In SOCRATES, the chemical species are grouped into three categories: long-lived species and chemical families, intermediate lifetime species, and short-lived species. For long-lived species or families with chemical lifetimes comparable to or longer than transport timescales, the full chemical continuity/transport equation is solved:
where Xi represents the mixing ratio of gas i, Pi is the chemical production rate of gas i, and LiXi is the chemical loss rate of gas i. The transport of tracers by small scale mixing process is represented by a diffusive term DXi, written as
The intermediate species are chemicals with lifetimes shorter than the transport timescales, with timescales relatively insensitive to dynamical process, but sufficiently long that photochemical equilibrium cannot be assumed. These species are solved from the continuity equation without involving transport:
For the short-lived chemical species with lifetimes much shorter than the dynamical time constants, photochemical equilibrium conditions apply and the concentration of the trace gas i is derived from
The list of the constituents included in the standard version of SOCRATES is given in Table 4 .
2.3.1 Chemical reactions
More than 160 chemical reactions describing HOx, NOx, Clx, Brx, Ox, and hydrocarbon chemistry are included in SOCRATES. The majority of the chemical reaction rate constants are based on on the compilation published by the Jet Propulsion Laboratory (JPL) in 1997 (DeMore et al., 1997). A list of the reactions and rates is given in Table 5 .
a. Heterogeneous chemistry on polar stratospheric clouds
The parameterization of heterogeneous processes occurring on the surface of polar stratospheric clouds is based on the methods described by Chipperfield et al. (1993). Two types of PSC are considered: type II PSCs, mainly composed of water ice, and type I PSCs mainly composed of nitric acid trihydrate (NAT). For type I PSCs, the formula of Hanson and Mauersberger (1988) is used to estimate the saturation vapor pressure of HNO3 over NAT and hence the number density of condensed HNO3.3H2O species:
where and . The vapor pressure is converted into units of number density from
Thus the number density of condensed HNO3 3H2O species is then estimated by subtracting the "saturation number density" from the total number density of HNO3. In the case of NAT, the condensed particles are assumed to have a radius of 1 µm, with a sedimentation velocity of 0.015 km/day. Similarly, the formula for the saturation vapor pressure over ice from Murray (1967):
is used to predict the occurrence of type II PSCs. These type II PSCs are assumed to have a radius of 10 µm, and a sedimentation velocity of 1.5 km/day. The condensed HCl number density is deduced from the mole fractions of condensed HNO3 and H2O according to Hanson and Mauersberger (1990) :
If sedimenting particles reach a level where the ambiant temperature is higher than the condensation threshold, evaporation takes place and the condensed species are returned to the gas phase. In the presence of PSCs, the following five heterogeneous reactions are assumed to occur:
vA/4 (Cadle et al. 1975), where is the reaction probability, A the PSC surface area density, and v the mean molecular velocity given by v=(8kT/
m)1/2. The reaction probabilities for these reactions are given in Table 6 for the two types of PSCs. Assuming that the particles are spherical, the surface area density A can be calculated knowing the radius of the two types of PSCs, and their mass and number densities.
| Reaction | Type I | Type II |
| het1 | 0.006 | 0.3 |
| het2 | 0.3 | 0.3 |
| het3 | 0.0006 | 0.03 |
| het4 | 0.003 | 0.03 |
| het5 | 0.1 | 0.3 |
b. Sulfate aerosol heterogeneous chemistry
For heterogeneous reactions on sulfate aerosol particles, six reactions are considered:
vA/4 . The surface area density (A) of sulfate aerosols is generally attainable from extinction measurements. The reaction probability () of the above reactions are based on works described in Hanson et al. (1994) and Hanson and Ravishankara (1995). The reaction probability for the g1 reaction rate is expressed as a function of sulfate aerosol composition (W: H2SO4 weight %) as
where the aerosol composition which depends primarily on the temperature and water vapor mixing ratio is evaluated based on the study of Steele and Hamill (1981) and has been fitted to a formula as described in Hanson et al. (1994) as
where ph2o is the partial pressure for water vapor. The reaction probability of g2 is specified as 0.14, independent of the aerosol and composition, and hence, of the temperature. The reaction probability for g3 reaction is expressed as:
where [HCl]* is the HCl solubility in droplets calculated from the equation:
For g4, the reaction probability is set to be 19.1 times that of 3. For the bromine reactions, the values adopted for the reaction probability are based on the work by Hanson and Ravishankara (1995), with 5=0.6, and =10*4.
c. NOy production.
In addition to the major stratospheric NOy production resulting from N2O+O(1D)-> 2NO reaction, the production source of NOy by lightning, cosmic ray, and ionic reactions are included in the model.
