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Greenhouse gas (GHG) emissions affect precipitation worldwide. The response is commonly described by two timescales linked to different processes: a rapid adjustment to radiative forcing, followed by a slower response to surface warming. However, additional timescales exist in the surface-warming response, tied to the time evolution of the sea-surface-temperature (SST) response. Here, we show that in climate model projections, the rapid adjustment and surface mean warming are insufficient to explain the time evolution of the hydro-climate response in three key Mediterranean-like areas--namely, California, Chile, and the Mediterranean. The time evolution of those responses critically depends on distinct shifts in the regional atmospheric circulation associated with the existence of distinct fast and slow SST warming patterns. As a result, Mediterranean and Chilean drying are in quasiequilibrium with GHG concentrations, meaning that the drying will not continue after GHG concentrations are stabilized, whereas California wetting will largely emerge only after GHG concentrations are stabilized. The rapid adjustment contributes to a reduction in precipitation, but has a limited impact on the balance between precipitation and evaporation. In these Mediterranean-like regions, future hydro-climate-related impacts will be substantially modulated by the time evolution of the pattern of SST warming that is realized in the real world. [ABSTRACT FROM AUTHOR]