The Berkeley Earth group has developed a new mathematical framework for producing maps and large-scale averages of temperature changes from weather station data for the purposes of climate analysis. The details of the mathematical framework used are described in the Methods paper available here.
The Berkeley Earth mathematical framework allows one to include short and discontinuous temperature records, so that nearly all temperature data can be used. The framework contains a weighting process that assesses the quality and consistency of a spatial network of temperature stations as an integral part of the averaging process. This permits data with varying levels of quality to be used without compromising the accuracy of the resulting reconstructions. The Berkeley Earth averaging process presented is extensible to spatial networks of arbitrary density (or locally varying density) while maintaining the expected spatial relationships.