The Naval Research Laboratory (NRL) family of SSI models is based on the premise that changes in solar irradiance from background-quiet Sun conditions can be described by a balance between bright facular and dark sunspot features on the solar disk. These two contributions are determined by linear regression between solar proxies, and direct observations of TSI and SSI by satellite missions such as SORCE . These models are thus empirical.

Both the TSI and the SSI consist of a baseline solar contribution, with a wavelength-dependent contribution. The Magnesium (MgII) index, for example, represents the contribution of bright faculae, whereas the sunspot area represents the contribution of sunspots. The time dependency in TSI and SSI thus emerges from the temporal variability in the solar proxies. SORCE measurements at solar-minimum conditions are the basis for the adopted quiet Sun irradiance in NRLSSI2.

The recently updated version of the NRL models, named NRLTSI2 (for TSI) and NRLSSI2 (for SSI), have been transitioned to the National Centers for Environmental Information (NCEI) as part of their Climate Data Record (CDR) program (see http://www.ngdc.noaa.gov), and operational updates are provided on a near-quarterly basis. describe the model algorithm, the uncertainty estimation approach, and comparisons to observations in detail. Please note that our version differs slightly from the one published by by using a different scaling factor between the sunspot area as measured by the Royal Greenwich Observatory (from 1874 to 1976) and the NOAA/USAF Solar Observing Optical Network (SOON) since 1966. The future release of NRLSSI2 will use the same scaling factor as the version we use.

In NRLSSI2, a multiple linear regression approach of solar proxy inputs with observations of TSI from SORCE/TIM , and observations of SSI from the SORCE/SOLSTICE and SORCE/SIM instruments is used to determine the scaling coefficients that convert the proxy indices to irradiance variability. Because the wavelength-dependent scaling coefficients used in the NRLSSI2 model are derived for solar rotation timescales (i.e., the SSI observations and the proxy indices are detrended with an 81-day running mean), concerns with respect to the long-term stability of the SORCE SSI observations are not shared with regard to the SORCE TSI record. However, because regression coefficients derived from detrended SSI time series differ from those developed from nondetrended SSI time series, a further adjustment is required to extend the SSI variability from solar-rotational to solar-cycle timescales. In NRLSSI2, this adjustment is made by a linear scaling that is constrained by the TSI variability. This adjustment is made in the separate facular and sunspot proxy records and the magnitude of the adjustment is smaller than the assumed uncertainty in the proxy indices themselves. In this approach, the integral of the SSI tracks the TSI; however, the relative facular and sunspot contributions at any given wavelength are not constrained to match their specific TSI contributions.

The NRLTSI2 and NRLSSI2 irradiances also include a speculated long-term facular contribution that produces a secular (i.e., underlying the solar activity cycle) net increase in irradiance from a small accumulation of total magnetic flux. This secular impact is specific to historical timescales (i.e., prior to 1950) and is consistent with simulations from a magnetic flux transport model .

The SATIRE (spectral and total irradiance reconstruction) family of semi-empirical models assumes that the changes in the solar spectral irradiance are driven by the evolution of the photospheric magnetic field . The model makes use of the calculated intensity spectra of the quiet Sun, faculae, and sunspots generated from model solar atmospheres with a radiative transfer code . SSI at a particular time is given the sum of these spectra, weighted by the fractional solar surface that is covered by faculae and sunspots, as apparent in solar observations.

The implementation of SATIRE employing solar images in visible light and solar magnetograms (magnetic field intensity and polarity) is termed SATIRE-S , and that based on the sunspot number (SSN) is SATIRE-T . Individual records are accessible at http://www2.mps.mpg.de/projects/sun-climate/data.html. We use here SATIRE-S for the satellite era (available from 1974 to 2015).

Prior to 1974 the CMIP6 SATIRE data were calculated with the SATIRE-T model , although this was done using annual SSN (Version 1) instead of daily Group SSN (GSSN) while keeping all other inputs (including sunspot area) identical to the original version. SSI variability on subannual timescales, taken from the SATIRE-T model, was added afterwards. We shall henceforth call this model SATIRE in the following.

On decadal to centennial timescales, SATIRE reproduces observations such as the composite of the Lyman-α line at 121.6 nm since 1947,, the measured solar photospheric magnetic flux (since 1967), the empirically reconstructed solar open magnetic flux since 1845,, and the 44Ti activity in stony meteorites .

SATIRE and NRLSSI2 are internally consistent, in the sense that the integral of the modeled spectral irradiances equals the TSI. These are among the best model reconstructions we currently have. Note, however, that both models reconstruct the SSI prior to the satellite era by assuming the relationship between sunspot number and SSI to be time-invariant. The model uncertainty associated with this assumption is difficult to quantify. For that reason, it is not included in the uncertainties that are provided with the model datasets, which may therefore be underestimated.

Both NRLSSI2 and SATIRE rely on the sunspot number when no other solar proxies are available. For the CMIP6 composite, we decided to rely on version 1.0 of the international sunspot number (from http://www.sidc.be/silso), even though a newer version 2.0 recently came out . Indeed, SSI models have not yet been thoroughly trained and tested with this new sunspot number. Recent results by suggest that this revision has little impact after 1885, and leads to greater solar-cycle fluctuations prior to that. Note that the NRLSSI version employed here uses the GSSN , while SATIRE uses the annually averaged international sunspot number (v1.0). This affects the long-term trend of the final product in the presatellite era (see Sect. 2.1.2).

In NRLSSI2 the proxy index for facular brightening is the composite MgII index from the University of Bremen. The MgII index is the core-to-wing ratio of the disk-integrated MgII emission line at 280 nm. This quantity is used by many models as a UV proxy. The MgII index is available from 1978 onwards; values prior to that are estimated from the sunspot number.

In NRLSSI2 and in SATIRE, the proxy index for sunspot darkening is the sunspot area as recorded by ground-based observatories in white light images since 1882 . The sunspot darkening prior to 1882 is estimated from the sunspot number.

The task at hand – to determine the most likely temporal variation in SSI – is challenged by the paucity of direct SSI observations, and the numerous instrumental artifacts that affect these observations. Recently, this task has been addressed by an international consortium, which has produced an observational SSI composite . This SOLID

FP7 SPACE Project First European Solar Irradiance Data Exploitation (SOLID); http://projects.pmodwrc.ch/solid/

NRLSSI and SATIRE are not the only available models for reconstructing the SSI . However, they are the only ones that have been widely tested, and can easily cover the 1850–2300 time span for CMIP6 with one single and continuous record. The resulting homogeneity in time is a major asset of our reconstructions, and a necessary condition for obtaining a realistic solar forcing.

NRLTSI2 and SATIRE-TSI agree well on timescales of days to months and show the same long-term trend before 1986 in their original versions. Note, however, that in the CMIP-adapted version of SATIRE (see Sect. 2.1.1), the long-term change over this period is slightly weaker. In contrast to NRLTSI2, SATIRE-TSI declines after 1986. NRLSSI2 and SATIRE-SSI show significantly different spectral profiles of the variability between about 250 and 400 nm. This has fueled a debate e.g., that is unlikely to settle soon. The two models have been derived independently, and as of today there is no consensus regarding their relative performance. In this context, and for the time being, the most reasonable approach (in a maximum-likelihood sense) consists of averaging their reconstructions, weighted by their uncertainty. Since, in addition, we are lacking uncertainties that can be meaningfully compared, our current recommendation is to simply take the arithmetic mean of the two model datasets: (i) the empirical model NRLTSI2 and NRLSSI2 and (ii) the semi-empirical model SATIRE . Note that multimodel averaging is a widely used practice in climate modeling e.g.,.

For historical data (1 January 1850–31 December 2014) both models rely, as described above, on one or several of the following: the international sunspot number V1.0, sunspot area distribution (after 1882), solar photospheric magnetic field (after 1974), and the MgII index (after 1978). Since NRLSSI2 and NRLTSI2 have yearly averages only before 1882, we reconstructed subyearly variations by using an ARMAX (autoregressive–moving-average with exogenous input) model that uses the sunspot number as input.

