Effects of Dynamics on Chemical Species Transport

Note that the source term Si (expressed here in mass per unit volume and time) is often expressed as the difference between rates of photochemical production P and loss L . Introducing the mass fraction or mass mixing ratio pi — pi/p where p is the air mass density, and making use of the mass conservation equation for air (3.3b), it is easy to show that equation 

The continuity equations can also be expressed in terms of number density n = p /m and mole fraction or volume mixing ratio X = n /n, where n = p/m is the air number density, m = M/Na is the molecular mass of air, Na is Avogadro s number (6.02 x 1026 molecules per mol) and M is the molar mass of air. In the homosphere, where M 29 kg/mol is approximately constant, 

In Chapter 2, the time constant appropriate to photochemical processes (rchem) was discussed, and it was shown that this time constant can be readily derived from knowledge of the rate of loss of chemical species. The time constants for dynamical effects on chemical species are somewhat more difficult to evaluate. 

If we consider only the effects of advection and chemistry, the continuity equation for a chemical species i can be written as  

Consider, for the purpose of illustration, transport only by vertical winds  

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