A feature reconstruction-based multi-task regression model for cyanobacterial distribution forecasting along the water column

Abstract

Cyanobacterial water pollution has been threatening the cleaner ecosystem and urban sustainability due to the harmfulness to aquatic ecosystems and human health, which triggers the development of an effective forecasting tool for cyanobacterial blooms. Along the water column, the variations in cyanobacteria cell densities show various distribution patterns and are influenced by multiple environmental factors. Most data-driven models treat cyanobacteria forecasting at a specific water depth as a single task, which fails to share knowledge amongst water depths, resulting in unfavourable forecasting accuracy. This is why an increasing number of nonlinear black-box models have been built for cyanobacteria forecasting but at the expense of model interpretability. This study aims to investigate whether forecasting accuracy and model interpretability can be enhanced by (i) using easily accessible predictors and (ii) developing a feature reconstruction-based multi-task regression model with knowledge sharing amongst water depths. Real-world data from a tropical lake are used to evaluate the effectiveness of the model. For the studied lake, the highest average cyanobacteria cell density occurs at 1.0 m, after which it decreases by over 30% at 5.5 m. The correlation coefficients of time-serial cyanobacteria cell densities between adjacent water depths are greater than 0.95 (P < 0.001). The forecasting results indicate that, compared to single-task nonlinear models, 20.59%, 16.25%, and 22.70% error reductions, measured by the mean square error, are achieved for one-day-ahead, two-day-ahead, and three-day-ahead cyanobacterial bloom forecasts. The accurate bloom and non-bloom signals under the proposed model are up to 94.81% and 98.28%. Based on the proposed model, the relative importance of predictors, the sparsity of regression coefficients, and the covariance relationship of regression coefficients can interpret the model adequately and elucidate the mechanism of knowledge sharing and forecasting accuracy improvement.