Let $X$ be a strictly $K$-analytic space and $L$ a line bundle on $X$. A metric $\|\cdot\|$ on $L$ is called piecewise $\mathbb{Q}$-linear if for every $x\in X$ there is an open neighbourhood $W$ of $x$ and a non-zero $n\in\mathbb{N}$ such that $\|\cdot\|^{\otimes n}\Big|_{W}$ is a piecewise linear metric on $L^{\otimes n}\Big|_{W}$.
A piecewise $\mathbb{Q}$-linear metric on $L$ is called semipositive in $x\in X$ if in the above $\|\cdot\|^{\otimes n}\Big|_{W}$ is semipositive in $x$.