Interactive comment on “ Modelling the effects of ( short-term ) solar variability on stratospheric chemistry ”

The manuscript describes the chemical response to solar irradiance variability obtained with photochemical model and its parametrization using statistical models. The subject of the study is relevant to ACP scope. The authors applied a relatively simple 1-D photochemical model driven by the spectral solar irradiance data for the solar activity maximum and minimum as well as their combinations. The obtained response of different chemical species is compared with previously published model results and observation data analysis to validate the applied model. Then, the authors introduced the parametrization of the odd oxygen mixing ratio response using linear statistical model with 2 and 3 predictors. The properties of these regression models are presented and their accuracy is estimated using original photochemical model with different definitions of the solar spectral irradiance variability. The applied approach is reasonable for this particular task. The manuscript is reasonably well written and structured, however C14395


Abstract
The photochemical response of the stratosphere to short-term solar variability is investigated using a photochemistry column model with interactive photolysis calculation.The solar variability is here simply represented using the Lean (1997) solar minimum and maximum spectra.In order to isolate the photochemistry effect, simulations are devoid of diffusion or any other external forcing and the temperature is held constant.The solar mininum/maximum response is estimated for all chemical families and partitioning ratios, and the underlying photochemical mechanisms are described in detail.
The ozone response peaks at 0.18 ppmv (approximatively 3 %) at 37 km altitude.In an attempt to find the simplest statistical model able to represent the effect of solar variability in the stratosphere, the diurnal-average response of ozone from an ensemble of 200 simulations is regressed linearly following two auto-regressive models.In the simplest case, an adjusted coefficient of determination R2 larger than 0.97 is found throughout the stratosphere using two predictors, namely the previous day's ozone perturbation and the current day's solar irradiance perturbation.A better accuracy ( R2 larger than 0.9992) is achieved with an additional predictor, the previous day's solar irradiance perturbation.The skills of the two auto-regressive models at representing the effect of solar variability are then evaluated independently when coupled either on-line or off-line with the comprehensive photochemistry column model driven by the solar average spectrum.In all cases, the magnitude of the bias and the RMS error are found smaller than 5 % and 20 % of the ozone response, respectively.When used on-line, the 3-predictor model captures the ozone response to solar variability throughout the stratosphere with bias and RMS error lower than 1 % and 15 % of the ozone response, respectively.The results are found to be insensitive to an increase in the magnitude of the solar variability by a factor three, when this increase is applied uniformly throughout the solar spectrum.These statistical models offer accurate, computationally inexpensive parameterisations of the effect of solar variability in the stratosphere for climate-chemistry models with simplified chemistry that can be driven 1 Introduction Solar ultra-violet (UV) radiation is the primary energy source for stratospheric photochemistry.Ozone is formed by photolysis of molecular oxygen O 2 at wavelength λ smaller than 240 nm (e.g.Dessler, 2000).In addition to the oxygen cycle's termination reaction, it is destroyed by a variety of catalytic cycles involving nitrogen oxides, hydrogen oxides, chlorines and bromines.Ozone's absorbtion of UV radiation at λ ≤ 320 nm is the main heat source in the stratosphere and is responsible for the positive vertical lapse rate and, together with the dynamical heating, for the meridional temperature gradient and its associated thermal winds.Hence, variations in incoming solar radiation may indirectly affect stratospheric circulation via changes produced in ozone distribution (e.g.Williams et al., 2001;Rozanov et al., 2004).The response of the stratosphere to solar variability has gained much interest over the past decade.Indeed, it is a useful indicator for the influence of solar variability on the atmosphere (e.g.WMO, 2007;Intergovernmental Panel of Climate Change, WGI, 2007).In addition, amplification mechanisms of the solar signal on climate are being sought for, and a possible candidate may involve a feed-back between the stratosphere and the troposphere via stratospheretroposphere dynamical coupling (e.g.Egorova, 2005;Semeniuk et al., 2011).
The solar variability can be represented, to some extent, as a superposition of a multi-decadal variation (the quiet Sun variability), an eleven-year cycle, and short term components that are related to the 27-day rotation period of the Sun.These short term variations may be approximated as a 27-day cycle with its harmomics, the 13.5, 9, 6.7 and 4.5-day periods (Fioletov, 2009).Analysis of the stratospheric response to the 11-yr cycle is limited by the length of observational records of both solar irradiance and the stratosphere, covering about three and four cycles respectively (e.g.Egorova, 2005;Fioletov, 2009).Furthermore, the combination of the large inter-annual variability Figures in stratospheric dynamics, the two major volcanic eruptions, El Chichon and Pinatubo, and the satellite instrument changes makes it even more challenging.Soukharev and Hood (2006) and Fioletov (2009) analysed satellite observations with multivariate linear correlation to estimate the stratospheric response to the 11-yr cycle.Both studies found a largest minimum-to-maximum difference around 40 km with a range of values within 1-3 % of the ozone concentration.Numerical modelling studies have also been performed using one-dimensional chemical-radiative-convective models (Rozanov et al., 2002), two-dimensional chemical-dynamical-radiative models (Brasseur, 1993;Haigh, 1994), and three-dimensional chemistry-climate models (Shindell et al., 1999;Tourpali et al., 2003;Egorova et al., 2004;Rozanov et al., 2004;Austin et al., 2007).Amongst these models, the largest minimum-to-maximum difference occurred around 40 km and ranges from approximately 2-3 %.One-dimensional models produced values at the high end of the range, whereas 2-D models and Climate-Chemistry Models (CCMs) produced values at both high and low ends of the range.In general, results from numerical models fall within the large range of results from satellite observations.
The study of short-term variability is of particular interest since observational records are long enough to provide robust statistics on both solar irradiance and stratospheric ozone on this time scale.Furthermore, since the chemical mechanisms responsible for the ozone response to the short-term variability are identical to those involved in the 11yr-cycle (Brasseur et al., 1987), the characterisation of the ozone response to the shortterm solar variability can be of relevance to the 11-yr-cycle, as noted by Fioletov (2009).This relevance is however limited to the pure photochemical response, as the coupling of ozone photochemistry with radiation and dynamics will depend on the competition between chemical, radiative and dynamical time scales.Radiative damping time scales for a temperature perturbation which extends through the stratosphere go typically from the order of a week in the upper stratosphere to the order of tens of days in the lower stratosphere (e.g.Fels, 1982).In the upper-stratosphere, since the 27-day cycle is slower than both the photochemical and radiative damping time scales, photochemistry and radiation are able to adjust to variations related to irradiance and ozone changes Figures as the cycle progresses.In this case, the minimum to maximum ozone response may be close to that of the 11-yr cycle.This is however not true for lower altitudes and/or with shorter periods of variability, and in such conditions the ozone response is likely to be influenced by additional radiative-chemical feed-backs.
Observational studies of the response to the 27-day cycle have been performed by Keating et al. (1987), Hood and Zhou (1999) and Fioletov (2009).They found the maximum ozone sensitivity1 to occur around 40-45 km and range from approximately 0.25-0.7 %, depending on the time period that was observed.Numerical simulations of the 27-day cycle response have been performed using one-dimensional chemical-radiative models (Brasseur et al., 1987), two-dimensional chemical-dynamical-radiative models (Brasseur, 1993), and three-dimensional climate-chemistry models (Williams et al., 2001;Rozanov et al., 2006;Austin et al., 2007).Amongst these models, the maximum ozone sensitivity was found around 40-45 km and had large variations ranging from approximately 0.2-0.8%.In an attempt to remove dynamical feedbacks, Fleming et al.
(1995) used a two-dimensional photochemical model with specified temperature and transport fields and found a maximum value of 0.5 %.Using the Lean (1997) solar variability spectra as a rough reference, where the 205 nm wavelength varies by 8.2 %, the 0.2-0.8% range of ozone sensitivity translates into a response between 1.6-6.5 % of the ozone concentration.This range emcompasses the 11-yr cycle ones but also includes responses with magnitudes twice as large.
Overall, the ranges of ozone responses from model and observational studies are equally large (factor three), even in the tropical upper stratospheric region which is expected to be photochemically controlled, and therefore not subject to significant dynamical variability.On the one hand, the representation of solar variability in numerical models is very variable, whether on the incorporation of the irradiance variability or on photochemistry aspects.Only very few models feed their radiation scheme with the irradiance variability (Semeniuk et al., 2011).The solar variability is usually represented Figures

