A New Hybrid Deep Sequence Model for Decomposing, Interpreting, and Predicting Sulfur Dioxide Decline in Coastal Cities of Northern China

Guoju Wang, Rongjie Zhu, Xiang Gong (), Xiaoling Li, Yuanzheng Gao, Wenming Yin, Renzheng Wang, Huan Li, Huiwang Gao and Tao Zou ()
Additional contact information
Guoju Wang: School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China
Rongjie Zhu: Tandon School of Engineering, New York University, Brooklyn, NY 10012, USA
Xiang Gong: School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China
Xiaoling Li: School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China
Yuanzheng Gao: School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China
Wenming Yin: School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China
Renzheng Wang: College of Environmental Science and Engineering, Ocean University of China, Qingdao 266071, China
Huan Li: National Marine Data and Information Service, Ministry of Natural Resources, Tianjin 300171, China
Huiwang Gao: Frontiers Science Center for Deep Ocean Multispheres and Earth System, Ocean University of China, Qingdao 266071, China
Tao Zou: Key Laboratory of Coastal Environmental Processes and Ecological Remediation, Yantai Institute of Coastal Zone Research, Chinese Academy of Sciences, Yantai 264003, China

Sustainability, 2025, vol. 17, issue 6, 1-30

Abstract: The recent success of emission reduction policies in China has significantly lowered sulfur dioxide (SO 2 ) levels. However, accurately forecasting these concentrations remains challenging due to their inherent non-stationary tendency. This study introduces an innovative hybrid deep learning model, RF-VMD-Seq2Seq, combining the Random Forest (RF) algorithm, Variational Mode Decomposition (VMD), and the Sequence-to-Sequence (Seq2Seq) framework to improve SO 2 concentration forecasting in five coastal cities of northern China. Our results show that the predicted SO 2 concentrations closely align with observed values, effectively capturing fluctuations, outliers, and extreme events—such as sharp declines the Novel Coronavirus Pneumonia (COVID-19) pandemic in 2020—along with the upper 5% of SO 2 levels. The model achieved high coefficients of determination (>0.91) and Pearson’s correlation (>0.96), with low prediction errors (RMSE < 1.35 μg/m 3 , MAE < 0.94 μg/m 3 , MAPE < 15%). The low-frequency band decomposing from VMD showed a notable long-term decrease in SO 2 concentrations from 2013 to 2020, with a sharp decline since 2018 during heating seasons, probably due to the ‘Coal-to-Natural Gas’ policy in northern China. The input sequence length of seven steps was recommended for the prediction model, based on high-frequency periodicities extracted through VMD, which significantly improved our model performance. This highlights the critical role of weekly-cycle variations in SO 2 levels, driven by anthropogenic activities, in enhancing the accuracy of one-day-ahead SO 2 predictions across northern China’s coastal regions. The results of the RF model further reveal that CO and NO 2 , sharing common anthropogenic sources with SO 2 , contribute over 50% to predicting SO 2 concentrations, while meteorological factors—relative humidity (RH) and air temperature—contribute less than 20%. Additionally, the integration of VMD outperformed both the standard Seq2Seq and Ensemble Empirical Mode Decomposition (EEMD)-enhanced Seq2Seq models, showcasing the advantages of VMD in predicting SO 2 decline. This research highlights the potential of the RF-VMD-Seq2Seq model for non-stationary SO 2 prediction and its relevance for environmental protection and public health management.

Keywords: Variational Mode Decomposition (VMD); Sequence-to-Sequence model; input sequence length; prediction; interpretation (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2025
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