Chemistry of the Global Troposphere' Fluorocarbons as Tracers of Air Motion

Winds and convective mixing from a general circulation model of the atmosphere have been applied in a chemical tracer model (CTM) to simulate the global distribution and temporal variability of chlorofluorocarbons (CFCs). The seasonal cycle in moist convection, with maximum activity over continents in summer, leads to an annual cycle in the surface concentration of CFCs. Emissions are retained in the lowest levels of the atmosphere during winter, and surface concentrations peak near sources. In this season, CFCs from European sources are carried by low-level winds into the Arctic. During summer, vertical exchange is more efficient, and pollutants are transported more rapidly to the middle atmo- sphere. Consequently, concentrations of CFCs during summer are relatively low near the surface and elevated in the middle troposphere. Time series analysis of data from Adrigole, Ireland, indicates that the model accurately simulates long-range transport of air pollution. The model reproduces global distributions and trends for CFC-11 and CFC-12 observed by the ALE experiment; however, subgrid diffu- sion must be introduced into the model in order to reproduce the observed interhemispheric gradient. Interhemispheric exchange occurs mainly in the upper tropical troposphere, producing a profile which increases with altitude in the southern hemisphere, in agreement with observations. The distribution of CFCs is such that it is necessary to apply important corrections to observations at surface stations in order to derive global distributions.

sphere. The concentration of OH depends on solar irradiance and on the abundances of 0 3, CO, CH,•, H20, NO•,, and hydrocarbons. Concentrations of these gases may vary widely on relatively short spatial and temporal scales. This paper is the first of a series intended to provide a global model for the physical and chemical processes responsible for the distribution of tropospheric NO x and 0 3. Budgets of these chemically active trace gases involve sources and sinks in the troposphere, exchange with the stratosphere, and complex interactions with surface and subsurface environments.
We approach this task in a sequential fashion. The first step, in the present paper, is to examine the role of atmospheric motions in the dispersal of the industrial chlorofluorocarbons (CFCs): CFC13 (CFC-11) and CF2Cl 2 (CFC-12). Modeling the distribution and variability of CFCs provides a test for threedimensional tracer models on both global and regional scales [Lovelock, 1971]. Rates for emission and removal of CFCs are moderately well known. Most importantly, the distribution in the troposphere has been carefully documented over the past eight years in the Atmospheric Lifetime Experiment (ALE) [Prinn et al., 1983;Cunnold et al., 1986], and limited data are available back to 1970 [Lovelock, 1971]. The recent study by Golombek and  was the first to examine the ALE data set with a three-dimensional model, focusing on stratospheric distributions and global lifetimes of CFCs; their model has insufficient vertical and horizontal resolution in the troposphere to simulate in detail the observed tropospheric concentrations.
The present paper examines the tropospheric distribution of 6579 CFCs. We use a GCM developed at the Goddard Institute for Space Studies to calculate structure and wind fields for the atmosphere and to describe the vertical exchange of air by convection . The model was formulated initially for efficient simulation of climate. It was designed to allow ready investigation of the effect of spatial resolution and to study schemes for parameterization of processes operating on small scales involving the boundary layer and cumulus convection. In the present series of studies the GCM is used to provide a set of wind fields and other variables which are employed to solve three-dimensional continuity equations for selected chemical species. It is assumed that air motions are unaffected by the trace gases considered in the chemical investigation. Early versions of the GISS model have been used in a variety of studies by Funt7 et al. [1983], Pinto et al. [1983], and Heimann et al. [1986]. We shall refer to the model as a chemical tracer model (CTM).
We have made a choice here to use the most accurate, stable, and positive definite algorithm for tracer transport [Russell and Lerner, 1981;Prather, 1986]. The wind fields used in the CTM, whether from the GCM or from other sources, are assumed accurate; the advantage of the GCM lies in providing a globally self-consistent set of winds, convergences, convective fluxes, temperatures, humidities, and cloud cover. There would be little advantage in solving the linear continuity equation for tracers with the same numerical method used for nonlinear momentum equations in the GCM. We use here novel numerical techniques which provide high resolution of the tracer distribution, consistent with the dynamical fields.
We shall show that the CTM provides an excellent simulation for most of the observed features of global and regional transport of CFCs. The model reproduces observed year-toyear trends as well as seasonal and shorter period fluctuations. Long-range transport of pollutants is accurately represented. Results are in good agreement, for example, with episodic enhancements of CFCs observed at Adrigole, Ireland, and wintertime pollution of the Arctic is simulated. The results show that the CTM can play a valuable role in the interpretation of sparse ground-based data to refine global budgets. It can also provide useful guidance in the design of optimal observing strategies. For example, the model indicates that anthropogenic sources result in higher than average concentrations of pollutants in the planetary boundary layer over the northern hemisphere. The reverse situation occurs in the southern hemisphere, where transport from the northern tropics introduces elevated levels of CFCs to the upper troposphere. Thus the model highlights the importance of vertical soundings to define the distribution of CFCs. Otherwise, one may infer an interhemispheric gradient considerably larger than the tropospheric mean.
It appears that transport of trace gases between hemispheres, as resolved by the parent GCM, is too slow to account for the CFC concentrations observed in the southern hemisphere. The problem can be resolved if we assume that deep convective mixing in the vertical has associated with it mixing in the horizontal over scales not resolved by the global model. In this paper we ascribe all discrepancies in interhemispheric transport to this diffusive mixing. Introduction of a simple parameterized diffusion, effective mainly near convergence zones in the tropics, allows satisfactory modeling of interhemispheric exchange for CFCs. We show by scale analy-sis that diffusion of this magnitude should have little effect on the general circulation. These CFC simulations provide a quantitative evaluation of the impact of subgrid, mesoscale mixing on global tracer transport and place upper limits on its magnitude. Elsewhere, it is shown that this empirical approach also gives good agreement for the latitudinal distribution of SSKr [Jacob et al., this issue]. We are continuing to assess the importance of subgrid diffusion for other chemical tracers and for the circulation itself, through direct inclusion in the GCM.
Background material on the model is given in the appendices. The parent GCM is discussed in Appendix A; the CTM, in Appendix B; and initialization procedures, release rates, and stratospheric loss for CFCs, in Appendix C. Global characteristics of the CFC simulations are discussed in section 2. Comparisons with observations at specific sites are presented in section 3. Potential applications of the CTM are described in section 4.

