Let $X$ be a smooth $n$-dimensional projective variety over $K$ with a closed $(1,1)$-form $\theta$. Let $\mathscr{L}$ be a line bundle on a ${K^{\circ}}$-model $\mathscr{X}$ of $X$ defining $\theta$ and with $L=\mathscr{L}|_{X}$ ample. We assume that $(\mathscr{X},\mathscr{L})$ is the base change of $(\mathscr{X}_{R},\mathscr{L}_{R})$ for a line bundle $\mathscr{L}_{R}$ of a projective integral scheme $\mathscr{X}_{R}$ over a subring $R$ of ${K^{\circ}}$ and that $R$ is a discrete valuation ring defined geometrically by a $d$-dimensional normal variety $B$ over a perfect field $k$ (as in Remark 7.2). If resolution of singularities holds over $k$ in dimension $d+n$, then ${P}_{\theta}(0)$ is a uniform limit of $\theta$-psh model functions and hence ${P}_{\theta}(0)$ is continuous on ${X^{{\mathrm{an}}}}$.