  NASA's Global Ecosystem Dynamics Investigation (GEDI) is a key climate
mission whose goal is to advance our understanding of the role of forests in
the global carbon cycle. While GEDI is the first space-based LIDAR explicitly
optimized to measure vertical forest structure predictive of aboveground
biomass, the accurate interpretation of this vast amount of waveform data
across the broad range of observational and environmental conditions is
challenging. Here, we present a novel supervised machine learning approach to
interpret GEDI waveforms and regress canopy top height globally. We propose a
probabilistic deep learning approach based on an ensemble of deep convolutional
neural networks(CNN) to avoid the explicit modelling of unknown effects, such
as atmospheric noise. The model learns to extract robust features that
generalize to unseen geographical regions and, in addition, yields reliable
estimates of predictive uncertainty. Ultimately, the global canopy top height
estimates produced by our model have an expected RMSE of 2.7 m with low bias.
