Why? Basic physics. Warmer air can hold more water. All other things equal, the same thunderstorm will bring more water in a warmer world. Argues Clausius in 1834, Clapeyron in 1850.
Early models showed this many decades ago.
Of course not all other things are equal, but to first order the argument still holds.
Bottom line 1: mean precipitation is difficult because it's a mix of thermodynamics and dynamics. But precipitation variability robustly increases in most places, from seasonal to daily timescales
Bottom line 2: Heavy precipitation intensity and frequency increases in most places, and has already been linked to human-induced warming. Damage is typically nonlinear, so every °C disproportionately increases the potential risk.
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