The length-scaling properties of topography

The scaling properties of synthetic topographic surfaces and digital elevation models (DEMs) of topography are examined by analyzing their "structure functions', i.e., the qth order powers of the absolute elevation differences: Δhq(l) = E {|h(x + l) - h(x)|q. We find that the relation Δh1(l)≃ clH describes well the scaling behavior of natural topographic surfaces, as represented by DEMs gridded at 3 arc sec. Average values of the scaling exponent H between ~0.5 and 0.7 characterize DEMs from Ethiopia, Saudi Arabia, and Somalia over 3 orders of magnitude range in length scale l (~0.1-150 km). Differences in apparent topographic roughness among the three areas most likely reflect differences in the amplitude factor c. Hypsometric curves, which probably reflect the relative importance of tectonic and erosional processes in shaping topography, clearly show that statistical moments higher than the second are important in describing topographic surfaces. Scaling analysis is a valuable tool for assessing the quality and accuracy of DEM representations of the Earth's topography. -from Authors

Duke Scholars

Author Lincoln F. Pratson Earth and Climate Sciences