Stochastic modelling of annual rainfall data

Rainfall data are generally required in computer simulations of rainfall-runoff processes, crop growth and water supply systems. The length of historical climate data is usually not long enough to describe the complete range of variability that might be experienced during the life of a water resources or agricultural project. Using the statistical characteristics of historical data, it is possible to generate many sequences of data that better represent the climatic variability. In developing the stochastic models, the data are generally assumed stationary in the broad sense and any long-term fluctuations in the data are ignored. Typically, only in monthly, daily and sub-daily models, is the seasonal variation within a year considered explicitly in stochastic models. However, there is a growing interest and concern about the role of interdecadal variability in climate and its influence on rainfall. One approach is to identify any long-term fluctuations in the observed rainfall and model them explicitly. Empirical Mode Decomposition (EMD) was used to identify any low frequency fluctuations in annual rainfall data from 44 sites in Australia. The results did not allow easy identification of low frequency fluctuations in the data. As a means of aiding interpretation of the EMD results, the following ploy was adopted. The AR1 model, the most widely used model for the generation of annual rainfall data, was used to generate stochastic data based on the statistics of the observed sequences and the EMD analysis was performed on the stochastic data sets. The results of the analysis comparing both the historical and generated data showed that, in general, both the data sets have similar low frequency characteristics except for Perth