Let $L$ be a semiample line bundle on the normal projective variety $X$ over $K$. Assume that $L$ has a ${K^{\circ}}$-model ${\mathscr{L}}$ on the ${K^{\circ}}$-model ${\mathscr{X}}$ of $X$. Let $\mathfrak{a}_{m}$ be the base-ideal of ${\mathscr{L}}^{\otimes m}$. If $\frac{1}{m}{\log|\mathfrak{a}_{m}|}$ converges pointwise to $0$ on $X^{\rm div}$, then ${\|\hskip 4.30554pt\|}_{\mathscr{L}}$ is semipositive.