NOy production, ozone loss and changes in net radiative heating due to energetic particle precipitation in 2002-2010

We analyze the impact of energetic particle precipitation on the stratospheric nitrogen budget, ozone abundances and net radiative heating using results from three global chemistry-climate models considering solar protons and geomagnetic forcing due to auroral or radiation belt electrons. Two of the models cover the atmosphere up to the lower thermosphere, the source region of auroral NO production. Geomagnetic forcing in these models is included by prescribed ionization rates. One model 5 reaches up to about 80 km, and geomagnetic forcing is included by applying an upper boundary condition of auroral NO mixing ratios parameterized as a function of geomagnetic activity. Despite the differences in the implementation of the particle effect, the resulting modeled NOy in the upper mesosphere agrees well between all three models, demonstrating that geomagnetic forcing is represented in a consistent way either by prescribing ionization rates or by prescribing NOy at the model top. Compared with observations of stratospheric and mesospheric NOy from the MIPAS instrument for the years 2002–2010, 10 the model simulations reproduce the spatial pattern and temporal evolution well. However, after strong sudden stratospheric warmings, particle induced NOy is underestimated by both high-top models, and after the solar proton event in October 2003, NOy is overestimated by all three models. Model results indicate that the large solar proton event in October 2003 contributed about 1–2 Gmol (10 mol) NOy per hemisphere to the stratospheric NOy budget, while downwelling of auroral NOx from the upper mesosphere and lower thermosphere contributes up to 4 Gmol NOy. Accumulation over time leads to a constant particle15 induced background of about 0.5–1 Gmol per hemisphere during solar minimum, and up to 2 Gmol per hemisphere during solar maximum. Related negative anomalies of ozone are predicted by the models nearly in every polar winter, ranging from 10– 50% during solar maximum to 2–10% during solar minimum. Ozone loss continues throughout polar summer after strong solar proton events in the Southern hemisphere and after large sudden stratospheric warmings in the Northern hemisphere. During mid-winter, the ozone loss causes a reduction of the infrared radiative cooling, i.e., a positive change of the net radiative heating 20 (effective warming), in agreement with analyses of geomagnetic forcing in stratospheric temperatures which show a warming in the late winter upper stratosphere. In late winter and spring, the sign of the net radiative heating change turns to negative (effective cooling). This spring-time cooling lasts well into summer and continues until the following autumn after large solar proton events in the Southern hemisphere, after sudden stratospheric warmings in the Northern hemisphere.

2007; Sinnhuber et al., 2011). However, these observations were mostly limited to sunlit areas, and thus did not observe deep into polar night. Observations from the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS, Fischer et al. (2008)), which covered also the polar night region, show that NO x produced by energetic particle precipitation (called EPP NO x in the following) reaches down to altitudes below 30 km in both hemispheres, in nearly all winters observed (Funke et al., 2014a). Particularly high values of EPP NO x are observed in Northern hemisphere late winters after the strong sudden 5 stratospheric warming events in winters (Randall et al., 2006Funke et al., 2014a;Sinnhuber et al., 2014;Funke et al., 2017). These warmings were followed by long-lasting downwelling in the mesosphere and upper stratosphere enabled by a strong polar vortex re-forming after the event. It was shown both from observations (Siskind et al., 2007;Orsolini et al., 2010) and model results (Limpasuvan et al., 2016) that this period of enhanced downwelling was characterized by the formation of an elevated stratopause in the upper mesosphere. 10 The so-called EPP indirect effect  due to downwelling of auroral NO x into the stratosphere leads to an increase in the catalytic ozone loss in the upper and middle stratosphere progressing from the upper to the lower stratosphere during polar winter. Lower values of ozone in the upper stratosphere are observed during winters characterized by large particle forcing or enhanced values of NO y (Natarajan et al., 2004;Randall et al., 2005), and downwelling negative ozone anomalies have been observed for the first time by (Fytterer et al., 2015a;Damiani et al., 2016). However, quantification of the particle 15 induced ozone loss by observations is difficult, because a) MIPAS observations of EPP NOx show that EPP-induced ozone loss must occur in every year, so only relative differences can be obtained from observations; b) stratospheric ozone is quite variable anyway, and c) a much longer timeseries than used by Fytterer et al. (2015a) would be necessary to attribute the observed anomalies clearly to the particle precipitation. Model studies are more suited to study the ozone loss, as models can do on/off experiments with and without particle precipitation in a clearly defined way.
In this paper we analyze results from three chemistry-climate models considering proton and electron forcing over the period from mid-2002 to mid-2010, e.g, covering 11 polar winters in both hemispheres. NO y 1 in the middle atmosphere from all three models is compared to MIPAS observations to evaluate the model results. The ozone loss at high latitudes in the middle atmosphere is quantified from the difference of model runs with and without particle impact, and changes in the net radiative heating are estimated from these results. 5 The models used are described in Sec. 2.1, MIPAS data are described in Sec. 2.3. NO y intercomparison with MIPAS data and the impact of energetic particle precipitation on middle atmosphere NO y are shown in Sec. 3, ozone intercomparisons with MIPAS data and the quantification of the EPP impact on ozone and stratospheric heating rates based on model results are discussed in Sec. 4.
2 Description of models and observations 10

Models
We use results from three different models in this study which have been used to determine the impact of energetic particle precipitation in the past (e.g., Funke et al. (2011Funke et al. ( , 2017) to analyze differences in the model results due to the implementation of the particle impact and the model transport schemes, and to derive a range of possible model results. The models used are 3dCTM , KASIMA (Reddmann et al., 2010), and EMAC (Joeckel et al., 2010). The models cover 15 different vertical regimes: 3dCTM and KASIMA cover the altitude region from roughly the tropopause up to the lower thermosphere (called high-top models in the following), the EMAC model covers altitudes from the surface up to the mesopause (called medium-top models in the following). All three models have a detailed description of middle atmosphere chemistry, and use temperatures and wind fields which are relaxed to meteorological analysis data provided by ECMWF in the stratosphere and below. However, the models differ in the treatment of energetic particles on the atmospheric composition, and in the 20 treatment of the impact of non-resolved gravity waves on atmospheric transport. 3dCTM and KASIMA cover the source region of particle-induced NO x production, and NO x production is driven by prescribed ionization rates; 3dCTM additionally also considers photoionization. EMAC does not cover the source region of NO x production, and the indirect effect is considered by prescribing NO y at the model upper boundary.
KASIMA and EMAC are chemistry-climate models internally calculating temperatures and wind fields, which however are 25 nudged to meteorological analysis data below the stratopause; 3dCTM is a chemistry-transport model driven by prescribed temperatures and windfields. KASIMA and EMAC use standard parameterizations of the gravity wave drag, while in 3dCTM, only resolved gravity waves are considered, restricting the spectrum to wavelengths ≥500 km.
The models are described in more detail in the following subsections. In Sec. 2.2, the different model scenarios used are described.

