Nonlinear Response of Stratospheric Ozone Column to Chlorine Injections

With a reasonably complete and up-to-date photochemical model of the stratosphere, we find that the calculated stratospheric ozone-column response to chlorine injections is highly nonlinear. The model calculations assume that the background inorganic (or odd) chlorine, C1X, is due to CH3CI and CC1, v Additional C1X is added to the stratosphere by varying input fluxes ofCC12F e and CC13F. The sensitivity, AO3/AClX , of the stratospheric 0 3 column to added C1X is relatively small forCIX (cid:127)< 3 ppb orAC1X (cid:127)< 2 ppb; slight ozone increases with CIX are possible over a limited range of CIX if the formation of chlorine nitrate proceeds rapidly. This may have important implications for total ozone-column trend assessment. As C1X increases beyond 3 ppb, the stratospheric O3 column decreases with C1X increasingly rapidly. This marked departure from the linearity calculated in past years is largely due to presently accepted faster rates of reaction of OH with HNO3, HNO,(cid:127), HOe, and HeO e. If stratospheric C1X increases to about 9 ppb due to continued usage of CCIeF e, CC13F, and CH3CC13, the stratospheric O 3 colttmn depletion is calculated to be 6.7-9.0%. Principal uncertainties in these calculations, including the rate of formation of chlorine nitrate, the products of its photolysis, and the present day mixing ratio of C1X are discussed. Calculated ozone decreases due to increased NeO concentrations are also presented.


INTRODUCTION
The identification of human activities that can affect globalscale atmospheric chemistry has led to an intensification of research aimed at understanding both the natural and perturbed systems. Man's potential impact on stratospheric ozone, on the entire stratospheric photochemical system, and indirectly on climate has been recognized to involve a rich variety of coupled chemical and physical phenomena. Accordingly, efforts to understand the future impact of continued usage of chlorofluoromethanes (CFM), CH3CC13, and of nitrous oxide have broadened in scope to consider the coupled effects of increasing atmospheric CO2 and CFM concentrations [Luther eta!., 1977; Haigh and Pyle, 1979-1 and of stratospheric dynamics and chemistry [Harwood and Pyle, 1977;Garcia and Solomon, 1983]. Recently documented trends in atmospheric CH,• levels [Rasmussen and Khalil, 1981;Blake eta!., 1982] have been shown [Owens eta!., 1982] to be capable of influencing stratospheric response to CFMs. Further, the potential interactions of simultaneous increases in N20 and CFMs were investigated by Logan et al. 1-1978] even before the convincing documentation of an upward secular trend in N20 concentrations appeared in print [Weiss, 1981]. Further, Logan et al. [1978] demonstrated the potential effects of combustion-produced gases on tropospheric 03 and OH and through these OH changes, the effects on stratospheric chlorine and ozone concentrations. The more speculative but plausible increases in tropospheric ozone due to commercial aircraft operations [Liu eta!., 1980;Derwent, 1982] would necessitate a still broader view of atmospheric ozone perturbations, especially from the point of view of trend assessment in ground-based total ozone-column measurements. Simultaneous variations in CFMs, N20, CH,•, and tropospheric NO0, were investigated by Wuebhies et al. [1983].
Since 1974 when the CFM-O3 problem was identified by Molina and Rowland [ 1974], there have been many attempts to calculate future changes in stratospheric 0 3. Although more emphasis has been placed on potential decreases in the total ozone column (both in one-and two-dimensional models) the potential redistribution of ozone (large decreases at high altitudes and small changes or increases at altitudes below 30 km) is also of great scientific interest and possibly important to climate [Crutzen, 1974;Ramanathan and Dickinson, 1979]). During the 8-year period 1974-1982, the estimated sensitivity of total stratospheric ozone to CFM injections has varied [see, e.g., NAS/NRC, 1982] as model parameterizations and laboratory photochemistry and kinetics data improved. However, three features of the CFM-O 3 problem remained in updated calculations as originally estimated: (1) large O3 decreases were projected near 40 km altitude; (2) as CFMs were added to the atmosphere, the total 03 column diminished; and (3) an essentially linear response was observed between total 03 column and the amount of added CFM, or equivalently stratospheric odd chlorine, C1X. For a representative statement on the linearity of the response, see Miller et al. [ 1978].
