The employment of polynomial chaos expansion approach for modeling dissolved oxygen concentration in river

  • Behrooz Keshtegar
  • Salim HeddamEmail author
  • Hamidreza Hosseinabadi
Original Article


This article proposes a novel methodology based on polynomial chaos expansions (PCE) for predicting dissolved oxygen (DO) concentration in rivers using four water quality variables as predictors: water temperature, turbidity, pH, and specific conductance. The proposed model is compared to the multilayer perceptron neural network (MLPNN), multilayer perceptron neural network optimized particle swarm optimization (MLPNN_PSO) and the standard multiple linear regression (MLR) with respect to their capabilities for predicting DO. The model results were evaluated using coefficient of correlation (R), Nash–Sutcliffe efficiency (NSE), root mean squared error (RMSE), and mean absolute error (MAE). Using data from more than three stations, operated by the United States Geological Survey (USGS), we demonstrated that that PCE model provides better predicting performance among the different models. Using the four water quality variables led to the best performances of PCE model for modelling DO at all three stations with R and NSE ranging from 0.931 to 0.970, and 0.866 to 0.938, respectively. MLPNN_PSO ranked next with R and NSE which ranged between 0.931 and 0.967, and 0.867 to 0.934, respectively. MLPNN ranked in the third place with R and NSE ranged between 0.921 and 0.966, and 0.849 to 0.931, for the three stations respectively. MLR models led to the worst results with R and NSE ranged between 0.907 and 0.961, and 0.822 to 0.922, respectively. According to the obtained results, PCE model is considered to be a good alternative to the direct measurement of DO concentration in river.


Polynomial chaos expansions Neural network Particle swarm optimization Multiple linear regression Dissolved oxygen Water quality 



Many thanks to Stewart Rounds from Oregon water science center (USGS) for providing the necessary information related to the description of the study area and details of the stations. We would like to thank all scientists from USGS for allowing permission for using the data that made this study possible. We would like to thank anonymous reviewers and the editor of Environmental Earth Science journal for their invaluable comments and suggestions on the contents of the manuscript which significantly improved the quality of the paper.

Supplementary material

12665_2018_8028_MOESM1_ESM.docx (77 kb)
Supplementary material 1 (DOCX 77.078 KB)


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Civil Engineering, Faculty of EngineeringUniversity of ZabolZabolIran
  2. 2.Faculty of Science, Agronomy DepartmentHydraulics Division UniversitySkikdaAlgeria

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