3dCTM
The three-dimensional chemistry and transport model (3dCTM) is an advanced version of the 3dCTM described in Sinnhuber et al. (2012). The model is based on a combination of the stratospheric transport model as described in  and a chemistry and photolysis code adapted from the SLIMCAT model (Chipperfield, 1999). The model operates on isobaric surfaces and reaches from the tropopause to the lower thermosphere (317.00 hPa -5 · 10 −6 hPa, approximately 10 -140 km) 5 with a vertical resolution of 1-3 km. The horizontal resolution is 2.5 • ×3.75 • .
Temperatures, densities and wind fields are prescribed using output data from the Leibniz Institute Middle Atmosphere Model LIMA (Berger, 2008). LIMA is nudged to tropospheric and stratospheric data from ECMWF-ERA40 below 45 km which introduce realistic short-term and year-to-year variability. LIMA applies a triangular horizontal grid structure with 41804 grid points in every horizontal layer (∆x ≈ ∆y ≈ 110 km). This allows to resolve the fraction of the large-scale internal 10 gravity waves with horizontal wavelengths of ≥ 500 km. Temporal LIMA data are made available to 3dCTM every six hours.
3dCTM uses a family approach for neutral gas-phase constituents in the stratosphere at altitudes below the 0.33 hPa level, but not in the mesosphere and lower thermosphere. The impact of energetic particles is considered by prescribed ionization rates for precipitation of electrons, proton and alphas from the AIMOS model (Wissing and Kallenrode, 2009), version v1.6.
Photoionization of N 2 , O 2 , N and O in the EUV and NO photoionization in the Ly-α band has been included as well. EUV 15 photoionization rates are calculated based on the parameterization of Solomon and Qian (2005). Ionic reactions are not included in the chemistry scheme, but the production of odd nitrogen species as a function of ionization rates and atmospheric state is calculated using the parameterization of Nieder et al. (2014), adapted for photoionization by implementing a dependency on the primary ion composition. The production of HO x is considered using the parameterization of Solomon et al. (1981), an approach which is widely used and has been validated both in comparison to observations of ozone loss, and in comparison to 20 ion chemistry model results, see, e.g., (Funke et al., 2011;Sinnhuber et al., 2012).

KASIMA
The Karlsruhe Simulation of the Middle Atmosphere (KASIMA) is a 3-dimensional mechanistic model of the middle atmosphere solving the primitive equations including middle atmosphere chemistry (Kouker et al., 1999). For the simulations presented here, the model was run on isobaric surfaces from 7 to 120 km with a vertical resolution of 750 m in the stratosphere, 25 gradually increasing to 3.8 km at the upper boundary. The horizontal resolution in the simulation is ≈5.4°× 5.4°(T21). The model is coupled to the specific meteorological situations by using the analysed geopotential field at the lower boundary (7 km) and applying analysed vorticity, divergence and temperature fields from ECMWF ERA-interim (Dee et al., 2011) below 1 hPa.
The parameterization of the gravity-wave drag is based on the formulation of Holton (1982). The parameterization has been 30 modified compared to the version described in Kouker et al. (1999) in order to better describe the cross mesopause transport often observed after sudden stratospheric warmings. The spectral distribution of the vertical momentum flux is now described with a Gaussian function of centroid of 7 m/s and a standard deviation of 50 m/s with phase speeds of 0, 20, 40, 60 an 80 m/s. The filter condition for critical phase speeds has been extended to be applied when the absolute difference between the speeds is less than 10 m/s. The latter condition effectively prevents gravity waves of low phase speed from propagating and breaking in the lower mesosphere. Only gravity waves of higher phase speed then break at higher altitudes, causing an elevated stratopause to build. In addition, the numerical implementation of the vertical diffusion has been re-formulated for better mass conservation according to Schlutow, Becker and Körnich (2014). The model includes a full middle atmosphere chemistry scheme based on a 5 family concept. In the mesosphere, the family members are transported separately. To consider the impact of energetic particle precipitation, proton and electron ionization rates from the AIMOS model (Wissing and Kallenrode, 2009) version v1.6 are prescribed. 1.25 NO x per ion pair are produced with a partitioning between N and NO of 45% and 55% as described in (Porter et al., 1976;Jackman et al., 2005). 0-2 HO x per ion pair are formed following (Solomon et al., 1981).

10
The ECHAM/MESSy Atmospheric Chemistry (EMAC) model is a numerical chemistry and climate simulation system that includes sub-models describing tropospheric and middle atmosphere processes and their interaction with oceans, land and human influences (Joeckel et al., 2010 (Hines, 1997) from ECHAM5 in a modularised structure. For the parameter rmscon (root-mean-square wind-speed at bottom launch level of 20 642.90 hPa), which controls the dissipation of gravity waves, we use a value of 0.92 m/s. For gas phase reactions the submodel MECCA is used , and for photolysis the submodel JVAL (Sander et al., 2014). 218 gas phase reactions and 68 photolysis reactions are included. Most of the reaction constants are taken from Sander et al. (2011b). A family concept for NO x is applied in the whole model domain. Geomagnetic forcing of NO y in the mesosphere is considered by applying an upper boundary condition (UBC) of NO y , parameterized by the geomagnetic Ap index (newly develope submodel UBCNOX).

25
This applies an online version of the upper boundary condition for the amount of NO x described in  and (Matthes et al., 2017 at midpoint 0.01-0.09 hPa) instead of NO y , and NO 2 is set to 0 in those levels to balance NO x (see (Matthes et al., 2017)).
For solar proton events we use the submodel SPE , incorporating daily values of precalculated ionization rates as described in (Jackman and Fleming, 2000) which are available updated to 2015 based on observed proton fluxes at http://solarisheppa.geomar.de/cmip6. Full ionization rates are applied where the geomagnetic latitude is greater than  Jackman et al. (2005). Between zero and 2 OH are formed per ion pair based on Solomon et al. (1981) as described in Baumgaertner et al. (2010). Note that effects from the SPE submodel in NO and NO 2 are overwritten by the UBCNOX submodel in the four highest model levels.

Model experiments
The model scenarios used in the following are listed with their main properties in Tab All models carried out one reference scenario with no particle impact, called Base in the following. Additionally, all models carried out one scenario including full particle forcing as available to the respective model: 3dCTM including protons and 10 electrons from the AIMOS model v1.6 and photoionization (v1.6 phioniz); KASIMA including protons and electrons from the AIMOS model v1.6 (v1.6); and EMAC including protons from the Jackman et al. (2005) database and NO y upper boundary conditions as a constraint for the EPP indirect effect (UBC, Funke et al. (2016)).

