Obviously this is a very simplified approach, and its application is limited. Nonlinear processes such as chemical reactions and spatial or temporal changes in the emission patterns are not accounted for explicitly in the rollback model formulation. Nonreacting gases have also been tracked by receptor modeling methods Yamartino Receptor models compare the measured chemical composition of particulate matter concentrations at a receptor site with the chemical composition of emissions from the major sources to identify the source contributions at ambient monitoring sites.
There are three major categories of receptor models: chemical mass balance, multivariate, and microscopic. Receptor models are powerful tools for source apportionment because of the vast amount of particulate species characterization data routinely collected at many sampling sites within the United States.
Most of the information available is for elemental concentrations for example, lead, nickel, aluminum although recent measurements are leading to increased data on concentrations of compounds such as ionic species and carbon compounds. At a sampling or receptor site, the aerosol mass concentration of each species i is. The mass concentration c i measured at the receptor site of interest and the coefficients a ij that describe the chemical composition for the major sources are the inputs from which S j , the mass apportioned to source j , is determined.
Because a ij characterizes the source, it is referred to as the source fingerprint and should be unique to the source. When the chemical composition of the emissions from two source categories are similar, it is extremely difficult for receptor models to distinguish between the sources. The categories of receptor models are differentiated by the techniques used to determine S j. Chemical Mass Balance Methods. This is the basis of the chemical mass balance CMB method Miller et al.
If each source emits a particular species unique to it commonly called a tracer species , then a very simple tracer technique can be used Friedlander Examples of tracers commonly used are lead and bromine from mobile sources, nickel from fuel oil, and sodium from sea salt. Often the necessary condition to use the latter method—that each source have a tracer species unique to itself—is not met in practice.
Microscopic identification models are similar to the CMB methods except that more information is included that distinguishes the source of the aerosol. Such chemical or morphological data include particle size and individual particle composition and are often obtained by electron or optical microscopy. Multivariate Models. Multivariate models, including factor analysis models Henry and Hidy , ; Hopke , , rely on finding the underlying structure of large sets of particulate air quality data in order to determine the sources of the aerosol.
Models based on factor analysis are the most widely used.
For example, lead and bromine concentrations are usually highly correlated because they are emitted primarily by the same sources automobiles burning leaded gasoline. Thus, multivariate techniques identify groups of pollutants whose concentrations are correlated, and thus suggest the nature of the source. They do not rely on a detailed knowledge of the source fingerprint, a ij, and can be used to refine estimates of the fingerprint. Research intended to extend the power of receptor models for source apportionment is continuing, including development of methods to integrate measurement uncertainties into the analysis, incorporation of aerosol properties other than elemental composition, and inclusion of the effect of chemical reactions on secondary aerosol formation.
Friedlander has proposed a method that includes a decay factor in the formulation of equation 3 to take into account the chemical transformation of aerosols such as PAHs. This method is limited to first-order decay and assumes a knowledge of the average pollutant residence time in the atmosphere. A more general technique that can be used to estimate the source contributions to secondary aerosol mass loadings using receptor modeling techniques would be of use.
Attempts to circumvent some of the limitations of receptor models include hybridization with source-oriented models that rely on mass emission rate data from the pollutant sources.
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Applications of this sort have met with varying success Gartrell and Friedlander ; Pace ; Yamartino and Lamich Yamartino and Lamich used a hybrid model to identify areas with noninventoried emissions of CO. In theory, the source strengths of noninventoried or unknown emitters could be estimated using a hybrid technique, although uncertainty and sensitivity analyses need to be conducted on this type of model.
Pace used a microinventory approach, assuming that most of the aerosol mass at a receptor is derived from nearby emitters, and was able to account for total suspended particulate concentrations TSP with a standard error of 17 percent. Note that hybrid models require additional data that is, source strengths and meteorological data , but the prospects of added accuracy can justify the added effort. Hybrid models potentially could account for the secondary aerosols present in source apportionment studies.
Further development and use of hybrid models is clearly warranted, since they potentially retain the strength of receptor-oriented as well as source-oriented analytical models. Research should continue on the development of receptor models, especially on the hybridization of these models with other types of models.
The inclusion of aerosol properties and formation should also be pursued. Deterministic air quality models describe in a fundamental manner the individual processes that affect the evolution of pollutant concentrations. R can also be a function of the meteorological variables.
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In essence, this equation states that the time rate of change of a pollutant term 1 depends on convective transport 2 , diffusion 3 , chemical reactions 4 , and emissions 5. As discussed in the chapter on pollutant transport Samson, this volume , the closure problem makes it necessary to approximate this equation, usually by K -theory Lamb :.
Pollutant dry deposition and ground level emissions enter the system as boundary conditions. If equation 5 can be simplified for a particular application, it is usually advantageous to do so. This is the basis of the transport only and transport with linear chemistry models which, for brevity, will be called transport models. Transport models are suitable for studying the effects of CO sources and primary particulate emissions sources on air quality, but not for studying reactive pollutants such as O 3 , NO 2 , HNO 3 , and secondary organic species.
