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With the increasing availability of observational data from different sources at a global level, joint analysis of these data is becoming especially attractive. For such an analysis – oftentimes with little prior knowledge about local and global interactions between the different observational variables at hand – an exploratory, data-driven analysis of the data may be of particular relevance. In the present work we used generalized additive models (GAM) in an exemplary study of spatio-temporal patterns in the tropospheric NO2-distribution derived from GOME satellite observations (1996 to 2001) at global scale. We focused on identifying correlations between NO2 and local wind fields, a quantity which is of particular interest in the analysis of spatio-temporal interactions. Formulating general functional, parametric relationships between the observed NO2 distribution and local wind fields, however, is difficult – if not impossible. So, rather than following a modelbased analysis testing the data for predefined hypotheses (assuming, for example, sinusoidal seasonal trends), we used a GAM with non-parametric model terms to learn this functional relationship between NO2 and wind directly from the data. The NO2 observations showed to be affected by winddominated processes over large areas. We estimated the extent of areas affected by specific NO2 emission sources, and were able to highlight likely atmospheric transport “pathways”. General temporal trends which were also part of our model – weekly, seasonal and linear changes – showed to be in good agreement with previous studies and alternative ways of analysing the time series. Overall, using a non-parametric model provided favorable means for a rapid inspection of this large spatio-temporal NO2 data set, with less bias than parametric approaches, and allowing to visualize dynamical processes of the NO2 distribution at a global scale.
We construct a family of admissible analysis reconstruction pairs of wavelet families on the sphere. The construction is an extension of the isotropic Poisson wavelets. Similar to those, the directional wavelets allow a finite expansion in terms of off-center multipoles. Unlike the isotropic case, the directional wavelets are not a tight frame. However, at small scales, they almost behave like a tight frame. We give an explicit formula for the pseudodifferential operator given by the combination analysis-synthesis with respect to these wavelets. The Euclidean limit is shown to exist and an explicit formula is given. This allows us to quantify the asymptotic angular resolution of the wavelets.