In this paper, we show that an updated photochemical model of the stratosphere now predicts a highly nonlinear response of total stratospheric ozone to C1X increments. It is shown further that a change in the sign of the response might occur, at least over a limited range of C1X increments. Before presenting these results in section 3 and discussing them in section 4, we describe essential features of the model in section 2. This paper is not subject to U.S. copyright. Published in 1983 by the American Geophysical Union.

THE PRESENT MODEL
Despite its obvious meteorological shortcomings, the onedimensional eddy-diffusion/photochemical model of atmosvheric chemistry has been proven to be useful especially to

(km) (cm -3) (øK) (cm 2 s -•) (cm 2 s -•)
explore chemical sensitivities [see, e.g., WMO, 1982]. The present model adopts this approach wherein all vertical transport is parameterized as being proportional to concentration gradients with a common proportionality constant, K(z). The spatial domain under consideration, 10-80 km, the spatial grid points, and the adopted values for K(z), atmospheric temperature (fixed with time) and for atmospheric N 2 and 02 densities are shown in Table 1. The distinction between K•(z) and K2(z ) is as follows. K•(z) is essentially twice the values of the 1975 Hunten profile [Massie and Hunten, 1981] below 30 km but slightly greater still above 30 km. We constructed K2(z ) to provide better agreement between calculated and measured values of CF2C12, CFC13, N20 , and CH 4 than was attainable with K•(z). Note that K2(z ) is not more than 28% lower than K•(z) and is closer to K •(z) at most altitudes.
Photodissociation reactions included in this model are listed in Table 2 along with the reaction products adopted for standard case calculations; nonstandard-case assumptions are discussed later and in Table 4. Rates of photodissociation were calculated by subdividing the wavelength spectrum 175-1100 nm into 76 unequal subintervals. In the Schumann-Runge bands of 02, the transmission formulation of Hudson and Mahle [1972] was employed. From 295 to 315 nm, A2 was taken as 2 nm. Photodissociation by Lyman-alpha radiation was included for CH4, HC1, and H20. In all calculations, absorption by 02 and 03 and multiple scattering optics were included, the latter with essentially the formulation of Luther [1980]. Luther's method is a two-stream approximation that permits a variable number of calculations (or passes) through the scattering field. We adopted a threepass approximation; it agreed with more accurate six-pass calculations to within 1% for J values with the largest disagreement (about 1%) near the lower boundary, 10 km. Mid-latitude equinox geometry and 30 ø latitude were assumed. A planar atmosphere was assumed in these calculations; corrections for a spherical atmosphere would significantly affect zenith angles over 89 ø . We have accounted for the variation of sunrise (sunset) time with altitude, however. For example, with our model geometry sunrise occurs at 0540 at 25 km (0600 at ground level) and sunset occurs at 1820 at 25 km (1800 at ground level).
The present model does not follow a chemical-family grouping. Instead, a mass-conservation equation is solved for each individual chemical species, and, thus, assumptions of chemical equilibrium are avoided. In particular, for steady state calculations, solutions are calculated for 32 species, and as discussed in the appendix a flux-divergence term is included in each individual species equation . These are H20 , H2, CH4, CO, N20 ,   CH3C1 , CC14, CFC13, CF2C12, 03, O, N(4S), NO, NO2, NO3,   N205, HNO3, HNO½, H, OH, HO2, H202, C1, C10, HC1,  C1ONO2, HOC1, CH3, CH30 , CH302, CH3OOH, and CH20. For O(•D), HCO, and C1OO photochemical equilibrium is assumed, i.e., no flux-divergence term is carried in the equations. In our time-dependent calculations, 23 species are calculated as per the appendix, and the first nine species of the 32 listed above are held fixed at specified self-consistent initial conditions.
