The assignment that, to a local section $s$ of $L$ gives the function defined as $\|s(\theta_{0}\rho_{0}(p)\|$ for $p\in X^{{\text{\rm an}}}_{\Sigma}$, is a toric metric on $L^{{\text{\rm an}}}$, that we denote $\|\cdot\|_{\mathbb{S}}$. Moreover, $\psi_{\|\cdot\|}=\psi_{\|\cdot\|_{\mathbb{S}}}$.