2.1 ATLAS-3-based reference spectrum

The SSI data set used in this study for the solar minimum reference state between 0.1 and 2395 nm is the Atmospheric Laboratory 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 the space shuttle (see Thuillier et al., 2004, for more details). The ATLAS-3 SSI data set covers wavelengths up to 2395 nm only. We use the NRLSSI1 data set for wavelengths between 2395 and 99 975 nm and the SATIRE-S data set from 99 975 to 165 000 nm to extend the spectrum to the infrared and to derive the TSI for the ATLAS-3 spectrum. To assure smooth transitions at 2395 and 99 975 nm, the NRLSSI1 and SATIRE-S data sets are scaled accordingly. The extended ATLAS-3 spectrum was then scaled with a constant factor 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 been added to get the respective SSI data sets for solar maximum conditions.

2.2 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 disc with SSI changes. Indices which are derived from observations and proxies for sunspot darkening and faculae are used in regression models to determine the coefficients required to 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). The required model coefficients are determined from a multiple linear regression of the proxy time series on the observed TSI from SORCE/TIM and observed SSI from SORCE/SOLSTICE and SORCE/SIM for NRLSSI2 and UARS/SOLSTICE for NRLSSI1. For facular brightening the composite MG II index of the University of Bremen (Snow et al., 2014) and as an index for sunspot darkening the sunspot area as recorded by ground-based observatories are used (Lean et al., 1998).

2.3 SATIRE

The SATIRE (Spectral And Total Irradiance REconstructions) model (Krivova et al., 2009; Yeo et al., 2014) for the reconstruction of SSI and TSI is a semi-empirical model that is based on variations in the solar surface magnetic field. The intensity 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 the estimation of 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 to 160 000 nm, 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 the reconstruction of 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 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 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.

2.4 CMIP6 data set

The SSI and TSI data sets of the NRLSSI2 and SATIRE (i.e. SATIRE-S and SATIRE-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 recommended SSI–TSI data set for CMIP6 has been derived by averaging the NRLSSI2 reconstructions with the SSI and TSI of SATIRE-S and SATIRE-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 consist of an average of output from NRLSSI2 and SATIRE-S.

Figure 1(a) Solar cycle SSI variations from November 1989 to November 1994 relative to November 1994 (ΔSSI) in percent for wavelengths ranging from FUV to the visible bands; (b) as in (a) for the Lyman-α (121.5 nm), far-UV (121–200 nm), Herzberg continuum–Hartley bands (201–242 nm), and Hartley and Huggins bands (243–380 nm) (multiplied by a factor of 10) and visible (381–780 nm) (multiplied by a factor of 100).

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Figure 2(a) Averaged SSI variations for solar cycle amplitudes relative to ATLAS-3 (ΔSSI) in percent for the Lyman-α (121.5 nm), far-UV (121–200 nm), Herzberg continuum and Hartley bands (201–242 nm), Hartley and Huggins bands (243–380 nm) (multiplied by a factor of 10), and visible (381–780 nm) (multiplied by a factor of 100) spectral ranges, with the 95 % confidence interval given as error bar. (b) Anomaly of SSI variations for solar cycle 22 (descent-2) with respect to the averaged solar cycle shown in (a).

