a. Governing equations

b. Poleward ozone transport expressed by eddy heat flux

a. Approximation by horizontal flux

Here, we compare the time series of the four terms on the rhs of Eq. (10) to try to justify the approximation to Eq. (21). The latitude ϕ_m and altitude z_p are temporarily set to 50° and 100 hPa, respectively, referring to Weber et al. (2011). The results from other choices are examined when necessary.

Figure 5 shows the ensemble-mean time series of each term on the rhs of Eq. (10). The time series of the first (black, denoted H.F), second (blue, V.F), and third (green, S) terms are calculated from model outputs, whereas in the present study we do not calculate ∇ ⋅ M explicitly as was done by Randel et al. (1994). Instead, the fourth term (red, Res) is estimated as the residual obtained by subtracting the above three terms from the lhs of the equation, assuming negligible errors in the estimated terms. We readily confirm that the vertical flux crossing the tropopause z_p (=100 hPa) is small in all cases. In the NH (top panels), the poleward ozone flux crossing the latitude ϕ_m (black) is the dominant term year-round, increasing from a minimum in summer to a maximum in January. This annual cycle is explained as the seasonal dependence of the planetary wave breaking and/or wave transience that take a maximum in winter. There is little difference between ODS1960 (left) and ODS2000 (right), except for an enhancement of chemical ozone loss (green) during winter to spring under ODS2000.

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Tendency of polar stratospheric ozone above z_p = 100 hPa integrated poleward of latitude ϕ_m = 50° (×10⁸ DU km² day⁻¹) as shown by time series of 500-member ensemble-mean values on the rhs of Eq. (10). Black, blue, green, and red lines are the first, second, third, and fourth terms, respectively. Vertical bars are the spread (standard deviation) drawn by thinning out by 5 days for visual clarity.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0023.1

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In the SH (bottom), the poleward ozone flux owing to the residual circulation (black) is dominant in most of the year, as in the NH. However, the flux is suppressed in winter, creating dual maxima in fall (March) and spring (November). What is distinct from the features in the NH is the increased eddy transport (fourth term, red) surpassing the poleward flux by the residual circulation from October to December. However, this eddy transport is nearly canceled by simultaneously activated chemical ozone loss. Details of this phenomenon are analyzed in section 6b. Owing to this cancellation, the polar ozone tendency described by Eq. (10) is approximated by the horizontal flux (first term, H.F) also in the SH.

b. Approximation by eddy heat flux

For the validation of Eq. (23), we investigate if the poleward ozone flux crossing the latitude ϕ_m above the altitude z_p is approximated by the eddy heat flux at P_ref(ϕ_m, z_p). Specifically, we examine whether or not Eq. (22) is a good approximation of Eqs. (16) and (20).

The top panels of Fig. 6 show the poleward ozone flux [lhs of Eq. (16); black, denoted H.F] decomposed into the latitudinal divergence of EP flux (blue, F_y), the first (red, F_z1) and the second (light blue, F_z2) terms originating from integration by parts of $\overline{\chi }(\partial F^{(z)}/\partial z)$, the component associated with zonal wind deceleration (orange, U_t), and the transport attributed to unresolved eddies (green, Res) under ODS1960. Those of ODS2000 are omitted as the dynamical fields are essentially similar to those of ODS1960 (section 2). We can see that the eddy heat flux term (red, F_z1) shows some enhancement in winter in the NH, although it does not constitute the major component of the poleward ozone flux (black, H.F) being smaller than the second term (light blue, F_z2) that arises from integration by parts.

