Let $G$ be a reductive group over a $p$-adic field $k$, $S \subset G$ a maximal $k$-split torus and $\Phi(G,S)$ the relative root system. Let $\Phi^+$ be a subsystem of positive roots.

There is a group homomorphism : $$S \to \mathbb{Z}^{\Phi^+}, s \mapsto (\mathrm{ord_p} \alpha(s))_{\alpha \in \Phi^+}$$ with finite cokernel and kernel equal to $S_0 (Z \cap S)$ where $S_0$ is the maximal compact subgroup and $Z$ the center of $G$.

This is used in many papers (e.g. Tit's "Reductive groups over local fields") but I could not find a reference for the proof.