Let $L$ be a toric line bundle on $X_{\Sigma}$. A metric on $L^{{\text{\rm an}}}$ is called toric if, for any toric section $s$ of $L$ over $X_{0}$, the function $p\longmapsto\|s(p)\|$ is $\mathbb{S}^{{\text{\rm an}}}$-invariant.