Journal of the Meteorological Society of Japan, Vol. 78, No. 5, pp ,

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1 Journal of the Meteorological Society of Japan, Vol. 78, No. 5, pp , Modeling of Chemistry and Chemistry-radiation Coupling Processes for the Middle Atmosphere and a Numerical Experiment on CO2 Doubling with a 1-D Coupled Model By H. Akiyoshi National Institute for Environmental Studies, Tsukuba, Japan (Manuscript received 19 August 1999, in revised form 6 June 2000) Abstract A family method chemical scheme, and a chemistry-radiation coupling scheme for the middle atmosphere, have been developed. These schemes are also applicable to a future atmosphere where concentrations of greenhouse gases and halogen gases will be different from the present atmosphere. A onedimensional, chemically radiatively coupled model has been constructed to test the scheme. A method of photolysis rate calculation flexible enough for any radiation calculation scheme on plane-parallel atmosphere, a definition of globally averaged solar zenith angles for the 1-D model, and development of a chemical scheme to which heterogeneous reactions on aerosols or Polar Stratospheric Clouds are easy to incorporate are presented. The model includes 163 gas phase chemical reactions of oxygen, hydrogen, nitrogen, hydrocarbon, chlorine, and bromine species for the stratosphere. Although heterogeneous reactions are not considered in this paper, the schemes are flexible for including these reactions. Vertical profiles of concentrations and photolysis rates of chemical constituents at a steady state of the model, and the temperature profile are presented and discussed. Comparison of these profiles with reference profiles in JPL-97, shows that they were successfully calculated by this scheme in the model. Numerical experiments on C02 doubling with the 1-D model shows that total ozone variation after C02 doubling is different between the coupled model, and in a fixed photolysis rate model. Mechanism of the slow, extended variation of total ozone in the coupled model is discussed. It is shown that reduction in solar radiation penetration into the atmosphere by 03 increase due to the C02 doubling, made considerable effects on chemical constituent concentrations in the lower stratosphere. 1. Introduction 3-D chemical transport model is a useful tool to study global chemical processes and transport processes in the atmosphere (e.g., Lefevre et al. 1994; Rasch et al. 1995; Zhao 1995; Chipperfield et al. 1996a, Chipperfield 1999). However, a chemical transport model is insufficient to study future trends and variations in atmospheric chemistry and transport, because atmospheric temperature and winds are not predicted in the model, but given as data. Not only chlorofluorocarbons, but also other greenhouse gases such as C02 change ozone concentration through the radiation process. The ozone change causes temperature change, which causes change in transports of ozone and other chemical constituent Corresponding author: Hideharu Akiyoshi, Global Environment Group, National Institute for Environmental Studies, Tsukuba, , Japan. hakiyosi@nies.go.jp 2000, Meteorological Society of Japan transport. Thus in the real atmosphere, chemical processes, dynamical (transport) processes, and radiation processes interact complicatedly. We do not know to what degree these interactions are important in the present atmosphere and in the future atmosphere, where concentrations of halogen gases and greenhouse gases will be considerably different from those of the present atmosphere. Several studies on these interaction mechanisms have been done by developing interactive 3-D chemistry models. Austin et al. (1992) showed by their chemistry GCM, in which effects of ozone radiative feedbacks were included, that C02 doubling would cause a severer Arctic ozone depletion due to an increase in PSC amount and the duration through stratospheric temperature decrease, and polar vortex intensification. Zhao et al. (1996, 1997) showed volcanic aerosol effects on the Arctic chemistry and on the Arctic polar vortex persistence in winter and early spring by their coupled chemistry GCM. Thus

2 564 Journal of the Meteorological Society of Japan Vol. 78, No. 5 an interactive chemical-radiative-dynamical model is necessary for understanding interaction mechanisms of the atmosphere, and for prediction of the future atmosphere. For developing a fully interactive chemicalradiative-dynamical model, a chemical-radiative coupling scheme and a chemistry scheme based on the family method for the middle atmosphere were developed. A 1-D chemical-radiative coupling model was constructed, and a steady state was calculated to test the developed coupling scheme. The purpose of the 1-D model construction is to check the vertical distributions of all the chemical component concentrations and the photolysis rates calculated by the coupling scheme, and to understand some interaction mechanisms between stratospheric chemistry and radiation by making C02 doubling experiments in the model. It is easy to incorporate this coupling scheme into a 3-D model which has fewer radiation spectrum bins, although some modifications are needed on radiation parameters such as spectral mean absorption cross sections of chemical species. The chemistry-radiation coupling schemes are given in Section 2. The 1-D coupled chemistryradiation model is described in Section 3. Results of a steady state calculation for the present atmosphere, and C02 doubling experiments are shown in Sections 4 and 5, respectively. Discussion is made in Section 6. Concluding remarks are given in Section Chemistry-Radiation coupling in the middle atmosphere Four chemical-radiative coupling processes were explicitly considered in the model: (1) Photolysis rates calculated directly from solar radiation transfer equations, (2) Temperature dependence of chemical reaction coefficients, (3) Temperature dependence of absorption cross sections of chemical constituents, and (4) Renewal of radiatively active chemical constituent profiles in the radiation calculation. The inclusion of temperature dependence of chemical reactions into the model was quite easy, by directly using the Arrhenius form or other mathematical expressions in JPL-97 publication (DeMore et al. 1997), and is not mentioned particularly in this text. 2.1 A direct photolysis rate calculation from radiation transfer equations It was assumed in the model that solar energy absorbed by all chemical constituents was used to photolyze chemical constituents as well as to heat the atmosphere. This assumption is justified with sufficient accuracy in the stratosphere, because almost all of the atmospheric heating in the stratosphere is due to ozone, and because atomic oxygen produced by ozone photodissociation immediately recombines with oxygen molecules and deposits the reaction heat at almost the same place. Furthermore, the other radicals produced by photodissociation have either much shorter lifetimes than the transport time scales, like atomic oxygen, or little effects on the heat budget due to the much smaller amounts or the much smaller absorption cross sections than those of ozone. Solar radiation spectrum was divided into 131 spectral bins in the model. Since solar radiation flux per unit area on the plane-parallel atmosphere obtained by a radiation scheme only contains information on the total amount of absorption energy by all chemical species involved with the absorption, it is necessary to distribute the total absorption energy into energy absorbed by each chemical species. Thus absorption weight function oixi was defined, and photolysis rates of chemical species i, J(z), were calculated as a function of chemical species and altitude as follows: J(z)=Ji(aj, z), J(,z)-qi(A)zF(,3,z) nabsi(ai,t(z))xi(z) i.labsn(a,t(z))x(z) jn n=1 xi(z)nair(z)lzhe zf(,j,z)=[tf(aj,z+liz)-t'f(1,z)} -[F(a,z+Oz)-j,F(A;,z)], where Ji (A, z) is spectral photolysis rate of the chemical constituent i at the spectral bin a at altitude z, qi P') is the quantum efficiency for photolysis of chemical constituent i at A3, OF(A, z) is the spectral net radiative energy divergence of a plane-parallel atmosphere at z, crabs i (Ai, T (z)) is the spectral absorption cross section of constituent i at the temperature T (z) at z, xi (z) is the volume mixing ratio of constituent i at z, nair(z)lz is the column density of the air molecule in the layer at z, h is the Planck constant, c is the light velocity, N is the number of species which have the absorption bands in the spectral bin ), and t F(z) and, F(z) are upward and downward radiation fluxes at z, respectively. They were defined as the normal component of radiance per unit area at the boundaries of plane-parallel atmospheric layers. Note that z F(), z) was calculated from the solar radiation transfer equations, and also used to calculate heating rates of the atmosphere by OizJ 'g LXrA,zJ &t(l(zlan(zl where g is the acceleration of gravity, Cp is the specific heat of air, and Lip is the pressure difference

