Recurrence lacunarity of spatial data

Abstract

Abstract Quantifying the structure and heterogeneity of complex spatial patterns remains a key challenge in spatial data analysis. Recurrence plots (RPs) offer a powerful method for visualizing the recurrent spatial patterns in such data. To quantify the structure of spatial recurrences, we extend the normalized recurrence lacunarity (nRL), a measure of the homogeneity of an RP, to the analysis of spatial RPs. Even though RPs can be derived from data with a topological dimension larger than one, their nRL has yet to be evaluated. To address this gap, we evaluate the nRL of spatial RPs, validate the method using synthetic test patterns and model data, and then apply it to analyze the hillslope gradients of 47 river catchments near the Mendocino Triple Junction. The results suggest that the nRL effectively detects and quantifies subtle differences in the spatial structure of the catchments. We show indications that these relate to local uplift rates, a previously identified possible driver of the structural differences. The nRL provides a robust and scale-sensitive tool for comparing diverse spatial data sets and for detecting and quantifying how their spatial structure may relate to external parameters.