  Let $P, Q$ be Heegaard surfaces of a closed orientable 3-manifold. In this
paper, we introduce a method for giving an upper bound of Hempel distance of
$P$ by using the Reeb graph derived from a certain horizontal arc in the
ambient space $[0,1]\times[0,1]$ of the Rubinstein-Scharlemann graphic derived
from $P$ and $Q$. This is a refinement of a part of Johnson's arguments used
for determining stable genera required for flipping high distance Heegaard
splittings.
