# Consolidating ICESat-2 Ocean Wave Characteristics with CryoSat-2 during the CRYO2 ICE Campaign
## 5 Discussion  
The comparison between the histogram model, which fits the high-resolution data of ICESat-2 photons, and the radar CryoSat-2 data gives a correlation of 0.95, with a mean difference of 0.14 m and an RMSE of 0.42 m. The study presented in [3], which compared a model derived from the individual waves observed by ICESat-2 with data from the European Centre for Medium-Range Weather Forecasts, gave a median difference of 0.07 m, correlation of 0.91, and RMSE of 0.38 m. The comparison in [3] has a lower time lag compared to this study; however, it was based on a gridded model. While this method has a higher difference than the methods based on the standard deviation (both ATL12 and the standard deviation model), it shows the possibilities of extracting additional information from surface observations of the oceans. Some effects of the observed waves, such as the wave direction, were corrected for in [3] but were not considered in our study to allow the determination of the SWH without using external tables. The metrics from this study can be seen in Table 4, along with those of the three models used in [3]. ATL08-Ocean is equivalent to the histogram model in this paper, and CryoSat-2 and ATL12 are the standard data output. ATL12 in [3], when ERA-5 is used as a reference, has a comparable performance to ATL12 in this paper, although we found that ATL12 has a more negative bias when it is compared to CryoSat-2. The overall performance of the different models, independent of the observed wave height, can be estimated using the scatter index, as shown in Table 3. Using all the observations, the SI of the histogram model is 17.6%, and it is 14.2% for the standard \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline
**SWH** & & \multicolumn{3}{c}{**0–1.5 m**} & \multicolumn{3}{c}{**1.5–2.5 m**} & \multicolumn{3}{c}{**2.5–11 m**} \\
**Models** & **Diff.** & **SD** & **SI** & **N** & **Diff.** & **SD** & **SI** & **N** & **Diff** & **SD** & **SI** & **N** \\ \hline Histogram & 0.18 m & 0.23 m & 39.5\% & 9883 & 0.18 m & 0.31 m & 17.7\% & 18,390 & 0.01 m & 0.59 m & 8.75\% & 9583 \\ Standard Deviation & 0.19 m & 0.19 m & 35.7\% & 9883 & 0.17 m & 0.23 m & 14.5\% & 18,390 & 0.13 m & 0.43 m & 6.67\% & 9583 \\ ATL12 & \(-\)0.06 m & 0.14 m & 19.77\% & 9750 & \(-\)0.11 m & 0.17 m & 10.2\% & 18,225 & \(-\)0.22 m & 0.45 m & 7.36\% & 8788 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean difference (Diff. ), standard deviation (SD), and scatter index (SI) from the comparison between the models and CryoSat-2, as well as the number of data points (N) for each SWH segment. deviation model and 12.7% for ATL12. ATL12 overall has fairly good agreement with CryoSat-2, while the other models experience slightly higher errors, but ATL12 deviates in the Q-Q plot. While this could be caused by a larger number of observations at lower SWHs, we have not proved that this is the case. The performance was estimated on the in situ corrected CryoSat-2 data; however, the difference was not large (approximately 3%). Comparisons with in situ measurement stations have previously been done for multiple satellite missions, with [2] using seven satellite missions in their comparison. Their study showed a high correlation for all missions (above 0.982) and an RMSE between 0.15 and 0.21 m, which is comparable to the crossover comparisons done in this paper (Table 1). However, when using CryoSat-2 as a baseline for ICESat-2, such a high correlation is not possible due to the average time lag between the satellites of 2.8 h, because in this amount of time, the sea state can change significantly. This is clear in Figure 6; however, within the known constraints, the correlations are still just below the expected correlation, as shown by the crossover analysis. A disadvantage of using the observed waves to determine the SWH is the necessity of observing an entire wave or large parts of it.