Abstract

High-resolution topographic data greatly facilitate the remote identification of geomorphic features, furnishing valuable information concerning surface processes and characterization of reference markers for quantifying tectonic deformation. Marine terraces have been used as long baseline geodetic markers of relative past sea-level positions, reflecting the interplay between vertical crustal movements and sea-level oscillations. Uplift rates may be determined from the terrace age and the elevation of its shoreline angle, a geomorphic feature that can be correlated with past sea-levels positions. A precise definition of the shoreline angle in time and space is essential to obtain reliable uplift rates with coherent spatial correlation. To improve our ability to rapidly assess and map shoreline angles at regional and local scales, we have developed TerraceM, a MATLAB® graphical user interface that allows the shoreline angle and its associated error to be estimated using high-resolution topography. TerraceM uses topographic swath profiles oriented orthogonally to the terrace riser. Four functions are included to analyze the swath profiles and extract the shoreline angle, from both staircase sequences of multiple terraces and rough coasts characterized by eroded remnants of emerged terrace surfaces. The former are measured by outlining the paleocliffs and paleoplatforms and finding their intersection by extrapolating linear regressions, whereas the latter are assessed by automatically detecting peaks of sea-stack tops and back-projecting them to the modern sea cliff. In the absence of rigorous absolute age determinations of marine terraces, their geomorphic age may be estimated using previously published diffusion models. Postprocessing functions are included to obtain first-order statistics of shoreline-angle elevations and their spatial distribution. TerraceM has the ability to process series of profiles from several sites in an efficient and structured workflow. Results may be exported in Google Earth and ESRI shapefile formats. The precision and accuracy of the method have been estimated from a case study at Santa Cruz, California, by comparing TerraceM results with published field measurements. The repeatability was evaluated using multiple measurements made by inexperienced users. TerraceM will improve the efficiency and precision of estimating shoreline-angle elevations in wave-cut terraces in both marine and lacustrine environments.

INTRODUCTION

Recent increases in the availability of high-resolution topographic data have greatly helped the accuracy of quantitative analyses of landforms and the processes generating them, particularly by furnishing valuable information on geomorphic markers that may help to constrain the spatiotemporal characteristics of tectonic deformation processes. Marine terraces along tectonically active coasts, either related to constructional or erosional processes, are commonly used as long baseline geodetic markers of relative past sea-level positions, reflecting the interplay between vertical tectonism and superposed sea-level oscillations. By studying terrace elevation and dating their exposed surfaces or associated sediments, geologists have discovered an extensive archive of information about past sea-level variations and temperatures, as well as paleogeographic and paleoenvironmental change (e.g., Bloom et al., 1974; Cabioch and Ayliffe, 2001; Chappell et al., 1996; Cornée et al., 2006; Sasaki et al., 2004; Zecchin et al., 2009). Marine terraces have been also used as reference horizons to track tectonic deformation and associated fault-slip rates along tectonically active coasts. In numerous studies on marine terraces, detailed topographic information has provided the necessary data to infer earthquake recurrence at millennial time scales (e.g., Armijo et al., 1996; Athanassas and Fountoulis, 2013; Bloom and Yonekura, 1985; Fairbanks and Matthews, 1978; Gesch et al., 2002; Matsuda et al., 1978; Melnick et al., 2009; Ota et al., 1991; Plafker and Rubin, 1978; Shikakura, 2014; Strecker et al., 1986; Valensise and Pantosti, 1992; Yildirim et al., 2013). Furthermore, the staircase morphologies of differentially uplifted marine terraces have also helped to identify coastal seismo-tectonic segments that sustain their geomorphic characteristics over much longer time scales (Chen et al., 2011; Gesch et al., 2002; Taylor et al., 1987; Victor et al., 2011). Similarly, lacustrine terraces have provided detailed records of lake-level variations associated with the local effects of climate change (e.g., Garcin et al., 2012; Kliem et al., 2013). As in the marine environment, if lacustrine shorelines can be dated, they potentially constitute geomorphic marker horizons that can be used to infer rates of tectonic deformation and tectonic segmentation (e.g., Melnick et al., 2012). In this study, we focus on morphometric analyses of marine terraces, but the broad spectrum of methods presented here may be equally applied to analyze their lacustrine counterparts.

