Statistical Models for Global Processes

This talk explores some of the issues that arise in statistical modeling of atmospheric phenomena on a global scale, using total column ozone as measured by the satellite-based Total Ozone Mapping Spectrometer (TOMS) as a case study. A basic issue in all statistical models for natural phenomena is finding statistical regularities that enable one to take meaningful averages. Since the statistical characteristics of total column ozone strongly depend on latitude, we consider the use of axial symmetry (invariance of statistical properties to rotations about the Earth's axis) as a possible exploitable regularity. Methods for summarizing, modeling, estimating and visualizing spatial dependence for axially symmetric processes are addressed. A computationally convenient approach to modeling using truncated expansions of spherical polynomials is shown to capture much of the larger-scale latitudinal variation in spatial dependence. However, the approach performs disastrously in terms of describing the local behavior of the process, leaving a need for the development of statistical models that provide good descriptions of the data and computational methodologies that allow one to fit these models with reasonable degrees of statistical efficiency. Lessons learned from this only partially successful modeling effort, including suggestions for new data products based on TOMS, are described.