The poleward shift of the mid-latitude storm track and jet stream is one of the most robust features of the atmospheric circulation change as the climate warms under the influence of greenhouse gases. A team of scientists, led by a DOE researcher at Pacific Northwest National Laboratory, found the reasons and the mechanisms for the shift turned out to be a complex matter because the mid-latitude atmospheric circulation is governed by a dynamical system which is fundamentally nonlinear and chaotic. This study employs a novel diagnostic approach based on finite-amplitude wave activity–a quantity that naturally encompasses both small and large disturbances associated with our everyday weather–to the problem of the atmospheric circulation response to global warming-like or El Niño-like tropical heating profiles. In comparison with the traditional linear approach, the team reveals the limitation of the linear thinking and unveils the irreversible nature in the dynamical circulation response to tropical, upper-tropospheric heating. In the finite-amplitude wave activity budget, the irreversible mixing of potential vorticity is simply a quantification of the Rossby wave breakings, the latter linked intimately to the extreme weather events in the subtropics and mid-latitude. They unveiled an inextricable relationship between the jet shift and the changing statistics of the wave breakings, which translates the robustness in the former under global warming to that in the change of precipitation extremes: as the jet stream shifts poleward, the concurrent weather extremes such as the atmospheric rivers should shift poleward as well.