Stratospheric ozone responses to the 11-year solar flux variation are calculated from two different decadal scale satellite ozone data sets by multiple regression analysis. The results show consistent dipole structures with solar regression coefficients that are positive in midlatitudes and negative in the equatorial lower stratospheric region. Because of the limited duration of the data record, the regression analysis may not completely separate variability from other processes. Other phenomena that could contribute to the observed pattern include the ozone variations associated with the quasi-biennial oscillation (QBO) and with two major volcanic eruptions: El Chichón in 1982 and Mount Pinatubo in 1991. A fully interactive NCAR two-dimensional chemical-dynamical-radiative model (Simulation of Chemistry, Radiation, and Transport of Environmentally Important Species (SOCRATES)) is used to investigate the effects of the equatorial QBO and the major volcanic eruptions on the 11-year solar cycle analysis. When both effects are considered in the model simulation, the resulting ozone solar signal shows a dipole pattern similar to that observed. When the 11-year solar flux variation is considered as the only external forcing, the resulting ozone solar cycle shows a monopole structure whose maximum is located in the equatorial upper stratosphere and whose response is uniformly positive.
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 Both observational analyses and modeling have shortcomings. The most serious problem in the data analysis is the limitation of the data records. Although more than two decades of stratospheric ozone data have now been accumulated [Rind et al., 1999], they are from different instruments which have different instrumental and retrieval errors. This makes it very difficult to verify trends and variations, even in the case where their errors are systematic and each data record is more than 11 years. This is further complicated because other factors like the quasi-biennial oscillation (QBO), the long-term trend of ozone, and two major volcanic eruptions in 1982 and 1991 in the tropical region interfere with the 11-year ozone solar signal.
 Determination of the ozone solar cycle from observations normally uses either a simple deduction method that calculates the difference between the ozone distribution during solar maximum conditions and that during solar minimum conditions or a multiple linear regression method. Both methods are influenced by other factors like the QBO or volcanic eruptions. The QBO of ozone has a well-documented characteristic structure [Baldwin et al., 2001] and has a periodicity that closely follows that of the equatorial zonal wind QBO. The stratospheric ozone perturbation induced by the zonal wind QBO is the most dominant component of interannual variation of stratospheric ozone and its periodicity and magnitude are variable. Although the ozone QBO is produced by dynamics associated with the equatorial zonal wind QBO and its interaction with the annual oscillation [Gray and Dunkerton, 1990], its magnitude is not linearly proportional to that of the zonal wind QBO. This makes it hard to remove the ozone QBO component, which is much bigger than the reported ozone solar cycle, from the interannual variation of ozone.
 In addition, two major volcanic eruptions in the equatorial region separated by 9 year intervals also cause ozone changes that are hard to isolate from the ozone solar cycle [Solomon et al., 1996; Callis et al., 1997; McCormack et al., 1997] and the longer-term ozone trend [Fusco and Salby, 1999; Randel et al., 2000]. Although there have been frequent volcanic eruptions like Sierra Negro in 1979, St. Helens in 1980, Nevado del Ruiz in 1985, and Kelut in 1990, not all of them have strong effects on stratospheric aerosol [Thomason et al., 1997a]. Two volcanic eruptions, El Chichón in 1982 and Mount Pinatubo in 1991, occurred during or right after sequential solar maxima; the resulting enormous increases in sulfate aerosol in the equatorial lower stratosphere induced significant lower stratospheric ozone decrease by augmented upward motion for several years [Tie et al., 1994; Rosenfield et al., 1997; Seol and Yamazaki, 1998]. These lead to another long-term variation of ozone that interferes with ozone solar cycle analysis. Yet another difficulty is that ozone variations induced by trends in anthropogenic gases that are not linear with time can be difficult to distinguish from cyclic changes with a short data record.
 Numerical simulations can isolate individual effects, but have their own limitations. Results are affected by inaccuracies in the simulated circulation and wave processes. In the stratosphere, a key limitation is the problem that even the most complex models have in simulating the QBO. Another is that the suite of compounds measured is incomplete, so it is not possible to fully validate the complete set of chemical processes. Nevertheless, models provide useful tools for examining physical processes and their roles in affecting variability.
