Characterizing Spatiotemporal Variability in Phosphorus Export across the United States through Bayesian Hierarchical Modeling

Phosphorus inputs from anthropogenic activities are subject to hydrologic (riverine) export, causing water quality problems in downstream lakes and coastal systems. Nutrient budgets have been developed to quantify the amount of nutrients imported to and exported from various watersheds. However, at large spatial scales, estimates of hydrologic phosphorus export are usually unavailable. This study develops a Bayesian hierarchical model to estimate annual phosphorus export across the contiguous United States, considering agricultural inputs, urban inputs, and geogenic sources under varying precipitation conditions. The Bayesian framework allows for a systematic updating of prior information on export rates using an extensive calibration data set of riverine loadings. Furthermore, the hierarchical approach allows for spatial variation in export rates across major watersheds and ecoregions. Applying the model, we map hotspots of phosphorus loss across the United States and characterize the primary factors driving these losses. Results emphasize the importance of precipitation in determining hydrologic export rates for various anthropogenic inputs, especially agriculture. Our findings also emphasize the importance of phosphorus from geogenic sources in overall river export.