Let $\|\cdot\|$ be an algebraic metric on $L$ and set ${\overline{L}}=(L,\|\cdot\|)$. We say that ${\overline{L}}$ is semipositive if there is a model $(\mathcal{X},\mathcal{L},e)$ of $(X,L)$ that induces the metric such that, for every vertical curve $C$ in ${\mathcal{X}}$,