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                               17
As a further complication, any dry, windy area may experience the greatest
participate problem under extremely strong wind conditions when natural
particles are carried aloft (i.e., duststorm conditions).
     For urban areas, stable, anticyclonic conditions are prerequisites for
high TSP levels.   Some success in correlating to TSP has  been shown  with
temperature [16,33], pressure [15] and 850-mb temperatures [11].
 2.1.2   Availability of Meteorological  Data
     Perhaps  the single most  limiting  factor in  performing successful air
 quality  data adjustment  is the  availability of  meteorological data.  Certain
 areas  of the  country, primarily  the larger  urban centers, are  fortunate to
 have extensive sources of meteorological  data.   Other areas more removed from
 the urban complexes  are  subject to limited  meteorological data.
     The following list will  serve as  a  guide to potential sources  of meteo-
 logical  data:
 Upper  Air Data
     National Climatic-Center (catalogue  listing #TDF 56)
     Research Libraries  (e.g., Daily Weather Map Series)
 Surface Data
     National Climatic Center (catalogue  listing #TD1440)
     Pollution Control Agencies
     Flood Control Agencies
     U.S. Forest Service  stations
     Schools/Universities

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                                   .18
 2.1.3  Representativeness  of Meteorological Data
      The success  of any methodology  for  producing weather-adjusted air
 quality trends  depends upon  the  representativeness of available meteorolo-
 gical  data.   "Representativeness", in  this context, implies those meteorolo-
 gical  data which  can adequately  define meteorological conditions at the air
 monitoring location.  Ideally, both meteorological and air quality data,
 measured at the same location, provide the best combination of conditions.
 Usually, however, such data  are  not measured at common locations (or at
 least  a  variety of meteorological parameters are not measured at the same
 location).  It  then  becomes  a problem of locating sources of meteorological
 data   and the subsequent selection of appropriate parameters.
     This section will describe  some of the conditions necessary to estimate
 the representativeness of meteorological data from sources which are not co-
 located  with available air quality data.  Although the treatment of data
 "representativeness" is of proportions to warrant a separate study (cur-
 rently in progress by the EPA), an overview is presented here in order to
 highlight pertinent  considerations supporting meteorological adjustment tech-
 niques.  Meteorological  parameters will be considered with respect to three
conditions:  (V) horizontal distance, (2) topographical  effects, and
 (3) weather-type effects.
1.  Surface temperature
     In general, surface  temperature  is an  excellent  meteorological  parameter
to utilize, partly due to  the availability of data  and  partly  due  to  known
correlations  with specific contaminants.   In  flat  terrain, isolated  from
land/sea breeze effects,  surface  temperature  can be representative for large
distances (>  100 km).  In  irregular terrain,  caution  must be taken to  ensure

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                                    19
the representativeness of the temperature data; however, it is possible that
data from an elevated location may serve as an indicator of warming  or
cooling aloft, which in turn can affect the stability of the  air mass.
     Locations near large bodies of water are not usually representative  of
locations 10-25 km inland when local sea breezes  prevail.   It is recommended
that sources of temperature data be used which represent similar micro-
climatology.
2.  Surface winds
     Perhaps the most consistently usable meteorological parameter is surface
winds.  Relationships between low wind speeds and pollutant concentration in-
creases are well documented.  Surface winds can also be used to define
source-receptor transport patterns.  Consequently, wind data from distant
locations can be useful, if pollutant transport is a primary mechanism for
affecting a particular monitoring site.
     Extreme variability in wind conditions can occur in areas with elevated
terrain and.to a lesser extent, in micro-meteorological regimes  (i.e., land/sea
breezes).   It is not advisable, therefore,  to use a  single source Of  wind
information.  Rather, an area  composite  of  available stations should  be used.
3.   Upper air data
     The major advantage of using  upper  atmospheric  temperature/humidity/and
wind data  is  the  tendency  toward  homogeneity  of  conditions at or above 850 mb
 ("•1500 m).   It is  sufficient to say that such conditions  are probably repre-
 sentative of areas within  a 100-km radius.  Because  the horizontal  variations
 in meteorological  conditions tend to decrease with  altitude, such parameters
 may be most useful in mountainous  terrain,  where surface  measurements may
 reflect extremely localized conditions.

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                                   20
4.   Inversion and mixing height data
     Unlike standard atmospheric conditions, where temperature decreases
with height, a temperature inversion is defined as a layer of air in which
temperature increases with height.  Thus the lifting of an air parcel from
the surface, undergoing adiabatic cooling, is inhibited from rising above
the inversion due to the changes in buoyant properties between the parcel
and its surrounding environment.  This is especially important in air
pollution considerations because of the vertical dilution limitations
caused by the inversion.
     Another term reflecting limitations to vertical dilution is "mixing
height."   In,this report,  "mixing height" is defined as that level at which
an  air parcel with  a given surface temperature is lifted and cooled at the
adiabatic  lapse  rate of 9.8°C  km"  until it achieves the same temperature
as  the surrounding  ambient air with a more stable lapse rate.  The exis-
tence of a definite mixing height does not imply the existence of an inver-
sion; however, the  existence of a low-level inversion does identify limited
mixing.
     When inversion/mixing height data are available, definite implications to
pollutant concentrations can be made.  While vertical air-mass properties may
be representative within 100 km, the effects of mixing are governed by surface
heating (i.e., as the surface  temperature increases, the level  at which equi-
librium occurs between the lifted air parcel and the ambient air also increases)
and general atmospheric stability.  As a result, the cautions mentioned for the
widespread geographical use of temperature parameters also apply for inversion/
mixing height data.

