Plant biodiversity supports life on Earth and provides a range of important ecosystem services, but is under severe pressure by global change. Structural diversity plays a crucial role for carbon, water and energy cycles and animal habitats. However, it is very difficult to map and monitor over large areas, limiting our ability to assess the status of biodiversity and predict change. NASA's Global Ecosystem Dynamics Investigation (GEDI) provides a new opportunity to measure 3D plant canopy structure of the world's temperate, Mediterranean and tropical ecosystems, but its potential to map structural diversity is not yet tested. Here, we use wall-to-wall airborne laser scanning (ALS) to simulate GEDI data (GEDIsim) over 7380 km2 in the southern Sierra Nevada mountains in California, and evaluate how well GEDI's sampling scheme captures patterns of structural diversity. We evaluate functional richness and functional beta diversity in a biodiversity hot spot. GEDIsim performed well for trait retrievals (r2 = 0.68) and functional richness mapping (r2 = 0.75) compared to ALS retrievals, despite lower correlations in complex terrain with steep slopes. Functional richness patterns were strongly associated with soil organic carbon stocks and density as well as variables related to water availability, and could be appropriately mapped by GEDIsim with and without cloud cover. Functional beta diversity was more strongly related to local changes in topography and more challenging to map, especially with decreasing sampling density. The reduced number of GEDIsim shots when simulating cloud cover lead to a strong overestimation of beta diversity and a reduction of r2 from 0.64 to 0.40 compared to ALS. The ability to map functional richness has been demonstrated with potential application at continental scales that could be transformative for our understanding of large-scale patterns of plant canopy structure, diversity and potential links to animal diversity, movement and habitats.