Back Close
Full by a simple superposition of 11-yr and 27-day cycles, whilst the observed frequency spectrum shows a continuum of frequencies down to daily time scales (Fr öhlich and Lean, 2004;Fioletov, 2009).The spectral representation of solar variability is usually uniformly linear between solar maximum and minimum spectra (Lean, 1997), ignoring any decorrelation or anticorrelation of variability between different wavelengths.The photolysis response is usually simplified to the linear combination of two pre-calculated states representing solar maximum and solar minimum, to avoid on-line photolysis calculations (Austin et al., 2007).Some numerical studies use simplified representation of stratospheric chemistry (Shindell et al., 1999).On the other hand, the observational multivariate analysis shows large uncertainties due to length and accuracy of observational records, as well as the non-independence of predictors.This makes the improvement and validation of numerical models using observational results in general difficult as far as solar variability is concerned.Despite these uncertainties, the pure photochemical response (i.e.free of radiativedynamical effects) in the stratosphere is supposed to be well constrained and should be consistent among numerical models as long as they have an adequate representation of the underlying photochemical processes.The level of complexity of the photochemical representation required to accurately capture the effect of solar variability on ozone is however not clearly known.Such knowledge is key since simplifications of some sort are necessary to allow solar variability studies on long time-scales.
In an attempt to fill this gap, this study aims at characterising the pure photochemical response of the stratosphere to solar variability and to build the simplest statistical model (or parameterisation) representing this response with some accuracy.We focus on the pure photochemical response of the stratosphere to short-term solar variability using a comprehensive photochemistry column model which includes a fully interactive photolysis scheme.Although the focus is on short-term solar variability, the results are expected to be of relevance for long-term solar variability too, since the photochemical mechanisms are identical.In order to identify the pure chemical response without distorsions by possible external forcing effects, the chemistry is left to evolve alone with Figures

Back Close
Full time as an initial condition problem, without any external sources/sinks nor any diffusion/advection representation.This transient chemistry framework imposes a limit to the duration of the numerical experiments of about ten days (see Sect. 2.2), after which the chemical concentrations are not relevant anymore for stratospheric purposes.It is worth noting that this response is different from the climatological response expected in the atmosphere as it ignores radiative and dynamical effects.As a first step, we limit the study to fixed solar maximum and minimum spectra from Lean (1997) and represent solar variability using uniform linear combinations thereof.
Response to solar variability is first characterised for all relevant chemical families and partitioning ratios using fixed solar minimum and maximum simulations.Then, the response of odd oxygen (which can be identified with ozone in the stratosphere) is analysed statistically using ensembles of 10-day simulations of the photochemistry with daily updated random solar irradiances.The analysis shows that the diurnal average response can be represented as a linear function of the solar irradiance perturbation on the current day, the concentration of the previous day, and for more accuracy, the irradiance perturbation of the previous day.The sensitivity of regression coefficients against initial conditions is tested and is non-negligible only for the temperature.The capacity of this simple autoregressive model to predict the odd oxygen perturbation is validated on-line and off-line with the comprehensive photochemical model representing solar average conditions.It shows to represent the odd oxygen perturbation with a good accuracy (bias and RMS error smaller than 1 % and 15 % of the ozone signal, respectively, in the 3-predictor model).The ozone response is also found to be linear with respect to an increase in the magnitude of the solar variability by a factor three uniform through the solar spectrum, which allows the statistical models to keep their accuracy through a larger range of solar variability.However, it is found that departures from a simple representation of the solar variability change the coefficients of the statistical models.It is argued that the ensemble-based statistical method introduced here provides an effective gauge for studying the implications of such departures as suggested in recent literature (e.g.Haigh et al., 2010) The next Section describes the numerical model employed, the initial conditions, the simulations and the statistical methodology.Section 3 presents the stratospheric chemical state for an average solar activity and discusses the results from the fixed solar minimum and maximum simulations for all relevant chemical families and partitioning ratios.Section 4 presents the results for odd oxygen from the ensemble simulations with daily random solar variability.It includes regression analyses with two and three predictors, the sensitivity to initial conditions, and the independent evaluation of the autoregressive models on-line and off-line, and with magnified solar variability.Finally, the conclusions are drawn in Sect. 5.

