EPA-6QO/4-77-002b
Februdry 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 reports 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-600/4-77-002b
February 1977
AN OBJECTIVE ANALYSIS TECHNIQUE
FOR THE REGIONAL AIR POLLUTION STUDY
PART II
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 is concerned with the application of objective analysis
techniques to the computation of trajectories from surface wind observations
of the Regional Air Pollution Study in St. Louis. Trajectories were computed
over a one hundred kilometer square grid centered on St. Louis for two five-
hour periods during July 1975. The variability of the surface wind field was
investigated by examination of the temporal and spatial variability of
computed trajectories. Also, the sensitivity of the computed trajectories
to the amount of data employed in the analysis was examined in some detail.
The results showed a general lack of sensitivity of the computed trajectories
to a single missing observation. However, computed trajectories were very
sensitive to missing adjacent observations.
In addition to the trajectory analysis, a set of tapes containing gridded
winds and temperatures for the St. Louis area were generated.
111
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CONTENTS
Abstract iii
Figures and Table, vi
Abbreviations and Symbols viii
1. Introduction 1
2. Conclusions and Recommendations 3
3. Objective Computation of Trajectories 4
4. Wind Trajectory Examples 9
5. Sensitivity of Computed Trajectories . . . ; 27
References 37
Appendices
A. Program Listings 38
B. Program Documentation 42
C. User Guide to Archive Tapes 44
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FIGURES AND TABLE
Number Page
1. Diagram of trajectory computation 4
2. Logical construction of the trajectory analysis program; overall
construction 7
3. Logical construction of the trajectory analysis program; detailed
flow chart of trajectory displacement computation 8
4. St. Louis RAMS observations on a square grid 10
5. Hourly averaged surface winds for Day 197, 1975, plotted on the
grid of Figure 4 11
6. Hourly averaged surface winds for Day 210, 1975, plotted on the
grid of Figure 4 12
7. Trajectory- starting points on the grid of Figure 4 13
8. Inner trajectories for Day 197 on the grid of Figure 4 14
9. Outer trajectories for Day 197 on the grid of Figure 4 15
10. Inner trajectories for Day 210 on the grid of Figure 4 16
11. Outer trajectories for Day 210 on the grid of Figure 4 17
12. Spatial variability of air parcel vector displacements for
trajectories of Day 197 19
13. Spatial variability of air parcel vector displacements for
trajectories of Day 210 20
14. Temporal variability of the wind field for Day 197 as indicated
by the scatter of trajectory end points for six individual hourly
wind patterns; inner trajectories ..... 22
15. Temporal variability of the wind field for Day 197 as indicated
by the scatter of trajectory end points for six individual hourly
wind patterns; outer trajectories .... 23
16. Temporal variability of the wind field for Day 210 as indicated
by the scatter of trajectory end points for six individual hourly
•wind patterns; inner trajectories 25
vi
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FIGURES AND TABLE (continued)
Number Page
17. Temporal variability of the wind field for Day 210 as indicated
by the scatter of trajectory end points for six individual hourly
wind patterns; outer trajectories 26
18. Departures of inner trajectory end points from reference values
for Day 197 as the amount of data used in the analysis is varied. . 29
19. Departures of outer trajectory end points from reference values
for Day 197 as the amount of data used in the analysis is varied. . 30
20. Departures of inner trajectory end points from reference values
for Day 210 as the amount of data used in the analysis is varied. . 31
21. Departures of outer trajectory end points from reference values
for Day 210 as the amount of data used in the analysis is varied. . 32
22. Dependence of the error, e, in trajectory end points with the
distance, A, of closest approach of the computed trajectory to
the missing station for Day 197 34
23. Dependence of the error, e, in trajectory end points with the
distance, A, of closest approach of the computed trajectory to
the missing station for Day 210 35
TABLE
1. Sequence of station combinations employed in the analysis leading
to Figures 18, 19, 20, and 21 28
vii
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ABBREVIATIONS AND SYMBOLS
ABBREVIATIONS
RAMS
RAPS
SYMBOLS
Regional Air Monitoring Systein
Regional Air Pollution Study
r.
i
u.
At
(Ay)
e
A
-- starting point of the i-th iteration in the computation of a
trajectory
-- time associated with point r.
-- west-east component of the wind at point r. and time t.
-- south-north component of the wind at point r. and time t.
-- vector wind at point ir. and time t
-- west-east coordinate at point r.
-- south-north coordinate at point r^
-- trajectory displacement associated with point r.
-- time interval between iterations in trajectory computation
-- west-east component of displacement (Ar).
-- south-north component of displacement (Ar).
-- trajectory end point displacement error
-- distance of closest approach of a trajectory to the location of
a station with missing data.
viii
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SECTION 1
INTRODUCTION
The 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 twenty-
five automated meteorological and air quality monitoring stations located
in St. Louis, MD. Data from this Regional Air Monitoring System (RAMS)
are recorded routinely and checked for quality in St. Louis. The data
used as input to the trajectory analysis described here are hourly averages
of wind from all stations in the network. The surface data are supple-
mented 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.
An objective analysis program has been developed (Hovland, et al..
1976) to transform data at unequally spaced observation points to evenly
spaced grid points. This program utilizes the scan weighting technique
for the horizontal interpolation of observed data. Basically, this method
is one of applying corrections to a first guess field where each observa-
tion provides a correction to the initial guess at each grid point lying
within a circle of influence of an observation point. Successive correc-
tions are then made to the field until reasonable consistency is realized
between observations and computed values at the grid points.
This report is concerned with the application of the objective
analysis program presented in Part 1 of this Final Report to the computation
of trajectories. Only the surface data are used since the RAMS network
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provides a much better defined wind field than can be obtained from only a
few upper air soundings.