The linked effects of tectonic uplift, sea-level variations, and erosional and depositional processes are responsible for shaping coastal landscapes. Marine terraces are ephemeral coastal landforms characterized by flat and generally smooth surfaces or paleoplatforms that dip gently seaward. The terrace surfaces are bounded by scarps or paleocliffs inland that delimitate each terrace level (Figs. 1A and 1B) formed during protracted sea-level highstands (Anderson et al., 1999; Lajoie, 1986). Such coastal geomorphic sequences include wave-cut or wave-built terraces, rasas, strandflats, and compound paleocoasts (e.g., Guilcher et al., 1986; Jara-Muñoz and Melnick, 2015; Keskin et al., 2011; Pedoja et al., 2014; Regard et al., 2010). Active wave-cut platforms and sea cliffs are generated by the effects of wave erosion, which in stable sea-level conditions may be intensified depending on the morphology of the shore profile, such as slope, concavity, and external climatic factors (e.g., Kline et al., 2014; Komar and Allan, 2008). During episodes of sea-level rise or stable sea levels, wave-erosion processes along rocky coasts are more pronounced, resulting in the carving of wave-cut platforms above bedrock associated with rapid cliff retreat (Fig. 2A; Anderson et al., 1999; Challinor, 1949; Sunamura, 1983; Trenhaile, 2000). Conversely, during sea-level lowstands, previously cut terraces may be obliterated by river incision, slope diffusion, and eolian deposition (Figs. 2B, 2C, and 3A). The shoreline angle is located at the intersection between the wave-cut platform and the adjacent landward cliff. According to Lajoie (1986), the shoreline angle defines the elevation of sea level at the time of terrace formation, and as such, this is an important datum for any kind of morphologic or tectonic reconstruction along the coast. After several millennia, surface uplift may preserve these snapshots of past sea-level positions and subsequent processes impacting the terraces, creating a staircase morphology, such as that observed along the California coast (e.g., Anderson and Menking, 1994; Bradley and Griggs, 1976; Gurrola et al., 2014; Merritts and Bull, 1989; Muhs et al., 2014; Rosenbloom and Anderson, 1994) and other areas along the Pacific Rim (e.g., Bloom et al., 1974; Hsu, 1992; Ota et al., 1991).

The analysis of marine terraces has benefited enormously from the recent advances in high-resolution topography led by light detection and ranging (LiDAR; Meigs, 2013). LiDAR technology uses a pulsed laser to measure distance to the surface of Earth. The return time of these pulses combined with global positioning system (GPS) and an inertial navigation system allows three-dimensional point clouds of Earth’s surface to be generated. One of the main advantages of LiDAR is the possibility of generating “bare-earth” digital terrain models (DTM) using only the last returns of the laser survey. This method allows vegetation to be filtered out, imaging the terrain morphology in great detail (e.g., Fig. 1B). LiDAR DTMs have enabled remote identification of geomorphic features at submeter scale, providing valuable information for earthquake geology and tectonic geomorphology (e.g., Cunningham et al., 2006; Fritz et al., 2012; Kondo et al., 2008; Zielke and Arrowsmith, 2012; Zielke et al., 2015).

Here, we present a new tool for the analysis of wave-cut terraces using high-resolution topography. By combining the concepts of marine-terrace analysis, statistical methods, and high-resolution topography, we have developed TerraceM (Fig. 4), a MATLAB® graphical user interface (GUI) that can be used to analyze wave-cut terraces with efficiency, precision, and accuracy over large regions. This GUI can produce repeatable measurements by analyzing bulk topographic swath profiles in sequence. Swath profiles are studied using descriptive geometry and statistics to obtain the location of the shoreline angle (see next section).

We describe the different functions of TerraceM in the context of a case study based on the marine terraces at Santa Cruz, California, where climatic conditions relative to deformation rates have been favorable for creating and preserving flights of emerged marine terraces uplifted during repeated earthquakes along the San Andreas fault system (Anderson and Menking, 1994). We further compare the results of TerraceM with terrace elevations measured in the field compiled by Anderson and Menking (1994). We also include examples of rough coasts and staircase-terrace morphologies along the coast of central Chile. Furthermore, we discuss the accuracy and precision of TerraceM measurements by comparing our results using digital elevation models (DEMs) with different resolution, and we assess the repeatability of measurements with an experiment carried out by 10 inexperienced users.