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(top) Time series of poleward ozone flux (×10⁸ DU km² day⁻¹) expressed by Eq. (16). The 500-member ensemble-mean values under ODS1960 of the horizontal flux above P_ref(ϕ_m, z_p) (H.F; black), the latitudinal convergence of EP flux (F_y; blue), the eddy heat flux at P_ref (F_z1; red), the additional term coming from integration by parts (F_z2; light blue), the zonal wind deceleration (U_t; orange), and the frictional term estimated as the residue (Res; green). (bottom) As in the top row, but for those expressed by Eq. (20): the horizontal flux (H.F; black), the latitudinal (${\tilde{F}}_y$; blue) and vertical (${\tilde{F}}_z$; red) convergences of $\tilde{F}$, the zonal wind deceleration (${\tilde{U}}_t$; orange), and the residual term (Res; green). ϕ_m and z_p are taken to be 50° and 100 hPa, respectively. Vertical bars are the spread (standard deviation) drawn by thinning out by 5 days for visual clarity.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0023.1

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The bottom panels of Fig. 6 are the same as the top, but for those obtained from Eq. (20). There is scarcely any difference if Eq. (19) is used. Note that the first three terms on the rhs of Eq. (20) representing latitudinal and vertical convergences of $\tilde{F}$ (blue, ${\tilde{F}}_y$, and red, ${\tilde{F}}_z$) and zonal wind deceleration (orange, ${\tilde{U}}_t$) are nearly the same as the first (blue, F_y), second (red, F_z1), and fourth (orange, U_t) terms of Eq. (16), respectively, meaning that the fourth term (vertical integral of ${\rho }_0\tilde{Y}$) estimated as the residue in Eq. (20) roughly corresponds to the sum of the second term from integration by parts (light blue, F_z2) and the unresolved eddy term (green, Res) in Eq. (16). In the NH (bottom left), the poleward and equatorward ozone fluxes driven by the vertical (red, ${\tilde{F}}_z$) and latitudinal (blue, ${\tilde{F}}_y$) convergences, respectively, of $\tilde{F}$ tend to cancel each other, and the residual term (green, Res) is the major contributor to the poleward ozone flux due to ${\overline{\upsilon }}^{*}$. In the SH (bottom right), the vertical convergence of $\tilde{F}$ (red, ${\tilde{F}}_z$) is generally small throughout the year with a slight enhancement in winter, whereas the latitudinal convergence (blue, ${\tilde{F}}_y$), contributing to the equatorward transport, is activated in winter to spring. The enhanced equatorward transport associated with the zonal wind deceleration (orange, ${\tilde{U}}_t$) in spring reduces the poleward transport carried by the residual term (green, Res). Overall, we can see that the vertical integral of ${\tilde{F}}^{(z)}$ above z_p, that is, the eddy heat flux at the altitude z_p, is not a good approximation to the poleward ozone flux but that the term associated with $\tilde{Y}$, estimated as the residue, appears a better proxy for the meridional ozone flux on the seasonal time scale.

Further investigation is made on the vertical profiles of the quantities discussed above. Figure 7 shows the time–height section of each term of Eq. (15) at 50°N (left) and 50°S (right) under ODS1960. No appreciable difference is found for ODS2000, and similar features are confirmed from ERA-Interim analysis (not shown). Top panels show the poleward ozone flux due to ${\overline{\upsilon }}^{*}$ (lhs) indicating a stratospheric enhancement in winter and a persistent ozone transport at around 100 hPa. This spatiotemporal structure suggests the contribution by planetary wave driving for the former and synoptic waves and quasi-horizontal isentropic eddy mixing for the latter (e.g., Plumb 2002). Latitudinal convergence of EP flux (F_y), Figs. 7c and 7d, contributes to equatorward ozone transport in the lower stratosphere all year round and in the middle to upper stratosphere in winter. The poleward ozone transport is brought about by the vertical convergence of EP flux (F_z), Figs. 7e and 7f, exhibiting a similar structure to Figs. 7a and 7b, respectively, but with reduced magnitude. The zonal wind acceleration term (U_t), Figs. 7g and 7h, contributes to equatorward transport in spring. The dominant term is associated with unresolved eddies (Res), Figs. 7i and 7j. Because this term is obtained as the residue of all other terms, it also includes both physical and numerical diffusion and a variety of errors arising from transformation from spectral to gridpoint data and others. Model dependence especially on the parameterization of unresolved processes is a problem left for future studies.