Photochemical model
The chemistry column model used here is an adapted version of the stratospheric photochemical scheme developed for BASCOE (Errera et al., 2008;Viscardy et al., 2010) with updated JPL06/09 chemical rates (Sander et al., 2006(Sander et al., , 2010)).The scheme calculates the temporal evolution of 57 chemical species described by a system of 199 chemical reactions.The corresponding chemistry module is built by the Kinetic PreProcessor (Damian et al., 2002) and is integrated using a third-order Rosenbrock solver (Hairer and Wanner, 1996).For the purpose of this study, this chemical model was modified to include an on-line calculation of the photolysis rates.The scheme has 171 spectral wavelengths between 116.3-730 nm and includes 55 photodissociation processes that are solved using a two-stream radiative transfer method (Chabrillat and Fonteyn, 2003) and a simple parameterisation of the absorption of the solar Lyman-alpha line by molecular oxygen (Chabrillat and Kockarts, 1997).This interactive coupling allows photolysis rates to respond to vertically changing concentrations in absorbing species and removes the dependence on an a priori vertical profile of ozone.(Hedin, 1991).The solar spectrum comes from SOLSTICE (Lean, 1997) and includes maximum, minimum, and average solar irradiance at each wavelength interval.
In order to account for absorption of solar irradiance above 55 km (above the upper boundary of the chemistry solver), an artificial standard upper atmosphere is added which is composed of 4 levels at 60, 80, 100, and 120 km.Similarly, to account for tropospheric absorption of reflected solar irradiance at the surface, an artificial standard troposphere is added with 5 levels at 0, 2, 4, 6, and 8 km.Extensive testing showed that these upper and lower levels were enough to represent photolysis rates between 10 and 55 km altitude without loss of accuracy.

Numerical simulations
All simulations start at midnight and occur in January at the Equator.We chose the Equator, where dynamical effects on ozone are smallest, to make our experiments more (although not entirely) comparable to CCMs.The initial concentrations and temperature are set to monthly and zonally averaged values taken from a 22-yr simulation with the Canadian Middle Atmosphere Model (Semeniuk et al., 2011) with greenhouse gases and halogen concentrations fixed to year 1979 (courtesy Kirill Semeniuk).The values used at all altitudes for the long-lived species are listed in Table 1, and the vertical profiles of the other chemical species, along with temperature can be seen in  2 as a percentage of the initial concentration.In order to keep the chemical system in a regime which is relevant to the stratosphere, all simulations in this study are thus limited to 10 days (maximum change smaller than 20 % for the families and most of the reservoir species).In order to facilitate the discussion of the results, the focus will be placed on day 5 hereafter and variations of the results between days 3 to 9 will be discussed as required.This variation is of interest as it provides some additional insight into the sensitivity of the results to variations in chemical concentrations.The first set of numerical experiments simulates the chemical response to various strengths of solar irradiance, with the solar irradiance kept constant through the simulations to: solar maximum, solar minimum, and solar average levels.The irradiance spectra represent the 11-yr maximum, minimum, and average solar irradiance for each wavelength interval (Lean, 1997).
The second set of numerical experiments investigates statistically the chemical response to daily solar variability and allows to build a simple auto-regressive model of the ozone perturbation.An ensemble of 200 transient simulations is performed, each forced by a different pseudo-random solar variability sequence.Solar irradiance is updated daily and held constant for 24 h.Updates are at midnight to avoid a sudden change in the photolysis rates.Here again, the irradiance spectrum ranges between the solar minimum and solar maximum spectra of SOLSTICE's 11-yr cycle following the linear formula in Eq. ( 1).
where from λ, so that the entire spectrum is linearly varying between the solar minimum and maximum.To ensure good statistical independence between the 200 members, a sequence of 2000 successive pseudo-random numbers (without re-seed) is used and partitioned into the 200 members.Two auto-regressive models are discussed here for odd oxygen (i.e.ozone).The two-predictor model determines the diurnal average concentration for the current day, knowing the diurnal average concentration of the previous day and the solar irradiance perturbation of the current day.The three-predictor model is similar to the two-predictor model, but with the addition of the solar irradiance perturbation of the previous day as the third predictor.The details are discussed in Sect. 4. Note that as a first step, we chose here to focus on Equatorial January conditions, and the study can be later generalised by allowing the regression coefficients to vary with latitude and month.
Since chemical concentrations and temperatures vary significantly over longitudes and within seasons, it is useful to test the sensitivity of the latter results to the initial conditions.To do this, a third set of numerical experiments is performed, where temperature and initial conditions of relevant species are perturbed, one variable at a time.The same approach is employed as before, but with ensembles of 100 simulations.The perturbations represent the intra-month and zonal variability, averaged over the 22 yr of the CMAM simulation of the two-standard deviations of three-daily values of the variable taken at the given altitude and latitude.Note that these standard deviations are used here merely as an estimate of the possible range of variation of the variables.The sensitivity analysis is performed for odd hydrogen (HO x = {H, OH, HO 2 }) by perturbing Then, a fourth set of experiments is made to test the performance of the autoregressive model at representing the ozone perturbation due to solar variability.For this purpose, five additional ensembles of 200 simulations are designed as follows using a new pseudo-random solar variability sequence adjacent to the first sequence.The same pseudo-random sequence is used in all these new ensembles, so that they can be inter-compared on a member-by-member basis.
1. Control ensemble with daily random solar variability performed as before using the photochemical model; 2. Two-predictor auto-regressive model used off-line on top of a solar average simulation with the photochemical model; 3. Two-predictor auto-regressive model used on-line with the photochemical model representing the solar average conditions; 4. Same as 2, but with the three-predictor auto-regressive model; 5. Same as 3, but with the three-predictor auto-regressive model; Note that in the two on-line experiments 3 and 5 above, the auto-regressive model is curtailed by its previous day's concentration component since this memory is carried over by the photochemical model itself.The results of these five simulations are discussed in Sect.4.3.Finally, a last set of solar maximum/solar minimum experiments is performed with the photochemical model, the 2-and the 3-predictor models, using solar maximum and minimum spectra such that their difference centered around the solar average spectrum is magnified by a factor between 0.1 to 3.0.This magnifying factor is applied either uniformly to the whole spectrum or to the range 200 to 400 nm (see Sect. 4.4).Introduction

