Let $X$ be a projective variety over $K$. We say that a model function $\varphi\colon X^{\mathrm{an}}\to\mathbb{R}$ is defined over $R$ if there exists a projective variety $Y$ over $F$, with an isomorphism $Y\otimes_{F}K\simeq X$, an $R$-model ${\mathscr{Y}}$ of $Y$, a vertical divisor $D_{0}$ on ${\mathscr{Y}}$ such that $\varphi=\frac{1}{m}\varphi_{D}$ where $m\in\mathbb{N}_{>0}$ and $D$ is the vertical divisor on ${\mathscr{Y}}\otimes_{R}K^{\circ}$ obtained by pullback from $D_{0}$. Likewise we define the notion of a vertical ideal sheaf defined over $R$.