Research papersAccounting for uncertainty in volumes of seabed change measured with repeat multibeam sonar surveys
Introduction
The topology of the seabed in the nearshore zone varies over a wide range of temporal and spatial scales as unconsolidated sediment is transported by tide- and wave-induced currents (Roy et al., 1994). These changes often impinge on artificial structures, affecting economic and recreational activity, which results in significant financial efforts being required to monitor, limit or compensate for sediment transfers. To date the key economic reasons for quantifying seabed change include the needs to monitor dredged shipping channels (Knaapen and Hulscher, 2002); the dispersal and fate of dumped dredge spoil (Stockmann et al., 2009); the volume of marine aggregate resources (Birchenough et al., 2010); and the seafloor response to engineering works introduced into the marine environment such as cables, pipelines and energy infrastructures (Ying et al., 2012). Scientific drivers include the needs to calibrate bedload transport equations and to gain insights into natural geomorphological dynamics such as bedforms (Barrie et al., 2009), delta channels (Hughes Clarke et al., 2009), landslides (Smith et al., 2007), lava flows (Le Friant et al., 2010), earthquake displacement (Fujiwara et al., 2011) and implications for benthic habitats (Rattray et al., 2013).
Fortunately, the tools available to precisely measure the change in seafloor topography have much improved since Langhorne (1982) hammered steel stakes into a sandwave to monitor its evolution—nowadays, swath sonars systems such as multibeam echosounders (MBES) provide suitable data for most hydrographic studies (Mayer, 2006). A modern seabed change monitoring methodology consists in calculating and analysing the difference between two co-registered Digital Elevation Models (DEMs) obtained from repeat MBES surveys. The resulting “DEM of Difference” (DoD) quantifies the change in elevation with positive values showing deposition (or fill), negative values showing erosion (or cut, scour) and null values showing an unchanged surface. Table 1 presents a review of marine studies that computed DoDs from repeat MBES surveys to visualise seabed change and gain insights in a variety of phenomena affecting seabed elevation.
The volumes associated with surface change can be quite simply obtained by integrating the DoD over the areas of interest (that is, summing the depth-change grid cell values and multiplying by the area of one grid cell). However, the uncertainty in MBES bathymetry datasets often prevents the computation of reliable volume estimates. Many sources of errors affect the accuracy of MBES soundings, including the sonar system used, vessel configuration, vessel motion, tide, parameters of the water-column affecting sound velocity and absorption, low signal-to-noise ratio, bottom detection algorithm, etc. (Hare et al., 1995, Lurton, 2003, Lurton and Augustin, 2010). In addition, DEMs acquired with different systems, geo-positioning techniques, tide corrections or vessel configurations can present vertical or horizontal offsets that would translate into large errors when integrated over large areas (Smith et al., 2007, Brothers et al., 2011). As a consequence, many studies of seabed elevation change do not supplement their visual analysis of the DoDs with an estimation of the transferred volumes (9 out of the 28 cited in Table 1), or do not account for uncertainty in their calculations (11 out of the 28 cited in Table 1).
In the few studies that accounted for uncertainty in volume computations (8 out of the 28 cited in Table 1), two different approaches were used. A first approach consisted in limiting the volume computations to grid cells that showed an elevation change over a threshold, under the assumption that smaller elevation changes are more likely to be due to errors in the DEMs rather than actual change (Table 1). For example, Smith et al., 2005, Smith et al., 2007 and Mazières et al. (2014 ) used an ad hoc threshold purposefully adapted to the magnitude of the datasets’ uncertainty (±1 m), while Caress et al. (2012) used a value equal to twice the vertical precision of the system used (±0.2 m) and Le Friant et al. (2010) used the standard deviation of the DoD over an area where it was assumed that no change had occurred (±3.80 m). The alternative approach consisted in calculating a confidence interval for any volume estimate as the total area of interest multiplied by the depth-change uncertainty, with different studies implementing a different measure of that uncertainty (Table 1). For example, Smith et al. (2005) used the mismatch in the depth of known features on the seabed (±0.50 m), Xu et al. (2008) used the DEMs' vertical precision (±0.20 m) and Lepland et al. (2009) used an estimate of the vertical offset between the two DEMs (±0.10 m).