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Time–height sections of the poleward ozone flux (×10⁻⁹ kg m⁻² s⁻¹) at (left) 50°N and (right) 50°S described by Eq. (15). (a),(b) The ozone flux due to ${\overline{\upsilon }}^{*}$ is decomposed into the (c),(d) latitudinal and (e),(f) vertical convergences of EP flux, (g),(h) zonal wind acceleration, and (i),(j) the residual including those associated with small-scale eddies Y. Poleward (equatorward) flux is color-coded in red (blue). 500-member ensemble mean for ODS1960.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0023.1

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Figure 8 is the same as Fig. 7 except that those constituting Eq. (18) are shown with the terms contained in $\tilde{Y}$ expanded:

${\rho }_0\overline{\chi }{\overline{\upsilon }}^{*}=-\frac{1}{fa\cos \varphi }\left[\frac{1}{a\cos \varphi }\frac{\partial }{\partial \varphi }({\tilde{F}}^{(\varphi )}\cos \varphi )+\frac{\partial {\tilde{F}}^{(z)}}{\partial z}\right]+\frac{1}{fa\cos \varphi }\left(\frac{F^{(\varphi )}}{a}\frac{\partial \overline{\chi }}{\partial \varphi }+F^{(z)}\frac{\partial \overline{\chi }}{\partial z}\right)+\frac{{\rho }_0\overline{\chi }}{f}\frac{\partial \overline{u}}{\partial t}-\frac{{\rho }_0\overline{\chi }}{f}Y.$(25)

We can see that the latitudinal divergence of $\tilde{F}$ (${\tilde{F}}_y$), first term on the rhs of Eq. (25), Figs. 8c and 8d, is quite similar to that of the EP flux (Figs. 7c,d) and the contribution of the term proportional to $\partial \overline{\chi }/\partial \varphi$, third term denoted F × χ_y shown in Figs. 8k and 8l, is relatively small. The vertical convergence of $\tilde{F}$ (${\tilde{F}}_z$), second term shown in Figs. 8e and 8f, contributes to poleward ozone transport in the stratosphere above 20 hPa during fall to spring, whereas it is directed equatorward in the lower stratosphere except for the summer season, contributing to the transport opposite to the vertical convergence of the EP flux (Figs. 7e,f). This lower-stratospheric equatorward transport results from the positive vertical gradient of ozone mixing ratio and is compensated for by the poleward transport by the term proportional to $\partial \overline{\chi }/\partial z$ (fourth term, F × χ_z) of Eq. (25), as can be seen from Figs. 8m and 8n.

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As in Fig. 7, but those expressed by Eq. (25). Figures 7a and 7b are not replicated. (k),(l) The third term and (m),(n) the fourth term.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0023.1

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The fact that $\tilde{F}$ is divergent in the lower stratosphere while it is convergent in the upper stratosphere suggests that the eddy heat flux at 100 hPa is not a good proxy for the poleward ozone flux in the whole stratosphere and that the choice of 100 hPa for z_p in constructing the Weber plot is too low to best express the fall-to-spring polar ozone buildup by the midlatitude eddy heat flux. On the other hand, higher values of z_p will make the correspondence to total ozone weaker. Time series similar to those shown in the bottom panels of Fig. 6 but for z_p taken as 50 hPa are shown in the top panels of Fig. 9. We can see some improvement from Fig. 6 (bottom) especially in the NH. That is, the contribution of the vertical convergence of $\tilde{F}$ is larger than that in the case of 100 hPa, and the seasonal enhancement during winter to spring is synchronized with the increase of poleward ozone transport due to ${\overline{\upsilon }}^{*}$. If we want to make the contribution larger still, the choice of ϕ_m = 60° in addition to the change to z_p = 50 hPa (bottom panels) is effective. In this case, the poleward ozone flux owing to vertical convergence of $\tilde{F}$ (red, ${\tilde{F}}_z$) surpasses the total flux (black, H.F) numerically. This is made possible because the latitudinal convergence of $\tilde{F}$ (blue, ${\tilde{F}}_y$) drives a strong equatorward ozone flux. As the latitudinal convergence of C-EP flux has nothing to do with the Weber plot, the choice of ϕ_m = 60° and z_p = 50 hPa may improve the appearance of the linear relationship.

