Let us assume that $K$ is discretely valued. Let $X$ be a proper scheme over $K$ with a line bundle $L$. We assume that the model metric ${\|\hskip 4.30554pt\|}$ on $L^{\rm an}$ is a pointwise limit of semipositive model metrics on $L^{\rm an}$. Then ${\|\hskip 4.30554pt\|}$ is a semipositive model metric.