DRAFT WORKBOOK FOR THE COMPARISON OF AIR QUALITY MODELS - APPENDICES - (After public review and comment this document will become part of the OAQPS Guideline Series) November 1977 Monitoring and Data Analysis Division Office of Air Quality Planning and Standards U. S. Environmental Protection Agency Research Triangle Park, North Carolina DRAFT ------- DRAFT Workbook for the Comparison of Air Quality Models Appendices by Albert E. Smith, Kenneth L. Brubaker, Richard R. Cirillo, and Donald M. Rote Energy and Environmental Systems Division Argonne National Laboratory Argonne, Illinois 60439 November 1977 Interagency Agreement No. EPA-IAG-D6-0013 EPA Project Officer: Joseph A. Tikvart Prepared for ENVIRONMENTAL PROTECTION AGENCY Office of Air and Waste Management Office of Air Quality Planning and Standards Monitoring and Data Analysis Division Research Triangle Park, North Carolina 27711 DRAFT ------- 1 TABLE OF CONTENTS Page APPENDIX A A 7 A.1 EMISSION CHARACTERISTICS A 7 A.1.1 GENERAL A 7 A. 1.2 TREATMENT OF SOURCE-RECEPTOR RELATIONSHIP A 8 A.1.3 TREATMENT OF EMISSION RATE A13 A.1.4 TREATMENT OF COMPOSITION OF EMISSIONS CHEMICAL COMPOSITION A18 A.2 PLUME BEHAVIOR A2O A.2.1 GENERAL A20 A.2.2 TREATMENT OF PLUME BEHAVIOR A23 A. 3 HORIZONTAL AND VERTICAL WIND FIELDS A27 A.3.1 GENERAL A27 A. 3.2 TREATMENT OF HORIZONTAL AND VERTICAL WIND FIELDS A3O A.4 HORIZONTAL AND VERTICAL DISPERSION A34 A.4.1 GENERAL A34 A.4.2 TREATMENT OF HORIZONTAL AND VERTICAL DISPERSION A43 A.4.2.1 Treatment Classification A44 A.4.2.2 Benefits and Limitations A48 A. 4.2. 3 Parameterization A54 A.5 QIENISTRYANDREACTIONMECHANISM . A56 A.5.l GENERAl..... A56 A.5.2 TREATMENT OF CHEMISTRY AND REACTION MECHANISM A61 A.6 PHYSICALREMOVALPROCESSES ................... A66 A.6.1 GENERAL A66 A.6.2 TREATMENT OF DRY DEPOSITION A68 A.6.3 TREATMENT OF PRECIPITATION SCAVENGING A71 A.7 BACKGROUND, BOUNDARY AND INITIAL CONDITIONS A73 A.7.1 GENERAL A73 A. 7.2 TREATMENT OF BACKGROUND, BOUNDARY AND INITIAL CONDITIONS A77 A. 8 TEMPORAL CORRELATIONS A8O A.8.1 GENER.A.IJ A8O A. 8.2 TREATMENT OF TEMPORAL CORRELATIONS A82 ------- II TABLE OF CONTENTS (Cont’d) Page A. 9 IMPORTANCE RATINGS FOR APPLICATION ELEMENTS A83 APPENDIX B B 1 B. 1 REFERENCE )DEL TREATMENTS OF APPLICATION ELEMENTS B 7 B. 2 REFERENCE MODEL ABSTRACTS AND EQUATIONS B 35 B.2.1 CDM B37 8.2.2 pjj B38 B.2.3 SINGLE SOURCE (CRSTER) B41 B.2.4 VALLEY B44 8.2.5 ATM B46 B.2.6 STRAN B47 B.2.7 APRAC—1A B48 B.2.8 HIWAY B50 B.2.9 DIFKIN B51 B.2.1O SAl 852 GLOSSARY OF SYMBOLS B55 APPENDIX C C 1 C.1 EXAMPLE 1: SCIM/1243 C 7 C.2 EXAMPLE 2: AQDM/1143 C23 C.3 EXAMPLE 3: PTDIS/1213 C37 C.4 EXAMPLE 4: PTMAX/1213 C49 C.5 EXAMPLE 5: PTMTP/1213 C61 C.6 EXAMPLE 6: HANNA—GIFFORD/1243 C73 C.7 EXAMPLE 7: HANNA—GIFFORD/1143 C87 C.8 EXAMPLE 8: APPENDIX J/6243 ClOl APPENDIX D D 1 REFERENCES ------- 111 LIST OF TABLES Number Page A.l Comparison of Widely Used Plume Rise Formulae A 25 A.2 General Atmospheric Stability Classification According toTemperatureLapseRate A.3 Commonly Used Measures of Atmospheric Stability and and Turbulence Intensity A 41 A.4 Factors Affecting the Level of Atmospheric Turbulence and the Rates of Horizontal and Vertical Dispersion A 43 A.5 Factors Determining Meandering Contribution to Horizontal Dispersion A 43 B.l Reference Model Classification B 9 B.2 Treatment of Source—Receptor Relationship by Reference Models B 10 B.3 Treatment of Emission Rate by Reference Models B 14 B.4 Treatment of Composition of Emissions by Reference Models . B 16 B.5 Treatment of Plume Behavior by Reference Models B 18 B.6 Treatment of Horizontal Wind Field by Reference Models B 19 B.7 Treatment of Vertical Wind Field by Reference Models B 21 B.8 Treatment of Horizontal Dispersion by Reference Models B 22 B.9 Treatment of Vertical Dispersion by Reference Models B 24 B.lO Treatment of Chemistry and Reaction Mechanism by Reference Models B 26 B.ll Treatment of Physical Removal Processes by Reference Models.... B 27 B.l2 Treatment of Background, Boundary and Initial Conditions byReferenceModels B29 B.13 Treatment of Temporal Correlations by Reference Models B 34 ------- iv ------- V LIST OF FIGURES Number Page A.l Dependence of Crosswind Pollutant Distribution from a Continuous Point Source on Averaging Time A 36 B.l Mixing Height Algorithm Used in RAN B 40 B.2 Mixing Height Algorithm Used in CRSTER. B 43 ------- vi ------- Al APPENDIX A TECHNICAL SUPPORT MATERIAL ------- A2 ------- A3 CONTENTS OF APPENDIX A Page A.1 EMISSION CHARACTERISTICS A 7 A.1.1 GENERAL A.1.2 TREATMENT OF SOURCE-RECEPTOR RELATIONSHIP A.1.3 TREATMENT OF EMISSION RATE A.1.4 TREATMENT OF COMPOSITON OF EMISSIONS A. 2 PLUME BEHAVIOR A 7 .A 8 •A13 .A 18 .A2 0 A.2.1 GENERAL A 20 A.2.2 TREATMENT OF PLUME BEHAVIOR A 23 A.3 HORIZONTAL AND VERTICAL WINDFIELDS A .3.1 GENE RAL A.3.2 TREATMENT OF HORIZONTAL AND VERTICAL WINDFIELDS A27 •A27 •A30 A. 4 HORIZONTAL AND VERTICAL DISPERSION A.4.1 GENERAL A.4.2 TREATMENT OF HORIZONTAL AND VERTICAL DISPERSION •A34 A.51 GENERAL A 56 A.5.2 TREATMENT OF CHEMISTRY AND REACTION MECHANISM A 61 A.6 PHYSICAL REMOVAL PROCESSES A.6.1 GENERAL A.6.2 TREATMENT OF DRY DEPOSITION A.6.3 TREATMENT OF PRECIPITATION SCAVENGING A.7 BACKGROUND, BOUNDARY AND INITIAL CONDITIONS A.7.1 GENERAL A.7. 2 TREATMENT OF BACKGROUND, BOUNDARY AND INITIAL CONDITIONS •A66 A66 A68 ‘A 7]. .A73 .A73 A.4.2.l Treatment Classification A.4.2.2 Benefits and Limitations A.4.2.3 Parameterization •A34 A 43 •A44 ‘A48 ‘A54 A.5 CHEMISTRY AND REACTION MECHANISM A 56 ‘ ‘ ‘ •A77 ------- A4 ------- A5 CONTENTS OF APPENDIX A (Cout’d) Page A.8 TEMPORAL CORRELATIONS A 80 A.8.1 GENERAL A 80 A.8. 2 TREATMENT OF TEMPORAL CORRELATIONS A 82 A.9 IMPORTANCE RATINGS FOR APPLICATION ELEMENTS A 83 ------- A6 ------- A7 Appendix A: TECHNICAL SUPPORT MATERIAL Sections A.1—A.8 of this Appendix contain technical discussions of the application elements and describe methods of treating them in models. Brief discussions of the rationale for the importance ratings are given in Section A.9. A.l EMISSION CHARACTERISTICS A.l.l General To predict the concentration of a pollutant, a model must treat the emissions of that pollutant and its precursors, if any, as well as the emissions of those substances which react with the pollutant or its precursors. The emissions and their distribution can be characterized by specifying the: • Source—receptor relationships, • Emission rates, and • Composition of the emissions. These three application elements are discussed together here but the user should make separate comparisons of their treatments. The source—receptor relationship includes: • Source location, • Height at which emissions are released into the atmosphere, • Receptor location, • Receptor height, • For line and area sources, the orientation of the source to a fixed direction, and • Downwind and crosswind distances between source—receptor pairs. Thus defined, source—receptor relationship comprises the positional factors which determine the extent to which dispersive, chemical, and removal pro- cesses affect pollutant concentrations. Once released at a particular loca- tion and height, pollutants travel downwind and are dispersed, ultimately to ------- A8 be detected at the receptors of interei t. It is during this time of flight that dispersion, secondary generation, and removal processes are active in altering the concentrations of the pollutant of interest. Emission rates are clearly important because they determine the total quantities of materials emitted into the atmosphere during the time of in- terest. A source’s emission rate generally varies with time. For example, emission rates from a stack generally vary over time scales ranging from minutes to years. For line and area sources, spatial variation within a single source may also be important. The treatment of these temporal and spatial variations must be considered when two models are compared and are discussed in Appendix A.l.3 dealing with the treatment of emission rates. Finally, Uie composition of emissions must be considered in some applications. Chomical composition is important for secondary or reactive pollutants and in some situations where several species of particulate matter are of interest. The size distribution of particulate emissions is also important when fallout, deposition, or precipitation scavenging must be considered. It should be noted that the identification of possible sinks and secondary production mechanisms can depend upon knowing the composition of emissions other than those with which the user is mainly concerned. The following three subsections describe the treatments of these application elements. A.l.2 Treatment of Source—Receptor Relationship In this discussion, location means a specification of the source’s horizontal position. The release height specifies the vertical position of the release of emissions to the atmosphere, and does not include a specific discussion of treatments of plume rise, which are discussed as a separate element, plume behavior, in Appendix A.2. For point sources, there are basically two levels of detail with which horizontal location can be treated. The first allows each source to be accurately located at its true position with respect to some horizontal grid system, thus allowing a maximum degree of spatial resolution. The second and less detailed approach locates each point source only to the extent of identi- fying a grid cell containing the source, thus sacrificing some degree of spa- tial resolution. This latter treatment is used by numerical models that treat all point sources lying within a given basic grid cell without regard to their ------- A9 precise location but that do distinguish between sources located in different cells. The loss of resolution between the first and second levels is essen- tially the same as that incurred in developing an emissions inventory when small point sources are aggregated to area sources. For the purpose of this workbook, however, the inventory is assumed to be given and the less detailed treatment then involves the assignment of the point sources to grid cells despite the availability of more precise information. If the aggregation to area sources is part of the inventory, it should not be considered when coin— paring models. The comparison should be based on the treatments of the point, area, and line sources given in the inventory. The location of point sources by grid cell can, of course, be treated at various levels of detail, the most detailed treatments preserving signif 1— cant spatial resolution on a relatively fine grid and the least detailed sacrificing all spatial resolution and not distinguishing between sources regardless of their location within the region of interest. Models using the least detailed treatment cannot adequately treat situations involving alt era— tions in the spatial distribution of emissions. Detailed treatments also frequently permit a finer grid to be used in areas where the user desires a high degree of spatial resolution. This treatment is somewhat more detailed than one using a fixed grid size, if the block size is smaller while allowing the user the added flexibility of matching the degree of resolution to the needs of the specific application. Occasionally, a model may aggregate sources on a basis not directly related to location. This occurs when sources are aggregated, for example, by industrial category. Unless this type of treatment is used in conjunction with one of the locational treatments described above, it provides no infor- mation on the location of sources and is equivalent to the least detailed treatment of horizontal location. The release height of point sources is treated in its most detailed form when both the physical stack height (without plume rise) and the elevation of the base of the stack above some reference elevation can be specified for each source. A less detailed treatment assumes flat terrain and considers only the physical stack height or release height above grade. These treatments can be used even when the horizontal locations of the sources are tgriddedlt by the model onto subareas of the region of interest. Less detailed treatments are ------- AlO frequently used when the model grids the point sources. These involve specifying one or several representative release heights, which may include an elevation correction, for each subarea of the grid. Less detail is available when the same release heights are applied to all the subareas. (When representative release heights must be assigned, the user frequently calculates a representative plume rise and adds it to the physical release height, since models using such treatments generally make no provision for the internal calculation of a typical plume rise.) At the least detailed level release height is not treated explicitly; all emissions are treated as if they are released at the same height. This non—explicit treatment is used in numerical models in which all emissions are treated as part of the boundary condition at ground level. Before proceeding, it is convenient to discuss receptor location br cause receptors are usually taken as points. As is the case with point sources, the horizontal locations of receptors can be specified as precise points or as locations in some grid block. When the receptors are located precisely two methods or a combination of the two are generally used. The first allows the user to locate the receptors arbitrarily. The second places the receptors at the intersections of a grid network, the spacing or scale of which may be fixed or under the user’s control. Both methods may provide equivalent levels of detail and the user must decide which is better suited to the particular application. It may also be, of course, that specifying receptor locations by subarea only is sufficient to the user’s purpose, but here such treatments will be rated as less detailed than treatments that locate receptors precisely in the horizontal. The level of detail of receptor locations also depends upon whether the elevation of the receptor can be spe- cified. Given comparable specification of horizontal receptor locations, a treatment which allows the user to specify arbitrary receptor heights is more detailed than one which assumes that all receptors are at the same height (usually ground level). in the context of source and receptor locations, it must be stressed that the user should not always rate one treatment against another solely on the level of detail. Consideration should also be given to whether the level of detail provided is necessary in the particular application. For instance, if the application involves the impact of a single source at a ------- All specific location, the ability to locate numerous sources and receptors precisely is irrelevant as long as the pair to be studied can be located as desired. Thus, the comparisons made by use of the tables in the workbook should be modified to reflect the specific requirements of the application of interest. The table assumes that it is desired to locate a number of sources and receptors at arbitrary locations. Since all required cases could not be foreseen, the user must modify this general list to reflect the application of interest. For area sources, the treatments of source location and release height follow the same general progression as for point sources, that is, a full specification in three dimensions (both horizontal location and release height) at the most detailed level and a complete lack of explicit recognition of different source locations and heights at the least detailed level. Two additional considerations must be given to area sources, however, because of their two dimensional nature. First, a model which accepts area sources at arbitrary locations provides more detail than one which places all area sources on a fixed grid even if the size of the grid can be changed by the user. In the latter case, the user’s area sources must be mapped onto the model’s gridded areas and hence the differences between areas tend to be averaged out. Such a loss of detail may be unimportant when the difference in emission rates in adjacent areas is small. The user must decide this based on his knowledge of the situation of interest. Second, models which treat arbitrarily sized area sources generally allow greater flexibility than those which limit area sources to one or several set sizes. This can be particularly important when dealing with “true” area sources such as open pit mines or dusty fields. Again the user must decide when comparing models whether this consideration is important in the particular application of interest. Another difference between point and area sources arises because an area can have an arbitrary orientation with respect to the wind direction. Most models treat area sources on some type of grid system that is fixed in space and hence the orientation of an area cannot be adjusted even when the real physical source is tilted with respect to the model grid. For computa- tional purposes, some models assume a specific orientation which may be unrelated to the actual orientation of the source. This assumption is ------- Al 2 frequently reasonable when the area sources are aggregates of many small point or line sources. A somewhat more detailed treatment permits the area sources to assume an arbitrary orientation; such treatments may be useful when dealing with true area sources where the orientation of the actual sources can be arbitrary. The most detailed treatment of line sources specifies the precise location and orientation of the line by, for example, using its endpoints and provides for some width and height for the line (thus really treating it as an elongated volume source). For infinite lines, only the orientation of the line is specified. Curved lines are usually approximated as series of straight line segments and for highways some width can be provided by allowing the number of lanes, medial strip width, and roadway width to be specified. Less detailed treatments specify only the horizontal location and fail to allow for width; a release height may be specified. Care must be taken with line source models to ascertain whether they allow the line to assume an arbitrary orientation with respect to the receptor. Some models, for example, require that the receptor be located near the perpendicular bisector of the line and will not properly treat a receptor lying near the axis of the line source. As with point and area sources, increasing degrees of aggregation within the model produce less detailed treatments. En applications involving a combination of source types, the degree of detail of the treatment can be different for different source types. However, an overall evaluation can still be made by comparing the reference model treatment with the study model treatment for each source category and making some assessment of the importance of each category to the particular application. Some modeling parameters determined by the source—receptor relation- ship may depend explicitly on the downwind or crosswind distances between source—receptor pairs. For instance, in Gaussian plume models the dispersion parameters are normally functions of the downwind distance. When this is the case, these distances must be calculated. It should be noted, however, that a model may not ever need to calculate the downwind or crosswind distance explicitly. For example, a numerical dynamic model may move an air parcel along a trajectory but never use the distance along the trajectory. In such cases, the downwind/crosswind distances are not calculated and their treatment ------- A13 can be ignored. When required by the model these distances are usually assumed to be determined by the horizontal separation between pairs and hence do not depend upon release height or receptor height. When point sources are involved and both the sources and receptors are located as points, the capability exists to calculate a unique downwind and crosswind distance for each source—receptor pair either along a curved trajectory or assuming a steady—state wind in a single direction. When a model grids either sources or receptors, less detail is available, since only average or representative separations can be determined. This is also the case for area and line sources. Finally, no downwind or cross- wind distances can be determined if no distinctions between sources and recep- tors are made on the basis of location. This is the case, for instance, when a box model includes an entire region in a single box. These treatments of source—receptor relationship are listed by their level of detail in Table 5.1. Treatments by the reference models are given in Table B.2. A.l.3 Treatment of Emission Rate Once the positional relationships between sources and receptors have been determined, the emission rate of each source must be specified. Two aspects of the element emission rate are important: — Spatial distribution of emissions and — Temporal variation of emissions. The treatment of the spatial distribution of emissions is closely related to the treatment of horizontal location discussed in Appendix A.l.2, since the degree of spatial resolution available depends upon how close to their real positions the model locates sources. For point sources, no additional infor- mation is required to describe the spatial distribution beyond what is already given in the treatment of source—receptor relationship. In the case of line or area sources, however, the manner in which the distributed nature of the source is taken into account requires consideration and is discussed in this section. Two points of view exist regarding the treatment of distributed sources. In determining the treatment of distributed sources by a model it is useful to identify which point of view is adopted simply in order to clarify the treatment. In many cases, there is no intrinsic difference in the level of detail associated with the two possibilities. ------- Al4 From the first point of view, the total contribution of the entire emission distribution is estimated by adding up estimates of the contributions from many individual parts, each consisting of a uniformly emitting area or line segment. For example, sulfur dioxide emissions from residential space heating in an urban area are most commonly represented as a rectangular array of square area sources, each characterized by a given emission rate per unit area. Another example is the representation of automotive emissions as a set of finite line sources, each of which is characterized by a given emission rate per unit length. Each part is considered to be a separate source, and the contribution from each of these parts to the pollutant concentration is estimated. The total contribution from the entire distribution is then esti- mated by summing all these individual contributions. From the other point of view, the overall distribution is regarded as a single entity in which, however, the local emission rate may vary from point to point. A single estimate of the total contribution from the given emission distribution is made without explicitly estimating the contribution from each of the individual parts comprising the source inventory, even though the source inventory may have exactly the same form as before. This point of view may be adopted for an array of square area sources as in the first example above, as well as in cases in which only one line or area source is of interest. In the latter situation, the emission rate per unit length or per unit area may be allowed to vary within the source itself. There is no intrinsic difference in the levels of detail associated with these two points of view if only the total contribution to the estimated pollu- tant concentration is of interest. If the individual contributions are desired, a treatment which adopts the first point of view is likely to be superior to one which adopts the second, although much depends upon the level of detail of the methods used to make the individual estimates in the two treatments. In order to estimate individual contributions within a model adopting the second approach, an algorithm for allocating the total calculated contribution among the indivi- dual parts must be incorporated, whereas in the first approach the individual contributions are independently estimated. Whatever point of view is adopted, some technique must be used to esti- mate the contribution of either the overall distribution or of each of its component parts. The rest of the discussion addresses methods of making these ------- A15 estimates. The various possible methods fall into two general categories: — Analytic or numerical integration, and — Source substitution — the replacement of a line or area source with a small number of point sources. In principle, the most detailed treatment of the spatial distribution of emissions involves the integration over the given distribution of the con- tribution from an infinitesimal area or line segment, assumed to contribute as a point source. If the spatial distribution and the infinitesimal contribution have a sufficiently simple form, the integral may be evaluated analytically. Thus, for example, the pollutant concentration downwind of a uniform horizontal line source of specified length oriented perpendicular to the wind may be esti- mated by means of a formula obtained by integrating the Gaussian plume expression for the contribution from each infinitesimal segment of the line. In general, however, the spatial distribution and the point source concentration estimates are sufficiently complicated that such an analytic expression cannot be derived. En such cases, alternative methods must be used. One alternative is to evaluate the integral by some appropriate numerical procedure. If the numerical procedure is sufficiently detailed that the spatial variation present in both the emissions and the point source formula is taken into account, the result may be equivalent to that which would be obtained by an analytic integration. The level of detail of the treatment is directly related to the distance between sampling points at which the emission rate and point source estimate are evaluated; the smaller the distance, the higher the level of detail. Since for a given receptor the nearby emissions are expected to contribute n re heavily than those father away, treatments which incorporate high resolution near the receptor and progressively lower resolution at greater distances involve a relatively high level of detail. Another alternative is to simplify the integration by introducing additional approximations so that either an analytic expression may be derived or the numerical integration is made significantly easier. For example, a common approximation used in dealing with an array of area sources is to assume that emissions are uniformly distributed in the crosswind direction. In most urban areas, this may be a reasonable assumption; in general, the level of the treatment depends upon the appropriateness of the assumptions in the user’s ------- A16 specific application. The example just given corresponds to what is often called the narrow plume approximation. In this approximation, only the emissions from those area sources which are directly upwind of the receptor, or in general those which are intersected by a trajectory which subsequently passes through the receptor location, have an effect on the estimated pollu- tant concentration. Further discussion may be found in Appendix A.4.2. The least detailed treatments involve the replacement of a line or area source by a small number of point sources having a combined emission rate equal to that of the source they are replacing. The smaller the number of effective point sources is, the less detailed is the treatment; a treatment involving the use of a large number of points amounts to the use of a numeri- cal integration procedure. The position of the effective points may be chosen to approximate the spread of emissions within the source being replaced, and the strength of each may depend upon their position. There are two components to the treatment of temporal variation of emission rates: — The degree of temporal resolution which the model allows and — The suitability of the technique for treating the variations to the particular application. The degree of temporal resolution is determined by the interval at which emission rates can be changed in the model. Even the most detailed treatments can usually handle properly at most hourly variations in emission rates. The overall temporal resolution of a model is often limited by the temporal reso- lution of the meteorological data. The emission data should reflect a similar resolution at the most detailed level. If a large number of time intervals must be treated, say all 8760 hours in a year, some models take a sample of all the hours and thus treat only a subset of all available time intervals. This approach provides somewhat less detail than accounting for all time intervals but may give results which are equivalent to those obtained from a fully de- tailed treatment particularly when the accuracy of the model is considered. Less detail is offered by treatments which allow no temporal variation, per— mitting only constant emission rates to be specified. Within these limits, the shorter the interval over which changes in emission rates can be specified, the more detailed the treatment. ------- A17 For those models which allow some temporal variation in emission rates, the suitability of the technique of handling the variations must also be considered. One technique is commonly used in dynamic models. The total time period of interest is divided into intervals. Each time interval is modeled in succession, the pollutant distribution at the end of one interval serving as the initial distribution for the next. This type of detailed approach is necessary when significant variations in emission rates occur over the averaging time of interest. In simpler situations, a second tech- nique treating the situation as a set of steady states is applicable; the steady—state approach is generally simpler to implement. This approach looks at each time period separately. it can account for the time sequence, but it ignores the pollutant distribution remaining at the end of each interval when a new interval is considered. The steady state treatment is the more common. Some models allow the entire set of steady—state situations to be treated. Others simulate only a single situation at a time and must be applied repeti- tively when longer time periods are of interest. The repititious application of a model allows temporal variations in emission rates to be treated using only constant rates. For example, if it is desired to use a climatological model designed to estimate annual averages from average emissions rates and the sources have significant monthly varia- tions, the model could be run twelve times with emission rates appropriate for each month and the twelve individual results averaged. It would, of course, also be necessary to use meteorological data appropriate to each month in the individual runs. As was the case with spatial variation, a model that aggregates sources is inherently less detailed than one which treats each source individually. In aggregating, each source’s emission pattern is masked in an average value and some details of the situation are lost. One further aspect of emission rate must be discussed: the treatment of the amount of emissions based on other input parameters such as VMT, vehicle mix, or population. When actual emission rates (or a sequence of rates) are supplied to the model, the degree of detail depends upon the degree of detail used in generating these numbers and is not limited by the model itself. When the model itself calculates the emission rates, a model requiring more de- tailed input generally provides a more detailed treatment. For example, a model ------- A18 which estimates vehicular emissions based on VMT, average speed, and vehicle mix is less detailed than one which uses VMT, vehicle mix, and allows a different average speed to be assigned to each class of vehicles. Since the number of possibilities is large, no attempt to rank treatments will be made here. As a general guideline, the user should compare the levels of detail required in the inputs of the models being evaluated. It should also be noted that evaluating this aspect of emission rate may be impossible as, for example, when the one model requires specific emission rates to be input and a second calculates emission rates from other information. Table 5.2 gives the general treatments of emission rates in order of decreasing level of detail; the specific treatments used by the reference model are given in Table B.3. A.l.4 Treatment of Composition of Emissions Chemical Composition In applications involving chemical reactions (secondary generation or reactive pollutants), the chemical composition of emissions is important. At the most detailed level, the emissions of all relevant individual compounds are treated. Somewhat less detail is obtained when several or many related compounds are “lumped” together into a single class and only the total emissions of all members of the class are treated. Two things must be con- sidered when a model treats the emissions of at least some of the relevant compounds in terms of lumped classes. First, the criterion for determining in which class a particular compound belongs must be appropriate for the chemistry to be modeled. Second, the compound chosen to represent the class must also be chosen appropriately; in some cases, it may not be an actual compound but a hypothetical representative compound. For example, in the case of photochemical oxidants, it would be impractical to use full detail and treat the emission of every possible organic compound individually. Con- sequently, they may be lumped into classes depending upon their degree of photochemical reactivity. Thus, if five reactivity classes were used, each source could have associated with it up to five different emission rates for organic compounds, one emission rate for each reactivity class. This classi- fication would also be appropriate to the oxidant problem whereas classifica- tion by, for instance, molecular weight may not be. In general, the greater ------- A19 degree of classification into appropriate, distinct