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Non-linear fuzzy-set based uncertainty propagation for improved DO prediction using multiple-linear regression

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Abstract

In this paper, a new non-linear fuzzy-set based methodology is proposed to characterize and propagate uncertainty through a multiple linear regression (MLR) model to predict DO using flow and water temperature as the regressors. The output is depicted as probabilistic rather than deterministic and is used to calculate the risk of low DO concentration. To demonstrate the new method, data from the Bow River in Calgary, Alberta from 2006 to 2008 are used. Low DO concentration has been occasionally observed in the river and correctly predicting, and quantifying the associated uncertainty and variability of DO is of interest to the City of Calgary. Flow, temperature and DO data were used to construct five MLR models, using different combinations of linear and non-linear fuzzy membership functions. The results show that non-linear representation of variance is superior to the linear approach based on model performance. Normal and Gumbel based membership functions produced the best results. The outputs from two non-linear fuzzy membership models were used to calculate risk of low DO. The predicted risk was between 3.9 and 4.9 %. This is an improvement over the traditional method, which can not indicate a risk of low DO for the same time period. This study demonstrates that water resource managers can adequately use MLR models to predict the risk of low DO using abiotic factors.

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Acknowledgments

The authors would like to thank the Natural Sciences and Engineering Research Council of Canada for funding this project, Dr. Cathryn Ryan (Department of Geoscience, University of Calgary) and Dr. Angus Chu (Department of Civil Engineering, University of Calgary) for providing the data sets used in this work. The authors are also grateful for the helpful feedback and comments from two anonymous reviewers.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Victoria, PO Box 3055, Stn. CSC, Victoria, BC, V8W 3P6, Canada

    Usman T. Khan & Caterina Valeo

  2. Department of Civil Engineering, Lakehead University, 955 Oliver Road, Thunder Bay, ON, P7B 5E1, Canada

    Jianxun He

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  1. Usman T. Khan
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  2. Caterina Valeo
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  3. Jianxun He
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Correspondence to Caterina Valeo.

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Khan, U.T., Valeo, C. & He, J. Non-linear fuzzy-set based uncertainty propagation for improved DO prediction using multiple-linear regression. Stoch Environ Res Risk Assess 27, 599–616 (2013). https://doi.org/10.1007/s00477-012-0626-5

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  • DOI: https://doi.org/10.1007/s00477-012-0626-5

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