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As in Fig. 6 (bottom), but (ϕ_m, z_p) is (top) (50°, 50 hPa) and (bottom) (60°, 50 hPa).

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0023.1

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a. Description by horizontal flux

Integrating Eq. (21) from t₀ to t₁ for a given set of ϕ_m and z_p, we have

$m_d({⟨X_{\text{st}}⟩}_{t_1}-{⟨X_{\text{st}}⟩}_{t_0})=2\pi a\cos {\varphi }_m{\displaystyle {\int }_{t_0}^{t_1}{\displaystyle {\int }_{z_p}^{\infty }{\rho }_0{(\overline{\chi }{\overline{\upsilon }}^{*})}_{\varphi ={\varphi }_m}dzdt}}.$(26)

The interannual variations of the variables on the lhs and rhs of the equation are shown as the scatterplots in Fig. 10. If we take ϕ_m = 50° and z_p = 100 hPa (top row), the scatterplots obtained from CCM simulations show a well-aligned linear relationship between the two variables irrespective of the ODS levels. The fact that the slope of the regression line is less than 1 means that the amount of polar stratospheric ozone does not fully increase in response to the transported amount. As the downward flux across the bottom boundary is small (V.F shown in blue in Fig. 5), we expect that a part of the transported ozone is lost by chemical reactions and small-scale mixing. The importance of chemical ozone loss is also recognized by the smaller averages in ODS2000 than in ODS1960. As the standard deviation of ozone accumulation along the ordinate (y) is larger in ODS2000 than in ODS1960 [e.g., 0.5 for ODS1960 and 0.7 for ODS2000 (10⁹ DU km²) in the NH], whereas that of the poleward ozone flux along the abscissa (x) does not change appreciably [e.g., 1.4 for ODS1960 and 1.3 for ODS2000 (10⁹ DU km²) in the NH], the slope of the regression line is larger in ODS2000. The finding that the interhemispheric unified structure still holds under ODS2000 (Fig. 10b) suggests that the springtime polar ozone depletion, more pronounced in the Antarctic stratosphere (Fig. 3), has a limited effect, whereas the gas-phase ozone chemistry is important (section 6c). The results from ERA-Interim (Fig. 10c) do not show a unified structure and the regression line for the SH strongly depends on the value for 2002; the scatterplot shows no correlation if the year 2002 is excluded from the statistics.

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Scatterplots of polar stratospheric ozone accumulation against the fall-to-spring integral of the poleward ozone flux across latitude ϕ_m above altitude z_p [Eq. (26), (×10⁹ DU km²)]. (top to bottom) (ϕ_m, z_p) = (50°, 100 hPa), (50°, 50 hPa), and (60°, 50 hPa) under (left) ODS1960 and (center) ODS2000 CCM simulations, and (right) ERA-Interim from 1996 to 2010. Northern Hemisphere is in black and Southern Hemisphere is in red. Dashed red lines are derived by excluding the year 2002 that lies far to the right along the abscissa. Calculations are made referring to daily mean values on log-pressure coordinates taking the integration period [t₀, t₁] from 1 Sep to 31 Mar of the next year in the NH and from 1 Mar to 30 Sep for the SH.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0023.1