BACKGROUND AND MOTIVATION

The elevation of a marine terrace is usually estimated from its surface morphology, and it is used as a proxy for estimating the amount of relative sea-level change, or tectonic uplift since the terrace was formed. There are several extended methods and markers that have been used to estimate terrace elevations (Fig. 2D), for instance, by manually picking slope changes along topographic profiles that include the foot of a sea cliff, commonly referred to as the terrace inner edge (e.g., Armijo et al., 1996; Regard et al., 2010; Roberts et al., 2013; Saillard et al., 2009), or with more sophisticated methods, such as isolating terrace-platform surfaces from a combined analysis of slope and roughness of the terrain from high-resolution DTMs (i.e., Bowles and Cowgill, 2012; Palamara et al., 2007). However, terrace elevations estimated from different markers may result in disparate estimates and large ranges in the derived uplift rates.

In modern, actively forming wave-cut platforms, the shoreline angle is located at the base of the cliff, and in emerged wave-cut terraces, it should coincide with the intersection between paleocliff and paleoplatform (Fig. 2D). The uplift rate (Ur) may be estimated from (Lajoie, 1986): 
graphic
or (Pedoja et al., 2008) 
graphic
where Te is the present-day terrace elevation, and Sl is the sea-level position at the time of formation, t. If we assume Sl = 0, following Pedoja et al. (2008), we can discard errors attributed to past eustatic sea-level positions, obtaining a relative uplift rate with respect to present-day sea level (Eq. 2); however, this approach may introduce a substantial bias in areas of slow tectonic uplift. Clearly, from both equations, uplift rates estimated for younger marine terraces will strongly depend on the precision of the terrace elevation measurements (Te).

The difficulty of estimating uplift rates from marine terraces lies in the correlation of the deformation markers in time and space. For instance, the inner edge calculated from slope maps (e.g., Palamara et al., 2007) often represents the contact between a colluvial wedge and the paleocliff, which is systematically located at a higher elevation than the shoreline angle (Fig. 2D; e.g., Matsu’ura et al., 2014). Along these lines, supervised surface classification models (SCM; e.g., Bowles and Cowgill, 2012), which have been used to map the elevation of terrace paleoplatforms, will tend to underestimate uplift rates because these markers usually form below mean sea level and prior to the highstand period when the cliff actively retreats (Fig. 2D). Thus, inappropriate assessment of geomorphic markers may lead to disparate uplift rates with underestimated uncertainties. Therefore, and following the definition of Lajoie (1986), we consider the shoreline angle as the most adequate marker to use for estimating uplift rates from terrace-elevation data, as it can be compared directly with past sea-level positions.

The shoreline angle of emerged older marine terraces is commonly concealed when the paleocliffs and/or paleoplatforms are affected by (1) scarp diffusion, (2) river incision, or (3) eolian depositional processes, or a combination thereof (Figs. 2B, 2C, and 3A–3D). Next, we assess these different effects on terrace morphology:

(1) Scarp diffusion is one of the processes that transfers material from the upper parts of the cliff to the foot and ultimately covers the shoreline angle. Scarp diffusion processes were modeled by Hanks et al. (1984) using Equation 3 and applied to marine terraces based on the assumption that mass transport resulting from erosional processes occurs exclusively in the downhill direction at a rate (M), which is proportional to the local gradient of topography (δux). The conservation of mass holds at a local scale and is defined by the constant of proportionality (K), which depends on the diffusivity (k) and the density of the bedrock (ρ) (see Eq. 4). The material removed from the top of the scarp and accumulating at the base is thus adjusted symmetrically along the profile over time, implying that the shoreline angle might be covered by an increasing amount of colluvium as the slope of the cliff progressively decreases (Figs. 2C and 3A).

(a) Mass transport equation (Hanks et al., 1984): 
graphic
(b) Proportionality constant (Hanks et al., 1984): 
graphic

(2) River incision of terrace surfaces is a response to changes in base level, which in these settings is determined by oscillations in sea level (Bishop et al., 2005). Thus, most of the river incision observed on marine terrace surfaces occurs during sea-level lowstands, when stream power is greater (Talling, 1998). Consequently, oscillating sea levels will force different fluvial adjustments to new base levels and may be expressed by retreating fluvial knickpoints in the river long profiles (Crosby and Whipple, 2006; Loget and Van Den Driessche, 2009). As the channel network evolves, incision into the landscape increases, progressively reducing the spacing between the main tributaries and obliterating the terrace morphology (Anderson et al., 1999). Along uplifting coasts, incision generally increases with terrace age and height, progressively degrading the morphology of both paleoplatforms and paleocliffs (Figs. 1B and 3A).

