STANFORD RESEARCH INSTITUTE
Final Report
                                 September 1970
 A  PRACTICAL, MULTIPURPOSE URBAN
 DIFFUSION MODEL FOR CARBON  MONOXIDE
By: F L. LUDWIG
    ALBERT E. MOON
WARREN B. JOHNSON
ROBERT L. MANCUSO
Prepared for:
COORDINATING RESEARCH COUNCIL, INC.
30 ROCKEFELLER PLAZA
NEW YORK, NEW YORK  10020

NATIONAL AIR POLLUTION CONTROL ADMINISTRATION
411  WEST CHAPEL HILL STREET
DURHAM, NORTH CAROLINA  27701
                           CONTRACT CAPA-3-68
                         CONTRACT CPA 22-69-64
SRI  Project 7874
Approved:

R. T. H. COLLIS, Director
Aerophysics Laboratory

RAY L. LEADABRAND, Executive Director
Electronics and Radio Sciences Division
                                                 Copy No.

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                                  ABSTRACT
     This report describes  the development and current status of a receptor-




oriented diffusion model that can be applied to urban areas to give the fol-




lowing outputs:  (1) carbon monoxide (CO) concentration isopleths for a given




set of meteorological conditions and times of day, (2) sequences of hourly CO




concentrations at specific  locations for given sequences of meteorological




conditions, and  (3)  climatological summaries of CO concentration for specific




locations if an historical  record of meteorological data is available.  The




model can be used to obtain the frequency distributions of concentrations aver-




aged over various time  intervals for specific hours of the day or days of the




week.





     Model  inputs are traffic volumes on major streets and highways in the




urban area, atmospheric stability,, mixing depth, and wind speed and direction.




Traffic volumes  can  be  obtained from either past measurements or forecast




values.  Methods are described for obtaining atmospheric stability and mixing




depth from  conventional (i.e., airport) hourly meteorological measurements and




twice daily radiosonde  data.  Meteorological parameters are assumed uniform




throughout  the urban area.  When the airport winds are calm the model uses a




small finite value of wind  speed and the last observed wind direction.





     The concentrations calculated with the model are compared with observations



of CO concentration  from Continuous Air Monitoring Program (CAMP) stations. Al-




though the  agreement is not good—the model generally calculates concentrations




lower than  those observed—improvement is obtained by empirical corrections.




Possible reasons are given  for the disagreement between calculations and obser-




vations, and a field measurement program is described that the authors feel




will help to define  the sources of the discrepancies and provide the infor-




mation necessary for their  correction.

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                                SUMMARY
     If city planners and highway planners are  to  include air pollution




effects among the factors to be considered in the  urban and highway de-




sign processes,  then some method must be made available that will allow




them to estimate the magnitude and nature of the effects that will arise




from implementation of various plans.  This report describes the results




of the first year's efforts to develop a method for determining the air




pollution consequences of various city and highway planning alternatives.




The approach taken has been that of the numerical  model, i.e., a scheme




for calculating  air pollution concentrations from  information about air




pollution sources and meteorological conditions.





     The long-term objectives of the program are to develop a model that




will accurately  calculate the concentrations of any pollutant at virtually




any point in any city, if meteorological conditions and pollution sources




are known.  The  objectives include being able to calculate the statistical




distributions of concentrations at a point, as well as single values




appropriate to some specific set of conditions.





     During this first year we limited ourselves to developing a calcu-




lational scheme  for carbon monoxide concentrations, largely because this




pollutant is relatively nonreactive, permitting us to focus our efforts




on the meteorological side of the problem.  After  this is in hand, work




to extend the model to chemically active pollutants will be in order.




The model as presently developed incorporates diffusion submodels based




upon both Gaussian and uniform (to the top of the mixing layer) vertical





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monoxide at any point in a city using readily available meteorological




and traffic data.  Techniques have been developed to estimate,, from ob-




served quantities, those model inputs that are not directly observed.




The model can provide statistical summaries and estimates for individual




situations.  The model has been applied to five different cities (St.




Louis, Washington, Chicago, Cincinnati, and Denver) in several different




ways to demonstrate its versatility.  This report contains examples of




the following different types of calculations:





     (1)  Maps of concentration isopleths for the five cities,




          based on calculated concentrations at 625 points




           (25 * 25 grid).  Inputs were specific observed meteoro-




          logical conditions from 1964 or 1965 weather records




          and historical, diurnally corrected 1965 average




          traffic data.





     (2)  Week-long sequences of calculated hourly concentrations




          at single points in each of the five cities.  Inputs




          were historical average traffic data and hourly




          meteorological observations.





     (3)  Maps of concentration isopleths for St.  Louis based on




          forecasts of 1980 traffic, two hypothesized levels of




          exhaust emission control, and specific meteorological




          conditions corresponding to those used for a 1964




          case.





     (4)  Ten different concentration frequency distributions for




          a location in St. Louis,  based on a five-year (1960-64)




          meteorological record and historical average traffic




          data.  The frequency distributions presented include



          those of

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          •    Concentrations during  all  hours





          •    Concentrations during  weekday, Saturday,  or




               Sunday hours





          •    Concentrations at  the  following hours:  0800,




               1200, 1800, or 2400  local  time (includes  day-




               light savings time corrections)





          •    8-hour and 12-hour averages of concentration.





      (5)  The same  ten frequency distributions based on  St. Louis




          traffic forecasts and the same  five-year meteorological




          record.





      (6)  The median and 90-percentile values of hourly  concen-




          trations  at nine St. Louis  locations, based on the same



          data as Item (4).





      (7)  The median and 90-percentile values of hourly  concen-




          trations  at nine St. Louis  locations, based on the same




          data as Item (5).





     When the concentrations calculated by the model are compared with




those measured at Continuous Air Monitoring Program (CAMP) stations, the




agreement is found  to be generally poor,  with observations usually




higher than calculations.  There are many possible sources for the dis-




crepancies, but each falls into one or more of three categories:





      (1)  Inadequate input data for the model





      (2)  Inappropriate assumptions used  in the modeling





      (3)  Unrepresentative or inaccurate  CAMP observations.





     The consequences of several possible sources of error in the first





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to its various inputs.  The inputs include source strength (determined




from traffic data)^ wind speed and direction  (measured at the local air-




port), atmospheric stability (determined from conventional airport




meteorological observations),  and mixing depth  (determined from airport




radiosonde temperature measurements).  The calculated concentrations




are directly proportional to source strengths, but, in general, sources




nearest the receptor are the most important in determining the calcu-




lated concentration.





     Calculated concentrations are inversely proportional to wind  speed.




Stability changes can cause large changes in calculated concentration,




particularly when the mixing layer is deep.  If the air is relatively




unstable so that mixing proceeds rapidly and if the mixing layer is




relatively shallow, then calculated concentrations are almost propor-




tional to the mixing depth used.  As the stability and mixing depth in-




crease, the sensitivity of the model to changes in the mixing depth




becomes less and less.





     The possible sources of error that can be included in the category




of inappropriate assumptions include those that would arise from taking




airport meteorological observations to be valid throughout the city.




from the assumption of Gaussian dispersion, and from our handling of the




calm-wind case.  The report concludes that local values of input meteoro-




logical parameters would provide an improvement over the present assump-




tion of uniform meteorology.  The Gaussian dispersion assumption is also




discussed, and it is concluded that the dispersion rates used may not be




seriously in error, but further study is needed.  As presently constituted,




the model takes a measured (airport) calm to correspond to an urban wind




of small finite speed (1 m/s)  from the most recently measured (airport)




direction.  Better methods of  treating this difficult case are being



sought.

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     The only CO data available  for  checking  our model  in  the  five




cities to which it was applied are the CAMP station  data.  The model




evaluation thus depends upon  the representativeness  and  accuracy of




these data.  Some of the CAMP stations are located near  parking lots




or large buildings, where aerodynamic effects are likely to be a signi-




ficant factor.  All measure CO concentrations at single  points rather




than over areas comparable to the spatial resolution of  the model.




These factors could contribute importantly to differences  between ob-




served and calculated concentrations.  Other possible sources of error




include water vapor interference and the relatively  poor precision




(1 ppm) of the observations.





     Attempts have been made  to  correct some of the  model's discrepancies




using a least squares statistical method in conjunction  with St. Louis




CAMP Station observations.  These attempts focused on errors that might




arise because of differences between winds observed  at the airport and




those in the city, and on errors that might come from poor estimates of




the fractions of the total daily traffic that occur  during individual




hours.  After the statistical adjustments have been  made,  the model can




reproduce the high concentration parts of the observed frequency dis-




tribution of independent data with good accuracy.  Its performance on




individual hourly values is slightly better than "predictions" based




upon a long-term mean value of concentration.   The model also performs




about as well as "persistence,"  i.e., assuming that  concentration has




the value observed 24 hours earlier-





     The report concludes with a discussion of our plans for a program




of field measurements that should help to define the most  serious sources




of discrepancies between observed and calculated concentrations.  This




measurement program should also provide much of the  information neces-




sary to correct the discrepancies.

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     Meteorological and CO measurements are planned for several loca-



tions and at several heights above street level in and around downtown



intersections in San Jose and St. Louis.  These should help define the



characteristics of aerodynamic flow effects around buildings and oi



differences in meteorology between the airport and the downtown area.



When combined with the detailed traffic data available from downtown



San Jose, these data should also provide a test of the accuracy of the



relationship used to determine CO emissions from traffic data.  Study



of the detailed traffic data should provide intormation on the probable



representativeness of historical traffic data, which are based on very



limited counting periods.   We also plan field measurements of CO con-



centrations at various points in the vicinity of the St.  Louis CAMP



Station.   These should serve as a check on the accuracy and representa-



tiveness of the available  CAMP data.

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                               CONTENTS
ABSTRACT	        iii

SUMMARY 	          v

LIST OF ILLUSTRATIONS	         xv

LIST OF TABLES	        xix

  I  INTRODUCTION 	          1
     A.   Scope and Objectives	          1
     B.   Fundamental Concepts	          3

 II  ELEMENTS OF THE BASIC MODEL	          5

     A.   Spatial Partitioning of Emissions 	          5
     B.   The Gaussian Model	          7
     C.   The Box Model	          9
     D.   Transition from Gaussian to Box Models	          9
     E.   Required Inputs for the Basic Model	         10
     F.   Simplifying Assumptions 	         11

III  DETERMINATION OF THE INPUTS	         15

     A.   Emission Inventory Design 	         15
          1.   General	         15
          2.   Calculation of Primary Network Emissions
               Using Historical Data	         22
          3.   Calculation of Secondary Traffic Emissions
               Using Historical Data	         24
          4.   Calculation of Emissions Using Forecast
               Traffic Data	         25

     B.   Meteorological Inputs 	         28

          1.   Gaussian Standard Deviation Function 	         28
          2.   Stability Category 	         30


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          3.   Mixing Depth	        32
          4.   Wind Speed and Direction	        33

 IV  ORGANIZATION AND APPLICATIONS OF THE SYNOPTIC AND
     CLIMATOLOGICAL MODELS	        37

     A.   Introduction	        37

     B.   The Synoptic Model	        38
          1.   Description	        38
          2.   Applications	        40

     C.   The Climatological Model	        58

          1.   Background	        58
          2.   Description	        59
          3.   Applications	        62

  V  TESTING AND IMPROVING THE MODEL	        77
     A.   Sensitivity Tests 	        77
          1.   Source Strength	        78
          2.   Wind Speed	        80
          3.   Wind Direction	        80
          4.   Location of the Receptor	        81
          5.   Stability and Mixing Depth 	        83
     B.   Use of Observations to Improve the Model	        88
          1.   Introduction	        88
          2.   Attempted Improvements 	        89
          3.   Example	        93

 VI  DISCUSSION AND FUTURE PLANS	        99

Appendix A—PRINCIPAL SOURCES OF CO IN URBAN AREAS	       107

Appendix B—THE URBAN TRANSPORTATION PLANNING PROCESS ....       113

Appendix C—METHODS FOR DETERMINING STABILITY CATEGORY.  . .  .       121

Appendix D—METHODS FOR DETERMINING MIXING DEPTH	       129

Appendix E—INCREASING THE SPATIAL RESOLUTION FOR EMISSIONS
            IN THE FIRST SEGMENT	       143

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Appendix F—TREATMENT OF EXTRAURBAN SOURCES AND
            STREET EFFECTS	        147

Appendix G—PROGRAM FOR PREPROCESSING OF THE DATA FOR THE
            CLIMATOLOGICAL MODEL	        155

Appendix H—THE EQUIVALENCE OF CERTAIN COMBINATIONS
            OF STABILITY AND MIXING DEPTH  	        161

Appendix I—CONTINUOUS AIR MONITORING PROGRAM STATIONS.  .  .  .        167

ACKNOWLEDGMENTS  	        177

REFERENCES	        179

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                             ILLUSTRATIONS
Figure 1

Figure 2



Figure 3

Figure 4

Figure 5



Figure 6
Diagram of Segments Used for Spatial
Partitioning of Emissions	
Figure 7
Figure 8

F i gur e 9


Figure 10


Figure 11


Figure 12


Figure 13


Figure 14
Computer-Generated Display of Traffic
Links in a 24-by-24-Mile Central Portion
of the Primary Network for Washington, D.C..
Hourly Distribution of Trips in
Washington, D.C	
Hourly Distribution of Traffic for Two
Facility Types in St. Louis	
Simplified Schematic Diagram of Traffic Link
Assignment Subroutine Used for the Five
Segments Closest to the Receptor 	
Illustration of the Grid-Point
Transformation Technique Used for Computing
the CO Emissions within the Four Most
Distant Segments 	
a  Functions Used in the Model 	
 z
Simplified Flow Chart for Synoptic Model
Calculations 	
Simplified Flow Chart for Concentration
Calculations 	
Calculated Washington, D.C., Concentration
Patterns 	
Calculated St. Louis Concentration Patterns
0700-0800, 15 October 1964 	
Calculated Concentration Patterns Based on
Forecast of 1990 St. Louis Traffic ....
Calculated St. Louis Concentration Patterns
for Two Grid Sizes 	
16
18
18
20
Calculated Carbon Monoxide Concentrations
(PPM) for Chicago	
21

31

39


41


43


44


45


47


48

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Figure 15      Calculated Carbon Monoxide Concentrations
               (PPM) for Cincinnati 	

Figure 16      Calculated Carbon Monoxide Concentrations
               (PPM) for Denver 	
Figure 17      Observed and Calculated CO Concentrations
               at the St. Louis CAMP Station, 18-24
               January 1965 	

Figure 18      Observed and Calculated CO Concentrations
               at the St. Louis CAMP Station, 19-25
               October 1964 	

Figure 19      Observed and Calculated CO Concentrations
               at the Washington, B.C., CAMP Station,
               19-25 October 1964 	

Figure 20      Observed and Calculated CO Concentrations
               at the Cincinnati CAMP Station, 14-20
               December 1964	
Figure 21      Observed and Calculated CO Concentrations
               at the Chicago CAMP Station, 20-26
               July 1964	

Figure 22      Observed and Calculated CO Concentrations
               at the Denver CAMP Station, 19-25
               April 1965 	

Figure 23      Simplified Flow Chart of Climatological
               Model	,

Figure 24      Simplified Flow Chart for a Program to
               Determine Ten Different Frequency
               Distributions	

Figure 25      Calculated St.  Louis CAMP Station CO
               Concentration Frequency Distribution for
               1965 Traffic Conditions; Weekday, Saturday,
               and Sunday Hours 	

Figure 26      Calculated St.  Louis CAMP Station CO
               Concentration Frequency Distribution for
               1965 Traffic Conditions; 0800, 1200, and
               1800 Hours 	

Figure 27      Calculated St.  Louis CAMP Station CO
               Concentration Frequency Distribution for
               1965 Traffic Conditions; 1-Hour,  8-Hour,
               and 24-Hour Averages 	 ,
49
50
51
52
54
55
56
57
63
65
67
68
69

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Figure 28      Spatial Variations of Calculated St. Louis
               Median and 90 Percentile Concentrations
               for 1965 Traffic Data	

Figure 29      Calculated St. Louis CAMP Station CO
               Concentration Frequency Distribution
               for 1990 Traffic Conditions; Weekday,
               Saturday, and Sunday Hours 	

Figure 30      Calculated St. Louis CAMP Station CO
               Concentration Frequency Distribution
               for 1990 Traffic Conditions; 0800, 1200,
               and 1800 Hours 	

Figure 31      Calculated St. Louis CAMP Station CO
               Concentration Frequency Distribution
               for 1990 Traffic Conditions; 1-Hour,
               8-Hour, and 24-Hour Averages 	
Figure 32      Spatial Variations of Calculated St. Louis
               Median and 90 Percentile Concentrations
               for 1990 Traffic Conditions	
Figure 33      Effect of Wind Direction on Concentrations
               Computed for the Washington, D.C., CAMP
               Station	
Figure 34      Effect of Moving Receptor Point	
Figure 35      Normalized Concentration as a Function
               of Stability and Mixing Depth	

Figure 36      Diurnal Emission Patterns for St. Louis. .
Figure 37      Observed and Calculated Frequency
               Distributions for Five Months of
               Independent Data 	

Figure D-l     Schematic Representation of the Diurnal
               Temperature/Time Interpolation of Mixing
               Depth	

Figure G-l     Simplified Flow Chart of Program for
               Converting Holzworth's Mixing Depths
               to Hourly Values 	

Figure G-2     Simplified Flow Chart of the Data
               Processing Program Used with the
               Climatological Model 	
 70
 71
 72
 73



 74



 82
 84


 86
 94



 98



140



158



159

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Figure 1-1     St.  Louis CAMP Station	        171



Figure 1-2     Cincinnati CAMP Station	        172



Figure 1-3     Chicago CAMP Station	        173



Figure 1-4     Washington CAMP Station	        174



Figure 1-5     Denver CAMP Station	        175

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                                TABLES
Table I
Average Speeds for Washington,  D.C.,
Table II
Table III
Table A-I
Table C-I
Table H-I
Table H-II
Percentage Increase in Calculated CO
Concentration Resulting from the Doubling
of Emission Rates in Different Segments. . . .
Results of Model Calibration 	
Percent CO Contribution by Source Category . .
Stability Categories . 	

Values of (x/Q). . for Unit Wind Speed . . .
79
96
110
124
164
166

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                             I   INTRODUCTION





A.   Scope  and  Objectives



     There  is a need  for an  objective,  practical  method  of  simulating


the  current and future  impact  of motor  vehicles on  air pollution  in


urban  communities.  Such a technique  could be used  to assess  current


concentration patterns  of primary vehicular  pollutants in cities,  and


to predict  the  effects  of exhaust emission controls and  expressway


routings  on future concentration patterns.   This  report  describes  our


progress  in developing  a simulation model designed  to meet  these  ob-


jectives.   Further refinements  of this  model are  indicated  and will be


made in the course of our continuing  study.  In this sense, the model


is not yet  a completely finished product, and any present applications


should be carried out with caution.



     In developing the  model, we have been aided  considerably by pre-


vious urban diffusion modeling  studies, which have  been  reviewed and

                           *
summarized  by Wanta (1968),  Stern (1969), Moses  (1969), and Neiburger


(1968).  An investigation of carbon monoxide diffusion in Washington,


D.C., by Ott et  al. (1967) and  Clarke's (1964) model could be considered


prototypes  for  the model described here.



     For simplicity, the modeling effort has been restricted to carbon


monoxide  (CO),   since  (1) the gas is relatively inert in  the atmosphere
*

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                                                                  *
with no known significant natural sources or sinks in urban areas,

(2) motor vehicles are known to be the most important source of the CO

in urban air, and (3) CO is an important pollutant in terms of health

effects.

     Our goal has been to develop a versatile, practical model to pre-

dict street-level CO concentrations at any point in a city.  Calculations

of the following types can be made using the model:

     (1)  Hourly concentrations as a function of time, for veri-

          fication use and possible operational applications, and

     (2)  The frequency distribution of concentrations for

          selected averaging times, including statistical pre-

          diction of the frequency of occurrence of specified

          high concentrations for planning purposes.

     To improve the accuracy of the model, we have developed calculation

schemes to assess the concentration contributions resulting from diffu-

sion on various scales,  including the treatment of:

     (1)  Extraurban transport and diffusion,  mainly from upwind

          cities, and

     (2)  General intraurban diffusion from arterial and feeder

          streets.

     Too little is yet known about the effects of nearby buildings and

streets to permit these influences to be included in the model, but
*
 Although evidence is mounting that such sources and sinks may be found
 in the biosphere (Swinnerton et al.,  1969;  Went, 1966; Robinson and
 Robbins, 1967).   Concentrations arising from such sources could be in-

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studies currently underway should substantially add to our knowledge in




this area.





     In developing the model we have attempted to:





     (1)  Bring together into a single model the best features




          of previous efforts and supplement these with original




          contributions where necessary.





     (2)  Maintain simplicity unless additional complexity is




          required to achieve greater accuracy, and is clearly




          justified in terms of the accuracy of the available




          input data and the resulting increased computing




          costs.








B.   Fundamental Concepts





     Our plan has been to develop the model around individual pieces,




or "modules."  These modules were to be organized in different ways to




accomplish different objectives.  In computer programming terms, this




means that several subroutines were used in the program.  This approach




has been useful, although it has been applied differently than originally




anticipated.  The same general organization is used in all the applica-




tions,  but modules are changed to reach the different objectives.  This




characteristic has allowed us to change different aspects of the model,




and to experiment with a minimum of disruption of the overall system.





     The organization of this report reflects the modular nature of the




diffusion model it describes.  We have chosen to describe the basic




model and then the various forms that the subunits of that model have




taken.   Much of the detailed description of the subunits is confined to




the appendices of this report.  Results obtained with the model are also





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the available input information, and of the data available to verify the




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                    II  ELEMENTS OF THE BASIC MODEL





A.   Spatial Partitioning of Emissions



     Our diffusion model is a modified form of the receptor-oriented


model developed by Clarke (1964).  The concentration at the receptor


is considered to be due only to emissions located within logarithmically


spaced segments, such as shown in Figure 1.  This arrangement of seg-


ments allows more precise selection of effective emissions near the re-


ceptor.  The closest segment extends from the receptor to 125 m, roughly


comparable to the size of a city block, and the farthest segment extends


to 32 km, approximately the diameter of a large city.



     The 22.5° sector width is convenient and fits reasonably well the


angular plume widths, between ±2 a points, predicted by Gifford's (1961)


model for slightly unstable conditions.  The sector width is expanded


to 45° within the closest 1 km to allow for the large initial lateral


dispersion observed during the St. Louis tracer studies (Pooler, 1966;


McElroy, 1969).



     Because nearly all urban carbon monoxide emissions are from internal


combustion vehicles (see Appendix A), the model assumes emissions to be


at ground level.  Furthermore, the emissions within each segment are


assumed to be uniformly distributed.  Thus the total emission from all


the highway links and parts of links that lie within a segment is averaged


over the area of that segment.  The emissions from the smaller and resi-


dential streets are also included.  The methods for determining emissions


are described in a later section of this report.   Here, it is sufficient


to note that each upwind segment is assigned an average emission rate

                                                             -2  -1

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16km
                                 8
                                                                    RECEPTOR
                                                                    POINT
                                             1000m
                                                        500
                   EXPANDED VIEW  OF
                   ANNULAR SEGMENTS
                   WITHIN 1 km  OF
                   RECEPTOR
                                                             250
125
     RECEPTOR
     POINT
                                                                      TA-7874-1S

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The small size of the segments near  the receptor provides  good  spatial


resolution for the close sources, where such resolution  is  important.


For farther areas the detailed location of  individual  sources is not


very important because diffusion processes  during  transport  intermingle


the individual emissions before they reach  the receptor.  The sacrifice


of resolution at greater distances simplifies the  calculations, but


does not substantially affect the results.





B.   The Gaussian Model



     Gifford  (1961) has developed a  generalized diffusion model to


describe the plume from a  continuous ground-level  point  source, assuming


perfect reflection at the  ground.  In  its simplest form, the ground-


level concentration from a ground-level source is  given  by
                            Q        /  2   2

                     c =    -    exp -
where


                                             3
          C -  ground-level concentration  (g/m )



          Q =  source  strength  (g/s)



          u =  average wind speed  (m/s)



          y =  lateral (crosswind) distance from the plume axis  (m)



     a , Q  =  lateral and vertical standard deviations of plume con-
      y   z

               centration  (m);  these parameters are functions of distance


               between the source  and the receptor and of atmospheric


               stability.



