Appendix B.2 Space-time spectral analysis

In order to clarify possible relationships between the sequences of precipitation events at the equator and equatorial waves, wavenumber-frequency power spectra are discussed in subsection 3.2 and subsection 4.2. In this appendix, we briefly summarize the calculation method, which follows the methods by Takayabu (1994) and Wheeler and Kiladis (1999), that is used to obtain those spectra.

1. 10 set of time series data with the period of 90 days are produced by shifting the starting day by every 30 days from one year data from day 1040 to day 1400 of calculated time serie.
2. Subtract the mean and the linear trend by the use of least square method from each time series.
3. Smoothing is applied to each time series to reduce erros in spectral estimation. Hanning window is adopted as a spectral window.
4. For each set of time series, FFT is applied both in the londituinal direciton and in time to have wavenumber-frequency power spectra (space-time spectra).
5. Taking the average over 10 spectral data obtained form the 10 time series, the following three types of data are produced.
   
   A_SYM(φ) = ( A(φ) + A(-φ) ) / 2 (symmetric component),
   A_ASYM(φ) = ( A(φ) - A(-φ) ) / 2 (anti-symmetric component),
   A(φ) = ( A_ASYM(φ) + A_SYM(φ) )
   
   Here A indicates the physical quantity concerned, and φ is latitude.
6. A background spectrum is produced by taking a moving filter with the weight of 1-2-1 on A.
7. The enhanced wavenuber-frequency power spctrum is obtained by deviding the symmetric (or antisymmetric) component of a wavenuber-frequency power spctrum A_SYM (or A_ASYM) by the backgoround spectrum.