MODEL RESULTS: GLOBAL PROPERTIES
The series of global CFC simulations using the CTM are summarized in Table 1 and Figures 1-13. The distributions of CFC-11 and CFC-12 were initialized in model year 1976. A uniform concentration was assumed for each hemisphere, and an initial interhemispheric difference was adopted from early measurements as described in Appendix C. Annual release rates were taken from CMA estimates, as shown in Table C1.
Loss rates were based on photochemical destruction integrated over the stratospheric layers of the model for each latitude and season (see Table C4). The method of calculating advection and convection of tracers is described in Appendix B, sections B1-B5. Horizontal mixing, occurring on scales not resolved by the grid, is parameterized in the CTM by a diffusion coefficient which is proportional to the local intensity of deep convection and to the square of a length parameter D (see Appendix B, section B6). Values of D in the range 177-250 km were chosen in order to reproduce the observed CFC interhemispheric gradients; the area D e may be regarded as a measure of the size of a region disturbed by the largest tropical convective complexes. Winds and dynamical fields were taken from a 4 ø x 5 ø GCM.
The CTM was run with both 4 ø x 5 ø and 8 ø x 10 ø resolution, as discussed later.

Interhemispheric Transport: Effects of Resolution and Diffusion
Detailed comparison between model runs and observed concentrations was made primarily for the period 1980-1982, using data from the Atmospheric Lifetime Experiment FPrinn et al., 1983; Cunnold et al., 1986] and from the Australian station at Cape Grim [Fraser et al., 1985]. Results from model years 1980 and 1981, using the global 8 ø x 10 ø CTM with D = 250 km, are given in Table 1. We include also in Table 1 results from a CFC-11 calculation which used the second year of winds from the GCM for the 6-year simulation and from a CFC-12 calculation in which the parameterized diffusion was reduced by a factor of 2 (D = 177 km).
Concentrations of CFCs are significantly higher in the northern hemisphere than in the southern hemisphere, reflecting the predominance of the northern source. Air moves southward across the equator carrying a relatively high concentration of CFCs, balanced by a northward flow of air containing, on average, a lower concentration. This exchange re- where M s and M s denote the total mass of tracer in the northern and southern hemispheres, respectively. In the event that emissions were suspended, the interhemispheric difference (M s --Ms) would decay exponentially with a time constant initially equal to •re•. If the hemispheres could be represented by well-mixed boxes with a barrier between, tl)s_• s would be proportional to the absolute difference in mixing ratios (M s --Ms), and Ze• would have a constant value independent of tracer distribution. In a three-dimensional model, however, spatial variations of mixing ratio may be quite complex, particularly in the tropics where the exchange occurs. The value of Zex in this case can vary for different species, depending on the spatial and temporal distribution of sources and sinks.
In the CFC experiments summarized in Table 1, the annual mean interhemispheric flux is approximately half the magnitude of the northern source and greatly exceeds the size of both southern sources and stratospheric losses. Values of Z ex are similar for CFC-11 and CFC-12, reflecting the overall similarity of emission patterns and distributions. Two successive years of GCM winds produce nearly identical exchange times. The difference in Tex between the two CFC-12 experiments, D--250 km versus D--177 km, reflects a change in M s --Ms; the value of (I)s_, s is virtually identical for all values of D, reflecting a near steady state balance between emissions and tropospheric redistribution.
There is a large seasonal variation in tI)s_• s associated with the annual migration of the convergence zone in the tropics. For example, during January and February the Hadley cell of the northern hemisphere follows the sun and crosses the equator into the southern hemisphere, bringing high levels of CFCs with it. Most of this air is not incorporated directly into the circulation of the southern hemisphere and remains in the northern branch of the Hadley circulation. This annual cycle leads to a maximum in the formally defined flux across the equator during northern winter, as shown in Table 1. The second year of GCM winds produces maximum exchange in December rather than in January. Choice of D does not change the basic seasonal pattern. The seasonal amplitude of interhemispheric mixing is much smaller than the seasonal variations in (I)N_• s indicated by Table 1; the true annual cycle in interhemispheric mixing may be inferred from the modest  [Weiss et al., 1983].
The effect of grid resolution on the CTM was tested in a pair of 1-year simulations, using both 4 ø x 5 ø and 8 ø x 10 ø global CTMs, with results shown in Figure 2. The winds in both cases are based on the same run of the 4 ø x 5 ø GCM, and horizontal diffusion has been eliminated (D = 0). Computational costs of the global 4 ø x 5 ø CTM did not permit a multiyear simulation of CFCs, and in order to make meaningful 1-year runs, electric power consumption (described in Appendix C, section C1, and given in Table C2) was used to define a continuous source of emission for an atmosphere initially without tracer. Comparing zonal mean profiles of tropospheric concentrations at the end of 1 year, we note that the 8 ø x 10 ø CTM has a greater latitudinal domain of high concentrations, which may be thought of as defining the northern hemisphere. north in the 4 ø x 5 ø CTM, but the total content of each hemisphere has not been substantially altered. Net interhemispheric exchange is equivalent in both runs. The same CTM experiment was repeated for the 8 ø x 10 ø resolution including diffusion, with D = 250 km; the amount of tracer transported into the southern hemisphere doubled. These experiments demonstrate that (1) small values of D chosen for our standard models enhance the rate of interhemispheric exchange by 50-100%, and (2) increased resolution of the CTM does not substantially alter either interhemispheric transport or latitudinal distributions in the case where the same 4 ø x 5 ø wind field is used for both coarse and fine resolutions.

