A simplified compartmental model for assessing nitrogen flows and losses in dairy effluent management systems: evidence from intensive farms in the Po Valley (Italy)

Introduction Nitrogen management in dairy production systems is a major determinant of environmental performance and nutrient use efficiency, as substantial nitrogen losses can occur along the manure management chain. Although life cycle assessment and nutrient balance approaches are commonly used to estimate emissions, they often provide limited insight into internal nitrogen transformations and provide restricted support for farm-scale decision making. This study aimed to develop a simplified compartmental model to quantify nitrogen flows and losses across the main components of intensive dairy farms. Methods The model combines process-based relationships with a limited set of farm-specific input data, including herd composition, feeding strategy, housing systems, and manure management practices. Nitrogen dynamics are represented through interconnected compartments describing the animal, barn, treatment, storage, and land application phases, enabling the identification of key stages contributing to gaseous nitrogen losses. The model was applied to ten commercial Holstein dairy farms located in the Po Valley (Northern Italy). Results Total gaseous nitrogen losses averaged 7.20 ± 6.43% of nitrogen intake in untreated systems, with ammonia volatilization representing the dominant loss pathway. Farms adopting anaerobic digestion showed increased nitrogen retention in digestate, despite higher overall losses associated with subsequent handling stages. A preliminary comparison between simulated and measured nitrogen concentrations in selected manure and digestate matrices indicated a generally consistent representation of nitrogen partitioning, although systematic overestimations were observed for liquid matrices during the early management stages. Discussion Given the limited number of monitored farms and the absence of a comprehensive quantitative validation, the results should be interpreted as indicative of nitrogen flow patterns rather than precise emission estimates. Nevertheless, the proposed framework provides a transparent and data-efficient tool for exploring farm-specific nitrogen balances, supporting scenario analyses and nutrient management strategies, and contributing to the transition toward more circular and environmentally efficient dairy production systems.