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Fractal Properties of Greenland Isolines

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Abstract

The shape of Earth’s surface topography is determined by numerous competing processes that act to either roughen or smoothen the surface. Hence, calculating topographic roughness is a useful technique for understanding the relative importance of these processes. This study analyzes the relative surface roughness of the Greenland Ice Sheet by calculating the fractal dimension of surface elevation isolines. It is shown that the fractal dimension of isolines decreases at higher elevations for nearly all the ice sheet catchments. However, the magnitude of fractality, which represents the relative complexity or roughness of the surface, is spatially variable. Catchments in the central-east of the ice sheet have the highest fractal dimension, and the north catchment has the lowest fractal dimension. Multi-fractality at lower elevations for several catchments is observed including the southeast catchment, indicating that these catchments have variable dominant forcings at different length scales. Exploring the local variation of fractal dimensions shows that the majority of isolines with high fractal dimension are clustered in the central-east region and persist in contours up to 2500 m elevation. However, it is shown that local fractal dimensions are related to surface elevation, bed elevation, and ice thickness. It is also shown that local fractal dimensions are correlated with the ruggedness of basal topography (defined as the difference between the highest and lowest elevation in a window of \(3\times 3\) pixels on a 150 m grid). This analysis serves as a qualitative approach for investigating the processes that control the geometry of ice caps on other terrestrial planets.

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Acknowledgements

The authors thank the editor-in-chief Roussos Dimitrakopoulos and two anonymous referees whose comments greatly improved the clarity of the manuscript. The authors acknowledge the contribution of Logan C. Byers for sharing and extensive help with his fractal code. We also like to thank Steve Rector at Center for Remote Sensing of Ice Sheets (CReSIS) for technical support. The Python code that was developed for this study is available at https://bitbucket.org/soroushr/fractal-dimension-greenland.

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Authors and Affiliations

  1. Department of Geology, University of Kansas, Lawrence, KS, USA

    Soroush Rezvanbehbahani & Leigh A. Stearns

  2. Center for Remote Sensing of Ice Sheets, University of Kansas, Lawrence, KS, USA

    Soroush Rezvanbehbahani & Leigh A. Stearns

  3. Department of Geography and Atmospheric Science, University of Kansas, Lawrence, KS, USA

    C. J. van der Veen

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  1. Soroush Rezvanbehbahani
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Correspondence to Soroush Rezvanbehbahani.

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Rezvanbehbahani, S., van der Veen, C.J. & Stearns, L.A. Fractal Properties of Greenland Isolines. Math Geosci 51, 1075–1090 (2019). https://doi.org/10.1007/s11004-019-09788-7

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