Global Trends and Budgets
The calculated trends for the global mean tropospheric concentration (C N + Cs, where CN is the concentration in the northern hemisphere, and C s the concentration in the southern hemisphere) of CFC-11 and CFC-12 are compared with those derived from the ALE network and from the National  ALE surface stations, located relatively near continental souces (i.e., Europe, North America, Atlantic Ocean), tend to overestimate abundances of CFCs in the northern hemisphere, even when pollution e,•ents are carefully removed, as in the ALE analysis. This particular location of sites may explain partly the lower values for interhemispheric differences observed from the NOAA sites, located predominantly over the mid-Pacific (see Figure B1). Model results demonstrate that CFC data from surface sites may be systematically biased with respect to true atmospheric means, as seen in Figure 3 by comparing values derived from ALE sites with true tropospheric means. The sampling error associated with use of ALE surface sites is less than 2% for the global abundance C N q-C s , but it appears to be as large as 35% for the hemispheric difference CN-C s. When pollution episodes from nearby a uniform gradient, C N -C s, over the 4-year period suggests that a steady state has been reached between the release of CFCs in the north and transport to the south. Such a steady state is to be expected, since the release rate was essentially constant (_ 10%) over the period 1978-1982 (see Table C1) and since the time scale for interhemispheric mixing is about 1 year.
It is unfortunate that CFC-11 and CFC-12 are so nearly in steady state with respect to the redistribution of the gases in the troposphere, since an empirical determination of the rate of interhemispheric transport requires then an accurate measurement of the difference in concentrations between hemispheres. As we have seen, the hemispherically averaged absolute difference CN-C s is a difficult quantity to measure, because of unavoidable sampling bias. A better method might be based on the study of a gas characterized either by an instantaneous release or by a rapid growth in emissions. In this case the rate of rise in the two hemispheres would be different, providing a more direct means for measurement of the rate of interhemispheric transport. Figure 4 summarizes the rates of change in CFC abundance (i.e., tendency) within each latitude band due to emission, stratospheric loss, mean transport, eddy transport, and diffu- predicted near the surface. Some structure, attributed to convective activity over the continents, is observed at 500 mbar in summer. The 500-mbar contours in winter are more zonally symmetric, however, and show little indication of sources below. Convective activity is most prevalent over continents in summer and over oceans in winter (see Figure B2). Vertical gradients in CFCs are thus largest over land in winter, when CFC emissions are most effectively contained in the lowest layers of the atmosphere. This confinement accounts also for the extensive plume of CFC-rich surface air extending northeast from Europe into the Arctic during January, as illustrated in Figures 5 and 7. Other pollutants are expected to be transported along with CFCs from the same source regions, contributing to the Arctic haze phenomenon, discussed further later.
Gradients of CFC mixing ratio across the equator are steeper at the surface than at 500 mbar, and gradients are sharper over oceans than over continents. This pattern, seen in Vertical motions are sufficiently strong in the region of tropical convergence to ensure that CFC mixing ratios are approximately uniform from the surface to the upper troposphere. To the north of this convergence zone, concentrations decline with altitude, reflecting inputs from sources. To the south they increase with altitude, reflecting interhemispheric exchange. In January 1981 the CFC convergence zone was calculated to be near the equator at the 165-ppt contour for CFC-11. In the following July, average concentrations increased about 5 ppt, and the convergence zone is seen to occur at about 15øN, near the 170-ppt contour. The zone of tracer convergence mimics the seasonal movement of the Intertropical Convergence Zone, following the sun, as discussed in section 2.1. It usually remains in the northern tropics.
Seasonal cycles in tracer concentrations may be generated both from the annual migration of the convergence zone and from seasonal variations in transport within a hemisphere when the sources and sinks are not uniformly distributed throughout the atmosphere [e.g., Levy et al., 1982]. We have shown that such seasonality depends on geographic location  for the years 1978-1981. As noted in section 2.2., calculated concentrations of CFC-11 are lower than observed values by about 5%. This difference is greatest in the northern hemisphere (11 ppt) and least in the southern hemisphere (7 ppt). Computed values for CFC-12 match the ALE data within + 2% at all sites.
We recognize two problems which may occur when comparing simulations using average concentrations from the CTM with observations at a particular ALE site' horizontal gradients may not be well resolved with the 8 ø x 10 ø grid; and the ALE data have had pollution episodes removed by an algorithm involving simultaneous measurement of short-lived pollutants, a process which cannot easily be simulated in the present model runs. An important question is how well the model predicts monthly mean background concentrations (i.e., typical clear air) observed at sites adjacent to sources. These issues, horizontal resolution and pollution episodes, are examined in sections 3.2-3.3, using the high-resolution 4øx 5 ø CTM which is applied to the European window (and which cannot be used for lengthy global simulations). We show that for Ireland, and possibly for Oregon, background air simulating the "unpolluted" data reported by ALE lies 4-6 ppt below the average value at the site. Thus a best comparison with the reported ALE data would be made with values which lie between the mean concentrations calculated from the 8 ø x 10 ø grid box at the site and those from the less polluted grid box immediately to the west (dashed lines in Figures 11 and 12 The seasonal cycle in CFC-11 at southern mid-latitudes (40øS) is predicted to have a peak-to-peak amplitude of about 1 ppt (D = 250 km), which is not readily seen on the scale of Figure 11. The minimum occurs about February and the maximum near August. The phase of the variation is consistent with observations from Cape Grim, Tasmania, but the observed peak-to-peak amplitudes are greater, about 2 ppt [Fraser et al., 1985]. The ALE data from Samoa have opposite phase, with relative maxima in CFCs every January-February and peak-to-peak amplitudes in excess of 2 ppt for CFC-11 [Cunnold et al., 1986]. This period corresponds to the southernmost extent of the tropical convergence zones and is the most likely time for Samoa to observe northern hemispheric air with higher concentrations of CFCs. Modeled values at Samoa have nearly the same phase as the data, reaching a maximum during February-March, but have smaller amplitudes, of the order of 1.4 ppt. Calculations with reduced diffusion (D = 177 km) have increased seasonal amplitudes for CFC-12 in the southern hemisphere by about 50% and are in closer agreement with the data.
Observations of CFCs at Oregon exhibit a large, possibly seasonal, variation, but unfortunately the data record for this

