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Abstract Structural diversity—the volume and physical arrangement of vegetation within the three‐dimensional (3D) space of ecosystems—is a predictor of ecosystem function that can be measured at large scales with remote sensing. However, the landscape composition and configuration of structural diversity across macrosystems have not been well described. Using a relatively recently developed method to quantify landscape composition and configuration of continuous habitat or terrain, we propose the application of gradient surface metrics (GSMs) to quantify landscape patterns of structural diversity and provide insights into how its spatial pattern relates to ecosystem function. We first applied an example set of GSMs that represent landscape heterogeneity, dominance, and edge density to Lidar‐derived structural diversity within 28 forested landscapes at National Ecological Observatory Network (NEON) sites. Second, we tested for forest type, geographic location, and climate drivers of macroscale variation in GSMs of structural diversity (GSM‐SD). Third, we demonstrated the utility of these metrics for understanding spatial patterns of ecosystem function in a case study with NDVI, a proxy of productivity. We found that GSM‐SD varied in landscapes within macrosystems, with forest type, geographic location, and climate being significantly related to some but not all metrics. We also found that dominance of high peaks of height and vertical complexity of canopy vegetation and the heterogeneity of the vertical complexity and coefficient of variation of canopy vegetation height within 120‐m patches were negatively correlated with NDVI across the 28 NEON sites. However, forest type always had a significant interaction term between these GSM‐SD and NDVI relationships. Our study demonstrates that GSMs are useful to describe the landscape composition and configuration of structural diversity and its relationship with productivity that warrants further consideration for spatially motivated management decisions. 

The species – area relationship (SAR) is a common pattern in which diversity increases with the area sampled, but ecosystems are three‐dimensional (3D) and diversity – volume relationships (DVRs) may exist in ecosystems that vary substantially in their vegetation volume. We tested whether forest vegetation volume, as a 3D extension of area in SARs, was a significant predictor of taxonomic (species) and structural (arrangement) diversity in five groups of organisms across the National Ecological Observatory Network (NEON). Vegetation volume and four structural arrangement metrics within the area of NEON plots were measured using NEON's discrete return lidar. Species richness was measured as the number of species within the respective NEON plot sampling area for understory plants, trees, breeding land birds, small mammals, and ground beetles. We found that volume negatively predicted understory plants and positively predicted tree and beetle species richness across the USA forest macrosystem, but not bird and small mammal species richness. Furthermore, volume was a significant predictor of several metrics that describe the internal and external heterogeneity of vegetation in forests (structural arrangement) within the ecosystem across the USA forest macrosystem. There were several significant within site‐level relationships, but not at all sites, between volume and species richness or structural arrangement in organism groups. Our study indicates that previous work that has focused on a 2D conceptualization of habitat can be expanded to 3D habitat space, but that the strength and the positive or negative direction of DVRs may vary taxonomically or geographically.