Gaussian processes retrieval of LAI from Sentinel-2 top-of-atmosphere radiance data

Retrieval of vegetation properties from satellite and airborne optical data usually takes place after atmospheric correction, yet it is also possible to develop retrieval algorithms directly from top-of-atmosphere (TOA) radiance data. One of the key vegetation variables that can be retrieved from at-sensor TOA radiance data is leaf area index (LAI) if algorithms account for variability in atmosphere. We demonstrate the feasibility of LAI retrieval from Sentinel-2 (S2) TOA radiance data (L1C product) in a hybrid machine learning framework. To achieve this, the coupled leaf-canopy-atmosphere radiative transfer models PROSAIL-6SV were used to simulate a look-up table (LUT) of TOA radiance data and associated input variables. This LUT was then used to train the Bayesian machine learning algorithms Gaussian processes regression (GPR) and variational heteroscedastic GPR (VHGPR). PROSAIL simulations were also used to train GPR and VHGPR models for LAI retrieval from S2 images at bottom-of-atmosphere (BOA) level (L2A product) for comparison purposes. The BOA and TOA LAI products were consistently validated against a field dataset with GPR (R² of 0.78) and with VHGPR (R ² of 0.80) and for both cases a slightly lower RMSE for the TOA LAI product (about 10% reduction). Because of delivering superior accuracies and lower uncertainties, the VHGPR models were further applied for LAI mapping using S2 acquisitions over the agricultural sites Marchfeld (Austria) and Barrax (Spain). The models led to consistent LAI maps at BOA and TOA scale. The LAI maps were also compared against LAI maps as generated by the SNAP toolbox, which is based on a neural network (NN). Maps were again consistent, however the SNAP NN model tends to overestimate over dense vegetation cover. Overall, this study demonstrated that hybrid LAI retrieval algorithms can be developed from TOA radiance data given a cloud-free sky, thus without the need of atmospheric correction. To the benefit of the community, the development of such hybrid models for the retrieval vegetation properties from BOA or TOA images has been streamlined in the freely downloadable ALG-ARTMO software framework.