A nonlinear autoregressive exogenous (NARX) model to predict nitrate concentration in rivers

Environ Sci Pollut Res Int. 2022 Jun;29(27):40623-40642. doi: 10.1007/s11356-021-18221-8. Epub 2022 Jan 27.


Forecasting nitrate concentration in rivers is essential for environmental protection and careful treatment of drinking water. This study shows that nonlinear autoregressive with exogenous inputs neural networks can provide accurate models to predict nitrate plus nitrite concentrations in waterways. The Susquehanna River and the Raccoon River, USA, were chosen as case studies. Water discharge, water temperature, dissolved oxygen, and specific conductance were considered exogenous inputs. The forecasting sensitivity to changes in the exogenous input parameters and time series length was also assessed. For Kreutz Creek at Strickler station (Pennsylvania), the prediction accuracy increased with the number of exogenous input variables, with the best performance achieved considering all the variables (R2 = 0.77). The predictions were accurate also for the Raccoon River (Iowa), although only the water discharge was considered exogenous input (South Raccoon River at Redfield-R2 = 0.94). Both short- and long-term predictions were satisfactory.

Keywords: Machine learning; NARX; Nitrate forecasting; Raccoon River; River water quality; Susquehanna River.

MeSH terms

  • Environmental Monitoring
  • Neural Networks, Computer
  • Nitrates*
  • Nitrogen Oxides
  • Rivers*
  • Water


  • Nitrates
  • Nitrogen Oxides
  • Water