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                                   21
 5.  Weather types
      No  one single meteorological  parameter can adequately describe the pre-
 vailing  weather conditions  at  the  time of a particular air quality measurement.
,To  get a true  picture  of the cause-effect phenomena of meteorology upon air
 quality, several  independent or  interrelated  variables should be gathered
 to  obtain the  most representative  meteorological  assessment at  a given air
 quality monitoring location.   While  individual parameters may not be represen-
 tative due to  terrain  or localized influences, their use with other parameters
 may be significant.  For example,  a  certain mixing height may not indicate a
 definite relationship  to a  pollutant concentration; however, the mixing
 height coupled with  temperature, relative humidity, and wind speed may  per-
 fectly describe a weather condition  which results in a consistent pollutant
 distribution and concentration.   It  suffices  to  say that combinations of
 meteorological variables tend  to become  more  representative of  dominating
 weather  types than  the individual  parameters, provided that logical meteoro-
 logical  processes are  considered.
     No  specific list describing the representativeness  of available meteor-
ological data can be compiled for every possible location  across the country.
For every rule given, there will  always be an  exception.   The  general  "common
sense" guidelines presented here are intended to stimulate  the  reader toward
a goal of thoughtful, rather than haphazard, selection  of available
meteorological data.   An empirical  method is presented in. Section 4.0  to
assist in the selection process.

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                                   22
 2.2  VARIATIONS IN AIR QUALITY DATA DUE TO METEOROLOGY
      The-relationship of specific pollutants  to various meteorological
 parameters, cited in Table 2.1, suggest that  variations in  pollutant
 concentrations, especially on a daily basis,  are primarily  due to
 meteorology.  Except in the case of specific  point  sources, where
 daily changes in emissions can affect air quality in a substantial man-
 ner,  the general uniformity in daily emissions over  most  urban areas dictates
 that  short-term changes of measured concentrations are  caused  by  meteoro-
 logical fluctuations.  To quantify the amount of variation  attributed  to
meteorology  is a difficult and complex problem.  Certainly if techniques  using
meteorological parameters  could explain all of the  daily pollutant variance,
then  one would have achieved  a perfect forecast mechanism.  Nothing approaching
this  level of achievement  has  been  accomplished to  date.  This does not imply
that such near-perfect relationships  do not exist;  but rather the  implication
is that the explicit combination of meteorological  parameters necessary to
determine the variation is too complex to identify and measure exactly.
     The longer the period of  analysis,  the greater the potential  for pollutant
 variances  to be  complicated by both meteorological  and emission factors.   For
 example,  in  one  study  [39], the statistical variance for year-to-year nation-
 wide N02  values  during 1970-1975 was  found to  be  ±20% for the annual Inhour
 maximum,  ±13% for  the  99th percentile of hourly concentrations, and ±11% for
 the annual mean.   No attempt, however,  was made to  distinguish that part of the
 total variance due to  meteorology,  illustrating the complexity of the problem.
      While the quantitative  assessment of meteorological  variations  affecting
 a variety of pollutants can  perhaps  best be  dealt  with in  a  lengthy  investi-
 gation of historical variations of specific  meteorological parameters (beyond

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                                     23
 the  scope  of  this  report),  the following subsections will explain some of
 the  known  meteorological  factors affecting air pollutant concentrations as
 well as  the subsequent  effects inherent in the type of air quality para-
 meter(s) chosen for analysis.
 2.2.1   Variation in Meteorological  Effect-Among Pollutants
      The  effect of  meteorology on pollutant concentrations may differ
 from  one  pollutant  to another.  For example, higher wind speeds tend to
 result  in lower concentrations for  primary pollutants such as CO.  But this
 is not  necessarily  true  for  oxidants or S02 which may be affected to a greater
 degree  by large point sources and transport phenomena.  In addition, seasonal
 effects can account for  significant variability of pollution concentration.
For example, in the winter, S02  concentrations  tend to increase,  but oxidant
concentrations  decrease.
      Table  2.2 presents  sample seasonal patterns of three primary pollu-
 tants resulting from fuel  combustion, S02, CO, and NO, and that of the
 secondary pollutant, oxidant.  In Table 2.3 sample diurnal .patterns of the
 same  pollutants as  those in  Table  2.2 are presented.  From these two tables,
 one can deduce a role of meteorology in pollutant concentration levels.
      The  three fuel combustion pollutants, S02, CO, and NO, exhibit higher
 concentrations in winter and lower  concentrations  in summer.  This is a
 function  not only of meteorological conditions conducive to pollutant
 build-up, but  also  of emissions.  Colder winter temperatures bring greater
 fuel-burning requirements, which in turn lead to greater seasonal dif-
 ferences  in pollutant concentrations.  On the other hand, the diurnal pattern
 of these fuel combustion pollutants may be explained more by meteorology than
 by emissions.  The  concentrations of the three pollutants generally increase in

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                                   24
   Table 2.2   Sample Seasonal  Patterns  of Pollutant Concentrations
                For Urban Areas
Pollutant
so2
CO
NO
°x
Spring
(M.A.M)
Medi urn
Medium
Medi urn
Medi urn
Summer
(J,J,A)
Low
Low
Low
High
Fall
(S,0,N)
Medium
Medium
Medium
Medium
Winter
(D,J,F)
High
High
High
Low
   Table 2.3   Sample Diurnal Patterns of Pollutant Concentrations
Pollutant
so2
CO*
NO
°x
Morning
(6-12)
High
High
High
Medium
Afternoon
(12-18)
Low
Medium
Low
High
Evening
(18-24)
Medium
High
Medi urn
Low
Night
(0-6)
Medi urn
Medi urn
Medi urn
Low
*  CO typically (but not at all  locales)  has  three  peaks:  around 0700;
   around 1700; and, with surprising regularity,  around 2400.

