We propose a tree-level biomass estimation model approximating allometric equations by LiDAR data. Since tree crown diameters estimation is challenging from spaceborne LiDAR measurements, we develop a model to correlate tree height with biomass on the individual tree level employing a Gaussian process regressor. In order to validate the proposed model, a set of 8,342 samples on tree height, trunk diameter, and biomass has been assembled. It covers seven biomes globally present. We reference our model to four other models based on both, the Jucker data and our own dataset. Although our approach deviates from standard biomass-height-diameter models, we demonstrate the Gaussian process regression model as a viable alternative. In addition, we decompose the uncertainty of tree biomass estimates into the model- and fitting-based contributions. We verify the Gaussian process regressor has the capacity to reduce the fitting uncertainty down to below 5%. Exploiting airborne LiDAR measurements and a field inventory survey on the ground, a stand-level (or plot-level) study confirms a low relative error of below 1% for our model. The data used in this study are available at https://github.com/zhu-xlab/BiomassUQ .

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