The Regionalization of National‐Scale SPARROW Models for Stream Nutrients1

Gregory E. Schwarz, Richard B. Alexander, Richard A. Smith, Stephen D. Preston

This analysis modifies the parsimonious specification of recently published total nitrogen (TN) and total phosphorus (TP) national-scale SPAtially Referenced Regressions On Watershed attributes models to allow each model coefficient to vary geographically among three major river basins of the conterminous United States. Regionalization of the national models reduces the standard errors in the prediction of TN and TP loads, expressed as a percentage of the predicted load, by about 6 and 7%. We develop and apply a method for combining national-scale and regional-scale information to estimate a hybrid model that imposes cross-region constraints that limit regional variation in model coefficients, effectively reducing the number of free model parameters as compared to a collection of independent regional models. The hybrid TN and TP regional models have improved model fit relative to the respective national models, reducing the standard error in the prediction of loads, expressed as a percentage of load, by about 5 and 4%. Only 19% of the TN hybrid model coefficients and just 2% of the TP hybrid model coefficients show evidence of substantial regional specificity (more than ±100% deviation from the national model estimate). The hybrid models have much greater precision in the estimated coefficients than do the unconstrained regional models, demonstrating the efficacy of pooling information across regions to improve regional models.