 This study was motivated by an effort to understand why the simulated response of stratospheric ozone to the 11-year UV solar cycle differs from the response deduced from observations. To investigate this, two different satellite ozone data sets are analyzed: the Solar Backscatter Ultraviolet (SBUV) and the Stratospheric Aerosol and Gas Experiment (SAGE) II. The solar cycle in stratospheric ozone induced by the 11-year solar flux variation simulated using a fully interactive chemistry-radiation-dynamics model is compared with that from satellite data. To understand the effects of the QBO and major volcanic eruptions on the ozone solar cycle analysis, additional model simulations are executed. The model and data used for this study are described in section 2. In section 3, the ozone solar cycle signal from the observed data is presented and the analysis limitations and problems are discussed. Section 4 shows the simulated ozone solar cycle and its budget analysis. Comparison of model output and the observational data and discussion of the problems in the solar regression analysis are given in section 5, followed by discussions in section 6.
2. Model and Data Description
 The model used in this study is a fully interactive two-dimensional chemical-dynamical-radiative model [Brassuer et al., 1990; Granier and Brasseur, 1992; Tie et al., 1994]. It is a NCAR community model, called SOCRATES (Simulation of Chemistry, Radiation, and Transport of Environmentally Important Species), on the web at http://acd.ucar.edu/models/open/socrates/socrates.html. Recent improvements in the model are described by Brasseur et al.  and Khosravi et al. . Its vertical range is from the surface to 120 km with 1 km vertical resolution. Its latitudinal range is from 85°S to 85°N with 5 degree interval. The time step for the thermodynamic and chemical transport equations is 1 day in this study. The time step for the radiative heating calculation is 5 days. To consider the diurnal variation of chemical species, the chemical reactions and vertical diffusion are calculated 8 times a day. Advective chemical transport and horizontal eddy transport are calculated on zonal mean fields once per day. In this model, more than 160 chemical reactions describing HOx, NOx, Clx, Brx, Ox, and hydrocarbon chemistry are included. All species are treated individually; i.e., the family method is not used. Ozone is calculated using a full chemical continuity/transport equation [Huang et al., 1998]. To estimate the volcanic effect on the ozone chemistry, heterogeneous reactions on sulfate aerosol particles are considered but heterogeneous reactions on polar stratospheric clouds are ignored in this study. In order to estimate the radiative effects of the volcanic cloud, the aerosol is assumed to be an absorber of solar and longwave radiation. Three levels of randomly overlapped clouds (fractional coverage of 0.37 at 761 hPa, 0.25 at 496 hPa, and 0.35 at 226 hPa) are assumed to represent the perturbation in the longwave aerosol heating rate [Tie et al., 1994].
 Two kinds of interannual forcing, the equatorial QBO and the 11-year solar cycle, are included in the model for this study. To include the effect of the QBO, the following temperature perturbation over the equatorial region is included in the stream function equation as a diabatic forcing, which results in the modification of the meridional circulation.
where H is a scale height (7 km), Ω is an earth rotational frequency, R is an universal gas constant, a is an earth radius, and ϕw is a Gaussian latitude radius (15°). qbo is a composite QBO for zonal wind, expressed by
where max is the maximum zonal wind QBO perturbation (25 ms−1), zmax = 28 km, hqbo is the QBO vertical extent of 24 km, tqbo is a wind descent period (27 months), and zhfwd is a QBO vertical half width (27 km). The zonal wind perturbation is centered over the equator and varies sinusoidally in altitude between 16 km and 40 km with a node between easterlies and westerlies that descends with time [Politowicz and Hitchman, 1997]. With this parameterization, the stratospheric ozone responds to variations in chemical reaction rates induced by the temperature QBO perturbation and to meridional transport induced by the QBO secondary circulation. Note that the modeled equatorial zonal wind responds to the QBO thermal forcing; there is no direct driving by eddy momentum deposition. With this parameterization, the simulated magnitude of the QBO equatorial zonal wind is less than the observed magnitude.