Window Calculations for Europe
Studies of long-range transport and dispersal of air pollution on a continental scale require a CTM with the finest possible resolution. In this case the global calculation may prove to be too expensive computationally and, furthermore, unnecessary. We have implemented a subset of the global CTM simulation in which the calculation is performed only within a window on the globe. In this section we demonstrate that window calculations of CFCs for Europe are indeed a valid subset of the global model and examine the impact of improved resolution and numerics on the simulations.
The European window covers one-sixteenth of the globe, as shown in Figure 14a. Winds are computed with the global  [Prather, 1986], which offers greater resolution and accuracy for both transport and emissions. Mixing ratios of CFCs were initialized throughout the volume to a concentration of 100 ppt, as were the boundary values along edges of the window. Reduced stratospheric concentrations were included, as described earlier.
High-resolution models require correspondingly fine source grids. We constructed a high-resolution 4 ø x 5 ø emission grid for CFC-11 over the European window. Countries were resolved in a 1 ø x 1 ø grid; electric power consumption for each country [Central Intelligence Agency (CIA), 1984] was distributed equally by area; scale factors relating CFC-11 emission to electric power were 1.0 for Western Europe and 0.2 for Eastern Europe, Africa and Asia; total emissions were 120 x 10 6 kg yr-•, equivalent to the amount released within the European window during year 1981 of the global simulation.
The second-order moments of the sources within each 4 ø x 5 ø grid were calculated by aggregating the 1 ø x 1 ø elements according to (B17). We used three source grids in these window calculations: (1) the 8 ø x 10 ø global grid, as defined in Table  C2 Figure 16b shows the same simulation, using the slopes method for advection and uniform emission over 4 ø x 5 ø (grid 2), and Figure 16c gives results from the same 4øx 5 ø model with 8øx 10 ø sources from Table C2. Figure 16d

AC(f, A)=• [f(t + A)--f][f(t)--f] dt (2) where f(t) denotes the mixing ratio at time t, A denotes the lag, and the average value off is • which may also include a linear trend where appropriate. The value A C(f, 0) is equal to the variance (ppt •) in the time series. The normalized autocorrelation function, defined as AC(f, A)/AC(f, 0), describes the probability that elevated concentrations will be observed at times A before or after the peak event.
Autocovariances of the ALE data for CFC-11 (S) at Adrigole have been presented by Prather [1985], and similar calcu-  Figure 16b) and the second-order moments method (solid line, time series in Figure 16a). Both of these simulations result in pollution episodes which are statistically very similar to those observed at Adrigole. The 4 ø x 5 ø SOM simulation has more narrowly defined episodes than the 4 ø x 5 ø with first-order moments, producing variances which are 20% higher at the peak (A = 0) and 20% lower on the shoulder (A = 4 days); the autocovariance has a half-height half-width of 2 days and a shoulder extending to 10 days, in excellent agreement with the ALE observations. The highest mixing ratios observed at Adrigole cannot be simulated with the current model. The most intense events have durations less than 8 hours; they correspond to air masses with horizontal scales of 100 km or less which would be diluted over a larger grid size in our model, even in the 4 ø x 5 ø SOM model. These events are likely to be plumes from major urban centers, contribute about 20% of the variance at the Adrigole site, and represent less than 5% of the observations [Prather, 1985].

SUMMARY AND CONCLUSIONS
The three-dimensional chemical tracer model incorporates geographic emission patterns and simulates the distributions of CFC concentrations over latitude, longitude, altitude, and time. We summarize the major findings as follows.

The model indicates that seasonal cycles in moist convection, with a maximum over the continents in summer, lead to
an annual cycle in the surface concentration of compounds with a land source. In winter, when vertical mixing is weakest over land, concentrations peak near sources, and these high surface values are carried far downwind in the lower atmo-

