###### Abstract  
The Amazon rainforest plays an important role in the global carbon cycle. However, due to its structural complexity, current estimates of its carbon dynamics are very imprecise. The aim of this study was to determine the forest productivity and carbon balance of the Amazon, particularly considering the role of canopy height complexity. Recent satellite missions have measured canopy height variability in great detail over large areas. Forest models are able to transform these measurements into carbon dynamics. For this purpose, about 110 million lidar waveforms from NASA's GEDI mission (footprint diameters of -25 m each) were analyzed over the entire Amazon ecoregion and then integrated into the forest model FORMIND. With this model-data fusion, we found that the total gross primary productivity (GPP) of the Amazon rainforest was 11.4 Pg C a\({}^{-1}\) (average: 21.1 Mg C a\({}^{-1}\) a\({}^{-1}\)) with lowest values in the Arc of Deforestation region. For old-growth forests, the GPP varied between 15 and 45 Mg C a\({}^{-1}\) a\({}^{-1}\). At the same time, we found a correlation between the canopy height complexity and GPP of old-growth forests. Forest productivity was found to be higher (between 25 and 45 Mg C a\({}^{-1}\) a\({}^{-1}\)) when canopy height complexity was low and lower (10-25 Mg C a\({}^{-1}\) a\({}^{-1}\)) when canopy height complexity was high. Furthermore, the net ecosystem exchange (NEE) of the Amazon rainforest was determined. The total carbon balance of the Amazon ecoregion was found to be \(-0.1\) Pg C a\({}^{-1}\), with the highest values in the Amazon Basin between both the Rio Negro and Solimoes rivers. This model-data fusion reassessed the carbon uptake of the Amazon rainforest based on the latest canopy structure measurements provided by the GEDI mission in combination with a forest model and found a neutral carbon balance. This knowledge may be critical for the determination of global carbon emission limits to mitigate global warming. t 17 September 2021 5 November 2021 5 November 2021 11 November 2021  
these forests are very heterogeneous and reveal complex structures. Thus, estimates for aboveground biomass in the Amazon rainforest diverge by a factor of two and range from 40 to 90 Pg C [12]. Based on the fact that variations in estimates of aboveground biomass in the Brazilian Amazon account for 60% of the variation in estimated net carbon flux for the region [13], it is important to estimate aboveground biomass and gross primary productivity for the Amazon as accurately as possible to determine the forests' carbon balance. Variations in aboveground biomass and productivity estimates primarily result from forest disturbance and recovery [14] but also from the limitations of the methods used so far. Previously, aboveground biomass maps were mainly produced based on passive optical satellite data, such as Landsat or MODIS in combination with sparse lidar measurements from the Geoscience Laser Altimeter System (GLAS) located on the ICESat (Ice, Cloud, and land Elevation Satellite) [11; 15; 16; 17]. However, there is a limitation to using measurements from passive optical satellites because they are only sensitive to tree cover, leaving the vertical structure of a forest unknown. Aboveground biomass estimates are thus saturated for high density forests. Lidar measurements, on the other hand, allow for the vertical structure of a forest to be measured. A new generation of satellites could bring tropical forest surveying to a new level. GEDI is the first spaceborne lidar mission optimized for measuring ecosystem structures [15]. The lidar measurements of GEDI (with a diameter of ~25 m each) can be used for determining the forest canopy structure, forest aboveground biomass, and topography [15]. The dataset contains an average of 27 waveforms per 1 km\({}^{2}\). With millions of lidar waveforms in the Amazon, GEDI provides the opportunity to decrease inaccuracy in the determination of forest attributes such as aboveground biomass [18].