classes, the greater the level of detail of the treatment. Less detail is available when assumptions regarding the composition of emissions are built into the model, such as when a phoiochemical oxidant model assumes a certain percentage of the organic emissions to be reactive regardless of the actual nature of the sources in— volved. Still less detailed treatments describe the emissions of only one of several compounds known to interact. Model treatments must also be checked to ascertain whether all relevant emissions have been treated. For example, models for photocheinica]. oxidants that treat reactive organic compounds but not NO and NO emissions are inher- ently less detailed than those which treat NO and/or NO, because NO can act as an ozone scavenger and the NO/organics ratio is important in determining the extent of ozone formation. Expert advice may be needed in making these determinations. With regard to this last point, care must be exercised to consider here only compounds which are actually “emitted tt by the sources. These may only be a subset of the total number of compounds which are in- volved in the chemical kinetics and may not even include the pollutant of interest. For example, ozone “emissions” are negligible or zero but the emissions of the organic precursors must be treated in models for photochemical oxidant. The user would not deem a photochemical model inappropriate because ozone emissions are not treated. Size Distribution of Particulate Matter The most detailed treatment of the size distribution of emitted partic- ulate matter would take into account a continuum of particle sizes by allowing the functional form of the particle size distribution to be specified. In somewhat less detail an appropriate distribution is assumed and the parameters necessary to describe that distribution are input. Less detail is available in treatments which treat all particles within a given range of sizes as if they had the same representative size. This treatment is analogous to the lumping of various chemical species described above. Similarly, a treatment using smaller size intervals offers more detail (generally, more size intervals) than a treatment that divides the total range of sizes into fewer, wider inter- vals. Even less detail is contained in treatments that assume that some fraction of the particulates are affected by the mechanism of interest. This is really a two—class treatment: a fraction of the particulates, for example ------- A2 0 might be assumed large enough to fall out of a plume, while the remaindeç are assumed to behave like a gas. The least detail, of course, is offered by treatments which fail to treat the size distribution explicitly in situations in which it may be important. Such is the case when all particulate emissions are treated as a gas, including that fraction which is sufficiently large to be subject to significant gravitational settling. It should be noted that a complete characterization of the composition of emissions may require a joint treatment of chemical composition and the size distribution. In such cases, the appropriate size distribution may not only vary from source to source but may also vary from chemical compound to chemical compound. Such detail is beyond the level at which models presently operate but the user should be aware of the complexity of a complete specifica- tion of the application. Tables 5.3 and B.4 give the treatments of the composition of emission in general and by the reference models, respectively. A.2 PLUME BEHAVIOR A.2.l General Upon release, an effluent generally has some upward momentum and buoy- ancy. Mixing with the ambient air begins immediately and continues as the effluent travels downwind and disperses. In the initial phases of this travel, the plume centerline is determined simultaneously by the rise due to the initial momentum and buoyancy and the downwind advection. As mixing continues, the plume centerline is determined by the initial conditions to progressively lesser degrees until it is determined predominantly by the downwind advection. The height to which the initial momentum and buoyancy carry the effluent is called the “plume rise” and this height plus the physical release height is termed the “effective stack height.” As these definitions indicate, some models treat plume rise only for point sources. When area and line sources are aggregates of small point sources, the plume rise associated with each individual area or line source is an average or representative value. This discussion focuses on plume rise from point sources and certain other types of plume behavior. The user should be aware, however, that the same factors as discussed herein must be considered if a model explicitly treats plume rise from area or line sources. ------- A21 Many interacting factors affect plume behavior. When the stack exit velocity is small compared to the wind speed, the plume may bend over immediately after release and downwash may occur behind the stack. This is one of several special situations to be considered when plume behavior is treated. If the stack exit velocity is large, mixing of the effluent and ambient air will be increased, rapidly dissipating the plume’s buoyancy and momentum and causing a low plume rise. The same effect also occurs with increasing atmospheric turbulence and may be represented as a dependence of plume rise on stability, atmospheric temperature gradient, or wind speed. The buoyancy of a hot plume is determined by the heat release rate ; hotter plumes rise higher than colder plumes, other conditions being the same. The heat release rate depends on the stack exit velocity, the effluent’s temperature, molecular weight, and specific heat, on the stack diameter, and on the atmospheric temperature and pressure. A formula relating these variables may be found in Moses and Kraimer (1972). In addition, the relative humidity and moisture content of the plume may be important. Many plumes contain some water and after release the condensation of gaseous water or vaporization of liquid water adds or removes heat from the plume and hence affects buoyancy. The condensation of water vapor can be large enough to cause a very low plume rise, as can be the case with cooling tower plumes. The momentum of the plume depends upon the mass of the effluent and the stack exit velocity. The density of the plume is thus important and the product of velocity and stack diameter is a measure of the square root of the momentum release rate. For stacks with very high exit velocities, the momentum term may be much larger than the buoyancy term. This “momentum only” case is not en- countered in most common applications, in which the principal interest is in buoyancy effects. There are other factors which also affect plume rise: • Terrain and nearby buildings, • Number of nearby stacks and local heat sources, • Shape of the stack opening, • Wind direction in directionally inhomogenous situations, • Wind shear, and • Precipitation. ------- A22 No single treatment of plume rise deals with all these factors and there is no generally accepted treatment; over twenty separate formulae are available and new ones continue to appear. Most analytical formulations make the plume rise directly proportional to the reciprocal of the wind speed at the top of the stack. Two terms, one proportional to the square root of momentum and the other to some power of the heat release rate, are also included but the momentum term Ls frequently omitted, its effect being negligible in many common situations. When plume rise is treated as a function of distance, data for power plant plumes indicates that the plume rise varies as the 2/3 power of the downwind distance. There may be separate formulae for different sized stacks and different stabi- lities but the treatment of special plume behavior is generally not included in the treatment of plume rise. The special plume behaviors usually considered include: • Dowawash • Plume trapping, and • Inversion breakup fumigation. The conditions leading to downwash were noted above. A rule—of—thumb says that downwash should be considered whenever the physical stack height is less than about 2 1/2 times the height of the building it is on or the height of nearby obstacles to airflow or whenever the stack exit velocity is less than about 1 1/2 times the windspeed at the top of the stack. This rule—of—thumb is only a rough guide and in many situations, for instance, with a cold plume having little buoyancy, downwash may need to be considered even for stacks whose heights exceed those indicated. Plume trapping occurs when a stable layer exists above a neutral or unstable layer. A plume emitted into the lower neutral or unstable layer will rise until it reaches the base of the stable layer where it becomes trapped between the stable layer and the ground. Very hot or fast plumes may be able to “punch through” the stable layer and thus may not be trapped. Fumigation occurs when a stable surface—based inversion is broken up by heating from the ground. Pollutants that were emitted into the stable layer are then thermally mixed in the vertical and relatively high ground level con- centrations can result, as discussed in Appendix A.4. ------- A23 A.2.2 Treatment of Plume Behavior As noted previously, there is no generally accepted method of treating plume rise. Several types of treatments of various degrees of detail exist. Within each type, the appropriateness of a given treatment depends upon whether the method has been verified in the field for the application of interest. In fact, the best comparison of two plume rise formulae is obtained by comparing their predictions with observed plume rise values under the conditions of in- terest. If such data are available they should be used in preference to the method described below. In general, a formula validated for the application of interest and producing gpod agreement with observed values is to be preferred to one for which no validatic i data is available or ft r which validation data show poor agreement with observations. It would not be proper to rank treat- ments simply by counting the number of parameters they handle, because some simple formulae perform better than more complex ones using many parameters. The most detailed level of treatment would account for the simultaneous rising and dispersing of the plume. This problem is extremely complex and has been treated only in very specialized applications such as self—contamination of buildings where the behavior of the plume immediately after release is of pri- mary concern. Most andels are unable to handle dispersion during the initial rising phase of plume travel and usually treat the situation by separating the rising plume from the dispersing plume and considering two distinct steps: First, the plume rise is determined based on stack and meteorological parameters. This plume rise may be a function of the downwind distance. Second, dispersion is treated by assuming a virtual source emitting at an effective stack height equal to the physical release height plus the plume rise. This is the type of treatment found in most dispersion models for primary pollutants. However, many formulae are used to estimate the plume rise. As noted above, comparison to a reference model’s treatment should be based upon which treatment gives better agreement with observed plume rises for the application under consideration. Such comparative results are scanty and another method must normally be used if a comparison is to be made. ------- A24 Without prejudice to other treatments, models using the following plume rise formulae can be considered applicable in many situations, unless comparative field studies indicate otherwise for the case at hand: • Briggs’ 2/3 power law or a later modification, • Holland, • cONCAWE or WNCAWE simplified, and • ASME. The Briggs’ and Holland formulae have been “verified’ t for power plants. Only Holland has a separate immentum term and correction factors have been suggested to account for stability. Briggs uses separate formulae for different stability classes and is the only one which treats plume rise as a. function of downwind distance. The ONCAWE formulations consist of single formulae and are the only ones in which plume rise is inversely proportional to a fractional power of the wind speed. It must be stressed that this list does not mean that other formulae should not be used. These four are widely used and do a fairly good job of prediction in many cases. Other formulae may be better in specific applications, but the only valid evidence of this is direct comparison with observations. If the user has an unverified formula in a study model, the following general guidelines, valid for hot, buoyant plumes only, may be helpful: • Plume rise should be proportional to the reciprocal of wind speed to some power between 1.0 and 0.70, • A buoyancy term must be included (heat release rate should be raised to a power between 1/3 and 1), • Other things being equal, a formula with an additional nxmentum term would be preferred, • Other things being equal, a formula giving plume rise as as function of downwind distance would be preferred. (This consideration is n re important for low level sources than for elevated sources.) It must again be stressed that verification in the field for the application of interest is the preferred decision parameter, followed by use of one of the four widely used formulations. Use of the guidelines is recommended only as a last resort. For ease in comparison, the widely used formulae are corn— pQred under these guidelines in Table A.1. ------- Table A.l. Comparison of Widely Used Plume Rise Formulaea 1.. , Formula Wind Speed Proportionality Buoyancy Proportionality Momentum Term Included? Function of Stability? Function of Downwind Distance? Briggs (lf )” stable 1/u neutral, unstable Q 1 ’ 4 stable ’ neutral, unstable no yes yes Holland if u q yes yesC vu CONCAWE (1/u) °’ 7 ° Q 0 ’ 58 no no no CONCAWE simplified (ifu) ° 75 q” 2 no no no ASNE (1/u)1 ’3 stable 1/ u neutral, unstable stable neutral, unstable no yes ! no an = wind speed at top of stack Q = heat release rate bA momentum term is included in the formulations used in models. literature but is omitted in the most co non en recommended correction factors are used. ------- A2 6 The next lower level in detail still uses the two—step procedure but does not attempt to estimate a specific plume rise based on stack parameters. Instead, the user specifies a value for the product of some power of the wind speed and plume rise. The model then calculates a plume rise for each wind speed. This method usually assumes that plume rise is inversely proportional to the wind speed but does not allow differences between sources or other meteorological parameters to affect the plume rise. A still less detailed treatment allows plume rise to be considered but only permits a small number of specific values. This treatment is used frequently for aggregate sources and hence is common in the treatment of area sources in urban models. The values of plume rise chosen are average or re— piesentative values and are often included in the release height (see Appendix A.l.2). The least detailed treatment does not deal with plume rise explicitly. This is the case, for example, in proportional models and models which treat vertical dispersion by assuming uniform mixing. There are only a limited number of treatments of the special plume behavior. Downwash is typically not treated explicitly. Treatments of down— wash are normally developed expressly for that problem alone. Halitsky (1965, 1968) and Turner (1969) discuss downwash in general and should be consulted if downwash is expected to be significant. Plume trapping can be accommodated in two—step models by assuming that the plume is reflected from the base of the stable layer aloft and from the ground. Repeated reflections lead to uniform mixing. The plume is assumed to be unaffected by the inversion lid until its vertical spread reaches the stable layer and to be uniformly mixed after some suitable downwind distance there- after. Between these two distances, interpolation of concentrations is used. (See the discussion of boundary conditions in Appendix A.7.) Carpenter et al. (1971), Pooler (1965), and Turner (1969) give treatments that can be used for trapping and Turner’s treatment frequently is used in Gaussian plume models. Inversion breakup is generally not treated by models. Carpenter et al. (1971), Turner (1969), and Pooler (1965) give formulas which can be used to estimate ground level concentrations during inversion breakup if the user must consider this condition. (See the discussion in Appendix A.4.) ------- A27 One further treatment of plume behavior used to treat the deposition of particulate matter for which gravitational settling is important should be noted. This is called the “tilted plume” approximation and is discussed in Appendix A.6.2. The various general treatments of plume rise are given in Table 5.4. Treatments of special plume behavior are n:.jL rated. The user should note how the study model compares to the reference model in the number of special cases of plume behavior each treats and compare these treatments to those given in the references cited above. Treatments by the reference models are described in Table B.5. A.3 HORIZONTAL AND VERTICAL WIND FIELDS A.3.l General The primary mechanism for the transport of pollution in the atmosphere is advection, the horizontal motion of air which carries pollutants along from one place to another. This transport of pollution by the wind must be accounted for by any deterministic model which attempts to predict the spatial distribution of some material being emitted from a set of known sources. In certain circum- stance, there may also be a significant vertical component to the mean atmos- pheric motion and in these cases pollutants may be transported in the vertical direction as well. This appendix describes the general features of and methods for treatment of the horizontal and vertical transport of pollution by the wind. Horizontal Wind Field This term refers to the magnitude and direction of the horizontal compo- nent of the wind velocity as functions of horizontal position, height above ground, and time. Hereafter, when the terms wind speed and direction are used they will refer to the horizontal component, in accord with common usage. The general properties of the wind speed and direction most relevant for pollutant transport are: • A systematic increase in speed and shift in direction with height above ground which — Is very pronounced within an inversion, ------- A28 — Becomes less and less pronounced as the atmosphere ranges from stable through neutral to unstable con- ditions, and — Is significantly affected by variations in surface properties upwind and possibly downwind of the location in question; • A sensitivity to the presence of topographic features such as — Hills or mountains — River valleys, and — Large bodies of water; • A significant diurnal variation, reflecting the diurnal variation of atmospheric stability; and • Significant seasonal variations, reflecting seasonal changes in the weather. The variation with altitude is due to the frictional interaction between wind and the surface of the earth. Its effects are most pronounced near the surface and becomes less evident at higher elevations until at some altitude the surface effects become negligible. The effects of variations in atmos- pheric stability on the rate at which wind speed and direction change with altitude simply reflect variations in the extent to which the air at different levels is being mixed by turbulence. Enchariced vertical mixing such as exists under unstable conditions tends to smooth out and decrease the dependence of wind speed and direction on height. In stable conditions, vertical mixing and with it the influence of one layer of air on another is decreased. As a result, both wind speed and direction can have a significant dependence on height in stable, and especially inversion, conditions. The gross effect of hills, mountains, or river valleys on wind speed and direction is to channel the airflow and to promote the formation of local, organized circulation patterns. More subtle effects can occur as well, such as mountain and valley breezes and drainage flows, and the possibilities are numerous and varied. A useful summary and discussion is given by Slade (1968). The principal effect of large bodies of water is similar to certain topographic effects in the sense that it is due to differences in air temperature above ad- joining land and water surfaces. A breeze, called a lake or sea breeze depending ------- A29 on the body of water involved, tends to blow from the water toward the land during the day. This breeze may blow in a direction opposite to the prevailing wind and may extend a considerable distance inland. En situations in which the lake or sea breeze acts against the prevailing wind, a convergence zone in which there are significant upward vertical motions is formed and pollutants may be blown inland near the surface, rise in the convergence zone, and be blown back out over the water at heights of several hundred meters. Situations in which the lake or sea breeze acts in the same direction as the prevailing wind are less complex and “circulation cells” such as were just described do not form, although the movement of cooler air onto an adjacent land surface can result in a temperature inversion extending some distance inland, often terminating in a zone in which there is an essentially continuous fumigation situation. It should also be pointed out that urban areas themselves have a sig- nificant effect on the wind field, ranging from modification of the flow when regional wind speeds are high to the establishment of local circulation patterns due to the urban heat island effect when regional winds are weak. Systematic changes in wind direction and speed occur over urban areas and even in strong regional flows there is a systematic tendency of the air to rise over cities, accompanied by a net m l low at low levels. Both seasonal and diurnal variations in the mean wind speed and direc- tion occur. We will not discuss seasonal variations except to point out that they depend on the location of the region of interest and can be significant. Dramatic variations may also occur during frontal passages or other weather changes. Diurnal variations are related to the diurnal variation of stability and the effect of stability on the variations of the wind field with altitude. Diurnal variations are most important during periods of cloudless weather, in which there are strong diurnal variations in stability and correspondingly large variations in the extent of atmospheric mixing. In stable conditions at night, the wind speed near the ground may be very low while at the same time at heights of a few tens of meters it is often quite high. In unstable conditions the wind speed, although usually rather low, is not strongly dependent on altitude. Both high and low wind speeds may occur under neutral conditions, although high wind speeds tend to produce neutral conditions even on clear days and nights, as discussed in Appendix A.4. ------- MO The horizontal wind speed and direction are in fact randomly fluctuating quantities with fluctuations occurring over time scales from much less than a second up to years and beyond. Qualitatively, short—term fluctuations are perceived as turbulence while long—term fluctuations are perceived as part of the day—to—day changes in the weather. For the purposes of describing the transport of pollution, the interest is normally in the mean wind speed and direction over some specific time interval, or over each of a sequence of time intervals. The transport of pollutants by the mean wind is the opera- tional definition of advection, and the transport of pollutants by the fluc- tuations about this mean is the operational definition of dispersion. In any given situation, the averaging time for which mean wind measurements are available determines the distinction between ad.vection and dispersion. Typical averaging times in practice range from about 10 minutes up to about 3 hours. Vertical Wind Field The vertical component of the wind velocity is in many cases much less important than the horizontal components, for the simple reason that in many cases it is zero over the averaging time of interest. In some situations, however, primarily those in which there are significant topographic features in the region of interest, significant vertical wind components may be pre- sent. When they are, they provide an effective mechanism for vertical trans- port of pollution and should be taken into account. A.3.2 Treatment of Horizontal and Vertical Wind Fields The treatment of the wind field by an air quality model depends on the type of model according to the classification scheme introduced in Appendix A.4. For example, dynamic models treat the time dependence of the wind field in addition to its spatial dependence, numerical models can generally handle more complex spatial variations than semiempirical models, and so on. Thus, treat- ments of wind field may be classified by the way both spatial and temporal variations are handled. Spatial. variation in either horizontal or vertical directions is usually handled in numerical models by specifying the wind velocity components at discrete points defined by a suitable grid, the grid spacing being chosen to reflect the actual spatial resolution available in the data from which the ------- A3 1 model wind field is calculated. This grid spacing then determines the spatial resolution of the model as a whole. The grid may be one, two or three—dimen- sional depending on the model. Similarly, in dynamic models the temporal variation in wind speed and direction at a given point is usually handled by specifying a sequence of mean values representing averages over some basic time step, typically one hour. An alternative to the use of measured wind speeds and direction in combination with an interpolation procedure is to model the wind flow within the region of interest in a separate calculation using fluid flow modeling techniques and to thereby determine the wind field in a manner suitable for use in the air quality simulation model. This approach is often used with dispersion models for complex terrain, and in principle allows great flexibility in the spatial and temporal variations in the wind field that can be described by the model. The user should be aware, however, that not only are simplifying assumptions generally introduced in practice, but also that the manner in which the basic equations are implemented in a computer code must be carefully con- sidered in order to minimize numerical errors. Expert advice may be necessary to properly take these considerations into account. Treatments at lower levels of detail involve progressively larger numbers of simplifying assumptions regarding both spatial and temporal variations. Most semiempirical models incorporate such assumption in their formulation and, if sufficient information is available, the user should consider whether they are appropriate or acceptable for the specific application of interest. Expert advice may be necessary in these considerations. Often the utility of a semiempirical model designed for use in a limited set of circumstances is ex- tended by making additional assumptions. An example illustrating this practice will be given below. The nature of the desired results may affect the amount of detail necessary in the treatment of the wind field, particularly in regard to the size of the region of interest and whether or not the entire spatial and tem- poral distribution of pollutant is desired. It is more important, for example, to be able to describe the spatial variations in the wind field over a large area than over a smaller one simply because the variations are expected to be more significant in the former case. Another example is the situation in which the maximum concentration for a given averaging time is to be estimated, rather ------- A3 2 than the expected mean concentration value. In this case, assumptions or information on wind persistence may be required. Another major factor which determines the required level of detail in treating the wind field is the extent to which it is necessary to describe the vertical component. As mentioned above, it is often a reasonably good approxi- mation to assume that the mean vertical component of the wind velocity is zero over the averaging time of interest. If this assumption is made, the practical treatment of the wind field is very much simplified; only the horizontal wind need be treated. The horizontal variation of the wind speed and direction is constrained by the physical requirement that air cannot accumulate anywhere, and normally the simplest possible approximation is made, i.e., that the wind speed and direction are independent of horizontal position over the region of interest and depend only on the height above ground. In practice, the depen- dence of wind direction on height is often ignored as well. The dependence of wind speed on height is usually given by an assumed functional form which may depend on the surface roughness and atmospheric stability. The most common form is a simple power law dependence with different exponents for different stabi- lities although a logarithmic form may be used near the ground under neutral conditions. Finally, the simplest treatment in the zero vertical component case is to assume that the wind speed and direction are uniform within the mixing layer over the region of interest. This treatment is often adopted in semiempirical models. The wind speed is normally chosen to be that which would be observ2d at a height equal to the emission height and this value is often estimated using a measured or assumed value at some lower reference height, usually 10 meters, in combination with an assumed wind profile. This proce- dure results In a different effective wind speed for each different emission height and potentially each different source as well. Alternatively, a single effective wind speed can be used for all sources regardless of individual differences in emission height. If the vertical component of the wind cannot be assumed to be zero, the treatment of the entire wind field is complicated again by the requirement that air cannot locally accumulate, except that now there is no constraint on the vertical component. In practice, this requirement provides a relationship between the horizontal and vertical components which Is used to calculate the vertical wind speed, given measurements of the horizon components at several ------- A33 locations within the region of interest. Wind fields which satisfy this non— accumulation requirement are often called 1t mass consistent’ wind fields because the requirement is derived from the concept of the conservation of mass. Any wind field used in a dispersion model should be mass—consistent; otherwise, errors in the estimated concentration will result. Wind fields determined by fluid—flow models are generally designed to satisfy the mass—consistency require- ment. It is relatively easy to satisfy the mass consistency requirement if the vertical wind component may be assumed to be zero. In this case, for example, if the wind speed and direction do not depend on the horizontal position coordi- nates x and y, the mass consistency requirement is automatically satisfied regardless of the dependence of either speed or direction on height above ground. An air quality model designed for use in complex situations may either require the wind field to be input and therefore place the burden of determining the proper wind field on the user or require the necessary measurements so that the wind field may be calculated internally. In the latter case, the wind field may be determined prior to or concurrently with the actual dispersion calcula- tions. As indicated above, simplifying assumptions are often incorporated. For example, a model designed for use in flat terrain may be combined with assumptions regarding the flow of air over topographic features to produce a new model which may give results of sufficient validity for the user’s purpose. Often such treatments of the vertical component are implicit , being incorporated, for example, in the form of assumptions about the height of the plume centerline above the terrain without an explicit determination of the vertical component that would result in such behavior. For the purpose of this workbook, such assumptions represent an implicit treatment of the vertical wind speed and should be evaluated as such. The situations in which treatment of the vertical component is desirable are those in which the region of interest contains significant geographic complexities such as mountains or hills, river valleys, large bodies of water, and so on. In the first two cases, the usual problem is to describe the chan- neling and vertical displacement effects of the terrain on the general wind flow. Models which are capable of doing this have been developed and are in current use. Near large bodies of water, the problem is to describe the effect of a temperature difference between adjacent surfaces. Although models of this ------- A34 situation have been developed, they are primarily of a research nature and have not been incorporated into a dispersion model. In applications involving averaging times of a month or more, a climatological approach is often used. The entire range of possible wind directions is divided into several (usually 16 or 36) sectors, and the entire range of possible wind speeds is divided Into several (typically six) discrete classes. At the same time, the possible range of atmospheric stabilities is also divided into some number (usually six) of discrete classes. The proba- bility of observing simultaneously the wind direction in a given sector, the wind speed within a given class, and the stability within a given class is determined from local observations for each possible combination of wind direction, wind speed, and stability class. The resulting joint frequency distribution is called a stability wind rose. Each combination of the three elements