## 5 Validation
In the case of the data resulting from the ship-based experiment, the validation was split into two parts. First, the deep water segments and second the shallow water segments were compared with the reference values. In Figure 7b, the results from the 122 deep water segments are plotted against  
Figure 6: Time series of the interpolated wave model SWH values (blue) and of the SWH calculated with the hourly averaged damping coefficients (red). Figure 7: SWH estimated with averaged damping coefficients \(\delta\) plotted against reference values from a numerical wave model. Point shading with respect to the \(\sigma\) of the estimated SWH. Function course for a perfect positive correlation (red). (**a**) Data from the static antenna. (**b**) Data from the ship-based antenna. the reference values. The mean difference was \(-0.030\,\mathrm{m}\), hence similar to that of the static antenna, but the RMS increased to \(0.210\,\mathrm{m}\). On average, the \(\sigma\) of the estimated SWH values was \(0.083\,\mathrm{m}\) and therefore double the size of the value found for the static antenna. Again, the \(\sigma\) increased for higher SWH, reaching a maximum \(\sigma\) of \(0.438\,\mathrm{m}\). The correlation coefficient between both datasets was \(0.90\). In Figure 8, the results of both water depth classes, sorted according to the reference SWH, are shown. In the case of the segments with a water depth of more than \(25\,\mathrm{m}\) (see Figure 7(a)), \(29\%\) differed more than \(0.20\,\mathrm{m}\) from the reference. More than \(50\%\) from these were measured when the SWH was above \(1.0\,\mathrm{m}\). For the \(184\) segments where the water depth was less than \(25\,\mathrm{m}\), the mean difference was significantly larger, reaching \(-0.108\,\mathrm{m}\) (see Figure 7(b)). Forty two percent of all segments analyzed showed differences of \(0.20\,\mathrm{m}\) and more. For SWH below \(0.5\,\mathrm{m}\), the empirical model results tended to be significantly higher than the reference values. It can be stated that a significant difference between the validation results of the two water depth classes was found. The reason for the worse performance in shallow water could be searched for by either the reference values or by the results from the empirical model. It cannot completely be ruled out that the reference value from the NWM was only vague estimations in the shallow regions crossed by the ship. In this region, no in situ measurements were available for model verification. Nevertheless, it is unlikely that the discrepancies were caused by the reference values. This is because of the good validation results for the static antenna and because of a comparison done with in situ data in shallow water where no systematic effects were found (see Section 3.3.2). It is therefore more likely that the empirical results were responsible for the systematic differences. These results depend on a precise and accurate estimation of the damping coefficient \(\delta\). The estimation requires reliable SNR observations and information about the reflector height \(h_{ref,i}\). Erroneous observations would result in incorrectly-solved \(\delta\) values or may be unsolvable. Such outliers would be down weighted in the average process and would only cause higher noise, but no offset. Because of this, it is most likely that the differences were caused by a systematic effect during the \(h_{ref,i}\) calculation. The hydrodynamic squat effect can cause such a systematic change of \(h_{ref,i}\) and therefore a false oscillation frequency in Equation (1). In shallow water, the depth dependence cannot be neglected, and the squat computation becomes more complicated. Better knowledge of the ship specific squat in shallow regions, as well as of the necessary input parameters will lead to improved validation results.