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2.5 SSI amplitudes

The quantification of the uncertainties of the solar responses in the CCMs is based on an exemplary solar amplitude with decreasing solar irradiances from the maximum of solar cycle 22 in November 1989 to a state near the solar minimum in November 1994, which is motivated by the timing of the ATLAS-3 measurements. 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, 121–200 nm), 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 (ΔSSI) represents the percentage SSI change from solar minimum to maximum relative to the ATLAS-3 solar minimum SSI in November 1994 and is also shown in Fig. 1b. The second value represents ΔSSI relative to the TSI change from solar minimum to maximum ($\frac{\mathrm{\Delta }\mathrm{SSI}}{\mathrm{\Delta }\mathrm{TSI}}$) in percent. Whereas ΔSSI emphasises the large variability of the solar irradiance at Lyman-α and in the Schumann–Runge continuum and bands over the 11-year solar cycle, the ΔSSI weighted by ΔTSI emphasises the large solar cycle variation in absolute energy in the UV and visible wavelengths. High ΔSSI variability in the FUV is leading to large increases in the photolysis of oxygen and water vapour in the upper mesosphere during solar maximum. More important for the solar response of stratospheric ozone mixing ratios are the two UV spectral regions. While the irradiance increases in the 201–242 nm spectral region lead to more oxygen photolysis and subsequent ozone production in the stratosphere during solar maximum, the irradiance increases between about 243 and 380 nm lead to more ozone destruction through photolysis during solar maximum, further discussed in Sect. 5.1. The NRLSSI1 and NRLSSI2 data sets have the lowest $\frac{\mathrm{\Delta }\mathrm{SSI}}{\mathrm{\Delta }\mathrm{TSI}}$ ratio in the Hartley–Huggins UV band among the SSI models used here, whereas the SATIRE-S data set shows the highest and also has the highest $\frac{\mathrm{\Delta }\mathrm{SSI}}{\mathrm{\Delta }\mathrm{TSI}}$ ratio in the Lyman-α, FUV, and Herzberg continuum–Hartley band spectral regions.

Table 1Solar cycle spectral solar irradiances changes from November 1989 to November 1994 relative to November 1994 (ΔSSI) in percent and relative contribution of SSI changes to the TSI change ($\frac{\mathrm{\Delta }\mathrm{SSI}}{\mathrm{\Delta }\mathrm{TSI}}$) in percent for the Lyman-α (121.5 nm), far-UV (121–200 nm), Herzberg continuum–Hartley bands (201–242 nm), Hartley–Huggins bands (243–380 nm), and visible (381–780 nm) spectral ranges.

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The magnitude of the applied solar amplitude in this study can be regarded as representative for the second half of the 21st century when the solar cycles 19 to 23 showed relatively large 11-year solar cycle amplitudes. However, the individual solar cycles show different, spectrally resolved characteristics in their amplitudes, which also differ among the individual SSI data sets. Compared to other solar cycle amplitudes in the satellite era (see Table S1 in the Supplement), the one used in this study is neither especially weak nor especially strong. The averaged ΔSSI is shown in Fig. 2a, with the error bars indicating the 95 % confidence interval of the ΔSSI within each spectral region. The main characteristics of the solar amplitude chosen here are also present in the averaged solar cycle amplitude, such as the small solar amplitude of SATIRE-T in the FUV and most of the ranking of the SSI data sets within the spectral regions. All deviations of the chosen solar cycle amplitude from the averaged solar cycle amplitude are within the range of the 95 % confidence intervals (Fig. 2b). Therefore, the selected solar cycle amplitude can be regarded as representative for most of the solar cycle amplitudes of the satellite era.

Besides the ATLAS-3 reference SSI data set, more recent SSI reference data sets are available such as SOLAR-ISS (Meftah et al., 2020, 2018), which is representative of the 2008 solar minimum. The usage of an alternative SSI reference data set 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 SW heating rates, thus affecting the temperature and potentially also the zonal wind of the CCMs. As the reference SSI data set serves as a common base state for the solar minimum of all other SSI data sets, we do not expect significant differences in the uncertainties of the solar responses when using a different SSI reference spectrum.

