The mountain wave scheme is described by Dean et al. (2007) and computes the maximum negative ΔTSSO- and positive ΔTSSO+ temperature fluctuations associated with the positive and negative vertical parcel displacement of gravity waves generated by flow passing over subgrid-scale orography (SSO) in a climate or general circulation model. The approach assumes that the vertical propagation is described by linear hydrostatic mountain waves, generated by steady-state stratified flow over an isolated two-dimensional ridge; i.e. in the absence of wave dissipation mechanisms the change in wave amplitude and displacement with height is controlled by variations in the air density, the horizontal wind speed U (resolved in the direction of the wave vector) and the buoyancy frequency N. The scheme includes critical-level absorption and wave breaking to prevent the wave amplitude from exceeding the local “saturation amplitude”, defined as U/NFsat (where Fsat is the critical Froude number for saturation). The scheme also includes the effects of low-level flow blocking (Bacmeister et al., 1990), such that the initial wave amplitude is set equal to the “effective” mountain height heff of the SSO (i.e. h-hb, where h=nσσ is the height of the SSO and hb=h-U0/N0FC is the height of the blocked layer, σ is the standard deviation of the SSO, nσ is a constant, FC is the critical Froude number at which flow blocking is deemed to first occur, and the subscript “0” refers to quantities averaged between the ground and h).

As mentioned above, the scheme was previously inserted into the UM-UKCA global chemistry–climate model. UM-UKCA uses a quasi-equilibrium PSC scheme which models two types of PSC particles: NAT and mixed NAT–ice, both calculated assuming thermodynamic equilibrium with gas-phase HNO3 and H2O (following Chipperfield, 1999). For NAT particles, the saturation vapour pressure of HNO3, calculated following Hanson and Mauersberger (1988), is used to calculate the mass of HNO3 in the solid phase, while for mixed NAT–ice the saturation vapour pressure of water vapour over ice is calculated following Goff (1957). Surface area density for both PSC types is calculated assuming spherical particles with fixed density and radii. For NAT particles these are 1.35 g cm-3 and 1 µm and for mixed NAT–ice particles 0.928 g cm-3 and 10 µm, respectively. As a result, in this scheme each individual NAT or mixed NAT–ice particle is assumed to be the same size, while the number density, and so surface area density, changes with the availability of HNO3 and H2O, as well as temperature and pressure.

Only the cooling-phase ΔTSSO- computed by the mountain wave scheme is coupled or passed to the PSC scheme; i.e. the PSC scheme uses as input a “total” temperature T=TUM-UKCA+ΔTSSO-, where TUM-UKCA is the temperature explicitly resolved by the UM-UKCA model. The cooling phase only is used because, in the simple quasi-equilibrium PSC scheme, an instantaneous temperature rise will evaporate particles immediately if the temperature increases above the PSC formation threshold – when in reality this would take some time. This configuration – referred to from now on as the “perturbation” simulation – was run for 30 years (following a spin-up period of 30 years) for a perpetual year 2000 simulation at a horizontal resolution of N48 (equivalent to a grid spacing of 2.5∘ × 3.5∘) and 60 vertical levels (up to 84 km), using prescribed sea ice fraction and sea surface temperature. Note that values of the constants and parameters used by the scheme were set to nσ=3, Fsat=2 and FC=4, which were selected following initial analysis to optimise its performance over the Antarctic Peninsula by best matching the magnitude of the parameterised stratospheric temperature fluctuations with those explicitly resolved by a high-resolution regional configuration of the UM (see Orr et al. (2015) for further details). A control experiment – referred to from now on as the “control” simulation – was also run, which is identical to the perturbation run but with the exception that the mountain wave scheme is switched off. Orr et al. (2015) provide more details of both experiments. Output from both the model runs are at 6-hourly intervals (including values of ΔTSSO- from the perturbation run) and are used as the basis for all subsequent analysis.

Note that earlier studies such as those of Orr et al. (2012) and Keeble et al. (2014) show that this model represents the high-latitude Southern Hemisphere circulation and temperature structure well. Nevertheless, of particular importance is an accurate representation of circumpolar westerly flow at pressure heights of around 850 hPa because of its role in generating wave activity over the Antarctic Peninsula (Orr et al., 2008). To test this here, the 30-year mean wind at 850 hPa for austral winter (June–July–August) from the control experiment was computed and found to be in excellent agreement with the climatological mean from the reanalysis product ERA5 (i.e. the fifth-generation reanalysis product from ECMWF; Hersbach et al., 2020) over the 1979 to 2019 period (not shown).