The technique for computing trajectories is presented in Section 3.
Application of the trajectory analysis to the St. Louis data is presented in
Section 4. An analysis of the sensitivity of computed trajectories to the
amount of data included in the analysis is reported in Section 5. Appendices
A and B contain program listings and documentation.
Appendix C contains documentation for a set of RAPS data archive tapes
generated with the objective analysis program described above. The seven
archive tapes contain gridded upper air winds and gridded surface winds and
temperatures for the period 14 July through 15 August, 1975. These tapes
are available at the Environmental Science Research Laboratory of the
Environmental Protection Agency.
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SECTION 2
CONCLUSIONS AND RECOMMENDATIONS
An objective technique for computing trajectories utilizing objectively
analyzed wind fields has been developed and applied to surface winds observed
during the Regional Air Pollution Study in St. Louis. The computed trajectories
are not too sensitive to the amount of data included in the analysis provided
the wind field is well sampled. The wind field is very well sampled in the
center of the grid, where stations are less than ten kilometers apart.
However, the wind is not as well sampled in the outer regions of the grid
where a station may be as far as 30 km from its nearest neighbor. If it
should happen that more than one of these outlying observations is missing,
the wind field analysis may be seriously degraded and the trajectory computa-
tions will be in error. Every effort should be made to keep the key outermost
observing stations in operation for the remainder of RAPS.
The sensitivity analysis reported here provides further evaluation of
the objective analysis technique reported in Part 1 (Hovland, e_t al. , 1976).
The evaluation presented in Part 1 was based primarily on the appearance of
contour patterns. Although contour patterns appear rather sensitive to the
amount of data employed in the analysis, computed trajectories appear much less
so. At least for the limited amount of data examined in this report the
sensitivity analysis supports the conclusion that the wind field is sufficiently
well sampled that computed trajectories are not significantly degraded when
data from any single station are lost. The results of the analysis also
inspire confidence in the adequacy of the objective analysis technique
reported in Part 1.
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SECTION 3
OBJECTIVE COMPUTATION OF TRAJECTORIES
The objective computation of trajectories requires a time sequence of
gridded wind fields. A program to transform unequally spaced wind observations
to a regular grid has been described earlier in Part 1 (Hovland, _e£,al., 1976).
Trajectories computed for this report use surface wind fields objectively
analyzed by this technique. Wind observations are from a month of RAMS data
(14 July through 15 August, 1975). The computed trajectories are confined to
a horizontal plane to which all surface wind data have been assigned.
A trajectory is generated as a series of short line segments such as those
in Figure 1 which run from point r. to r.- and from r. , to r _.
(Ax)!
Figure 1. Diagram of trajectory computation. The trajectory displacement
(Ar). is the average of displacements (Ar)I and (Ar)V.
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A point, r., on the trajectory is defined by a west-east coordinate, x ,
and a south-north coordinate, y.:
r. = (x.,y.)
Associated with each point r. is a time
tt = t + iAt (2)
The initial time, t , is the time of the first gridded wind field. The time
step, At, is chosen smaller than the time interval between the gridded wind
fields.
The wind at point r. and time t. is defined by a west-east component, u.,
and a south-north component, v.:
V± = VCr^t.) = (Ui,Vi) (3)
V. is interpolated from the gridded wind fields, since, in general, r. is not a
grid point and t. is not the time of one of the wind fields. The three-dimen-
sional (x,y,t) linear interpolation function is given in Appendix A which contains
a listing of the complete trajectory progran . This interpolation function is an
extension of the two-dimensional linear interpolation function which is derived
in Part 1 (Hovland, e_t al., 1976).
The wind changes in both time and space along a trajectory. Each short
trajectory segment should be computed with the average wind along its path.
Since the exact average wind cannot be known until the segment is defined, a
two stage procedure is used to approximate each segment. The trajectory calcu-
lation can be made as exact as desired by using a sufficiently small time step
it. A first displacement, (Ar) ! , is computed using the interpolated wind V.:
(4)
where (Ax)! = u.At (5a)
and (Ay)^ = v±At (5b)
The displaced location, r!, in Figure 1 is then
r| = r. + (Ar)| (6)
i.e., xl = xi +
-------
The -wind interpolated at the displaced location r! is
V[ = V(r[,t. + At) = (u[,vp (8)
which is then used to compute a second displacement:
l (9)
where (Ax)^ = u^At (lOa)
and (Ay)^ = v!At (lOb)
The displacement, (Ar) . , in Figure 1 used to advance the trajectory is the
average of the first and second displacements:
A = r(Ax)l + i
2 2 (11)
then ri+]_ = r± + (Ar)1 (12)
and ti+1 = t£ + At = tQ + (i+l)At (13)
The above iterative procedure is repeated until point r.+1 is outside the grid
or until t. , is greater than the time of the last gridded wind field.
The logical construction of the trajectory computation program is shown in
Figures 2 and 3. In general, more than one trajectory will be generated but all
trajectories must start at time t (Equation 2). The time step, At, in the
trajectory computation is adjustable. Tests have shown that trajectories computed
from the hourly averaged RAMS data are not very sensitive to the magnitude of
the time step, provided it is chosen to be less than one hour. All trajectories
computed for this report have been generated with a time step of ten minutes.
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READ FIRST
MAP
V
LOOP FOR
EACH MAP
V
READ SECOND
MAP
V
LOOP FOR EACH
TIME STEP
V
ADVANCE ALL
TRAJECTORIES
ARE
L TRAJEC
FFMAP?
YES
REPLACE FIRST
MAP WITH
SECOND MAP
COMPUTE: - SEVERAL TRAJECTORIES
- USING SEVERAL TIME STEPS BETWEEN MAPS
- USING SEVERAL MAPS
COMPUTATIONS ARE STOPPED IF ALL TRAJECTORIES ARE OFF THE MAP
Figure 2. Logical construction of the trajectory analysis
program; overall construction.
