Evaluation of various relationships of reaeration rate coefficient for modeling dissolved oxygen in a river with extreme flow variations in Pakistan

Mathematical relationships have been developed for reaeration rate coefficient (K_a) by various researchers. These relationships have a number of variables such as depth, velocity, width, slope, Froud number, molecular diffusion coefficient, kinematic viscosity and the gas‐transfer Reynolds number. From these variables, 29 relations have been developed and divided into four groups. To evaluate their predictive capability for highly variable flow rivers receiving high pollution loads form large cities, these relationships have been used to model dissolved oxygen (DO) in the River Ravi. Such rivers are either saturated with DO during high flows or anaerobic during critical low‐flow conditions. The evaluation is based on the agreement between model DO values calculated using K_a obtained from the available equations and the measured DO concentrations in the river samples in terms of sum of square of residuals (SSR) and coefficient of determination (R²). It has been found that in general, the group of equations containing depth and velocity as the only two variables affecting K_a performed better than the equations in other groups as reflected by lower SSR and higher R² values. The study results also reveal that the turbulence‐based reaeration rate coefficient equation containing additional variables also resulted in close agreement between DO model results and the measured values. The study results identify the most important parameters affecting the reaeration rate coefficient and the suitability of various K_a relationships as well for rivers with highly variable flows. Copyright © 2012 John Wiley & Sons, Ltd.