A New Approach to Predict Daily pH in Rivers Based on the “à trous” Redundant Wavelet Transform Algorithm

  • Taher Rajaee
  • Masoud Ravansalar
  • Jan F. Adamowski
  • Ravinesh C. Deo


Prediction of pH is an important issue in managing water quality in surface waters (e.g., rivers, lakes) as well as drinking water. The capacity of artificial neural network (ANN), wavelet-artificial neural network (WANN), traditional multiple linear regression (MLR), and wavelet-multiple linear regression (WMLR) models to predict daily pH levels (1, 2, and 3 days ahead) at the Chattahoochee River gauging station (near Atlanta, GA, USA) was assessed. In the proposed WANN model, the original time series of pH and discharge (Q) were decomposed (after being split into training and testing series) into several sub-series by the the à trous (AT) wavelet transform algorithm. The wavelet coefficients were summed to obtain useful input time series for the ANN model to then develop the WANN model for pH prediction. The redundant à trous algorithm was used for data decomposition. Model implementation indicated the values of 1-day-ahead pH predicted by the WANN model closely matched the observed values (with a coefficient of determination, R2 = 0.956; Root Mean Square Error, RMSE = 0.019; and Mean Absolute Error, MAE = 0.015). It is therefore possible that the WANN model’s accuracy can be attributed to its better predictive ability (due to the use of the AT) to remove the noise caused by pH shifts (e.g., acid precipitation). Peak pH values predicted by the WANN model were also closer to observed values compared to the other machine learning models.


Artificial neural network Multiple linear regression ‘à trous’ algorithm River water quality pH 


Funding Information

This research was partially funded by an NSERC Discovery and Accelerate Grant held by Jan Adamowski.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Taher Rajaee
    • 1
  • Masoud Ravansalar
    • 1
  • Jan F. Adamowski
    • 2
  • Ravinesh C. Deo
    • 3
  1. 1.Department of Civil EngineeringUniversity of QomQomIran
  2. 2.Department of Bioresource EngineeringMcGill UniversitySainte-Anne-de-BellevueCanada
  3. 3.School of Agricultural, Computational and Environmental Sciences, Institute of Agriculture and Environment (IAg& E)University of Southern QueenslandSpringfieldAustralia

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