defines a particular meteorological situation for which dispersion calculations are done, normally using a semiempirical model. The long—term average pollutant distribution is obtained by multiplying the results for each meteorological situation by the probability of observing that particular situation and summing over all possible cases. Thus, more information about the wind field than just the mean wind speed and direction over the averaging time of interest is used, although in each meteorological situation the assumption is commonly made that the wind is uniform and constant. The climatological approach is not necessarily restricted to semiempirical models; in principle, any type of model could be used to do the basic dispersion cal- culations as long as discrete wind field “classes” could be suitably defined and the probability of observing each determined. The various treatments of the horizontal wind field are listed in Table 5.5 and the treatments of the vertical wind field are given in Table 5.6. Treatments used by the reference models can be found in Tables B.6 and B.7 for horizontal wind field and vertical wind field, respectively. A.4 HORIZONTAL AND VERTICAL DISPERSION A.4.l General One of the most important elements in assessing the impact of emissions on air quality is the estimation of the extent to which the effluent ------- A35 from sources is dispersed by the atmosphere. In comparing the treatments of dispersion by two different models, the user should keep the following three factors in mind: • The operational definition of dispersion, • The duration and size of the emission and the source—receptor distance or travel time, and • The connection between the extent or rate of dispersion and the level of atmospheric turbulence. These factors determine the applicability of the various treatments of dispersion and the physical features of the problem which need to be taken into account. The term “dif fusionit is used by some authors in exactly the same sense that the term “dispersion” is used throughout this workbook. The term dis- persion is used here to avoid any confusion with the process of molecular diffusion, in which the spread of one substance in another is the result of entirely different phenomena than those responsible for atmospheric dispersion. The operational definition of dispersion is interrelated with that of advection and depends upon the averaging time of interest. The wind speed and direction at a point are randomly fluctuating quantities; rapid fluctua- tions are perceived as turbulence and very slow fluctuations as part of the day—to—day variations in the weather. The operational definition of advection is the transport of pollutant by the mean wind as measured over some specified averaging time. The operational definition of dispersion is the transport of pollutant by fluctuations about this mean which occur over times less than the averaging time. In other words, advection is the overall downwind movement of the emission as a whole and dispersion is the spreading of the pollutant about this overall motion. To fix these ideas, consider two photographs of the same continuous lume taken from above: one is a snapshot and the other is a time exposure (Figure A.l). The plume in the snapshot is observed to follow a meandering path and the width at any point is simply the actual physical spread of material about the instantaneous position of the plume centerline. In the time exposure, however, the plume follows a much straighter path and is characterized by a much wider and more smoothly varying cross—section. The longer the exposure, the wider the cross—section appears. The time exposure ------- 2 HOUR AVERAGE PLUME Figure Al, Dependence of Crosswind Pollutant Distribution from a Continuous Point Source on Averaging Time . I RELATIVE CONCENTRATION LA ) 0 ’ ------- A3 7 shows only the mean wind speed and direction over the exposure time, and the observed dispersion about the apparent plume centerline represents not only the physical spread but also the time—averaged effects of the meandering of the plume. Thus, meanders in the plume which take place over periods of time shorter than the exposure, or averaging, time are considered part of the dispersion. The snapshot clearly exhibits the effects of the short—term wind fluctuations responsible for meandering. The practical consequence is that for the horizontal case the extent of the dispersion about the mean plume centerline depends on the averaging time. This effect does not occur for vertical dispersion for averaging times longer than about ten minutes due to absence of fluctuations in the vertical component of the wind over these time scales. The example just given considered the case of a continuous release. A snapshot of the pollutant distribution following an instantaneous release shows a cloud of material at some point generally downwind of the source, and a time exposure shows a meandering path originating at the source. In both pictures, the observed extent of the dispersion represents the actual crosswind spread of material in the cloud, although dispersion in the downwind direction is not shown in the time exposure. Meandering in the path followed by the cloud should clearly not be treated as part of the dispersion of the cloud. Based on this type of consideration, and assuming that only the mean wind speed and direction are known over the averaging time of interest, meandering should be considered part of the process of horizontal dispersion from a point source when both the following conditions are met • The duration of the release is greater than the averaging time, and • The averaging time is greater than the source— receptor travel time. If these conditions are not met, more information about the wind field is required so that a more realistic description of the actual trajectory followed by the pollutant emission may be obtained. In particular, variations in the wind which occur over times greater than the averaging time but less than the travel time should be explicitly taken into account either by assump- tion or by actual calculation of the trajectory. (See Appendix A.3 for a dis- cussion of treatments of the wind field.) ------- £38 The initial size of the emission determines the relative importance of any further dispersion in either the horizontal or vertical direction. The larger a plume or cloud of pollutant, the slower is the relative rate of growth due to the action of atmospheric turbulence because as the plume grows an increasingly large part of the turbulence acts over too small a scale to be effective. The effect on the horizontal dispersion estimates of changing the averaging time is also diminished for extended sources such as lines and areas for the same reason. In order to quantitatively estimate the extent or rate of dispersion under specified conditions, the effect of those factors which determine the intensity of atmospheric urbulence must be suitab...y parameterized, because dispersion is a direct result of the action of turbulence. The most important factors governing the production of turbulence are: • The wind speed, • The roughness of the ground surface, and • The flux of heat being transferred between the ground surface and the air. The first two factors govern the mechanical generation of turbulence by friction due to the variation of wind speed with height (wind shear), itself caused by the frictional interaction between the general flow of the wind and the rough- ness of the surface. The third governs the thermal generation of turbulence due to surface heating. The surface heat flux itself depends on: • The solar angle (during the day), • The extent of cloud cover (both day and night), • Thermal properties of the ground surface, and • The extent of anthropogenic heat generation (in urban areas). In discussing atmospheric turbulence and dispersion, it is convenient to introduce the concept of atmospheric stability. At a given height, the atmosphere may be classified as unstable, neutral, or stable according to whether the rate of decrease of temperature with height (the lapse rate) is less than, equal to, or greater than a critical value called the dry adiabatic lapse rate (equal to approximately l°C/lOO meters), as shown in Table A.2. The significance of this classification is that near the ground, high levels of ------- £39 Table A.2. General Atmospheric Stability Classification According to Temperature Lapse Ratea Relation of Actual Lapse Rate to the Dry Adiabatic Lapse Rate Atmospheric Stability Classification Greater than Unstable Equal to Neutral Less than Stable aTh S classification is not the same as the widely used Pasquill stability classification scheme. turbulence and high rates of dispersion are generally associated with unstable conditions and low levels of turbulence with stable conditions. The terms used in the classification are in fact descriptive of the effects of the different types of temperature gradient on vertical turbulent motions, vertical notion being enhanced under unstable conditions and suppressed under stable conditions. A temperature inversion is said to exist when the lapse rate is negative (temperature increasing with height). The atmosphere is extremely stable within an inversion and turbulence is strongly suppressed. As a con- sequence both the rate of vertical dispersion and the actual physical spread of a plume in the horizontal direction are strongly suppressed, although considerable meandering of the plume can occur. The temperature profile near the ground is itself determined by the same factors listed above as being significant determinants of atmospheric turbulence. At any given time, the difference between the actual lapse rate and the dry adiabatic lapse rate is determined by the balance between two competing effects: 1) the addition or removal of heat energy from the air due to solar heating or radiational cooling of the ground surface, tending to produce unstable or stable conditions respectively, and 2) the tendency of the turbulence itself, whether mechanically or thermally generated, to smooth out the temperature profile and produce neutral conditions. In order for an atmospheric dispersion model to be useful in a variety of meteorological situations, some convenient measure of atmospheric stability ------- A4 0 or turbulence intensity is used to determine the appropriate values of those model parameters (such as a and a in Gaussian plume models) which determine the predicted extent or rate of dispersion. A number of different mt Leorolo— gical parameters or classification schemes have been used for this purpose and an increasing number of models make use of the more fundamental r’easures of turbulence intensity. Some of the more commonly used ones are given in Table A.3. The user should consult a standard reference (e.g., Slade, 1968) or an air pollution meteorologist tor L1 1e definitions of the Richardson number or the Monin -Obukhov length if the model being evaluat d makes use of one of these parameters. A discussion of the Pasquill—Gifford cl3ssification scheme is given by Turner (1969). and the Brookhaven scheme is discussed by Singer and Smith (1966). A review of various systems for characterizing turbulence is given by Gifford (1976). The basic factors which determine atmospheric stability near the ground have already been mentioned. The dependence of these factors on the time of day, the nature of the topography, and the nature of the ground sur- face gives rise to certain characteristics of which the user should be aware. Atmospheric stability near the ground undergoes very significant diurnal variations due to the rising and setting of the sun. On sunny days, the ground is warmed and heat is added to the air near the surface, causing the air temperature to rise and producing unstable conditions. On clear nights, the ground cools more rapidly than the air, heat is removed from the air near the ground, and a ground—based “radiation inversion” is produced. At any time, cloud cover tends to balance the exchange of heat and produce neutral conditions. The phenomenon of fumigation is due to the morning breakup from the ground of pollutants emitted into and trapped within the inversion during the night. There are important differences between urban and rural areas. Urban areas are normally much rougher than the surrounding rural areas, and the heat produced by anthropogenic activity in the city is an important factor at night all year round as well as during the daytime in winter. The combination of these factors results in substantially higher levels of turbulence, and correspondingly higher rates of dispersion, over cities during both day and night. The frequency of surface inversions is much lower in cities than in rural areas; when a surface inversion exists in the surrounding countryside, ------- A4 1 Table A.3. Commonly Used Measures of Atmospheric Stability and Turbulence Intensity Continuous Measures 1. Te 1 aperature gradient or, equivalently, temperature difference between two reference heights. 2 T az = (dry adiabatic lapse rate)—(ambient lapse rate) = (1°C/lOOm + T/ z) g = acceleration due to gravity. T = ambient temperature. (S is negative in unstable conditions, zero in neutral conditions and positive in stable conditions.) 3. Standard deviation of the horizontal component of the wind direction (os) or of the vertical component (ci ). 4. Richardson number. 5. Monin—Obukhov length. Discrete Classification Schemes 1. Pasquill—Gif ford stability classification. 2. Brookhaven gustiness classification. the temperature profile within an urban area generally corresponds to neutral or weakly stable conditions. Topography may significantly affect stability. The nocturnal in- version within a valley, for example, may be much deeper and longer lasting in the morning than that over flat terrain. This is caused by a combination of uneven heating of the ground surface due to the variable angle with which the sun’s rays strike the ground and the tendency of cooler air to settle in low places in the terrain. The presence of fog also delays the heating of the ground and prolongs the existence of stable conditions. Forested areas and regions of complex terrain also have surface roughness comparable to those ------- A4 2 of urban areas, and rates of dispersion are correspondingly higher than over gently rolling grassland, for example. The stability of the atmosphere at higher elevations is also an im- portant factor for atmospheric dispersion. At any given time the stability of the atmosphere at heights above a few hundred meters is determined mainly by the large scale features of the weather as well as by the general properties of the atmosphere as a whole. Below 10—15 km, the atmosphere is on the average slightly stable, so that turbulence generated at the surface can propagate up- wards only so far before it is damped out. This results in an upper limit, called the mixing height, to the altitude to which pollutants will disperse over a short period of time. In the absence of an elevated inversion, this mixing height is determined by the same variables that determine the stability. An elevated inversion may exist, however, usually in association with a large high pressure area. Such inversions are called subsidence inversions and are very effective in limiting vertical dispersion. Subsidence inversions exist at altitudes of the order of 1000 m and the maximum mixing height on any given day is limited by the height of the base of these inversions. Since relatively low wind speeds are also associated with these large high pressure areas, they cause some of the worst pollution episodes. An additional factor, relating primarily to vertical dispersion, is the fact that the earth’s surface forms a barrier which limits not only the extent of mixing in the vertical direction but also the physical size of the turbulent fluctuations which cause the dispersion. The first effect is normally handled as a boundary condition, but the second implies that the higher the altitude above ground, the greater the size of fluctuation that can exist. In addition, the relative importance of mechanically generated turbulence compared to ther- mally generated turbulence decreases with altitude. Thus, the rate of vertical dispersion from elevated sources is somewhat different from that ground level sources, at least until the emission from the elevated source reaches the ground. Since horizontal and vertical dispersion are considered to be separate elements in this workbook, and in order to tie the previous discussions together, it is useful to summarize here those factors which relate specifically to either horizontal or vertical dispersion, or both. These summaries are given in Tables A.4 and A.5. ------- A4 3 Table A.4 Factors Affecting the Level of Atmospheric Turbulence and the Rates of Horizontal and Vertical Dispersion • Wind shear, itself dependent on — Wind speed, and — Surface roughness • Surface heat flux, itself dependent on — Solar angle, — Cloud cover, — Surface thermal properties, and — Anthropogenic heat prcduction. • Atmospheric stability, itself dependent on — The factors listed above, and — Synoptic weather feati.res (particularly above a few hundred meters altitude) Table A.5. Factors Determining Meandering Contribution to Horizontal Dispersion Duration of pollutant release Source—receptor travel time . Desired averaging time f Dr pollutant concentrations . Initial size of the e nission A.4.2 Treatment of Horizontal and Vertical Dispersion In order to evaluate the tr atments of horizontal and vertical dis— persion in a specific model, the user should know: • The technical benefits and limitations of the different types of treatments and • The various ways of pararneterizing the effects of the important meteorological variables in each type. The remainder of this section addresses these points. ------- A4 4 A.4.2.l Treatment Classification Treatments of dispersion may be usefully classified in the following two ways: 1) According to the general modeling approach adopted: • Numerical methods, which involve the numerical solution of equations describing the conservation of mass, • Semiempirical methods, which assume a particular functional form for the pollutant distribution, and • Methods which do not treat dispersion explicitly; and 2) According to the way the time dependence of the pollutant distribution is treated: • Dynamic treatments, which predict the pollutant con- centration as a function of time as well as position, • Steady state treatments, which predict the average pollutant concentration as a function of position only for short averaging times, and • Climatological treatments, which predict the average pollutant concentration as a function of position only for long averaging times using a statistical distribution of meteorological conditions. Methods which do not explicitly treat horizontal dispersion, vertical dispersion, or both may still in some cases be simulation models and examples will be discussed below. Empirical or statistical models, which also do not generally contain explicit treatments of dispersion, are discussed in Section 7. Numerical Methods The most advanced and sophisticated models of atmospheric dispersion fall into this category. The current state of the art is represented by “closure models t which consider both the concentration and the flux of pollutant as well as most of the meteorological variables as unknown functions of position and time to be determined by numerical solution of the relevant equations. The flux obtained in this approach is directly related to the rate of dispersion. This type of treatment is still in its formulative stage and has not yet been used in practical applications. For this reason, closure models will not be discussed further here. ------- A4 5 The usual approach in numericaL models is to describe the flux in terms of the concentration distribution, so that the flux is no longer an independent quantity. This is done by making the “gradient—transfer” approximation, which assumes that the pollutant flux is proportional to the concentration gradient. The proportionality factor is called the eddy diffusivity and is usually symbolized by the letter K, hence this approach is often referred to as “K—theory.’ t The result of making this approximation is an equation, called the advection—diffusion equation , which predicts the pollutant concentration as a function of position and time. Treatments of the wind field are discussed in Section A.3. The advection—diffusion equation must usually be solved by any of a variety of numerical methods, Including, for example, finite—difference or particle—in—cell techniques, but the user should not be too concerned with the details of the numerical method used by a model being evaluated. There are certainly advantages and disadvantages with the various approaches, but the focus here is more on the parameterization and treatment of meteorological and other factors. The eddy diffusivities for dispersion in different directions are not necessarily equal, but this discussion will be restricted to what is by far the most common case, that in which only two eddy diffusivities are used, one for vertical dispersion and one for horizontal dispersion. The eddy diffusivity values reflect the level of atmospheric turbulence and their parameterization in terms of observable meteorological quantities should be considered by the user in evaluating a numerical model. Semiempirical Methods This category includes all treatments in which an explicit functional form is assumed for the concentration distribution. The assumed form may be based on observation, theoretical considerations, numerical simulation, or a combination of these. It may be a function determined elsewhere and assumed appropriate for the given application or it may be determined specifically for the application of iiiterest in the process of running the model Itself. The most common example of a semiempirical method is the Gaussian plume treatment of dispersion from a continuous source as described by Turner (1969). This particular approach involves the assumption that the horizontal crosswind pollutant distribution from such a source may be ------- A4 6 described, on average, by a Gaussian function and that, except for the effects of the ground, so can the vertical distribution. The only parameters beside the wind speed which appear explicitly in these functions and which reflect the prevailing meteorological conditions are the horizontal and vertical standard deviations, or dispersion coefficients, corresponding to the assumed horizontal and vertical Gaussian distributions. Another example of a semiempirical model is the simple box model, which assumes a spatially uniform pollutant distribution within some region. Dispersion is not explicitly treated in such a model, but additional assumptions are implicitly being made. If the pollutant distribution is taken to be uniform in the vertical direction up to some specified height, the process of vertical dispersion is implicitly being assumed fast enough to justify that treatment over the time scale of the problem. The assumption of uniformity in the horizontal crosswind direction is often used and is justified if the distribution of emissions is relatively uniform; this approximation, when used in connection with the determination of pollutant levels due to area source emissions, is called the narrow—plume approximation. A type of narrow—plume approximation may also be used for treating point sources in climatological models and will be discussed in that context later in this section. Dynamic Treatments This category includes all methods in which the concentration is pre- dicted explicitly as a function of time. Treatments in which one or more trajectories of pollutant releases are calculated from wind field data, or are simply assumed on any reasonable basis, are also included under the definition of dynamic models followed in this workbook. Dynamic treatments may be either numerical or semiempirical in nature. Dynamic models must be able to properly handle situations involving changing meteorological conditions and the resulting changes in the rate of dispersion. There is usually no difficulty in doing this in numerical models, but if a time—dependent generalization of a semiempirical steady—state method is used, problems can arise in making sure that the model parameters which describe the extent of dispersion at any given time are continuous functions of time. For example, if the horizontal crosswind pollutant distribution ------- A4 7 about some trajectory is assumed to be Gaussian, the horizontal standard deviation should be a continuous function of time. Most commonly used formulae or graphs give the standard deviation as a function of downwind distance or travel time only for the case in which the meteorological con- ditions are constant, and are not directly applicable under changing conditions. A treatment which uses a description of the rate of change of the standard deviation as a function of meteorological conditions is usually preferable for dynamic models. Examples of numerical/dynamic treatments are 1) those using the numerical solution to the full time—dependent three—dimensional advection— dif fusion equation and 2) those using the narrow—plume approximation for a grid of area sources over which a trajectory is calculated and treating vertical dispersion by numerically solving the one—dimensional (vertical) time—dependent diffusion equation. An example of a semiempirical/dynamic treatment would be one in which a trajectory originating at the location of a point source is calculated and the pollutant distribution about the tra— lectory is assumed to be Gaussian. Gaussian puff models, in which a plume is treated as a series of puffs which follow their own trajectories, are also semiempirical/dynamic models. Steady—State Treatments This category includes all methods in which temporal variations of all relevant quantities are ignored and in which the treatment of advection uses only the mean wind speed and direction for the averaging time of interest. This type of treatment predicts the average concentration as a function of position only. Steady—state methods may be either numerical or semiempirical in nature. The most familiar example of a semiempirical/steady—state treatment is the basic Gaussian plume model and an example of a numerical/steady—state treatment is one in which the time—independent version of the advection—diffusion equation is solved numerically. Climatological Treatments This category includes methods which predict the average pollutant distribution for long averaging times, typically a month, season, or year, using a joint frequency distribution which gives the probability of simulta- neously observing specified wind speed, wind direction, and other meteorological ------- A48 variables. In this approach, more information about the wind field than just the mean wind speed and direction over the desired averaging time is used in order to avoid treating variations which occur over time scales less than the averaging time as part of the horizontal dispersion process. Climatological models may in principle use either a numerical or semiempirical approach for the individual calculations, although in practice semiempirical/steady—state treatments are almost always used. A.4.2.2 Benefits and Limitations Numerical Methods The nh .1fl benefit to be gained by using a numerical approach is flexibility in the specification of the wic d field and the meteorological variables determining atmospheric turbulence levels as functions of position and time and in the specification of boundary conditions. In principle, numerical methods allow the description of dispersion for a realistic wind field in complex situations. They are also, in principle, capable of treating the spatial distribution and temporal behavior of chemically reactive pollu- tants. The main technical limitation is one of spatial resolution. Numerical methods calculate concentration values at only a finite number of points in space, normally corresponding to some conveniently defined grid, and the resolution which can be achieved is fixed by the grid spacing. In addition, the grid spacing should not be considered arbitrary, since it may be determined to a large extent by the way the wind field Is determined (see Appendix A.3). Variations in the concentration distribution, in the wind speed and direction, and in the emissions themselves which occur over distances smaller than the grid spacing cannot be resolved. This lack of resolution has several conse— quences: • Emissions from point or line sources into a specific grid cell are in effect dispersed instantaneously within the cell, rather than described in terms of a sub—grid scale distribution; • The value of the eddy diffusivity must reflect the intensity of turbulent fluctuations up to the size of the grid spacing and is therefore partially determined by that spacing; and ------- A4 9 Pollutant concentrations cannot be predicted at arbitrary receptor locations, except by interpolation from concen- tration values at grid points. The seriousness of these consequences depends on the specific application, and on the existance of practical limits to the amount of computational effort required and to the computer storage requirements. In general, however, the numerical approach is inappropriate for the treatment of dispersion when the size of the emission being dispersed is smaller than the grid spacing. Another way of stating this conclusion is that the numerical approach using the eddy diffusivity concept is inappropriate when the size of the pollutant distribution being dispersed is smaller than or comparable to the size of any turbulent eddies contributing significantly to the dispersion. As a result, the eddy diffusivity approach is not fundamentally suitable for describing horizontal dispersion, and in particular the meandering contribution, but because of constraints on the size of vertical fluctuations due to the presence of boundaries at the ground and at the mixing height, can be justified for the treatment of vertical dispersion from ground level sources or from elevated sources after the plume has reached the ground. Treatments of hori- zontal dispersion using the eddy diffusivity approach do exist, however, in spite of the physical fact that dispersion by meandering cannot be considered a gradient—transfer process. Such treatments describe horizontal dispersion in a phenotnenological way, rather than in a manner which reflects the basic physical processes, and the selection of an appropriate value for the horizontal eddy diffusivity must be based on more empirical grounds than is the case for the vertical diffusivity. (See the discussion of parameterization in numerical models later in this appendix.) It is sometimes possible to describe the pollutant distribution on a scale smaller than the grid spacing in an empirical or theoretical way, and use the numerical approach to describe the large scale distribution. This is in fact desirable in the case of point sources in order to minimize the numer- ical errors resulting from the poor resolution near the source. Another limitation in most cases is the lack of fundamental knowledge and appropriate meteorological data upon which to base the prediction of eddy diffusivity values, particularly at heights above 100 meters or so. This means that further assumptions must be made regarding the appropriate values to use in a model. ------- Aso Semiempirical Methods The principal technical benefit gained in this type of approach is that the assumed shape of the pollutant distribution may be based upon actual observational data. Furthermore, the distribution observed experimentally may be assumed to be the same under similar meteorological and topographical conditions, thus eliminating the need for new observations for each new application. In some cases, the assumed distribution may be derived on the basis of theoretical considerations. The semiempirical approach has two advantages over the numerical approach from a technical point of view: • Better spatial resolution can often be achieved in practice and • The effect of meandering may be treated in a more appropriate way. The general limitation on this type of approach is that it should not be used in situations in which there is insufficient observational data or theoretical results from which to determine the proper functional form. If the assumed shape is derived theoretically, its suitability depends on the nature of the assumptions made in the derivation. These may not be appropriate for the real situation. As indicated above, the most coimnon example of this type of approach is the Gaussian plume treatment of continuous emissions. En their basic form, Gaussian—plume based methods are inherently restricted to: • Flat or gently rolling terrain for a considerable distance upwind and downwind of the source, • Primary pollutants, and • Conservative pollutants, i.e., no significant physical or chemical sinks. It is possible to extend the utility of Gaussian models to applications in- volving complex terrain by making various assumptions regarding the extent to which the plume follows the terrain and by making modifications to the basic formulae. These models all fall within the category of semiempirical models and in view of the wide range of possible modifications and interpretations expert advice may be required in making a comparison. The only general guide- line that can be given is that the basis or justification for the assumed ------- AS 1 pollutant distribution should be scientifically sound. Ideally, modifications to the basic Gaussian distribution should be based on appropriate observational data, often in combination with theoretical considerations. If no information is available regarding the basis for any particular assumed pollutant distri- bution, it is difficult, if not impossible, to assess its validity. It should be pointed out that, given certain approximations, the standard Gaussian plume formula represents the steady—state solution to the advection—diffusion equation for a single point source. The conditions which have to be met are that 1) the wind field must be uniform, constant, and have no