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    Pressure–latitude cross section of estimated annual-mean, zonal-mean percentage change in ozone volume mixing ratio per 100 units of F10.7 cm radio flux for the period 1979–2005, from a regression analysis of SAGE data, adapted from Fig. 12 of Randel and Wu (2007). Values shown in this figure should be multiplied by 1.25 to obtain the average solar minimum to maximum solar changes over the period. Shaded areas are not statistically significant. Contour interval is 1%; dashed contours denote negative values.

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    Pressure–latitude cross section of annual-mean, zonal-mean change in temperature (K) using fixed dynamical heating calculations with (a) imposed spectrally resolved solar irradiance changes from Lean (2000) and (b) imposed zonally averaged ozone changes from Randel and Wu (2007). (c) The sum of the imposed solar irradiance and ozone changes. The annual means were calculated as the average of the individual monthly-averaged values. Contour interval is 0.1 up to 0.6 and 0.2 thereafter. Three additional contours of 0.0125, 0.025, and 0.05 have been inserted in (a) for clarity.

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    Pressure–latitude cross section showing the ratio of the FDH temperature response due to the imposed ozone changes (Fig. 2b) vs the total response due to both irradiance and ozone changes (Fig. 2c), expressed as a percentage. Contour interval is 10%; the thick line denotes the 50% value.

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    Pressure–latitude cross sections showing seasonal evolution of the imposed ozone changes and FDH model temperature response. (left) Imposed ozone changes (%) from Randel and Wu (2007), multiplied by 1.25 to obtain minimum-to-maximum change. Contour interval is 1%. (middle) FDH temperature response (K) when these ozone changes are imposed. (right) FDH temperature response (K) when both solar irradiance and ozone changes are imposed. Contour interval is 0.1 K up to 0.6 K and 0.4 K thereafter. Dashed contours denote negative values.

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    Annually and zonally averaged radiative forcing (W m−2) at the tropopause from the FDH model, including the effect of stratospheric temperature adjustment. Forcing due to (a) the spectrally resolved change in total solar irradiance (solid line) and the sum of the irradiance and ozone changes (dashed line) and (b) the solar cycle–induced ozone change, showing the net forcing and the individual shortwave (SW) and longwave (LW) components. The annual means were calculated as the average of individual monthly averaged values.

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    Latitude–month variation in the ratio between the shortwave radiative forcing at the tropopause and the net change in shortwave irradiance at the top of the atmosphere for the change in total solar irradiance between solar minimum and solar maximum.

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    Spectral variation in shortwave radiative forcing (W m−2 nm−1) for the change in TSI between solar minimum and solar maximum for (top) the equator in October and (bottom) 76°N in April. The dotted curve shows the change in downwelling irradiance at the top of the atmosphere (TOA), the solid black curve shows the change in the net irradiance at the TOA, and the gray curve shows the change in the net irradiance at the tropopause.

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    Cross section of SC change in temperature (K) from minimum to maximum estimated from (a) SSU/MSU data, 1979–96, reproduced from Ramaswamy et al. (2001a); (b) NCEP/NCAR reanalysis, 1979–2001, adapted from Haigh (2003); and (c) ERA-40 reanalysis dataset, 1979–2001, from Crooks and Gray (2005) but corrected for an error in monthly-mean calculations; see text. Contour interval is 0.25; dashed contours denote negative values. Shading represents 95% statistical significance.

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    Pressure–latitude cross section showing the annual-mean, zonal-mean FDH temperature response (K) due to both the imposed irradiance and ozone changes (as in Fig. 2c) but sampled using the SSU/MSU weighting functions. Contour interval is 0.25 K to allow comparison with Fig. 8a.

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Stratospheric Temperature and Radiative Forcing Response to 11-Year Solar Cycle Changes in Irradiance and Ozone

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  • 1 Department of Meteorology, University of Reading, Reading, United Kingdom
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Abstract

The 11-yr solar cycle temperature response to spectrally resolved solar irradiance changes and associated ozone changes is calculated using a fixed dynamical heating (FDH) model. Imposed ozone changes are from satellite observations, in contrast to some earlier studies. A maximum of 1.6 K is found in the equatorial upper stratosphere and a secondary maximum of 0.4 K in the equatorial lower stratosphere, forming a double peak in the vertical. The upper maximum is primarily due to the irradiance changes while the lower maximum is due to the imposed ozone changes. The results compare well with analyses using the 40-yr ECMWF Re-Analysis (ERA-40) and NCEP/NCAR datasets. The equatorial lower stratospheric structure is reproduced even though, by definition, the FDH calculations exclude dynamically driven temperature changes, suggesting an important role for an indirect dynamical effect through ozone redistribution. The results also suggest that differences between the Stratospheric Sounding Unit (SSU)/Microwave Sounding Unit (MSU) and ERA-40 estimates of the solar cycle signal can be explained by the poor vertical resolution of the SSU/MSU measurements. The adjusted radiative forcing of climate change is also investigated. The forcing due to irradiance changes was 0.14 W m−2, which is only 78% of the value obtained by employing the standard method of simple scaling of the total solar irradiance (TSI) change. The difference arises because much of the change in TSI is at wavelengths where ozone absorbs strongly. The forcing due to the ozone change was only 0.004 W m−2 owing to strong compensation between negative shortwave and positive longwave forcings.

Corresponding author address: Professor Lesley J. Gray, National Centre for Atmospheric Science, Dept. of Meteorology, University of Reading, P.O. Box 243, Reading RG6 6BB, United Kingdom. Email: l.j.gray@rdg.ac.uk

Abstract

The 11-yr solar cycle temperature response to spectrally resolved solar irradiance changes and associated ozone changes is calculated using a fixed dynamical heating (FDH) model. Imposed ozone changes are from satellite observations, in contrast to some earlier studies. A maximum of 1.6 K is found in the equatorial upper stratosphere and a secondary maximum of 0.4 K in the equatorial lower stratosphere, forming a double peak in the vertical. The upper maximum is primarily due to the irradiance changes while the lower maximum is due to the imposed ozone changes. The results compare well with analyses using the 40-yr ECMWF Re-Analysis (ERA-40) and NCEP/NCAR datasets. The equatorial lower stratospheric structure is reproduced even though, by definition, the FDH calculations exclude dynamically driven temperature changes, suggesting an important role for an indirect dynamical effect through ozone redistribution. The results also suggest that differences between the Stratospheric Sounding Unit (SSU)/Microwave Sounding Unit (MSU) and ERA-40 estimates of the solar cycle signal can be explained by the poor vertical resolution of the SSU/MSU measurements. The adjusted radiative forcing of climate change is also investigated. The forcing due to irradiance changes was 0.14 W m−2, which is only 78% of the value obtained by employing the standard method of simple scaling of the total solar irradiance (TSI) change. The difference arises because much of the change in TSI is at wavelengths where ozone absorbs strongly. The forcing due to the ozone change was only 0.004 W m−2 owing to strong compensation between negative shortwave and positive longwave forcings.

