EPA-600/4-77-0023
January 1977
Environmental Monitoring Series
AN OBJECTIVE ANALYSIS TECHNIQUE FOR THE
REGIONAL AIR POLLUTION STUDY
Parti
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
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RESEARCH REPORTING SERIES
Research report^ of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into five series. These five broad
categories were established to facilitate further development and application of
environmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the ENVIRONMENTAL PROTECTION
TECHNOLOGY series. This series describes research performed to develop and
demonstrate instrumentation, equipment, and methodology to repair or prevent
environmental degradation from point and non-point sources of pollution. This
work provides the new or improved technology required for the control and
treatment of pollution sources to meet environmental quality standards.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/4-77-002a
January 1977
AN OBJECTIVE ANALYSIS TECHNIQUE
FOR THE REGIONAL AIR POLLUTION STUDY
PART I
by
D. Hovland
D. Dartt
K. Gage
Control Data Corporation
Minneapolis, MN 55440
68-02-1827
Project Officer
R. E. Eskridge
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
Research Triangle Park, NC 27711
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NC 27711
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DISCLAIMER
This report has been reviewed by the Environmental Science Research
Laboratory, U. S. Environmental Protection Agency, and approved for
publication. Approval does not signify that the contents necessarily
reflect the views and policies of the U. S. Environmental Protection
Agency, nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
ii
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. . ABSTRACT
This report documents the development of an objective analysis
program for the mesoscale gridding of wind and temperature for the
Regional Air Pollution Study being conducted in St. Louis by the Environ-
mental Protection Agency. The program is designed to produce a 5-km
spaced horizontal grid analysis from a distribution of observations which
are sparse at the boundaries of the grid and dense near the center. An
iterative scan procedure is used successively to correct an initial guess
field until the analysis agrees reasonably well with observations. A
procedure is used where widely spaced observations and a large scan radius
are first used to approximate the field. This is successively followed
by the addition of more observational data and reduction in scan radius
until the field converges to the desired analysis (usually five iterations
are required). This procedure of simultaneously adding more data and
shrinking the scan radius insures that the small-scale variability in
areas of dense observations does not propagate into the surrounding
areas where there are few data.
The special problems of producing three-dimensional fields of gridded
data from the observation network are discussed. They include the incon-
sistency of the surface and upper air observation networks, the non-
uniform density of the basic observing network, and the difficulty of
producing a reliable analysis when data from one or more key stations are
missing.
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CONTENTS
ABSTRACT iii
FIGURES vi
ABBREVIATIONS AND SYMBOLS viii
1. Introduction 1
2. Conclusions 2
3. Recommendations 3
4. The Interpolation Problem 4
Survey of possible techniques 4
Application of scan weighting to St. Louis 7
5. The Objective Analysis Program 9
Outline of the program ..... 9
The interpolation function 12
The weighting function 14
The scan circle 16
The first guess field . 28
Error rejection 31
6. Evaluation of the Program 34
•DO
REFERENCES °°
APPENDICES
A. Program Listings 39
B. Program Documentation 43
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FIGURES
Number Page
1. Unequally spaced sampling stations (*) on an equally spaced
grid 5
2. Scan circle centered at a grid point, enclosing 5 sampling
stations (*) 6
3. St. Louis stations on a square grid (grid interval = 5 km).
Surface stations are 101 to 125, upper air stations are
141 to 144 8
4. Flow chart illustrating the logical structure of the
Objective Analysis Program 10
5. Scan circle centered at a sampling station (*), enclosing
29 grid points 11
6. Interpolation to a station, Z(nri-p,n+q) , within a grid.
Nine-point interpolation uses all nine grid points, whereas
four-point interpolation uses the four grid points surround-
ing the interpolated point (*) 14
7. Various weighting functions tested for use in
scan weighting 15
8. Objectively analyzed u-component field after first iteration.
Scan radius is 17 grid units 18
9. Objectively analyzed u-component field after second iteration.
Scan radius is 12 grid units 19
10. Objectively analyzed u-component field after third iteration.
Scan radius is 7 grid units 20
11. Objectively analyzed u-component field after fourth iteration.
Scan radius is 2 grid units 21
12. Station network for Figures 8 to 11. Data used are 975 mb
winds (m/sec) of 20 February 1964, 1130Z as reported in
Scoggins and Smith (1973). (See Section 6 ) 22
vi
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FIGURES (Continued)
Number Page
13. Objectively analyzed u-component field after four
iterations. Data are the same as in Figures 9 to 12, but
the scan radii are 11, 8, 5, and 2 grid units 24
14. Objectively analyzed temperature field using scan radii of
13, 10, 7, 4, and 1 grid units. Data used are 1500 CDT mean
surface temperatures (°F) for August 1972 as shown in Huff
(1973). (See Section 6) 25
15. Objectively analyzed temperature field using scan radii of
20, 15, 7, 4, and 1 grid units. In addition, all observations
are not used for each iteration. Data are the same as in
Figure 14 26
16. RAMS stations on a 100 x 100 km grid. The number for each
station is the iteration in which the station is first
used 27
17. Objectively analyzed temperature field. This is like
Figure 15, except for a different first guess field .... 29
18. First guess field for Figure 17 30
19. V-component grid with two rejected (in rectangles) data
values (1.2 and -.1). Data used are RAMS winds (m/sec) for
Hour 11, Day 67, 1975 32
20. Hand analyzed temperature field, No. 1. Data used are
0600 CDT mean surface temperatures (°F) for August 1972 as
shown in Huff (1973) 35
21. Hand analyzed temperature field, No. 2. Data are the same
as in Figure 20 35
22. Objectively analyzed temperature field using scan radii of
11, 8, 5, and 1.5 grid units. Contours drawn by hand to fit
the objectively analyzed gridded values (not shown). Data
are the same as in Figure 20 36
via
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ABBREVIATIONS AND SYMBOLS
ABBREVIATIONS
km
mb
NMC
NSSFC
RAMS
RAPS
kilometer
millibar
National Meteorological Center
National Severe Storms Forecast Center
Regional Air Monitoring System
Regional Air Pollution Study
SYMBOLS
C.
J
D.
J
i
J
J
m
MS
n
Value interpolated at data point j from surrounding
grid values.
The difference between observed and interpolated values
at data point j.
