Statistical perspectives on stratospheric transport

Abstract

Abstract. Many long-lived stratospheric chemical constituents enter the stratosphere through the tropical tropopause, are transported throughout the stratosphere by the Brewer-Dobson circulation, and are photochemically destroyed in the upper stratosphere. These chemical constituents, or "tracers," can be used to track mixing and transport by the stratospheric winds. Much of our understanding about the stratospheric circulation is based on large-scale gradients and other spatial features in tracer fields constructed from satellite measurements. The point of view presented in this paper is different, but complementary, in that transport is described in terms of tracer probability distribution functions. The probability distribution function is computed from the measurements and is proportional to the area occupied by tracer values in a given range. The flavor of this paper is tutorial, and the ideas are illustrated with several examples of transport-related phenomena, annotated with remarks that summarize the main point or suggest new directions. The examples illustrate how physically based statistical analysis can shed some light on aspects of stratospheric transport and dynamics that may not be obvious or quantifiable with other types of analyses. The dependence of the statistics on location and time is also shown to be important for practical problems related to statistical robustness and satellite sampling. An important motivation for the work presented here is the need for synthesis of the large and growing database of observations of the atmosphere and output generated by atmospheric models. INTRODUCTIONFor a comprehensive view of how the atmosphere works and how it responds to anthropogenic forcing over a range of length scales and timescales, we must look at both observational and model data from many different perspectives, using a variety of physically relevant analysis tools. Common among these are field maps that emphasize the patterns in field contours, the zonal mean structure of the field, and mean vertical profiles (see, for example, "Evaluation of the UARS Data," a special issue of Journal of Geophysical Research, 101 (D6), 9539-10, 476, 1996). There is no doubt about the value of these pictures in developing an understanding about stratospheric transport, particularly the spatial structure of a "tracer," a dynamical or chemical quantity that is conserved on the transport timescales of interest.Tracer-rich air enters the stratosphere in the tropics, where it is lofted to higher altitudes by the upwelling branch of the circulation. At high altitudes the air becomes depleted of tracer through photochemical loss, and tracer-poor air is then carried poleward and downward in the extratropics by the downwelling branch of •Also at NASA Goddard Space Flight Center, Greenbelt, There are also practical problems related to the collection and analysis of observations of the atmosphere and their comparison with models. Since models cannot be expected to reproduce all of the structural details in a tracer fiel...

From molecules to meteorology via turbulent scale invariance

“…Meteorological assimilation by operational weather forecasting models also shows such long-tailed PDFs, for example tropopause temperatures between 30 • N and 30 • S during northern winter, shown in Figure 2. Sparling (2000) has shown nonGaussian distributions prevailing in stratospheric satellite data. Non-Gaussian PDFs are also evident in the vertical from global positioning system (GPS) dropsonde data; see Hovde et al (2010).…”

Probability density functions of long-lived tracer observations from satellite in the subtropical barrier region: data intercomparison

“…Sparling, 2000;Palazzi and Fierli, 2010) to estimate the latitude of the subtropical boundary from the subtropical minimum in the probability distribution function (PDF) of a long-lived tracer χ, P (χ ). Given a set of observations of a tracer field χ , P (χ ) can be calculated as the fraction of observations having mixing ratios in the range from χ − χ to χ + χ in a given region of the atmosphere, normalized by the total area of the region.…”

“…Tracer PDFs represent an alternative to the use of mean tracer gradients with the advantage that they are less sensitive to the effects of the intrusions that can shift means and they allow avoiding latitudinal smearing without necessarily relying on equivalent latitude. Sparling (2000) discussed the global statistical properties of long-lived tracers PDFs using nitrous oxide (N 2 O) satellite measurements and introduced the statistics of the "support" region to calculate a single characteristic latitude for the barrier regions. This approach was then applied by Neu et al (2003) to identify the edges of the subtropical barrier and analyze their seasonal and interannual variability in the stratosphere, using N 2 O and CH 4 satellite measurements from the Cryogenic Limb Array Etalon Spectrometer (CLAES) and the Halogen Occultation Experiment (HALOE), respectively, both aboard the Upper Atmosphere Research Satellite (UARS).…”

“…Shuckburgh et al (2009) used the Lyapunov diffusivity diagnostic to investigate the seasonal and interannual variability of the transport and mixing structure of the Upper Troposphere Lower Stratosphere (UTLS) region. Sparling (2000) has advocated the use of probability distribution functions (PDFs) of long-lived tracers (i.e. the histogram of the tracer field) to quantify mixing regions and mixing barriers.…”

Variability of stratospheric mean age of air and of the local effects of residual circulation and eddy mixing

“…Therefore, the hemispheric probability distribution functions (pdfs) of simulated mean age for the respective level have been constructed for all months of the considered period. The minimum of the pdf indicates the mean age value at the transport barrier, from which the corresponding barrier latitude can be derived (for details, see Sparling [2000]). The transport barrier latitude shows a distinct undulation, consistent with the findings of Palazzi et al [2011] of a wintertime shift of the subtropical barrier toward the summer hemisphere during QBO westerly phase.…”