## 1. Introduction

[2] As reviewed by *Komen et al.* [1998], correct parameterization of the drag over the ocean has considerable impact not only on a synoptic scale (the development of cyclones) but also on the climate. Although considerable efforts have been spent on the issue, the problem is far from settled, different experiments reported in the literature (see below for details) giving seemingly contradicting results. In particular, the effect of swell on the resulting drag is still far from understood. In this paper several years' worth of concurrent measurement of turbulent flux, mean atmospheric “profiles,” and wave data are analyzed in order to obtain further understanding of how the state of the sea influences the drag. The data have been gathered at the marine site Östergarnsholm in the Baltic Sea during the years 1995–1999. The general criteria for selection of data have been wind from sector with long undisturbed fetch, near-neutral conditions, and completeness of the data. Overall, 375, 60-min data have been used in the analysis, see section 2.

[3] During neutral atmospheric conditions it is generally assumed that there is a logarithmic wind profile in the lowest 10 m or more. Over a solid surface, this is a well-established fact, supported by innumerable measurements in the laboratory as well as in the atmospheric surface layer. Thus for flow over an aerodynamically rough surface we get (see e.g., *Monin and Yaglom* [1971], for a derivation):

where *U* is mean wind speed at height *z*, and *u*_{*} is the friction velocity = . Here τ is shearing stress, which, above the viscous sublayer can be expressed as τ/ρ = where is the correlation between the longitudinal wind fluctuations and the vertical wind fluctuations, is the corresponding correlation between the transverse (lateral) wind fluctuation and the vertical wind fluctuations, ρ is air density, κ is von Karman's constant = 0.40 [*Högström*, 1996], and *z*_{0} is the roughness length. Over a solid surface, *z*_{0} is related to the size and geometry of the roughness elements at the surface.

[4] Equation (1) is usually assumed to be valid over the ocean as well during neutral conditions. It is however not self-evident that this is the case over a moving and undulating surface in dynamic interplay with the overlaying atmosphere. From the equation of motion it is easy to show that the vertical flux of momentum, τ, in the layers near the surface is approximately height constant. However, in the marine surface layer, τ can be written as the sum of three components:

where τ_{t} is the turbulent flux of momentum, τ_{w} is the wave-induced flux, and τ_{visc} is the viscous (molecular) flux. The logarithmic wind law is thought to be related to the turbulent flux so that τ_{t} = ρ*u*_{*}^{2} [*Kitaigorodskii*, 1973]. However, τ_{visc} is of importance only in the lowest millimeter, and calculations, for example, *Belcher and Hunt* [1996], indicate that during wind sea conditions, τ_{w} is an important part of τ only in the lowest meter or so above the surface (the “wave boundary layer”). Then τ = τ_{t} above this height, and we expect the logarithmic law to be valid, with *z*_{0} being a measure of the local roughness of the sea. Measurements by *Drennan et al.* [1999] at 2 m above mean water level indicate that there is no measurable effect from the waves at this height during pure wind sea conditions, supporting the idea that the wave boundary layer is very thin during such conditions.

[5] However, *Hare et al.* [1997] have made concurrent measurements of fluctuating pressure, wind, and surface waves, and plot the wave-induced pressure field as a function of the nondimensional parameter *kz*, where *k* is wave number, in bins of the wave-age parameter *u*_{*}/*c*_{p}, where *c*_{p} is the phase velocity of the dominating waves. For cases with swell, defined as *u*_{*}/*c*_{p} < 0.04, they observe significant influence up to *kz* = 4, so that effects of waves with a wavelength of say 50 m would be felt as high as 30 m. Note, however, that this argument is based on the proposed validity of the similarity arguments presented by *Hare et al.* [1997], their actual atmospheric measurements being made at 3 m.

[6] Measurements of wind profiles in neutral conditions over the ocean at reliable sites are rare. Most oceanic measurements report in fact only data from one level, usually 10 m and assume that equation (1) is valid. Introducing the drag coefficient

assuming neutral conditions and that equation (1) is valid, gives

i.e., a unique relation between the neutral drag coefficient *C*_{DN} and the roughness length *z*_{0}. Note, however, that if the wave boundary layer should extend to an appreciable height, as suggested by the results of *Hare et al.* [1997], the logarithmic law may be invalid, and then a drag coefficient determined from concurrent measurements of *u*_{*} and *U*_{10} is not likely to give physically meaningful values for *z*_{0} with the aid of equation (4).

[7] Section 2 describes the measuring site and the data and section 3 criteria for characterizing sea state. In section 4, the neutral wind profile is described and discussed. In section 5, the variation of the drag with sea state is studied, first for pure wind sea conditions and then for conditions with mixed sea/swell. Section 6, finally, is a discussion of the results and conclusions.