Let $L$ be an ample line bundle on $X$. A singular metric $\|\cdot\|$ on $L$ is semipositive if it is of the form $\|\cdot\|=\|\cdot\|e^{-\varphi}$, where $\|\cdot\|$ denotes a model metric and $\varphi$ is $c_{1}(L,\|\cdot\|)$-psh.