Dry and moist convective upper bounds for near-surface temperatures

Abstract. The current pace of climate change challenges the statistical methods used for bounding heatwave intensities, prompting the need for a physics-based upper bound to extreme surface temperatures (T_s). A recently proposed approach for deriving such a bound uses the hypothesis that convective instability limits the development of heat extremes. Here, we show that under this hypothesis, the absolute upper bound for extreme T_s — obtained in the limit of zero surface humidity — is set by dry convection. This bound is reached when the mid-troposphere and the surface are connected by a dry adiabat. Previous work suggested that this upper bound is instead set by moist convective instability and exceeds the dry convective limit. We resolve this discrepancy by showing that moist convection only limits heatwave development when surface specific humidity is larger than a threshold, and that the moist convective upper bound cannot exceed the dry limit. Yet, numerous temperature profiles in observational and reanalysis records do exceed the dry convective limit. We show that these occur exclusively in regions where daytime superadiabatic layers develop near the surface and the boundary layer top reaches deep into the mid-troposphere. Our work underscores the need for a finer understanding of the structure of dry convective boundary layers to constrain the intensity of future heatwaves. We conclude with an overview of the different upper bounds applicable in dry and moist scenarios, including the roles of processes such as entrainment and convective inhibition.