# Assessing the Performance of the Multi-Beam Echo-Sounder Bathymetric Uncertainty Prediction Model
## 1 Introduction  
Reliable representation of the sea- and river-floor bathymetry is of high importance for a large number of applications, such as maintaining safe navigation, marine geology, off-shore construction, and habitat mapping [1; 2; 3]. Acoustic remote sensing with Multi-Beam Echo-Sounder (MBES) systems has been extensively used for delivering such information due to the systems' capability to map large areas in a relatively short period of time. The system transmits an acoustic pulse (ping) in a wide swath perpendicular to the sailing direction [4]. Beamforming at reception enables determining the Two-Way Travel Time (TWTT) of the received signal for a set of predefined beam angles. The depth measurements are derived from the TWTT per beam and speed of sound in the water [5]. However, similar to any type of measured parameter, the derived depths are affected by varying sources of uncertainty, such as those in the sound speed, motion, and rotation sensors. Obtaining a realistic a priori estimate of the depth uncertainties is of importance for a number of applications. Approaches to obtain these estimates, and subsequently to use them, are described in the literature. [PERSON] [6; 7] developed an a priori vertical uncertainty prediction model to quantify the contribution of various sources. The developed model has been widely used for predicting the uncertainties prior to a survey, as implemented in the A priori Multi-beam Uncertainty Simulation Tool (AMUST) used throughout this paper. Therefore, in this paper, the term uncertainty prediction model refers to the model of [6; 7]. This model has been also employed for producing bathymetry maps(for example in the Combined Uncertainty and Bathymetry Estimator (CUBE) algorithm) [8; 9; 10] and for bridge risk management and coastal inundation modeling [11; 12]. Moreover, a realistic bathymetric uncertainty description is key for survey planning to assess whether the required survey standards can be met in a specific measurement campaign. Apart from the direct application of the depth measurements for map production, derivatives of the bathymetric measurements, such as the slope and bathymper position index, can be used for sediment classification [13; 14]. As an example, [PERSON] et al. [15; 16] combined the so-called depth residuals (related to the depths' standard deviation) with backscatter strength measurements to increase the discrimination performance of the sediment classification methods and to solve the ambiguity in the relationship between backscatter value and median grain size [17]. Recently, [PERSON] et al. [18] used the bathymetry uncertainty to assess the statistical significance of the changes in the measured depth differences between the various frequencies with the incident angle. Lacking information with regard to the uncertainties inherent to the MBES can lead to misinterpretation. As an example, on might mistakenly classify the uncertainties and assign different sediment types to measurements having actually the same sediment composition, but different uncertainties. Effort has been put forward to address the contribution of the uncertainty sources, of relevance to the MBES bathymetric measurements, not accounted for in the uncertainty prediction model of [6; 7]. These contributions can result from developments that have been since then realized in MBES systems, such as enabling the use of Frequency Modulated (FM) pulse shapes or using sophisticated bottom detection methods or filters [19; 20]. [PERSON] et al. [21; 22] quantified the vertical uncertainties induced by the use of FM pulse shapes and assessed their relevance for MBES bathymetric uncertainty predictions. [PERSON] and [PERSON] [4] proposed a unified definition of a quality factor for sonar bathymetry measurements, which is a posteriori estimator of the relative depth uncertainty induced by the signal features.