Surface Wave-Aerodynamic Roughness Length Model for Air–Sea Interactions

Abstract A new model to evaluate the equivalent hydrodynamic length or surface roughness, z 0 , of ocean waves is developed and tested. The proposed Surface Wave-Aerodynamic Roughness Length (SWARL) model requires maps of the wave surface height at consecutive times and the airflow characteristic Reynolds number as inputs. Pressure drag is accounted for by approximating the relative velocity in a frame moving with the local wave phase speed assuming ideal inviscid ramp flow. Drag from viscous and unresolved ripples is modeled using the standard equilibrium model. The SWARL model is tested using over 300 datasets for monochromatic and broad-spectrum wave surfaces. The model-predicted z 0 and drag coefficients are compared to measured values, as well as commonly used wave parameterization methods found in the literature. For datasets with well-characterized surfaces, the proposed model shows significantly better agreement with data compared to prior models. For data that did not include a full characterization of the wave fields (typically field data), the model yields predictions with accuracy similar to prior models. Results highlight that including detailed flow physics and extensive wavefield characterization in the modeling of z 0 can provide significant improvements in roughness-length-based modeling of air–sea interactions. Significance Statement This paper introduces a new method to predict the surface drag force of wind over ocean waves, a key parameter for weather forecasting, climate modeling, and offshore engineering. Drag is typically quantified by a roughness length (a measure of the resistance to the wind at the wind-wave interface due to moving surface waves), which conventional methods estimate using empirical formulas or assumptions that fail to capture the dynamics accurately. Our model predicts the roughness length based on geometric knowledge about the moving surface. It performs well on both simple and complex wave shapes, showing significantly better agreement with data than traditional approaches. By improving drag predictions, this method can enhance simulations of hurricane evolution, climate modeling, and offshore wind farm design.