  We introduce a long-period generic spatial modulation into a typical model of
the Thouless pump, namely, the Rice--Mele (RM) model, to examine the lattice
analog of the fermion charge in quantum field theory. We derive a Diophantine
equation relating the fermion charge and the pumped charge, which leads to the
one-dimensional (1D) analog of the Streda formula in the quantum Hall effect
(QHE). This formula implies that an adiabatic change of the periodicity of the
spatial modulation yields a spatial charge pump such that the rightmost charge
is pumped to the right by the Chern number compared with the leftmost charge.
This causes a change in the length of the fermion chain by an integer, thus
providing the opportunity for direct measurement of the Streda formula in 1D
systems.
