Gaussian Process Regression for the Calibration of Satellite-based Above-ground Biomass Estimates

The same tree size or photosynthetic activity can correspond to different biomass in different biomes, because of differences in wood density and allometry. Rather than training one model per biome, BioFiLM adapts a single fully convolutional, Xception-style network (1M parameters, trained with sparse GEDI L4A supervision) with Feature-wise Linear Modulation. The biome (Copernicus land cover) and region are embedded by a small network, and FiLM layers predict a per-channel scale and shift for the activations $F_{i,c}$: $$\mathrm{FiLM}(F_{i,c} \mid \gamma_{i,c}, \beta_{i,c}) = \gamma_{i,c}\, F_{i,c} + \beta_{i,c}.$$ Inputs are Sentinel-2 L2A, ALOS PALSAR-2, the ALOS DSM, land cover and canopy height from the AGBD dataset, plus added topographic (slope, aspect) and temporal (acquisition date, day of year) features.

Like other models of long-tailed vegetation variables, the network over-estimates low biomass and under-estimates high biomass, and the errors are spatially structured. For every Sentinel-2 tile (100×100 km), we:

1. predict a dense AGB map and its ensemble standard deviation with BioFiLM;
2. extract the quality-filtered GEDI L4A footprints in the tile;
3. compute the residuals $AGB_{pred} - AGB_{GEDI}$ at each footprint;
4. fit an exact GP (Matérn kernel) to interpolate the residual field across the tile, using auxiliary variables;
5. correct the map with the interpolated residuals.

The GP inputs are the pixel position, the predicted AGB and its ensemble STD (base), neighbourhood statistics (local mean, standard deviation, coefficient of variation and range; local), and Sobel and Laplacian edges (texture). Footprints are split into train / validation / test sets by geographically separated patches, the $x$/$y$ length-scales are set per tile from the footprint spacing, and low-biomass outliers are removed before fitting.

We generate calibrated AGB maps for 2020 over all 11 AGBD regions, from yearly Sentinel-2 composites, about 3 million km² in total. The maps follow ecological gradients, such as the forest belts of the Sierra Nevada and the Himalayan foothills, or the transition from the Qinling Mountains to the Wei River plains in Shaanxi, and they keep anthropogenic structure: plantations, agricultural mosaics and deforestation edges appear as sharp discontinuities. In Ghana, protected forest reserves stand out sharply from the surrounding cultivated land.

Explore the maps in Google Earth Engine

Global error measures are dominated by the many low-biomass samples. To capture the effect of calibration across the whole range, we split AGB into ten 50 Mg/ha bins and count the bins whose median bias the calibration reduces: $$\Delta B = \sum_{b=1}^{10} \mathbf{1}\big[\,|\rho^b_{post}| < |\rho^b_{map}|\,\big],$$ where $\rho^b$ is the median residual in bin $b$. Only configurations with $\Delta B = 10$ reduce bias across the full range. Removing out-of-distribution samples before fitting matters most for reaching $\Delta B = 10$; interpolating residuals rather than absolute AGB fixes the difficult 150–200 Mg/ha bin; and each added group of auxiliary variables lowers the RMSE further. The calibration still helps with only 5K footprints per tile.

To test against independent reference data, we turn to Jambi province in Sumatra, Indonesia. No part of Southeast Asia is in AGBD, so our model never saw this region during training. The reference is a 100 m AGB map built from 80 field plots and airborne LiDAR (May et al., 2024). We calibrate both our map and the ESA CCI v6 product with GEDI L4A footprints from the same period (May 2021 – April 2022) and compare everything at 100 m.

Our map agrees much better with the reference than ESA CCI, before and after calibration. Kriging greatly improves the CCI map (RMSE −30%) and lowers our map's bias, with a small RMSE gain; the moderate agreement between GEDI and the reference data here caps what GEDI-based calibration can achieve. At a matched 100 m grid, our calibrated map still keeps finer spatial structure than CCI.

The AGBD-GPR repository contains the BioFiLM model and training scripts (src/model), dense map generation (src/inference, src/data_prep), the per-tile GPR calibration (src/kriging), and the Sumatra experiments (src/sumatra). A notebook runs the whole pipeline (compositing → inference → kriging) on a single Sentinel-2 tile, and the Sumatra analysis notebook runs from a fresh clone with its bundled data.

git clone https://github.com/ghjuliasialelli/AGBD-GPR.git
cd AGBD-GPR
uv sync --extra notebook          # pinned environment: PyTorch, GPyTorch, rasterio, ...
export AGBD_ENV=local             # picks configs/local.yaml; see DATA.md for the inputs
uv run jupyter lab                # example/single_tile_pipeline.ipynb

The calibrated maps can be explored in Google Earth Engine. The post-calibration AGB and standard-deviation layers, as well as the pre-calibration BioFiLM AGB and ensemble standard deviation, are released as Cloud-Optimized GeoTIFFs on the ETH Research Collection. The training data is the AGBD dataset.

Calibrating each tile independently keeps the GP tractable but can leave tiling artifacts in very homogeneous, cloudy regions such as French Guiana, and the GP uncertainty is not on a common scale across tiles. The calibration also needs GEDI footprints, so it does not apply north of 51.6°, and it inherits the known weaknesses of GEDI L4A, such as under-estimation on steep slopes and in complex forests. Promising next steps are calibrating against other reference data (e.g. ESA Biomass, NISAR) and merging the two stages into a single end-to-end model.