The Dependence of Sea Surface Roughness on the Height and Steepness of the Waves

Abstract

It is proposed that the sea surface roughness z o can be predicted from the height and steepness of the waves, z o /H s ϭ A(H s /L p ) B , where H s and L p are the significant wave height and peak wavelength for the combined sea and swell spectrum; best estimates for the coefficients are A ϭ 1200, B ϭ 4.5. The proposed formula is shown to predict well the magnitude and behavior of the drag coefficient as observed in wave tanks, lakes, and the open ocean, thus reconciling observations that previously had appeared disparate. Indeed, the formula suggests that changes in roughness due to limited duration or fetch are of order 10% or less. Thus all deep water, pure windseas, regardless of fetch or duration, extract momentum from the air at a rate similar to that predicted for a fully developed sea. This is confirmed using published field data for a wide range of conditions over lakes and coastal seas. Only for field data corresponding to extremely young waves (U 10 /c p Ͼ 3) were there appreciable differences between the predicted and observed roughness values, the latter being larger on average. Significant changes in roughness may be caused by shoaling or by swell. A large increase in roughness is predicted for shoaling waves if the depth is less than about 0.2L p . The presence of swell in the open ocean acts, on average, to significantly decrease the effective wave steepness and hence the mean roughness compared to that for a pure windsea. Thus the predicted open ocean roughness is, at most wind speeds, significantly less than is observed for pure wind waves on lakes. Only at high wind speeds, such that the windsea dominates the swell, do the mean open ocean values reach those for a fully developed sea.

Coupled wave and surge modelling for the eastern Irish Sea and implications for model wind-stress

“…With the development of high frequency recording devices such as the sonic anemometer it has been possible to directly measure the surface stress (Reynold' stress) by means of eddy correlation and/or dissipation methods from the turbulent velocity fluctuations e.g. Smith and Banke (1975) and Taylor and Yelland (2001). These have led to various parameterisations of the stress in terms of the more readily available wind-speed at 10m above the sea surface, U 10 , giving the much-used empirical bulk formula such as S&B, and Wu (1982), among others.…”

“…The Charnock parameter, α, is thought to be related to wave-age (Janssen, 2004), although this has been disputed (Taylor and Yelland, 2001), but it is often treated as constant in models with values between 0.0112 and 0.035 (Wu, 1980). Although α = 0.0185 seems to provide accurate representation of the surface stress for all sea states (Wu, 1982), a larger value is imposed for young (steep) wind-seas due to increased wave-wind coupling (Janssen, 1991) in WAM.…”

The FuGas 2.3 Framework for Atmosphere–Ocean Coupling: Comparing Algorithms for the Estimation of Solubilities and Gas Fluxes

“…Applying four iterations were enough for an excellent convergence of the full data array. The coefficients proposed by Taylor and Yelland [68] yielded implausibly high z 0 when applied to steep young waves originated by a storm over the central Mediterranean Sea and by strong Mistral blowing off-shore of southern France, corresponding to 2.85% of our observations. These extreme z 0 led to absurdly high u * and k w , and thus we imposed a maximum roughness length of 0.01 m. This value roughly matches the maximum expected from the application of alternative formulations for the estimation of z 0 from the wave field [70][71][72][73][74].…”

“…It is more difficult to determine over water than over land as there is a strong bidirectional interaction between wind and sea surface roughness. Taylor and Yelland [68] proposed a dimensionless z 0 dependency from the wave field, increasing with the wave slope (Equation (15)) as estimated from the significant wave height (H s ) and peak wave period (L p ). Due to the bidirectional nature of the z 0 and u * relation, we also tested an iterative solution (iWLP) where Equation (15) was used as a first guess for the z 0 and Equation (14) for its subsequent u * .…”

“…Due to the bidirectional nature of the z 0 and u * relation, we also tested an iterative solution (iWLP) where Equation (15) was used as a first guess for the z 0 and Equation (14) for its subsequent u * . A second iteration re-estimated z 0 from the COARE 3.0 [69] adaptation of the Taylor and Yelland [68] formulation, whereby a term for smooth flow was added (Equation (16)), and u * was estimated back again from Equation (14). Applying four iterations were enough for an excellent convergence of the full data array.…”