Estimation of Global Temperature Fields from Scattered Observations by a Spherical-Wavelet-Based Spatially Adaptive Method

This paper considers the problem of estimating the entire temperature field for every location on the
globe from scattered surface air temperatures observed by a network of weather stations. Classical
methods such as spherical harmonics and spherical smoothing splines are not efficient in representing the data that have inherent multiscale structures. This paper presents an estimation method that has the capability of adapting to the multiscale characteristics of the data. The method is based on a spherical wavelet approach recently developed for multiscale representation and analysis of scattered data. Spatially adaptive estimators are obtained by coupling the spherical wavelets with different thresholding (selective reconstruction) techniques. These estimators are compared for their spatial adaptability and extrapolation performance using the surface air temperature data.