vertical, component, 2) the rate of pollutant dispersion along the direction of the wind must be negligible compared to the rate of pollutant transport by advection, and 3) the horizontal and vertical eddy diffusivities must also be uniform and constant. The extent to which the application of interest deviates from these assumptions determines the need for modifications to the formula or for a different modeling approach, e.g., a numerical model. It is also possible to extend the basic Gaussian model to non—conser- vative pollutants. (See Appendices A.5 and A.6 for discussions of possible treatments.) Limitations to the basic Gaussian plume model also exist because of the steady—state nature of the model. These are discussed in the subsection on dynamic treatments. The narrow plume approximation mentioned earlier deserves further comment at this point. This approximation can be used for either point or area sources, although its use for point sources is restricted to climatological models. For area sources, the narrow plume approximation amounts to the assumption that emission rates from nearby sources are sufficiently similar that the pollutant distribution may be assumed to be horizontally uniform. In the narrow plume approximation, pollutant concentrations along some well— defined trajectory are functions of height above ground and possibly travel time but not of horizontal crosswind position. The narrow plume approximation may be used in either a steady—state or a dynamic approach and the trajectory may be a straight line, a constant path determined, for example, by topography, or it may be determined from actual wind field data. The accompanying treat— ment of vertical dispersion may be either semiempirical or numerical. ------- A5 2 Dynamic Treatments The main benefits are: • The ability to describe the temporal variation of the pollutant concentration and • The ability to treat the effects of time variations in and correlations between emissions, meteorological parameters, and removal processes. Technical limitations depend upon how the time dependence is handled. Time dependence may be incorporated in an empirical or ad hoc way, In which case the suitability of the treatment in a given application depends on the observational or theoretical basis for that particular treatment, as with the empirical methods discussed ahove. Time dependence is more commonly treated .y dividing the total period of interest into a number of sequential time steps. The variation of some quantity such as an emission rate is then simulated by prescribing a sequence of values, one for each time step. Such an approach predicts the concentration at a finite number of points in time and the temporal resolution of the method is determined by the size of the time step. Time variations more rapid than the time step cannot be resolved. Steady State Treatments No significant technical benefits are gained by using a steady—state model in preference to a dynamic approach. Steady—state models are generally simpler and easier to use, however, and the decision to use such an approach is based on these considerations as well as on the fact that the most widely used semiempirical approach, the Gaussian plume method, is a steady—state method. Limitations include the assumptions of a constant emission rate and a constant level of atmospheric turbulence. The specified averaging time should be greater than the source—receptor travel time, as pointed out in the general discussion, so that the effect of meandering is properly treated. The assumption of constant emission rate guarantees that the duration of the re- lease is longer than the ave aging time, and the steady—state approach is clearly limited to the treatment of those sources which satisfy this require- ment. Instantaneous or very short releases must be treated using dynamic ------- A53 methods. Within its limitations, the steady—state approach is just as applicable as the dynamic approach for the calculation of average concen- tration values. Climatologic al Treatments This type of approach is used in practice only for the calculation oi long—term average concentrations, the principal benefit being one of con- venience compared with the alternatives of using a dynamic model or a sequence of a large number of steady—state calculations. A calculation is done for each set of meteorological conditions which is represented in the joint distribution being used, and the average pollutant distribution is obtained with the contribution from each set of conditions being weighted by its probability of occurrance. Limitations of the method may be divided into two categories: • Limitations of the nodel used to do each separate calculation, and • Limitations of the climatological approach, per se. The former are described in other parts of this section and the only additional remark that needs to be made here is that the model used must be of sufficiently general applicability to be able to handle the variety of meteorological con- ditions represented in the climatological frequency distribution. The latter include the approximations incurred by representing the wide range of con- ditions that occurs in nature by a finite number of specific situations, by the suitability of those situations which are used, and by the omission of meteorological variables such as precipitation and mixing height from the joint frequency function. Regarding treatments of dispersion at least one of the parameters defining the frequency function should be some measure of the level of at- mospheric turbulence. The measure of turbulence most commonly used in climatological models is the Pasquill stability classification, although others could be used. It is also common to use the narrow plume approximation for point sources, which amounts to the assumption that the crosswind or angular distribution of pollutant from a point source over a sufficiently long period of time is given simply by the frequency distribution of the wind ------- A54 direction, or in other words by the wind rose. This assumption is reasonable if the variation in the wind direction frequency function is negligible over an angular interval corresponding to the angular width of the plume. Since the wind direction frequency function takes the form of probabilities of observing wind from within well defined sectors (commonly 10° or 22.5° wide), this approach is also referred to as u’sector averaging.” A summary of the different general types of treatment is given in Table 5.7. It should be pointed out that in any given model, horizontal and vertical dispersion may be treated in completely different ways (although both will be either dynamic or steady—state) and the treatments in any case should be evaluated separately. In Table 5.7, the treatments are ranked in order of decreasing level of detail, but the user is cautioned that in the cases of horizontal and vertical dispersion the relative level of detail of two treatments is not by itself a reliable indication of their relative tech- nical. performance . As discussed above, there are limitations on the applica- bility of certain approaches, and the user must determine for his specific application if these are violated. If they are, those approaches should not be used. If the two models being compared use the same, or two equally applicable approaches, the relative level of detail may be used as a valid indicator. A.4.2 .3 Parameterization Atmospheric dispersion models are generally designed for use in a variety of conditions, each characterized by a different level of atmospheric turbulence and consequently different rates of dispersion. Various meteorolo- gical conditions are handled within a given model by using different numerical values for the relevant model parameters such as eddy diffusivities or Gaussian standard deviations. The determination of the appropriate values from meteoro- logical and other data is an important part of the total procedure by which predictions of pollutant concentrations are made. In an evaluation, the user should take into account any constraints on these parameters that are inherent in or built into the model, particularly if they clearly preclude the use of the correct values. An example of such a constraint is a built—in eddy diffusivity or standard deviation value which is not appropriate for the user’s application and which the user cannot conveniently ncdify. The determination ------- AS 5 of the appropriateness or correctness of any such specific parameter value may require expert assistance but a general guideline is that the value in question should be obtained from observations or theoretical analysis as closely associated as practicable with the specific location and meteorological conditions of interest. If sufficient information about the source of the values used in a given model is available, the appropriateness of those speci- fic parameter values should be considered in making the evaluation. Table 5.10 provides a list of some of the possibilities for both numerical and semiempi— rical models. Some general remarks regarding the way in which atmospheric stability and surface roughness are treated by various types of models are in order here. Numerical Models Confining our attention to gradient—transfer models only, the horizontal and vertical eddy diffusivities are the parameters through which the influences of stability and surface roughness on dispersion are manifested. As indicated above, the eddy diffusivity approach is not in general appropriate for the treatment of horizontal dispersion. For this reason, the basis for choosing a specific value of the horizontal diffusivity needs to be considered further. It is possible, by appropriate selection of the time or space dependence of the horizontal diffusivity, to force a numerical model to reproduce approximately the results of a more sophisticated calculation, or of a semlempirical model. If this is the case, the parameterization of the horizontal diffusivity needs to be judged on the basis of the treatment being reproduced. In general, the horizontal diffusivity may be expected to be roughly independent of horizontal position except when significant terrain features are present. The vertical diffusivity near the ground may be reasonably estimated in terms of the wind speed, surface roughness (given in terms of a parameter called the ‘ t roughness length”, see Slade (1968) or Pasquill (1974) for the definition and estimates for different situations), and parameters which determine the rate of heat—exchange between the earth’s surface and the air. An expert should be consulted for the details of the formulation. ------- A56 At higher altitudes, there is very limited data and the exact para— meterization of the vertical diffusivity is a subject of current research. Consequently, any parameterization must be based on further assumptions and it is not uncommon to simply use a convenient functional form having the desired qualitative behavior and having the correct behavior near the ground. Seniiempirlcal Models Since the Gaussian plume model is by Ear the most common example, the discussion will be restricted to t1 is case. The user should be able to follow a similar line of thought for other treatments. In the Gaussian plume approach as described by Turner (1969), the horizontal and vertical standard deviations need to be parameterized. Atmospheric stability is divided into several discrete classes and the sta il,ity class to be used in a given situation is determined from the wind speed, solar angle, and the extent of cloud cover. The horizontal and vertical standard deviations are then prescribed functions of the stability c .ass and downwind distance from the source. The effects of surface roughness may be accounted for in the nature of the prescribed functions or by additional, modification of the basic stan- dard deviation or may not be treated explicitly. Tables 5.8 and 5.9 list various treatuients of atmospheric stability and surface roughness, respectively. Tables B.8 and B.9 list treatments of horizontal and vertical dispersion, respectively, used by the reference models. A.5 CELEMISTRY AND REACTION MECBANIS) A.5.l General There are two common situations in which chemistry plays a role in determining atmospheric pollution levels. On one hand, the pollutant of interest may undergo chemical reaction with some other atmospheric component; that is, a chemical sink exists for that pollutant and it is referred to as being reactive. (If the pollutant undergoes no reaction, It is called inert.) On the other band, the pollutant of interest may be produced in the atmosphere by chemical reactions involving other pollutants (precursors); such a substance is called a secondary pollutant. (If the pollutant is directly emitted by ------- i 57 sources, it is called primary.) Clearly, in each case the chemical reactions involved affect the concentration of the pollutant of interest. In the first case they provide a process for the removal of that pollutant and serve to decrease its ambient concentration, while in the second case they serve to generate the pollutant and increase its concentration. Examples of primary reactive pollutants are the hydrocarbon precursors of photochemical smog. Examples of secondary, relatively inert materials are sulfate and photochemical aerosol. A pollutant may be both secondary and reactive; examples are nitrogen dioxide (NO) and ozone (03). If the pollutant of interest is both primary and inert, the element of atmospheric chemistry is irrelevant and does not need to be considered. As pointed Out lfl Section 3.3, the decision to regard a pollutant as being either reactive or inert depends upon the effective rate of reaction compared to the length of time that the pollutant spends within the region of interest. If the user is interested in a short—range application involving a slowly reacting material, that pollutant may be regarded as effectively Inert for the application even though over a longer range this would be a poor approx- imation. An example of such a pollutant is sulfur dioxide (SO ). 2 In the case of a secondary pollutant, some treatment of the chemical reactions which produce that pollutant will be required. Otherwise, the connection between precursor emissions and the concentration of the pollutant of interest is completely lost. The subject of atmospheric chemistry encompasses an extremely wide range of topics and only those very basic or general aspects that are directly rele- vant can be described in this workbook. If atmospheric reactions play a signi- ficant role in the user’s application, the advice of an expert should be sought regarding the level of detail with which the particular set of chemical reactions used by the model represents the system to be simulated. This discussion will refer primarily to reactions between gaseous materials. The extent to which atmospheric particulate matter actually participates in chemical reactions with gaseous components is not at present well understood but if this possibility exists, the advice of an expert should again be sought. However, many of the same considerations apply as in the completely gaseous case. ------- A5 8 The basic problem in modeling the dispersion of reactive systems is to describe the rates of production and removal of various pollutants and, equally as important, the interaction between the chemical reaction processes and the dispersion process. En order to assess the treatment of chemical reactions by a model, the user must consider two different aspects of that treatment: • The level of detail with which the chemical reaction mechanism is described, and • The manner in which the effects of spatial inhomogeneity on the average rates of change of the pollutant concen- trations are treated. It will be useful for the user to understand a few basic facts re- garding the general nature of chemical reaction rates. The rate of a chemical reaction may be defined with sufficient precision for the purpose of this workbook as the magnitude of the time rate of change of the concentration of a reactant or product of the reaction in question. (The reactants are the chemical species actually undergoing reaction.) The reaction rate depends on the concentrations of all of the atmospheric components participating in the reaction. Reactions can be classified as either elementary or complex. An “elementary reaction” is one in which the chemical reaction as written reflects the true sequence of events on the molecular level. For example, an important reaction in photochemical smog is that between ozone and nitric oxide (NO). This reaction involves the collision of a molecule of NO with a molecule of 0 3 followed by a reaction and the separation of the products, one molecule each of NO and oxygen (0 ). The most important property of elementary reactions is 2 that the rate of such a reaction is a predictab ç, simple function of the reactant concentrations. In the example above, the rate of the reaction is simply equal to a constant (the rate constant) times the product of the ozone and nitric oxide concentrations. On the other hand, a “complex reaction” is essentially a state- ment of the net effect of some (possibly large) number of elementary reactions operating simultaneously, with only the initial reactants and final products being explicitly written. In general, the rate at which the initial reactants disappear is not equal to the rate at which the final products appear, and neither rate is a predictable function of the concentrations of only the initial and final chemical species. The sequence of elementary reactions whose net ------- A59 effect is of interest forms what is called the “reaction mechanism” and the description of the pollutant concentrations as functions of time must usually be made in terms of what is known about the reaction mechanism. It should be pointed out that the mechanism of a complex reaction usually involves the existence of other chemical species in addition to the main reactants and products of interest and that, in general, these need to be treated also. An extreme example of a complex reaction is the generation of photo— chemical smog from nitric oxide and hydrocarbons under the action of sunlight. In this case the reaction mechanism involves literally hundreds or even thou- sands of ,react ions. As mentioned above, the expression for the rate of an elementary reaction can be predicted in an a priori way. In practice only three cases need to be considered; these three cases are outlined in Table A.6, in which the “order” of each type of reaction is also defined. The constant appearing in the rate expression for a given reaction is called the rate constant for that reaction. The most important feature in Table A.6 of which the user should be aware is that the rate of a first—order reaction is a linear function of the pollutant concentration whereas the rates of second and third—order reactions are nonlinear functions of the pollutant concentrations. This fact has signi- ficant consequences when the spatial distribution of reactive pollutants is of interest. Table A.6. Elementary Reaction Rate Expressions Rate Expression Reaction Order (constant) x (the concentration of one single reactant) First (constant) x (the product of the reactants) concentrations of two Second (constant) x (the product of the reactants) concentrations of three Third ------- A6 0 En order to describe the evolution of a complex reacting system, it is normally necessary to know the reaction mechanism, which consists of a set of (elementary) reactions whose rates are known functions of the pollutant con- centrations. If the initial pollutants are uniformly mixed within some closed volume, their concentrations as functions of time may be predicted by numerical solution of a set of coupled ordinary, non—linear differential equations, which may be derived from the reaction mechanism. In practice, a simplified mechanism may be used in which many of the reactions of lesser importance have been omitted or in which the net effect of many has been expressed in terms of just a few characteristic reactions using some kind of average or composite rate constant. The level of detail with which the reaction mechanism is treated affects the accuracy of the results and the mechanism being used should be justified by comparison with experimental studies. Knowledge of the reaction mechanism includes not only knowledge of the reactions which can occur but also knowledge of the values of the rate con- stants of these reactions. The appropriate values are normally supplied with the model so that the user generally does not need to supply them, but there is often considerable uncertainty in the experimental measurement of rate constants and the values of ones important in atmospheric chemistry are continually being redetermined. Obviously, in a practical application the values used should be as up—to—date as possible. In addition, rate constants depend on temperature and in some cases it may be important to use values appropriate for the ambient temperature in the user’s specific application. Further complications arise when dispersion is considered. It is impor- tant to emphasize at this point that chemical reactions are local phenomena in the sense that the rate of an elementary reaction at some point in space depends upon the reactant concentration(s) at that point . Thus, the rate of a given reaction is in general a function of position and time, reflecting the spatial and temporal variation in reactant concentrations. For most reactions of in- terest, the rate expression is a nonlinear function of pollutant concentrations, because most reactions of interest happen to be second—order. This implies that in most cases of interest the average rate of a given reaction within some finite volume of interest cannot be obtained from the rate expression simply by in- serting the average reactant concentrations, unless all reactants are uniformly mixed within this volume. En this case, there is no spatial variation in the ------- A 61 reactant concentrations and hence no spatial dependence of the reaction rate. The only other situation in which the average reaction rate is given by the rate expression using the average pollutant concentration is that of a first— order reaction, in which case this is always correct no matter what the spatial distribution. In most cases of interest, spatial inhomogeneity in the reactant concentrations causes the chemical and dispersion processes to be coupled in a very complicated way. The nature of turbulent dispersion and the small size of most real emission sources guarantee that in applications of practical interest there are significant variations in the concentrations of reactive pollutants over distances much smaller than the spatial resolution of most current models. The degree of inhomogeneity depends on the level of atmospheric turbulence and on the spatial distribution of the sources. In principle, the effect on the average reaction rate of this inevitable inhomogeneity at distance scales below the resolution of the model should be taken into account. In practice, however, this has proved to be a difficult problem and is still fundamentally unsolved. A.5.2 Treatment of Chemistry and Reaction Mechanism It is convenient to divide the discussion of treatments into two separate parts, the first dealing with the special case in which all relevant reactions are first—order reactions, the second with the more general situation. As pointed out in the general discussion, most chemical reactions of importance in air pollution are second—order reactions. This being the case, it may seem unrealistic to consider an application in which all the reactions of interest are first—order. There are two situations, however, in which only first—order reactions need be considered. The first involves the treatment of radioactive rather than chemical transformations; radioactive decay is rigorously a first—order process. The second arises as a result of approx— imating the disappearance of one pollutant and the appearance of its reaction products as a first—order process with some empirically derived effective rate constant. A first—order process has the property that the rate of that process is a linear function of the concentration of the reactant involved. As a result, it turns out that the effect of one or more first—order processes on ------- A 62 the reactant and product concentrations may be determined independently from the effect of dispersion; in other words, first—order transformation processes and the dispersion process are completely separable and any of the many treat- ments of dispersion may be used. Furthermore, in cases where more than one source is involved, the contribution from each may be evaluated and the total predicted concentration obtained by simply adding the individual source con- tributions. The simplest case arises with a primary pollutant subject to some first—order removal process. In this case, the effect of the process is simply to cause the pollutant concentrations to decay exponentially with a half—life which may be easily determined from the rate constant for the process. Many dispersion models now in use have the capability of simulating this situation. More often, however, the user’s application involves a system of chemical reactions, most of which are second—order; the most common example is photochemical smog. In general, a numerical/dynamic model is required, since the chemical mix evolves in time in a nonlinear way. The observational basis for a semiempirical approach is not usually available, although statis- tical models have been developed for some limited applications. Two aspects of the treatment by a given model should in principle be evaluated: • The level of detail used in the reaction mechanism, and • The treatment of the effect of inhomogeneous mixing on average reaction rates. With regard to the treatment of reaction mechanism, little can be said in general, because so much depends on the specific details of the chemistry. The simplest case is that in which either the disappearance of a particular pollutant, or the appearance of its reaction products, or both are of in- terest. En this case, if the reaction time scale is rather long compared to the dispersion time scale and if the reaction products are relatively inert so that, for example, the original pollutant is not regenerated by further reaction, it may be sufficient to approximate the reaction by a first—order process using an effective rate constant determined empirically. In this approximation, all details of the actual reaction mechanism are ignored. The ------- A63 conversion of sulfur dioxide to sulfate aerosol over long distances is commonly treated in this manner. In more complex cases, such as that of photochemical smog, the mechanism should be treated at some more appropriate level of detail. The required level of detail depends on the nature of the reactions being des- cribed and the number of different chemical species involved. The user should seek expert advice in evaluating a model with respect to the mechanism being used. In any case, the assumed mechanism should be sufficiently valid so as to give reasonable agreement with experimental observations. In the photochemical smog case, three approximations are commonly used and will be discussed briefly as examples of the possibilities that can arise. The first deals with the treatment of highly reactive intermediates which are present in photochemical smog. These intermediate species can be treated just like any other pollutant in that their concentrations may be des- cribed explicitly as functions of time. Due to their high reactivity, how- ever, the approximation is usually made that they exist in a steady or stationary state such that for each the rate of removal equals the rate of production. Making this approximation allows their concentrations to be expressed mathema- tically in terms of those of measurable pollutants and thus eliminated from the rate expressions altogether. By eliminating these species from the equations, considerable simplification occurs. This approximation, called the steady—state or stationary—state approximation, should be tested for validity in any specific case and there are indications [ Farrow and Edelson (l974)J that it is not necessarily valid for the photochemical smog case even though it is commonly used. This approximation is not restricted to applications involving photochemical smog but may be used in describing any reactive system in which highly reactive intermediate species are present. A second and less detailed treatment is sometimes used when the reaction mechanism may be approximated by a small number of fast reactions such that each one in the set is accompanied by its reverse reaction. For example, over a short period of time the photochemical smog system may be approximated by a mechanism consisting of only two reactions: 1) the photolysis (absorption of light, followed by chemical reaction) of NO to produce NO and 03 and 2) the reverse reaction of NO and 0 to produce NO . If each reaction in the set is 3 2 fast enough, the entire system responds very rapidly to changes in composition ------- A 64 brought about by dispersion, and the chemical composition of the pollutant mixture at any point may be predicted by assuming the system of chemical reactions to be in equilibrium. This approximation, called the equilibrium approximation, is equivalent to the assumption that the rate of removal equals the rate of production for every chemical species present, not just the re- active intermediates. The equilibrium approximation is valid when the reaction time for each reaction in the system is much shorter than the time required for significant concentration changes resulting from dispersion processes. The equilibrium approximation may be used in steady—state as well as dynamic models and allows the prediction of the chemical composition of the pollutant mixture at a given point given the composition of the original pollu- tant emission, the composition of the surrounding air into which that emission is being dispersed, and the concentrations predicted on the basis of the dis- persion model alone. The third approximation deals with the very large number of hydrocarbons which are actually present in the polluted atmosphere, all of which participate in the formation of photochemical smog. As a practical matter it is impossible to model the concentration of each even if their emission rates were known, which they are not in general. The approximation is made that classes of hydro- carbon may be defined such that all members of a given class share some de- sirable property, such as having similar reaction rates or reaction products. The total concentration of all members of each class is then modeled using a simplified reaction mechanism involving the use of average class rate constants. This technique is termed “lumping” of hydrocarbons. The validity of the pro- cedure should be determined by comparison of predictions with observations from experiments. For the purpose of comparing two models it should be assumed that, all other things being equal, it is better to treat reactive intermediates ex- plicitly than to employ the steady—state approximation (unless it can be shown explicitly that the error introduced thereby is truly negligible) and that the more accurate the reaction mechanism being used the better. If the detailed spatial and temporal evolution of a dispersing reactive system is to be described, the system of chemical reactions should be treated in some detail. For other purposes, particularly involving secondary pollutants, experimental and/or observational data may be used to provide the necessary link ------- A65 between the concentration of the pollutant of interest and the precursor levels at an earlier time. This may be especially useful for cases in which not enough Is known about the reaction mechanism or in which only a maximum con- centration regardless of location Is desired. The other aspect that needs to be evaluated is the way in which the rates of change of the average pollutant concentrations are evaluated. Dis- persion models for reactive pollutants generally attempt to predict the average concentrations of all relevant pollutants within some suitably defined volumes or cells as functions of time and need to be able to evaluate the time rates of change of these quantities. As discussed earlier, if the pollutants are uniformly distributed within a given cell the appropriate rates of change may be calculated from the elementary reaction rate expressions, using the average concentrations appropriate to the given cell. Errors will be intro- duced if this procedure is used In cases In which spatial Inhomogeneities exist in the pollutant concentrations over distances smaller than the cell size. At present, this effect is generally not treated at all. This is not to imply that modelers are unaware of the effect, but the problem of providing an adequate general treatment is still essentially unsolved. En summary, most dispersion models for reactive pollutants use elementary reaction rate expressions which are truly valid only In homogeneous regions and make no attempt to account for imperfect mixing at sub—grid distances. If the user is confronted with a model which does in fact treat the effect of inhomogeneities In some fashion, expert advice should be sought on the manner of treatment before making an evaluation but In general any reasonable treatment would be better than none at all. Table 5.12 gives the treatments of chemistry and reaction mechanism that have been discussed. No table of treatments of the effect of spatial inhomogeneities on the rate of change of average pollutant concentrations is provided, since at this writing no practical general treatments exist except In models developed solely for the purpose of doing basic research. Table B.lO gives the treatments of chemistry and reaction mechanism used by the reference models. ------- A66 A.6 PHYSICAL REMOVAL PROCESSES A.6.i. General The two major physical removal processes which affect ambient at- mospheric pollution levels are dry deposition and precipitation scavenging. In identifying them as physical processes, the intention is to distinguish