The extreme ultraviolet (EUV) band (10–121 nm) is required for CMIP6 but is not provided by NRLSSI2 and SATIRE, whose shortest wavelength is 115.5 nm. We thus added it with spectral bins from 10.5 to 114.5 nm by using a nonlinear regression from the SSI in the 115.5–123.5 nm band, trained with TIMED/SEE data from 2002 to 2011. This is further detailed in Appendix .

In some climate models the EUV flux is parameterized as a function of the F10.7 index, which is the daily radio flux at 10.7 cm from Penticton Observatory, adjusted to 1 AU, and measured daily since 1947 . For practical purposes, we also provide this index. Values prior to 1947 are obtained by multilinear regression to the first 20 principal components of the SSI and application of minor nonlinear adjustments. Let us note that while the F10.7 index is a good proxy for EUV variability on daily to yearly timescales, this may not be true anymore on multidecadal timescales. As of today, the lack of direct EUV observations does not allow us to constrain its long-term evolution, whereas the F10.7 index at solar minimum has not significantly varied since 1947, when its first measurements started.

The dataset, together with a technical description, and a routine for how to read and integrate the SSI data to the radiation bands used in climate models can be found at http://solarisheppa.geomar.de/cmip6. In addition, a recommendation on how to implement the SSI changes in the models is provided in the Appendix . A detailed description of the CMIP6 solar irradiance forcing in TSI and SSI and a comparison to the CMIP5 recommendation are presented in the following.

Figure presents time series of the TSI from the CMIP5, CMIP6, and the CMIP6-adapted versions of NRLTSI2 and SATIRE datasets, along with one observational composite from PMOD (version 42.64.1508)

https://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant

All TSI records agree well on daily to yearly timescales, and in some cases (e.g., NRLTSI1 and NRLTSI2) they match as well on multidecadal timescales. The major difference arises in the long-term behavior of SATIRE and NRLTSI2 (see Sect. 2.1.1), which impacts the CMIP6 composite, and leads to a weaker trend compared to the CMIP5 recommendation (which was based on NRLTSI1 only). In both models, the historical reconstructions are sensitive to the assumptions made when constraining them to direct (satellite era) observations that suffer from large uncertainties. There is no consensus yet as to which one better represents long-term solar variability, and this is what motivated us to average them for making the CMIP6 composite.

More subtle differences between the different TSI datasets arise in the satellite era, especially with the unusually deep solar minimum that occurred in 2008–2010: the NRLTSI2 model has a weak negative trend between successive solar minima, whereas the SATIRE reconstruction exhibits a larger one. The resulting trend in the CMIP6 composite is comparable to the observational TSI composite from PMOD (grey area). Figure  does not show any model uncertainties, because these are either absent or difficult to compare. We do provide uncertainties, however, for the observational PMOD composite, based on an instrument-independent approach that is described in . Note that both models are mostly within the ±1σ confidence interval, which highlights how delicate it is to constrain them by observational data.

After CMIP5, the recommended value of the average TSI during solar minimum was reduced from 1365.4 ± 1.3 W m-2 to a lower value of 1360.8 ± 0.5 W m-2 after reexamination by , later confirmed independently by . Based on this, the International Astronomical Union recently recommended 1361.0 ± 0.5 W m-2 as the nominal value of the TSI, averaged over solar cycle 23, which lasted from 1996 to 2008 . Our CMIP6 composite complies with this recommendation.

To summarize for the TSI, the CMIP6 and CMIP5 recommendations are comparable on decadal and subdecadal timescales. They differ, however, by a weaker secular trend in CMIP6. Between 1980 and 1880, the difference between TSI(CMIP6) and TSI(CMIP5) progressively increases from 0.1 to 0.4 W m-2 (after correcting the aforementioned 5 W m-2 offset in CMIP5). This results in a weaker change in solar forcing, which will be detailed in Sect. .

To estimate the impact of these different trends on the radiative forcing, we have conducted a high-spectral-resolution calculation using a single profile with a line-by-line radiative transfer code (libradtran) described in more detail below. This indicated an instantaneous change in downward solar flux of -0.16 W m-2 over the 1986–2009 period for the combined CMIP6 dataset. A crude estimate of the global mean forcing from this change is -0.04 W m-2, which is relatively small in comparison to other forcings over this period.

To investigate differences and similarities between the SSI datasets, following , we concentrate on four specific wavelength ranges: 120–200 nm (UV1), 200–400 nm (UV2), 400–700 nm (VIS), and 700–1000 nm (NIR), with special emphasis on the CMIP5 (i.e., NRLSSI1) and the CMIP6 (average of NRLSSI2 and SATIRE) datasets. These ranges are relevant for climate studies; see for example Table  below. Figure  shows the SSI time series from 1880 through 2014. Note that we added vertical offsets by adjusting the mean values to facilitate their comparison, using CMIP6 as a reference. We note the following:

The long-term increase from 1880 to 1980 is similar in NRLSSI2, SATIRE, and CMIP6, but NRLSSI2 predicts a slightly larger increase in the VIS and NIR. NRLSSI1 predicted a larger increase in the VIS, compensated by a smaller increase in the NIR and UV2.

In Fig. , the apparently less regular solar-cycle reconstruction by NRLSSI2 between 1940 and 1960 is most likely caused by the transition from one sunspot record to another in that model see.

Figure  compares our CMIP6 dataset with the observational SOLID composite (see description above) and some direct SSI satellite observations. Generally speaking, the observations and observation-based composite agree very well with each other, and the CMIP6 dataset up to 200 nm. Larger cycle variations than in the CMIP6 SSI occur above about 200 nm in the observations. Such discrepancies are inherent to the observation of small variations over 11 years. On the right panel of Fig. , one can notice the different influences of the various datasets on the SOLID composite, as a consequence of their uncertainty at different scales. For example, the SORCE/SIM data have only a minor (but significant) effect on the long-term variations of the composite. In the VIS and NIR part of the spectrum, the only available measurements are from the SORCE/SIM instrument, whose solar-cycle variation is controversial and hence should be considered with great caution.

Figure  shows the contribution of the different wavelength ranges to TSI variations between solar maximum on November 1989 (solar cycle 22) and solar minimum on November 1994 (between cycles 22 and 23) for the different solar irradiance models. Both extrema are averaged over 81 days. We use the same spectral bands and color coding as in Fig. 2 of the review by . The latter figure, though, applies to the next solar cycle, when SORCE/SIM is operating. Our dates coincide with the ones chosen in the CCM time-slice experiments; see Sect. . Please note that the sum of the SSI variability of the various models is not equal to the TSI variability because the IR part is missing in Fig. .

Both SSI models agree very well for the 120–200 nm wavelength range. Discrepancies arise for wavelengths longer than 200 nm, as already discussed in Fig. . In the 200–400 nm range, the SATIRE model shows the largest variability, followed by NRLSSI2 and NRLSSI1. This results in a CMIP6 variability that is larger than for CMIP5, 45 % compared to 32 % (Fig. ). In the VIS range this reverses, with CMIP6 showing a smaller variability than CMIP5 (30 % compared to 40 %). Also remarkable is the very good agreement between NRLSSI2 and SATIRE. In the NIR, CMIP6 shows slightly larger variability than CMIP5. The implications of these different spectral variabilities on the atmospheric heating and ozone chemistry and subsequent thermal and dynamical effects, with respect to both climatological differences between CMIP5 and CMIP6 and the solar cycle signals in CMIP5 and CMIP6, will be discussed in Sect. .

Figure  illustrates the reconstruction of the EUV band by comparing spectra obtained at high and low levels of solar activity, and by showing the historical reconstruction of the band-integrated flux. As explained in Sect. , we estimate the EUV flux by nonlinear regression from the SSI at longer UV wavelengths, using the first 7 years of observations from TIMED/SEE. Not surprisingly, this reconstruction agrees well with the observations from TIMED/SEE. However, due to a lack of other long-duration EUV observations that are of sufficient radiometric quality, it is very difficult to assess the quality of our reconstruction. For the same reason, multidecadal variations are poorly constrained, and in particular, the presence of trends remains largely unknown. Note that wavelengths below 28 nm require more caution, since they rely on TIMED/XPS observations that were partly degraded . One future improvement of our dataset involves reconstructions of the EUV band that are based on more advanced models such as NRLEUV2 .

