The 2-D approach to atmospheric modeling relies upon the high zonal symmetry of most dynamical and chemical quantities in the stratosphere and mesosphere. This symmetry is due to photochemical forcing and strong zonal wind components in this region. A 2-D model uses winds, temperatures and mixing ratios averaged over a zonal (constant latitude) ring and calculates the global development of the concentration of important chemical trace gases as a function of the two dimensions latitude and pressure (altitude).

The two dimensional photochemical transport model used here at the Physical Research Laboratory (PRL), was developed at the Max Planck Institute for Chemistry (MPIC) at Mainz, Germany. The model had been written in Fortran utilising some special features of the CRAY machine. The code was first made compatible to run on the IBM RS-6000 machines at PRL. At times the source code had to be changed. After an extensive modification, the model could run successfully on the IBM machine. Thereafter, SF₆ was incorporated as a new species in the model by giving its annual emission rates and OH and O¹D chemistry.

The PRL-MPIC 2-D model has a grid of 18 latitude points from 85^oS to 85^oN with a 10^o latitude spacing and 34 pressure levels from the ground upto 0.18 hPa (~ 61 km altitude), with about 2 km spacing in the stratosphere and mesosphere and finer spacing (~ 0.6 km) in the lower troposphere (upto about 2.5 km). The model time step is 2 hours. It was developed from the model described by Gidel et al. (1993)

The 2-D MPIC model at Mainz had 72 chemical species while one species namely SF₆ was incorporated here at PRL in the PRL-MPIC model. The chemistry module of the model consists of 128 chemical gas phase reactions and 52 photolysis reactions. Out of the gas phase reactions, 113 two-body and 13 three-body reactions were built in at Mainz while 2 two-body reactions (that of SF₆ with OH and O¹D) were incorporated at PRL.

The chemistry module uses an integration algorithm based on the family concept. The chemical families of the 2-D model are :

1. Odd oxygen (O_x) : O, O₃
2. Reactive chlorine (ClO_x)
3. Total inorganic bromine (Br_x)
4. Odd nitrogen (NO_y)

The redistribution of species inside a family is achieved by integrating the differential equations analytically over the given 2 hour time step. A combination of explicit and implicit integration schemes (Euler forward/backward) was chosen to get best agreement with other more accurate models with shorter time steps, such as box model. Different integration schemes are used for day and night time conditions, since the corresponding differential equations are very different in the absence of photolysis.

The temperatures in the 2-D model are based on a climatology by Barnett and Corney (1985) as a function of latitude and pressure for every month of the year.

The photolysis rates needed in the integration of the chemical equations are calculated using a radiative transfer algorithm, based on a modified two-stream method developed by Zdunkowski et al. (1980). It includes multiple scattering by air molecules, aerosol particles and a climatology for clouds (Brühl and Crutzen, 1988;1989). The cloud cover and distribution are estimated from Warren et al. (1986). The zonal average surface albedo is also taken from climatological data (Robock, 1980). Both cloud cover and surface albedo are given as a function of latitude and season.

The ultraviolet and visible wavelength regions are split into 176 spectral intervals with a higher resolution of 1 nm between 300 and 320 nm. This high resolution is needed to get the correct photolytical production of O¹D, which determines the OH and HO₂ concentration (Madronich and Weller, 1990). In the Schumann-Runge bands of O₂ between 180 and 200 nm the attenuation and absorption of the sunlight is calculated by the parameterisation of Allen and Frederick (1982).

The calculation of the photolysis rates is performed for a symmetrical diurnal cycle with 2 hour time intervals. The calculation of the diurnal cycle of photolysis rates is updated every 15 days of the model integration.

The chemical species combined in a family are transported together, similar to the other species whose concentrations only vary slowly. These include H₂O, CH₄, H₂, H₂O₂, N₂O, O_x, HCl, ClO_x, HF, Br_x, CO and the different CFC species. The transport of NO_y species is divided into two groups, HNO₃ and the remaining odd nitrogen species (NO_y-HNO₃). Similarly H₂O₂ is not counted in the HO_x family and is transported separately. Since the lifetime of HO_x is much shorter than the time scales of transport, the HO_x concentrations are calculated from photochemical steady state assumptions only.

The transport between the model grid boxes is described by the continuity equation. In a 2-D model, the large scale non-zonal fluxes between the model grid points are calculated from mean motions and their variability using an eddy diffusion parameterisation (Reed and German, 1965). The eddy diffusion coefficients that refer to transport in meridional direction (K_yy), vertical direction (K_zz) and slanted direction (K_yz) are derived empirically for each season. Typical values are K_yy=5 �10⁹ cm² s^-1 K_yz= ± 5 � 10⁵ cm² s^-1, and K_yy=4 � 10³ cm² s^-1 at the 50 hPa pressure level.

