A Bayesian approach for estimating phosphorus export and delivery rates with the SPAtially Referenced Regression On Watershed attributes (SPARROW) model

- We use SPARROW to estimate phosphorus delivery rates in the Bay of Quinte.
- Areal export rates from urban sites are higher than those from agricultural lands.
- Agricultural phosphorus export varies considerably among the various crop types.
- Attenuation rates in low flow streams are greater than those with high flow.
- Predictive uncertainty of phosphorus export can delineate “hot-spots” in watersheds.

The SPAtially Referenced Regression On Watershed attributes (SPARROW) model is used to predict total phosphorus (TP) export and delivery rates from different subcatchments in the Bay of Quinte watershed. Bayesian inference techniques were used to account for the uncertainty associated with the existing knowledge from the system as well as the sampling/analytical error of the calibration data. Our analysis suggests that urban areas are characterized by a fairly high areal phosphorus export with an approximate mean estimate of 120 kg of TP per km2 on an annual basis. The contribution of phosphorus from agricultural land can vary considerably among the various crop types (30-127 TP kg per km2), but is generally lower than the impact of urban areas. Crop-specific (oat, wheat, corn, alfalfa, and fallow) export coefficient values were generally on par with those typically reported in the literature. Our analysis also suggests that the attenuation rate in low flow streams (3.7% of TP per kilometer) is distinctly greater than in those with high flow (1.1% of TP per kilometer). Using posterior simulations, we obtained TP loading estimates from ungauged subwatersheds in the area that were twice as high relative to values historically used. The predictive uncertainty of phosphorus export from different sub-basins was also used to delineate “hot-spots” in the Bay of Quinte watershed that may be responsible for significant nutrient fluxes, due to their landscape attributes and soil characteristics. Our predictions can be used as pointers for maximizing the value of information of additional monitoring by determining locations where data collection efforts should focus on. The key findings of the present modelling study will be ultimately linked with process-based models developed for the receiving waterbody to shed light on the causal connections among phosphorus loading, sediment-water column interactions, and plankton community response.