(transcendence of canonical heights)

Is the Néron-Tate canonical height for an Abelian variety $A$ over a global function field $K$, $\hat{h}: A(K) \times A^\vee(K) \to \mathbf{R}$ known to always lie in $\bar{\mathbf{Q}}$?

Edit: I am looking for a reference that the height is always rational.