3 October 2000 H. Akiyoshi 565 between the upper boundary and the lower boundary of the atmospheric layer. In the photolysis rate equations, the third factor on the right hand side of the second equation represents the ratio of energy absorbed by constituent i to that by all N radiatively active species, the fourth factor gives the energy absorbed by one molecule of the species i, and the fifth factor translates the absorption energy into the photon number. This is an equation for photolysis rate calculation flexible enough for any radiation scheme on a plane-parallel atmosphere. See Section 6 for detail. The absorption cross section data of the chemical species were taken from JPL-97, and used for photolysis rate calculation. Mean cross sections of chemical species in each spectral bin of the model were obtained by interpolating the JPL-97 data logarithmically or linearly with respect to wavelength, case by case, and averaging within the bin. Ozone cross section data at wavelengths longer than nm, the data at 203 K between nm and nm were taken from WMO-85 (World Meteorological Organization 1986), because they were not listed in JPL-97. Note that the data of JPL-97 is the same as those of the WMO-85 except for wavelengths between and nm. Photolysis rates of chemical constituents except for 02, NO, and H2O were calculated by the 2-stream approximation in the radiation subroutine. The photolysis rate of 02, NO, and H2O in the 02 Schumann-Runge bands were computed by the parameterization of Minschwaner (1993), of Allen and Frederick (1982), and of Nicolet (1984), respectively, because in the 02 Schumann-Runge bands it is difficult to define effective spectral mean absorption cross sections of these species for the 2-stream calculations. Column abundance of 02 and 03 from the top of the atmosphere to each atmospheric layer along the light pass, is used for these parameterizations. 2.2 Temperature dependence of absorption cross sections o f chemical constituents Temperature dependence of absorption cross sections of the following species was taken into account in the model: 03, CH2O, H202, N20, NO2i HN03, N205, ClON02, CFC13, CF2C12, CH3CC13, CH3C1, CCIF2CC12F, CHC1F2, C12, CHBr3, CF2C1Br, CBrF3, CF2Br2, and BrCI. The spectral temperature dependence data of DeMore et al. (1997) were averaged with respect to wavelength within the model spectral bin, and fitted linearly or quadratically with respect to temperature except for CH3C1 and CHC1F2. Linearly and quadratically mathematical fittings of these two species over the whole temperature range were difficult. Then the linear dependence between each data point was assumed. If temperature in the model rose or fell outside the regions appropriate for the temperature dependence parameterization, maximum or minimum temperature within the valid range were used instead. See Akiyoshi (1997) for detailed description of parameterizations for the temperature dependence. 2.3 Renewal o f radiatively active chemical constituent profiles in the radiation subroutine New distributions of chemical component concentrations were calculated by the chemical subroutine of the model, and directly used by the radiation subroutine with the time resolution of one hour. In the thermal radiation calculation, the new vertical profiles of 1120 and 03 volume mixing ratios were used, while in the solar radiation calculation, the new profiles of all the photolysis species were used. Volume mixing ratios of chemical constituents were converted into the number densities, using the latest temperature profile calculated in the radiation subroutine. 3. Model description A 1-D coupled chemistry-radiation model was constructed to test the chemistry-radiation coupling scheme described in Section 2. Vertical distributions of the chemical constituent concentrations, photolysis rates, and temperature at a steady state were calculated and discussed. 3.1 General description of the 1-D coupled chemistry-radiation model In the 1-D coupled chemistry-radiation model, most basic data, such as solar spectrum data, spectral absorption cross section data of chemical constituents, chemical reaction coefficients, and vertical eddy diffusion coefficients for the atmosphere were given. No other artificially assumed parameters were given. Hence, this model is able to calculate photolysis rates of chemical constituents self, consistently, even if vertical profiles of temperature and chemical constituent concentrations, and solar radiation fields in the atmosphere are changed by CO2 increase, by stratospheric aerosol increase, or by halogen concentration increase/decrease. The model consists of plane-parallel atmospheric layers of 2.5 km thickness on the log-pressure coordinates with a bottom layer of 1.25 km thickness. The pressure scale height is 7 km. The model atmosphere was set from the ground surface up to 60 km on the log-pressure coordinates. Vertical transport of chemical constituents was calculated with timeindependent eddy diffusion coefficients. Transport by vertical advection was not considered. Water vapor mixing ratio in the troposphere below 17.5 km was calculated from a fixed vertical distribution of relative humidity presented in Table 5 of Owens et al. (1985), while in the stratosphere above 17.5 km, water vapor was predicted chemically with vertical diffusion. At 17.5 km, water vapor mixing ratio was fixed to 3.5 ppmv. An equinox condition of 12 hour