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                                  25
the morning and decrease in the afternoon, despite the fact that the emission
levels remain high in that period.  The probable cause of this difference in
morning and afternoon concentrations will be found in meteorology.   Under
stable, limited mixing, early-morning meteorology, concentrations will  in-
crease.  In the afternoon, solar radiation and wind speeds increase the at-
mospheric ventilation, thus resulting in dilution of pollutant concentrations.
     The secondary pollutant, oxidant, is formed by complex photochemical re-
actions of precursor pollutants, hydrocarbons and oxides of nitrogen.   The
oxidant concentration level is higher in summer than in winter (Table  2.2),
and is higher in the afternoon than in the morning (Table 2.3).   The high
oxidant concentrations during the summer season and afternoon period are pri-
marily due to the unfavorable meteorology (high temperature and  strong  inso-
lation) during those periods rather than due to the slightly increased
hydrocarbon emissions (i.e., increase in evaporative emissions).
     Smelters and power plants are often responsible, for much of the S0?
emissions.  Peak S02 concentrations occur when the wind blows from these
point  sources to a recepter site. Therefore, S02 concentrations originating from
point  sources are more sensitive  to wind direction than wind speed.  To fur-
ther complicate matters, breakdowns of modern, efficient pollution control
equipment can result in substantially higher concentrations at a monitoring
location under a'variety of meteorological conditions.  Thus in certain
areas  of the country, such as Los Angeles,, current SCL concentrations may
be more of a function of industrial control-equipment-breakdown status than
of any specific set or sets of meteorological conditions.

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                                     26
     Consideration must be given to the elevation of point-source emissions.
Ground-level emissions, such as CO from vehicular traffic, would be affected
by meteorological conditions which caused strong low-level inversions with
very light wind speeds.  Stack emissions could easily penetrate those types
of inversion conditions.  Strong off-the-surface inversions might trap stack
emissions, but would not be conducive to high concentrations of ground-based
emissions.
     The type of pollutant examined will affect the horizontal  difference
and geographical complexity of the meteorology to be considered.  The
concentration of primary pollutants is determined by local emissions
and local meteorological conditions.  Therefore, meteorological ad-
justment of air quality trends for the primary pollutants should be made by
using the local meteorological data collected as near as possible to the air
monitoring station.  On the other hand, the concentration level of secon-
dary pollutants is  determined by regional  emissions  and  meso-scale  or
synoptic scale meteorological conditions.   In the long-range transport of
secondary pollutants, such as oxidant, it may be necessary to examine the
meteorological conditions nearer the source area than the receptor area.  In
some analyses, this may require investigation of meteorological data 100 km
or more from the monitoring location.

2.2.2  Variation in Meteorological Effect Among Air Quality Parameters
     Currently used air quality parameters can be categorized into three types:
mean concentration at various averaging times; extreme concentrations such as
daily maximum, annual maximum or annual second maximum;  and frequency of

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                                 27
hourly or daily maximum hourly concentrations exceeding air quality stan-
dards.  Meteorology-may affect these air quality parameters differently.
     The level of a maximum concentration is largely dominated by a particu-
lar meteorological condition, rather than an emission level.   Variation in
annual 1-hour maximum concentrations reflects the variability in annual "worst-
case" meteorology.  On the other hand, the level of an average concentration
is a more stable parameter:  the longer the averaging period, the more stable
the parameter.  Anomalous meteorological years tend to be smoothed out in
annual average pollutant statistics, although significant seasonal anomalies
can seriously affect the results.  Regardless of the parameter selected,  it
is difficult to extract direct emission-related air quality trends without
an examination of the underlying meteorological conditions.
     Similarly, the number of violations of a standard, or the frequency of
concentrations exceeding a given threshold level can be affected in much the
same manner as a maximum concentration or an average concentration, depend-
ing upon the level of the standard or that of the threshold chosen.  When
the threshold level chosen is very high, frequency of concentrations ex-
ceeding the threshold may vary greatly from year to year, similar to the
annual maxfmum concentration.  When the threshold level is low, the fre-
quency of concentrations exceeding the threshold may vary as that of an average
concentration.
     Whichever air quality parameter is used, a specific set of logical
 meteorological parameters must be specified.   It is rather unlikely that an
 identified meteorological parameter used in analyzing an air quality parameter
 (such as annual average concentrations) could  be used to explain another air
 quality parameter.  For example, an abnormally large number of winter surface

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                                     28
inversions might explain an increase in annual CO averages, but could not,
of itself, explain an unusually high single CO hourly average.   Specific
meteorological parameters must be identified to explain the individual  case.

