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Volume 9 Issue 4

Oct.  1992

Article Contents

An Easy Algorithm for Solving Radiative Transfer Equation in Clear Atmosphere


doi: 10.1007/BF02677081

  • An accurate and rapid method for solving radiative transfer equation is presented in this paper. According to the fact that the multiple scattering component of radiance is less sensitive to the error of phase function than the single scattering component is, we calculate the multiple scattering component by using delta-Eddington approximation and the single scattering component by solving radiative transfer equation. On the ground, when multiple mattering com-ponent is small, for example, when the total optical depth τ is small, the accurate radiance can be obtained with this method. For the need of the space remote sensing, the upward radiance at the top of the atmosphere is mainly studied, and an approximate depression is presented to correct the multiple scattering component. Compared with the more precise Gauss-Seidel method, the results from this method show an accuracy of better than 10% when zenith angle θ < 50o and τ ≤ 1. The computational speed of this method is, however, much faster than that of Gauss-Seidel method.
  • [1] Li Jun, 1994: Temperature and Water Vapor Weighting Functions from Radiative Transfer Equation with Surface Emissivity and Solar Reflectivity, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 421-426.  doi: 10.1007/BF02658162
    [2] ZHENG Qin*, SHA Jianxin, SHU Hang, and LU Xiaoqing, 2014: A Variant Constrained Genetic Algorithm for Solving Conditional Nonlinear Optimal Perturbations, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 219-229.  doi: 10.1007/s00376-013-2253-6
    [3] Yi Zengxin, T. Warn, 1987: A NUMERICAL METHOD FOR SOLVING THE EVOLUTION EQUATION OF SOLITARY ROSSBY WAVES ON A WEAK SHEAR, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 43-54.  doi: 10.1007/BF02656660
    [4] Qin XU, Jie CAO, 2021: Iterative Methods for Solving the Nonlinear Balance Equation with Optimal Truncation, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 755-770.  doi: 10.1007/s00376-020-0291-4
    [5] DAI Qiudan, SUN Shufen, 2006: A Generalized Layered Radiative Transfer Model in the Vegetation Canopy, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 243-257.  doi: 10.1007/s00376-006-0243-7
    [6] DAI Qiudan, SUN Shufen, 2007: A Simplified Scheme of the Generalized Layered Radiative Transfer Model, ADVANCES IN ATMOSPHERIC SCIENCES, 24, 213-226.  doi: 10.1007/s00376-007-0213-8
    [7] ZOU Han, LI Peng, MA Shupo, ZHOU Libo, ZHU Jinhuan, 2012: The Local Atmosphere and the Turbulent Heat Transfer in the Eastern Himalayas, ADVANCES IN ATMOSPHERIC SCIENCES, 29, 435-440.  doi: 10.1007/s00376-011-0233-2
    [8] Feng ZHANG, Yadong LEI, Jia-Ren YAN, Jian-Qi ZHAO, Jiangnan LI, Qiudan DAI, 2017: A New Parameterization of Canopy Radiative Transfer for Land Surface Radiation Models, ADVANCES IN ATMOSPHERIC SCIENCES, 34, 613-622.  doi: 10.1007/s00376-016-6139-2
    [9] Liu Jinli, Lin Longfu, 1994: Microwave Simulations of Precipitation Distribution with Two Radiative Transfer Models, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 470-478.  doi: 10.1007/BF02658168
    [10] DUAN Minzheng, Qilong MIN, LU Daren, 2010: A Polarized Radiative Transfer Model Based on Successive Order of Scattering, ADVANCES IN ATMOSPHERIC SCIENCES, 27, 891-900.  doi: 10.1007/s00376-009-9049-8
    [11] Qiu Jinhuan, 1999: Constraint Inversion Algorithm of Lidar Equation for Deriving Aerosol Optical Property, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 216-228.  doi: 10.1007/BF02973083