4 566 Journal of the Meteorological Society of Japan Vol. 78, No. 5 daytime and 12 hour nighttime was assumed without any seasonal variation. The family method was used for photochemical calculations, and both daytime and nighttime chemistries were formulated separately. Chemical families and long-lived chemical species were predicted numerically with a time resolution of 1 minute. For radiation calculation, time resolution was 1 hour. The 2-stream approximation was used for solar radiative transfer calculations on 131 spectral bins, while the Malkmus band model for absorptions and emissions by H2O, C02, and 03 was used for the terrestrial infrared radiative transfer calculations in 31 spectral bins. A radiativeconvective adjustment process was considered to calculate temperature in the troposphere. Clouds were not considered in the model. The ground surface albedo for solar radiation was adjusted to 0.26 to make a realistic surface temperature. Ground surface temperature was calculated assuming that the ground was a black body, and that the outgoing upward thermal flux from the ground instantly balanced the downward solar flux and thermal flux into the ground. The temperatures and photolysis rates necessary in the photochemical subroutines were calculated every hour by the radiation subroutine, while vertical profiles of ozone, water vapor, and the other chemical constituent concentrations necessary in the radiation subroutines were also renewed every hour by the photochemical subroutine. 3.2 A definition of globally annually averaged solar zenith angles Diurnal variation of solar zenith angle is a necessary factor for a chemically radiatively coupled model, since the vertical distribution of ozone changes in response to solar zenith angles, and that results in a change in the vertical temperature distribution. In a 1-D model with a fixed vertical profile of ozone concentration, there was no appreciable difference in temperature distributions between the result from the fixed solar zenith angle of 60 and that from the diurnally variable solar zenith angle. However, the difference could not be neglected in the coupled model. In the coupled model, vertical distributions of temperature and ozone became more realistic with the diurnal cycles, compared to those with unrealistically high altitude maxima without diurnal cycle of a fixed solar zenith angle of 60. This is the reason why at least diurnal variation effect was taken into account in this model. However, an accurate simulation of the diurnal cycle is not the purpose: For example, an accurate calculation at sunrise or sunset when the solar zenith angle is close to 90 degrees is out of purpose for this paper. For this global mean 1-D model, solar zenith angles were originally defined from a global mean point of view on an equinox condition. The zenith angles were calculated quite geometrically considering the 6:00-7:00 hours and 17:00-18:00 hours 7:00-8:00 hours and 16:00-17:00 hours 8:00-9:00 hours and 15:00-16:00 hours 9:00-10:00 hours and 14:00-15:00 hours 10:00-11:00 hours and 13:00-14:00 hours 11:00-12:00 hours and 12:00-13:00 hours Fig. 1. Longitudinal belts for calculation of global mean solar zenith angles. See the text for details. energy absorbed by the earth as follows: Equally divided N longitudinal belts in the daytime hemisphere were considered. The solar zenith angle for the i-th longitudinal belt 8 was defined as follows; cos 8 (projected area o f longitudinal belt)i 2=, 2ira2 N where i indicates the i-th longitudinal belt, and a is the radius of the earth. The numerator on the right-hand side of the equation means the projected area of the longitudinal belt onto the plane perpendicular to the incident sunlight. This definition gives the global mean, globally energy conserved solar zenith angles; that is, the sum of the solar energy received by each longitudinal belt on which the solar zenith angle 8i was defined, is equal to the solar energy actually received by the whole daytime hemisphere of the earth. N =12 was taken for calculations presented here, which means solar zenith angles were defined every hour in the longitudinal belt of 15 width as shown in Fig. 1. The projected area was evaluated geometrically by calculating the area of plane ellipses. If just one longi-

5 October 2000 H. Akiyoshi 567 tudinal belt (N=1) is considered in the daytime hemisphere, the equation gives the zenith angle of 60 with the projected area of rra2. This is the global mean zenith angle in the daytime hemisphere as used in some traditional radiative equilibrium calculations and radiative-convective adjustment calculations (Manabe and Strickler 1964; Manabe and Wetherald 1967). The global mean zenith angles evaluated for N= 12 were: 01 and 012=84.13 (from 6:00 to 7:00 hours, and from 17:00 to 18:00 hours, respectively), 02 and On=72.56 (from 7:00 to 8:00 hours, and from 16:00 to 17:00 hours, respectively), 83 and 810=61.53 (from 8:00 to 9:00 hours, and from 15:00 to 16:00 hours, respectively), 84 and 99=51.59 (from 9:00 to 10:00 hours, and from 14:00 to 15:00 hours, respectively), 05 and 88=43.65 (from 10:00 to 11:00 hours, and from 13:00 to 14:00 hours, respectively), and 96 and 07=39.06 (from 11:00 to 12:00 hours, and from 12:00 to 13:00 hours, respectively). 3.3 Photochemistry The family method was used for the chemical calculations. Five families were defined in this model as follows: OX=O(3P) -f- O(1D)+03, HO X = , NOX=N+NO+NO2+NO3, C10X=C1+C10+2C1202+C100+OC10, BrOX=Br+BrO. Initially, Yang et al. (1991) was referenced for formulations of prediction equations for these families and long-lived species, such as methane and nitrous oxide, and equilibrium equations for shortlived species. A temporary version of our 3-D chemical model without heterogeneous chemistry essentially followed their photochemical formulation (Takigawa et al. 1999), but Yang et al.'s formulation is valid only for a gas phase photochemical system; some of the photochemical equilibrium equations and even the prediction equations for long-lived species should be modified, when heterogeneous reactions have deeper effects on the gas phase chemistry. To make a more flexible formulation for a chemical system with heterogeneous reactions, chemical species of reactants and products from heterogeneous reactions on sulfuric acid and Polar Stratospheric Clouds such as HNO3, N205, C1ONO2, HCI, HOCI, C12, HOBr, BrCI, BrONO2, and Br2 were separated from families and treated as prediction variables. We used primitive photochemical equations: For example, HO X photochemical equilibrium equation was deduced by just considering the net chemical production/loss rates, without introducing any other photochemical equilibrium assumptions into the equation (See Appendix for detail). Furthermore, bromine chemistry was added to the model and some modifications to HO X, NO X, hydrocarbon, and CIOX chemistry were made, referring to the formulation of the SLIMCAT model of Cambridge University (Chipperfield 1996b) and Brasseur and Solomon (1984). OX, HOx, NOx, CHOX, and C10X chemical reactions considered in our original model were listed in Appendix 1 of Akiyoshi (1997). Newly added chemical reactions for the present model were listed in Table. In the table, k indicates reaction coefficient for two body reaction, l indicates that for three body reaction, and tc indicates a reaction that was added from the SLIMCAT model. Chemical families and long-lived chemical species were predicted numerically by the explicit Euler forward scheme with a time step of 1 minute. The chemical scheme developed here was stable with time steps shorter than 5 minutes of that explicit scheme. Calculation of photochemical equilibrium species was iterated 5 times in the chemical subroutine at the same time-step, because the concentrations were calculated in order of OX species, HO X species, NO X species, hydrocarbons, C10X species, and BrOX species in the model, and the concentration calculations of each family member need concentrations of other family members (See the [OH] equation in Appendix). Volume mixing ratios of 02, N2, 112, and CO2 were fixed to , , 0.5 ppmv, and 350 ppmv, respectively, at all the model pressure levels. Mass flows of chemical constituents at the top of the model were assumed to be zero. Volume mixing ratios of some of the chemical constituents were fixed at the surface to the values for the early 1990s atmosphere: N20=308 ppbv, CH4= ppmv, CO=100 ppbv, CH3Cl=600 pptv, CFC13=246 pptv, CF2C12=422 ppty, CC14= 105 pptv, CH3CC13 =136 pptv, CHC1F2 88 pptv, CCIF2CC12F=15.3 pptv, NO y=0.825 ppbv, 11202=18 ppmv, CH3Br=9.06 ppty, CHBr3= 1.84 ppty, CF2C1Br=2.77 ppty, CF3Br= 1.65 pptv, and CF2Br2=0.5 pptv. These boundary conditions for chlorine and bromine source gases resulted in concentrations of 3.1 ppbv for Cly and 20 ppty for Br y in the upper stratosphere at a steady state of the model. The value of CHBr3 was determined so that Br y in the upper stratosphere became 20 ppty. The value is consistent with the observations in the marine boundary layer and in the Arctic troposphere (Yokouchi et al. 1996, 1997, 1999). The 03 volume mixing ratio was not fixed at the surface, but calculated with the deposition velocity of 0.22 cm s-1. The 1120 volume mixing ratio at 17.5 km was fixed to 3.5 ppmv and relative humidity was fixed below 17.5 km, as described in Section 3.1.

