An understanding of the spatial variability in tropical forest structure and biomass, and the mechanisms that underpin this variability, is critical for designing, interpreting, and upscaling field studies for regional carbon inventories. We investigated the spatial structure of tropical forest vegetation and its relationship to the hydrological network and associated topographic structure across spatial scales of 10-1000 m using high-resolution maps of LiDAR-derived mean canopy profile height (MCH) and elevation for 4930 ha of tropical forest in central Panama. MCH was strongly associated with the hydrological network: canopy height was highest in areas of positive convexity (valleys, depressions) close to channels draining 1 ha or more. Average MCH declined strongly with decreasing convexity (transition to ridges, hilltops) and increasing distance from the nearest channel. Spectral analysis, performed with wavelet decomposition, showed that the variance in MCH had fractal similarity at scales of ∼30-600 m, and was strongly associated with variation in elevation, with peak correlations at scales of ∼250 m. Whereas previous studies of topographic correlates of tropical forest structure conducted analyses at just one or a few spatial grains, our study found that correlations were strongly scale-dependent. Multi-scale analyses of correlations of MCH with slope, aspect, curvature, and Laplacian convexity found that MCH was most strongly related to convexity measured at scales of 20-300 m, a topographic variable that is a good proxy for position with respect to the hydrological network. Overall, our results support the idea that, even in these mesic forests, hydrological networks and associated topographical variation serve as templates upon which vegetation is organized over specific ranges of scales. These findings constitute an important step towards a mechanistic understanding of these patterns, and can guide upscaling and downscaling.