A Machine Learning Approach for Probabilistic Multi-Model Ensemble Predictions of Indian Summer Monsoon Rainfall

Abstract

Due to the uncertainty associated with Indian summer monsoon rainfall (ISMR), probabilistic seasonal forecasts which can convey the inherent uncertainty of ISMR are more useful to the user community than a single deterministic forecast. While such probabilistic seasonal forecasts can be produced from general circulation model (GCM) output, one single model generally does not represent all sources of error. The probabilistic multi model ensemble (PMME) is a well-accepted way to improve on the skill of probabilistic forecasts by individual GCMs. PMME can be constructed with one of two approaches: non-parametric, or parametric with respect to the occurrence of three categories of seasonal total rainfall—below, near, and above normal as defined by the climatological base period. Both the methods have their limitations. Non-parametric PMME use a smaller ensemble size which results in overconfident forecasts, and parametric PMME make the inaccurate assumption that total rainfall follows a Gaussian distribution. To avoid these problems, we propose the use of the Extreme Learning Machine (ELM), a novel machine learning (ML) approach, to construct PMME for ISMR forecasting. ELM is a state-of-the-art generalized form of single-hidden-layer feed-forward neural network. However, since the traditional ELM network only produces a deterministic outcome, we use a modified version of ELM called Probabilistic Output Extreme Learning Machine (PO-ELM). PO-ELM uses sigmoid additive neurons and slightly different linear programming to make probabilistic predictions. The performance of such PO-ELM based PMME is assessed rigorously in terms of Generalized Receiver Operating Characteristic scores and reliability diagrams over a 37 years period spanning from 1982 to 2018 following a leave-three-year-out cross-validation scheme. It is demonstrated that our new strategy for PMME based on ML is capable of producing skillful MME forecasts over large regions of India.