Interpolation of GEDI Biomass Estimates with Calibrated Uncertainty Quantification

Robin Young; Srinivasan Keshav

cs.LGJan 23, 2026

Interpolation of GEDI Biomass Estimates with Calibrated Uncertainty Quantification

Authors: Robin Young, Srinivasan Keshav

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

Accuracy Metrics
Model	ANP	XGBoost	MLP w/ Dropout	Random Forest	IDW
Validation Log $R^{2}$	0.735 $\pm$ 0.053	0.707 $\pm$ 0.062	0.704 $\pm$ 0.061	0.692 $\pm$ 0.061	-0.266 $\pm$ 0.175
Test Log $R^{2}$	0.747 $\pm$ 0.043	0.737 $\pm$ 0.042	0.735 $\pm$ 0.046	0.724 $\pm$ 0.045	-0.229 $\pm$ 0.111
Test Log RMSE	0.199 $\pm$ 0.016	0.203 $\pm$ 0.014	0.203 $\pm$ 0.016	0.207 $\pm$ 0.015	0.440 $\pm$ 0.022
Test Log MAE	0.141 $\pm$ 0.012	0.142 $\pm$ 0.011	0.141 $\pm$ 0.011	0.148 $\pm$ 0.010	0.361 $\pm$ 0.026
Linear RMSE (Mg/ha)	50.56 $\pm$ 5.36	49.35 $\pm$ 2.53	50.02 $\pm$ 2.75	51.68 $\pm$ 3.52	76.27 $\pm$ 6.36

Table 1: Summary of model performance on Guaviare test set. Values are mean

\pm

standard deviation over 10 seeds. Best model for each metric shown in bold.

Figure 1: Performance in baseline methods. Each point represents a hyperparameter configuration evaluated across 5 random seeds. Horizontal line indicates ideal calibration (Z-score std = 1.0).

		Accuracy Metrics		Z-Score Metrics		Coverage Metrics
Region	Model	Test Log $R^{2}$	RMSE	Mean (0.0)	Std (1.0)	1 $\sigma$ (%)	2 $\sigma$ (%)	3 $\sigma$ (%)
Maine, USA	ANP	0.581 $\pm$ 0.019	51.37 $\pm$ 2.83	0.046 $\pm$ 0.060	0.952 $\pm$ 0.059	75.0 $\pm$ 3.3	95.4 $\pm$ 0.7	99.0 $\pm$ 0.3
	XGBoost	0.566 $\pm$ 0.020	51.59 $\pm$ 2.62	0.020 $\pm$ 0.132	1.383 $\pm$ 0.061	58.9 $\pm$ 2.0	89.1 $\pm$ 0.9	97.1 $\pm$ 0.3
	Random Forest	0.530 $\pm$ 0.023	54.53 $\pm$ 2.64	0.117 $\pm$ 0.198	7.044 $\pm$ 1.810	19.4 $\pm$ 2.1	38.6 $\pm$ 4.2	54.8 $\pm$ 5.6
	MLP w/ Dropout	0.527 $\pm$ 0.011	52.29 $\pm$ 2.20	0.384 $\pm$ 0.383	4.390 $\pm$ 0.288	24.5 $\pm$ 1.3	45.8 $\pm$ 1.7	61.9 $\pm$ 2.4
	IDW	-0.258 $\pm$ 0.053	72.45 $\pm$ 2.27	-0.058 $\pm$ 0.141	2.101 $\pm$ 0.324	49.6 $\pm$ 1.7	79.6 $\pm$ 2.2	91.1 $\pm$ 1.4

Table 2: Comparison of model performance across four additional testing regions. Values are mean

\pm

standard deviation.

Figure 2: Calibration diagnostics for ANP on Guaviare test set (representative run). a : Distribution of standardized residuals closely follows theoretical N(0,1). b : Prediction interval coverage shows slight conservatism. c : Binned uncertainty vs error plot shows positive correlation. Higher predicted uncertainty corresponds to larger actual errors. d : Quantile-quantile plot shows good agreement in central quantiles ( $\pm$ 2 $\sigma$ ), with slight divergence in tails.