When Eq. (II-l) is integrated  over y, we obtain the following basic form



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                                1/2
                                        -1  -1
In this formulation Q  has the units g m   s
                     L

     Estimates of c  as a function of atmospheric stability and pollu-
                   z
tant travel distance or time have been proposed by Gifford  (1961) and

Smith and Singer (1966), and urban observations of this type have been
                                                                     *
reported by Pooler (1966) and McElroy (1969).  We have used Gifford' s

values, but the model is flexible and can use any set of functions  that

can be reasonably approximated, over the intervals between  segment

boundaries, with expressions of the form

                                    b. .
                          a  = a   r 1J     ,                      (II-3)
                           z    ij


where r is the travel distance, the subscript i refers to annular seg-

ments upwind of the receptor point (see Figure 1), and j refers to dif-

ferent stability classes.   The determination of stability class is

discussed later in the report.  The a  functions are generally well
                                     z
approximated by this set of power functions.

     Substituting Eq. (II-3) into the line-source equation and inte-

grating with respect to r from r = r  to r    gives the contribution to
                                    i     i+1
                                       th
the calculated concentration from the i    segment area source tor

stability class j:
*
 Gifford's work is a modification of that by F. Pasquill (1961).  The
 Gifford-Pasqui11 curves are based upon data from open country, and
 probably underestimate the diffusion in urban areas.  We are examining

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                  0.8  ,
                            b
                        (l-
                        \
                 u a. .  x
                                                        b   =1   (II-4)
                                                         ij
where r. and r.   are, respectively, the distance to the downwind and
                          th
upwind boundaries of the i   segment.  In this expression Q  is the

                                th                              -2  -1
average emission rate from the i   segment and has the units g m   s


This basic Gaussian model applies when there is no effective limitation


to vertical mixing or when the cloud has not spread sufficiently to be


affected by such a limitation.
C.   The Box Model



     When the layer into which the pollutants are being dispersed is


restricted, then they will tend to become uniformly distributed in the


vertical after sufficient travel has taken place.  Under these conditions,
the "box" model is used.  According to the box model, the concentration


arising from a uniform area source ii


by  (see Miller and Holzworth, 1967):
                                           th
arising from a uniform area source in the i   annular segment is defined
                                r    - r
                                 i+l    i
                                	r	    ,                   (n-5)
                                   uh
where h is the depth of the layer into which the pollutants are mixed.





D.   Transition from Gaussian to Box Models



     We have chosen to change from the Gaussian model to the box model


at that point where the two (in their respective line source formulations)



-------
source is:
                            C = Q /uh    .                         (11-6)
                                 L
Setting the right-hand sides of Eqs. (II-2) and  (II-6) equal to each


other, and solving for r gives:




                                     \1/bi '
                       r  = (0.8h/a   1   1J    .                  (II-7)
                        T   \      ij/
     In Eq. (II-7), r  is that value of r for which the box and Gaussian


models give equivalent results.  At this distance, we change from Eq.


(II-4) to Eq.  (II-5) in calculating concentrations.  The part of an


annular segment downwind of r  is treated according to the Gaussian


model, and the part that is upwind, according to the box model.  If the


transition occurs in segment i, then r  is substituted for r    in the


Gaussian equation and for r. in the box equation.
E.   Required Inputs for the Basic Model



     Equations (II-4) and (II-5) are the basis of the model.  In order


to use these equations to calculate the concentration at a receptor,


the values of certain input variables are required.  These inputs are:



     (1)  The wind direction



     (2)  The average transport wind speed



     (3)  The average emission strength within each of the upwind


          segments



     (4)  The depth of the mixing layer



     (5)  The variation of a  with travel distance.
                            z

-------
     The last item requires that we select  some empirically or  theo-


retically determined function that describes  the dependence of  a  on
                                                                z

distance for the meteorological conditions  for which we are calculating


the concentration.  As will be discussed later, these  functions may be


conveniently approximated  in the form given by Eq.  (II-3).



     None of the necessary inputs are routinely measured, except wind


speed and direction.  To satisfy the requirement that  the model be


generally applicable in a variety of cities,  we have had to develop


methods of deriving the model inputs from readily available information.


Section III of this report describes the ways in which the inputs can be


determined from conventional traffic data and from routine meteorological


measurements.





F.   Simplifying Assumptions



     Before proceeding to  the next section, it should be noted  that two


broad simplifying assumptions have been made  with regard to the meteoro-


logical data.  First, the meteorological inputs have been taken to be


uniform throughout the urban area, and second, they have been assumed


to remain constant during  the travel of the pollutants between  source


and receptor.  For example, it may take two hours for pollutants to


travel to the receptor from the farthest segment, but we assume that the


meteorological parameters  such as stability and mixing depth have re-


mained constant at the value they have when those pollutants arrive at


the receptor.  The assumption of horizontal uniformity of the meteoro-


logical factors is made, in large part, because it represents the best


available estimate of the  situation.  Winds are seldom measured at more


than a very few locations in an urban area, so we must generally make


do with a single measured wind.  There appears to be no reason, in


principle, why the emission segments upwind of the receptor could not

-------
be laid out along a wind trajectory, if the trajectories were known and



the added complexity were warranted by improved results.





     Variations of mixing depth and stability almost certainly occur



through a city, but at present there are seldom, if ever, sufficiently



detailed data to determine such variations.  As a matter ot  tact,  the



measurements required to determine a mixing depth are usually made at



some distance outside the urban area.  A similar situation exists with



the information required for stability estimates.  We must therefore



assume the estimates of mixing depth and stability are  typical oi  the



area, although we do make some adjustments to account for the gross



effects of urbanization.





     The assumption that diffusing pollutants have been subjected,



throughout their trajectory, to the conditions prevailing at the time



of their arrival at the receptor is justified when the quality of  the



input data is considered.  We have already conceded our inability to



determine the spatial changes.  In general, we would expect  the temporal



changes to be comparable with the spatial, so treating one without



treating the other could constitute an unwarranted complexity.  Though



the winds are measured hourly, as are the data from which stability is



determined, mixing depths must be interpolated between values estimated



at half-day intervals.  Again the principle of consistency suggests that



added complexity to account for changes in conditions during the travel



period of the pollutants is unwarranted.





     One other factor that concerns the assumption of temporal constancy




of inputs is the relative importance of emissions at different distances



to the observed concentrations at a point.  Calculations with the model




indicate that contributions of emissions to the concentration at a point



decrease with increasing distance, other things being equal.  Thus, the



nearby sources, with correspondingly short travel times, are the major






-------
factors in determining the concentration.  The short travel times from




these sources minimize the likelihood of substantial change in the



meteorological parameters.  This factor alone is probably sufficient to



justify the simplification of taking meteorological factors to be con-



stant during the time that pollutants travel from their source to the



receptor.

-------
                   Ill  DETERMINATION OF THE  INPUTS








A.   Emission Inventory Design





     1.   General





          The emission inventory for the model consists entirely of  the




emissions from vehicular  sources,  since these sources  are responsible




for almost all urban CO emissions  (see Appendix A).  The inventory of




vehicular emissions has two components:   (1)  primary network  link




emissions from vehicles traveling  on the network of major arterial




streets and freeways, and  (2) secondary background emissions  from




vehicles traveling over the less densely traveled local and feeder




streets.





          The primary network links for which the emissions are computed




are the sections of major  arterial streets and freeways between inter-




sections with other major  arterials and freeways.  The average length




of the links on the primary network is approximately one mile, although




the links may be much shorter in densely traveled downtown areas, and




more widely spaced in outlying areas.  Figure 2 illustrates the network




used for the Washington, D.C., area.  Computer-generated displays of




the links, like that in Figure 2,  are very useful for  detecting errors




in coding.





          Traffic volumes  on links vary hour-by-hour over a day and  are




different for weekend days than for weekdays.  Further, there are




smaller seasonal variations.  Highway engineers and planners  average




these variations into a quantity that they call average daily traffic




(ADT).

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                                                                    TA-7874-18S

FIGURE 2   COMPUTER-GENERATED DISPLAY OF TRAFFIC LINKS IN A 24-BY-24-MILE
           CENTRAL PORTION OF THE  PRIMARY NETWORK FOR WASHINGTON, D.C.

-------
          For use in the synoptic model, the emissions must be expressed
as hourly averages, so the average daily traffic is expressed as a func-
tion of time.  The amount taken to occur within any given hour is based
on the hourly distribution of trips compiled by the traffic study
agencies of many areas.  A typical weekday diurnal pattern of trips is
shown in Figure 3.  There are, however, limitations to the accuracy of
the assumption that the traffic on each link is distributed like the
hourly trip pattern.  We know that trips taken during the morning and
evening peak hours are longer than those taken during other times of
the day, and that the pattern of use of different kinds of streets in
different parts of the city is different, as shown by the comparison in
Figure 4 of hourly volume on a freeway and a downtown arterial in the
St. Louis area.  It is preferable to use the data on hourly distribution
of trips, rather than hourly traffic volume, because it is easier to use
and more widely available.  In Section V of this report, an hourly
traffic pattern has been determined on the basis of statistical compari-
sons of calculated concentrations and those measured at the Continuous
Air Monitoring Program (CAMP) Station in St. Louis.  That diurnal pattern
clearly reflects the traffic in the central city area around the CAMP
Station.
          Urban transportation studies generally do not explicitly survey
or forecast weekend travel.  This is because peak traffic loads on most
of the facilities in the area occur on weekdays during the morning and
evening commute hours.  Urban highway networks are therefore designed
to handle these peak loads.  Because of this preoccupation with peak
weekday traffic, little weekend travel data is available.  It is known,
however, that peak loads occur on certain rural or suburban roads used
for travel to recreational areas during weekends, and that the traffic
patterns on Sunday vary significantly over time and space from weekday
patterns.

-------
                 04      08       12       16       20       24

                          HOUR OF DAY — LST

                                                   TA-7874-14



FIGURE 3   HOURLY  DISTRIBUTION OF TRIPS IN WASHINGTON, D.C.
        12
        10
      w
      O
      <
      cc
      LU
      u
      cc
      HI
              I
                      II    I    I   I    I    I    I
                                 RADIAL EXPRESSWAY


                                 CIRCUMFERENTIAL ARTERIAL
                                             I    I
         00
                 04
08       12       16

 HOUR OF DAY — LST
                                                 20
                                                         24
                                                   TA-7874-1S
    FIGURE 4   HOURLY  DISTRIBUTION  OF TRAFFIC FOR TWO

                FACILITY TYPES IN ST.  LOUIS

-------
          Data that show weekend travel patterns are based upon a very




limited sample—from five permanent locations  in Nashville, Tennessee




(Institute of Traffic Engineers, 1965).  These data show that total




Saturday traffic is about the same as  the average daily traffic (ADT),




and that total Sunday traffic is about 70 percent of ADT.  Hourly traffic




flows are also available from these counting stations.  From these data,




diurnal traffic patterns for Saturday  and Sunday have been prepared and




used in the diffusion model operation.





          In order to calculate the contribution of the emissions from




traffic links within the five closest  segments, the links are first




identified with the segments through which they pass.  Then the length




of the link that lies within a given segment is determined.  The compu-




tational scheme developed for making these determinations is illustrated




in Figure 5.  For these calculations,  the segment boundaries are taken




as straightline fits to the curved boundaries  illustrated in Figure 1.




The coordinate system is transformed to one that originates at the re-




ceptor and is oriented in the upwind direction.





          The emissions within the four segments farthest from the re-




ceptor are calculated by a different technique than that used for the




closer segments.  The outermost segments are larger than those nearby,




and it was felt that the spatial resolution achieved by the link assign-




ment technique was not necessary when  the emissions were to be averaged




over the entire large area, of each outer segment.  The scheme that was




developed requires less computation time than  the link assignment method.





          Before other computations begin, the city is divided into a




grid of one-mile (1.6 km) squares.  The traffic link data are used to




determine the average daily CO emission in each of these squares.   This




is accomplished by dividing each link  into small increments, less than




0.08 km long.   The average daily emission from each of these small pieces






-------
               READ IN X,  Y, 6
             COMPUTE SIN e. COS 6
          READ IN TRAFFIC LINK DATA
              *  •  *  »
             x,, Vr x2, y2, V, f, L
     TRANSFORM AND ROTATE COORDINATES
        x = (x*  X) cos 6   (y*  Y) sin 0
        y = (x*  X) sin 6 + (y*  Y) cos 0
                     T
           RECEPTOR
              POINT
        CHECK FOR LINK  FALLING WITHIN
       DIFFUSION SECTOR; DETERMINE AREA
       SEGMENTS CONTAINING END POINTS
                     1
         LOCATE INTERSECTIONS OF LINK
           WITH  BOUNDARIES DIVIDING
                AREA SEGMENTS
         LOCATE INTERSECTIONS OF  LINK
           WITH SIDE BOUNDARIES OF
               AREA SEGMENTS
LOCATES A's
LOCATES B's
      COMPUTE PROPORTIONATE LINK LENGTH
       FALLING WITHIN EACH AREA SEGMENT
         COMPUTE AND ACCUMULATE CO
      CONCENTRATION CONTRIBUTION FROM
         LINK TO EACH AREA SEGMENT
           REPEAT FOR OTHER LINKS
                                                             RECEPTOR
                                                               POINT
                                                                               TB-7874-4
FIGURE  5   SIMPLIFIED SCHEMATIC DIAGRAM OF  TRAFFIC  LINK ASSIGNMENT SUBROUTINE
            USED  FOR THE FIVE SEGMENTS CLOSEST TO THE RECEPTOR

-------
is determined by assuming emissions  are spread uniformly along  the  link.

Then,  the emissions  from all the  small pieces of  link within a  square

are  added together to give total  daily emissions  for that square.   This

total  is paired in the computer memory with the coordinates of  the  point

at the center of the square.  These  calculations  are done only  once for

the  city. <

           A trapezoidal grid system  is used in the  four outer emission

segments.  As the location of the receptor changes  or the wind  direction

changes, these trapezoidal grids  are superimposed on different  parts of

the  fixed city emission grid described in the preceding paragraph.

Figure 6 shows a superposition of a  movable trapezoidal grid (marked by
           +   4-   +  +   +
                                           Small section of fixed emission grid
                                           (crosses). The CO emission per unit
                                           area is initially  computed at these
                                           grid points from traffic link data.


                                           Eighth segment of diffusion sector
                                           and movable trapezoidal grid (circles).
                                           Emission values for segment grid are
                                           interpolated from the values of the
                                           fixed emission grid (crosses).
                                                           TA-7874-77

         FIGURE 6   ILLUSTRATION OF THE GRID-POINT TRANSFORMATION
                    TECHNIQUE USED FOR COMPUTING THE CO EMISSIONS
                    WITHIN THE FOUR MOST DISTANT SEGMENTS
the  circles) on  the fixed city  grid (marked by  the crosses).  The  average

emissions at each  point on the  trapezoidal grid are determined  by  inter-

polation between the values at  the  points on  the  fixed grid.  The  average

of the emission  values determined  for the points  on the trapezoidal grid

defines the emission rate for the  segment.


-------
          A technique similar to that just described was used  to determine




the emissions due "to traffic on the secondary streets.  The average




secondary emissions were determined for squares two miles  (3.6 km) on a




side (see Section III-A-3).  The secondary emissions were  then determined




from the value on the fixed two-mile grid for each of the  nine movable




segments, using basically the same superimposed-grid technique just




described.  However, for the small segments near the receptor, the trape-




zoidal grid was replaced by a single point at the segment  center.  Once




the emissions due to the secondary traffic were determined, they were




added to those already determined, either directly (for the first five




segments) or indirectly (for the outermost segments), from the primary




traffic link data.





          Traffic data sources and the data handling varied with the use




of the model.  Data obtained from measurements of past traffic were used




as inputs to produce comparisons with the CAMP Station data.  Traffic




forecasts were used to calculate pollution concentrations  for future




years.   The traffic data were obtained and treated as described below.








     2.    Calculation of Primary Network Emissions Using Historical Data





          Historical data for the network description, the node coordi-




nates,  and link distances are obtained from highway and street maps.




The network is described by assigning numbers to the intersections, or




nodes,  of the network and by identifying the pairs of nodes that are




connected by links.   The coordinates of the nodes establish the locations




of the traffic links in the network.  Link distances are measured along




the links, rather than as the shortest distance between the nodes, al-




though,  as noted in the preceding section, the assignment  of the emissions




assumes that the link is a straight line between the nodes.

-------
          Historical  link-volume data  are  obtained  from  traffic  depart-


ments in the cities,  towns, and counties  in  the  region being  studied.


These agencies sample  traffic volumes  by means of portable  counting


units and a few fixed  installations.   Their  observations may  be  almost


continuous, or as  infrequent as once every two or three  years.   Because


traffic varies according  to seasonal,  weekly, and daily  cycles,  an ob-


servation of volume for one day must be adjusted for  the weekly  and


seasonal fluctuations.  The resultant  corrected  value is recorded as  the


average daily traffic  (ADT) for that location.



          The emission rate, e  (g/vehicle-mile), is determined from the


equation
                                      8
                                e =  c  SM                          (III-l)
where S  is  the  average  speed  over  the  link,  in mi/hr,  and  c and 3 are


constants.  For vehicles  in use  before exhaust control  systems, c =  1121


and 3 =  -0.849, as  determined by Rose  et  al.  (1964)  from observations on


a number  of vehicles  in several  locations.



          Link  speeds for use in the emission rate calculation are de-


termined  from averages  for peak  and off-peak travel  hours  on various


kinds of  route  facilities.  Speed  data were  obtained from  the traffic


survey.   For example, speeds  used  in the  Washington,  D.C., area were


based upon  the  study  by Wilbur Smith and  Assoc.  (1958)  and are shown in


Table I.



          For other locations, the peak traffic  hour speeds were  taken


as equal  to 80  percent  of the off-peak speeds.   Peak-hour  speeds  were


generally assigned  to the four heaviest traffic  hours of the day.

-------
                                Table I
        AVERAGE SPEEDS FOR WASHINGTON,, D.C., HIGHWAY  FACILITIES




Facility Type
Suburban Freeway
Downtown Freeway
Suburban Arterial
Downtown Arterial
Local or Feeder Street
Average Speeds
(mi/hr )

Peak Traffic Hours
(0700-0900, 1600-1800)
42
33
30
24
10
Off-Peak Traffic Hours
(0000-0700, 0900-1500,
1800-0000)
48
39
36
30
12
          Accuracy of the historical data is  limited by  the  frequency


with which it is recorded and by the accuracy of  the factors used  to


correct it to average daily traffic.  However, since locations with
                                     /

heaviest traffic are generally monitored most often, the most confidence


may be placed in data of highest volumes.
     3.   Calculation of Secondary Traffic Emissions


          Using Historical Data



          The number of vehicle-miles traveled on streets not represented


by the primary network is computed from an estimate of  the  total vehicle-


miles traveled in the area and the total vehicle-miles  on the links of


the primary network.  The local street mileage is taken to  be the dif-


ference between the two.  It is distributed over the study  area by esti-


mating the relative density of local streets as opposed to  parks, open


spaces, or streets already coded, for each four-square-mile area in a


two-mile-by-two-mile grid covering the area.  The emissions from the


local street travel in a given square are assumed to emanate uniformly




-------
from that square.  Although the emission per mile per vehicle is high




on these local streets because of low speeds, the overall contribution




is small because of the small number of vehicles on these local streets.








     4.   Calculation of Emissions Using Forecast Traffic Data





          Most urban areas in the United States have completed or are




conducting an area-wide transportation study to determine traffic de-




mands and transportation facility needs for future years, e.g., 1980 or




1990.  Such studies are required for participation in federal highway




programs.  An important result of these studies is a design of a future




traffic network for the area and a forecast of the traffic volumes on




the links of this network.  The procedure for conducting these studies




has been highly developed and partially standardized (see Appendix B).




The emission inventory components of the model are designed so that the




network description (including link length and facility types), link




volume, and link speed data of the widely used traffic-planning com-




puter programs, in magnetic tape form, can serve as input for the diffu-




sion model.  In most cases, the only manual step required will be the




measurement and coding of node coordinates for the network.





          Traffic forecasts include travel on both primary and secondary




networks.  The primary network links are usually represented in the




analysis just as they appear on the street map.  However, local or




feeder streets are represented in the traffic forecast analysis as




connectors between the assumed center of population of a traffic zone,




where all traffic in that zone is assumed to originate, and points on




the primary network.  The vehicle-miles on connector links therefore




approximate those expected on local streets, but the traffic is concen-




trated on a few links, rather than spread over a broad area.  This is




compensated for in the model by averaging the emissions from these links








-------
over a background grid.  The connector links never explicitly appear  in




the spatial positioning process where individual links are analyzed.





          Accuracy of the forecast traffic data is difficult to estab-




lish.  One study that sought to appraise the accuracy of earlier  fore-




casts was unsuccessful in finding a case where the planning recommendations




had been followed sufficiently closely to make the actual situation




equivalent to the conditions for which the forecast was made (Highway




Research Board, 1968).  Checks made to establish the adequacy of  cali-




bration of the forecasting models are usually considered successful  if




the forecast for present conditions gives link volumes in wide corridors




within 10 to 20 percent of counted volumes.  Variations between the




volumes on individual streets within the corridor may be much wider since




the models do not distinguish between parallel routes as readily  as do




drivers.





          Historical emission rates were computed from a formula  derived




from emission data taken from actual highway driving.  Comparable data




for the 1966-70 model vehicles are not available.  It was therefore




necessary to develop a baseline of performance for the 1968-70 autos in




order to apply the proportional controls for future model years.  The




controls used in the 1968-70 era improved emission performance for




acceleration, deceleration, and idle conditions more than for steady




cruise conditions.   Since the acceleration, deceleration, and idle con-




ditions are more prevalent at the lower average speeds, the greatest




reduction in emissions due to new control devices is realized for the




lower average speeds.





          To determine the approximate nature of the improvement, data




on an engine with and without emission controls (Beckman et al.,  1967)




have been used together with data on driving conditions encountered on




various types of roads.   These driving data were collected by SRI for






-------
an earlier project.  A computer program was  developed  to  determine  the


carbon monoxide emissions per mile versus  average  speed for route seg-


ments sampled  in  the road-test data.



          One  hundred thirty-nine emission values  were calculated from


emission data  presented by Beckman et  al.  (1967) and from actual obser-


vations of speeds,  speed changes, and  stops  for a  variety of road types


and traffic  congestion conditions.  Regression analysis was used to


examine the  relation between emissions and average speed,  both with and


without controls.   The following power function proved to be the best


fit for 1969 model  year automobiles:
                                   -0.48
                          e = 245 S          ,                    (III-2)
where e  is  the  carbon monoxide emission  in grams per mile, and S is the


average  speed on  the network  link in miles per hour.



          Increasingly  stringent regulations on exhaust emissions will


require  further reductions  in CO emissions from automobiles.  The best


estimates of future levels  of controls are that allowable emission


values on the test cycle will be reduced from the equivalent of 34 grams


per mile  (1.5 percent by volume) in 1969, measured on the federal test


cycle, to 4.5 grams per mile  on the test cycle for 1980 and later model


year automobiles.  These values were derived from estimates provided by


Mr. Seward  of the Ford Motor Company and from work done at NAPCA (Rose


and Krostek, 1969).  Although it has been shown that emissions at lower


speeds were reduced more than at higher  speeds for the 1969 controls,


the best estimates of future emission control performance is that


emissions will be reduced by  the same amount under all engine perfor-


mance conditions.  Therefore, a proportional reduction of the emission


model coefficient, equal to the ratio of the allowable emission values





-------
 in  1969  and  1980, has  been  applied  to the 1969 emission model to make


 it  applicable  to post-1980  automobiles.   The resulting emission model


 for  1980 and later model  year  automobiles is:
                                   -0.48
                           e -  34  S                              (III-3)
where e  and S are as defined before.





B.   Meteorological Inputs



     1.   Gaussian Standard Deviation Function



          The Gaussian model requires that we know  how  the  standard


deviation, o , of the vertical distribution  of  the  concentration  Iron  a
            z

line source changes as the pollutants travel downwind.   There  are


several  authorities for these functions  (see Slade,  1968).   In one


approach different functions are  given for different  atmospheric  sta-


bilities.  In the other approach, a single function is  specified, con-


taining parameters whose values may depend on the stability  or turbulent


mixing conditions.