Corresponding author address: Professor Lesley J. Gray, National Centre for Atmospheric Science, Dept. of Meteorology, University of Reading, P.O. Box 243, Reading RG6 6BB, United Kingdom. Email: l.j.gray@rdg.ac.uk

1. Introduction

An understanding of the mechanisms of influence of the 11-yr solar cycle (SC) on climate and their inclusion in climate models is important to accurately model past climate change and predict future trends. Changes in stratospheric temperatures during the SC are believed to originate primarily from a combination of changes in the incoming solar irradiance and the resulting changes in ozone concentrations (Haigh 1994; Solomon et al. 2007). There are other suggested mechanisms, such as changes in odd nitrogen caused by energetic electron precipitation that then influences the ozone distribution (Callis et al. 2001), but observations do not appear to support a significant role for this mechanism (Hood and Soukharev 2006).

Extraction of the 11-yr SC in the observed temperature (e.g., Scaife et al. 2000; Ramaswamy et al. 2001a; Haigh 2003, 2004; Crooks and Gray 2005) and ozone records (e.g., Hood 1997; Soukharev and Hood 2006; Randel and Wu 2007) has been carried out, although the length of the reliable observations covers only two solar cycles and is therefore rather short. The fields show a maximum signal near the equatorial stratopause and, in several of them, an additional, smaller lower stratospheric maximum, thus forming a double maximum in the vertical. Recent coupled chemistry general circulation model (GCM) studies that impose 11-yr SC irradiance changes have been increasingly successful in reproducing the SC signal in ozone (e.g., Austin et al. 2008). There have been many improvements to these models compared to those used in earlier studies. These include (i) the coupling of chemistry with the radiation and dynamical codes so that the ozone fields are no longer imposed from simpler offline models, (ii) realistic time-varying integrations instead of the previous steady-state solar maximum/solar minimum runs, and (iii) time-varying sea surface temperatures instead of the usual repeated climatology. However, with such complicated models including many processes and interactions, it is not easy to assess which of these improvements has resulted in the improved representation. Without this knowledge, an understanding of the fundamental mechanisms of solar influence is difficult to achieve.

In this study, we aim to investigate mechanisms of solar influence on stratospheric temperatures. We use a simple “fixed dynamical heating” (FDH) model with a relatively sophisticated radiation code and explore the response to irradiance changes and ozone changes by separately imposing the estimated changes and then combining them to get an estimate of the total temperature change (McCormack and Hood 1996; Shibata and Kodera 2005). Our FDH approach is similar to the recent study of Shibata and Kodera (2005) except in one very important detail: We impose distributions of ozone changes from observations (Randel and Wu 2007) instead of 2D model estimates. This produces very different results and hence conclusions about the origin of the secondary temperature maximum in the lower stratosphere. McCormack and Hood were the first to employ this approach using observed distributions of ozone, but they had a much shorter ozone record and the observations did not extend into the lower stratosphere.

We also extend the study by sampling the modeled temperature responses as though they were measured by the Stratospheric Sounding Unit (SSU)/Microwave Sounding Unit (MSU) instruments and propose an explanation for an apparent discrepancy between the 11-yr SC estimates from the SSU/MSU and the National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) and 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) reanalyses. An additional output from the above calculations is the radiative forcing at the tropopause, which includes the so-called instantaneous radiative forcing due to the changes in irradiance and ozone, and also the effect of the FDH-derived temperature changes in the stratosphere, which together yield the adjusted radiative forcing.

The paper is laid out as follows: In section 2 the experimental approach is described in detail, including a description of the FDH model, the derivation method for radiative forcing estimates, and the spectral irradiance and ozone datasets employed in the study. In section 3 results from the model runs are presented in which the irradiance and ozone changes are first imposed separately and then combined. The radiative forcing results from each model run are presented in section 4. In section 5 the FDH results are compared with estimates of the SC temperature response from satellite and reanalyses datasets. The possible mechanisms for the FDH temperature response are discussed in section 6, and results are summarized in section 7.

2. Experimental approach

The stratospheric temperature change due to irradiance and ozone changes is determined using the fixed dynamical heating (FDH) approach. In the FDH model it is assumed that for each month, and at each latitude φ and height z, the diabatic heating Q(T, O3, φ, z) (where T is temperature and O3 is some measure of ozone concentration) and the dynamical heating D(φ, z) are in balance so that Q(T, O3, φ, z) + D(φ, z) = 0. The diabatic heating term Q(T, O3, φ, z) is computed using the radiation code and background climatology, which then yields D(φ, z) using the above equation. On perturbing the top-of-the-atmosphere (TOA) solar irradiance and/or the ozone (to O3′), a new temperature T ′ is computed by simple time stepping with the same radiation code and using the unperturbed value of D(φ, z) so that Q(T ′, O3′, φ, z) + D(φ, z) = 0. Tropospheric temperatures (and all other conditions) are held fixed at climatological values when the FDH is applied in the stratosphere, following normal practice.

FDH allows a useful estimate of the impact of diabatic heating perturbations on temperature as it incorporates the effects of both the diabatic heating perturbation and the variation of radiative relaxation time scale with height, latitude, and season. The first comparison of FDH-derived temperature response with that from a GCM for the stratosphere was by Fels et al. (1980). This and subsequent comparisons [e.g., Kiehl and Boville (1988), Rosier and Shine (2000), and particularly Shibata and Kodera (2005) in the context of solar-induced perturbations of diabatic heating)] have confirmed that GCM- and FDH-derived temperature changes are in good agreement, at least for realistic perturbations in low and middle latitudes. Further reasons for adopting the FDH approach are that it unambiguously separates out the cause of modeled temperature changes and also allows a detailed radiative transfer scheme to be used, which resolves the detail of the wavelength dependence of the irradiance change between solar maximum and minimum.

The radiative transfer schemes and FDH model used here are similar to those described in Forster and Shine (1997) except that the wavelength resolution in the UV and visible has been increased to 1 nm. In the thermal infrared, a 10 cm−1 resolution narrowband model is used. The baseline extraterrestrial solar irradiance is from LOWTRAN 7 (Kneizys et al. 1988). Calculations are performed for monthly- and zonal-mean conditions with 4° latitudinal resolution from 80°S to 80°N for the irradiance calculations and 56°S to 56°N for the ozone calculations (as the ozone changes were only available over this domain). The radiative calculations extend from the surface to 0.01 hPa, with about 37 levels in the vertical (depending on surface pressure). Of these, 23 levels are at pressures below 100 hPa. Note that the radiation codes do not simulate all processes necessary for modeling of the upper mesospheric radiation budget and, in any case, the imposed ozone changes do not extend to pressures less than 1 hPa: the choice of the upper boundary is simply to ensure that it is well away from our region of interest.