We use estimates of the amplitude of mountain-wave-induced cooling (i.e. maximum cooling) from Atmospheric Infrared Sounder (AIRS) measurements of radiance perturbations for a 16-year period from 2002 to 2017 (Hoffmann et al., 2016, 2017), as well as from radiosonde soundings for a 14-year period from 2002 to 2015 (Moffat-Griffin et al., 2011). The nadir-scanning AIRS instrument is on board NASA's Aqua satellite, which since 2002 has typically made four passes per day over the Antarctic Peninsula, performing an across-track scan covering a distance of 1765 km on the ground. Each scan consists of 90 individual footprints that vary in size between 13.5×13.5 km2 at nadir and 41 × 21.4 km2 at the scan edges. Here we use the 666.5 cm-1 radiance channel of AIRS, which peaks in sensitivity to atmospheric temperatures at an altitude of around 22 km and has a full width at half maximum of 9 km, i.e. encompassing an altitude range that is particularly favourable for the formation of PSCs. See Fig. 1 from Orr et al. (2015) for a plot showing the temperature weighting function for this channel. The minimum radiance perturbation values (i.e. maximum cooling) are calculated for each single footprint. Note that the relatively coarse vertical resolution of AIRS limits the detection of waves with vertical wavelengths less than approximately 12 km, resulting in the attenuation of the measured wave amplitude; i.e. AIRS underestimates the true wave amplitude at short vertical wavelengths (Hoffmann et al., 2017). Note also that AIRS observes temperature disturbances from both orographic and non-orographic source regions, which in the context of this study would include those generated by storms over the Drake Passage to the north of the Antarctic Peninsula (Plougonven et al., 2012). The radiosonde soundings were launched around two to four times per week from Rothera Research Station, which is located along the western side of the Antarctic Peninsula. See Moffat-Griffin et al. (2011) for more details of the soundings. Figure 1 shows a map of the Antarctic Peninsula, which includes the location of Rothera Research Station, as well as orography from the Bedmap2 dataset (Fretwell et al., 2013).

To verify the parameterised mountain-wave-induced stratospheric cooling phase, 6-hourly values of ΔTSSO- for May–June–July–August–September–October over the Antarctic Peninsula from the perturbation run were compared against brightness temperature fluctuations measured by AIRS and temperature fluctuations measured by the radiosonde soundings. The brightness temperature fluctuations measured by AIRS are determined by removing a fourth-order polynomial function, representing the background atmosphere, from the original brightness temperatures (see Orr et al., 2015). To facilitate a comparison with the AIRS-observed minimum brightness temperature fluctuations(ΔBTAIRS-) over the Antarctic Peninsula, the values of ΔTSSO- are converted into brightness temperature (ΔBTSSO-) by computing a weighted-sum of ΔTSSO- over all vertical model levels from 15 to 45 km, i.e. by summing the value of ΔTSSO- multiplied by the associated normalised weighting function for the 666.5 cm-1 radiance channel of AIRS over the range of vertical levels. Figure 1 shows the regions over the Antarctic Peninsula that were used to compute ΔBTAIRS- and ΔBTSSO-. Note that the weighting function of the 666.5 cm-1 radiance channel is largely insensitive to atmospheric temperatures at altitudes both above 45 km and below 15 km. For the radiosonde-based measurements, we focus on the temperature perturbations ΔTRS- observed at an altitude of between 20.2 and 20.6 km above sea level (chosen because this range is both in the lower stratosphere and includes the vertical level of the UM-UKCA model at a height of 20.4 km for comparison), which are computed by removing a third-order polynomial function representing the background atmosphere from the original profile (see Moffat-Griffin et al., 2011). The distributions for the parameterised fluctuations are compared with those for the measurements and the probability density functions generated using a kernel density estimation.

