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Abstract The effective characterization of topographic surfaces is a central tenet of geomorphology. Differences in land surface properties reveal variations in structural controls and the nature and efficacy of Earth‐shaping processes. In this paper, we employ the Hölder exponents,α, characterizing the local scaling behavior of topography and commonly used in the study of the (multi)fractal properties of landscapes and show that the joint probability distribution of the area of the terrain with a given elevation andαcontains a wealth of information on topographic structure. The conditional distributions of the hypsometric integrals as a function ofα, that is,Ihyp|α, are shown to capture this structure. A multivariate analysis reveals three metrics that summarize these conditional distributions: Strahler's original hypsometric integral, the standard deviation of theIhyp|α, and the nature of any trend of theIhyp|αagainstα. An analysis of five digital elevation models (DEMs) from different regions of the United States shows that only one is truly described by the hypsometric integral (Mettman Ridge from central Oregon). In the other cases, the new metrics clearly discriminate between instances where topographic roughness is more clearly a function of elevation, as captured by the conditional variables. In a final example, we artificially sharpen the ridges and valleys of one DEM to show that while the hypsometric integral and standard deviation ofIhyp|αare invariant to the change, the trend ofIhyp|αagainstαcaptures the changes in topography.
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Surface Variability Mapping and Roughness Analysis of the Moon Using a Coarse‐Graining Decomposition
Abstract The lunar surface contains a wide variety of topographic shapes and features, each with different distributions and scales, and any analysis technique to objectively measure roughness must respect these qualities. Coarse‐graining is a naturally scale‐dependent filtering technique that preserves scale‐dependent symmetries and produces coarse elevation maps that gradually erase the smaller features from the original topography. In this study of the lunar surface, we present two surface variability metrics obtained from coarse‐graining lunar topography: fine elevation and coarse curvature. Both metrics are isotropic, deterministic, slope‐independent, and coordinate‐agnostic. Fine (detrended) elevation is acquired by subtracting the coarse elevation from the original topography and contains features that are smaller than the coarse‐graining length‐scale. Coarse curvature is the Laplacian of coarsened topography, and naturally quantifies the curvature at any scale and indicates whether a location is elevated or depressed relative to its neighborhood at that scale. We find that highlands and maria have distinct roughness characteristics at all length‐scales. Our topographic spectra reveal four scale‐breaks that mark characteristic shifts in surface roughness: 100, 300, 1,000, and 4,000 km. Comparing fine elevation distributions between maria and highlands, we show that maria fine elevation is biased toward smaller‐magnitude elevations and that the maria–highland discrepancies are more pronounced at larger length‐scales. We also provide local examples of selected regions to demonstrate that these metrics can successfully distinguish geological features of different length‐scales.
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- PAR ID:
- 10596405
- Publisher / Repository:
- Journal of Geophysical Research
- Date Published:
- Journal Name:
- Journal of Geophysical Research: Planets
- Volume:
- 129
- Issue:
- 10
- ISSN:
- 2169-9097
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1029/2024JE008484
