# Estimating Significant Wave Height from SAR with Long Integration Times
## 3 Experiments of Estimating Significant Wave Height from SAR with Long Integration Times
### Case 1-Invisible Ocean Waves from SAR with Long Integration Times  
The situation where the ocean waves are invisible is common from SAR with long integration times. In this subsection, the proposed method is applied to the P-band field data. The experimental data comes from the sea trial experiment conducted by the Aerospace Information Research Institute, Chinese Academy of Sciences covering South China Sea. It was collected on 11 October 2014. The integration time is 23 s. The radar system parameters are shown in Table 1.  
The SAR image obtained by the traditional imaging method is shown in Figure 2a, and the image spectrum is shown in Figure 2b. As shown in Figure 2a, the ocean waves are  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parametric Name** & **Parametric Symbol** & **Parametric Value** \\ \hline Radar wavelength (m) & \(\lambda\) & 0.5 \\ Platform height (m) & \(H\) & 8600 \\ Slant range of scene center (m) & \(R_{0}\) & 18,000 \\ Platform speed (m/s) & \(V\) & 122 \\ Integration Times (s) & \(T_{0}\) & 23 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Radar system parameters.  
completely invisible. Meanwhile, the corresponding wave spectrum cannot distinguish the wave characteristics shown in Figure 2b.  
The azimuthal autocorrelation function obtained from the SAR image spectrum is shown in Figure 3. Gaussian fitting is performed according to the Equation (1), and the azimuth cutoff \(\lambda_{c}=86.72\) m is calculated, which will be used to estimate significant wave height later.  
Since the ocean waves are completely invisible, the estimation of significant wave height cannot be carried out. So it is necessary to refocus ocean waves. The SAR SLC data shown in Figure 2a is refocusing. By traversing the focus setting variation section \(\Delta V_{i}\in[V-50,V+50]\), the curve of the normalized peak-to-background ratio obtained changing with focus setting is shown in Figure 4.  
Figure 3: Azimuthal autocorrelation function and its Gaussian fitting results.  
Figure 2: SAR image with invisible waves acquired by traditional imaging method and corresponding spectrum. (**a**) SAR image with invisible waves. (**b**) Spectrum corresponding to SAR image.  
As shown in Figure 4, the normalized peak-to-background ratio has only one local maximum value, indicating that there is only one wave system on the the real ocean surface. When \(\Delta V_{opt}^{1}=10\) m/s, the refocusing quality of the ocean waves is best shown in Figure 5a. The corresponding wave spectrum is shown in Figure 5b.  
As shown in Figure 5a, it can be found that the wave texture is clearly visible. Meanwhile, the wave spectrum is highlighted in Figure 5b, which is more conducive to estimate significant wave height. Using the process shown in Figure 1, the wavelength \(\lambda_{p}^{1}=233.85\) m of ocean waves can be obtained. Due to \(\Delta V_{opt}^{1}>0\), the wave propagation direction after \(180^{\circ}\) ambiguity removal is \(\phi^{1}=299.19^{\circ}\). Finally, the significant wave height \(SWH^{1}=1.51\) m is calculated by Equation (19).