Reaeration Coefficient Empirical Equation Selection for Water Quality Modeling in Surface Waterbodies: An Integrated Numerical-Modeling-Based Technique with Field Case Study

Empirical equations were developed by many investigators to determine the reaeration coefficients (Ka) required for predicting dissolved oxygen concentrations (DO) in surface waters, especially rivers, lakes, and reservoirs. However, these equations yield a wide range of Ka values. In this paper, an integrated numerical-modeling-based technique was developed to check the validity of the equations before using them in water quality modeling for rivers, lakes, and reservoirs. Depending on direct field measurements at the Hilla River headwater (Saddat Al-Hindiyah Reservoir, Iraq), the temporal oxygen mass transport at the water surface was estimated numerically by solving the one-dimensional advection diffusion equation and then using each Ka empirical equation separately in the numerical model obtained the best specific-waterbody equation. The DO modeling results showed that using a reservoir reaeration coefficient of 0.1 day−1 at 20 °C predicts the best DO simulation with low MAEs of 0.4987 and 0.7880 mg/L during the study years 2021 and 2022, respectively, compared to the field data. However, using the Ka empirical equations simulates the DO with wide-ranging statistical errors even though the temporal Ka values have a similar trend during the year. It was noticed that the empirical equations produced maximum Ka values of (0.0080–0.0967 day−1) and minimum Ka values of (0.00052–0.0267 day−1) in 2021 and maximum Ka values of (0.0079 to 0.0951 day−1) and minimum Ka values of (0.00012 and 0.0231 day−1) in 2022. The present equation selection technique revealed that Broecker et al.’s equation followed by Smith’s equation, developed in 1978, are the best selection for water quality modeling at the Hilla River headwater (MAEs: 0.1347 and 0.1686 mg/L in 2021, respectively; and MAEs: 0.1400 and 0.1744 mg/L in 2022, respectively). Hence, it is necessary to find good agreement for the equation-based prediction of DO, DO source–sink, and Ka values compared to the validated model before making selection.