them from the chemical processes discussed in Appendix A.5, even though on a fundamental level there are chemical aspects to each. After defining these elements, each will be discussed in turn. For a more technical discussion the user is referred to the article by Hidy (1973) as well as the proceedings of the symposia on precipitation scavenging [ Engelmann and Slinn (1970)] and on atmosphere—surface exchange of particulate and gaseous pollutants [ Engelmann and Sehinel (1976)]. Technical but still introductory discussions are also given by Van der Hoven and Engelmann in Slade (1968). Dry deposition is defined as the removal of a gaseous or particulate pollutant at the earth’s surface by any of the several processes, including impaction, absorption, and chemical reaction. The important point is that this process occurs only at the surface. Precipitation scavenging is defined as the removal of a gaseous or particulate pollutant by precipitation. In the past, the distinction has been made between the absorption or other collection of pollution by cloud droplets before precipitation actually occurred (denoted by the term “rainout”) and the scavenging of pollutant by the precipitation itself as it falls through the polluted air (denoted by the term “washout”). For purposes of this work- book, this distinction will not be emphasized but the user should be aware of its existence. Dry Deposition The rate of removal of an atmospheric pollutant per unit area of ground surface is called the deposition rate (dimenflons: mass/time/area). It depends upon • The nature of the mechanism by which the pollutant, once transported to the ground, interacts with and is removed at the ground surface and • The rate of vertical transport of that pollutant. ------- A67 The pollutant is removed from the air near the ground, thereby creating a non—zero vertical concentration gradient near that surface. Vertical dispersion processes tend to smooth out this gradient by transporting pollutant downwards, thereby providing nvre for possible removal. The ambient pollutant concen- tration near the ground is lower than it would be otherwise, with the magnitude of the depletion depending on the relative rate of removal at the surface, -“d a corresponding net decrease per unit time in the total amount of pollutant being advected by the wind is also observed. The deposition rate depends on the nature of the interaction between pollutant and ground surface and as such depends on a wide variety of pollutant and surface characteristics. Although these are highly dependent on the specific application of interest, a few general statements can be made. The deposition of gaseous pollutants, for example, increases as the solubility or reactivity of the gas increases. The deposition of airborn particulate matter is highly dependent on particle size and if the pollutant of interest is found predominantly within a certain size range, this fact should be taken into account in the treatment, as discussed below. The deposition rate also depends strongly on the rate of vertical transport and therefore on the same factors as does vertical dispersion. (See Appendix A.4 for a discussion of these factors.) With regard to the deposition of particulate matter, these remarks ref er primarily to particles smaller than approximately 10 microns in size. Particles larger than this are sufficiently massive that gravitational settling becomes significant and these particles simply drift downward at a rate dependent on their size and weight. This deposition mechanism is very different from that described so far and in general must be treated differently; see for example the discussion in Slade (1968). Particulate matter smaller than 10 microns behaves much like a gas in many respects and gravitational settling is usually negligible. If the removal is efficient enough, a significant fraction of the pollutant may be removed before it is transported out of the region of in- terest and ambient atmospheric concentrations can be significantly affected. In some application, the deposition rate or the total deposition within a given area over some specified period of time may be of interest, in addition ------- A 68 to or instead of the actual ambient concentration. In either case, dry deposition is an important phenomenon. Precipitation Scavenging This term includes processes which take place within clouds, such as the formation of cloud droplc s about pollutant particles which serve as condensation nuclei and the absorption of pollutants into existing droplets, as well as the scavenging action of precipitation falling through polluted air. The importance of each of these processes depends strongly on the characteristics of the pollutant, as in the case of dry deposition, and again only very general comments can be made. For gaseo is pollutant, the solubility in water is the most important factor and this often depends to a sign Lficant extent on the presence of other dissolved material in the precipi- tation. The solubility of sulfur dioxide, for example, decreases as the acidity of the precipitation increases. The particle size is again the most important factor for the scavenging of aerosols. The rate of pollutant re- moval by falling precipitation is also determined to a significant extent by the size of the falling drops and the rainfall rate. A.6.2 Treatment of Dry D!position As indicated above, the removal of pollutant at the ground surface has two major effects on ambient pollutant concentrations: A depletion of the mass of pollutant being advected by the wind, resulting in lower concentrations than would otherwise be expected, and A reduction of ground level concentrations compared to those at higher elevations, resulting in a non—uniform vertical distribution. All treatments of dry deposition that are used in practice describe the first effect but not all describe the second. The net downward pollutant flux resulting from removal at ground level is commonly assumed proportional to the pollutant concentration at ground level, the proportionality constant actually being dependent on a variety of factors such as: ------- A 69 • The nature of the pollutant, • The nature of the ground surface, and • The prevailing meteorological conditions, particularly the atmospheric stability near the ground. The proportionality constant is called the “deposition velocity” and its value in any given situation determines the significance of the effect of dry deposition on pollutant concentration. Theoretical procedures exist whereby appropriate values may be estimated for a specific application but their accuracy is uncertain and values derived from field observations are nearly always used in practice. Assuming that the downwind flux of pollutant nay be parameterized in this way, the problem of treating dry deposition becomes one of describing its effect on atmospheric pollutant concentrations and of calculating the amount of pollutant deposited in the area of interest. Different types of models treat these effects in different ways, depending specifically on the way vertical dispersion is treated and on the way the dependence of the pollutant concentration on height above ground is predicted. Since pollutant removal occurs at the ground surface, the best treatment of dry deposition is to mathematically specify the appropriate boundary condition at the earth’s surface and to determine or describe the corresponding effects numerically or analytically. The mathematical statement of the boundary condition, which is used in models which treat vertical dis- persion by a numerical method, involves both the vertical eddy diffusivity and the deposition velocity and defines the relationship between the pollutant concentration and the concentration gradient at the ground. Numerical solu- tion of the diffusion equation in the vertical direction then determines the predicted pollutant concentration as a function of height as well as the pre- dicted rate of pollutant deposition on the ground. This procedure may be used in either dynamic or steady—state models. Models which treat vertical dispersion by a semiempirical method do not necessarily handle dry deposition in a less appropriate way than do numerical models. If, for example, the assumed form for the vertical concentration distribution is based on suitable analytic solutions of the vertical diffusion equation obtained using the correct boundary conditions, the treatment may be as appropriate as any other. Normally, however, semiempirical models incorporate ------- A7 0 certain assumptions which are to some extent invalid for the treatment of dry deposition. Most semiempirical models incorporate the perfect reflection boundary condition, as discussed in Appendix A.7. Mathematically, this corresponds to the assumption that there is no net vertical pollutant flux and no net removal of pollutant from the atmosphere at the ground and has the additional result that the pollutant concentration is nearly independent of height near the ground. It also corresponds to the special case of a zero value for the deposition velocity. A model incorporating the perfect reflection boundary condition cannot treat the effect of dry deposition on the iertical concen- tration profile. If this approximation is used in a model, as it is in most Gaussian plume models, but it is still desirable or necessary to allow for the depletion of the plume as it is advected along, a time or downwind distance— dependent factor may be applied to the concentration value calculated by the basic semiempirical formula. This factor serves to simulate a reduction In the total mass of pollutant in the plume and to model pollutant removal by dry deposition. In essence, this type of treatment involves the determination of an effective source strength which is a decreasing function of travel time or downwind distance. The simplest example of this treatment is the use of an exponential decay factor in several currently available models. By appropriate choice of the value of the decay constant, it is possible to simulate crudely the effect of the removal of pollutant. An implicit assumption in this treat- ment is that the shape of the vertical concentration distribution is unaffected by the removal process; this assumption Is valid only if the rate of vertical mixing is large compared to the rate of pollutant removal. A somewhat more detailed treatment, described in Slade (1968), involves the assumption that the pollutant is removed at a rate proportional to the ground level concentration but that this concentration is given by, say, the Gaussian plume formula with perfect reflection, modified by a factor to account for that mass of pollutant already lost. The effective source strength as a function of downwind distance must be determined by quadrature for the specific parameter values involved and presented for use in graphical or tabular form. As in the simpler and less detailed exponential decay treatment, the implicit assumption is made that the shape of the vertical pollutant distribution is unaffected. ------- A7 1 The special case of particulate matter for which gravitation settling is important is generally treated by what has come to be known as the tilted plume approximation. The vertical pollutant distribution is determined as a function of time or downwind distance using whatever model is appropriate and a downward motion with a velocity equal to the appropriate settling velocity is added to whatever other motion has been predicted for the distribution. For steady—state models, the effect is to tilt the plume centerline downwards with a slope determined by the ratio of the settling velocity to the horizon- tal wind speed. One should in principle use a different settling velocity, and hence a different slope, for particulate matter in different size ranges. Table 5.13 lists possible treatments of dry deposition. Table B.ll lists the treatments used by the reference models. A.6.3 Treatment of Precipitation Scavenging The various processes whose net effect is called precipitation scavenging are not usually modeled individually except perhaps in specialized research—level models. Instead, the total effect is generally treated in an approximate way, and we will be concerned here only with this type of approach. Both the removal of pollutants in clouds and the scavenging by falling precipitation are usually considered to be exponential processes. This may not be strictly true in all cases; for example, the uptake of 502 by cloud droplets is not really an exponential process because of chemical reactions which occur in the droplets themselves. Precipitation falling through a polluted layer may take up a soluble gas at one height and release it at a lower height because of evaporation of the drops exposed to a clean at- mosphere. These effects must be modeled on an individual case—by—case basis. If removal in clouds is treated as an exponential process, the decay constant is called the rainout coefficient and if removal by falling precipi- tation is treated as an exponential process, the decay constant is called the washout coefficient. These coefficients in principle depend on a wide variety of drop and pollutant characteristics. Empirical values are often used and it is often assumed that the relationship between the washout coefficient and the total rainfall rate may be expressed by a power law. The washout coefficient is a function of drop size, and a more detailed treatment would take this into ------- A7 2 account and determine the total rate of pollutant removal by integrating over an assumed drop size distribution function, but this is rarely done in practice. If the rainfall rate is variable, so is the washout coefficient and the pollutant concentration decreases in a manner reflecting this variability; the decrease is not represented by simple exponential decay. For the purpose of describing the effect of rainfall on pollutant concentrations, the washout coefficient must be known or assumed, including any time variation due to variations in the rainfall rate. If the application involves an averaging time sufficiently long that more than one rainfall occurrence needs to be treated, even simpler methods are often used. For example, the assumption may be made that every time it rains the ambient pollutant level is decreased by some constant factor which may be empirically derived or estimated from the average duration of rain- fall in the area. If a climatological model Is being used, the correlation between frequency of rainfall and other meteorological parameters, particularly wind direction, should be taken into account. Ignoring this correlation represents an even less detailed treatment and correspunds to simply super- imposing total rainfall contours on calculated concentration contours to estimate the effect on long—term average concentration values. This correlation Is most simply handled in climatological models by including precipitation in the set of meteorological variables for which the joint frequency function is used. In this case, exponential decay may be an appropriate treatment of the effects of precipitation. Many climatological models now available provide the option of specifying an exponential decay rate but do not specifically treat precipitation conditions separately. These models apply the exponential decay factor in every distinct meteorological condition modeled; this is not an appropriate treatment of precipitation scavenging due to the intermittancy of rainfall. Table 5.13 lists the possible treatments of precipitation scavenging which are within the scope of this discussion and Table B.ll lists the treatments used by the reference models. ------- A73 A. 7 BACKGROUND, BOUNDARY MID INITIAL CONDITIONS A.7.l General An air pollution model describes the pollutant distribution within a limted volume of space for a limited period of time. This volume is bounded on the bottom by the earth’s surface, on the sides by the perimeter of the region of interest, and on the top by the upper limit to vertical dispersion. Even for models which calculate only ground level concentrations explicitly, the three dimensional nature of dispersion is accounted for through inclusion of such parameters as stack height, plume rise, or mixing height. In any case, treatments of the following four aspects of the given application are required: • Effects due to the existence of a finite upper limit to dispersion, • The effect of the earth’s surface as a barrier to dis- persion and as a potential sink for atmospheric pollutants, • The contribution to pollutant levels within the volume of interest from upwind sources not included in the model, and • The initial concentrations throughout the volume of interest at the beginning of the time period of interest. Numerical and semiempirical models treat the first three aspects in different ways; dynamic and steady—state models treat the last aspect in different ways. The first two aspects are generally called boundary conditions in both numerical and semiempirical models, because they relate to effects at well defined physical boundaries. The upper limit to dispersion is commonly treated as an absolute barrier which keeps pollutants above it from entering the modeled volume and which prevents pollutants dispersing upward within the modeled volume from going any higher. In such cases, there is no net flux of pollutant through the boundary. This condition is called the perfect reflection boundary condition and is a common assumption used for the upper boundary; other assumptions regarding the upper boundary condition are less common. However, there are circumstances in which pollutants may enter the modeled region through the upper boundary. For example, pollutants lying above the mixing layer can be entrained within the modeled volume as the mixing height increases in the morning as a result of solar heating. In practice, only numerical/dynamic models treat ------- A7 4 such situations in detail. A great deal of imprecision exists in specifying the flux (or flow) of pollutant across the upper boundary due to the lack of reliable estimates of such transfer in real situations. Even when perfect reflection is assumed, the exact value of the mixing height is generally subject to error, being based on extrapolations from measurements made at different locations or times than those being modeled. Two effects determine the nature of the lower boundary condition: • The behavior of the earth’s surface as a barrier to downward dispersion, and • The rate of removal of the pollutant at that surface. These two effects are usually assumed to be related, because the rate of re- moval is proportional to the ground—level concentration. Various processes determine the degree of absorption and which are most important depends upon the particular situation. For example, large particulates can settle out (be perfectly absorbed) under the influence of gravity. Sulfur dioxide can be absorbed by vegetation and ozone can react chemically with various mate— rials on the earth’s surface. The ground can also serve as a source of pollutants as, for example, when settled particulates are reentrained in sufficiently strong winds or when some pollutant is being emitted by vegetation. It would be exceedingly complex to attempt to treat any of these processes in detail and models must rely on approximate treatments of the most important processes. When removal at the surface can be ignored, there is no net flux of pollutant through the lower boundary and the perfect reflection boundary condition is appropriate. When the removal rate is very large the situation approaches the condition which would be called “perfect absorption.” Between these two extremes both effects must be treated. Their relative importance is determined by the rate of removal compared to the rate of vertical transport. It is thus important that applications involving physical sinks at the earth’s surface handle vertical transport in an adequate manner. The removal of pollutants at the earth’s surface is termed “dry deposition” and is discussed in more detail in Appendix A.6. It should also be noted that numerical models generally treat at least some fraction of the emissions of pollutants by specifying the appropriate flux through the lower boundary as part of the lower “boundary condition.” In this discussion, the “boundary condition” refers to what happens to pollutants ------- A75 already emitted; emissions treated as occurring at the boundary should be considered as aspects of source location and emission rate (Appendix Al). The third aspcct, advection of pollutants into the volume of interest, is related to the concept of a background level. Such concentrations are due to natural and man—made sources not being modeled, because they are outside the modeled region. This definition of background differs from another sometimes sometimes used in which the background level is taken as the concentration which would exist if all sources in the modeled inventory ceased to emit. The latter definition would include contributions from sources within the modeled region but not included in the inventory. In the sense used here, background might be defined operationally as the pollutant concentration measured just outside the upwind boundary of the region of interest. Such a concentration would frequently depend on the direction of the wind, the location of the measurement, or the time when the measurement was made. For non—conservative pollutants, this concentration would be expected to change as the air is advected through the study region due to the operation of various removal mechanisms. For secondary pollutants, the incoming fluxes of precursors must also be taken into account, because they will generally interact significantly with emissions within the region and greatly affect the predicted levels of the pollutant of interest. Ozone, which is both reactive and secondary, illustrates the situation well. “Background” ozone concentrations measured just upwind of urban areas are frequently reduced within these areas due to the initial scavenging of ozone by precursor nitric oxide emissions. Downwind of the urban area, the precursors react and ozone concentrations rise again to high levels. Back- ground is thus usually not a simple additive tern but is a function of position and time within the region of interest. A single, additive background number can be defined only for primary conservative pollutants. Otherwise, the flux of pollutant and/or precursors into the study region at the vertical boundaries must be known. Even for primary conservative pollutants, the in- coming flux must be known as a function of position and time if significant variations occur over time or distance scales small compared with the averaging time and the size of the region of interest. Rural SO or sulfate levels pro— 2 vide examples of situations in which a single, additive background level is likely to be appropriate. ------- A76 It has been assumed in this discussion of background and the side boundary conditions that the study region has been chosen carefully to include all important sources. It would be improper, for example, to estimate the total 24—hour maximum SO concentration in the vicinity of a power plant 2 while treating the contribution of a nearby plant as a background value. Both plants would need to be included in the study region and modeled. The second plant could be excluded only if the contribution of the first plant alone, rather than the total concentration, were desired. One other point needs to be made about background. Circumstances may arise in which background is negligible, any background concentration being small in comparison to th’ concentration of interest. For example, in cases where the maximum short—term concentrations near a large, relatively isolated source are being estimated, background can usually be ignored. In such cases, models ignoring background are applicable. The user must consider the appli- cation carefully when making such a determination. The last aspect covers the initial conditions, those concentrations existing throughout the study region at the beginning of the time period of interest. These concentrations are not treated explicitly in steady—state models but must be specified in order to solve the equations used in dynamic models. Initial concentrations may be included implicitly in steady—state models when background levels are estimated. They are likely to be most important for short—term averages for which the initial concentrations can constitute a substantial part of the final time—averaged concentration. This situation would occur most frequently when the initial concentrations are large and travel time across the region of interest is equal to or greater than the averaging time of interest. As noted in Appendix A.4, this type of situation calls for a dynamic, rather than a steady—state, treatment. The concentrations of secondary and reactive pollutants are particularly sensitive to the initial concentrations and distributions of precursors and potential reactants, respectively. Initial conditions are thus important for such pollutants and a dynamic approach is better suited to their treatment. This is particularly true when short—term concentrations are desired as is the case, for example, with ozone. ------- A77 A.7.2 Treatment of Background, Boundary and Initial Conditiohs Since numerical and semiempirical models treat dispersion from different poiutb of view, they employ different methods for handling background and boundary conditions. Initial conditions are treated differently by dynamic and steady—state models. The user should be aware that both “boundary conditions” and “initial conditions” signify two related but not entirely equivalent concepts. First, they mean a set of mathematical expressions req’iired to solve the partial differential equations used in numerical models add second, the physical conditions being modeled. The mathematical expressions are the representations of the physical conditions in a form suitable for numerical models. Saniempirical models must treat the same physical conditions, still often referred to as the boundary conditions, using different methods. The discussion is conveniently divided by considering first the treatments of background and boundary conditions by numerical and semiempirical models and then the treatments of initial conditions by dynamic and steady—state models. Background and Boundary Conditions Part of the difference between the treatments of background and boundary conditions by numerical and semiempirical models is simply a difference in the methodologies used to express the same physical condition. As will be seen, however, the numerical approach generally provides a more detailed and flexible treatment of these conditions. At this point, the user should keep in mind that applicability of both approaches to the application as discussed in Appendix A.4. As noted above, many processes can take place when a pollutant contacts the earth’s surface. Perfect reflection or absorption are generally approx- imations to the real situation. The appropriateness of the approximation being used must be assessed by the user when comparing models. Numerical models treat perfect reflection mathematically by requiring that the vertical gradient of pollutant concentration be zero at the surface, that is, what comes down must go back up. Perfect absorption corresponds to the requirement that the concentration be zero at the boundary. Perfect reflection is normally assumed, because it is usually a much better approximation to the physical situation than is perfect absorption. Both of these situations may also be handled easily by semieinpirical models. Semiempirical models treat perfect reflection ------- A78 at the lower boundary by including an “image source” equivalent to the real source but located like its mirror image with the earth’s surface as the mirror. The “method of Images” Is the technique employed in the most widely used forms of the Gaussian plume model and can only be used to handle perfect reflection or absorption. Partial reflection at the earth’s surface is treated in numerical models by using the concept of a “dry deposition velocity.” This parameter is a measure of the rate of pollutant removal at the earth’s surface. In essence, the mathematical formulation allows part of the incoming pollutant to be ab- sorbed so that the total amount being dispersed is depleted after reflection. Most semietnpirical model? developed to date cannot treat partial reflection as a boundary condition. An approximate treatment of dry deposition as a pollu- tant removal process by assuming an exponential decay of the pollutant is fre- quently used. This is discussed in more detail in Appendix A.6. Dry deposition could also be treated as a boundary condition by semiempirical models if the assumed functional form of the pollutant distribution were based upon analytical solutions of the diffusion equations subject to the appropriate boundary condition. Numerical models can also change the amount of absorption to represent different conditions throughout the study region; semiempirical models can usually only deal with one overall average dry deposition rate throughout the region of interest. At the mixing height, perfect reflection is generally assumed. Numerical models use the same form of mathematical boundary condition as at the surface but apply it at the height corresponding to the top of the mixing layer, which can vary with location and time. These models could also be used in principle to cover the case of partial penetration of the mixing layer (partial reflection) simply by altering the boundary condition as is done to treat dry deposition at the surface. They can also account for the transfer of pollutants into the region of interest by suitable modifications of the upper boundary conditions and thus treat fumigation or entrainment. It should also be noted that numerical models require a finite upper limit to dispersion in order to solve the relevant equations. As at the ground, semiempirical models generally treat only the case of perfect reflection. Two methods are commonly used. The first is the method of images in which image sources are added above the mixing height to account ------- A79 for the reflections from that barrier, which is generally assumed to have a constant elevation. It turns out that an infinite number of images are required to account for the multiple reflections from the ground and the mixing height [ see Turner (1969)] and the result is expressed as an infinite sum. In most cases only the first few tens of the sum contribute significantly and the sum may be evaluated easily to sufficient accuracy. A more common treatment relies upon the observation that near the source the plume is not affected by condi- tions at the top of the mixing layer and that far enough downwind, the pollutant is uniformly mixed within the entire mixing layer. Between the distance at which the plume first feels the effects of the finite mixing height and the distance at which the vertical profile becomes uniform, the concentration is obtained by interpolation [ see Turner (1969)]. A variation of this treatment used in some Gaussian plume models treats the effect of the mixing height implicitly by limiting the vertical spread of the plume by requiring that remain constant after the vertical spread of the plume (o ) exceeds some fraction of the mixing height. Pasquill (1976) discusses the limitations of the undisturbed and uniform mixing approximations and has presented a table for use in interpolating results in cases where the sum must be evaluated. [ See also Yamartino (1977)]. Evaluating the sum will generally give more accurate results than interpolation. The gain in accuracy is slight considering the magnitude of other inaccuracies in modeling treatments and interpolation is used more frequently. Semiempirical models can also, in essence, ignore the upper boundary condition by using a functional form for the vertical concentration profile that places no limits on the height to which pollutants can disperse. This may be an appropriate repre- sentation of the real situation of the large mixing heights at short distances from the source. Sanienpirical models can be modified to account for fumigations by using equations (functional forms) for predicting concentrations during the time of the fumigation. (See, for example, the equations in the appropriate references cited in Appendix A.2.) Numerical models treat the conditions at the sides of the region as mathematical specifications of the pollutant flux into the region. As noted above, this is the most fundamental way of treating background levels. Semi— empirical models cannot treat these as boundary conditions and “background” can only be treated as a general additive term. This term may be a function of location within the region but is generally treated as a single constant value thus ignoring directional dependence and spatial variations. Any temporal variation is also generally ignored. ------- A80 Initial Conditions As pointed out previously, initial conditions are treated explicitly only by dynamic models. Any contributions to the concentrations due to pollutants initially present would be handled as part of the additive back- ground level by steady—state models. As such they would be indistinguishable from the concentrations assumed to be advected into the region as “true” background. In dynamic treatments, more detail is available when the initial conditions can be arbitrary functions of location than when single uniform values must be assumed throughout the region of interest. A final word is in order about clinatological models and temporal variations. As noted in Appendix A.4, this approach can make use of any of the basic types of models discussed although a steady—state method is most often used. Thus, the treatment of background, boundary and initial conditions by clinatological models will depend upon the nature of the model used for the dispersion calculations. Both dynamic and sequential steady—state models can, of course, account for temporal variations in background and boundary conditions. Dynamic models usually allow important parameters to change re- latively