Extreme events, such as drought, heat wave, cold wave, flood, and extreme rainfall, have received increasing attention in recent decades due to their wide impacts on society and ecosystems. Meanwhile, the compound extremes (i.e., the simultaneous or sequential occurrence of multiple extremes at single or multiple locations) may exert even larger impacts on society or the environment. Thus, the past decade has witnessed an increasing interest in compound extremes. In this study, we review different approaches for the statistical characterization and modeling of compound extremes in hydroclimatology, including the empirical approach, multivariate distribution, the indicator approach, quantile regression, and the Markov Chain model. The limitation in the data availability to represent extremes and lack of flexibility in modeling asymmetric/tail dependences of multiple variables/events are among the challenges in the statistical characterization and modeling of compound extremes. Major future research endeavors include probing compound extremes through both observations with improved data availability (and statistical model development) and model simulations with improved representation of the physical processes to mitigate the impacts of compound extremes.
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