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

Although dimensional analysis suggests sound functional forms (FFs) to calculate longitudinal dispersion coefficient (K_x), no attempt has been made to quantify both reliability of the estimated K_x 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 K_x 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 K_x calculation, mainly due to different sources of error in the K_x 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 K_x 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.