## 4 Results
### Validation  
For the validation, a case study and an overall comparison were performed separately. Figure 4 presents the case study using the collocated traditional altimeter data. In this case, SARAL and HY2A altimeter data were collocated with the InIRA data, according to the criteria mentioned above. The beginning time for the InIRA data acquisition is 31 January 2017 at 13:16:33 UTC. The collocated positions with HY2A data are located in deep-sea areas, while the positions with SARAL are in offshore areas. As the SWH values for these collocations are overlapping, we plotted every type of SWH data on a separate figure for a clearer comparison. Meanwhile, its collocated data track was plotted with a black line, to clearly determine the intersection position. As shown in Figure 4, the SWH data from the InIRA have good agreement with the two traditional altimeter collocations. The statistical errors were calculated (Figure 5). The RMSEs of the InIRA SWH compared with the SARAL and HY2A data are 0.18 m and 0.38 m, respectively, indicating that the SWH retrieval accuracy with the application of the proposed model is acceptable. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\(\theta\)} & \multicolumn{5}{c}{**Coefficients**} \\ \cline{2-6}  & **C00** & **C01** & **C02** & **C10** & **C11** \\ \hline
3.0 & 18.7429 & 1.2219 & \(-0.0674\) & \(-14.1237\) & 0.3946  
Furthermore, the statistical errors for all collocations were calculated. The InIRA SWH errors with WW3 data are first shown (Figure 6). The WW3 model data provide rich collocations and helped in analyzing the overall accuracy. The figure reveals consistency between the InIRA retrievals and WW3 data, with an RMSE of 0.43 m and a slight bias of \(-\)0.01 m. The differences mainly occur at two ends (smaller than 1.0 m and larger than 3.5 m). For the lower SWH range, the InIRA SWH is on the high side, whereas it is on the low side for the higher SWH range. We think that this is possibly due to the varying SWH dependence in different SWH ranges. Overall, the InIRA SWH retrievals are consistent with the WW3 data. The comparison with WW3 data was reanalyzed for determining the retrieval accuracy trends with different incidence angles and relative wave directions (Figure 7). Here, the incidence angle range is from 2.5\({}^{\circ}\) to 7.5\({}^{\circ}\), while some data at the edge of the beam were removed for ensuring data quality. Additionally, the relative wave direction range is from 0\({}^{\circ}\) to 90\({}^{\circ}\), for which the 0\({}^{\circ}\) and 90\({}^{\circ}\) represents the range direction and azimuth direction, respectively. It has the same definition as one in Figure 3. From Figure 7a,b, we found that both BIAS and RMSE vary with incidence angles. In particular, when the incidence angles were larger than 6.5\({}^{\circ}\), the accuracies were significantly degraded (but still acceptable). From RMSE trends, the central beam (about 5.0\({}^{\circ}\)) has better accuracy than beams at both  
Figure 4: SWH data from **(a)** InIRA, **(b)** SARAL, and **(c)** HY2A. The black lines are plotted to find the intersection positions. Figure 5: Comparisons between SWHs from InIRA retrievals and collocated **(a)** SARAL and **(b)** HY2A data. ends. It is probably due to the higher signal-to-noise ratio (SNR) of the central beam. From Figure 7c,d, we found that both BIAS and RMSE slightly oscillate with relative wave directions by an amplitude about 0.1 m. The accuracies at different relative wave directions are all acceptable. The BIAS at range and azimuth directions (0\({}^{\circ}\) and 90\({}^{\circ}\)) are better than ones at other directions, which are probably due to the model integration factors are more sensitive to wave components at the two directions. In addition, the RMSE in the azimuth direction (90\({}^{\circ}\)) is significantly higher than ones in other directions, which may be due to the residual cutoff effects from velocity bunching modulation.