poor fit with too few knots. Consider the case of a Gaussian kernel with bandwidth $\tau=1$ and knots on a large rectangular grid with grid spacing $d$. Figure \[fextremal\] plots the extremal coefficient for points $(0,0)$ and $(0,h)$ as a function of separation distance $h$. The extremal coefficient has nearly an identical shape for all $d$ less than or equal to $\tau$. For $d=1.25\tau$, the extremal coefficient differs slightly from the fine grids, and for $d>1.25\tau$ the extremal coefficient deviates considerably from the fine grids, especially for small $\alpha$. These results will scale for other $\tau$, therefore, a rule of thumb is to select the knots so that the grid spacing is approximately equal to the kernel bandwidth. Knot selection is discussed further in Section \[ssim\].

![Extremal coefficient $\vartheta({\mathbf{s}}_1,{\mathbf{s}}_2)$, where ${\mathbf{s}}_1 =
(0,0)$, ${\mathbf{s}}_2=(0,h)$, the kernel bandwidth is $\tau=1$, and the knots form a rectangular grid with grid spacing $d$.[]{data-label="fextremal"}](591f02.eps)

Adaption for the NARCCAP data {#sST}
-----------------------------

In Section \[stemp\] we analyze climate model output for $T>1$ years, which requires additional notation. Denote $Y_t({\mathbf{s}})$ as the response for year $t$ and site ${\mathbf{s}}$. Assuming the years are independent and identically distributed (over years, not space) gives $$\begin{aligned}
\label{auxmodel2} Y_t({\mathbf{s}}_i) | 