Providing a first assessment of implications employing the SSI recommended for CMIP6 in comparison to CMIP5, we present results of two state-of-the-art chemistry–climate models (CCMs): the Whole Atmosphere Community Climate Model CESM1(WACCM); and the ECHAM/MESSy atmospheric chemistry model EMAC;. Additionally, we include results of single-profile radiative transfer calculations performed with the line-by-line radiative transfer code “libradtran” . We use the latter to present estimates of direct shortwave (SW) radiative heating impacts neglecting the ozone chemistry feedback which is included in the CCM results.

WACCM, the Whole Atmosphere Community Climate Model version 4;, is an integrative part of the Community Earth System Model (CESM) suite version 1.0.6;. 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 Community Atmospheric Model CAM4; with all its physical parameterizations. For this study the model is integrated with a horizontal resolution of 1.9∘ latitude × 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;. It contains all members of the Ox, NOx, HOx, ClOx, and BrOx chemical groups as well as tropospheric source species N2O, H2O, and CH4 as well as CFCs and other halogen components (59 species and 217 gas-phase chemical reactions in total). Its photolysis scheme resolves 100 spectral bands in the UV and VIS range (121–750 nm; see also Table ). The SW radiation module is a combination of different parameterizations. Above approx. 70 km the spectral resolution is identical to the photolysis scheme (plus the parameterization of , , based on F10.7 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 5000 nm . For the transition zone (60–70 km) SW heating rates are calculated as weighted averages of the two approaches. Table  contains an overview of the SW radiation and photolysis schemes in comparison to EMAC, the second CCM utilized for this study. CESM1(WACCM) features relaxation of stratospheric equatorial winds to an observed or idealized Quasi-Biennial Oscillation QBO;.

EMAC, The ECHAM/MESSy atmospheric chemistry (EMAC) model, is a CCM that includes submodels describing tropospheric and middle atmospheric processes and their interaction with oceans, land, and human influences . It uses the second version of the Modular Earth Submodel System (MESSy2) to link multiinstitutional computer codes. The core atmospheric model is the fifth-generation European Centre Hamburg general circulation model ECHAM5,. For the present study we applied EMAC ECHAM5 version 5.3.02, MESSy version 2.51, in the T42L47MA resolution, i.e., with a spherical truncation of T42 (corresponding to a quadratic Gaussian grid of approx. 2.8 × 2.8∘ in latitude and longitude) with 47 hybrid pressure levels up to 0.01 hPa (∼ 80 km). The applied model setup comprises, among others, the following submodels: MECCA, JVAL, RAD/RAD-FUBRAD, and QBO. MECCA (Module Efficiently Calculating the Chemistry of the Atmosphere) provides the atmospheric chemistry model. JVAL provides photolysis rate coefficients based on updated rate coefficients recommended by JPL . RAD/RAD-FUBRAD provides the parameterization of radiative transfer based on and (RAD). 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 1 band to 106 bands . Table  presents more details of the SW radiation and photolysis schemes in comparison to WACCM. The submodel QBO is used to relax the zonal wind near the equator towards the observed zonal wind in the lower stratosphere .

The CCM simulations with CESM1(WACCM) and EMAC are identically conducted in an atmosphere-only time-slice configuration. This means that the external forcings such as the solar and the anthropogenic forcing are fixed for the whole simulation period, i.e., 45 model years plus spin-up (∼ 5 years for EMAC, ∼ 3 years for CESM1(WACCM)). Concentrations of greenhouse gases (GHGs) and ozone-depleting substances (ODSs) are set to constant conditions representative for the year 2000. The lower-boundary forcing is specified by the mean annual cycle of SSTs and sea ice of the decade 1995–2004 derived from the HadISST1.1-dataset . All simulations are nudged towards an observed (EMAC) or idealized 28-month varying (CESM1(WACCM)) QBO. The only difference between the simulations is in the solar forcing. Four simulations for each of the following SSI datasets have been performed with EMAC and WACCM: CMIP6-SSI, its constituent datasets NRLSSI2 , and SATIRE , as well as NRLSSI1 . The latter was recommended as solar forcing for CMIP5 including a uniform scaling of the spectrum to match TSI measurements of the Total Irradiance Monitor (TIM) instrument. As one emphasis of this study is to highlight differences to the previous phase of CMIP, we employed NRLSSI1 (including this scaling) and refer to it as NRLSSI1(CMIP5) in the following. Runs for each of the four datasets have been performed with both CCMs for a solar-minimum time slice and a solar-maximum time slice, respectively. For solar-maximum time slices, SSIs averaged over November 1989 are used (maximum of solar cycle 22) while for the solar-minimum time slices averages over November 1994 are chosen. The latter does not match the absolute minimum of solar cycle 21–22 (June 1996). However, solar activity in November 1994 was already close to the minimum. The differences in solar activity between our solar-minimum and solar-maximum time slices for the respective datasets are within a range of 0.988 W m-2 for NRLSSI1(CMIP5) to 1.057 W m-2 for NRLSSI2.

It should be noted that these experiments will illustrate only one part of solar influence on climate. Given the atmosphere-only set-up of the runs, oceanic absorption of (mainly visible) solar irradiance and subsequent heating and feedbacks to the atmosphere – the so-called bottom-up mechanism seeand references therein – is not represented in our simulations. Therefore we focus only on stratospheric signals and “top-down” dynamically induced responses in the troposphere. A second constraint of this study's experimental set-up is the choice of one solar cycle. Solar activity and hence spectral irradiance vary between different solar cycles. However, these differences are relatively small compared to a typical solar-cycle amplitude and will probably not affect the main results of this study. It should also be noted that the time-slice simulations were designed as a sensitivity study to test the impact of the different solar input datasets. They do not represent the full feedbacks of transient CMIP6 simulations.

Radiative transfer calculations were performed with the high-resolution model libradtran , which is a library of radiative transfer equation solvers widely used for UV and heating-rate calculations (www.libradtran.org). Libradtran was configured with the pseudo-spherical approximation of the DISORT solver, which accounts for the sphericity of the atmosphere, running in a six-streams mode. Calculations pertain to a cloud- and aerosol-free tropical atmosphere (0.56∘ N), the surface reflectivity is set to a constant value of 0.1 and effects of Rayleigh scattering are enabled. The atmosphere is portioned into 80 layers extending from the surface to 80 km. The model output is annual averages of spectral heating rates from 120 to 700 nm in 1 nm spectral resolution, calculated according to the recommendations for the Radiation Intercomparison of the Chemistry–Climate Model Validation Activity (CCMVal) . As for the CCM simulations described above, calculations of the heating rates were performed for CMIP6-SSI, SATIRE, NRLSSI2, and NRLSSI1(CMIP5). The same climatological ozone profile is specified for both solar-maximum and solar-minimum conditions in order to assess the direct effects in atmospheric heating by SSI variations only. As such, the line-by-line calculations do not take into account the positive ozone feedback with the solar cycle, and SW heating-rate changes are expected to be weaker compared to the signatures in the two CCM simulations.

The analyses presented in the following consist of differences between climatologies derived from the various simulations. Given the time-slice configuration of the CCM runs with all external forcings equal except for the SSI dataset, we assume that statistically significant differences of two climatologies are the result of the differing solar irradiance forcings. Confidence intervals (95 %) as presented in Figs.  and , as well as statistical significance (p<5 %) as marked in Figs.  and , are based on 1000-fold bootstrapping. Confidence intervals in Figs.  and are only given for the CCM results related to CMIP6 SSI.

Although all solar irradiance reconstructions subject to this analysis agree fairly well in TSI (see Fig. ), they disagree significantly with respect to the spectral distribution of energy input, i.e., the shape of the solar spectrum. This is obvious from the offsets noted in Fig.  for the different spectral regions above 200 nm. Hence, we focus first on the climatological differences between the solar forcing in CMIP5 and CMIP6. We therefore compare the minimum time-slice simulations from the two CCMs and libradtran in Fig.  with respect to the climatological annual mean SW heating rates, as well as the temperatures and ozone concentrations between the two CCMs resulting from CMIP6-SSI, NRLSSI2, and SATIRE, respectively, as differences to equivalent simulations forced by NRLSSI1(CMIP5). The profiles represent the tropical (averaged over 25∘ S–25∘ N) stratosphere and mesosphere (100–0.01 hPa) for annual mean conditions for the CCMs and libradtran.