The baseline temperature and water vapor climatologies used for the FDH calculations from the surface up to 1 hPa are from the ERA-40 reanalysis (Uppala et al. 2005). The baseline ozone climatology from the surface to 1 hPa is from McPeters et al. (2007). Temperatures are extended up to 0.01 hPa using the Stratospheric Processes and Their Role in Climate (SPARC) climatology (http://www.sparc.sunysb.edu/html/temp_wind.html); water vapor is from the Upper Atmosphere Research Satellite (UARS) Reference Atmosphere (http://code916.gsfc.nasa.gov/Public/Analysis/UARS/urap/home.html), as is ozone, except at pressures between 0.1–0.01 hPa where Li and Shine (1995) is used. Cloud amounts, heights, and optical depths are taken from Rossow and Schiffer (1991). The radiation scheme used here was found to agree closely with an alternative scheme when calculating the solar-induced ozone radiative forcing (Isaksen et al. 2008).

The solar minimum to maximum irradiance changes are taken from Lean et al. (1997) and Lean (2000) and cover the region from 200 to 855 nm at 1-nm resolution. Lean et al. (2005) show that these changes are in good agreement with more recent observations. The actual change imposed corresponds to the irradiance at a particular solar minimum (September 1986) and solar maximum (November 1989). The wavelength-averaged change in total solar irradiance (TSI) imposed here is 1.21 W m−2.

Figure 1 shows the percentage ozone change from solar minimum to solar maximum employed in the calculations, taken from a regression analysis of Stratospheric Aerosol and Gas Experiment (SAGE) data by Randel and Wu (2007). Although there is little statistical significance in the equatorial midstratosphere, the overall structure indicates local maxima near 50 and 25 km at the equator and relatively deep maxima between ∼20 and 40 km in the subtropics, with a local minimum in the equatorial midstratosphere near 25–40 km. Corresponding analyses of solar backscatter ultraviolet (SBUV), SAGE, and Halogen Occultation Experiment (HALOE) data by Hood (1997) and Soukharev and Hood (2006) also have a midstratosphere minimum and local maxima in the subtropics in the 20–25-km height region. A similar latitudinal structure is also seen in independent column ozone measurements from ground-based and total ozone mapping spectrometer (TOMS)/SBUV observations (e.g., see Fig. 12 of Randel and Wu 2007; Tourpali et al. 2007). The origin of the local minimum in the equatorial midstratosphere has been the subject of recent debate (Lee and Smith 2003; Hood 2004). However, it is a feature of all recent regression analyses of ozone, and our approach has been to employ the most up-to-date available observational analyses of the ozone change rather than 2D model fields as employed by Shibata and Kodera (2005).

We note that the imposed irradiance changes correspond to ∼160 units of F10.7 cm flux, which is rather larger than the average over the last two solar cycles (125 units). To be consistent with the imposed ozone changes, which are taken from an analysis of observed data over the past two solar cycles, the results of the irradiance experiments have been scaled by 125/160.6.

The FDH calculations are performed only above the (latitudinally and seasonally varying) tropopause. The baseline climatology and baseline solar irradiance are assumed to be representative of solar-neutral conditions so that solar maximum and minimum conditions are simulated by either adding or subtracting 50% of the irradiance or ozone perturbations.

Experiments were performed to assess the possible nonlinearity of the responses to the combined irradiance and ozone changes. The temperature response calculated with both irradiance and ozone perturbations present was compared with the sum of the results from the individual irradiance-only and ozone-only perturbation experiments. There was found to be negligible difference between the combined runs and the sum of the individual runs, suggesting that a simple addition of the individual runs was an adequate approximation, so all results presented here use the latter.

3. Temperature response

a. Annual average

In Fig. 2 the annually averaged temperature responses are shown from the experiments in which the irradiance changes and ozone changes were imposed separately (Figs. 2a and 2b) and the sum of these (Fig 2c). As expected from previous studies (e.g., McCormack and Hood 1996; Shibata and Kodera 2005), the main response to the irradiance changes (Fig. 2a) is in the upper stratosphere/lower mesosphere, with warmer temperatures in the solar maximum than the solar minimum. The peak amplitude of 0.6 K is just above the stratopause. The latitude of the peak value shifts from month to month, following the solar declination (not shown). Below the stratopause the temperature response drops off rapidly so that it is only 0.1 K at approximately 10 hPa and is much smaller in the lower stratosphere. Note that extra contour values have been used in this plot compared with the others to show that the values are very small but not zero. There is virtually no latitudinal structure in the lower stratosphere response.

The annually averaged temperature response to the ozone changes (Fig. 2b) has a similar structure in the upper stratosphere, with warmer temperatures in the solar maximum. The equatorial maximum temperature response is 1 K at around 1 hPa, which is the upper limit of the available satellite ozone data. This is a similar magnitude to the imposed irradiance response in Fig. 2a. Below the stratopause, however, the response is very different. Although the amplitude decreases, it does so much less rapidly and has a latitudinal structure, with local maxima in the subtropics centered around 20°–30° at 30–70 hPa (∼20–25 km). There is also a negative region at the equator between 3 and 20 hPa (∼30–40 km) that mirrors the equatorial minimum in the imposed ozone change fields (see Fig. 1).

The temperature response to the combined irradiance and ozone changes (Fig. 2c) shows that in the upper stratosphere the two effects produce peak values of up to 1.6 K over the equator and subtropics just above the stratopause. In the midstratosphere the response is much weaker but is positive everywhere, showing that the negative response due to the ozone changes has been cancelled out by the positive response due to the irradiance changes. This result is very similar to the result of McCormack and Hood (1996), who calculated a response of 1.5–2.0 K in the upper stratosphere and showed that the temperature response minimum in the middle stratosphere (∼30 km) could be explained as a radiative consequence of the insignificant ozone response there. In the lower stratosphere, which McCormack and Hood were unable to analyze owing to lack of ozone data, there is a local temperature maximum between 30 and 70 hPa (∼20–25 km), with a latitudinal structure that is driven by the response to ozone changes, with local maxima at 20°S and 20°–30°N.

The relative contributions of the irradiance and ozone changes are illustrated in Fig. 3, which shows the temperature response to the ozone changes (shown in Fig. 2b) divided by the temperature response to both changes (shown in Fig. 2c), expressed as a percentage. Figure 3 shows that below 10 hPa the response is dominated by the imposed ozone changes.

Between ∼1 and 10 hPa, on the other hand, the temperature response is primarily a result of the changes in irradiance but with an ∼30%–40% contribution from the ozone changes.

b. Seasonal evolution

The left column of Fig. 4 shows the ozone percentage changes from solar maximum to solar minimum in selected months (W. Randel and F. Wu 2008, personal communication) to illustrate the seasonal evolution of the perturbations. Note that these are the actual percentage changes imposed on the model to represent the change from solar minimum to solar maximum and not the percentage change per unit 100 units of F10.7 cm flux as shown in Fig. 1.