(3) Erosion and sediment transport along coasts either result in the formation of rocky platforms or sandy beaches, respectively, depending on the shore morphology, the amount of sediments transported, tidal range, and wave exposure (e.g., Ruz and Meur-Ferec, 2004; Trenhaile, 2001; Twidale et al., 2005). Eolian transport usually increases during sea-level lowstands due the seaward retreat of the shoreline (e.g., Bradley and Addicott, 1968; Cantalamessa and Di Celma, 2004; Masselink et al., 2014). Remobilization of fluvial and marine sediments is determined by local winds and sediment availability, leading to coastal dune systems that usually migrate inland (Bailey and Bristow, 2004; Carr et al., 2006). Similar to the other processes, dunes may cover the terrace platforms and even the paleocliffs, burying the shoreline angle (Figs. 2B and 3B).

The aforementioned features of marine terraces have been compared worldwide in order to understand their origin and the genesis of uplifted paleocoasts in the context of the history of sea-level changes (e.g., Pedoja et al., 2014). However, the influences of surface processes affecting the morphology of marine terraces, and consequently the errors concerning uplift rates, have not yet been fully addressed quantitatively. To quantify these processes in light of the increased availability of high-resolution topographic data, we have developed TerraceM. This new approach allows us to: (1) explore different methodologies to quantify and isolate erosive and depositional processes that usually mask the exact position of the shoreline angle; (2) extract shoreline angles continuously along terrace exposures using a large number of profiles; and (3) visualize and export the results.

TerraceM: SPECIFICATIONS AND CALIBRATION SITE

GUI Interface

TerraceM is designed to run on standard desktop computers with MATLAB® 2011b or higher; the Mapping Toolbox is required for exporting results in ESRI® shapefile and Google Earth® formats and to display the DEM; online Google-Maps® terrain and satellite images can also be displayed in the main interface (Fig. 4). TerraceM includes open-source functions for coordinate transformations, exporting options, and DEM visualization (Table 1). (Files are included in Supplemental File 11.)

Shoreline angle processing, analysis, and postprocessing functions are designed interactively in a workflow (Fig. 4). The user is guided through the workflow by a console-style interface that prompts interactive information to follow each step. TerraceM inputs are ESRI® shapefiles containing rectangular polygons and a floating-point DEM in either Asciigrid or Geotiff formats (Fig. 5B), in Universal Transversal Mercator (UTM) projection; these files can be created in any geographic information system (GIS) platform. TerraceM extracts swath topographic profiles that allow distinctive elements of the landscape to be isolated. By analyzing the ranges of topography, the fluvial incision may be isolated from the pre-incision relief, which is usually marked by the maximum distribution.

Swath profiles should be oriented orthogonal to the trace of the paleocliff or the terrace inner edge, encompassing the paleoplatform and extending beyond the paleocliff (Fig. 6B). One profile may include as many terrace levels as needed. The width of the rectangular profiles must be set according to the raster resolution and the terrace morphology. At the calibration site (see “TerraceM Calibration Site: The Santa Cruz Marine Terraces” section), for instance, we used 100-m-wide rectangular profiles with variable length (Fig. 6B). The obtained swath profiles can be visualized using the “swath profile viewer,” which also allows the data to be exported.

Structure and Workflow

TerraceM is designed to process and analyze many profiles in a systematic manner, organized in a tree structure of subfolders (Fig. 5B). Stations (or sites) are arranged in independent folders that contain the inputs and outputs of TerraceM. We recommend defining a four-letter station code for each site (e.g., CRUZ), which will also be the name of the station folder. Each input file is named according to the corresponding station; for instance, the DEM for station CRUZ would be named CRUZ_dem.tif, and the associated shapefile with polygons for swath profiles would be named CRUZ_clip.shp (Fig. 5B). This shapefile should include all desired polygons and should be in the standard two-dimensional format.

The TerraceM workflow consists of eight steps that should be executed sequentially to analyze the set of profiles (Fig. 4). Steps 1–5 (Input, Display, Processing, and Analysis tools) allow raw shoreline angles to be obtained, which can be filtered, exported, and projected along profiles in the following steps 6–8 (Editing, Projecting, and Export). While TerraceM is running, information messages are prompted inside the command bar, guiding users through the different steps to calculate shoreline angles (Fig. 4A).

TerraceM Calibration Site: Santa Cruz Marine Terraces

We compared shoreline angles estimated with TerraceM with field measurements made along the coast of Santa Cruz, California (Figs. 6A and 6B), in an area characterized by excellent and continuous exposures of several levels of marine terraces. In addition, this area is well suited as a test site, because LiDAR data are available from the OpenTopography portal (www.opentopography.org) and National Oceanic and Atmospheric Administration (NOAA; www.noaa.gov).

