The data from their TOWARD experiment showed that the mean square slope increases gradually with wind friction velocity u* at low winds, U0126 followed by rapid growth near u* = 20 cm  s−1 and beyond, which resulted in mean square slopes much higher than those reported by Cox & Munk. According to Hwang & Shemdin, the swell is the primary factor that modifies this relationship. Usually, the wind-generated sea

is characterized by the wave age Cp/U10 (Cp is the phase speed of the peak component); when Cp/U10 > 1, swell conditions predominate. The measurements of surface slopes during the TOWARD experiment indicate that the presence of swell can either enhance or reduce surface roughness: in particular, for a low wind speed, when C/U10 > 3, there was a reduction in the mean square slope of up to 40%. Another possible primary factor influencing Bcl-2 inhibitor the mean square slope is the atmospheric stability, which is generally expressed in terms of the Monin-Obukhov parameter: equation(6) zL=gkzw′Ta′¯u*3T¯a,where L   is the Monin-Obukhov length scale, κ   ≈ 0.4 is the von Kármán constant, w  ′ is the fluctuation component of the vertical velocity, z   is the elevation above sea level, Ta′ is the fluctuation in air temperature, and T¯a

is the mean air temperature. Hwang & Shemdin’s (1988) data showed a reduction of the mean square slope for stable conditions (when z/L > 0). This reduction is nearly linear for mildly stable conditions with some limit at z/L ≈ 0.2. Beyond this value, the slope does not decrease any more. It should be noted that the direction of the slope vector deviates from that of the wind due to the presence of long waves. The steering of short waves away from the wind direction by long waves depends on the wave age, such that the greater the wave age, the more effective the steering. Up till now sea surface slopes have been discussed ioxilan without any relation to the form of the frequency spectrum S(ω) (ω is the frequency)

and directional spreading D(θ) (θ is the angle of wave propagation against the wind direction). Sea surface waves are fully described by the two-dimensional frequency-direction spectrum S1(ω, θ), usually given as the product of the frequency spectrum S(ω) and the directional spreading D(θ, ω): equation(7) S1(ω,θ)=S(ω)D(θ,ω).S1(ω,θ)=S(ω)D(θ,ω).Waves longer than the peak wavelength make only a very small contribution to the surface slope, and the influence of high frequency wave components on the statistics of sea surface slopes is substantial. In the classical JONSWAP spectrum ( Massel 1996), the high-frequency tail is represented in the form of a ω−5 dependence. There are many other representations for this frequency region, which results in different estimates of the wave slope statistics (see, for example, Bjerkas & Riedel 1979, Apel 1994, Hwang & Wang 2001). In order to reduce these discrepancies, Elfouhaily et al.