3D-SHI index for quantifying 3D spatial heterogeneity in big Earth data

Investigating spatial heterogeneity is a crucial aspect of spatial analysis. Existing studies have primarily focused on measuring 2D geographic distribution, which cannot be directly applied to extensive 3D big earth datasets. To address this gap, we propose a novel 3D spatial heterogeneity index (3D-SHI) to explore 3D spatial heterogeneity in big earth data. First, we introduce some new concepts including the Earth cube model and connected components to effectively capture 3D spatial heterogeneity. Second, we derive the formulation for 3D-SHI and propose a connected component model (CCM) to facilitate near real-time computation of the index. To elucidate the geographic significance of this index, we analyzed its characterization in comparison with three traditional methods. In our experiments, we simulated 3D datasets to demonstrate the efficiency and capacity of the proposed 3D-SHI. Additionally, we used a real-world sea temperature dataset from the North Atlantic were conducted to quantify high dimensional spatial heterogeneity. The experimental results illustrated that 3D-SHI can effectively capture changes in spatial heterogeneity and reveals patterns that exist across both temporal and spatial dimensions.