# Validation of Drifting Buoy Data for Ocean Wave Observation
## 4 Discussion
### Comparison with the Moored GPS Buoy Data  
The agreement between the GPS and drifting buoy-observed wave heights was good. Although the drifting buoy data were contaminated by low-frequency noise [8], the effect on wave height was small. A difference can also be found in the wave sensors between the drifting and moored GPS buoys. The wave sensor of the drifting buoy was an accelerometer. The wave parameters from the accelerometer and from the GPS sensor agreed very well [31]. The good agreement between the two types of buoy was particularly notable considering that they employ different wave sensing instrumentation. The difference in the wave parameters of the moored GPS buoy and the drifting buoy caused by the different sensors was small compared with that caused by the horizontal variability of the wave parameters. The difference between GPS wave height and drifting buoy wave height has various factors other than the difference in buoy position. Among them, the contribution of the wave height resolution and the sampling variability in the zero-up crossing method to the RMSD is evaluated. The variance of the drifting buoy-measured wave height by the (0.1 m) resolution was \(0.1^{2}/12\) m\({}^{2}\), because the variance of a uniform random number with a range of 0.1 is \(0.1^{2}/12\). The RMSD between \(H_{g}\) and \(H_{b}\) associated with the resolution was \((0.1^{2}/12+0.01^{2}/12)^{1/2}\simeq 0.03\) m. The mean wave height in Figure 2a was approximately 1.8 m. The sampling variability of the zero-up crossing method (Figure 1, black solid and dashed lines) was approximately \(S_{d}(H_{1/3})\simeq 0.13\) m for the drifting buoy and \(S_{d}(H_{1/3})\simeq 0.07\) m for the GPS buoys, where \(S_{d}(H_{1/3})\) is the sample standard deviation of \(H_{1/3}\). Their sum was approximately \((0.03^{2}+0.13^{2}+0.07^{2})^{1/2}\simeq 0.15\) m, which is approximately half of the RMSD between \(H_{g}\) and \(H_{b}\). The RMSD, correlation, and SI of the wave heights showed that the accuracy of the drifting buoy-observed wave height was better than that of the ERA5 wave heights. The statistical significance was explored using the bootstrap method explained in Appendix B. This method accounts for the resolution of the wave parameters (e.g., 0.1 m for \(H_{b}\)) and the sampling variability of the zero-up crossing method (Figure 1, black solid and dashed lines). The probabilities of \(R_{d}(H_{g},H_{b})<R_{d}(H_{g},H_{e})\), \(r_{c}(H_{g},H_{b})>r_{c}(H_{g},H_{e})\), and \(SI(H_{g},H_{b})<SI(H_{g},H_{e})\) were almost 100 % for \(R_{dmax}\)=15 km (Figure 2c). The drifting buoy-observed wave height was more accurate than the ERA5 wave heights at more than 99% confidence levels. A bias was observed between \(T_{g}\) and \(T_{b}\) in Figure 2b, which was mainly caused by the spatial variability of the wave periods and the low-frequency noise of the drifting buoys [8]. We checked the dependency of the drifting current speeds on the difference of the wave periods in Figure 2b. However, no clear relationships were observed between them. The contribution of the wave period resolution and the sampling variability in the zero-up crossing method to the RMSD from the linear regression line in Figure 2b is evaluated. The RMSD from the regression line was \(R_{d}(a_{p}T_{g}+b_{p},T_{b})=0.78\) s, where \(a_{p}\) is a slope, and \(b_{p}\) is an intercept of the regression line (Figure 2b). The RMSD between \(T_{g}\) and \(T_{b}\) associated with the resolution was \((1/12+0.1^{2}/12)^{1/2}\simeq 0.3\) s. The mean wave period was approximately 8 s in Figure 2b. The values of \(S_{d}(T_{1/3})\langle T_{1/3}\rangle^{-1}\) were approximately 0.03 and 0.02 for the drifting and GPS buoys, respectively (Figure A1, red lines). The RMSD between \(T_{g}\) and \(T_{b}\) associated with the sampling variability was \((0.24^{2}+0.16^{2})^{1/2}\simeq 0.3\) s. They sum up to approximately \(0.3\sqrt{2}\simeq 0.4\) s, which is greater than half of the RMSD from the linear regression line (\(R_{d}(a_{p}T_{g}+b_{p},T_{b})\)).