There is a substantial interhemispheric and seasonal asymmetry in these ozone changes. In March and June there are much larger changes in the Northern Hemisphere than in the Southern Hemisphere throughout the whole depth of the stratosphere. A similar mirror image interhemispheric difference is evident in September and December, although the overall hemispheric asymmetry is less in this latter period. These interhemispheric and seasonal asymmetries in the imposed ozone changes are reflected in the calculated temperature response. The middle column of Fig. 4 shows the temperature response when only the ozone changes are imposed; the right column shows the temperature response when both solar irradiance and ozone changes are imposed. A comparison of these confirms that the ozone changes dominate the response in the lower stratosphere and are responsible for producing the interhemispheric and seasonal asymmetries.

We note that a small subtropical ozone anomaly is present (Fig. 4, left column) in the northern lower stratosphere (∼20–25 km) at the end of winter (March), with a corresponding feature in the temperature response: these features remain throughout the summer until at least September. A similar but smaller local maximum is also present in the southern subtropics at ∼20–25 km in September and is still present in December. The longevity of these features may be a reflection of the long chemical lifetime of ozone at these levels, which means that an anomaly produced each spring, perhaps by an anomalous Brewer–Dobson circulation strength, may still remain throughout the summer (Fioletov and Shepherd 2005). On the other hand, the double maximum structure in the subtropics of the lower stratosphere, which is particularly evident in Fig. 4 in June through December, is also similar to the observed structure of the ozone quasi-biennial oscillation (QBO) (Gray and Pyle 1989; Baldwin et al. 2001), so there may be contamination due to nonlinear interaction between the 11-yr solar cycle and the QBO that cannot easily be separated by the linear regression analysis employed to extract the solar cycle variations in ozone. Caution is also required in the interpretation of features in the individual months owing to the limited data record; however, it is encouraging that the features are coherent from one month to the next and thus do not appear to be random noise.

4. Radiative forcing

The RF of climate change due to changes in total solar irradiance, and the associated ozone changes, is an important aspect of the impact of solar variability. The adjusted RF at the tropopause (see, e.g., Hansen et al. 2005; Forster et al. 2007) is the principal metric reported here; the impact of stratospheric temperature changes, calculated using FDH, is accounted for in the calculation of RF. It is recognized that RF is an imperfect measure of the size of climate change mechanisms, but nevertheless it remains a valuable and widely used indicator (e.g., Hansen et al. 2005; Forster et al. 2007). Of particular importance here is that the 11-yr SC forcings are not directly comparable to the effects of slowly varying forcings (such as those due to the steady increase in carbon dioxide); the oscillatory nature of the SC forcing, at a frequency which is high compared to the response time of the climate system, means that the climate system only has time to partially respond to this forcing (see, e.g., section 2 of Wigley et al. 2005).

One further issue concerns the so-called “efficacy” of climate change mechanisms, which is a measure of the climate sensitivity for a given climate forcing relative to that for a doubling of carbon dioxide. The only published estimate for spectrally varying solar irradiance changes, known to us, is from Hansen et al. (2005); they find that the efficacy varies from 0.83 to 0.92 depending on the size of the forcing, indicating that, per W m−2 of forcing, solar variability is slightly less effective in changing surface temperature than carbon dioxide. However, as shown by Forster et al. (2007; see especially their Fig. 2.19), the intermodel spread in efficacies is large for other forcings, although in the case of spectrally constant changes in solar irradiance there is at least some consistency in that all available model results indicate that the efficacy is equal to or less than 1.

There appear to be surprisingly few reported calculations of the RF due to spectrally varying solar forcing. Haigh (1994) reports calculations but does not separate out the impact of TSI changes from her model-derived changes in ozone due to the SC. Hansen et al. (2005) briefly report forcings, derived using the Lean et al. (1997, 2005) spectrally varying TSI, and compare these to the effect of spectrally constant changes.

More commonly, the SC RF is reported as
i1520-0469-66-8-2402-e1
where the factor of 4 comes from the ratio of the actual surface area to the cross-sectional area of the planet. [See, e.g., Forster et al. (2007). As noted in their footnote 11, this method of estimation neglects any wavelength dependence of the TSI changes and absorption within the stratosphere. It also assumes that the spectrally averaged planetary albedo is appropriate for the albedo at wavelengths at which the solar variability occurs.]

The solar minimum to maximum irradiance changes used here are taken from Lean et al. (1997) and Lean (2000) and cover the region from 200 to 855 nm at 1-nm resolution. Lean et al. (2005) show that these changes are in good agreement with more recent observations. As described in section 2, the actual change imposed corresponds to the irradiance at a particular solar minimum (September 1986) and solar maximum (November 1989). The wavelength-averaged change in TSI imposed here is 0.96 W m−2, which takes into account the 125/160.6 scaling (discussed in section 2) to make the values more applicable to a typical solar cycle.

a. Spectrally averaged radiative forcing due to solar irradiance change

Figure 5a shows the annual and zonal-mean spectrally averaged RF from solar minimum to solar maximum for the irradiance changes alone, as well as the sum of the irradiance and ozone RF. The global-mean irradiance RF is 0.136 W m−2, of which 93% is the direct effect of TSI changes (i.e., this is the instantaneous RF of 0.127 W m−2) and 7% is the longwave RF owing to the warming of the stratosphere due to the increased TSI.

Since the TOA forcing is 0.175 W m−2, this indicates that the RF is only 78% of the TOA forcing. The mechanisms that lead to this reduction will be discussed in section 4c. The reduction of the TOA forcing is not taken into account in, for example, the Intergovernmental Panel on Climate Change RF estimates (Forster et al. 2007), although they estimate, giving few details, that the RF/TOA ratio would be about 0.81 (see their footnote 11). The reduction calculated in our study is slightly greater than that reported by Hansen et al. (2005). For the 1880–2000 spectrally resolved TSI change, they give an RF of 0.30 W m−2 for a 0.36 W m−2 TOA forcing (M. Sato and R. Ruedy 2008, personal communication), giving an RF/TOA ratio of 0.83. This can be considered an update to a very brief discussion in Hansen et al. (1997) (and referred to in Forster et al. 2007), where a value of 0.86 is postulated (based on calculations for “a typical zenith angle”). Possible reasons for the lower value derived here include the fact that this study uses a higher spectral resolution (1 nm versus 5 nm in the ultraviolet) and has a better resolved stratosphere; other possible reasons include differences in such factors as the ozone climatology and the derived planetary albedo in each of the studies.