MIPAS
The  Clarmann et al. (2013). The retrieval of NO and NO 2 is described in Funke et al. (2005Funke et al. ( , 2014a. Updates in the ozone retrieval scheme since von Clarmann et al. (2013)  An overview of the particle and dynamical forcing throughout the time-period investigated here is provided in Fig. 1. Shown are the daily sunspot number as a proxy for solar activity, the daily AE index as a proxy for geomagnetic activity, and temperatures in the mid-stratosphere at high latitudes in both hemispheres as a proxy of the dynamical state of the middle atmosphere. Also marked are days with known solar proton events.  Days of known solar proton events as provided by http://umbra.nascom.nasa.gov/SEP/ as mean fluxes of protons with energies larger than 50 MeV are marked as red lines in the middle panel of Fig. 1. Only events where the mean flux is larger than 50 pfu 2 are shown here. Very large events with fluxes of ≥ 50 MeV protons larger than 1000 pfu occur on April 21, 2002;October 28-29, 2003;November 02-03, 2003;July 25-26, 2004, January 16-17, 2005May 14-15, 2005;September 08-11, 2005;and December 06-07, 2006. The strongest event, with mean proton fluxes of 29500 pfu, was the so-called Halloween Daily mean stratospheric temperatures in high Southern and Northern latitudes are shown in the bottom panel of Fig. 1 for 15.216 hPa (about 25 km). Temperatures are based on ECMWF ERA-40 re-analysis data taken from output of the 3dCTM model (see Sec. 2.1.1). In the Southern hemisphere, stratospheric temperatures show a smooth annual cycle following a more 10 or less sinusoidal behaviour with maxima during polar summer, minima during mid-winter. Small excursions from this behaviour occur in early summer, denoted by short-term increases of stratospheric temperatures of up to 20 K. These are the final warmings denoting the break-down of the meridional circulation in spring. In the Northern hemisphere, a similar annual cycle is observed, though the amplitude is lower -summers are colder, winters warmer. Also, late winter and spring in the Northern hemisphere is dominated by strong excursions from the smooth behaviour of up to 50 K. These are mid-winter 15 sudden stratospheric warmings, strong disturbances of the mean circulation. Sudden stratospheric warmings throughout the time-period observed here are listed, e.g., in (Kuttipurath and Nikulin, 2012;Kishore et al., 2016). Nine warmings are listed from early 2002 to mid-2010, occuring between late December and late February. Sudden stratospheric warmings lasting for more than 10 days occurred in January 2004, January 2006, and January 2009. These warmings were followed by an elevated stratopause and strong and long-lasting mesospheric and upper stratospheric descent (Randall et al., 2006Orsolini et al., 20 2010; Limpasuvan et al., 2016). They will be called strong sudden stratospheric warmings in the following. Changes of the temperature structure and dynamics of the middle atmosphere during and after these events have been investigated in a number of studies (e.g., Manney et al. (2005Manney et al. ( , 2008Manney et al. ( , 2009a). In the daily temperatures shown here, these three events are easily distinguished as increases of temperatures by more than 40 K over a few days (more than 50 K in 2009), and a slow recovery to cold winter temperatures in the weeks afterwards. It has been shown that the onset of these events is driven by planetary wave 25 activity (Pancheva et al., 2008(Pancheva et al., , 2009a, while downward transport from the thermosphere after the event is driven mainly by non-orographic gravity waves (McLandress et al., 2013).

Modeled and observed EPP-NO y
In the following, modeled EPP NO y is investigated in detail. In a first step, model simulations in the upper mesosphere at 0.01 hPa are compared to investigate how the implementation of particle impacts affects the model results (Sec. 3.1). The tem- Absolute differences between models and observations are discussed to evaluate how well models reproduce the EPP impact quantitatively (Sec. 3.3). In a last step, the total hemispheric amount of EPP NO y is derived from model results, and compared to previous derivations from observations (Sec. 3.4).

Model-model intercomparison in the upper mesosphere
In Fig. 2, model results are shown at 0.01 hPa (≈ 80 km) respectively, for high latitudes in both hemispheres (first and third 5 panel). 0.01 hPa corresponds to the center of the uppermost layer of the medium-top EMAC model, and also corresponds to an altitude just below the mesopause where thermospheric NO y enters the middle atmosphere.
At 0.01 hPa, all three models display a consistent behaviour. All show an annual cycle with strong maxima during winter, when NO y mixing ratios are roughly two orders of magnitude larger than during polar summer. All three models show an additional daily variability of NO y related to strong, sporadic events in particle fluxes (3dCTM, KASIMA) respectively ge-10 omagnetic activity (EMAC). This day-to-day variability is reproduced consistently by all three models during polar winter.
During polar summer it is missing in EMAC as the Ap-dependent contribution in the UBC parameterization is much smaller than the background NO y contribution during summer. Absolute values of NO y at 0.01 hPa do not show systematic differences between models in the Southern hemisphere, but in the Northern hemisphere, NO y from EMAC is higher than NO y from 3dCTM and KASIMA throughout most winters. 15 The relative difference between NO y from EMAC and from the other two models is also shown in Fig. 2 (second and fourth panel). The relative differences confirm that on average, values during Southern hemisphere winter are consistent in all three models, while in Northern hemisphere winters, EMAC shows systematically higher values than the other two models. Another systematic feature is observed during polar winter: The relative differences show a kind of U-shape during most winters, with more negative values (EMAC larger than other models) during mid-winter, more positive values (EMAC lower than other  To summarize, at the source region of particle forcings in the upper mesosphere (0.01 hPa), all three models show a reasonable, consistent behaviour. We conclude that the upper boundary condition in a medium-top model, or prescribed ionization rates in the mesosphere and lower thermosphere from the AIMOS model (version 1.6) in a high-top model, lead to a generally consistent description of particle-induced NO y in the upper mesosphere. However, small systematic differences between the model using the upper boundary condition (EMAC) and the models using AIMOS data (3dCTM, KASIMA) indicates possible  EPP signal, both between the different models, and between (all) models, and observations. These differences will be discussed in detail in the following subsection. clarity. These contours are chosen because they envelope the EPP NO y signal observed by MIPAS in the upper stratosphere and lower mesosphere (10-0.1 hPa) in many winters quite well, in particular in SH winters 2003, 2008, and in NH winters 2002 In the source region of the particle precipitation, the upper mesosphere above 0.1 hPa, no clear picture emerges. 3dCTM overestimates NO y in the Southern hemisphere in this region in mid-and late winter, but sometimes underestimates NO y in early winter. For KASIMA and EMAC, periods of overestimation and underestimation vary throughout most winters. In the Northern hemisphere, 3dCTM overestimates NO y in the upper mesosphere in early to mid-winter 2007-2008, 2008-2009, and 2009-2010, but underestimates NO y in most late winters, and throughout winter  underestimates NO y compared to MIPAS in the uppermost mesosphere in all Northern hemisphere winters, while in EMAC, again periods of over-and underestimation are observed in all winters. Despite the strong similarities of the modeled NO y in the upper mesosphere during winters discussed in the previous section, the indirect effect in the upper stratosphere to mid-mesosphere (10-0.1 hPa) is captured rather differently by the three models.