Observed value at data point j.
Index referring to- grid point.
Index referring to data point.
The number of data points.
Integer values of horizontal coordinate on analysis grid.
Mean square value of C..
Integer values of vertical coordinate on analysis grid.
Fractional distance so that m + p defines horizontal coordinate
of data point j; see Figure 6.
Fractional distance so that n + q define vertical coordinate
of data point j; see Figure 6.
viii
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ABBREVIATIONS AND SYMBOIS (Continued)
r. . Distance between grid point i and data point j.
R Radius of the scan circle.
t Tolerance criteria for rejecting observational errors
u West-east velocity component.
v South-north velocity component.
X. Grid point value.
W. . The weighting function.
ij
Z A two-dimensional function.
ix
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SECTION 1
INTRODUCTION
Ihe Regional Air Pollution Study (RAPS) was initiated in 1972 by
the Environmental Protection Agency to collect the necessary data base
for the development and verification of mathematical air quality models.
The primary source of data for the RAPS program is a surface network of
25 automated meteorological and air quality monitoring stations
located in St. Louis, MO. Data from the surface network are recorded
routinely and checked for quality in St. Louis. The data to be used as
input to the objective analysis program described here are hourly averages
of wind and temperature from all stations in the network. The surface
data are supplemented by a less dense network of upper air soundings.
Routinely, these consist of four rawinsonde soundings per day at each of
two locations (one urban and one rural), plus pibal wind soundings at these
same two locations every hour that rawinsonde ascents are not scheduled.
These two upper air sounding stations are supplemented during intensive
periods of data collection by an additional two stations operating on the
same schedule.
This report documents the development of an objective analysis
program designed to interpolate meteorological variables to a regularly
spaced grid from an irregularly spaced array of observations. Section 4
contains a discussion of the interpolation problem. The elements of the
program are presented in Section 5 and an evaluation of the program is
given in Section 6. The Appendices contain program listings and docu-
mentation.
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SECTION 2
CONCLUSIONS
The program documented in this report, when properly applied to
reliable data sets, should yield satisfactory analyses on the scale of
RAPS. Error rejection can be accomplished whenever there are sufficient
data to check on inter-station consistency. This can be done for the
surface RAMS network but cannot be done with the sparse network utilized
to collect the upper air data for RAPS. In the RAMS surface network,
having reliable data at the outermost stations is crucial for a successful
analysis of the entire field. This is due to the varying density of the
observing network of the Regional Air Monitoring System.
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SECTION 3
RECOMMENDATIONS
One of the special features of the Objective Analysis Program presented
in this report is the ability to provide on a uniform grid an objective
analysis from data recorded at a network of surface stations the density
of which varies greatly over the analysis grid. This analysis generally
provides gridded values which are consistent with the quality of the
observed data. The variability of this analyzed field appears to reproduce
the variability of the observed field over a range of scales. The
procedure for accomplishing this is discussed in Section 5.
Unfortunately, an analysis of available surface data from the Regional
Air Monitoring System (RAMS) reveals a considerable amount of missing data
from one or more of the outlying stations. This is especially trouble-
some since the success of the present analysis technique is highly
dependent on the presence of reliable data from the outermost ring of
stations. It is strongly recommended, therefore, that throughout the
remainder of RAPS special attention be given to maintaining the reliable
operation of these key stations.
No matter how much care is taken to collect reliable data, periods
will inevitably occur when data at key stations are missing. The objec-
tive analysis program presented here has no provision for missing data
other than the trivial one of ignoring it. Ignoring missing data presents
no problem in the center of the grid where stations are closely spaced.
However, if the data observed at an outlying station is missing, the
analysis may be seriously degraded. It is, therefore, recommended that
some further attention be given to the impact of missing data on the quality
of the analysis and that sojie way be found to provide to a potential user
a measure of the reliability of the analysis.
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SECTION 4
THE INTERPOLATION PROBLEM
SURVEY OF POSSIBLE TECHNIQUES
The numerical processing of meteorological information generally
requires the data field to be defined on an equally spaced grid. How-
ever, meteorological observation stations are seldom spaced at regular
intervals. Figure 1 shows an example of a grid to be defined from data
recorded at several unequally spaced sampling stations. One effective
technique is to subjectively analyze the field, drawing isolines based
on the data at the stations. Grid point values can then be generated by
manually interpolating between isolines. When large amounts of data are
involved, as in RAPS, manual methods are not practical. An objective
analysis procedure is necessary, and even then, the technique must be
simple enough to run efficiently on a computer. Several possible
objective analysis methods are discussed below:
Optimum Interpolation
This technique is attractive because the statistics of the naturally
occurring variability of the parameter to be interpolated are used to
define the interpolation function. Gandin (1965) discusses the overall
optimum interpolation method, while Dartt (1972) gives an application to
automated large-scale wind analysis. The overwhelming disadvantage of the
technique is that the statistical properties (correlations and variances)
necessary to specify the interpolation function are not known a priori as
a function of such meteorological variables as lapse of temperature, wind
speed, wind direction, etc. These statistical properties can only be
deduced from a careful analysis of long records of data comparable to the
data to be objectively analyzed.
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*
*-
Figure 1. Unequally spaced sampling stations
on an equally spaced grid.
Surface Fitting
Polynomials of a degree smaller than the number of data points can
be computed and used to define meteorological parameters at grid points.
Techniques vary from simple linear interpolation to complex multi-
dimensional polynomials of higher degree. The polynomial approach can
give exaggerated values at distances considerably removed from data points
especially if these points are unevenly distributed over the grid. Also, if
the distribution of data points varies considerably with time, there can
be problems with time continuity of successive analyses. Computationally,
polynomials of higher degree can be quite costly to evaluate.
Scan Weighting
This analysis method starts with a first guess field. In the usual
application,each observation within a circle of influence provides a
correction to the first guess grid point values. Figure 2 shows the scan
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circle centered at a grid point. A scan is made through the station
locations, and all data within a distance R of the grid point are used to
compute a correction for the grid point. Close observations are weighted
more heavily than distant observations. Successive corrections are made
to the previous field until a reasonably close consistency exists between
observations and computed values at the grid points (Belmont, et al.,
1966) . When the number of grid points greatly exceeds the number of obser-
vations, it is much more efficient to center the scan circles at observa-
tion points.