          There are several criteria for  the selection  of one  set oi


functions over another.  First, the functions should  describe  dittusive


behavior as accurately as possible.  For  our model,  they must  be capable


of being accurately approximated by power functions over the intervals


defined by the boundaries of the model's  emission segments.  Finally,


and very importantly,  the proper function or parametric  values  lor a


given atmospheric stability must be easily determinable  from routine


meteorological observations.   With regard to the last item,  it  is


preferabie that  the functions be determinable Irom  observations made


at short intervals,  rather than from those made only  once or twice a


day.   The observations should also be made within the environs of the




-------
city being studied.  Thus  functions  dependent  upon  hourly  suri'ace  meteoro-

logical observations are preferable  to  those based  on  the  twice-daily

upper air observations.

          Several  authors  have  given estimates of a as  a  function of
                                                    z
atmospheric stability  and  the distance  that a  cloud or plume  has  traveled

(e.g.., Hilsmeier and Gifford,, 1962;  Smith,  1968; Pooler,  1961).  On the

basis of the criteria  presented  earlier,  we have selected  a  set of curves
developed by Gifford (1961)  from Pasquill's  (1961)  work.   In  this  pre-

sentation^ atmospheric turbulent conditions are divided  into  six cate-

gories, and a curve of O   versus distance traveled  is  given  for each of
                        Z
the six.  Methods  for  selecting  the  proper  stability category have been

developed; these are discussed  in  the next  section.

          After selecting  the Pasquill-Gifford curves, they were approxi-

mated by power functions as  required by  the model.  The  behavior of the
cloud has not been defined by Pasquill or Gifford for  distances less
than 100 m.  Pooler (1966) and McElroy  (1969)  have  found that there is
an initial rapid mechanical  mixing of pollutants released  from ground
level sources in urban areas.  To  approximate  this  effect  the pollutants

were assumed to mix immediately  upon release to the point  where a   was
                                                                 z
equal to its value at  125  m  according to  the Pasquill-Gifford curves.

It then remains constant at  that value throughout the  first segment.
Using this assumption,  the Pasquill-Gifford curves  were extended to very

short travel distances.

          For those conditions where  there  is  rapid mixing, a quickly

becomes very large.  The Pasquill-Gifford  curves do not extend lo  values
of O  greater than 3 km.   Because  the box model will generally be  in
    z
effect for such large  values of  0  ,  and because the ground level con-
                                 z
centrations accompanying these large  o 's will, in  any event,  be very

-------
small-, it was felt that the curves could be arbitrarily extrapolated

beyond a  values of 3 km without serious consequence  to the  calculated
        z
results.

          Figure 7 shows the a  curves used for the calculations with
                              z
the model.  For the first segment (i = 1, r < 125 m), a   is  a  constant

for each stability type, j.  Beyond that the Pasquill-Gifford  curves

have been approximated by the power law representations—shown as

straight line segments on the log-log plot.

          Although the model currently is based on the Pasquill-Gifford

specification of a  as a function of travel distance, it would be a
                  z
simple matter to change to another specification should that be desired.

All that is required is a new set of constants, the a  's and  b 's in
                                                      ij         ij
Eq. (II-3), to describe the new functions.  As long as the new functions

are described by exponential expressions, the rest of the basic model

remains the same.
     2.   Stability Category

          Once we have a set of a  functions, we must be able to select
                                 z
the proper one for the calculations.   Methods were sought for determining

atmospheric stability from conventional meteorological measurements.  To
be useful, any method chosen had to define stability in a way that was

consistent with the definitions used originally to determine the a
                                                                  z
functions.  Other sets of a  functions might require different approaches
                           z
than those given in this section.                                  '

          Two methods of stability determination have been used with

this model.   One was developed from Pasquill's criteria by Turner (1964)

for use with another model and was simply cast in computer-compatible

form for these studies.   Turner's technique was used for the examples

-------
CO
10J
 8
 6
           10
            8
            6
                                   10
                                                                     i  = 1
                                                                  EXTREMELY
                                                                   UNSTABLE
                                                                                            SLIGHTLY
                                                                                            UNSTABLE
MODERATELY
UNSTABLE
                                                                                                              NEUTRAL
                                                                                                              SLIGHTLY
                                                                                                              STABLE
                                                                                                        MODERATELY
                                                                                                        STABLE
                                                           — 2
                                                         ^4^5^6-^-^S^-^
                                                                                                 10"
                                                      r, DISTANCE FROM SOURCE — m
                                                                                                           10=
                                                                                                                TA-7874-46

-------
of synoptic calculations given in later sections.  Because  this method




was rather complicated, we returned to the original definitions of




stability used by Pasquill to classify his data and developed  a some-




what simpler approach directly from these.  This technique  was used  for




the climatological examples presented in  later sections.  The  two methods




generally, but not always, give the same  stability category for a given




set of data.  The methods are described in more detail in Appendix C.








     3.   Mixing Depth





          To apply the box model it is necessary to know the depth to




which the pollutants will be mixed.  Considerable effort was expended




to find a method of estimating mixing depth that required only surface




meteorological observations.  Our attempts started with the  assumption




that the daytime mixing depth should be closely related to  the amount




of heat added to the lower layers of the  atmosphere and to  the resulting




change in temperature during the period of heating.  When mixing depths




were determined by these methods and compared with mixing depths deter-




mined from temperature soundings, it was  found that the two  sets of




values were virtually uncorrelated.  For  this reason we were forced  to




use upper air data, either directly or indirectly, to determine mixing




depth.   We had hoped to avoid the use of  these extra data for reasons




of simplification.  At this time, that does not seem feasible.





          Two methods have been devised for calculating mixing depth.




They are described in detail in Appendix D.  The method used for the




synoptic calculations presented in later  sections of this report uses




the morning temperature sounding taken by the nearest U.S. Weather




Bureau station.   This sounding, when combined with the afternoon maximum




temperature, allows us to calculate an afternoon mixing depth.  Early




morning mixing depths make use of a simple model of the mixing layer







-------
over urban areas proposed by Summers  (1966) and an empirical relation-




ship among city size and urban and rural nighttime temperatures developed




by Ludwig (1970).  A single value of mixing depth is assumed to apply




throughout the urban area, although mixing depth variations have been




observed by Clarke (1969) and Bornstein  (1969), and modeled in limited




fashion by Summers (1966) and Leahey  (1969).





          The other method, which has been used with the climatological




model, is basically the same, but makes use of preprocessed mixing depth




data obtained from Mr. George Holzworth of the National Air Pollution




Control Administration.  Use of Mr. Holzworth's tabulations simplifies




the data processing.





          Neither method discussed above provides values of mixing depth




for all hours of the day, so interpolation must be used.  Again,  two




methods were employed.  For the climatological model, mixing depth was




interpolated on the basis of time between its early morning and its




afternoon values.  The synoptic model interpolated hourly mixing depths




on the basis of observed hourly temperatures for daylight hours and on




the basis of time for the premidnight evening hours.   Both interpolation




schemes assumed that mixing depth remained constant during the hours be-




tween midnight and dawn.  The reasons for this are discussed in Appendix




D.  In general, all the methods gave consistent, though not identical,




results.








     4.   Wind Speed and Direction





          The wind velocity is the only input parameter that is available




as a routine measurement.   However, these observations are mostly taken




at airports,  where the surface roughness and atmospheric stability are




generally quite different than within the built-up part of the city.  It




is known that these different conditions cause variations in wind speed






-------
and direction between the outskirts (where the airports  are  located)


and the center of "the city.  Available measurements of these wind


variations, however, are fairly meager.



          In one study, Graham (1968) found an urban/rural average wind


speed ratio for Ft. Wayne of 0.67 at 15-m height and 0.64 at 60 m.  These


observations also show the wind direction over the city  to be backed by


10° to 15° from that at the outskirts.  In Nashville, Schnelle et al.


(1969) found the roof-level wind speed (U ) to be related to the airport
                                         r

wind speed (U ) as
             a
                      U  = 0.33 U  + 1.0 m/s    ,               (III-4)
                       r         a
where the overbars refer to daily averages.  These results are mostly


for daytime conditions.  At night the wind speed at low levels over the


city is likely to be higher than that at the airport, due to the greater


mechanical and thermal mixing and the presence of convective local cir-


culations over the city.




          In view of the uncertainties in our knowledge of the modifica-


tion of the airflow by the city, we have used the airport surface wind


velocity measurements directly as the transport wind input for the model.


Particularly for daytime use, this may not be a bad approximation.  Al-


though the airport surface wind is generally higher (in daytime) than


the urban "surface" wind, the appropriate input for the model is a mean


wind in the layer between from 50 to 100 m above the surface.  Since the


wind speed increases with height, a higher wind speed than that at the


urban "surface" is appropriate, and the higher airport wind may help


compensate for this.

-------
                                                          *
          At any rate, we have used airport winds directly  in the model


trials, with the idea of correcting the winds for urban effects later by


using a statistical technique to adjust the wind input for the best


agreement between observed and calculated CO concentrations.  The re-


sults of this "calibration" procedure are given in Section V-B.



          A further point of some importance is that the present model


cannot handle the case of calm winds  (which are fairly common at air-


ports) without some adjustments.  The nocturnal urban circulation for


the stagnation case has been reasonably well documented (e.g., Pooler,


1963; Hilst and Bowne, 1966; Clarke,  1969) and takes the form of a con-


vective cell driven by the urban heat island.  On this basis, and taking


into account the fact that most anemometers will not respond to very


light winds, we assume in the model a minimum speed of 1.0 m/s  for an


airport wind reported as calm.  We assume further that the wind direc-


tion is the same as the most recently measured direction.  Other


approaches to this problem are possible, but they require the develop-


ment of special models, which was beyond the scope of this first-year's


work.
*                                        o
 In terms of direction, to the nearest 10  or sixteenth point of the

 compass, as appropriate for the different model configurations.



t
 In some of the early calculations, a minimum speed of 2.0 m/s was used.

-------
           IV  ORGANIZATION AND APPLICATIONS OF THE SYNOPTIC




                       AND CLIMATOLOGICAL MODELS








A.   Introduction





     The synoptic model takes the data for a single hour, calculates




and displays concentrations for one or more points within the city for




that hour, and then proceeds to the next hour.  This is repeated on an




hour-by-hour basis for some limited time period of interest.  The tem-




poral changes of concentration for a specific location can be compared




with the measured values during the same period.  The climatological




model provides the statistics of CO concentration for different loca-




tions and various averaging periods.





     It was originally planned that the two models would employ signifi-




cantly different approaches.  The synoptic model was to calculate con-




centrations, in sequence, using hour-by-hour meteorological observations,




whereas the climatological model was to use meteorological statistics to



determine the frequency of occurrence of different CO concentrations.





     As the work has proceeded, the constraints imposed on the clima-




tological model, particularly by the requirements for the statistics of




the concentrations averaged over periods longer than an hour, have caused




the climatological model to become very much like the synoptic model.




The two models are discussed in the following sections:  first the




synoptic, then the climatological model.  This order is important be-




cause the climatological model eventually developed through simplifica-




tion of the synoptic model.  In its final version, it appears that the




climatological model could very serviceably replace the synoptic model




with little sacrifice in accuracy.






-------
B.   The Synoptic Model





     1.   Description





          The organization of the synoptic model is shown  in Figure  8.




In this flow chart it is assumed that the traffic data for the city  are




already stored and that the inputs consist of the meteorological




parameters and the city population and latitude.  These items are neces-




sary for the application of the subroutines for computing  stability




category and the mixing depth.  The calculations start by determining




the afternoon and early morning mixing depths from the appropriate




sounding.   Then the meteorological parameters for the starting hour  are




read and the stability class determined.   Mixing depths are interpolated




by the appropriate method,  concentrations are calculated, and then the




next hour's data are read.





          The calculations referred to in the box with the double out-




line in Figure 8 are performed using the basic models.  The appropriate




form of the model, Gaussian or box,  must be applied in each oi the up-



wind segments.  Thus, the Gaussian formula,  Eq.  (II-4), is used for all




segments up to the distance, r ,  that marks the transition to the box




model.   The box model, Eq.  (II-5), is used for those segments beyond r .




If r  occurs in segment N,  then the model is summarized by the following




equation
    C = -



1
u

/
N-l

/ Q
^^^j i
\
/ l-ta 1-b \"
I i i i-j I
O.SIr J - r J I
\ i+1 i /
i-< i \
a .( 1 - b I



r - r
N+l T
h





i r\
+ QN

/ 1-b 1-b \
1 il ill
O.Slr J - r J 1
\ T N /
a. .(l - b. \
-
\
9
E-
Qi
i=N+l
r - r
i+1 i
h






"

                                                                 (IV-1)

-------
                                     READ POPULATION. LATITUDE. INITIAL TEMPERATURE
                                   SOUNDING, DATE, MAXIMUM AND MINIMUM TEMPERATURES,
                                           AND LAST OBSERVED  WIND DIRECTION
                                    CALCULATE  INITIAL VALUES OF AFTERNOON AND NIGHT
                                             MIXING DEPTHS (SEE APPENDIX)
                                     READ HOUR OF DAY. CEILING HEIGHT, CLOUD COVER,
                                        TEMPERATURE. WIND SPEED, AND DIRECTION
                                    IF WIND IS CALM ASSIGN SPEED THE VALUE 1.0 m/s AND
                                            USE THE LAST OBSERVED DIRECTION
                                               DETERMINE STABILITY CLASS
IS
IT
DAY'
                                                  HAS SUNSET OCCURRED WITHIN THE PAST HOUR?
                        DETERMINE MIXING DEPTH
                        FROM AFTERNOON VALUE
                        BY TEMPERATURE INTER-
                        POLATION
          DETERMINE MIXING DEPTH
          FROM AFTERNOON VALUE
          BY TEMPERATURE INTER-
          POLATION
                                                                          READ NEXT MORNING'S
                                                                         SOUNDING AND MAXIMUM
                                                                       AND MINIMUM TEMPERATURES
                                      DETERMINE MIXING DEPTH
                                       BY INTERPOLATION (ON
                                       BASIS OF TIME) BETWEEN
                                      NIGHT VALUE AND VALUE
                                       AT FIRST HOUR AFTER
                                              SUNSET
 USE
NIGHT
MIXING
DEPTH
 CALCULATE AFTERNOON
AND NIGHT MIXING DEPTHS
             CALCULATE CONCENTRATION
              FOR ONE  OR MORE POINTS
               AND DISPLAY  RESULTS
 STOP
                                                                                     TA-7874-13 R
FIGURE 8    SIMPLIFIED  FLOW  CHART  FOR  SYNOPTIC MODEL CALCULATIONS.
                Using  radiosonde  data, Turner's stability index and temperature interpolation.

-------
This equation can be expressed in simplified fashion  as
                               9

                                   !.rM      •                    (iv-2)
                                       ij

In the simplified version the terms Ex/Q]. . refer  to  the  appropriate
square-bracketed terms in Eq. (IV-1).

          The application of the equation  to the calculation of  concen-
tration is shown in the simplified flow chart of Figure 9.  This  flow
chart is a description of the calculations required in the box with the
double outline in Figure 8.


     2.   Applications

          The synoptic model, as described above,  has been used  in two
different types of application.   In one type, concentration is calcu-
lated for a single hour at 625 points in a square  grid covering all or
a selected area of a city.  These 625 values are then used for an iso-
pleth analysis.  The other application presents the calculated CO con-
centrations at hourly intervals for a week.

          We have taken advantage of computer techniques  for objective
contour analysis and graphical display.  In this work.we  have used
                                                   *
special subroutines called "CONTOOR" and "GRAPH 4"  with  the CDC 6400
computer and the CDC 280 cathode-ray tube  (CRT) peripheral display
system.  The CONTOOR subroutine furnishes  objective isolines describing
the CO concentration distribution over an urban area, on  the basis of
the grid point values calculated by the diffusion  model.  These automatic
graphical techniques expedite trial and evaluation procedures.
^
 These subroutines were developed, respectively, by S. Briggs and
 B. Sifford of Stanford Research Institute.

-------
                                     FROM PROGRAM IN FIG. 8

                                    	J
                                   CALCULATE POINT OF TRANSITION FROM
                                         GAUSSIAN TO BOX MODEL
                                   IS ANNULAR SEGMENT ENTIRELY BEYOND
                                        (Upwind of) TRANSITION POINT?
                    CALCULATE AND
                    STORE VALUE OF
                  THE CONCENTRATION-
                  TO-SOURCE STRENGTH
                  RATIO (x/Q) FOR THE
                    SEGMENT ON THE
                    BASIS OF THE  BOX
                        MODEL.
    IS SEGMENT ENTIRELY INSIDE
   (Downwind of) TRANSITION POINT?
      HAVE ALL ANNULAR
   SEGMENTS BEEN TREATED?
                                         CALCULATE AND STORE
                                             X/Q FOR THE
                                           SEGMENT ON THE
                                             BASIS OF THE
                                           GAUSSIAN MODEL.
                  CALCULATE x/Q FOR THAT
                   PART OF THE SEGMENT
                   INSIDE THE TRANSITION
                   POINT ON  THE BASIS OF
                    THE GAUSSIAN MODEL
                     AND  BEYOND THE
                    TRANSITION POINT ON
                   THE BASIS OF THE BOX
                   MODEL.  SUM AND STORE
                  AS x/Q FOR THE SEGMENT.
                CALCULATE THE AVERAGE
                  SOURCE STRENGTH  FOR
                EACH SEGMENT. MULTIPLY
                   BY THE APPROPRIATE
                   X/Q AND SUM OVER
                     ALL SEGMENTS.
    PROCEED TO NEXT
     RECEPTOR POINT.
                PRINT RECEPTOR LOCATION
               AND SUM OF CONCENTRATIONS
                FROM ALL SEGMENTS, PLUS
                   THE CONCENTRATION
                 FROM OUTSIDE THE CITY
                     (Background level).
HAVE ALL RECEPTOR POINTS
     BEEN TREATED?
                                                 RETURN TO PROGRAM
                                                 IN  FIG. 8
FIGURE  9    SIMPLIFIED  FLOW CHART  FOR CONCENTRATION CALCULATIONS.
               Corresponds approximately to the box with the double outline in Figure 8.

-------
          A sample product of these techniques  is  given  in Figure  10(a).


Here the GRAPH 4/280 display of the CQNTOOR objective  analysis  is  super-


imposed upon the primary traffic network for Washington, B.C.   The corre-


spondence between the CO concentrations and road density is evident.


The calculations used the values of wind, mixing depth,  and stability


shown in the figure.  The objective contouring may be  compared  with a


manual analysis of the identical data, presented in Figure 10(b).   Dif-


ferences between the two patterns were traced to plotting and drawing


errors by the analyst.  The hand analysis is smoother, but the  objective


analysis is substantially faster, cheaper, and more accurate.


          Figure 11 shows two concentration patterns calculated for the


meteorological conditions in St. Louis during the 0600-0700 hour of 16


October 1964.  The difference between these two cases  is in the traffic


data used.   Figure 11(a) illustrates the results based on historical


traffic data.  Figure 11(b) shows those results obtained using  emissions


based on the traffic forecast process when 1965 demographic data were

                 *
used as an input.    Comparison of the two cases shows  that the  traffic


"forecast" yields a slightly lower peak CO concentration.  This may arise


because the forecast program distributes traffic over  a different network


of highways and arterials.


          Figure 12 provides examples of analyses based on 1990 forecast
        *
traffic.    For easy comparison with the 1965 case the  same hour of  the


day and the same meteorological conditions have been used for the calcu-


lations.   Figure 12(a) shows the forecast concentrations for cars without


any emission control devices,  i.e.,  like the 1964 cars.  Comparison of
*
 The traffic forecasts were obtained on magnetic tape from the Missouri

 State Highway Department.

-------
-10
-12
                                              0700-0800 LSI
                                              WIND 270° M m I"1
                                              MIXING DEPTH 200m
                                              NEUTRAL STABILITY
  -12-10-8-6-4-2    0   2    4    6   8    10    12
             DISTANCE EAST OF CAMP STATION — miles
                                                    TB-7874-9S
                  (a)  MACHINE ANALYSIS
 12,	
 10
                                   0700-0800 LST
                                   WIND 270°/4 m r1
                                   MIXING DEPTH 200m
                                   NEUTRAL STABILITY
                                                               I
                                                               N
-12
  -12   -10
                       _8   -6   -4   -2   0    2    4   6    8   10   12
                       DISTANCE EAST  OF CAMP STATION — miles
                                                               TB-7874-8S
                            (b)  SUBJECTIVE ANALYSIS

FIGURE 10    CALCULATED WASHINGTON, D.C.,  CONCENTRATION  PATTERNS

-------
            12 r
            -12
             -12 -10  -8   -6  -4  -2   0   24   6   8   10  12
                    DISTANCE EAST OF CAMP STATION — miles
                                                    TA-7874-25S
                  (a)  BASED  ON HISTORICAL TRAFFIC DATA
            -12
FIGURE 11
-12 -10  -8  -6  -4  -2   0    2   4   6   8  10  12
       DISTANCE EAST OF CAMP STATION — miles
                                        TA-7874-60
 (b) BASED  ON SIMULATED FORECAST TRAFFIC DATA

CALCULATED ST. LOUIS CONCENTRATION PATTERNS  0700-0800,
15 OCTOBER 1964

-------
                o
                I-
                 Q.


                 <
                 o

                 LL

                 O
                 DC
                 O
                 z

                 111
                 o
                 z
                 co
                 D
                     -12 -10  -8  -6  -4  -2  0   2   4   6   8  10

                            DISTANCE EAST OF CAMP STATION — miles


                        (a)  WITHOUT EXHAUST  EMISSION CONTROLS
                                                   12
CO
Q_


<
CJ
                 I

                 cc
                    12


                    10


                     8


                     6


                     4


                     2


                     0


                    -2
                 LU   e
                 O  ~b


                 I  -8
                   -10
                   -12
                                     O.5
                     -12  -10-8-6-4-2  0   2   4   6   8   10  12

                            DISTANCE EAST OF CAMP STATION — miles

                                                             TA-7874-61

                         (b)  WITH EXHAUST EMISSION CONTROLS


FIGURE 12   CALCULATED CONCENTRATION PATTERNS  BASED  ON FORECAST OF 1990

             ST. LOUIS TRAFFIC.  Meteorological conditions  same as in  Figure 11.

-------
this pattern with that in Figure 11(a) shows a very large  increase  in
                  «
forecast concentrations.   Figure 12(b) shows the results for  the  case

where the hypothetical emission control  (as described  in Section  III)

has been applied.  The significant reduction in CO concentrations is


readily apparent.


          By choosing different grid point spacing, the spatial resolu-

tion of the model can be changed.  Figure 13 illustrates this.  The two

halves of the figure show analyses of CO concentrations in St. Louis for

the same hour.  In Figure 13(a) the grid point spacing is  1 mile; in

13(b), 0.1 mile.  Both are centered on the CAMP Station.  The figure

shows that the model is capable of providing concentration patterns in

considerable detail.  It is limited in its spatial resolution, however,

by the size of the emission segments, particularly those nearest  the

receptor.


          The model has been used to obtain concentration patterns in

five different cities.   Examples have already been shown for Washington

and St.  Louis.  Figures 14, 15, and 16 show results obtained for  Chicago,

Cincinnati, and Denver.  These figures are all based on 1965 historical

traffic data.  They show, as do the other figures, the expected high

concentrations downwind of congested downtown areas and major arterials.


          Results of trials using the synoptic model to calculate hourly

concentrations continuously for a week are presented in Figures 17 and

18.  To provide a true test of the model's capabilities, weeks were

selected during which a variety of concentration magnitudes were  ob-

served,  as shown by the dashed curves in the figures.  These figures

and those that follow do not necessarily show examples of  the best agree-

ment between calculations and observations, but are representative of the

kinds of results achieved.   In an attempt to treat the effects of nearby

sources  more accurately,  the closest diffusion area segment was divided




-------
                Q-

                <
                o
                I
                DC
                O
                •
                LU
                O
                CO
1500-1600 CDT
15 OCTOBER 1964
WIND 310°/1.5m s"1
MIXING DEPTH 1670m
UNSTABLE
                                -8-6-4-2    0    2    4    6    8   10  12

                                DISTANCE  EAST OF CAMP STATION — miles
                                                                       TA-7874-26s
                                (a)  1-MILE (1.6 km) GRID SPACING
                   -1.2
                      -1.2 -1.0 -0.8  -0.6 -0.4  -0.2   0   0.2  0.4  0.6   0.8  1.0  1.2
                               DISTANCE  EAST OF CAMP STATION — miles
                                                                       TA-7874-24S
                               (b) 0.1-MILE  (0.16  km) GRID SPACING

FIGURE 13    CALCULATED ST. LOUIS  CONCENTRATION PATTERNS FOR  TWO GRID SIZES

-------
        -20
-15
 -10      -50        5       10
DISTANCE EAST OF  CITY CENTER — miles
15
                                                                             TA-7874-62
FIGURE  14   CALCULATED CARBON MONOXIDE  CONCENTRATIONS (PPM)  FOR CHICAGO.
            (0700-0800  LST, wind 270°/4 ms~1,  mixing depth 200 m, neutral stability)

-------
-12     -10
-6-4-20      24      6

  DISTANCE EAST OF CAMP STATION — miles
10
                                                                                TA-7874-73
FIGURE 15    CALCULATED CARBON MONOXIDE CONCENTRATIONS  (PPM) FOR CINCINNATI.
             (0700-0800 LST, wind  270°/2 ms~1, mixing depth 200 m,  slightly stable)

-------
-12    -10
-6      -4-20       2       4       6
  DISTANCE  EAST OF  CAMP STATION —  miles
10     12
                                                                              TA-7874-63
FIGURE 16   CALCULATED CARBON MONOXIDE CONCENTRATIONS (PPM) FOR  DENVER.
             (0700-0800 LST,  wind 315°/2 ms~1, mixing depth  400  m, slightly stable)

-------
  o.
  o.
  o
  o
  o
  o
E  §
X

UJ
o
m o
      25  -
      20
  Q    15
       10
                                                          OBSERVED  -


                                                          CALCULATED
   Q.

