Interpretable CEEMDAN-FE-LSTM-transformer hybrid model for predicting total phosphorus concentrations in surface water

Abstract

The complexity of the biogeochemical cycle of phosphorus in lakes makes it challenging to produce efficient and accurate predictions of total phosphorus (TP) concentrations. In this study, a hybrid model is developed for TP predictions. This model combines the Complete ensemble empirical mode decomposition with adaptive noise, Fuzzy entropy, Long short-term memory, and Transformer (CF-LT). The introduction of data split-frequency reconstruction effectively solves the problems of over- and underfitting suffered by previous machine learning models in the face of high-dimensional data, while an attention mechanism overcomes the inability of these models to establish long-term dependencies between data when making long-term predictions. The CF-LT model is applied to predict TP concentrations from January 1, 2015, to December 31, 2020, at Yaoxiangqiao, Zhihugang, and Guanduqiao, three national water quality monitoring stations at the inlet of Taihu Lake, China. Moreover, the Shapley additive explanations are used to interpret the CF-LT model and identify the essential input features. The prediction results demonstrate that the CF-LT model achieves a coefficient of determination (R2) of 0.37–0.87 on the test dataset, representing an improvement of 0.05–0.17 (6%-85%) over the control models. In addition, the CF-LT model provides the best peak value predictions. The model interpretation results indicate that the turbidity and total nitrogen are the essential factors influencing TP predictions. This demonstrates that the TP concentrations at the inlet of Taihu Lake are closely related to the non-point pollution discharge and the status of aquatic plants. It's worth noting that these two indicators exert a more significant influence on the prediction of TP during wet season. This work provides a viable modeling strategy for predicting TP concentrations and guidance for early warning and treatment of surface water eutrophication in the Taihu Lake basin.