Digital surfaces were generated using both the triangulated irregular network (TIN) and interpolation-based raster methods. Three methods of raster interpolation were used: natural neighborhood, inverse distance-weighted with a 12-point radius, and the Kriging model. Applied methods of grid surface interpolation were chosen due to widely available and well developed tools for its further analyses in GIS environments.
In order to minimize the effect of data lost during creating a digital surface from the point cloud, two different raster cell size of 10 and 20 cm were tested. For final analysis, a 10 cm raster size was chosen. Within the Kriging method, only 90% of the original cloud point were used for the interpolation process. The remaining 10% were used for model cross-validation. On the basis of the normal quantile-quantile (QQ) plot graph, the quantiles of the difference between the predicted and measured values and the corresponding quantiles from a standard normal distribution were analyzed. The points distribution proved that the method used relied on normality.
A comparison of TIN and raster surfaces indicated no significant difference in the coherence of the terrain models generated using the two methods. According to the literature [11
], grid-based terrain models are a best fit due to a well-developed analysis framework, in cases where further analysis is performed, while TIN surface is a better fit for visualization purposes. TIN surface estimates single locations more robustly than grid; however it is not recommended for producing profiles [11
], which is a crucial issue in the notch analysis process. Although the TIN surface was found to be more detailed according to “fitness for purpose” [10
], due to limitations of further analyzes and accurate profile preparations, it was decided that the more continuous raster data were more suited for representing the notches. In order to choose the most appropriate surface among the three created raster surfaces, a test was conducted whereby rasters of height differences between the three raster surfaces were generated to identify the area of the cliff surface exhibiting the greatest difference. The analysis showed that Kriging interpolation was the most reliable of the three approaches, as it was smooth and had less noise. Based on these results, all further analysis was performed using the raster method through Kriging interpolation.
Genetic Notch Type Evaluation
Identification of the notch genetic type consisted of three steps: (1) notch identification in the cliff surface; (2) notch shape acquisition; and (3) surface roughness calculation.
Due to specific notch geometry and its concavity, structure identification of notches in the cliff surface was based on the hillshade of the cliff and on the contour map generated using the Kriging interpolation raster method. It was assumed that both contour and hillshade maps would indicate sudden values changes in the notch border. A contour map was generated using a contour interval of 10 and 20 cm directly from the Digital Surface Model (DSM). After the preliminary notch border identification process, the 10 cm interval was chosen for further analysis. However, it should be noted that because of the flipping of axes, contour lines did not represent height values, but rather isolines of cliff depth. Accordingly, areas that are convex had higher contour values. Hillshade was produced with azimuth and altitude angles of the light source above the horizon at 45 decimal degrees. It is also worth noting that because the cliff was positioned horizontally as result of the axis flip, shadow angles referred to a horizontal and not a vertical plane.
On the basis of contour map analysis, notches were identified where contour lines (isolines) were very dense. Although contour values did not represent heights, if their density (concentration) was higher than their surroundings, this denoted areas of marked change in both the vertical and horizontal dimensions. Because of this property, both concave and convex areas of marked change were represented by dense isolines. Therefore, further analysis of hillshade for identifying the concave areas was performed, based on a sudden slope change and high shade value of the hillside raster as described in Section 2.2
In addition to notch elevation, shape and surface texture are used to classify genetic notch type. To classify the shape of a notch as either U or V type, specific geometry parameters were determined for the notch profiles as represented in the raster terrain surface. Because of the variation encountered in a notch profile in the lateral direction, several profiles were created for each notch. Final values of total notch depth, average height of the retreat zone, and average notch height were calculated as mean values of these parameters for individual notch profiles.
Intervals between profiles for each notch were set to 1 m. The number of profiles per notch differed depending on notch length. For notch nb.1, five profiles were obtained, whereas for notches nb.2 and nb.3, eight profiles were acquired.
