Tropical forests play an important role in the global carbon cycle. High-resolution remote sensing techniques, e.g., spaceborne lidar, can measure complex tropical forest structures, but it remains a challenge how to interpret such information for the assessment of forest biomass and productivity. Here, we develop an approach to estimate basal area, aboveground biomass and productivity within Amazonia by matching 770,000 GLAS lidar (ICESat) profiles with forest simulations considering spatial heterogeneous environmental and ecological conditions. This allows for deriving frequency distributions of key forest attributes for the entire Amazon. This detailed interpretation of remote sensing data improves estimates of forest attributes by 20-43% as compared to (conventional) estimates using mean canopy height. The inclusion of forest modeling has a high potential to close a missing link between remote sensing measurements and the 3D structure of forests, and may thereby improve continent-wide estimates of biomass and productivity.