Comparison of Chebyshev and Legendre Polynomial Expansion of Phase Function of Cloud and Aerosol Particles
Chebyshev and Legendre polynomial expansion is used to reconstruct the Henyey-Greenstein phase function and the phase functions of spherical and nonspherical particles. The result of Legendre polynomial expansion is better than that of Chebyshev polynomial for around 0-degree forward angle, while Ch...
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Online Access: | http://dx.doi.org/10.1155/2017/1835169 |
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doaj-aa29becbacdb4e898551c5625117011a2020-11-24T21:24:59ZengHindawi LimitedAdvances in Meteorology1687-93091687-93172017-01-01201710.1155/2017/18351691835169Comparison of Chebyshev and Legendre Polynomial Expansion of Phase Function of Cloud and Aerosol ParticlesFeng Zhang0Kun Liu1Quan Yang2Kun Wu3Jian-Qi Zhao4Key Laboratory of Meteorological Disaster, Ministry of Education (KLME)/Joint International Research Laboratory of Climate and Environment Change (ILCEC)/Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disaster (CICFEMD), Nanjing University of Information Science and Technology, Nanjing 210044, ChinaShenzhen National Climate Observatory, Shenzhen 518040, ChinaKey Laboratory of Meteorological Disaster, Ministry of Education (KLME)/Joint International Research Laboratory of Climate and Environment Change (ILCEC)/Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disaster (CICFEMD), Nanjing University of Information Science and Technology, Nanjing 210044, ChinaKey Laboratory of Meteorological Disaster, Ministry of Education (KLME)/Joint International Research Laboratory of Climate and Environment Change (ILCEC)/Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disaster (CICFEMD), Nanjing University of Information Science and Technology, Nanjing 210044, ChinaState Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, ChinaChebyshev and Legendre polynomial expansion is used to reconstruct the Henyey-Greenstein phase function and the phase functions of spherical and nonspherical particles. The result of Legendre polynomial expansion is better than that of Chebyshev polynomial for around 0-degree forward angle, while Chebyshev polynomial expansion produces more accurate results in most regions of the phase function. For large particles like ice crystals, the relative errors of Chebyshev polynomial can be two orders of magnitude less than those of Legendre polynomial.http://dx.doi.org/10.1155/2017/1835169 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Feng Zhang Kun Liu Quan Yang Kun Wu Jian-Qi Zhao |
spellingShingle |
Feng Zhang Kun Liu Quan Yang Kun Wu Jian-Qi Zhao Comparison of Chebyshev and Legendre Polynomial Expansion of Phase Function of Cloud and Aerosol Particles Advances in Meteorology |
author_facet |
Feng Zhang Kun Liu Quan Yang Kun Wu Jian-Qi Zhao |
author_sort |
Feng Zhang |
title |
Comparison of Chebyshev and Legendre Polynomial Expansion of Phase Function of Cloud and Aerosol Particles |
title_short |
Comparison of Chebyshev and Legendre Polynomial Expansion of Phase Function of Cloud and Aerosol Particles |
title_full |
Comparison of Chebyshev and Legendre Polynomial Expansion of Phase Function of Cloud and Aerosol Particles |
title_fullStr |
Comparison of Chebyshev and Legendre Polynomial Expansion of Phase Function of Cloud and Aerosol Particles |
title_full_unstemmed |
Comparison of Chebyshev and Legendre Polynomial Expansion of Phase Function of Cloud and Aerosol Particles |
title_sort |
comparison of chebyshev and legendre polynomial expansion of phase function of cloud and aerosol particles |
publisher |
Hindawi Limited |
series |
Advances in Meteorology |
issn |
1687-9309 1687-9317 |
publishDate |
2017-01-01 |
description |
Chebyshev and Legendre polynomial expansion is used to reconstruct the Henyey-Greenstein phase function and the phase functions of spherical and nonspherical particles. The result of Legendre polynomial expansion is better than that of Chebyshev polynomial for around 0-degree forward angle, while Chebyshev polynomial expansion produces more accurate results in most regions of the phase function. For large particles like ice crystals, the relative errors of Chebyshev polynomial can be two orders of magnitude less than those of Legendre polynomial. |
url |
http://dx.doi.org/10.1155/2017/1835169 |
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