Figure 3: Spatial predictions and uncertainty for a 0.1 ${}^{\circ}\times$ 0.1 ∘ tile in Guaviare, Colombia. Left : Mean AGBD prediction shows dendritic patterns of high biomass (green) corresponding to remaining forest corridors, with low biomass in cleared areas (yellow). Right : Predicted standard deviation (uncertainty) is spatially heterogeneous, with highest uncertainty in structurally complex forested areas and lowest uncertainty in homogeneous cleared land. The spatial pattern of uncertainty adapts to land cover configuration, increasing in regions with complex forest structure and decreasing in simple agricultural landscapes.

Figure 4: Satellite imagery validation of spatial predictions in Guaviare, Colombia. Left : Overview of the prediction area showing landscape scale deforestation patterns. Dark green areas represent intact or planted forest, while tan/brown areas indicate cleared agricultural land. White circle indicates zoom area shown in right panel. Right : Detail of agricultural parcels interspersed with riparian forest corridors. Imagery from Google Maps, map data from Maxar.

Figure 5: Conceptual illustration of ensemble variance vs. context-aware prediction intervals at three landscape types. Top: each target pixel (red) and its nearby observations (blue). Rows: predicted

\mu\pm 1\sigma

(shaded) against the nearby observations (filled = inside the interval).

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 6 — Figure 6: Architecture of the Attentive Neural Process (ANP) model.

Product	Filter Variable	Condition / Threshold
L2A	quality_flag	$=1$
	degrade_flag	$=0$ (Non-degraded)
	surface_flag	$=1$
	sensitivity_a0	$\in[0.9,1.0]$
	sensitivity_a2	$\in[0.95,1.0]$
	elevation_difference_tdx	$\in[-150,150]$ meters (relative to TanDEM-X)

Appendix

Table 3: GEDI data filtering and merging criteria.

Category	Parameter	Value
Architecture	Hidden Dimension ( $d_{model}$ )	512
	Latent Dimension ( $d_{z}$ )	256
	Embedding Feature Dim	1024
	Attention Heads	16
	Context/Target Encoder Layers	3
Data	Patch Size	$3\times 3$ (30m)

Appendix

Table 4: Hyperparameter configuration for the ANP model.

Region Name	Coordinates (Lon / Lat)	Ecological Description	Biome
Guaviare	$72^{\circ}$ – $73^{\circ}$ W	Tropical lowland forest,	Tropical
(Colombia)	$2^{\circ}$ – $3^{\circ}$ N	deforestation frontier	Moist
Tolima	$74^{\circ}$ – $75^{\circ}$ W	Tropical montane forest,	Tropical
(Colombia)	$3^{\circ}$ – $4^{\circ}$ N	high relief	Montane
Maine	$69^{\circ}$ – $70^{\circ}$ W	Temperate mixed forest,	Temperate
(USA)	$44^{\circ}$ – $45^{\circ}$ N	secondary growth	Broadleaf

Appendix

Table 5: Geographic specifications and ecological characteristics of the five study regions. Coordinates are provided in WGS84 decimal degrees.

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

Appendix

Table 6: Summary of GEDI L4A shot statistics by region.

	Unfiltered		$\leq$ 500 Mg/ha		$\leq$ 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

Appendix

Table 7: Sensitivity of GEDI L4A data to AGBD filtering threshold. For each region, we report the number of retained shots, mean AGBD (Mg/ha), and percentage of shots removed relative to the unfiltered dataset.

