HHT Analysis of the Global Average Monthly precipitation Data
This paper uses the Hilbert–Huang transform (HHT) method to make time–frequency diagnostic analyses of four monthly time series of the global precipitation: MERG (1900–2008), REOF (1900–2008), GPCP (1979–2009), and CMAP (1979–2009). All these data are the global land and ocean average of precipitation anomalies with respect to the mean of the entire data period. The MERG and REOF are spectral reconstructions based on historical data. The GPCP and CMAP are based on station gauge data and satellite remote sensing data. We have made the following analysis of the four datasets: (a) extract intrinsic mode functions (IMF) by HHT empirical model decomposition (EMD) sifting, (b) calculate the mean frequency and energy of each IMF, (c) calculate the Fourier spectra to compare with the IMF spectral properties, (d) calculate the Hilbert spectra and display the time–frequency variation of the precipitation time series, and (e) calculate the basic statistics of the four datasets, including mean, standard deviation, skewness, kurtosis and inter-correlation among the datasets. Our analysis results indicate the following: (i) IMFs may contain physical signals of MJO (Madden–Julian oscillation), monsoon, annual cycle, and ENSO (El Nino southern oscillation), (ii) Hilbert spectra appears to be an effective tool to display the time-frequency change of a precipitation time series and can help identify critical characteristics for improving data aggregation method and climate models, (iii) among the four datasets, MERG is the smoothest data and has the smallest variance and hence the smallest IMF energies, while the CMAP has the largest, followed by GPCP and REOF, and (iv) the nonlinear and nonstationary annual cycle is the IMF3 for all the four datasets, which is modulated by ENSO signals.