Bayesian model averaging of AI models for the high resolution mapping of the forest canopy height
Authors: Besic Nikola , Picard Nicolas , Vega Cédric , Renaud Jean-Pierre , Schwartz Martin , Planells Milena , Ciais Philippe 
Published: March 2024

The development of high resolution mapping models of forest attributes based on employing machine or deep learning techniques has&#160;increasingly accelerated in the last couple of years. The consequence of this is the widespread availability of multiple sources of information, which can either lead to a potential&#160;confusion, or to a possibility to get an "extended&#8221; insight into the state of our forests by interpreting these sources jointly. This contribution aims at addressing the latter, by relying on the Bayesian model averaging (BMA) approach.BMA is a method that can be used in building a consensus from an ensemble of different model predictions. It can be seen as weighted mean of different predictions with weights reflecting the predictive performances of different models, or as a finite mixture model which estimates the probability that each observation from the independent validation dataset has been generated by one of the models belonging to the ensemble. BMA can thus be used to diagnose and understand the difference in the predictions and to possibly interpret them.The predictions in our case are the forest canopy height estimations for the metropolitan France coming from 5 different AI models [1-5], while the independent validation dataset comes from the French National Forest Inventory (NFI) disposing with some 6000 plots per year, distributed across the territory of interest. For every plot we have several measurements/estimations of the forest canopy height out of which the following two are considered in this study: h_m &#8211; the maximum total height (from the tree's base level to the terminal bud of the tree's main stem) measured within the plot, and h_dom &#8211; the average height of the seven largest dominant trees per hectare.In this contribution we present for every considered plot the dominant model with respect to both references i.e. the model having the highest probability to be the one generating measurements/estimations at NFI plot (h_m and h_dom). We present as well as the respective inter-model and the intra-model variance estimations, allowing us to propose a series of hypotheses concerning the established differences between predictions of individual models in function of their specificities.[1] Schwartz, M., et al.: FORMS: Forest Multiple Source height, wood volume, and biomass maps in France at 10 to 30&#8201;m resolution based on Sentinel-1, Sentinel-2, and Global Ecosystem Dynamics Investigation (GEDI) data with a deep learning approach, Earth Syst. Sci. Data, 15, 4927&#8211;4945,&#160;2023, https://doi.org/10.5194/essd-15-4927-2023[2] Lang, N., et al.: A high-resolution canopy height model of the Earth,&#160;Nat Ecol&#160;Evol&#160;7, 1778&#8211;1789, 2023. https://doi.org/10.1038/s41559-023-02206-6[3] Morin, D. et al.: Improving Heterogeneous Forest Height Maps by Integrating GEDI-Based Forest Height Information in a Multi-Sensor Mapping Process, Remote Sens.,&#160;14, 2079. 2022, https://doi.org/10.3390/rs14092079[4] Potapov, P.,&#160;et al.: Mapping global forest canopy height through integration of GEDI and Landsat data, Remote Sensing of Environment, 253, 2021, https://doi.org/10.1016/j.rse.2020.112165.[5] Liu, S.&#160;et al.: The overlooked contribution of trees outside forests to tree cover and woody biomass across Europe, Sci. Adv. 9, eadh4097, 2023, 10.1126/sciadv.adh4097.