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Land and sea surface temperatures are important input parameters for many hydrological and meteorological models. Satellite infrared remote sensing is an effective tool for mapping these variables on regional and global scales. A supervised approach, based on support vector machines (SVMs), has recently been developed to estimate surface temperature from satellite radiometry. However, in order to integrate temperature estimates into hydrological or meteorological data-assimilation schemes (e.g., in flood-prevention applications), a further critical input is often required in the form of pixelwise error statistics. This information is important because it quantifies inaccuracies in the temperature estimate computed for each pixel. This letter proposes two novel methods to model the statistics of the SVM regression error on a pixelwise basis. Both approaches take into account the nonstationary behavior of the error itself. This problem has been only recently explored in the SVM literature through the use of Bayesian reformulations of SVM regressions. The methods proposed in this letter extend this approach by integrating it with either maximum-likelihood or confidence-interval supervised estimators. In both cases, the goal is improved modeling of the error contribution due to intrinsic random variability in the data (e.g., noise). The methods are experimentally validated on Advanced Very High Resolution Radiometer (AVHRR) and Meteosat Second Generation-Spinning Enhanced Visible and Infrared Imager (MSG-SEVIRI) images.