
The change in temperature-mediated global-mean precipitation ( P) is suggested to be proportional to surface temperature ( T) increase 4, 9, 10, and the ratio is referred to as hydrological sensitivity ( \(\eta\)), defined as follows: For longer timescales, after the surface subsequently gets warmer, the ARC is enhanced, allowing for an intensification of the hydrological cycle 7, 8. Increasing greenhouse emissions will initially reduce global-mean rainfall 4, 6, corresponding to the decreased ARC when the surface temperature remains unchanged (that is, a rapid adjustment). The latent heat released from precipitation has to be balanced by the atmospheric radiative cooling (ARC) and the surface sensible heat flux in equilibrium. The Clausius–Clapeyron relationship provides a strong constraint on increasing water vapour content per unit temperature warming (at around 7% K −1), but it does not apply to the global-mean precipitation change, which is constrained by the atmospheric energy budget 4, 5. It is an essential but challenging goal to improve the projection of precipitation change under global warming 1, 2, 3. By accounting for the pattern effect, the global-mean precipitation over the past decades can be well reconstructed in terms of both magnitude and variability, indicating the vital role of the pattern effect in estimating future intensification of the hydrological cycle. Differences in warming patterns are as important as different treatments of atmospheric physics in determining the spread of \(\eta\) in climate models. Warming in tropical strongly ascending regions produces \(\eta\) values even larger than suggested by the Clausius–Clapeyron relationship (7% K −1), as the warming and moisture increases can propagate vertically and be transported globally through atmospheric dynamics.
Hydrological processes runoff Patch#
Here we apply warming patch experiments to a climate model to demonstrate that the spatial pattern of sea surface warming can explain a wide range of \(\eta\).

The increase in global-mean precipitation with global-mean temperature (hydrological sensitivity \(\eta\)) is constrained by the atmospheric energy budget, but its magnitude remains uncertain.
