A framework based on hidden Markov model with adaptive weighting for microcystin forecasting and early-warning

• Improved CHMM with AEW schemes is proposed as an extension of general CHMM.
• An AEW-CHMM is built to discern similar data patterns to forecast MCs robustly.
• Bayesian hierarchical model is proposed to transform MC problem into Chl-a forecast.
• A novel framework is proposed to integrate MC forecast and early-warning of risk.
• Real case is presented to show the validity of this intelligent decision support tool.

Harmful algal blooms during the eutrophication process produce toxins, such as microcystins (MCs), which endanger the ecosystems and human health. Accurate forecasting and early-warning of MCs can provide theoretical guidance for quick identification of risk in water management systems. The variation of MC concentration is affected by not only the status quo of numerous manifest biotic and abiotic factors, but also a hidden variable that represents the uncertainty of variations of these factors. Traditional approaches focus on fitting data precisely but less consider such a hidden variable, which would experience formidable barriers when encountering fluctuations in time-serial data. In this study, to address the forecasting problem with a hidden state variable and the problem of early-warning-of-risk, we build a novel integrated framework which is consist of three parts: 1) a forecasting model based on a Principal Component Analysis (PCA) and an improved Continuous Hidden Markov Model (CHMM) with adaptive exponential weighting (AEW), where the AEW-CHMM is proposed to forecast both the single-step-ahead concentration for general points and fluctuating points, and the three-step-ahead concentration existing immediately after the fluctuating point; 2) Bayesian hierarchical modeling for a ratio estimation; and 3) revised guidelines for the risk-level grading. The case study tests a real dataset of one shallow lake with the proposed approaches and other supervised machine learning methods. Computational results demonstrate that the proposed approaches are effective to offer an intelligent decision support tool for MC forecasting and early warning of risk by risk-level grading.