Land and sea surface temperatures are important quantities for many hydrological and meteorological models and satellite infrared remote sensing represents an effective way to map them on global and regional scales. A supervised approach, based on support vector regression, has recently been developed to estimate surface temperature from satellite images. Such a strategy requires the user to set several internal parameters. Moreover, in order to integrate the resulting estimates into hydrological or meteorological data-assimilation schemes, a further important input is the statistics of the regression error affecting each pixel. In this chapter, we propose a method to automatically set the input parameters and two techniques to model the statistics of pixelwise regression error. Parameter optimization is achieved by numerically minimizing a generalization-error bound that can be computed by using only the training set, and error modelling is performed by integrating a Bayesian support vector regression approach with maximum-likelihood or confidence-interval supervised parameter estimators. Some parts of this chapter have been derived from papers (Moser and Serpico