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    Abstract. Satellite remote sensing provides a global view to processes on Earth that has unique benefits compared to making measurements on the ground, such as global coverage and enormous data volume. The typical downsides are spatial and temporal gaps and potentially low data quality. Meaningful statistical inference from such data requires overcoming these problems and developing efficient and robust computational tools.We design and implement a computationally efficient multi-scale Gaussian process (GP) software package, satGP, geared towards remote sensing applications. The software is able to handle problems of enormous sizes and to compute marginals and sample from the random field conditioning on at least hundreds of millions of observations. This is achieved by optimizing the computation by, e.g., randomization and splitting the problem into parallel local subproblems which aggressively discard uninformative data. We describe the mean function of the Gaussian process by approximating marginals of a Markov random field (MRF). Variability around the mean is modeled with a multi-scale covariance kernel, which consists of Matérn, exponential, and periodic components. We also demonstrate how winds can be used to inform covariances locally.The covariance kernel parameters are learned by calculating an approximate marginal maximum likelihood estimate, and the validity of both the multi-scale approach and the method used to learn the kernel parameters is verified in synthetic experiments. We apply these techniques to a moderate size ozone data set produced by an atmospheric chemistry model and to the very large number of observations retrieved from the Orbiting Carbon Observatory 2 (OCO-2) satellite. The satGP software is released under an open-source license. 
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