Multi-stage hybridized online sequential extreme learning machine integrated with Markov Chain Monte Carlo copula-Bat algorithm for rainfall forecasting

To ameliorate agricultural impacts due to persistent drought-risks by promoting sustainable utilization and pre-planning of water resources, accurate rainfall forecasting models, addressing the dynamic nature of drought phenomenon, is crucial. In this paper, a multi-stage probabilistic machine learning model is designed and evaluated for forecasting monthly rainfall. The multi-stage hybrid MCMC-Cop-Bat-OS-ELM model utilizing online-sequential extreme learning machines integrated with Markov Chain Monte Carlo (MCMC) based bivariate-copula and the Bat algorithm is employed to incorporate significant antecedent rainfall (t-1) as the model's predictor in the training phase. After computing the partial autocorrelation function (PACF) at the first stage, twenty-five MCMC based copulas (i.e., Gaussian, t, Clayton, Gumble, Frank and Fischer-Hinzmann etc.) are adopted to determine the dependence of antecedent month's rainfall with the current and future rainfall at the second stage of the model design. Bat algorithm is applied to sort the optimal MCMC-copula model by a feature selection strategy at the third stage. At the fourth stage, PACF's of the optimal MCMC-copula model are computed to couple the output with OS-ELM algorithm to forecast future rainfall values in an independent test dataset. As a benchmarking process, standalone extreme learning machine (ELM) and random forest (RF) is also integrated with MCMC based copulas and the Bat algorithm, yielding a hybrid MCMC-Cop-Bat-ELM and a MCMC-Cop-Bat-RF models. The proposed multi-stage hybrid model is tested in agricultural belt region in Faisalabad, Jhelum and Multan, located in Pakistan. The testing performance of all three hybridized models, according to robust statistical error metrics, is satisfactory in comparison to the standalone counterparts, however the multi-stage, hybridized MCMC-Cop-Bat-OS-ELM model is found to be a superior tool for forecasting monthly rainfall. This multi-stage probabilistic learning model can be explored as a pertinent decision-support tool for agricultural water resources management in arid and semi-arid regions where a statistically significant relationship with antecedent rainfall exists.