A Wavelet-Based Second Order Nonlinear Model for Forecasting Monthly Rainfall

In this article, a rainfall forecasting model using monthly historical rainfall data and climate indices is developed by incorporating wavelet analysis (WA) and second order volterra nonlinear model. The monthly rainfall time series and large-scale climate index time series are decomposed using wavelets into a certain number of component subseries at different temporal scales. The lag relationship between the rainfall anomaly and each potential predictor is identified by cross correlation analysis with a lag time of at least 1 month at different temporal scales. The components of predictor variables with known lag times are then integrated using a second order Volterra model. Further, orthogonal least squares method is used to reduce the redundant variables and select the significant variables to be included into the final forecast model. The proposed multivariate wavelet nonlinear rainfall forecasting method is examined with over three places in India, and compared to the traditional ANN model based on the original time series and linear wavelet regression model. The models are trained with data from the 1916 to 1968 period and then tested in the 1968-1989 period. The results show that the proposed wavelet nonlinear model provides considerably more accurate monthly rainfall forecasts for the three selected places in India than the traditional regression model, neural networks model and the wavelet based linear model. It was seen that for the proposed models and other models also, both the past rainfall and the large-scale climate signals were useful in forecasting the future.