Comments on some recent measurements of anomalously steep N2O and O3tracer spectra in the stratospheric surf zone

Recent aircraft measurements, primarily in the extratropics, of the horizontal variance of nitrous oxide (N2O) and ozone (O3) in the middle stratosphere indicate that horizontal spectra of the tracer variance scale nearly as k−2, where k is the spatial wavenumber along the aircraft flight track [Strahan and Mahlman, 1994; Bacmeister et al., 1996]. This spectral scaling has been regarded as inconsistent with the accepted picture of stratospheric tracer motion; large-scale quasi-two-dimensional tracer advection typically yields a k−1 scaling (i.e., the classical Batchelor spectrum). In this paper it is argued that the nearly k−2 scaling seen in the measurements is a natural outcome of quasi-two-dimensional filamentation of the polar vortex edge. The accepted picture of stratospheric tracer motion can thus be retained: no additional physical processes are needed to account for deviations from the Batchelor spectrum. Our argument is based on the finite lifetime of tracer filaments and on the “singularity spectrum” associated with a one-dimensional field composed of randomly spaced jumps in concentration.

Transport in the middle atmosphere

An overview is provided of the current understanding of transport in the middle atmosphere. Over the past quarter century this subject has evolved from a basic recognition of the Brewer-Dobson circulation to a detailed appreciation of many key features of transport such as the stratospheric surf zone, mixing barriers and the dynamics of filamentation. Whilst the elegant theoretical framework for middle atmosphere transport that emerged roughly twenty years ago never fulfilled its promise, useful phenomenological models have been developed together with innovative diagnostic methods. These advances were made possible by the advent of plenty of satellite and aircraft observations of long-lived chemical species together with developments in data assimilation and numerical modeling, and have been driven in large measure by the problem of stratospheric ozone depletion. This review is primarily focused on the stratosphere, where both the interest and the knowledge are the greatest, but a few remarks are also made on the mesosphere.

Planetary-wave-induced transport in the stratosphere

In the stratosphere, chemical tracers are drawn systematically from the equator to the pole. This observed Brewer–Dobson circulation is driven by wave drag, which in the stratosphere arises mainly from the breaking and dissipation of planetary-scale Rossby waves. While the overall sense of the circulation follows from fundamental physical principles, a quantitative theoretical understanding of the connection between wave drag and Lagrangian transport is limited to linear, small-amplitude waves. However, planetary waves in the stratosphere generally grow to a large amplitude and break in a strongly nonlinear fashion. This paper addresses the connection between stratospheric wave drag and Lagrangian transport in the presence of strong nonlinearity, using a mechanistic three-dimensional primitive equations model together with offline particle advection. Attention is deliberately focused on a weak forcing regime, such that sudden warmings do not occur and a quasi-steady state is reached, in order to examine this question in the cleanest possible context. Wave drag is directly linked to the transformed Eulerian mean (TEM) circulation, which is often used as a surrogate for mean Lagrangian motion. The results show that the correspondence between the TEM and mean Lagrangian velocities is quantitatively excellent in regions of linear, nonbreaking waves (i.e., outside the surf zone), where streamlines are not closed. Within the surf zone, where streamlines are closed and meridional particle displacements are large, the agreement between the vertical components of the two velocity fields is still remarkably good, especially wherever particle paths are coherent so that diabatic dispersion is minimized. However, in this region the meridional mean Lagrangian velocity bears little relation to the meridional TEM velocity, and reflects more the kinematics of mixing within and across the edges of the surf zone. The results from the mechanistic model are compared with those from the Canadian Middle Atmosphere Model to test the robustness of the conclusions.

A closer look at chaotic advection in the stratosphere: part I: geometric structure

The relevance of chaotic advection to stratospheric mixing and transport is addressed in the context of (i) a numerical model of forced shallow-water flow on the sphere, and (ii) a middle-atmosphere general circulation model. It is argued that chaotic advection applies to both these models if there is suitable large-scale spatial structure in the velocity field and if the velocity field is temporally quasi-regular. This spatial structure is manifested in the form of “cat’s eyes” in the surf zone, such as are commonly seen in numerical simulations of Rossby wave critical layers; by analogy with the heteroclinic structure of a temporally aperiodic chaotic system the cat’s eyes may be thought of as an “organizing structure” for mixing and transport in the surf zone. When this organizing structure exists, Eulerian and Lagrangian autocorrelations of the velocity derivatives indicate that velocity derivatives decorrelate more rapidly along particle trajectories than at fixed spatial locations (i.e., the velocity field is temporally quasi-regular). This phenomenon is referred to as Lagrangian random strain.