In contrast to diverse momentum space topological invariants, the local Chern marker in two-dimensional time-reversal breaking systems is known to be a direct probe of topological order in real space. Using finite temperature linear response theory, we demonstrate that this Chern marker is equivalent to the lattice charge polarization susceptibility to a circularly polarized electric field. A Chern marker spectral function is also introduced to describe the frequency-resolved circular dichroism measurement. We find that the nonlocal charge polarization susceptibility naturally leads to the notion of a Chern correlator which provides a distinct measure of topological correlations present in the system. From the off-diagonal elements of the Chern operator, a nonlocal Chern marker is further introduced, and we show that it is equivalent to a previously introduced Wannier state correlation function, a sensitive probe of topological phase transitions. Our work thus highlights the deep connection between real space measures of topological order and topological correlations, and experimentally measurable observables.