   UJ

   Q
     4000
     2000
-  tt  400
      200
   S   20
—  uj
o  Q.
       10
       10
                                                          .,. ••««».•.,
                20
            WON
                       40


                     TUBS
                              60


                             WED
80     100     120     140     160 HOURS


THURS-4—  FBI  -I-  SAT   -|«  SUN  —-I
 FIGURE 17
                   ST.  LOUIS,  MO. DATA [JANUARY  18-24. 1965)

                                                               TA-7874-47


             OBSERVED AND CALCULATED CO CONCENTRATIONS AT THE


             ST. LOUIS CAMP STATION,  18-24 JANUARY 1965. The


             meteorological inputs to the model are also shown.

-------
  o.
  a


  1
  o
  o
  o
  o
     4000
J  £ 2000
   X

   i

  Q

  o
  o

  UJ
  Ld

  Q.
  Q

  2


  5
  in
  i
400






200






  0


 20







  10







  0



  10
o
z
i!
               20
           MON
                40



              TUES
 60


WED
80


THURS
                                         100
                                                120
                                                      140
                                            FRI  -!•" SAT —*+



                  ST. LOUIS. MO. DATA (OCTOBER 19-25.  1964)
  160 HOURS



SUN —|






TA-7874-49
 FIGURE  18  OBSERVED AND CALCULATED CO CONCENTRATIONS AT THE

            ST. LOUIS CAMP STATION, 19-25 OCTOBER 1964.  The

            meteorological inputs to the model are also shown.

-------
into two sections for these calculations  (see Appendix E).  One  segment

extends from the receptor to 62.5 m in range, and the other extends from

62.5 out to 125 m.  The calculations also include estimates of the ex-

traurban background, i.e., contributions  from emissions outside  the

city, made with the model described in Appendix F.  Figures 17 and 18

also show the values of the meteorological inputs to the model,  either

as observed or as calculated.

          The CO observations during the January period (Figure  17) were

anomalously high, and the model generally gives underestimates for this
     *
week.   A variety of weather conditions prevailed; cold fronts passed

St. Louis on the evenings of 17, 19, and  23 January.  The poorest per-

formance of the model occurs on 19, 21, and 22 January, when the wind

was generally southerly.  This suggests that the high observed concen-

trations may be caused by the nearby sources on the adjacent streets,

since the St. Louis CAMP Station is located on the northwest corner of

an intersection.

          Weather conditions during the October period (Figure 18) were

not so variable, and more typical CO concentrations were observed.  In

contrast to the January period, the predicted concentrations are often

too high.  The worst agreement occurs when the airport winds are reported

as very light or calm.  For these calculations, the model used a minimum

wind speed of 2 m/s and, as noted earlier, the last observed wind direc-

tion.  It is probable that much of the prediction error is due to this

uncertainty in winds.
 The possibility of water vapor  interference as a  source  of  some of  the
 discrepancy between observed and calculated concentrations  is discussed
 in Section VI of this report.

-------
          Many additional  calculations of the type illustrated  in Figures

17 and 18 for St. Louis  have  been carried out for Washington, B.C.;

Cincinnati, Ohio; Chicago,  Illinois;  and Denver, Colorado.   Some  ex-

amples of these  are  given  in  Figures  19 through 22.  Prevailing meteoro-

logical conditions are also shown in  Figures 20 through 22.   It can  be

seen that a wide variety of meteorological situations are represented.

In general, the  agreement between calculations and observations leaves

much to be desired.  The measurement  program to be conducted  during  the

coming year should help  us  to identify the sources of the discrepancies

and to make corrections.
                   40      60      80     100     120      140

        MON  -|-» TUES »[•  WED -|« THURS -| •   FBI—• | •  SAT—-|

                    WASHINGTON, D. C. DATA (October 19-25, 1964)
  160 HOURS

•SUN-


  TA-7874-48
   FIGURE 19   OBSERVED AND CALCULATED CO CONCENTRATIONS AT THE
               WASHINGTON, D.C., CAMP STATION, 19-25 OCTOBER 1964

-------
O> UJ
V OL

  5

  o
         UJ
         0.
         §
             0
             20
             10
       x
       UJ
       Q
                                                         •.-^ .«•""•" """



                                                         1,1,
       ^ 0

       =! 8
       CD -J
       20
                                                        140
|— MON •
                                                            SAT
                       CINCINNATI. OHIO DATA  (DECEMBER  W-20. 196^)
                                                               160 HOURS

                                                              SUN -~\





                                                             TA-7874-50
FIGURE 20   OBSERVED AND CALCULATED CO CONCENTRATIONS  AT THE CINCINNATI

             CAMP STATION, 14-20 DECEMBER 1964.  The meteorological  inputs to the

             model calculations are also shown.

-------
       o.
       Q.
       O
       O

       O
       o

       o
       o
           35
           30
           25
           20
15
            10
                                                           OBSERVED


                                                           CALCULATED
          4000-
          2000-
        x
        5
        p 400
        o
        LU
        Q:

        Q

        Q 20°
            0


            20
        Q
        UJ
        bj
        CL
        in
      E Q
10
     "  ^   0

     8  ™   10
        §
        o

        o

        o
                                          80     100     120     140


                                         -THURS-4—  FRI  -I'  SAT



                          CHICAGO. ILL DATA  (JULY  20-26.  1964)
                                                          160 HOURS


                                                         SUN -—I





                                                         TA-7874-51
FIGURE 21   OBSERVED AND  CALCULATED CO CONCENTRATIONS  AT THE CHICAGO

             CAMP STATION,  20-26 JULY 1964.  The meteorological inputs to the model

             calculations are also shown.

-------
                        DENVER.  COLO.  DATA  (APRIL 19-25. I965)
                                                     160 HOURS
                                                   SUN



                                                   TA-7874-52
FIGURE 22
OBSERVED  AND  CALCULATED  CO CONCENTRATIONS AT THE  DENVER
CAMP STATION,  19-25 APRIL 1965.  The  meteorological  inputs to the  model
calculations are also shown.

-------
C.   The Climatological Model

     1.   Background

          There are two different approaches to calculating climato-

logical summaries of the concentration of carbon monoxide at a  site.

The most commonly used approach starts with a joint frequency distribu-

tion of all the meteorological variables that affect the concentration.

For our model there are five variables:  wind speed and direction,  time

of day, mixing depth, and stability.  There would be 24 categories  of

time, and 16 of wind direction.  Six categories each for wind speed and

mixing depth, and five categories for stability would probably  provide

sufficient resolution for climatological purposes.  With these  numbers

of categories, the joint frequency distribution would have 69,120

entries.

          As will be shown in a later section, some combinations of

stability and mixing depth are essentially equivalent to others.  By

combining equivalent categories it should be possible to reduce the

number of categories by about a third to a half.  This reduction would

make the indexing of the variables slightly more difficult but would

reduce the number of entries in our joint frequency table to about
      4
4 X 10 .  If only eight wind-direction categories were used, this number
                               4
could be halved to about 2 X 10 .

          The method that has been described above gives the frequency

distribution of hourly values of CO concentration.  To obtain the fre-

quency distribution of the 8-hour or 24-hour average values requires

some statistical model, such as Larsen's (1969).  Since there is some

uncertainty about the validity of Larsen's model  (e.g., McGuire and

Noll, 1970) we felt that it might be better to approach the problem

more directly.  If the individual calculated hourly values of concen-

tration are available, in sequence, it is possible to use "running mean"


-------
type operators to get the distribution of concentrations  averaged  over
periods greater than an hour.

          We have already shown that a very  large number  of  categories

have to be considered for the conventional approach using the  joint  fre-

quencies of the input parameters.  In fact,  the number of categories

could be very nearly as large as the number  of hours  in a five-  to ten-

year period.  Thus, it seemed reasonable to  consider  the  possibility of
calculating hourly values in sequence.  This approach, which is  described

below, was found to be practical and was adopted.


     2.   Description

          a.   Simplifications

               To calculate a long series of concentrations economically

requires some simplification of the model.   It is possible to represent
the source strengths of the segments as the product of a  time-dependent

factor and a time-independent factor.  Thus
                           . ^ <.    +.
                           i,d,t    t i
where
                                               th                  th
          Q      = the source strength of the i   segment, in the d
           i)d>t                       th             -2  -1
                   direction, for the t   hour.  (gm m   s  )

            Q    = the average daily source strength, based on total
             i,d
                   traffic and average speeds on the different roads
                                             -2  -1
                   within the segment.   (gm m   s  )

-------
                                                                     th
              P  - a factor that gives the source strength for the  t


                   hour, based on daily distribution of traffic, and


                   changes in average speed during peak hours.  P   is


                   assumed to be independent of the location  in the


                   city.  In some of the previously presented synoptic


                   applications, P  has assumed different values for


                   different road types.



To further limit the number of conditions to be considered, mixing


depths have been classified into seven categories (<100 m, 100-200 m,


200-400 m, ..., >3200 m).  With these simplifications, the model can be


written as follows:


                               9
                           p  	
                            t V >

                       c = —
where



          C - CO concentration at the receptor



          u = wind speed


                                                               th
 CX/Q) .      = ratio of the CO concentration received from the i   seg-


              ment to the emissions in that segment (for unit wind


              speed).  The values of these ratios depend on stability


              class,  j, and mixing depth class, m.



               The values of 
-------
                              9




                    Xj m d ~X/'~'      Qj  -     '               (IV~5)

                             1=1    ->">™



Then, for a given receptor site, all possible values of X      can be


calculated and stored in a 5 X 7 X 16  (stability  type X mixing depth


category X direction) array.  These values need only be calculated once


for each receptor.  These numbers, when combined  with the 24-item list


of P  values, provide the information  necessary to calculate concentra-


tion at a given receptor.  The storage space required is less than 600


numbers.  The operating equation for the climatological model is




                                     (P \
                                       t\
                                     —     .                     (IV-6)

                                     u /
          b.   Preprocessing of the Meteorological Data



               Equation  (IV-6) can be applied most easily when we have


converted the usual meteorological observations to a sequence of records


of time  (t), stability (j), mixing depth category  (m), direction on a


16-point compass  (d), and wind speed  (u).  This preprocessing of the


data is described in Appendix G.  Five years (1960-1964) of St. Louis


meteorological data have been condensed and recorded on magnetic tape.


These five years of data constitute a reasonably stable climatological


description of that city, although anomalies of this duration do


occasionally occur.  Five years of data are used partly because


Holzworth's tabulations of mixing depth cover only a five-year period,


and partly because longer periods of record would  increase the calcu-


lation time disproportionately to the small increase in climatological


accuracy.  Although it is quite possible in principle to use radiosonde


data from the National Weather Records Center to extend the period of

-------
record, their data are not universally available on magnetic  tape  for

all U.S. stations, and the processing of large quantities of  punched
cards presents practical difficulties.


     3.   Applications

          The preprocessed data are used as the climatology of  the city.

The effects of changes in the transportation network or of emission con-

trols are then assessed by determining a set of values of Q   . which
                                                           i,d
are used to calculate X     .   The five-year meteorological data se-
                       j,m,d
quence is used with Eq. (IV-6) to determine a sequence of CO  concentra-
tions.  A simplified flow chart showing this process is given in Figure
23.

          In Appendix H it is shown that there are different combinations
of stability and mixing depth that give the same value of (X/Q)      for
                                                                i,j,m
all the upwind segments.   Because this is the case, we were able to re-
duce the stored number of values of (y/Q)     .   This results in a corre-
                                         i,J,m
spending reduction in the required number of values X     ,  from 560 to
                                                     j,m,d
400 per site.   The simplified model makes it feasible to calculate a
sequence of CO concentrations for each of a number of points in the city.
Once this is done, these sequences can be treated as though they were
sequences of real observations.   Thus, it is possible,  without resorting
to a statistical model, to calculate any of the statistical parameters
that can be determined from sequences of real hourly observations.   This

includes the frequency distribution of 8-hour averages, 24-hour averages,
or the frequency distribution of any special subset of the data.

          As noted above,  the output of the climatological model can be

treated in any way that observed data can be treated.  This means that

the potential  number of outputs is virtually unlimited.  For purposes

of illustration, a computer program has been written to determine ten


-------
yes
                                                       (
                                                             START
           No
                                                INPUT THE FOLLOWING DATA:




                       1.  Q   for 9 upwind segments d), 16 wind directions (d), and n number of city locations




                       2.  (X/Q). .    for upwind segments, stability classes (j), and mixing categories  (m)




                       3.  P   's for different hours of day (t) and days of week (w)
                           t,w



                       4.  Determine, and store values of X      for n city locations
                                                       J.m.d
                                 Read first record: year, month, day, and m, j, u, and d for 24 hours
                                           Determine if  it  is a  daylight savings time month
                         Determine  the day of the  week code:  w   1  is weekday, w   2 is  Saturday, and  w   3


                         is Sunday
                             Adjust t to account for daylight savings time and set  u  < 1.0  m/s to 1.0 m/s
Calculate
p t,W
u
or t 1,24 and fo
9 / Y \
S ( X I n
U/ .
1 = 1 M, m
,
r n number of city locations
+ extraurban contribution
,d
r
Record year, month, day of week, and C for 24 hours and n city locations
i
r
Read next record: year, month, day, m, j, u, and d for 24 hours


                                                                                                TA 7874-41 R
             FIGURE 23    SIMPLIFIED  FLOW  CHART OF CLIMATOLOGICAL MODEL

-------
different frequency distributions based on the output from  the  cliraa-




tological model:





          (1)  All hours, a frequency distribution based on




               the total five-year set of hourly calculated




               concentrations





          (2)  All weekday hours





          (3)  All Saturday hours





          (4)  All Sunday hours





          (5)  All 0800 hours





          (6)  All 1200 hours





          (7)  All 1800 hours





          (8)  All 2400 hours





          (9)  8-hour means; frequency distribution of the




               averages of the values calculated for all 8-




               hour periods in the five-year sequence





          (10) 24-hour means; same as (9), except for 24-



               hour averages.





          A simplified flow chart for the program used to calculate the




above frequency distributions is shown in Figure 24.  This program also




computes cumulative distributions, and determines median (50 percentile)




and 90-percentile values by log-linear interpolation between the points




calculated on the cumulative distributions.





          We used the climatological model to calculate a five-year




sequence of CO concentrations at nine locations, including the CAMP




Station in St. Louis.  For these calculations, a constant 0.25 ppm




background concentration was added, based on the observations of






-------
                                                                         SET FREQUENCY  0 FOR FACH DATA SUUTYPF
                                                                            AND EACH LOCATION WITHIN THE CITY
                                                                             READ FIRST 24 HOURLY VALUES OF
                                                                            CONCENTRATION FOR EACH LOCATION
                                                                          DETERMINE SUM OF CONCENTRATIONS TOR
                                                                           HOURS 1 THROUGH 2-1 AND 17 THROUGH
                                                                                '14 FOR EACH LOCATION
                                                                         READ AND DETERMINE CONCENTRATION CLASS
                                                                         (• 0 25 ppm . 0 76 - 0 5 ppm ,        >64 p»m )
                                                                            FOR NEXT HOUFtLY  CONCENTRATION
                                                                          ADO 1  TO FREQUENCY IN PROPER CLASS FOR
                                                                               TYPE I DISTRIBUTION (See Tax!)
                                                                                                 IS IT SATURDAY
IS IT A
WEEKDAY '
                                                                                                I YESING
ADD 1 TO FREQUENCY
IN PROPER CLASS FOR TYPE
2 DISTRIBUTION (See Texl)

ADD 1 TO PROPER
CLASS FOR TYPE 3
DISTRIBUTION (S«e Text!

ADO 1 TO PROPER
CLASS FOR TYPE A
DISTRIBUTION (See Text!
                                                                      ADD CONCENTRATION TO 24-HOUfl SUM AND SUBTRACT
                                                                     VALUE FOR 2-5 HOURS EARLIER ADD CONCENTRATION TO
                                                                     8-HOUR SUM AND SUBTRACT VALUE FOR 8 HOURS EARLIER
                                                                           DIVIDE 21- AND 0-HOUR SUMS BY 24 AND 8
                                                                        RESPECTIVELY AND DETERMINE THE CONCENTRATION
                                                                             CLASS OF THE  RESULTING AVERAGES
                                                                       ADD 1 TO THE FREQUENCIES IN THE PROPER CLASSES
                                                                         FOR THE TYPE 9 AND 10 DISTRIBUTIONS ISei- Text)
YES
YES
*
ADD 1 TO FREQUENCY
IN PROPER CLASS FOR
TYPE 7 DISTRIBUTION
(Sue Te*ll



ADD 1 TO FREQUENCY IN
PROPER CLASS FOR TYPE
6 DISTRIBUTION ISce Text)
                                             ADD 1 TO FREQUENCY IN PROPER
                                             CLASS FOR TYPE 8 DISTRIBUTION
                                                     (See Ten)
 I
a
                                 a —
                                                 IS IT END OF FILE
                                       SUM THE FREQUENCIES IN EACH CONCENTRATION
                                         CLASS TO DETERMINE TOTAL NUMBERS OF
                                          OCCURRENCES FOR EACH DISTRIBUTION
                                                 TYPF AND LOCATION
                                      DETERMINE RELATIVE CUMULATIVE FREQUENCIES
                                         if. TOTAL PERCENT OF OCCURRENCES LESS
                                         THAN EACH OF THE CLASS BOUNDARIES
                                        FOR EACH DISTRIBUTION TYPE AND LOCATION
                                       DETERMINE MEDIANS AND ")0 PFRCENTILF. VALUES
                                       BY LOG LINEAR INTERPOLATION BETWEEN CLASS
                                           BOUNDARIES, FOR EACH DISTRIBUTION
                                                 TYPE AND LOCATION
                                               PRINT STATISTICAL RtGULFS
                                                                                                    TA-7874-64

FIGURE  24     SIMPLIFIED  FLOW  CHART  FOR  A  PROGRAM  TO  DETERMINE  TEN  DIFFERENT
                     FREQUENCY  DISTRIBUTIONS

-------
Robinson and Robbins (1967).  The calculations used  traffic emissions




appropriate to 1965.  We then applied the program diagrammed  in Figure




24 to these results and obtained frequency distributions of the types




enumerated above for each of the nine sites.





          Figure 25 shows the calculated St. Louis CAMP Station fre-




quency distributions for weekday, Saturday, and Sunday hours.  The figure




shows the expected decrease in the frequency of the  higher concentrations




on the weekend, and the corresponding increase in the lower concentra-




tions.  Figure 26 shows the frequency distributions  of concentrations at




0800, 1200, and 1800 Local Standard Time.  The greater frequencies of




high concentrations at 1800 are quite evident.  The  0800 also shows a




considerably greater number of occurrences of concentrations above 2 ppm



than does the 1200 distribution.   Figure 27 shows the frequency distri-




butions of concentrations averaged over three different time intervals,




1-hour, 8-hours,  and 24-hours.  Qualitatively, the results are just as




expected.  The mode remains the same, between 1 and  2 ppm,  but the spread




of the distributions decreases appreciably with increased averaging time.





          The output of the program can also be used to determine spatial




variations of certain statistical parameters.   For example, Figure 28




shows the variation of the median and 90-percentile values for nine sites




along a north-south line passing through the St.  Louis CAMP Station.   As




expected, the highest values are calculated for the downtown area, where



the CAMP Station is located.





          The calculations described in the preceding paragraphs were




repeated using the emissions based on the 1990 traffic forecast for




St. Louis.   The results are displayed in Figures 29  through 32.  As was




evident in Figure 12,  the hypothesized emission controls result in a




decrease in CO concentration from 1965 to 1990, although the amount of




traffic increases.   Some of the same qualitative features are seen in






-------
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                  40
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1 . . i . .. ,1 	 l '
                    O.I   0.2    0.5   I     2     5   10   20


                          CO   CONCENTRATION 	  ppm
50
                                                     TA-7874- 93R
FIGURE  25   CALCULATED ST.  LOUIS CAMP  STATION CO CONCENTRATION  FREQUENCY

            DISTRIBUTION FOR  1965 TRAFFIC CONDITIONS; WEEKDAY, SATURDAY,

            AND SUNDAY HOURS

-------
  60



__, 50


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£ 40



w 30


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                                                (c)  1800 HOURS
                                           I
    O.I   0.2    0.5   I     2     5


           CO   CONCENTRATION  	
                                                      10   20
50
                                                      ppm

                                                        TA-7874-S4R
FIGURE  26    CALCULATED  ST. LOUIS  CAMP STATION CO CONCENTRATION  FREQUENCY

             DISTRIBUTION  FOR 1965 TRAFFIC CONDITIONS;  0800, 1200, AND 1800 HOURS

-------
   70





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•
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-
m
-
B

-
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                               0.5
                                                   10  20
                                              50
                                                 ppm
                                                     TA-7874-59R
FIGURE 27   CALCULATED  ST. LOUIS CAMP STATION CO CONCENTRATION FREQUENCY


            DISTRIBUTION FOR 1965 TRAFFIC CONDITIONS; 1-HOUR, 8-HOUR, AND


            24-HOUR  AVERAGES

-------

4.0

3.5


3.0

i
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2.5
7
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t
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- 2.0
j
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1.0
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\ -
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\ 90 PERCENTILE _
\
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\
\
\
X —
N
X
\
\ --- .» 	 -
\^^ 50 PERCENTILE
ill i i
-8-6-4-2 02 4 6 8
DISTANCE NORTH OF ST LOUIS CAMP STATION — miles
TA-7874-56F
FIGURE 28   SPATIAL VARIATIONS OF CALCULATED ST  LOUIS MEDIAN AND 90 PERCENTILE

-------
INTERVAL
CO o
0 §
s 60
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1 1 1 , 1 1 ll j 1 1 1 1 1 1 1 1 1 ,1

, ,1 • 1 , l| | , T | . . , , | |
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-
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0.2 0.5 1 2 5 10 20 5(
rr\ r*r\w^CMTD AT inw 	 nnm
                                                     TA-7874-65

FIGURE 29  CALCULATED ST. LOUIS CAMP STATION CO CONCENTRATION FREQUENCY
           DISTRIBUTION FOR  1990 TRAFFIC CONDITIONS;  WEEKDAY, SATURDAY,
           AND SUNDAY  HOURS

-------

100
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-------
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0.2 051 2 5 10 20 5<
r. r* f nki r* 1- kl -f n « -V , f\*t 	
                                                      TA-7874-67
FIGURE 31   CALCULATED ST. LOUIS CAMP STATION CO CONCENTRATION  FREQUENCY
            DISTRIBUTION FOR 1990 TRAFFIC CONDITIONS; 1-HOUR, 8-HOUR, AND
            24-HOUR AVERAGES

-------
u.a
0.8


0.7
. 0.6
i
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50 PERCENTILE

"
—
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1 1 1 1 1 1 1
-2-10                     1

                       DISTANCE NORTH OF ST. LOUIS CAMP STATION — miles
     FIGURE 32    SPATIAL VARIATIONS OF CALCULATED ST. LOUIS MEDIAN AND
                  90  PERCENTILE CONCENTRATIONS FOR 1990 TRAFFIC CONDITIONS
                  with emission controls

-------
the 1990 frequency distributions at  the CAMP  site  as were  seen  in  those




based on 1965 emissions.  Figure 29  shows  that  the higher  concentrations




occur more frequently on weekdays  than on  weekends, and Figure  30  shows




that higher concentrations are more  likely at 1800 than at 1200 or  0800.




