# Assessing the Performance of the Multi-Beam Echo-Sounder Bathymetric Uncertainty Prediction Model
## 4 Results and Discussion
### Comparison between Modeled and Measured Uncertainties
angle), in contrast to Figure 5, where an increase in the uncertainty with the beam angle was observed. This indicates that accounting for the baseline decorrelation in the approximate way as carried out in [6; 7] overestimates the uncertainties. It is also seen that although the total bathymetric uncertainty (cyan) decreases, the magnitude of the reduction is lower than that of the echosounder contribution, which is due to the compensation of the decrease by an increasing contribution of the Doppler effect with the beam angle. Compared to the situation where these contributions were not considered, the variations of the bathymetric uncertainty with the beam angle as seen in the measurements are captured better (compare the solid cyan curve corresponding to the total predicted uncertainty in this figure to that of Figure 5). Furthermore, for the 30 m water depth, a decrease in the contribution of the echosounder is observed (see Figure 8). With regard to the total bathymetric uncertainty, in contrast to the shallower depth where a decrease was seen, here, no noticeable change is observed except for the pulse length of 54 us where an increase occurred. The almost equal uncertainties (compare Figure 6 and Figure 8) means that the decrease in the contribution of the echosounder is canceled out by the increase in the contribution of the Doppler effect. Compared to the measured uncertainties, still an underestimation occurs; however, accounting for the Doppler effect and baseline decorrelation can improve the performance of the uncertainty prediction model in capturing the increase of the measured uncertainties with the beam angle; see Figure 8b. Although accounting for the baseline decorrelation and Doppler effect improved the performance of the prediction model in capturing the dependency of the depth uncertainties to the beam angle,  
Figure 8: Bathymetric uncertainty derived from the measurements (blue) and those predicted considering the uncertainty induced by the Doppler effect and baseline decorrelation without (cyan) and with (light pink) additive noise for a water depth of 30 m and a pulse length of (**a**) 27 us, (**b**) 54 us, and (**c**) 134 us. The change from amplitude to phase detection is shown by switching from square markers to asterisks with the same color. The location of this switch was similarly applied in the modeling. The depth uncertainty induced by motion sensor measurements, correction accuracy for misalignment, sound speed, and heave are equal to those of Figure 6 and are thus not shown here. still discrepancies between the predicted and measured vertical uncertainties remained. A potential contributor deteriorating the quality of the bathymetric measurements toward the outer parts of the swath is the decreased SNR, due to the additive noise [21; 43]. The uncertainty prediction model assumes an infinite SNR, which is violated in reality. Here, we will investigate to what extent the additive noise contribution modifies the vertical uncertainty predictions for the cases considered. The SNR expresses the relative importance of the contribution of the expected received echo level and the perturbing noise and is given by the sonar equation [44]. The nature of the additive noise makes its prediction complicated as it requires information on the backscatter strength returned to the MBES, which is dependent on the composition of the seabed, angle of incidence, acoustic frequency, seafloor roughness, volume heterogeneity, and bulk density [45]. The backscatter strength received is the result of a complex interaction of the transmitted acoustic signal and the often inhomogeneous seafloor [46; 47]. Here, the total backscatter strength was modeled as the result of a contribution from volume backscattering and rough interface backscattering based on the APL -model [48]. A priori knowledge of the surveyed areas indicated a very soft sediment, and thus, clayey sand was assumed in the APL-model.