The MPI-ESM consists of the coupled atmospheric and ocean general circulation models, ECHAM6 and MPIOM , the land and vegetation model JSBACH , and the model for marine bio-geochemistry HAMOCC . We use the “mixed-resolution” configuration of the model (MPI-ESM-MR). The ocean model uses a tripolar quasi-isotropic grid with a nominal resolution of 0.4∘ and 40 vertical layers. ECHAM6 is run with a triangular truncation at wave number 63 (T63), which corresponds to 1.9∘ in latitude and longitude. The vertical grid contains 95 hybrid σ-pressure levels resolving the atmosphere from the surface up to 0.01 hPa. The vertical resolution is nearly constant (700 m) from the upper troposphere to the middle stratosphere, and is less than 1000 m at the stratopause. The time steps in the atmosphere and ocean are 450 and 3600 s, respectively.

The model has been used for many simulations within the CMIP5 (Coupled Model Intercomparison Project Phase 5) framework . An overview of the dynamics of the middle atmosphere in these simulations is given by . In this study, the preindustrial CMIP5 simulation (piControl) is used as reference. The forcing is constant in time and uses pre-industrial conditions (AD 1850) for the greenhouse gases. Solar irradiance and ozone concentrations are averaged over a solar cycle (1844–1856 for the solar irradiance and 1850–1860 for ozone concentrations). No volcanic forcing is applied. A period of 150 years of this simulation is used.

In order to analyze the impact of ozone changes on the model climate, two additional experiments with reduced ozone concentration are carried out. In one experiment, the mesospheric ozone is reduced by 40 % between 0.01 and 0.1 hPa polewards of 60∘ N (this is called “meso-O3”). In the other experiment, stratospheric ozone is reduced by 20 % between 1 and 10 hPa polewards of 60∘ N (this is called “strato-O3”). We perform on–off experiments, whereas in reality EPP causes a constant (but variable) ozone loss. However, the magnitude of the prescribed ozone losses is based on satellite observations for winter conditions between years with high geomagnetic activity and years with low geomagnetic activity. In general, the impact of energetic particles is sporadic in the mesosphere; , however, showed that the direct HOx effect induces long-term variability in mesospheric ozone of up to 34 % from November to February in satellite data. and revealed an upper stratospheric ozone loss between 10 and 15 % due to energetic particles for the Antarctic high latitudes in long-term measurements. Note that the applied ozone losses are slightly larger than the EPP influence diagnosed from observations. We use the stronger forcing to obtain a clear signal-to-noise ratio. However, this implies a potentially overestimated climate response.

To facilitate experiment design, we fixed ozone losses to be constant over time. Although we concentrate our analysis on boreal winter high latitudes, this still allows us to gain insights into boreal spring (i.e., the transition time from polar night to polar day). Observed ozone losses in summer are in general smaller than during winter, but this idealized setting allows for easy comparison of potential effects during the different seasons. In order to test whether the winter response is influenced through preconditioning, in this experiment design we repeated the experiments with ozone losses prescribed only from December to March. However, as the results are qualitatively very similar and differ only in the magnitude of the responses, we discuss only the results of the experiments with ozone losses prescribed all year. Both experiments, with mesospheric and stratospheric ozone loss, are forced by the same conditions as the piControl experiment. Moreover, the simulations are restarted from the same year in the piControl experiment. This ensures that the ocean state is similar in all experiments. For both simulations 150 years are simulated.

The simplistic nature of our experiments is intentional and, we think, useful. We chose this idealized experimental design in order to separate the climate impact of stratospheric and mesospheric ozone loss due to EPP and to identify the relevant mechanism which determines how EPP affects the climate. Prescribing complex ozone reductions that vary in space, by season and year, or simulating the ozone reduction interactively might enable more realism, but they do not facilitate the identification of potential mechanisms. However, due to the simplification we cannot consider all features associated with EPP. In particular, three main effects are not taken into account: (a) energetic particles entering the atmosphere only over the auroral oval regions ; (b) the negative ozone signal due to EPP propagating from the stratopause in mid-winter to the lower stratosphere in spring within the polar vortex ; and (c) that the polar vortex can shift off the pole to regions with more solar radiation. We, instead, apply constant ozone reduction between the stratopause and mid-stratosphere (1–10 hPa) over the entire polar cap. The climate response in our simulations is likely overestimated as we reduce ozone over a larger latitudinal and altitude region than observations suggest.

