# Estimating Significant Wave Height from SAR with Long Integration Times
## 3 Experiments of Estimating Significant Wave Height from SAR with Long Integration Times
### Case 2-Multiple Ocean Waves from SAR with Long Integration Times  
In common, when long integration time SAR is used to observe the ocean with multiple wave systems, only a wave system can be observed in the SAR images obtained by traditional imaging methods. In order to verify the effectiveness of the proposed method for estimating significant wave height of multiple ocean systems, the proposed method is  
Figure 4: Normalized peak-to-background ratio curve with focus setting.  
Figure 5: Refocused SAR image of ocean waves and corresponding spectrum. (**a**) Refocused SAR image with invisible waves. (**b**) Spectrum corresponding to refocused SAR image.  
applied to the L-band field data in this subsection. However, since there are no SAR data of multiple wave systems, the SAR data of two wave systems is selected for experimental verification. 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 14 September 2014. The radar system parameters are shown in Table 2.  
The SAR image obtained by the traditional imaging method is shown in Figure 6, while the image spectrum is shown in Figure 6. As shown in Figure 6, it can be found that wave textures are very weak, and the corresponding wave spectrum characteristics are also relatively weak, which brings difficulties to estimating significant wave height. In addition, only a wave system can be observed in SAR images.  
The azimuthal autocorrelation function obtained from the SAR image spectrum is shown in Figure 7. Gaussian fitting is performed according to the Equation (1), and the azimuth cutoff \(\lambda_{c}=44.80\) m is calculated, which will be used to estimate significant wave height below.  
The SAR SLC data is refocusing shown in Figure 6. 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 8.  
As shown in Figure 8, the normalized peak-to-background ratio has two local maximum value, indicating that there are two wave systems on the the real ocean surface, namely \(Num=2\) and \(\Delta\mathbf{V_{opt}}=[\Delta V_{opt}^{1},\Delta V_{opt}^{2}]\). When \(\Delta V_{opt}^{1}=20\) m/s, the refocusing quality of the first ocean waves is best. When \(\Delta V_{opt}^{2}=-30\) m/s, the refocusing quality of the second ocean waves is best.  
\begin{table}
\begin{tabular}{c c c} \hline
**Parametric Name** & **Parametric Symbol** & **Parametric Value** \\ \hline Radar wavelength (m) & \(\lambda\) & 0.23 \\ Platform height (m) & \(H\) & 8100 \\ Slant range of scene center (m) & \(R_{0}\) & 13,000 \\ Platform speed (m/s) & \(V\) & 117 \\ Integration Times (s) & \(T_{0}\) & 6 \\ \hline \end{tabular}
\end{table}
Table 2: Radar system parameters.  
Figure 6: SAR image with two wave systems acquired by traditional imaging method and corresponding spectrum. (**a**) SAR image with two wave systems, but only a wave system can be observed. (**b**) Spectrum corresponding to SAR image.