We use output from the two simulations to examine the temperature distribution T-TNAT and T-Tice, where T is equal to either TUM-UKCA+ΔTSSO- (as used by the perturbation run) or TUM-UKCA (as used by the control run), and TNAT and Tice are the actual threshold temperatures for the existence of PSCs composed of NAT and water ice particles, respectively. The values computed for TNAT and Tice are sensitive to the temperature, pressure, HNO3 and water vapour mixing ratio (Hansen and Mauersberger, 1988; Marti and Mauersberger, 1993), which are taken from either the perturbation or control runs. We also compute for each run the FP of PSCs at an altitude of around 20.4 km, using a metric which depends on both the size of the temperature difference below either TNAT or Tice and the area of the region. For example, the FP for PSCs composed of NAT particles would be defined as 1FPNAT=0,T-TNAT>-0.1K∑i=1NAiT-TNATi,T-TNAT≤-0.1K, where i is an integer, N is the total number of model grid boxes within the region defined in Fig. 1, and Ai is the spatial area of the model grid box. An analogous equation exists for the FP for PSCs composed of water ice. Note that as the latitude–longitude grid used by the UM-UKCA model has non-uniform spacing and grid box area (due to varying longitude), the results from (1) are also scaled by the cosine of latitude. Note also that again the results are computed for the box situated over the Antarctic Peninsula shown in Fig. 1.

To identify the role of atmospheric conditions on controlling the parameterised stratospheric temperature fluctuations, the sensitivity of the amplitude of the cooling-phase ΔTSSO- to the vertical wind shear α is examined, with 2α=Uz2-Uz1Uz1, where z1=0.85 km, z2=21.0 km and here U is the zonal wind velocity (applicable because the large-scale wind regime over the region containing the Antarctic Peninsula is predominately zonal; Thompson and Wallace, 2000). Note that this approach would not represent the impact of more local variations in α that also influence vertical propagation (Kruse et al., 2016). Additionally, the sensitivity of ΔTSSO- to directional shear was also investigated by examining its relationship to a change in the direction of the wind with height, between z2 and z1. These results are again computed for the box shown in Fig. 1.

Finally, we investigated the local impact of the scheme on ozone chemistry by examining changes in both the surface area density of PSCs composed of NAT particles and the ClONO2 (chlorine nitrate) + HCl (hydrochloric acid) reaction. This heterogeneous reaction is crucial as in their gas phase HCl and ClONO2 are very unreactive, and so any chlorine they contain is unable to destroy ozone (Solomon, 1999). However, in the presence of a PSC surface (either solid or liquid) they can react with each other to produce Cl2 (chorine gas), as well as the removal of nitric acid (HNO3) from the atmosphere, resulting in the denitrification of the stratosphere, an effect which allows Cl2 to build up during wintertime. In the spring, the presence of solar ultraviolet radiation splits Cl2 into two chlorine atoms (so-called chlorine activation), which plays an important role in stratospheric ozone depletion (Solomon, 1999). Note that these results are calculated over the region 76–64∘ S and 75–55∘ W, which includes the Antarctic Peninsula but is not the box depicted in Fig. 1. Furthermore, to look at the non-local impacts we examined changes to ozone over the high-latitude Southern Hemisphere, as well as temperature and pressure changes in the lower stratosphere, i.e. the polar vortex. Keeble et al. (2014) previously showed that in the version of UM-UKCA used here polar ozone depletion can have significant impacts on the polar vortex.

Figure 2 compares the probability distributions of ΔBTSSO- and ΔBTAIRS- over the Antarctic Peninsula from May to October, showing that both distributions peak at similar values (around -0.5 K for ΔBTSSO- and -1 K for ΔBTAIRS-) but differ in terms of their shape, with ΔBTSSO- restricted to a relatively narrow range and a high peak compared to a broader range and lower peak for ΔBTAIRS-. However, the agreement between the two distributions improves over the lower and large cooling part of the tail, with both showing a lower bound of around -6 K, which is perhaps the region of the distribution that is critical for decreasing temperatures below the threshold for PSC formation (particularly during early winter and early spring). Note that possible reasons for the discrepancies between the two distributions could be that (a) the parameterised results only represent mountain-wave-induced disturbances, while AIRS results include contributions from both orographic and non-orographic source regions, and (b) the (vertical-only propagation) parameterisation scheme does not represent the horizontal propagation of waves (Preusse et al., 2002; Sato et al., 2012), which could be potentially important here and result in a horizontal shift of mountain wave activity away from the source region. There is a much better agreement between the distributions of ΔTSSO- and ΔTRS- over Rothera Research Station at an altitude of around 20.4 km (Fig. 3), with both distributions showing a relatively narrow range which peaks at a value of around -0.5 K, and the lower–cooling part of the tail extending to around -8 K. Note that the radiosonde results may also include contributions from non-orographic sources, such as from waves generated by the edge of the polar stratospheric vortex (Moffat-Griffin et al., 2011). Both Figs. 2 and 3 suggest that Antarctic Peninsula mountain waves with relatively large amplitudes of 5–10 K are uncommon (although it is noted that Eckermann et al. (2009) observed waves in this region with an amplitude of around 10 K for a particular case study).

