Let $X$ be a projective variety over $K$ with an ample line bundle $L$. We assume that $X$ has an SNC model ${\mathscr{X}}$ over $K^{\circ}$ with a line bundle ${\mathscr{L}}$ extending $L$. Let ${\|\hskip 4.30554pt\|}={\|\hskip 4.30554pt\|}_{\mathscr{L}}$ be the corresponding model metric on $L^{\rm an}$ which is assumed to be the pointwise limit over $X^{\rm div}$ of semipositive model metrics on $L^{\rm an}$. Then ${\|\hskip 4.30554pt\|}$ is a semipositive model metric.