Quantification of model-observation differences
-In 3dCTM, the indirect effect is overestimated throughout all polar winters in the Southern hemisphere mesosphere.
However, the timing of the downwelling from the mesosphere to the stratosphere is delayed compared to MIPAS observations, which leads to an underestimation of NO y in the early to mid-winter upper stratosphere in particular in winter -In KASIMA, the indirect effect in the upper stratosphere to mid-mesosphere is underestimated in all winters and both hemispheres. However, the timing of the downwelling seems to be captured quite well.
-In EMAC, the indirect effect in the upper stratosphere to mid-mesosphere is overestimated in nearly all winters and both 10 hemispheres. The timing of the downwelling NO y suggests that downwelling is too fast in the upper stratosphere / lower mesosphere.
-3dCTM and KASIMA strongly underestimate the indirect effect after the sudden stratospheric warmings in early 2004 and early 2009 by more than 100 ppb. The speed of downward transport after the warming is too fast in EMAC: the EPP NO y signal reaches the stratosphere too quickly, and proceeds to too low altitudes. However, the amount of NO y 15 transported down after the warming seems to be captured reasonably well. This is consistent with results of the EMAC model for Northern hemisphere winter 2008/2009 as shown in Funke et al. (2017).
These results suggest that in 3dCTM, transport through the winter mesosphere is restricted particularly in the Southern hemisphere, so that NO y accumulates there throughout the winter. In the Northern hemisphere, a similar overestimation in the upper stratosphere and lower mesosphere is observed in early and mid-winter from 2007-2010, but not in the early years. In 20 contrast, downward transport in EMAC through the lower mesosphere in early winter is too fast, leading to too low values in the mesosphere, too high values in the upper stratosphere.
Only one strong solar proton event is captured by MIPAS observations during this time-period (October 2003). In the Southern hemisphere, NO y during and after this event is overestimated by the models in the lower mesosphere (1-0.1 hPa), indicating an overestimation of proton ionization rates there. This is shown consistently in all three models. This might in- 25 dicate either a problem of the proton flux data used, or of the photochemical lifetime of NO y in the models after the solar proton event. However, it is probably not due to the calculation of the ionization rates, as different models are used by 3dCTM and KASIMA (AIMOS) respectively EMAC (Jackman rates). The impact of the different assumptions in ionization models (including AIMOS and Jackman rates) on NO y and Ozone is discussed, e.g., in . This overestimation continues well into the following polar summer. In the Northern hemisphere, modeled NO y is overestimated below ≈ 0.2 hPa 30 by KASIMA and EMAC, but underestimated above. The underestimation in the mesosphere seems to be due to an underestimation of the indirect effect, while the overestimation at altitudes below 0.2 hPa has already been discussed in a detailed model-measurement intercomparison of this event (Funke et al., 2011).
In the lower stratosphere below 20 hPa, positive differences occur during mid to late winter occasionally in all models, in particular in the Southern hemisphere, and strongest in 3dCTM. These are likely due to the models' representation of the formation of polar stratospheric clouds in the cold polar vortex, and their subsequent sedimentation out of the stratosphere (denitrification).
3dCTM underestimates NO y in the polar summer stratosphere by 3-30 ppb. This is observed in both hemispheres, and 5 in all polar summers. KASIMA and EMAC agree much better with observations in the polar summer stratosphere, though a small underestimation of NO y compared to MIPAS data is observed in these models also during some summers. However, the underestimation of stratospheric summer-time NO y in 3dCTM is likely connected to background NO y , not to particle precipitation, and will not be discussed further here.
To summarize, the EPP indirect effect in NO y in the upper stratosphere and lower mesosphere is captured quite differently 10 by all three models depending on the speed of the downward transport in the lower mesosphere and upper stratosphere, which ultimately depends on the different treatment of gravity wave drag in the models. 3dCTM and KASIMA strongly underestimate the indirect effect in NO y after the strong sudden stratospheric warmings in Northern hemisphere winters 2003-2004 and 2008-2009. This is consistent with results of a dedicated model-measurement intercomparison involving three high-top and five medium-top models investigating the January 2009 SSW . The impact of the warming is better represented 15 in EMAC, which however transports NO y down too fast after the warming. It should be noted that the downward transport is even faster than in the EMAC version shown in  due to a different setting of the gravity wave drag scheme.
Only one strong solar proton event was observed by MIPAS during this time-period; the impact of this event was overestimated by all three models in the Southern hemisphere.
Thus, when the impact of particle precipitation on total NO y , stratospheric ozone loss, and net radiative heating is deter-20 mined from these models, it should be kept in mind that the indirect effect during Southern hemispheric winters and Northern hemispheric dynamically quiet winters (i.e., winters without strong sudden stratospheric warmings) will likely be underestimated by KASIMA, but will likely be overestimated by 3dCTM and EMAC. However, after sudden stratospheric warmings the impact of the indirect effect will likely be underestimated by 3dCTM and KASIMA, but represented reasonably well by EMAC. The impact of large solar proton events might be overestimated, though it should be pointed out that this assumption 25 is based on observations of one strong solar proton event only.

Total NO y
The daily total amount of NO y in each hemisphere is calculated from the model results as follows: In a first step, the total column amount is calculated for daily zonal averages for each model run on the native latitude grid of the respective model. is derived as the difference between a model run with full particle forcing (3dCTM v1.6 phioniz, KASIMA v1.6, EMAC UBC) to the respective Base model run without particle forcing.
Results of the total EPP-NO y amount are shown for all three models in Figure 7. All three models show a similar behaviour.
The main features are: -In both hemispheres, EPP-NO y shows values between 0.5 and 5 Gmol, with a distinct annual variability favouring the 5 winter periods, and sporadic, short-lived increases of up to 2 Gmol per hemisphere related to strong solar proton events. -EPP-NO y is enhanced over the whole model period by more than 0.5 Gmol in both emispheres. This indicates that once NO y has reached the mid-stratosphere, its effective atmospheric lifetime is rather longer than one year. EPP-NO y accumulates over the solar maximum years, and does not drop to zero before the next maximum starts. This accumulation effect is emphasized by the very low values displayed by KASIMA at the beginning of the KASIMA model period in -Highest values of EPP-NO y are predicted by EMAC, lowest by KASIMA, in agreement with the results of the comparison to stratospheric NO y from MIPAS shown in the previous section.
-The annual variation is less pronounced in the Southern hemisphere NO y from KASIMA. This might be due to the stronger (and apparently, more realistic) denitrification in KASIMA compared to the other two models: Denitrification 25 redistributes NO y in the lowermost stratosphere very efficiently, taking NO y out of the gas-phase and sedimenting it out of the middle atmosphere completely. This becomes evident by comparing to the EPP-NO y from altitudes above the vertical range where denitrification occurs (9 hPa): this shows a comparable annual variation in all three models. To summarize, energetic particle precipitation provides a nearly constant background of EPP-NO y in both hemispheres, from a few tenth of Gmol during solar minimum, to 1-2 Gmol during solar maximum. Superposed on this background is a 30 distinct annual cycle with higher values during polar winter due to the EPP indirect effect, that is, downwelling of particle induced NO y probably originating in the aurora during polar winter at high latitudes. Additionally, there are sporadic increases Table 2. Comparison of modeled EPP NOy (Gmol) with data derived from MIPAS Funke et al. (2014b). For the models, the difference between the highest value of this winter minus the lowest value of the preceding summer is given; in brackets, the maximal value of the winter is given. of more than 1 Gmol per event due to strong solar proton events, and in the Northern hemisphere, also due to strong sudden stratospheric warmings.
Strongest  The winter-time increase due to the indirect effect is in the range of a few tenth of Gmol in solar minimum, to up to 1.5-3.7 Gmol in the transition from declining phase of the solar maximum. These values are higher than in previous studies summarized in Sinnhuber et al. (2012), which provide a range of zero to 1.5 Gmol per winter based on HALOE (Siskind et al., 2000;Randall et al., 2007) observations, but are in good agreement with studies based on MIPAS data (Funke et al., 2005;Reddmann et al., 2010;Funke et al., 2014b). In Funke et al. (2014b), the wintertime increase in EPP NO y due to the 15 indirect effect is derived from MIPAS observations for every Northern hemisphere and Southern hemisphere winter covered by MIPAS observations (mid-2002-early 2012

