Let $\|\cdot\|$ be a model metric on $L$, associated to a $\mathbf{Q}$-line bundle $\mathcal{L}$ on a model $\mathcal{X}$ of $X$. Then

• (i)

  the metric $\|\cdot\|$ is semipositive iff $\mathcal{L}$ is nef;

• (ii)

  a continuous metric $\|\cdot\|e^{-\varphi}$ is semipositive iff there exists a sequence of semipositive model metrics $\|\cdot\|_{m}=\|\cdot\|e^{-\varphi_{m}}$ such that $\varphi_{m}\to\varphi$ uniformly on $X$.