 In the analysis that follows, we account for the model QBO by using a QBO index. Two definitions of this index are applied. The first is the periodicity of the QBO forcing, i.e., an exact sinusoid with a 27-month periodicity. Because the Singapore zonal wind at 30 hPa is used as a QBO index for the satellite data, the second is an index similar to that used for real data, the equatorial wind at 25 km (∼30 hPa) whose annual oscillation is removed. Although a sinusoidal forcing with a 27-month periodicity is imposed in the model as described above, the variation of the resulting equatorial zonal wind at 25 km (∼30 hPa) includes not only this 27-month variation but also the annual oscillation and the volcanic eruption and solar variation effects (Figure 1). By using two different QBO indexes, we can check the sensitivity of the solar regression result to the QBO index.
 The solar flux in the model is assumed to vary in proportion to the solar radio flux at 10.7 cm (F10.7) with time. On time scales longer than one month, F10.7 has been found to be closely correlated with solar ultraviolet radiation variations at stratospherically important wavelengths [Donnelly, 1991]. Solar flux variations from 163.5 nm to 735 nm contain monthly mean spectra for September 1986 (solar minimum) and November 1989 (solar maximum) and show a change of about 8.5% near 205 nm. This is comparable to 7% [Donnelly, 1991] and 10% [Cebula et al., 1992], which are estimated from solar ultraviolet irradiance change near 205 nm between solar minimum in 1986 and solar maximum in 1990 based on the Mg II index range. To obtain statistical significance, a 30-year simulation from 1971 to 2000 is executed.
 To represent the volcanic effect on middle atmospheric chemical species, monthly zonal mean aerosol extinctions at 1020 nm and aerosol surface area density observed by the SAGE II from 1988 to 1997 are used as model input aerosol data between 6 km and 40 km. The SAGE II instrument measures solar irradiance at sunrise and sunset and provides 15 sunrise and 15 sunset profiles each day [McCormick et al., 1989]. Aerosol surface area density is converted from aerosol extinction data as described by Thomason et al. [1997b]. Aerosol data averaged from 1988 to 1990 is adopted as a background aerosol data [Hofmann et al., 1975; Hofmann and Rosen, 1981; Grant et al., 1994, 1996]. This period is free of major volcanic eruptions just prior to the Mount Pinatubo eruption in 1991. To simulate the effect of the aerosol increase after each volcanic eruption, SAGE II aerosol data from 1991 to 1997 is used. Because of insufficient aerosol data following the El Chichón eruption, we use the aerosol observations following Mount Pinatubo, but shifted in time to coincide with the eruption. Considering the weaker aerosol loading during El Chichón than during Pinatubo, the volcanic effect of El Chichón in the model simulation might be overestimated.
 To study the effects of each of these interannual forcings, three experiments are designed, and they are summarized in Table 1. Experiment 1 includes only solar flux variation; experiment 2 includes solar flux variation and the QBO, and experiment 3 adds volcanic effects to experiment 2.
Table 1. Summary of the Model Experiments
27 month oscillation
27 month oscillation
 To calculate the ozone solar cycle from the observation data, two ozone data sets are analyzed. Ozone profile data (Version 6) observed by the SBUV instrument onboard the Nimbus 7 spacecraft from November 1978 to June 1990 are obtained from the website, ftp://toms.gsfc.nasa.gov/pub/sbuv/. Note that the SBUV ozone values below 25 km mostly reflect the difference between total column ozone and profile amounts above 25 km [Bhartia et al., 1996]. Data from January 1979 to December 1989 is used in this study. The other data set is the ozone profiles observed by SAGE II from 1984 to 1998. Each vertical profile is processed to get the monthly mean ozone distribution [SPARC/IOC/GAW, 1998].
3. Ozone Solar Cycle From the Observational Data
 The method of calculating the ozone solar cycle from observation data by taking the difference between the ozone distribution during solar maximum and that during solar minimum has a high possibility of being contaminated directly by other factors like the trend or the QBO. Therefore, the multiple linear regression method, including a linear trend, an equatorial QBO, an 11-year solar cycle [McCormack and Hood, 1996], and their annual variation components [Randel and Cobb, 1994], is used in this study. First, the original monthly mean SBUV and SAGE II data are deseasonalized. The F10.7 solar flux data is adopted as the index for the solar cycle and the Singapore zonal wind at 25 km (∼30 hPa) for the QBO index. Because the quality of SAGE II ozone data immediately after the Pinatubo eruption is poor [Cunnold et al., 2000b], the first year of ozone data after the Pinatubo eruption is excluded from the analysis. The sunrise/sunset difference of SAGE II data that can induce some error in the long-term variation analysis in the upper stratosphere is ignored and both data are used in this study.
