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) 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 northest facing part of the coast we used an average MHW of 0.45 m. 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). In order to estimate the bias between these two types of shorelines, wave data from a nearby buoy is needed to calculate wave run-up. Many of the sheltered areas within the Massachusetts study area do not have nearby buoy data and a proxy-datum bias value cannot be calculated in these areas. Therefore when this new datum-based MHW shoreline is compared to historic proxy-based HWL shorelines in these sheltered areas, there may be some artificial landward offset of the historic data that has not been quantified and could potentially influence the rates. For example, the north facing shoreline of Martha's Vineyard tends to have lower wave energy, which would result in less run-up and yield a smaller offset between a proxy shoreline and a datum shoreline than would occur along open-ocean coasts.
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]
