A cluster-based virtual sensing framework for estimating total nitrogen and total phosphorus using sensor-measurable...

In large river basins, water-quality responses exhibit strong spatial heterogeneity because of differences in hydraulic and geomorphic conditions, pollutant-source distributions, and residence times, and this heterogeneity limits the estimation accuracy of single-model virtual-sensor approaches. Total nitrogen (TN) and total phosphorus (TP), in particular, show nonlinear behavior and site-specific responses, highlighting the need for an estimation framework that explicitly incorporates spatial structure. This study proposes a cluster-based virtual-sensing framework that divides a large river basin into spatial clusters with similar water-quality responses and builds independent machine-learning virtual sensors for each cluster to improve TN and TP concentration estimation. Water Quality Monitoring Network (WQMN) data from January 2016 to October 2025 were used. Hierarchical Cluster Analysis (HCA), K-means, and Gaussian Mixture Model (GMM) clustering were applied and compared using multivariate water-quality variables, and the resulting spatial cluster structure was incorporated into the virtual-sensor estimation stage. Random Forest (RF), XGBoost (XGB), and Multilayer Perceptron (MLP) regression models were constructed for each cluster and evaluated through validation. The cluster-based approach showed the clearest complementary effect under restricted input conditions in which direct nutrient-component variables were excluded or only basic sensor variables were used. Relative to the no-cluster framework, the RF-based main cluster framework improved R² by up to approximately 0.045 for TN and 0.029 for TP, with more evident improvements under the component-excluded and basic sensor input conditions. These results demonstrate that combining spatial clustering with machine-learning-based virtual sensors can improve the spatial precision and interpretability of nutrient estimation in large river basins.