Quantifying uncertainties of climate signals related to the 11–year solar cycle. Part I: Annual mean response in heating rates,temperature and ozone

Abstract. Variations of the solar spectral irradiance (SSI) with the 11-year sunspot cycle have been shown to have a significant impact on temperatures and the mixing ratios of atmospheric constituents in the stratosphere and mesosphere. Uncertainties in modelling the effects of SSI variations arise from uncertainties in the empirical models reconstructing the prescribed SSI data set as well as from uncertainties in the chemistry-climate model (CCM) formulation. In this study CCM simulations with the ECHAM MESSy Atmospheric Chemistry (EMAC) model and the Community Earth System Model 1 (CESM1) – Whole Atmosphere Chemistry Climate Model (WACCM) have been performed to quantify the uncertainties of the solar responses in chemistry and dynamics that are due to the usage of five different SSI data sets or the two CCMs. We apply a two-way analysis of variance (ANOVA) to separate the influence of the SSI data sets and the CCMs on the variability of the solar response in shortwave heating rates, temperature and ozone. The ANOVA identifies the SSI data set with the strongest influence on the variability of the solar signal in shortwave heating rates in the upper mesosphere and in the upper stratosphere/lower mesosphere. The strongest influence on the variability of the solar signal in ozone and temperature is identified in the upper stratosphere/lower mesosphere. The largest influence of the CCMs on variability of the solar responses can be identified in the upper mesosphere. The solar response in the lower stratosphere also depends on the CCM used, especially in the tropics and northern hemispheric subtropics and mid latitudes, where the model dynamics modulate the solar responses.


confined to the lower stratosphere, using stratospheric analyses based on radiosondes (Labitzke, 1987;Labitzke and van Loon, 1988). Enhanced evidence for an effect of solar variability on middle atmospheric temperatures and constituents has been achieved since satellite observations are available (e. g., McCormack and Hood, 1996). Modelling studies range from early investigations with 2-dimensional atmospheric and chemistry models (Garcia et al., 1984;Haigh, 1994) and 3-dimensional general circulation models (GCMs) (e.g., Matthes et al., 2004) to studies with advanced chemistry-climate models (CCMs) 5 (SPARC CCMVal, 2010) and CCMs coupled to an ocean model, as partly used within the 5th Coupled Model Intercomparison Project (CMIP5) Hood et al., 2015).
While a good understanding of the chemical and dynamical implications of the 11-year solar cycle on the middle atmosphere has been achieved (e.g., Gray et al., 2010Gray et al., , 2013Ermolli et al., 2013), there are still discrepancies between observed responses to the solar cycle and modelling studies, as well as between different models. As explained in the following, there are two 10 major sources for the uncertainty in the modelled solar signals: differences in the model formulation such as for example the implemented UV radiation parameterisations, photolysis schemes and dynamical characteristics of the models, and the prescribed solar irradiance data set. The impact of the 11-year solar cycle on the atmosphere can be separated into two parts: a) an influence via the absorption of UV-radiation by ozone and oxygen in the middle atmosphere, with the direct solar heating response inducing a dynamical signal that propagates downward through the so-called "top-down" mechanism (Kodera and 15 Kuroda, 2002), and b) an influence based on the absorption of the visible and infrared parts of the solar spectrum at the surface (often expressed by variations in TSI), which is amplified by the so-called "bottom-up" mechanism (van Loon et Meehl et al., 2009). A realistic modelling of the "top-down" effect therefore relies on prescribing spectrally resolved solar irradiances (SSI) for the radiation and photolysis parameterisations of the applied CCMs. The SSI variation over the 11-year solar cycle leads to a modulation of stratospheric ozone through photochemistry (e. g., Haigh, 1994;Ball et al., 2014), as well 20 as variations of the heating rates in the middle atmosphere through absorption of UV-radiation (e.g., Garcia et al., 1984). It has been shown that the spectral resolution of the radiation parameterisation has a large impact on the 11-year solar response of the short-wave (SW) heating rates (Nissen et al., 2007;Forster et al., 2011). Both SSI dependent changes, in ozone and in SW heating rates over the 11-year solar cycle, determine the resulting solar induced temperature signal. SPARC CCMVal (2010) identified a large model spread in solar responses for ozone and temperature of 18 CCMVal-2 CCMs, mainly caused by 25 differences in the spectral resolutions of the shortwave radiation parameterisation or the treatment of photolysis in the CCMs.
Besides their solar cycle response on the thermal structure and dynamics of the middle atmosphere, the different spectral distribution of a SSI data set can also have an impact on the averaged middle atmospheric temperature, as was found in studies comparing different SSI data sets. It was shown that differences in the energy distribution during the solar minimum phases of individual SSI data sets may cause significant differences in the simulated temperatures in the middle atmosphere (e.g., Zhong 30 et al., 2008;Oberländer et al., 2012). Even when scaled to the same TSI, the variable spectral distribution of energy within the SSI data sets can cause significant changes of the simulated climatological temperatures in the middle atmosphere. As shown in Matthes et al. (2017), climatological annual mean middle atmospheric temperatures in the tropics can be up to 1.6 K lower when using the CMIP6 recommended SSI data set instead of NRLSSI1. Therefore, to exclude the effect of different spectral distributions and to isolate the pure effect of the amplitude of SSI changes over the solar cycle, it is necessary to use a common 35 2 https://doi.org/ 10.5194/acp-201910.5194/acp- -1010 Discussion started: 31 January 2020 c Author(s) 2020. CC BY 4.0 License. SSI data set for solar minimum conditions that serves as a baseline for adding the solar amplitude of the different TSI/SSI data sets. By adding the solar amplitude, i.e. the differences of the TSI/SSI between the solar maximum and solar minimum state of the different SSI data sets, to the reference state, the effects of the 11-year solar cycle differences in spectral distribution and amplitude of the individual SSI data sets can be quantified in a more appropriate way than in previous work.
The aim of this study is to estimate the uncertainty of the solar cycle signal resulting from the two above described sources 5 of uncertainty: the specification of the 11-year solar cycle SSI amplitude and the models' shortwave radiation and photolysis schemes and their dynamical characteristics. We apply different SSI data sets in two CCMs, EMAC and CESM(WACCM), as described in Section 3 to identify regions where significant differences in the solar responses can be attributed to differences in either the SSI data sets or the CCMs. Both CCMs have participated and their solar responses have been evaluated in the CCMVal-2 activity (SPARC CCMVal, 2010). Here, we use five different SSI data sets that are all based on empirical or 10 semi-empirical models of SSI and TSI (see Section 2 for more details). In contrast to previous studies, we use a common observation based reference SSI spectrum for solar minimum conditions where the five SSI amplitudes are added to create the solar maximum forcings (s. Section 3.1). After analysing the solar response of the ensemble mean and its variance in Section 4, the individual solar responses are discussed in Section 5. To separate the influence of the SSI data sets and the CCMs on the solar responses in shortwave heating rates, temperature and ozone, a two-way analysis of variance (ANOVA) method has been 15 applied. While the ANOVA is a well established method in many scientific fields, it is used here for the first time to quantify the uncertainty of the atmospheric response to decadal solar variability. The climatological differences between both CCMs, that are partially responsible for differences in the solar responses, are discussed in Section 5.2. In Section 6 the solar response in total column ozone and its variability are analysed, followed by a summary and conclusions in Section 7.
2 Spectral solar irradiance data sets 20 The record of observed TSI covers a relatively short period of time, since the first satellite mission to monitor TSI was launched in 1978. The record of SSI observations is even shorter and does not cover the solar spectrum continuously, as required for climate modelling studies. The construction of a continuous SSI data set exploiting all available space-borne measurements was only recently addressed by the "First European Comprehensive Solar Irradiance Data Exploitation project" (SOLID) (Haberreiter et al., 2017). In order to perform multi-decadal simulations with GCMs and CCMs covering the recent past and 25 the near future, as done within CMIP5 and the Chemistry-Climate Model Initiative (CCMI), SSI and TSI data sets are needed that are based on reconstructions with empirical models. Such models rely on SSI and TSI proxy data, which are available for longer time periods.
The standard data set for TSI and SSI in recent model intercomparison studies like CMIP5, CCMVal-2, and CCMI was the NRLSSI1 data set (Lean, 2000;Wang et al., 2005). This data set is known to have the lowest solar cycle variability in the 30 spectral range from 200-400 nm, compared to other SSI reconstructions and measurements (Ermolli et al., 2013). This is of particular importance for the formation of ozone and the related heating rates in the middle atmosphere (Ermolli et al., 2013).
The low variability of the NRLSSI1 data set might lead to an underestimation of simulated 11-year solar cycle effects in global 3 https://doi.org/ 10.5194/acp-2019-1010Preprint. Discussion started: 31 January 2020 . CC BY 4.0 License. models (Ermolli et al., 2013 and motivated the compilation of a new TSI/SSI data set to be used for CMIP6 (Matthes et al., 2017) which is a combination of two data sets: NRLSSI2 (Coddington et al., 2016) and SATIRE (Krivova et al., 2009;Yeo et al., 2014). In the following subsection we give a brief introduction of the SSI/TSI data sets applied in this study.

