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Nelder-Mead单纯形算法改进及在气象上的应用

张正秋

张正秋. Nelder-Mead单纯形算法改进及在气象上的应用. 应用气象学报, 2011, 22(5): 584-589..
引用本文: 张正秋. Nelder-Mead单纯形算法改进及在气象上的应用. 应用气象学报, 2011, 22(5): 584-589.
Zhang Zhengqiu. Improvement on the Nelder-Mead simplex algorithm and its application to meteorology. J Appl Meteor Sci, 2011, 22(5): 584-589.
Citation: Zhang Zhengqiu. Improvement on the Nelder-Mead simplex algorithm and its application to meteorology. J Appl Meteor Sci, 2011, 22(5): 584-589.

Nelder-Mead单纯形算法改进及在气象上的应用

详细信息
    通信作者:

    张正秋, E-mail:zqzhang@cams.cma.gov.cn

Improvement on the Nelder-Mead Simplex Algorithm and Its Application to Meteorology

  • 摘要: Nelder-Mead Simplex (NMS) 算法是一种查找多元函数局地最小值的无微分算法,在现代科学计算中得到广泛应用,该文提出了一种对NMS算法的改进方法。改进后,大大简化了其计算过程,提高了该算法的收敛速度。利用改进后的算法对陆面过程参数进行了拟合计算,结果表明:改进的NMS算法对非线性公式具有非常高的拟合精度,可将其应用于气象学上非线性问题计算或非线性方程组求解。
  • 图  1  改进的NMS下山方向设置示意图

    Fig. 1  Searching direction setting for the improved NMS

    图  2  阔叶林近地面参数曲线拟合结果

    (a) 零平面位移D0, (b) 空气动力阻力Rd

    Fig. 2  Simulations on the variations of ground parameters for the broad leaf tree

    (a) zero plane displacement D0, (b) aerodynamic resistance Rd

  • [1] Mordecai Avriel. Nonlinear Programming, Analysis and Methods. New Jersey: Prentice-Hall Inc, 1976.
    [2] William H P, Saul A T, William T V, et al. Numerical Recipes 3rd Edition: The Art of Scientific Computing, Chapter 9. Cambridge: Cambridge University Press, 2007.
    [3] Powell M J D. A method for minimizing a sum of squares of non-linear functions without calculating derivatives. Computer Journal, 1965, 7: 303-307. doi:  10.1093/comjnl/7.4.303
    [4] Brent R P. Algorithms for Minimization Without Derivatives, Chapter 7. Dover, 2002.
    [5] Mathews J H, Kurtis K F. Numerical Methods Using Matlab, 4th Edition. New Jersey: Prentice-Hall Inc, 2004.
    [6] 钟爱华, 严华生, 李跃清, 等.青藏高原积雪异常与大气环流异常间关系分析.应用气象学报, 2010, 21(1):37-46. doi:  10.11898/1001-7313.20100105
    [7] 郑栋, 张义军, 孟青, 等.北京地区雷暴过程闪电与地面降水的相关关系.应用气象学报, 2010, 21(3):287-297. doi:  10.11898/1001-7313.20100304
    [8] 陈正洪, 王海军, 张小丽.水文学中雨强公式参数求解的一种最优化方法.应用气象学报, 2007, 18(2):237-241. doi:  10.11898/1001-7313.20070240
    [9] 窦贤康, Amaye P.机载雷达定量测雨中雨滴谱参数的优化.应用气象学报, 1999, 10(3):293-298. http://qikan.camscma.cn/jams/ch/reader/view_abstract.aspx?file_no=19990371&flag=1
    [10] 曾庆存.数值天气预报的数学物理基础 (第一卷).北京:科学出版社, 1979.
    [11] Nelder J A, Mead R. A simplex method for function minimization. Computer Journal, 1965, 7: 308-313. doi:  10.1093/comjnl/7.4.308
    [12] Tomick J, Arnold S F, Barton R R. Sample Size Selection for Improved Nelder-Mead Performance. 1995 Winter Simulation Conference (WSC'95), 1995: 341-345.
    [13] Russell R B, John S I Jr. Nelder-Mead Simplex Modifications for Simulation Optimization. Management Science, 1996, 42(7): 954-973. doi:  10.1287/mnsc.42.7.954
    [14] David G H, James R W. A revised simplex search procedure for stochastic simulation response surface optimization. Informs Journal on Computing, 2000, 12(4): 272-283. doi:  10.1287/ijoc.12.4.272.11879
    [15] 王体健, 李宗恺.不同方案求解非线性化学动力方程组的比较.应用气象学报, 1996, 7(4):466-472. http://qikan.camscma.cn/jams/ch/reader/view_abstract.aspx?file_no=19960471&flag=1
    [16] Yarbro L A, Stanley N D. Selection and preprocessing of factors for simplex optimization. Analytica Chimica Acta, 1974, 73: 391-398. doi:  10.1016/S0003-2670(01)85476-3
    [17] Xue Y, Sellers P J, Kinter J L Ⅲ, et al. A simplified biosphere model for global climate studies. J Climate, 1991, 4: 345-364. doi:  10.1175/1520-0442(1991)004<0345:ASBMFG>2.0.CO;2
    [18] Sellers P J, Randall D A, Collatz G J, et al. A revised land surface parameterization (SiB2) for atmospheric GCMs. Part Ⅰ: Model formulation. J Climate, 1996, 9: 676-705. doi:  10.1175/1520-0442(1996)009<0676:ARLSPF>2.0.CO;2
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出版历程
  • 收稿日期:  2010-10-09
  • 修回日期:  2011-05-20
  • 刊出日期:  2011-10-31

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