6 568 Journal of the Meteorological Society of Japan Vol. 78, No Radiative transfer The radiation flux in a plane-parallel atmosphere was calculated as a function of wavelength and altitude. Spectral range from tam to 100 tam was divided into 162 spectral bins. The fluxes were calculated on the upper and lower boundaries of each homogeneous atmospheric layer. The boundaries were set at 0.0 km, 1.25 km, 3.75 km, 6.25 km, 8.75 km, km,..., and km on the logpressure coordinates. Absorbed fluxes were converted into atmospheric heating rates, and photolysis rates as described in Section 2.1. In the solar spectra between tam and 5 tam, the 2-stream method (Hybrid modified Eddingtondelta function method formulated by Meadow and Weaver (1980)) was used to calculate absorption and scattering effects due to the air molecules. Solar spectrum was divided into 131 spectral bins finely so that the absorption bands of any chemical constituent can be sited over at least a few bins of the model. See Akiyoshi (199.7) for the spectral bins and the solutions of upward and downward monochromatic diffusive fluxes. Solar heating rates were obtained by integrating monochromatic flux convergence over the full wavelength range of the solar spectrum, as shown by the last equation in Section 2.1. Photolysis rates were also obtained from the same flux convergence using the three equations in Section 2.1. In the thermal spectral region between 4.7 um and 100 tam, absorptions and emissions of the thermal radiations due to the H2O rotational bands, the H2O 6.3 tam vibrational-rotational bands, the H2O continuum, the CO2 15 tam bands, and the tam bands were considered. The thermal spectrum was divided into 31 spectral bins in accordance with those used by Roewe and Liou (1978), but note that the parameters for 03 in Table 1 of their paper were wrong; see Table 4.1 of Liou (1980) for the correct values, which were used in this study. These spectral mean parameters of Lorentzian line shapes for the Goody random model can be applicable for the Malkmus model with the same parameter values (Malkmus 1967; Brasseur 1997). Thus instead of using the Goody model, the Malkmus model was actually used, because the Malkmus model is more accurate than the Goody random model especially in weak or medium absorption bands. To calculate absorptions and emissions along the optical pass in an inhomogeneous atmosphere where pressure and temperature varies, the Curtis-Godson two parameter approximation was employed. Net heating rates over the whole spectrum from UV to far infrared were then calculated by summing up each heating rate. Then temperature was predicted numerically with the time step of 1 hour. Furthermore, a radiatioe-convective adjustment process was applied in order to make the temperature distribution realistic in the troposphere. The scheme described by Wang et al. (1984) was used, which was that described in Manabe and Wetherald (1967) with some modifications. Geometric heights of log-pressure levels were calculated from the hydrostatic balance equation, and used in the radiativeconvective adjustment scheme, assuming the lapse rate of -5.6 K km-1, which can be a global average value from Table 2 of Wang et al. (1984). 3.5 Vertical transport Vertical transports of long-lived chemical species were considered in the model with time-independent eddy diffusion coefficients. Figure 2 shows the diffusion coefficient distribution used in the model. 4. Results of a steady state calculation Steady state calculation started from the tentative initial profiles of temperature and chemical constituents based on observations and 1-D model calculation results (McClatchey et al. 1972; McPeters et al. 1984; Brasseur and Solomon 1984). A twenty year numerical calculation was performed to obtain a steady state of the model, because at least 10 years was needed for this model to reach a quasi-steady state in which appreciable variations of temperature, ozone, and the other chemical constituents disappeared but smaller and slower variations still existed. Strictly, the steady state is not the real one, because the model contains chemical species with atmospheric lifetimes more than 20 years, such as CF2C12. Also note that the steady state has the repetition of an almost identical diurnal cycle. Hereafter in this paper, the term "steady state" is used as the meaning mentioned above. Vertical distribution of the steady state temperature at local noon is shown by the solid line in Fig. 3. The surface temperature was K and the minimum temperature in the lower stratosphere was K around 19 km. Outgoing infrared radiation flux at the top of the model was 256 W m-2. Note that the vertical axis of Fig. 3 indicates real altitude, not the log-pressure coordinate, and the lapse rate in the troposphere was set to -5.6 K km-1. Figure 4 shows total (direct+diffusive) downward flux spectra calculated at 5 vertical levels in the model. The solar spectral flux at the top level is also shown. Solar zenith angle was set to 30 degrees to make a comparison with the spectra of JPL-97. Comparing Fig. 4 with the spectra shown in JPL-97, the flux was successfully calculated except that the flux at 39.5 km was larger around 250 nm than that of JPL-97. This is because the ozone amount in the steady state of our 1-D model was a little less above 40 km than that of JPL-97. Total ozone amount at the steady state at local noon was 371 DU. Calculated vertical profiles of volume mixing ratio of bromine source gases and

7 October 2000 H. Akiyoshi 569 Table 1. List of Newly added Photochemical Reactions bromine species at local noon are shown in Figs. 5(a) and 5(b), respectively. Note that vertical axis is the log-pressure coordinates with 7 km scale height, as mentioned in Section 3.1, that corresponds well to real altitudes up to about 70 km. The vertical gradient of CHBr3 mixing ratio in the troposphere shown in Fig. 5(a) was due to the photolysis, because absorption cross section of CHBr3 extends over 300 nm, where solar radiation penetrates into the troposphere and reaches the ground surface. However, the vertical gradient was not appreciable in data obtained by an aircraft measurement between the surface and 7 km around Japan from January to April (Tamaru and Yokouchi, private communication). The result shows that the transport, or some tropospheric chemical reaction with shorter time scale than that of the photolysis process, is working to make the different distribution in the troposphere from that of the steady state of the 1-D model. Our calculation showed the time scale of CHBr3 photolysis were between 10 days and 15 days in the troposphere. Volume mixing ratio of total reactive bromine in the model stratosphere approached 20 pptv as shown by Fig. 5(b). Ver-

8 570 Journal of the Meteorological Society of Japan Vol. 78, No. 5 Fig. 2. Profile of vertical eddy diffusion coefficients used in the 1-D coupled model. Fig. 3. Steady state temperature profile at local noon by the 1-D coupled chemistry-radiation, radiative-convective adjustment model. Solid line shows the temperature profile of the atmosphere with 350 ppmv C02, and dashed line shows that with 700 ppmv C02. The dotted line shows the temperature distribution of the 700 ppmv C02 atmosphere calculated by the fixed chemical constituent concentration model. Vertical axis is altitude (km), and the lapse rate in the troposphere was assumed to be 5.6Kkm-1. tical profiles of the other chemical species were almost the same as those of Akiyoshi (1997), where bromine species were not considered. However, concentrations of NO3 and a few chlorine species such as C100 and OC10 were largely different between the bromine-free model and the bromine-included model. Some of the calculated number density profiles and photolysis rate profiles of chemical species at local noon were shown in Figs. 6(a), 6(b), and 6(c), and Figs. 7(a) and 7(b), respectively. The vertical axis is again real altitude for convenience of the com-

