The Transit-Time Distribution from the Northern Hemisphere Midlatitude Surface

1. Introduction

The Northern Hemisphere (NH) midlatitude surface is a source of major greenhouse gases, ozone-depleting substances, tropospheric ozone (and its precursors), and aerosols. To better predict tropospheric air quality, stratospheric ozone depletion, and changes in Earth’s radiative balance, therefore, it is important to determine the factors that control the distributions of species emitted from NH midlatitudes. Trace gas distributions, however, are hard to interpret, owing to the complex interplay between species’ emissions, chemistry, and transport, which are difficult to disentangle even for long-lived species.

Partly owing to long-standing gaps in our understanding of tropospheric transport, climate models struggle to accurately represent present (and project future) distributions of a broad range of tropospheric trace gases and aerosols, including carbon monoxide, tropospheric ozone, and black carbon (e.g., Shindell et al. 2008; Young et al. 2013; Lee et al. 2013). Uncertainties in tropospheric transport persist largely because the transport circulation is not directly observable and reflects the complicated combination of the slow mean diabatic circulation and rapid isentropic mixing (Plumb and Mahlman 1987). Thus, while several studies have contributed significantly to our understanding of interhemispheric transport (e.g., Holzer 1999; Bowman and Erukhimova 2004), isentropic transport to the Arctic (e.g., Klonecki et al. 2003; Stohl 2006), and extratropical mixing (e.g., Leibensperger and Plumb 2014; Chen and Plumb 2014), many fundamental aspects of the tropospheric transport circulation remain poorly understood.

One fundamental aspect of transport that is important for understanding the distributions of species emitted in the NH is the time that it takes for transport to occur from the NH midlatitude surface to different regions in the troposphere. Waugh et al. (2013) used surface measurements of sulfur hexaflouride (SF₆) to infer the average time since the air in different regions in the troposphere last contacted the NH midlatitude surface or the “mean age.” The mean age, which is calculated for locations throughout the troposphere, provides a richer description of transport than the hemispherically integrated interhemispheric exchange time (e.g., Levin and Hesshaimer 1996; Geller et al. 1997) and presents the advantage that, while it is equal to the SF₆ age (Waugh et al. 2013), it can be calculated in models independent of SF₆. Thus, unlike the SF₆ age—which reflects intermodel differences in prescribed chemical emissions and is validated using SF₆ measurements that often vary between measurement datasets—the mean age is a tracer-independent diagnostic of the flow that is independent of any particular trace species (e.g., Holzer and Hall 2000; Haine and Hall 2002).

One limitation of the mean age is that it summarizes tropospheric transport in terms of a single time scale. Because of irreversible diffusive mixing, however, there is a broad range of times and paths for transport to occur from a region (here, the NH midlatitude surface), which can be summarized in terms of the transit-time distribution (TTD), where “transit time” refers to the elapsed time since last contact occurred at the surface (Holzer and Hall 2000). The TTD has been shown to be a far more powerful diagnostic than the mean age in understanding transport in the oceans (e.g., Primeau and Holzer 2006; Holzer and Primeau 2010) and the stratosphere, where it is commonly referred to as the age spectrum (Hall and Plumb 1994; Waugh and Hall 2002). By comparison, fewer studies have examined the TTD in the troposphere. Exceptions include a few studies that have used the TTD to examine interhemispheric exchange (Holzer and Boer 2001; Holzer 2009) and low-level transpacific transport (Holzer et al. 2003, 2005; Holzer and Hall 2007).

In addition to being a fundamental description of the flow, the TTD is also a propagator of boundary conditions applied over a control surface (in this case, the NH midlatitude surface, denoted throughout as ) (Hall and Plumb 1994; Holzer and Hall 2000). More precisely, the boundary propagator is a Green’s function that solves the continuity equation for the mixing ratio of a conserved and passive tracer, where is the receptor region, is the source time, or the time that tracer last had contact with , and t is the specific field time, or the time when tracer is sampled at . The boundary propagator can also be expressed in terms of the elapsed transit time τ [i.e., ].

The interpretation of the TTD as a boundary propagator can be seen by expressing the interior mixing ratio of a passive tracer by the following convolution:

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where the mixing ratio over the source region has been assumed to be uniform over (here ), and the decay term represents the special case of spatially uniform first-order loss acting at a constant time scale . Equation (1) shows that the TTD may be used to infer both the concentrations and chemical loss time scales of species that are difficult to measure directly, as has been done to infer total chlorine in the stratosphere (e.g., Waugh et al. 2001) and anthropogenic carbon dioxide in the oceans (e.g., Hall et al. 2002; Waugh et al. 2006; Khatiwala et al. 2009) as well to constrain global lifetimes of various chlorofluorocarbons (CFCs) and CFC replacement compounds (Holzer and Waugh 2015).

Another consequence of Eq. (1) is that the spatial patterns and time variations of tracers that are emitted over NH midlatitudes and subject to different loss rates are controlled by different properties of the TTD, such as its shape and temporal moments, which provide distinct summaries of how the air residing at is partitioned according to when it last contacted . This implies that suites of idealized loss tracers can be integrated in numerical models and used in combination to infer the TTD, which is not trivial to calculate in general circulation models, except under certain conditions (e.g., annually repeating cyclostationary flow).

