Mathematical Geosciences

, Volume 45, Issue 7, pp 819–835 | Cite as

Elliptically Symmetric Distributions of Elevation Gradients and the Distribution of Topographic Aspect



Characterizing the spatial variability of topography is essential when modeling landscape processes such as surface energy and water balances, and landslide and avalanche risk, to name a few. A probabilistic representation of topographic features is a parsimonious alternative to the more detailed but computationally demanding descriptions. In this work, an analytical expression for the theoretical distribution of topographic aspect is obtained that is based on the statistical parameters of the topographic elevation gradients, that is, the mean, standard deviation, and correlation coefficient. For this expression, an elliptically symmetric distribution of elevation gradients is assumed, and this assumption is validated with the resulting theoretical distribution of aspect using the data of six case studies in the continental United States with different geology, elevation range, climate, and vegetation. The comparison shows that the theoretical distribution of aspect is a suitable description for the observed distribution of aspect on a regional scale. Consequently, the theoretical expression for the distribution of aspect could be a useful tool in models that rely on aspect for the accuracy of surface energy and water balances, and other relevant processes.


Topography Random elevation field Change of variables Cauchy distribution Spherically symmetric distribution 



This work was partially funded by the National Science Foundation through grant NSF-CBET-1033467 and by the US Department of Energy through the Office of Biological and Environmental Research (BER) Terrestrial Ecosystem Science (TES) Program (DE-SC0006967). We thank the anonymous reviewers, the associate editor, and the editor, Professor Roussos Dimitrakopoulos, for their useful comments.


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Copyright information

© International Association for Mathematical Geosciences 2013

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringDuke UniversityDurhamUSA
  2. 2.Department of Crop Production EcologySwedish University of Agricultural SciencesUppsalaSweden

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