snoothly over time; sequential steady—state models allow parameters to assume new values at the beginning of each new time interval over which a steady—state is assumed to hold. Dynamic models most frequently treat the amount of material advected or entrained into the region of interest or the mixing height as time dependent; sequential steady—state models most frequently treat only temporal variations in the mixing height. The ranking of treatments of background, boundary, and initial condi- tions is given in Table 5.14. In treating these elements, almost any combination of types of treatments at the various boundaries can occur. In rating a model, the user should rate the model’s treatment of each element separately and combine them to arrive at an overall rating. Table B.l2 lists the treatments of back- ground, boundary and initial conditions used by the reference models. AM TE} ORAL CORRELATIONS A.8.l General As noted in previous subsections, many of the elements or quantities used to parameterize an element treated by a model can vary with time. The ------- MU variations of these quantities about their mean values are frequently correlated in the situation being modeled. For example, the application may involve a source with a diurnally varying emission rate and meteorology with the typical diurnal variations in atmospheric stability described in Appendix A.4. When such correlations occur it is usually important that the model correlate the tine—dependent quantities, that is, treat them in such a way that concentration estimates are made on the basis of values which do occur together in the application of interest. Implicit in the last statement is a realization that the treatment of correlations is closely related to the degree of temporal resolution obtainable in the model. In particular, the resolution time for the correlated quantities must be less than the tine over which the variations can occur. For example, if two correlated quantities vary hourly, the model must treat each of them with a tine resolution of one hour or less for the treatment of correlations to be possible. As pointed out previously, there is a limit, frequently based on practical considerations or data availability, to the resolution tine and hence to times over which correlations can be considered. The limiting factor is that element or quantity with the minimum degree of tine resolution among those elements which are important to the particular application and which exhibit sufficiently large temporal variability to affect the model results. The primary interest is generally in correlating emission rates, meteorological parameters, and rates of removal and transformation processes. of course, in applications where emission rates are almost constant, correlations involving them are small and may be ignored. Generally speaking, the correlations between the various meteorological parameters also need to be treated. Dynamic and sequential models handle temporal correlations automatically within the tine resolution used by the model. These models generally allow the values of most important parameters to be changed at each time step and since the data for each step are generally input as a unit by the user, they are automatically correlated. Steady—state models which treat one or several specific sets of emission and meteorological data treat correlations which occur on a tine scale longer than the averaging tine of the data automatically and ignore those which occur over shorter tines. The correlations are implicit in the structure of the input data as in the dynamic case. This type of treatment is frequently encountered in models which estimate short—term concentrations. ------- A82 On the other hand, cllinatological models use statistical wind roses and hence the only correlations inherent in this approach are between those parameters upon which the wind rose is based, typically atmospheric stability, wind speed, and wind direction. A three—hour resolution is typical of wind roses. All other correlations, particularly those involving emissions, must be treated separately. Two factors should be considered when evaluating the treatment of correlations: • The magnitude of the variations in the given application over time scales less than the averaging time, and • The importance to the application of the quantities involved. The first factor has been discussed above. As for the second, simply correlating many time-dependent quantities may be less important that correlating a few critical quantities, e.g., wind direction and emission rate when the effect of a peaking power plant at a specific location is desired. A.8.2 Treatment of Temporal Correlations Beginning with the most detailed, there are basically three levels at which temporal correlations can be treated: • Sequential and fully correlated, • Non—sequential with limited correlation, and • Not treated explicitly. The first type of treatment is found in dynamic models or in sequential models. In these models, the correlations are treated automatically. The second type of treatment is exemplified by cliinatological models. Although some statistical models may implicitly treat correlations by their choice of variables, they are classified here as using the third type of treatment and are discussed in Section 7. Within the first two treatments there is a variation in the level of detail depending on: • The degree of temporal resolution and The quantities allowed to vary. ------- A83 The determinants and importance of these aspects have been discussed in the general discussion in Appendix A.8.1. Table 5.15 lists the treatments of temporal correlations and the treatments by the reference models are given in Table B.13. A .9 IMPORTANCE RATINGS FOR APPLICATION ELEMENTS Source — Receptor Relationship The source—receptor relationship is assumed to be of at least medium importance in all applications. Many factors influencing transport and dispersion depend on the source—receptor separation and orientation. The relationship is somewhat more important for secondary pollutants, because of the need for a detailed description of the mixing of various precursors. For similar reasons, it is also somewhat more important when chemical sinks are involved. Short—term concentrations are more sensitive to this relationship than long—term concentrations, since changing meteorological conditions tend to average differences in concentrations from point to point. The concentra- tion distribution in situations involving limited numbers of sources depends heavily on the source—receptor relationship. In situations invo1vin multiple sources where small inaccuracies in one relationship are likely to be balanced by inaccuracies in another, this relationship is less important. Area source applications require a little less detail than point or line applications, because the spatial extent of an area source makes an error in the source— receptor relationship less significant in affecting concentration estimates. The importance of this element is somewhat enhanced in complex geographic situations which place considerable importance on the precise relationship between source, receptor, and geography. Short—range applications are more sensitive to the source—receptor relationship than long—range applications. At long distances emissions have usually become relatively uniformly mixed and a change in separation or orientation that would be critical at short range produces only a negligible effect. The importance of the source—receptor relationship to each of the applications is given in Table 4.2. Emission Rate Other things being equal, concentrations of primary pollutants are proportional to emission rates. For secondary pollutants, the relative ------- A84 concentrations of the precursors are very important factors in determining concentrations. Emission rates were thus always rated as of at least medium importance to all applications, and as somewhat more important for secondary than for primary pollutants. The same consideration applies to reactive pollu- tants, making emission rate slightly more important when chemical sinks are in- volved than when only physical sinks or inert pollutants are modeled. Emission rates must generally receive more attention in short—term or short—range appli- cations than in long—term or long—range applications where other factors such as changing meteorology and removal processes normally can assume greater fin— portance for determining concentrations. Emission rates are rated as somewhat more important in situations involving a limited number of sources, because of the likelihood of compensating errors in the multiple source case. No distinction is made between different source geometries nor between the importance of emission rates in simple and complex geographic situations. Ratings of the importance of emission rates to the various applications are given in Table 4.3. Composition of Emissions This discussion deals only with the chemical composition of emissions. If the user’s application requires the specification of a size distribution for particulate matter, the importance ratings in Table 4.4 should be reconsidered. No general statements can be made in this case, and the user should consult an expert to determine importance ratings appropriate to the application of interest. Chemical composition of emissions is critically important when secondary pollutants or chemical sinks are involved and of little importance when dealing with primary pollutants and either no sinks, or physical sinks only. No difference in importance between long-term and short—term applications is assumed. A slight extra importance is assigned to applications involving multiple sources or long—range transport, because of the increased possibility for chemical re- actions when many different emissions are mixed or a long time is allowed for reactions to occur. The importance in simple and complex geographic situations is the same. The importance ratings for the chemical composition of emissions are given in Table 4.4. ------- A85 Plume Behavior Table 4.5 gives the importance of plume behavior to each of the indexed applications. Plume behavior is equally important for both primary and secondary pollutants but is rated more important in cases where physical sinks are present than when chemical or no sinks are present. This is because the plume behavior determines how easily the plume contacts the ground, allowing the physical removal process to operate. Chemical removal can occur through- out the entire volume of mixing. Plume behavior is also rated more important in short—term than in long—term averages, because over short—time spans small variations, masked by averaging over long time spans, may be significant. The greater spatial inh mogeneities associated wth point sources make plume behavior more important for point sources than for line sources. Similarly, it is somewhat more important for line than for area sources. In complex geographic situations, plume behavior is important in determining whether the plume will be affected by the complex situation or rise above its influence. Over a long range, vertical mixing tends to become uniform and hence plume behavior is relatively unimportant. Horizontal Wind Field The horizontal wind field is generally an important element in any application, because advection is the principal process for pollutant transport. It is considered somewhat more important when chemical reactions are important and when short—term rather than long—term averages are desired, because of the need to know the wind field more precisely. The determination of the horizontal wind field is more important in complex terrain due to the channeling of the wind and other effects. The horizontal wind field is some- what more important in limited point or line source cases than area or multiple source cases. Finally, the horizontal wind field is considered to be very important in those situations in which the actual trajectory of a parcel of air must be determined, because the temporal and spatial variation must be reproduced. This is the case for long range transport and for very short re- lease times (puffs). Table 4.6 gives the importance rating of horizontal wind field for each application. ------- A86 Vertical Wind Field The vertical wind field is considered generally unimportant in many cases of interest, because it is nearly zero on average. Vertical wind field is important in situations requiring the estimation of concentrations at moderately short ranges in regions containing complex terrain due to the effect of the terrain on the (three—dimensional) wind field. Vertical wind field is considered slightly more important in applications involving chemistry than those in which chemistry is unimportant due to the need for a more accurate description of the wind field. Vertical wind field is also considered more important in estimating short—term rather than long—term estimates. No dis- tinction was made for different source geometries or numbers. Table 4.7 gives the importance ratings of vertical wind field for the indexed applications. Horizontal Dispersion Table 4.8 gives the importance rating of horizontal dispersion for each of the indexed applications. Horizontal dispersion is considered to be of at least medium Importance in every application. Horizontal dispersion is more important at short range than at long range, because the dispersion process is the most rapid and produces the greatest changes in concentration estimates at short ranges. Horizontal dispersion is considered less important for area sources than for line sources, and less for line than for point sources due to the emission size effect. In the case of secondary pollutants and/or the case of chemically reactive pollutants, it is very important to be able to describe the mixing of emissions with the ambient air, since chemical reaction rates are sensitive to local concentrations; therefore horizontal dispersion is considered quite important in these cases. Similarly, if physical sinks are present, it is generally more important to handle horizontal dispersion properly, depending on the nature of the removal process. The importance of horizontal dispersion is considered to be higher for short—term averages than for long—term, because the averaging which can occur over long times generally allows simpler treat- ments to be adequate. Finally, horizontal dispersion is considered to be equally important in either simple or complex terrain. Vertical Dispersion Table 4.9 gives the importance rating of vertical dispersion for each of the indexed applications. Vertical dispersion is given at least a medium ------- A87 rating for every application. Its importance is considered independent of averaging time, and approximately independent of the type of terrain. Vertical dispersion is considered much more important at short range than at long range, and more important for secondary and/or chemically reactive pollutants or if physical renvval processes, particularly dry deposition, are operative. Finally, the importance of vertical dispersion is considered independent of source type or number. Chemistry and Reaction Mechanism The importance of chemistry and its treatment is determined primarily by the chemical nature of the pollutants involved and to some extent by the travel distance; no other characteristics of the application need be considered. Chemistry is irrelevant for primary inert pollutants, is of importance for primary reactive or secondary inert pollutants, and is of even more importance for secondary reactive pollutants. The importance of chemistry is rated lower for primary reactive and secondary inert pollutants than for secondary reactive pollutants. If chemical reactions provide both a source and a sink for a given pollutant, chemistry is more important than if they provide either source or sink, but not both. This is a somewhat arbitrary ranking; the real importance of a detailed treatment of chemistry depends on the complexity of the system of re- actions and the number of pollutants involved. Chemistry is considered slightly more important f or long—range than for short—range applications due to the longer travel time and greater opportunity for reactions to occur. Table 4.10 gives the list of importance ratings of chemistry and reaction mechanism for each of the indexed applications. Physical Removal Processes We consider two processes in this category: dry deposition and pre- cipitation scavenging. Physical removal is important, by definition, in those applications for which the user has taken the physical or chemical/physical sink branch on the Application Tree. Physical removal is also slightly more important for pollutants with chemical sinks than conservative ones. Physical removal is more important for long—range than for short—range applications, because of the cumulative effects of the process. Its importance is considered roughly independent of source type and averaging time. Physical removal is ------- A88 considered slightly more important in complex rather than simple terrain, due to the increased surface roughness. It should be pointed out that the importance of precipitation scavenging, as a removal process, depends primarily on the fraction of the time during which precipitation occurs in the application of interest. Thus, for short—term applications precipitation scavenging may usually be neglected, while for long—term, or possibly long—range, applications a convenient measure of its importance is the rainfall probability. Table 4.11 lists the importance ratings of physical removal for the indexed applications. Background, Boundary and Initial Conditions The importance rat ngs of background, bound.ry and initial conditions to the indexed applications are given in Table 4.12. These conditions were rated as highly important for secondary pollutants where precursor background levels can significantly influence the pollutant concentrations in the region of interest and for applications involving sinks where the advected concentra- tions might be significantly depleted during transit. These elements are crucial for applications involving reactive pollutants where the details of the pollutant mix must be known. These elements are equally important for short and long—term averaging times and for short and long—range transport. They are independent of the specific source characteristics and geography and are assumed to be of at least medium importance to all applications. Temporal Correlations Temporal correlations relate the time variations of the other application elements in their proper sequence. The importance of temporal correlations to the indexed applications is given in Table 4.13. They are rated more important for secondary than for primary pollutants, because the exact sequence and correlation of emissions and meteorology determine whether the pollutants are brought into contact so that reactions can occur. The ambient concentration is less sensitive to correlations for primary pollutants. Similarly, when physical and chemical sinks are involved, it is important to treat correlations. When treating short—term averages, it is generally important to know the detailed short—term fluctuations in the relevant factors and to correlate them properly; such detail is usually unnecessary when treating long—term averages. Thus, correlations are more important in short—term than in long—term applications. No distinctions are made between the various source types. More importance is ------- A89 associated with temporal correlations in complex geographic situations. Here correlations between emissions and dispersion factors can determine whether a particular emission passes within the perturbing influence of the complex geography. Short—range applications usually require more attention to temporal correlations. At short range, rapid changes normally occur in plumes whereas at long range these changes are slower and require less detail to treat adequately. ------- A90 ------- Bi APPENDIX B BAQ(GROUND MATERIAL ON REFERENCE } )DELS ------- B2 ------- B3 Appendi’z B. BACKGROUI4ID MATERIAL ON REFERENCE MODELS Apper d1.x B is divided into two parts. The first, Appendix B.l, consists of Table B.l giving the classification of each reference model, and Tables B.2—B.13 giving the treatment of each of the twelve application elements used by the reference models. The second part, Appendix B.2, provides abstracts of and the working equations used by the reference models. A glossary of symbols is provided at the end of Appendix B.2. ------- B4 ------- B5 CONTENTS OF APPENDIX B Page B .1 REFERENCE MODEL TREATMENTS OF APPLICATION ELEMENTS B 7 B.2 REFERENCE MODEL ABSTRACTS AND EQUATIONS B35 B .2.1 DM B37 B .2.2 RAIl . . . . . . . . . . . . . . . B38 B.2.3 Single Source (CRSTER) B4l B.2.4 Valley B44 B .2.5 AT?.! B46 B .2.6 STRAI}1 . . . B47 B.2.7APRAC—1A . B48 B .2.8 HIWAY B50 B .2.9 DIFKIN B5l B .2.10 SA l B52 Glossary of Symbols . . . . . . . . . . . . . . . . . . B55 ------- B6 ------- U B.1. REFERENCE MODEL TREATMENTS OF APPLICATION ELEMENTS This appendix provides the classification of each reference model in Table B.l and the treatment used by each reference model of each of the twelve application elements in Tables B.2-B.13. ------- B8 ------- B9 Table B.1. Reference Model Classification Reference Model Classification APRAC—lA Semiempirical/Sequential (steady—state) ATM Semiempirical/Climatological (steady—state) CDM Semiempirical/Cllaatological (steady—state) Single Source (CRSTER) Semieznpirical/Sequential (steady—state) DIFKIN Numerical (vertical)/Seiniempirical (horizontal) / Dynamic HIWAY Semiempirical/ Steady—state RAM Semiempirical/Sequential (steady—state) SAl Numerical/Dynamic STRAM S emiemp ir ical/Dynamic Valley (short—term) Semiempirical/Steady—state (long—term) Semiempirical/Climatological (steady—state) ------- B 10 Table B.2. Treatment of Source—Receptor Relationship by Reference ide1s a. Horizontal Source and Receptor Location Reference Source Model Geoe’etfl Method of Treatment APRAC—1A Line and area User specifies line sourcee (traffic links) with arbitrary locations and lengths. Area sourcee (off link traffic) allocated to 2 ci x 2 mi grid. For each receptor both are aggregated onto wedge—ehaped areas of a polsr grid centered on a receptor (a different grid is used for each receptor) such that: 1) Radii of circular boundaries increase in geoaetric progression. 2) Radial boundaries art 22.50 beyond 3.000 a and 450 under 1000 a from receptor. (3,3 for ares, line)a Up to 10 arbitrarily Located receptors. Street canyon eubmodel: Four interna 1y located receptors on each user designated street. (2 for line)a (lI) ATM Point, area, Arbitrary location for all souccea. (1 for all source types)a and tine Areas should be roughly square or circular. Arbitrary receptor location. (l)b Assumes flat terrain; elevation not treated. Treats multiple point, area, and line sources. Treste up to ten receptors. 6DM Point and area Arbitrary location for point sources. (1 for point)a Area sources are a uarea of uniform size in user—defined grid, user nay specify sources which are integer multiples of the grid size, but these must be auper- isposable directly on the grid. (2 for area) Receptors located arbitrarily. Single Source 8 Point Up to 19 sources aLl assumed to be located at same user—specified, arbitrary (CRSTER) position. ( 1 .. 2 )a Receptor locations restricted to 36 azimutha (every 3. 0) and five user—specified radial distances. ( 3 )b DIFKIN Point and area All aourcas aggregated to square 2 m i x 2 ci grid cells in an array 25 cells x 25 cells. (2,2 for point. area) 3 Sources classified as points (power plants, refineries), distributed stationary, and mobile. Receptors located arbitrarily within boundaries of emission grid. ( 2 )b HIWAY tine Straight finite line segments (will treat up to 24 parallel segments), srbitrarily located. (2) Arbitrarily located receptors. Cut aection node: Emissions treated as coming f ton 10 lines at top of cut. (2—3) Receptors cannot be i tt cut. ------- Bll Table B.2 (Cont’d) a. (Cont’d) Raference Source Model Geometry Method of Treatment RAM Point end area Arbitrary location for point sourcea. (1 for POiflt)a Receptora may be: 1) Located arbitrarily, ( 1 )b 2) Located internally near individual source maxima, (4Y’ 3) Located on internally generated hexagonal grid to give good coverage in user— defined portion of region of interest. (4)0 Area aources are multiples of unit equarea on a grid; uaer controls ecele of Rrid. (2 for aree)a SAX Point end area All sources aggregated to square grid of arbitrary spacing and up to 25 x 25 cells. (2,2 for point, area)a Sources classified as points (power plants), distributed stationary and mobile. Multiple receptors located arbitrarily within boundaries of emission grid. ( 2 )b Concentrations alao calculated in each grid cell (up to 25 x 25 x 5 estimates) STRAN Point Arbitrary location for each source. Up to 10 arbitrarily located receptors plus receptors at intersections of a grid of up to 13 a 13 equally spaced boundaries. ( 1 , 3 )b Valley Point and area Arbitrery location and elevation for each point source. (1 for point)a Arbitrary location, elevation, end size for square area sources. (1 for aree)a Must be lees then 51 sources. Receptors (112) on 16 direction radial grid; relative radial distances fixed internally, scale and origin of grid defined by user. ( 3 )b b. Release end Receptor Heights Reference Source Model Geometry Method of Treatment APRAC—lA Line end area Sources assumed at ground level. (3,5 for line, aree)c Receptors assumed at ground level. ATM Point, area Arbitrary release height for each source. (2,3,2 for point, line, area)c and line Receptors at ground level. ())d 0DM Point and area Assumes flat terrain; arbitrary stack height for each aource. (2,3 for point, area) c Chooses larger of input stack height or 1 a. Receptors at ground level. Single Sourceg Point Arbitrary stack height for each source. (CRSTER) Unique topographic elevation for each receptor: must be lees then each stack height. Receptors must be at ground level. (combination of 2 , 7 )d ------- 312 Table 3.2 (Cont’d) b. (Cont’d) Reference Source Model Geometry Method of Treatment DIPEDI Point and area Emissions treated aa upward pollutant fluxes at ground surface. (5,5 for point. area) C Receptors at equally spaced hetghts from the ground to the mixing height. ( 4 yi HIWAY Line Arbitrary release heights. ( 2 )t Arbitrary receptor heights. RAM Point and area Arbitrary release height for each point source. (2 for Up to three effective release heights (appropriate for Sm/sec winds) may he specified for area sources. (2 for area)t Value for a particular ares must be one of these three. Receptors all of same height at or above groLnd level; flat terrain assumed. (fit S U Point and area Arbitrary release height for point sources (power plants). (1 for point)c Point source emissions assumed untformly mixed throughout vertical column in which emission takes place. Other emissions treated as upward fluxes at ground surface; arbitrery topographic elevatLon. (Combinstion of 1,3 for area)c Receptors at ground level. STRAtI Point Arbitrsry telease height for each source. ( 2 )c Roceptors at ground levei; flat terrain assumed. (flu Valley Point arid area Arbitrary release height for each source. (1, combination of 1, 3 for point, ares) RecePaore at ground level with s unique topographic elevation. (Combinstion of 2, 7) c. Downwind/Crosswind Distancese Reference Source Model Geometry Method of Treatment APR.AC—lA Line and ares Uses exact downwind distances to the two radial boundaries of each gridded area source. (1 for area) ATM Point, ares Uniqus downwind and crosswind distances for each point source—receptor pair, for three points within each area source, and for nine points slong each line source. (1 for all source types) CDM Point and area Calculates unique downwind distance for each point source—receptor pair. Cslculates representative distances for ares source—receptor pairs. (1, 2 for point, eras) Single Sour e Point Calculated fron source to each receptor locstion. (1) (CRSTRR) DIFEIN Point snd ares Not applicable. Distance traveled along computed trsjectory not used explicitly. HIWAY Line Precise downwind end croqswind distsncea for each point aloeg line. (1) ------- B 13 Table B.2 (Cont’d) c. (Cont’d) Reference Source Model Geometry Method of Treatment RAN Point and aree Unique downwind and croaewind dietences for eech point source—receptor peir. (1 for point) Downwind distance calculated for points along rays which intereect area sourcee. (1 for area) SA l Point and area Not applicable. STRAN Point Not applicable, concentration calculated et each receptor based upon distance along and distance from trajectory centerline. Valley Point and area Exact downwind distance calculated for each point—source receptor pair. (1 for point) Single representative downwind distance used for area sources. (2 for area) d. orientation Ref erence Source Model Geometry Method of Treatment APRAC— 1A Line and area Traffic links (lines) may have arbitrary horizontal orientation but this detail is lost when links are gridded onto the receptor—centered polar grid. (2.2 for area, line) ATM Point, area Orientation of areas not treated explicitly. (3 for area) and line Lines horizontal, arbitrary orientation. (2 for lines) CDM Point snd ares Sides of areas must lie along grid directions. Single Point Not applicable. (CRSTER) DIFKIN Point and area Areas oriented by fixed grid boundaries. (2) HIWAY Line Line assumed horizontal with arbitrary orientation. (2) RAN Point and area Sides of areas must lie along grid directions. (2) SAX Point and area Areas oriented by fixed grid boundaries. (2) STRAN Point Not applicable. Valley Point and area Area sources assumed oriented with one side parallel to wind direction. (Somewhat less detailed than 2) aNumbars in parentheses refer to treatments of horizontal source location for the appropriate source type as given in Table 5.1 a. bNu ers in parentheses refer to treatments of receptor location as given in Tsble 5.1 a. cNumbars in parentheses refer to treatments of release height for the appropriate source typa as given in Table 5.1 b. Sumbers in parentheses refer to treatments of receptor height as given in Table 5.1 f. 5 Numbers in parentheses refer to treatments of downwindfcroaswind distances for the appropriate source type as given in Table 5.1 c. Numbers in parentheses refer to treatments of source orientation for the appropriate source type as given in Table 5.1 d. ¼RSTER ahould be used only when the receptor is below stack height. ------- B 14 Table B.3. Treatment of Emission Rate by Reference Models Arbitrary line aource amiaaions aggregated onto grid deacribed under source—receptor relationship (Table B.2). Arbitrary off—link grid squares assumed uniform and aggregated to same grid. Area source contributions from grid obtained by numerical integration of narrow plume approximation formulas; contributions calculated from sll upwind sources located within the wedge—shaped grid. (2 for gridded sres sources) Ares sources transformed into polar sress each of which is represented by three effective point sources; shape of ares depends upon angle subtended by ares at each receptor. Totsl area source contribution estimated as a sum of individual contributions. Line sources treated as ten effective points. Areas and lines assumed uniform. (1, modified 4,4 for point, ares, line) Trests “windblown” source as an ares source of TSP with emission rate determined by user input values of type of mstarial, density, saltation diameter. snd suspension diameter appropriate to each source snd the wind speed. (“Windblown” source: modified 4) Point and Arbitrary emission rate for each point and ares ares source. Ares sources assumed uniform. Daily trafic volume for each link and off—link grid square is input and modified to produce hour—by— hour emissions. (Equivalent to 2b) Street canyon submodel: Hourly emission rats for link of interest is input by user. (5) Day/night vsriations in emissions; same vsristion for all sources. (2b) c Single Source (CRSTER) DIFKIN Point Point end ares Area source contributions integrated numaricelly one 22.50 sector at a time, based on ssmpling points located at specific angular and radial intervals on a polar grid centered st receptor (1, 3 for point, ares) Arbitrary emission rate for each source. (1) Emissions treated as upward pollutant fluxes at ground surface. Monthly variation in emission rats sllowed. (3) Sequence of hourly average rates for mobile sources. Individual rats for esch 2 mi x 2 mi grid square: Rates for mobile sources determined from ussr— supplied emission factors and traffic data. Rates for stationary sources input by user. Calculates contributions from grid squares along trajectory. (1, modified 3 for point, ares) Program option allows user to input drcctly ar- bitrary surface pollutant fluxes for up to three pollutants (not necssssrily photochemically re- active). Stationary source rates assumed constant. (1,3) APRAC—lA Line and Raference Model Method of Treatment Source b Geometry Spatial Varistiona Temporal Variation Point, area, and line Arbitrary rate for each point, line and ares source. Constant emission rates. (5) ATM CDM ------- 815 Table 8.3 (Cont’d) Reference I lodel Source Geometry Method of Treatment Spatial Variationa b Temporal Variation HIWAY Line Uniform emiesion rate for each traffic lane. Constant emission rates. (5) Each lane integrated cLacilcally to obtain con- tribution. (3) RAM Point and area Arbitrary emission rate for each point and area source. Constant emission rates. (5) Area source contributions obtained by numerical inte- gration along upwind distance of narrow—plume approxi- mation formulae for eras source with given effective releas,. height. Includes only those areas intersected by the upwind ray. (1 for point; 4,5 for area) SAt Point and area Point source emiasions distributed homogeneously throughout entire vertical column above grid square containing the source; emission rates supplied by user. Other emissions treated as upward pollutant fluxes at ground surface. Sequence of hourly for mobile sources Stationary source constant (1,3) average rates rates assumed Rates for mobile sources determined from user— supplied emission factors and traffic data. Rates for stationary sources input by user. (Mod- ified 1,3 for point, area) STRA t I Point Arbitrary emission rate for each sourcs. (1) Constant emission rstes. (5) Valley Point and area Arbitrary rate for each point and area source. Area sources treated as single effective point sources. Constant emission rates. (5) Total sres source contribution estimated as a sum of individual contributions. (1,4 for point, area) umbers in parentheses refer to treatments of spatial variation as given in Table 5.2. bNumbers in psrentheses refer to tTestments of temporal variation as given in Table 5.2. cC 5TER should be used only when the receptor is below stsck height. ------- Table B.4. Treatment of Composition of Emissions by Reference Models Nethod of Treatment Reference )bdel Chemical Composition Size Distribution APRAC—1A Not applicable; model designed for primary, unreactive Not applicable; model designed for gase,us pollutants. pollutant. ATM Not applicable; model designed for primary, unreactive User inputs single particle size (and density) for use pollutant. in calculating terminal velocity for particulates. Treats three types of sand (uniform, naturally graded, wide size range) and single saltation and suspension diameters (and single density) for windblown sources. ( 4 )b CDM Not applicable; model designed for primary pollutants. Not treated explicitly. (7)1 Sin 1e Sourcec Not applicable; model designed for primary, unreactive Not treated explicitly. (7)1) (CRSTER) pollutant. 