TITLE & AUTHORSHIP:  Spatial Scaling of Extremes in Climate Models.
Dan Cooley, National Center for Atmospheric Research, Geophysical
Statistics
Project and CU-Boulder Applied Mathematics Department
Philippe Naveau, CU-Boulder Applied Mathematics Department and Laboratoire
des Sciences du Climat et de l'Environnement, IPSL-CNRS, Gif-sur-Yvette,
France
Paul Poncet, Ecole Nationale Superieure des Mines de Paris, France

ABSTRACT:  Climate data is recorded at many different scales; global
climate models yield data for a grid cell while weather stations record
data at point locations. The extremes of climate data are of interest as
they have significant impacts, but little work has been done relating the
extreme values of the different scales. We propose a one-parameter model
which relates the annual maximum at a point location to the annual maximum
on the grid cell, after both have been rescaled to have standard Frechet
marginals.  Our model preserves the desired property of max-stability, and
is flexible enough to accommodate spatial structure.  The parameter of the
model can be understood intuitively and can be shown to be related to the
extremal index of the random variables.  Finally, we propose an estimate
to the extremal index (and thus the model's parameter) which is based on
the madrogram.