Conclusions References
Tables Figures

Back Close
Full  .To place in context the response of chemical families to solar variability, it is useful to first briefly map the chemical state for average solar irradiance (SI) conditions.This is represented in Fig. 2 by the diurnal cycle of day 5 of the simulation using average SI.The variation in the pattern of this diurnal cycle through the ten days of the simulation is minor and its diurnal average change is provided in Table 2.Note that these diurnal cycles are consistent with Brasseur et al. (1990) and Dessler (2000), for instance.
Figure 3 shows the diurnal cycle difference between the solar maximum and the solar minimum experiments, taken on day 5.Note that in both the solar maximum and solar minimum experiment, the entire chemical system may slowly adjust to the solar perturbation, and therefore a slow temporal drift may occur in addition to the diurnal response.However, above 35 km, where the photochemistry is in steady state, and therefore the O x response should stay constant in the absence of such an adjustment, a change in the O x response smaller than 10 % was found from day 5 to day 10 (not shown).Below this altitude, the ozone response changes by 60 % over this period between 15 and 25 km altitude due to the ozone chemistry becoming slower at low altitudes, and not because of an adjustment of the overall chemical system.Hence, it is sound to focus on the day 5 of the simulation, keeping in mind that the steady state response is only achieved above 35 km.
O x : Fig. 3 shows that the minimum-to-maximum difference is positive for both O x and . The peak difference for O x is approximately 0.18 ppmv (∼3 %) at 37 km, just above the ozone peak altitude, and remains throughout the diurnal cycle.Note that the relative change peaks slightly higher (3.2 % at 42 km) due to the decreasing O x concentration with altitude (Fig. 9, top panel).These results are within the range of the minimumto-maximum differences calculated from the observations by Soukharev and Hood (2006) and Fioletov (2009), and is in agreement with the largest minimum-to-maximum Introduction

Conclusions References
Tables Figures

Back Close
Full differences calculated from simulations by 1-D models (e.g.Rozanov et al., 2002), 2-D models (e.g.Haigh, 1994) and CCMs (e.g.Shindell et al., 1999;Tourpali et al., 2003;Egorova et al., 2004;Rozanov et al., 2004).The difference for O O x is only seen during the day above 48 km, and the peak difference is a change in the partitioning ratio of approximately 1.6×10 −3 (∼1 %) near the top of the model (55 km).The peak change in O O x occurs at the top of the model because this is where the UV irradiance is strongest, allowing for an enhanced photolysis of O 3 .The increased O 2 photolysis is the reason for the increase in O x during solar maximum conditions.The peak difference occurs a few kilometers above the maximum O x mixing ratio due to a change in the optical depth and in the O x loss processes.An increase in HO x above 40 km during solar maximum conditions (see below) results in an increased destruction of O x , thus limiting the response of O x to SI above 40 km.Similar results were obtained for the upper stratosphere and mesosphere in simulations by 2-D models (e.g.Brasseur, 1993;Khosravi et al., 2002) and CCMs (e.g.Egorova et al., 2005), and in observations by Zhou et al. (1997).
HO x : as expected, Fig. 3 shows that the minimum-to-maximum difference occurs mostly during the day for HO x and OH HO x . The difference for HO x is positive and occurs above 40 km, reaching a peak value of 0.03 ppbv (∼2.5 %) at the top of the model.A similar increase in HO x during solar maximum conditions is found in the CCM simulations of Egorova et al. (2005).For OH HO x , the difference is negative and is found in the middle stratosphere, with a peak difference of approximately −3 × 10 −3 (∼−1 %) at 38 km.The difference found at night above 50 km should be ignored as there is no HO x present here, and the difference is simply a result of a near-zero denominator.The peak increase in HO x is the result of an increase in the oxidation of water vapour and methane, and is found where the SI is strongest.The decrease in OH HO x in the middle stratosphere is a result of the increase of O x at these altitudes, as well as the decrease in NO.In the middle stratosphere, the conversion of OH to HO 2 (via O 3 ) and the conversion of HO 2 to OH (via NO) dominate the HO x cycle (Dessler, 2000).Thus an increase in O x leads to an enhanced conversion of OH to HO 2 , and a decrease in Introduction

