The reference line that was used for the first National Assessments shoreline was used for this work (except for a couple of areas where there were gaps in the reference line which were filled). The reference line is made of straight segments and is roughly coast-following with points every 20 meters. At each point a profile line (or transect) is defined that is perpendicular to the reference line. A program written by Amy Farris using Matlab version 2012b loads the cloud of (x,y,z) lidar points and finds all the data points within 2 meters of each profile line. The shoreline was extrapolated from data on each of these profiles.
The Matlab program described by Stockdon et al. (2002) was further developed by Laura Fauver, Jeff List and Kathy Weber at USGS. It was run on the profile data using Matlab version 2012b. This code works with one profile at a time. The code identified points located on the foreshore and fit a linear regression through them. The slope of the regression is an estimate of the slope of the foreshore. The intersection of the regression line with Mean High Water (MHW) is the calculated shoreline position. If the MHW elevation was obscured by water points, or if a data gap was present at MHW, the linear regression was simply extrapolated to the MHW elevation.
The MHW values used for the three regions of California are: Northern California: Oregon/California border to Cape Mendocino 1.81 meters, Central California: Cape Mendocino to Point Buchon 1.46 meters, and Southern California: Point Buchon to U.S./Mexico Border 1.33 meters (Weber et al., 2005 and Hapke et al., 2006).
The shoreline code has a graphical user interface (GUI) which plots all the data for a given profile, indicates which points were determined to be on the foreshore, plots the regression line and the calculated shoreline position. The information was visually checked and then the solution was either accepted or rejected. This manual verification process was repeated for each profile.
Each lidar shoreline point has an error associated with it. This error has three components: the error due to the linear regression, the error associated with the lidar data collection system, and the error due to extrapolation (if the shoreline point was determined by extrapolation). The error due to the linear regression is simply the 95% confidence interval about the regression estimate.
Sallenger et al. (2003) determined that the vertical accuracy of NASA's Airborne Topographic Mapper lidar system is about 15 centimeters. This vertical error is converted to a horizontal error using the beach slope as determined by the linear regression. The final part of the total shoreline error is the error due to extrapolation. If the shoreline point was determined by extrapolation, this error term is calculated as the amount of uncertainty in horizontal shoreline position due to the variability of the beach slope between the last point on the linear regression and the MHW elevation. These three error terms are then added in quadrature, yielding a total error for each shoreline point.
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, n.3, pp.502-513.
Sallenger, A.H., Krabill, W., Swift, R., Brock, J., List, J., Hansen, M., Holman, R. A., Manizade, S., Sonntag, J., Meredith, A., Morgan, K., Yunkel, J.K., Frederick, E., and Stockdon, H., 2003. Evaluation of airborne scanning lidar for coastal change applications: Journal of Coastal Research, v. 19, pp. 125-133.
After the shoreline code was run, the resultant shoreline was fed into another GUI for further quality checking. This GUI created a map view plot of the profile data color-coded by z values with a color jump at z = MHW so the approximate location of MHW is easily visible. The shoreline solutions were added to this plot. The shoreline data were visually scanned to look for incorrect solutions. For example the shoreline point was occasionally on the back of a barrier island or on a groin. These solutions were flagged and later removed. Small gaps on straight beaches were identified and later filled using linear interpolation but gaps at inlets or large gaps on curved beaches were not interpolated over. A visual quality check using imagery was conducted at a later stage.
This datum-based shoreline is often used in conjunction with proxy-based shoreline positions. There is a recognized offset between datum-based and proxy-based shorelines, therefore the proxy-datum bias as defined by Ruggiero and List (2009) was calculated for these shorelines. The formula for the bias is based on an equation for wave run-up which depends on beach slope and the recent wave climate (specifically, wavelength and wave height). The beach slope was calculated by the shoreline code (described in a previous process step). It was averaged alongshore in 1-kilometer non-overlapping blocks. The wave climate was estimated from averages of historical data. Historical wave lengths were obtained from offshore buoys. The buoy data were downloaded from the National Buoy Data Center (
https://www.ndbc.noaa.gov/). Buoys were chosen that had at least 10 years of data in at least 100 meters of water. Historical wave heights were obtained from wave information studies (WIS) stations (
http://wis.usace.army.mil/). At least 10 years of data were averaged. The formula for the proxy-datum bias also needs MHW and Mean Higher High Water, which were taken from the OFR mentioned in a previous Process Step (USGS OFR 2005-1027).
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, n.5, pp. 1069-1081.
The output file from the shoreline code, the map-view checker and the bias code were merged and saved as an American Standard Code for Information Interchange (ASCII) text file to be loaded by DSAS.
