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## Abstract

Tracers without feedback on the atmosphere are used to probe tropospheric transport. Such passive tracers are considered for two important anthropogenic sources, Europe and eastern North America. The linearity of passive tracer continuity allows transport to be formulated in terms of a Green function, *G.* A coarse-grained Green function is defined that is suitable for numerical investigation with a GCM. An ensemble of independent realizations of the atmosphere is used to obtain the model’s ensemble mean, or “climate” Green function. With increasing time, the individual realizations of *G* converge to their climate mean and this convergence is quantified in terms of the decay of ensemble fluctuations. Throughout, *G* is analyzed with the goal of gaining new insight into the tracer climate that results from constant sources.

The climate Green function is used to identify transport timescales, pathways, and mechanisms. The Green function is zonally mixed after about 3 months. The time to mix *G* to within 10% of its asymptotic value exceeds 1 yr at high-latitude lower levels, while the interhemispheric two-box exchange time is ∼7 months. Tracers from Europe and eastern North America follow different pathways with distinct seasonality. Eddies play a key role in transport. Transport in the Southern Hemisphere is dominated by transient eddies resulting from tracer injected ∼4 months earlier. These transient eddies extend throughout much of the troposphere, and align to a large degree with contours of zonally averaged mixing ratio. Large seasonal changes of the mean-motion part of the tracer flux are primarily compensated by the standing-eddy transport. Ensemble fluctuations of *G* decay with an approximate *t*
^{−3} power law. Eddy conversion provides a source of fluctuations, while dissipation damps ensemble fluctuations with a timescale of ∼10 days. In the GCM context, the relative importance of parameterized versus resolved vertical transport is examined.

## Abstract

Tracers without feedback on the atmosphere are used to probe tropospheric transport. Such passive tracers are considered for two important anthropogenic sources, Europe and eastern North America. The linearity of passive tracer continuity allows transport to be formulated in terms of a Green function, *G.* A coarse-grained Green function is defined that is suitable for numerical investigation with a GCM. An ensemble of independent realizations of the atmosphere is used to obtain the model’s ensemble mean, or “climate” Green function. With increasing time, the individual realizations of *G* converge to their climate mean and this convergence is quantified in terms of the decay of ensemble fluctuations. Throughout, *G* is analyzed with the goal of gaining new insight into the tracer climate that results from constant sources.

The climate Green function is used to identify transport timescales, pathways, and mechanisms. The Green function is zonally mixed after about 3 months. The time to mix *G* to within 10% of its asymptotic value exceeds 1 yr at high-latitude lower levels, while the interhemispheric two-box exchange time is ∼7 months. Tracers from Europe and eastern North America follow different pathways with distinct seasonality. Eddies play a key role in transport. Transport in the Southern Hemisphere is dominated by transient eddies resulting from tracer injected ∼4 months earlier. These transient eddies extend throughout much of the troposphere, and align to a large degree with contours of zonally averaged mixing ratio. Large seasonal changes of the mean-motion part of the tracer flux are primarily compensated by the standing-eddy transport. Ensemble fluctuations of *G* decay with an approximate *t*
^{−3} power law. Eddy conversion provides a source of fluctuations, while dissipation damps ensemble fluctuations with a timescale of ∼10 days. In the GCM context, the relative importance of parameterized versus resolved vertical transport is examined.

## Abstract

Interhemispheric transport from the earth’s surface north of 32.4°N (region Ω*
_{N}
*) to the surface south of 32.4°S (region Ω

*) is quantified using the path-density diagnostic developed in Part I of this study. The path density is computed using the Model of Atmospheric Transport and Chemistry (MATCH) driven by NCEP reanalyses. The structure of both the Ω*

_{S}*→ Ω*

_{N}*and Ω*

_{S}*→ Ω*

_{N}*zonally averaged path densities is examined in detail for air that had last Ω*

_{N}*contact (“Ω*

_{N}*air”) during January and July. The path density provides the joint probability that Ω*

_{N}*air will make its next surface contact with either Ω*

_{N}*or Ω*

_{N}*, that it will have surface-to-surface transit time*

_{S}*τ*∈ (

*τ*,

*τ*+

*dτ*), and that it can be found in volume element

*d*

^{ 3}

*r*during its surface-to-surface journey. The distribution of surface-to-surface transit times, the probability of Ω

