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A framework to quantify uncertainties of seafloor backscatter from swath mapping echosounders

Abstract

Multibeam echosounders (MBES) have become a widely used acoustic remote sensing tool to map and study the seafloor, providing co-located bathymetry and seafloor backscatter. Although the uncertainty associated with MBES-derived bathymetric data has been studied extensively, the question of backscatter uncertainty has been addressed only minimally and hinders the quantitative use of MBES seafloor backscatter. This paper explores approaches to identifying uncertainty sources associated with MBES-derived backscatter measurements. The major sources of uncertainty are catalogued and the magnitudes of their relative contributions to the backscatter uncertainty budget are evaluated. These major uncertainty sources include seafloor insonified area (1–3 dB), absorption coefficient (up to > 6 dB), random fluctuations in echo level (5.5 dB for a Rayleigh distribution), and sonar calibration (device dependent). The magnitudes of these uncertainty sources vary based on how these effects are compensated for during data acquisition and processing. Various cases (no compensation, partial compensation and full compensation) for seafloor insonified area, transmission losses and random fluctuations were modeled to estimate their uncertainties in different scenarios. Uncertainty related to the seafloor insonified area can be reduced significantly by accounting for seafloor slope during backscatter processing while transmission losses can be constrained by collecting full water column absorption coefficient profiles (temperature and salinity profiles). To reduce random fluctuations to below 1 dB, at least 20 samples are recommended to be used while computing mean values. The estimation of uncertainty in backscatter measurements is constrained by the fact that not all instrumental components are characterized and documented sufficiently for commercially available MBES. Further involvement from manufacturers in providing this essential information is critically required.

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Acknowledgements

Authors wish to thank two anonymous reviewers whose comments improved the manuscript significantly. The study was partly supported by NOAA awards NA17OG2285, NA16RP1718, NA04OAR4600155, NAOS4001153, ONR award N00014-00-1-0092 and IFREMER Foreign Fellow scientist Grant.

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The scientific results and conclusions, as well as any views or opinions expressed herein, are those of the author(s) and do not necessarily reflect the views of NOAA or the Department of Commerce. Mention of a commercial company or product does not constitute an endorsement by NOAA.

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Appendix: Statistical uncertainty in measured EL

Appendix: Statistical uncertainty in measured EL

The statistical fluctuation of the EL is an inherent property of backscattered signals and therefore an unavoidable source of random uncertainty. However, confidence in the mean echo level reliability can be improved by increasing the number of samples used in averaging. In MBES data, this is done most often by averaging across-track and along-track samples. However, this should only be done for homogeneous seafloor as the mean angular response can be corrupted at the transition between two seafloor types. Mosaic segmentation into areas showing similar backscatter can help in selecting regions of the same seafloor type over which the samples can be averaged (Rzhanov et al. 2012). The number of samples available for each beam is controlled by the across-track footprint extent, so the largest number of samples is obtained for the outer-most beams. Assuming that the time series is being sampled at a high enough rate compared with the pulse duration, the number of statistically-independent samples N s inside a beam is computed as the ratio of the length of the receive beam footprint in the across-track direction and the projected pulse duration (Simons and Snellen 2009):

$${N_s}(\theta ) \approx {{\left( {\frac{{z\omega }}{{{{\cos }^2}\theta }}} \right)} \mathord{\left/ {\vphantom {{\left( {\frac{{z\omega }}{{{{\cos }^2}\theta }}} \right)} {\left( {\frac{{cT}}{{2\sin \theta }}} \right)}}} \right. \kern-0pt} {\left( {\frac{{cT}}{{2\sin \theta }}} \right)}}$$
(29)

where z is the water depth, ω the Rx across-track beamwidth, c the sound speed, T the pulse length and θ the incidence angle. Equation (29) holds for long-pulse regime, excluding the angles around nadir. Obviously, the benefit of averaging over several samples exists only when N s > 1. Figure 9 presents the number of statistically independent samples for a MBES with ω = 0.5° and 2°; and z = 50 m (with T = 0.05 and 0.15 ms) and 1000 m (with T = 5 and 10 ms). N s increases with decreasing T and increasing ω.

Fig. 9
figure 9

Estimated number (Eq. 30) of statistically independent samples for each beam for a multibeam echosounder at water depths 50 and 1000 m; beamwidths of 0.5° and 2°; and pulse lengths (0.15; 0.5; 5 and 10 ms)

The standard deviation of N averaged independent samples is given as:

$${\sigma _{\bar {x}}}=\frac{{{\sigma _x}}}{{\sqrt N }}$$
(30)

where \({\sigma _{\bar {x}}}\) and \({\sigma _x}\) are the standard deviations of averaged and individual samples respectively. Eq. [30) is valid provided that the N averaged values are statistically independent, are derived from a same population, and have the same variance (Mandell 1964). Assuming the standard deviation of individual samples is 5.57 dB (Rayleigh distribution) and averaging over the dB values, more than 30 individual samples are required to achieve a 1 dB standard deviation (Fig. 10). If the envelope squared amplitudes (i.e. intensity) in natural units is considered for the averaging (which is a preferable way to do it), the dB value of the standard deviation referenced to the mean is \(10{\log _{10}}\left( {1+1/\sqrt N } \right) \approx 4.34/\sqrt N\) dB (Bjørnø 2017, p. 527). In this case, to reduce the standard deviation to 1 dB, only ~ 20 samples are required (Fig. 10). Although the uncertainty is lowered by averaging over larger number of samples, the spatial resolution is adversely affected which may or may not be important depending on the type of application (compare high resolution mapping, with large scale mapping).

Fig. 10
figure 10

Estimated number of statistically independent samples to be averaged in order to obtain a given standard deviation (in dB). The initial distribution is Rayleigh, with a standard deviation of 5.57 dB

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Malik, M., Lurton, X. & Mayer, L. A framework to quantify uncertainties of seafloor backscatter from swath mapping echosounders. Mar Geophys Res 39, 151–168 (2018). https://doi.org/10.1007/s11001-018-9346-7

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Keywords

  • Multibeam echosounder
  • Calibration
  • Incidence angle