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 interannal correlation coefficient is more （less） distinctive. A meteorological example is given.
To better understand the physical mechanism of the climate change on interdecadal-centennial timescale, this paper focuses on analysing and modelling the evolution characteristics of the climate change. The method of wavelet transform is used to pick out the interdecadal timescale oscillations from long-term instrumental observations, natural proxy records, and modelling series. The modelling series derived from the most simplified nonlinear climatic model are used to identify whether modifications are concerned with some forcings such as the solar radiation on the climate system. The results show that two major oscillations exist in various observations and model series, namely the 20- 30a and the 60-70a timescale respectively, and these quasi-periodicities are modulated with time. Further, modelling results suggest that the originations of these oscillations are not directly linked with the periodic variation of solar radiations such as the 1-year cycle, the 11-year cycle, and others, but possibly induced by the internal nonlinear effects of the climate system. It seems that the future study on the genesis of the climate change with interdecadal-centennial timescale should focus on the internal nonlinear dynamics in the climate system.
