a. Model description

The CCM2 (Hack et al. 1993; Hack et al. 1994) is a three-dimensional atmospheric general circulation model developed at NCAR for the purpose of climate simulation studies and medium- to long-range forecast studies. The simulation analyzed here uses the standard resolution of the CCM2, with triangular wavenumber T42 spectral resolution and 18 vertical levels (992.5, 970.4, 929.3, 866.4, 786.5, 695.2, 598.2, 501.3, 409.0, 324.8, 251.2, 189.2, 138.7, 99.0, 63.9, 32.6, 13.1, 4.8 mb). The T42 resolution corresponds to 128 longitudes and 64 latitudes on a Gaussian spectral transform grid. The vertical coordinate of the model is a hybrid-sigma coordinate that follows the terrain near the surface and becomes purely a pressure coordinate above 100 mb. The model time step is 20 min. The dry dynamical equations are solved by a spectral transform method in the horizontal and finite differences in the vertical. Horizontal diffusion at all model levels except the top three is applied to vorticity, divergence, and temperatures, using a ∇⁴ diffusion operator with a coefficient of 10⁶ m⁴ s⁻¹. Diffusion at the upper model levels is applied with a ∇² operator (Hack et al. 1994).

Constituent transport is accomplished by means of a shape-preserving, semi-Lagrangian method (Williamson and Rasch 1989; Rasch and Williamson 1990) applied on the latitude–longitude grid. Horizontal diffusion is not applied to constituents transported by the model. CCM2’s constituent transport abilities have been utilized in studies of water vapor transport (Williamson and Rasch 1994), the seasonal cycle of CO₂ (Erickson et al. 1996), and the transport of CFCl₃ (Hartley et al. 1994). Zapotocny et al. (1996) and Zapotocny et al. (1997) examine the transport and conservation abilities for inert trace constituents in the CCM2.

Several alterations to the standard configuration of the CCM2 were made for the simulations in this study. An adiabatic version of the model was used, which eliminated radiative heating and moist physical processes (convection, precipitation, evaporation, and temperature adjustment due to latent heating). At each time step of the simulation, model fields were truncated to retain only their zonal mean, zonal wave 6, and wave 6 harmonic values. An aquaplanet was simulated by setting the surface type and boundary conditions to oceanic values everywhere on the model surface.

b. Initial conditions

Since the model simulations are done with adiabatic, aquaplanet conditions, there is no difference between the two hemispheres simulated by the model. Given this, and the fact that the timescales of the integrations are short enough such that there is little interhemispheric interaction, one model run can be used to simulate two life cycles simultaneously, one in each hemisphere. The initial zonal wind fields for the NH and SH of the model simulation, shown in the top panel of Fig. 1, were designed to be similar to the wind fields of the LC1 and LC2 cases of THM, respectively. The wind field in the SH is identical to that of the NH, but with an added barotropic component that is −10 m s⁻¹ at 50°C and 10 m s⁻¹ at 20°S. The jet core in each hemisphere is near the 200-mb level with maximum velocities of 43 m s⁻¹ in the NH and 35 m s⁻¹ in the SH. The NH of the model will be used to simulate the LCn (“n” for no additional horizontal shear and north) case and the SH for the LCs (“s” for increased horizontal shear and south) case. Subsequent plots show both cases simultaneously, LCn in the NH and LCs in the SH.

The initial perturbations in the zonal and meridional wind, temperature, and surface pressure fields were obtained from a model calculation using a linear version of CCM2 (G. Branstator 1994, personal communication). The fastest growing zonal wave 6 structure from this model output was normalized to a 1-mb surface pressure perturbation and added to the initial zonal mean fields.

