A multivariate EMD-LSTM model aided with Time Dependent Intrinsic Cross-Correlation for monthly rainfall prediction

Abstract

Accurate prediction of rainfall is a complex problem because of the large number of controlling factors, complex interrelationships between them and the multiscaling behaviour of the process. Because of the multiscaling behaviour of the problem, the use of hybrid modelling involving decomposition techniques is preferable over strenuous physical models and standalone driven techniques for accurate rainfall predictions. This study proposes a novel hybrid modelling framework integrating Long Short Term Memory (LSTM) and Multivariate Empirical Mode Decomposition (MEMD) aided with Time Dependent Intrinsic Cross-Correlation (TDICC) analysis algorithm for monthly rainfall predictions. The application of the proposed model is demonstrated for monthly rainfall prediction of 2005–2015 period at All India spatial domain considering El-Niño Southern Oscillation(ENSO), Indian Ocean Dipole(IOD) and five antecedent values of rainfall are the input variables. The proposed framework first uses MEMD to obtain a set of orthogonal components namely Intrinsic Mode Functions (IMFs) identifying and aligning the common scales embedded in the multiple input variables considered. Subsequently, scale specific rainfall information are predicted by incorporating them on relevant IMFs and their significant lags identified through TDIC and TDICC analyses. Final aggregation of predicted rainfall components from different scales gives the monthly rainfall of a generic time step ahead. The efficacy of the proposed MEMD-TDICC-LSTM framework is compared with five other hybrid models such as MEMD-TDIC-ANN, MEMD-TDICC-ANN, MEMD-ACO-ANN, MEMD-ACO-LSTM and MEMD-TDIC-LSTM, which used Time Dependent Intrinsic Correlation (TDIC) and Ant Colony Optimization (ACO) for predictor selection and Artificial Neural Network (ANN) as modelling tool. The study has used different graphical representations and ten different statistical performance evaluation measures for the prediction of validation period, it is observed that the proposed model could achieve a predictive skill of 0.98, Nash-SutcliffeEfficiency (NSE) of 0.95 and Index of Agreement (IA) of 0.91 which is better than all the five remaining models. The capability of MEMD-TDICC-LSTM model to predict the extremes is also confirmed by using the bar graph for the drought year rainfall of 2009 and is observed that the model is successful in capturing the extremes with an annual rainfall 975.16 mm closer to observed value 927.3 mm. MEMD algorithm facilitates the inclusion of multiple large scale climatic oscillations as inputs and their multi time scale decomposition, TDICC helps to fix the relevant inputs at different time scales and the LSTM functions as the robust modelling tool. Further, the framework using this specific combination resulted in substantial reduction in modelling complexity and faster execution, as the approach considers only the most relevant and significant inputs in the process.