Chaotic Modeling of Stream Nitrate Concentration and Transportation via IFPA-ESN and Turning Point Analyses

Increased concentrations of nitrogenous compounds in stream networks are detrimental to the health of both humans and ecosystems. Monitoring, modeling, and forecasting nitrate concentration in the temporal domain are essential for an in-depth understanding of nitrate dynamics and transformation within stream networks. In this study, an advanced chaotic modeling and forecasting approach integrated with turning point analysis is proposed. First, the time-series daily nitrate concentrations in the form of nitrate-nitrite were reconstructed based on the chaotic characteristics and then input into the forecasting models. Second, an echo state network (ESN) was developed for one-day-ahead nitrate concentration forecasting, and the hyperparameters were optimized through an improved flower pollination algorithm (IFPA) to achieve a high efficiency. Furthermore, turning point analysis was performed to quantify the relationship between discharge and peak nitrate concentration. The Ricker function was fitted, and the parameters were estimated for turning points using the forecasted nitrate concentration and measured discharge. Field data, including daily stream nitrate concentration and information on discharge collected from eight different monitoring sites in the southern Sichuan Basin, China, were utilized for case studies. A comparative analysis was performed under three modeling scenarios, viz. conventional time-series modeling, temporal signal decomposition, and data reconstruction and embedding with chaotic characteristics. Four benchmark time-series forecasting algorithms were compared against the proposed IFPA-ESN in the above-mentioned scenarios. For each site, parameters of the Ricker functions were estimated, and turning points were computed based on the forecasted nitrate concentration and discharge. Computational results validated the superiority of the proposed approach in improving the accuracy of stream nitrate concentration prediction. The limitations to the supply and transportation of nitrogenous compounds were quantified, which would be valuable for pollution mitigation in the future.