Marine-terrace studies in the Santa Cruz area started with the pioneering work of Alexander (1953) and Bradley and Griggs (1976), who first described and mapped several flights of marine terraces. Subsequently, Anderson and Menking (1994) integrated both surveys, estimating uplift rates and earthquake recurrence of the adjacent San Andreas fault (Fig. 6A). The Highway terrace level is the lowest in the area with an estimated marine isotope stage (MIS) 5e age (ca. 125 ka; Anderson and Menking, 1994), and it is characterized by well-developed paleocliffs that can be followed over distances of hundreds of kilometers along the coast (Figs. 1A and 6B). The elevation pattern of the Highway terrace increases southward from ∼30 to ∼70 m (see “Precision and Accuracy of Measurements” section). According to Anderson and Menking (1994), errors of shoreline estimations arise from: (1) low precision of shoreline-elevation measurements; (2) measurement errors of the initial investigators (for example, Bradley and Griggs [1976] reported 1–2 m error, whereas Alexander [1953] reported 5 m error); and (3) the error in reading the data from the plots provided in these publications.

ANALYTICAL TOOLS

TerraceM includes four functions that use different methods to determine the shoreline angle in different geomorphic scenarios. These functions are included in step 5 of the workflow (Fig. 4).

Staircase Marine Terraces

Multiple marine terraces across a vertical transect are analyzed using the Staircase function, which is based on the concept of shoreline angle defined by Lajoie (1986) (see “Background and Motivation” section). This is particularly useful when working with well-preserved paleoplatform and paleocliff morphologies (e.g., Figs. 5A and 7A). The determination of the shoreline angle can be accomplished using the maximum or minimum topographic distribution obtained from topographic swath profiles. The maximum distribution of elevation in topographic swath profiles allows the pre-incision topography to be deciphered; however, the maximum topography may be biased locally by climbing dunes. In this particular case, the minimum elevations can be used to isolate the base of the dune field that should represent a maximum estimate of the original paleoplatform surface (see “Background and Motivation” section). Examples of the analysis of terraces with staircase morphologies and covered by dunes can be found at the Chile convergent margin, as described by Jara-Muñoz et al. (2015).

The Staircase function is designed to analyze swath profiles interactively, calculating the shoreline angle by clicking directly above the topographic swath profiles (Fig. 5A). Two user-defined points along the steepest part of the profile define the paleocliff, and two additional points delineate the extent of the paleoplatform (Fig. 7B). Linear regressions are then calculated upon the enclosed segments on the profile and extrapolated to find the intersection that marks the position of the shoreline angle. Vertical errors of shoreline angles are based on the extrapolation of the 2σ ranges in the linear regressions (Fig. 7B).

Sea Stacks at Rough Coasts

The Sea-Stack Analysis function allows shoreline-angle elevations along rough, rocky coasts to be analyzed. Sea stacks and stumps form where portions of a retreating coast become isolated through erosion and dissection of the cliff base (Bird and Bird, 2000; Trenhaile et al., 1998); these features are detached from the cliff, forming isolated promontories (Figs. 8A and 8B), columns, stack-arcs, and caves, which represent fragments of partly eroded terrace levels (Bishop, 1985; Gesch et al., 2002; Saillard et al., 2011).

The maximum elevation of the swath profiles highlights stack morphology and the location of peaks, which delineate the degraded terrace platform (Fig. 8A). By using a peak-detection algorithm (Billauer, 2008), individual stack positions and their maximum elevations are extracted along the profile (Fig. 8C). Peaks are grouped in classes and linearly interpolated to reconstruct the paleotopography of the platform. The user defines the roof or upper limit of each range interactively, and then the linear regression of peaks is extrapolated backward toward the cliff to find the elevation of the shoreline angle and the associated 2σ error (Fig. 8C). Spatially consistent distributions of shoreline angles have been estimated using this method for a partly degraded MIS 5e terrace in central Chile (Fig. 8A; Gesch et al., 2002).