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LOOP FOR EACH
TRAJECTORY
YES
IS
TRAJECTORY
OFF MAP?
FIND FIRST DISPLACEMENT
BASED ON WIND
AT CURRENT TIME
AND CURRENT POSITION
WILL
DISPLACEMENT
PUT TRAJECTORY
OFF MAP?
I FIND SECOND DISPLACEMENT
I BASED ON WINDS AT TIME + AT
j AND CURRENT POSITION
FIND SECOND DISPLACEMENT
BASED ON WINDS AT TIME + AT
AND DISPLACED POSITION j
(DISPLACEMENT COMPUTED ABOVE)!
ADVANCE TRAJECTORY
BY THE AVERAGE OF THE
FIRST AND SECOND
DISPLACEMENTS
NO
MORE
TRAJECTORIES?
YES
Figure 3. Logical construction of the trajectory analysis
program; detailed flow chart of trajectory
displacement computation.
8
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SECTION 4
WIND TRAJECTORY EXAMPLES
The St. Louis RAMS network of surface stations is shown in Figure 4. Also
shown is the grid used for the objective analysis. Note that the density of
stations decreases outward from the center of the city. As a result, smaller
scale variability of winds can inherently be described near the center of the
grid than at the external grid boundaries. Two five-hour periods have been
chosen for detailed analysis of the trajectories and their sensitivity. Figure
5 shows the wind fields for the first period which is from Hour 00 to Hour 05
on Day 197, 1975. Figure 6 shows the wind fields for the second period which
is from Hour 00 to Hour 05 on Day 210, 1975. On Day 197, data were missing
from Stations 116, 120, and 124. On Day 210, data were missing from
Stations 101, 109, 112, 119, 120 and 124. In addition, data from Station 102
were rejected for both days as unreliable. Thus, substantial fractions of the
St. Louis grid are devoid of observations.
Two sets of trajectories were computed for each period. The trajectories
had starting points as shown in Figure 7. Inner trajectories and outer
trajectories computed for Day 197 are reproduced in Figures 8 and 9 respec-
tively. For Day 210, inner and outer trajectories are shown in Figures 10
and 11. Trajectories can indicate convergence/divergence in the wind field
if the area enclosed by a fixed distribution of trajectory starting points is
greater/less than the area enclosed by the same respective distribution of
trajectory end points. Figure 8 indicates a general convergence downwind of the
central urban area during the five hour period of air passage on Day 197. The
outer trajectories of Figure 9 indicate convergence in the southwest part of
the grid but divergence in the eastern portion. The northern trajectories (G)}
(S)and(l) leave the grid during the five-hour period so they cannot be used to
diagnose the wind convergence pattern. The flow patterns of Figure 5 illustrate
the same basic pattern of convergence over the St. Louis grid as revealed by
the trajectories. Here divergence is also indicated on the northern grid
perimeter resulting from the increase in wind speed from about 2 to 4 meters/sec
downwind of the urban area in the outer two rows of wind barbs. However, the
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20
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14
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Figure 4. St. Louis RAMS stations on a square grid (grid interval = 5 km)
The grid is positioned so that Station 101 is at the center
point (11,11).
10
-------
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Figure 5.
Hourly averaged surface winds for Day 197, 1975, Hours 00 to 05L, plotted on the grid of
Figure 4. The length of each wind barb is proportional to the speed: ? . . , , f meters/sec.
-------
/ / /
\ I
f-T-- .
v^—e
«—•«—*-
/ X «-" «—• *•*-*•
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Hour 00
Hour 01
Hour 02
,/
s
Hour 03
Hour 04
Hour 05
Figure 6. Hourly averaged surface winds for Day 210, 1975, Hours 00 to 05L, plotted on the grid of
Figure 4. The length of each wind barb is proportional to the speed: o ^meters/sec.
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20 -
18 -
16 -
14 —
12 -
10 —
8 -
6 -
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Figure 7.
8
10
12
I
14
I
16
18
20
Trajectory starting points on the grid of Figure 4. Squares denote
inner starting points; circles denote outer starting points. The
starting point names are arbitrary; e.g., there is no connection
between @and I Aj.
13
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SB
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Figure 8. Inner trajectories for Day 197 on the grid of Figure 4.
Arrows indicate positions after each hour.
14
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.,;,..« ^ «.,..«««.4«.«««H»««»«..»«««*.*««..«•.««• «..«.«t"».
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Figure 9. Outer trajectories for Day 197 on the grid of Figure 4.
Arrows indicate positions after each hour.
15
-------
cH
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B C
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Figure 10. Inner.trajectories for Day 210 on the grid of Figure 4.
Arrows indicate positions after each hour.
16
-------
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Figure 11. Outer trajectories for Day 210 on the grid of Figure 4.
Arrows indicate positions after each hour.
17
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perimeter grid winds in the current analysis are suspect because of a general
lack of observations.
Figure 10 for Day 210 shows basically the same pattern of convergence
downwind of the central urban area as on Day 197. The nocturnal flow patterns
of Day 210, Figure 6, also exhibit cyclonic curvature of the wind at the center
of the grid (city). Both downwind convergence and central cyclonic curvature
with respect to urban St. Louis have recently been modeled theoretically by
Vukovitch, et al., (1976) for light wind speed conditions. Cyclonic curvature
is also evident on Day 197 surrounding the area of light winds which is
displaced slightly downwind of the central urban area, Figure 5 (03, 04, 05L).