 For the ozone solar cycle analysis, the calculated solar regression coefficients from the SBUV and SAGE II data are shown in Figure 2. The regression results show similar dipole structure in both SBUV and SAGE II cases, which show peak values at the upper stratosphere middle latitude regions as found by several previous reports [Hood et al., 1993; McCormack and Hood, 1996; SPARC/IOC/GAW, 1998]. The altitude of the maximum value is higher in SBUV than in SAGE II and their latitudes are different. The regions of negative regression coefficients are observed at the equatorial middle stratosphere in both cases. McCormack and Hood  noted that the “double-lobed” structure is a superposition of seasonally varying ozone solar signals in both hemispheres. Due to the seasonality, the ozone changes due to solar flux variation are largest at middle to high latitudes in the winter hemisphere [Haigh, 1994]. Although ozone solar anomalies show hemispheric asymmetry depending on the season, the interannual variation component of the stratospheric ozone has its maximum values at the equatorial region [Dunkerton, 2001]. An aspect of Figure 2, and of previous studies, that does not accord well with the physical understanding is that the most sensitive latitude of ozone response to the 11-year solar flux variation is not the equatorial region, where the stratospheric ozone has its maximum values, but rather in the mid latitude region. Another inconsistency is the negative solar regression coefficient in the equatorial lower stratosphere. Even when the solar UV shielding effect by an ozone increase in the upper stratosphere is considered, a significant amount of negative anomalies at the equatorial lower stratospheric region is hard to explain. These inconsistencies lead us to suspect that other factors like the equatorial QBO or the two major volcanic eruptions contaminate the analysis. Figure 3 shows the temporal variation of the Singapore zonal wind at 30 hPa and the F10.7 solar flux variation. Each solar maximum and minimum period lasts for 3 to 4 years, which is not an exact multiple of the QBO period and therefore can lead to a biased QBO phase. During the solar maximum periods in 1980 and 1990, the easterly phase of the QBO is dominant. Since most of the interannual variation of the stratospheric ozone can be explained by the QBO and its reported structure has large anomalies at the equatorial upper and lower stratosphere [Dunkerton, 2001], its remaining signal, which cannot be appropriately removed by the regression method, might have an influence on the derived solar cycle in ozone.
Figure 4 shows the SBUV and SAGE II data periods and the dates of the two volcanic eruptions. Because the two major volcanic eruptions were separated by about a 9 year interval and both occurred during or right after a solar maximum, their effect on the ozone solar cycle analysis using multiple regression analysis is expected to be significant. These major volcanic eruptions enhanced the amount of stratospheric aerosol loading in the equatorial lower stratosphere, which induced intensified upward motion and reduced the equatorial lower stratospheric ozone for three to four years after the eruptions. In addition, the modification of the equatorial zonal wind by processes associated with the volcanic eruption has to be considered [Salby and Callaghan, 2000]. As indicated in Figure 1, the equatorial zonal wind itself, which is used as a QBO index in the multiple regression, responds to a range of processes and can act as another error source to the ozone solar cycle analysis.
4. Simulation Using 11-Year Solar Flux Variation (Experiment 1)
 To determine the effect of solar flux variation on stratospheric ozone, the ozone variation is simulated using monthly mean solar flux from 1971 to 2000. In this case, neither the QBO effect nor the volcanic effect is included in the simulation (experiment 1). In Figure 5, the annual mean ozone solar anomaly distribution derived from experiment 1 is plotted from 1981 to 1992. To calculate the anomalies, the seasonality of the ozone is removed from the 30 year data and the resulting interannual variation component is annually averaged. In 1981, the ozone anomaly distribution shows a monopole structure whose peak values are located in the equatorial upper stratosphere. The peak magnitude varies from more than 1.5% during solar maximum to about −1.5% during solar minimum. As the solar flux decreases, dipole structures are observed in 1982 and 1985. During solar minimum in 1986, the minimum value is located at the equatorial upper stratosphere. The patterns from 1981 to 1990 are observed repeatedly for 30 years. The magnitude of ozone solar signal is not directly proportional to the magnitude of solar flux. Although a similar magnitude of solar flux is observed for two to three years at each solar maximum and minimum periods, the strongest ozone perturbation is observed at the late stage of each period.