Scarp Diffusion

The geomorphic age of a paleocliff abutting a terrace (Kt) may be estimated from the linear diffusion equation (Hanks et al., 1984; Eq. 3 herein; see “Background and Motivation” section). The first step of the Scarp Diffusion function is to define the temporal resolution of the model by specifying the range of iterations and the geometry of the profile, which is defined by the upper-slope break, the extent of the paleoplatform, and the profile center (Fig. 9). Finally, the cliff height (2a), and the far-field slope (fs) are calculated from the parameters; the best-fitting model is selected by minimizing the root mean square error, obtaining the geomorphic age of the cliff (Fig. 9).

Cliff Free-Face

The Cliff Free-Face function allows the shoreline angle to be located by using the slope distribution of modern cliffs as input angle to extrapolate the slope of a paleocliff below the colluvial wedge to find the shoreline angle (Fig. 10). The concept of free-face refers to the exposed part of fault scarps above colluvium (e.g., McCalpin, 2009), which we extend to a wave-cut scarp features in this study. This analysis is recommended for terraces with well-defined colluvial wedges below exposed cliffs with restricted heights, but sculpted into resistant bedrock, or for smoothed paleocliffs with marked transitions at the top of colluvium. This method is furthermore recommended for terraces covered by calcrete or beach rock, where low diffusion rates are favorable to preserving the free-face morphology over longer periods of time.

The Cliff Free-Face function is analogous to the Staircase function. However, in this case, the slope of the cliff is not estimated by linear regression, but is defined by the user and incorporated by graphically selecting a single point on the paleocliff. This point should be defined at the lower limit of the free face or at the contact between colluvium and exposed bedrock (Fig. 10D). Two additional points enclosing the paleoplatform are defined beyond the wash slope to find the shoreline angle and its associated 2σ error.

We present an example of this method at Pelluhue in south-central Chile with the analysis of modern cliffs and emerged terraces, where we estimated the slope of 107 Holocene cliffs and used the mean value and standard deviation as input to obtain the elevation of buried shoreline angles of emerged terraces levels (Fig. 10). At Pelluhue, the bedrock consists of homogeneously distributed schist; however, in case of variable bedrock lithologies, we recommend estimating cliff-slope distributions for each lithologic unit.

POSTPROCESSING TOOLS

TerraceM involves straightforward procedures for rapid visualization of shoreline-angle distributions and the filtering of outliers. A projection routine is included to display shoreline angles along a user-defined line, and an additional filtering routine has been included to remove outliers and improve the interpolation results for multiple shoreline angles and terrace levels. Errors in measurements may increase due to incorrect profile orientation, due to presence of sedimentary bodies near the base of the cliff, or due to incorporation of artificial structures (see “Repeatability of Measurements” section). Filtering is based on a nearest-neighbor interpolation with a user-defined bin size and exclusion range. The exclusion range is usually the standard deviation of the shoreline distribution and can be adjusted to improve the smoothness of the profile; we usually adjust this value by removing less than 10% of the shoreline-angle population. Along the terrace flights in Santa Cruz, we obtained shoreline angles for 90 profiles, excluding five of them (6% of the population) after filtering. (Shoreline angles in Google-Earth® format are included in Supplemental File 22.)

Visualization of shoreline-angle distributions is useful when comparing spatially disparate locations. The statistics routine calculates a histogram for each station, depicting the distribution of the elevation of shoreline angles or Kt values, including mean and standard deviation. Topographic profiles with shoreline angles determined from the analysis functions can be formatted inside 8 × 2 subplots and presented as a ready-to-print data repository in Adobe® pdf format. (Shoreline angle data used for plots of the Santa Cruz case study are included in Supplemental File 33.)

PRECISION AND ACCURACY OF MEASUREMENTS

We compared the results of shoreline-angle morphometry from the Santa Cruz Highway terrace using TerraceM, and different DEM resolutions, with actual field measurements (Anderson and Menking, 1994). This comparison allowed us to evaluate the errors and determine the precision and accuracy of TerraceM.

Accuracy and precision are defined in terms of systematic and random errors, respectively. Field measurements of shoreline angles were first compared with the results of TerraceM using a 2.5-m-resolution LiDAR DTM by linearly interpolating the shoreline angles using a 2 km bin size (Fig. 11A). Residuals calculated from the difference between the linear interpolations were not significantly different from a Gaussian distribution with a mean of 0.16 m and a standard deviation of 2.5 m. The obtained mean value is very low and smaller than the vertical error reported in the field measurements; the standard deviation is equal to the horizontal resolution of the DTM. Consequently, we assume the 0.16 m mean value to represent the accuracy and the 2.5 m standard deviation to represent the precision of TerraceM measurements for this case study.

