Numerical Model Description

From our basic definitions and theory we have,


for the concentration change(DC) in a time Dt.  Equation (1) can be used to find the concentration C at anytime if its initial value and the total emissions are known.  The model described by equation (1) has been created for you to use, explore, and have fun.   

The emission rate S is assumed to be increasing at a specific growth rate (r) each year , i.e.  


Here S(t+1) is the emission rate at a time 1 year after time t.

A value of r = 0.0  corresponds to a constant emission rate (S(t+1) = S(t)), and a value of r = 0.01 would be a 1% growth rate in atmospheric emissions each year.




The flow diagram above describes the model in more detail.  The key parameters of the model Co (initial concentration), So (initial emissions), r (emissions growth rate), and t (atmospheric lifetime) are all adjustable at the beginning of each model run.

The change in atmospheric concentration of a pollutant is controlled by the amount added to the atmosphere (emissions) and the amount removed.  The removal rate RR depends on how much is in the atmosphere at any time and on the atmospheric lifetime; i.e. the removal rate is  RR= C/tThat is why the removal rate has a connector arrow from the concentration and the lifetime in the above flow diagram.

The increase in emissions is controlled by the emissions growth rate.  The amount of increase depends on the present emission level and on the growth rate, rNotice the link between emissions growth and the emissions and the growth rate icons.

The connection between Emissions  and Emission rate is simply stating that the source of pollution (emissions) at any given time is also identical to the flow of material into the atmosphere (emissions into atmosphere).