Ozone intercomparison, quantification of ozone loss and net radiative heating change
In the following, modeled ozone is compared to MIPAS observations, and the particle impact on stratospheric ozone and net radiative heating will be quantified from model results by comparing the model runs with full particle forcing (3dCTM v1.     Southern hemisphere, by 0.5-1.5 ppm in the Northern hemisphere. KASIMA and EMAC generally reproduce the values of the stratospheric maximum well, with differences less than ± 1 ppm. The strong overestimation of ozone in this region by 3dCTM might be due to the underestimation of NO y discussed in the previous chapter. Below the main amount of the stratospheric ozone layer (100-10 hPa during late winter and spring) ozone is overestimated by all models in the Southern hemisphere, possibly due to underestimation of the ozone loss in the Antarctic ozone hole region. This is most pronounced 5 in 3dCTM (more than 2 ppm), with much lower values of 0.5-1 ppm in KASIMA and EMAC, and much less pronounced in the Northern hemisphere. In summary, all models display systematic differences (biases) in ozone compared to observations. However, it is unlikely that these biases are related to the treatment of energetic particles in the models, as the impact of energetic particle precipitation is usually -with the exception of strong solar proton events -masked by the much larger dynamical variability of ozone. In the next subsection, we will investigate this interannual variation of ozone, and how it 10 relates to energetic particle precipitation; in the following subsection Sec. 4.3, the energetic particle impact is extracted from the model results by comparing the model runs with full particle forcing with the Base model scenarios.

Comparison of modeled and observed ozone anomalies
Due to the large dynamical variability of ozone particularly in the stratosphere, an impact of energetic particle precipitation on ozone can be difficult to derive from observations. Previous studies based on observations have compared observations of 15 ozone in situations with and without elevated amounts of NO y on the same day and in the same latitude range (Natarajan et al., 2004), the evolution of ozone in years with high energetic particle fluxes compared to years with low particle fluxes (Randall et al., 2005), and the composite difference of years with high minus years with low particle fluxes (Fytterer et al., 2015a;Damiani et al., 2016). All methods have yielded lower values of ozone in the upper stratosphere presumably related to the energetic particle precipitation; the composite method also shows negative ozone anomalies proceeding downwards from 20 the stratopause to the mid-stratosphere during polar winter. In the following, we will analyze ozone anomalies for the time-   poleward motion during polar winter. Below 10 hPa, very strong anomalies of more than ± 40 % occur mainly during winter and spring, particulary in the Southern hemisphere, and possibly related to interannual variations in the Antarctic ozone hole.
A strong positive anomaly is observed, e.g., in late 2002 in the Southern hemisphere below 20 hPa which likely is related to the ozone-hole split during this Antarctic winter (B-M. . A clear negative downwelling signal of 5-30 % is observed in Antarctic winter 2003 from the lower mesosphere (≈ 0.3 hPa) in mid-winter to the lower stratosphere 5 (below 10 hPa) in spring, preceded by a weaker (5-10 %) positive signal. The structure and strengths of this signal is similar to the downwelling anomalies derived from global satellite observations for the Southern hemisphere (Fytterer et al., 2015a;Damiani et al., 2016) when comparing composites of years with high minus low geomagnetic activity, and are interpreted as particle impacts there. In the Northern hemisphere, a similar negative downwelling signal starts in the lower mesosphere in early winter 2003-2004, but is interrupted by a strong (> 40 %) positive anomaly in late 2003 and early 2004 probably related 10 to the onset of the sudden stratospheric warming. In late winter and spring 2004, after the sudden stratospheric warming, an even stronger negative anomaly of more than -50 % descends down from the upper mesosphere (0.02 hPa) to the stratopause (1 hPa) in spring. However, from the observations it is not clear whether the strong anomalies during and after the warming are related to dynamical changes related to the warming, or due to the strong NO y signal observed after the warming. This will be investigated in the following by comparing anomalies obtained in the same way from model results with and without particle 15 forcing.
For the model data, anomalies are obtained in the same way as for the observations. First, a daily climatology is derived for  Fig. 10 and Fig. 11 for the model runs including full particle forcing, in the lower right panels for the Base model runs. anomaly as well as the apparent speed of its downward motion vary from model to model, consistent with differences in the descent rate in the stratosphere already discussed in section Sec. 3.3 for NO y . Transport across the stratopause is restricted in 3dCTM, leading to too high anomalies in the lower mesosphere (1-0.1hPa) and a too small anomaly in the stratosphere; the 30 downwelling speed is well captured in KASIMA, though the amplitude of the anomaly is too small compared to observations; while the stratospheric anomaly is too large in EMAC. In the Northern hemisphere, again all three models show very large negative ozone anomalies of more than -50 % in the upper mesosphere (≥ 0.1 hPa) in winter [2003][2004]. The general structure of the anomalies from the lower mesosphere to lower stratosphere is also well captured by all three models, with a sequence of positive anomalies in the early winter stratosphere (≈10-1 hPa) followed by a negative signal moving down from the 35 mesosphere to the upper stratosphere, which is interrupted due to the sudden stratospheric warming in December 2004, by a very strong positive signal, followed again by a negative signal after the sudden stratospheric warming. While the strengths of the positive signals seems to be well captured by all three models, the strengths of the negative signal preceding the warming again varies from model to model, with values generally lower than observed in 3dCTM, higher than observed in KASIMA and EMAC. The strong negative signal after the warming in the mid-stratosphere to lower mesosphere is strongly underestimated 5 by 3dCTM and KASIMA, but well captured by EMAC, in good agreement with results shown for the downwelling signal of NO y discussed in Sec. 3.3.
The Base model runs without energetic particle precipitation show a very similar pattern of anomalies as the model runs with full particle forcing discussed in the previous paragraph, indicating that most of the anomalies observed are not due to chemical changes due to the particle forcing, but due to changes in dynamics (temperature and large-scale transport) from year to year. 10 In particular, the anomalies below 10 hPa are nearly identical in model runs with and without particle forcing, indicating that all anomalies below this pressure level are due to dynamical changes. This includes a negative signal which moves down from about 10 hPa in late Southern hemisphere winter 2003; though this appears to be connected to the negative anomaly moving down from the mesosphere to the mid-stratosphere throughout the winter, it is apparently not due to chemical changes due to the energetic particle precipitation. As the specified temperatures and wind fields in all model experiments are based on the 15 meteorological analyses in the stratosphere, it can not be ruled out that changes in dynamics from year to year are related to the particle precipitation, particularly in the years of strong particle forcing (2002)(2003)(2004); however, it is not possible to assess this with these model experiments. A negative anomaly moving down from the mesosphere to the mid-stratosphere during Southern hemisphere winter 2003 and Northern hemisphere winter 2003-2004 is also observed in all three models in the model runs without particle forcing, indicating that these negative anomalies are partly due to changes in the downward transport speed or 20 horizontal mixing. However, the strength of the negative anomalies is larger in the model runs including particle precipitation, indicating that energetic particle precipitation also contributes to these anomalies. In particular in Southern hemisphere winter 2003 and in the Northern hemisphere winter 2003-2004 after the sudden stratospheric warming, negative anomalies are much larger in the model runs with particle forcing than in the respective Base model runs, indicating that during these periods the particle impact plays a significant role. In most other winters, the differences between ozone anomalies in the model runs with 25 and without particle forcings are much smaller (not shown here). The large negative anomalies in the upper mesosphere in Southern hemisphere winter 2003 and Northern hemisphere winter 2003-2004 are not observed in the model runs without particle forcing, so they are probably due solely to particle forcing. Because of the apparent quite strong year to year variations in ozone due to changes in the vertical and poleward transport during polar winters even in the Southern hemisphere seen here as downwelling positive/negative anomalies, it is very difficult to extract a signal of particle precipitation from stratospheric 30 and mesospheric ozone by comparing years with and without particle precipitation; as the comparison of the analysis of model runs without particle forcing shows, downwelling negative anomalies can be produced due to dynamical reasons, and falsely attributed to particle forcing. In the following Section we investigate the impact of energetic particle precipitation on ozone in the stratosphere by comparing model runs with and model runs without particle forcing; as the model runs use specified  Figure 12. Relative Ozone anomalies due to energetic particle precipitation at high Southern latitudes (70-90 • S), calculated as the difference of model runs with to without particle impact (%). Top: 3dCTM (v1.6 phioniz-Base), middle: KASIMA (v1.6 -Base), third: EMAC (UBC -Base). The gray shaded area in the middle figure denotes the time-period before the start of the KASIMA model runs. Dashed and dotted vertical gray lines mark zero, one-quarter, one-half, and three-quarters of each year. The thin black contours refer to -1.5 (solid), -1 (dashed) and -0.5 (solid) ppm. dynamics, the dynamical variability of ozone from year to year is the same in both model experiments, and the difference between the model experiments highlights the particle impact only.

