Error Analysis

Shoreline Uncertainty

In order to determine the uncertainties associated with individual shorelines, a methodology following Morton and Miller (2005) and Hapke and others (2006) was used to estimate a positional error value for each shoreline. Total shoreline positional error was a function of the errors inherent in the source data/data collection and errors generated in the interpolation or creation and identification of the vector shoreline.

Interpolated MWH Shorelines: October 2012–December 2013

The terms used for the interpolated shorelines derived from October 2012 to December 2013 were (1) predicted MHW uncertainty—an estimate of interpolated shoreline position accuracy based on the slope and distance between track lines (1–2.5 m); (2) average measured MHW error—the positional difference between the interpolated MHW shoreline and the location of the MHW elevation on the cross-shore profiles from the same survey date (1–7.5 m); (3) collection and equipment error—derived from static portions of each survey (0.07–0.12 m); (4) a term to account for horizontal positional variation found when driving the GPS (horizontal to the ATV) on a sloped surface (0.02–0.1 m). Individual shoreline uncertainties are available in the shapefile “ACCURACY” attribute and in the metadata file.

Extracted MHW Shorelines: January 2014–September 2014

For the two surveys conducted in January 2014 and September 2014, the MHW elevation (0.46 m NAVD 88) was extracted from a surface generated from field collected data points. The terms used to estimate error for the extracted shorelines were (1) average measured MHW—the positional difference between the extracted MHW shoreline and the location of the MHW elevation on the cross-shore profiles from the same survey date (2.2–3.2 m; September 2014 used an average of previous time periods, as a large displacement of MHW due to high waves that occurred in the day between shoreline and profile surveys); (2) collection and equipment error—derived from static portions of each survey (0.07–0.1 m); and (3) uncertainty of the interpolated surface estimated by withholding 10 percent of the original data points and calculating a root mean square error (RMSE) of the difference between the withheld points and the surface (0.04–0.06 m). Individual shoreline uncertainties are available in the shapefile “ACCURACY” attribute and in the metadata file.

Profile Uncertainty

Horizontal and vertical uncertainties from the XYZ profile data were calculated based on the equipment limitations (0.01–0.02 m) and the post-processed data uncertainty (0.04–0.05m). The total horizontal uncertainty for the profile data is +/- 0.04 m, and the total vertical uncertainty is +/-0.05 m.

To estimate vertical uncertainties that resulted from variations in the path along which data were collected from one survey to another, a variance methodology (Plant and others, 2002) was used by creating an interpolated continuous 2-D beach surface from the raw GPS xyz data for each survey date. Individual profile elevation data were compared to the interpolated surface, and a RMSE error of 6.3 cm was calculated by determining the elevation differences between the interpolated surface and the data points. This uncertainty value can be found in the attribute table as “DASVert_Uncert” and is only applied to the profile elevation when plotted using the “distance along profile” attribute to compare one or more surveys. Visit http://coastal.er.usgs.gov/fire-island/research/sandy/beach-profiles.html to see how cross-shore data are plotted using distance along profile values.