 Using monthly mean F10.7 values, solar regression coefficients are calculated from the monthly values of ozone (Figure 6) using a simple regression method. The structure of the solar regression coefficient shows a clear monopole structure whose maximum is located at the equatorial region, which is quite different from the dipole structure in Figure 2. The regression result is statistically significant at the 99% level. To check the sensitivity of ozone to the solar flux variation, the correlation coefficients between annual mean ozone solar anomalies and annual mean F10.7 data are calculated at different time lags. In the equatorial region, the correlation coefficients are more than 0.95 with no time lag even in the troposphere. In high latitudes, the ozone variation lags the solar flux variation by one year. As a result, the global total ozone is nearly in-phase with sunspot number [Angell, 1989]. The higher correlation coefficients at low latitudes throughout the stratosphere are consistent with the reported high correlation coefficient between solar flux and total ozone [Zerefos et al., 1997].
 The temperature response to the solar flux variation is determined from an Empirical Orthogonal Function (EOF) analysis of the year-to-year annual mean temperature perturbations. Figure 7 shows the primary EOF mode and the principal component of temperature. The sensitivity of temperature to the solar flux variation becomes higher with altitude in the stratosphere, and shows a difference of almost one degree between solar minimum and maximum. Although its magnitude is similar, the structure of temperature anomaly, especially its meridional gradient in the extratropical region, is quite different from that given by World Meteorological Organization (WMO) . Considering that the volcanic effect on stratospheric temperature is also significant, it is very hard to compare two results directly. When the temperature solar cycle is calculated using the data from experiment 3, the resulting temperature solar cycle shows a structure that is more similar to that given by WMO , i.e., larger meridional gradient of temperature at extratropical region (not shown). Due to the thermal wind relationship, the first EOF mode of zonal mean zonal wind also has a 11-year solar cycle but its magnitude is very small (not shown). The meridional circulation in the model does not show any 11-year solar cycle variation (not shown).
 In the model, the ozone concentration is determined by four processes: transport by the mean residual circulation (MRC), chemical reactions, vertical diffusion due to gravity waves, and horizontal eddy transport by planetary waves. As shown in Figure 8, the net effect of transport by the MRC is almost cancelled out by the effect of chemical reactions. Although transport shows a strong solar cycle signal, the related meridional wind fields do not show any solar cycle variation. This implies that it is the meridional and vertical gradients of ozone that account for the solar cycle variation in transport. Chemical reactions of ozone in this model include two production terms and eleven loss terms. Each term reacts to the solar flux variation and the combined effects show the structure in Figure 8b. During solar maximum, annual mean ozone is reduced by chemical reactions in the equatorial upper stratosphere and increased in the extratropical upper stratosphere region. The change to ozone due to vertical diffusion indicates that this process tends to increase the ozone perturbation in the upper stratosphere but reduce it in the middle and lower stratosphere. Unlike the other terms, the first EOF mode of horizontal eddy transport does not show a dominant solar cycle signal. Its second EOF mode shows a temporal variation with superposition of a solar flux variation and a two or three year oscillation. The horizontal eddy transport is largest in the Northern Hemisphere high latitude.
Figure 9 shows the difference of the monthly mean simulated ozone distribution by SOCRATES and the observed climatology ozone from the UARS Reference Atmospheric Project (URAP, “http://code916.gsfc.nasa.gov/Public/Analysis/UARS/urap/home.html”) for January and July. Probably as a result of insufficient wave forcing in the middle atmosphere, the meridional circulation produced in the model is weak and the resulting ozone transport is less than observed.