These results are certainly as expected, considering that  we have not




changed the diurnal or weekend values of P used in Eq. (IV-6).  If




there were a foreseeable change in working hours,  a change in these




values might be justified.





          Figure 31 for 1990 corresponds to Figure 27  for  1965.  Again




we see the reduction in the spread of the  frequency distribution as the




averaging period is increased.  In this case  the change is not  so pro-




nounced because there are so few high concentration cases  in the dis-




tribution of the hourly values.





          Figure 32 shows the change in the 1990 median and 90-percentile




concentrations along a north-south line through the CAMP site.  The




scales on this figure are different  than those on  the  corresponding




figure for 1965, Figure 28.  Some of the pronounced features of the 90-




percentile curve may be artifacts caused by the log-linear  interpola-




tion used to determine the values.   It suggests that smaller class




intervals should be used when we know that the calculated  concentra-




tions will not reach high values.   Regardless of the artifacts, the




data show that the concentrations remain very nearly the same along




this line for several miles through  the downtown area.

-------
                  V  TESTING AND  IMPROVING THE MODEL








     In the preceding sections, the design of the  basic model was pre-




sented along with the techniques  used  to determine its inputs,  and




examples of the types of output that the model is  capable of producing.




In this section, we will discuss  the way in which  input accuracy affects




the accuracy of the resultant outputs,  i.e., the sensitivity of the




model.  We will also present the  results of an attempt to "calibrate"



the model by comparing its output to the observed  concentrations.








A.   Sensitivity Tests





     It is important to know the  effects in output values caused by




changes in the inputs.  If a very small change in  a certain input re-




sults in a large change in the output,  then the model is very sensitive




to that input and we will be required  to provide values of the  input




that are very accurate, if we are to avoid large errors in the  output.




On the other hand, if large changes in  an input have little effect on




the output, then little effort need be  expended to achieve high input




accuracy for that particular variable.  Of course,  sensitivity  is not




likely to remain constant over the whole range of  values that a par-




ticular variable can assume.  Thus it  is possible  that for certain com-




binations of parametric values,  the model output will be totally




independent of the changes in one  or more inputs.   This, as will be




seen in this section,  occurs with  this model, and  we have referred to




it in earlier sections.   This characteristic has allowed us to  treat




several different combinations of variables as though they were the




same.

-------
     In the following we will discuss the inputs to the model  and  try




to illustrate their interdependence and their effects on  the output.








     1.   Source Strength





          If source strength were to increase or decrease by some  factor




uniformly throughout the city, then the resultant change  in the  calcu-




lated concentration would be quite straightforward.  The  calculated




concentration would increase or decrease by the same factor.   Similarly,




if our emission estimates were uniformly in error, then that error would




show proportionally in our calculations.





          A more realistic situation would be the case where the




emissions are poorly estimated for individual upwind segments  of the




model.  In this case the change in the output will depend not  only on




the relative magnitude of the error in emission, but also on the seg-




ment in which the error occurs and on mixing depth and stability.  The




relative effect also depends on the average emission rates in  other




segments.





          To test the effects of errors in the different segments, cal-




culations were made for a case where the true source strength was taken




to decrease linearly away from the receptor and to reach zero  at 32 km




upwind.  For a site at the center of the city, this is probably a




reasonable approximation of the distribution of emissions.  To test the




sensitivity of the model to changes in source strength in the different




segments,  we doubled the emissions (relative to those specified by the




assumption of a linearly decrease with distance) in one segment at a




time.   The results of these calculations are given in Table II.  This




table shows the percentage increases in the total calculated concentra-




tions that result from the doubling of the source strength in  the




individual segments.  Four stability types and two different mixing




depths are represented in the table.





-------
                               Table II
     PERCENTAGE INCREASE IN CALCULATED CO CONCENTRATION RESULTING

       FROM THE DOUBLING OF EMISSION RATES IN DIFFERENT SEGMENTS
Stability
Class*
1
2
3
4
1
1 2
3
4
Mixing
Depth
(m)
50
50
50
50
3000
3000
3000
3000
Segment with Doubled Emission
1
1.4
2.1
3.1
4.5
26.9
22.3
14.6
9.8
2
1.0
1.5
2.1
3.3
17.8
15.9
10.2
7.3
3
1.5
1.6
2.2
3.7
15.2
16.0
10.4
8.2
4
3.0
3.0
3.0
4.3
9.1
14.4
11.1
9.4
5
5.9
5.8
5.7
5.5
3.5
11.2
11.7
11.2
6
11.2
11.1
10.8
10.1
3.6
6.6
12.3
13.4
7
20.1
20.0
19.4
18.1
6.4
4.0
12.5
15.5
8
31.0
30.6
29.8
28.0
9.8
5.3
11.4
16.1
9
24.8
24.4
23.9
22.4
7.8
4.4
5.7
9.1
 1 = Extremely unstable
 2 - Moderately unstable
3 = Slightly unstable
4 = Neutral.
          For the low mixing depth case  (50 m) there is a general in-

crease in the contribution caused by changes in source strength as one

progresses toward the segments farthest  from the receptor.  The box

model is employed for most of the calculations when the mixing depth is

low, and it specifies that the contribution from a segment is propor-

tional to the upwind distance subtended  by that segment.  Since the

outer segments are considerably larger than the nearby segments, their

contribution is consequently greater.  This effect is suppressed in the

larger mixing depth cases where contributions from the nearer segments

are mixed through a shallow layer compared to those from the further

segments.

          The table indicates that for some combinations of stability

and mixing depth,  appreciable uncertainties can be introduced into the

calculations by uncertainties in the specification of source strength.


-------
Other factors to be considered include the possibility  that errors  in




specifying emissions may be compensating and therefore  not so  important.





          Finally, errors in emission values due to  improper location  of




highway links are much more apt to be large, relative to the total  source




emission in the smaller, close segments, than they are  in the  large




outer segments.  When the mixing depth is low, Table II shows  that errors




in nearby source strengths cause relatively small errors in the calcu-




lated concentration.  It is only for the larger mixing  depths  that the




errors in the nearby segments produce large relative errors in the cal-




culated concentrations.  However, for large mixing depths the  concentra-




tions tend to be lower and of much less importance to planners.








     2.   Wind Speed





          Of all the inputs,  the most straightforward effect on the model



output comes from wind speed.   Since both the Gaussian and box models




yield concentrations that are inversely proportional to the wind speed,




then the overall model will also have this characteristic regardless of




where the transition occurs between the two submodels.   As the model is




presently constituted,  observed wind speeds less than 1 m/s are not used,




so for observed wind speeds less than this value the model output would




not change.   For higher wind  speeds the calculated concentrations will




vary inversely as the wind speed,  providing the other parameters remain



invariant.







     3.   Wind Direction





          With regard to model sensitivity, wind direction and source




strength are closely related parameters.  Variations in wind direction




only change the values used for the emissions in the segments  upwind of




the receptor, so the effects of changes of segment source strengths dis-




cussed earlier can, to some extent, be interpreted in terms of wind






-------
direction effect.  However, this requires  that we  know  something  of  the




changes in source strength as a function of direction from  the receptor.




If the receptor is located at the edge of  the city,  then  changes  in  wind




direction can shift the emissions in the segments  from  large  to small  as




the wind shifts from the city to the countryside.  Such changes would  be




likely to occur in almost all the segments, for  such a  case.





          For locations near the center of the city, the  farther  and




larger segments are not likely to change much with direction  because




the large numbers of streets within the larger areas will tend to smooth




out the fluctuations.  However, for the nearby segments that  may  on  the




average contain only a few streets, the variations are  likely to  be




large.  Since the nearby segments contribute appreciably  to the calcu-




lated concentrations, we may expect substantial  variations.





          To provide an example of the kinds of  changes that  might be




expected to arise from changes in wind direction,  some  sample calcula-




tions have been made; they are illustrated in Figure 33.  Two sets of




meteorological conditions are shown; we can see  that the relative




changes are about the same in both cases.  There is about a 3:1 dif-




ference between the largest and the smallest calculated concentrations.




The calculations were made at 22.5° increments,  and it can be seen that




the largest difference between adjacent directions amounts to about  60




percent.  Thus, it seems reasonable to estimate  that an error in  wind




direction specification of 22.5" could result in errors as  large  as  a




factor of two.





     4.   Location of the Receptor





          Another factor that is closely related to source  strength  is




the accuracy with which we can specify the location of  the receptor




relative to the traffic links.  The arguments are  essentially the same




as those given above for direction, i.e., moving the receptor relative




to the links changes the location of the various upwind segments,  and




hence changes the source strengths used for the  calculations.





-------
               Q.
               O.
oo
to
O



I


O
O
                     6
                                             I
                                         I
I
I
I
                                 50
                             100        150       200       250

                                WIND  DIRECTION 	 deq from N
                    300
                    350



                    TA-7874-6R
                        FIGURE 33   EFFECT OF WIND DIRECTION ON CONCENTRATIONS COMPUTED FOR

                                    THE WASHINGTON, D.C., CAMP STATION.  (0700-0800 LST, neutral


-------
          A study was made  to determine  the  sensitivity  of  the model  to




errors in the location of the receptor.  The  study was conducted  by




moving the coordinates of the receptor point  from its original location




in increments of 0.1 mile and determining  the effect of  the  displacement




on the concentration.  Increments of 0.1  (0.16  km) mile  were chosen be-




cause this is the coding precision for most  of  the areas studied,  al-




though in crowded central areas, coordinates have been coded to the




nearest 0.01  (0.016 km) mile.  Figure 34 shows  changes in the calculated




CO concentration arising from displacements  of  the receptor  in the down-




wind (x) and crosswind (y)  directions.  The  initial location corresponds




to the Washington, D.C., CAMP Station.  In this area, with  its dense




network of major streets, concentrations are fairly sensitive to  the




location of the receptor relative to the streets.  Outside  the densely



packed downtown area, the sensitivity to location is much less.





          The figure shows  that changes in calculated concentration of




more than a factor of two do occur within 0.1 mile (0.16km).  However,




for a precision of location of about 0.01 mile  (16 m), the changes would




be limited to a few tens of percent or less, regardless  of wind speed.




The model would probably be more sensitive to these errors for the cases




of low mixing depth and high stability.








     5.    Stability and Mixing Depth





          Stability and mixing depth interact to determine which  of the




two submodels are used for  the calculation of the contribution of




emissions from a given segment.  To determine the effects on the model




output of variations in stability and mixing depth, calculations were




made using two different configurations of carbon monoxide emission.




In the first case, source strengths were assumed to be the same in all




nine segments of the model.   It was assumed that there were  no emissions







-------
Q.
Q.
z
o
i
LJ
O
O
O
o
o
       -1.0
  -0.5               0
RECEPTOR LOCATION  DISPLACEMENT (X)
          (a)  ALONG-WIND
 a.
 a
UJ
o
o
o
o
o
       -l.O               -0.5               0                 0.5
                       RECEPTOR LOCATION  DISPLACEMENT M 	 mi
                                 (b)  CROSS-WIND
     FIGURE  34   EFFECT OF  MOVING RECEPTOR POINT
                  (Washington,  D.C., CAMP  Station; 0700-0800 LST, wind 270°/4 ms
                  neutral  stability,  mixing depth  200 m)
                                                         1.0
                                                   TA-7574-5R
                                                      -1

-------
beyond the outer boundary of  the  last  segment,  32  km  from  the  receptor.




The results of calculations for this source  configuration  and  for




various combinations of stability  and  mixing depth are  shown in Figure




35(a).  The results have been normalized  to  represent unit wind speed




and unit source strength.  In this figure we see that all  the  results




are essentially the same for  low values of mixing  depth, regardless of




stability.  For very shallow  mixing layers,  the box model  is used for




almost the entire distance upwind  of the  receptor.  Since  the  box model




results are independent of stability,  the fact  that the results converge




at small mixing depths is to  be expected.





          The neutral and slightly unstable  cases  shown in Figure 35(a)




are unaffected by mixing depth for the larger values of the parameter.




This  too is quite reasonable  because mixing  of  the emitted material




proceeds rather slowly under  the more  nearly stable conditions and the




mixing is uninhibited by the  top of the mixing  layer, if it is suffi-




ciently high.  In such cases, the  Gaussian model is used for the con-




centration calculations throughout the entire 32-km upwind distance.




The results of Gaussian model calculations are  independent of mixing




depth.





          For the moderately unstable  and extremely unstable cases the




box model is used in the calculations, for at least some segments, for




mixing depths to 3000 m.   However, the number of segments  for which the




box model is applicable decreases with increasing mixing depth, so that




calculated concentrations become less dependent on mixing  depth as that




parameter increases.  This is reflected in the continual approach of the




slope of the curves toward zero.    It also suggests that the 4000 m upper




limit that was placed on mixing depth, in some applications of the model,




will have very little effect on the results.

-------
oo
05
                 1000
                  800
                  600

                  400
   200

a
O 100
    80
    60

    40


    20


    10
\   I  I  I  I I I
                             MODERATELY UNSTABLE
                                        EXTREMELY UNSTABLE
                         (a) UNIFORM SOURCE STRENGTH

                        I II  I I I	I	I  I   I  I I  I
                       50      100
                                               500    1000
                                               T	1	1—I  I  I I I
                                                                               MODERATELY UNSTABLE
                                                                                              EXTREMELY UNSTABLE
                                  (b) SOURCE STRENGTH DECREASING
                                     LINEARLY FROM RECEPTOR

                                          	I    I   I  I  I  I I  I I	I    I
                                50     100
                     MIXING DEPTH — m
                                                                                                   500     1000
                                                                                                                 TA-7874-38
                           FIGURE 35   NORMALIZED CONCENTRATION AS A FUNCTION OF STABILITY AND

-------
          As noted  before,  the  assumption of a uniform source strength




over  the  city  is probably  less  realistic than an assumption of a source




strength  that  decreases from the center  of  town  to  its  edge.   We  recal-




culated the cases used for  the  curves  in Figure  35(a),  but  used  a source




strength  that  linearly decreased from  two units  at  the  receptor  to zero




32-km upwind.  The  results  of these calculations are  shown  in Figure




35(b).  Again, the  results  have been normalized  to  represent  unit wind




speed and unit average source strength.   Qualitatively,  the  two  source




configurations produce similar  results.   However, the dependence  on




mixing depth is less for all cases.  This is  because  the mixing  depth




dependence is  the result of those parts  of  the calculation based  on the




box model.  The Gaussian model  is used for  calculations  of concentrations




due to emissions from segments  close to  the receptor.  The box model,  if




used at all, applies to the farther segments.  In this  source  configura-




tion the emission rates in  the more distant segments are less  than those




in segments close to the receptor.   Thus, the contributions  that  the box




model makes to the  results  are  smaller than those for the uniform area




case.  This decreases the effect of mixing depths upon  the normalized




concentrations.





          The results displayed in Figure 35(a)  suggest  that  for  some




values of mixing depth,  the results obtained  from the model are nearly




independent of stability.   For  certain stability types,  changes  in the




mixing depth produce no changes in the results,  if  the mixing depth is




sufficiently large.   We have made use of  this latter fact in  the  de-




velopment of the climatological model.    It allows us to consider  certain




combinations of stability and mixing depth to be identical with certain




others.   As noted earlier,  this simplifies calculations and reduces the




amount of computer memory required.

-------
B.   Use of Observations to Improve  the Model





     1.   Introduction





          The formulation of the model given in earlier  sections  of  this




report was based entirely on empirical and  theoretical considerations




of traffic emissions, and meteorological diffusion and transport.  No




adjustable constants have been used.  It is clear that the  accuracy  of




this model could be improved if we were to make some use  of  observed




carbon monoxide concentration data.  In this section we will discuss a




method whereby this information can be incorporated into  the model.  In




developing a method, we have attempted to make statistical  adjustments




with as little damage to the physical basis of the model  as  possible.




If the model is to be useful in a variety of cities, it should be de-




veloped from sound physical principles, rather than by purely statistical




means.  The physical phenomena underlying the model will  remain the  same




from city to city, but we cannot assume the same to be true  of the




statistics.  Of the inputs to the model, source strength, wind speed,




and wind direction have been chosen as the most amenable  to  study




through the use of statistical comparison with observed CO concentra-




tions.  Mixing depth and stability were discarded, partly because neither




is amenable to statistical correction.   Both are involved in the model




in such nonlinear fashion that they cannot be isolated from  the rest of




the model for statistical treatment.  Also,  model results are not very




sensitive to mixing depth under most conditions, as was shown in the




preceding sensitivity analysis, so that if the mixing depth  is specified




incorrectly,  it may be less serious than an incorrect wind speed or




source strength,  which are directly related to the output.





          In considering source strength,  we have assumed that it is




directly related to the total daily traffic and to the average speeds,




but there is uncertainty about how the emissions are distributed through






-------
the day.  This uncertainty inseparably includes considerations of the



proportionality of emission rates and traffic amounts.  As will be seen



in the following sections, uncertainties in source strength can be mini-



mized by statistical techniques.





          We know that wind speed has a very significant and direct



effect on concentration.  We also know that the transport wind that



moves and dilutes pollutants in the city may be different than the air-




port wind that we have used for our calculations.  The relationship be-



tween the two winds can be determined so as to minimize the differences



between calculated and observed concentrations.





          Finally, wind direction probably plays a part in determining



the background concentrations entering the segment farthest from the re-



ceptor and in determining the aerodynamic effects of structures near the



measuring point.  The gross effects of wind direction at a given loca-



tion can be checked through comparison of calculated and observed



concentrations.





          In the following section an approach to the "calibration" of




the model is presented along with some results.  This approach is by no



means the only one possible,  but we feel that it has a sound physical



basis, and encouraging results have been achieved.








     2.    Attempted Improvements





          As was shown in Section IV-C,  the model can be most simply




expressed in the following form
                                                                 (V-l)

-------
where



          C = calculated concentration due to emissions within  the  city



     X      = the sum of the products of average daily emissions  in the
      j,m,d

              upwind segments and the dilution ratios for  the segments;


              depends on stability  (j), mixing depth  (m),  and wind


              direction (d)


                                                              th
         P  = a factor used to give source strengths for the t    hour,


              based on the daily distribution of traffic and changes  in


              average speed during peak traffic hours



          u = wind speed.





          a.   Background Concentration



               The above equation can be related to the observed  concen-


tration C  for a given time by the following
                      C  = C + e
                       o
                         = x-   ,,  — I + en    ,                  (v-2)
                            j,m,d \u I    1



where e  is the error in specifying the concentration.  If we assume

that part of the error arises from a background concentration 13 entering

the farthest upwind segment of the model, then Eq. (V-2) can be written




                    c  = c + 3 + e


                                 (p \

                                 ;T  + » + «2    •               
-------
In this formulation (3 is a constant, although  it can be made  a  function


of wind direction; e  is the error remaining after  the background has
                    £i

been added to C.






          b.   Wind Speed



               Let us assume that effective urban transport wind speed


u is not correctly represented by the wind measured at the airport, u
                                                                     a

and that the true value of its reciprocal can be approximated by a linear


expression depending upon the reciprocal of the measured wind speed at


the airport, i.e.,
                            1       b
                            - = a + —    ,                      (V-4)
                            u       u
                                     a



where a and b are constants to be determined, and u  is the measured air-
                                                   a

port wind, assumed to have a minimum value of 1 m s  .   Assuming the


dilution factor 1/u to be a linear function of the dilution due to the


airport wind makes it much easier in practice to minimize errors than if


we assumed a linear relation between the winds themselves.



               Making the substitution in Eq. (V-3) gives
                                     \ P
                                     /  t
                              au  +

                 c  = x	'•	 + 3 + e    ,            (v-5)
                  o    j,m,d      u
                                   a



where e is the residual after adjustments have been made.



               The problem is then to use the observed data to determine


the values of the constants.   To do this we used the conventional approach


and minimized the sum of the squares of the residuals.  This procedure


gives the following equations:

-------
                                      X     P \


                                       J;I";d 1  = EC              (V-6)
                                         Ua
                                       2
                                            P
         (3Sx     P  + aSx     p  + bS  J'm'     = EC x.    P      (v-7)
            j,m,d t      j,m,d t     I   u     I     o j,m,d t
    pE. J^Zt) + .flp^L* | + bEM^I = Ef ° J'°'d 1  ,  (v-8)



      \   Ua         .         -      -     a




where N is the total number of cases over which the summations are per-




formed.   The above simultaneous  linear equations were solved for 3, a,




and b using a standard  matrix inversion computer program.  This minimizes




the root-mean-square error for the hypotheses represented in Eq. (V-5),




and for the available data set.








          c.   Diurnal  Distribution of Emissions





               The values of P  have been specified for the model on the




basis of only a few measurements in a limited number of cities.  After




the wind speed corrections have  been made, it is a simple matter to




correct the values of each of the 24 values of P  to minimize the total




differences between observed and calculated values.  After a new set of




P  values has been calculated, they can be used to recalculate the a, b,




and 3.  This iterative  procedure has been used on a set of St. Louis data



(see the examples given in Section V-3);  the correlation and root-mean-




square error were found to stabilize after four repetitions.








          d.   Wind Direction





               The wind direction effect could most easily be included




in the background constant term.  The data could be stratified according

-------
to wind direction and values of (3 calculated for each case.  The average


of these 3 values (weighted by the number of occurrences of each wind


direction in the data set) would be the same as the value of (3 calcu-


lated from the procedure outlined in the preceding sections.  We have


not had sufficient data to stratify according to wind direction, so the


example that follows has not considered that correction.





     3.   Example



          The approach to calibration outlined on the preceding pages


has been applied to data from St. Louis.  The earliest CO concentration


records that we have available from the CAMP Station in St. Louis were


for the month of March 1964.  The records were fairly complete for the


rest of that year.  This provided us with ten months of concentration


data that were concurrent with values that had been calculated using


the climatological model.  We chose to determine the calibration con-


stants on the basis of the available odd-numbered months and to use the


even numbered months as independent data for checking the results.



          To determine if there was an annual variability to the values


of the constants &, b, and $, they were calculated separately for the


weekdays in each of the odd numbered months.  There appeared to be no


regular changes in a and b, but |3 did seem to have a seasonal change.


The seasonal change was incorporated into the corrections.  For the


independent months, values of 3 were interpolated between those found


for the odd numbered months.  The resulting calibrated equation is



                     0.07 u  + 1.4

                 C =	 P X      + 0     ,            (V-9)
                          u         t j,m,d    m
                           a

-------
where


          P  = the adjusted traffic emission  factors determined


               statistically


          3  = background concentration  adjusted for monthly variations.
           m


          The adjusted values of P  are  shown in Figure 36.   This figure


also shows the values of P  derived from trip data.   The corrected curve


shows greater midday emission and lower  night emissions than had been
    0.10  —
                                         Statistically

                                          determined
                                10            15


                                  HOUR OF DAY
                                                                 TA-7874-70
           FIGURE 36   DIURNAL  EMISSION PATTERNS FOR ST. LOUIS



-------
originally postulated.  This probably reflects  the  traffic conditions


in the downtown area near the CAMP Station.  Downtown areas attract


considerable traffic during operating hours but very little at night.


This is reflected in the very rapid  increase in the value of P  at the


beginning of the business day and the corresponding rapid decrease at


its end.



          The performance of the model was considerably  improved by the


derived constants.  Table III shows  the correlation coefficient and


root-mean-square errors of the calibrated and uncalibrated models for


the ten months studied.  The table also shows the values of (3  used for
                                                             m

each month.  With these calibration  factors included, the model predicts


the hour-by-hour concentrations for  the independent months with a root-

                 *
mean-square error  of 3.1 ppm.