The scan weighting method is used in numerical weather forecasting
and is described by Cressman (1959) and Bedient and Vederman (1964). The
Joint Numerical Weather Prediction Unit adopted the method of Bergthorsson
and Dtttts (1955) because the polynomial scheme previously in use ran into
trouble in areas of sparse data. Bergthorsson and Dotts (1955) point out
that in such areas a previous analysis or even climatology may be a better
representation of the field than an interpolated analysis. In the scan
weighting scheme, the final analysis will strongly reflect the first guess
field in areas with few data points.
Figure 2. Scan circle centered at a grid point,
enclosing 5 sampling stations Of).
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APPLICATION OF SCAN WEIGHTING TO ST. LOUIS
The scan weighting technique was chosen for the objective analysis
of the St. Louis data because of its flexibility in accommodating various
horizontal distributions of observations. Figure 3 shows the locations
of the St. Louis stations on a 100 km square grid. The grid spacing
is 5 km for a total of 21 times 21 = 441 grid points. The grid is
positioned so that Station 101 is at the center grid point. The density
of observational stations is greatest near the center of the grid and
sparse at the external boundaries of the grid. Only 357o of the grid
points are within the area enclosed by the stations. Data at the remaining
65% of the grid points are computed by extrapolation not interpolation.
It is required that the horizontal scale of variability at grid points
conforms to similar patterns indicated by the local distribution of obser-
vations. The small-scale variability that may occur near the middle of
the grid should not propagate outwards to the external boundaries where
there are few observations. This can be prevented by either of two methods:
1) using telescoping grids or 2) gradually adding observations at various
iterations in the scan procedure.
In the case of telescoping grids, a complete large-scale analysis
is made first on the largest mesh grid. Grid point values for the next
smaller mesh grid are interpolated from this large-scale analysis. These
interpolated values are then used as the first guess field for a complete
re-analysis of observational data within the small-scale grid. This
process can be repeated for as many nested grids as necessary.
A second approach is to use one small-scale grid and add observations
at various iterations in the scan procedure. First, widely spaced observa-
tions and a large scan radius are used to approximate the field. This is
successively followed by the addition of more observations and a reduction
in scan radius until the field converges to the desired analysis. This
procedure of simultaneously adding more data and shrinking the scan radius
insures that the small-scale variability in areas of dense observations
does aiot propagate into the surrounding area where there are few data.
It is this approach which has been adopted here.
7
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20 -
IB -
16 _
14 -
12 -
10 ~
ilf
a
"t?
6 -
4 -
/J?V
I I I I I I I I I I ! I I I I 1 I
2 46 8 10 12 14 16 18
Grid Points
Figure 3. St. Louis stations on a square grid (grid interval
= 5 km). Surface stations are 101 to 125, upper
air stations are 141 to 144.
20
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SECTION 5
THE OBJECTIVE ANALYSIS PROGRAM
OUTLINE OF THE PROGRAM
The objective analysis program, SUBROUTINE GRID, is listed in Appendix
A. A flow chart outlining the logical construction of this routine is
shown in Figure 4.
It is necessary for the objective analysis to start with a value at
each grid point. This first guess field may be a previous analysis, a
forecast, or simply a uniform field. Computations are initiated in the
location of the first observational data point. A scan circle is centered
at this data point as shown in Figure 5. The value A. at the observation
point is then interpolated from the initial guess field. If the observed
value at the data point j is referred to as D., then the difference
C. = D.- A. (1)
J J J
provides a correction to be supplied to the grid point values, X., within
a neighborhood of the data point. Note that i is an index associated with
the grid points and j is an index associated with the observation points.
The number of observation points is J.
The actual correction supplied to a grid point within the vicinity of
point j is weighted by the dist
This weighting function is given by
data point j is weighted by the distance, r.., between the two points.
ij -
-------
BEGIN
END
SPECIFY FIRST
GUESS FIELD
LOOP FOR
EACH ITERATION
LOOP FOR
EACH STATION
YES
NO
INTERPOLATE VALUE
AT STATION LOCATION FR01*
SURROUNDING GRID POINTS
YES
NO
COMPUTE AND SAVE
CORRECTIONS FOR EACH
GRID POINT WITHIN SCAN
CIRCLE
YES
NO
APPLY CORRECT 101
TO ALL
GRID POINTS
YES
Figure 4. Flow chart illustrating the logical structure of the Objective
Analysis Program.
10
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Figure 5. Scan circle centered at a sampling station
, enclosing 29 grid points.
where R is the preselected radius of the scan circle. If the distance
r.. exceeds R, then the weighting function is assigned a value of zero.
Therefore, each grid point lying within a circle of radius R from data
point j will receive a correction W..C.. The objective analysis program
computes corrections to all grid points lying within the scan circles sur-
rounding each of the J data points. Only after corrections from all data
points have been computed are the values of grid points adjusted. The new
values, X. at each grid point are given by
new
J
2 W. .C.
xi = xi + ^T—— • <3>
new old
£ W. .
11
-------
J
The quantity Z W. . appearing on the right hand side of (3) serves to
j=l 1J
normalize the corrections to grid points. Without this normalization
grid points receiving corrections from many close observations will be
"over-corrected" whereas grid points far from any observations will be
"under-corrected".
The procedure outlined above is repeated a fixed number of times or
until the corrections made to the grid points are less than some small
value. The analysis after each iteration is used as the first guess field
for the next iteration. The size of scan circles is often decreased
from one iteration to the next. The goal is to obtain an objective analysis
of the gridded values which is reasonably consistent with the observed
data field. The variability of the analyzed field should then be reason-
ably consistent with the variability of the observed data even when the
density of the observing network varies over the grid.
THE INTERPOLATION FUNCTION
To establish the value A. at each observation location (Equation 1),
an interpolation is required from the surrounding grid points. Several
options are available for defining this interpolation function which is
used at each observation point before each scan iteration (Figure 4).
Indeed, the National Meteorological Center (NMC) uses three different
interpolation functions depending on the location of the observation on
the analysis grid (McDonell, 1974). The three functions are a sixteen
point 2-dimensional function, a four point 2-dimensional function and a
three point arithmetic average.
Figure 6 illustrates the four point 2-dimensional (bilinear)
interpolation function used in the analysis. It can be derived as follows.