9 October 2000 H. Akiyoshi 571 Fig. 4. Total (direct+diffusive) downward flux spectra calculated by the 1-D coupled chemistry-radiation model at 5 vertical levels. Solar spectral flux at the top level is also shown by solid line. Solar zenith angle is 30 degrees. parison. The JPL-97 profiles are local noon profiles on March 15 at 40 N, and the zenith angle is almost the same as the local noon zenith angle of this model, 06 and 87= All the number densities and photolysis rates were generally consistent with the JPL-97 profiles, showing the calculation by the coupled chemistry-radiation model was successful except for H2O photolysis rate photolysis rate was calculated non-interactively in the model by using Nicolet's parameterization on 02 column density (Nicolet 1984), because the absorption cross section data listed on p. 153 of JPL-97 gave much smaller photolysis rates in the lower stratosphere of the model than those of the reference profile on p. 263 of JPL-97. It is not certain whether or not the discrepancy arose from a direct use of spectral mean absorption cross section values in the Schumann- Runge Band radiation fields. 5. C02 doubling experiments 5.1 Transient variation In order to examine how the chemistry-radiation coupling process works in the model, C02 volume mixing ratio was doubled suddenly from 350 ppmv to 700 ppmv at all the vertical levels of the model. The solid line labeled "cpl" in Fig. 8 shows the total ozone variation in the coupled model, while the dotted line labeled "fj" shows that in the photolysis rate fixed model where all the photolysis rates of chemical species were fixed to the initial values. The total ozone at the initial state was 371 DU. Temperature in the stratosphere was decreased by the C02 increase. Then ozone was increased through the negative temperature dependence of photochemical equilibrium ozone concentration, which is easily understood from a photochemical equilibrium ozone concentration equation on the Chapman cycle, for example. The figure indicates that total ozone variation after C02 doubling was different between the coupled model and the fixed photolysis rate model. Total ozone was apparently overestimated by the fixed photolysis rate model, because the feedback of ozone increase through UV radiation was not considered. Another interesting result from the coupled model is that total ozone continued to increase for a longer period than in the fixed photolysis rate model. Since lower stratospheric ozone mostly contributes to the total ozone, the prolonged variation of the coupled model indicates a prolonged ozone variation in the lower stratosphere. This is due to a slower variation in NO y in the lower stratosphere in the coupled model than in the fixed photolysis rate model. The perturbation process is; C02 t=ir emission t= Temperature 4= Column 03 above the level T UV. 0(1D),-= NO NO X 03 1', where 1 and indicate increase and decrease, respectively. The rate-determining step of this process is NO y production from O(1D) and N20. In order to check the rate-determining step, two more C02 doubling experiments were made, where total reactive nitrogen (NOr) mixing ratio or O(1D)

10 572 Journal of the Meteorological Society of Japan Vol. 78, No. 5 Fig. 5. (a) Steady state volume mixing ratio profiles of CF3Br (Halon-1301, solid line), CF2Br2 (Halon-1202, dotted line), CF2C1Br (Halon-1211, dashed line), CH3Br (dash-dot line), and CHBr3 (dash-dot-dot-dot line) at local noon. (b) The profiles of Br Y (solid line), BrO (dotted line), Br (dashed line), HBr (dash-dot line), HOBr (dash-dot-dot-dot line), BrONO2 (long dash line), BrCI (solid line), and Br2 (solid line). mixing ratio was fixed respectively. Total ozone amounts of the fixed NO y model and the fixed O(1D) model reached the equilibrium values much faster than in the full-coupled model, as shown by dashed line labeled "fnoy" and dash-dot-dot-dot line labeled "fold" in Fig. 8, indicating that NO y variation, and hence O(1D) variation is the main cause of such a prolonged variation in the total ozone. N and NO are also important for NO y budget, but the effects on the prolonged variation was small. Photolysis processes of chlorofluorocarbons in the lower stratosphere also have similar time scales to that of the NO y variation. Thus Cl,, should be changed with a comparable time scale. To check whether or not the Cly variation have an important effect on the slow ozone variation, one more CO2 doubling experi-

11 October 2000 H. Akiyoshi 573 Fig. 6(a). Steady state number density profiles of 03 (solid line), Hx10+8 (dotted line), OH (dashed line), HO2 (dash-dot line), O(3F) (dash-dot-dot-dot line), O(1D)x10+8 (long dash line), CH4 (solid line), H2O (dash-dot-dot-dot line), and H2O2 (long dash line) between 10 km and 50 km at local noon. The vertical axis expresses altitude (km), and the horizontal axis expresses number density on the log scale. Fig. 6(b). Same as Fig. 6(a), but profiles of Nx10+8 (solid line), NO (dotted line), NO2 (dashed line), NO3x10+6 (dash-dot line), N205 (dash-dot-dot-dot line), N20 (long dash line), HNO3 (solid line), HNO4 (dotted line), and C1ONO2 (dashed line).

12 574 Journal of the Meteorological Society of Japan Vol. 78, No. 5 Fig. 6(c). Same as Fig. 6(a), but profiles of Cl (solid line), C10 (dotted line), C1ONO2 (dashed line), HCl (dash-dot line), and HF (dash-dot-dot-dot line). Fig. 7(a). Steady state photolysis rate coefficient profiles of C1ONO2 (solid line), N205 (dotted line), HNO3 (dashed line), HNO4 (dash-dot line), HOCI (dash-dot-dot-dot line), HOBr (long dash line), and C1ONO2 (solid line) at local noon.

13 October 2000 H. Akiyoshi 575 Fig. 7(b). Same as Fig. 7(a), but profiles of 03 that produces O(3P) (solid line), 03 that produces 0('D) (dotted line), NO2 (dashed line), BrO (dash-dot line), and NO3 (dash-dot-dot-dot line). Fig. 8. Total ozone variation after sudden CO2 doubling. The variation in the coupled model (solid line, labeled "cpl"), in the fixed photolysis rate model (dotted line, labeled "fj"), in the fixed NO y model (dashed line, labeled "fnoy"), in the fixed C1 model (dash-dot line, labeled "fcly"), and in the fixed O(1D) model (dash-dot-dot-dot line, labeled "fold"). ment with fixed total reactive chlorine (Cli) mixing ratio was made. However, there was little difference in the total ozone variation between the fixed Cly model and the full-coupled model, as shown by dash-dot line labeled "fcly" in Fig. 8, indicating that effects of Cly species on lower stratospheric ozone was small. In a bromine-free coupled chemistryradiation model, the prolonged ozone increase after the CO2 doubling was a little more larger, which indicated that NO X effects on ozone in the lower stratosphere were relatively larger in the brominefree atmosphere.

