The importance of the wind-drag coefficient parameterization for hydrodynamic modeling of a large shallow lake

Abstract

Wind strongly impacts the hydrodynamic and biogeochemical process of large shallow lakes, therefore wind stress also plays an important role in modeling the hydrodynamics and water quality of shallow lakes. In large shallow lakes, it may be necessary to modify the empirical wind-drag coefficient formula derived from ocean surface experiments because lake current velocities may be seriously underestimated in inland waters. To resolve this limitation, we added a wind-drag multiplier (α) to the wind drag formula in a lake hydrodynamic model. We used the Environmental Fluid Dynamics Code (EFDC) to model the hydrodynamics of Upper Klamath Lake (UKL), Oregon. The moment-independent method for global sensitive analysis (GSA) based on sampling of input parameters was utilized. We found that the original model underestimated lake current velocities when compared to field observations, so we developed a modified model with a wind-drag multiplier. This model was calibrated to observed data from June 21–September 12, 2005, and verified with data from May 24–September 25, 2006. The results showed the calibrated modified model resolved the underestimation problem, e.g., at three sites in UKL the water velocity increased by 59–85%, and the relative error for the model decreased by 15–32%. Sensitivity analysis showed the modeled current velocities were more sensitive to the α coefficient than to the bottom roughness height z0 and the coefficients in the original wind-drag formula. We believe the wind-drag multiplier affects wave propagation in the model and reconciles the mismatch between large shallow lake and open ocean conditions. Our results show that a relatively simple modification can alleviate the fundamental mismatch between modeling the hydrodynamics of the open ocean and large shallow lakes.