          The correlation and root-mean-square error resulting from the


use of "persistence" values have been calculated for the weekdays of the


five independent months.  For these  calculations, the observed CO con-


centration at the CAMP Station was compared with the concentration ob-


served during the same hour of the preceding weekday.  The correlation


was 0.64, with a root-mean-square error of 3.0 ppm, so the calibrated


model performed very nearly as well  as persistence.  Of course, the per-


sistence method cannot be used with  forecast traffic data to estimate


conditions in future years.
*                            /           2
 Root-mean-square error - ~\ /[2(C  - C ) ]/N
                            y    o    c


 where



          N - number of cases
         C  = observed concentration
          o


         C  — calculated concentration.
          c



-------
                                                      Table  III
                                            RESULTS OF MODEL  CALIBRATION
CD
CT)
Month
(1964)
Calibration Months
March
May
July
September
November
Independent Months
April
June
August
October
December
(ppm)

4.2
5.6
7.0
5.6
4.2

4.9
6.3
6.3
4.9
3.5
Uncalibrated
Correlation
Coefficient

0.45
0.29
0.26
0.27
0.45

0.28
0.32
0.16
0.26
0.39
Root— Mean-Square
Error
(ppm)

5.5
6.2
8.8
5.7
5.9

6.9
8.1
5.0
4.7
5.4
Calibrated
Correlation
Coefficient

0.59
0.61
0.63
0.58
0.61

0.58
0.50
0.63
0.53
0.61
Root-Mean-Square
Error
(ppm)

2.0
2.2
2.3
3.8
3.4

2.3
3.7
3.2
3.3

-------
          A second comparison is also available  for  judging  the model's




performance.  We can compare it to climatology.  The root-mean-square




difference between the observed concentrations and the mean  concentra-




tion is the standard deviation of the observed values.  For  the inde-




pendent data this is 3.5, somewhat greater  than  the  model's  root-mean-




square error of 3.1.  As with persistence,  the concentration climatology




is not a useful tool for estimating future  conditions.





          One final check can be made of  the performance of  the cali-




brated model.  We can see how well it reproduces the frequency distri-




bution of observed concentrations.  This  has been done for the independent




weekday hours used in the above calculations; the results are shown  in




Figure 37.  In this figure, cumulative  frequencies are plotted on a  log-




probability graph.  On such a graph, log-normal  distributions appear as




straight lines.  It can be seen that both the calculated and observed




distributions differ somewhat from the  ideal log-normal.  For the high




percentile values, the two frequency distributions agree quite well.




Between the 50 percentile and the 99.9  percentile, the agreement between




the observed and calculated concentrations  is generally within 25 percent.




It is the high percentile concentrations  that are of greatest importance




to planners, and for these the calibrated model  appears to perform very




well.

-------
       1
        0.5 1
                      10       30    50    70      90  95   98 99
                       PERCENT OF HOURLY VALUES < ORDINATE VALUE
99.9    99.99
                                                                    TA-7874-69
FIGURE 37   OBSERVED AND CALCULATED FREQUENCY DISTRIBUTIONS FOR FIVE MONTHS
            OF INDEPENDENT DATA

-------
                    VI  DISCUSSION AND FUTURE PLANS








     This report has presented an approach  to modeling urban CO concen-




trations that meets most of the established objectives.  The model can




calculate hourly concentrations at one or many points in a city.  It




can determine frequency distributions and other statistical information




about CO concentrations.  Source strengths  can be determined from esti-




mates of traffic, either historical or forecast, but assumptions have




to be made about the CO emissions to be expected from the automobiles




of the future.  The meteorological inputs for the model can be deter-




mined from readily available weather data.





     The model is quite versatile, in that  a wide variety of parameters




can be calculated without the need for esoteric input data.  In these




respects the model is satisfactory, but its performance has been dis-




appointing in one most important respect.  For those few places from




which data are available, the hourly concentrations calculated with the




model and those observed are generally in poor agreement.





     The discrepancies between observed and calculated concentrations




may be due to many different causes.   In general, these causes can be




divided into three categories:  (1) inadequate or inaccurate input data




for the model, (2) invalid assumptions used in the formulation of the




model, and (3) unrepresentativeness or inaccuracy of the CAMP observa-




tions.  Specific examples that fall into these categories are discussed




in the following paragraphs.





     The first category of observation/calculation discrepancy is errors




in input data.  Errors in source strength specification immediately come




to mind as an example in this category.   Source strength errors can






-------
arise from erroneous or unrepresentative historical traffic data,  or




from inaccurate relationships between average speeds and emission  rates.




Such errors can come from anomalous traffic situations such as  accidents




or large sporting events, or from assuming an incorrect distribution  of




the total daily traffic among the individual hours of the day.  The re-




sults given in Figure 36 suggest that there may be significant  dif-



ferences between the assumed and the actual distributions in central




St. Louis.  The calculated concentrations are directly proportional to




the emissions from traffic, so inaccuracies in its specification can




contribute substantially to the differences between observed and model




results.





     Meteorological observations from a single station,  usually at the




airport outside the city, are used for the inputs to the model.  Except




for wind, these observations are not used directly, but are transformed




to give the basic inputs to the model, i.e.,  stability type and mixing



depth.   Thus the sources of potential input error are twofold.   First




the meteorological observations themselves may not represent conditions




in the city, and secondly the methods used to transform the observations




into values of mixing depth and stability may not be totally appropriate.




The sensitivity analyses in the report have shown some of the effects of




such errors on the calculated concentrations.   Wind speed and calculated




concentration are inversely proportional.   The relationship among mixing




depth,  stability, and concentration is more complicated.   For unstable




conditions and small mixing depths,  the calculated concentration is al-




most inversely proportional to mixing depth,  other things being equal.




For large mixing depths, calculated concentration increases quite




rapidly with increasing atmospheric stability.  In any event,  the re-




sults achieved with the model can be quite sensitive to the inputs, so




inaccuracies in their specification represent potentially important




sources of the discrepancies between model results and observations.





-------
     The second category  for possible  causes  of  the  discrepancies be-




tween calculations and observations  includes  those that might  arise  from




any invalid assumptions used in  the  formulation  of the model.  The first




assumption made is that the Gaussian model provides  a reasonably accurate




description of the diffusion of  pollutants from  sources near the receptor




and the next  is that  the  rates for this  Gaussian diffusion  can be defined




by the Pasquill-Gifford empirical functions based on data from nonurban




areas.  While it would be difficult  to change  the model to  remove the




Gaussian assumption,  it would be quite easy to use other functions to




describe the  diffusion rates.  Because of increased  mechanical and ther-




mal turbulence in cities  we might expect the diffusion to proceed more




rapidly than  given by the Pasquill-Gifford functions, which would mean




that the presently calculated concentrations are biased to  the high  side




by this effect.  However,  the presence of large  buildings in downtown




areas restricts the volume into  which  the pollutants can mix,  and such




an effect might counteract those caused  by increased turbulence.





     Another  assumption that is  included in the  model in its current




form is that  of uniform meteorology  throughout the urban area.  It is




certain that winds in cities are not uniform,  and the same  is  true of




mixing depth  (e.g., Clarke, 1969).  The  stability index also changes




between the edges of  a city and  its  center.  It  may  be that these factors




are not so serious as it  first appears because the results  that have been




achieved with the model seem to  indicate that  sources close to the re-




ceptor are the most important in determining concentrations.   If this is




indeed true, then wind,  stability, and mixing  depth  close to the receptor




are very important, but their values at  greater  distances are  much less




so.   This would mean  that different values of  the inputs could be used




for different receptor locations, but  the basic  form of the model would




not have to be changed to accommodate  changes  of the parameters with




distance upwind of each individual receptor point.





-------
     One of the most serious remaining weaknesses of the fundamental




model is the assumption that it can be applied to calm conditions  (if




such conditions ever actually exist) by assuming that some slight




organized air movement is present.  After we identify and correct  other




possible sources of discrepancy between observations and calculations,




it may be feasible to develop a better method for treating this  important




special case.  Studies of air motions within cities during calm  and near




calm conditions would probably be of some help.





     The third possible source of error is unrepresentative observations




of CO concentrations.  Before discussing examples,  the term should be




defined.  for our purposes, a representative observation is one  that has




very nearly the same value as most of those that would have been obtained




if the measurements had been made simultaneously at many other points in




the same "general area."  For studies with this model,  the  general area"




to be considered should have dimensions comparable  to the resolution of



the model, or about 100 to 200 m.  Thus, we would consider observations




to be unrepresentative of an area if significantly  different results




were likely to be obtained by moving the instrument to some randomly




chosen points within about 200 m of its original location.   This defini-




tion of representativeness implies that a monitoring station should be




located at a point where its surroundings are reasonably uniform for




about 200 meters in all directions.  Such locations are virtually  im-




possible to find in most cities.  The CAMP Stations that served  as data




sources for the examples given in this report are probably located about




as well as is possible (see Appendix I), but their  locations cannot be




considered "representative" in the above defined sense.  The readings




from these stations are likely to be biased or otherwise made unrepre-




sentative by the presence of parking lots, traffic  signals, and  the




aerodynamic effects of large nearby buildings.

-------
     The accuracy of the available observations of CO concentration is


somewhat limited by the precision to which observations are reported.


Values are given to the nearest part-per-million, resulting in an un-


certainty of about 0.5 ppm.



     Interferences from other atmospheric constituents are also possible


with the instruments.  The most likely interferent is water vapor, so


the usual measurement procedures either remove the water vapor itself


from the air to be analyzed, or else neutralize its infrared absorption


interference with optical filters.  Nevertheless some questions of


possible interference remain.  For instance, at the Washington CAMP


Station it has been found that the removal of CO from ambient air by


Hopcalite does not produce the anticipated readings of zero ppm when the


CO-free air is analyzed; instead, the instrument indicates CO levels of

           *
2 to 3 ppm.   If the instruments consistently indicate CO concentrations


higher than those actually present, then the actual discrepancies between


observed and calculated concentrations would be somewhat smaller than


presently indicated.  However, only a small portion of the disagreement


can be explained by CO measurement errors.



     A continuation of the work described in this report is currently


underway.   It is directed toward determining the source of the dis-


crepancies discussed above.  The major portion of the program will be


devoted to field measurements of carbon monoxide concentrations and


meteorological parameters within urban areas.  Results from the earlier


experimental studies of diffusion through cities (e.g.,  Stanford
*
 Letter to W.  B.  Johnson, dated 10 October 1969, from C. E. Couchman,

 Chief, Air Pollution Division, District of Columbia Department of Public

 Health.

-------
University Aerosol Laboratory, 1953 a, b, c, d; Perkins,, 1962; Pooler,




1966; Hilst and Bowne, 1966) will continue to be used for the  further




development and refinement of the CO model, along with the new data  to




be obtained.  Although these previous studies are generally limited  to




point and line-source releases of tracers and their determinations of




diffusion in the vertical are limited, they should be useful in refining




the Gaussian model for urban applications.





     To test the representativeness of CAMP Station measurements, we




plan to measure CO concentrations at various locations around the St.




Louis CAMP Station using a mobile instrument.   Mobile measurements will




also be made in other areas of St. Louis and San Jose in order to study




the small-scale spatial variability of concentration.





     Other studies of spatial variability are also planned.  These will




involve CO, wind, and temperature measurements around downtown inter-




sections in St. Louis and San Jose at several levels from rooftop to




about ten feet above street level.  These studies should help to relate




rooftop concentrations, which we believe are better represented by the



model, with concentrations at lower levels, where measurements are




usually made and where most people are exposed to the pollutants.  The




observations should also help to determine the nature and importance of




aerodynamic effects caused by airflow around buildings and through the




street canyons.  These measurements will test the validity of using




airport meteorological data to represent conditions throughout a city.




Additional observations of temperature profiles and mixing depth varia-



tions across the urban area will check the methods we have used for



estimating mixing depths.





     Another input that will be tested during the program is the rela-




tion of observed traffic to the rate at which CO is generated.  It is




planned to use the detailed traffic data available from a relatively






-------
dense, computer-monitored network of sensors in downtown San Jose.  By



knowing the details of the traffic flow near the CO measuring stations,



it should be possible to test the validity of the relationships between



traffic and CO generation that have been used with the model.

-------
              Appendix A
PRINCIPAL SOURCES OF CO IN URBAN AREAS

-------
                              Appendix A





                PRINCIPAL SOURCES OF CO IN URBAN AREAS








     The model considers only the mobile sources of carbon monoxide.




The literature was surveyed to determine the  importance of other sources




of CO.  Table A-I shows the fraction of total CO emissions arising from




various sources for nine individual American  cities and a 28-city average.




The table shows that transportation CO emissions range from about 77 to




99 percent of the total for the different cities.  According to Mason's




(1969) data, about 98 percent of the CO emissions due to transportation



are from motor vehicles.





     San Francisco is the only city shown in  the table that has non-




transportation emissions greater than ten percent of the total.  The




major nontransportation source in the San Francisco Bay Area was incin-




eration.  As of 1 January 1970, incineration  has been banned in the Bay




Area.  If we assume that the other CO sources remained the same, but all




CO generated by incineration was eliminated,  then the San Francisco Bay




Area CO emissions from transportation would be about 92 percent of the




total.  This is very nearly the same as the other cities shown.





     Inasmuch as more than 90 percent of the  CO in urban areas is




generated by traffic, we ignore fixed sources in our model.  In the




future we may treat some of the diffuse sources (such as space heating)




in the same way that we now treat residential area streets.  Very strong




individual point sources, if they exist, may  have to be treated separately




at a later time.  For now, we feel that inclusion of the more  than 90




percent of the total CO emissions arising from traffic will give results

-------
                 Table A-I
PERCENT CO CONTRIBUTION BY  SOURCE CATEGORY
City
Washington, D.C.
Area, 1965-1966
Los Angeles Metropolitan
Area, 1967
Boston, Massachusetts
Area, 1967
San Francisco
Bay Area, 1967
Pittsburgh Metropolitan
Area, 1967
Cleveland Metropolitan
Area, 1967
Kansas City Metropolitan
Area, 1966
Metropolitan
Baltimore
Hartford-Springfield
Area, 1967
Average of 28 Major
Metropolitan Areas
Category
Transportation
98.7
98.2
91.3
77.2
92.1
94.3
95.2
95.7
94.2
91.5
Industry
—
—
—
6.5
—
2.0
—
1.2
1. 1
2.6
Incineration
0.8
1.8
8.4
16.3
1.0
2.1
4.3
1.8
3.8
1.9
Power Plants,
Space Heating,
and Other Sources
0.5
—
1.2
—
6.9
1.5
0.5
1.3
0.9
4.0
References
NAPCA
(1968a)
NAPCA
(1968b)
NAPCA
(1968c)
NAPCA
(1968d)
NAPCA
(1969a)
NAPCA
(1969b)
NAPCA
(1969c)
NAPCA
(1969d)
NAPCA
(196 9e)
Mason
et al.

-------
that are quite consistent with the accuracies of the other  input



parameters.





     Other potentially important nontraffic sources of carbon monoxide




are the airports.  Carbon monoxide emissions at airports are comparable



with those of surrounding communities  (Bastress, 1969).  Increased air



traffic may increase these levels.  One of the problems to  be considered



in the modeling of airports as CO sources is that they do not constitute



a ground level source.  Much of the emission occurs in a volume above



the area occupied by the airport.  For this reason, the box model would



seem appropriate to the treatment of emissions from an airport regardless



of its distance from the receptor.





     The distribution of airport emissions through the mixing layer



appears to minimize their contribution to ground level concentrations.



However, this should be checked and if airports contribute  significantly



to ground level concentrations, they should be added to future versions



of the model.

-------
               Appendix B
THE URBAN TRANSPORTATION PLANNING PROCESS

-------
                              Appendix B





               THR URBAN TRANSPORTATION PLANNING PROCESS








     The purpose of this appendix  is  to describe the urban  transporta-




tion planning process so that its  capabilities and limitations may be




assessed, and to show how data generated  in the planning process can be




used as  inputs to the urban diffusion model.








1.   Background





     The first major urban transportation planning effort was undertaken




for the Detroit area by the Detroit Metropolitan Area Transportation




Study (DMATS) in the early 1950's.  Dr. Douglas Carroll and his staff




developed many of the concepts and the methodology that are still used.




The Carroll study team staffed subsequent studies in Chicago, Pittsburgh,




and New York.  The methods and techniques have been developed and re-




fined in the succeeding years, strongly aided by increasingly efficient




data processing equipment.   It is  a requirement of the Federal Aid




Highway Act of 1962 that every community with a population over 50,000




have a transportation plan to participate in federal highway programs.








2.   Structure of a Transportation Study





     A transportation study produces  a plan for future transportation




facilities.   A five-step process is generally followed:  (1) inventory.




(2) model development,  (3)  forecast,   (4) system design, and (5) system




evaluation.   There is considerable iteration and feedback among these




steps,  as described below.

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3.    Inventory





     Three kinds of data are collected:





     (1)  Complete descriptions of present transportation




          facilities





     (2)  Numbers of trips presently taken, their purposes, and




          demographic data that may serve as trip-predicting




          variables





     (3)  Descriptions of land uses in the study area.





     The study area is divided into small "traffic zones,  and the trip-




taking and land use data are collected for the traffic zones.  Traffic



zones are usually related to census tracts, with one or more tracts in




each traffic zone.  Census tracts are used because they provide the




most readily available historical and forecast data on population, in-




come, and other demographic variables.





     The transportation system inventory is a description of the local




highway network of major arterial streets and freeways.  A map of the



highway network is prepared.  The network is described by the inter-




sections, or nodes, and the characteristics of the links that connect



the nodes.  For example, traffic capacity, observed speed, observed




volume, and type of facility are recorded for each link in the network.




Public transportation facilities are described by their frequency of




service, kind of equipment, capacity, and current patronage.





     The trips taken at the present time are determined from a household




survey in each traffic zone.  Households are asked to report the number




of trips taken by household members on a specified day, the purpose of




the trips, and the destinations.  Household income, number of persons  in




the household, ages of household members, and number of automobiles are



also determined.





-------
     Land use and employment  in each  traffic  zone  are  determined from


planning agencies,, surveys, and in  some  cases from field observations.





4.   Model Development



     To develop the model, the data collected in the  inventory  are  re-


lated in such a way that  trips between zones  can be predicted from  demo-


graphic and land-use data.  Three submodels are used:   the  trip


production model, the trip attractions model,  and  the  trip  distribution


mode 1.



     The trip production  model relates the number  of  trips  originating


in a zone to characteristics  of the zone, e.g., population,  average


household income, etc.  The trips are characterized by  their purpose,


e.g., to work, to social  or recreational  activity,  to health or medical


treatment, etc.  The trip production model is  a statistical regression,


concerned only with the number of trips  that  originate  in the zone, not


their destinations.



     The trip attraction  model relates the number  of  trip destinations


in a zone, by purpose, to zone characteristics, e.g., land use,  total


employment,  etc.  The trip attraction model is concerned statistically


only with the number of trips that  end in a zone,  not their points of


origin.



     The trip distribution model describes the relation  between trip


productions and attractions:   i.e., the number of  trips  between each


zone pair.  The distribution model  describes  the number  of  trips between


each zone pair by a formula of the  form:
                                     , k
                          t   = p a /d       .
                           ij    i J  iJ

-------
where


          t   = the number of trips from zone i to zone j
           ij

           p  = the number of productions in zone i
            i

           a  = the number of trip attractions in zone j
            j

          d   = the impedance between zones i and j, usually expressed
           ij
                as the travel time between the zones, but occasionally

                as distance or cost


            k = an exponent that depends upon the travel characteristics

                of the area's residents.


Because of its form, the trip distribution model is commonly called  the

"gravity" model.  The exponent k is determined from the frequency dis-

tribution of trips between zone pairs as revealed by the household

interview data.
5.   Forecast


     In the forecast step, the land use, employment, population, and

income are forecast for some future year.  The travel in that future

year is forecast from these variables, using the models developed  in

the previous step.  The demographic variables must be forecast  for  each

zone.  Frequently, this is done by allocating overall population and

income projections among  the zones, using models that have been developed

for that purpose.


     Future land use may  be a function of the transportation  system

adopted, so there is feedback between the transportation system design

and the land use forecast.  Further, zone-to-zone  travel time will be

influenced by  the transportation system, so  there  must  be  iteration

between the forecast and  the design.  The division of trips between




-------
private automobiles and public  transit  is  estimated  by using  a model




based on relative time and cost.








6.   System Design





     In the system design step,  alternative  changes  to the  existing




transportation system are postulated.   These must meet the  forecast




travel demand.  They may include addition  of freeway links, increase  in



capacity of arterials or freeways by widening,  or the addition of new




public transportation facilities.  A network description  is prepared




for each of the alternatives.








7.   System Evaluation





     In the system evaluation step, the costs of the alternative systems




are determined and compared.  Costs include  the costs of  construction,




costs of rights-of-way, costs of equipment,  annual maintenance and




operating costs, and user and community costs.  User costs  include those




of operating, parking, and owning an automobile; the costs  of accidents;



transit fares; and the value of  all travelers'  time.  Community costs in-




clude disruption, noise and emission pollution, and  the cost  of limited




access to employment and other opportunities.  Because these  costs occur




at different times, and the expenditure patterns may be different for




different alternatives, future costs are discounted  according to com-




pound interest formulas to obtain comparable values  for all outlays.




Costs that cannot be expressed in dollar terms are described  qualitatively





     The heart of the evaluation process is  the series of computer pro-




grams that make up the traffic assignment model.  This model  is capable




of determining the minimum time path between zone pairs for a given




transportation network and can assign zone-to-zone trips  to the links




along that minimum path.   Thus,  the total traffic volume  on each link






-------
is predicted.  This defines the needed capacity, the traffic speed, and




finally the total travel time and vehicle operating cost.  The diffusion




model uses link volume and link speed outputs.   These are obtained




directly from the magnetic tape outputs of the  traffic assignment pro-



grams.   The network descriptions are also on magnetic tape.   Thus, it




is possible to forecast future pollution concentrations from the fore-




cast traffic.   The pollution forecasts will provide additional informa-




tion for the transportation planners to evaluate alternatives.

-------
                Appendix  C
METHODS FOR DETERMINING  STABILITY CATEGORY

-------
                              Appendix  C




              METHODS FOR DETERMINING STABILITY  CATEGORY






     This appendix discusses  two methods  for  determining  stability


category for use with the model described in  this  report.   One  of the


methods has not been presented elsewhere  in the  literature.






1.   Turner's Method




     Turner (1964) developed  criteria for determining  stability from



routinely available meteorological data.   His procedure estimates the



stability class on the basis  of cloud cover,  ceiling height, wind speed,



and solar elevation.  In his  paper, Turner presents a  series of compu-



tational steps that effectively constitute the flow chart for a computer


program.  His model requires  the following inputs:  cloud cover, ceiling



height, wind speed, and, if daytime, solar elevation.  The  parameters,


other than solar elevation, that are required for  the  application of


Turner's stability determination method are all  available from  routine


hourly meteorological measurements.  For  application of Turner's approach


with the synoptic model, an approximate formula  was used to determine



solar elevation.   The approximation assumes that the earth  has  a circular



orbit and that the station lies at the  center of its time zone.  With



these simplications the following useful  relation  is obtained:
                     f          *      /12 - H\
                     L sin 8 sin $ + cosl—	It
           a = arcsinjsin 6 sin $ + cos(———Jcos 6 cos $ |        (C-l)


and

                                         /2rr(N + 10)

                                             365
                5 = arctan -tan 23.5° cosl	—	)|             (C-2)

-------
where


          Ot - the solar elevation


          5 = the solar declination


          $ = station latitude


          H = the hour of the day (24 is midnight)


          N - the number of days since 1 January.




2.   Method Based More Directly on Pasquill's Classifications


     In the work that Pasquill (1961) did to determine the spread  of  a


plume with distance traveled, atmospheric conditions were classified


according to prevailing insolation strength and wind speed,  for daytime


conditions, and according to cloud cover and wind speed for  night  condi-


tions.  His classification scheme, which Turner also used in developing


his method, is summarized in Table C-I.  The table, as presented here




                               Table C-I

                                             *
                         STABILITY CATEGORIES
Surface Winds
(knots)
S3
3-6
6-10
10-12
>13
Daytime Insolation
Strong
1
1
2
3
3
Moderate
2
2
3
3
4
Slight
2
3
3
4
4
Night Clouds
>5/10
5
4
4
4
4
^4/10
5
5
4
4
4
         1 = extremely unstable, 2 = moderately unstable,

         3 = slightly unstable, 4 = neutral, 5 =  slightly  stable.

-------
has been changed slightly from the  form presented  by  Slade  (1968).  First,




that table contains some cases where  the  stability falls  between  the




accepted classes; these have been assigned  to  a  single  category.   Second




the moderately unstable case in  the original table has  been  redefined  as




slightly unstable and the two slightly unstable  cases have been rede-




fined as neutral.  We feel this  is more appropriate to  urban conditions,




where very stable conditions are uncommon.  In the original  scheme, no




categories were defined for the  near-calm wind cases  at night.  We have




assumed such cases to be slightly stable  over  an urban  area.





     The next problem was to define an objective method for  determining



the strength of insolation.  The strength of the insolation  depends on




the solar elevation, the cloud cover, and the  atmospheric turbidity.