14 576 Journal of the Meteorological Society of Japan Vol. 78, No Profiles in 7 years after CO2 doubling The 1-D coupled chemistry-radiation system seems to have reached a quasi-steady state in 7 years after the CO2 doubling, where most of the large variations disappeared, but smaller and slower variations and oscillations still existed. Since the possibility that a large variation happens seems so small after 7 years, profiles at 7 years from the initial point of the numerical integration are shown below. The vertical distribution of temperature of the C02 doubled atmosphere are shown by the dashed line in Fig. 3. Warming due to the C02-doubling at the surface was 1.3 K. This magnitude of warming occurred below 17.5 km, while cooling occurred above 17.5 km, and the cooling reached 10.8 K at 45 km. Since temperature profile of the fixed photolysis rate model was almost the same as that of the coupled model, it was not shown in this figure. The temperature profile of the fixed chemical constituent model was also shown by the dotted line in the same figure. The maximum cooling was 15.3 K at 50 km. The cooling difference between the coupled model, and the fixed chemistry model was due to an additional heating caused by ozone increase through the temperature dependence of ozone chemical reactions of the coupled model. Figure 9(a) shows the vertical distribution of relative values of NON, Cly, Br, 1120, HNO3, and C1ONO2 volume mixing ratios at the 7 years to those of the initial model atmosphere. A CO2 doubling experiment with fixed photolysis rates was also made in order to reveal temperature change effects of the C02 doubling on chemical constituent concentrations. The ratio distributions of the fixed photolysis rate model are shown in Fig. 9(b). The difference between the fixed photolysis rate model and the coupled model means the difference is due to the solar radiation change, because the temperature changes were almost the same between both models. Rosenfield and Douglass (1998) suggested that NO y was decreased through the strong temperature dependence of the reaction N+02-f NO+0 in a doubled CO2 atmosphere. The NO y decrease mechanism is; CO2 t=t, k(n+02) NT (N+NO-N2 +0)t=NO, where t and, indicate increase and decrease, respectively, as in Section 5.1, and k(n+02) is the reaction coefficient of N+02-NO+0. Similar NO y decreases were seen in the upper stratospheres both of the coupled model and of the fixed photolysis rate model. As shown in Fig. 9(b), the NO y decrease is confined above 25 km in the photolysis rate fixed model. In the coupled model, however, NO decrease extended down to 15 km level due to O(1D) decreases at all altitudes below 40 km (Fig. 10(a)) due to ultraviolet radiation reduction. The mechanism of NO y decrease described in Section 5.1 is effective in the lower stratosphere. The stratospheric cooling increased HNO3 at almost all altitudes in the stratosphere due to the acceleration of the HNO3 production reaction, OH+NO2+M-HNO3+M, (Fig. 9(b)), while in the coupled model HNO3 was decreased in the lower stratosphere following the NO2 and OH decreases due to the ultraviolet radiation reduction. Similar explanation is possible on C1ONO2 concentration difference in the fixed photolysis model, and in the coupled model. In the stratosphere of the fixed photolysis model, CO2 T=Tk(C10+NO2+M-} C1ONO2+M) C1ONO2 t, where k is the reaction coefficient, while in the lower stratosphere of the coupled model, CO2 t=t4= Column 03 above the level t=uv.j.=c10,, NO24=C1ONO2,. Cly and Br y variations in the lower stratosphere were a little larger in the coupled model than in the fixed photolysis rate model. Reduction in ultraviolet penetration into the lower atmosphere due to the ozone increase made the reduction in NO y, Cly, and Br y species in the lower stratosphere. Figures 10(a) and 10(b) show vertical distributions of relative values of 03, O(1D), NO2, C10, BrO, OH, and HC1 volume mixing ratios in the coupled model and in the fixed photolysis rate model, respectively. Nitrogen dioxide was decreased in the lower stratosphere as NO y was decreased. O(1D) and OH perturbations were quite opposite between the two models. They were increased by the temperature change (Fig. 10(b)), but decreased by the solar radiation reduction (Figs. 10(a) and 10(b)). Positive ozone perturbation, which was seen below 40 km in the fixed photolysis rate model, was reduced in the coupled model, because the ratio of j 1 to that is, 02 photolysis rate to produce 0 to 03 photolysis rate to produce 0 and 02, was reduced below 40 km in the coupled model (Fig. 11), which is directly related to the photochemical equilibrium concentration of ozone (Hantmann 1978). This led to an overestimated positive total ozone perturbation of 30 DU in the fixed photolysis rate thodel compared to 13 DU in the coupled model. All these results show that the perturbations in the solar radiation, as well as in temperature due to CO2 increase, have considerable effects on concentrations of chemical constituents. 6. Discussion In this paper, photolysis rates were calculated following the equation originally deduced in Section 2.1. On the other hand, there is a more straightforward conventional equation for photolysis rate calculation using radiation influx into atmospheric layers; Jaz)=q(A)F(, z)inabs (A7, T(z where F(A z)2n is radiation flux coming into an atmospheric layer located at z.,. F(z+zz) (down-

15 October 2000 H. Akiyoshi 577 Fig. 9. Change in chemical constituent volume mixing ratios of the 700 ppmv CO2 atmosphere at noon after a 7 year numerical integration from those of the 350 ppmv CO2 atmosphere (a) by the coupled model and (b) by the fixed photolysis rate model. Solid line shows the NO y mixing ratio change, dotted line Cli, dashed line Br, dash-dotted line H2O, dash-dot-dot-dotted line HNO3, long dashed line ClONO2. ward flux on the upper boundary at z+oz), and t F(z) (upward flux on the lower boundary at z) are used for the flux. In this method, however, the direct and diffusive components of the downward flux should be treated separately, and a solar zenith angle factor and a diffusive factor are necessary for the photolysis rate calculations, because those flux outputs from radiation transfer equations are defined as the normal components of radiance per unit area on the boundaries of plane-parallel atmospheric layers. For photolysis rate calculation, the direct component should be multiplied by a factor of 1/ cos 8, and the diffusive components of the 2-stream approximation method should be multiplied by a factor of 2. (Bruhl and Crutzen 1988). Our equation for photolysis rate calculation in Section 2.1 has

