Dynamic regression modeling of daily nitrate-nitrogen concentrations in a large agricultural watershed

Nitrate-nitrogen concentrations in rivers represent challenges for water supplies that use surface water sources. Nitrate concentrations are often modeled using time-series approaches, but previous efforts have typically relied on monthly time steps. In this study, we developed a dynamic regression model of daily nitrate concentrations in the Raccoon River, Iowa, that incorporated contemporaneous and lags of precipitation and discharge occurring at several locations around the basin. Results suggested that 95 % of the variation in daily nitrate concentrations measured at the outlet of a large agricultural watershed can be explained by time-series patterns of precipitation and discharge occurring in the basin. Discharge was found to be a more important regression variable than precipitation in our model but both regression parameters were strongly correlated with nitrate concentrations. The time-series model was consistent with known patterns of nitrate behavior in the watershed, successfully identifying contemporaneous dilution mechanisms from higher relief and urban areas of the basin while incorporating the delayed contribution of nitrate from tile-drained regions in a lagged response. The first difference of the model errors were modeled as an AR(16) process and suggest that daily nitrate concentration changes remain temporally correlated for more than 2 weeks although temporal correlation was stronger in the first few days before tapering off. Consequently, daily nitrate concentrations are non-stationary, i.e. of strong memory. Using time-series models to reliably forecast daily nitrate concentrations in a river based on patterns of precipitation and discharge occurring in its basin may be of great interest to water suppliers.