Modeled Ozone anomalies due to particle precipitation
Ozone anomalies due to energetic particle precipitation only are derived from the model results as the difference of model runs with (3dCTM v1.6 phioniz, KASIMA v1.6, EMAC UBC) to the respective Base model run without particle impacts.  Figure 13. Relative Ozone anomalies due to energetic particle precipitation at high Northern latitudes (70-90 • N), calculated as the difference of model runs with to without particle impact (%). Top: 3dCTM (v1.6 phioniz-Base), middle: KASIMA (v1.6 -Base), third: EMAC (UBC -Base). The gray shaded area in the middle figure denotes the time-period before the start of the KASIMA model runs. Dashed and dotted vertical gray lines mark zero, one-quarter, one-half, and three-quarters of each year. The thin black contours refer to -1.5 (solid), -1 (dashed) and -0.5 (solid) ppm.
In high Southern latitudes, all three models show a consistent behaviour with a distinct annual/vertical variation in the ozone loss, as well as a few sporadic events of short-lived ozone loss: -In the upper mesosphere above 0.1 hPa, all three models predict strong ozone losses during polar winter. The vertical structure and strength of these winter-time mesospheric ozone losses vary from year to year, and between models from 10-30 % in winter 2009 (KASIMA, 3dCTM) to 70-90 %/50-70 % in winter 2003 (EMAC/KASIMA). In KASIMA and 5 EMAC, mesospheric ozone loss is constant or increases with altitude above 0.1 hPa, while in 3dCTM, the ozone loss decreases again above ≈ 0.03 hPa, maximizing around 0.1 hPa.
-The negative ozone anomaly simulated in every winter moves downward from the mesospheric ozone loss region in early winter, to the mid-stratosphere (≈10 hPa) in late winter. Again, values vary from winter to winter and between models, -Small regions of a positive ozone change are observed in the lower mesosphere in early and late winter below the regions 30 of strong mesospheric winter-time ozone loss (3dCTM, EMAC); these are likely due to self-healing, i.e., stronger ozone formation below regions of ozone loss because of the stronger UV radiation.
Mesospheric ozone loss has been observed related to strong energetic electron precipitation events (Andersson et al., 2014b) and also related to the 27-day cycle of the geomagnetic activity (Fytterer et al., 2015b). It is also predicted by model studies (Semeniuk et al., 2011;Fytterer et al., 2016;Arsenovich et al., 2016), and is likely related to the increase in HO x during electron precipitation events. Is is restricted mainly to polar winter because during summer, the background in HO x is higher, therefore the relative increase in HO x due to the electron precipitation is rather smaller (Fytterer et al., 2015b(Fytterer et al., , 2016. The 5 values simulated here are in range of the observations, which show ozone losses of about 10 % averaged over one winter, up to 90 % in individual strong events (Andersson et al., 2014b). The mesospheric ozone loss also agrees well with model results by the CMAM model driven with prescribed auroral and medium-electron ionization for the period 1979period -2006period (Semeniuk et al., 2011. They show a multi-annual mean of 10-30 % (Northern hemisphere) respectively 30-80 % (Southern hemisphere) of ozone loss compared to model runs without particle impacts in mid-winter (DJF respectively JJA) in the upper mesosphere 10 above ≈65 km (about 0.1 hPa). Particle-induced ozone loss in the mesosphere is mainly due to catalytic cycles involving HO x , which is released from positive water cluster ions formed by incorporating water vapor, thus depends on the availability of water vapor (Solomon et al., 1981;Sinnhuber et al., 2012). It has been shown recently that during polar winter, mesospheric ozone loss can also be initiated by NO x , indirectly by changing the partitioning of HO x from HO 2 to OH (Verronen and Lehmann, 2015). Differences in the vertical structure of the ozone loss between KASIMA and EMAC might therefore denote 15 different gradients in the mesospheric water vapor and NO y content in the models. However, the strong mesospheric ozone loss predicted by EMAC is more likely due to the implementation of the upper boundary condition: in every time-step, NO in EMAC is overwritten by the upper boundary NO y . To balance NO x , other NO x species like, e.g., NO 2 are set to zero. This leads to realistic values of NO y as shown in Sec. 3.4; however, in every chemistry time-step, the reactions NO + O 3 −→ NO 2 + O and NO + HO 2 −→ NO 2 + OH are also processed, changing the partitioning of HO x and destroying larger amounts of 20 ozone than in the Base run.
Ozone loss in the mid-stratosphere is mainly due to catalytic cycles involving NO x , and the stratospheric ozone loss predicted by the models can be directly related to the EPP-NO y brought into the stratosphere by the indirect effect and by large solar proton events. The winter-time ozone loss seems to be mainly due to the indirect effect, and this continues well into summer in agreement with the long-term accumulation of EPP-NO y discussed in the previous chapter. Strong summer-time ozone loss, 25 e.g., in summer 2003-2004 and 2004-2005, nevertheless seems to be due mainly to strong solar proton events.
In the Northern hemisphere, mesospheric ozone loss throughout the winter is predicted by all models similar to the Southern hemisphere. Solar proton events in October 2003, January 2005 and September 2005 lead to instantaneous ozone loss from the mid-stratosphere to the upper mesosphere in all models. However, the annual variation of the stratospheric ozone loss due to the indirect effect looks distinctly different. In the Southern hemisphere, a continuous downwelling negative anomaly 30 reaching down to the mid-stratosphere (10 hPa) is observed in every winter. In the Northern hemisphere, this is not the case.
In the solar minimum winters (2006-2007 to 2009-2010), stratospheric ozone loss is significantly lower than in the Southern hemisphere winters, and the signal does not reach down to 10 hPa in most of these winters. In the solar maximum winters, strong stratospheric ozone loss of more than 50 % (late winter in EMAC), 30-50 % (winter 2003in KASIMA and early winter 2003 or 10-30 % (winters 200310-30 % (winters -200410-30 % (winters in 3dCTM, 200410-30 % (winters -2005 in 3dCTM and EMAC) is 35 predicted, and this ozone loss continues well into summer. However, the structure of the downwelling signals in these winters is distinctly different to the structure in Southern hemisphere winters with two distinct peaks of ozone loss, one in early winter, one in late winter. The second peak in late winter 2003-2004 is due to the strong downwelling of NO y from the mesosphere after the strong sudden stratospheric warming. It is stronger in EMAC than in KASIMA, and weakest in 3dCTM, following the differences in NO y in the models. In EMAC, downwelling ozone losses of 10-30% are also observed outside solar maximum 5 related to the sudden stratospheric warmings in early 2006 and early 2009; these are weaker in KASIMA, and not observed in 3dCTM. After the sudden stratospheric warmings in early 2004, early 2006, and early 2009, stratospheric ozone loss of 5-30 % continues throughout Arctic spring and summer in EMAC. However, in other summers, continuing stratospheric ozone loss from the EPP indirect effect is lower than in the Southern hemisphere, less than 1 % in some summers in 3dCTM, 2008. Absolute differences during winter again range from less than 0.5 ppm (all but 2003-10 2004in 3dCTM, all but 2003in KASIMA, 2002-2008 to more than 1 ppm (KASIMA) respectively more than 1.5 ppm (EMAC) after the sudden stratospheric warming in winter [2003][2004]. These values are in good agreement with observations of ozone variations of 1-2 ppm in longitudes with enhanced NO y compared to airparcels without enhanced NO y in early April 2004 at 2 hPa (Natarajan et al., 2004) as well as with observed differences of about 1 ppm of ozone mixing ratios in March and April 2004 compared to previous winters 15 at ≈ 40 km (Randall et al., 2005). The structure of the downwelling signal appears to be consistent with a previous model study incorporating MIPAS NO x in the lower mesosphere and showing 2-3 ppm ozone loss between 35-40 km compared to a model run without excess NO 2 in Northern hemisphere winter (Reddmann et al., 2010. These results agree well with EMAC results which also reach more than 2 ppm, but are higher than KASIMA or 3dCTM results. On average, ozone loss in the mid-to upper stratosphere during mid-winter agrees well with results from the CMAM model (5-30 % during JJA To summarize, stratospheric ozone loss due to energetic particle precipitation is predicted by all three models in most winters in both hemispheres, but the vertical range, temporal structure, and strength of the ozone loss varies from year to year, between models, and between hemispheres. Stratospheric ozone loss often continues into polar summer. In the Southern hemisphere, strong summer-time ozone losses are related mainly to strong solar proton events, while in the Northern hemisphere they are 25 related mainly to strong sudden stratospheric warmings. In the Northern hemisphere, wintertime stratospheric ozone loss seems to be dominated by sudden stratospheric warmings as well, and is small in winters without strong warmings. In contrast, in the Southern hemisphere, the wintertime stratospheric ozone loss is dominated by continuous downwelling of NO y from the mesosphere, and is predicted by all models to occur in every winter.