sphere. For example, during January, contributions from the European source of CFCs are blown into the Arctic, as shown by the surface contours in Figures 5 and 7. It is difficult at present to test the model's simulation of concentrations in air adjacent to or over a source region, since data records equivalent to the ALE series are scarce for polluted environments.
Such data are clearly important as a benchmark in development of CTMs. The model provides excellent simulation of synoptic-scale pollution episodes at observing sites 400-2000 km removed from major sources, Point Barrow and Adrigole, for example. The modeled climatology for Adrigole was statistically very similar to the observed climatology, provided that the highestresolution model was used, i.e., 4 ø x 5 ø with SaM. Simulation of such sites requires high resolution for both sources and transports as well as time series analysis to characterize the distribution of observed concentrations, not just the mean. It appears that data from stations adjacent to source regions, in conjunction with the CTM, allow a direct estimate of regional rates of emission to the atmosphere. The model can be used to predict trace gas climatologies for projected monitoring sites.
Parameterized diffusion, to mimic mixing in the horizontal dimension associated with deep vertical convective activity, was introduced and adjusted to match the interhemispheric exchange observed for CFC-11. It had little impact on intrahemispheric transport but resulted in an increase of 50-100% in the rate for cross-equatorial transport. The parameterization gave an excellent simulation of the north-south distribution of 85Kr as well as CFCs.

tent of the unstable layer is insufficient for condensation, vertical motion proceeds on a dry adiabat until the level of stability is reached; complete mixing of layers is assumed along this path.
Moist convection is associated with formation of thick cumulus clouds. The cumulus clouds are assumed to extend throughout grid points for which condensation is expected. They account statistically for about 10% of the global cloud cover. Clouds in the model are more commonly associated with vertical motions and supersaturation on larger scales. Large-scale clouds are treated on a probability basis. The chance that a cloud occurs within a given grid element is described by a probability distribution which depends on the temperature variance and the local relative humidity. This function is sampled randomly and gives a larger chance for cloud cover as the relative humidity increases. Clouds, if they occur, are assumed to cover a grid square completely [-see Hansen et al., 1983]. reactive tracers. The present model augments procedures introduced by Russell and Lerner [1981]. It incorporates a revised first-order advection scheme, adding a second-order moments method for transport [Prather, 1986] allowing calculations to be carried out at high resolution on a limited "window" of the globe. Advection is treated over extended polar zones in order to improve numerical stability. A more detailed treatment of moist convection is incorporated. Photochemical losses in the stratosphere are properly accounted. A brief review of the basis for the model with a documentation of the added features follows.

B1. The Three-Dimensional Grid
The distribution of a trace gas is calculated at a discrete set of latitudes, longitudes, and pressures defining the grid boxes of the CTM. We carried out several calculations using a horizontal resolution of 4 ø x 5 ø, corresponding to the GCM's fine grid (as in the works by Russell and Lerner [1981] and Hansen et al. [1983]), 46 latitude zones, with boundaries at 4 ø intervals extending from 88øS to 88øN, and 72 longitudinal elements, from 177.5øW at 5 ø intervals to 177.5øE (see Figure B1). The vertical levels are defined by pressure according to the a coordinates used in the GCM, as summarized in Figure A1

Here AX defines the east-west extent of the box (in meters), A Y refers to the north-south dimension (in meters), and a denotes the radius of the earth. The mass M•, of air contained in the grid box (in kilograms) is M k = (100/q) Apk AS A r (B4)
where a = 6375000 m and g = 9.81 m s-2 Many calculations were made with a subset of the 4 ø x 5 ø CTM, using a resolution of 8 ø x 10 ø with 24 latitude zones with 36 meridional elements. The same polar boxes and vertical layers were used, but four horizontal grid elements of the 4øx 5 ø model were combined into a single 8øx 10 ø box. Winds from the 4 ø x 5 ø GeM were integrated along the sides of the 8 ø x 10 ø box, and physical quantities (Ps, T, q) were averaged over the four 4 ø x 5 ø elements comprising the larger box. The relationship of these grids is shown in Figure B1 Our method for solving the three-dimensional continuity equations is often called operator splitting or alternating directions [e.g., Dahlquist and Bjorck, 1974]. It is applied consistently in the CTM for the various processes affecting trace gases' advection moves the tracer for a 4-hour period, convection vertically distributes tracer mass for the same interval, tracer from sources during the 4-hour period is added to each box, and tracer is removed allowing for local chemical loss.

