Extremely Wrong: When Limited Data Leads to Biases in General Extreme Values Distribution Estimates

Abstract:

Notable climate-related extremes include, but are not limited to, hurricanes, floods, sea level changes, heat waves, and drought and have been associated with countless deaths, destruction, and ecological changes. Although extremes, by definition, do not occur frequently and generally as the magnitude of the extreme increases, its probability for occurrence decreases, the damage such extreme can cause increases. The modeling of such extremes is, of course, of interest for social, academic, and economic purposes. In order to model maxima of random variables using extreme value theory, many assumptions have to be satisfied for the fitting of the generalized extreme value distribution to be appropriate. In particular, the underlying theory is asymptotic and based upon the maxima being drawn from independent and identically distributed random variables, but the length of our climate time series is limited and climate data typically exhibits substantial within-season autocorrelation. Here we explore the importance of such assumptions and the potential for mischaracterization of extremes as we relax these constraints. We use model data, real data, and synthetic data to further understand the limitations of our ability to understand and model extremes appropriately.