Let $X$ be a paracompact strictly $K$-analytic space and $L$ a line bundle on $X$. A formal metric $\|\cdot\|$ on $L$ is semipositive in every $x\in X$ if and only if there exists a nef formal $K^{\circ}$-model $\mathfrak{L}$ of $L$ inducing $\|\cdot\|$. In particular we regain the original global definition of semipositivity by Zhang ([Zha95]).