The diabatic circulation in the stratosphere is calculated in advance, based on the radiation scheme described by Brühl and Crutzen (1988). The heating rates for this calculation are derived from the infrared absorption calculation of CO₂, O₃, H₂O, CH₄, N₂O and the CFCs by a modified broadband model (Ramanathan, 1976; Kiehl and Ramanathan, 1983), using climatological mixing ratios of these constituents and the radiation scheme described above. From the heating rates, the stream function Y is derived by an iterative solution method of the zonally averaged residual Eulerian thermodynamic equation (Solomon et al., 1986) using climatological zonal mean temperatures (Barnett and Corney, 1985).

The tropospheric mean winds are taken from observations and the two schemes are connected with stream function and global vertical mass flux. The wind fields are calculated by differentiating the given stream function Y . This method guarantees the conservation of mass, because the continuity equation if fulfilled automatically. The calculated wind fields are updated every month of the model integration.

There are two possibilities for treating transport at the upper and lower boundary of the model. Either the flux of a species through the boundary level can be specified or the mixing ratio of the species can be assigned to a fix value. The first method is better for example, when the emissions at the Earth's surface are well known, while the second method is preferred when observed concentrations at the boundary are available. The model uses a mixture of both methods, but mainly the flux boundary condition (Gidel et al, 1983). The treatment of tropospheric deposition of water soluble species through rainout is described in detail in (Crutzen and Gidel, 1983).

The NO_x emissions by lightnings and by aircraft are incorporated in the model. The emissions of CFC and other long lived species are derived from the surface concentrations taken from WMO (1995), except for SF₆ which is derived from Maiss et al. (1996).

Allen M., and J.E. Frederick, Effective photodissociation cross sections for molecular oxygen and nitric oxide in the Schumann-Runge bands, J. Atmos. Sci. 39, 2066- 2075, 1982.

Barnett, J.J. and M. Corney, Middle atmosphere reference model derived from satellite data, Hand book for MAP 16 (eds: K. Labitzke, J.J. Barnett, B. Edwards), 47-85, 1985.

Brühl, Ch. and P.J. Crutzen, Scenarios of possible changes in atmospheric temperatures and ozone concentrations due to man's activities, estimated with a one-dimensional couple photochemical climate model, Climate Dynamics 2, 173- 203, 1988.

Brühl, Ch. and P.J. Crutzen, On the disproportionate role of tropospheric ozone as a filter against solar UV-B radiation, Geophys. Res. Lett. 16, 703-706, 1989.

Brühl, Ch. and P.J. Crutzen, MPIC Two-dimensional model, in : The atmospheric effect of stratospheric aircraft, NASA Ref. Publ. 1292 (eds: M.J. Prather and E.E. Remsberg), p.103-104, 1993.

Crutzen, P.J., and L.T. Gidel, A two-dimensional photochemical model of the atmosphere; 2; The tropospheric budgets of the anthropogenic chlorocarbons CO, CH₄, CH₃Cl and the effect of various NO_x sources on tropospheric ozone, J. Geophys. Res., 88, 6641- 6661, 1983.

Gidel, L.T., P.J. Crutzen, and J. Fishman, A two-dimensional photochemical model of the atmosphere; 1; chlorocarbons emissions and their effect on stratospheric ozone, J.Geophys. Res., 88, 6622-6640, 1983.

Kiehl J.T., and V. Ramanathan, CO2 radiative parameterisation used in climate models: Comparisons with narrow band models and laboratory data, J. Geophys. Res. 88, 5191- , 1983.

Madronich, S. and G. Weller, Numerical integration errors in calculated tropospheric photodissociation rate coefficients, J. Atmos. Chem. 10, 289-300, 1990.

Maiss, M., and I. Levin, Global increase of SF₆ observed in the atmosphere, Geophys.Res. Lett., 21, 569-572, 1994.

Maiss, M., L.P. Steele, R.J. Francey, P.J. Fraser, R.L. Langenfels, N.B.A. Trivett, and I. Levin, Sulfur hexafluoride-A powerful new atmospheric tracer, Atmosph. Environ., 30, 1621-1629, 1996.

Ramanathan V., Radiative transfer with the Earth's troposphere and stratosphere: A simplified radiative-convective model, J. Atmos. Sci. 33, 1330-1346, 1976.

Reed R.J., and K.E. German, A contribution to the problem of stratospheric diffusion by large scale mixing, Monthly weather review 93, 313-321, 1965.

Robock, A., The seasonal cycle of snow cover, sea ice and surface albedo, Monthly weather review 108, 267-285, 1980.

Solomon S., J.T. Kiehl, R.R. Garcia and W. Grose, Tracer transport by the diabatic circulation deduced from satellite observations, J. Atmos. Sci. 43, 1603-1617, 1986.

Warren, S.G., C.G. Hahn, J. London, R.M. Chervin and R.L. Jenne, Global distribution of total cloud cover and cloud type amounts over land, NCAR technical notes TN-273+STR, 229 pp., Boulder, CO, 1986.

WMO, Scientific assessment of ozone depletion; 1994, Report No. 37, World Meteorological organisation, Geneva, 1995.

Zdunkowski, W., R.M. Welch and G. Korb, AN investigation of the structure of typical two-stream methods for the calculation of solar fluxes and heating rates in clouds, Contr. Phys. Atmos. 53, 147-166, 1980.