Similar approaches have been implemented in other research fields concerned with measuring volumes involved in the change of subaerial terrain elevation. In coastal geomorphology for example, Ierodiaconou et al. (In Press) estimated volumes of sediments eroded from the shoreline based on airborne photogrammetry data using for threshold the standard deviation of the DoD within an area where no change had occurred. In fluvial geomorphology, it has become commonplace to calculate volumes of sediments transferred in braided rivers using a threshold that varies with each DoD grid cell, under the reasonable assumption that the uncertainty of a DEM varies spatially (James et al., 2012). The spatially variable threshold – often termed a “Limit of Detection” (LoD) – is calculated as follows: First, a spatially variable uncertainty is obtained for each of the two DEMs involved in the differencing. The spatially variable uncertainty of the DoD is then calculated as the propagation in quadrature of the uncertainty of each DEM. Finally, the LoD is defined as the product of the DoD's uncertainty and a factor depending on the desired level of confidence (Lane et al., 2003, Brasington et al., 2003, Wheaton et al., 2010). The DoD's spatially variable uncertainty can also be used instead of a fixed uncertainty value in the computation of volumetric confidence intervals (e.g. Erwin et al., 2012; Wheaton et al., 2013; Eekhout et al., 2014). The main obstacle in these improved techniques is the first step of calculating a spatially variable uncertainty for each DEM, and a number of approaches have been explored to tackle this challenging task (e.g. Milan et al., 2011; Wheaton et al., 2010; Schürch et al., 2011).
These methodological improvements are immediately applicable to the estimation of volumes involved in seabed change as measured by MBES, with one additional advantage: a measure of the spatially variable uncertainty of a DEM is one of the standard outputs of the CUBE algorithm implemented by most hydrographic software to obtain DEMs from raw MBES data (Calder and Mayer, 2003). Through its implementation of the soundings error budget model devised by Hare et al. (1995) and methodologies for uncertainty propagation and multiple depth hypotheses, the CUBE algorithm produces an uncertainty layer that accounts for many sources of errors such as the survey system used, its auxiliary sensors, configuration and conditions of operation, sounding depth, sound velocity, bottom detection algorithm, seabed slope, sounding density and sounding distance from the DEM grid nodes (Calder and Mayer, 2003).
This article sets out to explore how uncertainty affects the spatially variable thresholding and volumetric confidence intervals techniques for calculating the volumes involved in bathymetric change. We defined the DoD's uncertainty in two manners, as a fixed value obtained from a reference area and as a spatially variable grid based on the DEMs’ CUBE uncertainty, and compared the results. A shallow, high-energy sedimentary system consisting of a harbour enclosed by a breakwall on a high-energy open-ocean coast in Victoria, Australia is used as a field site. The complexity of the system derived from the breakwall interrupting longshore transport makes it an ideal setting to test the techniques on both sediment erosion and deposition areas.
Section snippets
Study site
The study site is Warrnambool Harbour (38.40°S 142.48°E), located on the exposed southern shoreline of Victoria, Australia (Fig. 1). Warrnambool Harbour lies at the western end of an open bay bound at its western edge by a rocky headland (Thunder Point) that extends seaward as a subtidal reef system. A breakwall over 400 m long extends from this point delineating the southern edge of the harbour. At the northern edge, the shoreline is dominated by Holocene foredunes up to 10 m high. The coast
Study site, beach area and reef area
The MBES bathymetry map shows that a sheet of unconsolidated sediment covers the seafloor inside the bay in the lee of the breakwall and extends southward past the breakwall over a rocky seafloor (Fig. 1). A large area of the bathymetry map inside the bay displays a rough, patchy texture that was later identified by a short drop camera survey to be sand mounds with patches of seagrass. The sediment sheet extends southwestward over the complex rocky reef south of the breakwall, and southeastward
Discussion
The widespread availability of MBES systems has made the formation of a DoD from repeat bathymetric surveys an increasingly common technique providing much needed insights in marine geomorphology. Investigations of seabed change occasionally require volume calculations to provide the quantitative information to back up visual interpretation (Table 1). However, as our study illustrated, the uncertainty of the bathymetric DEMs have a large impact on the calculations. In modern MBES systems, the
Conclusions
The capability to quantify the change experienced by the seafloor under the influence of sedimentation processes provides insights into the mechanisms that drive these processes. Undertaking repeat and frequent MBES surveys, differencing the successive DEMs, and computing the associated volumes provide such quantitative information. Our research showed that thorough considerations of uncertainty result in valuable improvements in the computation of volumes of sediment displaced and their
Acknowledgements
We are grateful to Sean Blake (Deakin University) for his help in data acquisition. The Warrnambool City Council funded this project but was not involved in study design, data collection, analysis and interpretation, in the writing of the manuscript or in the decision to submit the article for publication.We are grateful to the editors and an anonymous reviewer for their excellent comments and suggestions to improve this article. The Matlab functions used in this research are available for
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