Fig. 1.

Example confounder adjustment for the bivariate Matérn: $X\left(s\right)$ is generated from Matérn with ${\varphi }_x=1$ and $v_x=1$ on a 50 × 50 grid with grid spacing one. The panels show the confounder adjustment $\hat{Z}\left(s\right)$ for ${\varphi }_{xz}={\varphi }_x$ and $v_{xz}=c{v}_x$ for $c\in \{1,3,5\}$. For $c=1,\hat{Z}\left(s\right)=X\left(s\right)$.