5. Effects of QBO and Volcanic Eruptions on Ozone Variation
 It is well documented that the effect of the equatorial QBO on the ozone distribution is significant. Although modeling of the QBO in zonal wind is so far not successful, simulation of the ozone QBO has been successful with fixed QBO phase [Politowicz and Hitchman, 1997]. Following this lead, we impose an equatorial QBO in the model with a period of exactly 27-month. To isolate the effect of the equatorial QBO, the ozone variation of experiment 1 is subtracted from that of experiment 2. The principal components of the first and the second EOF modes in Figure 10 result from taking annual means of the 27-month oscillation. The difference between their phases can be interpreted as the interaction between the annual oscillation and the QBO. The first two EOF modes explain more than 94% of the ozone QBO variation and their time coefficients are the same as those of the temperature QBO signal (not shown). The interaction of the annual oscillation and QBO can induce a decadal scale oscillation [Salby et al., 1997] as well as subbiennial variability [Dunkerton, 2001]; the decadal variation is seen in the third EOF mode. Note that its magnitude is much smaller than the first two modes. The third EOF mode has a decadal scale oscillation that happens to be 180° out of phase with the solar flux variation in the upper stratosphere during this 20 year period. When we focus on the upper stratosphere, the ozone variation associated with this QBO signal has a negative relationship with the ozone solar cycle and a magnitude of half that of the ozone solar cycle signal. When the ozone data is analyzed with a regression method, this QBO related mode has an effect on the solar cycle regression results. This QBO ozone variability disappears in model run without solar cycle variability (not presented).
 The other process that is expected to have an influence on solar regression analysis is volcanic eruptions. Both the radiative heating, which modifies the meridional circulation, and heterogeneous chemical reactions caused by the increase of stratospheric aerosol particles after the El Chichón and Mount Pinatubo eruptions have strong influences on the stratospheric ozone. The eruptions are separated by a 9-year interval and the effects of each remained for three to five years [Fusco and Salby, 1999]. To demonstrate the model simulation of reasonable radiative heating induced by the aerosol perturbations, the radiation heating variation of experiment 2 is subtracted from that of experiment 3. The first EOF of radiative heating and its principal component from experiment 3 are displayed in Figure 11.
 The estimated stratospheric radiative heating rates due to the El Chichón and Pinatubo eruptions are reported to be 0.3 K/day and 0.25 K/day, respectively [Anderson et al., 2001]. The model results show a similar range of values. The altitude of the peak heating and the latitude range of the radiative heating perturbation are also consistent with the reported values [Stenchikov et al., 1998]. The main difference between the El Chichón and Pinatubo eruptions is their latitudinal locations. The heating due to the El Chichón eruption is located in the Northern Hemisphere subtropical region versus the more equatorward heating by Mount Pinatubo. In this study, this hemispheric difference is neglected due to lack of suitable data for the El Chichón eruption.
 After the volcanic eruptions, ozone decreases abruptly following the increase of stratospheric aerosol loading [Grant et al., 1994; Herman and Larko, 1994; Tie et al., 1994; Zhao et al., 1997; Rosenfield et al., 1997] although no decrease of total ozone was reported in some low-latitude regions [Chakrabarty and Peshin, 1997]. The first EOF mode in Figure 12 is mainly induced by the anomalous vertical motion at the equatorial region after the volcanic eruption. The second mode is caused by the combined effects of diffusion, chemistry, and transport. The contributions of transport by the MRC and chemistry show different temporal variations. Right after the volcanic eruption, both transport and chemical reactions reduce ozone at the equatorial lower stratosphere. After that, transport by the MRC contributes to reduce ozone values in that region but chemical reactions and diffusion act in the opposite sense.
 To compare the solar regression coefficient of the model output to those of observed data, subsets of the model ozone results are selected during the periods that correspond to the data periods from the SBUV and SAGE II ozone, as shown in Figure 4. The solar regression coefficients are calculated from the model output in experiment 3 for the time periods corresponding to each observation data sets. The results in Figure 13 show dipole structures that are similar to the observations but very different from the monopole structure in Figure 6. The difference in the altitude of the negative ozone anomaly is related to the relative phase of the QBO; since the model QBO phase does not correspond to that in the atmosphere, the altitude of the negative regression coefficient does not correspond exactly between the observations and simulation. Nevertheless, the negative ozone anomaly at the equatorial region and the dipole structure in the upper stratosphere are simulated. The magnitude at the peak region is about half of the observed values. This may be a result of differences in the QBO phase and magnitude. As shown in Figure 10, the QBO induces a decadal variation in ozone that, for the model case, partially cancels the solar cycle variation. Another possibility is that uncertainties in the spectral distribution of the solar flux changes and the penetration of radiation to the stratosphere lead to an underestimate of the variable ozone production.
