All of the modelled data depicted are averaged to form annual means, or the two- monthly averages of July/August (JA) and December/January (DJ). The focus
lies on the JA and DJ averages because during these months E39/C yields the strongest and most robust tropical and higher-latitude dynamical NH response, respectively (not shown). Then, the 20 individual averages of the model period 2000 to 2019 are averaged to obtain 20-year inter-annual means, either “absolute” means representing one of the two scenarios, or “anomalous” means representing the difference of the scenarios, WARM-COLD. The term “response” is identified with “anomalous”. Finally, the three WARM realisations result in 60, the two COLD realisations in 40 samples per absolute inter-annual mean.
2.3.1
EP cross-sections
The modelled EP fluxes and EP divergences shown (Figure 2.3, for instance) are calculated from 12-hourly fields of instantaneous model data and then averaged as described above. Here, calculation method and scaling of the modelled EP flux are adopted from Edmon et al. (1980), the EP flux arrow patterns thus visually correspond to their respective divergence, times a plot-specific scaling factor, referred to as eddy activity scaling. Acceleration scaling better accounts for wave mean-flow interaction, especially in case of polar stratospheric warmings (Gray et al., 2003), but does not properly consider the eddy conservation properties being of interest here. In the cross-sections depicted, thin iso-lines quantify the respective EP divergence patterns, thick iso-lines demonstrate the position of the zero-wind line.
Eddy attenuation causes the EP flux to strongly drop off with height and only a small fraction of the flux, mostly of planetary-scale, actually enters the strato- sphere (Andrews et al., 1987). To overcome this visualisation problem many stud- ies apply a logarithmic ordinate and scale the EP flux by the inverse of density, thereby neglecting the eddy conservation properties mentioned above. Here, the EP cross-sections are separately generated for three different scale heights each of which obeying eddy activity scaling, but with respectively different scaling factors for the lower stratosphere (100−10 hPa), the uppermost troposphere lowermost
stratosphere (UTLS) (300−100 hPa), and the troposphere (1000−400 hPa). To
improve the visual traceability of eddy activity ascending across the tropopause, EP flux arrows at 100 hPa are plotted twice using the respective scaling factor, once in the stratospheric and once in the UTLS cross-sections.
A-geostrophic corrections are not applied to the modelled EP diagnostics and as such the latter is probably unreliable close to the equator where the weak horizontal Coriolis force cannot maintain a sufficiently tight geostrophic balance (Andrews et al., 1987). According to Edmon et al. (1980), however, the hor- izontal component of the EP flux may still specify horizontal Rossby-like flow across the equator. Also, the instantaneous EP flux represents a more qualitative measure of eddy activity propagation through the northern polar region during
et al., 2003), albeit yearly or two-monthly averaging should cope with this prob- lem (Newman et al., 2001). Finally, the EP flux better describes stratospheric than tropospheric eddy activity because eddies tend to be more Rossby-like above the tropopause then below (Son et al., 2007).
The net eddy-related northward transport of heat and momentum across a lat- itudinal circle consists of two components, a quasi-stationary part due to the time mean departure from the zonal-mean and a transient part due to the zonal-mean departure from the time mean (Lee, 1999, for instance). As an example, Figures 2.3b and 2.3c depict such quasi-stationary and transient EP flux contributions.
The monthly mean chosen here represents a filter in the sense that those in- ternal atmospheric wave modes can contribute to the quasi-stationary part whose constant-phase surfaces travel sufficiently slowly in a longitudinal direction and whose amplitudes vary slowly enough (Toth, 1992). This spontaneously-generated quasi-stationary contribution physically differs from that due to forced quasi-sta- tionary eddies showing, on the averaging time scale, geographically near-fixed phase surfaces and amplitudes. The transient eddy-related transport is thought to be mainly made up of travelling or standing oscillating eddies but can also con- tain other time-dependent mechanisms, such as changes in the mean state during polar warmings or breaking planetary eddies (Andrews et al., 1987). Because the life cycles of quasi-stationary and transient eddies tend to differ, a separate con- sideration helps to more profoundly validate the modelled EP diagnostics, and identify causal relationships connecting both modelled anomalous EP diagnostics and model boundary conditions.
2.3.2
Transformed Eulerian mean (TEM) stream function
Transformed Eulerian mean (TEM) residual velocities define the residual circu- lation which well represents Lagrangian mass transport, the latter differing from the Eulerian velocity field via the Stokes drift (Dunkerton, 1978); in the strato- sphere that residual circulation is commonly identified with the BD circulation, even though the latter is specifically calculated from observed atmospheric fields of chemical trace species and temperature because stratospheric vertical veloc-
ity is weak and cannot be measured (Andrews et al., 1987). Here, the terms
“residual” and “Brewer-Dobson” circulation are used interchangeably.
The computation of TEM residual velocities involves modelled values of Eule- rian meridional and vertical velocities, the northward eddy flux of heat, and the vertical buoyancy-gradient. A TEM stream function can then be obtained which has the advantage over residual velocities in that it simultaneously provides in- formation on strength and latitude height structure of the residual circulation.
Here, the calculation of the TEM stream functions follows the approach by Ed-
data. The residual circulation (Figure 2.2c, for instance) is parallel to the TEM stream function iso-lines, clockwise around a stream function maximum, counter- clockwise around a minimum, and its strength is proportional to the density of the iso-lines.