3.1 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 fifth-generation European Centre Hamburg general circulation model (ECHAM5, Roeckner et al., 2006). For the present study we applied EMAC (ECHAM5 version 5.3.02, MESSy version 2.52; Jöckel et al., 2016) in T42L47MA resolution, i.e. with a spherical truncation of T42 (corresponding to a quadratic Gaussian grid of approx. 2.8^∘ latitude by 2.8^∘ longitude) with 47 hybrid pressure levels up to 0.01 hPa (∼80 km). EMAC includes the MECCA (Module Efficiently Calculating the Chemistry of the Atmosphere) (R. Sander et al., 2011) chemical mechanism, which contains 155 species with 224 gas-phase, 12 heterogeneous, and 74 photolytic reactions. The photolysis rate coefficients are calculated with JVAL (Sander et al., 2014) using updated rate coefficients recommended by JPL (S. P. Sander et al., 2011) and resolves the solar Lyman-α line and eight spectral bands in the UV and visible ranges (178–683 nm). RAD and RAD-FUBRAD (Dietmüller et al., 2016) provide the parameterisation of radiative transfer based in the SW on Fouquart and Bonnel (1980) and Roeckner et al. (2003) (RAD) with four bands from 250 to 4000 nm. For a better resolution of the UV–vis spectral band RAD-FUBRAD is used for pressures lower than 70 hPa, increasing the spectral resolution in the UV–vis from one band to 55, 81, or 106 bands (Nissen et al., 2007; Kunze et al., 2014). Here we use the updated version of RAD-FUBRAD with 81 bands which substitutes the single-band parameterisation for the heating rates in the Schumann–Runge bands (Strobel, 1978) by the parameterisation based on 19 bands, as given in Strobel (1978), and 14 bands in the Chappuis bands (407.5–690 nm). The stratospheric equatorial zonal winds are relaxed towards an observed Quasi-Biennial Oscillation (QBO) with the sub-model QBO (Giorgetta and Bengtsson, 1999). With an upper boundary in the upper mesosphere, EMAC is not able to capture the thermospheric influx of NO_y. Therefore, 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 the thermosphere by auroral and medium-energy electrons.

3.2 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 $\mathrm{5}\times {\mathrm{10}}^{-\mathrm{6}}$ hPa, equivalent to approx. 140 km. It is an extension of the 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 ionisation reactions and 14 ion-neutral and recombination reactions. Its photolysis scheme resolves 100 spectral bands in the UV and visible 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 extreme-ultraviolet (EUV) irradiances). Below approx. 60 km the SW radiation of CAM4 is retained, employing 19 spectral bands between 200 and 5000 nm (Collins, 1998). For the transition zone (60–70 km), SW heating rates are calculated as weighted averages of the two approaches. CESM1(WACCM) features relaxation of stratospheric equatorial winds to an observed or idealised (used here) 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 an 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 sub-model UBCNOX.

3.3 CCM simulations

All EMAC and WACCM simulations have been made explicitly for this study, to ensure that the differences in the solar responses are exclusively related to the SSI data sets prescribed or the CCM applied, and not due to differences in the scenario. For both CCMs (EMAC and WACCM) time slice simulations have been performed with the same basic scenario in all simulations, except only for the prescribed SSI data set. The basic scenario consists of year 2000 conditions for prescribed greenhouse gas (GHG) mixing ratios, ozone-depleting substances (ODSs), and monthly climatological sea surface temperatures (SSTs) and sea ice concentrations (SICs) (average from 1995 to 2004). After dismissing 5 or 3 years of spinup for EMAC and WACCM, respectively, 45 years of data are available from each simulation for analyses. The QBO is included in all simulations by relaxation of the zonal wind in the tropical lower stratosphere between 90 and 10 hPa with the strongest nudging applied from 50 to 15 hPa in EMAC. Whereas EMAC uses the time series of the observed zonal winds (Naujokat, 1986), an idealised 28-month 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; see Sect. 2.1). To our knowledge, this is the first time that this observational SSI data set 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 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 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.

