Abstract
Directional spreading function of the gravity-capillary wave spectrum can provide the high-wavenumber wave energy distribution among different directions on the sea surface. The existing directional spreading functions have been mainly developed for the low-wavenumber gravity wave with buoy data. In this paper, we use radar observations to derive the directional spreading function of the gravity-capillary wave spectrum, which is expressed as the second-order Fourier series expansion. So far the standard form of the second-order harmonic coefficient has not been proposed to correctly unify the gravity and gravity-capillary wave. Our strategy is to introduce a correcting term to replace the inaccurate gravity-capillary spectral component in Elfouhaily’s directional spreading function. The second-order harmonic coefficient at L, C and Ku band calculated by the radar observation is used to fit the correcting term to obtain one at the full gravity-capillary wave region. According to our proposed the directional spreading function, there is a spectral region between the gravity and gravity-capillary range where it signifies the negative upwind–crosswind asymmetry at low and moderate speed range. And this is not reflected by the previous models, but has been confirmed by radar observations. The Root Mean Square Difference (RMSD) of the proposed second-order harmonic coefficient versus the radar-observed one at L, C band Ku band is 0.0438, 0.0263 and 0.0382, respectively. The overall bias and RMSD are −0.0029 and 0.0433 for the whole second-order harmonic coefficient range, respectively. The result verifies the accuracy of the proposed directional spreading function at L, C band Ku band.
Highlights
The gravity-capillary wave plays an important role in air-sea interaction because it affects the mass, momentum and energy flux through the air-sea interface
The directional spreading function of the gravity-capillary wave spectrum is related to the radar observation through sea surface backscatter model
If the directional wave spectrum is expressed as a Fourier series, the directional spreading function should contain only even harmonics: D(k, φ) =
Summary
The gravity-capillary wave plays an important role in air-sea interaction because it affects the mass, momentum and energy flux through the air-sea interface. 2017, 9, 361 is pillaged by the gravity wave and wind wave will grow [1,2]. The energy propagation is colinear with gravity crests propagation in absence of currents and internal gravity waves. The directional spectrum is used to describe the gravity-capillary waves, which can give the wave energy distribution among different directions on the sea surface. There are two main ways to observe the azimuthal behavior of the directional spectrum: in situ measurement and remote sensing measurement. Buoy and its array provided two main types of directional spreading functions of ocean wave spectrum. The cosine-shape spreading function was first proposed by Longuet-Higgines et al [3]
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