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Remote Sens. 2017, 9(4), 361;

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

National Key Laboratory of Microwave Imaging Technology, Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China
Key Laboratory of Marine Geology and Environment, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266061, China
Laboratory for Marine Geology, Qingdao National Laboratory for Marine Science and Technology, Qingdao 266200, China
Shanghai Radio Equipment Research Institute, Shanghai 200090, China
College of Information Science & Engineering, Ocean University of China, Qingdao 266100, China
National Satellite Ocean Application Service, Beijing 100081, China
Author to whom correspondence should be addressed.
Academic Editors: Xiaofeng Li, Ferdinando Nunziata, Alexis Mouche, Raphael M. Kudela and Prasad S. Thenkabail
Received: 3 December 2016 / Revised: 19 March 2017 / Accepted: 1 April 2017 / Published: 12 April 2017
(This article belongs to the Special Issue Ocean Remote Sensing with Synthetic Aperture Radar)
Full-Text   |   PDF [3841 KB, uploaded 12 April 2017]   |  


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. View Full-Text
Keywords: directional spreading function; gravity-capillary wave; radar observations directional spreading function; gravity-capillary wave; radar observations

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Zhou, X.; Chong, J.; Bi, H.; Yu, X.; Shi, Y.; Ye, X. Directional Spreading Function of the Gravity-Capillary Wave Spectrum Derived from Radar Observations. Remote Sens. 2017, 9, 361.

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