  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 the leaf area index (LAI) if algorithms account for
variability in the 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-6S 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 VHGPR models led to consistent LAI maps at BOA and TOA scale. We
demonstrated that hybrid LAI retrieval algorithms can be developed from TOA
radiance data given a cloud-free sky, thus without the need for atmospheric
correction.