Besides indicating the movement of air parcels and the convergence pattern
in the flow field, trajectories can also be used to reveal the space and time
variability of wind within an area. A measure of the spatial variability
of trajectories is revealed by the variation of the air parcel vector
displacements (trajectory end point minus starting point) for various locations
across the field. If the wind field were uniform, all air parcel displacements
Would be identical. The displacements for inner and outer starting points for
Day 197 presented in Figure 12 are seen to vary greatly; indeed the variation
is of the same magnitude as the displacements themselves. Also, the air parcel
displacements for outer trajectory starting points tend to bracket the displace-
ments for inner trajectory starting points.
Simulating the variability of air parcel displacements as a function of the
density of input data is useful for estimating the actual trajectory errors for
various distributions of observations. The variability in Figure 12, based on
all available observations for Day 197, is thus a baseline measure of spatial
variability for comparing sampling networks with fewer observations. In the
extreme case, with a uniform wind field based on only one observation, the
estimated trajectory error would be equivalent to the spatial variability
(scatter) of displacements indicated on this diagram.
Note that trajectories started east of St. Louis ({c], ©,©) are displaced
to the west, and trajectories started to the west of the city (JB], (U, (§)) are
displaced more to the east. This pattern is consistent with convergence in
the boundary layer over the city as discussed earlier. The corresponding air
parcel displacements for Day 210 are reproduced in Figure 13. Again there
18
-------
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123456
East-west displacement in grid units
(5 km interval)
Figure 12. Spatial variability of air parcel vector displacements for
trajectories of Day 197. The starting points of inner
trajectories (p) and outer trajectories (O^ are shown
in Figure 7.
19
-------
©
-8 -7 -6 -5 -4 -3 -2 -1
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^ &0
East-west displacement in
grid units (5 km interval)
- -1
_ -2
„ -3
. -4
_ -5
. -6
_ -7
- -8
- -9
- -10
Figure 13. Spatial variability of air parcel vector displacements for
trajectories of Day 210. The starting points of inner
trajectories (D) and outer trajectories (O) are shown
in Figure 7.
20
-------
appears to be some evidence for convergence in the urban boundary layer. For
example, note that trajectories starting to the north of the city (d3,E3,®)
are generally displaced further to the south than trajectories starting from
south of the city (ID, EJ ,(§)).
The urban boundary layer convergence noted above is consistent with the
circulation patterns expected due to the "heat island" effect. However, some
of the observed variability is undoubtedly associated with the local topo-
graphy. The influence of topography on the mesoscale wind field in a non-
urban environment has been studed by Wendell (1972, 1975). Recently,
Vukovich, et al., (1976) have taken into account both the "heat island" effect
and the influence of topography in a theoretical study of the St. Louis wind
field. The results reported here seem consistent with circulation patterns
deduced from the theoretical study.
One method of analyzing the time variation of the wind field is to
analyze the variation of air parcel displacements from a fixed starting point
as a function of chronologically observed wind patterns. Thus, each of the
hourly wind patterns of Figure 5 is used to construct a separate vector dis-
placement of five hours duration. The resulting six terminal points of these
displacements for wind fields at 00, 01, 02, 03, 04, and 05L are then plotted
on the St. Louis grid along with the end point of the conventional trajectory
based on the time variation of winds throughout the five hour period (Figure 14).
As the wind field changes from one hour to the next, the six trajectory end
points based on the hourly wind patterns change. Only in the unlikely event
that the wind field remains steady over the entire period will the end points
be equal to one another and identical to the conventional trajectory end point.
Figure 14 (15) illustrates the trajectory end point analysis for the inner
(outer) city trajectories of Figure 8 (9) for Day 197. The letters refer to the
end points of the conventional trajectories whose starting points are given in
Figure 7. The numbers 0-5 refer to trajectory end points generated with the
analyzed wind fields of Hour 00 through Hour 05. The lines connect these
end points based on hourly wind patterns with their corresponding conventional
trajectory end points. The scatter of trajectory end points of the hourly wind
patterns about a conventional trajectory end point is indicative of the tem-
poral wind variability occurring in various portions of the field. Figures 16
21
-------
20 —
Figure 14. Temporal variability of the wind field for Day 197 as indicated by
the scatter of trajectory end points for six individual hourly
wind patterns (0, 1, 2, 3, 4, 5 local time). The letters indicate
the location of the associated end points of the conventional inner
trajectories of Figure 8 on the grid of Figure 4. Insets are used
to show the temporal variability where the trajectory end points
overlap. See text for further explanation.
22
-------
20
18 -
16
i
14 H
12
I
1
10 -
-
8
6 —
Figure 15.
8
10
12
1 --- y
14
16
18
20
Temporal variability of the wind field for Day 197 as indicated by
the scatter of trajectory end points for six individual hourly wind
patterns (0, 1, 2, 3, 4, 5 local time). The letters indicate the
location of the associated end points of the conventional outer
trajectories of Figure 9 on the grid of Figure 4. See text for
further explanation.
23
-------
and 17 show that the time variability of winds on Day 210 is similar to that
on Day 197. If the time variability of wind is accurately depicted by the
spatial variability of trajectory end points as shown above, then the scatter
of these end points about the end point of the conventional trajectory is rep-
resentative of the error in trajectory displacement that would occur if
observations were available only once within the five hour period. It is
possible to simulate errors of trajectory displacement as a function of various
distributions of observations in time as well as space.
24
-------
20
18 -
16 -
14 -|
12
10
8 -
6 -I
4 -
8
10
12
14
16
18
20
Figure 16.
Temporal variability of the wind field for Day 210 as indicated by
the scatter of trajectory end points for six individual hourly wind
patterns (0, 1, 2, 3, 4, 5 local time). The letters indicate the
location of the associated end points of the conventional inner
trajectories of Figure 10 on the grid of Figure 4. Insets are used
to show the temporal variability where the trajectory end points
overlap. See text for further explanation.