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                                  29
     3.0  APPROACHES TO METEOROLOGICAL ADJUSTMENT OF AIR QUALITY  TRENDS

     The adjustment of observed air quality for meteorological  variability
to reflect true trends requires three basic elements:
     (1)  Selecting an air quality index:   What annual  measurement of
          air quality do we wish to adjust?  Candidates include (a) values
          corresponding to the standards (e.g., the second-highest eight-
          hour average CO value in the year); (b) averages of values re-
          lated to the standards (e.g., the average of daily maximum
          eight-hour-average CO over the year); (c) the averages  of values
          related to the standards over a portion of the days of  the year
          (e.g. only the high-pollution season);(d)  the number  of days or
          hours of the year in which the standard is exceeded;  and (e) var-
          iations  on the above themes.
     (2)  Relating meteorological  variables to  air quality:   If air
          quality  measurements are to be adjusted for meteorology, the
          effect of available meteorological  variables  on air quality
          must be  expressed at least qualitatively,  but preferably quan-
          titatively.
     (3)  Adjusting measured air quality:   The  relationship  between air
         .quality  and meteorological  variables  must  be  used  to  adjust
          observed values.   Preferably, the adjusted values  should repre-
          sent annual  pollution measurements  which would have occurred if
          meteorology  were  the same each year.

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                                   30
       These three components of a meteorological  adjustment procedure are
  closely interrelated; the best choice of one component may depend on the
  choices we make of the other components.  In this section, we discuss some
  choices suggested in the literature, indicate their relationship to one
  another, and outline their strengths and weaknesses.   In Section 4.0, we
  recommend an approach which is an extension of the best ideas in the liter-
  ature.
      The remainder of  this  section is organized by the way  in which  the
 proposed methodology relates meteorology to air quality:
      (a)  Postulation from basic principles;
      (b)  Regression techniques;
      (c)  Classification techniques;  or
      (d)  Meteorologically invariant  statistics.
 3.1  POSTULATION FROM BASIC PRINCIPLES
      Section 2.0 discusses qualitatively typical relationships of indi-
 vidual meteorological variables to the concentration of various pollutants.
 Using these and similar ideas, one might combine meteorological variables
 to develop an "index" indicating the  likelihood of high pollution levels
 in a given day or year.
     For example, an Environmental Protection Agency (EPA) report  [42]  used a
method of meteorological adjustment of oxidant trends in the Los Angeles area
which compared annual ventilation criteria and yearly hydrocarbon emissions to
the annual average of daily one-hour oxidant maxima (a composite of three key
monitoring locations).  Ventilation data represented the number of days per

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                                   31
 year with specified limited mixing and low wind speeds (Los Angeles County
 APCD  "Rule 57" days).  A day meets the "Rule 57" criteria if the following
 all occur on that day:
      (1)  Morning inversion < 1500 feet MSL;
      (2)  Afternoon mixing height £ 3500 feet MSL; and
      (3)  6 A.M. - 12 noon average wind speed £ 5 mph.
     One potential difficulty in the annual agglomeration of Rule 57 days
against annual oxidant data is that poor ventilation in the off-season winter
months does not relate well to high concentrations of oxidant.  As a result,
seasonal biases  can occur  by achieving an unusually high number of winter
Rule 57 days or  an unusually low number of summer Rule 57 days.  This problem
is  partly solved by treating the "smog season" alone rather than the full year,
     Horie and Trijonis [20] used a conceptually similar approach to estimate
the effect of meteorology on annual values of oxidant and N02 in Los Angeles.
If a parameter value in a given year was  sufficiently above its long-term
average,  it was assigned a "+1" value;  if sufficiently below, a "-1" value.
A "score" was calculated for each year to indicate which years had an above-
or below-average propensity for high pollutant concentrations.  The results
were used qualitatively to comment on the likely underlying pollution trends.
       Another index was developed by Davidson [15] using the product of
  mixing height and wind speed in, Los Angeles.  This combination reflected
  atmospheric conditions conducive to photochemical pollution.  Thus, the
  lower the index value, the greater the seasonal potential for increased
  oxidant concentrations.  Ozone trends in the Los Angeles area were norma-
  lized based on the seasonal index value.  Results showed that adjusted

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                                   32
seasonal daily one-hour maxima were improving slightly less rapidly than
actual trend data due to the more favorable meteorological conditions in
the early 1970' s.
     An index for S02 near Rotterdam was used by van Dop and Kruizinga [43]
based upon a measure of the strength of the inversion (A6), the maximum
mixing height (L), and the average daytime surface windspeed (U).   The
form was
A =
A8
                                      + C2/LU
where C, and C2 were chosen so that the two terms have equal values for
average conditions.  The daily value of A was averaged over each year for
use in normalizing that year.
     Zeldin [44,46] developed a method for meteorological adjustment using
weighted class- intervals for specific meteorological parameters.  Based on
known cause-effect relationships between oxidant and meteorological parameters
of inversion strength, temperatures aloft, inversion height, and surface pres-
sure  gradients, a stratified system was devised which numerically evaluated
the meteorological potential for each day.  Table 3.1 illustrates the
"scoring" structure.  A high score indicated a high pollution potential.
    Zeldin averaged daily meteorological  index-values for the smog season months
of June through September.  Resultant values were therefore a numerical evalua-
tion of the severity of the entire smog season.  Statistical comparisons were
then made to oxidant data for various cities in the Los Angeles Basin.  In one
study [44], correlations were performed using the number of hours exceeding
the California Air Resources Board (ARE) stage-one episode level of 0.20 ppm.

