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)
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
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.
Received: 21 March 2006
Revised: 29 May 2006
Accepted manuscript online:
Fund: Project supported by the National
Natural Sciences Foundation of China (Grant Nos 40275031 and
90411008).
Cite this article:
Shi Neng(施能), Yi Yan-Ming(易燕明), Gu Jun-Qiang(顾骏强), and Xia Dong-Dong(夏冬冬) On the correlation of nonlinear variables containing secular trend variations: numerical experiments 2006 Chinese Physics 15 2180
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