Conclusions References
Tables Figures

Back Close
Full NO leads to a diminished conversion of HO 2 back into OH .The small decrease seen at the top of the model is due to the increase in O atoms at the top of the model, resulting in an increased conversion of OH to HO 2 via O.In the CCM simulations by Egorova et al. (2005), an increase in HO 2 is found between 25 to 55 km, in agreement with the decrease in OH HO x found here.
NO x : in Fig. 3 it can be seen that there is both a positive and negative difference in the minimum-to-maximum NO x .The negative difference peaks at a value of −0.1 ppbv (∼−1 %) late in the night at around 40 km.There is also a slightly smaller negative difference above 40 km that remains throughout the diurnal cycle and peaks above 50 km.The positive difference in NO x is seen during the day and has a peak value of approximately 0.03 ppbv (∼0.5 %) at about 32 km.The minimum-to-maximum difference for NO NO x is negative and is mainly found in the middle stratosphere during the day, with a peak difference of −4 × 10 −3 (∼−1 %) at around 37 km.During the night, the decrease in NO x at around 40 km is a result of the increase in O x at this altitude during solar maximum.An increase in O x results in an increased conversion of NO 2 to NO 3 (via O 3 ), which then results in an increase in the conversion of NO x to its reservoir N 2 O 5 (through the combination of NO 2 and NO 3 ).The negative minimum-to-maximum difference above 40 km during the day is due to an increase in N atoms (via an increased photolysis of NO), resulting in an enhanced conversion of NO to N 2 (via N), thus causing a loss in NO x .The increase of NO x seen during the day is due to an increase in the conversion of the NO x reservoirs (specifically HNO 3 ) back into NO x (specifically NO 2 ) due to enhanced photolysis.The strongest response is located at around 32 km.This is due to the combination of HNO 3 decreasing at higher altitudes and the photolysis of HNO 3 slowing down at lower altitudes.The decrease found in the middle stratosphere is due to the increase in O x at these altitudes, which results in an increased conversion of NO to NO 2 (via O 3 ).Again, in the simulations by Egorova et al. (2005), an increase in NO 2 is found at these altitudes, and is thus in agreement with the decrease in NO for use in predicting the effect of solar variability on the stratosphere.The regression model's dependent variable (y) is taken as the daily (24 h) average concentration of each ensemble member for days 3-9.Days 1 and 2 are left out to allow for a spinup in the simulations.In order to verify that the regression coefficients do not vary significantly over the course of the simulations, separate regressions are performed every day.The ensemble size of 200 members was found to be large enough so that results are not significantly sensitive to it.Two auto-regressive models are tested: a 2predictor and a 3-predictor model.In the 2-predictor model, the independent variables are taken as the previous day's daily average concentration (x 1 ), and the current day's SI (x 2 ).The dependence on the previous day's daily average concentration is referred to as the memory and the current day's SI as the SI for simplicity.In the 3-predictor model, the additional independent variable is the previous day's SI (x 3 ).The previous day's SI is added in an attempt to include the effects of SI on the chemistry that are too slow to be captured by the current day's SI regression term.Such effects include for instance changes in other species that indirectly affect O x .The multiple linear regression models can be written in the standardised form as, respectively: (2) with standardised regression coefficients are always between −1 and +1 and show the relative contributions of predictors at every altitude, without regard to the actual ozone response.The intercept coefficient α is zero in these standardised forms.Note that although the two regression models have distinct values of the coefficients β and γ, we use the same notation for simplicity.The ensemble averages can be expected to represent solar average conditions under the hypothesis of large ensembles and a linear ozone response.The difference between the ensemble average ȳ (or equivalently x1 ) and the solar average simulation is smaller than 0.1 % of the solar average O x everywhere (not shown) and therefore these two quantities can be assumed equal.The following form will also be used for the regression models, which measures the centered, non-normalised contribution of the different predictors to the ozone response: where by definition, the intercept α equals ȳ, i.e. to a good approximation the ozone concentration in average solar conditions, and the regression coefficients β , γ and δ are related to the standardised ones by: , and r = rσ y . (7) These regression coefficients provide the actual contribution to y − ȳ of a positive perturbation by one standard deviation in the previous day's ozone concentration, the current day's SI and the previous day's SI, respectively.The two predictors x 1 and x 2 are independent.As a result, in the 2-predictor model, the corresponding coefficients β and γ can be interpreted independently from each other, as the ozone response to a positive perturbation by one standard deviation in the previous day's ozone concentration and the current day's SI, respectively.By contrast, since the ozone concentration on the previous day depends on the previous day's SI, the third predictor x 3 is expected Introduction

Conclusions References
Tables Figures

Back Close
Full to have some collinearity with x 1 .The degree of this collinearity is indeed measured by the 2-predictor coefficients β and γ.If a perfect collinearity exists somewhere in the column between x 1 and x 3 , we will have β = 0 and γ = 1.Such a situation would make the third predictor useless and the corresponding regression coefficients β and δ in the 3-predictor model ill-defined with only their sum being well-constrained.As will be seen below, the 2-predictor model's β never goes to zero.This means that the third predictor brings additional information at all altitudes, and that the coefficients β and δ in the 3-predictor model can be expected to be well-constrained everywhere.A more formal confirmation of this was made by calculating the variance inflation factor (VIF) for the third predictor, defined by (Wilks, 2006): where R 2 x 3 is the coefficient of determination for the regression of the previous day's SI on the memory.Usually, VIF > 10 is considered the cut-off threshold where multicollinearity is too large in a regression and will lead to ill-defined coefficients.In our case, VIF is smaller than 10 at all altitudes where the previous day's SI has a significant effect, and thus multicollinearity is not making the regression ill-defined.However, it is important to note that the collinearity between x 1 and x 3 makes the intepretation of the corresponding regression coefficients less straightforward.The two regression coefficients must be interpreted together to the extent of the correlation between the two predictors.
The error of a regressive model in representing the ozone response can be simply measured by the coefficient of determination R 2 (Wilks, 2006).However, the comparison of this coefficient between the two models may lead to a bias favouring the 3-predictor one, simply due to the addition of an explanatory term and its effect in decreasing the number of degrees of freedom in the regression estimation.To take this effect into account, we use the coefficient of determination adjusted for the number of predictor variables ( R2 ) (Wilks, 2006): Introduction

Conclusions References
Tables Figures

Back Close
Full where n is the sample size and p is the total number of predictor variables in the regression.By definition, R2 is always smaller than R 2 .As the number of predictors increases, the adjusted coefficient R2 increases only if the new predictor adds significantly to the fit, and may decrease if it does not.

Regression coefficients
Figures 4 and 5 show both the standardised and non-normalised regression coefficients determined from the multiple linear regression using 2-and 3-predictors, respectively (for each day).In each plot, altitudes at which the standard deviation (amongst the ensemble) in the observed variable y was smaller than 5 % of the maximum standard deviation in the column are hatched out, and are considered insignificant response to solar variability.Note that the regression analysis was performed on all species discussed in Sect.3, and all species could be reasonably well regressed with the 3predictor model, with an adjusted coefficient of determination larger than 0.8 at all altitudes (not shown).
Figure 4 shows that the adjusted coefficient of determination for the 2-predictor model is larger than 0.97 throughout the column, demonstrating that the 2-predictor linear model provides a reasonable representation of the response.Consistently with Fig. 2, the intercept term (from the non-normalised regression) shows that the peak daily average mixing ratio of O x in solar average conditions occurs around 32 km (∼9 ppmv).The standardised regression coefficients shows that the current day's SI is dominant in the upper stratosphere (above 40 km) where the UV irradiance is intense and chemical life-times are short, whereas the memory is dominant in the mid to lower stratosphere where chemical lifetimes of O x are longer.Nevertheless, both these 2predictors appear to have a significant effect at all altitudes considered here.The nonnormalised regression coefficients confirm that the current day's SI dominates in the Introduction