*air making next contact with Ω*

_{N}*, and the probability of finding Ω*

_{S}*air destined for Ω*

_{N}*in the stratosphere are computed from suitable integrations of the path density. Approximately one-third of the Ω*

_{S}*air undergoes interhemispheric transport to Ω*

_{N}*, with a ∼20% probability of being found in the stratosphere during its surface-to-surface journey. The stratospheric fraction has about equal contributions from the part of the stratosphere that is isentropically isolated from the troposphere and from the part that is isentropically connected to the troposphere (i.e., from the overworld and the stratospheric middleworld in the terminology of Hoskins). The flow rate through the stratospheric middleworld is about twice as large as the flow rate through the overworld.*

_{S}## Abstract

Interhemispheric transport from the earth’s surface north of 32.4°N (region Ω*
_{N}
*) to the surface south of 32.4°S (region Ω

*) is quantified using the path-density diagnostic developed in Part I of this study. The path density is computed using the Model of Atmospheric Transport and Chemistry (MATCH) driven by NCEP reanalyses. The structure of both the Ω*

_{S}*→ Ω*

_{N}*and Ω*

_{S}*→ Ω*

_{N}*zonally averaged path densities is examined in detail for air that had last Ω*

_{N}*contact (“Ω*

_{N}*air”) during January and July. The path density provides the joint probability that Ω*

_{N}*air will make its next surface contact with either Ω*

_{N}*or Ω*

_{N}*, that it will have surface-to-surface transit time*

_{S}*τ*∈ (

*τ*,

*τ*+

*dτ*), and that it can be found in volume element

*d*

^{ 3}

*r*during its surface-to-surface journey. The distribution of surface-to-surface transit times, the probability of Ω

*air making next contact with Ω*

_{N}*, and the probability of finding Ω*

_{S}*air destined for Ω*

_{N}*in the stratosphere are computed from suitable integrations of the path density. Approximately one-third of the Ω*

_{S}*air undergoes interhemispheric transport to Ω*

_{N}*, with a ∼20% probability of being found in the stratosphere during its surface-to-surface journey. The stratospheric fraction has about equal contributions from the part of the stratosphere that is isentropically isolated from the troposphere and from the part that is isentropically connected to the troposphere (i.e., from the overworld and the stratospheric middleworld in the terminology of Hoskins). The flow rate through the stratospheric middleworld is about twice as large as the flow rate through the overworld.*

_{S}## Abstract

As a characterization of the variability of observed geopotential height fluctuations, their probability density function (PDF) and its skewness are studied in the global domain for winter and summer. The PDF of the geopotential, Φ, is skewed toward low anomalies at midiatitudes and toward high anomalies in polar and tropical regions. When Φ is filtered spatially by discarding planetary wavenumbers less than ∼8, the skewness is small in the Tropics and in polar regions and large and negative in zonal bands approximately centered on the latitudes of the climatological jets. Where the skewness is large and negative, the zonally averaged PDF of Φ has an approximately exponential tail for negative anomalies.

From a diagnostic study based on computing Φ from the observed winds through the balance equation, the negative skewness bands can clearly be attributed to the rectification of near-symmetric velocity fluctuations by the advective nonlinearity. This mechanism implies that where winds are highly variable, large synoptic-scale negative Φ anomalies are more likely than large positive Φ anomalies. The maximum of the (negative) zonally averaged skewness in the summer hemisphere tends to be larger than that in the winter hemisphere, and in both hemispheres these maxima lie ∼150 mb below the velocity variance maxima. The fact that skewness extrema do not precisely match maxima in the nonlinearities is attributed to asymmetries in the winds themselves. Interactions of the velocity fluctuations with the mean flow have a small but observable effect in modulating the skewness.

The subtle dependence of the skewness on key flow parameters is illustrated through an analytic model for idealized fluctuations on a beta plane. General expressions for the PDF, its asymptotic form, criteria for the presence of exponential tails, and the generic dependence of the skewness on a generalized Rossby number are derived. For the case of a δ-function velocity spectrum, closed-form expressions for the PDF and skewness are obtained and compared to observations.