Here, we present an analysis of the transit-time distribution connecting the NH midlatitude surface to the free troposphere, based on simulations of the NASA Global Modeling Initiative Chemistry Transport Model driven with MERRA meteorological fields. Our main goal is to present a rigorous tracer-independent description of transport from the NH midlatitude surface, which roughly corresponds to the region of largest emissions of greenhouse gases and ozone-depleting substances, and which we define here as surface latitudes spanning 30°–50°N. As such, our analysis focuses primarily on documenting the main properties of the TTD in terms of its characteristic time scales (section 3) and on using the TTD to infer transport pathways from the NH midlatitude surface to the free troposphere (section 4).

While our analysis focuses on one particular model, we note that the simulations in this study were performed as part of the International Global Atmospheric Chemistry (IGAC)/Stratospheric Processes and their Role in Climate (SPARC) Chemistry-Climate Model Initiative (CCMI). In section 5, therefore, we also explore the relationship between the TTD and idealized loss tracers that were requested by CCMI as standard model output and are similar in spirit to idealized carbon monoxide tracers that have been examined in previous studies (e.g., Shindell et al. 2008; Monks et al. 2015). Specifically, we examine the behaviors of tracers that are emitted uniformly over and subject to uniform exponential loss outside at rates of 5 and 50 days⁻¹ and are denoted throughout as the 5- and 50-day loss tracers and , respectively. The 5-day loss tracer mimics the loss experienced by a short-lived ozone-depleting substance like bromoform (Liang et al. 2010); by comparison, the 50-day loss tracer may be regarded as an idealization of carbon monoxide and ethane, which experience similar atmospheric loss and are important for determining the oxidizing capacity of the troposphere (Guenther et al. 2000). Following a brief exposition of the methodology in section 2, we present the model results in sections 3–5, followed by conclusions in section 6.

2. Methods

b. Idealized tracers

We examine two types of idealized tracers that are carried in the integration: 1) tracers that are used to infer the TTD and 2) tracers subject to spatially uniform exponential loss. All tracers’ boundary conditions are defined over the same zonally uniform surface NH midlatitude region , defined as the first model level spanning all grid points between 30° and 50°N. A summary of the tracers’ boundary conditions and sources is presented in Table 1.

Table 1.

Table of tracers integrated in the GMI–MERRA simulation. All tracers satisfy the tracer continuity equation, , in the interior of the atmosphere (i.e., outside of ), where is the linear advection–diffusion transport operator, and S denotes interior sources and sinks. Here, is taken to be the NH midlatitude surface , which is defined throughout as the first model level spanning latitudes between 30° and 50°N.

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1) TTD tracers

We construct the boundary propagator using four boundary impulse response (BIR) tracers, each of which corresponds to a particular instance (in ) of the boundary propagator (Haine et al. 2008). We use the pulse tracer method, which is direct and easy to implement, compared to the Lagrangian trajectory and Eulerian adjoint approaches used in Schoeberl et al. (2005) and Haine et al. (2008). More precisely, a pulse of a conserved and passive tracer is placed in at a specific source time , and the model’s time-evolving response is the BIR. Four BIRs are released at source times t′ = 1 January, 1 April, 1 July, and 1 October during the first year of the integration (2000) and integrated for 10 yr. Unlike in the stratosphere, where 20–30-yr integrations are needed to guarantee convergence everywhere (Schoeberl et al. 2005; Li et al. 2012), we find that 10 yr is more or less sufficient to capture the evolution of the BIR tracers in the troposphere: that is, their eventual exponential decay to zero at large transit times. To ensure that the long-term asymptotic behavior of the TTD is captured, however, we extrapolate the exponential tails for transit times τ > 10 yr.

After shifting each BIR at each grid cell about τ = 0, we treat the average of the centered BIRs as our approximation to the TTD, designated throughout as . (Note that after averaging we have dropped the explicit dependence on source time .) The resulting quantity is then normalized so that . Physically, the normalization of means that the total fraction [Eq. (1)] of air at had to last have contacted sometime in its history (Holzer and Hall 2000).

The TTD is summarized in section 3 in terms of its modal age , its first temporal moment (i.e., the mean transit time) , which is defined as

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and its second moment (i.e., the spectral width) , which is defined as

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Throughout, we refer to the mean transit time as the “mean age” for consistency with the presentation in Waugh et al. (2013), and this needs to be distinguished from the mean age presented in other studies (Ray et al. 1999; Engel et al. 2006; Patra et al. 2009), which conceptually are similar but are defined with respect to transport from the tropical tropopause or tropical surface, not the NH midlatitude surface layer.

One important caveat of our approach is that, while for unsteady flow the statistics of the TTD and the BIR are identical, the direct time-evolving product of the pulse tracer method is not the TTD (Holzer et al. 2003; Haine et al. 2008). In this study, however, we are interested in the annual-mean behavior of the TTD, for which represents a suitable approximation. We demonstrate this by comparing with the mean age derived from an idealized “NH clock” tracer that is initially set to a value of zero throughout the troposphere. Thereafter, it is held to be zero over and subject to a constant aging of 1 yr yr⁻¹ in the rest of the model surface layer and throughout the atmosphere (Waugh et al. 2013). The statistically stationary value of the clock tracer is equal to the mean age from the NH midlatitude surface and thus provides an independent check on . In accordance with its use in oceanographic applications, the mean age calculated from the clock tracer is hereafter referred to as the “ideal age” (e.g., Thiele and Sarmiento 1990; England 1995) and designated throughout as .