Employing CMIP6-SSI results in significantly decreased radiative heating of large parts of the mesosphere and stratosphere (above 10 hPa) compared to NRLSSI1(CMIP5). Whereas the largest differences can be found at the stratopause with approx. -0.35 K day-1 according to both CCMs, and even more, -0.42 K day-1, for libradtran (without any ozone chemistry feedback), libradtran and EMAC yield slightly increased SW heating rates below ∼ 7 and 10 hPa, respectively. This weaker SW heating in the new CMIP6 SSI dataset in the upper stratosphere and the stronger heating in the lower stratosphere are confirmed by the wavelength-dependent percentage changes between the CMIP6 and CMIP5 SSI datasets with respect to the radiation and photolysis schemes (Fig. ). Regardless of the number of bands in the radiation code, both models show a smaller percentage difference of -5 % below about 300 nm and weaker or negligible differences above 300 nm (Fig.).

Significant differences in radiative heating throughout the stratosphere related to the three state-of-the art SSI reconstructions are produced only with radiation codes of high spectral resolution such as in libradtran or – to a lesser degree – in EMAC (for the middle to lower stratosphere). Comparisons between CMIP6-SSI and its constituents NRLSSI2 and SATIRE in WACCM and EMAC lead to the conclusion that the choice of the CCM and its specific radiation and photolysis scheme is more important than the choice of the SSI dataset with respect to SW heating rates. In addition the ozone chemistry damps the SW heating response in the CCMs compared to libradtran, which misses the ozone feedback. Less SW radiation below 300 nm reduces ozone production (note also the reduced photolysis rates around 240 nm in Fig. ), and hence less ozone is available to absorb SW radiation and results in a relative cooling of the upper stratosphere.

Corresponding to the SW heating-rate differences, large parts of the stratosphere and mesosphere are significantly cooler (up to -1.6 K at the stratopause) in simulations using CMIP6-SSI compared to NRLSSI1(CMIP5) irradiances. Note that libradtran results are shown for the SW heating-rate differences only, as temperature and ozone profiles are prescribed for the radiative transfer calculations. No significant differences in temperature are found when employing NRLSSI2 or SATIRE instead of CMIP6-SSI in CESM1(WACCM) which has a coarser spectral resolution in the SW heating parameterization than EMAC (Table  and Fig. ). EMAC instead simulates significantly lower (higher) temperatures in the stratosphere when using NRLSSI2 (SATIRE) than CMIP6-SSI forcing and in general a warmer stratosphere (and cooler stratopause and mesosphere) than CESM1(WACCM).

The impact of CMIP6-SSI, compared to NRLSSI1(CMIP5) irradiance changes on ozone, is more complicated. In the middle tropical stratosphere, ozone concentrations are significantly lower (peaking at ∼ 7 hPa with approx. -3.2 %). In contrast, ozone concentrations around the stratopause are significantly higher for CMIP6-SSI (+0.8 and +1.6 % according to EMAC and CESM1(WACCM), respectively) than under NRLSSI1(CMIP5) irradiances. Despite the considerable differences in spectral resolution of the photolysis schemes (Table  and Fig. ), for larger parts of the stratosphere below about 3 hPa, CESM1(WACCM) and EMAC agree fairly well. For both models the SATIRE irradiances show larger signals than NRLSSI2 irradiances, with the signal for CMIP6 in between. The ozone signals start to differ at and above the stratopause, probably due to the more detailed photolysis code and the higher model top in CESM1(WACCM) compared to EMAC. The ozone signal is much more uncertain with respect to the different SSI forcings than the SW heating rate and the temperature signals.

In summary, the CMIP6-SSI irradiances lead to lower SW heating rates and lower temperatures as well as smaller ozone signals in the lower stratosphere and larger ozone signals in the upper stratosphere and lower mesosphere than the CMIP5-SSI irradiances. Differences between the three tested SSI datasets occur in the SW heating rates only with a very high spectral resolution of the radiation code (libradtran, EMAC), and the differences are more prominent for ozone in a similar way for both CCMs, i.e., stronger effects occur for SATIRE than NRLSSI2. These direct radiative effects in the tropical stratosphere lead to a weakening of the meridional temperature gradient and hence to a statistically significant weakening of the stratospheric polar night jet in early winter (not shown).

The second question tackled by this evaluation is the atmospheric impact of the 11-year solar cycle using different SSI irradiance reconstructions. A special focus lies on the comparison of the new CMIP6 dataset with its predecessor NRLSSI1(CMIP5). Figure  provides annual mean tropical (25∘ S–25∘ N) profiles analogous to Fig.  but now illustrating differences between perpetual solar-maximum and perpetual solar-minimum conditions according to simulations forced by the various SSI-datasets.

All models and SSI-forcings produce the well-known solar-cycle impact of enhanced SW heating at solar maximum throughout the upper stratosphere and mesosphere. Differences to solar-minimum forcing peak at the stratopause with approx. +0.19 to +0.23 K day-1. Only the libradtran-calculations – that do not include any ozone feedback – yield considerably weaker responses.

According to libradtran and CESM1(WACCM), CMIP6-SSI produces slightly higher SW heating-rate differences than NRLSSI1(CMIP5). However, for EMAC this is not the case. For both CCMs and libradtran, the usage of SATIRE leads to the strongest solar-cycle-induced SW heating-rate signals, while NRLSSI2 is associated with the weakest response (though not significantly different from NRLSSI1(CMIP5) for EMAC and libradtran).

Temperatures in the tropical stratosphere and mesosphere are generally higher during solar maximum than during phases of low solar activity. A local maximum of temperature differences is found at the stratopause with positive differences of 0.8–1.0 K compared to solar minimum. According to both CCMs, CMIP6-SSI forcing yields slightly higher temperatures (up to +0.2 K in the mesosphere in CESM1(WACCM)) for the stratopause region and the (lower) mesosphere than NRLSSI1(CMIP5). However, most of these differences are not statistically significant. Comparing CMIP6-SSI-forced results with its components NRLSSI2 and SATIRE yields heterogeneous results. According to EMAC, NRLSSI2 leads to a slightly weaker solar-cycle response throughout the stratosphere, while the mesospheric response is stronger than SATIRE and CMIP6-SSI. CESM1(WACCM)-results show that the stratospheric (up to approx. 2 hPa) solar-cycle response to CMIP6-SSI-forcing in temperature is slightly weaker than in both NRLSSI2- and SATIRE-driven simulations. As opposed to that, simulations forced by SATIRE and CMIP6-SSI yield very similar warming signals in the mesosphere while NRLSSI2 produces a (significantly) weaker response in the mesosphere.

The solar-cycle signal in ozone is very consistent for most parts of the stratosphere and mesosphere, with respect to the SSI datasets. More important for the solar ozone signals seems to be the choice of the CCM (with its specific photolysis scheme; see also Fig. ), especially for the lower stratosphere (10 hPa and below). In the lower mesosphere, however, the dataset-induced differences are larger than the model-induced ones. All analyzed combinations of CCMs and forcing datasets agree very well on the (relative) peak of the ozone response (+2.3–2.5 %) to the solar cycle at 3–5 hPa. In the lower mesosphere (0.2–1 hPa), CMIP6-SSI (and SATIRE) leads to a significantly weaker solar-cycle ozone response (+0.3–0.5 % at 0.5 hPa) than NRLSSI1(CMIP5) (and NRLSSI2; +0.6–0.8 % at 0.5 hPa). For the lower stratosphere (below 7 hPa), both CCMs agree that SATIRE leads to the strongest solar-cycle ozone signals, though still within the uncertainty associated with CMIP6-SSI-forced simulations. The comparison between CMIP6-SSI and NRLSSI1(CMIP5) yields no unequivocal result: CESM1(WACCM) exhibits a secondary maximum ozone response at approx. 70 hPa that is weaker with CMIP6-SSI than with NRLSSI1(CMIP5) while the opposite is seen in EMAC. Given the large uncertainty in the lower stratospheric solar ozone signal, we can only conclude that the signal is positive.

