We will say that a $\mathbb{T}$-Cartier divisor on a toric scheme is semipositive if it is generated by global sections. Let $X_{\Sigma}$ be a proper toric variety over $K$ and let $D_{\Psi}$ be a $\mathbb{T}$-Cartier divisor generated by global sections. A toric model $({\mathcal{X}},D,e)$ is called semipositive if $D$ is semipositive.