A wavelet-based multiple linear regression model for forecasting monthly rainfall

In this article, a rainfall forecasting model using monthly historical rainfall data and climate indices is developed by incorporating the multi-resolution analysis (MRA) and multiple linear regression (MLR) model. The monthly rainfall anomaly and large-scale climate index time series are decomposed using MRA into a certain number of component subseries at different temporal scales. The hierarchical lag relationship between the rainfall anomaly and each potential predictor is identified by cross correlation analysis with a lag time of at least one month at different temporal scales. The components of predictor variables with known lag times are then screened with a stepwise linear regression algorithm to be selectively included into the final forecast model. This MRA-based rainfall forecasting method is examined with 46 stations over South Australia, and compared to the traditional MLR model based on the original time series. The models are trained with data from the 1959-1995 period and then tested in the 1996-2008 period for each station. The performance is compared with observed rainfall values, and evaluated by common statistics of relative absolute error and correlation coefficient. The results show that the proposed MRA-based model provides considerably more accurate monthly rainfall forecasts for all of the selected stations over South Australia than the traditional regression model. For the MRA-based method, historical rainfall is consistently useful for all examined stations, while the large-scale climate signals are only partly useful for some stations.