In summary, the CMIP6-SSI irradiance forcing leads to slightly enhanced solar-cycle signals in SW heating rates, temperatures, and ozone than the CMIP5-SSI irradiance forcing. In general, differences between the different SSI datasets are not statistically significant. Note that statistically significant differences in the irradiance amplitude between CMIP5 and CMIP6-SSI irradiances are observed between 300 and 350 nm in particular, a wavelength region important for ozone destruction (below 320 nm), consistently in both CCMs (Fig. ).

The direct radiative effects in the tropical stratosphere from the CMIP6-SSI dataset, i.e., enhanced solar-cycle signals in SW heating rates, temperatures, and ozone in the tropical upper stratosphere lead to the expected strengthening of the meridional temperature gradient and hence to a statistically significant stronger stratospheric polar night jet which propagates poleward and downward during winter from December through January (Fig. ) and significantly affects the troposphere with a positive AO-like signal developing in late winter, i.e., January and February (Fig. ). This signal is very similar and statistically significant for both CCMs, and therefore the ensemble mean of both models is shown. Besides the radiative impact of the solar cycle, energetic particles also have an impact on the atmosphere and will be discussed in the following.

Energetic particles are trapped in the space around the Earth dominated by the geomagnetic field (known as the magnetosphere). The loss of electrons into the atmosphere is termed “electron precipitation”. Due to the Earth's magnetic field configuration, electron precipitation occurs mainly in the polar auroral and subauroral regions, i.e., at geomagnetic latitudes typically higher than 50∘. Enhanced loss fluxes are associated with geomagnetic storms, which can occur randomly, and also with periodicities ranging from the ∼ 27 day solar rotation to the 11-year solar cycle, and even to multidecadal timescales. The altitudes at which precipitating electrons deposit their momentum are dependent on their energy spectrum, with lower energy particles impacting the atmosphere at altitudes higher than those with higher energies e.g.,. Auroral electrons, originating principally from the plasma sheet, have energies < 10 keV and affect the lower thermosphere (95–120 km). Processes that occur in the outer radiation belt typically generate mid-energy electron (MEE) precipitation within the energy range ∼ 10 keV to several MeV, affecting the atmosphere at altitudes of ∼ 50–100 km .

Odd nitrogen, produced by precipitating electrons, is long-lived during polar winter and can then be transported down from its source region into the stratosphere, to altitudes well below 30 km. This has been postulated already by and observed many times . This so-called EPP “indirect effect” contributes significant amounts of NOy to the polar middle atmosphere during every winter in both hemispheres, although with varying magnitude ranging from a few percent up to 40 % . Its consideration in climate models with their upper lid in the mesosphere, thus not covering the entire EPP source region, requires the implementation of an upper-boundary condition (UBC) that accounts for the transport of NOx into the model domain, as discussed below.

Stratospheric ozone loss due to electron-induced NOx production in the upper mesosphere–lower thermosphere and subsequent downward transport has been postulated by model experiments many times . However, observational evidence for EPP-induced variations of stratospheric ozone linked to geomagnetic activity, characterized by a negative anomaly moving down with time during polar winter, have been given only very recently .

In addition, mesospheric ozone effects have been observed which are caused by HOx increases during MEE precipitation . Although the HOx-driven response is short-lived, the frequency of MEE events is large enough to cause solar-cycle variability in ozone . HOx response is seen at magnetic latitudes connected to the outer radiation belts, with, for example, the yearly amount of HOx varying with the observed magnitude of precipitation . The consideration of the effects of MEE on atmospheric species other than NOx, HOx, and ozone have not been investigated in detail to date, but they can be expected to be qualitatively similar to those caused by solar proton events .

The impact of magnetospheric particles on the atmosphere is strongly linked to the strength of geomagnetic activity; this has been shown both for the direct production of NO in the thermosphere and mesosphere , for mesospheric OH production , and for the EPP indirect effect . Geomagnetic activity can be constrained over centennial timescales by means of proxy data provided by geomagnetic indices. Since our forcing dataset for magnetospheric particle precipitation relies on these indices, their reconstruction and homogenization is discussed first.

Geomagnetic indices provide a measure of the level of geomagnetic activity resulting from the response of the magnetosphere–ionosphere system to variability in the solar and near-Earth solar wind forcings. Many geomagnetic indices have been constructed and different indices are sensitive to different aspects of magnetospheric and ionospheric dynamics . The Kp and Ap geomagnetic indices are directly related by a quasi-logarithmic conversion; they are proxies for the global level of geomagnetic activity, and are used as inputs to parameterizations of magnetospheric particle precipitation. For the historical solar forcing data, daily values of the Kp and Ap indices from 1850 to 2014 are required. However, these indices, provided by the International Service of Geomagnetic Indices (http://isgi.unistra.fr/), have only been produced from 1932 onwards. It is not possible to directly and consistently extend the Kp and Ap indices prior to 1932, as they use data from 13 geomagnetic observatories around the globe, and these data are unavailable further back in time. So, before 1932 the Kp and Ap indices must be estimated from other geomagnetic indices. The aa index is the most appropriate choice, as it was constructed to be as similar as possible to the Ap index on annual timescales . However, the original aa index only extends back to 1868 (also available from http://isgi.unistra.fr/), and so an extension to the aa index is also employed, extending it back to 1844 by use of the Ak indices from the Helsinki geomagnetic observatory, spanning 1844–1912. In addition, we implement a correction to the aa index to account for a change in the derivation of the index in 1957; see .

On larger than annual timescales, the response of the aa and Ap indices is similar, and the indices are positively linearly correlated. However, on daily timescales the relationship between aa and Ap is not linear, and also displays a regular annual variation. Therefore, to estimate the daily Ap indices during the period 1868–1931, we used piecewise polynomial fits between the daily Ap and aa values for the period 1932–present, for each calendar month. These fits were then extrapolated to estimate the Ap values between 1868 and 1931 from the aa values. This process was repeated to estimate the relationship between the Ak indices provided by , and the Ap values estimated from the aa index. The piecewise polynomial fits for each calendar month were calculated using the overlap period between the Ak and estimated Ap records, 1868–1912. These were then extrapolated to estimate Ap in the period 1850–1867. Figure  shows the time series of the reconstructed Ap index and the aa and Ak indices used for extension, back to 1850.

The daily Kp index for the period 1868–1931 was estimated by using the monthly piecewise polynomial aa–Ap fits to estimate the 3-hourly ap index values from the aa index values. These 3-hourly ap values were then converted to the corresponding Kp indices, from which the daily mean was calculated. Since only daily Ak data are available, such an approach is not possible for the period 1850–1867, and so here the daily estimates of Ap, derived from Ak, are directly converted into daily Kp. The quasi-logarithmic nature of the conversion between the hourly Kp and ap indices, means that calculating daily values of Kp in this manner results in lower values than the standard method of averaging the eight 3-hourly values in a day, resulting in a slight bias in the Kp estimates. A statistical correction for this bias was employed by estimating the bias using the difference between the aa-derived Kp and the Ak-derived Kp for the period 1868–1912. The estimated bias was then subtracted from the Ak-derived Kp estimates for the period 1850–1867.

Lower thermospheric nitric oxide production by auroral electron precipitation can only be considered explicitly in CCMs extending up to 120 km or higher. There were only a few Earth system models of this characteristic in CMIP5 and it is expected that the number of such models will not increase significantly within CMIP6. Most of the models falling into this category use parameterizations for the calculation of auroral ionization rates or NO productions in the polar cusp and polar cap . Those parameterizations are typically driven by geomagnetic indices and we hence recommend the use of the extended Ap or Kp time series described above.