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                                    33
Point
Score
0
1
2
3
1 (°C) ! (°C) ' (feet)
Inv. Strength t 95Q_mb Temo. Inversion
< 5.0 | < 5.
5.1 - 7.0 , 5.1 -
• 7.1 - 9.0 ; 8.1 -
i
- j
9.1 - n.o ! n.i -
i
i i
4 11.1 - 13.0 i 14.1 -
I
• 5
6
i
i
i
i
8
13.1 - 15.0 17.1 -
!
!
f
I
!
15.1 - 17.0 j 20.1 -
i
i
17.1 - 19.0 ; 24.1 -
i
19.1 - 21.0 • 28.1 -
9 21.1 - 23.0 i 32.1 -
i >
0 5,000+
8.0 4,001 - 5,000
1
;
11.0 | 3,001 - 4,000
14.0 ! 2,501 - 3,000
i
2,001 - 2,500
17.0
i Surface
20.0 I 1,501 - 2,000
i
24.0 1,001 - 1,500
i
|
28.0 I 701 - 1,000
i
!
32.0 501 - 700
36.0 301 - 500
i
(millibars)
Prpssure Gradient
< -10.0
< +20.0
- 9.0 to - 9.9
+16.0 to +19.9
- 8.0 to - 8.9
+12.0 to +15.9
- 7.0 to - 7.9
+12.0 to +11.9
- 6.0 to - 6.9
+ 8.0 to + 9.9
- 5.0 to - 5.9
+ 6.0 to + 7.9
- 4.0 to - 4.9
+ 4.0 to + 5.9
+ 2.0 to + 3.9
- 3.0 to - 3.9
+ 1.0 to + 1.9
- 2.0 to - 2.9
0.0 to + 0.9
i
  10
> 23.1
36.1
150 -   300 !   - 1.9 to - 0.1
            l
Table 3.1   Zeldin's Point Classification Table.  (Each of the four meteorological
            variables yielded a score.   The daily score was the sum of the
            scores for each variable.)

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                                34
 In a second study [46], similar evaluations were made using the averages
 of the daily maximum hourly average.  Results for common locations with
 both air quality parameters exhibited similar trends.
      Using the -postulation approach, some of the indices evolve in rather
 arbitrary units which cannot be related directly to pollutant concentra-
 tions.  To achieve a more desirable result, most of the referenced authors
 used a single-variable linear regression of the annual pollution values
 against annual values (or averages) of the meteorological index in order
 to translate arbitrary meteorological index values into pollution concen-
 tration units (Fig. 3.1).  Suppose the resulting best-fit equation is
                                y " ax + b   ,                      (3-1)
 where y is the annual pollution measure and x the annual meteorological
• index.  Then this equation is intended to give the value of y which would
 be "expected" to result in a year when meteorology yielded a value x.  it is
 assumed that the differences between the expected value and observed value
 in a given year (the "residuals") are primarily the result of emission
 trends.  Zeldin [44,46] used this concept directly and plotted the resid-
 uals to elucidate the true trend.
      Mtist of the other references cited in this section took the more pre-
 ferable approach of attempting to indicate what the pollution level  would
 have been in each year if the meteorology index took its average value
 each year.   The  references are uniform in a lack of specificity as to how
 this adjustment  of measured values  was accomplished.   It appears that
 the procedure used is  as  follows:    Let  x" be the overall  mean  value  of
      ^
       Verified by conversation  for two  references  [15,41].

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                                            35
(Annual

Pollution

Measure)
                                                                        Best-fit Line:

                                                                        y = ax + b
                                                         x (Value  of Meteorological  Index)
                 Figure 3J   Annual Value of Pollution Measure Versus  Annual  Values
                              of Meteorological  Index.   (Five years  are assumed  in
                              this figure.)

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                                 36
 the meteorological  index (over all  years),  and "x* the average value

 for the k   year.  Assuming Eq. (3-1) holds,
                             a  x  +  b


 is  the  pollution  level  due  to  meteorology  in year  k and



                             a x" +  b


 is  the  average pollution  level due  to meteorology  over all years.  The

 excess  amount of  pollution  due to meteorology in year k is found by sub-

 tracting these two quantities, yielding


                            a (x* -  x)

                                    /N.
The meteorologically adjusted  value yk for year k  is found by subtracting

this excess from  the observed  value y.:
                       yk = yk - a (x  - x)
(3-2)
     Equation (3-2) has built-in insurance against the use of a poor

meteorological index.  If the correlation between pollution levels and

the meteorological index is zero, the coefficient "a" will be zero, and the

adjusted value will be the observed value.
      «
      Equation  (3-2) can be  interpreted as the residual error in the re-
gression for year k,

                         yk  - a 3^ - b
added to the overall average of y,

                          y = a x" + b
Thus, except for a change of origin, a plot of the residuals will look
exactly like a plot of values adjusted by Eq. (3-2).

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                                  37

      The major technical weakness of this approach is that the slope of
 the regression line (the constant "a") is affected by the underlying emis-
 sion trend,  as well as  by meteorology.  To see that this  is  true,  one need
 only examine the  extreme case  where  only two years  are  considered.   Since
 the regression line in  this  case  will  go through both points,  the  residuals
 will  be  zero.  .Thus, this  method  will  always indicate no  trend in  the
 meteorologically  adjusted  values, irrespective of their value,  for two
years.  This problem is  discussed in more general terms in the  following
subsection.
3.2  THE REGRESSION APPROACH
      In  the  previous subsection,  we  described  meteorological indexes which
 were  postulated from basic principles.   The underlying objective of  this
 subsection is  the derivation and  use of  such indexes by objective methods.
 Meteorological Adjustment  for  Two Time Periods
      A study of S02 trends in  Oslo, Norway, is typical of this  approach [17],
A study was  undertaken  to meteorologically adjust S02 air quality to com-
 pare  the periods  1959-1963 and 1969-1973.  The meteorological  conditions
 during the former period were  considerably different from those during the
 later period;  hence one  could  not expect a change in air quality to be
directly related to a change in emission potential.
     Data from the earlier period (1959-1963)  were used to do a linear re-
gression analysis for daily values.   It was discovered that two variables
dominated the estimate of S02 concentration:   (1) a temperature difference
between a low-altitude and high-altitude measuring  station,  and (2) the
temperature at the lower station.   For example, a typical  regression  equa-
tion for one station was

