Spatially referenced watershed models for the binational Red–Assiniboine River Basin: Bayesian vs frequentist comparison

Excess nutrient loading remains a leading cause of declining water quality in lakes, estuaries, and coastal waters worldwide, with global economic costs of US\$200 billion – US$2 trillion annually from impacts on fisheries, tourism, freshwater resources, and water treatment. Our study focuses on total phosphorus (TP) in Lake Winnipeg and its binational Red-Assiniboine River Basin, where nutrient inputs have degraded water quality and increased cyanobacterial blooms. These changes pose ecological, public health, and economic risks. We applied a spatially referenced watershed model with a hybrid statistical-mechanistic structure partitioning annual nutrient loads into land-use export, land-to-water delivery, and in-reservoir decay. Bayesian and traditional frequentist model calibrations were compared. In the frequentist model, coefficients for agricultural inputs, forests /wetlands, stream channels, precipitation, and reservoir losses were statistically significant, whereas coefficient for wastewater was not. In contrast, all variables were successfully calibrated using the Bayesian approach. Model results delineate TP-export hotspots across the basin, showing that 54–62% of TP originates from the U.S., with agricultural sources ranging 62–72%—highlighting the importance of agriculture-focused Best Management Practices. Given the global relevance of nutrient-driven water-quality challenges, our results highlight Bayesian calibration for robust risk assessment and adaptive nutrient management.