Modeling the Atmosphere 



AIRBORNE CHEMICALS 



The purpose of the models in ques- 

 tion is to allow quantitative assess- 

 ment of "air quality" — i.e., the con- 

 centration of pollutant gases and 

 particles — at all or chosen points 

 within an area of the order of 100 

 square miles which contains (and is 

 bordered by) numerous pollutant 

 sources. Models are required both for 

 the assessment of abatement tactics 

 (What sources are responsible for 

 what degree of pollution in what 

 areas?) and for the planning of de- 

 velopment (What will be the effect of 

 a new highway or new industrial com- 

 plex on pollutant concentrations in 

 the area and how, given that a pollu- 

 tant must be emitted, can its impact 

 be minimized by the siting of the 

 source?). 



Existing models, when classified 

 only according to the nature of their 

 output, are of two types: short-term 

 models and long-term models. The 

 objective of a short-term model is to 

 compute air quality averaged over 

 periods of about one hour to one day. 

 Long-term models produce averages 

 of air quality over periods of one 

 month to one year. Statistics of short- 

 term averages of air quality may be 

 derived from the output of long-term 

 models by the application of empirical 

 distribution functions. Long-term 

 models are, therefore, applicable to 

 planning and to assessing the broad 

 impact of land-use changes on air 

 quality; but if models are to be used 

 in the day-to-day management of 

 air quality — e.g., during air-pollution 

 alerts and incidents — short-term 

 models are required. Long-term aver- 

 ages and statistics can, of course, be 

 derived by the repeated use of short- 

 term models, at the expense of com- 

 puting effort. 



Physical and Mathematical 

 Basis of Air Quality Models 



To compute the concentration of a 

 pollutant, we must know where and 



in what quantity it is emitted and 

 what happens to it in the atmosphere. 

 If the source inventory is inadequate, 

 the model cannot be expected to be 

 adequate. An adequate source in- 

 ventory must account for the total 

 emission of pollutant over the area, 

 and it must have the same resolution 

 in time and space as the required out- 

 put of the models, so that if we re- 

 quire, for example, the one-hour aver- 

 age concentration of sulfur dioxide 

 (SO-) over an area one mile square, 

 we must have an inventory of emis- 

 sions of SOj hour by hour, averaged 

 over areas not greater than one mile 

 square. 



Once in the atmosphere, the pol- 

 lutant travels with the wind. It may 

 react chemically with other pollutants 

 or normal atmospheric constituents, 

 it may fall out or be washed out, or it 

 may change by radioactive decay. 

 Traveling with the wind is conven- 

 tionally divided into transport by the 

 average wind (the average being taken 

 over times and areas larger than those 

 resolved by the model) and diffusion 

 by the turbulent eddies (i.e., by wind 

 variations on time or space scales 

 smaller than those resolved by the 

 model). 



The mathematical basis of short- 

 term air-quality models is the so- 

 called continuity or conservation 

 equation — a balance sheet of the 

 pollutant in a box in space, with terms 

 representing transport in and out by 

 the mean wind, transport in and out 

 by turbulent diffusion, emissions on 

 the surfaces of and within the box 

 (i.e., the "source inventory"), and 

 chemical or radioactive transforma- 

 tion within and deposition out of the 

 box. 



Specification of the mean wind, the 

 coefficients of diffusion terms, and 

 the nature of the transformation, de- 

 position, and decay is the task of the 



atmospheric scientist. Efficient or- 

 ganization of the calculations calls 

 for mathematical and computational 

 skills. Solution of the continuity equa- 

 tion is essential for a rigorous compu- 

 tation of the concentration of pollu- 

 tants produced by chemical reaction, 

 such as the oxidants in photochemical 

 smog, but no such model of an exten- 

 sive area has yet been produced be- 

 cause of the computational complexity 

 of solving a set of simultaneous con- 

 tinuity equations. The short-term 

 models that have been successfully 

 applied have been based on formulae 

 that are formal solutions of a continu- 

 ity equation with diffusion terms. 

 Such solutions are typified by the 

 "Gaussian plume" distribution of ma- 

 terial continuity emitted by a point 

 source. This has the form 



X(x,y,zJTL 



2ttiJjU z u 



exp 



Mm 



where X is the concentration of 

 pollutant at a height z, distant x in 

 a direction along the mean wind 

 and y in a direction across the mean 

 wind from a source at height H 

 emitting material at a uniform rate 

 Q into a mean wind of strength u. 

 The factors cr y and o- Z/ which meas- 

 ure the diffusive dispersion of the 

 material in the horizontal and verti- 

 cal directions, depend both on the 

 meteorological conditions and on 

 the distance from the source. They 

 have been determined empirically 

 many times and standard tables 

 exist. 



Various integrations of this formula 

 adapt it for use with line sources and 



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