  We rederive the spectral asymmetry of the Wilson-Dirac model in external
fields, paying attention to the Chern number due to the Berry connection. We
interpret the smooth part of the spectral asymmetry as the Streda formula that
is originally derived for the two-dimensional quantum Hall effect (QHE). We
show by numerical calculations that the Streda formula reproduces the known
first and second Chern numbers in a weak magnetic field limit. We conjecture
that the Streda formula is valid even for stronger fields and for more generic
systems in higher dimensions.
