Background In recent years, with the intensification of human agricultural and industrial activities, water pollution had become increasingly prominent, which seriously affects human health. How to establish a reliable water quality prediction model to forecast future water quality trends is a critical scientific issue that urgently needs to be addressed. The Zuli River, as a first-class tributary of the Yellow River, is severely polluted, and the trend of its water quality changes remains unknown.

Methods Taking Zuli River Basin as the study area, we collected the monitoring data (from 2001 to 2021) of ten indicators, including salinity, total hardness, dissolved oxygen (DO), permanganoate index (COD_Mn), chemical oxygen demand (COD), five-day biochemical oxygen demand (BOD₅), ammonia nitrogen (NH₃-N), volatile phenol, hexavalent chromium, and total phosphorus (TP) from five water quality monitoring sections (i.e., Jingyuan, Dayangying, Chankou, Dingxi, and Huining). The main pollution indicators were selected in each section by principal component analysis method. Combined the water quality data of the main pollution indicators with three prediction models, that is, the ARIMA model, GM (1,1) model, and GM (1,1) and Markov combined model, we predicted the water quality of five monitoring sections of the basin from 2001 to 2021.

Results 1) Among three models, GM (1,1) and Markov combined model yielded the most accurate simulations in predicting water quality. Therefore, GM (1,1) and Markov combined model was selected as a reliable water quality prediction model to forecast future water quality trends in the study area. 2) GM (1,1) and Markov combined model was adopted to predict the water quality change of Zuli River Basin in the next ten years. The pollution indicators of water quality in different sections presented a downward trend in the future. In other words, the water quality of the Zuli River was gradually improving, but the water quality was still relatively poor. 3) Among five sections, most of the water quality indicators in the Huining and Chankou section were still worse than class V standard, so it was necessary to pay more attention to the water pollution control work in the areas controlled by Chankou section and Huining section.

Conclusions The result of this study enriches the research of water quality prediction model in the upper reach of the Yellow River Basin and can provide technical reference for soil and water conservation, ecological protection and high-quality development in the Yellow River basin.