中国物理B ›› 2006, Vol. 15 ›› Issue (9): 2180-2184.doi: 10.1088/1009-1963/15/9/046

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On the correlation of nonlinear variables containing secular trend variations: numerical experiments

易燕明1, 施能2, 夏冬冬3, 顾骏强4   

  1. (1)Guangzhou Institute of Tropical and Oceanic Meteorology,Guangzhou 510080, China; (2)Key Laboratory of Meteorology and Environment, Nanjing University of Information Science and Technology, Nanjing 210044, China; (3)National Marine Environment Forecast Center, Beijing 100081, China; (4)Zhejiang Meteorological Science Research Institute, Hanzhou 310017, China
  • 收稿日期:2006-03-21 修回日期:2006-05-29 出版日期:2006-09-20 发布日期:2006-09-20
  • 基金资助:
    Project supported by the National Natural Sciences Foundation of China (Grant Nos 40275031 and 90411008).

On the correlation of nonlinear variables containing secular trend variations: numerical experiments

Shi Neng(施能)a)†, Yi Yan-Ming(易燕明)b), Gu Jun-Qiang(顾骏强)c), and Xia Dong-Dong(夏冬冬)d)   

  1. a Key Laboratory of Meteorology and Environment, Nanjing University of Information Science and Technology, Nanjing 210044, China; b Guangzhou Institute of Tropical and Oceanic Meteorology,Guangzhou 510080, China; c Zhejiang Meteorological Science Research Institute, Hanzhou 310017, China; d National Marine Environment Forecast Center, Beijing 100081, China
  • Received:2006-03-21 Revised:2006-05-29 Online:2006-09-20 Published:2006-09-20
  • Supported by:
    Project supported by the National Natural Sciences Foundation of China (Grant Nos 40275031 and 90411008).

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摘要： Due to global warming, the general circulation, underlying surfaces characteristics, and geophysical and meteorological elements all show evident secular trends. This paper points out that when calculating the correlation of two variables containing their own obvious secular trends, the interannual correlation characteristics between the two variables may be distorted (overestimated or underestimated). Numerical experiments in this paper show that if two variables have opposite secular trends, the correlation coefficient between the two variables is reduced (the positive correlation is underestimated, or the negative correlation is overestimated); and if the two variables have the same sign of secular trends, the correlation coefficient between the two variables is increased (the positive correlation is overestimated, or the negative correlation is underestimated). Numerical experiments also suggest that the effect of secular trends on the interannual correlation of the two variables is interchangeable, that is to say, as long as the values of the two trends are not changed, the two variables interchange their positions, and the effect of the secular trends on the interannual correlation coefficient of the two variables remains the same. If the two variables have the same-(opposite-) sign trends, the effect of secular trends on the interannual correlation coefficient is more (less) distinctive. A meteorological example is given.

关键词: correlation analysis, secular trend, trend coefficient, numerical experiment

Abstract: Due to global warming, the general circulation, underlying surfaces characteristics, and geophysical and meteorological elements all show evident secular trends. This paper points out that when calculating the correlation of two variables containing their own obvious secular trends, the interannual correlation characteristics between the two variables may be distorted (overestimated or underestimated). Numerical experiments in this paper show that if two variables have opposite secular trends, the correlation coefficient between the two variables is reduced (the positive correlation is underestimated, or the negative correlation is overestimated); and if the two variables have the same sign of secular trends, the correlation coefficient between the two variables is increased (the positive correlation is overestimated, or the negative correlation is underestimated). Numerical experiments also suggest that the effect of secular trends on the interannual correlation of the two variables is interchangeable, that is to say, as long as the values of the two trends are not changed, the two variables interchange their positions, and the effect of the secular trends on the interannual correlation coefficient of the two variables remains the same. If the two variables have the same-(opposite-) sign trends, the effect of secular trends on the interannual correlation coefficient is more (less) distinctive. A meteorological example is given.

Key words: correlation analysis, secular trend, trend coefficient, numerical experiment

中图分类号:  (Thin film structure and morphology)

  • 68.55.-a
73.50.Jt (Galvanomagnetic and other magnetotransport effects) 73.61.Cw (Elemental semiconductors) 79.20.Fv (Electron impact: Auger emission) 68.55.Ln (Defects and impurities: doping, implantation, distribution, concentration, etc.) 78.30.Am (Elemental semiconductors and insulators) 78.66.Db (Elemental semiconductors and insulators)