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Based on the outputs of 30 models from Coupled Model Intercomparison Project Phase 5 (CMIP5), the fractional changes in the amplitude interannual variability (sigma) for precipitation (P) and vertical velocity () are assessed, and simple theoretical models are constructed to quantitatively understand the changes in sigma(P) and sigma(). Both RCP8.5 and RCP4.5 scenarios show similar results in term of the fractional change per degree of warming, with slightly lower inter-model uncertainty under RCP8.5. Based on the multi-model median, sigma(P) generally increases but sigma() generally decreases under global warming but both are characterized by non-uniform spatial patterns. The sigma(P) decrease over subtropical subsidence regions but increase elsewhere, with a regional averaged value of 1.4%K-1 over 20 degrees S-50 degrees N under RCP8.5. Diagnoses show that the mechanisms for the change in sigma(P) are different for climatological ascending and descending regions. Over ascending regions, the increase of mean state specific humidity contributes to a general increase of sigma(P) but the change of sigma() dominates its spatial pattern and inter-model uncertainty. But over descending regions, the change of sigma(P) and its inter-model uncertainty are constrained by the change of mean state precipitation. The sigma() is projected to be weakened almost everywhere except over equatorial Pacific, with a regional averaged fractional change of -3.4%K-1 at 500hPa. The overall reduction of sigma() results from the increased mean state static stability, while the substantially increased sigma() at the mid-upper troposphere over equatorial Pacific and the inter-model uncertainty of the changes in sigma() are dominated by the change in the interannual variability of diabatic heating.