ATLAS3 based reference spectrum
The SSI data set used in this study for the solar minimum reference state between 0.1-2,395 nm is the Atmospheric Laboratory 5 of Applications and Science-3 (ATLAS-3) SSI reference spectrum (Thuillier et al., 2004), obtained during the third ATLAS mission in November 1994 near the minimum of solar cycle 22. It is a composite spectrum that comprises SSI measurements from instruments on three space platforms, including measurements with the SOLar SPECtrum instrument (SOLSPEC) and the Solar Ultraviolet Spectral Irradiance Monitor (SUSIM) experiment on board of the space shuttle (see Thuillier et al., 2004, for more details). The ATLAS-3 SSI data set covers wavelengths up to 2,395 nm only. We use the NRLSSI1 data set for 10 wavelengths between 2,395-99,975 nm and the SATIRE-S data set from 99,975-165,000 nm to extend the spectrum to the infrared and to derive the TSI for the ATLAS-3 spectrum. The extended ATLAS-3 spectrum was then scaled to obtain the integrated TSI of 1361.05 W m −2 for November 1994, derived from Total Irradiance Monitor (TIM) TSI measurements on NASA's Solar Radiation and Climate Experiment (SORCE) (Kopp and Lean, 2011). The resulting compiled and scaled SSI data set serves as a reference state for solar minimum conditions to which the solar amplitudes of all other SSI data sets have 15 been added to get the respective SSI data sets for solar maximum condition.

NRLSSI
The Naval Research Laboratory (NRL) SSI models (Lean et al., 1997;Lean, 2000;Coddington et al., 2016) are based on the empirical, wavelength-dependent relationship between sunspot darkening and facular brightening on the solar disk with SSI changes. This relationship is decribed by indices, which are used in regression models to determine the coefficients required to 20 estimate the time-varying SSI changes. The SSI changes of the empirical model are added to a quiet sun reference state, based on the WHI (whole heliosphere interval) SSI reference spectrum and the ATLAS-1 measurements (Thuillier et al., 1998). The TSI changes are added to a quiet Sun reference state of 1365.5 W m −2 (NRLSSI1) and 1360.45 W m −2 (NRLSSI2), based on SORCE/TIM measurements (Kopp and Lean, 2011 (Viereck et al., 2001) and as index for sunspot darkening the sunspot area as recorded by ground-based observatories are used (Lean et al., 1998).

SATIRE
The SATIRE (Spectral And Total Irradiance REconstructions) model (Krivova et al., 2009;Yeo et al., 2014) for the recon- 30 struction of SSI and TSI is a semi-empirical model that is based on variations of the solar surface magnetic field. The intensity 4 https://doi.org/ 10.5194/acp-2019-1010 January 2020 c Author(s) 2020. CC BY 4.0 License. spectra of the quiet Sun reference state, faculae, network, sunspot umbrae, and sunspot penumbrae are derived by applying a radiative transfer code (Unruh et al., 1999;Yeo et al., 2014). The resultant SSI is given as a weighted sum of these five contributions, where the weights (filling factors) are retrieved from magnetograms and continuum images that allow to estimate the fractional solar surface that is covered by the brightening (faculae and network) and darkening (sunspot umbrae and penumbrae) features. Two different data sets from the SATIRE model that both span a wavelength range from 115 -160000 nm, 5 SATIRE-T (telescope era) and SATIRE-S (satellite era), are used in this study. Differences between SATIRE-T and SATIRE-S arise from the estimation of the filling factor that describes the fractional surface coverage of the quiet Sun and the brightening and darkening features. SATIRE-S relies on full-disc magnetograms and intensity images, which allow to reconstruct TSI and SSI back to 1974. Satire-T (Krivova et al., 2010) is intended to reconstruct the SSI/TSI in the pre-satellite era when only lower quality data for the estimation of the state of the photosphere are available. Whereas for SATIRE-S detailed information of the 10 photospheric structure can be used, it is assumed to be homogeneous for SATIRE-T. The SATIRE-T filling factors for sunspot umbrae and penumbrae are calculated from the observed sunspot areas. The filling factors for faculae and network are derived from the evolution of the solar photospheric magnetic flux estimated by a coarse physical model (Solanki et al., 2000). As our study is based on the SSI/TSI data of November 1994, the most reliable reconstruction of the SATIRE model is given by the SATIRE-S data set, however SATIRE-T is also included for comparison. The direct comparison of SATIRE-T and SATIRE-S 15 for the same time frame can be beneficial for modelling studies using SATIRE-T in the pre-satellite era (e.g., the Maunder Minimum) and comparing to simulations for present-day conditions, which also use SATIRE-T SSI.