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                                      38
                        qSQ   =61.5  (Tg-T.,)  -  n.6T] + 472
(3-3)
 where
                                                          Q
      qso  = daily mean value of S02 concentration  in  yg/m  at the  particular
             station
        T2 = temperature at higher station  at 7  P.M.
        TI  = temperature at lower station at 7 P.M.  .
      The temperature-difference term is related to  the  strength  of the  inver-
 sion  and hence  the dispersion,  while the temperature  term is  related  to the
 variation  in  the  emission  of S02 due to space heating.    Since the daily tem-
 perature data for the  later time period is  known, the daily mean S02  expected
 for the meteorological  conditions  during that time  period can be estimated
 by Eq.  (3-3).   This was done for each day  on which  data was available in
 the later time  period; the predicted values were consistently higher  than
 observed values.   Thus, it was  easy to conclude that  emission  potential
 was reduced.
     A  quantitative statement was made in the report that the S02  pollution
was reduced 50%to 60%.  According to a conversation with one of the authors
of the  report, this latter  statement was derived by looking at the ratio of
the coefficient on the  temperature-difference term in the early time period
      This equation explained the observed values of S02 concentration with
a multiple correlation coefficient of .80; that is, the correlation between
values predicted by this equation and observed values for the period was
0.80.

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                                   39
 to the coefficient of the temperature-difference term in a similarly derived
 equation for the later time period.  The intuitive justification for such a
 statement is that the coefficient measures the degree to which a given tem-
 perature inversion will  be translated into S02 concentrations.  Thus a 50%
 or 60% reduction in that coefficient might be thought of as a meteorologically
 adjusted measure of the trend .in air quality.  This approach to quantifying
 the reduction is not easily generalized or of clear mathematical validity.
      Meisel suggested a more general approach to comparing the air quality
 in two time periods [28],  He suggested that equations relating daily air
 quality to daily meteorology be derived for the two time periods.  In the
 first period, suppose the best-fit equation is
where q, is an air quality parameter, m-j , ... m^ are meteorological param-
eters and F-, is some function of
suppose the best-fit equation is
  eters and  F-,  is  some  function  of  those  parameters.   In  the second period,
Then we examine the ratio of the equations:
                                P2(m-\ .....
                                                                     (3.5)
This can be calculated for any set of meteorological conditions.  If emis-
sion potential is unchanged, we would expect air quality to be about the

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                              40
same in both periods, assuming that all significant meteorological param-
eters have been identified.  Hence, the ratio q2/q-| will be about 1 for
all meteorological conditions if the emission potential is unchanged.  If
q2/q, is approximately constant over all meteorological conditions, but at
a value other than 1, then emission potential has increased or declined by
an amount given by that constant.  (If the constant is 0.90, meteorologically
adjusted air quality, i.e., emission potential, is 90% of its former value;
that is, it has improved 10%.)
     If q2/q-| is highly variable, then the improvement in emission potential
depends on the meteorological condition, i.e., the meteorological parameters
used do not adequately relate to the pollutant, and a more detailed examin-
ation is required.  One might find, for example, that there is a degradation
in adjusted air quality when the wind blows from the direction of a newly
constructed power plant, but an improvement otherwise.
     Mathematically,' one could calculate q2/q-| bY Eq- (3-5)  for the meteoro-
logical conditions of each day during both periods.  The median of all
these values might be taken as representing the meteorologically adjusted
change in air quality between the two periods.  The 95th and 5th percentile
values of q2/q-| might be used to indicate the range of uncertainty in this es-
timate.
Meteorological Adjustment for Multiple Time Periods
     Sidik and Neustadter [33] proposed a linear regression to correct a
series of annual pollution values for the Cleveland area.  A linear regres-
sion of pollutant levels was performed against 29 predictor variables; the
variables were meteorological, except for two rough indicators of economic

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activitys a seasonality variable, and the number of days from the inception
of the monitoring.  Because this last variable increases linearly with time,
it has the potential of accounting for a linear trend in emissions.
     A  similar method of meteorological  adjustment was  described by the
EPA  [41]  using seasonally  adjusted averages of wind  speed, temperature, and
rainfall  for  the  Los Angeles area.   Statistical analyses were .performed with
a nine-station  composite of seasonally adjusted  values  of  SC^  and TSP.  It
was  shown that SOp  was  correlated to inverse  wind  speed and  that TSP  was
negatively correlated with rainfall.   Observed quarterly levels were  nor-
malized to the average  meteorological  conditions for each  calendar quarter.
A variable corresponding to the year was used to model  a linear emissions
trend.   Since only  one  meteorological  variable was considered  significant
 for each pollutant, that variable was used to adjust observed  values  using
 Eq. (3-2).
      In the last two studies referenced, a "dummy"  variable  was  used  to rep-
 resent a linear trend in emissions.   This procedure  deserves further  discussion.
 In reference to Figure 3.1, we noted earlier that  direct regression over
 several years could result in a coefficient which  incorporated changes in
 emissions rather than meteorology alone.  In Appendix A, we  generalize this
 problem to the regression  of daily values in several years.   Our conclusion
 is that it is inadvisable to use data for several  years in a regression against
 meteorological  variables alone.  Instead, one should either use dummy variables
 or do  a separate regression in each year.
      If dummy variables are used, we  recommend using one for each year rather
  than a single linear trend variable.   (See Appendix A  for details.)   If the