The simulation included four passive tracers (χ₁–χ₄) to be advected by the transport scheme of the CCM2. The numerical values representing the mixing ratios of these passive tracers are arbitrary. The midlatitude tracer χ₁ has a maximum in each hemisphere at 45° and decreases in value symmetrically toward the poles and equator with decreasing pressure. Although idealized, χ₁’s structure represents a tracer with a low-level, midlatitude source (such as fossil fuel CO₂). The tracer χ₂ is a vertically stratified tracer with an initial vertical gradient of 10 km⁻¹, and χ₃ is a horizontally stratified tracer with its largest values occurring at the equator and a meridional gradient of 2 (deg lat)⁻¹. The tracers χ₂ and χ₃ were constructed to be orthogonal to each other such that we could assess the influence of the meridional and vertical tracer gradients on the transport characteristics associated with the baroclinic wave event. The tracer χ₄ is a step function tracer, initialized with a value of unity in the stratosphere (above the tropopause) and zero in the troposphere. The tropopause was defined here by the PV = 2 PVU (1 PVU = 10⁻⁶ m² K s⁻¹ kg⁻¹) location in the middle and high latitudes and the 380-K potential temperature surface in the Tropics. Poleward of 60°, the 2 PVU-surface is at approximately 8 km. The 2 PVU- and 380-K surfaces intersect near 15° and 14 km. The stratospheric tracer is used to analyze the effect of the baroclinic waves on transport near the tropopause.

a. Zonal mean description

The transport that occurs during the life cycles can be observed in changes in the tracer fields and in regions of positive and negative tracer tendency. Figure 6 shows meridional cross sections of the horizontally stratified tracer, the vertically stratified tracer, and the midlatitude tracer at the start and end of the life cycle. The difference in the tracer field over this time period is shown as the time-averaged tendency (Fig. 6b). Sharper meridional gradients are formed for all three tracers during the life cycles near the 60°–70° latitude range of LCn and LCs above 600 mb. Positive tendency values are seen in this region that peak at 300–400-mb altitude, corresponding to an increase in tracer value over the life cycle. LCn has a broader region of positive tendency, with two peaks about 10° apart, than that seen in LCs. The region extends from 40°–70°N, with the exception being the midlatitude tracer, which has a somewhat narrower structure. The region of positive tendency in LCs is confined to the 55°–75°S range. Negative tendencies exist at the lower levels in the 30°–60° latitudinal range and extend upward from the surface in narrow bands centered near 30°N and 45°–50°S. The net effect displayed in Fig. 6 is that of upward and poleward transport in the troposphere for latitudes ∼30°–75° for both the LCn and LCs life cycles. This transport is downgradient with respect to the background tracer distributions. The strongest tracer transport effects are seen near the high-latitude tropopause, poleward of the peak regions of eddy activity. The three tracers show very similar tendency structures despite the substantial differences in their initial configurations. Because of this similarity, we focus on the details of transport for the horizontally stratified tracer only.

Figure 7 shows a latitude versus time plot of the horizontally stratified tracer on the 315-K surface, highlighting the change in the meridional gradient of the tracer. The gradient in LCs is increased poleward of 60° but is weakened in the midlatitudes. The meridional tracer gradients of LCn on this surface were increased in two bands centered at 55°N and 75°N. The largest changes occur between days 5 and 8. In both cases, the field changes relatively little after day 10. The second pulse of eddy activity in the LCs case (see Fig. 2) has the effect of decreasing the meridional tracer gradients near 30°N.

b. Tracer budget analysis

In order to study the transport of the zonal mean mixing ratio in the meridional plane associated with the developing baroclinic waves, we make use of the tracer conservation equation based on the TEM formalism in log pressure (z) coordinates [Andrews et al. 1987, Eq. (9.4.13)]:

View Expanded

Here υ* and w* are components of the residual mean circulation, ρ⁻¹₀∇ · M is the eddy transport term, and S is a source or sink term, equal to zero for the passive tracers used here. The TEM eddy flux vector M has components

View Expanded

Note that these terms are related to the negative of the Eulerian mean tracer fluxes. Here M^(y) and M^(z) are also dependent on the product of the eddy heat flux and the vertical or meridional tracer gradient.