Figure 4 shows maps detailing the location and frequency of instances when ΔBTSSO-<-0.1 K and ΔBTAIRS-<-0.1 K, i.e. the regions that contribute the most to the probability distributions shown in Fig. 2. The peak source region of the parameterised values is over the midsection and highest region (see Fig. 1) of the Antarctic Peninsula, i.e. centred over Alexander Island and Graham Land, which are regions of maximum σ (standard deviation of the SSO) in the UM-UKCA model (not shown). Note that here there are some contributions/waves from regions over the sea, which is due to the smoothness of the UM-UKCA mean orography (due to its relatively coarse resolution), which results in non-zero values of mean orography and associated SSO values over sea points around the coastline. By contrast, the AIRS-observed values show the peak source region to be more over the northern section of the Antarctic Peninsula. Note that the AIRS-observed values also show some contributions from over the sea surrounding the peninsula, which as discussed earlier is a possible reason for some of the disagreement between the distributions of parameterised and AIRS-observed cooling phase in Fig. 2.

The distributions of temperature difference T-TNAT and T-Tice from the perturbation and control runs are shown in Fig. 5 for the combined months of May to October, and reveal that the addition of ΔTSSO- to the explicitly resolved synoptic-scale temperature TUM-UKCA (i.e. T=TUM-UKCA+ΔTSSO-) in the perturbation run is particularly important for temperatures to drop below Tice, as without this the temperature rarely falls below the ice frost point temperature by more than a few degrees kelvin. For PSCs composed of water ice particles, the addition of ΔTSSO- to the synoptic-scale temperature in the perturbation run extends the lower bound of the distribution from around T-Tice=-2 or -3 K to T-Tice=-10 K. For PSCs composed of NAT particles it is extended from around T-TNAT=-10 K to T-TNAT=-20 K. Figure 6 is analogous to Fig. 5, but comparing the distributions of the temperature differences T-TNAT and T-Tice for the individual months of May to October for the perturbation and control runs, indicating that the additional cooling ΔTSSO- in the perturbation run is vital if T is to drop below Tice during the months of May, June, September and October – as during these months in the control run T=TUM-UKCA alone is too warm, i.e. late austral autumn–early austral winter, as well as early austral spring (consistent with the findings of McDonald et al., 2009). Note however that during July and August the cold side of the tail extends to T-Tice<0 K in the control run using T=TUM-UKCA. For PSCs composed of NAT particles the impact of the parameterisation in the perturbation run is particularly important for October (and to a lesser degree September), as this is the only month that the additional cooling ΔTSSO- is required for T to drop below TNAT, increasing the likelihood of PSC formation in early austral spring. However, it should be noted that the impact on PSC formation is also dependent on the local mixing ratios of HNO3 and H2O, which in part are affected by PSC formation and sedimentation earlier in the winter. We explore the impacts of the parameterisation on PSC surface area density in Sect. 3.4.

Using (1), Fig. 7 shows the FP for PSCs composed of both water ice and NAT particles at an altitude of 20.4 km for the individual months from May to October from both the perturbation and control runs. This shows that the FP of PSCs composed of NAT particles is around 2 orders of magnitude larger than that for PSCs composed of water ice particles due to them having a higher threshold temperature for formation (i.e. roughly around 195 K for TNAT and 188 K for Tice at this altitude). Thus it is much more likely that the temperature falls below the threshold temperature (cf. Figs. 5 and 6). The results show FP values for NAT particles peaking at around -4×106 K km2 in June and July, but with little sensitivity in any of the months to the inclusion of the additional cooling ΔTSSO- in the perturbation run. However, consistent with Fig. 6 is that the FP of PSCs composed of water ice particles is highly sensitive to the inclusion of the additional cooling ΔTSSO- in the perturbation run, with FP values around 4–5 times larger in July and August if the additional cooling is included compared to it being neglected in the control run, as well as significant increases also occurring during June and September, which otherwise show a negligible FP for the control run. For PSC composed of NAT particles, the FP values obtained from the perturbation and control run are much more similar (cf. Figs. 5 and 6), although the inclusion of the added cooling in the perturbation run does still result in increases. To further understand this, Fig. 8 shows maps of the difference in FP between the perturbed and control runs for the two types of PSCs examined, revealing that the differences evident in Fig. 7 (i.e. due to the addition of ΔTSSO- to the synoptic-scale temperature) are dominated by the contribution from mountain waves originating from the high-altitude base of the Antarctic Peninsula (which Hoffmann et al., 2013, showed was a hotspot of mountain wave activity).