Figure  demonstrates the improvement in 2004–2009 wintertime polar NOy modeling when production due to electron precipitation is included. The simulations are from the SD-WACCM model version 4 nudged to the NASA Global Modeling and Assimilation Office Modern-Era Retrospective Analysis for Research and Applications (MERRA) dynamics, and they are compared to observations from the ACE-FTS instrument . The auroral electron contribution was calculated with a Kp-based parameterization and was further controlled through eddy diffusion affecting the NOx descent from lower thermosphere. MEE ionization and NOx production was calculated using electron flux observations from the NOAA SEM-2 medium energy proton and electron detector (MEPED) instrument onboard the POES spacecraft , using methods described in more detail in the following MEE section. Enhancing the transport of auroral NOx from the lower thermosphere and including the mesospheric NOx production by MEE clearly improves the wintertime NOy near the stratopause. Around 0.1 hPa, modeled NOy increases by 100 % in both hemispheres, which leads to better agreement with ACE-FTS. Both auroral electrons and MEE have a clear impact, although the auroral contribution is larger. However, it should be noted that 2004–2009 was a period of weak MEE in general, and during other periods of stronger MEE the contributions become more equal such that the effect on model NOy is stronger (not shown).

Highly energetic particles trapped in the radiation belts mainly consist of electrons and protons, forming inner and outer belts separated by a “slot” region . The outer radiation belt (located 3.5–8 Earth radii from the Earth's center) is highly dynamic, with electron fluxes changing by several orders of magnitude on timescales of hours to days e.g.,. These changes are caused by the acceleration and loss of energetic electrons, through enhancements in radial diffusion and wave-particle interactions, during and after geomagnetic storms e.g.,. Storm-driven dynamic variations in the underlying cold plasma density influence the effectiveness of such processes in different regions of the inner magnetosphere e.g.,.

In order to characterize the electron precipitation into the atmosphere since 1850, it is necessary to develop a model that uses in situ satellite observations from the modern era. The most comprehensive, long-duration, and appropriate set of observations is provided by the NOAA SEM-2 MEPED instrument onboard the POES spacecraft . The MEPED instrument covers an energy range from 50 eV to 2700 keV. In this study we are primarily concerned with measurements made with the three medium energy integral electron detectors, i.e., > 30, > 100, and > 300 keV, as the lower “auroral” energy range has been well characterized in previous work. The SEM-2 instrument has been flown on low-Earth-orbiting (∼ 800 km) Sun-synchronous satellites since 1998, with up to six instruments operating simultaneously on occasion. Electron precipitation fluxes from the outer radiation belt are measured with the 0∘ detectors, which are mounted approximately parallel to the Earth-center-to-satellite vector.

Improved calibration of the SEM-2 detectors has been undertaken by using modeling techniques contained in the GEANT-4 code to determine the detector geometric conversion factor, or detector efficiency following the original work described in.

Further treatment of the data requires correction for the false counts caused by incident proton fluxes, which we undertake using the technique described in . These calibrations and corrections have been tested through comparison with other satellite e.g., and ground-based observations e.g.,. We convert the satellite position into the geomagnetic latitude parameter L using the International Geomagnetic Reference Field (IGRF; see Appendix ) and bin the precipitating flux data into zonal means with 0.25 L resolution from L=2–10 (40–75∘ geomagnetic latitude).

Using observed electron flux data in 2002–2012, a precipitation model for radiation belt electrons was created by . The precipitation model was fitted to the corrected observations of the MEPED/POES detectors following the approach outlined in . In the CMIP6 application of this model, the Ap index is used as the driving input parameter. Ap defines the level of magnetospheric disturbance and the location of the plasmapause, both of which are needed to calculate precipitating-electron fluxes at different magnetic latitudes. Thus, the reconstructed Ap record, as described earlier, can be readily used to create a continuous electron precipitation time series for the whole CMIP6 period. As output, the model provides daily spectral parameters of precipitation: integrated flux at energies above 30 keV and a power-law spectral gradient. A test of high-energy resolved precipitating electron flux measurements made by the DEMETER satellite found that the power-law fit consistently provides the best representation of the flux . The model output has been shown to compare well with the spectral parameters derived from POES satellite data .

An atmospheric ionization dataset has been calculated based on the Ap-based precipitation model, using a computationally fast ionization parameterization and atmospheric composition from the NRLMSISE-00 model . This calculation considered MEE (30–1000 keV) with maximum energy deposition at altitudes between about 60 and 90 km . Note that the ionization parameterization does not consider the contribution of Bremsstrahlung, which could be significant only at altitudes below 50 km .

Figure  shows examples of solar-cycle variability of the modeled atmospheric MEE ionization rates at ≈ 80 km altitude. At 68∘ magnetic latitude (L shell 7.25), MEE precipitation is mostly driven by magnetic substorms and the solar-cycle variability is relatively weak, except in around 2009 and the mid-1960s when extended periods of very low geomagnetic activity occurred. At 64∘ (L shell 5.25), precipitation is driven by high-speed solar wind streams. A more clear solar-cycle variability can be seen with maximum ionization lagging the sunspot maximum by 1–2 years. At 56∘ (L shell 3.25), precipitation is mainly driven by coronal mass ejections which lead to more of an event-type behavior. Relatively infrequent ionization peaks are contrasted with long periods of very low ionization. Similar behavior is seen at other altitudes as well (not shown).

In the following, we demonstrate with examples the MEE impact in WACCM simulations. The purpose is to present a proof of concept, i.e., show that the MEE ionization dataset can be used in chemistry–climate modeling and is producing the expected direct effect in the mesosphere. We simulated the 2002–2012 period, including the Ap-driven MEE ionization rates, and analyzed mesospheric OH and ozone responses at 0.040–0.015 hPa (approx. 70–80 km in altitude). This altitude region was selected because of the clear and direct MEE impact seen in satellite observations e.g.,. WACCM version 4 (see above) was used with 1.9∘ × 2.5∘ horizontal resolution extending from the surface to 5.9×10-6 hPa (≈ 140 km geometric height) in the specified dynamics mode, nudged to MERRA reanalysis at every dynamics time step below about 50 km.

Figure a and b shows global differences in yearly median OH mixing ratios due to MEE. Distinct features on the map are the stripes of enhanced values at magnetic latitudes between 55 and 75∘ (both hemispheres) which connect through the magnetic field to the outer radiation belt. The impact decreases from 2005 to 2009 due to the decline in geomagnetic activity and MEE precipitation (as shown in Fig. ). These features are of expected quality and magnitude, and similar to those based on Microwave Limb Sounder (MLS) data analysis .

Figure c and d show relative differences in wintertime mean ozone due to MEE in the Southern Hemisphere. As expected, ozone is affected at high polar latitudes. In 2009, when MEE precipitation was weak, a maximum of 5–10 % decrease is seen near the South Pole relative to a reference WACCM simulation. In 2005, with much stronger MEE precipitation, the effect reaches up to 10–20 % and covers the whole polar cap above about 60∘ latitude. The magnitude of the 2005 response, tens of percent, is comparable to that seen in MLS observations .

Those models with their upper lid in the mesosphere, i.e., those which do not represent the entire EPP source region, require an odd nitrogen upper-boundary condition, accounting for EPP productions higher up, in order to allow for simulating the introduced EPP indirect effect in the model domain. Odd nitrogen UBCs have been previously used in CCMs. In some model studies, the UBC was taken directly from NOx observations e.g.,, which, however, implies the restriction to the relatively short time period spanned by the observations. In other cases, a simple parameterization in dependence of the seasonally averaged Ap index was employed e.g.,, enabling extended simulations over multidecadal time periods. We recommend the use of the UBC model described in which is designed for the latter application and represents an improved parameterization due to its more detailed representation of geomagnetic modulations, latitudinal distribution, and seasonal evolution. This semi-empirical model for computing time-dependent global zonal mean NOy concentrations (in units of cm-3) or EPP-NOy molecular fluxes (in units of cm-2 s-1) at pressure levels within 1–0.01 hPa is available at http://solarisheppa.geomar.de/solarisheppa/cmip6.

The UBC model has been trained with the EPP-NOy record inferred from Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) observations . Inter-annual variations of the EPP indirect effect at a given time of the winter are related to variations of the EPP source strength, the latter being considered to depend linearly on the Ap index. A finite impulse response approach is employed to describe the impact of vertical transport on this modulation. Interannual variations of the EPP-NOy seasonal dependence, driven by variations of chemical losses and transport patterns, are not considered in the standard mode of the UBC model. Optionally, episodes of accelerated descent associated with elevated stratopause (ES) events in Arctic winters can be considered by means of a dedicated parameterization, taking into account the dependence of the EPP-NOy amounts and fluxes on the event timing . Although its application is recommended in principle, we note that it requires the implementation of the UBC model into the climate model system since ES events cannot be predicted in free-running model simulations. Further, the ES detection criterion might need to be tuned for each individual model system.