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If 50 hPa is chosen for z_p (Fig. 10, middle row), the sensitivity to ODS loading becomes higher in the SH (Fig. 10e); the ozone accumulation is negative and the regression line is no longer aligned with that of the NH. This is due to the increase of the slope associated with the decrease of the average and the increase of standard deviation (from 0.6 ± 0.2 to −2.2 ± 0.3) of the ozone accumulation; there is little change in the poleward ozone flux. In the ERA-Interim case (Fig. 10f), the polar stratospheric ozone accumulation becomes almost insensitive to the poleward ozone flux in the NH, and it is also true in the SH if the year 2002 is excluded. If ϕ_m is taken to be 60° (Fig. 10, bottom row), the unified structure between the two hemispheres is disrupted in all cases including ODS1960, ODS2000, and ERA-Interim without 2002 due to the appreciable decreases of the variation of the poleward ozone flux in the SH (Figs. 1 and 2).

b. Description by eddy heat flux

From Eq. (23), we have

$m_d({⟨X_{\text{st}}⟩}_{t_1}-{⟨X_{\text{st}}⟩}_{t_0})=2\pi a\cos {\varphi }_m{\displaystyle {\int }_{t_0}^{t_1}{\left({\rho }_0\overline{\chi }\frac{\overline{{\upsilon }^{\prime }{\theta }^{\prime }}}{{\overline{\theta }}_z}\right)}_{\varphi ={\varphi }_m,z=z_p}dt}.$(27)

The interannual variations of the variables in the two sides of this equation are shown as the scatterplots in Fig. 11. In the case of ϕ_m = 50° and z_p = 100 hPa (top panels), the regression lines shift appreciably to the left along the abscissa (note the change of scale from Fig. 10) and, in the case of CCM simulations (Figs. 11a,b), there are interhemispheric differences in the y intercept of the regression lines, although the parallel structure is maintained. The steepening of the regression lines in Fig. 11 suggests that the variations are smaller in the eddy heat flux than in the poleward ozone flux (Fig. 10) implying that the eddy heat flux at P_ref is not the major driver of the poleward ozone flux on an interannual time scale. Data from ERA-Interim (Fig. 11c) do not exhibit systematic dependence of polar ozone accumulation on the eddy heat flux in the NH.

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As in Fig. 10, but with polar stratospheric ozone accumulation approximated by eddy heat flux [Eq. (27)].

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0023.1

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If we select 50 hPa for z_p (middle panels), the variance of eddy heat flux becomes larger than that of 100 hPa whereas that of polar ozone accumulation becomes smaller (Figs. 11d,e). This improves the linearity of the scatterplot. The situation appears the same for ERA-Interim (Fig. 11f) if the 2002 data are excluded. The improvement is still greater if we take ϕ_m = 60° and z_p = 50 hPa (bottom panels). In the case of ODS1960 (Fig. 11g), increased variance of the eddy heat flux and reduced interhemispheric difference in the polar ozone accumulation improve the alignment of the regression lines for NH and SH. However, the negative ozone accumulation under ODS2000 disrupts the alignment by shifting the plots downward in the SH (Fig. 11h) even though high linearity is maintained in each hemisphere. The results from ERA-Interim (Fig. 11i) also shows a structure similar to that of ODS2000 if the year 2002 is excluded.

In summary, the linear relationship between the interannual variations of the fall-to-spring buildup of ozone integrated above and poleward of P_ref and the eddy heat flux during the corresponding period at P_ref is realized for each hemisphere; latitudinal averaging of the eddy heat flux between 45° and 75° (Weber et al. 2011) is not essential. By choosing P_ref at higher latitude and altitude such as P_ref(60°, 50 hPa), the linearity between the two variables and the interhemispheric unified structure are improved. Under ODS2000, however, the unified structure is disrupted owing to the enhanced ozone depletion in the SH. These findings are interpreted using the fact that the eddy heat flux at P_ref is derived from the vertical integral above P_ref of the vertical convergence of $\tilde{F}$ and that the interannual variation of the wintertime poleward ozone flux is well-captured by $\tilde{F}$ in the upper stratosphere.

