Supplementary Information: Tornado outbreak variability follows Taylor’s power law of fluctuation scaling and increases dramatically with severity

Tornadoes cause loss of life and damage to property each year in the United States and around the world. The largest impacts come from ‘outbreaks’ consisting of multiple tornadoes closely spaced in time. Here we find an upward trend in the annual mean number of tornadoes per US tornado outbreak for the period 1954–2014. Moreover, the variance of this quantity is increasing more than four times as fast as the mean. The mean and variance of the number of tornadoes per outbreak vary according to Taylor’s power law of fluctuation scaling (TL), with parameters that are consistent with multiplicative growth. Tornado-related atmospheric proxies show similar power-law scaling and multiplicative growth. Path-length-integrated tornado outbreak intensity also follows TL, but with parameters consistent with sampling variability. The observed TL power-law scaling of outbreak severity means that extreme outbreaks are more frequent than would be expected if mean and variance were independent or linearly related.

每年，龙卷风都会在美国及全球范围内造成人员伤亡与财产损失。影响最为严重的灾害事件源自“群发事件”——即时间上紧密接连的多起龙卷风集群。本文针对1954年至2014年的时段展开研究，发现美国单次龙卷风群发事件的年均龙卷风数量均值呈上升趋势。不仅如此，该指标的方差增长速率是均值的四倍有余。单次群发事件的龙卷风数量均值与方差遵循泰勒涨落标度幂律（Taylor’s power law of fluctuation scaling，TL），其参数符合乘性增长规律。与龙卷风相关的大气代理变量也呈现出相似的幂律标度与乘性增长特征。路径积分的龙卷风群发事件强度同样遵循泰勒幂律，但其参数符合采样变异性特征。观测到的群发事件严重程度的幂律标度表明，极端群发事件的发生频率要高于均值与方差相互独立或呈线性相关时的预期水平。