25
-------
20 —
18 -
16
14
12
10 -I
8 -
6 —I
0
2 —
8
10
12
14
16
18
20
Figure I/. Temporal variability of the wind field for Day 210 as indicated by
the scatter of trajectory end points for six individual hourly wind
patterns (0, 1, 2, 3, 4, 5 local time). The letters indicate the
location of the associated end points of the conventional outer
trajectories of Figure 11 on the grid of Figure 4. See text for
further explanation.
26
-------
SECTION 5
SENSITIVITY OF COMPUTED TRAJECTORIES
Although trajectories can be generated without much difficulty, the
degree to which the computed trajectories are representative of actual trajec-
tories of material elements advected by the wind field will depend upon the
quality of the analyzed wind fields. The quality of an analyzed wind field is
dependent on the objective analysis technique, the accuracy of individual wind
observations, and the adequacy of the observing network to resolve the varia-
bility of the field. One way to check the validity of computed trajectories
would be to compare them with actual trajectories measured by tracking tetroons
or tracers.
The approach followed here is to evaluate the sensitivity of analyzed
trajectories to the amount of data employed in the analysis of the wind field.
This sensitivity analysis should provide a good internal consistency check on
the RAMS wind data and the objective analysis of the wind field.
The first test of the sensitivity of computed trajectories is to explore
their convergence to the final trajectory as data are successively added to the
wind field analysis starting with data from a single station and ending with all
available data. The trajectory end points using all available data are used
for reference. Trajectory end points computed using lesser amounts of data
are compared to the reference values and their differences calculated. Table
1 lists the observations used for the sets of trajectories computed for the
two days. For each trajectory, the vector differences in end point locations
are plotted for all the data sets of Table 1. The results are reproduced in
Figures 18, 19, 20, and 21. Figure 18 shows the inner trajectory end point
differences for Day 197 and Figure 20 shows the inner trajectory end point
differences for Day 210. These inner trajectory end points with a few
exceptions converge to the final end points with the fifth data set.
Although some cases can be found where adding more data actually displaces
trajectory end points further from their final value, the general trend is for
convergence toward the final value as more data are added.
27
-------
TABLE 1.
SEQUENCE OF STATION COMBINATIONS EMPLOYED IN THE
ANALYSES LEADING TO FIGURES 18, 19, -20, AND 21
DATA SET
DAY 197
DAY 210
1
2
3
4
5
6
7
Missing from
all data sets
101
101, 122-125
101, 114, 117, 119, 122-125
101, 114-125
101, 108-125
101, 104, 106, 108-125
101-125
102, 116, 120, 124
103
103, 122 - 125
103, 116, 118-125
103, 114-125
103, 110-125
103, 104, 106, 108-125
103-125
101, 102, 109, 112, 119,
120, 124
28
-------
T4
•5
'i
-2
-2
-2
-2
-2
0) V
s a
•U -H
at 6
a, ,2
-2
•u
o
CO
i
o n
3 toO
.3
2 4
East-west departure
-2
grid units
in
(5 km interval)
T4
2
-2
6
-2
Figure 18. Departures of inner trajectory end points from reference values
Basing all available data) for Day 197 as the amount of data used
in the analysis is varied. Numbers refer to the data set of
Table 1 employed in each analysis. Low numbers not shown are
off-scale. High numbers not shown are essentially equal to the
reference value.
29t'
-------
T 4
i
-2
—i
4
-2
C «
" t
0) (1)
3 C
•U -i-l
0)
•O m ••
•U CO
O -H
co C
i 3
.C
4J T3
I-l -H
O t-l
2 00
--2
-2
• 2
—t
4
-2
(i)
-2 f
-2
-2
-2
2 4
East-west departure in
grid units (5 km interval)
-2
.f
+ -2
Figure 19.
Departures of outer trajectory end points from reference values
(using all available data) for Day 197 as the amount of data used
in the analysis is varied. Numbers refer to the data set of
Table 1 employed in each analysis. Low numbers not shown are
off-scale. High numbers not shown are essentially equal to the
reference value.
30
-------
.. 2
-2 '•* 3 I
- -2
-2
a) a)
i-l 4J
3 C
4J -i-l
flj 6
0. 42
0)
'O in
T 4
- 2
5*
•• -2
4J
3
0
to
i
4-1
M
O
1 r-
cn
4J
•H
a
3
•a
-r-l
1-1
60
6
. 2
.5"
- -2
2 4
East-west departure in
grid units (5 km interval)
T 4
-2
-2
©
-2 *'
>
2
•-i
4
-2
ioj dj
Figure 20. Departures of inner trajectory end points from reference values
(using all available data) for Day 210 as the amount of data used
in the analysis is varied. Numbers refer to the data set of
Table 1 employed in each analysis. Low numbers not shown are
off-scale. High numbers not shown are essentially equal to the
reference value.
31
-------
-2
A 2
i
-2
®
-2
-2
0)
4J
C
.C
4-1 CO
3 4J
O -H
CO C
I 3
4J T3
60
T 4
2
-2
3'
•
Z
'* 'I
3
t -2
©
East-west departure in
_2 grid units (5 km interval)
T
I 2
• I
-2
-2
-2
H
4
Figure 21_
Departures of outer trajectory end points from reference values
(using all available data) for Day 210 as the amount of data used
in the analysis is varied. Numbers refer to the data set of
Table 1 employed in each analysis. Low numbers not shown are
off-scale. High numbers not shown are essentially equal to the
reference value.
32
-------
The outer trajectory end point differences for the two days_are plotted in
Figures 19 and 21, respectively. The outer trajectory end points are seen to
converge somewhat more rapidly to their final values than the inner trajectory
end points do. The reason for this is that the objective analysis is accom-
plished in such a way that the variability of the wind field from the dense
inner network does not propagate into the outer regions. Therefore, adding
more data from the interior stations does little to affect trajectories which
do not pass through the interior region. The inner trajectories converge more
slowly to their final values because the data which are added to higher
numbered data sets contain information from the innermost stations which will
refine the analyzed wind field in the inner region.