This distinction between the BIR approximation and the TTD becomes important when considering seasonal variations in the TTD or, more generally, for unsteady flows (Holzer et al. 2003; Haine et al. 2008). For flows that are not stationary, one can recover the TTD by constructing a boundary propagator map using a large number of BIR tracers (Holzer et al. 2003; Haine et al. 2008), an approach that can be simplified by assuming that interannual variations in transport are sufficiently small compared to seasonal variability (Li et al. 2012). More about the simplified BIR method and distinctions with the TTD can be found in these studies.

In addition to looking at annual averages of the modal age and the moments of the TTD, we examine their seasonal cycles in section 5. Note that we use the ideal age tracer , which depends explicitly on field time t, to infer seasonal variations in the mean age that otherwise would not be recoverable from the TTD-based mean age . Furthermore, the seasonal cycle of the modal age is defined with respect to source time and is constructed by linearly interpolating the BIR tracers to a monthly interval (in ), in order to accommodate for the fact that only four pulse tracers are carried in the simulation. It is important to note that the seasonal cycle of is not necessarily—and most often not—the same as . Hence, in section 5 we only examine in regions where the modal age is young and the TTD is skewed to young transit times—that is, in regions where most of the air residing at had recent contact at the surface —in effect rendering . As this approximation is crude, however, we take care in section 5 to ensure that only qualitatively guides our interpretation of the idealized loss tracers.

Finally, an alternative way to summarize the TTD is in terms of transport pathways inferred from the responses of the individual BIR tracers. First, we normalize each BIR to unity so that the integral of over transit times in the interval corresponds to the fraction of air at that left the midlatitude surface at time sometime in the interval . More precisely, we define the BIR fraction as

View Expanded

in order to provide a gross measure of the transport pathways that trace back to and how they depend on the time when last contact at the midlatitude surface occurred. BIR fractions are presented for the four source times in section 4.

2) Loss tracers

The idealized loss tracers and are emitted uniformly over and undergo spatially uniform exponential decay at loss rates of 5 and 50 days⁻¹, respectively. We analyze the decay tracer values in the last year of the integration (2010), at which point they have reached a statistically stationary state. Both tracers were requested as output variables in the CCMI model intercomparison, and our study therefore provides a framework for interpreting and in other models in terms of fundamental transport time scales.

Throughout, we normalize the 5- and 50-day tracer concentrations by their average concentrations over the NH midlatitude source region . This normalization ensures that the spatial patterns and amplitudes of the 5- and 50-day tracers, expressed throughout as percentages, can be meaningfully compared. Furthermore, we only consider normalized concentrations, and, for convenience, we refer to for τ_c = 5 and τ_c = 50 days simply as and , respectively. Throughout we use an asterisk to refer to normalization by .

3. Transit-time distribution

We first describe the shape of (or, simply, ) at different latitudes in the upper troposphere (Fig. 1, top row) and near the surface (Fig. 1, bottom row). Throughout the troposphere, is characterized by a peak at young transit times and by long flat tails. While the shape of the TTD is most asymmetric over NH high latitudes, the peak of the TTD shifts to older transit times moving equatorward and upward into the NH subtropical troposphere. In the Southern Hemisphere (SH) the TTD approaches a more symmetric distribution resembling an inverse Gaussian (IG). All signatures of fast transport disappear south of ~20°S, where by “fast” we mean relative to the mean of the TTD. For example, in the tropics, fast transport paths corresponds approximately to transit times τ < 50 days.

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The TTD since last contact at the NH midlatitude surface layer in (top) the upper troposphere (312 hPa) and (bottom) the lower troposphere (873 hPa). The TTD has been zonally averaged and evaluated in (left two columns) the SH and (right two columns) the NH. The red dashed and solid lines mark the modal age and mean age , respectively. The ratio of the spectral width and the mean age is shown in the top-right corner of each panel.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0289.1

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Changes in the shape of the TTD are reflected by changes in the relationship between the mean age [Fig. 2a; Eq. (2)], the modal age (Fig. 2b), and the spectral width [Fig. 2c; Eq. (3)]. (For convenience, the dependencies on and are suppressed throughout, except when they add clarity to the text.) We begin with the mean age, which increases from ~3 months at the NH mid- and high-latitude surface to ~1.8 yr at SH high latitudes. Note that is overall consistent with the annually averaged mean age calculated from the idealized NH-clock tracer, which indicates that the BIR pulse approximation reproduces the mean statistics of the TTD [Fig. A1; see also Fig. 7 in Waugh et al. (2013)].

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The (a) mean age , (b) modal age , and (c) spectral width , calculated from the approximation of the TTD . (d) The shape parameter . The thick dashed black line and gray contours denote the annually averaged climatological-mean thermal tropopause and isentropes, respectively (the 300-, 330-, and 360-K isentropes are shown). In all panels, the vertical axis ranges from 100 to 900 hPa, and the horizontal axis spans latitudes from 90°S to 90°N. Note the nonlinear color bar in (b).

