R. Alan Plumb

On the Three-Dimensional Propagation of Stationary Waves

Abstract A locally applicable (nonzonally-averaged) conservation relation is derived for quasi-geostrophic stationary waves on a zonal flow, a generalization of the Eliassen-Palm relation. The flux which appears in this relation constitutes, it is argued, a useful diagnostic of the three-dimensional propagation of stationary wave activity. This is illustrated by application to a simple theoretical model of a forced Rossby wave train and to a Northern Hemisphere winter climatology. Results of the latter procedure suggest that the major forcing of the stationary wave field derives from the orographic effects of the Tibetan plateau and from nonorographic effects (diabatic heating and/or interaction with transient eddies) in the western North Atlantic and North Pacific Oceans and Siberia. No evidence is found in the data for wave trains of tropical origin; forcing by the orographic effects of the Rocky mountains seems to be of secondary importance.

Interrelationships between mixing ratios of long-lived stratospheric constituents

Recent analyses have revealed simple relationships between the simultaneously measured mixing ratios of certain stratospheric constituents. In some cases, the relationship appears to be nearly linear, so that measured concentrations of one can be used to predict the other. We argue here that such relationships are to be expected for species of sufficiently long lifetime. Species whose local lifetimes are longer than quasi-horizontal transport time scales are in climatological slope equilibrium, i.e., they share surfaces of constant mixing ratio, and a scatter plot of the mixing ratio of one versus that of the other collapses to a compact curve whose slope at any point is the ratio of the net global fluxes of the two species through the corresponding surface of constant mixing ratio. Species whose local lifetimes are greater than vertical transport time scales are in gradient equilibrium and their mixing ratios display a linear relationship. For species whose atmospheric lifetimes are determined by removal in the stratosphere, the slope of this relationship in the lower stratosphere can be related to the ratio of their atmospheric lifetimes. These statements are illustrated using results from a two-dimensional chemistry-transport model.

Age as a diagnostic of stratospheric transport

Estimates of stratospheric age from observations of long-lived trace gases with increasing tropospheric concentrations invoke the implicit assumption that an air parcel has been transported intact from the tropopical tropopause. However, because of rapid and irreversible mixing in the stratosphere, a particular air parcel cannot be identified with one that left the troposphere at some prior time. The parcel contains a mix of air with a range of transit times, and the mean value over this range is the most appropriate definition of age. The measured tracer concentration is also a mean over the parcel, but its value depends both on the transit time distribution and the past history of the tracer in the troposphere. In principle, only if the tropospheric concentration is increasing linearly can the age be directly inferred. We illustrate these points by employing both a one-dimensional diffusive analog of stratospheric transport, and the general circulation model (GCM) of the Goddard Institute for Space Studies (GISS). Within the limits of the GCM, we estimate the time over which tropospheric tracer concentrations must be approximately linear in order to determine stratospheric age unambiguously; the concentration of an exponentially increasing tracer is a function only of age if the growth time constant is greater than about 7 years, which is true for all the chlorofluorocarbons. More rapid source variations (for example, the annual cycle in CO2) have no such direct relationship with age.

A “tropical pipe” model of stratospheric transport

A conceptual model of global stratospheric transport is described, based on the assumption of rapid isentropic mixing within midlatitude “surf zones” but weak mixing into the tropics. Thus the tropical region is isolated from middle latitudes, and trace species budgets there are balances between mean upwelling and local chemical sources and sinks. In middle latitudes, where long-lived species are assumed to be in “slope equilibrium,” the budgets are more complex, being influenced by isentropic mixing, mean downwelling, entrainment from the tropics, and local chemistry. The one-dimensional vertical flux-gradient relation obtained in previous studies in which mixing was assumed to be global is lost in this model. Tracer correlations are compact separately in each region, with substantial differences between tropical and midlatitude relationships. The result discussed by Plumb and Ko linking the slope of the correlation diagram to net global fluxes (and thus to lifetimes) is valid in this model only at the midlatitude tropopause.

Contour advection with surgery : a technique for investigating finescale structure in tracer transport

Abstract We present a trajectory technique, contour advection with surgery (CAS), for tracing the evolution of material contours in a specified (including observed) evolving flow. CAS uses the algorithms developed by Dritschel for contour dynamics/surgery to trace the evolution of specified contours. The contours are represented by a series of particles, which are advected by a specified, gridded, wind distribution. The resolution of the contours is preserved by continually adjusting the number of particles, and finescale features are produced that are not present in the input data (and cannot easily be generated using standard trajectory techniques). The reliability, and dependence on the spatial and temporal resolution of the wind field, of the CAS procedure is examined by comparisons with high-resolution numerical data (from contour dynamics calculations and from a general circulation model), and with routine stratospheric analyses. These comparisons show that the large-scale motions dominate the defor...