A slightly different approach is to investigate the sensitivity of
computed trajectories to the effect of dropping observations from selected
individual stations. An error, e, is defined as the distance between end
points of two trajectories originating from the same starting point; one
trajectory is computed from complete data and the second is computed from the
same data base less one station. The error, e, should be inversely proportional
to the distance, A, of closest approach of the second trajectory to the location
of the station with missing data. A plot of e versus A will reveal the signifi-
cance of missing data in various portions of the observational network.
Observations are dropped individually from the following sequence of stations:
105, 108, 121, and 125. This sequence proceeds from the dense parts of the
observing network to the sparse areas. The results of this analysis are
presented in Figure 22 (Day 197) and Figure 23 (Day 210). Inspection of
these figures reveals that the errors are generally less than one grid interval
(5 km) except in the case where data from an outer station (121 or 125) is
missing. In fact for the two five-hour periods, there is only one case where
dropping the data from an inner station leads to an error in the trajectory
end point which is greater than one half grid unit. Figure 23 shows that, on
Day 210 when the data from Station 125 is dropped from the analysis, most
trajectories depart significantly from their reference values. This would
appear to represent an extreme case since on Day 210 data from Stations 112,
119, 120, and 124 are already missing, and dropping data from Station 125
creates an analysis without any observation in a large area to the west and south
of the city. This occurrence tends to confirm the importance of certain key
33
-------
(grid
units)
ui
7 -
6 -
5 -
4 -
3 -
2 -
1 -
I,
G
O
0
^
6
O
X - 105 missing
® - 108 missing
O - 121 missing
• - 125 missing
-oo-j
9
A (grid units) -*
Figure 22.. Dependence of the error, e, in trajectory end points with the distance,A, of closest
approach of the computed trajectory to the missing station for Day 197.
-------
(grid
units)
6 -
5 -
«5
r\
o
--K-
o
o
-0< 9
56
O -
- 105 missing
- 108 missing
121 missing
- 125 missing
A (grid units)
Figure 23. Dependence of the error, e, in trajectory end points with the distance, A, of closest
approach of the computed trajectory to the missing station for Day 210.
-------
stations in the outermost regions of the network especially when the data from
some of the adjacent stations are already missing. With this exception noted,
the sensitivity analysis supports the conclusion that the wind field is suf-
ficiently well sampled that computed trajectories are not significantly
degraded when data from any single station is lost. The results of the analysis
also inspire confidence in the adequacy of the objective analysis routine
reported in Part 1 (Hovland, ie_t al., 1976).
36
-------
REFERENCES
Hovland, D., D. Dartt and K. Gage: An Objective Analysis Technique for the
Regional Air Pollution Study. Final Report, Part 1, Contract No. 68-02-
1827 for Environmental Protection Agency, Research Triangle Park, NC,
1976. 52 pp.
Vukovich, F. M., J. W. Dunn III, and B. W. Crissman: A Theoretical Study
of the St. Louis Heat Island: The Wind and Temperature Distribution.
J. Appl. Meteor., 15, 417-440, 1976.
Wendell, L. L.: Mesoscale Wind Fields and Transport Estimates Determined
from a Network of Wind Towers. Mon. Wea. Rev., 100, 565-578, 1972.
Wendell, L. L.: An Evaluation of Data Requirements and Objective Analysis
Techniques Appropriate for Regional Scale Atmospheric Transport.
Battelle Pacific Northwest Laboratories, BNWL-SA-5234, 1975.
37
-------
APPEKD1X A: PROG5&M LISTINGS
SUBROUTINE TRACKS
DIMENSION TRAJX(M,N)»TRAJY(M»N)»LEN(N),U(I,J»K)fV» TRAJY(1»L)» L=1»...»N. REMAINING POINTS OF
C A TRAJECTORY WILL BE IN TRAJX(LL,L>» TRAJY(LL»L>,
C LL=2f...»LEN(L>. THE LEN(L) WILL BE GENERATED BY TRACKS.
C IPT WILL GET THE LENGTH OF THE LONGEST TRAJECTORY.
C «DATA MAPS WILL BE READ INTO COMPONENT ARRAYS U AMD V FROM
C TAPE LU. GRIDSP IS THE DISTANCE BETWEEN GRID POINTS IN KM.
C NSTEPS IS THE NUMBER OF TIME STEPS BETWEEN MAPS» HOURS IS
C THE NUMBER OF HOURS BETWEEN MAPS, AND NMAPS IS THE NUMBER
C OF MAPS TO USE.
C
C «IPT IS THE INDEX OF THE CURRENT TIME STEP
I P T = 0
IF(N.LE.O .OR. I.LE.l .OR. J.LE.l .OR. K.LE.1)RETURN
C
C *CHECK THAT TRAJECTORY ARRAYS ARE LONG ENOUGH
MAX=NSTEPS»NMAPS+1
IF(MAX.GT.M)RETURN
C
C *LEN(L> MAY BE MADE SMALLER LATER
DO 10 L=1»N
10 LEN(D=MAX
I P T = 1
C
C »WIND SPEEDS ARE IN METERS /SEC. CONV CONVERTS
C TRAJECTORY INCREMENTS TO GRID UNITS.
CONV=3.6/GRIDSP*HOURS
C
C *DT IS THE TIME BETWEEN TRAJECTORY STEPS.
DT=1./NSTEPS
C
C »READ FIRST MAP.
