HHT analysis of the nonlinear and non-stationary annual cycle of daily surface air temperature data

The empirical mode decomposition (EMD) method is used to analyze the nonlinear and non-stationary annual cycle (NAC) in climate data. The NAC is defined as an intrinsic mode function generated in the EMD process and has a mean period equal to a year. Both Hilbert and Fourier spectra of the NAC are examined to validate the power density at the frequency of one cycle per year. The NAC differs from the strictly periodic thirty-year-mean annual cycle (TAC), which is now commonly used in climate anomaly analysis. It is shown that the NAC has a stronger signal of the annual cycle than that of the TAC. Thus, the anomalies derived from the NAC have less spectral power at the frequency of one cycle per year than those from the TAC. The marginal Hilbert spectra of the maximum daily surface air temperature of ten North America stations demonstrate the expected characteristics of an annual cycle: the NAC’s strength is proportional to the latitude of the station location and inversely proportional to the heat capacity of the Earth’s surface materials around a station. The NAC of the Niño3.4 sea surface temperature analysis indicates that El Niño events correspond to a weaker annual cycle, as suggested by wavelet analysis.