We recommend prescribing NOy concentrations, as this has already been tested successfully in a CCM. As an example, Fig.  shows the NOy concentrations from the UBC model at 0.1 hPa in comparison with the MIPAS observations. Care has to be taken when balancing [NOy] = [NO] + [NO2] + [NO3] + [HNO3] + 2[N2O5] + [ClONO2] in order to avoid model artifacts at the upper boundary (primarily triggered by the loss reaction of NO2 with atomic oxygen). The simplest way to achieve this is to set [NO] = [NOy] while forcing the concentrations of all other NOy species to be zero. Note that below the vertical domain where NOy is prescribed, MEE ionization still might occur and its consideration (as described before) is recommended. However, its consideration should be strictly limited to this vertical range since at and above the UBC, MEE is already implicitly accounted for by the prescribed NOy from the observation-based UBC model.

The UBC was tested in the EMAC CCM version 2.50 see also Sect.  and with a T42L90 resolution. NOy concentrations were prescribed as NO in the uppermost four model boxes at pressure levels from 0.09 to 0.01 hPa. There, NO2 was set to zero to suppress artificial NO2 buildup. The model was run from 1999 to 2010 in the specified dynamics mode, nudged to ERA-Interim reanalysis data below 1 hPa. A special treatment of ES events was disabled in the UBC model and SPEs were not considered. A comparison of polar NOy from EMAC with MIPAS observations is shown in Fig.  for 0.1 hPa (just below the prescription altitudes) and 1 hPa. A very good agreement between model predictions and observations is found at 0.1 hPa in both hemispheres, with the exception of periods of large SPEs (October/November 2003) in both hemispheres and ES events (January 2004 and February 2009) in the Northern Hemisphere. At 1 hPa, the agreement is still very good during winter, but EMAC underestimates the summer maximum of NOy slightly. This is also observed in the base model run without employing the UBC (see Fig. ).

The interannual variation of ozone in the stratosphere and lower mesosphere has been investigated in this model in a similar way to a three-satellite composite . The ozone difference between austral winters with high and low geomagnetic activity during 2005–2010 is shown in Fig.  for 27-day running means relative to the mean of all years. This period has been chosen because of its low SSI variability. Cross-correlations between SSI and particle impact are thus minimized. EMAC results are in excellent agreement with the observations provided in Fig. 5, showing a clear negative ozone anomaly of 5–10 % moving down from the upper stratosphere to below 10 hPa (∼ 30 km) from July to October. Below, a positive anomaly of smaller amplitude is observed both in EMAC and the three-satellite composite, which might be due to a combination of self-healing, dynamical feedbacks, and chemical feedbacks (NOx-induced chlorine buffering in the processed “ozone hole” area).

Solar eruptive events sometimes result in large fluxes of high-energy solar protons at the Earth, especially near the maximum and declining periods of activity of a solar cycle. This disturbed time, wherein the solar proton flux is generally elevated for a few days, is known as a solar proton event. Solar protons are guided by the Earth's magnetic field and impact both the northern and southern polar-cap regions > 60∘ geomagnetic latitude, e.g., see. These protons can impact the neutral middle atmosphere (stratosphere and mesosphere) and produce both hydrogen radicals and reactive nitrogen constituents.

The ozone response due to very large SPEs is fairly rapid and substantial and has been observed during and after numerous events to date e.g.,. Ozone within the polar caps (60–90∘ S or 60–90∘ N geomagnetic) is generally depleted to some extent in the mesosphere and upper stratosphere e.g., within hours of the start of the SPE and can last for months beyond the event at lower altitudes in the stratosphere.

Decreases in mesospheric and upper stratospheric ozone are mostly caused by SPE-induced HOx increases, which were predicted to occur over 42 years ago e.g., see. Direct measurements of SPE-caused OH and HO2 enhancements have confirmed these early predictions e.g.,. Other observations of increased H2O2 and of chlorine-containing constituents HOCl an increase; see and HCl a decrease; see support the SPE-caused HOx enhancement theory. Since HOx constituents have relatively short lifetimes (hours), these SPE-enhanced species have only a short-term impact on ozone.

The SPE-induced NOy enhancements, on the other hand, cause a much lengthier reduction in ozone, given their much longer atmospheric lifetime (months) in the stratosphere. SPE-caused NOx increases have been shown in several studies e.g.,. Other NOy constituents like HNO3, HNO4, N2O5, and ClONO2 e.g., as well as the total NOy family e.g., have also been shown to increase as a result of large SPEs. Additionally, N2O has been measured to increase as a result of large SPEs .

Solar proton fluxes have been measured by a number of satellites in interplanetary space or in orbit around the Earth. The National Aeronautics and Space Administration (NASA) Interplanetary Monitoring Platform (IMP) series of satellites provided measurements of proton fluxes from 1963 to 1993. IMPs 1–7 were used for the fluxes from 1963 to 1973 (Jackman et al., 1990) and IMP 8 was used for the fluxes from 1974 to 1993 . The National Oceanic and Atmospheric Administration (NOAA) Geostationary Operational Environmental Satellites (GOES) were used for proton fluxes from 1994 to 2014 e.g.,.

Other precipitating particles are associated with SPEs, besides protons. These include alpha particles, which comprise, on average (but this value may vary from event to event) about 10 % of the positively charged solar particles; other ions, which account for less than 1 % of the remainder; and electrons e.g.,. Only solar protons are included in energy deposition computations given in this paper. Please note that other charged particles could add modestly to this energy deposition in the middle atmosphere during SPEs.

The proton fluxes of energies 1–300 MeV were used to compute daily average ion pair production profiles using an energy deposition scheme first discussed in . The scheme includes the deposition of energy by the protons and assumes 35 eV is required to produce one ion pair . Note that this approach misses development of the atmospheric cascade (Sect. ). This process, crucial for GCRs, is minor for SPEs in the upper atmosphere but may contribute modestly to the energy deposition in the lower stratosphere.

The dataset for daily average ion pair production rates at 60–90∘ geomagnetic latitudes from SPEs was computed over a 52-year time period (1963–2014), when proton flux measurements from satellites were available. A longer-term dataset for these SPE-caused ion pair production rates was created for the 1850–1962 time period using activity levels of the measured sunspots over the solar cycles. SPEs are much more frequent during years of maximum solar activity and vice versa. This longer-term dataset was reconstructed for years 1850–1962 in a random way using solar activity levels combined with the 52-year calculated SPE-caused ion pair production. Thus, an historical record of atmospheric forcing by SPEs in the form of a daily average ion pair production rate is available over the entire period 1850–2014 for use in global models.

The Earth's atmosphere is continuously irradiated by galactic cosmic rays, which consist mostly of protons and α-particles with a small amount of heavier fully ionized species up to iron and beyond. These cosmic rays originate from galactic (mostly supernova shocks) and exotic extra-galactic sources and may have an energy up to 1020 eV but the bulk energy is in the range of several GeV per nucleon. While the GCR flux can be assumed (at timescales shorter than thousands of years) constant and isotropic in the interstellar space, it is subject to strong modulations within the heliosphere (the region of about 200 AU across, hydromagnetically controlled by the solar wind and the heliospheric magnetic field). This modulation is driven by solar magnetic activity – the stronger the solar activity, the lower the GCR flux near the Earth. This flux is often described by the so-called force-field model parameterized via the time-variable modulation potential ϕ and the fixed shape of the local interstellar spectrum see, e.g.,for more details. Typically, the value of the modulation potential is defined by fitting data from the worldwide network of ground-based neutron monitors calibrated to fragmentary space-borne measurements of GCR energy spectra. These data are available since 1951 or, with caveats of using the ground-based ionization chambers, since 1936 .

Before impinging on the Earth's atmosphere, GCR are additionally deflected by the geomagnetic field.

