# Estimating Significant Wave Height from SAR with Long Integration Times
## 4 Validation of the Experimental Results With ECMWF and Sensitivity Analysis  
### Validation of the Experimental Results With ECMWF  
In order to verify the effectiveness of the proposed method, the experimental results of the proposed method are compared with the European Centre for medium-Range Weather Forecast (ECMWF) data. The spatial resolution of the ECMWF data is \(0.5^{\circ}\times 0.5^{\circ}\). The time resolution is \(1h\). The comparison of SAR image significant wave height estimation results and ECMWF data are shown in Table 3.  
Figure 10: Refocused SAR image of the second ocean waves and corresponding spectrum. (**a**) Refocused SAR image with two wave systems. (**b**) Spectrum corresponding to refocused SAR image. Figure 9: Refocused SAR image of the first ocean waves and corresponding spectrum. (**a**) Refocused SAR image with two wave systems. (**b**) Spectrum corresponding to refocused SAR image. As is shown in Table 3, it could be found that significant wave heights are estimated for the cases of invisible waves and two wave systems. The time separation between the SAR acquisition time and the ECMWF time is within half an hour. The significant wave heights are very close to that of ECMWF, which fully demonstrates the effectiveness of the proposed method. The space-time analysis is of great significance to verifying the accuracy of the proposed method [29, 30, 31]. In order to further illustrate the effectiveness of the proposed method, 10 sets of airborne SAR data with long integration times collected at different times are processed, and the estimation results of significant wave height are compared with the ECMWF data. The scatter plots of the significant wave height derived by the proposed method and the ECMWF data are shown in Figure 11. Quantitative analysis is performed by bias (BIAS), the root mean square error (RMSE), scatter index (SI) and correlation coefficient (COR). The equations are as follows:  
\[\text{BIAS}=\frac{1}{N}\sum\limits_{j=1}^{N}\left(x_{j}-y_{j}\right) \tag{21}\]  
\[RMSE=\sqrt{\frac{1}{N}\sum\limits_{j=1}^{N}\left(x_{j}-y_{j}\right)^{2}} \tag{22}\]  
\[SI=\frac{1}{\left\langle x_{j}\right\rangle}\sqrt{\frac{1}{N}\sum\limits_{j=1} ^{N}\left[\left(y_{j}-\left\langle y_{j}\right\rangle\right)-\left(x_{j}- \left\langle x_{j}\right\rangle\right)\right]^{2}}\times 100\% \tag{23}\]  
\[COR=\frac{\sum\limits_{j=1}^{N}\left[\left(x_{j}-\left\langle x_{j}\right\rangle \right)\left(y_{j}-\left\langle y_{j}\right\rangle\right)\right]}{\sqrt{\sum \limits_{j=1}^{N}\left(x_{j}-\left\langle x_{j}\right\rangle\right)^{2}\sum \limits_{j=1}^{N}\left(y_{j}-\left\langle y_{j}\right\rangle\right)^{2}}} \tag{24}\]  
among them, \(x_{j}\) and \(y_{j}\) represent the significant wave height in ECMWF data and that obtained by the proposed method, respectively. \(N\) is the number of verification data, and \(\left\langle\cdot\right\rangle\) represents the average operator. As shown in Figure 11, compared with the ECMWF data, the results of the significant wave height obtained by the proposed method have a bias of 0.06 m, a root mean square error of 0.2 m, a scatter index of 14.4%, and a correlation coefficient of 0.95. It can be found that the results of the proposed method are in good agreement with the ECMWF data. In addition, according to Figure 11, it can be seen that the estimation error of the significant wave height is basically stable within 0.2m, and the maximum error is about 0.5 m. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Case**} & \multicolumn{2}{c}{**Case 2-Two Wave Systems**} \\  & **1-Invisible Waves** & & \\ \hline SAR acquisition time (UTC) & 2014.10.11 01:22 & 2014.9.14 01:29 \\ SAR image central location & \((109.46^{\circ}\text{E},17.27^{\circ}\text{N})\) & \((109.58^{\circ}\text{E},17.27^{\circ}\text{N})\) \\ Corresponding time of ECMWF (UTC) & 2014.10.11 01:00 & 2014.9.14 01:00 \\ SWH from SAR image (m) & 1.51 & 0.45 & 0.40 \\ Corresponding SWH from ECMWF (m) & 1.52 & 0.51 & 0.30 \\ \hline \hline \end{tabular}
\end{table}