In our steady state model, a proper 24-hour averaging is included according to the procedure of Turco  As noted in the appendix, two distinct types of boundary conditions are employed for the chemical species. In the steady state model at 10 km fixed-flux boundary conditions (as opposed to fixed densities) are used for N20, CH3Cl, CCl,•, CF2C12, and CFCl 3. The exact flux values are adjusted to yield volume mixing ratios at 10 km as follows: N20 (0.30 ppm), CH3Cl (0.68 ppb), CC14 (0.125 ppb). As model parameters such as chemical reaction rates are varied, the input fluxes of these species must be readjusted to yield the stated mixing ratios. A fixed mixing ratio of 1.6 ppm is used for CH4 at 10 km except as noted in Table 4. Assuming a constant flux for species like CH3C1 (with appreciable tropospheric loss) is not an essential procedure; one might select a constant mixing ratio instead.  Table 4 describes fourteen different configurations of the photochemical models that we used to calculate the response of stratospheric ozone to chlorine injections. Except as noted in Table 4, the reaction rates listed in Table 3 and the photochemical data of Table 2 were Table 3. All models used K:(z) from Table 1  Because of the remaining uncertainties in laboratory kinetic data for k?2 and k67 , it is not completely clear as to which of the models of Table 4 are to be preferred. Models A, B, C, D, F, G, H, and I are not defensible based on available data; they were employed to study sensitivities. Further, model J, while possible, is hard to defend as available evidence suggests that C1ONO2 + hv-• C1 + NO3, not C10 + NO2. Models E, K, L, M, N are most likely, but k?2 is probably not the intermediate, standard value adopted in Table 3 and models E and K; it is either the NASA/JPL [1982] fast rate or the slow rate. Assuming that k67 is best chosen as the new, faster rate, our preferred models are M and N. Note once again that the rate, k72, of formation of chlorine nitrate is four times faster in model M than in model N.  Hudson and Kieffer [1975] Where no reference is shown, the critical review recommendations from NASA/JPL [1982] were adopted. Deviations from these standard rates and photodissociation products in certain of our calculations are noted in Table 4.    . An asterisk after a reference (e.g., a*) indicates that the adopted rate constant or reaction product is within the ra. nge of that recommended by reference a.  Table 5). In models E and M where presently accepted reaction rates and cross sections but different values for k?2 and k67 were used•, Figure lb shows that 03 decreased at altitudes above about 25 km and increased below about 25 km as C1X increases. Table 5 lists the values of C1X and of the ozone column (above 10 km) for each calculated point within each model group for these three models and the 11 others characterized in Table 4.

CIO + NO 2 + M • CIONO2 + M CIONO 2 + O--, C10 + NO + O 2 C1ONO 2 + OH • HOC1 + NO a H2CO + CI--} HCI + HCO
The nonlinearity of the calculated response of the stratospheric 03 column to added C1X is documented in Table 5. The slope of the O3-C1X curve is listed in the right-hand column of    Table 1) Standard rates and products of kinetic and photochemical reactions are shown in Tables 3 and 2' differences from standard choices are indicated here. Standard eddy-mixing coefficient is K2(z ) (see Table 1) except for model H. Methane was held at 1.60 ppm by volume at 10 km except in model D, where a fixed flux of 7.4 x 109 cm -2 s-x was used. In models K, M, and N the rate forHC1 + OH--, H20 + CI, i.e.,k67 is from  The C1X mixing ratio (ppb) is the high altitude asymptote of the C1X vertical profile [see Figure 1  Intermediate C1X values resulted from portions of these CFM fluxes. Within each model group, fluxes of CH3C1, CC14, and N20 were held fixed at the value that yielded the desired mixing ratios (listed above) when no CC12F 2 or CC13F was present.