30
In the following, changes in the net radiative heating due to changes in ozone are derived from the modeled ozone changes discussed in the previous paragraph. All three models calculate radiative heating and cooling rates, but use different spectral resolutions and parameterizations. To obtain results for all three models independent of differences in the parameterizations, the shortwave heating rate in the Hartley bands of ozone (λ ≤ 320 nm) and the longwave radiative cooling in the ν = 001 → ν = 000 transition of ozone at 1042 cm −1 (9.6 µm) are estimated using the daily zonally averaged ozone and temperature fields of the respective model as follows.
In a first step, the change in radiative flux in each model box is calculated depending on the temperature in the box center, and the column density of ozone between the upper and lower box boundaries for each model scenario.
For the shortwave radiation in the Hartley bands of ozone, the change in radiative flux is derived from the amount of 5 downwelling solar radiation absorbed in the box: where J O3 is the daily mean Hartley band photolysis rate, O 3,col is the column density of ozone between upper and lower box boundaries, ∆E is the energy transferred into heat, and ∆F is the change in radiative flux in W m −2 . The amount of energy transferred into heat is estimated as the mean energy of a photon in the Hartley bands, at 260 nm (7.64 × 10 −19 J) 3

10
The daily mean photolysis rate is calculated using the photolysis scheme of 3dCTM for the respective latitude and day of year using fixed ozone, density, and temperature profiles by calculating photolysis rates every five minutes and averaging over a full day. The Huggins and Chappuis bands have not been taken into account here because they contribute to solar heating only in the lower stratosphere and below (Brasseur and Solomon, 2005).
For the longwave radiation, in a first step the upwelling flux is calculated from 200 hPa up to 0.01 hPa, and the downwelling 15 flux from 0.01 hPa down to 200 hPa. The limits are chosen to make results from all three models comparable: from the upper limit of EMAC down to the lower limit of 3dCTM. As we are interested only in the mid-to upper stratosphere, the emission of thermal radiation at the surface is not considered, and the upward and downward fluxes can be calculated as Heating or cooling rates are obtained from the fluxes as where c p is the specific heat capacity of air, g the acceleration of gravity taken to be constant as 9,81 m/s, ∆p the pressure width of the box, and ∂T ∂t is the heating rate in K/s. It should be pointed out that above about 60 km altitude, non-LTE effects as well as the diurnal variability of ozone become increasingly important both for the shortwave heating and for the longwave 5 cooling terms. These are not considered here, and only results below ≈ 0.1 hPa are considered in the following.
The changes in net radiative heating and cooling rates due to particle precipitation are calculated as the difference between model runs with to without particle impacts, and the net heating rate change is the sum of changes in heating and cooling rates.
The net changes in heating rates due to the particle-induced ozone loss are shown for high Southern (70-90 • S) and high Northern (70-90 • N) latitudes in Figs. 14 and 15. For all three models and in both hemispheres, changes in the net heating are 10 confined to the upper stratosphere and above (above 20 hPa), and peak around the stratopause (around 1 hPa). Net heating rate changes show a clear annual variation with positive values (a net heating) during winter, and negative values (a net cooling) during spring. The net heating during winter is due to a decrease in radiative (longwave) cooling due to the ozone reduction, while the net cooling during spring is due mainly due to a decrease in radiative (shortwave) heating, which is balanced to some extent by the decrease in radiative (longwave) cooling. In some years, the net cooling of the spring upper stratosphere continues 15 well into summer. In the Southern hemisphere, these are years with strong solar proton events in spring or summer (2004,2005,2007); in the Northern hemisphere, these are mainly years with strong sudden stratospheric warmings (2004,2006,2009), but also one year with with a solar proton event in late winter (2005). The strongest and longest-lasting impacts of more than 0.6 K/day (EMAC) respectively more than 0.1 K/day (KASIMA) for several month is predicted for the sudden stratospheric warmings in Northern hemisphere winters 2003-2004, 2005-2006, and 2008-2009. The solar proton event of October 2003 20 has an impact comparable with the sudden stratospheric warmings as predicted by EMAC on net heating rates of more than 0.5 K/day, but lasting a few days only, and predicted by all three models. Values of 0.1-0.2 K/day are then predicted to continue throughout the summer. In the lowermost panels of Figs. 14 and 15, the daily averaged sum of all shortwave and longwave contributions to radiative heating and cooling (called net radiative heating rate in the following) are shown for comparison for the EMAC Base scenario. The strongest changes of the net radiative heating rate due to energetic particle precipitation during 25 mid-winter occur in the upper stratosphere and lower mesosphere (10-0.1 hPa), at the lower edge of a region of strong radiative cooling in the lower mesosphere. The net radiative heating rates increase from 1 K/day at 10 hPa to more than 10 K/day at 1 hPa. Changes due to particle precipitation are in the order of magnitude of 0.1 K/day in this altitude range, reaching more than 0.5 K/day in Southern hemisphere winter 2003 (EMAC). This amounts to relative changes of 1-10 % in most winters, up to 50 % in winter 2003 (EMAC). In contrast, negative changes to the net radiative heating during spring after strong solar proton 30 events or sudden stratospheric warmings occur in a region of low net radiative heating rates ranging from less than 0.5 K/day  Figure 14. Changes in daily net radiative (short-wave and long-wave) heating rates (K/day) due to particle-induced ozone changes derived from all three models (top: 3dCTM, second from top: KASIMA, second from bottom: EMAC) at high Southern latitudes (70-90 • S). Bottom: The net radiative heating rate (sum of the shortwave and longwave contributions) in the EMAC Base scenario (K/day). Black dashed lines are the -0.1 and -0.5 K/day contours of the net radiative heating rate change in EMAC, black solid lines are the +0.1 and +0.5 K/day contours.  