The main aim of the present work is to search for periodicities in the monsoon rainfall data. A new method that combines multi-resolution analysis (MRA) and classical Fourier spectral methods to identify peaks in the power spectral density of a given time series is proposed. The method is validated on specially designed test signals. The proposed method is then applied to the rainfall time series, especially to help separate closely spaced periodicities. In this procedure, using MRA the stationary component of the rainfall time series is first identified. Then (partially) reconstructed time series are derived over each wavelet scale band in the stationary component. The significance of the detected peaks is then determined using a chi-squared test against the reference spectra, which together represent a noise process spectrally close to rainfall. A new quantitative definition of spectral homogeneity is also proposed which identifies new spectrally homogeneous region in Indian sub-continent. This work is done under the incredible guidance of Prof. Roddam Narasimha, I greatly acknowledge his support.

Sarita Azad received her Master's (Mathematics) from the Indian Institute of Technology (IITD), Delhi, India, in 1999. She did her PhD (2008) in Applied Mathematics from Delhi University,India, under Prof. Roddam Narasimha (FRS) at Indian Institute of Science, Bangalore, India. She was visiting fellow at University of Cambridge, UK (2009).