Transport of nonreactive pollutants is described in detail by Samson this volume and will be discussed here only briefly. Lagrangian Models. There are two distinct reference frames from which to view pollutant dynamics. The most natural is the Eulerian coordinate system which is fixed at the earth's surface.
In that case, a succession of different air parcels are viewed as being carried by the wind past an observer who is fixed to the earth's surface. The second is the Lagrangian reference frame in which the frame of reference moves with the flow of air, in effect maintaining the observer in contact with the same air parcel over extended periods of time. Because pollutants are carried by the wind, it is often convenient to follow pollutant evolution in a Lagrangian reference frame, and this perspective forms the basis of. Lagrangian trajectory and Lagrangian marked-particle or particle-in-cell models.
In a Lagrangian marked-particle model, the center of mass of parcels of emissions are followed, traveling at the local wind velocity, while diffusion about that center of mass is simulated by an additional random translation corresponding to the atmospheric diffusion rate Lamb and Neiburger ; Cass Lagrangian trajectory models can be viewed as following a column of air as it is advected in the air basin at the local wind velocity.
Simultaneously, the model describes the vertical diffusion of pollutants, deposition, and emissions into the air parcel figure 3.
The underlying equation being solved is a simplification of equation Schematic diagram of a Lagrangian trajectory model: A The column of air being modeled is advected at the local wind velocity along a trajectory path across the modeling region. Within the moving air parcel, the model describes the important processes more Trajectory models require spatially and temporally resolved wind fields, mixingheight fields, deposition parameters, and data on the spatial distribution of emissions. Lagrangian trajectory models assume that vertical wind shear and horizontal diffusion are negligible.
Other limitations of trajectory and Eulerian models are discussed by Liu and Seinfeld Gaussian Plume Model. One of the basic and more widely used transport models based on equation 5 is the Gaussian plume model figure 4. Gaussian plume models for continuous sources can be obtained from statistical arguments or can be derived by solving:. Diffusion of pollutants from a point source. Pollutant concentrations have separate Gaussian distributions in both the horizontal y and vertical z directions.
For a source with an effective height H, with emission rate Q, and a reflecting nonabsorbing boundary at the ground, the solution is:. The standard deviations are the directional diffusion parameters, and are assumed to be related simply to the turbulent diffusivities, K yy and K zz. Gaussian plume models are easy to use, require relatively few input data, and are very quick computationally. Multiple sources are treated by superimposing the calculated contributions of individual sources to ambient concentrations at a given receptor site.
It is possible to include the first-order chemical decay of pollutant species within the Gaussian plume framework. For chemically more complex situations, however, the Gaussian plume model simply fails to provide an acceptable solution. Because of its simplicity and because of its use by regulatory agents, the search for improvements to Gaussian plume models is still an active area of research.
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Eulerian Models. Of the Eulerian models, the box model is the easiest to envision conceptually. Simply, the atmosphere over the modeling region is perceived as a well-mixed box, and the evolution of pollutants in the box is calculated following conservation-of-mass principles including emissions, deposition, chemical reactions, and a changing mixing or inversion-base height figure 5.
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Schematic representation of a box model based on the conservation-of-mass equation. The stationary box allows pollutants to be advected into and out of the modeled region. The height of the modeling region can increase, accounting for an increase in the more Grid models attempt to solve a finite approximation to equation 5, including temporal and spatial variation of the meteorological parameters, emission sources, and surface characteristics. Grid models divide the modeling region into a large number of cells, horizontally and vertically, that interact with each other by simulating diffusion, advection, and sedimentation for particles of pollutant species.
Input data requirements for grid models are similar to those for Lagrangian trajectory models but, in addition, require data on background concentrations boundary conditions at the edges of the grid system used. Eulerian grid models produce pollutant concentration predictions throughout the entire airshed, which can be examined over successive time periods to observe the evolution of pollutant concentrations and how they are affected by transport and chemical reaction.
Modeling Chemically Reactive Compounds. A number of compounds, regulated as well as unregulated, are formed in the atmosphere by a series of complex, nonlinear chemical reactions. Often the compounds formed are more harmful than their precursors. Such models are also required to study the dynamics of chemically reactive primary pollutants such as benzene, and pollutants that are primary as well as secondary in origin, for example, NO 2 and formaldehyde.
Addition of the capability to describe a series of interconnected chemical reactions greatly increases the computational requirements for computer storage as well as for time, and also the input data requirements. The increased computational demands arise because the evolution of some species must be followed simultaneously.
One major difficulty encountered when numerically calculating the change of pollutant concentrations due to chemical reaction is that the characteristic lifetimes of the different pollutants are distributed over many orders of magnitude.
A suitable numerical solution scheme must be chosen when confronted by a stiff system.