Let Z be a field defined on a-square grid. The value Z(m+p,n+q) is to
be interpolated from four grid points. The values of p and q are measured
as fractions of the grid length. One dimensional linear interpolation
between point (m,n) and point (m+l,n) gives
12
-------
Z(m+p,n) = Z(m,n) + p[Z(m+l,n) - Z(m,n)]. ' (4)
Similarly, one -dimensional linear interpolation between point (m,n+l)
and point (m+l,n+l) yields
Z(m+p,n+l) = Z(m,n+l) + p[Z(m+l,n+l) - Z(m,n+l)]. (5)
Another linear interpolation between points (m+p,n) and (m+p,n+l) leads to
Z(m+p,n+q) = Z(m+p,n) + q[Z(m+p,n+l) - Z(m+p,n)]. (6)
When (4) and (5) are substituted into (6), it is found that
Z(m+p,n+q) = [l-p][l-q] Z(m,n) + p[l-q] Z(m+l,n) + q[l-p] Z(m,n+l)
+ pq Z(m+l,n+l), (7)
which is the desired relation. Note that
[l-p][l-q] + p[l-q] + q[l-p] + pq = 1. (8)
Also, note that it is assumed here that all data points lie within the
analysis grid. The objective analysis program has been tested using
both four point and nine point interpolation functions. The four point
function usually gives comparable results and is always faster.
13
-------
Z(m,n+l)
Z (nri-p, n+q)
Z(m-l,n) • Z(m,n) • ' •Z(nri-l,n)
Z(m-l,n-l) * Z(m,n-l) * * Z(irri-l,n-l)
Figure 6. Interpolation to a station, Z(nri-p,n+q), within a grid.
Nine-point interpolation uses all nine grid points,
whereas four-point interpolation uses the four grid
points surrounding the interpolated point (*).
THE WEIGHTING FUNCTION
In order to obtain an analyzed field which is consistent with the
field of observed data, it is necessary to weight the influence of a
data point upon a given grid point according to the distance between the
two points. Maximum weight at any grid point is given to the closest
observing point. If no data point lies within a distance R of a given
point, that initial grid point value will remain unchanged by the analysis.
The desired weighting function is a monotonically decreasing function
of the distance r. . between observation point j and grid point i. This
function, W.., is defined to be one when r.. is zero and vanishes when
ij ij
r.. exceeds the scan-circle radius, R. Several alternative weighting
functions are reproduced in Figure 7. They correspond to
14
-------
1.0
0.5
0.0
1.0
0.5
0.0
1.0
R
0.5
Figure 7. Various weighting
functions tested for use in scan
weighting. Equations defining
weighting functions given in
text.
0.0
r -»
(c)
R
15
-------
1 r. . < R
W.. t ^ (9a)
0 r >R,
<9b)
0 r . . > R
and
'f*2-^2'4
- -1
lj 1
I
RVr.2
L LJ J
= 0
r . . «< K.
1J -
r. . > R
i-J
(9c)
respectively. The weighting function used for this objective analysis
program is defined by (9c) and reproduced in Figure 7. This function
decreases rapidly with increasing distance which allows the use of a
large scan radius, R, and still gives nearby observation points much more
influence than distant observation points. When there are large areas of
grid with few data points, it is necessary to begin with a large scan
radius to ensure that all grid points are influenced by at least one
observation point.
THE SCAN CIRCLE
The choice of the scan radius, R, determines which observation points
enter into the analysis at a particular grid point. The size of the scan
radius can even influence the propagation of observational errors. Random
errors will be somewhat averaged out if the scan radius is chosen large
enough for the values at grid points to be influenced by many observation
points. However, an error in an individual observation will be confined
16
-------
to only a few grid points if a small scan radius is used.
The best strategy for selecting the size of the scan radius and even
varying it from one iteration to the next can be determined by experimenting
with any given observation network. An especially attractive approach
is to start with a fairly large scan radius for the first iteration and
to reduce its size in successive iterations. This procedure has the effect of
producing a smooth large-scale analysis while retaining the smaller scale
variability in regions of dense observations. Figures 8 to 11 show an
analysis after each of four iterations using scan radii of 17, 12, 7 and
2 grid units. The data are 975 mb winds on 20 February 1964, 1130Z,
measured at the stations shown in Figure 12. Only the u-component
analysis is given. The isolines of Figures 8 to 11 were drawn by manually
interpolating (linearly) between the grid point values generated by the
objective analysis. The observed data values are shown for reference.
The first guess field has value zero at each grid point. After one
iteration (Figure 8) the basic pattern is defined, but the analysis does
not match the observed data. With each succeeding iteration the analysis
more closely matches the data. Since the field is quite smooth and the
stations are fairly uniformly spaced, there is not much change from the
third to the fourth iteration. A measure of the consistency of the analyzed
field of grid values and the observed data field is given by MS, the mean
square difference of the interpolated A. and the observed D.. That is,
MS is defined by
J 2 J 2
MO ISC. 12 (D.- A.) ,.„
"* = J j-i J = 3 j-i J J • (10)
The convergence of the objective analysis can be evaluated by examining
the computed MS values. In particular the analysis is said to converge if
MS approaches zero in a finite number of iterations. In practice the
objective analysis converges rapidly in a few iterations. For example, in
the analyses corresponding to Figures 8 to 11, MS at the start of each of
the four iterations is 32.12, 10.46, 1.62 and .01 respectively.
17
-------
-z.
00
~z
-a.i/' -1-7 -1.3 -.6 -/o
2.7 3.S / -i.3 5.1 5.8
3.0 3.0 / 4.5 b.2 5.R
/ (2S>
3.3 3.97 4,6 b.2 5.8
3.4 4/0 4.6 b.2 5.7
1.1 1.5 1.7
.8 l.l 1.5
2.6 3.0 3.3 3.7
l.C 1.4 1.8
H.3 2.6 2.9 3.2
1.0 !„* 1.
-2,3 :~>>-0^ -i.7 -1
-3.1 -3." -J. -2.6
-3.? -J.b -3.3 -3.0
-1.5 -1.0 -.5
-4.6 -«.5 -4.4 -4.2
3.3 -2.9 -2.5 -2
-V
Figure 8. Objectively analyzed u-component field after first iteration. Scan radius is
17 grid units.