It is also useful to compare the TOA forcing with that estimated using Eq. (1), as this routinely uses the spectrally averaged planetary albedo. In our case, the global-mean spectrally averaged albedo is 0.26 and application of Eq. (1) would yield an RF of 0.178 W m−2 compared to the TOA forcing of 0.175 W m−2 calculated using the detailed radiation code; this indicates that the use of the spectrally averaged albedo does not lead to a significant bias, at least in the global mean.

b. Spectrally averaged radiative forcing due to ozone change

The RF due to the solar-induced changes in ozone is 0.004 W m−2, computed over the latitude range 56°S–56°N for which the ozone data is available, and so represents a small enhancement of the irradiance forcing. Figure 5b indicates that the forcing is greatest in northern midlatitudes where the ozone signal is largest. There are only a few contemporary estimates, which have used observed SC-induced ozone changes, with which to compare this value. Hansen et al. (2005) report that they consider it “small.” Isaksen et al. (2008) also find a small forcing and show that the sign of this forcing depends on the source of solar-cycle-induced ozone data used, with a range from −0.005 to 0.008 W m−2. The small ozone forcing is, in fact, due to strong compensation between a shortwave forcing of −0.038 W m−2 and a longwave forcing of 0.042 W m−2, as shown in Fig. 5b. Both shortwave and longwave forcings peak locally with magnitudes of 0.15 W m−2 at 30°N in springtime (not shown), coincident with the largest ozone changes. These individual forcings are much more substantial fractions of the irradiance forcing. As it is possible that the longwave and shortwave forcings do not have the same efficacies, some caution is necessary in assuming that they are negligible, and careful GCM experiments would be necessary to help establish this.

c. Mechanisms for differences between TOA forcing and radiative forcing

In this section, the mechanisms leading to the reduction of the tropopause RF below its TOA value are considered. The focus will be on the direct solar forcing (rather than the net solar plus longwave forcing), as it is the reduction in the solar forcing that is the key issue. In this case, for the global mean, the shortwave RF/TOA value (henceforth SWRF/TOA) ratio is 0.72, a smaller ratio than for the total forcing, because the contribution of the longwave forcing partially compensates for the shortwave reduction.

Figure 6 shows the SWRF/TOA ratio as a function of month and latitude. Clearly, for much of the planet, the value is in excess of 0.65. However, at high latitudes values significantly lower than 0.5 can be seen. To understand the processes leading to this reduction, Fig. 7 shows the spectrally resolved irradiances at two times and locations: the equator in October, where the spectrally averaged SWRF/TOA ratio is 0.75, and 76°N in April, where the ratio is 0.41. Figure 7 shows the change in incoming TOA irradiance between solar minimum and solar maximum, the change in the net (i.e., downwelling minus upwelling) TOA irradiance, and the change in the net tropopause irradiance (i.e., the spectrally resolved solar RF). The figure focuses on the wavelength region 190–690 nm, as at longer wavelengths the SWRF/TOA ratio is 0.9998 and 0.9892 at the two locations, respectively; this indicates that near-infrared absorption does not contribute significantly to the reduction of the solar forcing at the tropopause. Table 1 summarizes the results of Fig. 7 over wide spectral intervals.

Figure 7 (top) shows, as expected, that at wavelengths less than 300 nm, the strong ozone bands absorb almost all of the incoming radiation so that a negligible SC variation directly reaches the tropopause; Table 1 shows that SWRF/TOA is less than 0.004. Since almost 20% of the wavelength-integrated SC variability is at these shorter wavelengths, it is little surprise that the total SWRF/TOA ratio is less than 0.8. Figure 7 (top) also shows a small effect of the Chappuis ozone absorption band, most marked between 500 and 600 nm, which further contributes to the reduction of the SWRF over its TOA value; Table 1 shows the SWRF/TOA ratio is 0.96 in the 450–691-nm region.

The situation at 76°N in April (Fig. 7, bottom) is dramatically different. First, and most importantly, the spectrally averaged planetary albedo (0.65 compared to 0.20 in October at the equator) is much higher. The increase in planetary albedo is almost all at wavelengths greater than 300 nm—the planetary albedo at shorter wavelengths is essentially zero because of the near-complete absorption of solar radiation by ozone. Hence, although the proportion of the SC TSI variations in the ultraviolet is, of course, the same as at lower latitudes, the contribution of these ultraviolet changes to the wavelength-integrated change in the net TOA irradiance is much larger. Table 1 shows that wavelengths less than 300 nm contribute almost 40% to the TOA change: As this 40% is almost entirely absorbed before it reaches the tropopause, the SWRF/TOA ratio is consequently much smaller than at lower latitudes. Figure 7b also shows that the impact of the Chappuis bands is much enhanced compared to lower latitudes because of both the much higher total-column ozone at high latitudes and the longer mean path length through this ozone. Table 1 shows that the SWRF/TOA ratio is about 0.6 in the 450–691-nm region, which further lowers the SWRF/TOA ratio when averaged over all wavelengths. It is notable that, in this case, the spectrally averaged albedo is 0.65, whereas the effective albedo for solar cycle variations, which can be derived from Table 1, is somewhat less (0.59) since at high latitudes a higher proportion of the absorbed radiation is in the ultraviolet.

In summary, this section has shown that the assumption that the solar cycle RF can be approximated using Eq. (1) leads to a significant error. There is negligible error (at least for the global mean) in assuming that the wavelength-averaged planetary albedo is appropriate, despite the fact that the SC changes are such a strong function of wavelength, but a significant error arises because of the absorption of solar radiation in the stratosphere.

On the global average, the wavelength-averaged SWRF is 0.72 of the change in TOA net irradiance. The reduction in SWRF is partially compensated by the increased temperature and hence infrared emission from the stratosphere at solar maximum, giving a RF/TOA ratio of 0.78 in our calculations.

Forster et al. (2007) adopt Eq. (1) on three grounds: first, that the RF/TOA ratio (which they estimate to be 0.81) is a small correction; second, because it may to some extent be compensated by SC-induced ozone changes; and third, because “the corrections are not routinely reported in the literature.” Our work shows that, while their estimate of 0.81 is quite close to the value estimated using the detailed analysis here, application of Eq. (1) leads to a significant bias in the reporting of the solar cycle RF, and we can see no reason for not applying the correction, despite the fact that it hitherto has not been done. Although the SC-induced ozone RF calculated here does, indeed, partially compensate for the reduction, the effect is small (the ozone RF is 4% of the irradiance forcing) and is much more uncertain—the net ozone RF is a small residual of opposing shortwave and longwave forcings and hence even the sign of this forcing must be in some doubt.

Clearly, there may be a dependence of our results on both the radiative transfer code used here and the background climatology; hence, further work in this area is justified.