In Sects.  and  the differences between the experiments and the control simulation (i.e., piControl) are analyzed. Statistical significance is calculated using the 95 % confidence intervals assuming normally distributed regression errors and using the 0.975 and 0.025 percentile of Student's t distribution with the appropriate degrees of freedom. Properties of two simulations are considered statistically significantly different if the mean value of the control simulation is outside 95 % confidence interval of the experiment.

The radiative transfer scheme of MPI-ESM is based on the rapid radiation transfer suite of models optimized for general circulation models (RRTMG; ). The RRTMG is widely used and its ability to calculate radiative forcing has been evaluated by . In its stand-alone version here, it is used to study the impact of ozone on heating rates. It is divided into 16 bands in the longwave (1000–3 µm) and 14 bands in the shortwave (12 195–200 nm; ). The spectral bands are chosen to include the major absorption bands of active gases. The major ozone absorption bands – Hartley band (200–310 nm), Huggins bands (310–350 nm), and Chappuis bands (410–750 nm) – are considered. However, absorption of oxygen at shorter wavelengths than 200 nm is missing, which could lead to an underestimation of the total heating rate in the mesosphere. The radiative transfer scheme is further described in and , and further on we will refer to it as the radiative transfer model “PSrad”.

The shortwave and longwave components are calculated separately. Furthermore, optical properties for gases, clouds, and aerosols are computed separately for longwave and shortwave components and, finally, combined to compute the total heating rates. PSrad expects profiles of gases (H2O, N2O, CH4, CO, O3), profile of cloud parameters as well as additional parameters (e.g., albedo and zenith angle) as input. Additionally, CO2 and O2 are set to fixed values invariant with height. For all other gases, we use multi-year monthly means representative of the late 20th century provided by the atmospheric and chemistry model HAMMONIA (Hamburg Model for Neutral and Ionized Atmosphere; ). For the albedo and cloud properties (e.g., cloud fraction, cloud water/ice content), multi-year monthly means from the piControl experiment are used. All quantities are extracted for 75∘ N. The zenith angle is calculated for 12:00 UTC at 75∘ N, 0∘ E for the 15th of each month. The latitude of 75∘ N is chosen to be exemplary for polar latitudes. The results are insensitive to the actual latitude, the main difference at other polar latitudes is the length of the polar night. Note that the length of the polar night for an air pocket also depends on the altitude and on atmospheric dynamics (e.g., movement of the polar vortex). Both effects are omitted in this study. In our simulations ozone is reduced independent of actual dynamics, over the entire polar cap (60–90∘).

To quantify the impact of ozone on the heating rates, we perform multiple runs in which for each run the ozone concentration of a single layer is set to 0. Then we take the differences between a control run and each single run. The differences of each run are, finally, added up for the estimation of the total heating rate. This method allows us to consider that layers of reduced ozone will lead to increased absorption of shortwave radiation in the layers directly below.

Ozone loss directly alters the atmospheric energy transfer. Before analyzing circulation and climate impacts due to ozone losses, we study the heating rate response using the radiative transfer model PSrad. The heating rates are calculated for the polar latitude of 75∘ N (see Fig. ). As the effect of EPP is most important at the winter polar cap, we will concentrate our analysis on boreal winter high latitudes.

In the shortwave part of the spectrum, ozone strongly absorbs solar radiation and heats the whole atmosphere. The strongest heating (about 12 K day-1) occurs in the uppermost stratosphere around 1 hPa. Ozone loss would, hence, result in relative cooling due to reduced heating. The ozone heating and, hence, the cooling caused by ozone reduction become smaller for larger zenith angles and vanish in polar night.

In the longwave part of the spectrum, the radiative effect of ozone is highly temperature dependent. Ozone cools the atmosphere via infrared emission in the stratosphere and in warm regions of the mesosphere below 0.1 hPa (see Fig. b). The strongest cooling (about -2 K day-1) occurs at the stratopause. In the troposphere and in the cold regions of the mesosphere above 0.1 hPa, the absorption of outgoing radiation exceeds the infrared emission resulting in a heating of the atmosphere due to ozone.

In total, the shortwave heating dominates all sunlit months. During polar night, ozone cools the atmosphere between 0.1 and 100 hPa and, hence, ozone loss in the stratosphere and lower mesosphere results in warming. Near the terminator (e.g., at 75∘ N in November and February), the net influence of ozone is more complex: at some altitudes ozone heats the atmosphere and at some ozone cools it. The net radiative forcing of ozone loss depends on when and where ozone is reduced. For example, in November, stratospheric (1 hPa) ozone loss leads to a heating, but mesospheric (0.1 hPa) ozone loss leads to cooling.

