Playfair's Law and the Width of Glacial Valleys
Abstract
Valleys produced by glaciers are morphologically distinct from those created by rivers, but these differences are surprisingly difficult to detect using digital topographic data. In this contribution, we determine whether glacial and fluvial valleys can be discriminated in topographic data using the scaling between watershed area and valley width between these two classes. Specifically, we present a method for estimating valley width at each point in a digital topographic dataset by determining the cross-valley scale at which normalized principal curvature is minimized. Calculations are performed in the frequency domain, which enables an iterative search to determine minimum curvature at each point and the corresponding valley width (cross-valley scale). Synthetic valley cross-sections are used to assess how well this approach measures valley width in idealized valleys subject to topographic noise. Valley width estimates are validated against manual measurements of valley width in glacial and fluvial valleys. Finally, we assess the sensitivity of these quantities to the pixel dimension of the input data to determine the detection limits of the method for moderate (20 m) and coarse resolution (> 30 m) digital topographic data. We find that valley widths are under-predicted by a factor of 2.5 to 4; nonetheless, they are well correlated with both synthetically prescribed and empirically measured widths, and so can be used as reliable measures of valley width when adjusted for this under-prediction.
This methodology was applied to basins in the Olympics (Washington), Sawtooths (Idaho), and Sierra Nevadas (California), where previous work has identified fluvial and glacial valley morphologies in close proximity to one another. We find that fluvially and glacially dominated basins follow fundamentally different trajectories of Playfair's Law, which describes the scaling between watershed area and valley width. These deviations should be large enough to discriminate fluvial and glacial valley morphologies, which may allow us to produce topographic global inventories of glacial landscapes. We speculate that the difference in scaling of Playfair's law can be understood in terms of the viscosity of ice and water, which causes the former to occupy far larger portions of the valley floor than the latter.- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2019
- Bibcode:
- 2019AGUFMEP43E2408H
- Keywords:
-
- 1630 Impacts of global change;
- GLOBAL CHANGE;
- 1807 Climate impacts;
- HYDROLOGY;
- 1824 Geomorphology: general;
- HYDROLOGY;
- 1861 Sedimentation;
- HYDROLOGY