Meteo 465/565 -- The Middle Atmosphere
Chemical Composition

1.  We know that eddies are effective at mixing gases in the lowest 100 km of the atmosphere.  Why is it then, that we see gases that have mixing ratios that change dramatically well below 100 km?

• By the Law of Atmospheres (from the hydrostatic approximation), p = p(z=0)exp(-Mg/R*T), where M is the molar mass, R* is the gas constant, and T is the temperature.  If gases did not collide with each other, then each would be distributed with height according to its molar mass.
• Eddy mixing in the lowest 100 km keeps gases mixed up.
• How can gases not have uniform mixing ratios throughout the lowest 100 km?  They can have:
• a source at the surface
• a source in the atmosphere
• a sink at the surface
• a sink in the atmosphere
• If the gas's lifetime is shorter than the time it takes to transport it from one place to another, then the gas may not  be uniformly distributed throughout the atmosphere.

2.  Mixing ratios:  Mass mixing ratio is the fraction of the total air mass that is a certain gas; volume mixing ratio is the fraction of the total number of molecules that is a certain gas.

3.  The molar mass and volume mixing ratio for some important stratospheric species:

gas	molar mass	volume mixing ratio
nitrogen (N2)	28.01	0.781
oxygen (O2)	31.99	0.209
argon  (Ar)	39.95	0.0093
water vapor	18.0	3 - 8 ppmv
carbon dioxide (CO2)	44.00	365 ppmv
ozone  (O3)	48	0-10 ppmv
methane  (CH4)	16.0	1800 ppbv
nitrous oxide (N2O)	44	320 ppbv
chlorofluorocarbons	> 50	~ 3 ppbv total
bromine compounds	> 50	<~ 20 pptv total

4.  90% of all atmospheric ozone is in the stratosphere.  Peak mixing ratios are in the tropics near 30 km; peak concentrations are near 15 km at high latitudes; peak column amounts are at high latitudes.

5.  Particles are located primarily in the troposphere.  However, sulfur species do make it into the stratosphere in the form of long-lived sulfur compounds (OCS) and as SO2 injected by volcanoes.  These sulfur gases are converted to sulfuric acid (H2SO4), and then form particles.  These particles stay in the lower stratosphere, just above the tropopause, forming what is known as the Junge Layer.

6. Upper atmosphere. A transition occurs at about 100 km. Below about 100 km, the mixing of air parcels and thus air molecules is dominated by eddy motions.  Above, 100 km, the mixing of air parcels is dominated by molecular diffusion.  With molecular diffusion in control, molecules of different mass are no longer uniformly mixed.  Thus, the region below 100 km is called the homosphere, while the region above 100 km is called the heterosphere.

Look at the concept of diffusion. In the vertical, molecular flux F = - D (ÑN), where D is the diffusion coefficient and N is the molecular number density. Note that fluxes by diffusion are down-gradient.

Now, the time rate of change of N is given by the ¶N/¶t = - ÑF = D Ѳ N. In the vertical, F = -D ¶N/¶z. We can estimate the diffusion caused by eddies, the eddy diffusion: F_eddy = - K_eddy ¶N/¶z.

The solution to this diffusion equation for atmospheric conditions results in a time scale for diffusive travel: time = <x²> / 2 D.

Now, we can use kinetic theory to tell us something about the molecular diffusion coefficient D. The resulting expression for D is:

D µ (T )^3/2/ (p) (1/m)^1/2,

where k_B is the Boltzman constant, T, is the temperature, p is the pressure, and m is the molecule mass.

At the surface, D = 2 x 10^‑5 m² s^-1

When p = 5 x 10^-7 atm, T is about the same, D ~ 40 m s^-1.

When eddy diffusion dominates over molecular diffusion, the gases are well mixed. When molecular diffusion dominates over eddy diffusion, the gases separate according to mass, as we can see in the figure for the upper atmosphere.

7. Ionosphere. The ionosphere is a region where there are a significant number of electrons and positive ions. The electron number densities reach as high as 10⁶ electrons cm^-3.