These results are in line with previous work. It is widely accepted that ozone loss in spring and summer leads to stratospheric cooling e.g.,. Some studies analyzed the radiative forcing of winter stratospheric ozone loss. showed that the observed stratospheric ozone loss in the late 20th century led to winter warming and summer cooling in a global climate model. Using a radiative transfer model with fixed dynamical heating, confirmed that stratospheric ozone loss over the winter pole results in small stratospheric radiative warming and dominating stratospheric dynamical cooling. showed that the shortwave cooling of the stratosphere due to ozone loss dominates, in all sunlit months, infrared heating due to ozone loss. Recently, simulated warming in mid-winter and cooling in late winter and spring in the upper stratosphere for ozone losses explicitly induced by EPP.

The results above are confirmed by the actual heating rate anomalies induced by the applied ozone losses in the experiments meso-O3 and strato-O3 (not shown). The heating rates are calculated at the first time step of the model at which the radiation is updated (1 January) excluding any feedbacks occurring only at later time steps. Note that the exact values may change for other months, especially depending on the sunlit area. Compared to the total heating rates of piControl, the changes in heating rates caused by a 40 % reduction of mesospheric ozone in polar night are very small (on average about -0.01 K day-1 and -0.4 %), and by a 20 % reduction of stratospheric ozone on average are about 0.12 K day-1 and 2.6 %. This agrees with the estimate of , who simulated a change of 0.1 K day-1 in the winter stratospheric heating rate due particle-induced ozone loss. The change in heating rates due to the stratospheric ozone change is in the range of solar UV forcing (0.1 K day-1) .

As changes in heating rates due to reduced ozone during polar night are small, one might reason that climate impact of winter polar ozone loss is small. But large effects may occur in regions slightly outside the polar night. Furthermore, several studies suggested that changes in the heating rates due to winter polar ozone loss leads to dynamical cooling e.g.,, whereas the initial radiative forcing suggests warming. Hence, we further analyze the climate impact of winter polar ozone loss. As large variations in the polar vortex can propagate downward and affect the surface climate, we first concentrate on the circulation changes of the middle atmosphere due to ozone loss, which are a prerequisite for a potential climate impact of EPP. In the following, we analyze the climate effect of idealized polar mesospheric ozone loss, while in Sect.  we analyze the climate effect of idealized polar stratospheric ozone loss.

Figure a and d show the zonal mean temperature and zonal wind simulated for boreal winter (December–February). Main observed characteristics of the zonal mean temperature, e.g., the stratopause tilt from the summer towards the winter pole, are well reproduced. The changes in the zonal mean zonal wind are consistent with the temperature changes via the thermal wind balance. In most regions, the difference between meso-O3 and piControl is very small (see Fig. b and e).

Near the winter pole, a dipole structure emerges with cooling in the upper stratosphere and warming in the mesosphere. According to our radiative transfer calculations mesospheric winter polar ozone loss should lead to cooling. However, the temperature differences are small (below 1 K) and not significant at the 95 % level. As the applied forcing is very small, small and barely significant values are expected. At the winter pole, the polar vortex slightly weakens, whereas the mesospheric winds strengthen; these differences are not significant. The signal is only slightly stronger but still insignificant if winters with major sudden stratospheric warmings (SSWs) are excluded (not shown). As stated above, large variations in the winter polar vortex can propagate to the surface influencing the surface climate. However, the changes reported here are small. The anomalies reaching the troposphere are statistical artifacts. Indeed, the surface temperature reveals no statistically significant change (not shown).

The temperature and wind signals are not statistically significant after 150 simulated years; it nevertheless makes sense to analyze if the signals could have a physical explanation and not be purely accidental. Note that with fewer simulation years apparently very different results can be obtained. Upon analyzing different simulation periods, we obtain mesospheric warming and cooling of apparent significance. Particularly, we calculated a statistically significant weakening of the polar vortex when using only the first 80 simulation years. We cannot identify a model drift in the experiments, which could explain the disagreement between the 150-year and 80-year runs. However, the model simulates variability on timescales up to multi-decadal, which is common in many climate models , and might cause the apparently different responses to ozone reduction in different sub-periods of the 150-year simulation. The high degree of internal variability of the winter polar stratosphere can obviously create incorrect apparent signals. The most dramatic demonstration of this variability are major sudden stratospheric warmings (SSWs), which occur on average about six times per decade in the Northern Hemisphere (see , for more information on SSW). A short simulation period may lead to an over-representation or under-representation of SSWs. Over our whole simulation period (150 years) the number of major SSWs is balanced in all three experiments. In total, there are 102 events in piControl, 99 events in meso-O3, and 109 events in strato-O3 (using a reversal of the zonal wind at 60∘ N and 10 hPa as the criterion for major SSW occurrence).