0 ’ DIFKINd Treats emissions of CO. NO, and reactive hydrocarbons. Not applicable; model designed for gaseous pollutants. Emissions of NO in inventory assumed to be entirely NO 2 ; converted internally entirely into NO. Hydrocarbons in inventory assumed to be total hydro- carbons; reactive fraction of mobile source hydrocarbon emissions assumed to be 70.4% by weight. Stationary source hydrocarbons assumed to be 100% reactive. ( 4 , 5 )a Program option: User directly input fJ.uxes up to three arbitrary pollutants (for applications not involving photochemical smog). (Not applicable: chemical reaction not treated.) HIWAY Not applicable; model designed to treat primary, unre— Not applicable; model designed for gaseous pollutants. active pollutant. RAM Not applicable; model designed to treat primary, unre— Not treated explicitly. ( 7 )b active pollutant. ------- Table B.4 (Cont’d) aNumbers in parentheses refer to treatments of chemical composition in Table 5.3. bNumbers in parentheses refer to treatments of size distribution in Table 5.3. ccRSTER should be used only when receptor height is below stack height. dDesigned specifically to treat photochemical oxidants. Reference Method of Treatment Model Chemical Composition Size Distribution 1 d Treats emissions of reactive hydrocarbons, unreactive Not applicable; model designed for gaseous pollutants. hydrocarbons, NO, 1402, and CO. User imputs mobile source emissions of hydrocarbons, NOR, and CO. Mobile source hydrocarbon emissions split internally into 67.4% (mole fraction) reactiwe fraction and 32.6% unreactive fraction. Mobile source NOx emissions assumed to be 99% NO 2 ; converted internally to NO. User inputs stationary source (both point and area) emissions of reactive hydrocarbons, unreactive hydro- carbons, NO, 1402 and CO. ( 4 , 5 )a STRM4 Treats two compounds; one is assumed to be 502 the other, sulfate (504). ( 4 )a Not treated explicitly. (7)1 Valley Treats only one compound. Not treated explicitly. ( 7 )b Capable of treating at most one compound or a single representative compound in cases where chemical reactions occur. ( 6 )a I - . ------- B18 Table B.. . Ireatm nt of Plume Rise by Reference Modt.ls Reference Treatment of Model Treatment of Plume Risea Downwash/Fumigation APRAC—lA Not treated explicitly. (5) Does not treat either. For each point source, user inputs a value representing Does not treat either. the product of plume rise with 1) wind speed end 2) the cube root of the wind speed for neutral and stable cond- itions, respectively. Maximum effective stack height limited to 1500 m. (Modified 4b) No plume rise for area and line sources; a constant value could be included in user—supplied release height. (4e,5) Uses “tilted plume” approximation to treat deposition of particulates (see Table 5.13). CDM Briggs’ 2/3 (1971) neutral/unstable formula used for Does not treat either. point sources. If (stsck height) + (plume rise) exceeds mixing height, ground level concentrations are assumed equal to zero. (Modified 4a) Aa an alternative to Brigge’, the user may input a value of the product of plume rise and wind speed for each point source. (Alternative : 4e) No plume rise calculated for area sources; a constant value could be included in user—supplied release height. (4e,5) Single sourceb Rriggs’ (1971, 1972) final plume rise formulas; plume rise Does not treat either. (C aSTER) not treated as a function of downwind distance. If plume height exceeds mixing height, concentrations further downwind assumed equal to zero. (4a) DIFKIN Not treated explicitly. (5) Does not treat either. HIWAT Not treated explicitly but could be included in release Does not treat either. height. (4e,5) RAN Uses Briggs’ (1971, 1972) downwind distance dependent Does not treat either. plume rise formulse for point sources. If plume height exceeds mixing height, ground level concentrations assumed zero. (Modified 4s) No plume rise calculated for sres sources; could be included in release height. (4e,5) SkI Uses Briggs’ formulae (1971) for point sources (power Does not treat either. plants only) to determine if plume penetrates inversion. If plume height exceeds mixing height, emissions from source are not treated. Other power plant emissions included in ground level flux. (4a) Treats emissions as ground level fluxes; plume rise not treated explicitly. (5) STRA t I Not treated explicitly; could be included in release Does not treat either. height for each source. (4e,5) Valley Uses Briggs’ (1971, 1972) plume rise formulae for Does not treat eithsr. both point end eres sources. Option: A single constant plume rise value may be input for any or all sources. (OptionS 4e) If plume height exceeds mixing height: A. For long—term calculations, ground level concentra- tions assumed equal to zero. B. For short—term calculations, maximum plume height is llzsited to the mixing height. (Modified 4a) aNumbers in parentheses refer to treatments as given in Table 5.4. bCRSTER should be used only if receptor height is below stack height. ------- Table B.6. Treatment of Horizontal Wind Field by Reference Models Reference Model Method of Treatmenta APRAC— 1A Constant, uniform wind speed and direction assumed for each of a sequence of hours. Wind speed, direction values input by user. (4,7,2) Street canyon sub—model: specific positional and height dependence built in; constant in time. (3,5,4) ATM Constant, uniform wind speed and direction. Climatological treatment with sixteen wind sectors, S wind speed classes used. (4,7,3) CDM Constant, uniform wind speed and direction. Wind speed is estimated value at release height, correction from value at reference height (1Gm) dependent only on stability class. Climatological treatment with sixteen wind sectors, 6 wind speed classes used. (4,6,3) Single sourceb Constant, uniform wind speed and direction assumed for each of a sequence of hours. (CRSTER) Wind speed, direction values input by user;c speed corrected for release height depend— ing on stability class. (4,7,2b) DIFKIN Trajectory model. Wind speed and direction specified for each of a sequence of time steps at point on a horizontal grid, interpolated from nearest 1, 2, or 3 surface measurements. Discrete user—specified number (n) of wind directions allowed, 4< n <99 Arbitrary wind speed values allowed. Wind speed, direction independent of height. (2,7,2b) Program option allows direct user input of trajectory. HIWAY Constant, uniform wind speed and direction. Wind speed, direction values input by user for the hour of interest. (4,7,4) RAM Constant, uniform wind speed and direction assumed for each of a sequence of hours. Wind speed, direction values input by user.c Wind speed is modified to correspond to value at release height, modification dependent only on stability class. (4, modified 6,2b) SA l Fixed grid model. Wind speed and direction specified for each of a sequence of hours at point on a horizontal grid, interpolated from surface measurements. Arbitrary wind speed, direction values allowed. Wind speed, direction independent of height. (2,7,2b) ------- Table B.6 (Cont’d) Reference Model Method of Treatmenta STRM4 Trajectory model. Wind speed and direction specified at 12—hour intervals on a horizontal grid, inter- polated from radiosonde measurements. Wind speed and direction interpolated in time between measurements. Arbitrary wind speed, direction values allowed. Wind speed, direction independent of height. (2,7,2a) Valley 1. Long—term calculations: Constant, uniform wind speed and direction. Climatological treatment with sixteen wind sectors, 6 wind speed classes. Wind speed class values input by user, used without correction for height. (4,7,3) C ’ 2. Short term calculations (24—hour maximum only): User—defined direction used. Wind speed assumed 2.5 rn/sec . with persistence of 6 hours out of 24. Stable conditions in complex terrain with receptors at or above plume centerline: Implicit treatment of locational and height dependences — effect of plume deflection by terrain accounted for by linear interpolation of centerline concentration values between the lOm value at point of impingement and zero at 400m above point of impingement. (6,8,5) Stable conditions with receptor below plume centerline: Uniform wind direction assumed. (4,7,5) Does not treat neutral or unstable conditions. aNumbers in parentheses refer to the dependence on horizontal location, height above ground, and tine as given in Table 5.5. bCRSTER should be used only if the receptor height is less than the stack height. cAssumes wind directions given to nearest 10°, randomizes wind direction by addition of the amount (n—4) 0 where n is a random number between 0 and 9. ------- Table B.7. Treatment of Vertical Wind Field by Reference Models Reference a Model Method of Treatment APRAC—lA Assumed equal to zero. (4b,4b,3) Street canyon sub-model: specific positional and height dependence built in, assumed constant in time. (3,3,3) ATM Assumed equal to zero. (4b,4b,3) CDM Assumed equal to zero. (4b,4b,3) Single sourceb Assumed equal to zero. (4b,4b,3) (CRSTER) DIFKIN Assumed equal to zero. (4b,4b,3) HIWAY Assumed equal to zero. (4b,4b,3) I . ’ , RAM Assumed equal to zero. (4b,4b,3) SAT Vertical wind speed specified for each of a sequence of hours at points on a three—dimensional grid. Values assumed linearly increasing functions of height, values near surface determined from horizontal wind speed and directions using mass consistency requirements. (2 ,3,2b) STRA]4 Assumed equal to zero. (4b,4b,3) Valley 1. Long—term calculations: Assumed equal to zero for stable atmospheric conditions. (4b,4b,3) Implicit treatment for neutral and unstable conditions: plume assumed to remain at a constant height above terrain. No time dependence. (4a,4a,3) 2. Short—term calculations (24—hour maximum only): as in long—term calcula- tions for stable conditions. (4b,4b,3) Does not treat neutral or unstable conditions. awumbers in parentheses refer to the dependence on horizontal location, height above ground, and time as given in Table 5.6. bCRSTER should be used only if the receptor is Less than the stack height. ------- B 22 Table B.8. Treatment of Horizontal Dispersion by Reference Models Reference Model classification Method of Treatment APRAC— 1A Semiempirical /sequentisi Sector averaging (narrow plume approximation) (steady—state) 45.00 less than 1 km. 22.5° beyond 1 km. Atmospheric stability not treated explicitly. Surface roughness not treated explicitly. (4b,3,3 ,na)a ATM Semiempirical/climatological Uniform horizontal distribution assumed within each of 16 (steady—state) 22.50 sectors (sector avereging). Atmospheric stability not treated explicitly. Surface roughness not treated explicitly. Averaging time assumed long enough for sector averaging to be valid. (Sc,3,2a,na)a CDM Semiempirical/climatologicel Uniform horizontal distribution assumed within eech of 16 (steady—state) 22.5° sectors (sactor averaging). Atmospheric stability not treated explicitly. Surface roughness not treated explicitly. Averaging time assumed long enough for sector averaging to be valid. (Sc,3,3,ns) 5 Single Sourcet Semiempirical/sequential Gaussian plume function assumed. CCRSTER) (steady—state) Atmospheric stability divided into seven classes. Surface roughness not explicitly treated. One hour averaging tine used. (4a, 2 b, 3 ,3)a DIPKIN Numerical Cvertical)/ Narrow plume approximation about calculated trajectory. Semiempirical (3c ,3,3 ,na)a (horizontal) /dynami c HIWAY Semiempirica1/ ’ r .cady—state Gaussian plume function assumed for each point along line; numerical integration along line. Atmospheric stability divided into six (Paaquill—Gif ford) classes. Dispersion coefficients from Zimmerman and Thompson (1975) less than lOOm, from Turner (1969) beyond lOOm. Level grade mode — initial value of dispersion coefficient set at 3.0 m. Cut section mode — initial value of dispersion coefficient an empirical function of wind speed. Surface roughness not treated explicitly. One hour averaging time used. (4a,2b.3,3) 5 RA I l Semiempirical/sequentisi Gaussian plume function assumed. (steady—state) Atmospheric stability divided into six (Pasquill—Gif ford) classea. Dispersion coefficients from Turner (1969) or McElroy and Pooler (1968) at user option. Surface roughness not treated explicitly. One hour averaging time used. Point sources: (4a,2b ,3,3) 5 ; Area sources: (4b,3,3,ne) 5 ------- B23 Table B.8 (Conttd) Reference Model Classification Method of Treatment SA l Numerical/dynaaic Numerical solution of advection—diffusion equation in three dimensions. Horizontal eddy diffusivity value assumed uniform and constant and is fixed in the code. (lb,3,3,3)a.(4.4,3)b STR.AM Semiempirical/dynamic Crosswind distribution about calculated trajectory assumed Gaussian. Atmospheric stability divided into six (Paaquill—Gifford) classes. Same atability claaa assuned to hold over entire region of interest. Surface roughness not treated explicitly. Diapersion coefficianta determined by integration of expres— eiona for ratee of change; based on Turner (1969) up to bObs, Heffter and Ferber (1975) beyond 100 km. Averaging time specified by user. (3b,2b,3,3 and S) Valley Semiempirical/climatological Long—term calculations: (steady—state) Uniform horizontal diatribution assumed within each of 16 22.50 sectors (sector averaging). Atmospheric stability not treated explicitly. Surface roughness not treated explicitly. Averaging time assumsd long enough for sector averaging to be valid. (5c,3,3,na)a Semiempirical/steady—state Short—term calculations (24—hour maximum only): Uniform horizontal distribution assumed within each of 16 22.5° sectors (sector averaging). Atmospheric stability not treated explicitly. Surface roughness not treated explicitly. Averaging time: 24 hours. (Sc,3 ,3,na)a LiNumbars in parentheses refer to treatments listed in Tables 5.7, 5.8, 5.9 and 5.10 respectively. The user should refer to the appropriate aection (numerical or samiempirical) of Table 5.10 according to the modal classification. bNumbera in parentheses refer to the dependence of the horizontal eddy diffusivity on horizontal location, height above ground. and time as given in Table 5.11. c CRZTER should be used only when the receptor is below stack height. ------- B24 Table B 9. TrcaL ,iient of Vertical Dis’ rsion by Reference Mo’kls ReferenLe Model Clasalfication Method of Treatment APRAC— 1A Semiempirical /sequential Gaussian plume function assumed. (steady—state) Atmospheric stability divided into six (modified Pasquill—Gifford) classes. Dispersion coefficient modif ted from McElroy and Pooler (1968). Surface roughness not treated explicitly. Downwind distance dependence of dispersion coefficient assumed axb for purposes of doing analytic integration. In street—canyon submodel, semiempirical function of wind speed, street width, and direction is used. (4a, Zb,3,3) 5 ATM Semiempirical/climatological Gaussian plume function assumed. (steady—state) Atnoapheric stability divided into six (Pasquill— Gifford) classes. Dispersion coefficients from Turner (1969) or Hosker (1973). (user option). Surface roughness characterized by a user—specified roughness parameter (Hosker dispersion coefficients only) (4a,2b,2a,3)a CDM Semiempirical/climatological Gaussian plume function assumed. (steady—state) Atmospheric stability divided into six (Pasquill— Gifford) classes, with neutral stability divided into day and night cases. Stability class decreased by one class (more unstable) for area sources. Surface roughness not treated explicitly. Dispersion coefficients from Turner (1969). (4a,2a,3,3) 5 Single Sourcec Semiempirical/sequentisl Gaussian plume function assumed. (cRSTER) (steady—state) Atmospheric stability divided into seven (P—G) classes. Surface roughness not treated explicitly. Dispersion coefficients from Turner (1969). (4a,2b,3,3)a DIFKIN Numericai (verticsl)f Numerical integration of diffusion equation in Seniempirical (horizontal)f vertical direction. drtamic Vertical eddy diffusivity values specified hourly by user at user—defined discrete heights above ground. (lb,Za,3,2)a, (4,3,2b)b RIVA l Semiempirical/steady—state Gaussian plume func ion assumed. Atmospheric stability divided into six (Pasquill— Gifford) classes. Dispersion coefficient from Zimmerman and Thompson (1975) less than lOOm, from Turner (1969) beyond lOOm. Level grade mode — initial dispersion coefficient set at l.5m. Cut section mode — initial dispersion coefficient an empirical function of wind speed. (4a,2b,3,3)a ------- F2 Table 1’. J (Coot’d.) Reference Model Classification Method of Treatment RAN Semiempirical/sequential Gaussian plume function assumed. (steady—state) Atmospheric stability divided into six (Pasquill— Gifford) classes. Dispersion coefficients from Turner (1969) or McElroy and Pooler (1968) at user’s option. Surface roujhnssa not treated explicitly. (4a.ab,3.3Ya SAl Numerical/dynamic Numerical solution of advection—diffusion equation in three dimensions. Vertical eddy diffusivity an empirical function of wind speed and height above ground. (lb,3,3.2) 5 , ( 4 ,S, 2 b)b STRAM Semiempirical/dyneetic Two options are available to the user: 1) Gaussian plume function assumed. Atmospheric stsbility divided into six (Pasquill— Gifford) classes. Same stability class assumed to hold over entire region of interest. Surface roughness not treated explicitly. Dispersion coefficients determined by integration of expressions for rates of change; based on Turner (1969) up to 100 kit, Beffter and Ferber (1975) beyond 100 km. 2) Uniform vertical distribution up to mixing height assumed. (3b or 3d,2b,3,3)a Vslleye Semiempiricel/climetological Long—term calculations: (steady—state) Gaussian plume function assumed. Atmospheric stability divided into six (Pasquill— Gif ford) classes. Surface roughness not treated explicitly. Dispersion coefficients fron turner (1969). (4a,2b, 33 )S Semiempirical/steady—atste Short—term calculations (24—hour maximum only): Gaussian plume function assumed. One stability class (stable Pasquill—Gif ford “F”) used. Surface roughness not treated explicitly. Dispersion coefficients from Turner (1969). (4a,2c,3,3)a aNumbers in parentheses refer to treatments listed in Tables 5.7, 5.8, 5.9 and 5.10, respectively, The user should refer to the appropriate section (Numerical or Semiempirical) of Table 5.10 according to the model classification. bNnmbers in parentheses refer to the dependence of the vertical eddy diffusivity on horizontal location, height above ground and time is given in Table 5.11. CCRSTER should be used only when the receptor is below stack height. ------- B2’ rable B.1() Treatment of Chemistry and Reaction Mechanism by Refsrcnce Models Reference a Models Method of Treatment APRAC—lA Not treated explicitly. (7) ATM Not treated explicitly. (7) CDM Treats only first—order removal processes: exponential decay. Single, constant user—supplied halflife used. (6) Single Source 1 ’ Not treated explicitly. (7) (CRSTER) DIFRIN Photochemical smog system: (4) Sixteen reactions involving 10 chemical species (NO, Hc, NO 2 03, HNO 2 , NO 3 , N20 5 , OH, R02, CO). Lumping approximation for 2 species (Hc, R0 2 ). Steady—state approximation for 4 species (NO 3 , N 2 0 5 , OH, R0 2 ). User specifies NO 2 photolysis rate constant as function of time (up to 300 sequential values). No adjustment made for effects of imconplete turbulent mixing below the resolution of the grid. Program option allows user to prescribe arbitrary chemical reaction mechanism (up to 20 chemical species, up to 20 reactions). HIWAY Not treated explicitly. (7) R AN Treats only first—order removal process: exponential decay. Single, constant user—supplied half life used. (6) SA l Photochemical smog system: (4) Fifteen reactions involving 10 species (NO, NO 2 , Oj, Mc, 0, OH, 1102, R0 2 , NO 3 , 1*102). Lumping approximation for 2 species ( Mc, RO 2 ). Steady—state approximation for 6 species (NO 3 , 0, RO , OH, HO 2 , HNO 2 ). NO 2 photolysis rate calculated internally as a function of time. No adjustments made for the effects of incomplete turbulent mixing below the resolution of the grid. STRAM 5O 2 —sulfate aerosol system: SO 2 to sulfate conversion approximated by a first—order process with internally defined value of the rate constant. (6) Valley Treats only first—order removal processes: exponential decay. Single, constant user—supplied halflife used. (6) a Numbers in parentheses refer to treatment numbers in Table 5.12. 1’ CRESTER should be used only if receptor height is less than stack height. ------- ‘r?tbis li i. ‘ircatmiant f Ph’si al Itemoval Processes t’, kefetence Models Reference Model Method of Treatment APRAC—]A Not treated explicitly. (415) ATM Dry deposition : (2a)b Pollutant removal simulated by effective source treatment. Multiplicative factor determined by downwind integration of removal rate. Rate of removal determined from ground—level pollutant concentration and a constant deposition velocity. Deposition velocity (gases) adjusted within internally defined range of values by user—supplied measure of surface roughness, related to extent and type of vegetation cover. Effect of atmospheric stability not treated explicitly. ( . 1 Deposition velocity (particulate matter) is the greater of the gravitational settling velocity or 0.01 rn/sec. Tilted plume approximation used for particulate matter if gravitational settling velocity is greater than 0.01 rn/sec. (3)b Effect on vertical concentration profile not treated explicitly except in tilted plume case. Precipitation scavenging : ( 2 )c Exponential decay with constant washout coefficient. Removal occurs only for fraction of time equal to frequency of occurrence of rainfall (input by user); not correlated with any other meteorological variables. Washout coefficient calculated imtermally from user supplied mean rainfall rate. CDM Treats only first—order removal processes; exponential decay. Single, constant user—supplied halflife used. (2b,5)a Single Source ’ Not treated explicitly. (4, 5 )a (CRSTER) D IPKIN Not treated explicitly. ( 4 ,s)a ------- 1MI1L 5.11 (Cont’d) Reference Model Method of Treatment RIWAY Not treated explicitly. ( 4 , 5 )a RAM Treats only first—order removal processes: exponential decay. Single, constant user—supplied halflife used. (2b .5)a SA l Not treated explicitly. (4,s)a STRAM Dry deposition : (2a)b Pollutant removal simulated by effective source treatment. Multiplicative factor determined by downwind integration of removal rate. Rate of removal determined from ground—level pollutant concentration and constant deposition velocity. Deposition velocities for SO 2 , sulfate aerosol are fixed in the program at 1.0 and 0.1 cm/sec., respectively. Effects of surface roughness or atmospheric stability not treated explicitly. Effects on vertical concentration profile not treated explicitly. Precipitation scavenging : (S) Not treated explicitly. Valley Treats only first—order removal processes: exponential decay. Single, constant user—supplied halflife used. (2b,5)a aFirst number refers to treatments of dry deposition in Table 5.13, second number refers to treatments of precipitation scavenging in Table 5.13. bNumbers refers to treatments of dry deposition in Table 5.13. cNumbers refers to treatments, of precipitation scavenging in Table 5.13. dCRSTER should be used only if receptor height is less than stack height. ------- Table B 0 i2, raatment of Lackgrouitd, P.jund r’ nd Initial Conditions by Reference Models a. Backgrounda Reference Model Classification Method of Treatment APRAC—1A Semiempirical/sequential Value calculated for each receptor; box model used to estimate contributions from upwind (steady—state) sources beyond 32 km based on wind speed, mixing height and annual fuel consumption. (2) in street csnyon sub—model, contribution from other streets is included in the back- ground. (2) Semiempiricel/climatological Not treated explicitly. (3) (steady—state) CDM Semiempirical/climatological Single constant input values for each pollutant. (2) (steady—state) Single Source g Semiempirical/sequential Not treated explicitly. (3) (CKSTER) (steady—state) DIFKIN Numerical (vertical)/ Not applicable. Semiempirical (horizontal) /dvnamic RIWAY Semieepirical/ateady—state Not treated explicitly. (3) 0 RAM Semiempirical/sequential Not treated explicitly. (3) (steady—state) SA l Numerical/dynamic (Treated as a boundary condition on flux at vertical boundanea.) STRA It Seieiempirical/dynasaic Not treated explicitly. (4) Valley Semiempirical/climatological Long—ten calculations. Not treated explicitly. (3) (steady—state) Semiempirical/steady—state Short—term calculations (24—hour maximum only). Not treated explicitly. (3) b. Upper Boundary Condition (at Mixing Height)b APRAC—lA Semiempirical/sequential Perfect reflection: ignores effect until concentration equals that calculated using box (steady—state) model; usea box model (uniform vertical distribution) thereafter. (intermediate between 2—3) Mixing height determined from morning radiosonde data and during day, surface temperature variations Midnight to dawn: constant at ore—dawn value obtained uaine minimum urban temperature; Dawn to sunset: afternoon maximum temperature used to obtain maximum height; hourly values obtained from surface temperature variations; Sunaet to midnight: linear interpolatinn over time. ------- Table B.lz (C.nt’d) b. (Cont’d) Reference Model Classifications Method of Treatment ATh Semiempirical/cllmatological Treated implicitly by limiting vertical disperaion coefficient to be no larger than (steady—atate) mixing height. (4) CON Semiempirical/climatological Perfect reflection: no effect until vertical disperaion coefficient equala 0.8 of (ateady—atate) the mixing height, uniform vertical mixing assumed thereafter. (2) Single Semiempirical/aequential Perfect reflectionS method of multiple images trested by summation of aeriea until (CRSmR) (steady—state) vertical dispersion coefficient = l. 6 x (mixing height), uniforn vertical mixing thereafter. (1) Mixing height for a given hour obtained by interpolation of radiosonde data (see Appendir 8.4 for algorithm). DIFICIN Numerical (vercical)/ Perfect reflectionS flux required to be equal to zero at boundary. (3) Seniempirical Mixing height can change at hourly intervals. (horizontal) /dynamic HIWAY Semiempirical/steady—state Perfect reflection: 1) Stable conditions or mixing height greater than 500Dm. assume no effect (treats only reflection from ground); (3) 2) Neutral or unstable conditions with mixing height less than 500Dm: method of multiple imagee treated by aununation of infinite aeriea until vertical dispersion coefficient > 1.6 x (mixing height), uniform vertical distribution thereafter (1) RAM Semiempirical/sequential Perfect reflectionS (steady—state) 1) Neutral and unstable conditions method of multinle images treated by summation of infinite series until l.6x (mixing height); uniform mixing assumed thereafter; (1) 2) Stable conditions: mixing height sasumed to have no effect. (3) Mixing height for a given hour obtained interpolation of radiosonde data (see Appendix 8.8 for algorithm). SA l Numerical/dynamic Perfect reflection for pollutants within region of interest (turbulent diffusive flux = 0). Allows for entrainment of pollutants from above mixing layer (1) STRAM Semiempirical/dynam]c Two options. 1) Uniform mixing (perfect reflection) (4) or 2) Mixing height assumed to have no effect. (3) Valley Semiempirical/climatological Perfect reflection: (eteady—state) and 1) Neutral and unstable conditions perfect reflection; method of multiple images Semiempiricsl/steady—state treated by summation of infinite series; (1) 2) Stsble conditions: ignores effect of upper boundary. (3) ------- Table L.12 (Cont’d) c. Lower Boundary Condition (at Earth’s Surface)c Reference Model Classification Method of Treatti ent APRAC— 1A Semiempirical/sequentitl Perfect reflection; single image source. (Intermediate between 3—4). (steady—state) ATM Semienpirical/climatological Perfect reflection; single image source. (4) (steady—state) ON Semiempirical/climatological Perfect reflection; single image sourcei (3) (steady—state) Single sourceg Semiempirical/sequential Perfect reflection in plane at same height as receptor; multiple Image sources. (2) (CRSTER) (steady—state) DIflIN Numerical/ (vertical) I Emissions treated as upward fluxes at the ground. (horizontal)/ Implicit perfect reflection; no adjustment made to fluxes to account for removal. (3) HIWAT Semiempirical/steady—state Perfect reflection by method of multiple images. (2) RAM Semiempirical/sequential Perfect reflection by method of multiple images. (2) (steady—state) F-’ SA l Numerical/dynamic All non—point source (power plant) emissions treated at upward fluxes at ground. Implicit perfect reflection; no adjustment made to fluxes to account for removal. (3) STR.AM Semiempirical/dynamic Perfect reflection by method of single image source. (4) Valley Semiempirical/climatological Perfect reflection by method of multiple images in stable cases and single image source (steady—state) and in neutral and unstable casesJ (stable: 4; other: 2). Semiempiricalf steady—state d. Boundary Condition at Vertical Sidesd APRAC—lA Semienpirical/sequential Not applicable; treated as background. (steady—state) A T M Semiempirical/climatological Not applicable; treated as background. (steady—state) CM Semiempirical/climatological Not applicable; treated as background. (steady—state) Single gour Semiempirical/sequential Not applicable; treated as background. (CRSTER) (steady—state) ------- 1.? (Je_Lt ‘‘ d (Cont’d) Reference Model Classification Method of Treatment DIFKIN Numerical (vertical)! Not treated explicitly, horizontal uniformity assumed (5) Semiempirical (horizontal)! dynamic HIWAY Sesiempirical/ateady—atate Not applicable, treated aa background. RAM Semiempirical/sequential Not applicable, treated as background. (steady—state) SA l Numerical/dynamic Treated as a function of position and elevation, total flux normal to aide of region required to be continuoua across boundary at each point. (1) STRA}1 Semiempirical /dynamic Not applicable, treated as background Valley Semiempirical/climatological Not applicable, treated as background. (steady—state) and Semiempirical/steady _stete e. Initial Conditionee APRAC-lA Semiempirical/sequential Not applicable (steady-state) ATM Semiempirical/climatological Not applicable. (steady—state) COP ! Semiempirical/clinatologicsl Nor applicable. (steady—state) Single Sourceg Semiempirical/sequential Not applicable (CRSTER) (steady—state) DIFKIN Numerical (vertjcal)/ User specifies arbitrary initial concentrations for all specios not treated by steady—state Semiempirical (horizontal)/ assumption (all but NO 3 , N 2 0 5 , R0 2 , OH st each discrete height above ground (1) dynamic HIWAY Semiempiricsl/stesdy—stste Not applicable. RAN Semieepiricsl/sequentssl Not applicable (steady—state) SAl Nusericsl/dynamic Mean initial concentrations of 6 species (reactive HC, NO, 03, NO 2 , CO, unresctive He) specific for each grid cell. (1) STRAP! Semiempirical/dynsmic Not applicable Valley Semiempirical/climatological Not applicable (steady—state) and Semiesipirical/steady state ------- Table B.l2 (Cont’d) aNumbers in parentheses refer to treatments of background given in Table 5.l4a for models having the same classification as the reference model. bNumbers in parentheses refer to treatments of the upper boundary condition (at the mixing height) given in Table 5.l4b for models having the same classification as the reference model. cNumbers in parentheses refer to treatments of the lower boundary condition (at the earth’s surface) given in Table 5.l4c for models having the same classification as the reference model. dNumbers in parentheses refer to treatments of the boundary condition at vertical sides given in Table 5.l4d for models having the same classification as the reference model. eNumbers in parentheses refer to treatments of initial conditions given in Table 5.l4e for models having the same classification as the reference model. see also the description of the treatment of the upper boundary condition. CRSTER should be used only when the receptor height is below the stack height. ------- B 34 Table B.l3 Treatment of Temporal Correlations by Reference Models DIBRIN Sequentia] treatment up to 24 hours; correlations automatic. RIWAY Not appliceble. S A l Sequential treatnept up to 24 hours; correlations automatic. ST RM I Sequential treetment; cor- relations automatic for meteorological variables. Emissions a function of hour of the day snd day of the week. Wind speed, direction, stability and mixing height are func- tions of hour of the day. (la) Wind speed, wind direction, stability correlated via atabili— ity wind rose. Emiaeion rates constant, not corralated with other parameters. Mixing height correlated with atabilit ). class through limits on 0 m. different limit for each cleas. (2b) Wind speed, wind direction, atabit3ty correlated via stability wind rose. Mixing height adjusted according to stability class: Class A——l.5 x (afternoon climatoLogical value). Cleaa 0 (ni ht)-—average of morning and afternoon ciinato— logical values. Class B——Morning clliaatological value. Class B, c, D (day)——Appropriate climatological value. Emiaaion rater day—night veriationa allowed; all sources vary by same factor. (2b) User supplies hourly values of wind speed, wind direction, mixing height, and other meteorological variables required for determining stability class and plume rise. Monthly emiasion variation allows limited emission—meteorology correlations. (lc) Parameters updated each hour: mobile estisaiona from each grid square, wind speed and direction (trajectory); vertical diffusivity values at each height, mixing height, NO 2 phota— lyaie rate constant. Update based on user input values. (lb) Not applicable; user inputs specific parameter valuea for the hour of interest. User supplies hourly values of wind speed, wind direction, mixing height, and other meteorological variables required for determination of stability class and plume rise. Emission ratea constant, not correlated with other parameters. ( Ic ) Parameters updstei every hour: mobile aource emission for each ground—level grid square, point source (power plant) emissions, wind speed end direction, mixing height at every vertical column of grids, varrical eddy diffumivity at every vertical interface of grid cella, incoming fluxes at bound— ariea, 502 photalysie rate constant. Update based on user input values. (la) Stability class end mixing height changed each hour based on user—input values. Horizontal components of windfield updated at 12 hour inter- vals based om radioaonde date; changed eech hour by inter- polation between updates. Emission rates conatant; not correlated with other parameters. ( Ic) APRAC— 1A geference Degree Model Type of Treatment and of Temporal Resolution Quantitiea Correlatede Sequential; correlations automatic. ATM Non—sequential (clinatolog— icel) ; limited correlation between some meteorological parameters. CDM Non- equential (clinatolog— icai). limited correlation between total emission rate and meteorological parameters. Single Source ’ Sequential, correlations (CRSTER) automatic for meteorological parameters. RAM Sequential treatment; cor- relations automatic for meteorological parameters. Valley Non—aequential (climatolog— icel); limited correlation for meteorological variables. Wind speed, direction, atability correlated vie stability wind rose. Emisafon rates constant; not correlated with other parameters. Mixing height adjusted according to stability class (2b) thong—term mode Class D (night)——0.5 x (afternoon climatological value). Stnble classes—-Mixing height not cotaidared. Class A, B, C—Appropriate cliisatological value; •Short—ten mode—input value ignored, only F atability considered. 