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Data and Methodology

Radiosonde measured monthly mean temperature and zonal wind data at 1km interval for the altitude range 1-27 km during September 1971 to December 1992 over Thumba (Trivandrum) constitute the basic data for the present study. Beyond this period, the radiosonde data are not available in this station. Temperature anomalies of each month from the 256 month mean were computed for each level. Data of Indian Summer Monsoon Rainfall (ISMR) has been taken from Parthasarathy et al (1994). ISMR is the average June to September rainfall of 306 stations well distributed over India.

To analyse the multi-time scale oscillations present in zonal wind and temperature anomaly, Morelet wavelet transform is used. It is a useful tool to analyse the time series that contain non-stationary power at many different frequencies (Daubechies, 1990). Wavelet transform transforms a one dimensional time series into two-dimensional frequency-time domain. So it is possible to know the frequency content of the signal at every time-step. Wavelet transform uses generalized wave functions called wavelets that can be stretched and translated both in time and frequency.

Wavelet decomposes a signal s(t) in terms of some elementary function ?b,a (t) derived from a analyzing wavelet or mother wavelet ?(t) (Weng and Lau, 1994). The wavelet transform of a real signal s(t) with respect to the analyzing wavelet ?(t) may be defined as

 

W(b,a) = (1/?a) ? ?* (t-b/a) s(t) dt

 

            ?*        is the complex conjucate of ?

           

            b          is the position (translation)

 

            a(>0)    is dilation.

 

The analyzing wavelet ?(t) for Morelet wavelet transform is ?(t)=eik?t  e-?txt?/2, which is a plane wave modulated by a Gaussian. Complex Morelet wavelet transform was applied to zonal wind and temperature at each level. This transform provides information of signal on both amplitude and phase. Length of the data is kept as 256 (28) in order to avoid edge effects caused by data padding and voices per octave are set as 4. Zero octave was fixed as 8 months. Detailed mathematical treatment of the wavelet transform is available elsewhere (Lau and Weng, 1995; Torrence et al, 1998; Weng and Lau, 2000).

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