IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 10, NO. 3, MAY 2013 593 Estimation of the Sea-Surface Slope Variance Based on the Power Spectrum Width of a Radar Scatterometer Min-Ho Ka, Member, IEEE, Aleksandr I. Baskakov, Vladimir A. Terechov, and Anatoliy A. Kononov Abstract—In this letter, we introduce the possibility of the sea-surface slope measurements using second-order statistics of return waveforms from sea surface in a continuous-wave radar scatterometer. It has been shown that the estimation of the vari- ance of sea-surface slopes can be obtained by measuring the signal power or the power-spectrum width of return waveforms. We found that the power-spectrum-width-based estimation approach is more sensitive to the variance of the sea-surface slope for weak sea-surface disturbances in contrast to the power-based one. Index Terms—Correlation function, power spectrum, radar scatterometer, remote sensing, sea slope variance. I. I NTRODUCTION R EAL-TIME monitoring of the sea-state condition and other processes associated with the ocean surface dynam- ics is necessary for reliable weather forecasts over continents and oceans, as well as for other applications such as navigation, scientific study of air and sea interaction, and global climate phenomena [1], [2]. Thus, the development of methods and remote-sensing instruments for real-time sea-state condition measurement is of great current importance [3]–[6]. The inter- est in rapid, accurate, and global scale measurements of the sea state has favored the development of radar systems either in high frequency or in the microwave domain. The microwave sensors have the advantage of being usable in aircraft, as well as in space platforms [2] [4] [5]. One of the on-board sensors providing useful data on ocean surface (wind measurement) is the microwave radar scatterometer. It can even operate from small space platforms due to the advantage of low cost and low power requirements. In addition to ocean wind measurements, scatterometer data are also valuable in ice mapping, vegetation classification, soil moisture retrieval, etc. [1], [2]. Manuscript received February 8, 2012; revised July 3, 2012; accepted August 13, 2012. Date of publication October 11, 2012; date of current version November 24, 2012. This work was supported by the Ministry of Knowledge Economy under the “IT Consilience Creative Program” by the National IT Industry Promotion Agency Korea. M.-H. Ka is with the School of Integrated Technology, Yonsei University, Incheon 406-840, Korea (e-mail: kaminho@yonsei.ac.kr). A. I. Baskakov and V. A. Terechov are with Moscow Power Engineering Institute, 111250 Moscow, Russia (e-mail: baskakovai@mpei.ru). A. A. Kononov is with the STX Engine Corporation, Gyeonggi-do 449-915, Korea (e-mail: kaa50ua@gmail.com). Digital Object Identifier 10.1109/LGRS.2012.2215305 TABLE I RELATION BETWEEN NEAR-SURFACE WIND AND SEA SLOPE VARIANCE This letter addresses some issues related to the principle of measurement to be employed in a down-looking continuous- wave (CW) radar scatterometer that should be capable of pro- viding accurate data on the variance of the sea-surface slope from aircraft or small space platforms. The scatterometer does not directly measure the wind. Instead, it measures variance σ 2 θ of the sea-surface slope. To infer the wind speed, the σ 2 θ measurements should be then related to the near-surface wind via appropriate geophysical model function. An example of such a function in tabulated form is presented in Table I [7]. We will show that an estimate of the sea-surface slope variance σ θ2 can be extracted by measuring either the power- spectrum width or the power of return waveforms. It will be also shown that the spectral-width-based estimate exhibits high sensitivity to the sea slope variance for weak sea disturbance. II. RETURN WAVEFORM MODEL The geometry for near-vertical sea-surface illumination (in- cidence angle θ ≤ 15 ◦ ) in a down-looking radar scatterometer is shown in Fig. 1. The scatterometer, located at point A(0, 0,Z 0 ), which is at height H (Z 0 = H) above the mean flat sea surface, is assumed to radiate monochromatic microwave signals at frequency ω or wavelength λ. The XY plane corresponds to the mean flat surface. Origin O of the coordinate system corresponds to the projection of point A on the mean flat surface and moves 1545-598X/$31.00 © 2012 IEEE