If the response of total ozone to added C1X were linear the slopes in the right-hand column of Table 5 would be constant within each model group. Instead, the slopes are functions of C1X, often strong functions varying by factors of 5 or more or even changing sign in models L and M. Figure 2 shows the calculated ozone changes versus C1X for five different models. The responses are all nonlinear. Indeed, model M shows a net column ozone increase for AC1X less than about 3 ppb. The most nearly linear responses are found for models B, C, D, and G (see Table 5), all of which models are characterized by lower (and presently unaccepted) reaction rates for OH (i.e., not the standard rates of Table 3 To see more clearly how the nonlinearities arise requires more detailed analysis. We have examined ozone production and loss processes at several key altitudes. A term-by-term analysis of ozone production and loss terms at 26 km appears in Table 6 I  I  I  I  I  I  I  I  I  I  I  I Table 6 is purely diagnostic because have presented new evidence that the principal products (over 55%) are CI and NO3 in chlorine nitrate photolysis. Let us look more closely at the effects of adding chlorine to the stratosphere by focusing on two models, one (B) that is nearly linear in its response of column ozone to C1X and model M which is highly nonlinear. Figures 3a and 3b show the calculated change in 03 versus altitude for these models for three different levels of CIX. The linear scale (i.e., AO3 in units of 10 TM cm -3) allows one to see that the calculated nonlinear response of the stratospheric ozone column arises from the increase of ozone that appears below about 26 km. Qualitatively, the sequence of events that occur as CIX is increased is clear. First, the decrease in 03 above 30 km allows more UV light to penetrate to altitudes below 30 km, Wavelengths below 240 nm dissociate O2, and the ozone production rates increase. Larger UV fluxes (2 < 310 nm) also lead to elevated levels of O(•D) and thus increased OH and the ratio of HCI/CIO decreases. Further, the higher concentrations of C10 (elevated both by increased CIX and by the OH effect) allow more CIONO 2 to form, thus sequestering more NO 2. Higher CIO also increases the ratio NO2/qNO through reaction No. 60. Many other chemical feedbacks also begin, e.g., CF2C12, N20 , etc., are photodissociated more rapidly. Also, as the shape of the 03 profile changes, vertical fluxes of 03 change. Accord-    Table 4 Table 4. the actual calculation did not employ chemical families; the model equations were written for individual species and ratelimiting steps for odd-oxygen destruction, for example, were not identified or calculated in the model. Table 6 should be noted. First, the C1Xinduced increase in the 03 production rate, 2Jl[-Oe-I , is pronounced at 26 km. Second, the reaction NOe + O slows as C1X is added, largely due to the formation of additional C1ONOe. Also, the rates of the ozone-destroying reactions C10 + O and H OC1 + hv increase with C1X but at rates that are more than simple proportionality with C1X would predict. C10 and HOC1 densities increase for several reasons: (a) C1X increases, (b)NOe decreases as more of it is sequestered in C1ONOe, and (c) the increased penetration of UV light to 26 km leads to increased OH, thereby increasing the C10/C1X ratio, and to increased HOe. The increased HOe and C10 lead to increased HOC1 and to HOCI/C1X. Table 6   In  Table 6 exemplifies and in a one-dimensional steady state the divergence of the flux, (d/dz)[K(z)N(z) df/dz = P(z)-L(z) is nonzero, where f(z) is the ozone volume mixing ratio. This net photochemical production produces a downward flux that maintains the ozone concentrations at lower altitudes and feeds the troposphere. As chlorine is added to the stratosphere, ozone concentrations decrease above 30 km but the response below 30 km clearly depends both on photochemical processes and on transport. In our model B where the downward 03 flux decreases with added C1X at all altitudes, there is less incoming 03 at all altitudes below 29 km (see Table 7) and 03 concentrations are decreased there (see Figures lb and 3a). In our model M, 03 is decreased above 30 km as one adds C1X and 03 increases below there at first (see Figure 3b) largely due to the behavior of the downward 03 flux ( Table 7). As C1X increases further, the crossover altitude where AO3 = 0 moves downward. The downward movement of this crossover altitude is largely explained, at least in a one-dimensional ( ,-•,j model, by L,e sign of the change in the downward 03 flux (see Table 7) at each altitude as C1X increases.