-------
.-7.5 -6.9
.1 11.0 11.6
.1 10.9 11.5 II.
9.1 10\0 10.7 11.2 11.6
9.8\ 10.4 10.9 11.2 11.
10.4 10.6 1C.
-6.2
-6.4 -6.4 -6.3 -6.2
9.6
/O
3.3/ 5.57 7.5 9.0
.?/ 5.3 / 6.7
6.B 7.9\ 6.8 9.5 1
7.6 \8.4 fl.9 9.4 9.6 9.7
8.* 8,5 8.4 8
6.5 6.9 7.2 7.3 7.2 7.0
4.6 5.1 5.6 5.
4.3 4.6 4.fl 4.9 4.9 A.9
i^J? 2.4 ?.e 3,3
_a -3.H -3.3
3.0 3.4 3.6
Figure 9. Objectively analyzed u-component field after second iteration. Scan radius
is 12 grid units.
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-to
-a
tsJ
O
'>.7 /8.7 10.2 11.4
7.2 / 9.0 IJO.3 11.3 \2.1 12.7 13.2 13.
9.i 1J0.3 11.2 12\0 12.5 t',9 ,13.2
12.9 13.4 13.7
5
-6. -y -Z o a.
5.2 5.3 5.3
Figure 10. Objectively analyzed u-component field after third iteration. Scan radius
is 7 grid units.
-------
-2 O Z, V (, 9 10
/b.7 / 8.7 19.2 11.4 J2.2 12.9 13.4 13.7
7.2 / 9.0 U0.3 11.3 42.1 12.7 13.2 13.5
7.6/ 9.2 10.4 11.3 12\0 12.5 12.9 i3.2
7.8 9.2 ltt.2 11.1 11.7 ^W.l 12.5 12.7
\ ^^^
7.8\ 9.0 10\0 10.7 11.2 11.6 11.8
9.4 XO.l 10.6 10.8 10.9 10.8
6.9 7.9v fl.b 9.2 rJ.6 9.7 9.4 H.6
./ V 6..1 7.(J 7.5 7.9 7.9 7.<> 7.4 7.1
6.3 6.4 6.4 6.3
4.7 4.9 5.1 5.2 5.3 5.3 5.2
2.1 2.6 3.1 3.6
4.d 4.4 4.5 4.6
3.1 3.5 3.B
2.6 3.1 3.4
l.S \ 2.3 2.9
Figure 11. Objectively analyzed u-component field after fourth iteration. Scan radius
is 2 grid units.
-------
PC
I
a
41° J
40° J
39° -\
38l
37°-J
36°-
35°-
34l
DMA
•
PIA
TOP
CBI
BNA
•
OKC
LIT
100° 98° 96° 94° 92°
90° 88° 86° 84°
Figure 12. Station network for Figures 9 to 13.
Data used are 975 mb winds (m/sec) of
20 February 1964, 1130Z as reported in
Scoggins and Smith (1973).
(See Section 6)
22
-------
Convergence can be accelerated by using smaller scan sizes, but the
analysis may be degraded. Figure 13 is the final analysis of the same
data as in the preceding figure with R=ll, 8, 5 and 2 grid units. In
this case MS at the start of each iteration has values of 32.12, 1.82,
.02 and .00 respectively. The convergence is faster but the analysis is
somewhat different.
A special strategy has been worked out for applying the objective
analysis algorithm to the observation network of the St. Louis Regional
Air Monitoring System (RAMS), Figure 3. In the RAMS network the spacing
between observing locations varies greatly over the grid. Most of the
observations are concentrated near the center of the array. This large
variation in density of the observational network poses special problems in the
application of the objective analysis program. Figure 14 is an objective
analysis of a temperature field over St. Louis using R=13, 10, 7, 4
and 1 grid units. The tight gradients in the northwest and southeast
corners are generated by the program and are not seen in the data.
A much better objective analysis of the same data is shown in
Figure 15. It was obtained after making two changes in the application
of the program. For the first iteration only the four outermost observa-
tions are used. Twelve observations are used for iterations two and three.
All twenty-five observations are used for iterations four and five.
Figure 16 shows which stations are used during each iteration. In addition
the scan radii for the first two iterations has been increased so that the
entire sequence is R=20, 15, 7, 4, and 1 grid units.
The practice of mixing more data and simultaneously decreasing the
scan radii in successive iterations appears to optimize the analysis of
data observed from the non-uniformly spaced RAMS network. However, the
application of this technique relies heavily upon the existence of reliable
data at the outermost ring of stations. In this sense the outer stations
become key stations in the analysis.
23
-------
-a
0.4 10.9 11.1 11.2 11.1
0.3 10.8 11.0 11.1 11.2
0.2 10.7 10.9 11.1 11.1
9.2 1
-------
NJ
83.9 83.9 "3.9.—£3.9
83.7 83.7 83.8 83.8
83.3 83.4 83.5 ",3.5
83.1 83.1 83.1 J13.0
83.2 8.3.1 82.9 fU',4
83.5 83.4 MJ.O 82.6
0 B3.7 83.2 flJ.C
8't.U 83.6 H3.b Hj.b
84.6\H3.
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-£
85.0 85^.1
Hij.i^-HT. 1
83.9 83.9
83.7 83.6
83.3 83.1
82.8 82.7
82.7 82.7
83.0 83.0
fib.3 H6.3
Mo. 7 H6.7 (16.8 nij.H
87.0 87.0 HY.O R7.1
87.2 87.2 87.J
86.4 86.3
86.8 86.8
87.1 87.1
£17.3 87.3
Figure 14. Objectively analyzed temperature field using scan radii of 13, 10, 7, 4, and
1 grid units. Data used are 1500 CDT mean surface temperatures (°F) for
August 1972 as shown in Huff (1973). (See Section 6)
-------
68.
•£•-'
9 R3.3 .13.8
7 R.l. 7 3n.7
1 03.1 ^13. 3
83.5 _83.6
3.1.
83.7 ~e"3.7
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b 06.4 B6.2
8 H6.7 H6.6
0 87.0 S6.9
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2 8V.1 a7
3 87.£ 87.2
Figure 15. Objectively analyzed temperature field using scan radii of 20, 15, 7, 4, and 1
grid units. In addition, all stations are not used for each iteration. Data
are the same as in Figure 14.