5 Nuzabera in parentheses refer to treatment numbers in Table 5.15. should be used only when receptor height is below stack height. ------- B35 B.2. REFERENCE MODEL ABSTRACTS AND EQUATIONS This appendix provides abstracts and working equations for each of the reference models used in this workbook. A glossary of symbols is given at the end of this appendix. ------- B36 ------- 837 8.2.1 CD ) ! Reference : Busse and Zimmerman (1973), Brubaker, et. al. (1977). Abstract : The Climatological Dispersion Model (CDM) is a clitnatological steady— state Gaussian plume model for determining long—term (seasonal or annual) arithmetic average pollutant concentrations at any ground level receptor in an urban area. A statistical model based on Larsen (1968) is used to transform the average concentration data from a limited number of receptors into expected geometric mean and maximum concentration values for several different averaging times. Equations : N 6 6 = 2 L l m ]. ‘ ¼&m S jp)/P Xarea = tl 2l ltPin S (ø)] dp with = JQ( p ,e)de Sector k exp [ -4 (f) 2 ]ex [ _o.692o] for a ------- B 38 B.2.2 R.A}1 Reference : Hrenko and Turner (1975). Abstract : RAM is a steady state Gaussian plume model for estimating concen- trations of relatively stable pollutants for averaging times from an hour to a day in urban areas from point and area sourc9s. Level or gently rolling terrain is assumed. Calculations are performe for each hour. Equations : Contribution from single upwind area source x XA 2 f dx, integral evaluated numerically xl x 1 , x 2 = points of intersection of ray from receptor through area source in question. Stable conditions: f = — ___ — 2rrua a g 1 g 2 yz Neutral or stable conditions with a < l.6L z — = = 2rruaa g 1 g 3 Neutral or unstable conditions with a > l.6L z 1 L — ____ - 12 uLa y In which 2 Fly = exp L y ------- B39 2. 2 I 1 z—H I I 1 z+H + exP [ - - z z 2 2 ° r 1 z-H+2nL I 1 z+H+2nL g 3 = te L_ + exP [ z z Mixing Height Algorithm : Two different mixing heights can be calculated. One is for basically rural surroundings; the other is for urban locations. The user is given the option to specify which he wants to use. The way in which hourly mixing heights are determined from maximum mixing heights (MXDP) for yesterday (i—i), today (i) and tomorrow (i+1) and minimum mixing height (MNDP) for today (i) and tomorrow (i+l) is depicted in Figure B.l. For urban mixing height, between midnight and sunrise; if the stability is neutral interpolate between NXDP 1 _ 1 and MXDP. (i’), if stability is stable use MNDP. (s). For hours between sunrise and 1400, if the hour before sunrise was neutral, interpolate between MXDP _ 1 and MXDP. For sunrise to 1400, if the hour before sunrise was stable, interpolate between MNDP. and MXDP. (i). For 1400 to sunset, use MXDPj For hours between sunset and midnight; if stability is neutral interpolate between MXDP and DP + 1 ( , if stability is stable interpolate between MXDP. and MNDP 7 1 1+1 For rural mixing height between midnight and sunrise, interpolate between MXDP 11 and MXDP . For hours between sunrise and 1400, if the hour before sunrise was neutral interpolate between MXDP 1 _ 1 and MXDP ( . For sunrise to 1400, if the hour before sunrise was stable, interpolate between 0 and MXDP. . For 1400 to sunset, use MXDP. . For sunset to midnight, interpolate between MXDP. and MXDP.+i ------- (a) URBAN TODAY I 0 MXDP 1 - I (b) RURAL I I ® I I / I v _1 - MIDNIGHT S U FIR IS E I 400 TIME TOMORROW I I S... 5 S.... • • •• •• • SI SI ••s ‘ ‘ NEUTRAL —— STABLE I — BOTH MXDP I+ I I SUNSET MIDNIGHT YESTERDAY MXDP ... 1 Li.I x F- I -, U i = MXDP _ C, ‘C C Figure B.1. Mixing Height Algorithm Used in RAM ------- B43 B.2.3 Single Source (CRSTER) Reference : EPA (1977). Abstract : S ngJe Sourc : (CRSTER) is a sce—-ly state Gaussian plume technique applicable where terrain elevation does not exceed physic i stack h ht. The purposes of the technique are: 1) to determine the maximum 24—hout concen- tration from a single point source of up to 19 stacks for one year, 2) to de- termine the meteorological conditions which cause the maximum concentrations, and 3) to store concentration information useful in calculating frequency distributions for various averaging times. The concentration for each hour of the year is calculated and midnight—to—midnight averages are determined for each 24—hour period. Equations : X = 2irucjcy g 1 g 3 for y < l.6L x g fora >l.6L 2iruLG 1 z x 0 (stability class 7) L constant, independent of downwind distance D = (stack height + plume rise) — (difference in elevation between receptc r and base of stack) ex [ _ 4 2] g3 exp (2nL D)2] + exp [ (2nL÷D)2]} Mixing Height Algorithm : Two different mixing heights can be calc.lated. One is for basically rural surroundings, the other is for urban locations. The user is given the option to specify which he wants to use. The way in which hourly mixing heights are determined from maximum mixing heights (MXI)P) for yesterday (i-i), today Ci) and tomorrow (i+l) and mimimum mixing height (MNDP) for today (i) and tomorrow (1+1) is depicted in Figure B.2. ------- B42 For urban mixing height between midnight and sunrise; if the stability is neutral interpolate between MXDP. and MXDP.(?J, if stability is stable use MNDP 1 For hours between sunrise and 1400, if the hour before sunrise was neutral, interpolate between MXDP _ 1 and MXDP ( . For sunrise to 1400, if the hour before sunrise was stable, interpolate between MNDP. and MXDP. 4 . For 1400 to sunset, use MXDP 5 1 1 1 For hours between sunset and midnight; if stability is neutral interpolate between MXDP. and NXDPI+i ( , if stability is stable interpolate between MXDP. and MNDP 7 1 1+1 For rural mixing height between midnight and sunrise, interpolate between MXDP 1 1 and NXDP 1 (j. For hours between sunrise and 1400, if the hour before sunrise was neutral interpolate between MXDP 1 _ 1 and NXDP For sunrise to 1400, if the hour before sunrise was stable, interpolate between 0 and MXDP 1 . For 1400 to sunset, use MXDP 1 © For sunset to midnight, interpolate between MXDP 1 and MXDPi+l ------- (a) URBAN YESTERDAY MXDP 1 ..., 1 MXDP _ 1 TODAY I ..... MXDP —Q- ® —-. MNDP _________________ I I (b) RURAL 1 ® I I / I I, MIDNIGHT SUIRISE 1400 TIME TOMORROW I •. •. MXDP 1 ÷i •••‘• ••‘ NEUTRAL —— STABLE — BOTH MXDP 1 +, SUNSET MIDNIGHT w I — = I ., x Figure B..2, MLxi.; g Heigh Algorithm Used in CRSTER ------- B44 B.2.4. Valley Reference : Burt (1977), Abstract : Valley is a climatological, Gaussian model whose primary intended use is the estimation of the maximum 24—hour SO 2 and TSP concentrations from single facilities in complex terrain, although annual average SO 2 and TSP con- centrations may also be estimated in flat terrain applications. Equations : Long—term calculations: N 6 = I ,m with as follows: n=l m1 n Neutral or unstable conditions — 16 1 °. 693 P X —g expi— fl n m 2irp u L u T½ 1 [ 1 1 2iL—H 1 1 1 2iL+H g 3 = i i [ exp [ j + exp [ - a for . 2L g forcr >2L L z X =OifH>L. nR,m Stable conditions — 16 Q 1 r 1 H 21 1 °1 693 1)n Xn m = 2 n i exp L - exp [ u T½ Define D = (stack height + plume rise) — (receptor elevation) if 0 > 10 meters, set H D if D < 10 meters, set H = 10 meters and Interpolate concentration linearly to zero at a height of 400 meters above (stack height + plume rise). o Short—term calculations: (Maximum 24—hour concentration for a single elevated point source.) X = 24 ------- B45 with given by the stable conditions formula on the preceding page, and with n = 1 (single point source), 9. = wind speed class index corresponding to u 9. = 2.5 meter/sec, and in = 6 (Pasquill—Gifford “F” stability class). ------- B46 B.25. ATM Reference : Culkowski and Patterson (1976). Abstract : The Atmospheric Transport Model (ATM) is a climatological steady— state Gaussian plume model for use in mesoscale range (up to 50 1cm) modeling. This model includes the effect of surface roughness on dispersion coefficients, treats dry deposition and precipitation scavenging, and treats gravitational settling of heavy particulates using a tilted plume approximation. The model is primarily intended for calculating monthly averages but averages for other time periods can be estimated by the use of appropriate climatological data. Equations : = r 1 £ m l nim kZm S (p)/p with Qn tmthn) = n [ w exi (_APn/ul) + exp [ _(vg/u 1 ) m(Pn)]] = effective source strength = true source strength modified by depletion of pollution due to deposition and washout at distances less than A = washout coefficient = 5.55 [ Rainfall rate (mm/hr)]0 6 vg = dry deposition velocity (meter/sec) = 2/ir exp (_H 2 I2c1 2 )dx f = fraction of the time washout occurs w 2.032 2 2 = a u exp (-H /2a zZ o = vertical dispersion coefficient, a function of stability class (m) Z and downwind distance The equations for the emission rate from a windblown source are quite complex and will not be given here. ------- B47 B.2.6. STRAM Reference : Hales, et. al. (1977). Abstract : STRAM (Source—Transport—Receptor Analysis Model) is a trajectory model using a Gaussian crosswind pollutant distribution designed to estimate ground—level concentrations of pollutants over source—receptor distances of up to approximately 1000 km. STRAN is designed to treat SO 2 emissions from several elevated point sources and the conversion of SO 2 to sulfate aerosol. Equations : (1) Unlimited mixing height case: C = exp (....Y2/2 2){exP [ _ (z;h) 2 ]÷ exp [ — ( z+h) 2 ]} = R 1 — — if 7 ( i ’di ) exp (—h 2 /2cj 2 ) = Q = the emission rate of the ith source at x = 0. (2) For a limited mixing height (L): c. = , exp (—y 2 12a 2 ) dQ 1 — R ____ jVdi dx 1 u uL = Q 01 at x 0. Where C 1 = ground level concentration of species i. = total mass of species i in the plume passing a downwind plane per unit time R 1 = ffr.(x .Y z)dYdz r 1 rate of gain (or loss) of species I by chemical reaction A. = washout coefficient for species i Vdi dry deposition velocity for species i. ------- B48 B.2.7. APRAC—IA Reference : Ludwig and Mancuso (1972) and Ludwig and Dabbert (1972). Abstract : APRAC is a model which computes hourly average carbon monoxide concentrations for any urban location. The model calculates contributions from dispersion on various scales: extraurban, mainly from sources upwind of the city of interest; intraurban, from freeway, arterial, and feeder street sources; and local, from dispersion within a street canyons APRAC requires an extensive traffic inventory for the city of interest. Equations : —11 Extraurban — x = 5.15 x 10 F F = annual fuel consumption within 22.5° U sector extending from 32 km to 1000 km upwind of receptor. 1—b.. 1—b 0.8Q. x. 13 —x. Intraurban — x.. = 1 i+1 1 until this expression equals 13 ua,. 1—b.. 13 13 the “box model value” — X 4 X. uL Thereafter the box model formula is used. i = upwind area segment label j = stability class label b a.. and b.. from (c i ).. = a.. x 13 for x within segment i 1 ] 13 Z1J 13 KQ Street Canyon — Lee side XL = L (u+0.5) [ (x 2 + z 2 ) + L] KQ (B—z) Windward side ½ = ( u+o 5) SB Intermediate wind direction = 4 (XL + (less than ±30° from Street direction). ------- B49 In which x = horizontal distance from traffic lane z height above pavement K constant 7 a vehicle size 2 meters u = rooftop wind speed Q a CO emission rate/meter S street width B = average building height 38.8 meters ------- B 50 B.2.8. IIIWAY Reference : Zimmerman and Thompson (1975). Abstract : HIWAY is a Gaussian plume model that computes the hourly concentrations of non—reactive pollutants downwind of roadways. It is applicable for uniform wind conditions and level terrain. Although best suited for at—grade highways, it can also be applied to depressed highways (cut sections). Equations : x = fd2, integral along length of line segment, evaluated J° using trapezoidal rule. q = CO emission rate/unit length for stable conditions or if mixing height L > 5000 m 1 2ira g 1 g 2 , yz for neutral or unstable conditions, with a < 1.6 L z— 1 — 2iTcy a g 1 g 3 yz for neutral or unstable conditions, with a > l.6L z 1 — y i a L y with 2 = ex [ _4( _) ] g 2 2 +00 2 1 2nL g3=2 ex [ _. (. _) ] ------- B 51 B.2.9. DIFKIN Reference : Martinez. et.al. (1973). Abstract : The DIFKIN (Diffusion/Kinetics) model is a numerical/dynamic (trajectory) model for photochemical smog simulation. It determines the trajectory of an air parcel across an emission grid network and calculates pollutant concertrations as functions of time. The model obtains con- centrations and fluxes at up to ten mesh points between ground level and the top of the mixing layer. Equations: DIFKIN numerically solves the vertical diffusion equation = L( c j 1&) + for Q. = 1, 2, . . ., p Along a trajectory determined from surface wind measurements, subject to the following initial and boundary conditions; A. Initial Conditions CQ (z, tiiii) = f (z = initial concentration distribution for Species j ,, B. Boundary Conditions (1) z = 0 (at ground level) ac — = (t) (perfect reflection plus addition of emissions from ground level flux) (2) z = L(t) (at mixing height) ac, — K. = 0 (perfect reflection) where = mean concentration of species t = rate of production ( r depletion) of species Q. through chemical reaction vertical eddy diffusivity, a function of height z. q (t) = ground—level flux of species Z ------- B52 B.2.lO. SAt Reference : Reynolds (1973). Abstract : The SA l model is a numerical/dynamic model for studying the dispersion of photochemical pollutants, employing a fixed grid coordinate system and a finite difference solution of the atmospheric diffusion equation. The model calculates an emission inventory based on extensive traffic input data as well as stationary source emissions. It requires extensive meteorological data including both spatial and temporal variations and uses a kinetic mechanism for photochemical smog involving fifteen chemical reactions and ten chemical species. Equations : SAl numerically solves the advection—diffusion equation: h ( J1c ) + F (uMlcz) + i — (vAHc ,) + f- (Wc ) = ( + $&) + h ( i&) + R àH ÷ SLd H £ = 1, 2, where All = R(x,y,t) — h(x,y) = elevation difference between the mixing height and ground level, 3WO W = w — p 3t , and — z — h(x,y ) — H(x,y,t) — h(x,y) subject to the following: A. Initial Conditions = f (x,y,p) = initial concentration distribution for species £, ------- B53 B. Boundary Conditions (1) p = 0 (at ground level) Ky ac 2 — = q ,(x,y,t) (perfect reflection plus addition of emissions from ground level flux) (2) p = 1 (at mixing height) x a Wc 2 — Wg if W < 0 (material from outside of region entrained if mixing height is increasing) Ky — - — = 0 if W > 0 (perfect reflection with no entrainment p otherwise) (3) x = XE or x. (along the east or west vertical boundaries) . - uc 2 — K - -- = ua 2 if U • n < 0 (transport wind into region; material advected in from outside) ac - - — K.d 2 = 0 if U • n > 0 (transport wind out of region) ax (4) ‘ = or (along the north or south vertical boundaries) Similar to (3), except involving v, the y— component of the wind. where U = horizontal wind vector = outwardly directed unit vector perpendicular to the vertical boundary C 2 , = mean concentration of species 2. p = number of species u,v,w = components of wind in x, y, z directions = horizontal and vertical eddy diffusivities ------- B54 S 2 , = emission rate of species 2. from elevated source = production rate of species 2 , by chemical reaction = ground—level flux of species £ g 2 , = concentration of species 2. above region 2. = concentration of species 2. outside region XNIXS XE X.W = northern, southern, eastern, western boundaries of region h(x,y) = terrain elevation H(x,y,t) = elevation of inversion base. ------- B55 GLOSSARY OF SYMBOLS A, B Regression coefficients used in calibration procedures. h Stack height H Effective stack height = (stack height) + (plume rise) k Wind sector index Wind sector index corresponding to the sector containing the n—th point source 2 Wind speed class index L Mixing height m Stability class index n Point source index N Total number of point sources Q Emission rate Emission rate for the n—th point source T½ Pollutant half—life uZ Representative horizontal wind speed for the l—th wind speed class u, v Components of horizontal wind speed w Vertical wind speed x Downwind distance or distance In x—direction y Crosswind distance or distance in y—direction z Vertical distance p Do wind distance Crosswind, vertical dispersion coefficients P ‘ 1 m Meterological joint frequency function for wind in sub— n m cardinal direction k , k n ) Pollutant concentration ------- B56 ------- Cl APPEI 1DIX C APPLICATIONS TO SPECIFIC MODELS ------- C2 ------- C3 APPENDIX C APPLICATIONS TO SPECIFIC MODELS This appendix contains examples of the application of the methodology presented in this workbook to several specific atmospheric dispersion models. Each subsection deals with a different study model and illustrates the nature of the information required ‘about a study model, the factors involved in making individual element—by—element comparisons with a reference model, and the pro- cess of arriving at a final technical evalt;ation. Each subsection consists of a body of text in which the reasons for obtaining the various element—by—element comparisons and the final technical evaluation are explained. In the first example, the entire procedure is illustrated. In subsequent examples, it is assumed that the first five steps in the comparison need little additional ex- planation and that the Application Classification Form and the Evaluation Form — Part A have been completed. In each example, the application for which the study model is considered has been chosen so that the study model is in fact applicable in order to illustrate the methodology. A complete set of forms for each example, filled out in accordance with the discussion presented in the text, is located at the end of each subsection. The user should refer to these completed forms while reading the text. ------- C4 ------- C5 CONTENTS OF APPENDIX C Page C7 C23 C37 C4 9 C61 C73 C8 7 Clol C.1 EXMIPLE1: SCIM/1243. C.2 EXAMPLE 2: AQDM/1143 . . . . . . . . . C.3 EXAMPLE3: PTDIS/1213 C .4 EXAMPLE 4: PTMAX/1213. . . . C.5 EXAMPLE 5: PTMTP/1213. . . . C.6 EXAMPLE 6: HANNA—GIFFORD/1243 . C.7 EXAMFLE7: }IANNA—GIFFORD/1143. C,8 EXAMPLE 8: APPENDIX J/6243 . . ------- C6 ------- C7 C.l EXAMPLE 1: SCIM/l243 In this example, the application of interest involves estimating the maximum expected one—hour sulfur dioxide concentration in Sample City, a moder- ately sized urban area located in gently rolling terrain far from any large bodies of water • Each step in the entire methodology is illustrated. While reading the text, the user should refer to the completed forms at the end of the section. The first step involves the classification of the application as ex- plained in Section 3. with regard to pollutant characteristics, sulfur dioxide is a primary pollutant not subject to significant removal processes within the time scale of the application. The size of the region of interest is of the order of 50 km or less, and the residence time of a pollutant emitted within this region is less than 5—8 hours for typical wind speeds. As indicated in Table 3.1, the appropriate pollutant characteristics index number under these circumstances is one. The averaging time is short (under 24 hours); the appropriate averaging time index number is two, as discussed in Section 3.4. The Sample City emission inventory is assumed to contain both point and area sources and the appropriate source characteristics index number is there- fore four, as explained in Section 3.5. Finally, since the terrain in which Sample City is located is simple and the size of the region of interest is lass than 100 lan, the appropriate trans- port characteristics index number is three, as explained in Section 3.6. The completed Application Classification Form for this example can be found at the end of this section. As indicated, the appropriate application index is 1243. At this time, the basic information sections of the Evaluation Form — Part A are also completed by listing the reference documentation and preparing a short abstract describing SCTh’s mode of operation. This completes step 1. The next step in the comparison involves the documentation of the study model equations. The references listed on the front of the Evaluation Form — Part A are used to determine the working equations shown on the reverse side of the form to complete step 2. ------- C8 These references also indicate that SC m ! selects a sample of one—hour periods from the total number in some period of record, typically one year. The sample is obtained by taking every n—th hour where n is an integer speci- fied by the user. Having selected the sample, SC m ! applies a steady—state Gaussian model separately to each hour in the sample and estimates from these results both the long term average concentration and the frequency distri- bution of one—hour concentrations. With this information, SCIM may be classi- fied and its compatibility with the application of real interest checked (steps 3 and 4 in the comparison). It is assumed, in this example, that the Sample City emission inventory is structured in a manner compatible with SCIM input requiretnertts, specifically that all required source information is available, that area sources are de- fined in a suitable manner, that the number of point and area sources is within SC m ! limitations, and so on. It is also assumed that the necessary meteoro- logical and other data are available in the appropriate format. The user has already classified the application and in the process has determined that sulfur dioxide transformation and removal are not important enough to select any other pollutant characteristics branch than number one. As a consequence, no check need be made at this point to determine whether or not SCIM incorporates treatments of these elements. Had the application index begun with number three, for example, indicating that some physical removal process is important, the user would have been required at this point to de- termine whether SC m ! incorporates a treatment, however simplified, of that process. SCIM provides estimates of various percentile one—hour concentra- tions at each receptor, including the maximum expected value, and therefore does estimate precisely the quantity of interest. If the application had in- volved the estimation of the maximum 24—hour SO 2 concentration, SCIM would not have been found applicable, because it does not estimate this quantity directly, even though the necessary program modifications to do this calcu- lation may be straightforward or even though the necessary calculations could easily be done by hand. As a result of these checks and determinations, SCIM is found to be applicable to the application of interest. The “Applicable” hox on Part A is checked to indicate this determination. ------- C9 The description above also implies that SCIM is a simulation model and, in view of the guidelines for model classification in Section 4.3, the appro- priate classification is: semiempirical/Sequential (Steady—State). Step 5 simply involves referring to Table 4.1 to identify RAM as the reference model for application 1243. The next step (step 6) is to review the importance ratings of the appli- cation elements for application index number 1243 and to determine if modif i— cations to these ratings are necessary to more accurately define the relative importance of the elements in the situation of real interest. Expert advice may be necessary in this step. It is assumed here that the importance ratings as given in Tables 4.2 — 4.13 are appropriate with the exception of those for composition of emissions and chemistry and reaction mechanism, which are modi- fied from LOW to IRRELEVANT for purposes of this example. Notice that the rating for physical removal has not been changed from LOW to IRRELEVANT even though no physical removal process Is considered important enough to affect the application classification. The distinction between LOW and IRRELEVANT is that, as explained In Section 4.4, the treatments of IRRELEVANT elements are not taken into account at all in the evaluation, while the treatments of LOW elements may be considered In certain cases. It is assumed for this example that the involve— taent of sulfur dioxide in atmospheric chemical reactions in and around Sample City is considered so unimportant that it should play no role at all in evalu- ating simulation models. Therefore, the elements compo5jtjon of emissions” and “chemistry and reaction mechanism” are in fact irrelevant. In contrast, it is assumed that dry deposition of sulfur dioxide, while not important enough to affect the application classification, nevertheless does occur and is not in- significant enough to be totally irrelevant. Thus, the importance rating of physical removal is kept at LOW. Both initial and modified importance ratings for each element are inserted in Part B of the Evaluation Form. The next step (step 7) is the deterriination of the treatment by SCIM of all application elements not rated IRRELEVANT. Operating equations used by SCIM are reproduced on the reverse side of Part A of the evaluation form. Using these equations and the material in the references as sources, descriptions of the treatments by SCIM, together with the corresponding reference model treat- ments obtained from Tables B .2— B.l3 and the importance ratings for each ele- ment, are entered on Part C of the evaluation form. The treatments by SCIM ------- do were determined in accordance with. the guidelines given in Section 5, supple- mented by the discussions presented in Appendix A. After both the study model and reference model treatments of a given element have been entered on the Evaluation Form — Part C, the comparison of these two treatments may be made using the guidelines in Section 6.2.1. The level of detail involved in each treatment is examined with reference to the relative ranking of treatments in Tables 5.1—5.15. The result of each comparison con- sists of the single adjective from the set BETTER, COMPARABLE, WORSE which most accurately describes the treatment used by the study model in comparison with that used by the reference model. This result is then entered in the place provided in each section of Part C. The various treatments by SCIM and RAM of most application elements are clearly COMPARABLE, and are virtually identical in several cases. The ex- ceptions are the elements horizontal wind field and background, boundary and initial conditions. The two treatments of horizontal wind field are basically COMPARABLE. However, SCThI does not employ a randomization procedure for wind direction and RAN does, with the result that SCM only allows 36 different wind directions while RAM allows 360. Thus, SCIM be somewhat WORSE in its treat- ment of the horizontal wind field. In cases of doubt, both results are indi- cated on the form; the primary evaluation as usual, followed by a secondary evaluation in parentheses (see the entries on Part C). The same situation arises for background, boundary and initial conditions. The two treatments are basically COMPARABLE, but 5dB ’ ! may be a little WORSE because of its less detailed treatment of the upper boundary condition. On the other hand, SCIM allows a background value to be input. Both comparisons are indicated on Part C of the Evaluation Form. In the cases of emission rate and temporal correlations, it is necessary to judge the importance of area source emissions in Sample City before making the comparisons because SCIM and RAN differ in the level of detail with which the temporal variation of area source emissions are described. The comparisons actually made in the example assume that area source contributions are not sig- nificant enough to justify rating the SC 1M treatment BETTER. If these contri- butions were more Important in the application, the additional detail in the SCIM treatment might justify a BETTER rating. ------- Cl i The synthesis of these individual comparisons into a final technical evaluation (step 9) is documented on the Evaluation Ton — Part D. The guide- lines in Section 6.2.2 are used to arrive at this final evaluation. In the example, there are no CRITICAL elements. Therefore, the initial evaluation is based on the comparisons for the three HIGH—rated elements. All of these com- parisons are COMPARABLE, resulting in an initial comparative rating of COMPAR- ABLE. Of the elements rated MEDIUM, all five have COMPARABLE treatments; there- fore no change in the initial rating is indicated. Even if the secondary evalu- ations for horizontal wind field and background, boundary and initial con- ditions were used, they would not carry sufficient weight to alter the evalu- ation. Thus, the technical evaluation of SCIM for Application 1243 is that SCIM is COMPARABLE to the reference model, RAN. This evaluation is further supported by the distribution of comparisons for the LOW elements, although these would not be considered here, because the rating based upon HIGH and MEDIUM elements is unambiguous. ------- Cl 2 APPLICATION CLASSIFICATION FORM 0 A. POLLUTANT / C HA R ACT E R ISTICS \ \ SECONDARY CHEMICAL PHYSICAL CHEMICAL & N ON E 7’ CHEMICAL SIC AL \ CHEMICAL & INDEX NUMBERS INSERT APPROPRIATE NUMBERS IN THE BOXES PROVIDED: 2 3 PHYSICAL.. -v -5 -6 7 PHYSICAL 8 B. AVERAGING TIME C. SOURCE C HA RA CT ER IS TIC S < LONG—TERM -TERM LIMITED POINT 7 AREA LINE PLE/CO TIO COMPLEX D. TRANSPORT K CTERISTIC4 PLE SHORT — RANGE LONG—RANGE RA E Form the application index by transferring the four index the corresponding boxes below: \.,.,. APPLICATION IN DEX j I J 112 J 1 2J 1413 numbers into 2 2 3 4 2 3 4 ------- C 13 EVALUATION FORM Part A: Abstract and References Study Model : Sampled Chronological Input Model (5Cr!) References : Koch, R.C. and GH. tadsklev, A User’s Manual for the Sampled Chronological Input Model (3dM), GEOMET Report No. E—261, prepared for U.S. EPA under Contract No. 68—02—0281. (December 1974). Koch, R.C. and S.D. Thayer, Validation and Sensitivity Analysis of the Gaussian Plwne Multiple - Source Urban Diffusion Model, NTIS PB 206951, National Technical Information Service, Springfield, Va. 22151. (November 1971). Abstract : The Sampled Chronological Input Model (5Cr!) is a Gaussian plume—based model designed to estimate mean long—ten pollu- tant concentrations and the frequency distribution and maxi- mum of one—hour pollutant concentrations in an urban area. Classification : Semiempirical/Sequential (Steady—State) 4pplication Index : 1243 Reference Model : RAN Application Description : )là.x$jnun 1 —hour SO 2 concentration in an urban area. Model Applicability : Applicable Not Applicable ------- C 14 EVALUATION FORM Part A (reverse): Ej tions Study Model : SCfl4 Equations : Point sources: [ 2 qn Jex (... ) Xn=2 aa gexp 2Ia yz ‘ yg 2 2’ 1 I H—z u+z I I with g(x,z;H) = exp [ ] + exp [ — 4 [ j , ZI J Area sources: Xd 1 1 (x ) _ _ _ _ - — dx ;ll) exp ( i c c uçy g(x,z uJ 0 Z with (x) q(x,o), q(r,9) = emission rate per unit area at position (r,9) from receptor (Narrow plume approximation) Integral evaluated using trapezoidal rule. N Total estimated concentration = + n=l N = number of point sources Vertical dispersion coefficient: b a =ax x |