Reliability of functional forms for calculation of longitudinal dispersion coefficient in rivers - Noori, Roohollah; Mirchi, Ali; Hooshyaripor, Farhad; Bhattarai, Rabin; Torabi Haghighi, Ali; Kløve, Bjørn (The Science of the total environment, 2021)
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. [Display omitted] •We examined the reliability of mathematical functional forms (MFFs) to obtain Kx.•Wide range of predicted Kx for rivers demonstrates poor reliability of the MFFs.•Bandwidths similarity factor is introduced to quantify the reliability of MFFs.•Aspect ratio of the channel showed a greater impact on Kx than the friction term.•The accuracy of Kx estimations could be improved by accounting for river curvature.