Conclusions References
Tables Figures

Back Close
Full upper statosphere with a peak around 42 km, and the memory in the mid stratosphere with a peak around 38 km.Both memory and SI coefficients decrease to zero in the lower stratosphere as the chemistry becomes very slow and the overall response σ y converges to zero.As expected, the two regression coefficients are positive throughout the stratosphere, meaning that increases in previous day's concentration or in current day's SI, both increase the current day's O x .In Fig. 5, it can be seen that the addition of previous day's SI increases the adjusted coefficient of determination to 1 (more precisely ≥0.9992) throughout the entire column, making the 3-predictor linear model a very good representation of the response.As expected, the intercept term does not change from the 2-predictor results.From the standardised regression coefficients, it can be seen that the current day's SI remains unchanged by the addition of the extra predictor.In contrast, the memory has now less of an importance above 35 km and becomes negligible above 45 km.This contribution is now taken over by the previous day's SI, which relative contribution peaks around 41 km.The non-normalised memory has a slightly smaller peak, about one to two kilometres lower in altitude.The previous day's SI peaks around 40 km, similarly to the current day's SI, but with a magnitude three times smaller.This much lower magnitude suggests that this two-time level scheme for the SI term is accurate enough to include most chemical effects and that a three-time level scheme is unnecessary (as confirmed by the adjusted coefficient of determination).
The day-to-day variability of the non-normalised regression coefficients is insignificant for both the 2-and 3-predictor models.Consistently, it is only substantial in the standardised coefficients below 40 km, where the overall response is small, due to the magnifying effect of the decreasing σ y at lower altitudes.Hence, it appears that the results are robust to the changes in chemical conditions over the 10 days of the

Sensitivity to initial conditions and temperature
In order to understand how the initial conditions affect the chemical response to solar perturbations, additional multiple linear regressions were performed on simulations with perturbed initial conditions (Fig. 1).The chemical response of O x was found to be sensitive to perturbations in the temperature, while it showed no significant sensitivity to perturbations in H 2 O, NO x or O x (not shown).
Figure 6 shows the sensitivity to temperature of the non-normalised regression coefficients for the current day's SI and the memory from the 3-predictor model.The previous day's SI coefficient showed the same sensitivity to temperature as the current day's SI, but since its effect is both similar and of a much lesser magnitude, it was not deemed useful to show.The 2-predictor model's sensitivity (not shown) was similar to the 3-predictor model.For both coefficients in Fig. 6, a shift towards lower altitudes is observed for increasing temperatures, accompanied by a weakening of the effect.A similar result was found in the observational analysis by Fioletov (2009), such that the ozone response weakened for a temperature disturbance in phase with the solar variation.Brasseur (1993) and Keating et al. (1994) also found that an increase in upper stratospheric temperatures resulted in increased rates of ozone destruction, accompanied with a weaker ozone response to solar variability.This is explained by the temperature dependence of the NO x catalytic cycle, which leads to larger O x concentrations, and consequently a larger response to solar variability, at lower temperatures.

Evaluation of the error of the statistical model
As shown in Sect.4.1, the 2-and 3-predictor models fit the ensemble simulations with a good and excellent accurary, respectively.In this section, we perform an independent evaluation of their skills at representing the effect of solar variability on ozone.For this purpose, we use a new, independent pseudo-random solar variability sequence, started after the end of the one used for the regression.As described in Sect.2.2, these statistical models can be used either off-line or on-line with the photochemical Figures model (or similarly with a CCM).In the off-line mode, the statistical model takes care of the effect of the solar variability while the photochemical model simulates solar average conditions.The statistical model does not feed back into the photochemical model.While this mode provides the most direct evaluation of the predictive skills of the statistical models, it may not be appropriate when the feed back between radiation and photochemistry needs to be accurately resolved.In the on-line mode, the ozone perturbation generated by the statistical model is added to the ozone concentration in the photochemistry scheme when initialising the latter for the next day's calculation.However, since the photochemical model is initialised every day with the perturbed ozone concentration, it keeps memory of the previous day's perturbation in ozone.Thus, the memory term in the statistical model must be dropped in this mode, giving rise to potential additional errors.
Figure 7 shows the error in the two statistical models for the two modes of coupling with the photochemical model.The bias and RMS errors are estimated here using, respectively, the relative mean difference and the relative root mean square difference of the diurnal average ozone concentrations between the off/on-line and the control experiments.The control experiment is an ensemble of simulations where the solar variability is resolved by the photochemical model.The errors are relative to the ozone response in the sense that they are normalised by the root mean square difference between the control and the solar average experiments.Since the control experiment is centred around the solar average simulation, the normalisation factor is equal to the standard deviation of the solar variability effect in the ozone concentration (σ y ).In the regions where this normalisation factor (i.e. the ozone response) is smaller than one thousands of the solar average ozone concentration, the response and errors are set to zero (areas under the thick dashed lines in Fig. 7).This cut-off assumes that ozone responses smaller than 0.1 % can be neglected in a model.
As expected, the bias and RMS errors are smaller in the 3-predictor than in the 2predictor model, and are smaller in the off-line mode than in the on-line mode.In the best case, the off-line 3-predictor model offers an excellent accuracy throughout the Figures

Back Close
Full stratosphere with a bias smaller than 2 % and an RMS error smaller than 5 %.In the worst case, the on-line 2-predictor model still offers a reasonable accuracy with a bias smaller than 5% and an RMS error smaller than 20 %.This accuracy in the on-line mode is improved by the addition of one predictor to a bias smaller than 1 % and an RMS error smaller than 15 %.This absence of a systematic bias in the 3-predictor model when used on-line makes it an excellent candidate for a CCM.Note furthermore that, in contrast to the on-line 2-predictor model, the on-line 3-predictor model sees its relative error increasing at altitudes above 40 km, where the ozone response weakens.Hence, the absolute error in the on-line 3-predictor model is markedly smaller than in the on-line 2-predictor model.The time variation of errors is small in all cases, confirming the low sensitivity of the statistical models to the chemical changes that occur over the 10 day simulations.The performance of the statistical models, when used on-line, is illustrated in Fig. 8 for a randomly choosen member of the ensemble of 200 simulations at 37 km, the altitude where the ozone response is largest.Overall, the two statistical models provide an accurate, computationally inexpensive representation of the effect of solar variability on ozone, with the 3-predictor model being the most accurate.

Magnified solar variability
The Lean (1997)   3.0.The response is linearly proportional to the magnitude of the solar change within this range.Increasing beyond the factor 3.0 was attempted but led to instability of the photochemical model.This linearity allows the statistical models developed here, and in particular the 3-predictor model, to capture the response to solar variability, even when magnified by a factor three, with an excellent accuracy throughout the stratosphere, as confirmed in Fig. 9 (middle).Figure 9 (bottom) shows the responses in the photochemical and statistical models as a function of the magnifying factor at 37 km altitude, and compares them with the response found in the photochemical model when the magnifying factor is applied only within the range 200 to 400 nm.In the latter case, the response remains linear through the entire range but with a smaller slope and nonzero intercept.This is explained by the ozone production outside the 200 to 400 nm window which is kept constant in these experiments.Hence, the statistical models used here still apply in this case (though with slightly different coefficients).

