University of Oulu

Roohollah Noori, Ali Mirchi, Farhad Hooshyaripor, Rabin Bhattarai, Ali Torabi Haghighi, Bjørn Kløve, Reliability of functional forms for calculation of longitudinal dispersion coefficient in rivers, Science of The Total Environment, Volume 791, 2021, 148394, ISSN 0048-9697,

Reliability of functional forms for calculation of longitudinal dispersion coefficient in rivers

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Author: Noori, Roohollah1; Mirchi, Ali2; Hooshyaripor, Farhad3;
Organizations: 1Water, Energy and Environmental Engineering Research Unit, Faculty of Technology, University of Oulu, 90014 Oulu, Finland
2Department of Biosystems and Agricultural Engineering, Oklahoma State University, 111 Agricultural Hall, Stillwater, OK 74078, USA
3Department of Civil Engineering, Architecture and Art, Science and Research Branch, Islamic Azad University, Tehran, Iran
4Department of Agricultural and Biological Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 3.1 MB)
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Language: English
Published: Elsevier, 2021
Publish Date: 2021-09-17


Although dimensional analysis suggests sound functional forms (FFs) to calculate longitudinal dispersion coefficient (Kx), no attempt has been made to quantify both reliability of the estimated Kx value and its sensitivity to variation of the FFs’ parameters. This paper introduces a new index named bandwidths similarity factor (bws–factor) to quantify the reliability of FFs based on a rigorous analysis of distinct calibration datasets to tune the FFs. We modified the bootstrap approach to ensure that each resampled calibration dataset is representative of available datapoints in a rich, global database of tracer studies. The dimensionless Kx values were calculated by 200 FFs tuned with the generalized reduced gradient algorithm. Correlation coefficients for the tuned FFs varied from 0.60 to 0.98. The bws–factor ranged from 0.11 to 1.00, indicating poor reliability of FFs for Kx calculation, mainly due to different sources of error in the Kx calculation process. The calculated exponent of the river’s aspect ratio varied over a wider range (i.e., −0.76 to 1.50) compared to that computed for the river’s friction term (i.e., −0.56 to 0.87). Since Kx is used in combination with one-dimensional numerical models in water quality studies, poor reliability in its estimation can result in unrealistic concentrations being simulated by the models downstream of pollutant release into rivers.

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Series: Science of the total environment
ISSN: 0048-9697
ISSN-E: 1879-1026
ISSN-L: 0048-9697
Volume: 791
Article number: 148394
DOI: 10.1016/j.scitotenv.2021.148394
Type of Publication: A1 Journal article – refereed
Field of Science: 218 Environmental engineering
1172 Environmental sciences
Funding: The first author acknowledges the support from the Arctic Interactions (ArcI) Visit Grant program, Profi 4, University of Oulu.
Copyright information: © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (