Sea surface wind affects the fluxes of energy, mass and momentum between the atmosphere and ocean, and therefore regional and global weather and climate. With various satellite microwave sensors, sea surface wind can be measured with large spatial coverage in almost all-weather conditions, day or night. Like any other remote sensing measurements, sea surface wind measurement is also indirect. Therefore, it is important to develop appropriate wind speed and direction retrieval models for

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... t types of microwave instruments. In this paper, a new sea surface wind direction retrieval method from synthetic aperture radar (SAR) imagery is developed. In the method, local gradients are computed in frequency domain by combining the operation of smoothing and computing local gradients in one step to simplify the process and avoid the difference approximation. This improved local gradients (ILG) method is compared with the traditional two-dimensional fast Fourier transform (2D FFT) method and local gradients (LG) method, using interpolating wind directions from the European Centre for Medium-Range Weather Forecast (ECMWF) reanalysis data and the Cross-Calibrated Multi-Platform (CCMP) wind vector product. The sensitivities to the salt-and-pepper noise, the additive noise and the multiplicative noise are analyzed. The ILG method shows a better performance of retrieval wind directions than the other two methods. Many satellites have been launched with SAR onboard, e.g., Seasat, ERS-1/2, Envisat, Radarsat-1/2, and so on [14] [15] [16] [17] [18] . These sensors have acquired abundant SAR images containing many interesting features including coastal upwelling, typhoon/hurricane, atmospheric waves, atmospheric vortex street, and so on [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] . Some of SAR imaged features, e.g., Langmuir cells, boundary layer rolls, surfactant streaks, foam and water blown from breaking waves, or wind shadowing, align with wind direction. Wind direction (with an ambiguity of 180 • ) can be retrieved from these features by different methods including Fourier transforms, wavelet analysis, local gradients and so on. The 180 • ambiguity can be removed by referencing to weather model output, Doppler shift or land shadows [3, 16, 32] . The accuracy of various methods ranges from 15-40 • [33]. After wind direction is obtained, wind speed can be retrieved by physical or empirical models. Accordingly, estimating wind vectors directly from SAR images becomes feasible [34] . Both cross-polarization and co-polarization SAR images can be used for the retrieval of wind vectors [35] [36] [37] . There are two conventional methods of retrieving wind directions (with an ambiguity of 180 • which is removed later) from SAR images, namely, two-dimensional fast Fourier transform (2D FFT) method and local gradients (LG) method [34, 38, 39] . In the FFT method, the Fourier spectrum of SAR images is computed and the main spectral energy is located perpendicular to the orientation of the wind streaks. The reported standard deviations of FFT method are between 10-37 • and the method works fine on large image areas, e.g., 20 km by 20 km [34] . In the LG method, local gradients are computed with standard image processing algorithms, and the orthogonal of the most frequent gradient direction is chosen to be the likely wind direction. The reported directional error of LG method was about 20 • for ERS-1/2 images and the most frequent spatial sampling used was 20 km by 20 km and 10 km by 10 km [34] . The tests in [34] indicated that the LG method could provide a higher resolution of retrieved wind field than the FFT method. However, the current LG method has a problem; that is, the local gradients in the conventional LG method are computed with difference approximation like Sobel operators, and this process is easily affected by noise, e.g., speckle noise. Thus, SAR images are usually first smoothed before computing local gradients. In this study, we develop an improved local gradients (ILG) method for sea surface wind retrieval by combining smoothing and computation of the local gradients together in the frequency domain. In the method, the computation of local gradients is analytical as the Gaussian function can be expressed analytically in both spatial domain and frequency domain and it can avoid the errors of difference approximation which can be easily affected by noise. The new method is tested on the images acquired by the advanced synthetic aperture radar (ASAR) onboard Envisat, and its retrieved results show better agreement with both following kinds of interpolating wind directions than the other two methods. The interpolating wind directions from the European Centre for Medium-Range Weather Forecast (ECMWF) reanalysis data are obtained by interpolating the ECMWF reanalysis data to the SAR imaging times. The same procedure is applied to the Cross-Calibrated Multi-Platform (CCMP) data to obtain the interpolating wind directions from the CCMP data. The remaining sections are organized as follows. In Section 2, the ILG method is described in detail. In Section 3, the data sets used are introduced. In Section 4, we compare the three wind direction retrieval methods using the wind directions from the ECMWF reanalysis data and the CCMP wind products. The ILG method is also tested by using small images (thus high resolution) in this section. The performance of each retrieval method is analyzed while the images are corrupted by different types of noise in Section 5. Conclusions are given in Section 6. Improved Local Gradients Method The direction of the gradient should be the same as the direction of the strongest change in an image, and an ideal image of streaks should have nearly no change along the direction of streaks, and show the strongest variation in the orthogonal direction of streaks. Thus, the wind direction, which is assumed to be parallel to the wind streaks [40] , is also perpendicular to the direction of the gradient. Remote Sens. 2017, 9, 671 3 of 17 (9) Remote Sens. 2017, 9, 671 4 of 17 ∂ ∂x s (x , y ) and ∂ ∂y s (x , y ) are denoted as g x and g y , respectively, for convenience, so the gradients can be stored as complex numbers in the form of