A new article in Science provides observational evidence of the link between rising temperatures and extreme weather events:
These observations reveal a distinct link between rainfall extremes and temperature, with heavy rain events increasing during warm periods and decreasing during cold periods. Furthermore, the observed amplification of rainfall extremes is found to be larger than predicted by models, implying that projections of future changes in rainfall extremes due to anthropogenic global warming may be underestimated.
Of all the impacts of climate change, extreme weather seems especially likely to help spur mitigation action, especially when that weather occurs in rich states. Reasons for that include the visibility and newsworthiness of floods, droughts, hurricanes, and so forth. Another major factor is the importance of the insurance industry, especially insofar as their professional estimations of risk affect the cost and feasibility of different projects. That is, so long as policy-makers do not establish incentives for risky behaviour.