A model metric ${\|\ \|}$ on ${\mathcal{O}}_{X^{\mathrm{an}}}$ induces a continuous function $f=-\log\|1\|\colon X^{\mathrm{an}}\to\mathbb{R}$. The space of model functions

$${\mathscr{D}}(X)=\{f\colon X^{\mathrm{an}}\rightarrow\mathbb{R}\,|\,f=-\log\|1\|\mbox{ for some model metric }{\|\ \|}\mbox{ on }{\mathcal{O}}_{X^{\mathrm{an}}}\}$$

has a natural structure of a $\mathbb{Q}$-vector space. We say that a model function $f=-\log\|1\|$ is determined on a model ${{\mathscr{X}}}$ if the model metric ${\|\ \|}$ is determined on ${{\mathscr{X}}}$. A vertical divisor $D$ on ${{\mathscr{X}}}$ determines a model ${\mathcal{O}}(D)$ of ${\mathcal{O}}_{X}$ and an associated model function $\varphi_{D}\coloneqq-\log\|1\|_{{\mathcal{O}}(D)}$. Such model functions are called $\mathbb{Z}$-model functions. Let ${\mathfrak{a}}$ denote a vertical ideal of ${{\mathscr{X}}}$. Let $E$ denote the exeptional divisor of the blowup of ${{\mathscr{X}}}$ in ${\mathfrak{a}}$. Then $\log|{\mathfrak{a}}|:=\varphi_{E}$ is called the $\mathbb{Z}$-model function defined by the vertical ideal ${\mathfrak{a}}$.