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.