A continuous metric $h$ is semipositive if and only if, for any $\epsilon>0$, there is a positive integer $n$ such that, for all $x\in X^{\mathrm{an}}$, we can find $s\in H^{0}(X,L^{\otimes n})_{\hat{\kappa}(x)}\setminus\{0\}$ with $\|s\|_{h^{n},\hat{\kappa}(x)}\leq e^{n\epsilon}|s|_{h^{n}}(x)$.