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Abstract

Droughts and heatwaves are among the most damaging climate extremes, and their increasing co-occurrence poses a growing risk under global warming. Traditionally studied as distinct phenomena, both hazards arise from tightly coupled atmospheric and land-surface processes that operate across scales. Here we argue that understanding compound drought–heatwave events requires a shift from local Eulerian descriptions toward a Lagrangian process-based view of atmospheric connectivity, moisture transport, energy accumulation and land–atmosphere feedbacks. Based on recent findings, drought severity depends not only on precipitation deficits but also on disruptions in moisture transport, rising atmospheric evaporative demand, land evaporation, and soil-moisture–temperature coupling, while heatwaves reflect the combined effects of background warming, large-scale circulation anomalies, diabatic and adiabatic warming, and surface energy partitioning. We highlight how Lagrangian diagnostics of moisture and heat transport provide a unifying framework to identify causal pathways, disentangle physical mechanisms, and distinguish shared from independent drivers of compound drought and heatwave extremes. Integrating moisture and heat tracking offers new opportunities for improved attribution, early warning, and physically grounded projections of compound drought–heatwave risk in a warming climate through process-dependent analyses derived from shared atmospheric trajectory ensembles. However, important methodological challenges remain, including uncertainty propagation, framework dependence, and the difficulty of jointly resolving coupled moisture–heat pathways across scales.