and compare performance as the number of knots increases to provide recommendations on the number of knots needed to provide a good approximation to the limiting process.

$M=50$ data sets are generated for each simulation design. For each simulated data set, we fit the model with a varying number of knots. For the first four designs we compare $L=25$ knots at ${\mathcal{S}}(5,0,6)$ and $L=49$ knots at ${\mathcal{S}}(7,0,6)$ to compare fits with the true knots and either too few ($L=25$ for designs 1 and 2) or too many ($L=49$ for designs 3 and 4) knots. For the final design we compare fits with 8 knot grids: $L=25$ knots at ${\mathcal{S}}(5,-1,7), \ldots, L=144$ knots at ${\mathcal{S}}(12,-1,7)$. The spatial covariance parameters for the GEV location have priors $\delta_{\mu}^2\sim \operatorname{InvGamma}(0.1,0.1)$ and range $\rho_{\mu}\sim \operatorname{InvGamma}(0.1,0.1)$; for this relatively small spatial domain we fix the smoothness parameter $\nu_{\mu}=0.5$, giving an exponential covariance. The design matrix ${\mathbf{X}}$ includes only the intercept with $\beta_{\mu}\sim\mathrm{N}(0,100^2)$. The GEV log scale and shape are constant across space and have $\mathrm{N}(0,1)$ and $\mathrm{N}(0,0.25^2)$ priors, respectively. The residual dependence parameters have priors $\tau\sim \operatorname{InvGamma}(0.1,0.1)$ and $\alpha\sim \operatorname{Unif}(0,1)$.

The results are presented in Figure \[fsim\]. For each data set, we compute the posterior mean 