5.1 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 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 Sect. 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 data sets, averaged over both CCMs. Figure 5 shows vertical profiles of the solar cycle amplitude in SW heating rates, temperature, ozone, atomic oxygen (O(³P) and O(¹D)), NO_y, HO_x, and water vapour (H₂O), averaged from 60^∘ S to 60^∘ N between 100 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 ATLAS-3 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 Fig. 3, a t test is applied to the solar response of the complete ensemble. The 95 % confidence interval from this test is included as error bars in each panel of Fig. 5. To better assess the solar responses of the photochemically influenced quantities shown in Fig. 5, the solar responses of the photolysis rates of EMAC and WACCM (averaged over both CCMs as for Fig. 5) are shown in Fig. 6 for a single simulation time step in January at 180^∘ E, averaged from 60^∘ S to 60^∘ N. The shaded areas in Figs. 5 and 6 indicate the range of the solar responses between the EMAC and WACCM ensemble means, framed by the dotted and dashed black contours for the EMAC and WACCM ensemble means, respectively. By comparing the CCM averaged profiles for individual SSI data sets with the SSI averaged ensemble mean for each CCM (shading), the relative roles of the SSI data sets and the CCMs can directly be inferred for the different quantities and altitude regions.

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 (Fig. 5a, b). In the upper mesosphere, these differences are a direct consequence of the magnitude of the FUV amplitude over the solar cycle (see Table 1) with SATIRE-S showing the largest and SATIRE-T showing the smallest solar response in FUV heating by oxygen absorption/photolysis and subsequent temperature increase. In the stratosphere, the photochemical Chapman cycle is more effective during solar maximum, as shown with the positive solar responses of atomic oxygen (O(¹D), O(³P), Fig. 5d, e) and the photolysis rates of oxygen and ozone (JO₂, JO₃→O(¹D), JO₃→O(³P), Fig. 6a, c, d). This results in a positive solar response in ozone, peaking in the upper stratosphere near 7 hPa (Fig. 5c). The SATIRE-T solar response in ozone is the weakest in this comparison, as its SSI amplitude in the FUV and 201–242 nm spectral ranges, 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 simulations, the simulations using the remaining SSI data sets show solar responses in SW heating rates, temperature, and ozone that are relatively close to each other.

Figure 6Percentage change of the photolysis rates from solar minimum to maximum of (a) oxygen (JO₂), (b) ozone (JO₃ = $J{\mathrm{O}}_{\mathrm{3}}\to \mathrm{O}{(}^{\mathrm{1}}\mathrm{D})+J{\mathrm{O}}_{\mathrm{3}}\to \mathrm{O}{(}^{\mathrm{3}}\mathrm{P})$), (c) O₃-producing O(¹D) (JO₃→O(¹D)), (d) O₃-producing O(³P) (JO₃→O(³P)), (e) water vapour (JH₂O), and (f) nitric oxide (JNO) for a single time step at 180^∘ E averaged from 60^∘ S to 60^∘ N. Changes are derived for an average of WACCM and EMAC simulations using five SSI data sets at solar maximum NRLSSI1(CMIP5) (yellow), NRLSSI2 (red), SATIRE-S (blue), SATIRE-T (dark blue), and CMIP6 (black) relative to the average of the WACCM and EMAC reference solar minimum simulations. The shaded area indicates the range of the WACCM (long black dashed contour) and EMAC (black dotted contour) ensemble means.