 Since the regression structure of modeled ozone perturbations from experiment 3 more closely resembles the observational analyses than the experiment 1 results, we use the results from the three model integrations to investigate the processes responsible for the dipole structure. In Figure 14, the solar regression coefficients for several different simulated ozone data sets are displayed to check the sensitivity of the regression method to the forcing in the model. The data period of SAGE II is adopted in this analysis and three different combinations of forcings are tested. The results show how much effect the volcanic and the QBO perturbations can have on the solar regression analysis. First, consider the case where only the QBO and solar forcing are included (experiment 2) and the QBO index is the simulated zonal wind at 25 km, which is affected by volcanic eruptions and solar variability as well (refer to solid line in Figure 1). In this case (Figure 14a), the regression result shows a dipole structure to the ozone solar cycle. Alternatively, when the exact QBO forcing, which is sinusoidal (refer to dotted line in Figure 1), is adopted as the QBO index for analysis of the same data (Figure 14b), the resulting solar regression coefficients have a structure that is more similar to the results from experiment 1 (Figure 14e). There are several differences between the two QBO indices that could lead to the apparent difference in the regression analysis. In using the equatorial zonal wind, the estimated QBO amplitude is not constant nor does the time variation have a smooth sinusoidal shape.
 When the volcanic forcing is added to the simulation and the simulated zonal wind at 25 km is adopted as QBO index (experiment 3, Figure 14c), the clear dipole structure, the negative regression coefficient at the equatorial region, and the lobes of higher coefficients extending into the mid latitude lower stratosphere region are obtained (compare to Figure 2b). This is the case that we feel has the greatest similarity, both in processes included and in resulting regression coefficients, to the observations. Even when the sinusoidal QBO forcing is adopted as QBO index, the resulting structure continues to have a dipole structure in the upper stratosphere and the higher coefficients extending into the mid-latitude lower stratosphere. Assuming that the QBO effect has been adequately removed by adopting the sinusoidal QBO index, Figure 14d indicates that the dispersed pattern and the dipole structure appearing in Figure 2b are associated with the volcanic eruptions. Comparison of Figures 14a and 14d indicates that both the QBO and the volcanic forcing contribute to the double cell structure in the solar regression coefficient. The QBO alone is responsible for the regions of negative regression coefficient in the tropics. The modifications of solar regression results by the QBO and volcanic eruptions can be expected from the third EOF mode of ozone QBO signal (refer to Figure 10c) and the first and second modes of ozone volcano signal (refer to Figures 12a and 12b). In Figure 15, the regression coefficients are expressed in terms of the percent change from solar minimum to maximum. The solar cycle variation of ozone is almost 3% in the upper stratosphere, which is similar to the reported value, 3–4% [Hood, 1997]. By including the QBO and volcanic effects, the maximum variation in the upper stratosphere region is modified slightly but is still less than that of the observational data presented by Shindell et al .
 To understand the effect of the 11-year solar flux variation on stratospheric ozone, the ozone solar cycle from the observation data is compared with the simulated ozone response to the solar flux variation. Because the expected magnitude of the solar signal in stratospheric ozone falls within the data error range even under ideal circumstances, it is difficult to isolate the solar signal from the observation data. Although it is assumed that the data error is systematic and does not affect the long-term variation analysis, other factors like the equatorial QBO and major volcanic eruptions interfere with the analysis of the ozone solar cycle. The ozone QBO induced by the equatorial zonal wind QBO and its interaction with the annual oscillation is the most dominant part of the interannual variation of the stratospheric ozone. Its residual interferes with the ozone solar cycle analysis, whose magnitude is much smaller than that of the ozone QBO, due to the least-chi-square fitting characteristic of the multiple regression analysis. The persistence of the easterly QBO phase during the two recent solar maximum periods might be an explanation for the negative ozone solar anomaly in the lower stratospheric ozone solar cycle. Due to the phase variation of the ozone QBO with latitude, a monopole structure whose maximum is located on the equatorial upper stratosphere is not fit very well by the regression method.