The latter factor is not routinely measured and  was ignored  because its




attenuating influence should be  small compared to  cloud cover.  The




following equation approximately describes  the flux density  of solar




energy on a horizontal surface:








                 Insolation strength = k(l - AN)sin a             (C-3)








where





          k = a proportionality  factor, depending  on  the  solar constant,




              and atmospheric transmission





          A = the average albedo or reflectance  of the  clouds





          N = the fraction of the sky obscured by  cloud





          a. = the elevation angle of the  sun.





Of course, this equation applies only to  an average insolation over an




area sufficiently large that the effects  of the  irregular distribution




of clouds are minimized.






-------
     A reasonable value of A would be 0.5, so that Eq.  (C-3) becomes








                  Insolation = k(l - 0.5 N)sin a    .               (C-4)








Of necessity,, we assume that k is constant, i.e., the insolation is




proportional to (1 - 0.5 N)sin a.  This term can assume values from U




to 1.  If we divide that interval in three equal parts, corresponding




to Pasquill's three insolation categories, we then have the following




relationships:





     Slight Insolation:       0 < (1 - 0.5 N)sin a ^ 0.33





     Moderate Insolation:     0.33 < (1 ~ 0.5 N)sin a < 0.67





     Strong Insolation:       (1 - 0.5 N)sin a > 0.67.





These simple expressions are used to determine the insolation type.  When




combined with the wind speed information, they give the stability classi-




fication more directly than does the scheme devised by Turner (1964).




This method also seems somewhat more consistent with Pasquill's original



specification of the stability types.





     In using Table C-I and the insolation expressions given above, it




is still necessary to determine the solar elevation for the time of day;




cloud cover and wind speed are measured parameters.  To economize on




calculation time,  the subroutine using this scheme to preprocess the




data (see Appendix G) does not calculate a, but uses a table of values




of sin a obtained by means of Eq. (C-l).  Values are given for each




month of the year and each hour of the day.  The five cities studied in




this report are all within ±3° of 40° north latitude,  so a single table



for that latitude has served for all calculations.





     The procedure for determining stability has been improved by using




"opaque" cloud cover.  This is a regularly recorded parameter.  In






-------
determining the opaque cloud cover, the very thin semitransparent clouds




are ignored.  Thus, the assumption of an average cloud albedo of 0.5  is




probably more accurate when applied to these types of cloud  than when




applied to the total cloud cover.

-------
             Appendix  D
METHODS FOR DETERMINING MIXING DEPTH

-------
                              Appendix D

                 METHODS FOR DETERMINING MIXING DEPTH


     One of the model's required  inputs is mixing depth.  The most
commonly used method for determining  the top  of the mixing  layer  for
afternoon conditions is to assume that it is  at the height  where  the

potential temperature on the morning  sounding is equal  to the afternoon
surface maximum potential temperature  (e.g.,  Miller and Holzworth, 1967).
This is the method used with the  synoptic model.  Potential temperature,
9, is defined as

                                        R/c
                           0 = T(1000/p)   P                      (D-l)


where

          T = temperature (°K)

          p = pressure (mb)

       R/c  = the ratio of the gas constant for air to  its  specific heat
          P
              at constant pressure (0.287).
                                                              *
     To determine afternoon mixing depth,  the morning sounding  from the

nearest radiosonde station and the afternoon  maximum temperature were
used.  Potential temperature is calculated for the surface  maximum tem-
perature first,  and then for each of the successively higher reported
*
 For this model we used the pressures and temperatures at the significant
 levels,  Deck 505, available from the National Weather Records Center,
 Asheville,  North Carolina.

-------
radiosonde  levels until  the potential  temperature  at some level exceeds


the  surface maximum value.  The pressure  where  the surface maximum and



upper  level potential  temperatures  are equal  is determined by linear


interpolation between  values  for  the reported levels.   If we assume a


constant  average temperature T, through the mixing layer,  then we can


use  the thickness equation  (e.g.,, Panofsky, 1957)  to convert the pressure



at the top  of the layer, p  ,  to height
                          h





              h = ln(p /p ) (RT/g) = 29.3  T ln(p /p )     .          (D-2)
                    \  o  h'                   \  o  h/





In this equation, g is the  acceleration of gravity,  p   is the surface


pressure, and T is taken to be the  average of the  temperatures at the


surface and the top of the mixing layer.




     The  estimation of nighttime mixing depth over the  city for use with


the  synoptic model is  based on Summers' (1966)  model of  the urban heat


island and  Ludwig's (1968,  1970) empirical relationship  between rural


lapse rates and the intensity of urban heat islands.  If we assume T to


be a linear function of  the logarithm  of  pressure  (very  nearly the same


as Summers' assumption of T as a linear function of  height),  then the


temperature T  at some height h outside the city is  given  by:
                T  =T  + —	 Alnp K, T  + p —  In —              (D-3)
                 h    o   dlnp                    '   '





where T  and p  are the rural surface temperature and pressure,  respec-
       o      o                                                '

tively, p  is the pressure at h, and p is the average of  p   and  p  .
         h                                                oh


     If air moving into a city is heated from below  to  the  extent  that


complete mixing takes place through a depth h, then  the temperature  at


height h will remain T , and the lapse rate below h  will  become  adiabatic
                      h


The dry adiabatic lapse rate y   (in pressure coordinates) is given by






-------
                   Y  = 	  -  0.287 — K, 0.287 —
                    d   pc          p        p
                                                (D-4)
where T and p are absolute  temperature  and  pressure,  and T  and ^ are


their average values within the  layer from  the  surface  to height h.


For the urban situation, Eq.  (D-3)  becomes
                    /v
   T  = T  + p Y  ln|—
    h    u      d   \p  ,
                                                                   (D-5)
where T  is the surface air  temperature  in  the  center  of  the urban  area.
       u

Subtracting Eq. (D-5) from Eq.  (D-3)  gives:
Tu - TQ = p|ln( —1|[— -
                                                                   (D-6)
Substituting Eq.  (D-4) into Eq.  (D-6) gives:
                T  - T  =
                 u    o
                               o/J
                _ dT
                p — - 0.287 T
                  dp
                                 (D-7)
     Ludwig (1970) has shown that the urban-rural  temperature difference


(T  - T ) can be approximated within about ±2° C by the following
  u    o

equation:
                           1/4 /               dT
                T  - T  = $    0.0633 - 0.298 —
                 u    o       \               dp
                                               (D-8)
where $ is the population of the urban area and dT/dp is expressed in


"C/mb.   The equation is based on 85 sets of data from 18 different


cities.  Substituting Eq. (D-8) into Eq. (D-7) gives:
               ln(p /p
                 \  h  c
               dT\
0.0633 - 0.298 —
 	dp/


 p — - 0.287 T
   dp
                                               (D-9)

-------
The value of dT/dp is determined from the lowest portion  of  the  morning


sounding (using the differences in temperature and pressure  at  the  sur-


face and the first significant level above the surface; "p  and T  are the


averages of the pressures and temperatures at these points.



     To convert ln(p /p ) to mixing depth, we use Eq.  (D-2).  Making
                    h  o

that substitution gives


                         —  1/4 /      dT
                    29.3 T $   10.298 — - 0.0633

                h = 	*	—	     .           (D-10)
                            _ dT         —
                            p — - 0.287 T
                              dp


     This is the- equation that was used to determine the predawn  values


of urban mixing depth from 1200 GMT soundings.



     The above equation has an idiosyncracy that should be noted.   For


increasing positive values of dT/dp,  h becomes larger, as  it should, but


at some point where dT/dp is approximately adiabatic, h becomes  infinitely


large.   If dT/dp increased further still,  h becomes negative.  This  be-


havior arises because of the assumption that the observed rural  lapse


rate is less than the adiabatic rate.   Large positive lapse rates are


quite rare in the early morning hours,  so the assumptions are not


seriously misleading.   However,  it is necessary to provide for the


eventuality in the computer program.   This has been done by assigning a


large positive value to h whenever the above equation yields a negative


value.   The value chosen was 4000 m.   This same value was also assigned


to h whenever the equation gave a positive value larger than 4000 m.



     This assignment of a maximum mixing depth will not affect the  cal-


culations,  except for  moderately or extremely unstable conditions,  and


according to the stability classification system used  (see Appendix  C),


such stabilities cannot be assigned at night.

-------
     We have  also used  the  4000-m maximum mixing depth for afternoon


 calculations  in order to  limit  the amount of radiosonde data necessary


 to  apply  the  program.   As is  shown in Section V of this report,,  this has


 very little effect  on the results.



     Inspection of  the  mixing depth equation given above indicates  that


 there  is  a minimum  positive value that h can assume,  given a fixed  city


 size and  fixed values of  p  and  T.   This minimum occurs when dp/dT  is

                                           5
 infinitely negative.  For a city  of 9 X 10  population,  an average


 pressure  of 925 mb,  and an  average temperature of  280" K,  the  minimum


 nighttime urban mixing  depth  should be about 79 meters.



     This number appears  reasonable considering that  the heat  generated


 by  the city,  and the mechanical mixing produced by the airflow over  its


 rough  surface probably  set  a  lower bound on  urban  mixing depths.  From


 this it follows that daytime  mixing depths are also likely to  have  some


 minimum value in the city.  We  have arbitrarily chosen 50  meters as  that


 minimum,  although there is  no minimum intrinsic in the procedure used


 to  determine  afternoon  mixing depths.   This  choice seems to be physically


 reasonable.   However, its main  function is to prevent  h from assuming a


 value of  zero, which could  give an infinite  calculated concentration.



     The use  of radiosonde  soundings  for  mixing depth  computations  is


 time-consuming and  expensive  on the computer.   This is particularly  true


 for climatological  applications where  large  amounts of data are required.


The sounding  data are not universally  available on magnetic tape from the


National Weather Records  Center,  and  several  years of  punched-card data


 are very cumbersome to  process.   Fortunately,  Holzworth  (1967) has calcu-


 lated forenoon and  afternoon  mixing depths for a large number  of U.S.


 cities, using the morning (1200 GMT)  temperature soundings.  Mr. Holzworth


has been very cooperative and has  allowed  us  to use his  tabulations  of


mixing depth  for several  stations.  His  tabulations generally  cover  the




-------
period 1960-1965,, and most U.S. radiosonde stations  are  represented.


These data are considerably more convenient as a  source  for  mixing-depth


computations than the original radiosonde data.   This body of  data does


require some modification for use with the diffusion model.  These ad-


justments are described below.



     The afternoon mixing depths given in Holzworth's tabulations  were


determined by the conventional method described at the beginning of this


appendix, so we have taken his tabulated values and used them  without


change.



     Holzworth determines his forenoon mixing depth from the intersec-


tion, on a thermodynamic diagram,  of the morning  sounding and  an adiabat


passing through a surface temperature 5° C greater than the observed


early morning minimum temperature.   Thus, his forenoon mixing  depth, h


(meters), can be related to the morning vertical  temperature gradient


dT/dZ by the following approximation, which is exact if dT/dZ  is con-


stant to the height h ,  and if the  surface radiosonde temperature  is


the minimum temperature:
                                                                3      1
where (dT/dZ)  is the adiabatic temperature gradient, -9.8 X 10   "C m~
             £L


Substituting and simplifying,  Eq.  (D-ll)  becomes:




                dT    s°  C - (9.8  X 10~3  °C/m)h
     The gas law and the hydrostatic equation can be combined to give:




                            dZ     RT

-------
Using Eq. (D-13) we can reduce Eq.  (D-12)  to  the  following
|~9.

^
                    RT9.8  X  10~3  (°C/m)h   -  5"

                                   ~ - - - -    .           (D-14)
                                 Pghf
     Virtually all cities  in  the U.S.  are  located  at  altitudes  such  that


the atmospheric pressures  in  the lowest  layers  are between  about  850 mb


and 1000 mb.  Thus, we introduce an error  of  less  than  10 percent,


assuming p to be constant  and equal to 925 mb.



     Similarly, temperature can be assumed constant and equal to  280° K


without introducing errors greater than  about 10 percent.   Substituting


these, and the values for  the constants  gives:
                   dT    /        -2         \  C
                   — &  8.7 X 10   - 44/h   —     .              (D-15)
                   dp    \                 f/ mb
     We have already shown that the early morning mixing depth, h, over


the city can be related to this low level lapse rate.  Recalling Eq.


(D-10)
                h=
                         —  1/4 /      dT
                    29.3 T $    0.298 — - 0.0633
                            _ dT         —
                            p — - 0.287 T
                              dp
where f is the population of the urban area.  Using the same values of T


and p as used in the development of Eq.  (D-15) and substituting from


that gives:



                        1.1 X 10  + 307 h
                    1/4                  f
               h = $    - — — meters     .           (D-16)

                        4. 1 X 10  + 0.02 h



     For those cases of importance, where h  would be  less than about

  4
10  m,  the term 0.02 h  in the denominator will be very small compared

                        4
to the  constant 4.1 X 10  and can be ignored.  Then Eq. (D-16) becomes:

-------
               h « $   (2.6 + 7.5 X 10   h  I meters     .          (D-17)
                                          f /
This equation was used to convert Holzworth's tabulated forenoon mixing


depths to values appropriate to the early-morning hours for use with  the


climatological model.



     Equation (D-17) has the same characteristic as Eq. (D-10), in  that


there is a minimum value that h can have.  It is, as expected, the  same


as found with Eq. (D-10), if the conditions are the same.



     As with the methods based on radiosonde data, we have assigned the


same minimum and maximum values of mixing depth, when appropriate,  to


those obtained from Holzworth's tabulated values.



     The two methods described above provide values of mixing depth for


only two hours of the day,  one in the early morning, predawn hours and


one for the time of the afternoon temperature maximum.  To obtain values


for other hours of the day,  interpolation must be used.  Two schemes have


been employed with the model.   The first approach combines time and sur-


face temperature interpolations.  The second uses time only as the basis


of the interpolation.  The time-temperature interpolation has been used


with radiosonde data to obtain mixing depths for the examples that


illustrate the use of the synoptic model in this report.  The time-only


interpolation was used with Holzworth's mixing depths in the examples


that illustrate the climatological model.



     When the temperature interpolation scheme was used, the following-


equation gave mixing depths from the first hour after sunrise through


the first hour after sunset:
                          (T - T     N
                         	min

                         T    - T
                          max    min,
Ifh   - h  )  t  h                (D-18)
f\ d    n/    n

-------
where



               h  = mixing depth




       h   and h   - mixing depth  at  time of  maximum temperature  and  at
        d      n

                   time  of the morning sounding




   T, T    . T     = current,  maximum,  and minimum temperature.
       max  min


Temperature interpolation during the  day is reasonable  because  the  top


of the mixing layer  is usually marked,  on a thermodynamic  diagram,  by


the  intersection  of  the  morning  sounding and the adiabat passing  through


the  current surface  air  temperature.   If the slope of  the  morning


sounding is constant up  to this  height,  the change of mixing  depth  will


be very nearly proportional  to the  change of surface air temperature.



     From  the second hour past sunset through midnight, the mixing  depth


is interpolated by time.   At the first  hour past sunset it has  the  value


given by the above equation.  At midnight it has the value of h   deter-


mined from the next  morning's soundings.  Observations presented  by


Ludwig and Kealoha (1968)  for Dallas  and Ft.  Worth, Texas, show that the


urban heat island develops rather quickly in the evening and  then tends


to stabilize about midnight.  If  the  urban  heat  island and the urban


mixing layer are related,  as suggested  by Summers'  (1966)  model,  then


the mixing depth should  also reach  its  early morning value by the middle


of the night as does the  heat-island  intensity.   For this  reason  the


early morning value  of mixing depth is  assumed  to apply from midnight


until the  first hour past  sunrise on  the  next day.



     Figure D-l gives a  schematic representation  of the results of


applying the temperature-time interpolation  to a  typical day's data.



     The second interpolation scheme, based  on time alone,  has many of


the same features as the hybrid approach  described above.   For instance,

-------
0.
LU
Q

CJ
Z

X
    I


SUNRISE

SUNSET
                                      TIME OF  T
                                                max
       CONSTANT
                  INTERPOLATION BY
                  SFC TEMPERATURE

               I     I     I     I      I
INTERPOLATION  CONSTANT
                                                     j     BY TIME

                                                     I     I     I
                         8    10   12    14    16

                                    LOCAL TIME
                                          18    20    22   24
                    02
04
                                                                           TA-7874-28S
         FIGURE D-1   SCHEMATIC REPRESENTATION OF THE DIURNAL TEMPERATURE/TIME

-------
the early morning mixing depth, h  ,  is used  throughout  the  hours  from


midnight until sunrise.  We have assumed  that  the  afternoon mixing


depth, h , occurs at 1400  local standard  time.  The  hourly  mixing depths


h, are interpolated for the hours  between sunrise  and 1400  using  the


following equation



                               H - H
                                     sr
                                      sr



where



          H = current hour of the day



        H   = the first integral hour after  sunrise, determined from
         sr

              tables of solar elevation angle, e.g., 0600, 0700, etc.



From 1400 local standard time until midnight, a similar interpolation is


used between h  and the mixing depth for the following morning.
              d


     The advantage to using a time-based interpolation is that an hourly


sequence of mixing depths can be determined from either soundings or from


the Holzworth tabulated data without concurrently handling the hourly


surface temperature data.

-------
            Appendix E









 INCREASING THE SPATIAL RESOLUTION




FOR EMISSIONS IN THE FIRST SEGMENT

-------
                              Appendix  E



                   INCREASING THE  SPATIAL RESOLUTION


                  FOR EMISSIONS  IN THE  FIRST  SEGMENT





     For the first segment, which  covers  the  upwind area from the re-


ceptor to a distance of  125 m, the Gaussian model is used.   As noted in


the text, the standard deviation,  a  }  in  this segment is presumed to
                                   z

remain constant,  so  the  exponent,  b. .is zero in the exponential repre-
                                    •"v 3

sentation of cr  }  and the Gaussian  equation becomes:
              Z



                           0.8 • 125       100  El
                     C  .  = - Q  = - —                (E-l)
                      Lj     u a      1   u a   A
where



          C  . = the concentration due  to remissions  from  the  first  seg


                ment, for j type stability  (gm m   )



           Q  = the average source  strength in  the first  segment


                (gm m   s  )



          a   = a constant for  the  first segment,  for  j type  stability
           lj

                (m)



           E  = the emission rate in the first  segment (gm  s   )


                                                -2
           A  = the area of the first  segment  (m   ).



If we divide the first segment  in two, part A extending to  62.5 m and
\
part B from 62.5 to 125 m, then
                            a   = a   = a                          (E-2)
                             lj    Aj    Bj

-------
                             A  = A  + A                           (E-3)
                              1    A    B
                               A  = A /4                           (E-4)
                                A    1
                              A  = 3A /4                           (E-5)
                               B     1
                           E  = E  + E      .                       (E-6)
                            1    A    B
It follows that
                                         (E         E  \
                                          A         B
                                    62.5	h 62.5 	
                                         A         A
                                          A         is /
                             u a   A   \  A    3  B
                               100     12E  +=• E  I     .            (E-7)
     If we let
then we can use Q   as an  effective  source  strength  for  the first seg-
                 AJD

merit, replacing Q  in Eq.  (E-l), and we obtain  the  same  results that we


would had we divided the nearest segment  into two parts.   By using the


effective source strength, Q  , we do not have  to add  to the numbers of
                            Ar>

segments treated in many stages of the calculations.

-------
                    Appendix F
TREATMENT OF EXTRAURBAN SOURCES AND STREET EFFECTS

-------
                              Appendix  F





          TREATMENT OF EXTRAURBAN  SOURCES AND  STREET EFFECTS








 1.   Introduction





     In an earlier report  (Johnson, et  al.,  1969) we discussed  submodels




 to account for the amounts  of carbon monoxide  arriving  from outside  the




 city and for the aerodynamic effects associated with airflow  around




 buildings and through street canyons.   For  completeness,  the  submodel




 used to account for CO concentrations resulting from extraurban  sources




 is described below.  This model was used in the calculations  that  illus-




 trated the use of the synoptic model in the text of this  report.  A




 constant background was used for many of the calculations with  the




 climatological model.  In  the text it was shown that a  background could



 also be accounted for on the basis of statistical modeling, using ob-




 served CO concentrations.  At this time the statistical model appears




 to give the better results, if adequate data is available.  If not,  the




 model described in this section would be preferred.





     Because of a number of problems encountered in applying  the em-




pirical street effects submodel on a general basis, it  was judged in-




 adequate for our purposes and has not been  incorporated into  the




diffusion model.   No attempt was made to include street and building




effects directly in the calculations used as examples in  this report.








2.   Extraurban Model





     The development of the following model accepts, a  priori,  the




assumption that the treatment of extraurban transport and diffusion




should be considerably more gross than  the  treatment of nearby sources.





-------
     The first problem to be faced in the development  of  an  extraurban

diffusion model is that there is no convenient way of  knowing the  upwind

trajectory of the air arriving at a city.  We can either  determine the

trajectory from past and present meteorological data or we can assume

that the air has come from somewhere within a very large  upwind segment.

This latter approach is much more practical.

     We apply the box model to a quadrant centered on  the upwind direc-

tion and extending from 32 to 1000 km upwind of the receptor.   The source

strength is assumed to be constant in time and space throughout the

sector, and is estimated from yearly fuel consumption  for those states

(Federal Highway Administration,  1966) and Canadian provinces  (Dominion

Bureau of Statistics, 1968) whose centers fall within  the sector.  To

determine the total emission rate within the area, we  use the  total

amount of motor vehicle fuel consumed and the conversion  factor:
                                 3
1 gallon of fuel yields 1.32 X 10  grams of carbon monoxide.   If the
                 7
yearly (3.15 X 10  s) consumption of fuel within the quadrant  extending

to 1000 km is given by F,  then the average CO emission rate Q  in the
               11  2
area (7.86 X 10   m ) is given by:


                  Q = 5.32 X 10    F (g m~  s~ )     .              (F-l)


The extraurban model input for a given city includes a table  of  16

values of F, one for each wind direction used.  A different table  is

used for each city.   An average wind direction is used based  on the

direction observed with the highest hourly wind speeds.

     According to the box model,  the concentration C from some  upwind
segment is
                                r  - r
                                 2    I
                                  - -    ,                      (F-2)

-------
where r  and r   are  the  distances  to the outer and inner segment

                            6             3
boundaries  (in  this  case 10  and 32  X 10  m),  u is the wind speed,  and


h is the depth  of  the  layer through  which the  material is mixed.   Sub-


stituting Q from Eq.  (F-l)  and  the values of r  and r  gives the following


equation for concentration  from extraurban sources, C :
                                                      e



                             5.15 X 10" 1 F
                       C -	    .                    (F-3)
                         e          uh




     The afternoon mixing depth is used in Eq.  (F-3) because the pollu-


tants are likely to  have traveled  for long enough periods that they will


have had time to be  mixed through  the depth of the afternoon layer.  We


are aware that  the local mixing depth will not necessarily be appro-


priate to the region upwind of  the city,  but more detailed treatment of


this problem does  not  seem  to be warranted.  To approximate the  normal


increase in wind speed with height in the lower atmosphere,  we have


taken the average  transport wind velocity through the depth of the  mixing


layer to be 1.5  times  the maximum  airport winds for the  day.



     In addition to  the  material generated within the segment extending


to 1000 km, the  general  "worldwide"  background is included.   Robinson


and Robbins (1967) have  estimated  this to be about 0.2 ppm (about

        -4    -3
2.4 X 10   g m   )  at sea level  in  the midlatitudes of the northern


hemisphere.  This  value  is  added to  that  calculated from Eq.  (F-3)  to


give the total extraurban concentration,  which generally amounts  to a


few tenths ppm.   In  applying  the synoptic model,  the extraurban  con-


tribution was calculated once for  each 24-hour  period.   The  same  value


was used from one midnight  to the  next.

-------
3.   Street Effects Model





     Because of the finite spacing of sources within a  city,  area-source




simulation such as is used in the intraurban model  is best  applied  at




scales above a certain lower limit.   This minimum spatial scale  can be




considered to be on the order of a city block, hence the choice  of  62 m




as the finest resolution in the intraurban model.   For  shorter source-




receptor distances, an alternative technique is needed.





     Additional complications arise because, contrary to the  usual




situation in nonurban diffusion studies, the scale  of the largest urban




roughness elements (buildings,  etc. ) is very large  compared to the  local




scales of emission and reception.   This means that  the  aerodynamic




effects of structures become important.





     Models that do not include the effects of microscale diffusion will




normally undercalculate concentrations in comparison with those measured




at CAMP Stations,  which are often located near streets.  For  example,



the model used by Ott, et al.  (1967) gave average concentrations that



amounted to 36 percent of the CAMP average.