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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 $=\mathrm{N}+\mathrm{NO}+{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{NO}}_{\mathrm{3}}+$ $\mathrm{2}{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{HNO}}_{\mathrm{3}}+$ ${\mathrm{HNO}}_{\mathrm{4}}+{\mathrm{ClNO}}_{\mathrm{2}}+{\mathrm{BrNO}}_{\mathrm{3}}$, but in the mesosphere NO_y is very close to the active nitrogen defined as ${\mathrm{NO}}_x=\mathrm{NO}+{\mathrm{NO}}_{\mathrm{2}}$. 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 (Fig. 5f). The stratospheric and lower-mesospheric decrease is consistent with Hood and Soukharev (2006), who attributed the negative solar response of NO_y in the stratosphere at low latitudes to enhanced photolysis of nitric oxide (NO) by solar FUV irradiance during solar maximum. The major source of NO is the oxidation of nitrous oxide (${\mathrm{N}}_{\mathrm{2}}\mathrm{O}+\mathrm{O}{(}^{\mathrm{1}}\mathrm{D})\to \mathrm{2}\mathrm{NO}$) in the middle stratosphere at low latitudes where the abundance of O(¹D) is sufficiently high due to the photolysis of ozone at wavelengths <310 nm (e.g. Seinfeld and Pandis, 2006). The major sinks of NO are photolysis (NO +hν (183 nm $<\mathit{\lambda }<\mathrm{193}$ nm) → N + O) and the subsequent reaction of NO with atomic nitrogen ($\mathrm{N}+\mathrm{NO}\to {\mathrm{N}}_{\mathrm{2}}+\mathrm{O}$) in the upper stratosphere, mesosphere, and lower thermosphere (e.g. Minschwaner and Siskind, 1993). During solar maximum, O(¹D) increases (Fig. 5e), implying enhanced NO production from N₂O. However, at the same time a clear increase in the NO photolysis rates by 8 % to 9 % is found in the stratosphere and mesosphere at solar maximum (Fig. 6f). This increase is the result of the larger solar irradiance amplitude in the FUV in all applied SSI data sets (see Table 1). With enhanced photolysis at solar maximum, the NO_y abundances decrease (Fig. 5f). 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 in the NO photolysis rates and a weaker negative NO_y solar response. 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).

There are two possible reasons for the increase in NO_y in the uppermost mesosphere above 0.03 hPa during solar maximum compared to solar minimum. EUV photoionisation of neutrals increases during solar maximum, leading to an increase in 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 ($\mathrm{N}{(}^{\mathrm{2}}\mathrm{D})+{\mathrm{O}}_{\mathrm{2}}\to \mathrm{NO}+\mathrm{O}$) (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 ($\mathrm{N}{(}^{\mathrm{4}}\mathrm{S})+{\mathrm{O}}_{\mathrm{2}}\to \mathrm{NO}+\mathrm{O}$). 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).

The solar response in HO_x (defined as OH+HO₂) (Fig. 5g) is positive throughout the middle atmosphere in all CCM-averaged SSI simulations. In the stratosphere, HO_x is mainly produced by reactions of O(¹D) with H₂O,CH₄, or H₂ (e.g. ${\mathrm{H}}_{\mathrm{2}}\mathrm{O}+\mathrm{O}{(}^{\mathrm{1}}\mathrm{D})\to \mathrm{2}\mathrm{OH}$). Increasing abundance of O(¹D) (Fig. 5e) during solar maximum conditions is leading to a positive solar response in HO_x mixing ratios (Fig. 5g). A clear dependence of the O(¹D) and HO_x solar responses on the UV-SSI amplitude is found with the largest solar response in the simulations using the SATIRE-S SSI data set. This SSI amplitude dependence of the HO_x solar response continues in the upper mesosphere where it is mainly produced by photolysis of water vapour at wavelengths in the Schumann–Runge bands and Lyman-α.

Despite the loss of H₂O through reaction with the more abundant O(¹D) during solar maximum, the H₂O mixing ratios increase during solar maximum in the stratosphere, which is most pronounced when the SATIRE-S SSI data set is used (Fig. 5h). While this signal is not statistically significant for the complete CCM ensemble, there is a significant solar response in the stratosphere for the individual simulations of WACCM. This positive solar response of H₂O in the upper stratosphere and lower mesosphere has also been identified in HALOE satellite data by Remsberg et al. (2018). It is explained by chemical reaction of CH₄ and H₂ with OH, finally producing, after a reaction chain including photolytic reactions, H₂O (Remsberg et al., 1984). The positive solar response of H₂O in the lower stratosphere corresponds to the positive solar response of temperature in the tropical tropopause layer (TTL) region, which increases the saturation vapour pressure during solar maximum and thus counteracts the water-vapour-limiting freeze-drying mechanism. This is in contrast to the results of Schieferdecker et al. (2015), who analysed water vapour from MIPAS and HALOE satellite instruments and found an anti-correlation of a slightly time-shifted 11-year solar cycle proxy with lower-stratospheric water vapour. In the upper mesosphere, the solar response in H₂O is negative as a direct consequence of the stronger water vapour photolysis during solar maximum (Fig. 5h).