Conclusions
This study presents an analysis of the pure photochemical response of the stratosphere to solar variability, with no inclusion of dynamics, diffusion or radiation.This photochemical response is of special interest since it is common for the various cycles of solar variability, such as the 27-day or 11-yr cycles.Its coupling with the dynamical and radiative processes will however differ, depending on the duration of the solar variability cycle.The solar maximum-minimum response in O x shows a sharp peak of 0.18 ppmv (about 3 %) increase in O x around 37 km altitude and a rapid decrease of this response towards lower altitudes with a near-zero response below 27 km altitude.This pattern compares particularly well with estimates from Fioletov (2009) based on satellite observations of the 27-day cycle combined with the Mg II index (the orange lines in their Fig.9).In Climate-Chemistry Models, the ozone response to the 27-day cycle shows a smoother peak which typically extends at lower altitudes, and the response stays significant, though very variable, at altitudes even lower than 20 km (e.g.Austin Introduction

Conclusions References
Tables Figures

Back Close
Full  , 2007).Assuming that the CCMs achieve a similar photochemical response as here, this difference can come either from the effect of coupling photochemistry with radiation and dynamics, or from errors in the statistical separation between the solar impact and the dynamical variability.
The response in other chemical families is also discussed and is consistent with past studies (Egorova et al., 2005).It was found that HO x increased in the upper stratosphere-lower mesosphere up to 2 % and limited the increase in O x in this region.NO x was found to increase during the day below 40 km by 1 %, and Cl x was found to increase during the day above 35 km altitude, with a peak of 1 % at 40 km.Ensemble simulations were performed using daily pseudo-random sequences of solar variability.The O x response was then regressed following two auto-regressive models with 2-and 3-predictors.The two predictors, common to the two models, are the previous day's ozone concentration and the current day's solar irradiance.The additional predictor in the 3-predictor model is the previous day's solar irradiance.The regression leads to coefficients of determination larger than 0.97 and 0.9992, respectively.The relative contribution of the current day's SI is found to dominate above 40 km, while the memory dominates below 40 km and remains non-zero in the upper stratosphere.In the 3-predictor model, the relative contribution of the previous day's SI peaks at 40 km and takes over the upper-stratospheric contribution of the memory term.The sensitivity of the regression coefficients was analysed with respect to initial concentrations of H 2 O (i.e.HO x ), NO x , O x and the temperature.The results are found to be sensitive to the temperature only, with a shift of the peak towards lower altitudes accompanied by a weakening of the magnitude of the non-normalised regression coefficients.This sensitivity is attributed to the temperature dependence of the NO x catalytic cycle.
Then, the two statistical models were evaluated for the prediction of the ozone response to solar variability when used off/on-line with a photochemical model representing the solar average chemistry.The bias and RMS errors were estimated relative to the ozone response.As expected, errors are larger in the 2-than in the 3-predictor Introduction

Conclusions References
Tables Figures

Back Close
Full model, and in the on-line than in the off-line mode.When used on-line, the memory term must be dropped from the model since it is carried over by the photochemistry model itself.This is expected to introduce an additional error.Nevertheless, when used on-line the 2-and the 3-predictor models have a bias smaller than 5 % and 1 %, respectively, and an RMS error smaller than 20 % and 15 %, respectively.This makes the on-line 3-predictor model an accurate candidate for a simple, fast module representing solar variability.
Finally, the linearity of the O x response, and thereby the validity of the statistical models, in an extended domain of solar variability was tested with solar maximum and solar minimum experiments.It was found that within the range tested here, extending the solar variability magnitude of Lean (1997) by a factor three uniformly through the spectrum, the response remains fully linear and the statistical models identical.However, magnifying the solar variability within a limited range of wavelengths from 200 to 400 nm led to a different linear relationship between response and solar variability magnitude, and to slightly different regression coefficients.
It is concluded that the 3-predictor statistical model offers an accurate, inexpensive approach for parameterising interactively the solar variability in CCMs with simplified chemistry (e.g.Taylor and Bourqui, 2005).This parameterisation can be driven on a daily basis by any solar variability index.In order to port one of the statistical models developed here on-line with a CCM, it needs of course to be extended to different seasons, latitudes and for a range of temperatures.It is also important to note that since the memory contribution has to be taken over by the photochemical module of the CCM, it is necessary to build the statistical model using a photochemical model which is consistent to that of the CCM.
A worth noting limitation of this study arises from taking the spectral solar irradiance and its variability from Lean (1997).Haigh et al. (2010) suggest that the variability in the ultra-violet range from 200 to 400 nm may be underestimated by a factor 4 to 6 in Lean (1997).As shown in the present study, while the ozone response remains linear with a factor three applied uniformly through the spectrum, it is highly sensitive to the range of wavelengths forced.It is therefore expectable that variable correlations between pairs of wavelengths through the spectrum may affect the simple response discussed here, where all wavelengths were assumed to vary together.Bolduc et al. (2011) suggest that the pair of wavelengths 240 and 300 nm may have a correlation well below 1.0, which may particularly affect the stratospheric chemistry through a decorrelation of photolysis processes for O 2 and O 3 .More generally, the statistical approach presented here based on ensembles of transient photochemical simulations sets a useful framework to measure the implications on stratospheric chemistry of different representations of spectral solar variability.It will be valuable to extend this study by applying its methodology to more realistic time series of spectral solar variability, such as spectral time series from SIM or SOLSTICE, or from semi-empirical solar models (e.g.Bolduc et al., 2011), and comparing results with the present study.Introduction

Conclusions References
Tables Figures

Conclusions References
Tables Figures

Back Close
Full    Full Fig. 1.Initial conditions used in the simulations for the interactive species (upper row) and the specified temperature and species (lower row) that vary with altitude.Initial conditions for specified species that have a constant mixing ratio with altitude are provided in Table 1.Solid lines of different colours correspond to regular initial conditions, while the dashed and dotted lines represent the two-standard deviation perturbed initial conditions used in the simulations testing the sensitivity to the initial conditions (see text for more details).Chemical species are shown in units of volume mixing ratio, and the temperature in K. Introduction