This chain of events occurs in both B and M and similar net changes occur in ozone-production minus ozone-loss terms. For models B and M at 26 km, photochemical production (P) of 03 exceeds losses (L) for all C1X values. Indeed, P-L increases with C1X in model B and in model M except for the last increase of C1X in model M. While this term-by-term analysis is incomplete because some less important terms have been omitted (e.g., 2k3o[-HO2][O ] and 2Jal-NO3] [Johnston and Podolske, 1978] it does indicate that an analysis of photochemical terms at a single altitude is not capable of explaining why model B differs from model M and how the nonlinear response of total column ozone originates. An analysis similar to that in
The possibility of a strongly nonlinear response of the stratospheric zone column to added chlorine has important consequences for ozone trend detection. In Figure 4, Table 4, a fast k72 (rate of formation for CIONO2) is adopted in model M and a slow rate, about one-fourth as fast is adopted for k72 in model N. The NASA/JPL [1982] critical review of chemical rate constants states that both of these choices for k72 are presently acceptable, although in reality the true rate is either the fast rate or the slow rate, and not their average. If the fast rate applies, our model finds that ozone increases slowly until about A.D. 2010 and then ozone decreases rapidly with further increases of CIX. Table 5 shows that the total ozone decrease attained at C1X = 9.38 ppb (or AC1X = 8.23 ppb) is 6.78% in model M. In model N, total ozone decreased by 8.95% in going to C1X = 9.12 ppb (AC1X = 7.96 ppb).
The small, but potentially important, 03 increases shown for model M in Table 5 and Figure 4 and for model L in Table 5 are not due to numerical inaccuracy in our model as three facts indicate. First, our numerical convergence criterion, that each variable must converge to better than 10-3 at each spatial grid point before terminating the iteration (see appendix), forces the - .   I  I  I  I  •  I  I  I  I  •  I Table 4). Total i•o•a•ic chlorine, CId, mixin• •atio is ].• ppb at km i• FiSu•e 5a and 2.56 ppb i• Fisu•e 5•. conver•ed solution for the O3 vertical pm•le to be at least this accurate. Even ff the O3 densit• at each altitude were s•stematicall• in error in the same dkcction (hi•hl• unlikely), the column would be in error b• less than ]/1•0. Table 5 Table 4) with CIX = 2.44 ppb at 50 km. Figure 5b shows noontime concentrations of these species calculated with the photochemical data specified by model M of Table 4 and 2.56 ppb CIX. Compare the values for the Cl-containing species:relative to Figure 3a, the CIO concentrations in Figure   3b are 0.73, 0.82, 1.10, and 1.15 at 26, 30, 40, and 44 1.09, and 1.14. For HC1 they are 0.67, 0.68, 0.91, and 0 concentrations. In th,•, ß ca!cu-......... 1" ...... N20 lations the input flux of NeO was increased above the value needed to sustain a 300 ppb mixing ratio at 10 km. With all standard rate constants except for the new, faster k67 (i.e., model K) increasing the N20 input flux by 50% led to a 5.27% total ozone decrease. With k?2 twice as fast (i.e., model M) total ozone decreased 5.56% and with the slow rate of CIONO 2 formation (i.e., model N) total ozone decreased 5.04%. These calculations with 150% normal N20 flUX inputs lead to mixing ratios of 440 _ 3 ppb at 10 km. The calculations took fixed fluxes ofCH3CI , CC14, CF2CIe, and CFC13g C1X began at about 2.52 ppb and dropped to about 2.42 ppb as NeO increased. When the CIX background was raised to 5.3 ppb and the NeO flux subsequently increased by 50%, the added led to total ozone decreases of 3.05, 3.38, and 2.85 % for models K, M, and N rate constants, respectively. Further calculations were performed to examine the linearity of the 03 response to added N20. The input flux of NeO was varied between the value needed to produce 300 ppb NeO at 10 km in an unperturbed atmosphere to flux values 1.2, 1.5, and 2.2 times larger. With near-present CIX background, i.e., 2.52 ppb, a slight nonlinearity appeared in the sense that the percentage ozone loss per ppb of added NeO decreased as NeO levels increased. At higher, presumably future levels of stratospheric C1X (5.3 ppb), the nonlinearity switched sense (i.e., the 03 loss per unit of added N eO increased as NeO increased).
The corresponding increased production of stratospheric NO and downward flux of odd nitrogen into the troposphere would tend to increase the tropospheric odd nitrogen. This may in turn increase tropospheric ozone.