## Abstract

As a characterization of the variability of observed geopotential height fluctuations, their probability density function (PDF) and its skewness are studied in the global domain for winter and summer. The PDF of the geopotential, Φ, is skewed toward low anomalies at midiatitudes and toward high anomalies in polar and tropical regions. When Φ is filtered spatially by discarding planetary wavenumbers less than ∼8, the skewness is small in the Tropics and in polar regions and large and negative in zonal bands approximately centered on the latitudes of the climatological jets. Where the skewness is large and negative, the zonally averaged PDF of Φ has an approximately exponential tail for negative anomalies.

From a diagnostic study based on computing Φ from the observed winds through the balance equation, the negative skewness bands can clearly be attributed to the rectification of near-symmetric velocity fluctuations by the advective nonlinearity. This mechanism implies that where winds are highly variable, large synoptic-scale negative Φ anomalies are more likely than large positive Φ anomalies. The maximum of the (negative) zonally averaged skewness in the summer hemisphere tends to be larger than that in the winter hemisphere, and in both hemispheres these maxima lie ∼150 mb below the velocity variance maxima. The fact that skewness extrema do not precisely match maxima in the nonlinearities is attributed to asymmetries in the winds themselves. Interactions of the velocity fluctuations with the mean flow have a small but observable effect in modulating the skewness.

The subtle dependence of the skewness on key flow parameters is illustrated through an analytic model for idealized fluctuations on a beta plane. General expressions for the PDF, its asymptotic form, criteria for the presence of exponential tails, and the generic dependence of the skewness on a generalized Rossby number are derived. For the case of a δ-function velocity spectrum, closed-form expressions for the PDF and skewness are obtained and compared to observations.

## Abstract

A new path-density diagnostic for atmospheric surface-to-surface transport is formulated. The path density *η* gives the joint probability that air whose last surface contact occurred on patch Ω*
_{i}
* at time

*t*will make its next surface contact with patch Ω

_{i}*after a residence time*

_{f}*τ*∈ (

*τ*,

*τ*+

*dτ*)

*and*that it can be found in

*d*

^{3}

*r*during its surface-to-surface journey. The dependence on

*τ*allows the average surface-to-surface flow rate carried by the paths to be computed. A simple algorithm for using passive tracers to determine

*η*is developed. A key advantage of the diagnostic is that it can be computed efficiently without an adjoint model and using only a moderately large number of tracers. The nature of the path density is illustrated with a one-dimensional advection–diffusion model. In Part II of this study, the path density diagnostic is applied to quantify interhemispheric transport through the troposphere and stratosphere.

## Abstract

A new path-density diagnostic for atmospheric surface-to-surface transport is formulated. The path density *η* gives the joint probability that air whose last surface contact occurred on patch Ω*
_{i}
* at time

*t*will make its next surface contact with patch Ω

_{i}*after a residence time*

_{f}*τ*∈ (

*τ*,

*τ*+

*dτ*)

*and*that it can be found in

*d*

^{3}

*r*during its surface-to-surface journey. The dependence on

*τ*allows the average surface-to-surface flow rate carried by the paths to be computed. A simple algorithm for using passive tracers to determine

*η*is developed. A key advantage of the diagnostic is that it can be computed efficiently without an adjoint model and using only a moderately large number of tracers. The nature of the path density is illustrated with a one-dimensional advection–diffusion model. In Part II of this study, the path density diagnostic is applied to quantify interhemispheric transport through the troposphere and stratosphere.

## Abstract

Gibbs oscillations in the truncated spectral representation of the earth's topography are strongly reduced by determining its spectral coefficients as a minimum of a nonuniformly weighted, nonquadratic cost function. The cost function penalizes the difference between spectral and true topography with weights that are explicit functions of the topographic height and its gradient. The sensitivity of the Canadian Climate Centre general circulation model's climate to the presence of Gibbs oscillations is determined for T32 and T48 resolutions by comparing the climates with optimal spectral topography to those with standard spectral topography. The main effect of Gibbs oscillations in the standard spectral topography is to induce spurious grid-scale ripples in the surface fluxes, which, for the surface energy balance, can be on the order of several tens of watts per square meter. Ripples in the surface fluxes are nearly absent in the model climate with the optimal spectral topography.

