VART Model–Based Method for Estimation of Instream Dissolved Oxygen and Reaeration Coefficient

Dissolved oxygen (DO) is essential to maintaining flora and fauna in aquatic ecosystems. The DO replenishment through the surface reaeration mechanism is commonly described using the reaeration coefficient ($K_2$). This paper presents a new approach to modeling instream DO and estimating $K_2$. The new approach includes an extension of the Variable Residence Time (VART) model and optimization algorithms for inverse modeling. The VART model is modified in this paper to incorporate the DO reaeration mechanism across the air-water interface, forming the VART-DO model. A major advantage of the VART-DO model is that it is capable of simulating DO exchange across the water-sediment interface through the hyporheic exchange mechanism in addition to the air-water exchange. A sensitivity analysis is conducted to investigate the relative importance of key model parameters to DO modeling. It is found that the $K_2$ value increases markedly with the dispersion coefficient. The simplex-simulated annealing and the genetic algorithm are used to optimize the estimation of the parameter $K_2$. A comparison of the optimized $K_2$ value from the VART-DO model with those from existing empirical equations reveals that $K_2$ value could increase 1.5 to 6 times when the effects of the dispersion and hyporheic exchange mechanisms on DO are taken into account. The results from the VART-DO model provide new insights into the DO variation in streams and rivers. The VART-DO model also provides a general and effective tool for total maximum daily load (TMDL) calculations of DO.