We study collective attention paid towards hurricanes through the lens of $n$-grams on Twitter, a social media platform with global reach. Using hurricane name mentions as a proxy for awareness, we find that the exogenous temporal dynamics are remarkably similar across storms, but that overall collective attention varies widely even among storms causing comparable deaths and damage. We construct `hurricane attention maps' and observe that hurricanes causing deaths on (or economic damage to) the continental United States generate substantially more attention in English language tweets than those that do not. We find that a hurricane's Saffir-Simpson wind scale category assignment is strongly associated with the amount of attention it receives. Higher category storms receive higher proportional increases of attention per proportional increases in number of deaths or dollars of damage, than lower category storms. The most damaging and deadly storms of the 2010s, Hurricanes Harvey and Maria, generated the most attention and were remembered the longest, respectively. On average, a category 5 storm receives 4.6 times more attention than a category 1 storm causing the same number of deaths and economic damage.