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0289.1

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The largest gradients in span latitudes between 30°N and 30°S, with relatively weaker meridional gradients in the extratropics and middle and upper troposphere. In addition to large meridional variations in the extratropics, the mean age is characterized by positive (negative) vertical gradients in the NH (SH)—that is, younger upper-tropospheric air than near the surface in the SH—which is consistent with the fact that transport to the SH occurs primarily via the upper troposphere (e.g., Plumb and Mahlman 1987; Prather et al. 1987; Holzer 1999; Bowman and Erukhimova 2004). See section 4 below for more discussion.

Unlike the mean age, the modal age remains nearly uniform in the NH, ranging from a few days in the extratropics to only ~30 days at the equator (Fig. 2b). In the SH subtropics, increases sharply from ~30 days at the equator to ~150 days at 20°S, marking the disappearance of fast transport paths connecting back to the NH midlatitude surface . Correspondingly, it is interesting to contrast regions like the Arctic with the NH subtropical upper troposphere, where the modal ages are very similar (~5–10 days), while the mean age differs by as much as one year.

Unlike the modal age, the spectral width (Fig. 2c) features strong meridional gradients in the NH, where increases sharply from ~0.5 over high latitudes to ~1.1 at the equator and varies negligibly in the SH. In the NH extratropics, therefore, the large gradients in reflect large changes in . The fact that and vary with each other in the NH is expected, based on the behavior of the TTDs characteristic of the stratosphere and the ocean (Waugh et al. 2003). The close relationship between and , however, breaks down in the SH, where the large changes in instead reflect the rapid increase in , marking the absence of fast transport paths in the SH extratropics. As discussed in section 4, the disappearance of fast transport paths south of 20°S is related to the position of tropical convection.

The changing relationship between , , and between the hemispheres reflects the fact that transitions from a highly skewed distribution in the NH to an approximately inverse Gaussian in the SH. The systematics that relate , , and to changes in the shape of the TTD may be summarized in terms of the ratio Δ/Γ (here referred to as the shape parameter) (Fig. 2d). While the mean age merely sets the time scale for the dependence of on transit time, the combination of both and provides information on the shape in terms of how broad the TTD is relative to its mean.

In the NH, where Δ/Γ > 1, the TTD is broader (relative to mean age) than in the SH, where Δ/Γ < 1. Our physical interpretation of the broader TTD in the NH is that fast transport paths from , manifest as young modal ages (~5–10 days), result in a relatively lower mean age, while the tails of the TTD due to eddy-diffusive recirculations result in a broad tail. By comparison, in the SH fast transport paths from disappear (manifest as large gradients in ) and result in a TTD that is narrower relative to its mean, compared to in the NH. The decrease in from the southern tropics to the South Pole, as represented in the GMI–MERRA simulation, is consistent with the observed behavior of the spectral width and the mean age derived from measurements of SF₆, CFCs, and CFC replacement compounds (Holzer and Waugh 2015).

In the NH, the large gradients in align approximately with the isentropic boundary between the middleworld and the underworld, where Δ/Γ < ~1.5 and Δ/Γ > ~1.5, respectively. [The underworld is the region of the atmosphere where isentropes lie entirely in the troposphere, while the middleworld is the region of the atmosphere where isentropes cross the tropopause (Hoskins 1991).] Unlike in the SH, where changes in reflect changes in the modal age (i.e., the disappearance of fast transport paths), the large gradients in within the NH reflect changes in the tails of the TTD. Physically, the tails of the TTD reflect air that recirculates back into the NH underworld and can move isentropically back to the midlatitude surface, where it is stripped of its label. The probability that air is relabeled at the surface is much larger in the NH underworld (i.e., poleward of the ~300-K isentrope). As a result, in the underworld the tails of the TTD are much flatter than in the middleworld, reflecting only the small fraction of recirculating air parcels that survives recontact with .

4. Transport pathways

In the previous section, we showed that the relationship between the mean age, modal age and spectral width changes in the troposphere in concert with changes in the shape of the TTD, which we interpreted in terms of the disappearance of fast transport pathways (in the SH) and eddy-diffusive recirculations (in the NH underworld). We further examine this interpretation by explicitly examining the transport pathways that connect the NH midlatitude surface to the free troposphere, which we infer from the BIR fractions [hereinafter, simply ] [Eq. (4)]. For convenience, we refer to air that left the midlatitude surface at as air (i.e., “January air” or air that was last at on 1 January).

It is important to contrast with the path-density diagnostic introduced in Holzer (2009), which provides the joint probability of transit times and regions through which the air at passed since leaving and is a more rigorous, but also more computationally intensive, approach for diagnosing transport pathways. Nonetheless, by comparing the spatial patterns of evaluated over successive nonoverlapping transit-time intervals, we can obtain a gross sense for the paths along which air travels until its eventual return back to the NH midlatitude surface.

a. Fast transport pathways

The fast transport paths that trace back to depend sensitively on the source time when air last contacted the midlatitude surface. This is evident from the large spread between the individual BIRs that occurs for young transit times (Fig. 3). (Recall from section 3 that by “fast” we refer to transit times τ < 50 days.) For the particular flow and source times examined in the GMI–MERRA simulation, the largest differences between the BIRs occur over the Arctic and the tropics (Fig. 3, columns 2–4), which we now discuss separately. By comparison, the spread between the BIRs is relatively smaller over SH midlatitudes (Fig. 3, column 1) and negligible south of 30°S (not shown).

