Advective‐diffusive mass flux and implications for stratosphere‐troposphere exchange

Abstract

[1] We show that the flux of mass crossing in one direction (the ''gross'' flux) through any specified surface S that divides anadvective-diffusive flow in a closed domain is infinite. That is, the flux, F (t), through S of the fluid mass that spent at least time t on one side of S diverges like t À1/2 as t ! 0, in the continuum limit. The gross flux is completely dominated by fluid elements residing infinitesimally short times on one side of S before re-crossing to the other side. This general result puts into context the widely varying estimates of gross mass flux across the midlatitude tropopause. Such estimates are dominated by the smallest resolved scales, leading us to conclude that gross mass flux is not a useful diagnostic of stratosphere-troposphere exchange. The function F (t), however, provides important information on transport across the tropopause.

The Path Density of Interhemispheric Surface-to-Surface Transport. Part I: Development of the Diagnostic and Illustration with an Analytic Model

“…Plumb and McConalogue (1988) emphasized that the mixing ratio at a given point is determined by an admixture of fluid elements, each of which will generally have taken a different path from the source. More recent analyses using transport Green functions show that the lag in mixing ratio between the hemispheres can be understood in terms of the moments of the distribution of times since last contact with the source region (e.g., Hall and Plumb 1994;Holzer and Boer 2001).…”

Stratosphere‐troposphere exchange: A review, and what we have learned from STACCATO

“…For other implementations the net cross-tropopause fluxes, if averaged over great time or space scales, may be sufficiently accurate, but estimates for the instantaneous local STT or TST fluxes are very uncertain [Kowol-Santen et al, 2000], as they are highly sensitive to intrinsic parameters [Gettelman and Sobel, 2000]. Recently, Hall and Holzer [2003] have shown that for advective-diffusive flows the ''gross'' STT and TST fluxes are actually infinite, if no residence time limits in the troposphere and stratosphere are specified, thus explaining the great sensitivity of these fluxes to the numerical implementation of the diagnostic. With too much spatial or temporal averaging, on the other hand, the advantage of having a better resolution than global estimates is almost lost.…”

A new global real-time Lagrangian diagnostic system for stratosphere-troposphere exchange: evaluation during a balloon sonde campaign in eastern Canada

“…The residence time criterion requires the trajectories to stay for at least 12 h in the stratosphere and in the troposphere, just before/after the exchange time. This criterion efficiently avoids the selection of trajectories that oscillate around the tropopause due to numerical noise (Bourqui, 2006), and at the same time it eliminates the singularity problem of one-way STE fluxes (Hall and Holzer, 2003). This selection of trajectories reduces the number of trajectories that need to be considered by a factor of 100, from around 15 million to 150 000.…”

“…Bourqui (2006) suggests that consideration of hourly meteorological fields with horizontal resolution 0.5 × 0.5 • is necessary to resolve the most important contributions from these processes on STE. Furthermore, the nature of the separate S→T and T→S mass fluxes is such that they become infinite at infinitely small scales (Hall and Holzer, 2003). In a finite-grid representation, these fluxes are essentially determined by the smallest resolved scales and therefore do not provide relevant information on STE.…”

“…This ill-defined character is probably responsible for a good part of the large range of estimates of separated STE fluxes found in the literature (e.g., Hoerling et al, 1993;Gettelman and Sobel, 2000;Sprenger and Wernli, 2003). To render the fluxes well-defined, it is necessary to include an explicit scale constraint such as the residence time (Wernli and Bourqui, 2002;Hall and Holzer, 2003;Bourqui, 2006). In such a case, the parcel is required to reside on either side of the tropopause for a time interval larger than a given threshold.…”