READ(LU) < »JJ=1»J)»((V(II»JJ,1)»II = 1»I),JJ=1,J>
C
C *LOOP THROUGH MAPS
IMAPS=0
201 IMAPS=IMAPS+1
IF(IMAPS.GT.NMAPS)GO TO 381
C
C »READ SECOND MAP.
READ
-------
IPTsIPT+1
C
C »LOOP THROUGH TRAJECTORIES. ICT COUNTS ACTIVE TRAJECTORIES,
ICT = 0
DO 320 ITR=1,N
C
C *LENGTH LESS THAN MAX MEANS TRAJECTORY HAS GONE OFF MAP.
IF(LEN(ITR),LT.MAX)GO TO 320
ICT=ICT+1
C
C *FINO X AND Y INCREMENTS AND MOVE TRAJECTORY
CALL ADVECT(DX,DY»U»V,I,J,K»
1TRAJX(IPT-1,ITR)»TRAJY(IPT-ltITR),TIME»DT»CONV)
X=TRAJX(IPT-1»ITR)+DX
TRAJX(IPT,ITR)=X
Y=TRAJY(IPT-1.ITR)+OY
TRAJY(IPT»ITR)=Y
C
C ^TERMINATE TRAJECTORY IF IT IS OFF THE MAP
IF(X.LT.O .OR. X.GT.1-1)60 TO 315
IF(O.LE.Y .AND. Y.LE.J-DGO TO 320
315 LEN(ITR)=IPT
320 CONTINUE
C
C *RETURN IF ALL TRAJECTORIES ARE OFF THE MAP
IF(ICT.NE.O)GO TO 301
IPT=IPT-1
GO TO 3P1
C
C *REPLACE FIRST MAP WITH SECOND MAP.
351 DO 360 JJ=1,J
DO 360 11=1,1
U(II»JJ,1)=U
GO TO 201
381 RETURN
END
39
-------
SUBROUTINE ADVECT (DELX»DELY»U, V » 11 J»K»X» Y»T»DEl_T,CONV )
C DIMENSION U(I«JtK)*V(ItJ»K)
C
C *ADVECT FINDS DELX AND DELY WHICH ARE APPROXIMATIONS TO THE
C X AND Y DISPLACEMENTS OF AN AIR PARCEL BETWEEN TIME T
C AND TIME T * DELT
C *THE WIND FIELDS ARE DEFINED BY THE COMPONENT ARRAYS U AMD V.
C
-------
FUNCTION TRILI(A»L»M»N»XfY»Z)
DIMENSION A(L»M»N)
C
C «A IS AN ARRAY OF DIMENSION (L»M»N) HOLDING 3-DIMFNSIONAL GRID !
C POINT DATA. TRILI WILL INTERPOLATE A VALUE AT TH£ INTERNAL |
C POINT + (l.-0)*A(I,J,K*l) ) >
RETURN
END
41
-------
APPENDIX B: PROGRAM DOCUMENTATION
SUBROUTINE TRACKS will compute horizontal trajectories from a time
sequence of gridded wind fields. The wind fields are stored in component
form: u is the west-east component in meters/sec, and v is the south-north
component in meters/see.
The wind fields must be written one per record on a file such that they
can be read with the statement
READ (LU)((U(II,JJ,1),11=1,1),JJ=1,J),((V(II,JJ,1),11=1,1),JJ=1,J)
where LU, I, and J are explained below. Grid point (1,1) is in the south-
west corner. I increases to the east, and J increases to the north.
To compute backward trajectories the wind fields must be stored in reverse
chronological order. In addition, the components must be replaced by their
negatives.
The following elements are parameters to SUBROUTINE TRACKS:
Explanation
Element
TRAJX(M,N)
& TRAJY(M,N)
Input or
Output
Input & Output
Arrays which will contain the u and v
coordinates of the N trajectories to be
computed. M must be at least as large
as the number of points in the longest
trajectory. TRAJX and TRAJY are measured
in grid units relative to grid point (1,1)
Starting points must be supplied in
TRAJX(1,L),TRAJY(1,L), L=l, , N.
LEN(N)
Output
Array which will hold the lengths
(number of points) of the N trajectories.
42
-------
(Continued)
Element
M,N
IPT
LU
U,V
I,J,K
Input or
Output
Input
Output
Input
Input
GRIDSP
NSTEPS
HOURS
NMAPS
Input
Input
Input
Input
Explanation
Dimensions of arrays TRAJX and TRAJY
(and LEN).. N is also the number of
trajectories to be generated (at least 1)
Length of the longest trajectory
generated, i.e., IPT is the largest of
the LEN(L).
Tape number of the file on which the
wind fields are stored.
Component arrays into which the gridded
wind fields are read. Together U and V
are referred to as a map.
Dimensions of U and V. I,J,K must each
be greater than 1. K need be no greater
than 2.
Distance (in km) between grid points.
Number of time steps to use between
maps.
Number of hours between map times.
Number of maps to use. The first map
is map 0; therefore, NMAPS+1 maps must
be provided on TAPE LU.
43
-------
APPENDIX C: USER GUIDE TO ARCHIVE TAPES
The surface and upper air analyses are on seven reels of BCD tape written
in even parity at 556 BPI.
Reel Dates No. of Blocks
Surface 1 ' 7/14-8/15, 1975 1584
Upper Air 1 7/14-7/19, 1975 3465
Upper Air 2 7/20-7/25, 1975 3420
Upper Air 3 7/26-7/31, 1975 3455
Upper Air 4 8/01-8/06, 1975 2991
Upper Air 5 8/07-8/11, 1975 2880
Upper Air 6 8/12-8/15, 1975 2309
On each reel the data blocks are followed by a double end-of-file.
The surface analyses are based on observations from Stations 101-125.
The upper air analyses are based on pibal observations from Stations
141-144.