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The BIRs released over at source times = 1 Jan (blue), 1 Apr (cyan), 1 Jul (red), and 1 Oct (green), plotted with respect to the elapsed transit time . The responses are evaluated in (top) the upper troposphere (312 hPa) and (bottom) the lower troposphere (873 hPa). The black solid line shows the average of the BIRs .

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0289.1

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1) Arctic

The fastest transport paths into the Arctic are associated with air that leaves the NH midlatitude surface in January, with peaking at ~5–10 days throughout the Arctic troposphere (Fig. 3, column 4). By comparison, transport to the Arctic is relatively slower during boreal summer, as shown by the BIR , which peaks at ~10 days in the upper troposphere (312 hPa) and ~30 days near the surface (873 hPa). A comparison of the BIR fractions and evaluated over successive 10-day-transit-time bands spanning τ ∈ [1, 50] days, reveals that the young modal transit times during boreal winter reflect rapid isentropic transport to the upper Arctic, followed by diabatic descent to the surface (Figs. 4a–e).

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The zonal-mean BIR fraction corresponding to source times (a)–(e) = 1 Jan and (f)–(j) = 1 Jul. Here, is the fraction of air at that last contacted within the time interval and is calculated as . Transit-time bands span (left)–(right) 1–10, 11–20, 21–30, 31–40, and 41–50 days. Note that the horizontal axis extends from 40°S to 80°N.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0289.1

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The BIR-based indications of an “up and over” transport pathway from to the Arctic surface are consistent with previous Lagrangian-based studies that have shown that air parcels from midlatitudes tend to rise adiabatically to high latitudes before diabatically descending across isentropes over the pole (Stohl 2006; Law and Stohl 2007). Seasonal changes in isentropes at high latitudes—that form the so-called polar dome—have been invoked to interpret seasonal changes in the relative contributions of different midlatitude source regions to pollution transport into the Arctic (Stohl 2006).

In contrast to boreal winter, the fastest transport paths during summer connect the midlatitude surface to the midlatitude and subtropical upper troposphere. The patterns of the BIR fractions reveal that air initialized over is preferentially drawn upward and equatorward toward the subtropical upper troposphere before it moves poleward into the upper Arctic (Figs. 4f–j). Similar transport paths have been observed in both idealized tracers of airmass origin (Orbe et al. 2015) and carbon monoxide (Klonecki et al. 2003) and are consistent with enhanced summertime convection over the subtropics and midlatitudes.

2) Tropics and subtropics

Next, we discuss seasonal variations in the fast transport paths that connect the NH midlatitude surface region to the tropical and SH subtropical free troposphere (Fig. 3, columns 2–3). As discussed in section 3, the TTD in the NH subtropics and tropics is broader than in the SH extratropics because of the presence of fast cross-equatorial transport paths that extend to ~20°S, south of which . The evolution of the four BIR pulse tracers reveals that the fastest transport to the SH subtropical surface occurs during January, with peaking at ~30 days at 10°S. The fractions reveal that this rapid cross-equatorial transport reflects low-level convergence and ascent over the tropics and SH subtropics (Figs. 4a–e), consistent with the fact that during boreal winter the zonally averaged intertropical convergence zone (ITCZ) is in the SH, and surface inflow represents a fast path across the equator (e.g., Prinn et al. 1992; Holzer 1999; Bowman and Erukhimova 2004).

By comparison, the modal transit times in the SH subtropics corresponding to the other source times are much longer (~50–60 days). For example, the BIR fraction reveals that air that is released at the midlatitude surface during boreal summer largely avoids the deep tropics and reaches the tropical upper troposphere via the NH subtropics (Figs. 4f–j, 6a–d). This is consistent with the fact that trace gases of midlatitude origin are drawn into the ITCZ in the NH during boreal summer and enter the SH aloft via the upwelling branch of the Hadley cell (Holzer 1999).

Longitudinal sections of at 10°S (Figs. 5a–e) and maps of at 873 hPa, overlaid with the surface precipitation flux due to convection (Figs. 6a–d), more clearly illustrate the relationship between the position of the ITCZ and the rapid near-surface cross-equatorial transport during boreal winter. In particular, most of the air that arrives at 10°S within one month of leaving the midlatitude surface is concentrated over South America and the western Pacific, where the ITCZ is located farthest south and where strong surface winds prevail (Figs. 6a–d). Over the Indian Ocean, by comparison, surface convection is stronger but located farther north, ensuring that air released over is first picked up by convection before it reaches the SH subtropical surface.

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As in Fig. 4, but for the cross section at 10°S.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0289.1

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Maps of the BIR fractions at 873 hPa for source times (a)–(d) = January and (e)–(h) = July. The surface precipitation flux from convection is overlaid in the cyan contours and has been averaged over field times t corresponding to each panel, . The field-time-averaged winds at 873 hPa are also shown (black arrows). The transit-time bands are identical to those shown in Figs. 4 and 5 and span (top)–(bottom) 1–10, 11–20, 21–30, and 31–40 days. Only the last interval [i.e., days] is not shown.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0289.1

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Several studies have examined the relationship between cross-equatorial transport and the southward extent of tropical convection, invoking shifts in the ITCZ to interpret the seasonal cycles of surface SF₆ (Gloor et al. 2007) and mean age (Waugh et al. 2013; Holzer and Waugh 2015). By comparison, fewer studies have examined the underlying cross-equatorial transport pathways, especially in the upper troposphere. The BIR fractions evaluated for transit times τ ∈ (21, 50) days show that the air that left the midlatitude surface in January enters the SH over South America and the Indian Ocean (Figs. 5a–e). While the cross-equatorial paths over South America remain more or less confined below 200 hPa, the transport paths over the Indian Ocean extend higher, consistent with higher and stronger convective detrainment (Figs. 7a–d).