Equation (1) defines the zonal mean tracer tendency in terms of transport due to advection by the residual circulation (υ* and w* terms), transport due to eddy tracer flux divergence (ρ⁻¹₀∇ · M), and sources and sinks. The nontransport theorem (Andrews et al. 1987) states that for linear, steady, adiabatic, conservative waves, the residual circulation and the eddy flux divergence are identical to zero, and under these conditions, no net meridional transport occurs. However, the conditions of nontransport are violated by the lack of steadiness and the nonlinear dynamics of baroclinic waves, and we detail here the balances in Eq. (1) throughout the life cycles.

The four panels in Fig. 8 depict the tracer tendency, the advection by the residual mean circulation, the wave transport effects, and the calculated tendency, which is the sum of the latter two. The calculations are averaged over days 1–10 of the model run for the horizontally stratified tracer. A comparison of the measured and calculated tendencies (Figs. 8a and 8d) shows that the equation balances relatively well. The structure of the calculated and actual tendency is similar, although in magnitude, they are not a perfect match. Reasons for this difference may be the interpolation from the model levels to pressure surfaces and the finite difference approximations used for calculations of derivatives in the equation.

Figure 8 also shows that over the 10 days of the life cycles, the balance of the equation is approximately between the tendency and the eddy tracer flux divergence, ∂χ/∂t ≈ ρ⁻¹₀∇ · M. The advection by the residual mean flow plays only a small role. The tendency and eddy flux divergence attain their maximum values at the 300–400-mb level in the extratropics. There is convergence and negative tendencies at the lower levels equatorward of this. Overall, the eddy fluxes act to increase the constituent values in the upper troposphere at latitudes poleward of 50°.

Figure 9 displays the two dominant terms in Eq. (1), and the tracer tendency and the eddy flux divergence. The time evolution of the two quantities are displayed on latitude versus time grids at the 866- and 501-mb levels, showing the development of the eddy tracer transport and total tracer transport throughout the life cycles. Approximate balance between these two terms is seen with the eddy flux divergence being slightly larger in magnitude than the tendency term. On the lower surface, the region of negative tendency (and corresponding eddy flux convergence) in each life cycle moves equatorward with time from 45° to 25°, peaking on days 5–6. LCn has a broader meridional structure with negative tendencies extending poleward with time as well. In the middle troposphere, the region of positive tendency (or flux divergence) moves poleward with time from 55° to 70° in both cases. LCn again has a broader structure. The negative tendency region is equatorward and weaker than the positive region.

Also included in the diagram of eddy flux divergence (Fig. 8c) are vectors depicting the components of the TEM eddy flux vector, M^(y) and M^(z). These cross sections showing the direction and magnitude of the TEM eddy tracer flux and its divergence are analogous to EP flux cross sections (Edmon et al. 1980). In plotting the vectors, the density factor in Eq. (2) is omitted, and M^(z) is multiplied by a factor of 150 (the approximate ratio of N/f) so that M^(y) and M^(z) are plotted isotropically in the latitude–height plane [in analogy with EP flux diagrams; see Palmer (1982)]. Note that, by definition [Eqs. (1) and (2)], the vectors are in the opposite direction to the eddy tracer fluxes so that divergence of M corresponds to positive tracer tendency. The overall features of the eddy tracer flux and its divergence are similar for the two life cycles, showing M vectors that point downward and equatorward (signifying eddy tracer fluxes that are upward and poleward). Both the horizontal and vertical flux components contribute significantly to the eddy transport. However, the detailed transport characteristics are somewhat different between LCn and LCs. The wave transport for LCn displays a broader meridional region of convergence in the middle to high latitudes, and the wave flux patterns extend much more into the subtropics than those for LCs (which appear confined to high latitudes). This asymmetry is qualitatively similar to differences in the EP flux diagrams discussed above.

In analogy to Fig. 3, Fig. 10 breaks down the eddy flux divergence and vectors into two time segments to demonstrate the stages of development of the wave transport effects. The wave transport term was shown to be the dominant influence on the changes to the tracer field. Regions of divergence (positive contours) indicate increasing tracer values. Early on in the life cycles, the divergent and convergent regions peak at the lower levels of the midlatitudes with the convergence of eddy tracer flux occurring equatorward of the divergent regions. During the mature phase of the waves (days 5–7), strong eddy transports are found in the middle and upper troposphere, and more asymmetry is found between LCn and LCs. Peak values of the divergence remain at the lower levels, while the positive regions peak around 400 mb. During this time, the strongest changes in the zonal mean tracer field occur. The vectors of eddy flux point predominately downward and equatorward in both cases, indicating that eddy transports are upward and poleward.

