Interpolation of GEDI Biomass Estimates with Calibrated Uncertainty Quantification
Organizations: Department of Computer Science and Technology, University of Cambridge, Cambridge, CB3 0FD, Cambridgeshire, UK
Abstract
Wall-to-wall biomass density estimation from NASA's GEDI mission requires interpolating sparse LIDAR observations across heterogeneous landscapes. While Random Forest and XGBoost are widely used, they predict each location independently from satellite features, without adapting to the varying difficulty of heterogeneous landscapes. We introduce Attentive Neural Processes (ANPs), a probabilistic meta-learning architecture that explicitly conditions predictions on local observation sets as well as geospatial foundation model embeddings. ANPs learn a flexible spatial covariance approximator that is more uncertain in complex landscapes and less in homogeneous areas. We validate this approach across five distinct biomes ranging from tropical Amazonian forests to boreal, temperate, and alpine ecosystems, demonstrating that ANPs achieve competitive accuracy while maintaining uncertainty calibration. We demonstrate a scalable, empirically calibrated alternative to ensemble architectures for continental-scale biomass mapping.
Figures & tables
| Model | ANP | XGBoost | MLP w/ Dropout | Random Forest | IDW |
|---|---|---|---|---|---|
| Accuracy Metrics | |||||
| Validation Log | 0.735 0.053 | 0.707 0.062 | 0.704 0.061 | 0.692 0.061 | -0.266 0.175 |
| Test Log | 0.747 0.043 | 0.737 0.042 | 0.735 0.046 | 0.724 0.045 | -0.229 0.111 |
| Test Log RMSE | 0.199 0.016 | 0.203 0.014 | 0.203 0.016 | 0.207 0.015 | 0.440 0.022 |
| Test Log MAE | 0.141 0.012 | 0.142 0.011 | 0.141 0.011 | 0.148 0.010 | 0.361 0.026 |
| Linear RMSE (Mg/ha) | 50.56 5.36 | 49.35 2.53 | 50.02 2.75 | 51.68 3.52 | 76.27 6.36 |
| Accuracy Metrics | Z-Score Metrics | Coverage Metrics | ||||||
|---|---|---|---|---|---|---|---|---|
| Region | Model | Test Log | RMSE | Mean (0.0) | Std (1.0) | 1 (%) | 2 (%) | 3 (%) |
| Maine, USA | ANP | 0.581 0.019 | 51.37 2.83 | 0.046 0.060 | 0.952 0.059 | 75.0 3.3 | 95.4 0.7 | 99.0 0.3 |
| XGBoost | 0.566 0.020 | 51.59 2.62 | 0.020 0.132 | 1.383 0.061 | 58.9 2.0 | 89.1 0.9 | 97.1 0.3 | |
| Random Forest | 0.530 0.023 | 54.53 2.64 | 0.117 0.198 | 7.044 1.810 | 19.4 2.1 | 38.6 4.2 | 54.8 5.6 | |
| MLP w/ Dropout | 0.527 0.011 | 52.29 2.20 | 0.384 0.383 | 4.390 0.288 | 24.5 1.3 | 45.8 1.7 | 61.9 2.4 | |
| IDW | -0.258 0.053 | 72.45 2.27 | -0.058 0.141 | 2.101 0.324 | 49.6 1.7 | 79.6 2.2 | 91.1 1.4 | |
Appendix figures & tables11 assets
Supplementary material from the paper’s appendix.
