Adapting lacunarity techniques for gradient-based analyses of landscape surfaces

Typically, landscapes are modeled in the form of categorical map patterns, i.e. as mosaics made up of basic elements which are presumed to possess sharp and well-defined boundary lines. Many landscape ecological concepts are based upon this perception. In reality, however, the spatial value progressions of environmental parameters tend to be “gradual” rather than “abrupt”. Therefore, gradient approaches have shifted to the forefront of scientific interest recently. Appropriate methods are needed for the implementation of such approaches. Lacunarity analysis may provide a suitable starting point in this context. We propose adapted versions of standard lacunarity techniques for analyzing ecological gradients in general and the heterogeneity of physical landscape surfaces in particular. A simple way of customizing lacunarity analysis for quantifying the heterogeneity of digital elevation models is to use the value range for defining the box mass used in the calculation process. Furthermore, we demonstrate how lacunarity analysis can be combined with metrics derived from surface metrology, such as the “Average Surface Roughness”. Finally, the “classical” lacunarity approach is used in combination with simple landform indices. The methods are tested using different data sets, including high-resolution digital elevation models. In summary, lacunarity analysis is adopted in order to establish a gradient-based approach for terrain analysis and proves to be a valuable concept for comparing three-dimensional surface patterns in terms of their degree of “heterogeneity”. The proposed developments are meant to serve as a stimulus for making increased use of this simple but effective technique in landscape ecology. They offer a large potential for expanding the methodical spectrum of landscape structure analysis towards gradient-based approaches. Methods like lacunarity analysis are promising, since they do not rely on predefined landscape units or patches and thus enable ecologists to effectively deal with the complexity of natural systems.

Research highlights▶ We propose adapted versions of lacunarity techniques for analyzing ecological gradients. ▶ We combine lacunarity analysis with metrics derived from surface metrology. ▶ The techniques are valuable for comparing three-dimensional surface patterns. ▶ They are adequate for expanding the methodical spectrum of landscape structure analysis.