Definitions

Extreme weather includes unexpected, unusual, unpredictable severe or unseasonal weather. (...). Often, extreme events are based on a location’s recorded weather history and defined as lying in the most unusual ten percent.[2] In recent years some extreme weather events have been attributed to human-induced global warming,with studies indicating an increasing threat from extreme weather in the future. (Source: Wikipedia)

Hierarchy
Alternative labels:
extreme climate
extreme weather event
severe weather
weather phenomena