B3. Windows
Study of the dispersal of gases from source regions on continents requires the finest resolution attainable in the model, while much lower resolution may often be appropriate for global simulations. We designed the CTM so that highresolution calculations of tracer concentrations could be carried out using a restricted rectilinear subset, or window, of the global latitude-by-longitude grid. The winds and convection patterns are identical to those used in the full global model. Boundary conditions for the tracer are imposed at all layers along the edges of the window. Since tracer advection is treated using an upstream method, we chose to specify the mixing ratio of tracer in air which enters a particular window. In case studies of source regions, the United States or Western Europe, for example, the upwind boundaries were placed over the oceans, well away from continental sources. We are able thus to specify background mixing ratios at the upstream boundaries, using results for the CTM global run. Studies discussed in this paper demonstrate that results in the interior of the window are insensitive to the somewhat artificial treatment of the boundaries. Use of a window option results in considerable savings, more than a factor of 10, when compared with global studies of similar resolution. Simulation of time series for CFCs at Adrigole, Ireland, was performed using a window calculation for Europe, with the window located as shown in Figure B1.

B4. Extended Polar Zones
Extended zones near the poles can be defined so that the CTM grid allows nearly equivalent areas for the high-latitude grid-boxes, as shown in Table B1. This approach leads to numerical advantages similar to those attained with the equalarea grid employed at GFDL [Mahlrnan and Moxim, 1978]   ing air scales as the mass flux in the convective plume divided by the vertical velocity of the descending air. The area of this mesoscale system and the rate at which air passes through it determine the extent of horizontal mixing. This circulation is explicitly resolved in two-dimensional, nonglobal chemical models of these cloud systems [Gidel, 1983;Chatfield and Crutzen, 1984]. Unfortunately our global model cannot resolve these mesoscale systems, and we must average the advective transports of tracers in these systems, approximating the mean transports by eddy diffusion.
The GCM has not explicitly included this diffusion, and we shall argue that its effect on the dynamics is small but that its impact on chemical tracers with gradients across the equator is significant, even for small amounts of diffusion. In this paper we use CFCs to understand what levels of mesoscale mixing are plausible, to place limits on the role of subgrid diffusion which might be incorporated into the GCM.

AS(i) diff = [K,,(i) + Kx(i + 1)]At M(i)+ M(i + 1) 2 AX 2 2 [S(i + 1)/M(i + 1)-S(i)/M(i)] = --AS(i + 1) diff (B26)
where At is the time step and other symbols have been defined previously. Note that diffusive transport is calculated only from the zeroth moments; however, higher-order moments in the x direction are reduced by a factor corresponding to the extent of horizontal mixing,  •'Western Europe, Australia, South Africa, and Japan. Japan has been scaled down by a factor of 2 because of its higher electricity/CFC ratios. ed for initialization, and a summary of the individual experiments.

C1. Release Scenarios