In this section, we analyze the climate effect of idealized polar stratospheric ozone loss. Figure a and d show the zonal mean temperature and zonal wind simulated for boreal winter (December–February) for piControl, and Fig. c and f show the difference between strato-O3 and piControl. The winter stratosphere warms due to ozone loss as expected from the calculations with the radiative transfer model. As a consequence of the warming, the stratospheric winds weaken. The small mesospheric cooling likely results from enhanced eastward momentum deposition from gravity waves as shown by . Our results are in line with earlier studies. and identified warming in the polar winter upper stratosphere due to EPP in reanalysis data, but their magnitude is much stronger (5 K) than in our simulations. Regarding the zonal wind response, the two studies differ from each other. analyzed strengthening of the polar vortex with enhanced equatorward planetary waves, whereas analyzed weakening of the polar vortex. The statistically significant warming of the summer mesopause is an indication of inter-hemispheric coupling as discussed by and also persists for winters without a sudden stratospheric warming event.

Figure  shows only changes for the mean over December to February, while the radiative transfer model suggests that the month-to-month variability of the forcing is large. To study whether the impact of stratospheric ozone loss differs over the course of the winter, we analyze the monthly means of temperature and zonal wind (see Fig. ). Ozone loss during most of the polar night (except December) leads to warming, whereas at all other times and locations it leads to cooling. This agrees with the calculations of the radiative transfer model and with our assumption that the winter cooling is not affected by strong summer warming. However, the cooling in December is unexpected from the radiative transfer modeling. argued that the polar winter atmosphere transits from a radiatively controlled state in early winter to a dynamically controlled state in late winter. Given the opposite sign of the diabatic forcing, the simulated cooling must have been already dynamically created in December. This is in agreement with early model studies which showed that uniform ozone losses lead to dynamical cooling at the boreal winter polar latitudes e.g.,. suggested that the dynamical cooling is due to weakening of the mean meridional circulation related to reduced wave forcing caused by a reduction of midlatitude wave flux into the stratosphere. Similarly, in our simulations we find a (albeit not significant) reduction of the zonal mean eddy heat flux at 100 hPa in the midlatitudes from December to March (not shown). This may be caused by enhanced wave reflection as suggested by for the dynamical response to 11-year solar irradiance forcing. The dynamically induced cooling in December also occurs in simulations in which the ozone is only reduced from December to March (not shown). Also, reported dynamical cooling in the winter polar stratosphere due to EPP. However, in their model the cooling dominates the winter (DJF) signal, whereas we obtain small warming for the DJF average (see Fig. ). The magnitude of the signal decreases in our simulations, especially in late winter, if we exclude all seasons with a SSW (not shown).

The zonal wind changes consistently with the temperature changes via the thermal wind balance. Simultaneously with warming (cooling), the polar wind weakens (strengthens). Anomalies in the polar vortex occasionally reach the troposphere (e.g., the strengthening in November or the weakening in December or February). Although most of those changes are not significant, some disturbances in the polar vortex may still force the surface temperature (see Fig. ). In our simulations for boreal winter, stratospheric ozone loss cools large parts of the northern high latitudes from northern Europe to Eurasia and over North America. Excluding all winters with a SSW strengthens the cooling over North America (not shown). Over Greenland and the pole, the surface warms. This is consistent with the weakening of the zonal wind in December (see Fig. d). However, most changes are small and not significant. and analyzed statistically significant changes in surface temperature and found warming over Eurasia of about 1.5 K and cooling over North America of about -1 K. Compared to both studies the amplitude of our signal is much smaller. The weaker signal also persists if we exclude all winters with a SSW (not shown). However, based their study on only 9 simulated years and we have shown that the large variability in the polar winter stratosphere can cause incorrect apparent signals if the ensemble is not large enough. Note that another difference between our and their study is that our model is coupled to an interactive ocean. could not rule out that their results are by chance induced by the NAM.