Whenever possible, a profile method was used to extract the operational Mean High Water (MHW) shoreline from the lidar point cloud data, using a Matlab-based approach (Matlab version 2015b was used) similar to the one developed by Stockdon and others (2002). Elevation values for the height of MHW were determined from vdatum (version 3.8) provided by NOAA (https://vdatum.noaa.gov/)
. We continued the practice set out by Weber and others, (2005) of using one MHW value for a continuous section of coast (as opposed to using a continuously varying value). We chose this value such that it is always within 15 cm of the value returned by vdatum at any point along the coast. For example, we used MHW = 0.6 m for all of Buzzards Bay even though vdatum shows it varying slightly over the basin. For the shorelines of the South Shore of Massachusetts, we used an average MHW elevation of 1.22 meters. This profile method uses a coast-following reference line with 20 m spaced profiles. All lidar data points that are within 1 m of each profile are associated with that profile. All work is done on the 2 m wide profiles, working on a single profile at a time.
For each profile, a linear regression was fit through data points on the foreshore and the regression was evaluated at the MHW elevation to yield the cross-shore position of the MHW shoreline. If there was a data gap at MHW or if the MHW elevation was obscured by water points, the linear regression was simply extrapolated to the MHW elevation. Foreshore beach slope is defined as the slope of the regression line.
Each MHW shoreline point that was extracted using this profile method has an uncertainty associated with it. This uncertainty includes three components: 1) the 95% confidence interval on the linear regression estimate of the shoreline position; 2) the uncertainty associated with the elevation of the raw lidar data and; 3)the uncertainty due to extrapolation. These three components of uncertainty were added in quadrature to yield a total error for each shoreline point. For details on each component, see pp.12-13 under the section titled Lidar-Derived MHW Shoreline Position Uncertainty in Hapke and others (2011).
There is a known horizontal offset between the datum-based lidar MHW shoreline and the proxy-based historical shorelines on open-ocean sandy beaches that nearly always acts in one direction (Ruggiero and List, 2009). Wave data from offshore buoys is used with the beach slope in a run-up equation to estimate a proxy-datum bias correction to reconcile the unidirectional offset that the proxy-based historic High Water Line (HWL) shorelines, such as those derived from NOAA t-sheets or air photos, have in relationship to the lidar-derived, datum-based operational MHW line. An uncertainty associated with the bias was also computed, which can also be thought of as the uncertainty of the HWL shorelines due to water level fluctuations. For details on the proxy-datum bias and bias uncertainty, see pp.9-11 under the section titled The Proxy-Datum Bias Correction between HWL and MHW Shorelines in Hapke and others (2011).
Hapke, C.J., Himmelstoss, E.A., Kratzmann, M.G., List, J.H., and Thieler, E.R., 2011, National assessment of shoreline change—Historical shoreline change along the New England and Mid-Atlantic coasts: U.S. Geological Survey Open-File Report 2010-1118, 57 p., https://pubs.usgs.gov/of/2010/1118/
Ruggiero, P., and List, J.H., 2009, Improving accuracy and statistical reliability of shoreline position and change rate estimates: Journal of Coastal Research, v. 25, no. 5, p. 1069-1081. [Also available at https://www.jstor.org/stable/27752753
Stockdon, H.F., Sallenger, A.H., List, J.H., and Holman, R.A., 2002, Estimation of shoreline position and change using airborne topographic lidar data: Journal of Coastal Research, v.18, no. 3, p. 502-513. [Also available at https://www.jstor.org/stable/4299097