Error Analysis

Single Beam

The ASCII files from each vessel platform were imported into ArcMap version 10.3, merged into one shapefile, and reviewed for spatial and vertical agreement at line crossing zones. A Python script was written locally to calculate the elevation differences at the intersection of crossing lines. The script calculated the elevation difference between points at the intersection of tracklines using an inverse distance weighting equation and was run as an Esri ArcMap Ad-In program. Elevation values at line crossings should not differ by more than the combined instrument acquisition error (per manufacturer specified accuracies; tables 1–3). GPS cycle slips, stormy weather conditions, and rough sea-surface conditions can contribute to poor data quality. If discrepancies exceeding the acceptable error threshold (plus or minus [±] 0.30 m) were found, the line in error was statically adjusted or removed. A line in error constitutes one or more of the following: (1) a segment with values inconsistent with those from several crossing lines, (2) a known equipment problem logged at the time of acquisition, or (3) known bad GPS data identified in the post-processing steps. For this dataset, elevation differences at 1,000 crossings (90 percent of the total crossings) were within ±0.30 m.

Interferometric Swath

The stated horizontal accuracy of the Marinestar HP navigation subscription used during IFB acquisition is ±10 centimeters (cm) horizontally and ±15 cm vertically. The Coda Octopus F190R+ IMU integrated the Marinestar HP position and measured vessel motion. The Coda Octopus F190R+ has the following stated accuracies: velocity, ±0.014 meters per second (m/s); roll, ±0.025 degrees; pitch, ±0.025 degrees; heading, 2-m baseline (0.05 degrees); and heave, 5 cm or 5 percent of heave amplitude (on-line) (table 7). The vertical accuracy for the SWATHplus-H system varies with depth and across track range. At maximum swath width, the across-track resolution can be within 1 cm depending on water conditions and bottom type (table 8). 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 9). Sound velocity profile cast data were collected with the SonTek Castaway-CTD, which has a stated accuracy of ±0.15 m/s (table 6).

Vertical Transformation

In addition to positional accuracies inherent for different datums (for example, NAD83, standard deviation [σ] =2.0 cm; NAVD88, σ=5.0 cm; MLLW, σ=1.6 cm), error is introduced every time the data is transformed between datums. The transformation from ITRF00 (ellipsoid height) to NAVD88 (orthometric height) is σ=7.0 cm, and the maximum cumulative uncertainty (MCU) (quantified by standard deviation of the error) introduced when transforming from ellipsoid height to orthometric height to a tidal datum (MLLW) is 17.1 cm for the VDatum region listed as “Louisiana/Mississippi—Eastern Louisiana to Mississippi Sound” (https://vdatum.noaa.gov/docs/est_uncertainties.html). NOAA reports the vertical error associated with each conversion performed in VDatum version 3.6 (table 10). As stated earlier, the x,y,z point data files were transformed horizontally and vertically from ITRF08 into ITRF00 (IFB data only), from ITRF00 (ellipsoid height) into NAD83 (CORS96) and NAVD88 (orthometric height) using the GEOID12B model, and then from NAD83 (CORS96) and NAVD88 GEOID12B into NAD83 (CORS96) and MLLW (tidal datum).

Digital Elevation Model

A comparison of the DEM with the soundings (x,y,z point data) was performed to evaluate how well the DEM spatially represented the original soundings. This was done by comparing the cell node values of the DEM surface to the final processed x,y,z point data using the Esri ArcGIS Spatial Analyst Extract Values to Points tool. This produced a set of elevation differences between the gridded surface and the input data from which the root mean square (RMS) error was calculated using the following equation:

This dataset contains 4,715,011 SBB and IFB data points. The DEM boundary polygon used in this report was selected as an acceptable area with reliable data coverage for accurate, quantitative comparisons. Consequently, not all of the data points are represented by the DEM because they do not fall within the boundary or they are on the perimeter of the boundary and are not used in the interpolation. For this dataset, 4,136,171 (87 percent) of the data points in the NAD83 (CORS96) and NAVD88 GEOID12B dataset are represented by the DEM and have an RMS of 0.32 m. To express the differences between the point dataset and the extracted DEM values, the RMS values are color coded and shown in figure 12. This comparison demonstrates how well the model surface represents the original sounding and sample data.

In this dataset, there may be hundreds of samples in a 50-m by 50-m cell; however, they are represented on the surface by a single cell value. Therefore, in cases where terrain slope is high, the gridding formula reduces the actual variability in the sample data (Foxgrover and others, 2004; Fregoso and others, 2008; Finlayson and others, 2011). The larger differences between the DEM and the data points may also be caused by creating continuous surfaces over bathymetric datasets where trackline spacing is wide enough that it does not adequately represent overlap. The larger differences (either deep or shallow) are apparent in and around the tidal inlets and along steeper transitions in water depth, particularly on the Mississippi Sound side of East Ship Island. The highly variable seafloor elevations on the eastern side of the study area are coincident with higher RMS values around DA-10 (Sand Island), just west of Horn Island Pass (fig. 12). 

Figure 12. Map showing error values overlain upon the 50-meter (m) digital elevation model (DEM) referenced to North American Vertical Datum of 1983 Universal Transverse Mercator Zone 16 North, and North American Vertical Datum of 1988 (NAVD88) with respect to the GEOID12B model. The colored circles represent the difference in elevation between the DEM (bathymetry grid) value and the datapoint value (for positive values, the grid is deeper than the soundings; for negative values, the grid is shallower than the soundings). Transparent circles represent error within ±0.50 meter. The base map is derived from Landsat 8 imagery acquired January–February 2015 (Guy, 2015a, b). [Click figure to enlarge]