Directional Spreading Function of the Gravity-Capillary Wave Spectrum Derived from Radar Observations

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.

Modeling and SAR imaging of the sea surface: A review of the state-of-the-art with simulations

“…It should be noted that when wind speed is increased, the differences between gravity-capillary and short gravity waves are minimized. An example of this effect can be found in [108], p. 10.…”

Modeling and SAR Imaging of the Sea Surface: a Review of the State-of-the-Art with Simulations

“…It should be noted that when wind speed is increased, the differences between gravity-capillary and short gravity waves are minimized. An example of this effect can be found in [108], p. 10. All the spreading functions presented in this section can potentially be applied in conjunction with different omnidirectional spectra in order to offer exhaustive modalities of simulating SAR images.…”

Development of a New Tropical Cyclone Strip Segment Retrieval Model for C-Band Cross-Polarized SAR Data

“…The geophysical model functions (GMFs), which are the empirical relations between normalized radar cross-section (NRCS), wind speed, wind direction, and radar incidence angle, can be used to transform the NRCS from satellite-borne SAR images of the ocean surface into a wind field [9][10][11][12][13]. The GMFs exist just because a wind field would roughen the sea surface via the production of sea waves, which in turn enhance the backscattered NRCS at moderate incidence angles [14][15][16][17][18][19]. The works in [16][17][18][19] demonstrate that the GMFs for co-polarized SAR images have limitations to retrieve tropical cyclone-force wind speed because the co-polarized NRCS would be saturated when sea surface wind speed exceeds 20 m/s.…”