CMIP6 data set
The SSI and TSI data sets of the NRLSSI2 and SATIRE-S/T models, introduced in the previous sections, both cover the required time span (1850-2300) for CMIP6 simulations, and have been widely tested in modelling studies. The new recom-20 mended SSI/TSI data set for CMIP6 has been derived by averaging the NRLSSI2 reconstructions with the SSI and TSI of SATIRE-S/T as described in detail in Matthes et al. (2017). As we only use data for November 1989 and November 1994, the CMIP6 SSI and TSI data consists of an average of output from NRLSSI2 and SATIRE-S.
[  Table 1 gives an overview of the applied SSI data sets with details of their percentage solar cycle amplitude in the Lyman-α, far-UV (FUV,, UV in the Herzberg continuum (partly overlapping with the Hartley-bands) (201-242 nm), UV in the Hartley-/Huggins-bands (243-380 nm), and the visible (381-780 nm) spectral regions. The first value (∆SSI) represents the percentage SSI change from solar minimum to maximum relative to the solar minimum in November 1994. The second value represents ∆SSI relative to the TSI change from solar minimum to maximum ( ∆SSI ∆T SI ) in %. Whereas ∆SSI emphasises the large shows the highest and has also the highest ∆SSI ∆T SI ratio in the Lyman-α, FUV, and Herzberg continuum/Hartley bands spectral regions. Coddington et al. (2019) compare solar amplitudes of 11-year solar cycles in the satellite period produced with the NRLSSI2 and SATIRE-S for a number of broad wavelengths bands to SSI amplitudes derived from the SOLID composite. In the FUV spectral region they report the highest SSI amplitude for the SATIRE-S data set. Yeo et al. (2015) compare the SSI variability of NRLSSI1 and SATIRE-S with SSI obeservations over the satellite period and report the low UV variability of 10 NRLSSI compared to the SATIRE-S data set.

Chemistry-climate models and simulations
Two state-of-the-art CCMs have been used in this study to quantify the uncertainty of the modelled solar response related to the 11-year solar cycle. These are EMAC (ECHAM/MESSy Atmospheric Chemistry) (Jöckel et al., 2016) and CESM1(WACCM) (Community Earth System Model 1-Whole Atmosphere Chemistry Climate Model) (Marsh et al., 2013).

EMAC
EMAC is a CCM that includes sub-models describing tropospheric and middle atmospheric processes and their interaction with oceans, land and human influences (Jöckel et al., 2010). It uses the second version of the Modular Earth Sub-model System (MESSy2) to link multi-institutional computer codes. The core atmospheric model is the 5th generation European Centre Hamburg general circulation model (ECHAM5, Roeckner et al., 2006). For the present study we applied EMAC (ECHAM5  (Sander et al., 2011a) provides the atmospheric chemistry model. The chemical mechanism contains 155 species with 224 gas phase, 12 heterogeneous, 25 and 74 photolytic reactions. JVAL (Sander et al., 2014) provides photolysis rate coefficients using updated rate coefficients recommended by JPL (Sander et al., 2011b) and resolves the solar Lyman-α line and 8 spectral bands in the UV and VIS range (178-683 nm). RAD/RAD-FUBRAD (Dietmüller et al., 2016) provides the parameterisation of radiative transfer based in the SW on Fouquart and Bonnel (1980) and Roeckner et al. (2003) (RAD) with 4 bands from 250 to 4,000 nm. For a better resolution of the UV-VIS spectral band RAD-FUBRAD is used for pressures lower than 70 hPa, increasing the spectral 30 resolution in the UV-VIS from one band to 81 bands (Nissen et al., 2007;Kunze et al., 2014). With this updated version of RAD-FUBRAD the single band parameterisation for the heating rates of FUV in the Schumann-Runge bands (Strobel, 1978) 6 https://doi.org/ 10.5194/acp-201910.5194/acp- -1010 Discussion started: 31 January 2020 c Author(s) 2020. CC BY 4.0 License. is replaced by the parameterisation based on 19 bands, as given in Strobel (1978). A further update is introduced by using 14 bands for the Chappuis bands (407.5-690 nm). The submodel QBO is used to relax the zonal wind near the equator towards the observed zonal wind in the lower stratosphere (Giorgetta and Bengtsson, 1999). As EMAC, with an upper boundary in the upper mesosphere, is not able to capture the thermospheric influx of NO y , the simulations presented in this study employ the UBCNOX parameterisation (Sinnhuber et al., 2018;Funke et al., 2016) in the upper mesosphere to include NO y produced in 5 the thermosphere by auroral and medium-energy electrons.

WACCM
The Whole Atmosphere Community Climate Model (version 4; Marsh et al., 2013) is an integrative part of the Community Earth System Model suite (version 1. 0.6;Hurrell et al., 2013). CESM1(WACCM) is a "high-top" CCM covering an altitude range from the surface to the lower thermosphere, i.e. up to 5×10 -6 hPa, equivalent to approx. 140 km. It is an extension of the 10 Community Atmospheric Model (CAM4; Neale et al., 2013) with all its physical parameterisations. For this study the model has been integrated with a horizontal resolution of 1.9°latitude by 2.5°longitude and 66 levels in the vertical. CESM1(WACCM) contains a middle atmosphere chemistry module based on the Model for Ozone and Related Chemical Tracers (MOZART3; Kinnison et al., 2007) which includes a total of 52 species with 127 gas-phase, 17 heterogeneous, and 48 photolytic reactions.
A six constituent ion chemistry model is included with 13 ionization reactions and 14 ion-neutral and recombination reactions.

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Its photolysis scheme resolves 100 spectral bands in the UV and VIS range (121-750 nm). The SW radiation module is a combination of different parameterisations. Above approx. 70 km the spectral resolution is identical to the photolysis scheme (plus the parameterisation of Solomon and Qian, 2005, based on the F10.7 cm solar radio flux to account for EUV irradiances).
Below approx. 60 km the SW radiation of CAM4 is retained, employing 19 spectral bands between 200 and 5,000 nm (Collins, 1998). For the transition zone (60-70 km), SW heating rates are calculated as weighted averages of the two approaches. 20 CESM1(WACCM) features relaxation of stratospheric equatorial winds to an observed or idealised Quasi-Biennial Oscillation (QBO; Matthes et al., 2010). The ionisation in the auroral regions by energetic particles is parameterised according to Roble and Ridley (1987) using the Kp index as input parameter. To achieve a setup for low auroral activity, for WACCM the Kp index is set to a constant value of Kp = 0.67, as this corresponds to a geomagnetic index of Ap = 3, which is used in the EMAC submodel UBCNOX.  (Naujokat, 1986), an idealized 28-months varying QBO is used for WACCM. The reference simulation with perpetual solar minimum conditions, performed by each CCM, uses the ATLAS-3 based SSI reference spectrum (Thuillier et al., 2004, s. Section 2). To our knowledge, this is the first time that this observational SSI dataset has been used to force CCM simulations.
In addition, five sensitivity simulations with perpetual solar maximum conditions of the solar cycle 22 maximum in November 1989 from five different SSI data sets have been performed by each CCM. The five spectra for solar maximum conditions are 5 constructed by adding the difference of the SSI between the solar maximum in November 1989 and the near solar minimum in November 1994 of NRLSSI1 (Lean, 2000), NRLSSI2 (Coddington et al., 2016), SATIRE-T (Krivova et al., 2010), SATIRE-S (Yeo et al., 2015), and CMIP6-SSI (Matthes et al., 2017) to the common ATLAS-3 based observational reference SSI data set which is defined for the solar minimum state. By this procedure we ensure that we use a common spectral distribution of energy that only varies in the solar maximum sensitivity simulations by the genuine difference from solar minimum to solar 10 maximum of each SSI data set. Table 1 summarises the resulting percentage changes for five spectral regions, and also gives an overview of the five sensitivity simulations for solar maximum, which have been performed by WACCM and EMAC.
The solar minimum reference simulation as well as the solar maximum sensitivity simulations are performed for low auroral activity. Due to these model configurations, the NO y changes are expected to be caused by the SSI changes from solar minimum to solar maximum and not by variations in auroral activity.