Releases of CFCs to the atmosphere occur during primary manufacture, product application, and final disposition [-see McCarthy et al., 1977;Gamlen et al., 1986]. There are no known natural sources: total production provides thus an upper limit to emissions. Estimates for the industrial production of CFC-11 and CFC-12 have been given by the Chemical Manufacturers Association (CMA), [1982,1983,1984,1985]. Totals for Western reporting companies are believed to be accurate to better than 2%. Values for Soviet and Eastern European production for the period 1968-1975 are extrapolated from data given by Ye. P. Borisenkov and Yu. Ye. Kazakov (Effects of freons and halocarbons on the ozone layer of the atmosphere and climate, unpublished Russian manuscript, 1977; hereafter called Borisenkov and Kazakov, 1977). Large uncertainty is associated with the estimates of Soviet and Eastern European production. This has small effect on the CFC-11 budget, since these countries are minor sources of the gas. Production of CFC-12 in the U.S.S.R. and Eastern Europe could be quite important, especially if the growth rates reported for 1968-1975 (17% per year) persisted to later years. Original CMA reports included assumptions on the growth of emissions from the U.S.S.R. and Eastern Europe. More recent reports [CMA, 1984[CMA, , 1985 specifically avoided estimates for Soviet production. The problem of deriving CFC-12 sources has led to considerable discussion and to revision of recent estimates for global emission I• Rowland et al., 1982;Cunnold et al., 1983b;Cunnold, 1984]. We adopted the CMA estimates for production of CFCs between 1940-1982, as indicated in Table C1. Data on the seasonality of CFC release are lacking, and therefore the release was assumed to occur uniformly throughout the year. Our test of the global model focuses on its ability to reproduce observed spatial and seasonal patterns. If there was significant seasonal variation in emissions, we would expect observed concentrations to exhibit a noticeable annual cycle [-see Hyson et al., 1980]. Consumption patterns for CFC products in individual countries are not well established, and the spatial distribution for emissions cannot be defined with precision. Major CFC applications, such as use in aerosol propellants (52% of European market in 1983 [CEFIC, 1985]) rigid and flexible foams (20% and 11%, respectively) and refrigeration (12%), are associated with technologically advanced economies. We therefore used electric power consumption as a surrogate to construct a release pattern for CFCs. Electric power use reflects both national wealth and technology, and data are readily available for most countries. An 8øx 10 ø emission grid (1 unit = 6 x 106 kW) was defined, as illustrated in Table C2, and the world was subdivided into three economic groupings, each with its own coefficient relating CFC use to electrical power. The groupings selected were (1) the United States (U.S.A.) and Canada, (2) Western Europe, Japan, Australia, and South Africa, and (3) the rest of the world (ROW).
The weighting factor relating CFC emissions to consumption of electricity for each group is given in Table C2 for Table C3 summarizes the fragmentary information available for CFC production and use in various geographic regions for comparison with the scenarios adopted here. Note that recent reports from the Soviet Union [U.S.S.R., 1986] claim a much higher production of CFC-11 than used here. The quantity of CFCs released in the southern hemisphere is estimated to be between 4% and 8% of the total. Uncertainty in this number does not significantly affect model results (e.g., the north-south gradient of CFCs), provided that the southern hemispheric CFCs account for less than 10% of the total emissions. Emission of CFCs into the atmosphere is simulated in the CTM as a surface source. An amount equal to the emission (in kilograms per second) in a given grid square (P) over the time step (At) is added to layer 1, and the vertical slope is reduced accordingly to allow for the fact that the CFCs are added to the bottom of the layer,