16 578 Journal of the Meteorological Society of Japan Vol. 78, No. 5 Fig. 10. Same as Fig. 9, but profiles of 03 (solid line), O(1D) (dotted line), NO2 (dashed line), ClO (dash-dotted line), BrO (dash-dot-dot-dotted line), OH (long dashed line), and HCl (solid line) (a) by the coupled model and (b) by the fixed photolysis rate model. the same form as equations for atmospheric heating rate calculation by using another 2 outgoing radiation fluxes on the atmospheric boundaries as well as the 2 incoming fluxes. Neither the separation of the downward flux between the direct component and the diffusive component nor a diffusive factor is necessary in this equation, because outgoing fluxes themselves are results from scattering and absorption in the atmospheric layer. Thus the convergence of the energy from the four fluxes was used to calculate both photolysis rates and heating rates. This is a more consistent equation for photolysis rate calculation on plane-parallel atmosphere from a point of view that solar energy heats atmosphere as well as photolyzes atmospheric constituents at almost the same place in the middle atmosphere. This method is easily applicable to any coupled photochemistryradiation model which has radiation flux outputs at

17 October 2000 H. Akiyoshi 579 Fig. ll. Change in 02 photolysis rates to produce O (labeled "jl"), 03 photolysis rates to produce 0 and 02 (labeled "j3"), and the ratio of the 02 photolysis rate to the 03 photolysis rate (labeled "j1/j3") of the 700 ppmv CO2 atmosphere at noon after a 7 year numerical integration from the 350 ppmv CO2 atmosphere. the atmospheric layer boundaries. However, there is a limitation that the radiation scheme used here is only valid for plane-parallel atmosphere. And most of the radiation schemes which have explicit flux solutions, for example, the two stream approximation, are based on plane-parallel atmosphere. Therefore, a correction based on spherical geometry is necessary for applying this scheme in polar regions of 3- D models, particularly for simulation of polar ozone depletion. But at least, the scheme developed here directly can be applicable to low-latitude and midlatitude atmosphere studies in a 3-D model such as atmospheric response after volcanic eruptions, or CFC global transport and distribution studies. All the steady profiles of chemical species calculated for the present atmosphere were compared with JPL-97 profiles in Section 4. Note that the JPL-97 profiles were generated by a 2-D model, and they are profiles at 40 N on March 15. The good agreement between the results of our 1-D model, and the JPL-97 profiles of the 2-D model means that our globally averaged 1-D model corresponds well to an equinox condition at mid-latitude in the 2-D model. The zenith angles at noon are almost the same between the two models, and symmetry in transport circulation in the 2-D model must be high between both the hemispheres in this season. Note that a portion of the vertical diffusion coefficients of the 1-D model compensates for a time-independent advective transport in the 2-D model. However, there were still small differences between the profiles of the 1-D models and those of JPL-97. The difference was a little larger in the lower stratosphere and in the upper troposphere than in the upper and middle stratosphere. The difference may result from an inability of the 1-D model to include a time and latitude dependent advective transport of chemical species. The concentration of Br y (total reactive bromine) was 20 pptv above 30 km at the steady state of the model, which can be easily estimated by the surface concentrations of the bromine source gases described in Section 3.3. Inclusion of bromine chemistry increased C100 and OC10 by more than one order by reactions k131 and k132, NO3 as much as 70% by photolysis of BrONO2, and also increased N205, C1202, and C12 by 10%, and other chemical species such as HOCI and HNO4 by 5% at maximum in the troposphere. Most of the maximum perturbations were around 12.5 km. Figure 12 shows vertical profiles of 03, OH, NO2, and C10 concentration change of the bromine-included model from the bromine-free model after a 20 year numerical integration. The ozone change was larger in the troposphere because halons were easier to photolyze in lower altitudes than chlorofluorocarbons. NO2 was increased by the reaction k129, and OH and ClO were decreased due to HO X and CIOX decreases. The radiative-chemical equilibrium temperature profile was little changed with additional cooling within 0.1 K. Difference in photolysis rates with and without bromine species was less than 7% in the tropo-

18 580 Journal of the Meteorological Society of Japan Vol. 78, No. 5 Fig. 12. Ratio profile of 03 (solid line), OH (dotted line), NO2 (dash-dot line), and C10 (dashed line) mixing ratios of the bromine-included model to those of the bromine-free model after a 20 year numerical integration. sphere (about 7% difference in 02, HCI, N20, and chlorofluorocarbon photolysis rates, and about 3% difference in OC10 photolysis rate and 03 photolysis rate to produce O(1D), i.e., J03). Total ozone of bromine-included model was less by 6 DU (-1.6%) compared to that of the bromine-free model. Recently, Lipson et al. (1997) reported that the branching ratio for the reaction OH+C10-HCl+O2 could not be neglected but ranged from 0.05 at 298 K to 0.06 at 210 K. The underestimation problem of ozone concentration around 40 km and overestimation of ClO/HC1 ratio in the stratosphere may be resolved by the new branching ratio (McElroy and Salawich 1989; Natarajan and Callis 1991; Toumi and Bekki 1993; Chandra et al. 1993; Michelsen et al. 1996), because this reaction transforms active chlorine species such as Cl and C10, which destroys ozone by the catalytic cycles, to HCl as a reservoir of chlorine species. Figure 13 shows change in 03, OH, and C10 volume mixing ratio of the 6% branching ratio model after a 20 year numerical integration from the 0% model. 03 was increased as much as 10% at 40 km. Accordingly, the radiative-chemical equilibrium temperature was increased by 1.4 K at 42.5 km and decreased slightly below 30 km (not shown). C10 was decreased by 30% at 40 km, where ClO mixing ratio reaches its maximum. These results were consistent with the results of the space shuttle or satellite observational studies using chemical models by Michelsen et al. (1996) and Khosravi et al. (1998). 7. Concluding remarks A one-dimensional chemically radiatively coupled model was developed. Coupled chemistry-radiation processes and numerical schemes considered in the model were described. A method of photolysis rate calculation which is more flexible to any radiation schemes on plane-parallel atmosphere was proposed and used in the model. Also, diurnal variation was considered from a global-mean point of view for the global mean 1-D model. Globally averaged solar zenith angles were defined on an equinox condition quite geometrically from a point of view of energy equilibrium of the earth-atmosphere system. The model includes 163 OX, HOX, NOX, C10x, and BrOX gas phase chemical reactions, which were formulated on the family method so that heterogeneous reactions on aerosols and PSCS can be easily incorporated into them. Steady state profiles of temperature and chemical species of the model were presented. These profiles were compared with reference profiles in JPL-97 to show that the profiles of chemistry-radiation equilibrium of the coupled model were successfully calculated. The chemical scheme developed here was stable with time resolutions shorter than 5 minutes on the explicit forward time integration. The CO2 doubling experiments showed that total ozone variation after CO2 doubling is different between the coupled model and the fixed photolysis rate model. The fixed photolysis rate model overes-