Appendix
| Product | Filter Variable | Condition / Threshold |
| L2A | quality_flag | |
| degrade_flag | (Non-degraded) | |
| surface_flag | ||
| sensitivity_a0 | ||
| sensitivity_a2 | ||
| elevation_difference_tdx | meters (relative to TanDEM-X) |
| Category | Parameter | Value |
| Architecture | Hidden Dimension ( ) | 512 |
| Latent Dimension ( ) | 256 | |
| Embedding Feature Dim | 1024 | |
| Attention Heads | 16 | |
| Context/Target Encoder Layers | 3 | |
| Data | Patch Size | (30m) |
| Region Name | Coordinates (Lon / Lat) | Ecological Description | Biome |
|---|---|---|---|
| Guaviare | – W | Tropical lowland forest, | Tropical |
| (Colombia) | – N | deforestation frontier | Moist |
| Tolima | – W | Tropical montane forest, | Tropical |
| (Colombia) | – N | high relief | Montane |
| Maine | – W | Temperate mixed forest, | Temperate |
| (USA) | – N | secondary growth | Broadleaf |
| Region | Area (deg 2 ) | Tiles | Shots Total | Mean | Median |
|---|---|---|---|---|---|
| Maine (USA) | 1.00 | 100 | 305,457 | 3,054.6 | 2,877 |
| South Tyrol (Italy) | 0.80 | 80 | 337,455 | 4,218.2 | 3,733 |
| Hokkaido (Japan) | 0.70 | 70 | 134,564 | 1,922.3 | 1,628 |
| Tolima (Colombia) | 1.00 | 99 | 82,043 | 828.7 | 621 |
| Guaviare (Colombia) | 1.00 | 92 | 144,628 | 1,572.0 | 1,494 |
| Region | Std. Dev. | Min | Max | Q1 | Q3 |
| Unfiltered | 500 Mg/ha | 1000 Mg/ha | ||||
|---|---|---|---|---|---|---|
| Region | Shots | Mean | Shots | Mean | Shots | Mean |
| Maine (USA) | 305,457 | 85.13 | 305,046 (0.13%) | 84.00 | 305,326 (0.04%) | 84.57 |
| South Tyrol (Italy) | 337,455 | 129.41 | 334,798 (0.79%) | 124.65 | 337,107 (0.10%) | 128.10 |
| Hokkaido (Japan) | 134,564 | 93.91 | 134,467 (0.07%) | 93.49 | 134,555 (0.01%) | 93.83 |
| Tolima (Colombia) | 82,043 | 85.05 | 81,256 (0.96%) | 78.97 | 81,960 (0.10%) | 83.73 |
| Guaviare (Colombia) | 144,628 | 55.79 | 144,265 (0.25%) | 54.02 | 144,591 (0.03%) | 55.35 |
| Model | Max Depth | Test Log | Z-score Std | 1 Coverage (%) | Train Time (s) | |
|---|---|---|---|---|---|---|
| RF | 20 | 1000 | ||||
| RF | 20 | 500 | ||||
| RF | 20 | 200 | ||||
| RF | 20 | 100 | ||||
| RF | 10 | 1000 | ||||
| RF | 10 | 500 |
| Metric | Full | Deterministic | Latent |
|---|---|---|---|
| Accuracy Metrics | |||
| Log-space | 0.722 0.017 | 0.715 0.032 | 0.699 0.045 |
| Log-space MAE | 0.146 0.011 | 0.151 0.009 | 0.147 0.010 |
| Linear RMSE (Mg/ha) | 55.85 5.14 | 54.59 1.75 | 53.94 2.30 |
| Uncertainty Calibration | |||
| Z-score Std (Ideal: 1.0) | 1.03 0.06 | 1.05 0.14 | 1.05 0.07 |
| Model | Regression Kriging | ANP | Random Forest |
|---|---|---|---|
| Accuracy Metrics | |||
| Test Log | |||
| Test Log RMSE | |||
| Test Log MAE | |||
| Linear RMSE (Mg/ha) | |||
| Linear MAE (Mg/ha) | |||
| Model | Quantile Random Forest | ANP | Random Forest |
|---|---|---|---|
| Accuracy Metrics | |||
| Test Log | |||
| Test Log RMSE | |||
| Test Log MAE | |||
| Linear RMSE (Mg/ha) | |||
| Linear MAE (Mg/ha) | |||
| Model | Deep Ens. (NLL) | Deep Ens. (MSE) | ANP | MLP w/ Dropout |
|---|---|---|---|---|
| Accuracy Metrics | ||||
| Test Log | ||||
| Test Log RMSE | ||||
| Linear RMSE (Mg/ha) | ||||
| Uncertainty Calibration | ||||
| Z-Score Mean (0.0) | ||||
Uncertainty Quantification
Uncertainty quantification estimates how reliable predictions and scientific inferences are, and how uncertainty propagates into decisions.
See all 636 papers