Using (2), Fig. 9 compares the range of vertical wind shear α that was associated with the top 10 % (i.e. most cold) and bottom 10 % (i.e. least cold) of the distribution of the cooling phase ΔTSSO- at an altitude of 20.4 km. This shows that the largest negative cooling phases are associated with larger (positive) values of α, which is consistent with the understanding that waves with long vertical wavelengths in the stratosphere generate large temperature fluctuations and are associated with conditions where wind speed increases with height, i.e. causing wave refraction towards longer vertical wavelengths (Wu and Eckermann, 2008; Bramberger et al., 2017). Hoffmann et al. (2017) also showed that such conditions were conducive for the propagation of gravity waves into the lower stratosphere with long vertical wavelengths, which AIRS can best identify. Note that the top 10 % and bottom 10 % of the distribution were comparatively insensitive to the change in wind direction with height (not shown), which perhaps reflects that the wind regime is predominately unidirectional with height, i.e. a similar structure at many height levels in both the troposphere and lower stratosphere, consistent with an equivalent barotropic structure (Thompson and Wallace, 2000).

The impact of the additional cooling ΔTSSO- in the perturbation run on PSCs composed of NAT particles and chlorine activation is shown in Fig. 10. In the control run, the maximum surface area density of PSCs composed of NAT particles is modelled in June at an altitude of around 20 km, and extending from around 10 to 30 km. Between June and September, the surface area of the NAT particles decreases due to both rising (synoptic-scale) temperatures and the effects of denitrification and dehydration of the polar vortex by PSC sedimentation (Fahey et al., 1990; Teitelbaum et al., 2001). The result is that by August and September, little PSC surface area remains for chlorine activation. However, in the perturbation run, the surface area density of the NAT particles is increased at higher altitudes throughout the winter and early spring and reduced at lower altitudes. Importantly for chlorine activation in the late winter and spring (August and September), surface area density is increased by up to 20 %. Also shown in Fig. 10 is the flux through the ClONO2+ HCl heterogeneous reaction, a key reaction for the activation of chlorine from the major chlorine reservoir species. Surface area density changes of the NAT particles have only a modest impact on chlorine activation throughout the winter, but the small increases in surface area density in the late winter and early spring in the perturbation experiment result in large increases in chlorine activation throughout August and September, and thus enhancing ozone depletion (Solomon, 1999).

Figure 11 shows the impact of the additional cooling in the perturbation run on October monthly mean total column ozone. While Fig. 10 highlights the local impacts of the parameterisation scheme on PSC formation and chlorine activation, it can be seen from Fig. 11 that the impacts of the parameterisation scheme extend far beyond the region of the Antarctic Peninsula. This is unsurprising, as not only is the Antarctic Peninsula responsible for differences both upstream and downstream of the region, but other hotspots of mountain wave activity exist over Antarctica that can also play a role in PSC formation, such as the Transantarctic Mountains (e.g. Noel et al., 2009; Hoffmann et al., 2013, 2017; Alexander et al., 2017), which would also be sources of cooling via the parameterisation scheme. While perhaps it would be expected that October monthly mean total column ozone would be reduced above and downwind from the Antarctic Peninsula when the additional cooling ΔTSSO- is included in the perturbation run, there is little change to column ozone values here. Instead, total column ozone is reduced between 30 and 130∘ E and increased between 120 and 180∘ W. This is indicative of a shift of the polar vortex away from the Pacific sector of the Southern Ocean and towards the Indian Ocean sector. This result is supported by the 25 km pressure and temperature differences between the two simulations, which both indicate a change in the position of the polar vortex (Fig. 11).