A water quality model for distributed nutrient load estimation in sparsely monitored catchments

Nutrient pollution in freshwater systems remains a major environmental challenge, driving eutrophication, and ecological degradation, and requiring robust modelling tools to support effective water management. However, catchment-scale water quality modelling is often constrained by sparse and uneven monitoring networks, scale mismatches between processes and observations, and high parameter uncertainty associated with complex biogeochemical dynamics. These limitations hinder reliable load estimation, pollution sources identification, and scenario analysis, particularly in large and data-scarce catchments.

This study presents an integrated modelling framework combining the existing MOBIDIC hydrological model with a newly developed BIO–ALGAE reactive component, to simulate nutrient dynamics at the catchment scale. The model simulates eight key water quality constituents, including dissolved oxygen, carbonaceous biochemical oxygen demand, organic and inorganic nitrogen and phosphorus species, and algal biomass. To address parameter non-identifiability and spatial heterogeneity, the framework employs a spatially regularized ensemble calibration strategy using the PEST++ iterative ensemble smoother. This ensemble-based framework enables efficient estimation of spatially distributed diffuse loads while providing a robust quantification of predictive uncertainty. Tikhonov regularization is employed to enforce spatial smoothness of the parameters, while a combination of localization matrices and singular value decomposition is used to stabilize the inversion in high-dimensional parameter spaces.

The model was applied to the Arno River catchment (7990 km²) in central Italy, simulating water quality dynamics over a ten-year period (2011–2020) across a network of more than 3600 river reaches. Calibration relied on 8151 spot observations from 70 monitoring stations. Despite the sparse and discontinuous nature of the dataset, the model demonstrated good predictive capability across multiple constituents and successfully reproduced observed spatial and temporal patterns. The results revealed pronounced pollution hotspots, particularly associated with urban and peri-urban areas, characterized by elevated ammonium and organic loads, while phosphorus exhibited a more heterogeneous distribution indicative of multiple source contributions.

Despite limitations under low dissolved oxygen conditions, the approach captured first-order reactive processes and provided spatially explicit load estimates with uncertainty bounds. This framework offers a practical decision-support tool for targeted water quality management in data-scarce catchments.

 

Acknowledgements

This work was carried out within RETURN Extended Partnership and received funding from the European Union Next-GenerationEU (National Recovery and Resilience Plan – NRRP, Mission 4, Component 2, Investment 1.3 – D.D. 1243 2/8/2022, PE0000005). The authors also wish to acknowledge Fondazione Cassa di Risparmio Firenze for co-funding this work within the project ECO-C – “ECOidrologia dei corsi d’acqua urbani nel contesto dei Cambiamenti climatici e socioeconomici”.