Dry and moist convective upper bounds for extreme surface temperatures

How hot can heatwaves get in a given region of the world? The current pace of climate change challenges the statistical methods traditionally used to answer this question. An alternative approach is to seek a physics-based upper bound to extreme surface temperatures (T_s). Recent work proposed to address this problem using 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: that is, 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 is several degrees hotter. 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 with an extremely deep boundary layer and where a daytime superadiabatic layer develops near the surface. 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.