-------
21
19
17 ~
15 -
13 -
11 -
9 -
7 -
5 -
3 -
V V
\ \
3
I
5
I I
I
11
I
13
I
15
I
1 7
T
19
21
Figure 16. RAMS stations on a 100 x 100 km grid. The number for
each station is the iteration in which the station is
first used.
27
-------
THE FIRST GUESS FIELD
The first guess field affects the convergence of the objective analysis
procedure. When the first guess closely matches the data, MS (Equation 10)
is small since the C. are small. If all the C. are zero,there is no need
J J
to iterate since the analysis will not change (Equation 3). When the first
guess is quite different from the data, several iterations may be needed
to reduce the MS to some acceptable small value.
Brown (1973) suggests the use of a forecast or persistence field as
a first guess. Nearly any first guess field that is defined at all grid
points will work in the objective analysis program. However, the field
should be carefully chosen since features in the first guess field carry
over to the final analysis. When tests using first guess fields of random
noise are made, very noisy analyses are generated.
An example of the effect of the first guess field on the final analysis
can be seen by comparing Figures 15 and 17 which are analyses of the same
data using different first guesses. A field of all zeros is the first
guess for Figure 15. The field in Figure 18 is the first guess for
Figure 17.
According to Inman (1970) no good first guess fields exist for the
National Severe Storms Forecast Center (NSSFC) use, so a field of all
zeros is used. The use of a large scan size in the first iteration
essentially defines each grid point value as the local average of the data.
The zero first guess field is also preferred for the St. Louis grid. Then
the variability in the final analysis will be only that specified in the
data.
The use of a zero first guass field requires that the correction at a
grid point be normalized by dividing by the sum of the weights of all the
corrections contributed to it. With a zero first guess the C.'s in the
first iteration are the data values. However, E W. .C. could be a very
J J
large or a very small number. When the correction is normalized as in
28
-------
to
9 83.9 83.9
7 83.7 83.8 83.9
0 83.6 83.7 83
4 83. 6 83. 9/8*. 2
3 83.6 83.9\M.l
3 83.5 83.7 83.
? «3.5 83.5 83.*
J.8 8J.4
<£»£>
84.NJ 83.5
83.2 n3.6 H3.b
? •&!£&— -^4 . 2-
'J.-'fllTTX 85.4 84.&
86.5 86.4 86.3
36.8 8h.7 ft6.7
87.4 87.3 87. 3
Figure 17. Objectively analyzed temperature field. This is like Figure 15, except for
a different first guess field.
-------
Figure 18. First guess field for Figure 17.
-------
Equation (3) the new grid point values are of the proper magnitude.
ERROR REJECTION
Errors in data can sometimes be identified by examining C., the
magnitude of the difference between the interpolated and actual values at
data point j (see Equation 1). Since the grid point values are weighted
averages of the data at nearby observation points, the station value, D.,
if in error, will be quite different than the value interpolated from the
grid points, A.. Therefore, if a suitable tolerance, t, can be found, an
observation can be assumed to be in error (and ignored) whenever C. > t.
Cressman (1959) lists a set of liberal tolerances with t decreasing from
one iteration to the next. In addition, an analyst monitoring the procedure
can require the program to accept data tagged for rejection. Gandin (1965)
prefers completely objective error checking since an analyst may accept
or reject data simply because it does or does not fit his ideas.
The choice of t is obviously very important. When t is too large,
very few errors are detected. When t is too small, good data are rejected.
A value fixed for all eases is not desirable. A large value is needed
when the field is highly variable and a smaller value is needed when the
field is smooth. A tolerance based on the standard deviation, a, of the
observations seems reasonable. Tests using fictitious and real data, with
and without known errors, show a value of t = 2a to be effective. Obvious
errors are removed using this value. Brown (1973) gives throw criteria
of 2.2a where cj is computed for the C., not for the data. The throw
criteria are restricted to predefined maxima since very bad observations
generate an unrealistically large a.
Figure 19 shows an objective analysis of the surface v-component of
RAMS winds averaged over Hour 11, Day 67, 1975. Two of the 25 data values
are obviously inconsistent. The -.1 value is from Station 109 where the
wind speed was recorded as .1 mps for most of the day. The 1.2 value is
from Station 115 where a wind direction of 102° was recorded while all
other stations recorded directions near 340 . The program rejects the
31
-------
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-5.6
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—4 7
-3.3
Figure 19. v-component grid with two rejected (in rectangles) data values (1.2 arid -.1).
Data used are RAMS winds (meters/sec) for Hour 11, Day 67, 1975.
-------
two erroneous values and ignores them completely in arriving at the final
analysis. The u-components for Station 109 and Station 115 must be rejected
also since the two stations are identified as having erroneous winds for
the observation time of Figure 19.
The standard deviation for Figure 19 is quite large because it is
computed using the erroneous values. A preliminary screening may be used
to remove obviously bad data before determining t. For this preliminary
screening the mean and standard deviation cr are calculated for the set of all
stations with data. Then all data more than 4
-------
SECTION 6
EVALUATION OF THE PROGRAM
It would have been highly desirable to have had data available from
the St. Louis RAPS program as the entire objective analysis program was
being developed. As this data did not become available until rather late
in the development effort, it was necessary to find alternate sources of
data to check out the program. To this end, surface data for St. Louis
was readily available from the Metromex program (Huff, 1973), This source
was chosen because it presents the type of data which was expected from
the St. Louis RAMS network. Data values were read from the published
analysis of the mean temperature field at 1500 CDT for August 1972. The
twenty-five data points coincide with the RAMS station locations. This
was used as the source of data for Figures 14, 15, and 17.
The analysis of the mean temperature field at 0600 CDT for August
1972 was used in another test. Data values were read at twenty-five points
corresponding to the Metromex hydrothermograph sites. These sites are
more evenly distributed over the grid than are the RAMS stations. Hand
analyses were drawn for maps on which the twenty-five data values were
plotted. Figure 20 and Figure 21 are the patterns drawn by two different
analysts. Figure 22 is the objective analysis of the same data using four
iterations with scan radii of 11, 8, 5, and 1.5 grid units. Contours
are reproduced which are consistent with the objectively analyzed gridded
values. The objective analysis compares very well with the conventional
(subjective) analysis.
