Comparative study between linear and non-linear modelling techniques in rainfall forecasting for South Australia

Abstract

Australian rainfall is highly variable in nature and largely influenced by the several large scale remote climate drivers. Several past studies tried to establish the relationships between climate predictors (El Nino Southern Oscillation (ENSO), Indian Ocean Dipole (IOD) and Southern Annular Mode (SAM)) and rainfalls over Australia. However, the relationship between climate predictors and South Australian rainfall is still unclear. Most of the past studies in this region have been carried out based on the individual and concurrent relationship of climate drivers with rainfall. Moreover, the combined relationship considering lagged-time effects of multiple climate predictors has not previously been attempted in South Australia. This paper presents the application of linear Multiple Regression (MR) analysis and non-linear Artificial Neural Networks (ANN) modelling to forecast long-term seasonal rainfall in South Australia using the potential climate predictors. A rainfall station in South Australia was chosen as case study to broadly explore this present hypothesis. The use of combined lagged ENSO-IOD-SAM climate input sets for calibrating and validating the ANN and MR Models was proposed to investigate the effect of past values of these major climate modes on long-term spring rainfall. The ANN model was developed in the form of multilayer perceptron using Levenberg-Marquardt algorithm. Early stopping techniques were used to analyze the improvement in the network's generalization ability. Both the MR and ANN modelling were assessed statistically using root mean square error (RMSE), Pearson correlation (R) and Willmott index of agreement (d). Finally the superiority of rainfall predictability methods was established by comparing the both linear and non-linear techniques. The developed MR and ANN models were tested on out-of-sample test sets; the MR models showed poor generalization ability than non-linear ANN models. This study found that predicting spring rainfall using combined lagged ENSO-DMI-SAM climate indices with ANN can achieve better correlation as compared to multiple regressions. The study discovered that lagged DMI-SAM combined climate model has more effect on spring rainfall predictability than other combinations of climate model. It was observed that ANN modelling is able to provide higher correlations using the lagged-indices to forecast spring rainfall in compared to linear methods. Using the combination of DMI-SAM dual climate indices in an ANN model increased the model correlation up to 87%, 76% and 37% for the three combined climate predictor's models in forecasting South Australian spring rainfall. Whereas, those rainfall predictability was 52%, 49% and 18% respectively in case of linear MR modelling. The errors of the testing sets for ANN models are generally lower compared to multiple regression models. The statistical analysis suggested the potentials of non-linear artificial intelligence techniques (ANN) over linear MR models for rainfall forecasting using large scale climate modes. This method can be used for other parts of the world where a relationship exists between rainfall and large scale climate modes which could not be established by linear methods.