transfer code for fast approximation of multiplescatter fields // Journal of Quantitative Spectroscopy and Radiative Transfer, 2011. Vol. 112, # 16, pp. 2630–2637.
26. Van Oss R.F., Spurr R.J.D. Fast and accurate 4 and 6 stream linearized discrete ordinate radiative transfer models for ozone profile retrieval // Journal of Quantitative Spectroscopy and Radiative Transfer, 2002, Vol. 75, # 2, pp. 177–220.
27. Girolamo L. Di. Reciprocity principle applicable to reflected radiance measurements and the searchlight problem // Applied Optics, 1999, Vol. 38, # 15, pp. 3196.
28. On Rayleigh optical depth calculations / B.A. Bodhaine, N.B. Wood, E.G. Dutton, J.R. Slusser // Journal of Atmospheric and Oceanic Technology, 1999, Vol. 16, # 11, pp. 1854–1861.
29. Bohren C.F., Huffman D.R. Absorption and Scattering of Light by Small Particles/ Wiley, 1998.
30. Deirmendjian D. Electromagnetic Scattering on Spherical Polydispersions/ Elsevier, 1969.
31. Marquardt D.W. An Algorithm for Least-Squares Estimation of Nonlinear Parameters // Journal of the Society for Industrial and Applied Mathematics, 1963, Vol. 11, # 2, pp. 431–441.
32. Loyola D.G.R. Pedergnana M., García S. Gimeno. Smart sampling and incremental function learning for very large high dimensional data // Neural Networks, 2016, Vol. 78, pp. 75–87.
33. Halton J.H. On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals // Numerische Mathematik, 1960, Vol. 2, # 1, pp. 84–90.
34. Wang X., Hickernell F.J. Randomized Halton sequences // Mathematical and Computer Modelling, 2000, Vol. 32, # 7–8, pp. 887–899.
35. A Novel Ozone Profile Shape Retrieval Using Full-Physics Inverse Learning Machine (FP-ILM) / J. Xu, O. Schussler, D.G. Loyola et al. // IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2017, Vol. 10, # 12, pp. 5442–5457.
36. Amdahl G.M. Validity of the single processor approach to achieving large scale computing capabilities // Proceedings of the April 18–20, 1967, Spring Joint Computer Conference on – AFIPS67 (Spring). ACM Press, 1967.
37. Numerically stable algorithm for discrete-ordinatemethod radiative transfer in multiple scattering and emitting layered media / K. Stamnes, S.C. Tsay, W. Wiscombe, K. Jayaweera // Appl. Opt, 1988, Vol. 12, pp. 2502–2509.
38. Spurr R.J.D. LIDORT and VLIDORT: Linearized pseudo-spherical scalar and vector discrete ordinate radiative transfer models for use in remote sensing retrieval problems // Light scattering reviews / Ed. by A.A. Kokhanovsky, 2008, Vol. 3, pp. 229–275.
39. Numerical modeling of the radiative transfer in a turbid medium using the synthetic iteration / V.P. Budak, G.A. Kaloshin, O.V. Shagalov, V.S. Zheltov // Opt. Express, 2015, Vol. 23, # 15, p. A829.
Keywords

Buy

Recommended articles