Let $\mathcal{L}\in\Pic(\mathcal{X})$ and let $\|\cdot\|$ be the corresponding metric on $L:=\mathcal{L}|_{X}$. If $\mathfrak{a}$ is a vertical fractional ideal sheaf on $\mathcal{X}$ such that $\mathcal{L}\otimes\mathfrak{a}$ is generated by its global sections, then $\log|\mathfrak{a}|$ is a model $c_{1}(L,\|\cdot\|)$-psh function.