A model of $X$ is given by a proper flat scheme ${{\mathscr{X}}}$ over $S:={\rm Spec}\,K^{\circ}$ together with an isomorphism $h$ between $X$ and the generic fiber ${{\mathscr{X}}}_{\eta}$ of the $S$-scheme ${{\mathscr{X}}}$ which we read as an identification. Given a model ${{\mathscr{X}}}$ of $X$ there is a canonical surjective reduction map ${\mathrm{red}}\colon X^{\mathrm{an}}\longrightarrow{{\mathscr{X}}}_{s}$ where ${{\mathscr{X}}}_{s}$ denotes the special fiber ${{\mathscr{X}}}\otimes_{K^{\circ}}\tilde{K}$ of ${{\mathscr{X}}}$ over $S$.

Let $L$ be a line bundle on the proper variety $X$. A model of $(X,L)$ or briefly a model of $L$ is given by a model $({{\mathscr{X}}},h)$ of $X$ together with a line bundle ${\mathscr{L}}$ on ${{\mathscr{X}}}$ and an isomorphism $h^{\prime}$ between $L$ and $h^{*}({\mathscr{L}}|_{\mathscr{X}_{\eta}})$ which we read as an identification.

Given a model $({{\mathscr{X}}},{\mathscr{L}})$ of $(X,L^{\otimes m})$ for some $m\in\mathbb{N}_{>0}$ there is a unique metric ${\|\ \|}_{\mathscr{L}}$ on $L^{\mathrm{an}}$ over $X^{\mathrm{an}}$ which satisfies the following: Given an open subset ${\mathscr{U}}$ of ${{\mathscr{X}}}$, a frame $t$ of ${\mathscr{L}}$ over ${\mathscr{U}}$, and a section $s$ of $L$ over $U=X\cap{\mathscr{U}}$ we write $s^{\otimes m}=ht$ for some regular function $h$ on $U$ and get $\|s\|=\sqrt[m]{|h|}$ on $U^{\mathrm{an}}\cap{\mathrm{red}}^{-1}({\mathscr{U}}_{s})$. Such a metric on $L^{\mathrm{an}}$ is called a model metric determined on ${{\mathscr{X}}}$.