Let $K$ be a complete discrete valuation field of residue characteristic zero. Let $X$ be a smooth projective $K$-variety that is algebraizable. Let $L\in\Pic(X)$ be an ample line bundle and $\mu$ be a positive Radon measure on $X$ of mass $c_{1}(L)^{n}$. If we further assume that $\mu$ is supported on the dual complex of some SNC model of $X$, then there exists a continuous, semipositive metric $\|\cdot\|$ on $L$ such that

(1.1)

$$c_{1}\left(L,\|\cdot\|\right)^{\dim X}=\mu~.$$

This metric is furthermore unique up to a multiplicative constant.