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4 Annual mean solar response of heating rates, temperature, and ozone To analyse the solar signal, time series of anomalies have been calculated for each simulation performed by EMAC and WACCM using one of the five SSI data sets constructed for solar maximum conditions with respect to the time series of the reference simulations of both models using the ATLAS-3 based SSI near solar minimum. These five anomaly fields for each CCM can be interpreted as solar response of the model variables to SSI and TSI changes over the 11-year solar cycle. Figure 1 20 (left) shows the solar response of the ensemble mean, i.e. averaged over the simulations of both CCMs applying five different SSI data sets each, in (a) shortwave heating rate (HR), (b) temperature, and (c) ozone mixing ratio. The averaged solar response is significant at the 95% level in regions that are not masked by grey hatching. A t-test is applied to the complete concatenated ensemble (10 simulations in each group without performing an ensemble mean of the simulations at solar maximum and minimum in advance). By this procedure the variability of the solar response is maintained and the regions where the significance 25 reaches the 95% level are smaller compared to the results of a t-test for an ensemble average.
[ Figure 1 about here.] The solar SW heating rate response is significant throughout the middle atmosphere at pressures lower than 30 hPa with peaks in the tropics near the stratopause (∼0.2 K day −1 ) and in the upper mesosphere (∼0.38 K day −1 ) ( Figure 1a). Whereas the solar response in the upper mesosphere is due to enhanced solar radiation in the spectral range from Lyman-α to the evidence that the primary annual mean radiative response of the middle atmosphere is a robust feature and not particularly sensitive to the specified SSI data set or the CCM configuration.
A direct consequence of the stronger SW heating during solar maximum is a solar signal in temperature, which also peaks in the upper mesosphere with up to 2 K and near the stratopause in the subtropics with more than 0.8 K (Figure 1b, left). This is weaker than the more than 1 K solar temperature response derived from combined SSU/MSU4 satellite data reported by Randel 5 et al. (2009), but in the same order of magnitude as reported by SPARC CCMVal (2010) for CCMs and slightly larger than analysed by Mitchell et al. (2015) for an ensemble of CMIP5 high-top models. The secondary lower stratospheric maximum in the solar temperature response in the tropics, which has been identified in reanalyses (e.g., Frame and Gray, 2010), is not present in the ensemble mean. At high latitudes, the solar signal in temperature shows generally an enhanced spread between the ensemble members which is due to the high internal dynamical variability of the polar winter atmosphere. 10 The solar response in ozone mixing ratio has a first peak in the stratosphere near 7 hPa with two regions exceeding 2%,

Uncertainty in solar response due to SSI data sets and CCMs
To quantify the uncertainty of the mean solar response emerging from the usage of different SSI data sets on the one hand and different CCMs on the other, we apply a two-way analysis of variance (ANOVA) approach in this study (s. Appendix A 25 for details). The data set to analyse consists of the annual mean solar responses from simulations using the five SSI data sets in both CCMs, i.e. a time series with 450 years from 10 simulations with 45 years each, as shown for the ensemble average in Figure 1 (left). The overall variance of the solar response, as expressed by its annual standard deviation (Figure 1, left, white contours), is partitioned into a contribution arising from the applied SSI data sets and a contribution arising from the or exceed the limits of the colour coding. They indicate the percentage of the solar signal variance that can be explained by the differences between the SSI data sets or the CCMs, respectively. Superimposed grey hatching masks areas where the solar responses are not significantly different when grouped according to the SSI data sets or the CCMs. Note that the contributions of the variances explained by the SSI data set and the CCM in the middle and right columns of Figure 1 do not add up to 100%, as often the random contribution to the total variance is largest.
Significant differences in the solar signal can be identified when the simulations of the ensemble mean are grouped according to the SSI data sets (Figure 1, middle) and the CCMs (Figure 1, right). In the upper mesosphere, differences between the CCMs 5 explain more than 80% of the spread in the solar ozone signal -due to the change of sign in the ozone response between WACCM and EMAC -, more than 25% of the spread of the solar temperature signal, and up to 50% of the spread of the SW heating rate signal at high latitudes. In contrast, between 60 • S and 60 • N up to 70% of the spread of the solar signal in SW heating rates is explained by the different SSI data sets, due to large solar amplitude variations in the FUV between the SSI data sets. As a result, the SSI data sets also induce a significant fraction of the variability of the solar signal in temperature 10 (9%) at the mesopause.
In the upper stratosphere and lower mesosphere, the SSI data sets are responsible for a relatively large part of the variance of the solar responses, while the CCMs explain much less variance as the radiation schemes of both models possess a sufficient spectral resolution to capture the SW heating rate peak. The largest fractions of the SSI induced variance of the solar response in SW heating rates (30%) and ozone (30%) peak in the subtropics, while the SSI induced variance of the temperature solar 15 signal (10%) maximizes in the tropics.
In the lower stratosphere and troposphere, the SSI data sets do not contribute significantly to the variability of the solar signal in annual mean SW heating rates, temperature, and ozone. But some significant contributions of the applied CCMs to the variance of the solar response are found, which have similar vertical and latitudinal structures for all three variables, peaking in the tropics between 30 and 10 hPa and in the northern subtropics to mid-latitudes between 100 and 10 hPa. The 20 minor CCM contribution to the SW heating rate solar signal in the lower stratosphere (p > 10 hPa) is consistent with the CCM induced variance contribution of ozone and seems to be related to differences in ozone transport affecting shortwave ozone absorption.
The simulations performed with the SATIRE-T data set show considerable deviations in the solar response compared to simulations using the other data sets, as further discussed in Section 5.1. When omitting the simulations with the SATIRE-T 25 data set in the ANOVA (see Figure S1 in the supplement), less variability is explained by the SSI data set, revealing that a large fraction of the variability attributed to the SSI data set is caused by the specific behaviour of SATIRE-T.

