A Lacunarity‐Based Index for Spatial Heterogeneity

Abstract

Abstract Characterizing spatial heterogeneity is fundamental in numerous areas, yet defining spatial patterns often depends on qualitative assessments or a priori knowledge. Lacunarity analysis is a popular occupancy‐based method for identifying relevant length scales in spatially heterogeneous systems. From lacunarity, we identify the existence of a point which encapsulates the spatial heterogeneity of a given system. This value satisfies the conditions for the lacunarity cutoff function and forms the basis of a heterogeneity index. We evaluate the behavior of both parameters in monofractal, clustered, and periodic systems. In addition, we demonstrate the broad utility of our approach to the scientific community by classifying the spatial heterogeneity of fractured sea ice and comparing our findings to existing measures. The heterogeneity index produced a linear correlation with the area fraction of open ocean to ice with an R2 of 0.967.

Keywords

• lacunarity
• heterogeneity
• index
• spatial