     The street effects have great importance for two reasons.  First,




they must be considered if we are to use existing data  to verify the




performance of our model.  Most available observations  are taken near




streets in downtown areas where local effects are likely to be signifi-




cant.  The second reason for the importance of the  street effects is




that they contribute substantially to those concentrations to which



large parts of the population are exposed.





     Current knowledge about street effects on CO concentrations is




based largely upon the extensive measurements of Georgii, et  al.  (1967)




in Frankfurt/Main,  Germany;  McCormick and Xintaras  (1962),, Schnelle,




et al.  (1969),  and Rouse (1951) have also made experimental contribu-



tions in this area.




-------
     Georgii's experiment  involved  extensive measurements  of  CO  concen-




trations and wind speeds at different  levels above  three different




streets in built-up areas, along with  occasional  traffic counts.  A




major finding was that the CO concentrations on the  leeward sides of




buildings were considerably higher  than  those  on  the windward sides




implying a helical cross-street circulation component  in the  opposite




direction from the roof-level wind.  In  addition, the  averaged data




showed that  (1) the vertical concentration profiles  on either side of




the street assume an exponential form,  (2) the mode  of air circulation




above the street apparently changes when the roof-top  wind speed exceeds




about 2 m/s, and (3) the concentrations  are exponentially  related to




traffic density.  Examination of the measurements reported by Schnelle,




et al. (1969) also indicates general agreement with  (1) and (2)  above;




their data are insufficient for verifying (3).





     Georgii's observations show that  the roof-level concentrations




differ only slightly from windward  to  leeward  sides  of the street-side




buildings.  It is reasonable to assume that the urban  background con-




centrations calculated by  the intraurban model are approximately equiva-




lent to roof-level concentrations.  The  effect of the  street  is  to




increase incoming roof-level concentrations by a factor that  depends




upon the receptor location relative to the wind direction, the height




above the street, the wind speed at average roof level, and the  traffic




density.





     A street effects submodel, empirically derived  from Georgii's




observations, was discussed in an earlier report  (Johnson, et al., 1969).




Because of a number of problems encountered in applying the empirical




model on a general basis, it has not been incorporated into the




diffusion model.

-------
     The statistically derived adjustments to the model discussed  in




the text would probably account for much of the aerodynamic effects




associated with buildings and streets, but those parts of the results




that were directly attributable to street effects would not be easily




separated from those due to other causes.  Also, statistically derived




results could not be transferred with any confidence to other locations.





     Because of the importance of the street effects,  a program of field



measurements is planned.   The results of this program should provide




the data necessary for the development of an adequate  model of CO



diffusion on the microscale in a city.

-------
             Appendix G









PROGRAM FOR PREPROCESSING  OF THE DATA




    FOR THE CLIMATOLOGICAL MODEL

-------
                              Appendix G





                 PROGRAM FOR PREPROCESSING OF THE DATA




                     FOR THE CLIMATOLOGICAL MODEL








     The preprocessing of the meteorological data for use in the clima-




tological model is done in two steps.  First, the Holzworth tabulated




values of mixing depth for afternoon and forenoon are processed to give




a series of hourly values.  The equations used have been enumerated in




Appendix D to this report.  Figure  G-l shows a simplified flow chart




of the program used for converting  Holzworth's mixing depth tabulations



into a sequence of hourly values.





     After the magnetic tape records of hourly mixing depth are produced,




they are merged with conventional hourly meteorological records ob-




tained from the National Weather Records Center.   The methods used to




convert solar elevation,  opaque cloud cover, and wind speed to stability




index have already been discussed in Appendix C to this report and




need not be repeated here.  The organization of the preprocessing is




summarized in the simplified flow chart in Figure G-2.  The magnetic




tape record of the condensed historical meteorological data that results




from this program is then used as the climatological basis for calculating




extended sequences of CO concentrations.

-------
                                                                 START
                                                           INPUT CITY POPULATION
                                                READ STATION, DATE, AND HOLZWORTH'S VALUES OF
                                                    FORENOON AND AFTERNOON MIXING DEPTH
                                                   DETERMINE PRE-DAWN MIXING DEPTH FROM
                                              HOLZWORTH'S FORENOON VALUE — See Discussion in Text
              NO
                           YES
               IS THIS DATE IN
              THE SAME  MONTH
              AS THE PREVIOUS
                  DATE ?
                                NO
                                                 DETERMINE SUNRISE HOUR FOR CURRENT MONTH
                                                 FOR HOURS FROM 0100 TO  LAST PRE-DAWN HOUR,
                                                LET THE MIXING DEPTH EQUAL THE PRE-DAWN VALUE
                                                 FOR HOURS BETWEEN FIRST POST-DAWN AND 1400,
                                                 LINEARLY  INTERPOLATE BETWEEN PRE-DAWN AND
                                                   AFTERNOON VALUES ON THE BASIS OF TIME
                                                           READ NEXT DAY'S DATA
                                                 DETERMINE  NEXT DAY'S PRE-DAWN MIXING DEPTH
                                               FOR HOURS FROM 1500 TO 2400 INTERPOLATE BETWEEN
                                               AFTERNOON MIXING DEPTH AND NEXT DAY'S PRE-DAWN
                                                         VALUE ON THE BASIS OF TIME
                                                   RECORD DATA AND MIXING DEPTH FOR ALL
                                                         24 HOURS ON MAGNETIC TAPE
                                                       IS IT THE END OF THE DATA FILE ?
                                                                     YES
                                                                                   TA-7874-71
FIGURE  G-1    SIMPLIFIED FLOW CHART OF PROGRAM  FOR  CONVERTING  HOLZWORTH'S
                 MIXING  DEPTHS  TO HOURLY VALUES

-------
                                               START
          READ IN TABLES - STABILITY INDEX AS A FUNCTION OF RADIATION  INDEX AND WIND SPEED
            (SEE TEXT) AND SINE OF THE SOLAR ELEVATION AS A FUNCTION OF MONTH AND HOUR.
          READ MONTH, DAY, YEAR, HOUR, WIND SPEED, WIND DIRECTION, AND OPAQUE CLOUD COVER
        FROM SURFACE-OBSERVATION TAPE AND MIXING DEPTH FROM HOLZWORTH-BASED DATA (SEE TEXT).
             DETERMINE RADIATION INDEX FROM MONTH, TIME OF DAY, AND OPAQUE CLOUD COVER.
                                   DETERMINE WIND-SPEED CATEGORY.
             READ STABILITY CATEGORY FROM TABLE, AS A FUNCTION OF RADIATION INDEX AND
                                     AND WIND-SPEED CATEGORY.
                                PUT WIND DIRECTION IN 16-POINT FORM.
           DETERMINE MIXING DEPTH CATEGORY	1 : h<100m, 2 : 100
-------
              Appendix H








THE EQUIVALENCE OF CERTAIN COMBINATIONS




     OF STABILITY AND MIXING DEPTH

-------
                              Appendix H





                THE EQUIVALENCE OF CERTAIN COMBINATIONS




                     OF STABILITY AND MIXING DEPTH








     As was noted in the discussion of the climatological model  in  the




text of this report, it can be simplified to the following form:





                           P   9

                         	t


                           u


                              i=l    '""'"



where



                                                         _3

               C - CO concentration at the receptor  (gm m  ).





              P  = A factor that gives the source strength for the  t




                   hour, based on daily distribution of traffic, and



                   changes in average speed during peak traffic  hours.





               u - Wind speed (m s  ).



                                                                    th

                 - Ratio of the CO concentration received from the  i




                   segment to the emissions in that segment  (for unit




                   wind speed).   The values of these ratios  depend  on




                   stability class, j, and mixing-depth class, m.




            -                                            th
            Q    = Average daily source strength in the i    segment, and




                   the d   direction upwind of the receptor, based  on




                   the total daily traffic and the average speeds on




                   the different types of roads within the segment




                   (gm m   s  ).

-------
It is the term (v/Q)      that is of interest here.  It will  be  shown

              '      i,J,m

that, for some combinations of j and m, the values are independent  of


stability and mixing depth.



     First, the mixing depth class will be defined.  Table H-I shows


the mixing depth intervals for each class and geometric mean, h  , for


each of the classes.
                               Table H-I
                         MIXING DEPTH CLASSES
m, Mixing
Depth Class
1
2
3
4
5
6
7
Mixing Depth Interval
(meters)
<100
100-200
200-400
400-800
800-1600
1600-3200
>3200
hm, Geometric
Mean of Depth
*
70.7
141
283
566
1131
2262
4525
           For classes 1 and 7, the geometric mean was

           calculated as though the classes were bounded.
     We can calculate the values of (v/Q)      for all the combinations
                                         i,j,m

of j and m.  These values are based on the Gaussian model for those  seg-


ments totally inside that distance where the Gaussian and box models


give the same ground level concentration.  For those segments wholly


beyond that distance, the box model values are used.  For the segment


in which the transition occurs, (x/Q)      is based on a combination of
                                     i,j,m

the two models,  as discussed in Section II of this report.  Values of


           were  calculated using the values of h  shown in Table H-I
                                                m

-------
and the exponential approximations of  the Pasquill-Gifford  curves of


the vertical standard deviation as discussed  in  the  text.   These values


of (x/Q) .      are presented in Table H-II.
     The values in Table H-II are  those  that  are used  in  the  climato-


logical model.  Inspection of the  table  shows  that  there  are  rows  that


are identical.  For instance, the  rows of  (x/Q)      values are  identical
                                                i,j,m

when the stability class, j, is 5  and the  mixing depth  class, m, has any


value from 3 through 7.  The same  is true  for  stability class 4, except


that for i = 9 and m = 3 the value differs slightly from  the  values


found for m > 3.  In applying the  climatological model, this  slight dif-


ference was ignored.



     The last column of Table H-II gives a type number  that was  assigned


to each row.  Rows with the same type number  have been  taken  to  be


identical for purposes of applying the model.   Inspection of  the last


column shows that the number of rows that  need to be considered  separately


has been reduced from 35 to 25.  When this fact is  employed in the appli-


cation of the model, it results in a reduction of required memory  space


of about 28 percent.  This allows  for much more efficient use of the


computer.

-------
               Table H-II
VALUES OF (v/Q)
                     FOR UNIT WIND SPEED


Stability
Class, j
1
2
3
4
5
1
2
3
4
5
1

2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Mixing
Depth
Class,
m
1
1
1
1
1
2
2
2
2
2
3

3
3
3
3
4
4
4
4
4
5
5
5
5
5
6
6
6
6
6
7
7
7
7
7


Segment, i
1
4.60
6.89
10.38
16.11
23.0
4.60
6.89
10.38
16. 11
23.0
4.60

6.89
10.38
16. 11
23.0
4.60
6.89
10.38
16.11
23.0
4.60
6.89
10.38
16. 11
23.0
4.60
6.89
10.38
16. 11
23.0
4.60
6.89
10.38
16.11
23.0
2
3.04
4.92
7.22
11.91
16.67
3.04
4.92
7.22
11.91
16.67
3.04

4.92
7.22
11.91
16.67
3.04
4.92
7.22
11.91
16.67
3.04
4.92
7.22
11.91
16.67
3.04
4.92
7.22
11.91
16.67
3.04
4.92
7.22
11.91
16.67
3
3.60
4.99
7.49
13.48
18.96
2.62
4.99
7.49
13.48
18.96
2.61

4.99
7.49
13.48
18.96
2.61
4.99
7.49
13.48
18.96
2.61
4.99
7.49
13.48
18.96
2.61
4.99
7.49
13.48
18.96
2.61
4.99
7.49
13.48
18.96
4
7.07
7.07
8.24
15.74
22.50
3.54
4.60
8.08
15.74
22.5
1.96

4.55
8.08
15.74
22.5
1.58
4.55
8.08
15.74
22.5
1.58
4.55
8.08
15.74
22.5
1.58
4.55
8.08
15.74
22.5
1.58
4.55
8.08
15.74
22.5
5
14.14
14.14
14.14
19.17
27.6
7.07
7.07
8.79
19. 17
27.6
3.54

4.03
8.75
19.17
27.6
1.77
3.60
8.75
19.17
27.6
0.955
3.60
8.75
19.17
27.6
0.67
3.60
8.75
19, 17
27.6
0.604
3.60
8.75
19.17
27.6
6
28.3
28.3
28.3
28.5
34.9
14.14
14.14
14.14
24.2
34.9
7.07

7.07
9.65
24.2
34.9
3.54
3.54
9.65
24.2
34.9
1.77
2.38
9.65
24.2
34.9
0.884
2.88
9.65
24.2
34.9
0.442
2.28
9.65
24.2
34.9
7
56.6
56.6
56.6
56.6
56.6
28.3
28.3
28.3
31.5
47.1
14.14

14.14
14.16
31.1
47.1
7.07
7.07
10.89
31. 1
47. 1
3.54
3.54
10.9
31.1
47.1
1.77
1.83
10.89
31.1
47.1
0.884
1.28
10.89
31.1
47. 1
8
113.2
113.2
113.2
113.2
113.2
56.6
56.6
56.6
56.6
67.4
28.3

28.3
28.3
42.0
67.4
14. 1 4
14. 14
14.50
9
226.
226.



Type
1
2
226. ; 3
226.
226.
113.2
11X2
113.2
113.2
113.2
56.6
4
5
6
7
8
9
10
11
I
56.6 | 12
56.6
60.5
100.3
28.3
28.3
28.3
42.0 59.3
67.4
7.07
7.07
12.97
42.0
67.4
3.54
3.54
12.97
42.0
67.4
1.77
1.77
12.97
42.0
67.4
100.3
14. 14
14. 14
16.37
59.3
100.3
7.07
7.07
16.3
59.3
100.3
3.54
3.54
16.3
59.3
100.3
13
14
['•>
16
17
18
14
15
19
20
21
14
15
22
23
21
14
15
24
25
21
14
15

-------
                Appendix I
CONTINUOUS AIR MONITORING PROGRAM STATIONS

-------
                              Appendix  I





              CONTINUOUS AIR MONITORING PROGRAM STATIONS








     The only generally available  carbon  monoxide  measurements  that can




be used to verify  the performance  of  the  diffusion model  are  those




taken at the stations of the Continuous Air Monitoring Projects  (CAMP).




This appendix has  been included  to provide  some information about the




sites at which the measurements  were  taken.   In this  program  we  have used




data from the stations in St. Louis,  Cincinnati, Chicago, Washington




and Denver.  These stations are  pictured  in Figures 1-1 through  1-5.  All




are located in or  near the downtown sections  of their respective cities.





     The individual sites have certain  characteristics that make their




measurements not entirely comparable  to the computations  made with the




model.  As can be  seen from Figure 1-1, the St.  Louis site is adjacent




to a parking lot that has considerable  in and  out  traffic during business




hours.  This traffic, which is not included in the model  calculations,




undoubtedly influences the measured CO  concentrations.





     The location  of the Cincinnati CAMP  Station,  also in a parking lot




(Figure 1-2), is similar to that of the St. Louis  station, but there is




probably less in-and-out traffic during the day at the Cincinnati site.




The Cincinnati parking lot is near a  theater,  so that anomolously high




measurements may occur at times when  there are public events  at  that




theater.





     The Chicago site represents a different  type  of  problem.  Figure




1-3 shows that the station is situated  just at the foot of a  tall




building.   The airflow around that  building is likely  to  be considerably

-------
different than the airport wind used for the computations.  For example,




airflow around the building may cause the measurements to reflect the




high emission rates on the adjacent street, although the airport wind




may indicate that those emissions would be swept away from the site.




These aerodynamic effects are to be investigated during the coming year.





     The Washington and Denver CAMP Stations (Figures 1-4 and 1-5) are




probably better located than the others,  being somewhat farther away




from tall buildings and parking lots.   However,  their measurements may




not be entirely free of such interferences.

-------
FIGURE 1-1   ST. LOUIS CAMP STATION

-------
FIGURE  1-2   CINCINNATI CAMP STATION
                                                   TA-7874-73

-------
FIGURE  1-3   CHICAGO  CAMP STATION

-------
FIGURE  1-4   WASHINGTON,  D.C., CAMP STATION

-------
FIGURE  1-5   DENVER CAMP STATION
                                              TA-7874-76

-------
                            ACKNOWLEDGMENTS








     We are grateful  for  the  able  assistance  of  the  following  individuals




at Stanford Research  Institute:  the  late Mrs. Shirley Reid, who  secured




and supervised the reduction  of  the traffic data; Mr. Hisao  Shigeishi,




who programmed much of  the model and  carried  out computer  trials;




Miss Joyce Kealoha, who assembled  and cataloged  our  library  of urban




pollution model  studies,  and  who helped  with  numerous other  aspects of




the work; Mr. Elmer Robinson, who  aided  in planning  the model develop-



ment; and Mrs. E. Cox,  Miss S. Hanson, Miss M. Ray,  and Mrs. D. Orr, who




have typed the reports  required  on this  project.





     We also  thank the  members of  the CRC-APRAC  Urban Diffusion Project




Group for their  guidance  and  suggestions, and for supplying  useful tech-




nical information.





     The assistance of Messrs. Charles Hosier and George Holzworth of




NAPCA and of Messrs.  V. Hagarty  and D. Galloway  of the National Weather




Records Center are gratefully acknowledged for their cooperation  in




supplying us with special and conventional meteorological  data.





     Finally, we thank  all the state  and local traffic agencies that




were so cooperative in  supplying historical or forecast traffic data.




The following personnel and agencies  provided such information for St.




Louis:   Messrs. J. R.  Turner and R. Weldinger, Missouri State Highway




Department;  Mr. C. Sweet, St. Louis Land Use  and Transportation Study;




and Mr.  R. L.  Grady,  St. Louis Department of  Streets.  For the Washington,




D.C., metropolitan area, traffic data were supplied by:  Mr. L. E. Brett,




Jr., Virginia Department of Highways;  Mr. W.  C.  Scruggs, Arlington




County Traffic Engineering Division;  Mr. D. E. Tyler, District of






-------
Columbia Bureau of Administrative Services; and Mr. G. W. Cassell,




Maryland State Road Commission.  For Chicago traffic data, we acknowledge




the assistance of Messrs. E. W. Campbell and J. Miller, Chicago Area




Transportation study; and Mr. H. R.  Handley, Illinois Division of




Highways. Mr. C.  Ball, Denver Regional Council of Governments, and the




Colorado Department of Highways provided Denver traffic information.




Messrs. C.  Ball and A. H. Hessling,  Ohio-Kentucky-Indiana Regional




Transportation and Development Plan, provided traffic data for the




Cincinnati area.

-------
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Beckman, E. W., W. S. Fagley, and  Jorma  O. Sarto,  1967:   "Exhaust
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Bornstein, R.  D., 1969:  Observations of the  urban heat  island effect
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-------
Graham, I. R., 1968:  An analysis of turbulence statistics at Fort Wayne,
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-------
Ludwig, F. L. and J. H. S. Kealoha,  1968:  Urban Climatological Studies,
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-------
National Air Pollution Control Administration, 1969a:  Report for
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National Air Pollution Control Administration, 1969c:  Report for
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     Control Region, U.S. Dept. of HEW.

National Air Pollution Control Administration, 1969d:  Report for
     Consultation on the Metropolitan Baltimore Intrastate Air Quality
     Control Region, U.S. Dept. of HEW.

National Air Pollution Control Administration, 1969e:  Report for
     Consultation on the Hartford-Springfield Interstate Air Quality
     Control Region  (Connecticut-Massachusetts), U.S. Dept. of HEW.

Neiburger, M., 1968:  Diffusion Models of Urban Air Pollution, WMO
     Symposium on Urban Climates and Building Climatology, Brussels,
     15-20 October 1968.

Ott, W., J. F. Clarke, and G. Ozolins, 1967:  Calculating future carbon
     monoxide emissions and concentrations from urban traffic data,
     PHS Publ. No. 999-AP-41, National Center for Air Pollution Control,
     Cincinnati, Ohio.

Panofsky, H., 1957:  Introduction to Dynamic Meteorology, Pennsylvania
     St. U., University Park, Pennsylvania, 243 pp.

Pasquill, F., 1961:  The estimation of the dispersion of windborne
     material, Meteorol. Mag.  (London) 90, 33-49.

Perkins, W. A.,  1962:  Some effects of city structure on the  transport
     of airborne material in urban area, paper presented at Air over
     Cities Symposium, R. A. Taft Sanitary Engineering Center, Cincinnati,
     Technical Report A62-5, pp. 197-205.

Pooler, F., 1963:  Airflow  over  a city in  terraine of moderate relief,
     J. Appl. Meteorol., 2, 446-456.

Pooler, F., 1961:  A prediction  model  of mean urban  pollution for  use
     with standard wind roses, Intern. J. Air and Water Poll., 4,  199-211.


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Pooler, F., 1966:  A tracer study of dispersion over a city, J. Air
     Poll. Contr. Assoc., 11, 677-681.

Robinson, E. and R. C. Robbins, 1967:  Sources, Abundance, and Fate of
     Gaseous Pollutants, Prep,  for Amer. Petroleum  Inst. Final Report
     Proj. PR-6755, Stanford Research  Institute, Menlo Park, California.

Rose, A. H. and W. D. Krostek,  1969:   Emission Factors, U.S. Dept. of
     Health, Education and Welfare, National Air Pollution Control
     Administration, p. 5.

Rose, A. H., R. Smith, W. F. McMichael,  and R. E. Kruse, 1964:
     Comparison of Auto Exhaust Emissions  from Two  Major Cities, U.S.
     Public Health Service, Cincinnati,  Ohio.

Rouse, H., 1951:  Air tunnel studies of  diffusion in urban areas,
     Meteor. Mono., _1, 39-41.

Schnelle, K. B., F. G. Ziegler, and P. A.  Krenkel,  1969:  A study of the
     vertical distribution of carbon monoxide and temperature above an
     urban intersection, APCA Paper No.  69-152.

Slade, D. H. (Ed.), 1968, Meteorology  and  Atomic Energy U.S. Atomic
     Energy Commission, Div. Tech. Info.,  Oak Ridge, Tennessee.

Smith, M.  (Ed.), 1968, Recommended guide for the prediction of the
     dispersion of airborne effluents, Amer. Soc. Mech. Eng., New York.

Smith, M. E. and I. A. Singer,  1966:   An improved method of estimating
     concentrations and related phenomena  from a point source emission,
     J. Appl. Meteor., 5_, 631-639.

Smith, Wilbur and Associates, 1958:  Transportation Survey—National
     Capital Region, prepared for National Capital  Planning Commission
     by W. Smith and Assoc., 495 Orange  Street, New Haven, Connecticut.

Stanford University Aerosol Laboratory and The Ralph M. Parsons Co.,
     1953a:  Behavior of aerosol clouds  within cities, Joint Quarterly
     Report No. 3, January-March 1952, Contracts DA-18-064-CML-1856 and
     DA-18-064-CML-2282, DDC No. AD31711,  January.

Stanford University Aerosol Laboratory and The Ralph M. Parsons Co.,
     1953b:  ibid., Joint Quarterly Report No. 4, April-June 1953, DDC
     No. AD31508.

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Stanford University Aerosol Laboratory and The Ralph M. Parsons  Co.,
     1953c:  -ibid.,, Joint Quarterly Report No. G, Vol.  I,  October-
     December 1953,, DDC No. AD31510.

Stanford University Aerosol Laboratory and The Ralph M. Parsons  Co.,
     1953d:  ibid., Joint Quarterly Report No. 6, Vol.  II,  October-
     December 1953, DDC No. AD31711.

Stern, A. C., 1969:  The Systems Approach to Air Pollution  Control,
     Pub. No. 216, Dept. of Environ. Science and Engineering, Univ. of
     North Carolina, Chapel Hill, Presented at Clean Air Conference,
     Sydney, Australia, 21 May 1969.

Summers, P. W., 1966:  The seasonal, weekly, and daily  cycles of
     atmospheric smoke content in central Montreal, J. Air  Poll. Contr.
     Assoc., I6_, 432-438.

Swinnerton, J.  W., V. J. Linnenbom, and C. H.  Cheek, 1969:  Distribution
     of methane and carbon monoxide between the atmosphere  and natural
     waters, Environ. Sci. and Tech., 3^,  836-838.

Turner, D. B.,  1964:  A diffusion model for an urban area,  J. Appl.
     Meteor., 3_, 83-91.

Wanta, R. C., 1968:  Meteorology and air pollution, Chap.  7 of Air
     Pollution, Vol. 1, 2nd Edition, A. C. Stern, Ed., Academic Press,
     New York,  187-227.

Went, F. W., 1966:  On the nature of Aitken condensation nucleii, Tellus,
     18, 549-556.

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