The methods used in this analysis closely follow those of Hapke and Reid (2007), who developed a methodology for estimating regional-scale coastal bluff retreat for California. As in Hapke and Reid (2007), the modern bluff edge used in this analysis is interpreted from lidar data. Lidar from 1998 and 2006 were available for most of the Lake Erie, Pa., coastline. Additionally, a historical bluff edge (1938) was digitized from existing orthophotographs.

In order to interpret a bluff edge from the lidar data, digital elevation models with a 1-m-cell size were created from lidar data using standard geographic information system (GIS) methods.  A hillshade rendering for each grid was generated and used to digitize the interpreted bluff edge using the visual break in slope.  A hillshade, or shaded relief map, uses slope and aspect data to determine a hypothetical shaded surface that visually enhances surface features. Hillshades are useful for enhancing the visualization of a surface, and the resulting three-dimensional rendering was used to interpret and digitize the bluff edge using the visual break in slope.  This visual rendering approach has advantages over slope or second-derivative (gradient) methods of edge enhancement in that objects such as buildings or vegetation that are near the bluff edge are easier to identify and omit from the data set (Hapke and Reid, 2007). The bluff top along the Lake Erie, Pa., coastline is heavily vegetated with relatively tall trees that obscure the bluff edge in many places. Therefore, the slope and gradient methods are not regionally applicable.

Along most of the Lake Erie, Pa., coast, the bluff is a flat-topped, elevated terrace with a distinct lakeward edge (see figs. 1, 2, and 5).  In some areas, however, there is no well-defined break in slope, or the break is obscured by dense vegetation. In these situations, the interpretation of the bluff edge from the lidar data reverted to the same feature that was surveyed on the historical maps, as determined by superimposing the two data sets. Aerial photographs and the orthophotographs were frequently utilized when digitizing the bluff edges from the hillshades to resolve ambiguities in the identification of the bluff edge. 

Gaps in the bluff-retreat analysis occur primarily in areas where streams dissect the continuous bluff line or in lowland areas (such as Presque Isle). This pilot study presents bluff-retreat rates for 60 km of the Pennsylvania coast.  Gaps result when the bluff edge is ambiguous or absent.  In addition, single transects were eliminated in areas where there are long, narrow headlands or deep, narrow gullies, because these features represent singularities not representative of overall bluff change.

Rates of bluff retreat were generated in a GIS with the Digital Shoreline Analysis System (DSAS), an ArcGIS© extension (Thieler and others, 2005). This tool contains three main components that define a baseline, generate transects perpendicular to the baseline that intersect the bluff edges at a user-defined separation along the coast, and calculate rates of change based on measurement locations established by the transects.  A baseline was constructed lakeward of, and roughly parallel to, the general trend of the bluff edge. Using DSAS, transects were spaced at 20-m intervals.

In this study bluff-retreat rates were averaged over a 68-year time period for the western portion of the area and over a 60-year time period for the eastern portion (fig. 3).  Averaged rates of coastal change are frequently used in coastal-zone management and can provide information on the spatial distribution of regional bluff-retreat trends, but they provide little information on specific hazard zones because of the highly variable nature (both spatially and temporally) of coastal bluff-retreat process and response. The dominant influences on the temporal variation of coastal bluff retreat are related to weather variations (storm intensity and frequency), climate variations, and fluctuations in lake-water levels. Spatial variations in bluff retreat are related to the physical characteristics of the bluff-forming material (lithology and geologic structure) and anthropogenic impacts such as irrigation and the emplacement of protective structures. Because bluff retreat and rates of bluff retreat vary substantially in space and time, the averaged data presented in this report are not a good predictor of future annual change.

Following the methodology used by Hapke and others (2006) and Hapke and Reid (2007), the total cliff edge-position error (E_p) is calculated by adding in quadrature the orthorectification error (E_r), digitizing error (E_d), and lidar bluff-edge position uncertainty (E_l):

(Equation 1)

The orthorectification error represents the estimated maximum root mean square (RMS) error for orthophotographs at a scale of 1:12,000 in this study.  The digitizing error reflects the maximum error specified in past studies (Anders and Byrnes, 1991; Crowell and others, 1991; Moore, 2000; Hapke, 2004) and is applied to the historical bluff edge only. Lidar cliff position error is the maximum error associated with the lidar positioning and GPS errors (Stockdon and others, 2002) for the modern date.

A separate E_p is calculated for each time period and data source (E_p1 and E_p2). These values were combined and annualized to provide an error estimation for the bluff-retreat rate at each transect. The annualized error (E_a) is expressed by:

(Equation 2)