This section has focused primarily on analysis of the horizontally stratified tracer since, as noted in Fig. 6, the three different tracer tendencies were similar over the life cycles. Figure 11 displays the wave transport term of Eq. 1 for the vertically stratified tracer and the midlatitude tracer averaged over days 3–4 and 5–7. This should be compared with Fig. 10, which shows similar plots for the horizontally stratified tracer. The eddy flux divergence pattern is similar for the three tracers during the growth and mature stages of the life cycles, although the vertical extent of their features and the relative magnitudes of divergent and convergent regions varies among them. Some difference in the wave transport for the three passive tracers is found in the eddy flux vectors. As noted in Fig. 8c, both the horizontal and vertical flux components contribute to the eddy flux vectors. In addition, the two terms that make up M^(y) and M^(z) [see Eq. (2)] each contribute to the magnitude of the vector components. While in general the structure of the M^(y) and M^(z) fields is similar for the three tracers discussed here, the relative importance of the two components and the contributions of the terms that form them is sensitive to the distinct gradients of the tracers.

c. Isentropic calculations

The use of potential temperature as a vertical coordinate (isentropic coordinates) has the advantage that the “vertical velocity” (Dθ/Dt) simply equals the diabatic heating rate. Thus, for the adiabatic life cycles analyzed here, tracer transport is expected to occur primarily by eddy transfer along isentropic surfaces. Comparison of the time-averaged eddy transport vectors (M) for the horizontally stratified tracer with the time mean isentropes (shown in Fig. 12) confirms this expectation qualitatively: the M vectors are approximately parallel to the isentropes for both life cycles, suggesting the transport is primarily isentropic.

The isentropic transport is explored in further detail by analysis of the Eulerian zonal mean transport equation in isentropic coordinates [Andrews et al. 1987, Eq. (9.4.21)]:

View Expanded

Here, σ = g⁻¹∂P/∂θ is the density in isentropic coordinates, υ^σ = (συ)/σ is the mass-weighted mean meridional velocity, and diabatic heating and tracer source terms have been omitted.

Figure 13 shows separate terms in the isentropic transport balance [Eq. (3)] for the horizontally stratified tracer life cycle. Individual model fields were interpolated to isentropic levels, followed by explicit calculation of Eq. (3). The term −σ⁻¹∂(σ′χ′)/∂t is very small and is not included in Fig. 13. The results in Fig. 13 show reasonable agreement between the calculated and observed tendencies, confirming an approximate balance in Eq. (3). The isentropic eddy flux term dominates the transport in Fig. 13, with relatively small contribution from the mean meridional transport term (although there is no mean cross-isentropic velocity in this calculation, there is a nonzero υ^σ due to the redistribution of mass during the life cycle). We note that the tracer transport viewed in the Eulerian mean isentropic framework [Eq. (3) and Fig. 13] closely resembles the results in the transformed Eulerian mean log pressure coordinates [Eq. (1) and Fig. 8]. These results also confirm that the baroclinic wave tracer transport studied here is predominantly isentropic in nature.

d. Synoptic description

The PV and horizontally stratified tracer fields appear highly correlated in Fig. 14 and the description of the tracer matches the PV field on this surface (Figs. 4 and 5). In order to compare this more quantitatively, Fig. 15 displays a scatter diagram of the horizontally stratified tracer and the PV field at the start of the life cycle and during the peak transport period. These plots show the value of each field at every grid point (of both hemispheres) on the 315-K surface. The initial relationship shows a one-to-one correspondence between the constituent and PV. Although the two fields are still fairly well correlated on day 7, the exact initial relationship does not remain intact and the correspondence between the two fields is smeared out, particularly in the extratropical values. A similar result is found in comparing individual tracers (not shown).