a. Application of the constituent-based EP Flux to the transport problem

We have seen in Fig. 9 that the winter-to-spring enhancement of the vertical convergence of $\tilde{F}$ is accompanied by the simultaneous growth of the equatorward transport due to the latitudinal convergence of $\tilde{F}$. It is interesting to investigate such a mutual dependence in the interannual variations of the processes, not just the convergences of $\tilde{F}$, contributing to the poleward ozone transport. Such investigations will help us understand the physical processes underlying the linear relationship of the Weber plot. Figure 12 shows the scatterplots demonstrating the relationship between the time and altitude integrals of the poleward ozone flux due to ${\overline{\upsilon }}^{*}$ (ordinate) and those of each contributing process decomposed into the rhs terms of Eq. (25) (abscissa); integration is made from fall-to-spring above P_ref(ϕ_m, z_p), where (ϕ_m, z_p) is taken as (50°, 100 hPa), (50°, 50 hPa), and (60°, 50 hPa). The terms related to the latitudinal ozone gradient multiplied by F^(ϕ) and the zonal wind acceleration (third and fifth terms on the rhs, respectively) are omitted because they are small. The features for ODS2000 are similar (not shown). The latitudinal convergence of $\tilde{F}$ (first term, Figs. 12a1, 12a2, and 12a3, ${\tilde{F}}_y$) shows appreciably negative values (equatorward transport) with an enhancement at P_ref(60°, 50 hPa), although it shows little correlation with the ozone flux due to ${\overline{\upsilon }}^{*}$. The vertical convergence of $\tilde{F}$ (second term, Figs. 12b1, 12b2, and 12b3, ${\tilde{F}}_z$) is positive and contributes to the linear relationship showing a good correspondence to the poleward ozone flux. The magnitude of this term becomes larger as the altitude and latitude of P_ref increase. The vertical ozone gradient multiplied by F^(z) (fourth term, Figs. 12c1, 12c2, and 12c3, F × χ_z) is also positive and contributes to the linear relationship. Compared with the vertical convergence of $\tilde{F}$, the correlation coefficient with the poleward ozone flux is not as high; the magnitude of this term is larger at P_ref(50°, 100 hPa) but becomes smaller as the altitude and latitude of P_ref increase, especially at P_ref(60°, 50 hPa). Unresolved eddies (sixth, Figs. 12d1, 12d2, and 12d3, Y), estimated by subtracting the values of all rhs terms [and those of vertical advection of zonal momentum omitted in Eq. (25)] except the sixth term from those of the lhs, do not show positive correlation with the poleward flux due to ${\overline{\upsilon }}^{*}$. The magnitude of this term is comparable to the vertical convergence of $\tilde{F}$ at P_ref(50°, 100 hPa) but becomes smaller at P_ref(50°, 50 hPa) and P_ref(60°, 50 hPa). The description in the C-EP flux framework thus indicates that no single process can explain the linearity of the poleward ozone flux. Because the interannual variation of the springtime polar ozone accumulation results mostly from that of planetary wave breaking in the upper stratosphere rather than that of synoptic waves and unresolved eddies, the interannual variation of the transport features is captured by the convergence of $\tilde{F}$. The linear relationship demonstrated by Weber et al. (2011) is an approximation that relies solely on the vertical convergence of $\tilde{F}$.

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Decomposition, as in Eq. (25), of the fall-to-spring summed poleward ozone flux due to ${\overline{\upsilon }}^{*}$ integrated above P_ref(ϕ_m, z_p) (abscissa of Fig. 10 taken as ordinate) into terms representing (a) latitudinal and (b) vertical convergences of $\tilde{F}$, (c) the vertical gradient of ozone multiplied by F^(z), and (d) the contribution of unresolved eddies. (top to bottom) (ϕ_m, z_p) is (50°, 100 hPa), (50°, 50 hPa), and (60°, 50 hPa), respectively. NH (black) and SH (red) for ODS1960 condition.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0023.1

