Model - average mean local precipitation responses also roughly scale with the global mean temperature response across the emissions scenarios, though not as well as for temperature. (ipcc.ch)
Merlis, T. M., T. Schneider, S. Bordoni, and I. Eisenman, 2013: The tropical precipitation response to orbital precession. (climate-dynamics.org)
It's interesting to note that while the result of a muted precipitation response to global warming appears to be theoretically sound and robust across models, satellite observations suggest that precipitation is increasing closer to 7 % per K, instead of 3 % per K (Wentz et al 2007). (hannahlab.org)