Differences resolved by SSI data set
The ANOVA of the ensemble mean in the previous section has shown that significant differences in the solar responses can 30 be attributed to the SSI data sets mainly in the region of the most active ozone production in the upper stratosphere to lower mesosphere, whereas significant differences attributed to the CCMs are mainly located in the upper mesosphere and lower stratosphere, further discussed in Section 5.2. In this section, we examine the differences in the solar responses of EMAC and WACCM arising from the use of the different SSI data sets. The atmospheric response to solar irradiance variations is primarily determined by radiative and photochemical processes that are represented by a variety of parameterisations in climate models or CCMs. To separate the effects of differences in the input SSI data sets on the respective SW radiation and photolysis schemes of EMAC and WACCM, we first present profiles for simulations applying the five individual SSI datasets, averaged over both CCMs. Figure 2 shows vertical profiles of the solar cycle amplitude in SW heating rates, temperature, ozone, atomic oxygen (O( 3 P) and O( 1 D)), NO y , HO x , and water vapour (H 2 O), averaged from 60 • S to 60 • N between 100 5 hPa close to the tropopause and 0.01 hPa in the upper mesosphere. For each sub-figure, the 11-year solar response is at first calculated as the difference between the individual solar maximum simulations and the ATLAS3 solar minimum reference simulation for EMAC and WACCM, respectively. The differences are then grouped according to the SSI data set and averaged over EMAC and WACCM. As in Figure 1  The average over both CCMs shows the strongest stratospheric solar response in SW heating rates and temperatures when using the SATIRE-S data set, whereas SATIRE-T leads to the weakest solar response throughout the middle atmosphere ozone is the weakest in this comparison, as its SSI amplitude in the FUV and 201-242 nm spectral range, important for the photochemical ozone production, is considerably weaker (7.6% and 2.6%) than in the other SSI data sets (11.1-12.1% and 3.3-3.6%) (Table 1), whereas its SSI amplitude in the ozone-destroying UV-band (243-380 nm) is comparable to the other SSI data sets. The two competing, wavelength dependent effects of ozone production and ozone loss in the Chapman cycle lead to the relative weak solar ozone response in simulations using the SATIRE-T data set. Compared to the SATIRE-T-based 30 simulations, the simulations using the remaining SSI data sets show solar signals in SW heating rates, temperature, and ozone, that are relatively close to each other.
[ Besides the oxygen chemistry of the Chapman cycle, ozone depleting catalytic cycles, e.g. the HO x and NO x cycles, are involved in contributing to the solar response in ozone. Whereas the HO x catalytic cycle is the most important one in the upper mesosphere, the NO x catalytic cycle dominates in the middle and upper stratosphere. NO y is specified as NO y =N + NO + NO 2 + NO 3 + 2 N 2 O 5 + HNO 3 + HNO 4 + ClNO 2 + BrNO 3 , but in the mesosphere NO y is very close to the active nitrogen defined as NO x = NO + NO 2 . For all SSI-based averages, the solar response of NO y is negative in the stratosphere and lower mesosphere but positive in the uppermost mesosphere above 0.03 hPa (Figure 2f). The stratospheric and lower mesospheric decrease is consistent with Hood and Soukharev (2006)  applied SSI data sets (see Table 1). With enhanced photolysis at solar maximum, the NO y abundances decrease (Figure 2f).
The NO y solar response is of the same magnitude up to the lower mesosphere for all SSI data sets, except for SATIRE-T, which due to its weaker FUV solar amplitude produces a weaker increase of the NO photolysis rates and a weaker negative NO y solar response, respectively. The negative NO y solar response results in a slowdown of the catalytic NO x cycle of ozone destruction, which indirectly enhances the positive solar response in ozone (Sukhodolov et al., 2016). 20 There are two possible reasons for the increase of NO y in the uppermost mesosphere above 0.03 hPa during solar maximum compared to solar minimum. EUV photoionization of neutrals increases during solar maximum, leading to an increase of electron, ion and excited species production and subsequently, NO, above about 80 km. On the other hand, the response of NO y in the uppermost mesosphere could also reflect changes in the auroral NO production in the lower thermosphere. NO in the lower thermosphere is mainly produced by the reaction of an excited nitrogen atom with molecular oxygen (N( 2 D) + O 2 → NO + O) 25 (Marsh et al., 2004). As low auroral activity is prescribed for both the solar minimum reference and the solar maximum simulations, no solar response of thermospheric NO is expected from this reaction. However, NO in the lower thermosphere is also formed by the reaction of the ground-state of N with molecular oxygen (N( 4 S) + O 2 → NO + O). This reaction is strongly temperature dependent and thus more effective in the warmer lower thermosphere during the solar maximum (e.g., Sinnhuber and Funke, 2020). 30 The solar response in HO x (defined as OH + HO 2 ) (Figure 2g  An even larger part of the variability of the solar signal in the stratosphere can be attributed to the SSI data set for O( 3 P) (60%) and O( 1 D) (70%) (see Figure S2 in the supplement). In the upper mesosphere, the choice of the SSI data set has the largest influence on the solar signal variability of the SW heating rates (70%) for which the solar amplitude of the SSI data set in the FUV is the main driver.

