6533b7d3fe1ef96bd125fe5b

RESEARCH PRODUCT

Statistical biophysical parameter retrieval and emulation with Gaussian processes

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Abstract Earth observation from satellites poses challenging problems where machine learning is being widely adopted as a key player. Perhaps the most challenging scenario that we are facing nowadays is to provide accurate estimates of particular variables of interest characterizing the Earth's surface. This chapter introduces some recent advances in statistical bio-geophysical parameter retrieval from satellite data. In particular, we will focus on Gaussian process regression (GPR) that has excelled in parameter estimation as well as in modeling complex radiative transfer processes. GPR is based on solid Bayesian statistics and generally yields efficient and accurate parameter estimates, accompanied by confidence intervals for the estimations. We will first review the standard application of GPs for parameter retrieval and inverse modeling, which is based on regressing the parameter of interest on the concurrent observations. Secondly, noting that very often several parameters need to be estimated simultaneously, we review the field of multioutput GPR and illustrate its application in gap filling of multiple time series of parameters. The third GP modeling that we review here is that of combining real and simulated data. Very often a forward model encoding the well-understood physical relations is available. Inverting the model with GP is a standard practice known as hybrid modeling. In addition, we review a joint GP (JGP) model that combines both in situ measurements and simulated data in a single GP model and allows us to transfer information across spatial, temporal, and land cover modalities such as different crops. In recent years, forced by the data deluge, a plethora of large-scale GP models were introduced. We review recent advances and illustrate their performance for the estimation of surface temperature from infrared sounding data. Finally, we take a reversed pathway and focus on mimicking physical models with GPs. We present an automatic emulation scheme that approximates the forward physical model via interpolation, reducing the number of necessary nodes. Empirical evidence of the performance of these models will be presented through illustrative examples of land and vegetation monitoring.