Evaluation of transport in stratospheric models

We evaluate transport characteristics of two- and three-dimensional chemical transport models of the stratosphere by comparing their simulations of the mean age of stratospheric air and the propagation of annually periodic oscillations in tracer mixing ratio at the tropical tropopause into the stratosphere to inferences from in situ and satellite observations of CO2, SF6, and water vapor. The models, participants in the recent NASA “Models and Measurements II” study, display a wide range of performance. Most models propagate annual oscillations too rapidly in the vertical and overattenuate the signal. Most models also significantly underestimate mean age throughout the stratosphere, and most have at least one of several unrealistic features in their mean age contour shapes. In the lower stratosphere, model-to-model variation in N2O, NOy, and Cly is well correlated with variation in mean age, and the magnitude of NOy and Cly variation is large. We conclude that model transport inaccuracies significantly affect simulations of important long-lived chemical species in the lower stratosphere.

Baroclinic Instability of the Summer Mesosphere: A Mechanism for the Quasi-Two-Day Wave?

Abstract Observations of the “quasi-two-day” wave are reviewed and it is concluded that the weight of evidence indicates that the wave is a solstical phenomenon, with maximum amplitudes in low latitudes of the summer mesosphere. It is suggested that the properties of this wave and of a similar wave found in a numerical model of the middle atmosphere may be consistent with an origin via baroclinic instability of the easterly jet in the summer mesosphere. This suggestion is supported by the results of a stability analysis of a one-dimensional model of the summer mesospheric flow.

Three-Dimensional Propagation of Transient Quasi-Geostrophic Eddies and Its Relationship with the Eddy Forcing of the Time—Mean Flow

Abstract An approximate theory is developed of small-amplitude transient eddies on a slowly varying time-mean flow. Central to this theory is a flux MT, which in most respects constitutes a generalization of the Eliassen–Palm flux to three dimensions; it is a conservable measure of the flux of eddy activity (for small amplitude transients) and is parallel to group velocity for an almost-plane wave train. The use of this flux as a diagnostic of transient eddy propagation is demonstrated by application of the theory to a ten-year climatology of the Northern Hemisphere winter circulation. Results show the anticipated concentration of eddy flux along the major storm tracks. While, in a suitably transformed system, MT may be regarded as a flux of upstream momentum, it is not a complete description of the eddy forcing of the mean flow; additional effects arise due to downstream transience (i.e., spatial inhomogeneity in the direction of the time-mean flow) of the eddy amplitudes. The relation between MT and the...

The Brewer-Dobson Circulation: Dynamics of the Tropical Upwelling

Abstract Recent advances in our understanding of the dynamics of the stratospheric circulation have led to the concepts of “downward control” and the “extratropical pump.” However, under the assumptions on which these concepts are based, midlatitude wave driving cannot explain the fact that mean stratospheric upwelling is located in the Tropics. Nevertheless, using a nonlinear two-dimensional model it is shown here that a steady and (in the lower stratosphere) linear circulation with a qualitatively reasonable upwelling can be produced, provided the wave drag extends to within about 20° of the equator. In a linear analysis of the problem, it is shown that the effects of weak model viscosity (some 50 times weaker than thermal relaxation) are crucial in permitting flow across angular momentum contours within a tropical boundary layer whose width is of order LRP1/4, where LR is the equatorial Rossby radius and P a Prandtl number (the ratio of radiative to viscous relaxation times). Provided the wave drag ext...

Age of air in a “leaky pipe” model of stratospheric transport

We discuss the characteristics of analytical solutions for the mean age of air in a simple, one-dimensional conceptual model of stratospheric transport. This “leaky pipe” model is a version of the “tropical pipe” model which has been modified to include detrainment of surf zone air into the tropics. We examine the dependence of the mean age on advection, diffusive mixing, and quasi-horizontal mixing between the surf zones and the tropics. In the absence of vertical diffusion across tracer mixing ratio isopleths the age difference between the tropics and midlatitudes does not depend on mixing across the edge of the tropics, but only on advection. The age difference given by this nondiffusive limit is an upper bound on the tropical-midlatitude age difference. This work provides some insight into the results of recent modeling studies that have used the mean age as a diagnostic of stratospheric transport.