Building on the recent advent of the concept of finite-amplitude wave activity, a contour-following diagnostics for column water vapor (CWV) is developed and applied to a pair of aquaplanet model simulations to understand and quantify the higher moments in the global hydrological cycle. The Lagrangian nature of the diagnostics leads to a more tractable formalism for the transient, zonally asymmetric component of the hydrological cycle, with a strong linear relation emerging between the wave activity and the wave component of precipitation minus evaporation. The dry-versus-wet disparity in the transient hydrological cycle is measured, and it is found to increase at a super-Clausius–Clapeyron rate at the poleward side of the mean storm track in response to a uniform sea surface temperature (SST) warming. The meridional structure of the increase can be largely attributed to the change of the meridional stirring scale of the midlatitude Rossby waves. Further scaling indicates that the rate of the wavy hydrological cycle, measured by the ratio of to the CWV wave activity, is subdued almost everywhere in the extratropics, implying an overall weakening of the transient circulation. Extending the CWV wave activity analysis to the transient moist regions helps reveal some unique characteristics of atmospheric rivers in terms of transport function, minimum precipitation efficiency, and maximum hydrological cycle rate, as well as an overall weakening of the hydrological cycle rate in the atmospheric river regions under SST warming.