Let $X$ be a proper scheme over $K$ with a line bundle $L$ over $X$. We call an algebraic ${K^{\circ}}$-model $({\mathscr{X}},{\mathscr{L}})$ of $(X,L)$ numerically effective (briefly nef) if $\deg_{\mathscr{L}}(C)\geq 0$ for every closed curve $C$ in ${\mathscr{X}}$ which is proper over ${K^{\circ}}$. Of course, properness implies that $C$ is contained in the special fiber ${\mathscr{X}}_{s}$. An algebraic metric ${\|\hskip 4.30554pt\|}$ on $L^{\rm an}$ is said to be semipositive if there is a nef algebraic ${K^{\circ}}$-model $({\mathscr{X}},{\mathscr{L}})$ of $(X,L)$ such that ${\|\hskip 4.30554pt\|}={\|\hskip 4.30554pt\|}_{\mathscr{L}}$.