Error Analysis
Single Beam
The single-beam data were imported into ArcGIS, and an in-house Python script was created to evaluate the elevation differences at the intersection of crossing tracklines. The script calculates the elevation difference between points at each intersection using an inverse distance weighting equation. Elevation values at line crossings should not differ by more than the combined instrument acquisition error (manufacturer specified accuracies). GPS cycle slips, stormy weather conditions, and rough sea surface states may all contribute to poor data quality. If discrepancies were found that exceed the acceptable error threshold, then the line determined to be in error was either statically adjusted or removed. A line in error is considered to have one or more of the following: (1) a segment where several crossings are incomparable, (2) a known equipment problem, or (3) known bad GPS data seen in the post-processing steps. For this dataset, elevation differences at all crossings were less than or equal to 0.14 m, and the elevation differences were within plus or minus (±) 0.10 m for 99.3 percent of the 434 crossings at which the horizontal distance between soundings was less than 2 m.
Interferometric Swath
The manufacturer's stated accuracy of the OmniSTAR HP navigation subscription used during swath bathymetry acquisition is ± 10 centimeters (cm) horizontally and ±15 cm vertically. The Coda Octopus F190R IMU, which integrates the OmniSTAR HP position with motion, measures vessel velocity (± 0.014 m/s), roll and pitch (± 0.025 degrees), heading (1-m baseline – 0.1 degrees), and heave (5 cm per meter of depth) (table 3). The vertical accuracy for the SWATHplus-H system varies with depth and across track range. At 57 m it is accurate to 10 cm vertically (table 4). Sound velocity captured in real time at the transducer head was collected by a Valeport MiniSVS with a stated maximum error of ± 0.017 m/s (table 5). SOS water column data tables are also applied to the swath data, based on time and distance from the sound velocity cast to the vessel. The SOS profile data were captured with a Valeport MiniSVP with stated accuracy of ± 0.02 m/s (table 6).
Vertical Transformation
In addition to positional accuracies inherent for different datums (for example, NAD83, σ = 2.0 cm; NAVD88, σ = 5.0 cm; Mean Lower Low Water, MLLW, σ = 1.6 cm), error is introduced every time the data are transformed between datums. The transformation from ellipsoid height (ITRFXX) to orthometric height (NAVD88) is σ = 7.0 cm, and the maximum cumulative random uncertainty (quantified by standard deviation) introduced when transforming from ellipsoid height to orthometric height to a tidal datum (for example, MLLW) is 17.1 cm for eastern Louisiana (http://vdatum.noaa.gov/docs/est_uncertainties.html).
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Digital Elevation Model
Point data from both the interferometric swath system (5-m samples) and single-beam soundings were merged into a single dataset. Using the Spatial Analyst tool in ArcGIS, the soundings were compared to the final combined DEM by extracting values from the model at the precise sounding sample locations used to create the model. The difference between the point data and extracted model values were classified in 0.25-m intervals and color coded in order to visually articulate differences (fig. 7). This comparison demonstrates how well the surface represents the original sounding and sample data. There are a total of 603,372 samples, and the mean difference between the samples and the model is -0.0099, with a range of -1.95 to 2.28 m and a sample standard deviation of 0.15 m (95-percent confidence interval of 0.30 m). The interpolated resolution was constrained by a 50-m cell size and the distance between tracklines was generally in excess of 150 m (fig. 5). Depending on how coarse the DEM resolution is compared to sounding distribution greatly affects how well the DEM represents the data. In this example there may be hundreds of samples in a 50-m x 50-m cell; however, all of those sample are only represented on the surface by one value, typically the mean. Thus, in cases where terrain slope is high, the gridding formula mutes the actual variability in the sample data. This sacrifice is necessary when creating continuous surfaces over bathymetric datasets where trackline spacing did not allow for overlap. Foxgrover and others (2004), Fregoso and others (2008), and Finlayson and others (2011) also reported difficulty with gridding over steep slopes. Percent coverage of swath sample data relative to the elevation model area is approximately 58.58 percent, encompassing 33.96 km2. |
Figure 7. Error values representing the difference between the bathymetry grid (DEM) at each sample point (positive values – grid is deeper than soundings; negative values – grid is shallower than soundings). White or gray symbols represent error of +/- 0.25 centimeters. Island extent is derived from USGS lidar data collected in 2011. [Click to enlarge] |
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