###### Abstract  
Water is a critical resource globally, covering approximately 71% of the Earth's surface. Employing analytical models to forecast water quality parameters based on historical data is a key strategy in the field of water quality monitoring and treatment. By using a forecasting model, potential changes in water quality can be understood over time. In this study, the gated recurrent unit (GRU) neural network was utilized to forecast dissolved oxygen levels following variational mode decomposition (VMD). The GRU neural network's parameters were optimized using the grey wolf optimizer (GWO), leading to the development of a VMD-GWO-GRU model for forecasting water quality parameters. The results indicate that this model outperforms both the standalone GRU model and the GWO-GRU model in capturing key information related to water quality parameters. Additionally, it shows improved accuracy in forecasting medium to long-term water quality changes, resulting in reduced root mean square error (RMSE) and mean absolute percentage error (MAPE). The model demonstrates a significant improvement in the lag of forecasting water quality parameters, ultimately boosting forecasting accuracy. This approach can be applied effectively in both monitoring and forecasting water quality parameters, serving as a solid foundation for future water quality treatment strategies. water quality parametric forecast; variational mode decomposition; gated recurrent unit neural networks; grey wolf optimizer +
Footnote †: journal: _aciences_  
instance, [PERSON] et al. [9] aim to forecast the long-term effects of rapid population growth on the quality of a river water body in the near future using a deformed-derivative, cumulative, grey, multi-convolution model. In order to improve the accuracy of their model, they incorporated the accumulation of deformed derivatives. Research on the grey model has shown that the model is faster at forecasting small samples of data, yet the methodology employs a limited quantity of sample data, rendering it challenging to discern the long-term characteristics of the water quality parametric data. [PERSON] et al. [10] devised a method for assessing changes in water quality parameters and turning points in trends by integrating segmented regression and locally weighted polynomial regression methods. Good prediction results were obtained and the research records demonstrated that the method was efficient. Regression analysis is a highly scalable technique, but it does have a significant drawback: it necessitates the utilization of a substantial quantity of sample data, and it cannot be guaranteed that it will yield accurate results when forecasting long-term series [11]. As a matter of fact, water quality parameters are a dynamically changing time series with historical characteristics, and their prediction process is progressive, with strong correlation between current and historical water quality parameters [12]. Among time series domain forecasting methods, traditional methods such as the autoregressive integrated moving average (ARIMA) and modern machine learning methods such as the transformer each play their respective roles. A water quality prediction method combining ARIMA and clustering models was employed by [PERSON] et al. [13]. Their prediction object was selected to be the water quality TP index, and ARIMA was utilized for forecasting the water quality parameters, resulting in satisfactory water quality prediction outcomes. To enhance the accuracy and reliability of time series prediction, [PERSON] et al. introduced an integrated learning model known as GATE [14]. This model addresses overfitting in deep learning by optimizing parameters within the integrated structure. It utilizes sample loss and weight update functions, along with unsupervised learning strategies, to guide network output. Empirical findings demonstrate that the GATE model outperforms existing models when dealing with long-term prediction tasks.