Zapotocny et al. (1996) and Zapotocny et al. (1997) examined the ability of the CCM2 to transport and conserve distributions of PV and an inert tracer. Their findings suggest that the two do not remain highly correlated due to details of the numerical transport scheme, and that amplifying baroclinic waves, wherein three-dimensional transport in the presence of vertical wind shear must be resolved, leads to spurious decorrelation. This suggests that the reason the exact initial relationships between the tracers in Fig. 15 do not remain intact is due to the numerical transport scheme and is not caused by physical processes associated with the baroclinic waves, particularly since we are using an adiabatic version of the CCM2.

e. Stratospheric tracer

In the midlatitudes, isentropic surfaces traverse the troposphere and lowermost stratosphere, and isentropic mixing is an effective mechanism for stratosphere–troposphere exchange (see Holton et al. 1995). In this region, baroclinic waves are a predominant source of quasi-horizontal mixing on the isentropic surfaces (as shown in section 4c above). Recent studies have focused on the transport across the tropopause in the extratropics (Mote et al. 1994; Chen 1995; Rood et al. 1997). Mote et al. (1994) show that in the extratropics, exchange from the stratosphere to the troposphere occurs mainly in developing baroclinic waves and stationary anticyclones. In order to examine the issue of transport in the region of the tropopause during the two baroclinic wave life cycles of this study, a passive tracer is initialized with a value of 1 in the stratosphere (above the tropopause) and a value of 0 in the troposphere (this is a zeroth-order representation of ozone mixing ratio, for example). The tropopause is defined here by the 2-PVU level in the midlatitudes and the 380-K surface in the Tropics and is shown in the top panel of Fig. 16. A fundamental problem in quantifying transport across the tropopause (defined by the PV = 2 PVU surface) in these life cycles is that both the tracer and PV fields are deformed in time in a nearly identical manner (see Fig. 14 and discussion above), so that both the tracer and 2 PVU contours change coherently. Hence, there is zero net tracer transport across the tropopause (apart from small numerical changes). This behavior also occurs in the real atmosphere to some degree, but radiative and other diabatic effects act to dissipate small-scale PV structures and restore the tropopause close to a climatological location. These diabatic effects do not act to restore the transported tracer, so there is a net transport across the tropopause (see Lamarque and Hess 1994; Wirth 1995). Because the baroclinic wave simulations here are adiabatic, the restoring effect on the tropopause is not simulated, and we cannot calculate the details of the processes described above. However, a qualitative estimate of the behavior of stratosphere–troposphere exchange can be made by calculating the tracer transport with respect to the initial (day 0) tropopause location. This assumes that the final tropopause position (after dissipation of the baroclinic waves and diabatic restoring effects) will be near the initial position shown in Fig. 16. Thus, we treat the zonal mean transport of the stratospheric tracer as an estimate of stratosphere–troposphere exchange. Although this is admittedly only a qualitative calculation, we feel it is a reasonable estimate given the limitations of an adiabatic simulation.

During the model run, the stratospheric tracer is transported with respect to the day-0 tropopause as the baroclinic waves develop. The middle panel of Fig. 16 shows the tendency of the stratospheric tracer averaged over days 5–7 of the model ran. The tendency field indicates that the tracer value has increased, from an original null value, just below the tropopause and decreased just above it. In the LCn case, the tendencies are somewhat larger and the stratospheric tracer is transported to lower altitudes (down to 2 km in Fig. 16) than that seen in the LCs case. Figure 16 also displays the eddy tracer flux divergence and vectors for the stratospheric tracer. Again, good agreement is seen between the tracer tendency and the eddy flux divergence terms of Eq. (1), demonstrating that eddy transport is the dominant mechanism of the exchange. The eddy tracer flux vectors point upward and poleward signifying an equatorward and downward flux of tracer. Note this transport has increased the tracer mixing ratio in the (day 0) troposphere and decreased it in the (day 0) lowermost stratosphere; that is, there is a two-way exchange across the initial tropopause location. We quantify this exchange and find that nearly 4% of the tracer mass initially present in the lowermost stratosphere is located at altitudes below the initial location of the tropopause by day 10.