Figure 15. Changes in daily net radiative (short-wave and long-wave) heating rates (K/day) due to particle-induced ozone changes derived from all three models (top: 3dCTM, second from top: KASIMA, second from bottom: EMAC) at high Northern latitudes (70-90 • N). Bottom: The net radiative heating rate (sum of the shortwave and longwave contributions) in the EMAC Base scenario (K/day). Black dashed lines are the -0.1 and -0.5 K/day contours of the net radiative heating rate change in EMAC, black solid lines are the +0.1 and +0.5 K/day contours.  Figure 16. Daily changes in the net amount of energy absorbed or transmitted due to particle induced ozone destruction in the stratosphere (W/m 2 ), derived from the difference of model runs with to model runs without particle forcing, as a function of time and latitude. summer are in the range of 4-10 % of the net radiative rate of 1-2.5 K/day at this time. During spring the upper stratosphere approaches radiative equilibrium, so small changes in the net radiation budget -as after sudden stratospheric warmings or wintertime solar proton events -could potentially have a large impact.
To investigate the temporal-spatial structure of the particle impact onto the net energy absorbed or emitted, the changes in radiative flux derived above for both the shortwave and longwave component are added up over the vertical region from 200 hPa 5 to 0.2 hPa. The upper limit was chosen because above this region, the simplified approach used here is no longer valid, see above. The resulting changes in the net flux are shown in Fig. 16. Results confirm many of the findings already discussed for the heating rates: largest changes to the net energy absorbed are related to strong solar proton events in the Southern hemisphere, to sudden stratospheric warmings in the Northern hemisphere. Positive changes (net heating) are predicted for winter-time, but are restricted to high latitudes poleward of 60 • . Negative changes (net cooling) are predicted mainly for spring and summer, the Southern hemisphere, 2004 and 2005 in the Northern hemisphere). This latitudinal extent of the particle impact well into midlatitudes (up to 30 • ) is consistent with results of EPP NO y derived from MIPAS observations as shown in Funke et al.

Conclusions
Analysis of results from three global chemistry-climate models driven by geomagnetic forcing and solar protons shows that 5 solar proton events and the indirect effect due to downwelling of NO y presumably from the aurora contribute similar amounts of NO y to the stratosphere. Comparison to MIPAS NO y shows that on average, the indirect effect is captured well by the models in dynamically quiet winters, though the amount transported into the stratosphere depends on the treatment of gravity wave drag in the respective models. After sudden stratospheric warmings, the indirect effect is strongly underestimated by the two hightop models (3dCTM and KASIMA), while it is well represented by the medium-top model EMAC using the upper boundary 10 conditions from Funke et al. (2016). Ozone loss in the mid-to upper stratosphere related to the indirect effect is predicted by all three models for all polar winters, varying from 10-50 % during solar maximum, to 2-10 % during solar minimum.
Ozone loss maximizes in mid-winter to spring. The ozone losses lead to changes in the net radiative heating which change sign in late winter: a warming of the upper stratosphere at high latitudes dominates in mid-winters, while a cooling extending into midlatitudes dominates in late winter and spring. Analysis of several decades of re-analysis data show a warming of the 15 mid-to late winter upper stratosphere related to high geomagnetic activity (Lu et al., 2008;Seppälä et al., 2013) which is also reproduced in model experiments using free-running chemistry-climate models (Semeniuk et al., 2011;Baumgaertner et al., 2011). Based on older model experiments by (Langematz et al., 2005), Baumgaertner et al. (2011) and Seppälä et al. (2013) argue that the warming in the upper stratosphere and lower mesosphere is consistent with a direct radiative impact, while a cooling of the middle and lower stratosphere observed at the same time, during mid-winter (DJF in the Northern hemisphere), is 20 more likely the result of coupling between the vortex strength and wave propagation and reflection, an assumption strengthened by the apparent relation to the phase of the stratospheric quasi-biennal oscillation and the solar cycle (Lu et al., 2008;Seppälä et al., 2013). Our results are consistent with these earlier studies, and strengthen the assumption that the mid-winter warming is due at least partly to a direct radiative impact.
The indirect effect could contribute to the reformation of a strong and long-lasting vortex in late winter and spring after 25 sudden stratospheric warmings in years with high geomagnetic activity, as e.g. in winter 2003-2004. Sudden stratospheric warmings in Northern hemisphere winter and spring as well as solar proton events occuring during spring or summer can lead to an ongoing cooling from spring to late summer, possibly pre-conditioning the stratosphere in autumn.
Code and data availability. The model output used here as well as idl routines used to calculate heating and cooling rates are available from M. Sinnhuber (miriam.sinnhuber@kit.edu) on request. AIMOS v1.6 ionization rates due to protons and electrons have been