How heating tracers drive self-lofting long-lived stratospheric anticyclones: simple dynamical models

Abstract. Long-lived `bubbles' of wildfire smoke or volcanic aerosol have recently been observed in the stratosphere, co-located with ozone, carbon monooxide, and water vapour anomalies. These bubbles often survive for several weeks, during which time they ascend through vertical distances of 15 km or more. Meteorological analysis data shows that the smoke or aerosol is contained within strong, persistent anticyclonic vortices. Absorption of solar radiation by the smoke or aerosol is hypothesised to drive the ascent of the bubbles, but the dynamics of how this heating gives rise to a single-sign anticyclonic vorticity anomaly has thus far been unclear. We present a description of heating-driven stratospheric vortices, based on an axisymmetric balanced model. A highly simplified model includes a specified localised heating moving upwards at fixed velocity and produces a steadily translating solution with a single-signed anticyclonic vortex co-located with the heating, with corresponding temperature anomalies forming a vertical dipole, matching observations. A more complex model includes the two-way interaction between a heating tracer, representing smoke or aerosol, and the dynamics. An evolving tracer provides heating which drives a secondary circulation and this in turn transports the tracer. Through this two-way interaction an initial distribution of tracer drives a circulation and forms a self-lofting tracer-filled anticyclonic vortex. Scaling arguments show that upward velocity is proportional to heating magnitude, but the magnitude of peak vorticity is O(f ) (f  is the Coriolis parameter) and independent of the heating magnitude. Estimates of peak vertical velocity and vorticity from observations match our theoretical predictions. We discuss 3D effects such as vortex stripping and dispersion of tracer outside the vortex by the large-scale flow which cannot be captured explicitly by the axisymmetric model. The large O(f ) vorticity of the fully developed anticyclones explains their observed persistence and their effective confinement of tracers. To further investigate the early stages of formation of tracer-filled vortices, we consider an idealised configuration of a homogeneous tracer layer. A linearised calculation reveals that the upper part of the layer is destabilised due to the decrease in tracer  concentrations with height there, which sets up a self-reinforcing effect where upward lofting of tracer results in stronger heating and hence stronger lofting. Small amplitude disturbances form isolated tracer plumes that ascend out of the initial layer, indicative of a self-organisation of the flow. The relevance of these idealised models to formation and persistence of tracer-filled vortices in the real atmosphere is discussed and it is suggested that a key factor in their formation is the time taken to reach the fully-developed stage, which is shorter for strong heating rates.