 In addition to the QBO, the major volcanic eruptions in 1982 and 1991 had significant effects on the lower stratospheric ozone, and this interferes with the ozone solar signal analysis and makes a dipole pattern of the ozone solar signal in the upper stratospheric region and enhanced variability in the mid-latitude lower stratosphere. The modulation of the modeled equatorial zonal wind by the major volcanic eruptions and possibly also by the solar flux variations themselves deteriorates the precision of the equatorial zonal wind as a QBO index in the multiple regression analysis. We have emphasized how this QBO index uncertainty affects analysis of longer-period stratospheric ozone variations. However, a similar uncertainty would apply to any analysis of temporal trends in the middle atmosphere. Ozone is unique in that it responds not only to the secondary circulation associated with the QBO but also to the temperature variations because of the strong dependence of chemical loss rates on temperature. The simultaneous dependence on transport and on in situ temperature make it particularly difficult to separate the effects of different atmospheric forcing such as the QBO, the solar cycle and the occasional volcanic eruptions. The other problem with the QBO index is in the latitudinal phase difference of the ozone QBO, which is affected by the annual cycles at mid-latitudes. Although the observed interannual variation of ozone shows a strong QBO pattern extending from low to mid latitudes, the phase varies with latitude. When the equatorial zonal wind at 30 hPa, which represents the variation of the equatorial zonal wind QBO, is used as a QBO index in a regression analysis, the ozone QBO at each latitude cannot be removed completely.
 When both the effects of the QBO and the solar flux variation are included in the ozone simulation, the interaction between the equatorial QBO and solar flux forcing induces localized ozone variation with the opposite sign to the pure ozone solar variation.
 A final issue is whether the model simulates the observed features well enough to provide reliable analysis of the problems with analysis of the observational data. When the equatorial QBO, volcanic effects, and solar flux variation are considered in the model simulation of the stratospheric ozone, the multiple regression analysis shows similar dipole structure to those of the observed data but its magnitude is about half of that observed [Shindell et al., 1999]. In addition to the weak meridional circulation of the model, the inexact interannual forcings related to the QBO, solar flux, and volcanic eruptions can contribute to this magnitude discrepancy. The variation of the simulated equatorial QBO zonal wind is 17 m s−1, while the magnitude of the observed easterly Singapore zonal wind is more than 38 m s−1. This difference can lead to a weakened ozone QBO signal and a reduced interaction between the QBO and solar cycle. The assumed sinusoidal structure of the equatorial QBO forcing might be incorrect, which could affect the solar signal in the equatorial zonal wind [Salby and Callaghan, 1999]. The approximation that the solar flux variation follows the monthly mean F10.7 data could also contribute to the magnitude deficit in the simulated ozone solar signal. Another approximation is the use of monthly mean F10.7 data whereas the actual solar flux variation has a pronounced 27-day variation. Most of the limitations outlined here are believed to have a quantitative, rather than qualitative, effect and therefore not to affect the basic conclusions. The largest uncertainty is in the forcing of the QBO, but this is the most difficult to address with current observations.
 In spite of the limitations in the observation data analysis and model simulations, the resulting solar regression patterns show similar dipole structures for the ozone solar regression under similar conditions. The dipole structure from the model simulation comes from the interference of the QBO and two major volcanic eruptions and not from the direct solar forcing. The simulated ozone response to the 11-year solar flux variation shows a monopole structure with an equatorial maximum. The analysis in this paper indicates that this is consistent with the observational record, but is not sufficient to prove that the stratospheric ozone response is identical to that in the model. To isolate the observational solar cycle precisely and compare it with simulations, a longer observational data record with no major volcanic eruptions has to be accumulated. Analysis could be greatly aided by observations of the QBO forcing in the stratosphere.
 We thank Xuexi Tie for his professional advice on the model simulation of the volcanic eruption effect on chemical species. We also thank Bill Randel and Fei Wu for providing monthly mean SAGE II ozone data. The comments of two anonymous reviewers were helpful for the reorganization of this paper and its improvement. The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation.