Mariarosaria Natale

Tangible climate changes are experienced by the Earth. They refer to long-term changes in, e.g., temperature and precipitation, as well as other aspects of the Earth system. Essential Climate Variables (ECVs) are used to monitor climate changes, validate climate models and, ultimately, inform policy decisions; they are, therefore, essential markers that help scientists understand the Earth system dynamics. Fundamental contributions to the understanding and characterization of ECV values can be given by the analysis of data produced by current and next-generation Earth observation (EO) satellites, which, among other options, can be based on microwave remote sensing. EO sensors can directly characterize bio-geophysical variables connected to ECVs, such as, e.g., the soil moisture (SM), the above-ground biomass (AGB), and the freeze-thaw (FT) dynamics. While FT dynamics are primarily relevant in northern latitudes, SM and AGB are globally significant parameters. SM, AGB, and FT are also key variables for the ESA EO science strategy and the ESA Climate Change Initiative program, mainly due to their strong relevance in understanding the global hydrological and carbon cycles. This work aims to be a comprehensive review of retrieval techniques for SM, AGB, and FT, considering data collected with passive and active microwave remote sensing systems. An overview of the methods proposed in the last decades is reported and discussed, then future perspective and current challenges are outlined. This paper targets a very broad scientific community, not necessarily engineers, but rather any scientist with interest in microwave EO and satellite remote sensing. For that reason, some basic concepts are briefly reported and discussed throughout the manuscript.

The analysis and processing of satellite remote sensing data have established new paradigms to observe the Earth and to study climate changes. Data collected by sensors and systems operating across the entire frequency spectrum carry on enormous information content. They enable systematic retrieval and characterization of bio-geophysical variables. The retrieval of these variables, however, is often hindered by limitations such as missing data, low spatial and temporal resolutions, and insufficient co-located ancillary data. These challenges arise due to factors such as sensor limitations, dead pixels, cloud cover, and discontinuous data acquisition. To overcome these issues, numerous techniques have been proposed, ranging from classical interpolation methods and spectral transforms to modern artificial intelligence-based approaches. This paper presents a comprehensive and critical review of satellite remote-sensing data augmentation methods, focusing on how interpolation theory and artificial intelligence techniques can be effectively applied to reconstruct missing data and enhance the quality of retrieved bio-geophysical variables. This roadmap offers a comprehensive framework that categorizes and evaluates existing methods, highlights their strengths and limitations, and identifies promising areas for future exploration.

In this paper, we introduce the nonlinear exponential Kantorovich sampling series. We establish pointwise and uniform convergence properties and a nonlinear asymptotic formula of the Voronovskaja-type given in terms of the limsup. Furthermore, we extend these convergence results to Mellin-Orlicz spaces with respect to the logarithmic (Haar) measure. Quantitative results are also given, using the log-modulus of continuity and the log-modulus of smoothness, respectively, for log-uniformly continuous functions and for functions in Mellin-Orlicz spaces. Consequently, the qualitative order of convergence can be obtained in case of functions belonging to suitable Lipschitz (log-Hölderian) classes.