Compound extremes pose immense challenges and hazards to communities, and this is particularly true for compound hydrometeorological extremes associated with deadly floods, surges, droughts, and heat waves. To mitigate and better adapt to compound hydrometeorological extremes, we need to better understand the state of knowledge of such extremes. Here we review the current advances in understanding compound hydrometeorological extremes: compound heat wave and drought (hot-dry), compound heat stress and extreme precipitation (hot-wet), cold-wet, cold-dry and compound flooding. We focus on the drivers of these extremes and methods used to investigate and quantify their associated risk. Overall, hot-dry compound extremes are tied to subtropical highs, blocking highs, atmospheric stagnation events, and planetary wave patterns, which are modulated by atmosphere-land feedbacks. Compared with hot-dry compound extremes, hot-wet events are less examined in the literature with most works focusing on case studies. The cold-wet compound events are commonly associated with snowfall and cold frontal systems. Although cold-dry events have been found to decrease, their underlying mechanisms require further investigation. Compound flooding encompasses storm surge and high rainfall, storm surge and sea level rise, storm surge and riverine flooding, and coastal and riverine flooding. Overall, there is a growing risk of compound flooding in the future due to changes in sea level rise, storm intensity, storm precipitation, and land-use-land-cover change. To understand processes and interactions underlying compound extremes, numerical models have been used to complement statistical modeling of the dependence between the components of compound extremes. While global climate models can simulate certain types of compound extremes, high-resolution regional models coupled with land and hydrological models are required to simulate the variability of compound extremes and to project changes in the risk of such extremes. In terms of statistical modeling of compound extremes, previous studies have used empirical approach, event coincidence analysis, multivariate distribution, the indicator approach, quantile regression and the Markov Chain method to understand the dependence, greatly advancing the state of science of compound extremes. Overall, the selection of methods depends on the type of compound extremes of interests and relevant variables.
