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Global canopy height regression and uncertainty estimation from GEDI LIDAR waveforms with deep ensembles

Nico Lang, Nikolai Kalischek, John Armston, Konrad Schindler, Ralph Dubayah, Jan Dirk Wegner

arXiv:2103.03975v2cs.LGcs.CV

TL;DR

Interpreting GEDI waveforms globally is difficult because canopy structure, environmental conditions, noise, and instrument effects vary widely. The paper uses probabilistic deep ensembles of CNNs to regress canopy-top height from L1B waveforms while estimating predictive uncertainty, achieving an expected RMSE of 2.7 m with low bias. The approach generalizes to unseen regions, although tall-canopy underestimation and uneven reference-data coverage remain limitations.

  • Problem

    GEDI waveform interpretation for global canopy-height estimation is challenging because structural, atmospheric, environmental, and instrument effects are difficult to model across diverse conditions.

  • Method

    A probabilistic ensemble of CNNs maps full GEDI L1B waveforms to RH98 canopy-top heights and estimates aleatoric and epistemic predictive uncertainty.

  • Results

    2.7 m expected RMSE, compared with 4.4 m for the initial GEDI L2A product, with underestimation bias reduced from −1.0 m to −0.1 m.

  • Takeaways & Limitations

    The model produces global canopy-height maps, generalizes to unseen geographical regions, and provides calibrated uncertainty that can support accuracy–recall filtering.

  • Takeaways & Limitations

    The model systematically underestimates tall canopy heights above 70 m, and the reference dataset lacks South American and East Asian coverage while scarcely representing Europe.

Abstract

from arXiv · show

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.

1. Introduction

Global canopy-height estimation matters for carbon-cycle and ecosystem monitoring, but interpreting GEDI waveforms globally is difficult because structural and observational conditions vary widely. The paper addresses this with a probabilistic CNN approach that estimates canopy height and predictive uncertainty.

  • Motivation: 47% relative standard deviation underscores uncertainty in carbon-flux estimates, motivating improved forest biomass mapping.Annual global land-use-change emissions are reported as 1.5±0.7 GtC yr−1, while the terrestrial CO2 sink is 3.2±0.6 GtC yr−1.
  • Motivation: Canopy height supports aboveground-biomass estimation, ecosystem-change monitoring, biodiversity assessment, and species-richness prediction.It is also a key morphological trait for monitoring climate and land-use change and restoration.
  • Challenge: GEDI waveform processing must identify canopy-top and ground signals despite difficult-to-model effects and weak returns under dense canopies.Relevant effects include pulse shape, digitizer noise, slope, multiple scattering, background noise, and sparse leaf area near tree tops.
  • Challenge: GEDI’s global observations span diverse topographic, climatic, edaphic, structural, and laser-power conditions that challenge traditional signal-processing methods.High- and low-power beams interact with substantial waveform variability across temperate and tropical forests.
  • Approach: The proposed probabilistic CNN maps full GEDI L1B waveforms to RH98 canopy-top heights while modeling aleatoric and epistemic uncertainty.The network learns waveform peaks and patterns rather than explicitly modeling unknown atmospheric, environmental, and instrument effects.
  • Evaluation: 68,483 on-orbit GEDI waveforms were matched to ALS-derived RH98 references, with geographic cross-validation used to test transfer to unseen regions.Waveform-block correlation reduced first-release geolocation errors from approximately 20 m to a few meters on average.

2. Data

The study combines GEDI orbital measurements with airborne-LIDAR references to construct a geographically diverse training and validation dataset. The data cover broad terrain and forest conditions, but regional representation is uneven.

  • GEDI observations: GEDI measures along eight ground tracks from the ISS, with approximately 25 m footprints and 60 m along-track shot spacing.Four tracks use full-power lasers and four use a reduced-power coverage laser.
  • GEDI products: The L2A product derives elevation and relative-height metrics from L1B waveforms using six algorithm-setting groups for varied environmental conditions.It also provides lowest-mode ground locations and MODIS-derived non-vegetated-area percentages.
  • Reference dataset: The airborne-LIDAR reference dataset spans five continental regions and diverse canopy heights, canopy covers, plant functional types, and topography.Terrain ranges from flat to steep across −36.8 to 51.8 degree latitude.
  • Reference dataset: North America contributes more than half of the reference data, while South America and East Asia lack reference data and Europe is sparsely represented.This uneven geographic coverage constrains how broadly the dataset represents global forests.
  • Data construction: GEDI L1B waveforms from the first seven mission months were matched with ALS data, correcting systematic geolocation error through block correlation.Poor-quality offsets were filtered, and Pearson correlation between on-orbit and simulated waveforms assessed match quality.

3. Method

The method uses probabilistic one-dimensional CNN ensembles to regress canopy height from harmonized GEDI waveforms while estimating predictive uncertainty. Independently trained models produce a mixture prediction, evaluated with standard error metrics and geographic validation.

