Hierarchical Spatially Varying Coefficient Process Regression for Modeling Net Anthropogenic Nitrogen Inputs (NANI) from the Watershed of the Yangtze River, China

Abstract

The increasing discharge of nitrogen nutrients into watersheds calls for assessing and predicting nitrogen inputs, as an important basis for formulating management strategies. The traditional net anthropogenic nitrogen inputs (NANI) budgeting model relies on 45 predictor variables, for which data are sourced from local or national statistical yearbooks. The large number of predictor variables involved makes NANI accounting difficult, and the missingness of data reduces its accuracy. This study aimed to build a prediction model for NANI based on as few predictor variables as possible. We built a prediction model based on the last 30 years of NANI data from the watershed of the Yangtze River in China, with readily available and complete socio-economic predictor variables (per gross domestic product, population density) through a hierarchical spatially varying coefficient process model (HSVC), which exploits underlying spatial associations within 11 sub-basins and the spatially varying impacts of predictor variables to improve the accuracy of NANI prediction. The results showed that the hierarchical spatially varying coefficient model performed better than the Gaussian process model (GP) and the spatio-temporal dynamic linear model (DLM). The predicted NANIs within the entire catchment of the Yangtze River in 2025 and in 2030 were 11,522.87 kg N km−2 to 12,760.65 kg N km−2, respectively, showing an obvious increasing trend. Nitrogen fertilizer application was predicted to be 5755.1 kg N km−2 in 2025, which was the most significant source of NANI. In addition, the point prediction and 95% interval prediction of NANI in the watershed of the Yangtze River for 2025 and 2030 were also provided. Our approach provides a simple and easy-to-use method for NANI prediction.