and ice boundary conditions in the historical run. The boundary conditions for the future run are perturbations of the historical boundary conditions. The amount of perturbation is based on a lower resolution climate model. The perturbations assume the A2 emissions scenario \[Nakicenovic et al. ([-@Na00])\], which increases CO$_2$ concentration levels from the current values of about 380 ppm to about 870 ppm by the end of the 21st century.

![Grid cell centers for the NARCCAP output (left) and madogram extremal coefficient estimate (box width is proportional to the number of observations) for the historical run.[]{data-label="fdata"}](591f04.eps "fig:")\[t!\]

We analyze data for $n=697$ grid cells in eastern US as shown in Figure \[fdata\]. For grid cell $i$ with location ${\mathbf{s}}_i$ and year $t$, we take the annual maximum of the daily precipitation totals as the response, $Y_{t}({\mathbf{s}}_i)$. NARCCAP provides eight 3-hour precipitation rates each day, and we compute the daily total by summing these eight values and multiplying by three. To explore the form of residual spatial dependence, we use the madogram \[@cooley-2006a\] function in the `SpatialExtremes` package in $\mathtt{R}$ ([www.r-project.org](http://www.R-project.org)). The madogram converts the observations at each site to have unit ${\mbox{Fr\'{e}chet}}$ margins using a rank transformation, and then estimates the 