  • 3.1. Waveform preprocessing: GEDI waveforms are harmonized by noise subtraction, energy normalization, fixed-length padding, and standardization of inputs and canopy-height targets.Fixed waveform length allows the CNN to learn absolute canopy-height scale because consecutive returns are separated by 15 cm.
  • 3.2. Model architecture: The SimpleResNet adapts ResNet with one-dimensional convolutional, pooling, and normalization layers for canopy-height regression.The architecture uses eight residual blocks with repeated convolutional layers.
  • 3.3. Predictive uncertainty estimation: Each CNN predicts a conditional mean and variance, with Gaussian negative log-likelihood training modeling heteroscedastic aleatoric uncertainty.The predicted log variance is exponentiated to guarantee a positive variance, with ϵ = 10^-8 added for numerical stability.
  • 3.3. Predictive uncertainty estimation: An ensemble of independently initialized deterministic CNNs approximates epistemic uncertainty through Bayesian marginalization over models.Averaging member outputs forms an equally weighted Gaussian mixture whose variance combines epistemic and aleatoric uncertainty.
  • 3.6. Geographical cross-validation: The dataset is split into training, validation, and held-out test sets, with random 10-fold and geographic cross-validation assessing split stability and transfer to unseen regions.Geographic splitting reserves all samples from one region for testing while training on the remaining regions.
  • 3.7. Evaluation metrics: Performance is measured primarily with RMSE and mean error, while predictive uncertainty is assessed through ranking and calibration curves.Calibration compares binned predictive standard deviation with empirical RMSE, where closer agreement to the diagonal indicates better calibration.

4. Results

The CNN regresses GEDI canopy top height with stable performance across random splits and reasonable transfer to unseen geographic regions. Its predictive uncertainty is well calibrated, supports adaptive filtering that reduces error while preserving the height range, and reflects waveform ambiguity and underrepresented conditions.

  • Canopy top height regression: 3.6 m RMSE and −0.3 m ME were obtained under random cross-validation, with only 0.1 m standard deviations across ten folds.The estimates show slight underestimation relative to ALS references, while performance remains invariant to random data splits.
  • Geographic generalization: Geographic holdouts produced no higher RMSE and suggested reasonable generalization to regions unseen during training.Bias was −0.9 m in Australia, Africa, and the tropics, versus 0.7 m in Europe; MAPE varied with regional canopy-height distributions.
  • Predictive uncertainty: Removing the most uncertain predictions reduced RMSE from 3.6 m at 100% recall to 3.0 m at 90% recall and 2.7 m at 70% recall.The result indicates that predictive uncertainty ranks samples by expected empirical error, trading recall for lower overall error.
  • Predictive uncertainty: Predicted standard deviations were well calibrated, with samples assigned 3.5 m uncertainty achieving an empirical RMSE of approximately 3.5 m.Aleatoric uncertainty dominated random cross-validation, while epistemic uncertainty remained non-negligible and may increase for underrepresented cases.
  • Predictive uncertainty: Low uncertainty corresponded to waveforms with distinct canopy-top and ground signals, whereas high uncertainty marked ambiguous signals from noise, dense low canopy, or canopy shape.The qualitative examples separate predictive, aleatoric, and epistemic standard deviations.
  • Filtering canopy height estimates: Adaptive thresholds depending on predicted canopy height reduced error while preserving the full predicted height range.Absolute thresholds removed almost all high canopies and relative thresholds removed almost all low canopies; the adaptive rule also reduced underestimation bias.

5. Discussion

The discussion presents probabilistic CNN waveform processing as a data-driven alternative that generalizes across variable observation conditions and provides calibrated uncertainty for global canopy-height estimation.

  • Data-driven waveform processing: The CNN avoids manual calibration across beams, plant functional types, canopy covers, and other observation conditions by learning an adaptive waveform processor.The authors state that the approach generalizes across possible scenarios.
  • Uncertainty estimation: Predictive uncertainty is directly estimated and can be used to filter canopy-height predictions according to application-specific accuracy requirements.Filtering can reduce empirical error while preserving the range and geographical coverage of estimates.
  • Height range and bias: 97.2 m is the model’s maximum predicted canopy height, exceeding the 70.1 m maximum in training data while covering the relevant range for most forests.Epistemic uncertainty increases above 70 m, and tall canopy heights show systematic underestimation.
  • GEDI beam conditions: Coverage-beam power differences did not affect overall CNN performance, despite the beams’ lower signal-to-noise ratio and weaker ground and canopy returns.This may support less restrictive use of coverage beams in downstream products.
  • Extensions: The generic CNN can be applied directly to ground elevation, plant area index, biomass, and species richness from raw waveforms.The authors suggest that end-to-end biomass regression could bypass manually derived waveform metrics.

