# Assessing the Performance of the Multi-Beam Echo-Sounder Bathymetric Uncertainty Prediction Model
## 4 Results and Discussion
### Comparison between Modeled and Measured Uncertainties
As such, an underestimation of the contribution of the Doppler effect potentially leads to an optimistic expectation of the depth uncertainties; see [21]. This contribution increases with water depth and beam angle. 2. Baseline decorrelation: As shown by [PERSON] et al. [21], the phenomenon of baseline decorrelation occurs in the MBES interferometry step for phase detection due to slightly different received signals by the two sub-arrays resulting from different angular directions. Thus, the coherence between the two received signals is affected. As the water depth increases, this coherence is reduced (due to a larger signal footprint and consequently a more fluctuating directivity pattern), and thus, the quality of the phase estimates is negatively, affected resulting in an increase in the bathymetric uncertainty. The current expressions used for the depth uncertainty prediction has not accounted for the contribution of the Doppler effect. However, the baseline decorrelation has been accounted for in an approximate way, not accounting for the specific pulse characteristics [21]. Here, it will be investigated to what extent these two factors modify the model-data agreement for the cases considered. Figure 6: Bathymetric uncertainty derived from the measurements (blue) and those predicted for a water depth of 30 m and a pulse length of (**a**) 27 μs, (**b**) 54 μs, and (**c**) 134 μs. 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. As discussed by [PERSON] et al. [21], accounting for the contribution of the Doppler effect requires knowledge of the speed of the array center at emission and reception of the signal projected in the beam direction and the weather condition during the data acquisition. The weather condition during the survey was calm, and the same vessel and MBES as used in [PERSON] et al. [21] were employed. We thus made use of the values derived by them for the calm weather condition; see Figure 3 in [21]. To quantify the effect of baseline decorrelation on MBES bathymetric measurements in the interferometry step, the standard deviation of the phase difference needs to be calculated [42]. The parameters required for this calculation are the actual pulse shape of the transmitted signal (the CW pulse shape used here with the center frequency presented in Table 1) and the length of each sub-array used in the interferometry step, equaling 0.12 m for the case considered, i.e., one-third of the theoretical array length corrected for the shading. Shown in Figures 7 and 8 are the measured and predicted depth uncertainties for a water depth of 10 m and 30 m, respectively, with varying pulse lengths where both the Doppler effect (light green circles) and baseline decorrelation are considered. The baseline decorrelation has now been considered within the echosounder contribution (solid black line with circle markers). The depth uncertainty induced by the motion sensor, correction accuracy for misalignment, sound speed, and heave were equal to those of Figures 5 and 6 and are thus not shown here. From Figure 7, it is seen that the contribution of the echosounder decreases with an increasing beam angle (as the coherence between the two received signal increases with an increasing beam  
Figure 7: 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 10 m and a pulse length of (**a**) 27 μs, (**b**) 54 μs, and (**c**) 134 μs. 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 5 and are thus not shown here.