Model	Max Depth	$n_{\text{estimators}}$	Test Log $R^{2}$	Z-score Std	1 $\sigma$ Coverage (%)	Train Time (s)
RF	20	1000	$0.7147\pm 0.0262$	$1.652\pm 0.428$	$74.4\pm 1.8$	$904.16\pm 102.58$
RF	20	500	$0.7144\pm 0.0262$	$1.819\pm 0.537$	$74.2\pm 1.7$	$496.04\pm 59.42$
RF	20	200	$0.7136\pm 0.0266$	$2.220\pm 0.891$	$73.1\pm 2.0$	$258.15\pm 73.03$
RF	20	100	$0.7124\pm 0.0262$	$2.559\pm 1.022$	$71.4\pm 2.4$	$199.87\pm 28.59$
RF	10	1000	$0.7121\pm 0.0252$	$3.503\pm 0.898$	$75.1\pm 4.7$	$539.76\pm 56.43$
RF	10	500	$0.7120\pm 0.0252$	$3.666\pm 0.948$	$74.2\pm 4.7$	$281.99\pm 33.67$

Appendix

Table 8: Model hyperparameter sweep for RF and XGB across 5 seed runs sorted by Log

R^{2}

Accuracy Metrics
Metric	Full	Deterministic	Latent
Log-space $R^{2}$	0.722 $\pm$ 0.017	0.715 $\pm$ 0.032	0.699 $\pm$ 0.045
Log-space MAE	0.146 $\pm$ 0.011	0.151 $\pm$ 0.009	0.147 $\pm$ 0.010
Linear RMSE (Mg/ha)	55.85 $\pm$ 5.14	54.59 $\pm$ 1.75	53.94 $\pm$ 2.30
Uncertainty Calibration
Z-score Std (Ideal: 1.0)	1.03 $\pm$ 0.06	1.05 $\pm$ 0.14	1.05 $\pm$ 0.07

Appendix

Table 9: Ablation on the components of the ANP architecture.

Accuracy Metrics
Model	Regression Kriging	ANP	Random Forest
Test Log $R^{2}$	$0.723\pm 0.044$	$0.747\pm 0.043$	$0.724\pm 0.045$
Test Log RMSE	$0.208\pm 0.014$	$0.199\pm 0.016$	$0.207\pm 0.015$
Test Log MAE	$0.149\pm 0.010$	$0.141\pm 0.012$	$0.148\pm 0.010$
Linear RMSE (Mg/ha)	$51.65\pm 3.58$	$50.56\pm 5.36$	$51.68\pm 3.52$
Linear MAE (Mg/ha)	$28.00\pm 2.82$	$27.33\pm 3.44$	$28.01\pm 2.71$

Appendix

Table 10: Performance comparison of Regression Kriging against Attentive Neural Process and Random Forest on the Guaviare test set.

Accuracy Metrics
Model	Quantile Random Forest	ANP	Random Forest
Test Log $R^{2}$	$0.688\pm 0.057$	$0.747\pm 0.043$	$0.724\pm 0.045$
Test Log RMSE	$0.220\pm 0.018$	$0.199\pm 0.016$	$0.207\pm 0.015$
Test Log MAE	$0.130\pm 0.012$	$0.141\pm 0.012$	$0.148\pm 0.010$
Linear RMSE (Mg/ha)	$49.03\pm 3.57$	$50.56\pm 5.36$	$51.68\pm 3.52$
Linear MAE (Mg/ha)	$27.06\pm 2.79$	$27.33\pm 3.44$	$28.01\pm 2.71$

Appendix

Table 11: Performance comparison of Quantile Random Forest (QRF) against the Attentive Neural Process and Random Forest on the Guaviare test set.

Accuracy Metrics
Model	Deep Ens. (NLL)	Deep Ens. (MSE)	ANP	MLP w/ Dropout
Test Log $R^{2}$	$0.734\pm 0.049$	$0.712\pm 0.055$	$\textbf{0.747}\pm 0.043$	$0.709\pm 0.053$
Test Log RMSE	$0.204\pm 0.017$	$0.212\pm 0.018$	$\textbf{0.199}\pm 0.016$	$0.213\pm 0.017$
Linear RMSE (Mg/ha)	$\textbf{48.96}\pm 2.58$	$48.98\pm 3.14$	$50.56\pm 5.36$	$48.71\pm 2.84$
Uncertainty Calibration
Z-Score Mean (0.0)	$0.034\pm 0.087$	$-0.041\pm 0.112$	$\textbf{0.023}\pm 0.124$	$0.041\pm 0.249$

Appendix

Table 12: Performance comparison of deep ensemble variants against the Attentive Neural Process and MC Dropout baseline on the Guaviare test set.