5. Comparison with observational estimates

There is some discrepancy between the results of the various observational temperature analyses that are available to compare with the FDH results in Fig. 2. Figure 8 shows estimates of the observed solar maximum minus minimum temperature difference from multiple regression studies of three different datasets. In Fig. 8a, reproduced from Ramaswamy et al. (2001a), see also Randel et al. (2009), the SSU/MSU satellite observations for the period 1979–96 were used. The regression analysis included a linear trend term as well as the solar term. The input data have been adjusted to take into account jumps due to the transition from one satellite instrument to the next. Figure 8b shows a similar regression analysis of the NCEP/NCAR reanalysis for the period 1979–2001 by Haigh (2003) (see also Gray et al. 2005). In addition to the solar and linear trend term, this regression analysis included estimated contributions from the QBO, ENSO, volcanic aerosol, and the North Atlantic Oscillation (NAO). Note that the data extends only to 10 hPa. Finally, Fig. 8c shows the equivalent results for 1979–2001 from the ECMWF Reanalysis dataset (ERA-40) (Uppala et al. 2005), updated from Crooks and Gray (2005). (The monthly-mean processing in the original Crooks and Gray analysis was incorrect. The corrected results shown in Fig. 8c are very similar to those original results except that the lower stratospheric maximum has less variation with latitude so that the subtropical maxima are now less pronounced). The ERA-40 regression analysis included all the terms employed by Haigh. We note here that assimilation of the SSU/MSU observations is the main source of stratospheric temperature in both the NCEP/NCAR and ERA-40 datasets, in addition to radiosonde observations up to ∼30 km. However, the input SSU/MSU data were not corrected for instrumental changes in either the NCEP/NCAR or the ERA-40 data assimilations.

We note that the quality of the estimated SC signals from the ozone and temperature regressions in Figs. 1 and 8 is subject to considerable uncertainties. Ideally such regressions would be obtained over many solar cycles from either a single stable instrument or a series of carefully cross-calibrated instruments. In addition, since we employ the SC ozone regression estimates to drive the FDH model and then compare these with SC temperature regression estimates, there is a danger that any consistency may be due to the spurious presence of an 11-yr signal, unrelated to the SC, introduced by the regression method. Nevertheless, the available regression estimates represent our best observational evidence of the size of the SC-driven changes in the stratosphere while bearing in mind the limitations of the datasets employed.

The equatorial maximum near the stratopause in the SSU/MSU analysis (Fig. 8a) is barely half the amplitude of the corresponding ERA-40 signal (Fig. 8c) and the vertical structures are very different. The SSU/MSU data (see also Hood et al. 1993; McCormack and Hood 1996; Scaife et al. 2000; Hood 2004) show a single, deep equatorial maximum that extends from the stratopause down to ∼20 km, with a maximum near 4 hPa and little evidence of the secondary maximum at around 20 km seen in the ERA-40 analysis. These differences seem surprising at first. As already noted, the SSU/MSU satellite is the only source of assimilated data in the upper stratosphere of the ERA-40 analysis, so one might expect their solar signals to be very similar. However, the ERA-40 dataset is produced by a combination of the assimilated data and the internal model dynamics. Since the model extends into the lower mesosphere, it has the potential to respond to small changes in temperature and wind structure in the upper stratosphere through changes in planetary wave propagation (Kodera 1995). Changes in planetary wave propagation impact the Brewer–Dobson circulation, which has its greatest meridional flow near the stratopause level, and hence the strength of the solar signal maximum near the stratopause and also its vertical gradient could be influenced in this way.

At low and midlatitudes, the FDH modeled temperature response to the imposed irradiance and ozone changes (Fig. 2c) shows a marked similarity to the ERA-40 temperature distribution (Fig. 8c). The ERA-40 estimates have a maximum response of 1.25–1.75 K just below the equatorial stratopause at 2 hPa between ±20°, whereas the FDH modeled response is ∼1.2–1.6 K. The model does not reproduce the negative response near the stratopause at mid to high latitudes, suggesting that this is primarily controlled by direct dynamical influences on the temperature field that are not present in the FDH model. The local equatorial minimum at around 10 hPa (which is not statistically significant in the ERA-40 estimate) and the second maximum in the lower stratosphere are both reproduced by the FDH model. The latitudinal structure in the lower stratosphere in Fig. 2c is also similar to both the ERA-40 and NCEP/NCAR estimates (Figs. 8b and 8c), with local maxima in each of the subtropics, although the peak values are slightly smaller, with 0.3–0.4 K compared to ∼0.75 K in the ERA-40 and NCEP/NCAR estimates.

We note here that the reason for similarity of the FDH modeled results with the ERA-40 and NCEP/NCAR estimates is not because they are all produced by models with the same ozone fields. For example, the model employed to produce the ERA-40 dataset did not employ observed ozone distributions in its radiation scheme (Dethof and Holm 2002). Instead, the climatology of Fortuin and Langematz (1995) was used every year, thus excluding the possibility of an 11-yr cycle in the ozone fields. In addition, the radiative transfer code used in the ERA-40 analysis does not include the solar-cycle driven changes in TSI.

One possibility for the discrepancy between the SSU analysis and the ERA-40 and NCEP analyses is the relatively poor vertical resolution of the SSU/MSU data. To explore this hypothesis, Fig. 9 shows the FDH temperature response due to the imposed irradiance and ozone changes (i.e., Fig. 2c) but sampled as if the values had been measured by the SSU/MSU instruments. This was achieved by taking each individual vertical profile of the modeled temperature and weighting it by the value of the appropriate weighting function for each satellite channel. This gives the temperature profile that would be sensed by each satellite channel if the modeled results were the real atmosphere. These results were additionally degraded from 4° latitudinal resolution to the 10° latitudinal resolution of the SSU/MSU analyses. The resulting data were plotted in Fig. 9 by sampling the temperature profiles at the characteristic pressure for each channel and then contouring these point values, which is the usual way that the satellite results are presented. The results have also been plotted using the same axes and contours as Fig. 8a to aid comparison, although Fig. 9 only extends up to ∼46 km, as the information above this height comes from the 47X channel, which is centered on 0.5 hPa and has the majority of its weighting function in the mesosphere, so there is insufficient information from the FDH calculation to represent it.

A substantial degradation of both the structure and amplitude of the FDH model response is evident (cf. Figs. 2c and 9), and the overall response pattern now compares better with the SSU/MSU estimates than the ERA-40 estimates. The main temperature response in the region of the equatorial stratopause has been reduced in amplitude from 1.6 to 0.9 K and has been shifted down in height by 6–8 km so that the peak response is now at 2 hPa (∼44 km). The vertical gradient in the region of 40 km has been substantially reduced. Most notably, the structure in the lower and middle stratosphere has been severely degraded so that the double peak structure in the vertical has disappeared and the variation with height is now monotonic. Indeed, there is now even less height structure in the FDH response than in the SSU/MSU estimate, suggesting that the FDH model has, if anything, underestimated the lower stratosphere response, possibly because the FDH formulation excludes the dynamical response to the imposed irradiance changes. In addition, the latitudinal structure in the lower stratosphere has been severely degraded so that the double peaked structure is no longer evident.

