Stochastic modelling of periodicities and trends for multisite daily rainfall simulation

Trends and periodic movements in climatic series are treated as on-stationary components. A time series model and Bayesian statistics are combined through a Markov chain Monte Carlo procedure. Gibbs sampling is used in the Monte Carlo application. Monthly series of river flow, rainfall and temperature from northern Italy are used. Some late temperature rises are noted, otherwise there are no systematic increases or decreases in the series. Changes in periodicity are also of a random nature. From the results it is also possible to compare these properties between different locations and climatic indicator

Some considerations of periodicityand 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