Snowfall is an important element of the climate system, and one that is expected to change in a warming climate [1][2][3][4] . Both mean snowfall and the intensity distribution of snowfall are important, with heavy snowfall events having particularly large economic and human impacts [5][6][7] .Simulations with climate models indicate that annual-mean snowfall declines with warming in most regions but increases in regions with very low surface temperatures 3,4 . The response of heavy snowfall events to a changing climate, however, is unclear. Here I show that in simulations with climate models under a high-emissions scenario, by the late twenty-first century there are smaller fractional changes in daily snowfall extremes than in mean snowfall over many Northern Hemisphere land regions. For example, for monthly climatological temperatures just below freezing and surface elevations below 1000m, the 99.99th percentile of daily snowfall decreases by 8% in the multimodel median as compared to a 65% reduction in mean snowfall. Both mean and extreme snowfall must decrease for a sufficiently large warming, but the climatological temperature above which snowfall extremes decrease with warming in the simulations is as high as -9 • C as compared to -14 • C for mean snowfall. These results are supported by a physically based theory that is consistent with the observed rain-snow transition. According to the theory, snowfall extremes occur near an optimal temperature that 1 is insensitive to climate warming, and this results in smaller fractional changes for higher percentiles of daily snowfall. The simulated changes in snowfall that I find would influence surface snow and its hazards; these changes also suggest that it may be difficult to detect a regional climate-change signal in snowfall extremes.Extremes of daily precipitation (including liquid and solid precipitation) are found to increase in intensity with climate warming in observations and simulations [8][9][10] , and this is physically consistent with greater saturation specific humidities in a warmer atmosphere [11][12][13] . However, little is known about the physical basis for changes in daily snowfall extremes, their past changes on a global or hemispheric scale, or how they change in global climate-model simulations. Regional observational studies show large interdecadal variations in measures of snowfall extremes 14 , but not necessarily significant long-term trends 15 . Extremes of seasonal-mean snowfall have been studied previously 16, 17 , but extremes on shorter timescales may respond differently 14 . Physically we expect heavy snowfall events to occur in a relatively narrow range of temperatures below the rain-snow transition; at much lower temperatures it is not "too cold to snow", but low saturation specific humidities make heavy snowfall unlikely. However, it is not clear what this means for the response to climate change, and previous studies have differed in their findings as to whether heavy snowfall events are predominantly associated with anomalou...