    [12] Wu Guoxiong, Stefano Tibaldi, 1987: THE EFFECTS OF MECHANICAL FORCING ON THE MEAN MERIDIONAL CIRCULATION AND TRANSFER PROPERTIES OF THE ATMOSPHERE, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 24-42.  doi: 10.1007/BF02656659
    [13] Wu Beiying, John Gille, 1999: Retrieval of Tropospheric CO Profiles Using Correlation Radiometer: I. Retrieval Experiments for a Clear Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 343-354.  doi: 10.1007/s00376-999-0013-4
    [14] ZHANG Qiang, SONG Lianchun, HUANG Ronghui, WEI Guoan, WANG Sheng, TIAN Hui, 2003: Characteristics of Hydrologic Transfer between Soil and Atmosphere over Gobi near Oasis at the End of Summer, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 442-452.  doi: 10.1007/BF02690802
    [15] Efang ZHONG, Qian LI, Shufen SUN, Wen CHEN, Shangfeng CHEN, Debashis NATH, 2017: Improvement of a Snow Albedo Parameterization in the Snow-Atmosphere-Soil Transfer Model: Evaluation of Impacts of Aerosol on Seasonal Snow Cover, ADVANCES IN ATMOSPHERIC SCIENCES, 34, 1333-1345.  doi: 10.1007/s00376-017-7019-0
    [16] GUO Xia, LU Daren, LU Yao, 2007: A Simple but Accurate Ultraviolet Limb-Scan Spherically-Layered Radiative-Transfer-Model Based on Single-Scattering Physics, ADVANCES IN ATMOSPHERIC SCIENCES, 24, 619-630.  doi: 10.1007/s00376-007-0619-3
    [17] Fuzhong WENG, Xinwen YU, Yihong DUAN, Jun YANG, Jianjie WANG, 2020: Advanced Radiative Transfer Modeling System (ARMS): A New-Generation Satellite Observation Operator Developed for Numerical Weather Prediction and Remote Sensing Applications, ADVANCES IN ATMOSPHERIC SCIENCES, 37, 131-136.  doi: 10.1007/s00376-019-9170-2
    [18] Qiu Jinhuan, 2002: A Simple Yet More Accurate Model to Calculate Solar Radiative Flux in the Inhomogeneous Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 433-447.  doi: 10.1007/s00376-002-0077-x
    [19] Gao Shouting, Lei Ting, 2000: Streamwise Vorticity Equation, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 339-347.  doi: 10.1007/s00376-000-0027-4
    [20] Ji Zhongzhen, Wang Bin, Zhao Ying, Yang Hongwei, 2002: Total Energy Conservation and the Symplectic Algorithm, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 459-467.  doi: 10.1007/s00376-002-0079-8

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Manuscript History

Manuscript received: 10 October 1992
Manuscript revised: 10 October 1992
通讯作者: 陈斌, bchen63@163.com
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An Easy Algorithm for Solving Radiative Transfer Equation in Clear Atmosphere

  • 1. Institute of Atmospheric Physics, Academia Sinica, Beijing 100029,Institute of Atmospheric Physics, Academia Sinica, Beijing 100029

Abstract: An accurate and rapid method for solving radiative transfer equation is presented in this paper. According to the fact that the multiple scattering component of radiance is less sensitive to the error of phase function than the single scattering component is, we calculate the multiple scattering component by using delta-Eddington approximation and the single scattering component by solving radiative transfer equation. On the ground, when multiple mattering com-ponent is small, for example, when the total optical depth τ is small, the accurate radiance can be obtained with this method. For the need of the space remote sensing, the upward radiance at the top of the atmosphere is mainly studied, and an approximate depression is presented to correct the multiple scattering component. Compared with the more precise Gauss-Seidel method, the results from this method show an accuracy of better than 10% when zenith angle θ < 50o and τ ≤ 1. The computational speed of this method is, however, much faster than that of Gauss-Seidel method.

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