In summary, the analysis of CCM-averaged quantities has revealed a dependence of the solar responses on the SSI data sets, with solar responses for most quantities showing a clear relation to the SSI amplitude. Whereas the solar responses are relatively close to each other in the stratosphere and lower mesosphere when using NRLSSI1, NRLSSI2, and CMIP6, clear differences appear for SATIRE-T, which shows the smallest solar responses for all analysed variables. SATIRE-S produces an enhanced solar response for HO_x and H₂O but agrees well with NRLSSI1, NRLSSI2, and CMIP6 for the other variables. The differences in the SSI amplitude are responsible for 10 % of the temperature, 30 % of the ozone, and up to 40 % of the SW heating rate variability of the solar response in the stratosphere and lower mesosphere. An even larger part of the variability of the solar response in the stratosphere can be attributed to the SSI data set for O(³P) (60 %) and O(¹D) (70 %) (see Fig. S3 in the Supplement). In the upper mesosphere, the choice of the SSI data set has the largest influence on the solar response variability of the SW heating rates (70 %) for which the solar amplitude of the SSI data set in the FUV is the main driver.

Figure 7Annual mean temperature deviation of EMAC and WACCM to ERA-5 climatology. (a) EMAC – ERA-5 and (b) WACCM – ERA-5 climatology. The ensemble mean for each CCM consists of the solar minimum reference simulation (included five times in the ensemble mean) and the five simulations of the solar maximum. The ERA-5 data consist of annual mean data from 1982 to 2018. Grey hatching masks areas where differences do not pass a test for statistical significance (p>5 %), for differences relative to ERA-5.

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5.2 Differences resolved by CCM

Large differences in the variability of the solar response explained by CCM differences have been identified by the ANOVA (Fig. 3) 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 Figs. 5 and 6, also identifies the largest differences in the upper mesosphere.

Figure 8Annual mean differences for EMAC (ensemble mean) minus WACCM (ensemble mean) (shaded) of (a) SW heating rates, (b) temperature, (c) ozone mixing ratios, (d) atomic oxygen (O(³P)), (e) HO_x, and (f) NO_y. The ensemble mean for both CCMs consists of the solar minimum reference simulation (included five times in the ensemble mean) and the five simulations for the solar maximum. Grey hatching masks areas where differences do not pass a test for statistical significance (p>5 %).

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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. In particular the climatological temperature has a large effect on the chemistry in the middle atmosphere and lower thermosphere either directly on the chemical gas-phase reaction rates or indirectly, as the temperature in the tropical lower stratosphere determines the abundance of H₂O in the middle atmosphere and thereby also affects many chemical reactions. The climatological background state of a CCM is determined by a number of factors, ranging from the horizontal and vertical resolutions and the vertical model domain to the physical and chemical processes either resolved or parameterised by the models. In this section, we examine the uncertainty in the atmospheric solar response arising from the model specifications of the EMAC and WACCM models, regarded here as representatives for typical state-of-the-art CCMs. For this purpose, two ensembles of five simulations each for EMAC and WACCM have been constructed by averaging the simulations with different SSI data sets of each model to the respective model ensemble. To achieve an overall ensemble mean representative for a mean solar state, the reference solar minimum simulation in each model ensemble is weighted by a factor of 5, to balance the five simulations with the SSI data sets at solar maximum in each model ensemble.

