  Zhang introduced semipositive metrics on a line bundle of a proper variety.
In this paper, we generalize such metrics for a line bundle $L$ of a
paracompact strictly $K$-analytic space $X$ over any non-archimedean field $K$.
We prove various properties in this setting such as density of piecewise
$\mathbb{Q}$-linear metrics in the space of continuous metrics on $L$. If $X$
is proper scheme, then we show that algebraic, formal and piecewise linear
metrics are the same. Our main result is that on a proper scheme $X$ over an
arbitrary non-archimedean field $K$, the set of semipositive model metrics is
closed with respect to pointwise convergence generalizing a result from
Boucksom, Favre and Jonsson where $K$ was assumed to be discretely valued with
residue characteristic $0$.
