Research Article: Measuring (subglacial) bedform orientation, length, and longitudinal asymmetry – Method assessment

Date Published: March 20, 2017

Publisher: Public Library of Science

Author(s): Marco G. Jorge, Tracy A. Brennand, Yanguang Chen.


Geospatial analysis software provides a range of tools that can be used to measure landform morphometry. Often, a metric can be computed with different techniques that may give different results. This study is an assessment of 5 different methods for measuring longitudinal, or streamlined, subglacial bedform morphometry: orientation, length and longitudinal asymmetry, all of which require defining a longitudinal axis. The methods use the standard deviational ellipse (not previously applied in this context), the longest straight line fitting inside the bedform footprint (2 approaches), the minimum-size footprint-bounding rectangle, and Euler’s approximation. We assess how well these methods replicate morphometric data derived from a manually mapped (visually interpreted) longitudinal axis, which, though subjective, is the most typically used reference. A dataset of 100 subglacial bedforms covering the size and shape range of those in the Puget Lowland, Washington, USA is used. For bedforms with elongation > 5, deviations from the reference values are negligible for all methods but Euler’s approximation (length). For bedforms with elongation < 5, most methods had small mean absolute error (MAE) and median absolute deviation (MAD) for all morphometrics and thus can be confidently used to characterize the central tendencies of their distributions. However, some methods are better than others. The least precise methods are the ones based on the longest straight line and Euler’s approximation; using these for statistical dispersion analysis is discouraged. Because the standard deviational ellipse method is relatively shape invariant and closely replicates the reference values, it is the recommended method. Speculatively, this study may also apply to negative-relief, and fluvial and aeolian bedforms.

Partial Text

Longitudinal (or streamlined) subglacial bedforms form at the ice-bed interface and typically have their longitudinal axis oriented (sub)parallel to ice flow vectors. This study concerns positive-relief longitudinal subglacial bedforms (hereafter referred to as LSBs). Morphometric data from LSBs have been used to reconstruct paleoglacier geometry and dynamics (e.g., [1,2]) and to test morphological predictions from hypotheses of LSB genesis [3–6]. These data have been derived using a variety of methods [7–17], but there has been limited assessment of their differences and adequacy; thus, their comparability is uncertain. This study assesses different methods for measuring LSB orientation, length and longitudinal asymmetry, all of which require defining a longitudinal axis.

The a- and b-axes of ellipses defined from the area and perimeter of footprints using Euler’s approximation have been used to derive length and width for very large samples of drumlins [7–10]. The minimum bounding rectangle was used for deriving the length, width (rectangle length, width) and elongation (ratio of length to width) for over 10,000 LSBs from southern Sweden [15,16]. The longest straight line (LSL) fitting inside the LSB footprint has been used to analyze the longitudinal asymmetry of a very large sample of drumlins (44.5k) from northern Europe and North America [11,12] and to compute both length and planar asymmetry for 812 drumlins in southern Ontario, Canada [13]. Hillier and Smith [17] and Hillier et al. [19] derived drumlin length and width using the longest straight line crossing i) each footprint’s innermost point and ii) the drumlin’s highest point.

The morphometrics produced by the different automated methods are assessed against those derived from a longitudinal axis manually drawn based on visual interpretation of the topography. This axis is not an absolute reference due to the subjectivity of that process, but is the most typically used reference for evaluating data from automated methods [7,8,11,17]; synthetic bedforms are an alternative way of defining a reference, with both benefits and limitations [17,20]. Fig 1 shows the workflow used to derive the morphometric database.

With the exception of elliptical length (Euler’s approximation), absolute differences between the values for footprint orientation, length and longitudinal asymmetry computed with the various automated methods decrease with increasing footprint elongation (Fig 6). Elliptical lengths differed considerably (up to 100s of metres) from those of the other methods and independently of elongation (Fig 6B). With the exception of elliptical length, for LSBs with elongation > ~5, differences between methods were minimal (e.g., < ~1° in orientation). The results presented hereafter refer to LSBs with elongation < 5 (n = 64). For LSBs with elongation > ~ 5, differences between morphometrics from the different LAs (LSL, LSL-IP, RLA, SDE1-3) are negligible. Differences between LAs decrease as LSBs become more elongated (Fig 6A and 6B) because the possible range in orientation of a line extending between the footprints’ stoss and lee ends also decreases.

While for LSBs with elongation > ~5, differences between methods are minimal (Fig 6), for less elongated bedforms the relative performance of most methods (LSL, LSL-IP, RLA, elliptical length) depends on footprint shape (Figs 8, 10 and 11). The SDE methods most closely replicated the reference morphometrics (Tables 1 and 2; Fig 7) and are relatively shape-invariant (Fig 9). Due to the controlled vertex spacing and thus particular insensitivity to footprint shape, the SDE2-3 methods are, in principle, better than the SDE1 method.




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