Figure 7 shows the deviations of the climatological annual mean temperature of EMAC and WACCM from the climatological temperatures of the ERA-5 reanalysis (Hersbach et al., 2018). The ERA-5 climatology includes 37 years from 1982 to 2018 centred around the year 2000. The temperature deviations of both CCMs relative to ERA-5 are largely statistically significant on the 95 % level (all regions not masked by hatching), as estimated by Student's t test.

EMAC has a pronounced cold bias in the tropical upper troposphere–lower stratosphere (UTLS), where WACCM simulates slightly higher temperatures than the ERA-5 climatology. In the upper stratosphere and upper mesosphere, both models show a cold bias over large regions, which is more pronounced in the mesosphere of EMAC. In the lower mesosphere both CCMs show higher temperatures compared to ERA-5. At SH high latitudes, temperatures in WACCM are too low in the stratosphere and too high in the mesosphere compared to the ERA-5 climatology (Fig. 7).

Figure 8 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 SW heating rates, temperature, ozone, atomic oxygen (O(³P), O(¹D)), NO_y, HO_x, and H₂O. Substantially lower (by up to 1.2 K d⁻¹) SW 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 O₂ absorption parameterisation of Strobel (1978) with 19 bands (used in 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 (Fig. 5a, b). They lead to the patterns of solar response variance explained by CCMs in Fig. 3a, b which resemble the structure of the anomaly pattern in SW heating rates in the upper mesosphere (Fig. 8a). By contrast, in the lower mesosphere and large areas of the stratosphere, EMAC shows higher SW 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 (Fig. 8c). However, WACCM shows larger solar responses in ozone mixing ratios and JO₃→O(³P) 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 (Fig. 8b) are not congruent with those in SW 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-5 reanalyses. This shows that with the implementation of the modified gravity wave parameterisation of Garcia et al. (2017) in our WACCM simulations, 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 SW heating rates and temperatures between EMAC and WACCM, there are also large differences in the chemical composition (and the associated solar responses) in this region. The odd oxygen mixing ratios in the upper mesosphere are lower in EMAC by 50 % for ozone, 80 % for O(³P), and more than 50 % for O(¹D) (Fig. 8c–e). This is partly explained by the fact that oxygen photolysis in the Schumann–Runge continuum (O₂ +hν (λ<175.9 nm) → O(¹D)+O(³P)) is neglected in EMAC, because it becomes important only in the lower thermosphere, which is above the upper lid of EMAC. The larger abundances of O(¹D) and O(³P) in WACCM, which has a higher upper lid than EMAC, are the result of photochemical production in the lower thermosphere and downward transport into the mesosphere by the residual circulation during the winter seasons, where they affect the climatological averages as well as the solar responses of atomic oxygen, O₃, and HO_x. The model differences in January and July exhibit a clear enhancement of O(¹D) and O(³P) in the respective winter hemisphere of WACCM indicative of strong downward transport from the lower thermosphere (see Figs. S4 and S5 in the Supplement). As a result of the larger O(¹D) and O(³P) mixing ratios, the equilibrium of ozone-producing and ozone-destroying processes leads to higher ozone mixing ratios in WACCM, apparent in the climatology (Fig. 8c) as well as in the solar response (Fig. 5c) in the upper mesosphere. Due to the larger solar responses in the mixing ratios of O(¹D) and O(³P) (Fig. 5d, e), WACCM produces a strong ozone increase from solar minimum to maximum, in contrast to EMAC, where the more intense HO_x cycle at solar maximum (Fig. 5g) dominates and leads to a negative solar response. Noticeable are the higher ozone mixing ratios in the upper-mesospheric high latitudes of EMAC (Fig. 8c) compared to WACCM which result from a less effective catalytic HO_x cycle of ozone destruction during the winter seasons, due 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 chemical 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 seasons (Figs. S4 and S5 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 % (Fig. 5f). The solar response of NO_y in the upper mesosphere discussed in Sect. 5.1 is much stronger in WACCM than in EMAC, as obvious from the shaded area in Fig. 2f. In WACCM, the increased NO production during solar maximum in the uppermost mesosphere and lower thermosphere is driven by the increase in EUV photoionisation and lower-thermospheric temperatures as discussed in Sect. 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 and EUV radiation and thus suppresses a solar response in NO_y.

