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The pumping conductance of a disordered two-dimensional Chern insulatorscales with increasing size and fixed disorder strength to sharp plateautransitions at well-defined energies between ordinary and quantum Hallinsulators. When the disorder strength is scaled to zero as system sizeincreases, the "metallic" regime of fluctuating Chern numbers can extend overthe whole band. A simple argument leads to a sort of weighted equipartition ofChern number over minibands in a finite system with periodic boundaryconditions: even though there must be strong fluctuations between disorderrealizations, the mean Chern number at a given energy is determined by the {\itclean} Berry curvature distribution expected from the intrinsic anomalous Halleffect formula for metals. This estimate is compared to numerical results usingrecently developed operator algebra methods, and indeed the dominant variationof average Chern number is explained by the intrinsic anomalous Hall effect. Amathematical appendix provides more precise definitions and a model for thefull distribution of Chern numbers.

Pumping conductance, the intrinsic anomalous Hall effect, and statistics of topological invariants