ENERGY DECOMPOSITION OF RAINFALL IN THE TIME-FREQUENCY-SCALE DOMAIN USING WAVELET PACKETS

The time-frequency-scale features of high-resolution rainfall are inve stigated in an effort to gain more insight into the rainfall-generatin g mechanism. In particular, we look for the existence of persistent an d short-lived structures and their associated frequencies and time (le ngth) scales, as well as the energy they carry. We try to achieve this objective via the wavelet packet representation. The best representat ion for a signal from the point of view of minimum entropy (i.e. maxim um information in a few coefficients) is obtained, and, in the process , we define two measures: (1) best basis spectrum, which is analogous to the well-known Fourier spectrum; (2) frequency persistence spectrum , a new measure, which in essence gives an idea of what scale has been chosen to best represent a particular frequency; thus the localizatio n of that frequency in time, whether persistent or short lived, is kno wn. We discuss the implications of our analysis in separating stratifo rm and convective components of rain and in gaining insight into the r ainfall energy cascading mechanism for the purpose of model building.