Differences between EMAC and WACCM are also found in the climatological distribution of water vapour and the related HO_x mixing ratio. In the annual mean, EMAC has less H₂O than WACCM in the stratosphere and lower mesosphere – except for the upper mesosphere, where EMAC exceeds the WACCM values (Fig. 8h). The lower H₂O abundance of EMAC in the middle atmosphere is the consequence of a cold bias in the tropical UTLS region (Fig. 8b), a feature of EMAC also discussed in Jöckel et al. (2016). As a result, HO_x, which is produced by photolysis of H₂O, is also lower in EMAC (Fig. 8g). From solar minimum to solar maximum, the abundances of H₂O (Fig. 5h) and the photolysis rates of H₂O (Fig. 6e) increase in the stratosphere and lower mesosphere, leading to a HO_x increase by about 2 %–3 % in both models (see also Sect. 5.1). The smaller solar response of HO_x in EMAC in this height region can be attributed to differences in the model climatologies because of the lower HO_x and H₂O mixing ratios in EMAC. In the mesosphere, the magnitude of the solar responses of H₂O (negative) and HO_x (positive) grow fast with altitude. At solar maximum, strongly enhanced H₂O photolysis (Fig. 6e) induces a decrease in H₂O (Fig. 5h) and an increase in HO_x by about 11 % (Fig. 5g). The HO_x production in the upper mesosphere is dominated by H₂O photolysis at wavelengths in the Schumann–Runge bands and Lyman-α with the major reaction H₂O+hν ($\mathit{\lambda }<\mathrm{200})\to$ H+OH (70 %, $J_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}^a$) and two minor reactions, producing O+2H (12 %, $J_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}^b$) and H₂+O(¹D) (10 %, $J_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}^c$) (Nicolet, 1984). However, while the solar responses in H₂O photolysis (positive) and H₂O mixing ratio (negative) further increase towards the upper mesosphere, the positive solar response in HO_x peaks near 70 km and declines above, implying the existence of a HO_x-depleting process that increases with solar activity in the upper mesosphere and counteracts HO_x production by H₂O photolysis. In addition H₂O declines in the upper mesosphere, limiting the potential for HO_x production. The CCMs start to deviate more strongly in the upper mesosphere, with EMAC showing a less intense decrease in the solar response in HO_x than WACCM. This cannot be attributed to the H₂O photolysis as EMAC has a larger solar response in H₂O photolysis. The reason might be the combination of the up to 50 % larger upper-mesospheric H₂O mixing ratio in EMAC (Fig. 8h) and the stronger solar response of WACCM in O(³P) (Fig. 5d) which acts in WACCM as a more effective sink of HO_x through reaction $\mathrm{OH}+\mathrm{O}{(}^{\mathrm{3}}\mathrm{P})\to \mathrm{H}+{\mathrm{O}}_{\mathrm{2}}$. The smaller H₂O mixing ratio of WACCM in the upper mesosphere is a consequence of the larger O(¹D) mixing ratios in WACCM, leading to a more effective decomposition of water vapour through ${\mathrm{H}}_{\mathrm{2}}\mathrm{O}+\mathrm{O}{(}^{\mathrm{1}}\mathrm{D})\to \mathrm{2}\mathrm{OH}$. During solar maximum this H₂O decomposition is even enhanced, due to more abundant O(¹D) mixing ratios in the upper mesosphere (Fig. 5e), leading to a more pronounced negative H₂O solar response in WACCM (Fig. 5h).

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 responses deviate substantially, as shown for ozone, oxygen, HO_x, and NO_y. The comparison of the upper-mesospheric solar responses 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 be better achieved when the residual downward transport of thermospheric photolysis reactants is taken into account.