Differences resolved by CCM
Large differences in the solar signal variability explained by CCM differences have been identified by the ANOVA (Figure 1, right) in the upper mesosphere. The range of the solar responses between the EMAC and WACCM ensemble means over the SSI data sets, indicated by the shaded areas in Figures 2 and 3, also identifies the largest differences in the upper mesosphere.
[ Figure 5 about here.] 30 The changes in the chemistry and dynamics over the 11-year solar cycle are superimposed on the climatological reference states of the CCMs, and are influenced by the climatological temperatures and abundances of photochemically active species.   Figure 5 presents a direct comparison between the annual mean climatologies of the EMAC and WACCM ensemble means in the middle atmosphere in terms of zonal mean differences in shortwave heating rates, temperature, ozone, atomic oxygen (O( 3 P), O( 1 D)), NO y , HO x , and H 2 O. Substantially lower (by up to 1.2 K day −1 ) shortwave heating rates are found in the upper mesosphere of EMAC. This bias is indicative of less effective FUV-heating from oxygen absorption in the Schumann-Runge bands, presumably due to differences in the O 2 absorption parameterisation of Strobel (1978) with 19 bands (used in 25 EMAC) and the heating rates from the photolysis parameterisation based on Koppers and Murtagh (1996) (used in WACCM).
These differences in SW parameterisations between the CCMs also affect the solar response in the upper mesosphere which is smaller in EMAC for the SW heating rates and temperatures (Figure 2a,b). They lead to the patterns of solar signal variance explained by CCMs in Figure 1a,b (right) which resemble the structure of the anomaly pattern in SW heating rates in the upper mesosphere (Figure 5a). By contrast, in the lower mesosphere and large areas of the stratosphere, EMAC shows higher 30 shortwave heating rates, possibly an effect of the degraded spectral resolution of the SW radiation scheme in WACCM below 60 km or of the higher ozone mixing ratios in EMAC (Figure 5c). However, WACCM shows larger solar responses in ozone mixing ratios and JO 3 → O( 3 P) photolysis rates in the lower and middle stratosphere, possibly related to the finer spectral resolution of the photolysis scheme used in WACCM.
The temperature deviations in the mesosphere between EMAC and WACCM (Figure 5b) are not congruent with those in shortwave heating rates and, therefore, most likely have to be attributed to differences in dynamical heating by dissipating planetary or gravity waves. The largest temperature differences between EMAC and WACCM are located in high southern latitudes. The southern polar vortex is much colder in WACCM than in EMAC and the ERA-Interim reanalyses. This shows that with the implementation of the modified gravity wave parameterisation of Garcia et al. (2017) in our WACCM simulations, 5 the low temperature bias has been alleviated but still exists. Interaction between dynamics and chemistry in EMAC is leading to higher ozone mixing ratios in the lower stratosphere over the south pole, where a less intense and warm biased south polar vortex is avoiding more severe heterogeneous ozone depletion, compared to WACCM.
Besides the differences in the average mesospheric shortwave heating rates and temperatures between EMAC and WACCM, there are also large differences in the chemical composition (and the associated solar signals) in this region. The odd oxy-10 gen mixing ratios in the upper mesosphere are lower in EMAC by 50% for ozone, 80% for O( 3 P), and more than 50% for O( 1 D) (Figure 5c-e). This is partly explained by the fact that oxygen photolysis in the Schumann-Runge continuum to much lower HO x mixing ratios in EMAC in these regions.
As already discussed for atomic oxygen in the previous paragraph, the climatologies and solar responses of chemcial species in the upper mesosphere are strongly affected by differences in the vertical transport between WACCM and EMAC. With an upper boundary in the lower thermosphere, WACCM is capable to simulate the downward transport of NO y by the gravity wave driven, residual circulation from the thermosphere down to the lower mesosphere at high latitudes in the respective winter 30 seasons ( Figures S3 and S4 in the supplement). In EMAC we use the UBCNOX parameterisation to include NO y produced in the thermosphere by auroral and medium-energy electrons. Nevertheless, the NO y mixing ratios are up to 60% lower in EMAC than in WACCM in large parts of the upper mesosphere, except for northern polar latitudes where the WACCM NO y mixing ratios are exceeded by 100% (Figure 5f). The solar response of NO y in the upper mesosphere discussed in Sec. 5.1 is much stronger in WACCM than in EMAC, as obvious from the shaded area in Figure 2f. In WACCM, the increased NO production during solar-maximum in the uppermost mesosphere and lower thermosphere is driven by the increase in EUV photoionization and lower thermospheric temperatures as discussed in Sec. 5.1. In EMAC, the NO y mixing ratios in the uppermost four model levels are determined by the UBCNOX parameterisation, which depends on the prescribed, constantly low Ap index, but not on the solar UV/EUV radiation, and thus suppresses a solar signal in NO y .
Differences between EMAC and WACCM are also found in the climatological distribution of water vapour and the related  In summary, both models show for all quantities comparable solar responses to the different SSI data sets up to the lower mesosphere near 0.1 hPa. Above, the solar signals deviate substantially, as shown for ozone, oxygen, HO x , and NO y . The comparison of the upper mesospheric solar signals in EMAC and WACCM, as well as the differences in the climatologies in the upper mesosphere, shows that a realistic simulation of solar cycle effects might better achieved when the residual downward transport of thermospheric photolysis reactants is taken into account. 35 16 https://doi.org/ 10.5194/acp-201910.5194/acp- -1010 Discussion started: 31 January 2020 c Author(s) 2020. CC BY 4.0 License.
In this section we focus on the solar response in total column ozone (TCO) in our simulations and investigate to what extent it is influenced by the applied SSI data set and by the CCM. The solar signal in TCO is the vertically integrated solar signal in ozone mixing ratios. In the previous sections, we have identified differences in the solar signal in ozone mixing ratios depending on the applied SSI data set (Section 5.1) as well as on the applied CCM (Section 5.2), especially in the middle to 5 lower stratosphere which contributes most to the solar signal in TCO. Hood (1997) who analysed SBUV data for a relatively short period from 1979-1993, found an annual mean solar response of TCO in the tropics of 1-2%. For the same time period, Zerefos et al. (1997) detected a significant correlation of the solar activity with annual mean TCO from TOMS between 40 • S and 40 • N, whereas no significant correlation was found at higher latitudes, due to the large dynamically induced variability. Soukharev and Hood (2006) suggested that the solar response of 10 TCO is mainly caused by ozone abundances in the tropical lower stratosphere. A study of Randel and Wu (2007)  The latitudinal distribution of the solar response in TCO for the 10 simulations performed for this study is shown in Figure   15 6. Clear differences occur between both CCMs, with WACCM showing in general a larger solar signal in TCO at all latitudes ( Figures 6, 8). Between 40 • S and 40 • N significant solar TCO responses are simulated in both models, reaching 1.5% (3.9 DU) for WACCM and 1.1% (3.0 DU) for EMAC in the tropics (20 • S-20 • N). The chosen SSI data set has only a very minor impact on the solar TCO signal in both models, except for SATIRE-T. The WACCM and EMAC simulations using SATIRE-T show the smallest solar responses in the tropics, which reflects the small solar amplitude in the UV spectral region of this SSI data 20 set. At mid and high latitudes, differences in the solar TCO signals between the SSI data sets become larger, however remain generally smaller than the differences between the models, as particular evident for high southern latitudes.
[ Table 2 about here.] The solar response in TCO at high latitudes is strongly influenced by stratospheric dynamic variability during the respective winter seasons in both hemispheres. As a measure of this dynamic variability, we introduce in (Figure 7) the thickness of the 25 stratospheric layer between the 100 and 10 hPa pressure levels. High values of the 100-10 hPa layer thickness correspond to a warm layer and a weak polar vortex occurring in dynamically disturbed periods, such as minor or major sudden stratospheric warmings (SSWs). The associated downward transport of air in high latitudes leads to an increase in TCO. On the other hand, cold conditions in polar regions, represented by low values of 100-10 hPa layer thickness, can lead to enhanced chemical ozone depletion and low TCO values (Farman et al., 1985;Rex et al., 2002;Manney et al., 2011). While the 100-10 hPa layer latitudes where EMAC simulates a colder and stronger polar vortex during solar maximum and WACCM shows a warmer and weaker polar vortex (Figure 7). At northern polar latitudes, both models simulate warmer and weaker polar vortices at solar maximum -except for the SATIRE-S WACCM simulation.
The high correlation between the solar responses in TCO and 100-10 hPa layer thickness at high latitudes is reflected in Table 2 which gives the correlation coefficients between the solar maximum anomalies of the annual average 100-10 hPa layer 5 thickness in the polar region (70 • -90 • ) and the respective TCO anomalies for both hemispheres. The annual mean correlation at high latitudes is mainly a result of the high correlation during the winter/spring seasons of both hemispheres, with the highest correlation occurring in January/February/March (JFM) for the NH and in September/October/November (SON) for the SH (for seasonal correlation coefficients see Table S1 in the supplement). More intense downwelling of ozone during episodes of stratospheric warming events, or less intense downwelling during cold conditions in combination with a more effective 10 chemical ozone depletion, are the main driver of the TCO anomalies in high latitudes in both hemispheres. Although all anomalies shown in Figure 6 and 7 are derived for simulations during solar maximum conditions with respect to the simulation during solar minimum conditions, a consistent, significant solar response for TCO and lower stratospheric layer thickness in polar latitudes can not be found, implying that the derived changes at high latitudes are rather due to random internal dynamical variability in the models than to the external solar forcing.