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One may argue against the use of the C-EP flux system because it is simply a rearrangement of the equations and does not deserve to be given a specific name. In fact, $\tilde{F}$ is merely the EP flux multiplied by $\overline{\chi }$ and the terms shown in Figs. 12b1–12b3 and 12c1–12c3 are equivalent to the second and third terms, respectively, on the rhs of Eq. (16) which is derived without using $\tilde{F}$. Still, the C-EP flux system is useful for understanding the Weber plot as more than an empirical relationship: it provides a mathematical basis as to why the eddy heat flux at a particular reference point P_ref can approximate the poleward constituent (ozone) transport vertically integrated above P_ref. The divergence of $\tilde{F}$ that implies a contribution to the equatorward transport in the lower stratosphere tells us how P_ref should be chosen for better realization of the linearity. Despite the difficulty in generalizing the importance of the term $\tilde{Y}$, it is a framework with which to describe the poleward constituent transport in terms of the divergence of $\tilde{F}$ that sheds light on the role of eddy momentum flux as well as that of eddy heat flux. Ultimately, the usefulness of this system will depend on whether it provides an advantage over the system described by Eq. (16), recognizing it as a useful extension of the TEM momentum equation to the meridional constituent transport.

b. Enhanced ozone depletion in the Antarctic late spring

We found a remarkable enhancement of the eddy ozone flux (∇ ⋅ M) and the simultaneous activation of chemical ozone losses during October to December in the Antarctic stratosphere (Fig. 5). This takes place, accompanying the mixing of ozone-depleted air and ozone-rich air that had been separated by the PV mixing barrier along the vortex edge, associated with the transition to the summer circulation. The ozone losses are brought about by the mixing in of high-concentration NO_x (mostly NO and NO₂) from outside of the polar vortex (Akiyoshi et al. 2004). Some details on this process are shown in Fig. 13, taking the model year 2019 as an example. Note that there is no correspondence to the year 2019 of the real atmosphere. Figure 13a shows the time series similar to those of Fig. 5, but for one of the 500 ensemble members. Figure 13b is the time–height section of the chemical ozone production rate averaged in the area poleward of 50°S. We can see that the ozone depletion that appears at around the end of October on the 5 hPa level propagates downward until early December. Figures 13c–h show the horizontal distributions of the mixing ratios of ozone (left) and nitrogen oxides (center) and chemical production rate of ozone (right) superposed on the contours of potential vorticity on the 850 K isentropic surface (around 10 hPa) for 25 October (middle) and 5 November (bottom) 2019. Since daily values of NO_x are not available in our model output, nitrogen oxides in this figure are defined by subtracting HNO₃ from total reactive nitrogen. On 25 October when the polar vortex is still present, ozone is distributed in an almost axially symmetric structure and nitrogen oxides have extremely low values in the polar vortex, while the chemical ozone production rate has hardly any systematic features. When the vortex becomes unstable and the mixing associated with the vortex breaking is initiated (5 November), the area of low ozone concentration spreads in the elongated vortex and scatters around the small patches torn from the main vortex, while some organized structure emerges in the chemical ozone production rate. In general, the enhanced ozone depletion is seen in the region where the low-latitude air migrates closer to the pole along PV contours associated with the polar vortex deformation. What is interesting here is that the high depletion rates are distributed also inside the vortex. This will be due to the nitrogen oxides penetrating across the PV barrier marked by the contours around −200 PVU (labeled as −20, e.g., between 40° and 120°W). The longitude of penetration found in the Western Hemisphere on 5 November migrates day by day (not shown). This will be the source of chemical ozone depletion compensating for the ozone increase due to eddy ozone transport.

