# Assessing the Performance of the Multi-Beam Echo-Sounder Bathymetric Uncertainty Prediction Model
## 4 Results and Discussion
### Comparison between Modeled and Measured Uncertainties  
The modeled bathymetric uncertainties were derived using the characteristics of the MBES and its settings during the data acquisition (see Table 1), uncertainties of the sound speed measurements and motion sensors (Section 3), and environmental related parameters. It should be highlighted that the uncertainty predictions presented here were based on these specifications and are not to be viewed as the uncertainty predictions applicable to a different scenario. Generally, information regarding the majority of the input parameters is reliable. However, in the expression used for predicting the bathymetric uncertainty due to the uncertainty in the phase bottom detection, the number of phase samples, \(n_{p}\), is used [6; 7]. This was given in [40] as:  
\[n_{p}=\frac{\frac{d\Omega_{R}}{\cos^{2}\Theta}}{\frac{cT}{2\sin\Theta}}\, \tag{5}\]  
where \(\Theta\) indicates the angle between the received beam and nadir (depth-axis) [22]. \(\Omega_{R}\) is the across-track beam opening angle (the beam opening angle at reception), which increases with an increasing steering angle for the outer beams; see Table 1 for its value at nadir. How well this equation represents the actual number of phase samples is questionable as there is no information with regard to the approach taken by [PERSON] for deriving the number of phase samples per beam. Presented in Figure 4 with gray is the prediction of the bathymetric uncertainty for the situation in which the number of phase samples within the beam footprint was derived using Equation (5). Shown with black and green are the bathymetric uncertainties obtained using the number of phase samples extracted from the data [41] and those measured respectively. It is seen that in case of using the theoretical number of phase samples in the uncertainty prediction model, large discrepancies occurred between the modeled and measured uncertainties; compare the gray and green in Figure 4, in particular for the middle sector of the swath with the prediction overestimating the measured uncertainties. Using the number of phase samples obtained in practice for predicting the bathymetric uncertainties reduced this discrepancy to a noticeable extent. Therefore, for the comparison between the modeled and measured bathymetric uncertainties, the number of phase samples obtained in practice was used in the prediction model. Figure 3: Standard deviation of the depth measurements for water depths of (**a**) 10 m and (**b**) 30 m, with a pulse length of 27 μs (red), 54 μs (green), and 134 μs (blue). The transition from the amplitude (Ampl) to phase (Ph) detection is shown by changing the square marker to an asterisk. Shown in Figure 5 are the modeled and measured bathymetric uncertainties for the area indicated by the black dashed rectangle in Figure 1e for a water depth of 10 m with a pulse length of 27 us (a), 54 us (b), and 134 us (c). It should be noted that for the bottom detection method (amplitude or phase), the approach documented in the data was taken. Both the measured and predicted depth uncertainties increase with increasing pulse length. In general, the uncertainties derived from the prediction model are in a good agreement with those encountered in reality with larger discrepancies occurring for the beams where the amplitude detection was used. The measured bathymetric uncertainty slightly increases with an increasing beam angle which is captured by the prediction model. As discussed in Section 4.1, lengthening the pulse duration results in using the amplitude detection for a larger range of beams around nadir, and consequently, the model underestimates the bathymetric uncertainties for a broader range of beams; compare Figure 5a and Figure 5c. The most dominant source of uncertainty has been predicted to be the echosounder contribution; see the solid back line with circle markers. As discussed in Section 2.1, this contribution is divided into three terms (see [22; 25]):  
1. Uncertainties in the range measurements,
2.