Thermally forced updrafts over small hills

Thermally forced circulations driven by elevated mountain heating are critically important for initiating moist convection and regulating boundary-layer air quality. However, because of their formidable physical complexity, they remain inadequately understood. Although linear theory has shown promise for advancing this understanding, it thus far has only been used in highly idealized situations with limited real-world relevance. The current study advances this theory by considering more complex and realistic basic-state flows, which allow for the representation of a convective boundary layer as well as diabatic heating in a mid-level cloud layer. Focus is placed on the updrafts that form directly over mountain crest (aka the “convective cores”), which are typically responsible for cloud initiation. Non-dimensional parameters are derived to establish the boundaries of validity of linear theory and to categorize flows into four regimes based on boundary-layer stability, upstream winds, and the mountain geometry. These parameters quantify the sensitivity of the convective cores to a range of physically relevant parameters. The cores are found to be highly sensitive is found to the ambient winds and boundary-layer depth, which agrees with empirical results but was previously unexamined by linear theory. The feedback between the convective core and diabatic heating above it (associated with shallow moist convection) is found to strongly depend on the mountain dimensions. Idealized numerical simulations are presented to reinforce the linear results and identify the sensitivities that carry over to the nonlinear regime.