Assume that the absolute value $|\raisebox{1.72218pt}{.}|$ is non-trivial. Let $L$ be an ample invertible sheaf on $X$, equipped with a semipositive continuous metric $h$. Then there exists a sequence $\{(\mathscr{X}_{n},\mathscr{L}_{n})\}_{n\geqslant 1}$, where $\mathscr{X}_{n}$ is a model of $X$ and $\mathscr{L}_{n}$ is a nef invertible sheaf on $\mathscr{X}_{n}$ such that $\mathscr{L}_{n}|_{X}=L^{\otimes n}$ and that $h_{n}=(|\raisebox{1.72218pt}{.}|_{\mathscr{L}_{n}}(x)^{1/n})_{x\in X^{\mathrm{an}}}$ converges uniformly to $h$. This follows from Proposition 3.10 and the comparison between quotient metrics and model metrics (via the embedding into the projective spaces of lattices). Combining with Proposition 3.17 and Corollary 3.11, we obtain that, in the non-trivial valuation case, our semipositivity coincides with that of Zhang [12] and Moriwaki [8]. We refer the readers to [6, §6] and to [2, §6.8] for the descriptions of the semipositivity in terms of plurisubharmonic currents. Note that their semipositivity is also equivalent to our semipositivity.