The overall difference between the original FDH model response (Fig. 2c) and the degraded response (Fig. 9) is similar to the difference between the ERA-40 and SSU/MSU estimates. Based on these results, we suggest that the relatively poor sampling of the SSU/MSU instruments may be a major explanation for the apparent discrepancies between the ERA-40 and SSU/MSU solar responses.

6. Discussion

The primary proposed mechanism for a dynamical influence on the 11-yr SC signal in lower stratospheric temperature is through a modification of the Brewer–Dobson circulation—either its strength (Kodera 1995; Kodera and Kuroda 2002) or its timing (Gray et al. 2004). This change in circulation is associated with extratropical planetary wave propagation. Weaker wave forcing in the solar maximum than in the solar minimum gives rise to a weaker Brewer–Dobson circulation and, hence, reduced adiabatic heating and cooler temperatures at mid to high latitudes. Regions of negative temperature anomalies at high latitudes in the SSU/MSU and ERA-40 estimates (Fig. 6) support this hypothesis although statistical significance is difficult to achieve because of the high variability in this region. At low latitudes the corresponding weaker equatorial upwelling at solar maximum would cause warmer equatorial temperatures than at the solar minimum, which is again supported by the estimates in Fig. 8.

However, employing the FDH approach specifically excludes the direct influence of dynamical effects on the temperature field; yet, the FDH model response has a temperature maximum in the lower equatorial stratosphere whose structure compares reasonably well with the ERA-40 and NCEP/NCAR estimates. An explanation of this surprising result is that changes in the Brewer–Dobson circulation will also influence the transport of ozone that can then indirectly impact the temperature fields. Reduced tropical upwelling during solar maximum results in the decreased transport of ozone-poor air from below, and vice versa during solar minimum. Through diabatic heating this process would result in anomalously high temperatures in the solar maximum and low temperatures in the solar minimum, as seen in Figs. 2b and 8. Hood (2004) has shown that the decadal variation in υT ′ at 20 hPa, 60°N (see also Hood and Soukharev 2003), which is a measure of planetary wave activity, is inversely correlated with the tendency of tropical (20°S–20°N) column ozone amounts from TOMS/SBUV (see Fig. 10 in Hood 2004), which supports the presence of this mechanism. This indirect effect will be present in the FDH model integrations because we have imposed ozone from observations. Because many of the observed temperature characteristics are reproduced when the ozone fields are imposed, our results therefore suggest that the Kodera mechanism may act not only directly on the temperature field but also indirectly through the redistribution of ozone.

These results suggest that to reproduce the observed response of stratospheric temperature to the 11-yr solar cycle in the lower stratosphere, a realistic ozone distribution is essential. Our results contrast with the conclusion of Shibata and Kodera (2005), who stated that the FDH formulation could not reproduce the observed lower stratospheric warming in the tropics (see their abstract), thereby suggesting that direct dynamical influences on temperature may be the prime cause of the equatorial lower stratosphere signal. The major difference between the two studies is the imposed distribution of ozone changes. They employed estimated ozone changes from two different offline 2D model calculations (Haigh 1999; Shindell et al. 1999), whereas in this study estimations from observations were employed (Randel and Wu 2007). Two-dimensional modeled estimates of ozone changes associated with the solar cycle are now known to compare poorly with observations (Hood 2004). Our results suggest an important role for the indirect dynamical influence through the redistribution of ozone, which had been previously overlooked. We also note, therefore, the importance of including a realistic representation of the SC ozone changes in climate change scenarios (such as the IPCC “all forcings” scenario).

In addition to large-scale Brewer–Dobson circulation changes associated with the SC (Kodera 1995; Kodera and Kuroda 2002), modification of the QBO by the SC has been proposed (Salby and Callaghan 2000, 2006; McCormack 2003; McCormack et al. 2007; Pascoe et al. 2005; Soukharev and Hood 2006) and this may affect the local QBO-induced circulations in the lower equatorial stratosphere. Although the FDH approach excludes a direct influence of this on the temperature fields, it will include the indirect effect through the ozone distribution. Indeed, the latitudinal structure of both the ozone (Fig. 1) and temperature solar cycle responses (Fig. 2c) between 30°S and 30°N near 20–25 km are similar to the latitudinal structure of the ozone QBO (Gray and Pyle 1989; Baldwin et al. 2001), as noted earlier. In contrast to the induced circulation changes associated with the Brewer–Dobson circulation, which is broad and extends across the whole of the winter hemisphere, the circulation pattern of the QBO is much more confined to equatorial/subtropical latitudes (30°S–30°N). During a descending westerly phase of the QBO there is relative downwelling (reduced ascent) at the equator and a corresponding relative upwelling near 30°. This produces a positive ozone anomaly over the equator and negative anomalies in the subtropics. During a descending easterly, the reverse pattern is set up, with a negative ozone anomaly over the equator and positive anomalies in the subtropics. Recent evidence from radiosonde observations (Salby and Callaghan 2000, 2006) has suggested that the 11-yr solar cycle influences the length of the QBO period, although this has been questioned by Hamilton (2002). Specifically, the length of the easterly phase does not appear to be affected by the solar cycle, but the observed westerly phase of the QBO is shorter during solar maximum periods. This means that the effects of the westerly QBO phase anomaly on the ozone (more over the equator, less in the subtropics, as explained above) will be reduced during solar maximum, resulting in a local negative ozone anomaly over the equator and positive anomalies in the subtropics during solar maximum. This is in the correct sense to explain the latitudinal ozone distribution in Fig. 1, although more years of observations will be required to confirm whether the latitudinal double peak structure in the lower stratosphere ozone signal (Fig. 1) and the ERA-40 and NCEP/NCAR estimates (Figs. 8b and 8c) is real or not. There is a possibility that the local minimum near the equator could be due to an artifact of the poor sampling of the SAGE instrument at low latitudes owing to the solar occultation viewing. This results in sparse measurements and hence less statistical significance of the signal at these latitudes (Soukharev and Hood 2006). Nevertheless, the similarity between this structure in the FDH temperature response (Fig. 2c) and the NCEP and ERA-40 analyses (Figs. 8b and 8c) suggests that it may be real.

7. Summary and conclusions

A fixed dynamical heating (FDH) model has been used to determine the contribution to the 11-yr SC signal in temperature associated with (i) irradiance changes and (ii) ozone changes. The temperature response due to the combined irradiance and ozone changes (Fig. 2c) was approximately 1.6 K in the upper stratosphere, with a much weaker positive response in the midstratosphere. This is in good agreement with observations and previous FDH calculations. In addition, a secondary maximum of ∼0.4 K was present in the lower stratosphere, whose magnitude and structure compared well with results from the ERA-40 analysis of Crooks and Gray (2005). The temperature response in the upper stratosphere was shown to be primarily due to the imposed irradiance changes and in the lower stratosphere it was primarily due to the imposed ozone changes (Fig. 3).