15
In Figure 8 (top) we show the zonally averaged differences in TCO between the simulations for solar maximum and solar minimum conditions for the average of all simulations (black contour), the EMAC-(blue contour) and WACCM-simulations (red contour), the standard deviation (light grey shading), and the two-way ANOVA with SSI-(dark grey shading) and CCMtreatment (hatches). The range of the standard deviation shows the largest variability of the TCO anomaly in polar regions.
As discussed above, the high latitude TCO anomaly is mainly a result of the internal, dynamic variability of the CCMs. 20 Consequently in the north polar region, there is only a relatively small part of the TCO anomaly variability that can be explained by the SSI data set (1%) or the CCM (0.6%). Only in the southern polar region, a larger but still only small fraction of the variability can be explained by differences in the CCMs (1.4%), as there are systematic differences in the anomalies of the lower stratospheric layer thickness and TCO between WACCM and EMAC (Figures 6, 7). As in the northern polar region, the SSI data set can only explain a small fraction of the variability of the TCO anomaly in the southern polar region (0.8%). The 25 standard deviation of the solar TCO response is considerably smaller in the tropics, where also the fraction of the standard deviation that can be explained by either the choice of the SSI data set (22%) or the CCM (13%) is much larger, with a larger contribution of the SSI data sets. When approaching the northern mid-latitudes the influence of the CCMs on the variability of the solar response grows, whereas the influence of the SSI data set gets smaller. This is reflected by the pronounced minimum of the solar TCO response in the mid-latitudes of the EMAC simulations, whereas three out of five WACCM simulations show 30 a relatively large positive anomaly in this region.
The annual, global mean solar response of partial column ozone integrated for different pressure regions is shown in Figure   8 (bottom) with the same type of contour lines/shading as in Figure 8 (top). Averaged over all simulations, the largest solar response in ozone is in the lower stratosphere. In this region, simulations performed by WACCM show a much larger solar signal than the averaged EMAC simulations, with largest differences occurring in the lowest region with pressures higher than 35 18 https://doi.org/ 10.5194/acp-201910.5194/acp- -1010 Discussion started: 31 January 2020 c Author(s) 2020. CC BY 4.0 License. 32 hPa. In the WACCM simulations, this layer contributes 32.5% to the solar signal in TCO, whereas it is only 16.7% in the EMAC simulations. The analysis of SBUV-SBUV/2 (Solar Backscatter Ultraviolet Radiometer) data by Hood (1997) shows that 85% of the solar signal in TCO is from the contribution of the lower stratospheric layer (pressure > 16 hPa). The same analysis for the CCMs gives smaller contributions from the lower stratosphere with 52.8% on average, 57.8% for WACCM, and 45.3% for EMAC. This different behaviour of the CCMs in the lower stratosphere is also reflected in the relatively large 5 fraction of the standard deviation of the solar signal that can be explained by differences between the CCMs. A larger part of the standard deviation can be explained by differences between the SSI data sets in the middle stratosphere (16-4 hPa), although still the largest part of the standard deviation can not be attributed to either differences between the CCMs or the SSI data sets.

Summary and conclusions
This study aimed at investigating the uncertainty in simulations of the atmospheric solar response to 11-year solar cycle variability. In particular, the effects of two sources for uncertainty, i.e. the prescribed spectral solar irradiance (SSI) data set and potential differences in the CCM background state and configuration, were examined. For this purpose, simulations with two CCMs, each forced with five different SSI data sets, were performed. The CCMs EMAC and WACCM are representative 15 of state-of-the-art CCMs, including the prerequisites for simulating solar cycle variability, i.e. spectrally resolved shortwave radiation and photolysis schemes. Both models contributed to the evaluation of the simulated solar signature in the SPARC CCMVal-2 initiative (SPARC CCMVal, 2010). The SSI data sets represent the best available estimates of 11-year solar variability in electromagnetic radiation, and either have been used in previous model studies ( i.e., or are recommended for current model intercomparions (i.e., CMIP6). We apply a novel approach to extract the effects of the pure 20 SSI solar cycle amplitudes, as a common reference SSI distribution for solar minimum conditions was defined, based on AT-LAS3 measurements in November 1994, and SSI data sets for solar maximum were constructed by adding the solar amplitude of the five SSI data sets to the solar minimum reference distribution. To separate the influences of the SSI data sets and the CCMs, respectively, on the solar responses in shortwave heating rates, temperature and ozone, a two-way analysis of variance (ANOVA) was applied here for the first time in this context. 25 Our study revealed that differences in SSI data sets provide the largest fraction of solar cycle variance in the upper stratosphere/lower mesosphere, contributing 30% to the SW heating rate, 30% to the ozone and 10% to the temperature solar cycle variance. A second region with a considerable SSI induced spread in the SW heating rate solar signal up to 70% is the upper mesosphere (except for polar latitudes), affecting also the ozone solar signal in this height region. Differences between CCMs have a major effect in the upper mesosphere, where they explain more than 80% of the ozone, 25% of the temperature and 50% 30 of the SW heating rate variability of the solar signals. CCMs add a minor contribution to the SW heating rate and ozone solar cycle variance in the lower stratosphere.
To isolate the causes for the contributions to the solar signal spread, a detailed analysis was performed of the solar signal profiles of SW heating rate, temperature, ozone, different chemical compounds and photolysis rates for the five SSI-simulation ensemble means (each including 2 CCMs) on the one hand and for the two CCM ensemble means (each including 5 SSI data sets) on the other. The analysis of CCM-averaged quantities, involved in the radiative and photochemical processes, has revealed a dependence of the solar responses on the SSI data sets, with solar signals for most quantities showing a clear relation mixing ratios with the solar cycle throughout the stratosphere, emerging for all SSI data sets, can be explained by chemical 20 production in the upper stratosphere and enhanced H 2 O transport from the troposphere into the lower stratosphere in a warmer UTLS at solar maximum. In the upper mesosphere, the choice of the SSI data set has the largest influence on the solar signal variability of the SW heating rates (70%) for which the solar amplitude of the SSI data set in the FUV is the main driver.
In addition to the SSI induced spread in the solar signal, differences between the CCMs turned out to have their strongest impact on the solar signals in shortwave heating rates, temperature and ozone in the upper mesosphere at altitudes above about 25 60 km. The two CCMs used for this study are representative for the current CCM generation which consists primarily of models with a top level in the upper mesosphere around 0.01 hPa (or 80 km altitude), as the EMAC version used in this study, plus a few CCMs that also include the thermosphere, as WACCM with a top level at about 140 km. Resulting differences in the radiation parameterisations and the vertical transport of substances have been identified to cause the spread in the upper mesosphere solar signals. For example, the spread in the solar response of the upper mesosphere shortwave heating rates arises 30 from an underestimation of oxygen absorption in the FUV by the parameterisation of Strobel (1978) in EMAC, reaching up to -1.2 K day −1 compared to WACCM in the climatological annual mean. Moreover, the odd oxygen mixing ratios in the upper mesosphere are substantially lower in EMAC than in WACCM, as EMAC -due to its lower lid -does not capture the photochemical production of O( 1 D) and O( 3 P) in the lower thermosphere of WACCM nor their downward transport into the mesosphere by the residual circulation during the winter seasons. As a result, solar ozone responses of opposite sign are 35 20 https://doi.org/ 10.5194/acp-2019-1010Preprint. Discussion started: 31 January 2020 2020. CC BY 4.0 License. produced in the upper stratosphere where WACCM exhibits more ozone at solar maximum due to its enhanced odd oxygen abundances, while EMAC exhibits less ozone due to its more intense HO x cycle. This shows that a realistic simulation of solar cycle effects is better achieved when the residual downward transport of thermospheric photolysis reactants is taken into account.
For annual mean total column ozone (TCO) a significant solar response could be identified from the southern midlatitudes 5 to the northern polar region when all simulations from both CCMs are considered. In the southern high latitudes, these TCO anomalies are the result of natural dynamical variability of the Antarctic polar vortex. Distinct differences in TCO anomalies between the CCMs are also reflected by the relatively large fraction of the anomaly variability that can be explained by differences between the CCMs. The usage of the SSI data set has the largest influence on the variability of the TCO solar response in the tropics. The largest contribution to the annual mean TCO solar response is from the lower stratospheric layers 10 with pressures > 16 hPa which on average contributes 53%, or when analysed separately, 58% (WACCM) and 45% (EMAC).
Both CCMs underestimate the lower stratospheric contribution to the solar response in TCO, compared to the analysis of SBUV-SBUV/2 data by Hood (1997) who found a 85% contribution of the lower stratosphere to the TCO solar signal.
Note that the individual contributions of the SSI data sets and CCM configurations derived in our study are constrained by the choice of the CCMs. While the possible spread of solar cycle SSI variation is very well captured in our study by considering 15 the five currently usable SSI data sets, a similar coverage of the CCM induced spread cannot be achieved, given the number and diversity of available CCMs. Thus, the CCM contribution to the variance of the solar signal are, to some extent, determined by the specifics of the EMAC and WACCM models. For example, the CCM contribution to the solar SW heating rate signal would increase in models applying SW radiation schemes with low spectral resolution or employing TSI scaling procedures.
Besides the ATLAS3 reference SSI dataset more recent SSI reference datasets are available such as SOLAR-ISS (Meftah 20 et al., 2020(Meftah 20 et al., , 2018, which is representative of the 2008 solar minimum. The usage of an alternative SSI reference dataset may have an influence on the climatological state of the CCMs, as higher or lower SSI values in certain spectral bands lead to higher or lower shortwave heating rates, thus affecting the temperature and potentially also the zonal wind of the CCMs. As the reference SSI dataset serves as a common base state for the solar minimum of all other SSI datasets, we do not expect significant differences in the uncertainties of the solar signals when using a different SSI reference spectrum. The quantification of the Finally, as all simulations of this study were carried out under conditions of low auroral activity, only effects of 11-year variations in solar electromagnetic radiation have been considered in this study. The impact of variations of energetic particle precipitation for different levels of auroral activity will be subject of further studies.