## Abstract

Gibbs oscillations in the truncated spectral representation of the earth's topography are strongly reduced by determining its spectral coefficients as a minimum of a nonuniformly weighted, nonquadratic cost function. The cost function penalizes the difference between spectral and true topography with weights that are explicit functions of the topographic height and its gradient. The sensitivity of the Canadian Climate Centre general circulation model's climate to the presence of Gibbs oscillations is determined for T32 and T48 resolutions by comparing the climates with optimal spectral topography to those with standard spectral topography. The main effect of Gibbs oscillations in the standard spectral topography is to induce spurious grid-scale ripples in the surface fluxes, which, for the surface energy balance, can be on the order of several tens of watts per square meter. Ripples in the surface fluxes are nearly absent in the model climate with the optimal spectral topography.

## Abstract

Atmospheric “transport climate” characterizes how trace gases are distributed by and within the atmosphere, on average, as a consequence of the interaction of atmospheric flow with tracer sources and sinks. The change in transport climate under global warming is investigated using passive tracers. Experiments with constant localized surfaces sources, pulsed sources, and pulsed boundary conditions are analyzed using a Green-function approach in conjunction with a climatological budget calculation.

Under climate warming, interhemispheric exchange times, mixing times, and mean transit times all increase by about 10%. The main transport pathway between the hemispheres via the “tracer fountain” at the ITCZ is suppressed. Generally less vigorous flow manifests itself in higher tracer burdens in the source hemisphere and in downwind plumes of enhanced mixing ratio close to the sources; these increases are also about 10%. Resolved advection and subgrid transport do not cooperate for all sources in enhancing the near-source mixing ratio. The warmer climate has a reduced cross-tropopause gradient, primarily due to a slightly higher tropopause, which results in a reduction of about 25% in the average tropospheric tracer mixing ratio, and a corresponding enhancement in the stratosphere. A global variance budget shows increased mean and transient tracer variance due to increased generation from strengthened mean gradients near the source and weakened eddy and subgrid transport.

## Abstract

Atmospheric “transport climate” characterizes how trace gases are distributed by and within the atmosphere, on average, as a consequence of the interaction of atmospheric flow with tracer sources and sinks. The change in transport climate under global warming is investigated using passive tracers. Experiments with constant localized surfaces sources, pulsed sources, and pulsed boundary conditions are analyzed using a Green-function approach in conjunction with a climatological budget calculation.

Under climate warming, interhemispheric exchange times, mixing times, and mean transit times all increase by about 10%. The main transport pathway between the hemispheres via the “tracer fountain” at the ITCZ is suppressed. Generally less vigorous flow manifests itself in higher tracer burdens in the source hemisphere and in downwind plumes of enhanced mixing ratio close to the sources; these increases are also about 10%. Resolved advection and subgrid transport do not cooperate for all sources in enhancing the near-source mixing ratio. The warmer climate has a reduced cross-tropopause gradient, primarily due to a slightly higher tropopause, which results in a reduction of about 25% in the average tropospheric tracer mixing ratio, and a corresponding enhancement in the stratosphere. A global variance budget shows increased mean and transient tracer variance due to increased generation from strengthened mean gradients near the source and weakened eddy and subgrid transport.

## Abstract

Transport in the atmosphere and in the ocean is the result of the complex action of time-dependent and often highly turbulent flow. A useful diagnostic that summarizes the rate at which fluid elements are transported from some region to a point (or the reverse) via a multiplicity of pathways and mechanisms is the probability density function (pdf) of transit times. The first moment of this pdf, often referred to as “mean age,” has become an important transport diagnostic commonly used by the observational community.

This paper explores how to probe the flow with passive tracers to extract transit-time pdf’s. As a foundation, the literal “tracer age” is defined as the elapsed time since tracer was injected into the flow, and the corresponding tracer-age distribution, *Z,* as the fractional tracer mass in a given interval of tracer age. The distribution, *Z,* has concrete physical interpretation for arbitrary sources, but is only equivalent to a tracer-independent transit-time pdf of the flow in special cases. The transit-time pdf is a propagator, *Z* and ^{†}, as the pdf’s of transit times since fluid at point **r** had last contact with Ω, and until fluid at **r** will have first contact with Ω, respectively. In the limit as Ω is shrunk to a point, point-to-point transit-time pdf’s are well defined, but their mean transit time and higher-order moments become infinite. Several concrete geophysical examples are considered to illustrate under what conditions characteristics of tracer-age and transit-time pdf’s can be inferred from observations in the atmosphere or the ocean.

