Let $X_{\Sigma}\simeq\mathbb{P}^{1}_{K}$ be a one-dimensional toric variety over $K$. Let $(L,s)$ be a toric line bundle with a toric section and let $\|\cdot\|$ be a semipositive algebraic metric. Then $\|\cdot\|_{\mathbb{S}}$ is a semipositive toric algebraic metric and $\psi_{\|\cdot\|}$ is concave.