Data availability
The data of the EMAC and CESM1(WACCM) simulations, which have been performed for this study, are available for down-5 load on request.

Appendix A: Analysis of variance (ANOVA)
A two-way analysis of variance (ANOVA) (Fisher, 1925) is applied to time series of anomaly data, i.e. a data set consisting of the time series of the differences between the simulations performed by both CCMs for solar maximum conditions and the respective simulation of each CCM for solar minimum conditions. It is created by using the five simulations of each CCM with 10 solar maximum SSI data sets minus the simulations of each CCM with the ATLAS-3 SSI data set at solar minimum. Thus, the complete time series consists of 450 annual mean anomalies (n t ) from 10 simulations, each with a length of 45 years (n). The total sum of squares (SS t ) of this time series is calculated as with the individual annual mean solar response x k and the overall mean x. The SS t of the complete time series is further split 15 by applying two treatments as One treatment (A) takes into consideration the applied CCM, building two groups (N A = 2), the WACCM and the EMAC solar responses with n A = 225 elements each. The second treatment (B) takes into consideration the applied SSI data set, building five groups (N B = 5) with n B = 90 elements each. For each treatment (K = A, B) the sum of squares between the groups (SS bK ) 20 are calculated as with x j the mean solar response of each group, N K the number of groups within each treatment, and n K the number of elements within each group. The sum of squares emerging by the interaction of the treatments (SS b AB) is calculated as with x ijk the individual solar responses. By the ratios the coefficients of determination are calculated, which are a measure of the variance explained by the treatment (K = A, B) or by the interaction between both treatments. R 2 A and R 2 B are shown in Figure 1. The mean sum of squares within the groups MSS w is calculated as and the mean sum of squares between the groups MSS bK and the MSS interacting between the groups MSS bAB are calculated 10 as with n t − N A N B the degree of freedom within the groups, N K − 1 the degree of freedom between the groups, and (N A − 1)(N B −1) the degree of freedom of the interaction between the treatments. As MSS w and MSS bK are assumed to be unbiased estimators of the variance σ 2 we can use these estimators to calculate the F-statistics as  The white contours indicate levels of explained variance larger than the range of shading. Right column: as middle column but for systematic differences between CCMs. The grey hatching masks areas where signal or ratio of explained variance does not pass a test for statistical significance (p > 5 %). . . . . . . . . . . . . . . . 32 2 Annual mean 11-year solar cycle response (60 • S-60 • N) in (a) shortwave heating rates, (b) temperature, (c) Top: Ensemble average, annual and zonal mean 11-year solar cycle response in partial column ozone in % (solid black) and the 95% confidence interval as error bars; WACCM simulations only (solid red); EMAC simulations only (solid blue); light grey shading denotes the standard deviation of the ensemble mean solar response; hatched region denotes the part of the standard deviation explained by the models; dark shading denotes the part of the standard deviation explained by the SSI data sets. Bottom: As top for annual, global Left column: Annual mean 11-year solar cycle response (shaded) and signal variance (white contours) in terms of the solar response annual standard deviation for shortwave heating-rates (top), temperature (middle), and ozone mixing ratios (bottom). Solar signal derived as ensemble mean over both models and all SSI data sets; solar minimum SSI based on ATLAS3 reference state. Middle column: Percentage of signal variance (square of white contours of left figures) explained by systematic differences between forcing data sets (blue shading). The white contours indicate levels of explained variance larger than the range of shading. Right column: as middle column but for systematic differences between CCMs. The grey hatching masks areas where signal or ratio of explained variance does not pass a test for statistical significance (p > 5 %).