  In this paper, we derive a real-space topological invariant that involves all
energy states in the system. This global invariant, denoted by $Q$, is always
quantized to be 0 or 1, independent of symmetries. In terms of $Q$, we
numerically investigate topological properties of the nonchiral Rice-Mele model
including random onsite potentials to show that nontrivial bulk topology is
sustained for weak enough disorder. In this regime, a finite spectral gap
persists, and then $Q$ is definitely identified. We also consider sublattice
polarization of disorder potentials. In this case, the energy spectrum retains
a gap regardless of disorder strength so that $Q$ is unaffected by disorder.
This implies that bulk topology remains intact as long as the spectral gap
opens.