DISCUSSION AND CONCLUSION
In this report we have shown that a distinctly nonlinear response of the stratospheric ozone column to chlorine injections is likely, or at least, this is the response predicted by our updated 1-D photochemical models. Specifically, Table 5 and Figure 2 showed that the sensitivity of total stratospheric ozone to added CIX, AO3/ACIX, is a strong function of CIX, especially in the range of 1 < CIX < 4 ppb, or 0 < ACIX < 3 ppb, where ACIX is the CIX not attributable to CH3CI and CCI,•. The only model calculations that showed weak or moderate nonlinearities were•those that employed out-of-date rate constants for OH + HNO3, OH + HNO,• and OH + HOe or which assumed that C1ONOe + hv--• CIO + NO2, products not deduced in the NASA/JPL [1982] critical review. Given that the present CIX mixing ratio (at 50 km) is now approximately 2.5 ppb (i.e., ACIX = 1.4 or 1.5 ppb) and that CIX = 4 ppb (or ACIX about -3 ppb) is not predicted to be attained until A.D. 1995 or 2000 [Logan et al., 1978;Cicerone, 1981], the problem of ozone trend assessment takes on a new complexity. If our calculations are accurate (see caveats below), then CFMinduced stratospheric ozone depletions of order 1% will not materialize until after A.D. 2000 when CIX reaches 5 ppb or more. This latter figure comes from Table 5, models K, L, M, N, the models with presently most credible rate constants for chemical reactions. Further, as is shown in Figure 2 and Table  5, AO3/ACIX becomes very strongly negative for CIX > 5 ppb so that the rate of ozone decrease in the early 21st century could accelerate greatly. Eventual ozone column reductions due to continued release of CCIeFe and CCI3F are estimated to lie between 6.8 and 9.0% assuming a new, faster rate for OH + HCI--• H20 + CI from M. J. Molina (private communication, 1982).
The non!inearities evident in our results arose from an essentially controlled numerical experiment in which (1) a fixed CH,• mixing ratio was assumed at 10 km, (2) fixed fluxes of NeO, CH3CI, and CCI,• were input at 10 km, and (3) stratospheric COe and temperature were held constant. In reality, all of these factors appear to be varying; see discussion and references in section 1. Further, and very important for ground-based total ozone-column trend assessment, secular trends in tropospheric ozone are possible [see, e.g., Liu et al., 1980]. A 10% change in tropospheric 03 is about a 1% change in total ozone. The present calculations do predict large future decreases in 03 concentrations near 40 km altitude, however, as did previous calculations.
The possibility of small stratospheric ozone-column increases cannot be eliminated. Indeed our calculations (models L and M) found this kind of result for CIX < 3 or 4 ppb when the rate of formation, k7e , of C1ONO• (chlorine nitrate) was set equal to the faster of the two rates in NASA/JPL [1982]. With the slower rate for k72 , i.e., one-fourth the fast rate, no ozone increases were calculated nor were they when an intermediate rate (standard rate in Table 3) was assumed. Accordingly, it appears very important to (1) settle the issue of possible isomer formation in CIO + NO e + M--• products and to determine the rate of formation of C1ONOe at stratospheric pressures and temperatures, and (2) obtain quantitative measurements of stratospheric CIONOe. Many other photochemical processes, e.g., the products of HNO,• photodissociation need further investigations.
Our results do not depend on model assumptions such as chemical family groupings or on the exact choice of K(z), the eddy-diffusion coefficient. More rigorous calculations with models that embody stratospheric dynamical meteorology are clearly needed, however. Also, while it is well known that the efficiency of ozone destruction by chlorine atoms is an increasing function of altitude [Cicerone et al., 1974;Wuebbles, 1983] and that the stratosphere of the future will receive C1 atoms from an increasingly wide spectrum of chlorocarbons and chlorofluorocarbons, our present results will not be very sensitive to changes in this input-species spectrum. Further, our small adjustment to O e cross sections in the Herzberg continuum (see section 2) did not affect the nonlinear character of the 03 response to CIX. If present-day stratospheric C1X concentrations greatly exceed the commonly believed 2.5 ppb the total ozone response to added CIX could differ greatly from that shown in Figure 4 because of the strong dependence of AO3/ACIX on C1X shown in Figure 2 and Table 5.
Finally, our calculated loss of total stratospheric 03 due to 50% increases in upward NeO fluxes from the troposphere are about 5% when background C1X is near presently assumed values (2.5 ppb) and near 3% if CIX grows to 5.3 ppb. Small nonlinearities were observed in the ozone response to increases in NeO levels.  All symbols are the same as listed in Table 8.