Some considerations of periodicity and persistence in daily rainfalls

In formulating mathematical models for the evaluation of variability in daily rainfalls, periodicity and persistence are two of the main characteristics to consider. We review periodogram analysis ranging from the Whittaker–Robinson technique to the Schuster periodogram and recent practices such as the modified Daniell window and the autoregressive and entropy spectra. We also reconsider models of the Markovian type of dependence and methods of analysis. The objective is to demonstrate useful practical procedures with the aid of relevant graphical displays. Results from periodograms not based on sinusoids are shown to complement the findings from more conventional methods. Periodicity in rainfall is less effective than in other related phenomena but has wide climatic variations. Preference for the familiar two-state first-order Markov model is reconfirmed with a two-harmonic representation of the seasonal variation in the Markov parameters. Rainfall data from Italy and Sri Lanka are used with observations of temperatures and flow for comparison.