A toric metric on $L$ is a family $(\|\cdot\|_{v})_{v\in M_{\mathbb{K}}}$, where $\|\cdot\|_{v}$ is a toric metrics on $L_{v}^{{\text{\rm an}}}$. A toric metric is called adelic if $\psi_{\|\cdot\|_{v}}=\Psi$ for all but finitely many $v$.