6. Conclusion

The conclusion reports that end-to-end probabilistic learning derives global canopy heights from noisy GEDI L1B waveforms while avoiding explicit modeling of unknown effects and generalizing to unseen regions.

  • Global canopy-height retrieval: The model derives global canopy heights from complex on-orbit GEDI L1B waveforms with favorable accuracy that may exceed traditional waveform processing.The conclusion frames this as an end-to-end supervised learning task.
  • Learned waveform processing: End-to-end learning avoids explicitly modeling unknown atmospheric, environmental, and instrument effects by learning to isolate the desired signal from noisy data.The model learns robust features that generalize to geographical regions absent from training.
  • Uncertainty estimation: Probabilistic learning supplements canopy-height regression with predictive-uncertainty estimates that are empirically calibrated and reliable.These estimates support filtering highly uncertain predictions while preserving the full height range and global distribution.

7. Data availability

The paper provides access to generated canopy-height maps and describes the computational resources used to produce the global archive.

  • Data access: Generated canopy-height map data are available as georeferenced raster files through the cited Zenodo repository.Most source ALS data are open access, while non-public ALS datasets are subject to data-use agreements.
  • Computational scaling: A single orbit containing 1.2×10^6 waveforms can be processed in under 10 minutes for the complete model ensemble on one consumer-grade GPU.The stated hardware is an Nvidia GeForce GTX 1080Ti.
  • Computational scaling: Processing the four-month archive of 12.3 TB of raw GEDI L1B waveforms requires approximately 250 hours of GPU computing.

Appendix B. CNN architecture illustration

Appendix B illustrates the convolutional neural network architecture used by the paper through a ResNet-based graphical depiction.

  • CNN architecture: Figure B.8 graphically illustrates the convolutional neural network based on the ResNet architecture.
  • CNN architecture: The figure concerns the paper’s CNN architecture rather than a canopy-height result or uncertainty evaluation.
  • CNN architecture: The illustration provides an architectural view of the network used for GEDI waveform processing.

Appendix C. Performance regarding laser power for high canopies

The appendix examines performance for high-canopy samples under varying laser power, alongside solar-background noise, beam sensitivity, and geographic generalization experiments.

  • Laser power: Figure C.9 evaluates performance with respect to laser power for samples with canopy height >50 m.Results are shown for all test samples and for the 70% most certain predictions.
  • Noise and beam sensitivity: Figure D.10 evaluates performance under solar background noise and beam sensitivity.Beam sensitivity is defined as the maximum canopy cover that can be penetrated.
  • Geographic generalization: Figure E.11 presents geographic generalization experiments for regressing canopy top height (RH98).

Appendix F. Filtering with absolute and relative predictive uncertainty thresholds

The appendix compares filtering GEDI canopy-height predictions using absolute versus relative predictive-uncertainty thresholds. Adaptive thresholding is designed to preserve the full range of canopy heights.

  • Filtering criteria: Figure F.12 compares ALS reference canopy top heights with CNN estimates under absolute and relative uncertainty filtering.The filters retain samples with absolute predictive standard deviation <5 m or relative predictive standard deviation <20%.
  • Adaptive thresholds: Figure G.13 shows adaptive thresholds for canopy heights from 0 to 70 m using absolute and relative threshold functions.The adaptive approach preserves the full range of canopy heights.

Appendix H. Effect of the filtering with predictive uncertainty

The appendix evaluates how predictive-uncertainty filtering affects RH98 performance and examines uncertainty calibration, global uncertainty patterns, and out-of-distribution predictions.

  • Filtering effects: Figure H.14 compares RH98 performance across all test samples and the 70% most certain predictions.The two evaluations correspond to 100% recall and uncertainty-filtered predictions.
  • Uncertainty calibration: Figure I.15 plots estimated aleatoric and epistemic standard deviations against empirical RMSE for grouped subsets.These calibration plots use random cross-validation of RH98.
  • Global uncertainty: Figure J.16 maps mean aleatoric and epistemic uncertainty at 0.5-degree resolution.The maps use 346×106 waveform predictions from the first four months of the GEDI mission.
  • Out-of-distribution predictions: Figure K.17 compares epistemic uncertainty within the training-data range below 70 m with out-of-distribution predictions above 70 m.

Appendix L. Estimating RH70 and ground elevation with the same model architecture

The same CNN model architecture is also applied to regress RH70 and ground elevation from L1B GEDI full waveforms. The ground-elevation formulation predicts an elevation difference that is added to the first-return elevation.

  • RH70 regression: Figure L.18 evaluates RH70 regression by comparing ALS reference data with CNN estimates.It also reports precision–recall trade-offs while varying the maximum predictive-uncertainty threshold.
  • Ground elevation: Figure L.19 evaluates ground-elevation regression from L1B GEDI full waveforms.The final elevation is computed by adding the predicted elevation difference to the elevation corresponding to the first waveform return.
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