Unfortunately, LiDAR topography is not yet available along all coastlines of the world, and thus we tested the dependence of TerraceM results obtained using different resolutions from the 10 m National Elevation Data set (NED, U.S. Geological Survey) and 30 m Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model (GDEM, J-spacesystems) topographic data sets (e.g., Aster, 2011; Gesch et al., 2002; Maune, 2007; see details in Table 2). The comparisons between DEMs were performed using the same datum (North American Vertical Datum 1983 [NAD83]/NAVD88). We used the LiDAR-derived shoreline angles as base values to compare the deviations of the other data sets, and we calculated the residuals using linear interpolation (Fig. 11B). The distribution of errors was used to estimate the precision and accuracy of each topographic data set. As expected, precision and accuracy were inversely related to DEM resolution (Fig. 11D). During the analysis, we noticed that shoreline angles estimated using the ASTER DEM might result in erroneous interpolations of paleocliffs for short profiles, and consequently we recommend increasing swath sizes for low-resolution DEMs.

To quantitatively assess the differences between shoreline angle and inner-edge measurements (described in “Background and Motivation” section), we compared both geomorphic markers by means of their residuals (Fig. 11C). We started mapping the inner edge on LiDAR-derived slope maps using two slope ranges between 0° to 30° and 30° to 90°, following the method proposed by Palamara et al. (2007). We first extracted the elevation of the inner edge (e.g., Fig. 7A) and calculated the differences from the LiDAR-derived shoreline angles (Fig. 11C) by comparing linear interpolations. The obtained residuals had a mean of 14.1 m and a standard deviation of 5.8 m. These values suggest that the inner-edge measurements overestimate terrace elevation, and they are characterized by a relatively low precision and low accuracy with respect to the shoreline angles.

Another factor that may influence the precision and accuracy of TerraceM shoreline angle-elevations is the width of the swath profile. Channel incision will tend to reduce the maximum elevation of swath profiles, with the amount of reduction depending on the position of the swath with respect to the channels and on its width. We tested the influence of swath width by incrementally increasing the width of profiles along the Santa Cruz Highway terrace (Fig. 11D). First, we calculated the spacing of channels that cut the terrace riser, finding a minimum spacing close to 100 m (inset in Fig. 11D) and used this value to estimate reference shoreline-angle elevations. Then, we calculated shoreline angles by incrementally increasing the swath width from 20 to 340 m and compared them with the reference estimates.

This experiment shows that the range of shoreline-angle elevations is dependent on the swath width, although changes in median elevation change are rather limited (<1 m). As could be expected, the amplitude of the elevation change increases with swath width; the general tendency shows that narrower swaths result in predominantly lower elevations, and wider swaths result in higher values (Fig. 11D). Larger widths could be biased by irregularities along the strike of the terrace riser, causing an apparent seaward position of the cliff and thus lowering the shoreline angle; in turn, the higher probability to have greater elevations in the platform would cause the opposite effect, resulting in higher shoreline elevations. This could explain the increase in the dispersion of the shoreline elevations observed for larger widths. For narrower widths, lower elevations will arise in areas where both the platform and cliff have been dismantled by channel incision, whereas the higher probability to include drainages in the swath would result in an apparent increase of the platform slope, resulting in higher shoreline elevations. Based on these results, we suggest using a value close to the minimum drainage spacing for the width of swath profiles in TerraceM.

REPEATABILITY OF MEASUREMENTS

To evaluate the repeatability of shoreline-angle measurements, we performed an experiment with a group of 10 inexperienced users following the six conditions proposed by Bland and Altman (1986) to evaluate uncertainty: (1) the same experimental tool (TerraceM); (2) the same observer (we carried out the experiment and processed the data); (3) the same measuring instrument under the same conditions (the users carried out this experiment simultaneously using TerraceM); (4) the same location (the experiment was performed in a computer pool at the University of Potsdam); (5) repetition over a short period of time (the experiment consisted of repeating a series of four profiles continuously for 120 times); and (6) the same objective (map the shoreline angles in all profiles).

The profiles selected for the experiment exhibit small differences in topography that we used to evaluate possible sources for error in the measurements (Fig. 12A). For instance, profiles 1 and 2 are characterized by sharp subvertical paleocliffs with small artifacts along the paleoplatform due the intersection with Highway 1; profile 3 is characterized by high-roughness sections at the outer edge of the paleoplatform; and profile 4 has a relatively narrow paleoplatform and smoothed paleocliff, probably associated with eolian and/or colluvium accumulation.