Upper air data was taken from the NASA AVE I experiment as reported
by Scoggins and Smith (1973). This report provides a convenient source
of high frequency (three hour interval) rawinsonde soundings. The data
are observations from the NOAA Synoptic stations in the southeastern
United States. This data was utilized in Figures 8 to 11, and Figure 13.
34
-------
Figure 20. Hand analyzed temperature field, No. 1. Data
used are 0600 GDI mean surface temperatures
(°F) for August 1972 as shown in Huff (1973).
Figure 21. Hand analyzed temperature field, No. 2. Data are
the same as in Figure 20.
35
-------
Figure 22... Objectively analyzed temperature field using
scan radii of 11, 8, 5, and 1.5 grid units.
Contours drawn by hand to fit the objectively
analyzed gridded values (not shown). Data
are the same as in Figure 20.
36
-------
The Metromex and AVE data were used in developing and checking the
objective analysis program because RAPS data were not available. The
only RAPS data shown in this report are in Figure 19 which is an analysis
of the v-components at the RAMS stations (Figure 3) averaged over Hour 11,
Day 67, 1975. A full month of data, 14 July to 15 August, 1975, was made
available in December, 1975. This period has some missing data. In
addition, there are many bad values which will be removed by the error
rejection procedure outlined above.
Unfortunately, the removal of bad data changes the observation network
configuration. As mentioned in Section 5 the choice of scan sizes is
dependent on the network configuration. Perhaps the scan radii presented
in Section 5 will not produce a reliable analysis when many stations
are missing. The first iteration, when only the outermost four stations
are used, may be particularly troublesome. There are some observation
times when three of the four outermost stations are missing.
37
-------
REFERENCES
Bedient, H. A., and J. Vederman. Computer Analysis and Forecasting in
the Tropics. Mon. Wea. Rev., 92, 565-577, 1964.
Belmont, A. D., L. W. Engberg, and W. C. C. Shen. Network Influence
on Wind Interpolation in the Tropics. Final Report, Contract CWB-
11164, Control Data Corp., Minneapolis, MM, 1966. 33 pp.
Bergthorsson, P., and B. R. Dobs. Numerical Weather Map Analysis.
Tellus, 7, 329-340, 1955.
Brown, J. F. Tropical Analysis Model. AFGWC Technical Memorandum
73-3, 1973. 20 pp.
Cressman, G. P. An Operational Objective Analysis System. Mon.
Wea. Rev., 87, 367-374, 1959.
Dartt, D. G. Automated Streamline Analysis Utilizing "Optimum
Interpolation." J. Appl. Meteor., 11, 901-908, 1972.
Gandin, L. S. Objective Analysis of Meteorological Fields. Israel
Program for Scientific Translation^ Jerusalem, 1965. 242 pp.
Huff, F. A., Ed. Summary Report of Metromex Studies, 1971-1972.
Illinois State Water Survey, Urbana, 1973. 173 pp.
Inman, R. L. Papers on Operational Objective Analysis Schemes at the
National Severe Storms Forecast Center. NOAA Technical Memorandum
ERLTM-NSSL 51, 1970. 97 pp.
McDonell, J. E. Notes on Operational Objective Analysis Procedures.
Prepared for "Advanced Prediction Techniques Course" at National
Weather Service Headquarters, 1974. 76 pp.
Scoggins, J. R., and 0. E. Smith. Data for First NASA Atmospheric
Variability Experiment (AVE I) Part I: Data Tabulation. NASA
Technical Memorandum X-2938, 1973. 682 pp.
38
-------
APPENDIX A: PROGRAM LISTINGS
SUBROUTINE GRID(NDATAsXCOORD.YCOORD.STNVAL.
1 IDIM,JDIM.GRDVAL.SUMWT,SUMCOR.
2 ISTART.IEND.JSTART.JEND,
3 NSCANS.RSCAN.CRIT.REJECT)
C
C *GRID WILL TRANSFORM UNEQUALLY SPACED STATION DATA TO EQUALLY
C SPACED GRID POINTS. WHEN GRID IS CALLED THERE MUST BE A
C VALUE FOR EACH GRID POINT. THE FIRST GUESS FIELD MAY BE A
C PREVIOUS ANALYSISt A FORECAST* OR SIMPLY A CONSTANT. THE GRID
C MUST BE ARRANGED SO THAT GRID POINTS SURROUND EACH DATA POINT.
C
C *NDATA IS THE NUMBER OF STATIONS WITH DATA. XCOORD AND YCOORD THE
C STATION COORDINATES IN GRID UNITS RELATIVE TO GRID POINT (!.!)»
C AND STNVAL THE DATA VALUES AT THE STATIONS.
DIMENSION XCOORD(NDATA).YCOORD(NDATA).STNVAL(NDATA)
C
C «IDIM AND JDIM ARE THE DIMENSIONS OF THE GRID POINT ARRAYS. GRDVAL
C HOLDS THE GRID POINT DATA. SUMWT AND SUMCOR ARE ARRAYS OF THE
C SAME DIMENSIONS THAT MUST BE PROVIDED FOR TEMPORARY STORAGE.
DIMENSION GRDVAL(IDIM.JDIM).SUMWT
-------
c
C *FIND X AND Y DISTANCE FROM GRID POINT GO TO 50
IF(J.LT.JSTART)GO TO 50
IF(J+l.GT.JEND)GO TO 50
STNINT=GRDVAL(I»J)«(1.-P)«(1.-Q)
1 »GRDVALU*1»J)*P«(1.-Q)
2 »GRDVAL
-------
c
c CORRECTIONS ARE NOT APPLIED NOW SINCE A GIVEN
C WD POINT MAY GET CORRECTIONS FROM SEVERAL DATA POINTS.
~iJMWT(M»N)=SUMWT(M»N)+WT
5JMCOR(M,N)=SUMCOR(M«N)+WT»DIFF
3C CONTINUE
40 CONTINUE
C
C *ENO OF LOOP THROUGH DATA POINTS.
