Unsurprising Surprises: The Frequency of Record‐breaking and Overthreshold Hydrological Extremes Under Spatial and Temporal Dependence

Record‐breaking (RB) events are the highest or lowest values assumed by a given variable, such as temperature and precipitation, since the beginning of the observation period. Research in hydroclimatic fluctuations and their link with this kind of extreme events recently renewed the interest in RB events. However, empirical analyses of RB events usually rely on statistical techniques based on too restrictive hypotheses such as independent and identically distributed ( i / i d ) random variables or nongeneral numerical methods. In this study, we propose some exact distributions along with accurate approximations describing the occurrence probability of RB and peak‐over‐threshold (POT) events under general spatiotemporal dependence, which enable analyses based on more appropriate assumptions. We show that (i) the Poisson binomial distribution is the exact distribution of the number of RB events under i / i d , (ii) equivalent binomial distributions are accurate approximations under i / i d , (iii) beta‐binomial distributions provide the exact distribution of POT occurrences under spatiotemporal dependence, and (iv) equivalent beta‐binomial distributions provide accurate approximations for the distribution of RB occurrences under spatiotemporal dependence. To perform numerical validations, we also introduce a generator of spatially and temporally correlated binary processes, called BetaBitST. As examples of application, we study RB and POT occurrences for monthly precipitation and temperature over the conterminous United States and reanalyze Mauna Loa daily temperature data. Results show that accounting for spatiotemporal dependence yields strikingly different conclusions, making the observed frequencies of RB and POT events much less surprising than expected and calling into question previous results reported in the literature.