Stochastic export coefficient model to predict annual variation in phosphorus loading from diffuse runoff

A stochastic export coefficient (EC) model is needed to predict variation in annual diffuse or nonpoint source nutrient loads and develop realistic river basin management plans. This study aimed to develop such a model by using observed discharge occurrence probability to: a) select EC values from a probabilistic database covering all US river basins; and b) adjust the delivery ratio value, transforming edge of field loads into basin outlet loads via riverine storage. The model was tested in three river basins from Colorado, New York, and Ohio, with sizes ranging from 742 to 3450 km2, where observed loads of total phosphorus had been recorded for 27 to 38 years; the first three years of data were used to calibrate a single parameter, the base delivery ratio in the new model. The stochastic EC model was compared to the standard EC model, i.e., deterministic and temporally static. The stochastic EC model outperformed the standard EC model, with on average 74% lower root mean square error (RMSE) and had better coefficients of determination (R2), and statistically significant temporal correlation with observed loads (p < 0.01). The stochastic EC model has flexibility with observed discharge inputs, and based on statistical tests its predictions were equally accurate using discharge data from any representative tributary in a multi-tributary basin, and were only slightly less accurate when using annual in place of daily discharge time series. The stochastic EC model is within the i-Tree Buffer toolkit to assist river basin nutrient management plans by automating simulations, bounding estimates with uncertainty, providing default parameters, and allowing inputs of observed or predicted discharge time series.Research-impact statement: This study presents a Stochastic Export Coefficient Model within the i-Tree Buffer model to assist with nutrient management plans for river basins. This research is the first to utilize the high spatial resolution US federal dataset of export coefficients to generate variation in annual loading and match time series observations.