The canonical metric in Example 2.25 is semipositive: for a vertical curve $C$, its degree with respect to ${\mathcal{O}}_{\mathbb{P}^{n}_{K^{\circ}}}(1)$ equals its degree with respect to the restriction of this model to the special fibre. This restriction identifies with ${\mathcal{O}}_{\mathbb{P}^{n}_{k}}(1)$, the universal line bundle of $\mathbb{P}^{n}_{k}$, which is ample. Hence all the metrics obtained by inverse image of the canonical metric of ${\mathcal{O}}(1)^{{\text{\rm an}}}$ are also semipositive.