Conclusions References
Tables Figures

Back Close
Full Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Fig. 1 .
As mentioned above, in order to concentrate on photochemical processes and avoid any distorsion of the results by external forcing effects, the model is used in a pure photochemistry mode and includes no external sources and sinks, nor transport or diffusion.It also keeps temperatures and pressures constant over time, so that the Discussion Paper | Discussion Paper | Discussion Paper | effects of the diurnal cycle are included through the solar irradiances only.Simulations are therefore performed in a transient mode, where chemical concentrations change according to their individual lifetimes.The changes in individual families (as well as the reservoirs) over time in a control simulation with average solar conditions are given in Table is the solar irradiance spectrum on day i , I max (λ) is the maximum solar irradiance spectrum, and I min (λ) the minimum spectrum.The pseudo-random number x i is updated every midnight from a uniform distribution within [0,1].It is independent Discussion Paper | Discussion Paper | Discussion Paper | and temperature.These chemical species are chosen as they make the dominant contribution to ozone photochemistry.H 2 O is the main source of HO x , which dominates ozone destruction in the lower and upper stratosphere.NO x dominates ozone destruction in the middle stratosphere, and O x is chosen to see if different concentrations of ozone result in different responses to solar variability.Finally, temperature is chosen because of the temperature dependence of ozone destroying reactions.Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |Cl x : Fig.3shows that the minimum-to-maximum difference is positive for both Cl x and Cl Cl x .The increase in Cl x occurs during the day with a peak value of 3 pptv (∼1 %) around 40 km and slowly decays through the night.The difference for Cl Cl x is seen only during the day above 47 km, with a peak value of 2.4 × 10 −3 (∼0.4 %) at the top of the model.The increase in Cl x in the middle stratosphere is due to the enhanced conversion of Cl x reservoirs (mainly ClONO 2 ) back into Cl x due to enhanced photolysis during solar maximum conditions.Also, since photolysis is the primary decomposition channel for CFCs(Dessler, 2000) and the added Cl goes mainly into ClONO 2 and HCl, the increase in reservoirs results in a further conversion back into Cl x (via photolysis) during the day.The peak change in Cl Cl x at the top of the model (55 km) is due to increased O O x , resulting in an enhanced conversion of ClO to Cl (via O).Simulations by Egorova et al. (2005) found a decrease in ClO between 45 to 55 km, and are thus in agreement with the increase in Cl Cl x found here.Br x : Fig. 3 shows a negative difference in Br x occuring at night essentially above 45 km, reaching a peak value of −0.08 pptv (∼−0.3 %).For Br Br x , the difference is negative and is found during the day, with a peak value of −5 × 10 −3 (∼−2.5 %) around 42 km.Above 45 km, the large negative change in Br x during the night is due to the decrease in OH HO x (seen previously), resulting in an increased conversion of BrO to its reservoir HOBr (via HO 2 ), and thus a decrease in Br x .Similarly to stratospheric daytime is due to the increase in O x , resulting in an enhanced conversion of Br to BrO (via O 3 ).4 Results from ensemble simulations with daily random solar variability In this section, the effect of short-term solar variability on O x is approached from a statistical perspective using multiple linear regressions on ensembles of simulations.We focus on O x exclusively, with the underlying goal of building a simple statistical model Discussion Paper | Discussion Paper | Discussion Paper |

)
The superscript i is the day, overbars • represent the ensemble averages and σ • the ensemble standard deviation of the corresponding variable, and r is the residual.The regression coefficient β represents the standardised memory effect, γ the standardised SI effect and δ the standardised previous day's SI effect.By definition, these 32471 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | solar minimum and maximum spectra used in this study are reconstructions based on different proxies and are subject to large uncertainties.Haigh et al. (2010) showed that observed spectra from the Spectral Irradiance Monitor (SIM) and the Solar Stellar irradiance Comparison Experiment (SOLSTICE) instruments on satellite SORCE(Harder et al., 2005) differ very significantly from the Lean (1997) spectra for the period 2004 to 2007, with variability larger by factors of four to six in the range 200 to 400 nm, and an inversed variability between 400 and 700 nm.
Figure 9 (top) shows the results from additional pairs of simulations using the comprehensive photochemistry model with the departure between solar maximum and minimum spectra and the reference solar average spectrum magnified uniformly by a factor between 0.1 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | et al.
Discussion Paper | Discussion Paper | Discussion Paper | It is however difficult to evaluate how general these new results are, since the instruments SIM and SOLSTICE on satellite SORCE that are used in Introduction Discussion Paper | Discussion Paper | Discussion Paper | Haigh et al. (2010) only provide measurements since 2004 and show large differences in the range from 200 and 300 nm.

Fig. 9 .
Fig. 9. Normalised relative difference in O x concentration between solar maximum and solar minimum experiments for various solar variability magnitudes.The relative difference is calculated as the solar maximum-minimum difference divided by the O x concentration, and normalised by the solar variability magnitude.A solar variability magnitude of one corresponds to Lean (1997) solar maximum and minimum spectra.Top: photochemical model (PhM) with solar variability magnitudes from 0.1 to 3.0.Middle: photochemical model, 2-predictor model (2-PM) and 3-predictor model (3-PM) with solar variability magnitudes 1.0 and 3.0.Bottom: normalised relative difference at 37 km altitude as a function of the solar variability magnitude for the photochemical model and the 2-and 3-predictor models.In addition, the light blue line shows the response of the photochemical model with the solar variability magnified with respect to Lean (1997) only in the range 200-400 nm.
The coupled model is setup to calculate the photochemistry in each 1 km thick layer of a Figures

3 Results from simulations with constant solar irradiance
In this section results of constant solar irradiance simulations are presented for the following chemical families and partitioning ratios: O x , NO x , HO x , Cl x = {Cl, ClO}, Br x = {Br, BrO}, O

Table 1 .
Initial conditions for chemical species where mixing ratio is specified constant with altitude.Units are in mixing ratio.Initial mixing ratios that depend on altitude are given in Fig.1.

Table 2 .
Maximum percent change from initial condition throughout the stratosphere, after 5, 10, 15, and 25 days of simulation for the relevant chemical species, with corresponding altitude.