Statistical Models for Global Processes
- Date: 04/02/2007
Michael Stein (University of Chicago)
University of British Columbia
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.
10th Anniversary Speaker Series 2007