To obtain surface texture, two steps were performed: (1) extraction of the notch area data and (2) surface roughness calculation. Notch surface data were extracted from the raster data by identifying the upper and lower boundaries of each notch based on a combination of slope, hillshade, and contour data (Figure 7
). Contours of the final positions of the boundaries were approximate, given the method used to identify them (manual identification using hill shade and isolines).
Surface roughness has been described as a standard deviation of the pixel density of the profile–plan curve raster. The profile curve raster represents the curvature of the surface in the direction of the slope, whereas the plan curve raster shows a curvature perpendicular to the direction of slope. By combining these two morphologic attributes (represented as rasters), it was possible to extract and identify values of curvature in both directions, which from a theoretical perspective corresponded to surface roughness. Notch surface roughness was categorized according to statistical standard deviation ranges as smooth, moderately smooth, moderately rough, or porous (Table 4
Using the contour and hillshade map analysis and verification of distinguished features on a base of superimposed map of those parameters, three notch areas were identified (Figure 8
) within the areas of interest and selected for further testing both on a base of generated digital surface models and the original point cloud. Notch nb.1 was located in the middle part of the northern sector of the cliff (area “b”, Figure 5
and Figure 7
b), and notches nb.2 and nb.3 were located in the upper and middle sections of the southern sector of the cliff, respectively (area “a”, Figure 5
and Figure 7
The applied methodology enabled the identification of detailed characteristics of the notches. Notches nb.1 and nb.2 were U-shaped whereas nb.3 was V-shaped. Although all notches conformed to the general shape classification scheme, notch nb.1 had a rectangular morphology, as opposed to circular shapes exhibited by nb.2 and nb.3. The established threshold values for notch shape recognition do not take into account the possibility of occurrence of a rectangular form. This fact, as well as the observed regular shape, the almost horizontal slope of the boundaries, and large dimensions (Table 5
), led to the conclusion that notch nb.1 represented an unnatural feature. Notch nb.2 was an example of a perfectly symmetrical U-shaped notch (1.88 m deep and 1.86 m high). Notch nb.3 had the smallest dimensions (0.4 m deep and 0.25 m high), and if it were not for its continuity in the horizontal direction, it would not have been detected as a notch.
On the basis of the values of standard deviation as well as the value range of the profile-plan curvature raster, notch surface roughness values for the three notches were determined as follows: notch nb.1, moderately smooth; notch nb.2, smooth; and notch nb.3, moderately porous. According to the mechanisms of notch evolution, interior regions of notches created by wind or sand/pebble action were completely smooth, whereas interior parts of notches of marine origin (tidal and surf notches) were rougher.
Notch nb.1, with a moderately smooth surface, could potentially be classified as an abrasion or structural notch. However, because of the height of the notch on the cliff profile, its origin could not be satisfactorily explained as either of these two types. Also, structural notches have symmetric, U-shaped forms and, in typical conditions, would not attain a size as that presented by notch nb.1. The atypical combination of a moderately smooth surface and a rectangular, almost symmetrical notch located in the middle of a cliff suggests that this notch represented a discontinuity of anthropogenic origin in the cliff profile. The location of the notch as identified on photographs (Figure 2
and Figure 6
) appeared to be part of a human-made feature engraved in the cliff. Site inspection confirmed a non-natural origin for the detected notch. It proved to be a man-made corridor carved into the cliff wall, created as a tourist attraction accessible form the pocket beach.
Notches nb.2 and nb.3 were considered to be naturally occurring. Notch nb.2 had a smooth surface and accordingly could potentially be classified as an abrasion or structural notch. Due to its smooth surface and location on the upper part of the cliff, notch nb.2 was identified as a structural notch. Notch nb.3 had a moderately porous surface and should therefore be classified as a tidal notch. However, the small dimensions of this notch and its height above the intertidal zone did not support this classification. Two possible scenarios could apply: (1) the notch is tidal and developed at mean sea level (MSL), and subsequently the cliff section was tectonically uplifted or MSL decreased, or (2) the notch is structural and has developed by chemical reaction with sea spray in a rock layer of lower chemical resistance compared with the surrounding material.