Sz•(t q-At)= Sz•(t)-PAt (c1)
Subsequent upward transport (and vertical homogenization of layer 1) is provided by dry convection, moist convection, and large-scale convergence. When sources are resolved within a grid square by their second-order horizontal moments (i.e., P,,, Pxx, Py, Py•, Px•), the corresponding moments of the tracer distribution in layer 1 are augmented as per (C1). In order to avoid negative sources, limits are placed on the source moments in the same manner as on the tracer moments in the work by Prather [1986].

C2. Stratospheric Chemical Loss
Loss of a trace gas due to photochemical reactions in the stratosphere is an important component of the global budget of many species, particularly CFC-11 and 12. Destruction of CFCs may be represented as a first-order loss process (per second) with coefficient L. The value of L depends on local pressure, overburden of ozone, and solar angle. The rapid falloff with altitude of CFC mixing ratios reflects the increasing importance of chemical loss at high altitude. The scale height of CFC-11, for example, is about 2 km at an altitude of 25 km, less above.
It is difficult therefore to determine the profile of CFCs with any precision using the limited stratospheric resolution of the current GCM (see Figure A1). Issues of stratospheretroposphere exchange and the vertical distribution of CFCs in the stratosphere would require a model with greater vertical resolution above 150 mbar, one that is tuned for stratospheric studies as in the work by Golombek and Prinn [1986]. We are currently developing a 21-layer CTM which should address these questions.
For present purposes, though, we are concerned not with the details of the CFC distribution in the stratosphere, but rather with their abundance in the troposphere. This is set mainly by the geographic distribution of the source and by effects of tropospheric circulation. The removal mechanism in the stratosphere regulates the trend in global abundance over long time scales and can be treated adequately for present purposes as follows.
Observations  Table 4 Reference Source Thus the rate of loss in layer 9 of the CTM included also stratospheric loss above 10 mbar. Evaluation of L from the one-dimensional model is independent of the absolute scale of the mixing ratio. Most of the loss in layer 9 occurs near the top, and this effect is approximated by using the computed loss S9(t q-Af) --S9(t)-L9S9(t)At (C4) and reducing the vertical slope accordingly:

Sz9(t q-At) --Sz9(t)-L9S9(t)At (C5)
In some of the first numerical experiments with CFCs the vertical slope in the stratosphere (layer 9) was reset each time step to that value expected from the high-resolution onedimensional model which approximated the observations. This technique provided a more accurate subgrid parameterization of the distribution and loss of CFCs in the stratosphere, but it had the unwanted wide effect of introducing a numerical artifact at the lower boundry of layer 9, thereby enhancing CFC concentrations in layer 8 by a few percent, and it was dropped from the CTM.
Values for the loss frequency (L 8, L9) are calculated as a function of season and latitude at 15 ø intervals, using the onedimensional model, with results summarized in Table C4. The quantities at northern latitudes are used in southern latitudes at equivalent seasons. Losses are scaled according to the earth-sun distance, increasing by 3.3% in January and decreasing appropriately in July. A two-dimensional cubic spline is fitted through the latitude-by-season points as nodes. The