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                                    42
trend is not linear (e.g., is U-shaped), a linear trend variable can create
misleading results.
     If a separate regression for each year is performed, a method such as
that recommended by Meisel and discussed above must be applied to each sue-
                                                                                  y
cessive pair of years to obtain an adjusted trend.
Cautions Regarding Linear Regression
        Because linear regression is one of the best understood and easiest
to use statistical analysis techniques, it can be a.powerful tool in meteoro-
logical adjustment, as discussed.  Some cautions are in order, however; it is
not always the best approach.
     The most serious limitation of linear regression is that its effective-
ness depends on the relationship between the meteorological variables and
pollutant concentration being approximately linear.  As we discussed in
Section 2.0, many meteorological variables are nonlinearly related to pol-
lutant concentrations.  If nonlinearly related variables are avoided, only
a portion of the variation in pollutant concentrations explained by meteor-
ology will be modeled.  This omission can potentially result in distortions:
year-to-year differences  in nonlinear variables would not be reflected
in the adjusted values.
      A nonlinear variable which is monotonically related to the pollution
 concentration will result in a correlation with that variable.   The use of such   .
 a variable in a linear regression can result in biased residuals.  (See
 Figure 3.2.)  The resulting equation will predict high for some ranges of
 the meteorological variable and low for others.  This condition can often

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                                  43
                                            linear
                                                   underlying nonlinear
                                                   relationship
Figure 3-2   Example of Linear and Non-Linear  Relationships.   (The meteoro-
             logical variable x is nonlinearly related  to y, but fit with a
             linear equation.  The linear equation will  consistently over-
             predict for large values of x.)

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                                     44
be  detected by plotting the residuals  (difference between predicted and actual
values of y) versus y.  If the regression is legitimate, there should appear
to  be no relationship between the two.
     Nonlinearities can be handled through redefinition of variables, in
order to maintain the linear regression methodology.  For example, it is
common to use the logarithms of a meteorological variable.  More generally,
tabular definitions are possible, as in Table 3.1.  In this case, Zeldin has
transformed nonlinearly related variables into a linear point score.   One
then simply uses the redefined variable in a linear regression.
     Nonlinear transformation of the concentration variable y are also
possible, but care is required.  If we predict, for example, log y with
40% of the variance explained, we are not explaining the same 40% of the
variance in y.  The predictions must be transformed into predictions of y
to  calculate the error in predicting that quantity.  Explaining more of
the variance in log y than in y is not sufficient justification for using
log y.  Instead, the percentage of variance explained in y by the log y regres-
sion should be computed.
     On the other hand, since most pollution values can be reasonably ap-
proximated as lognormally distributed, the use of the log of the concentration
may cause the residuals to be less biased.  The equations in this section and
in Appendix A are valid if y is interpreted as the log of the pollutant con-
centration.
     Another typical  error in linear regression is to use too many varia-
bles.   One can overfit the data by adding variables which do not signifi-
cantly improve that fit;  this practice can cause anomalous  results.   A

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                                 45
further difficulty in using too many variables is that dependencies among
the variables can make the coefficients uninterpretable.  If linear regres-
sion is used, we recommend stepwise linear regression to avoid using any-
more variables than necessary.
 Nonlinear Regression
      In  general,  if a  relationship  is  nonlinear,  it  is  better  to  perform
 nonlinear regression directly rather than  use  a number  of  tricks  to make
 the  problem  linear.  However,  software for nonlinear regression is not  as
 common or automatic as  linear regression.   Techniques of the following
 sub-section,  however,  allow nonlinear  effects  to  be  incorporated  without
 nonlinear regression.
      CLASSIFICATION APPROACHES TO '-METEOROLOGICAL ADJUSTMENT
     The basic difficulty with the regression approach is finding a simple
relationship between meteorology and air quality which holds for the full
range of meteorological variables.  The approach of this subsection is to
reduce this difficulty by breaking up the problem.  In particular, we focus
attention on days falling in meteorological classes which are conducive to
high pollution levels.
     Such a method  of adjusting oxidant data in  the San Francisco area was
employed by the Bay Area Air Pollution Control District [1].  By taking two
meteorological parameters known to have a significant relationship to oxi-
dant levels on a daily basis, adverse days were  selected for seven locations.
For each location,  a limiting temperature and an inversion  base height were used
to classify days into the "adverse" category.  Annual averages of the daily  .