## Abstract

Transport in the atmosphere and in the ocean is the result of the complex action of time-dependent and often highly turbulent flow. A useful diagnostic that summarizes the rate at which fluid elements are transported from some region to a point (or the reverse) via a multiplicity of pathways and mechanisms is the probability density function (pdf) of transit times. The first moment of this pdf, often referred to as “mean age,” has become an important transport diagnostic commonly used by the observational community.

This paper explores how to probe the flow with passive tracers to extract transit-time pdf’s. As a foundation, the literal “tracer age” is defined as the elapsed time since tracer was injected into the flow, and the corresponding tracer-age distribution, *Z,* as the fractional tracer mass in a given interval of tracer age. The distribution, *Z,* has concrete physical interpretation for arbitrary sources, but is only equivalent to a tracer-independent transit-time pdf of the flow in special cases. The transit-time pdf is a propagator, *Z* and ^{†}, as the pdf’s of transit times since fluid at point **r** had last contact with Ω, and until fluid at **r** will have first contact with Ω, respectively. In the limit as Ω is shrunk to a point, point-to-point transit-time pdf’s are well defined, but their mean transit time and higher-order moments become infinite. Several concrete geophysical examples are considered to illustrate under what conditions characteristics of tracer-age and transit-time pdf’s can be inferred from observations in the atmosphere or the ocean.

## Abstract

A conceptually new approach to diagnosing tracer-independent ventilation rates is developed. Tracer Green functions are exploited to partition ventilation rates according to the ventilated fluid’s residence time in the ocean interior and according to where this fluid enters and exits the interior. In the presence of mixing by mesoscale eddies, which are reasonably represented by diffusion, ventilation rates for overlapping entry and exit regions cannot meaningfully be characterized by a single rate. It is a physical consequence of diffusive transport that fluid elements that spend an infinitesimally short time in the interior cause singularly large ventilation rates for overlapping entry and exit regions. Therefore, ventilation must generally be characterized by a ventilation-rate distribution, *ϕ*, partitioned according to the time that the ventilated fluid spends in the interior between successive surface contacts. An offline forward and adjoint time-averaged OGCM is used to illustrate the rich detail that *ϕ* and the closely related probability density function of residence times ℛ provide on the way the ocean communicates with the surface. These diagnostics quantify the relative importance of various surface regions for ventilating the interior ocean by either exposing old water masses to the atmosphere or by forming newly ventilated ones. The model results suggest that the Southern Ocean plays a dominant role in ventilating the ocean, both as a region where new waters are ventilated into the interior and where old waters are first reexposed to the atmosphere.

## Abstract

A conceptually new approach to diagnosing tracer-independent ventilation rates is developed. Tracer Green functions are exploited to partition ventilation rates according to the ventilated fluid’s residence time in the ocean interior and according to where this fluid enters and exits the interior. In the presence of mixing by mesoscale eddies, which are reasonably represented by diffusion, ventilation rates for overlapping entry and exit regions cannot meaningfully be characterized by a single rate. It is a physical consequence of diffusive transport that fluid elements that spend an infinitesimally short time in the interior cause singularly large ventilation rates for overlapping entry and exit regions. Therefore, ventilation must generally be characterized by a ventilation-rate distribution, *ϕ*, partitioned according to the time that the ventilated fluid spends in the interior between successive surface contacts. An offline forward and adjoint time-averaged OGCM is used to illustrate the rich detail that *ϕ* and the closely related probability density function of residence times ℛ provide on the way the ocean communicates with the surface. These diagnostics quantify the relative importance of various surface regions for ventilating the interior ocean by either exposing old water masses to the atmosphere or by forming newly ventilated ones. The model results suggest that the Southern Ocean plays a dominant role in ventilating the ocean, both as a region where new waters are ventilated into the interior and where old waters are first reexposed to the atmosphere.