The results of the experiment show narrow distributions of shoreline-angle elevations for all profiles (Fig. 12B), but χ2 tests indicate that these distributions are not Gaussian, suggesting the data are theoretically invalid for a repeatability analysis. Nevertheless, we used an heuristic approach to study the distribution and sources of errors using the standard deviation, the mean, and the median of each profile.

Geomorphic differences between profiles appear to be expressed in the standard deviation of shoreline-angle distributions (Fig 12B). For instance, profile 1, which has a sharp paleocliff and paleoplatform, yielded the lowest standard deviation (1.5 m). Instead, profile 4 has the highest standard deviation of 3.4 m, possibly associated with the ambiguity in interpreting smoothed paleocliffs, hence resulting in a more scattered distribution of shoreline angles. Artificial structures, such as the Highway 1 crossing the terraces along the paleoplatform in profiles 2 and 3 (Fig. 12A), are associated with a positive bias in shoreline angles. Profile 2 displays a bimodal distribution, and profile 3 displays a positive tail. We conclude that the incorporation of Highway 1 into the area used to interpolate the paleoplatform may bias shoreline-angle elevations toward higher values; these different criteria of shoreline angle mapping may be associated with inexperienced users.

To estimate the precision of measurements carried out by first-time users, we subtracted the shoreline-angle elevation from terrace measurements carried out by an experienced user (Fig. 12C). The mean and median of the centered distributions were used to estimate the precision of the measurements. Profiles 1, 3, and 4 are characterized by low mean and median values (mean: 0.04–0.5 m, median: 0.4–0.75 m), indicating higher accuracy when compared with profile 2, which yielded the highest mean and median values of 1.32 m and 1.19 m, respectively; the lower accuracy of this profile is associated with the bimodal distribution of elevations.

The distributions of shoreline angles for the different profiles are non-Gaussian and probably contain both systematic and random errors in an unknown proportion. However, through the comparison of morphologic elements of marine terraces with the statistics of shoreline-angle distributions in a heuristic manner, we detected possible sources for systematic errors. To minimize these errors, we suggest the following: (1) select the smoothest and most representative segment of the paleoplatform for fitting, avoiding the influence of artifacts; (2) for smoothed paleocliffs, try other mapping methods, such as the Cliff Free-Face function; and (3) maximize user experience, which is important to increase the accuracy of the measurements, by training first-time users with TerraceM in batch mode and with different case studies.

SUMMARY

Wave-cut terraces formed in marine as well as lacustrine environments are important geomorphic marker horizons that help researchers assess the impact of tectonic and climatic processes on landscape evolution. TerraceM is a Matlab GUI designed to study terraces in the marine and lacustrine realms quantitatively by incorporating several methods developed and tested using high-resolution LiDAR topography in different coastal settings. The interface and structure of TerraceM are designed to manage large amounts of profiles grouped in separated stations simultaneously. By comparing TerraceM measurements using LiDAR topography with a field survey of shoreline angles in the region of the Highway marine terrace in Santa Cruz, California, we estimated 0.16 m accuracy and 2.5 m precision. By taking advantage of high-resolution topography, TerraceM will help to expand and facilitate regional studies of marine terraces. For further information, please visit www.terracem.com.

We would like to thank Javier Quinteros for suggestions on graphical user interface (GUI) design, Kevin Pedoja for his advice on marine terrace analysis, and Cengiz Yildirim, Gino De Gelder, and Saptarshi Dey for their interest and valuable feedback on program performance and applicability. This study was developed within the framework of the project MARISCOS (MAule eaRthquake: Integration of Seismic Cycle Observations and Structural Investigations), financed by the German Science Foundation (DFG), grant STR 373/30–1. Melnick was supported by DFG grant ME 3157/2-2. The source code of the GUI and new updates can be downloaded from http://www.terracem.com.

1Supplemental File 1. TerraceM code, workspace, and example data. Please visit http://dx.doi.org/10.1130/GES01208.S1 or the full-text article on www.gsapubs.org to view Supplemental File 1.
2Supplemental File 2. Shoreline angles of Santa Cruz in Google Earth® format. Please visit http://dx.doi.org/10.1130/GES01208.S2 or the full-text article on www.gsapubs.org to view Supplemental File 2.
3Supplemental File 3. Shoreline angle fits of Santa Cruz in .pdf format. Please visit http://dx.doi.org/10.1130/GES01208.S3 or the full-text article on www.gsapubs.org to view Supplemental File 3.