Environmental Science and Pollution Research

, Volume 26, Issue 2, pp 1821–1833 | Cite as

Evaluation of the bias and precision of regression techniques and machine learning approaches in total dissolved solids modeling of an urban aquifer

  • Conglian Pan
  • Kelvin Tsun Wai NgEmail author
  • Bahareh Fallah
  • Amy Richter
Research Article


TDS is modeled for an aquifer near an unlined landfill in Canada. Canadian Drinking Water Guidelines and other indices are used to evaluate TDS concentrations in 27 monitoring wells surrounding the landfill. This study aims to predict TDS concentrations using three different modeling approaches: dual-step multiple linear regression (MLR), hybrid principal component regression (PCR), and backpropagation neural networks (BPNN). An analysis of the bias and precision of each models follows, using performance evaluation metrics and statistical indices. TDS is one of the most important parameters in assessing suitability of water for irrigation, and for overall groundwater quality assessment. Good agreement was observed between the MLR1 model and field data, although multicollinearity issues exist. Percentage errors of hybrid PCR were comparable to the dual-step MLR method. Percentage error for hybrid PCR was found to be inversely proportional to TDS concentrations, which was not observed for dual-step MLR. Larger errors were obtained from the BPNN models, and higher percentage errors were observed in monitoring wells with lower TDS concentrations. All models in this study adequately describe the data in testing stage (R2 > 0.86). Generally, the dual-step MLR and hybrid PCR models fared better (R2avg = 0.981 and 0.974, respectively), while BPNN models performed worse (R2avg = 0.904). For this dataset, both regression and machine learning models are more suited to predict mid-range data compared to extreme values. Advanced regression methods (hybrid PCR and dual-step MLR) are more advantageous compared to BPNN.


Total dissolved solids Artificial neural network Principal component regression Multivariate statistical analysis Machine learning methods Bias and precision 


Funding information

The research reported in this paper was supported by a grant from the Natural Sciences and Engineering Research Council of Canada (RGPIN-385815). The authors are grateful for their support. The views expressed herein are those of the writers and not necessarily those of our research and funding partners.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Environmental Systems EngineeringUniversity of ReginaReginaCanada

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