Environment and Ecology Research 6(5): 397-412, 2018 http://www.hrpub.org DOI: 10.13189/eer.2018.060501 Geomorphometry in Landscape Ecology: Issues of Scale, Physiography, and Application Kirsten Erin Ironside 1,* , David J. Mattson 1 , Terence Arundel 1 , Tad Theimer 2 , Brandon Holton 3 , Michael Peters 4 , Thomas C. Edwards, Jr. 5 , Jered Hansen 1 1 U.S. Geological Survey, Southwest Biological Science Center, United States 2 Biological Sciences Department, Northern Arizona University, United States 3 National Park Service, Grand Canyon National Park, Science and Resource Center, United States 4 Pterylae Systems, Arizona, United States 5 U.S. Geological Survey, Utah Cooperative Fish and Wildlife Research Unit, Department of Wildland Resources, Utah State University, United States Copyright©2018 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of the Creative Commons Attribution License 4.0 International License Abstract Topographic measures are frequently used in a variety of landscape ecology applications, in their simplest form as elevation, slope, and aspect, but increasingly more complex measures are being employed. We explore terrain metric similarity with changes in scale, both grain and extent, and examine how selecting the best measures is sensitive to changes in application. There are three types of topographic measures: 1) those that relate to orientation for approximating solar input, 2) those that capture variability in terrain configuration, and 3) those that provide metrics about landform features. Many biodiversity hotspots and predators have been found to coincide with areas of complexity, yet most complexity measures cannot differentiate between terrain steepness and uneven and broken terrain. Currently characterizing terrain in landscape-level analyses can be challenging, especially at coarser spatial resolutions but developing methods that improve landscape-level assessments include multivariate approaches and the use of neighborhood statistics. Some measures are sensitive to the spatial grain of calculation, the physiography of the landscape, and the scale of application. We show which measures have the potential to be multi-collinear, and illustrate with a case study how the selection of the best measures can change depending on the question at hand using mountain lion (Puma concolor) occurrence data. The case study showed a combination of infrequently employed metrics, such as view-shed analysis and focal statistics, outperform more commonly employed singular metrics. The use of focal statistics as a measure of topographic complexity shows promise for improving how mountain lions use terrain features. Keywords Habitat, Topography, Terrain, Ruggedness, Mountain Lion, Puma concolor 1. Introduction Techniques for characterizing and quantifying land and benthic surfaces have been utilized by many biological and ecological fields of study, in addition to the fields of geomorphology, soil science, and remote sensing from which they are typically derived. A wide assortment of measures has been developed as a result of a cross-disciplinary approach required to capture landscape or seascape features. With the coming of the digital age, geomorphology and geography gave rise to geomorphometry, the science of topographic quantification where the primary objective is to quantify surface parameters from digital elevation models (DEMs) [1]. Currently, many software tools and parameters have been developed with advances in Geographic Information Systems (GIS). Measures first developed for geomorphological or remote sensing applications are now being applied to ecological questions, such as evaluating species’ resource selection of “rugged” terrain [2]. As with many fields of study, semantics in geomorphometry [1] have been problematic for describing what a topographic measure captures. Topographic features can play a fundamental role in many biological, ecological, and evolutionary processes. Some features such as large mountain ranges or low elevation valleys may form barriers to movement and gene flow for some species. Terrain aspect determines amounts of energy input in the form of solar radiation, in turn affecting evapotranspiration rates and contributing to the evolution of plant phenology and adaption to xeric or mesic conditions. Similarly, in animals, terrain has contributed to the evolution of