19 October 2000 H. Akiyoshi 581 Fig. 13. Ratio profile of 03 (solid line), OH (dotted line), and C10(dashed line) volume mixing ratios of the model with 6% branching ratio for the reaction C10+OH-HCl+02 to those of the model with the 0% branching ratio after a 20 year numerical integration. timated the ozone increase and underestimated the variation time scale. Vertical distribution of chemical species at 7 years after the sudden CO2 doubling showed that the solar radiation change as well as the temperature change caused by 03 increase due to the CO2 doubling had considerable effects on chemical constituent concentrations. A simplified stratospheric chemical code without bromine species has been successfully incorporated into CCSR/NIES GCM (Center for Climate System Research, University of Tokyo / National Institute for Environmental Studies General Circulation Model) by Takigawa et al. (1999). The coupling processes between chemistry and radiation have been also incorporated into the GCM in the same way as those in the 1-D coupled model, with some rearrangements of spectral mean absorption cross section data of chemical constituents. The new chemistry scheme with bromine species developed here is also being incorporated into the GCM with a more sophisticated PSC scheme. The chemistry-coupled GCM will be a useful tool for studying various chemical and climate studies in near future. Acknowledgments The author thanks H. Nakane and 0. Uchino for their continuous encouragements and helpful suggestions, and K. Sudou in the Center for Climate System Research, University of Tokyo, for discussion about photolysis rate calculation. Thanks are extended to two anonymous reviewers for many useful comments. Computations were made on NEC SX- 4 of the Center for Global Environmental Research in the National Institute for Environmental Studies. This work was partly supported by the Global Environmental Research Program of the Japan Environment Agency and International Cooperative Study on Stratospheric Change and its Role in Climate of Japan Science and Technology Agency. Appendix Formulation of photochemistry The following families and long-lived species were predicted: OX (= O(1D)+0+03), NO X (= N+NO+NO2+NO3), CIOX (= Cl+C10+ 2C1202+C100+OC10), BrOX (= Br+BrO), CH4, CO, N20, CC14, CFC13, CF2C12, CH3CC13, CH3C1, CCIF2CC12F, CHC1F2, H2O, HF, H2O2i HNO3, HNO4, N205, C1ONO2, HC1, HOC1, C12, CF2C1Br, CF3Br, CF2Br2, CHBr3, CH3Br, HBr, HOBr, BrCI, BrONO2, and Br2. NO y, Cly, and Br y were defined as follows and predicted independently for numerically stable calculation: NOy=NOX+HNO3+HNO4+2N205 +C1ONO2+BrONO2, Cly=C10X+HC1+HOCI+C1ONO2 +BrCI+2C12, Bry=BrOX+HBr+HOBr+BrONO2 +BrCI+2 Br2.

20 582 Journal of the Meteorological Society of Japan Vol. 78, No. 5 Ox prediction equation was obtained by summing up chemical production/loss rate terms of 0(1D), 0, and 03. [0]xt=[0(1D)]t+[Oh+[03]t =2(J00+J01)[02]-2k04[0][03] -2106{M][0][0]-k28[H][03]-k27[0][OH] -k30[h02][0]-k26[03][oh] -k31[h02][03]+j42[n02]-k43[no][03] -k44[n02][0]-k45[n02][03]+j46[n03] -k57[c1][03]-k58[c10][0]+j91[ocio] -k92[c10][03]-k96[0][oc10]+j104[bro] -k121[br][03]-k125[0][bto] -(k134+k136)[hbr][0(1d)] -k137[0][hbr]-k141[bro][03], where [X]t means d[x]/dt. All the other prediction equations were derived in the similar way by summing the production/loss rates of each chemical species. Prediction equations for nighttime were obtained from the daytime equations by setting photolysis rates of all chemical species and concentrations of the following species to be zero; 0(1D), O, H, OH, N, NO, CH3, CH3O, Cl, ClOO, and CHO. Species within the families such as 03, OH, and N02 were considered as short-lived species and the concentrations were calculated from concentrations of the families and the long-lived species, assuming the photochemical equilibrium. For example, concentrations of HO x species were obtained as follows: H and OH are in photochemical equilibrium with the ratio, H]/[OH]=(k23[CO]+k27[O]+a19[H2]) /(k28[o3]+129[m][02]). And the ratio for OH and H02 is [H02]/[OH]=(k26[03]+l29[M][02][H]/[OH] +k33[h2o2]+k126[bro] +tc75a[c1o]) /(k30[o]+k31[03]+k41[no]). HOx(=H+OH+H02) was also assumed to be in photochemical equilibrium. 0=[HO]xt=[H]t+[OH]t+[H02]t. Substituting the two equilibrium equations for [H] and [H02] into the above equation, a quadratic equation for [OH] was derived; where a[oh]2+b[oh]-c=0, a=2k24b+2(k25b+k25c)ab+2k32b2+2a16 b=k13[ch4]+k15[ch302]b+k16[ch300h] +k19[ch2o]+148[m][n02]+k50[hn03] +151[M][N02]B+k52[HN04]+k61[Cl]B +k62[hcl]+k63[c1o]b+k65[hoc1] +k94[oc10]+k122[br]b+k127[bto] +k128[bto]b+k138[hbr]+tc75b[c10], c=2j09[h20]+2k10[h20][o(1d)] where +2k11[H2][O(1D)] +(k12a+kl2b)[ch4][o(1d)] +c03[ch3][o]+k18[ch3o][02] +c09[ch2o][o]+j20[ch2o]+2j34[h202] +J49[HN03]+b23b[HN04][M]+J53[HN04] +d08[cl][h2o2]+jhci[hc1]+j64[hoci] +J103[HOBr]+J105[HBr]+k123[Br][H2O2] +k134[hbr][o(1d)]+k136[hbr][o(1d)] +k137[hbr][0]+tc67[hoc1][0], A=(k23[CO]+k27[O]+a19[H2]) /(k28[03]+129[m][02]), B=(k26[03]+129[M][02]A+k33[H2O2] +k126 [BrO]+tc75a[C10]) /(k30[o]+k31[03]+k41[no]). Since the coefficients a, b, and c are positive, it is obvious that one of the solutions is positive and the other is negative. The positive one was chosen as the solution for [OH]. Similarly, concentrations of CH302i C1O, and Br0 were calculated by quadratic equations. Formulation for nighttime equilibrium concentration of H02, N02, N03, C10, Br, and Br0 was also made independently of the daytime formulation. Quadratic equation was used to calculate nighttime HO2, C10, and Br0 concentrations. References Akiyoshi, H., 1997: Development of a global 1-D chemically radiatively coupled model and an introduction to the development of a chemically coupled General Circulation Model, CGER's Supercomputer Monograph Report, 4,69pp.. Allen, M. and J. Frederick, 1982: Effective photodissociation cross section for molecular oxygen and nitric oxide in the Schumann-Runge bands, J. Atmos. Sci., 39, Austin, J., N. Burchart and K.P. Shine, 1992: Possibility of an Arctic ozone hole in a doubled-co2 climate, Nature, 360, Brasseur, G.P., 1997: The stratosphere and its role in the climate system, NATO ASI Series, Vol. 54, Springer, 368pp.. and S. Solomon, 1984: Aeronomy of the middle atmosphere, Second edition, D. Reidel Publishing Company, 452pp..

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