50 CONTINUE
C
C *MOW APPLY CORRECTIONS TO GRID POINTS
-0 80 M=ISTART,IEND
00 70 N=JSTART,JEND
!P(SUMWT(M,N),EO.O)GO TO 70
r3°DVAL RETURN
41
-------
-JNCTION TWILI(A,L,M,N,X,Y,Z)
I IPENSION A(L,M,N)
C
C *i 15 AN ARrtAY OF DIMENSION (L,M,N) HOLDING 3-DIMENSIONAL GRID
C =j!\T DATA. TRILI WILL INTERPOLATE A VALUE AT THE INTERNAL
C -3INT (X,Y,Z) WHERE X, Y, AND Z ARE MEASURED RELATIVE TO (1,1,1).
C "-ILI USES TRILINEAR INTERPOLATION. IT REDUCES TO
C 2-QIMENSIONAL BILINEAR INTERPOLATION WHENEVER Z IS AN INTEGER.
C
C *«IND INDEXES OF NEAREST GRID POINT IN THE DIRECTION OF (1,1,1)
C AND THE P, 0 AND R DISTANCES FROM THAT GRID POINT.
==Z-(K-1)
"-lLl=(l.-R)»*A(I*ltJ«K>)
1 *(l.-P)*(Q»A(I»J*l»K)*(l.-Q)*A(I»J»K)))
C
C *= IS 0 IF K IS AN INTEGER
IF (R.EQ.O)RETURN
T»ILl=THILI+R»(P*(Q*A(I*lfJ+l«K*l)*(l.-Q)»A(I*l,JfK*l»
I *(l.-P)
-------
APPENDIX B: PROGRAM DOCUMENTATION
The objective analysis program, SUBROUTINE GRID, is listed in
Appendix A. GRID was written for the CDC 6600, However, care was taken
to use FORTRAN statements that are also valid on the Univac 1110. A
useful reference is Garner (1973) which lists CDC and Univac FORTRAN
differences. A test run has been made on the EPA Univac 1110, and
SUBROUTINE GRID compiled and executed correctly.
The following elements are parameters of SUBROUTINE GRID and must
be supplied by the calling routine:
NDATA
XCOORD
YCOORD
STNVAL
IDIM
JDIM
GRDVAL
SUMWT
SUMCOR
ISTART
IEND
JSTART
JEND
The number of data stations
Arrays of station coordinates measured
relative to grid point (1,1). e.g., grid
point (5,7) has XCOORD = 4 and YCOORD = 6.
Array of data values. 999.0 = missing.
The dimensions of arrays GRDVAL, SUMWT,
and SUMCOR
Grid point array. On entry to GRID, GRDVAL must
contain the first guess field (see Section III-E)
On exit from GRID, GRDVAL contains the analysis.
Scratch arrays provided by the calling routine.
The arrays need not be defined before GRID is
called.
The range of subscripts for the parts of arrays
GRDVAL, SUMWT, and SUMCOR that are actually used.
1 < ISTART < IEND < IDIM
1 < JSTART < JEND < JDIM.
Usually ISTART = JSTART = 1, LEND = IDIM, and
JEND = JDIM.
43
-------
NSCANS
RSCAN
GRIT
REJECT
The number of iterations.
Array of scan radii measured in grid units
(see Section III-D).
The convergence criterion (see Section III-D).
GRID will stop iterating when MS (see Equation (5)),
the mean square difference at the stations, is
less than CRIT. Usually GRIT = 0 so that all
NSCANS iterations are completed.
Reject value (see Section III-F). If the first
guess field is zero, any data value greater than
REJECT will be rejected.
The following elements are programmed into SUBROUTINE GRID:
The interpolation function (see Section III-B).
The weighting function (see Section III-C).
A sample run using SUBROUTINE GRID is given in Appendix C. The
execution time is proportional to the number of stations and the number
of grid points and the number of iterations. GRID uses about .56
seconds of CDC 6600 central processor time for this sample run of 25
stations, 529 grid points, and 5 iterations.
FUNCTION TRILI is also listed in Appendix A. TRILI was developed
along with SUBROUTINE GRID, but it is not actually used here. TRILI may
be used for bilinear interpolation or for the extension to three dimen-
sions, trilinear interpolation. (See Figure 6 for the derivation of the
bilinear interpolation formula.)
44
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse befors completing}
1. REPORT NO.
EPA-600/4-77-002a
2.
3. RECIPIENT'S ACCESSION-NO. .
4. TITLE AND SUBTITLE
AN OBJECTIVE ANALYSIS TECHNIQUE FOR THE REGIONAL AIR
POLLUTION STUDY
Part I
5. REPORT DATE
January 1977
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
D. Hovland, D. Dartt, and K. Gage
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORG \NIZATION NAME AND ADDRESS
Control Data Corporation
8100 South 34th Avenue
Minneapolis, MN 5440
10. PROGRAM ELEMENT NO.
1AA603
11. CONTRACT/GRANT NO.
68-02-1827
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratories
Office of Research & Development
U.S. Environmental Protection Agency
Research Triangle Park, N.C. 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
EPA-ORD
15. SUPPLEMENTARY NOTES
Part II of this
1977.
report has been issued as EPA-600/4-77-002b, February
16. ABSTRACT
This report documents the development of an objective analysis program for
the mesoscale gridding of wind and temperature for the Regional Air Pollution Study
being conducted in St. Louis by the Environmental Protection Agency. The program is
designed to produce a 5-km spaced horizontal grid analysis from a distribution of
observations whicharesparse at the boundaries of the grid and dense near the center.
An iterative scan procedure is used successively to correct an initial guess field
until the analysis agrees reasonably well with observations. A procedure is used
where widely spaced observations and a large scan radius are first used to approxi-
mate the field. This is successively followed by the addition of more observational
data and reduction in scan radius until the field converges to the desired analysis
(usually five iterations are required). This procedure of simultaneously adding
more data and shrinking the scan radius insures that the small-scale variability in
areas of dense observations does not propagate into the surrounding areas where
there are few data.
The special problems of producing three-dimensional fields of gridded data
from the observation network are discussed. They include the inconsistency of the
surface and upper air observation networks, the non-uniform density of the basic
observing network, and the difficulty of producing a reliable analysis when data
from one or more key stations are missing.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. COS AT I Field/Group
*Air pollution
Meteorological data
*Wind (meteorology)
*Temperature
*Grids (coordinates)
*Atmospheric models
13B
04B
08B
04A
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (This Report)
UNCLASSIFIED
21. NO. OF PAGES
55
20. SECURITY CLASS (This page)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
45
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