varies by site following the Gaussian process with mean zero, variance one, and exponential spatial correlation $\exp(-\Vert {\mathbf{s}}_i-{\mathbf{s}}_j\Vert /2)$. Unlike the analysis of the NARCCAP data in Section \[stemp\], the GEV scale and shape parameters are assumed to be the same for all sites and fixed at $\sigma({\mathbf{s}})=1$ and $\xi({\mathbf{s}})=0.2$. We fix these parameters in the simulation study for computational purposes, and because these spatially-varying parameters will likely be hard to estimate for these moderately-sized simulated data sets. The simulations vary by the nugget effect ($\alpha$), the kernel bandwidth ($\tau$), and the number of knots used to generate the data ($L_0$). The simulation designs are numbered:

$L_0=49$ knots at ${\mathcal{S}}(7,0,6)$, $\alpha=0.3$, $\tau=3$,

$L_0=49$ knots at ${\mathcal{S}}(7,0,6)$, $\alpha=0.7$, $\tau=3$,

$L_0=25$ knots at ${\mathcal{S}}(5,0,6)$, $\alpha=0.3$, $\tau=3$,

$L_0=25$ knots at ${\mathcal{S}}(5,0,6)$, $\alpha=0.7$, $\tau=3$,

$L_0=10\mbox{,}000$ knots at ${\mathcal{S}}(100,-1,7)$, $\alpha=0.4$, $\tau=1$.

For the first four designs, the number of knots used to generate the data is small enough to permit fitting the model with the correct number of knots. We use these examples to explore sensitivity to knot selection. The final design with $L_0=10\mbox{,}000$ knots represents the limiting case with more knots than can be fit computationally. Here we fit several course grids of knots 