Uncertainty Quantification

Uncertainty quantification estimates how reliable predictions and scientific inferences are, and how uncertainty propagates into decisions.

See all 636 papers

Neural Processes Maintain Calibrated Biomass Estimates Across Spatiotemporal Gaps and Disturbance
Apr 4, 2026Robin Young, Srinivasan KeshavForest Aboveground Biomass Estimation Neural Processes
Department of Computer Science and Technology, University of Cambridge, Cambridge, CB3 0FD, Cambridgeshire, UK
Transferable Above-Ground Biomass (AGB) Estimation Model from Multi-Sensor Data with Sparse Field Calibration
Aug 12, 2026Pann Thinzar Seint, Bryan Atwood, Subas ChhatkuliForest Aboveground Biomass Estimation Remote Sensing
DAI Labs, K.K.
Multi-Modal, Multi-Temporal Geospatial Foundation Models Improve Global Above-Ground Biomass Estimation
Aug 5, 2026Ghjulia Sialelli, Linus Scheibenreif, Jan Dirk Wegner +1Geospatial Foundation Models Forest Aboveground Biomass Estimation
Photogrammetry and Remote Sensing, ETH Zurich, Zurich, 8049, Switzerland · ETH AI Center, Zurich, 8092, Switzerland · EcoVision Lab, Department of Mathematical Modeling and Machine Learning, University of Zurich, Zurich, 8057, Switzerland

Apr 4, 2026J/K move · Enter open · S save

Neural Processes Maintain Calibrated Biomass Estimates Across Spatiotemporal Gaps and Disturbance

Robin Young, Srinivasan Keshav

Department of Computer Science and Technology, University of Cambridge, Cambridge, CB3 0FD, Cambridgeshire, UK

Forest Aboveground Biomass Estimation Neural Processes Uncertainty Calibration Remote Sensing

Open paper AskPDF arXiv

Monitoring deforestation-driven carbon emissions requires both spatially explicit and temporally continuous estimates of aboveground biomass density (AGBD) with calibrated uncertainty. NASA's Global Ecosystem Dynamics Investigation (GEDI) provides reliable LIDAR-derived AGBD, but its orbital sampling causes irregular spatiotemporal coverage, and occasional operational interruptions, including a 13-month hibernation from March 2023 to April 2024, leave extended gaps in the observational record. Prior work has used machine learning approaches to fill GEDI's spatial gaps using satellite-derived features, but temporal interpolation of biomass through unobserved periods, particularly across active disturbance events, remains largely unaddressed. Moreover, standard ensemble methods for biomass mapping have been shown to produce systematically miscalibrated prediction intervals. To address these gaps, we extend the Attentive Neural Process (ANP) framework, previously applied to spatial biomass interpolation, to jointly sparse spatiotemporal settings using geospatial foundation model embeddings. We treat space and time symmetrically, empirically validating a form of space-for-time substitution in which observations from nearby locations at other times inform predictions at held-out periods. Our results demonstrate that the ANP produces well-calibrated uncertainty estimates across disturbance regimes, supporting its use in Measurement, Reporting, and Verification (MRV) applications that require reliable uncertainty quantification for forest carbon accounting.

Abstract

Uncertainty Quantification

Explore similar work

Neural Processes Maintain Calibrated Biomass Estimates Across Spatiotemporal Gaps and Disturbance

Transferable Above-Ground Biomass (AGB) Estimation Model from Multi-Sensor Data with Sparse Field Calibration

Multi-Modal, Multi-Temporal Geospatial Foundation Models Improve Global Above-Ground Biomass Estimation