The global pollution mass balance model that we use in this activity assumes that the change in concentration DC of a gas during one time step (Dt) is,


where C is the average concentration, t (the greek letter tau) is the atmospheric lifetime of the gas (in years), and S is the emission strength for the gas (in ppm/yr).  The removal rate is C/t (in ppm/yr) and is related to how fast the trace gas is removed by such processes as chemical reaction, absorption by the ocean, soils, or plants, or by photo dissociation.  The atmospheric lifetime is inversely proportional to the gas removal rate from the atmosphere.  For example, if t = 10 years, 0.1 (or 10%) of the gas is removed from the atmosphere each year and if t=4 years 0.25 (or 25 %) of the gas is removed from the atmospheric each year.  In words, equation (1) states that the net concentration change in a given time interval equals the amount of the gas that is added minus the amount that is removed.  Notice the Analogy with the water bucket model.

Typically, gases with very short life-times are highly reactive and also can be fairly toxic to humans.  These types of pollutants are of primary concern in urban air quality.

It is easy to see from equation (1) that when the emission source strength S equals the removal rate C/t then the concentration will not change; i.e. if S = C/t then DC=0.  The value of C that makes this true is called the equilibrium concentration Ceq.

                                 Ceq=St           (2)