Let $\theta$ be a closed $(1,1)$-form with nef de Rham class $\{\theta\}$ on the smooth projective curve $X$ over $K$ and let $f\colon X^{{\mathrm{an}}}\to\mathbb{R}$ be a model function. We assume that $\theta$ and $f$ are determined on the strictly semistable model $\mathscr{X}$ of $X$. Let $\tau\colon{X^{{\mathrm{an}}}}\to S(\mathscr{X})$ be the canonical retraction to the skeleton. Then the following properties hold:

1. (i)

   There is $F\colon S(\mathscr{X})\to\mathbb{R}$ which is affine on each edge and with ${P}_{\theta}(f)=F\circ\tau$.

2. (ii)

   If $\Gamma\subset\mathbb{Q}$ and if $\theta\in\mathcal{Z}^{1,1}(X)_{\mathbb{Q}}$, then ${P}_{\theta}(f)$ is a $\theta$-psh model function which is determined on $\mathscr{X}$.