44
-------
Station coordinates are given in grid units (5 km. spacing). Point
(1.00, 1.00) is in the southwest corner of the grid. The x coordinate
increases to the east and the y coordinate increases to the north.
Station No.
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
141
142
143
144
45
x Coordinate
11.00
10.67
11.68
11.63
10.90
9.90
10.20
11.84
13.32
11.61
9.93
8.95
9.71
11.03
13.59
14.72
14.28
10.78
8.12
6.78
8.65
10.49
17.63
12.02
1.65
10.75
5.30
14.22
13.34
y Coordinate
11.00
12.24
11.52
10.49
10.32
10.54
11.55
13.25
11.00
9.59
9.52
11.21
12.99
14.52
14.59
13.04
9.59
7.68
9.14
12.21
15.50
20.87
12.30
2.34
11.48
10.84
8.25
6.44
16.64
-------
ARCHIVE FORMAT FOR SURFACE WIND ANALYSES
FIEU)
1
2
3
4
5-54
55-936
937
FORMAT
12
13
12
A13
25(2F4.1)
441(2F4.1)
2X
CONTENTS
Year (75)
Day (1-365)
Hour (0-23)
,,SURFACEAWIND (BCD Characters)
Direction (degrees) and speed
(mps) for Stations 101-125.
999.0 (9990) represents missing.
Analyzed data: direction
(degrees) and speed (mps)
for 441 grid points.
999.0 (9990) represents missing.
Blank fill
Total block length is 3750 characters. Each block contains the
surface wind analysis for one observation time.
The analysis grid has 2 x 21 x 21 = 882 points:
((DIR(I,J),SPD(I,J),I=1,21),J=1,21). Grid point (1,1) is in the
southwest corner. I increases to the east, and J increases to the north.
Each surface wind analysis is followed by a surface temperature
analysis for the same hour.
46
-------
ARCHIVE FORMAT FOR SURFACE TEMPERATURE ANALYSES
30-470
471
FORMAT
12
13
12
A13
25F4.1
441F4.1
16X
CONTENTS
Year (75)
Day (1-365)
Hour (0-23)
ASURFACEATEMP (BCD Characters)
Temperature (C) for Stations
101-125.
999.0 (9990) represents missing.
Analyzed data: temperature (C)
for 441 grid points.
999.0 (9990) represents missing.
Blank fill
Total block length is 1900 characters. Each block contains the
surface temperature analysis for one observation time.
The analysis grid has 21 x 21 = 441 points:
((TEMP(I,J),I=1,21),J=1,21).- Grid point (1,1) is in the southwest corner.
I increases to the east, and J increases to the north.
Each surface temperature analysis is preceded by a surface wind
analysis for the same hour.
47
-------
ARCHIVE FORMAT FOR UPPER AIR WIND ANALYSES
FIELD
1
2
3
4
5
6
7-14
15-896
897
FORMAT
14
12
12
12
14
A6
4(2F5.1)
441(2F4.1)
12X
CONTENTS
Year (1975)
Month (1-12)
Day (1-31)
Hour (0-23)
Level, meters above mean sea
level.
MAW±ND (BCD Characters)
Direction (degrees) and
speed (mps) for Stations
141-144.
999.0 (A9990) represents missing.
Analyzed data: direction
(degrees) and speed (mps) for
441 grid points.
999.0 (9990) represents missing.
Blank fill
Total block length is 3600 characters. Each block contains the
analysis for one level, at one observation time. Only those levels for
which at least one station has data are included on the tape.
The analysis grid has 2 x 21 x 21 = 882 points:
((DIR(I,J),SPD(I,J),1=1,21),J=l,21). Grid point (1,1) is in the southwest
corner. I increases to the east^ and J increases to the north.
48
-------
TECHNICAL REPJfiT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/4-77-002b
2.
3. RECIPIENT'S ACCESSION>NO.
4. TITLE AND SUBTITLE
AN OBJECTIVE ANALYSIS TECHNIQUE
FOR THE REGIONAL AIR POLLUTION STUDY
Part II
5. REPORT DATE
1Q77
6.
G 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 Ave.
Minneapolis, MN 55440
10. PROGRAM ELEMENT NO.
1AA603
11. CONTRACT/GRANT NO.
68-02-1827
12. SPONSORING AGENCY NAME AND ADDRESS
13. TYPE OF REPORT AND PERIOD COVERED
Environmental Sciences Research Laboratories
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park. N.C. 27711
TYPE O
Final
14. SPONSORING AGENCY CODE
EPA-ORD
15. SUPPLEMENTARY NOTES
Part I of this report has been issued as EPA-600/4-77-002a, January 1977
16. ABSTRACT
This report discusses the application of objective analysis techniques to the
computation of trajectories from surface wind observations of the Regional Air Pol-
lution Study in St. Louis. Trajectories were computed over a 100-kilometer square
grid centered on St. Louis for two 5-hour periods during July 1975. The variability
of the surface wind field was investigated by examining the temporal and spatial
variability of computed trajectories. Also, the sensitivity of the computed tra-
jectories to the amount of data employed in the analysis was examined in some detail
The results showed a general lack of sensitivity of the computed trajectories to a
single missing observation. However, computed trajectories were very sensitive to
missing adjacent observations.
In addition to the trajectory analysis, a set of tapes containing gridded winds
and temperatures for the St. Louis area were generated.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COS AT I Field/Group
*Air Pollution
*Meteorological data
*Wind (meteorology)
*Temperature
*Grids (coordinates)
*Atmospheric models
*Applications of mathematics
St. Louis, Mo.
13B
04B
08B
04A
12A
13. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (ThisReport)'
UNCLASSIFIED
21. NO. OF PAGES
57
20. SECURITY CLASS (This page)
SECURITY CLASS (1
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
49
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