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As in Fig. 6, but for 164 hPa. The 164-hPa field-time-averaged reanalysis winds are shown in the black arrows.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0289.1

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During boreal summer there is a large increase in fast cross-equatorial transport above 200 hPa, with the fastest transport paths (i.e., τ ∈ [1, 10] days) passing through a narrow region over the Indian Ocean and relatively older transport paths (i.e., τ > 10 days) spanning a broader range of longitudes over the east Pacific (Figs. 5f–j). Maps of at 163 hPa (Figs. 7e–h) reveal that the rapid upper-tropospheric pathway over the Indian Ocean is consistent with advection by strong cross-equatorial winds at the southward edge of the monsoon anticyclone as far south as 30°S.

The rapid upper-tropospheric pathway over the Indian Ocean appears connected to the Asian monsoon. Previous studies have shown the important role of the Asian monsoon in supplying boundary layer constituents to the lower stratosphere (Park et al. 2004; Randel et al. 2010; Park et al. 2013; Bergman et al. 2013), but fewer studies have addressed the role of the monsoon in transporting NH surface air and trace species into the SH. How this occurs—via the meridional advection of convectively detraining air across the equator or through eddy-driven processes like the shedding of PV along the southward edge of the anticyclone (Popovic and Plumb 2001)—is not well understood and will be explored in future work.

b. Older transport pathways: Recirculation back into the Northern Hemisphere

In section 3, we discussed how large gradients in span the isentropic boundary between the middleworld and underworld in the NH, where the modal ages vary negligibly (Fig. 2b). We interpreted these changes in the shape of the TTD in terms of changes in the contribution of eddy-diffusive recirculations, with significantly weaker contributions in the underworld, where recirculating air parcels are more likely to move isentropically back to (and be relabeled at) the NH midlatitude surface. Similar signatures of a subtropical transport barrier in the NH middle and upper troposphere have been discussed in the context of Lagrangian-based approximations of the tropospheric transport climate (Bowman and Erukhimova 2004) and climatologies of carbon monoxide based on satellite data (Bowman 2006).

The BIR fractions evaluated for transit times between 3 months and 1 yr (Fig. 8) provide a gross sense for the advective-diffusive transport pathways that control the recirculation of air parcels between the hemispheres. Air that is released over in January, for example, is concentrated in the NH tropical upper troposphere within 3 months of leaving the surface (Fig. 8a). This is consistent with low-level convergence at the SH subtropics and ascent within the rising branch of the wintertime Hadley cell (Figs. 4a–d). The presence of strong horizontal gradients in in the NH subtropical upper troposphere is qualitatively consistent with the position of strong north–south gradients of potential vorticity at the subtropical jet stream that act as a barrier to meridional transport during late winter and early spring (here, t = March) (Mahlman 1997). Correspondingly, most of the mass is concentrated within the descending branch of the Hadley cell, providing a transport pathway back into the SH. Similar signatures of this path back into the SH through the Hadley cell appear in the 7–9-month-old fraction (Fig. 8g).

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The zonal-mean BIR fraction corresponding to source times (a)–(d) = 1 Jan and (e)–(h) = 1 July. Transit-time bands span (left)–(right) 3, 4–6, 7–9, and 10–12 months since air was released over . The corresponding field times are labeled above each panel. The thick dashed black line denotes the field-time-averaged thermal tropopause. Note that this figure is a continuation of Fig. 4 for all remaining transit times τ < 1 yr. For that reason, the upper limit on the color bar (20%) is different from than in Fig. 4 (30%).

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0289.1

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During boreal summer, by comparison, the mean sense of the circulation in the tropical upper troposphere acts to oppose transport back into the NH, which is reflected in the weak vertical gradients in that span the NH subtropics during the summer months (Figs. 8c,e). Nonetheless, reentry back into the NH may occur during summer via the lower stratosphere, as indicated by the weak horizontal gradients in that line the NH tropopause. Weaker horizontal gradients during boreal summer are consistent with a summertime relaxation in the lower-stratospheric tropical–extratropical mixing barrier (Chen 1995; Konopka et al. 2009), which enables air that left the midlatitude surface to reenter the NH troposphere above the subtropical jet (Figs. 8c,h).

It is more difficult to meaningfully infer pathways for τ > 1 yr, as older air parcels reflects more circuitous and less clearly defined paths, which is consistent with the diffusive nature of transport. Nonetheless, successive integrals of evaluated over older transit-time intervals (not shown) reveal that a large fraction of the air released at the midlatitude surface passes through the stratosphere before reentering the troposphere. This is qualitatively consistent with calculations of the interhemispheric transport pathways presented in Holzer (2009), who find that air at the SH surface has nearly a 20% probability of being found in the stratosphere since leaving the NH high-latitude surface.

