Stochastic Models for Monthly Rainfall Forecasting and Synthetic Generation

Abstract

The Integrated Autoregressive Moving Average (ARIMA) model was applied to the average monthly rainfall time series over 15 basins located in Indiana, Illinois and Kentucky, with areas varying between 240 and 4000 mi2 approximately. The record length varied from 492 to 684 months. The first-order, mixed, autoregressive, moving average model emerged as the most suitable one for forecasting and generation of cyclicly standardized monthly rainfall square roots series. The model passed the goodness-of-fit test in all cases studied. The seasonally differenced, multiplicative model applied to monthly rainfall square roots also passed the goodness-of-fit test in all cases. This model has the advantage of requiring fewer parameters than the previous one. However, the use of the differenced models is limited to forecasting of monthly rainfall series and cannot be used for the generation of synthetic rainfall time series, as it does not preserve the monthly standard deviations. Seasonal differencing is effective in removing the periodicities but distorts the spectral structure of the original rainfall series, whereas cyclic standardization only introduces a negligible distortion in the random component while effectively removing the circularly stationary part.