  Earth observation from satellites offers the possibility to monitor our
planet with unprecedented accuracy. Radiative transfer models (RTMs) encode the
energy transfer through the atmosphere, and are used to model and understand
the Earth system, as well as to estimate the parameters that describe the
status of the Earth from satellite observations by inverse modeling. However,
performing inference over such simulators is a challenging problem. RTMs are
nonlinear, non-differentiable and computationally costly codes, which adds a
high level of difficulty in inference. In this paper, we introduce two
computational techniques to infer not only point estimates of biophysical
parameters but also their joint distribution. One of them is based on a
variational autoencoder approach and the second one is based on a Monte Carlo
Expectation Maximization (MCEM) scheme. We compare and discuss benefits and
drawbacks of each approach. We also provide numerical comparisons in synthetic
simulations and the real PROSAIL model, a popular RTM that combines land
vegetation leaf and canopy modeling. We analyze the performance of the two
approaches for modeling and inferring the distribution of three key biophysical
parameters for quantifying the terrestrial biosphere.
