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Parameter retrieval and model inversion are key problems in remote sensing and Earth observation. Currently, different approximations exist: a direct, yet costly, inversion of radiative transfer models (RTMs); the statistical inversion with in situ data that often results in problems with extrapolation outside the study area; and the most widely adopted hybrid modeling by which statistical models, mostly nonlinear and non-parametric machine learning algorithms, are applied to invert RTM simulations. We will focus on the latter. Among the different existing algorithms, in the last decade kernel based methods, and Gaussian Processes (GPs) in particular, have provided useful and informative solutions to such RTM inversion problems. This is in large part due to the confidence intervals they provide, and their predictive accuracy. However, RTMs are very complex, highly nonlinear, and typically hierarchical models, so that often a shallow GP model cannot capture complex feature relations for inversion. This motivates the use of deeper hierarchical architectures, while still preserving the desirable properties of GPs. This paper introduces the use of deep Gaussian Processes (DGPs) for bio-geo-physical model inversion. Unlike shallow GP models, DGPs account for complicated (modular, hierarchical) processes, provide an efficient solution that scales well to big datasets, and improve prediction accuracy over their single layer counterpart. In the experimental section, we provide empirical evidence of performance for the estimation of surface temperature and dew point temperature from infrared sounding data, as well as for the prediction of chlorophyll content, inorganic suspended matter, and coloured dissolved matter from multispectral data acquired by the Sentinel-3 OLCI sensor. The presented methodology allows for more expressive forms of GPs in remote sensing model inversion problems.

Land Surface Temperature (LST) is one of the key parameters in the physics of land-surface processes on regional and global scales, combining the results of all surface-atmosphere interactions and energy fluxes between the surface and the atmosphere. With the advent of the European Space Agency (ESA) Sentinel 3 (S3) satellite, accurate LST retrieval methodologies are being developed by exploiting the synergy between the Ocean and Land Colour Instrument (OLCI) and the Sea and Land Surface Temperature Radiometer (SLSTR). In this paper we explain the implementation in the Basic ENVISAT Toolbox for (A)ATSR and MERIS (BEAM) and the use of one LST algorithm developed in the framework of the Synergistic Use of The Sentinel Missions For Estimating And Monitoring Land Surface Temperature (SEN4LST) project. The LST algorithm is based on the split-window technique with an explicit dependence on the surface emissivity. Performance of the methodology is assessed by using MEdium Resolution Imaging Spectrometer/Advanced Along-Track Scanning Radiometer (MERIS/AATSR) pairs, instruments with similar characteristics than OLCI/ SLSTR, respectively. The LST retrievals were properly validated against in situ data measured along one year (2011) in three test sites, and inter-compared to the standard AATSR level-2 product with satisfactory results. The algorithm is implemented in BEAM using as a basis the MERIS/AATSR Synergy Toolbox. Specific details about the processor validation can be found in the validation report of the SEN4LST project., Comment: 14 pages, 7 figures, 3 tables