# Unmanned Aerial Vehicle Depth Inversion to Monitor River-Mouth Bar Dynamics
## 4 Results
### Validation  
We compared the estimated water depth with transect survey data to validate the proposed method. The survey data was obtained by a remote control (RC) boat equipped with sonar and RTK GPS. Although there are time gaps between the UAV observations and the RC-boat surveys (Table 3), we treat the survey data as true values in the following discussion. The bathymetric change during the time gaps can be assumed to be small in  
Figure 9: Map of estimated seabed levels. (**a**) Case 1, (**b**) Case 2, (**c**) Case 3, and (**d**) Case 4.  
general. However, it should be noted that the river-mouth bar was in a rapid erosional phase just before the typhoon passage in Case 3. Therefore, the transects around the river mouth may not represent actual values due to the several-days gap. To compare the capability of the present method with an existing method, we also estimated water depth along the transects using the spectral method, cBathy [8]; the estimation parameters of cBathy are given in Appendix A. Since the computational cost of cBathy was relatively high, we set the analysis point spacing as 6 m in the cross-shore direction and 10 m in the alongshore direction for cBathy and the present method. The smoothing length scales of cBathy were chosen at 18 m in the cross-shore direction and 30 m in the alongshore direction. Therefore, cBathy uses signals within a rectangular area of 36 \(\times\) 60 m around each analysis point. In contrast, the present method uses signals along the circumference of \(r\) = 20 m, and the resulting water depth was subsequently smoothed by the 5 \(\times\) 5 Gaussian filter (30 \(\times\) 50 m). It should be noted that we cannot compare the two methods in a strict sense, as they involve different filtering processes. Figure 10 compares the seabed profiles from the present method, cBathy and the survey data. In Case 1, the two inversion methods produced similar profiles in good agreement with the survey data. In Case 2 with breakwaters along the shore, both methods underestimated the water depth in the deep area (<-5 m). The underestimation might be due to weak swell signals, and the cross-correlation analysis was significantly affected by non-swell signals. Moreover, there is also the possibility that a projection error affected the results, since the GCPs were available only along the shore for this case. In Cases 1 and 2, cBathy tended to produce larger fluctuations. In Cases 3 and 4, the two methods generated similar results, except in far-field from the camera (No. 56) where cBathy generated significant fluctuations. The discrepancy from the survey data in front of the river mouth (No. 53) in Case 3 might be partially due to the survey time gap, as mentioned above. Table 3 summarizes the overall estimation errors and relevant domain-averaged variables. The present method has a higher level of accuracy than cBathy for the tested cases. The domain-averaged wave periods range from 7.4 to 8.6 s, and thus, the error was supposed to be primarily due to an estimation error of wave celerity according to Equation (2). The domain-averaged cross-correlation coefficient ranges between 0.53 and 0.68. The present method tends to achieve higher accuracy when swells produce coherent signals. These results suggest that the present method works well under the condition that narrow-band swells are dominant, which is consistent with previous comparative studies of the temporal and spectral methods [19; 23].