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                                 46
maximum hourly concentrations were computed based on only those days clas-
sified as  "adverse."  The averages from year-to-year thus represented the
meteorologically adjusted oxidant trend.
     The applicability of this technique is apparent.  A specific subset
of days containing similar meteorological conditions approaches the ideal
situation  of holding meteorology constant.  The trend resulting from the
analyses can be regarded as a good representation of the downward oxidant
trend due  to effectiveness of emission control strategies.
     One potential problem, however, in employing this method is the varia-
bility of  meteorological conditions within the prescribed subset of days.
If the criteria selected are too broad, the variability within categorized
subsets may not adequately describe the desired "adverse" effect.  In
essence, meteorology is not held constant, and ultimately, results cannot
be regarded with confidence.  On the other hand, criteria set too strin-
gently can reduce the number of such days to the point of losing statisti-
cal confidence in the results.  Appropriate class definition is critical.
Again, even with good definitions, very large deviations from normal weather
patterns can seriously impact the accuracy of this model.  (See Appendix A.)
     A method for weather-correcting oxidant data in the San Gabriel  Valley
portion of the Los Angeles  Basin was developed by Kerr [24].   He classified
September meteorological  data for the years  1968 to 1973 into five meteoro-
logical  types:   (1) closed  high-pressure center aloft,  (2)  inversion  <  1100 ft.,
(3)  inversion 1100-3500 ft.,  (4)  surface Santa Ana wind  type, and (5)  closed
low or deep trough aloft.   These  definitions  involved some  subjectivity and

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                                  47
were not mathematically explicit.  A table was constructed depicting a fre-
quency distribution by weather category per year.  For each category, multi-
year averages of the maximum hourly averages were determined.
     Once the distribution of days by category was established, the weighted
averages of each year of record were computed; that is, Kerr summed the yearly
frequency of occurrence over all the categories  and multiplied by the concen-
tration mean for each category.  Thus, the expected concentration.value for
a year9 given the meteorology of that year, could be  calculated.  The resi-
duals  reflecting the difference between this  predicted value and the observed
value  were  used as  a measure of meteorologically adjusted trends.
3.4 METEOROLOGICALLY  INVARIANT STATISTICS
     Another method, presented by  Zeldin  et al.[46],  explores  the possi-
bility of performing meteorological  adjustment to  air quality  data  without
the use of  meteorological  data!
       In this  particular  study,  oxidant  data  were  analyzed in  the Los Angeles
area.   It  is  known  that meteorological variability affects annual ozone  con-
 centrations.   However,  even in  the most  favorable  of meteorological years,
 there  will  still occur a  number of particularly adverse days under  which
 elevated ozone concentrations  will occur.  The author found that,  by using
 the fifth-highest maximum hourly average at a given site for a particular
 year,  and then comparing that value to the same parameter in other years, the
 general meteorological patterns under which the ozone concentration occurred
 were nearly identical.  Thus no specific meteorological parameters were used,
 but the values reflect underlying emission trends.

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                                 48
     This method is basically untested.   It is not known whether the metho-
dology can be utilized more universally; however,  it does offer potential
use in areas where meteorological data are sparse.  If proven to be an ef-
fective method of providing a meteorological adjustment of air quality
data, the method allows one major advantage —simplicity.  Since this ap-
proach, strictly speaking, exploits meteorological invariance rather than
meteorological adjustment, we will not pursue it further here.

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                                   49
              4.0  RECOMMENDED PROCEDURES  FOR METEOROLOGICAL
                           ADJUSTMENT OF AIR QUALITY

      This section describes in detail a recommended methodology to achieve
a meteorological adjustment of air quality data,  which in turn can result
in an air quality trend based on meteorologically adjusted emissions,
i.e., emission potential.  Guidelines are  presented for the definition
of distinct meteorological classes and for the use of these classes to
determine a meteorologically adjusted trend.  By determining average
concentrations for each class, and then by relating the data to a "typical"
meteorological year, a pollutant concentration trend can be obtained which
provides an estimate of what would have occurred if all years had closely
comparable meteorology.
      It  should  be noted  that  these recommended procedures, while  based on
 extensions  of ideas  generated previously  in  the  literature, have  not been
 tested.   Thus,  until  adequate evaluation  programs  have  been undertaken,
 results  of these recommended  procedures should be  qualified.
  4.1  SELECTION  OF METEOROLOGICAL CLASSES
      In  Section  2.0, we  discussed meteorological parameters which affect
  given pollutants and  the  nature of  those effects.  Presuming that one has
  a  list  of  candidate meteorological  variables for  defining meteorological
  classes,  it  remains  to  define the classes  using all  or some of these
  candidate  variables.
      A  "meteorological  class" is a  set of  days which have a  specific set
  of meteorological  characteristics.   Such classes  can be naturally occurring

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                               50
weather categories such as those listed in Table 4.1.  In this type of
classification process it is quite possible for two weather classes to have
the same average pollution level, i.e., the same "pollution potential."
As in Table 4.1, classes 1 and 5, although meteorologically dissimilar,
both result in low pollutant concentrations.  It is clearly unnecessary,
therefore, to be concerned with fine distinctions between meteorological
classes which always result in low pollution concentrations.
     The simplest categorization possible is into two classes:  the "adverse"
class and the "non-adverse" class, as in the Bay Area APCD work [1] reviewed
in Section 3.3.  The adverse-class approach has the disadvantage of requiring
a very accurate definition of meteorologically adverse days.   If the defi-
nition misses many high-pollution days or includes too many low-pollution
days, the resulting trend estimate may be unreliable.  If a greater number
of classes are defined, the requirement for precision in defining each class
is reduced.
      The  definition  of meteorological  classes may  depend  to some extent
 on  the use made of the results  of the  analysis.   It  is  possible to  have
 distinctly different trends  in  each  meteorological class  if the major
 emission  sources  differ for  each  class  (due  to wind  direction, for  example).
 Even  if two  classes  which  are  meteorologically distinct have  approximately
 the same  average  pollution levels, one may wish  to preserve the distinction;
 doing so  may allow isolating the  effect on  the overall  trend  of specific
 emission  sources.