The rate of global lightning production is 8.7 Tg/yr, with productions occurring at latitudes less than 60o, and at altitudes between 0 and 16 km. Between latitudes of -30 to 30 deg, the NOy production rate is specified as 2000 cm-3/s. Beyond 30 deg latitude north and south, the NOy production is specified to decrease linearly from 2000 cm-3/s at 30 deg to zero at 60 degrees latitude.
Production of NOy associated with the deposition of galactic cosmic rays is parameterized as a function of latitude and altitude according to Heaps (1978) for solar maximum condition, with the production of 1.3 NO molecules per ion pair produced by the cosmic rays. At altitudes less than 8 km, NOy production by cosmic ray is assumed to be zero. At other altitudes:
Production of NOy by thermospheric ionic process including its production by N2 photolysis and N2 reaction with energetic electrons (e*) is specified as a function of height and latitude based on data presented by McEwan and Phillips (1975). NOy production by particle precipitation near the auroral zone in the thermosphere is confined to latitudes beyond 55 degrees, while the production by extreme UV radiation occurs at all latitudes except for night time conditions. The magnitude of the NOy production rate is on the order of 1000 cm-3/s by N2 + e*, and on the order of 10 cm-3/s by N2+hv in the lower thermosphere. NOy production rates by these processes are assumed to be negligible below 90 km.
d. Tropospheric species washout rates.
Computation of the rainfall rate and wet removal rate of soluble species in the troposphere for HNO3, H2O2, CH3OOH, HCl, HO2NO2, and CH2O, is based on the parameterization described by Hough (1991). For HBr, CCl2O, CClFO, CF2O, HF, Bry and Cly, the washout rate for HCl is used; for C2H5OOH, CH3COOOH, and C3H6OHOOH, the washout rate for CH2O is used; and for NOy, the washout rates for HNO3 and HO2NO2 is used.
As described in Appendix B of Hough (1991), the rainfall rate of water vapor is written as:
and the water from the rainout is assumed to move vertically down to the immediate lower layer and evaporate. The washout rates of species i is then:
where fxi is the fraction of species i in the aqueous phase derived from
and dh2o is the density of liquid water (g/cm3), while lwc is the liquid water content (g/cm3) of the clouds.
Hi is the dimensionless Henry's Law coefficient, derived from
where ki is the Henry Law coefficients, listed in Table 7 for different rainout species, while p is the local pressure and p0is the standard surface pressure, both in units of Pascal. The liquid water content, lwc (g/cm3),is calculated from the formula
where mh2o is the mean molecular mass of water (18 g/mole), and [H2O](sat) is the saturated concentration of water vapor derived from
where p is the pressure in units of Pascal.
| Species | k (mol l-1 atm-1) |
| HNO3 | 3.3e6 |
| H2O2 | 7.36e4 |
| CH3OOH | 221 |
| HCl | 3.3e5 |
| HO2NO2 | 3.3e6 |
| CH2O | 6.3e3 |
2.3.2 Vertical transport in the troposphere associated with convection and fronts.
Tropospheric vertical transport produced by convective and frontal activity is formulated in the 2-D model by a simple parameterization which ensures mass continuity. Assuming that the convective upward mass flux at the first model layer is known (which we shall call 
in units of g/m2/s), mass continuity dictates that at layer i:
if 
i is the fraction of boundary mass flux that is detrained into the layer i (sumation of i = 1 ) and 
is the downward mass flux out of layer i. At the top layer of the convective layer (denote by layer N), the continuity can be written as
Substituting into Eq.98 for layer N-1 yields:
Under the same token, at layer i, a recursive relationship can be obtained for the downward flux out of layer i:
The time rate of change of the transported chemical species, knowing the mass flux in and out of the layer i, can be written as:
where [n]i is the number density of species i, and Xi the mixing ratio of the transported species at layer i. Substituting the relationship (101) into (102), and after converting mass flux in units of g/m2/s to units of (cm-3s-1) by multiplying it with NA/mair/109 yields
which can be rewritten as
Thus, the convective transport effect is equivalent to a chemical production term: represented by the first term in the right-hand side of Eq. (104), and a chemical loss coefficient, represented by the coefficient of the second term on the right-hand side. These convective "production" and "loss "terms are added to the chemical production and loss rates in the continuity equation (79).
The input information needed for the transport parameterization is the upward boundary mass flux , and the fraction of that enters layer i (i). The convective mass flux out of the boundary layer for both deep convection and frontal circulation process is taken from Langner et al. (1990) (Table 7 in the paper). The detrainment percentages (or i) of the convective and frontal process as a function of season, altitude and latitude are also obtained from Langner et al. (1990) (Table 1 and 2 in the paper). The same data is used to estimate the top level (N) reached by convective and frontal vertical transport.