Energy decomposition of rainfall in the time-frequency-scale domain using wavelet packets

The time-frequency-scale features of high-resolution rainfall are investigated in an effort to gain more insight into the rainfall-generating mechanism. In particular, we look for the existence of persistent and short- lived structures and their associated frequencies and time (length) scales, as well as the energy they carry. We try to achieve this objective via the wavelet packet representation. The best representation for a signal from the point of view of minimum entropy (i.e. maximum 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 localization of that frequency in time, whether persistent or short lived, is known. We discuss the implications of our analysis in separating stratiform and convective components of rain and in gaining insight into the rainfall energy cascading mechanism for the purpose of model building.