the residual max-stable process model described here may be applicable to this type of analysis as well. We describe a model for a single realization of the process and extend to multiple independent realizations in Section \[sST\].

Assuming the process is max-stable, then the marginal distribution of $Y({\mathbf{s}})$ is $\operatorname{GEV}[\mu({\mathbf{s}}),\sigma({\mathbf{s}}),\xi({\mathbf{s}})]$, where $\mu
({\mathbf{s}})$ is the location, $\sigma({\mathbf{s}})>0$ is the scale, and $\xi({\mathbf{s}})$ is the shape (GEV distribution is described in Appendix \[appa1\]). Equivalently \[@resnick-1987\], we may express $Y({\mathbf{s}}) = \mu({\mathbf{s}}) + \frac{\sigma
({\mathbf{s}})}{\xi({\mathbf{s}})} [X({\mathbf{s}})^{\xi({\mathbf{s}})}-1 ]$, where $X({\mathbf{s}})$ is the residual max-stable process with unit ${\mbox{Fr\'{e}chet}}$ margins, that is, $X({\mathbf{s}})\sim \operatorname{GEV}(1,1,1)$. To allow for both nonspatial and spatial residual variability, we model $X({\mathbf{s}})$ as the product $X({\mathbf{s}})=U({\mathbf{s}})\theta({\mathbf{s}})$. Borrowing a term from geostatistics, we refer to $U({\mathbf{s}})$ as the nugget effect since it accounts for nonspatial variation due to measurement error or other small-scale features. The nugget is modeled as $U({\mathbf{s}}){\stackrel{\mathrm{i.i.d.}}{\sim}}\operatorname{GEV}(1,\alpha,\alpha)$, where, as described in detail below, the parameter $\alpha\in(0,1)$ controls the relative contribution to the nugget effect.

Residual spatial dependence is captured by $\theta({\mathbf{s}})$. We express the spatial process as a function of a linear combination of $L$ kernel basis functions $w_l({\mathbf{s}})\ge0$, scaled so that $\sum_{l=1}^Lw_l({\mathbf{s}})=1$ for all ${\mathbf{s}}$. The spatial 