An improved sea state dependency for surface stress derived from in situ and remotely sensed winds

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Abstract

An improved model is developed for the dependency of surface turbulent stress on wave characteristics. Recent studies have used differences between satellite and in situ observations to gain insights into the physical processes that might be related to air–sea interaction. Both scatterometers and buoys provide very accurate measurements of wind speed. Differences between these measurements can be explained in terms of the different mechanisms to which the instruments respond. A physically-based flux model is developed herein. Prior results suggest that, the stress parameterizations, converting neutral equivalent wind speed to stress, applied to in situ observations differ subtlety from those that should be used for scatterometer-derived winds. These differences are due to water waves modifying the surface stress. This model provides a physical explanation of the observed differences, and provides a model for calculating stresses from scatterometer winds. The model is validated with recent in situ observations gathered under severe conditions. The model explains more wave-related variability in surface stress than previous models.

Introduction

Surface stress over water is primarily dependent on the vertical profile of wind speed, which is dependent on stratification of the atmosphere (atmospheric stability) and sea state (i.e., characteristics of the surface wave field). A typical assumption in GCM modeling of surface fluxes is that the wind and the waves are in a state of local equilibrium or a prescribed state of non-equilibrium. This assumption is equivalent to specifying a sea state. Recent examinations (Bourassa et al., 1999; Taylor and Yelland, 2001) based on in situ data have shown that this assumption is invalid for most spatial and temporal scales where there is substantial variability in sea state. Physical mechanisms have been proposed to account for the dependency of stress on sea state (Kusaba and Masuda, 1988; Geernaert, 1990; Toba et al., 1990; Perrie and Toulany, 1990; Maat et al., 1991; Smith et al., 1992; Yelland et al., 1998; Bourassa et al., 1999; Bourassa et al., 2001); however, an empirical formulation based on a much wider range of wind speeds and non-directional sea states (Taylor and Yelland, 2001) has been shown to provide substantially better matches to observations that cover a wide range of conditions. Differences between satellite and in situ wind observations have been used to infer the relative importance of several wave characteristics (Quilfen et al., 2001). The results of this study are correlations, which do not explain the physical mechanisms through which these wave characteristics modify surface fluxes. These differences also indicate that different parameterizations should be used to convert the observed wind speeds to stresses. A physical mechanism that utilizes these satellite-derived insights is developed, and it is found to be largely consistent with the results of Taylor and Yelland’s (2001) empirical relation. One advantage of this physically-based mechanism is that it also considers directional sea state (i.e., the wind direction relative to the direction of wave propagation). This additional consideration makes the flux model consistent with observations over a wider range of conditions. The non-directional impacts on surface turbulent stress are developed and validated herein.

A stress-dependent model for significant wave height is coupled with a sea state dependent surface flux model to demonstrate the interdependence of surface fluxes and wave characteristics. It is shown that significant wave height can be used, in conjunction with wind speed, as an indicator for the departure from local wind wave equilibrium as well as the calculation of non-equilibrium fluxes. This result is largely consistent with the empirical formulation of Taylor and Yelland (2001); however, the physical impacts of sea state are parameterized through the influences of the surface’s orbital motion induced by waves, rather than the slope of the waves. Such a model has been successfully applied to capillary-wave related surface stress (Bourassa et al., 1999); however, such wave dominate stress for ten meter wind speeds (U10) <∼ 5 ms−1. The mechanism was not applied to gravity wave related surface stresses, which dominate greater wind speeds due to the lack of appropriate data for validation. A recent study (Quilfen et al., 2001) has shown that, the differences between observed and modeled scatterometer backscatter are well correlated to wave slope characteristics, but better correlated to the wave-induced surface motion. The modeled backscatter were found by inverting the geophysics model function (GMF) that was used to convert backscatter to vector winds. This model function has been shown be very accurate (Bourassa et al., 2003), indicating that small differences in wind speed (greater than ∼5 cm/s), or the equivalent in backscatter, are likely to be due to physical differences rather than noise. These differences were binned according to low, moderate, and strong wind speeds. The correlations between these differences in backscatter, and the wave characteristics (orbital velocity and significant slope) were similar for low and moderate wind speeds; however, for strong winds the correlation was much better with orbital velocity (the significance of these differences was not given). This finding supports the physical reasoning applied in the flux model developed herein, for low wind speeds as well as high wind speeds.

Section snippets

Data

The impacts of sea state on stress have previously been validated (Bourassa et al., 1999) for conditions dominated by capillary waves. The model reproduced observed changes in stress as a function of directional sea state. The developments in this study are applicable to conditions where stress is dominated by gravity waves. There are few observational data sets that contain both stress and wave observations. A preliminary version of observations from the storm wave study experiment (SWS-2;

Flux model

The downward momentum flux (τ) can be modeled in terms of the friction velocity (u*)τ=ρu*|u*|,where ρ is the density of the air. The upward surface turbulent fluxes of sensible (H) and latent heat (E) are:H=−ρCpθ*|u*|,E=−ρLvq*|u*|,where θ* and q* are scaling parameters analogous to u*, Cp is the specific heat of air, and Lv is the latent heat of vaporization. The goal of this study is to improve the accuracy of modeled values of u*, which will improve the accuracy of these surface turbulent

Comparisons to observations

The model is evaluated with SWS-2 observations, and it is compared to empirical relation (12) developed by Taylor and Yelland (2001) based on the observations from SWS-2 and data from a wide range of other conditions. The functional form of the gravity wave portion of (11) is far different than the empirical relation (12)z0=1200Hs(Hsp)4.5,where λp is the wavelength associated with the dominant waves. Eq. (12) has been shown (Taylor and Yelland, 2001) to be an excellent match to mean

Conclusions

Insights gained from examining the differences between satellite and in situ observations demonstrated a consistency with theory that had previously only been tested for low and moderate wind speeds. These observations and theory indicated that the orbital velocity of waves modifies wind shear, and consequently modifies oceanic surface turbulent stress. This concept had been difficult to verify because there were few appropriate in situ observations. The SWS-2 observations provide an excellent

Acknowledgements

I thank Peter Taylor for providing the SWS-2 data and advice on quality assurance. COAPS receives it base funding from ONR’s Secretary of Navy Grant to James J. O’Brien. Current support is from NASA’s Ocean Vector Winds Science Team, OSU’s Sea Winds project, and the NSF.

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