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(a) As in Fig. 5, but extracted for the model year 2019, (b) time–height section of the chemical ozone production rate integrated poleward of 50°S (×10¹⁸ m⁻¹ day⁻¹). (c)–(e) Horizontal distributions of the mixing ratios of ozone (ppmv) and nitrogen oxides (ppbv), and ozone production rate (×10⁶ cm⁻³ s⁻¹), respectively, superposed on contours of potential vorticity (×10 PVU) on the 850 K isentrope for 25 Oct 2019. The meridian of 0° longitude is directed from the center to the left. (f)–(h) As in (c)–(e), respectively, but for 5 Nov 2019.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0023.1

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c. ODS-dependent variations

We have seen that the effect of ozone chemistry appears as the smaller values of y intercept and the larger slope in ODS2000 than in ODS1960 in the Weber plot (Figs. 4 and 11). The former is the direct consequence of enhanced gas-phase ozone chemistry under ODS2000 (section 5). The improved linearity associated with the change of z_p from 100 to 50 hPa in Fig. 11, combined with the altitude dependence of the homogeneous and heterogeneous chemistry on stratospheric ozone (Fig. 3), supports this interpretation. This is also consistent with the notion that the long-term decrease of March total ozone relies mostly on halogen-driven ozone depletion occurring all year round rather than the winter-to-spring heterogeneous chemistry on PSCs (Chipperfield and Jones 1999). The latter comes from the growth of the variance of ozone accumulation even though the dynamical fields remain mostly unchanged. The investigation on this mechanism is left for future studies.

The ODS-dependent variations in polar-stratospheric ozone could be investigated further by using the linear relationship between the polar stratospheric ozone accumulation and the fall-to-spring poleward ozone flux caused by residual circulation [Eq. (26), Fig. 10]. The left panel of Fig. 14 is the same as Fig. 10c, except that all years from 1979 to 2018 available from ERA-Interim are shown. The dashed line superposed on the plots shows a slope of 0.28, which is the gradient of the regression line between the poleward ozone flux and associated ozone accumulation for ODS1960 (Fig. 10a). As the 1960 data are not available in ERA-Interim, the dashed line is configured to contain the 1979 data point of the NH, assuming that the effect of the 1960–79 increase in ODS on the slope is negligible. Almost all of the plotted data points fall below this line in both hemispheres, indicating that, for every year, the fall-to-spring seasonal accumulation of polar ozone was less than that of 1979 because of the enhanced ozone depletion under the ODS burden that increased from 1979 onward. The scatterplot of Fig. 14 (left panel) is converted to two time series, one for each hemisphere, in the top panel on the right by sorting the data points by time. The line plots connecting plus (+) symbols in the bottom panel are the same as those of the top panel, except that the deviations from the dashed line rather than the raw values in the left panel are presented. The time series of the plus symbols show the temporal evolution of the components attributable to the enhanced chemical ozone loss relative to 1979. However, the attribution is not exclusive because the fluctuations due to transport that appear to be aligned with the regression line are superposed. As the ODS levels changed over a decadal time scale and the dynamical fields remained almost the same between ODS1960 and ODS2000 despite the prevailing year-to-year variations, the ODS-dependent changes could be extracted with the aid of a low-pass filter. The heavy dashed lines are the 3-yr running means applied to the time series of the plus symbols, whereas the line plots connecting squares (□) are the residual obtained by subtracting the ODS-dependent changes (dashed line) from the raw time series (top-right panel). The residual time series approximately represent the variations in poleward ozone flux. Differences between the two hemispheres are attributable mainly to the ozone transport (□), and the small negative bias of the SH relative to the NH (dashed lines) is the result of enhanced ozone depletion in the SH. The slow decrease that persists until around 2000 and a possible recovery thereafter reflect the temporal development of ODS level. See, e.g., Figs. 1–18 of WMO (2018) as for its time evolution.

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(left) As in Fig. 10c, but showing all available data from ERA-Interim. The dashed line passes through the NH data point for 1979 (i.e., the period from September 1979 to March 1980), with the slope of 0.28 taken from Fig. 10a. (right) Time series of Arctic (black) and Antarctic (red) stratospheric ozone accumulation from fall to spring obtained by sorting the data in the left panel by time. (top right) Raw values and (bottom right) lines connecting plus (+) symbols show deviations from the dashed line in the left panel. The heavy dashed lines are 3-yr running means. The lines connecting squares (□) show deviations of the raw values (top panel) from the running means.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0023.1

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