We obtain a more quantitative measure of the importance of eddy-diffusive recirculations by fitting the tails of the TTD with an exponentially decaying mode . Here, refers to the eigentime of the lowest (i.e., slowest decaying) mode of the TTD and describes how fast transport alone can cause the eventual decay of the mixing ratio of a conserved tracer (Ehhalt et al. 2004). Exponential fits of the TTD for transit times larger than 10 yr reveal that τ ≈ 3 yr throughout the troposphere. This decay rate is similar to 2.8 yr, or the decay mode of stratospheric age spectra calculated using the free-running NASA chemistry climate model Goddard Earth Observing System Chemistry Climate Model (GEOSCCM; Li et al. 2012), and suggests that the long flat tails of the TTD most likely reflect air of stratospheric origin. The fact that is slightly older may indicate excessive mixing in the stratosphere in the GMI–MERRA integration, although we do not read much into this difference, as it is subtle and may partly reflect small differences in implementation between the studies. Further work is needed to quantitatively determine if this difference is statistically significant to separate out the stratospheric and tropospheric contributions to the tails of the TTD.

5. Idealized loss tracers

We now capitalize on the interpretation of the TTD as a propagator of chemical boundary conditions [Eq. (1)] in order to examine how short-lived tracers are controlled by different aspects of the TTD. Our approach is to examine the 5- and 50-day loss tracers, first in terms of their annually averaged distributions and (Fig. 9, top row), where the overbar denotes annual averages. Both the 5- and 50-day tracers decrease away from the source region and are largely concentrated in the NH. While is mainly confined to the NH underworld, however, extends into the tropics and SH subtropical upper troposphere.

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(top) The annually averaged concentrations of the (a) 5-day ( = 5 days) and (b) 50-day ( = 50 days) loss tracers, averaged over the last year of the integration and normalized by the -averaged surface concentration for each tracer . (bottom) Reconstructions of using Eq. (1) and the approximation to the TTD, The thick dashed black line and thin gray contours denote the annually averaged climatological-mean thermal tropopause and isentropes, respectively (the 300-, 330-, and 360-K isentropes are shown).

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0289.1

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To interpret the different spatial patterns of the idealized loss tracers in terms of the underlying TTD, we compare the spatial distributions of and with those of the mean age, the modal age, and the shape parameter (Figs. 2a,b,d). In the NH underworld, the pattern of (Fig. 9a, top panel) corresponds closely with the modal age (Fig. 2b), with both and featuring (relatively) strong horizontal gradients poleward of 60°N and a reversed vertical gradient over the pole, with larger (smaller) tracer concentrations (modal ages) in the upper troposphere compared to the surface. By comparison, varies weakly over the Arctic lower and middle troposphere (Fig. 9b, top panel).

There is also a close correspondence between the seasonality of the 5-day tracer and in the NH underworld (Fig. 10a, left column). [Note that in the overbar from the previous notation has been replaced with explicit dependence on field time t, and the asterisk denotes normalization by .] In particular, during boreal summer low concentrations of in the Arctic {large negative values of } correspond to large values of for the case of t′ = July. These low tracer concentrations reflect the disappearance of fast transport paths from the midlatitude surface during summer as isentropic transport weakens compared to during boreal winter (section 4).

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(a) The seasonal cycles of , , the modal age , and the mean age calculated from the ideal age tracer evaluated in the NH extratropics at 873 hPa. Note that the seasonal cycle of is shown with respect to pulse (source) time , while all other fields are expressed in terms of field time t. (b) As in (a), but evaluated over the NH and SH subtropics at 312 hPa. Note the different x axes in (a) and (b).

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0289.1

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By comparison, the seasonal cycle of the 50-day decay tracer is much weaker over the polar cap (Fig. 10a, right column) and more consistent with the seasonal cycle of the mean age inferred from the ideal age tracer (Fig. 10a, right column). This is because in the Arctic, where the TTD is highly asymmetric, the 50-day tracer and the mean age primarily reflect the long flat tails of the TTD and are not as sensitive to strong seasonal variations in the fast transport paths that control the shorter-lived 5-day tracer.

We can be more precise in describing the transition between a tracer with a strong seasonal cycle in the Arctic and a tracer with a weak seasonal cycle by looking at meridional profiles of at 712 hPa evaluated for spanning 5 days up to 1 yr (Fig. 11a). Here, has been constructed by propagating a uniform concentration (set to an arbitrary value) with our approximation to the TTD convolved with spatially uniform exponential loss [Eq. (1)]. In particular, we find that only species with τ_c ≤ 1 month exhibit strong meridional gradients in poleward of 60°N. By comparison, varies negligibly over the Arctic for species with chemical loss time scales > 3 months. Note that our use of the TTD to reconstruct the loss tracers is shown to be a reasonable approach in Fig. 9, where the reconstructions of and (Fig. 9, bottom row) correspond well with the explicitly simulated tracer concentrations (Fig. 9, top row), and gives us confidence that our approximation not only captures the mean age, but also other aspects of the TTD.

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The normalized concentrations evaluated at (a) 712 hPa and (b) 40°N for = 5 days (blue), = 1 week (black solid), = 1 month (black dashed), = 50 days (red), = 3 months (black circles), and = 1 yr (black asterisks). The normalized concentrations have been calculated using Eq. (1) and the approximation to the TTD .

