# Estimating Significant Wave Height from SAR with Long Integration Times
## 5 Conclusions  
When long integration time SAR observes the ocean, the motion of ocean waves will have a great impact on the imaging quality, resulting in waves blurred or even invisible in SAR images. For low-frequency SAR (such as P-band, L-band) data with long integration times, the following two problems are more prominent. (1) The ocean waves are usually invisible in SAR images. It is impossible to estimate significant wave height by means of the present methods. (2) In the case that there are multiple wave systems on the real ocean surface, significant wave height of only one wave system can be estimated for the reason that only a blurred wave system can be observed in SAR images. In order to solve the above two problems, a method of estimating significant wave height from SAR with long integration times is proposed in this paper. Firstly, the azimuth  
Figure 14: Sensitivity curve of significant wave height to propagation direction of ocean waves. cutoff is calculated from SLC data. Then, each ocean wave system is refocused based on the optimum focus setting, respectively. Next, the wavelength and propagation direction of each wave system are calculated from the refocused images. At the same time, the 180\({}^{\circ}\) ambiguity of wave propagation direction is removed without any additional processing. Finally, significant wave height is estimated. The proposed method has been verified by two airborne SAR data with long integration times. One is a case of invisible ocean waves. The other is a case of two ocean wave systems. Compared with the ECMWF data, the results show that the significant wave heights are very close to that of ECMWF, and the error is basically stable at 0.2 m, which sufficiently demonstrate the effectiveness of the proposed method. Further, the sensitivity of the significant wave height to the azimuth cutoff, the wavelength of ocean waves and propagation direction of ocean waves is analyzed. The results show that the sensitivity of the significant wave height to the azimuth cutoff is independent of the azimuth cutoff itself. With the increase of the wavelength of ocean waves, the influence of the wavelength error of ocean waves on the significant wave height is reduced. The sensitivity of the significant wave height to the propagation direction of ocean waves is nonlinear. Moreover, comparing Figures 12-14, it could be found that the wavelength error of ocean waves has the least influence on the estimation result of the significant wave height, the error of azimuth cutoff has the most obvious influence on the estimation result of the significant wave height, and the influence of the propagation direction error on the estimation result of the significant wave height depends on the actual propagation direction. When the wave texture is invisible in SAR images with the long integration times, the present methods cannot estimate the significant wave height. The proposed method can overcome the limitation of the present methods. Compared with the present methods, some steps such as ocean refocusing in Section 2.3 are added. Therefore, the proposed method increases the cost of computation compared with the present methods. However, the proposed method does not increase the time complexity compared with the present methods. For the SLC data of \(P_{azi}\times P_{rg}\) (point number in azimuth\(\times\)point number in range), the time complexity is \(O[P_{azi}\times P_{rg}\times l_{g}(P_{azi}\times P_{rg})]\). The proposed method is suitable for the significant wave height estimation of ocean waves when the waves are invisible in SAR images with long integration times. When the proposed method is applied to estimating significant wave height from SAR with long integration times, it needs to be satisfied that a sub-block data can be chosen in accordance with Section 2.1. In addition, the proposed method can be well applied to other SAR with long integration times, such as spotlight SAR, circular SAR and geosynchronous SAR under development.