The lower stratospheric maximum was not reproduced in a similar FDH study by Shibata and Kodera (2005), who imposed a simple ozone change from 2D model calculations. Because of this they concluded that FDH calculations could not reproduce this secondary maximum, suggesting that the presence of dynamical processes acting directly on the temperature field is required. We have shown that imposing more realistic ozone changes from observations allows the feature to be reproduced, albeit with reduced amplitude. Our results suggest that the impact of changes to the Brewer–Dobson circulation may be acting not just through its direct impact on the temperature field (a process excluded by the FDH approach) but also indirectly through its impact on ozone transport and hence diabatic heating. We therefore note the importance of including a realistic representation of SC ozone changes in climate change scenarios.

The height structure of the FDH temperature response was much closer to that of the ERA-40 analysis (Fig. 8c) (Crooks and Gray 2005) than that of the SSU/MSU estimate (Fig. 8a), which has a much weaker, broader distribution and does not display a double peak structure in the vertical. Degrading the FDH model results by sampling the temperature data using the SSU/MSU weighting functions gave temperature distributions that were much closer to the SSU/MSU results, suggesting that the poor vertical resolution of the SSU/MSU observations can explain much of this discrepancy (Fig. 9).

The radiative forcing calculations show the dominance of the irradiance change over the ozone change but indicate that the ozone forcing leads to a small enhancement of the forcing, in contrast to that suggested elsewhere (see, e.g., the discussion in section 6.11.2.1 of Ramaswamy et al. 2001b). In addition, use of the spectrally resolved irradiances shows that the standard definition of the forcing (at the tropopause, following stratospheric adjustment) is 78% of the instantaneous forcing at the top of the atmosphere, which is often quoted for the TSI forcing. We recommend that, in the future, the solar cycle forcings should take into account this reduction.

Acknowledgments

We should like to express our thanks to Judith Lean and Bill Randel for providing the irradiance and ozone data, respectively, and especially for the very helpful advice on the use of their data, and to Makiko Sato and Reto Ruedy for discussion of the solar forcings in their model and Tom Frame for the corrected version of the Crooks and Gray plot in Fig. 8c. S. T. Rumbold was supported by a Natural Environment Research Council (NERC) doctoral grant. L. J. Gray was funded through the NERC National Centre for Atmospheric Sciences. Support from NERC (Grant NE/C510383/1) is also acknowledged. We thank the referees and K. K. Tung for their comments.

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Fig. 1.
Fig. 1.

Pressure–latitude cross section of estimated annual-mean, zonal-mean percentage change in ozone volume mixing ratio per 100 units of F10.7 cm radio flux for the period 1979–2005, from a regression analysis of SAGE data, adapted from Fig. 12 of Randel and Wu (2007). Values shown in this figure should be multiplied by 1.25 to obtain the average solar minimum to maximum solar changes over the period. Shaded areas are not statistically significant. Contour interval is 1%; dashed contours denote negative values.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2866.1

Fig. 2.
Fig. 2.

Pressure–latitude cross section of annual-mean, zonal-mean change in temperature (K) using fixed dynamical heating calculations with (a) imposed spectrally resolved solar irradiance changes from Lean (2000) and (b) imposed zonally averaged ozone changes from Randel and Wu (2007). (c) The sum of the imposed solar irradiance and ozone changes. The annual means were calculated as the average of the individual monthly-averaged values. Contour interval is 0.1 up to 0.6 and 0.2 thereafter. Three additional contours of 0.0125, 0.025, and 0.05 have been inserted in (a) for clarity.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2866.1

Fig. 3.
Fig. 3.

Pressure–latitude cross section showing the ratio of the FDH temperature response due to the imposed ozone changes (Fig. 2b) vs the total response due to both irradiance and ozone changes (Fig. 2c), expressed as a percentage. Contour interval is 10%; the thick line denotes the 50% value.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2866.1

Fig. 4.
Fig. 4.

Pressure–latitude cross sections showing seasonal evolution of the imposed ozone changes and FDH model temperature response. (left) Imposed ozone changes (%) from Randel and Wu (2007), multiplied by 1.25 to obtain minimum-to-maximum change. Contour interval is 1%. (middle) FDH temperature response (K) when these ozone changes are imposed. (right) FDH temperature response (K) when both solar irradiance and ozone changes are imposed. Contour interval is 0.1 K up to 0.6 K and 0.4 K thereafter. Dashed contours denote negative values.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2866.1

Fig. 5.
Fig. 5.

Annually and zonally averaged radiative forcing (W m−2) at the tropopause from the FDH model, including the effect of stratospheric temperature adjustment. Forcing due to (a) the spectrally resolved change in total solar irradiance (solid line) and the sum of the irradiance and ozone changes (dashed line) and (b) the solar cycle–induced ozone change, showing the net forcing and the individual shortwave (SW) and longwave (LW) components. The annual means were calculated as the average of individual monthly averaged values.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2866.1

Fig. 6.
Fig. 6.

Latitude–month variation in the ratio between the shortwave radiative forcing at the tropopause and the net change in shortwave irradiance at the top of the atmosphere for the change in total solar irradiance between solar minimum and solar maximum.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2866.1

Fig. 7.
Fig. 7.

Spectral variation in shortwave radiative forcing (W m−2 nm−1) for the change in TSI between solar minimum and solar maximum for (top) the equator in October and (bottom) 76°N in April. The dotted curve shows the change in downwelling irradiance at the top of the atmosphere (TOA), the solid black curve shows the change in the net irradiance at the TOA, and the gray curve shows the change in the net irradiance at the tropopause.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2866.1

Fig. 8.
Fig. 8.

Cross section of SC change in temperature (K) from minimum to maximum estimated from (a) SSU/MSU data, 1979–96, reproduced from Ramaswamy et al. (2001a); (b) NCEP/NCAR reanalysis, 1979–2001, adapted from Haigh (2003); and (c) ERA-40 reanalysis dataset, 1979–2001, from Crooks and Gray (2005) but corrected for an error in monthly-mean calculations; see text. Contour interval is 0.25; dashed contours denote negative values. Shading represents 95% statistical significance.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2866.1

Fig. 9.
Fig. 9.

Pressure–latitude cross section showing the annual-mean, zonal-mean FDH temperature response (K) due to both the imposed irradiance and ozone changes (as in Fig. 2c) but sampled using the SSU/MSU weighting functions. Contour interval is 0.25 K to allow comparison with Fig. 8a.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2866.1

Table 1.

Solar minimum to solar maximum changes in TOA downward and net irradiance and the tropopause shortwave radiative forcing (SWRF) (W m−2) and the ratio of SWRF/TOA (net) for the equator in October and 76°N in April, averaged over various wavelength intervals.

Table 1.
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