Reconstructing ice‐flow fields from streamlined subglacial bedforms: A kriging approach

Abstract

The orientation of several landforms, e.g. drumlins, flutes, crag‐and‐tails, and mega‐scale glacial lineations, records the direction of the overlying ice flow that created them. Populations of such features are used routinely to infer former ice‐flow patterns, which serve as the building blocks of reconstructions of palaeo ice‐sheet evolution. Currently, the conceptualisation of flow patterns from these flow‐direction records is done manually and qualitatively, so the extractable glaciological information is limited. We describe a kriging method (with Matlab code implementation) that calculates continuous fields of ice‐flow direction, convergence, and curvature from the flow‐direction records, and which yields quantitative results with uncertainty estimates. We test the method by application to the subglacial bedforms of the Tweed Valley Basin, UK. The results quantify the convergent flow pattern of the Tweed Palaeo‐Ice Stream in detail and pinpoint its former lateral shear margins and where ice flowed around basal bumps. Ice‐flow parameters retrieved by this method can enrich ice‐sheet reconstructions and investigations of subglacial till processes and bedform genesis. © 2018 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.

Reconstructing basal ice flow patterns of the Last Glacial Maximum Rhine glacier (northern Alpine foreland) based on streamlined subglacial landforms

“…The kriging workflow of Ng and Hughes (2019) Kamleitner et al, 2023;Preusser et al, 2007), Rhine glacier exited the Alps at the mouth of Alpenrhein Valley (Figure 1), where it had been laterally confined and strongly funneled. Upon encountering a much flatter landscape on the foreland, it spread to the west, north and east, filled the Lake Constance basin and, from there, flowed uphill (Figure 1c) to its maximum position at the Schaffhausen stadial moraines (Figure 11a).…”

“…Orientations of streamlined subglacial landforms indicate glacier flow directions and are a powerful tool for constraining basal ice flow patterns during past glaciations (Clark, 1999; Greenwood & Clark, 2009; Hughes et al, 2014; Kleman & Borgström, 1996; Ng & Hughes, 2019; Shaw et al, 2010; Stokes & Clark, 2001). Highly elongated subglacial features can further inform about corridors of fast‐flowing ice (Jamieson et al, 2016; Stokes & Clark, 2002).…”

“…Ng and Hughes (2019) recently proposed a quantitative approach to infer continuous basal ice flow patterns (flow fields) from defined subglacial landform flowsets using a kriging interpolation method (Figure2). The herein implemented MATLAB workflow(Ng & Hughes, 2019) was specifically designed for deriving continuous flow fields from subglacial orientations.…”

“…In a variogram with a well-defined sill, the R value is chosen on the shoulder of the sill's rise. To guide the kriging process, we fit our model variogram using the equations presented byNg and Hughes (2019)…”

“…improve and speed up the curve-fitting process, in light of the multiple combinations of kriging ranges and sills tested, we implemented an additional python script. This included a curve-fitting function from the scipy library (scipy.optimize.curve_fit, scipy.org) and uses least squares (lm, Levenberg-Marquardt) or trust region reflective (trf) algorithms to fit the equation parameters (C values; seeNg & Hughes, 2019). Kriging output will be most sensitive to the rise of the model variogram curve close to h = 0, while fitting at higher h values will have weaker influence(Ng & Hughes, 2019).…”