Adaptation of Wind Drag Coefficient Parameterization: Improvement of Hydrodynamic Modeling by a Wave‐Dependent C_d in Large Shallow Lakes

Abstract

Wind is a critical driving force in hydrodynamic and water quality modeling of large shallow lakes, and is characterized by the wind drag coefficient Cd, representing the momentum transfer at the air‐water interface. Contemporary empirical formulae for Cd estimation were derived over oceans and some of which are solely wind velocity U10 dependent. These formulae were previously found to be inadequate in inland lake models often resulting in the water velocity underestimation. To address this problem, a physical scale experiment was designed, in which Cd was measured using a wind profile and eddy covariance methodology. A new wind‐induced wave‐dependent Cd parameterization was also established and validated in two lake studies. The driving force was modified by the wave‐dependent Cd formula in a hydrodynamic model of the shallow Upper Klamath Lake (UKL), OR, USA. The experimental Cd was negatively correlated to the wind velocity up until the critical U10 = 1.6 m s−1 which was 1.0~3.1 times previous empirical extrapolations at light winds. The variation partitioning results showed that wave parameters contributed to more than 30% of Cd variation combined with wind parameters. The modified wind stress field was spatially heterogeneous and the modeled water velocity was closer to the observations at two sites. Significant main circulation and outer bank circulation were modeled accompanied by higher surface vorticity, compared to the original UKL model. Overall, the wave‐dependent Cd formula provided an improvement of the surface flow field in the UKL model and will improve the management of the lake ecosystems.