Let $X$ be a proper scheme over $K$ and $L$ a line bundle on $X$. An algebraic $K^{\circ}$-model of $X$ is a proper flat scheme $\mathscr{X}$ over $K^{\circ}$ with a fixed isomorphism from the generic fibre $\mathscr{X}_{\eta}$ to $X$. An algebraic $K^{\circ}$-model of $(X,L)$ is a pair $(\mathscr{X},\mathscr{L})$ where $\mathscr{X}$ is an algebraic $K^{\circ}$-model of $X$ and $\mathscr{L}$ is a line bundle on $\mathscr{X}$ with a fixed isomorphism from $\mathscr{L}\Big|_{X}$ to $L$. An algebraic $K^{\circ}$-model of $(X,L)$ gives rise to a formal $K^{\circ}$-model of $(X^{\textup{an}},L^{\textup{an}})$ by formal completion. Hence by the above, an algebraic model of $(X,L)$ induces a formal metric on $L^{\textup{an}}$. We call such metrics algebraic metrics.