This shielding is usually parameterized in the form of the effective geomagnetic rigidity cutoff, so that only particles with rigidity (momentum per charge) exceeding the cutoff can penetrate to the atmosphere at a given location, while less energetic particles are fully rejected . When energetic cosmic rays enter the atmosphere, they initiate a nucleonic-muon-electromagnetic cascade in the atmosphere, ionizing ambient air. A subproduct of this cascade is the production of cosmogenic isotopes such as 14C, 10Be, and others. These cosmogenic isotopes are long-lived and can be used for the reconstruction of solar activity over several thousand years (see Sect. ).

Between the surface and 25–30 km, cosmic rays are the main source of atmospheric ionization causing the production of NOx and HOx. The influence of GCRs on atmospheric chemistry has been investigated in several model studies . GCR-induced ozone reductions of more than 10 % in the tropopause region and up to a few percent in the polar lower stratosphere have been reported. The potential impact on surface climate has been studied by and .

The process of development of the atmospheric cascade, initiated by energetic cosmic rays, is complicated and needs to be modeled using direct Monte Carlo simulations of all the processes involved in the development of the cascade, including all types of interactions, scattering, and decay of various species. We note that older models based on empirical parameterizations or on solution of Boltzmann-type equations may introduce significant biases in the results, especially in the lower atmosphere. Accordingly, we use a full Monte Carlo model, CRAC:CRII , based on the CORSIKA Monte Carlo package. A similar result can be obtained with the PLANETOCOSMIC based on the GEANT package. The agreement between the two models has been verified to be within 10 %.

GCR ion pair production rates are provided as a function of the barometric pressure and geomagnetic latitude and were calculated from the modulation potential values ϕ of the 9400-year long record by . Since this dataset has a 22-year time resolution, it has been interpolated to interannual timescales to resolve individual solar cycles, based on the sunspot numbers (see Fig. ). One can see that this agrees well with the values of ϕ reconstructed using data from the worldwide network of neutron monitors . An example of the calculated ionization rate is shown in Fig. . The ionization maximizes in polar regions at heights of 15–20 km, while in the equatorial region the maximum of ionization occurs at about 12 km (note that in case of using ionization per cubic centimeter, the ionization maximizes at about 10 km in the equatorial region and 12 km over the poles).

MEE, SPE, and GCR-induced atmospheric ionization is expressed in the CMIP6 forcing dataset in terms of ion pair production rates (IPRs). Note that IPR data are provided in units of ion pairs per gram per second as a function of the barometric pressure. These units are natural for the ionization processes and are mostly independent of the atmospheric conditions. Conversion into units of ion pairs per cubic centimeters per second (cm-3 s-1), by multiplying with mass density, should be done on the model grid ideally at each time step, but at least once per day. Recommendations for the projection of ion pair production rates onto geographic coordinates can be found in Appendix .

Particle-induced ionization causes, along with the generation of the ion pairs, the production of NOx and HOx. As a basic approach, we recommend considering these NOx and HOx productions in CCMs with interactive chemistry by using the parameterizations provided by and , respectively. More detailed information about these approaches is provided in Appendix  and . Recommendations for the implementation of EPP effects on minor species are given in Appendix .

The analogue forecast is calculated with a simple nonparametric technique, known across disciplines by various names including compositing, superposed-epoch analysis, conditional sampling, and Chree analysis. In a data sequence that exhibits a low-amplitude response to a specific trigger event, the response may be obscured by sources of random variability. The AF technique aims to reveal the response to a specific trigger event by averaging the responses to many occurrences of the trigger event, such that over many events random variability will be suppressed and the response will emerge . used this technique with the Φ record to estimate the possible future Φ evolution given the expected decline from the grand solar maximum that persisted through the late 20th century. Here we perform an updated version of the procedure employed by .

Defining grand solar maxima in the Φ record as any period above the 90th percentile of the Φ distribution (462 MV) identifies 23 grand solar maxima in the Φ record prior to the most recent one. Here the declines from the grand solar maxima are used as the event triggers from which the AF is calculated, and these times are marked on the Φ time series shown in Fig.  by red stars. Figure  also shows that the most recent values in the Φ record have not yet fallen below the grand solar maxima threshold. Therefore, as the end date of the most recent grand solar maxima is not known, it must be estimated, to provide a date from which the AF applies. The grand solar-maximum end date was estimated to be 2004, by extrapolating the regression of the 22-year smoothed annual geomagnetic reconstruction of the open solar flux onto the Φ record. So the construction of the scenarios was applied from 2004 onwards and interpolated onto the dates required to continue the 22-year sample sequence defined by the Φ record.

Autoregressive models are widely used in time series analysis . These linear parametric models assume that variations can be described by means of a linear stochastic difference equation, so that future values are expressed as a linear combination of present and past values. In our context, we have Φ^k+h=a1Φk-1+a2Φk-2+…+apΦk-p, where Φk is the heliospheric modulation potential (after subtracting its time average) at the kth time step, and Φ^k+h is its value predicted h≥0 time steps ahead. Since Φk is measured with a cadence of 22 years, each value of k corresponds to a 22-year time step. AR models are capable of describing a variety of dynamical behavior, including oscillations, red noise, etc. The main free parameter is the model order p, for which there exist several selection criteria . In our case, we obtain p=20. According to this value, our scenarios are based on observations that go back at most 440 years into the past.

Because AR models are linear, they cannot properly describe nonlinear dynamical effects such as the occasional occurrence of grand solar minima, which appear as a different mode of solar activity . To partly overcome this limitation, we train the model by considering time intervals whose conditions are similar to those prevailing at the end of the 20th century. More specifically, we train the model by using only observations that belong to either of the 23 time intervals [tGSM-1100 years, tGSM+1100 years] that are centered on the same occurrences, tGSM, of the 23 grand solar maxima as in the analogue forecast (see Sect.  and Fig. ). We exclude observations that follow tGSM by up to 300 years in order to give us a means for testing the prediction on a time interval that is (mostly) independent of the one the model has been trained on. The only exception in this list is the last grand solar maximum of the late 20th century, for which we do not have future observations available. The 2200-year duration of the time interval is the shortest one, below which the performance of the AR model starts degrading.

This independence of the intervals on which the model is trained and then tested (called cross-validation; ) is essential for it and allows the testing of the performance of the model and define confidence intervals that truly reflect the difference between the constructed and actual course of solar activity.

Using AR models, we now construct the heliospheric potential 22, 44, …, 308 years ahead by training a different model for each value of the scenario horizon h in Eq. (). The error, which is the usual metric for describing the performance of the scenario construction, is classically defined as s(h)=Φ^k+h-Φk+h2, where the ensemble average 〈…〉 runs over all 23 grand solar maxima. Clearly, the AR model can be improved in several ways. One of them consists of modeling the full record of the heliospheric potential and using threshold AR models to account for mode changes. These issues will be addressed in a forthcoming publication.

Several studies have reported the existence of periodicities in cosmogenic solar proxies, with outstanding periods of approximately 87 years (known as the Gleissberg cycle), 208 years (de Vries cycle), 350 years, and more . The origin of these elusive periodicities has been hotly debated, and is beyond the scope of our study. successfully used them to model solar activity on multidecadal timescales, and produced a 500-year extension of the heliospheric potential. We consider the same approach, and thus assume that the dynamical evolution of the heliospheric potential obeys a deterministic model. Φ^k=b0+∑i=1Nbisin⁡(2πtk/Ti)+cicos⁡(2πtk/Ti) We parameterize and train this harmonic model in a way that is similar to the preceding AR model. First, we select 2600-year intervals that are centered on the timings, tGSM, of each of the 23 grand solar maxima, and exclude the 300 years that follow each tGSM. In contrast to the AR model, however, we estimate the model coefficients separately for each interval in order to account for possible phase drifts. To select the periods T, and reduce their number, we start from an initial set of N=19 periods of less than 2200 years, taken either from or obtained from spectral analysis. We then estimate the error of this method after discarding one period at a time, only keeping those that do not lead to a significant increase of the error. Finally, we end up with a set of 12 periods of {88, 105, 130, 150, 197, 208, 233, 285, 353, 509, 718, 974} years. Likewise, the error is used to fix the 2600-year duration of the intervals. Longer intervals give a better statistic, but result in a poorer fit because of possible phase drifts in short-period oscillations.