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Advances in Meteorology
Volume 2017, Article ID 1835169, 10 pages
Research Article

Comparison of Chebyshev and Legendre Polynomial Expansion of Phase Function of Cloud and Aerosol Particles

1Key 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, China
2State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China
3Shenzhen National Climate Observatory, Shenzhen 518040, China
4State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China

Correspondence should be addressed to Jian-Qi Zhao;

Received 26 May 2017; Accepted 30 July 2017; Published 18 September 2017

Academic Editor: Jia Yue

Copyright © 2017 Feng Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.