## Abstract

The first climatology of airmass origin in the Arctic is presented in terms of rigorously defined airmass fractions that partition air according to where it last contacted the planetary boundary layer (PBL). Results from a present-day climate integration of the Goddard Earth Observing System Chemistry–Climate Model (GEOSCCM) reveal that the majority of air in the Arctic below 700 mb last contacted the PBL poleward of 60°N. By comparison, 62% (±0.8%) of the air above 700 mb originates over Northern Hemisphere midlatitudes (i.e., “midlatitude air”). Seasonal variations in the airmass fractions above 700 mb reveal that during boreal winter air from midlatitudes originates primarily over the oceans, with 26% (±1.9%) last contacting the PBL over the eastern Pacific, 21% (±0.87%) over the Atlantic, and 16% (±1.2%) over the western Pacific. During summer, by comparison, midlatitude air originates primarily over land, overwhelmingly so over Asia [41% (±1.0%)] and, to a lesser extent, over North America [24% (±1.5%)]. Seasonal variations in the airmass fractions are interpreted in terms of changes in the large-scale ventilation of the midlatitude boundary layer and the midlatitude tropospheric jet.

## Abstract

The first climatology of airmass origin in the Arctic is presented in terms of rigorously defined airmass fractions that partition air according to where it last contacted the planetary boundary layer (PBL). Results from a present-day climate integration of the Goddard Earth Observing System Chemistry–Climate Model (GEOSCCM) reveal that the majority of air in the Arctic below 700 mb last contacted the PBL poleward of 60°N. By comparison, 62% (±0.8%) of the air above 700 mb originates over Northern Hemisphere midlatitudes (i.e., “midlatitude air”). Seasonal variations in the airmass fractions above 700 mb reveal that during boreal winter air from midlatitudes originates primarily over the oceans, with 26% (±1.9%) last contacting the PBL over the eastern Pacific, 21% (±0.87%) over the Atlantic, and 16% (±1.2%) over the western Pacific. During summer, by comparison, midlatitude air originates primarily over land, overwhelmingly so over Asia [41% (±1.0%)] and, to a lesser extent, over North America [24% (±1.5%)]. Seasonal variations in the airmass fractions are interpreted in terms of changes in the large-scale ventilation of the midlatitude boundary layer and the midlatitude tropospheric jet.

## Abstract

The intimate relationship among ventilation, transit-time distributions, and transient tracer budgets is analyzed. To characterize the advective–diffusive transport from the mixed layer to the interior ocean in terms of flux we employ a cumulative ventilation-rate distribution, Φ(*τ*), defined as the one-way mass flux of water that resides at least time *τ* in the interior before returning. A one-way (or gross) flux contrasts with the net advective flux, often called the subduction rate, which does not accommodate the effects of mixing, and it contrasts with the formation rate, which depends only on the net effects of advection and diffusive mixing. As *τ* decreases Φ(*τ*) increases, encompassing progressively more one-way flux. In general, Φ is a rapidly varying function of *τ* (it diverges at small *τ*), and there is no single residence time at which Φ can be evaluated to fully summarize the advective–diffusive flux. To reconcile discrepancies between estimates of formation rates in a recent GCM study, Φ(*τ*) is used. Then chlorofluorocarbon data are used to bound Φ(*τ*) for Subtropical Mode Water and Labrador Sea Water in the North Atlantic Ocean. The authors show that the neglect of diffusive mixing leads to spurious behavior, such as apparent time dependence in the formation, even when transport is steady.

## Abstract

The intimate relationship among ventilation, transit-time distributions, and transient tracer budgets is analyzed. To characterize the advective–diffusive transport from the mixed layer to the interior ocean in terms of flux we employ a cumulative ventilation-rate distribution, Φ(*τ*), defined as the one-way mass flux of water that resides at least time *τ* in the interior before returning. A one-way (or gross) flux contrasts with the net advective flux, often called the subduction rate, which does not accommodate the effects of mixing, and it contrasts with the formation rate, which depends only on the net effects of advection and diffusive mixing. As *τ* decreases Φ(*τ*) increases, encompassing progressively more one-way flux. In general, Φ is a rapidly varying function of *τ* (it diverges at small *τ*), and there is no single residence time at which Φ can be evaluated to fully summarize the advective–diffusive flux. To reconcile discrepancies between estimates of formation rates in a recent GCM study, Φ(*τ*) is used. Then chlorofluorocarbon data are used to bound Φ(*τ*) for Subtropical Mode Water and Labrador Sea Water in the North Atlantic Ocean. The authors show that the neglect of diffusive mixing leads to spurious behavior, such as apparent time dependence in the formation, even when transport is steady.