It is proposed that the sea surface roughness zo can be predicted from the height and steepness of the waves, zo/Hs = A(Hs/Lp)B, where Hs and Lp are the significant wave height and peak wavelength for the combined sea and swell spectrum; best estimates for the coefficients are A = 1200, B = 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 (U10/cp > 3) were there appreciable differences betwe... Abstract It is proposed that the sea surface roughness zo can be predicted from the height and steepness of the waves, zo/Hs = A(Hs/Lp)B, where Hs and Lp are the significant wave height and peak wavelength for the combined sea and swell spectrum; best estimates for the coefficients are A = 1200, B = 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 (U10/cp > 3) were there appreciable differences betwe...

An automatic inertial dissipation system was used during three cruises of the RRS Discovery in the Southern Ocean to obtain a large dataset of open ocean wind stress estimates. The wind speed varied from near calm to 26 m s−1, and the sea-air temperature differences ranged from −15° to +7°C. The data showed that the assumption of a balance between local production and dissipation of turbulent kinetic energy is false and that the sign and magnitude of the imbalance depends critically on both stability and wind speed. The wide range of stability conditions allowed a new formulation for the nondimensional dissipation function under diabatic conditions. A minimum in the 10-m neutral value of the drag coefficient occurred at 6 m s−1. At lower wind speeds the data were fitted by the relationship where U10n. is the 10-m neutral wind speed (m s−1). At higher wind speeds which gives drag coefficients that are about 10% higher than those from previous open ocean studies (which assumed a balance between pro... Abstract An automatic inertial dissipation system was used during three cruises of the RRS Discovery in the Southern Ocean to obtain a large dataset of open ocean wind stress estimates. The wind speed varied from near calm to 26 m s−1, and the sea-air temperature differences ranged from −15° to +7°C. The data showed that the assumption of a balance between local production and dissipation of turbulent kinetic energy is false and that the sign and magnitude of the imbalance depends critically on both stability and wind speed. The wide range of stability conditions allowed a new formulation for the nondimensional dissipation function under diabatic conditions. A minimum in the 10-m neutral value of the drag coefficient occurred at 6 m s−1. At lower wind speeds the data were fitted by the relationship where U10n. is the 10-m neutral wind speed (m s−1). At higher wind speeds which gives drag coefficients that are about 10% higher than those from previous open ocean studies (which assumed a balance between pro...

The concept of an “equivalent surface roughness” over the ocean is useful in understanding the relation between wind speed (at some height) and the net momentum flux from air to sea. The relative performance of different physics-motivated scalings for this roughness can provide valuable guidance as to which mechanisms are important under various conditions. Recently, two quite different roughness length scalings have been proposed. Taylor and Yelland presented a simple formula based on wave steepness, defined as the ratio of significant wave height to peak wavelength, to predict the surface roughness. A consequence of this formula is that roughness changes due to fetch or duration limitations are small, an order of 10%. The wave steepness formula was proposed as an alternative to the classical wave-age scaling first suggested by Kitaigorodskii and Volkov. Wave-age scaling, in contrast to steepness scaling, predicts order-of-magnitude changes in roughness associated with fetch or duration. The existence of two scalings, with different roughness predictions in certain conditions, has led to considerable confusion among certain groups. At several recent meetings, including the 2001 World Climate Research Program/Scientific Committee on Oceanic Research (WCRP/SCOR) workshop on the intercomparison and validation of ocean–atmosphere flux fields, proponents of the two scalings met with the goal of understanding the merits and limitations of each scaling. Here the results of these efforts are presented. The two sea-state scalings are tested using a composite of eight datasets representing a wide range of conditions. In conditions with a dominant wind-sea component, both scalings were found to yield improved estimates when compared with a standard bulk formulation. In general mixed sea conditions, the steepness formulation was preferred over both bulk and wave-age scalings, while for underdeveloped “young” wind sea, the wave-age formulation yields the best results. Neither sea-state model was seen to perform well in swell-dominated conditions where the steepness was small, but the steepness model did better than the wave-age model for swell-dominated conditions where the steepness exceeded a certain threshold.

A large dataset of wind stress estimates, covering a wide range of wind speed and stability conditions, was obtained during three cruises of the RRS Discovery in the Southern Ocean. These data were used by Yelland and Taylor to determine the relationship between 10-m height, neutral stability values for the drag coefficient, and the wind speed, and to devise a new formulation for the nondimensional dissipation function under diabatic conditions. These results have been reevaluated allowing for the airflow distortion caused by the ship. The acceleration and vertical displacement of the flow have been modeled in three dimensions using computational fluid dynamics (CFD). The CFD modeling was tested, first by comparison with wind tunnel measurements on models of two Canadian research ships and second, by analysis of data from four anemometers on the foremast of the RRS Charles Darwin. Originally, the four anemometers gave drag coefficient values that differed by up to 20% from one to another and were... Abstract A large dataset of wind stress estimates, covering a wide range of wind speed and stability conditions, was obtained during three cruises of the RRS Discovery in the Southern Ocean. These data were used by Yelland and Taylor to determine the relationship between 10-m height, neutral stability values for the drag coefficient, and the wind speed, and to devise a new formulation for the nondimensional dissipation function under diabatic conditions. These results have been reevaluated allowing for the airflow distortion caused by the ship. The acceleration and vertical displacement of the flow have been modeled in three dimensions using computational fluid dynamics (CFD). The CFD modeling was tested, first by comparison with wind tunnel measurements on models of two Canadian research ships and second, by analysis of data from four anemometers on the foremast of the RRS Charles Darwin. Originally, the four anemometers gave drag coefficient values that differed by up to 20% from one to another and were...

The contemporary air‐sea flux of CO₂ is investigated by the use of an air‐sea flux equation, with particular attention to the uncertainties in global values and their origin with respect to that equation. In particular, uncertainties deriving from the transfer velocity and from sparse upper ocean sampling are investigated. Eight formulations of air‐sea gas transfer velocity are used to evaluate the combined standard uncertainty resulting from several sources of error. Depending on expert opinion, a standard uncertainty in transfer velocity of either ~5% or ~10% can be argued and that will contribute a proportional error in air‐sea flux. The limited sampling of upper ocean fCO₂ is readily apparent in the Surface Ocean CO₂ Atlas databases. The effect of sparse sampling on the calculated fluxes was investigated by a bootstrap method, that is, treating each ship cruise to an oceanic region as a random episode and creating 10 synthetic data sets by randomly selecting episodes with replacement. Convincing values of global net air‐sea flux can only be achieved using upper ocean data collected over several decades but referenced to a standard year. The global annual referenced values are robust to sparse sampling, but seasonal and regional values exhibit more sampling uncertainty. Additional uncertainties are related to thermal and haline effects and to aspects of air‐sea gas exchange not captured by standard models. An estimate of global net CO₂ exchange referenced to 2010 of −3.0 ± 0.6 Pg C/year is proposed, where the uncertainty derives primarily from uncertainty in the transfer velocity.

Wind velocity and air–sea turbulent flux measurements made from shipborne instruments are biased due to the effect of the ship on the flow of air to the instruments. The presence of the sh... Abstract Wind velocity and air–sea turbulent flux measurements made from shipborne instruments are biased due to the effect of the ship on the flow of air to the instruments. The presence of the sh...