# Estimating Significant Wave Height from SAR with Long Integration Times
## 1 Introduction  
Waves are the ocean's most obvious surface feature. Significant wave height (SWH) is defined as the average of the highest one-third of the observed waves [1]. As an important parameter reflecting the characteristics of ocean waves, the accurate estimation of the significant wave height is particularly important for marine engineering, ship designing and marine transportation. Synthetic aperture radar (SAR) has become one of the important ways to obtain ocean wave parameters with obvious advantages of all-day, all-weather, high resolution and wide swath coverage [1]. At present, the methods of estimating significant wave height can be divided into three major categories. The first type is theoretical-based methods, such as the Max-Planck Institute (MPI) [2, 3], numerical wave model [4], semi-parametric retrieval algorithm (SPRA) [5] and parameterized first-guess spectrum method (PFSM) [6, 7]. However, they are difficult and limited in implementation. The second is empirical methods, which are typically represented by CWAVE_ERS [8], CWAVE_ENVI [9], CWAVE_S1A [10]and QPCWAVE_GF3 [11]. These methods can only process specific SAR data. The third method is based on the relationship between the significant wave height and the azimuth cutoff [12; 13; 14]. However, all of the above methods are based on visible ocean waves in SAR images. Actually, due to the random motion of the ocean waves, the ocean waves in the SAR images will be extremely blurred or even invisible [15; 16]. For low-frequency SAR (such as P-band, L-band) data which have the characteristic of long integration time, the following two problems are more prominent. The ocean waves are usually invisible in SAR images. It is impossible to estimate significant wave height by means of the present methods. On the other hand, in the case that there are multiple wave systems, significant wave height of only one wave system can be estimated using the present methods for the reason that only a blurred wave system can be observed in SAR images. In order to solve the problems that the present methods cannot estimate the significant wave height when the ocean waves are invisible and that can estimate the significant wave height of only one wave system in the case of multiple wave systems, a method of estimating significant wave height from SAR with long integration times is proposed in this paper. The proposed method is suitable for SAR data with long integration times. The clear SAR images of ocean waves can be obtained by refocusing, breaking through the limitation that the present methods cannot estimate the significant wave height when the wave texture is invisible from SAR with long integration times. Firstly, the azimuth cutoff is calculated. Then, each ocean wave system is refocused from single-look complex (SLC) data, respectively. After obtaining the optimum refocused SAR image of different wave systems, the wavelength and propagation direction of each wave system are calculated. Meanwhile, according to the optimum focus setting, the 180\({}^{\circ}\) ambiguity of wave propagation direction is removed without any additional processing. Finally, significant wave heights are estimated. Two airborne SAR data with long integration times are employed to verify the proposed method. One case is that ocean waves are invisible in SAR images, the other is that there are two wave systems on the real ocean surface but only one is visible in the SAR images. The results are compared with the European Centre for medium-Range Weather Forecast (ECMWF) data, which demonstrate the effectiveness of the proposed method. The remainder of the paper is organized as follows. In Section 2, the proposed method is introduced in detail. In Section 3, the experimental results of airborne SAR data with invisible ocean waves and two ocean wave systems are given. In Section 4, the results are compared with ECMWF data, which verified the effectiveness of the proposed method, and the sensitivity of the significant wave height is analyzed. Finally, conclusions are drawn in Section 5.