Research on the relationship between rainfall and reference crop evapotranspiration with multi-time scales

Limited by Fourier analysis and the selection of different wavelet base functions, the wavelet analysis method shows some deficiencies. For that reason, the empirical mode decomposition method is applied to analyze fluctuating periods and local features of annual rainfall and reference crop evapotranspiration (ET0) from 1959 to 2002. With respect to the correlation between variables, the traditional time series analysis methods often assume that data sequences are stationary which result in "spurious regression." Therefore, the cointegration theory is introduced to describe the long-term equilibrium relationship of rainfall and ET0. At last, to understand the uncertainty between these two variables, the set pair analysis (SPA) method is used to present the identity, discrepancy, and contrary of rainfall and ET0 with multi-time scales. The results reveal that rainfall and ET0 have a complex relationship which may be related to El Nino, air-sea intersection, solar activity. Moreover, the fluctuation periods of rainfall and ET0 also have similar short and middle period level, and slightly different long period level. The changes of rainfall and ET0 present mainly the contrary and the discrepancy. This relationship will remain a long-term equilibrium.