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0289.1

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Outside of the NH underworld, the strong relationship between and breaks down in the NH subtropics and in the SH for different reasons. In the NH subtropics, is nearly negligible, despite the fact that the modal transit times are as young as in the Arctic ( ~ 5–10 days). This reflects the fact that the TTD is significantly narrower in the subtropics (relative to the mean age), compared to in the NH underworld (Figs. 1 and 2d). That is, in the NH middleworld the TTD is more evenly distributed over transit times τ > . The mass associated with short-τ transport paths in the NH middleworld therefore accounts for a much smaller fraction of the total integrated air mass, compared to in the underworld. Physically, the narrowing of the TTD (relative to the mean) in the NH middleworld reflects increases in the contributions of eddy-diffusive recirculations from the SH and the stratosphere (see discussion in section 4).

This point is illustrated more systematically by comparing vertical profiles of at 40°N (Fig. 11b). The largest spread between the tracer profiles occurs in the lower troposphere between species with short lifetimes (i.e., τ_c < 50 days); by comparison, in the upper troposphere (~300 hPa) the largest differences occur between species with lifetimes of 3 months and 1 yr. This reflects the fact that at 40°N the lower troposphere resides in the NH underworld, and the upper troposphere resides in the middleworld (Fig. 2d). In the lower troposphere, therefore, the TTD is skewed to young transit times, and only species with short chemical lifetimes will respond sensitively to changes in the fast transport pathways that trace back to the midlatitude surface. This is in contrast to the upper troposphere, where more of the air mass at a given location resides in the tails of the TTD.

The close correspondence between and also weakens in the SH subtropics, where the modal age increases sharply at ~20°S, reflecting the disappearance of fast transport paths (Fig. 2b). In the SH subtropical upper troposphere, therefore, where ≈ 30–60 days, the 5-day tracer simply does not survive transit to the SH, and the modal age is more important at controlling the pattern and time variations of (Fig. 10b). In particular, large seasonal variations in between 30°S and the equator reflect variations in the cross-equatorial transport paths in the upper troposphere that result in relatively young modal ages during boreal summer and are related to transport associated with the Asian monsoon (see section 4).

6. Conclusions

The main goal of this study has been to provide a rigorous analysis of transport from the NH midlatitude surface in terms of the transit-time distribution (TTD). In addition to documenting its main properties, we have also used the TTD to understand the spatial patterns and time variations of idealized loss tracers. To do this, we capitalized on the interpretation of the TTD as a propagator of chemical boundary conditions and focused on one class of idealized tracers: decay tracers subject to uniform exponential loss. Our analysis, based on calculations using the NASA GMI Chemistry Transport Model driven with MERRA meteorological fields, reveals the following:

• The mean transit time, or “mean age,” represents the average of a broad TTD that is characterized by long flat tails. This results in mean ages that are significantly larger than their corresponding modal transit times or “modal ages” .

• The shape of the TTD transitions from > 2 over NH high latitudes, to ~0.7 in the SH extratropics, where the TTD approaches a more symmetric distribution resembling an inverse Gaussian. Changes in in the NH are dominated by changes in the mean age, which increases from ~0.25 yr at high latitudes to ~1.25 yr in the subtropics, while remains nearly uniform. By comparison, changes in the shape of the TTD in the tropics and SH extratropics primarily reflect changes in the modal age, which increases sharply as fast surface transport paths disappear south of ~20°S.

• Physically, changes in the shape of the TTD signal changes in the contributions of fast transport pathways relative to slow eddy-diffusive recirculations. At the SH subtropical surface, large gradients in signal the disappearance of fast cross-equatorial transport paths; by comparison, large gradients in at the isentropic boundary between the NH middleworld and underworld reflect changes in eddy-diffusive recirculations.

• The spatial patterns and seasonal variations of idealized 5- and 50-day loss tracers ( and , respectively) are controlled by different aspects of the TTD. In the Arctic, corresponds closely to the modal age and has a strong seasonal cycle that reflects changes in fast isentropic transport from the midlatitude surface. The correspondence between and , however, weakens in regions where fast transport paths contribute less mass to the TTD, such as in the NH middleworld and the SH extratropics. In the SH subtropical upper troposphere, for example, the distribution of corresponds more closely to that of the 50-day loss tracer , which varies in concert with seasonal changes in upper-tropospheric cross-equatorial flow associated with the Asian monsoon.

One important caveat in our study is that our results represent the transport climate of one model, and our analysis will need to be repeated for other chemistry transport models and chemistry–climate models. Our focus in section 5 on the idealized loss tracers that were requested in the CCMI model intercomparison will provide an immediate opportunity to perform such a comparison. Our illustrations with the GMI–MERRA simulation, therefore, provide a benchmark for interpreting the 5- and 50-day idealized loss tracers in terms of fundamental TTD time scales that may be useful when assessing transport in models. In particular, the fact that and correspond closely in the tropical upper troposphere (fourth conclusion above) suggests that one way to assess the representation of fast cross-equatorial transport pathways inferred from the BIR pulse tracers in the GMI–MERRA simulation will be to compare time variations in between the CCMI models.

Another application of the idealized tracers that was not explored here but will be examined in future work is to identify real species that may be idealized as and and can provide observational constraints on the modal age and other aspects of the TTD. In particular, the nonmethane hydrocarbons butane, benzene, and propane, which have approximate lifetimes of 5, 8, and 10 days⁻¹, respectively, may represent a way to constrain the modal age in the NH. Several assumptions, however, need to first be tested before using idealized loss tracers to constrain the TTD, including our use of a simplified zonally averaged source region and the idealization of chemical loss as exponential decay. These will be examined in future work.