EPA-650/4-73-001
A MESOSCALE WINDFIELD ANALYSIS
OF THE LOS ANGELES BASIN
by
Gerald E. Anderson
The Center for the Environment § Man, Inc.
275 Windsor St.,
Hartford, Connecticut 06120
Contract No. 68-02-0223
Program Element No. 1A1009
EPA Project Officer: Kenneth L. Calder
Meteorology Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
June 1973
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This report has been reviewed by the Environmental Protection Agency and
approved for publication. Approval does not signify that the contents
necessarily reflect the views and policies of the Agency, nor does mention
of trade names or commercial products constitute endorsement or recommen-
dation for use.
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TABLE OF CONTENTS
Section Title Page
1 Introduction 1
2 Atmospheric Model 5
3 Flow Model 10
4 Computations 14
5 Empirical Constants 14
6 Data 15
7 Results 15
8 Recommendations 19
9 References 20
APPENDICES
A Mesoscale Influences on Wind Fields 21
B Los Angeles Windfield - ANAL70 Program Specifications 31
C Poisson Surface Data Fitting Technique 37
D Computer Output 42
LIST OF ILLUSTRATIONS
Figure Caption Page
1 Los Angeles Region and Surroundings 4
2 Model Determination of Inversion 7
3 Vertical Temperature Profiles for 29 September 1969 9
4 Circulation Pattern in Vertical Slice 11
5 Effective Topographic Surface at an Inversion 12
6 Constant Potential Lines for Flow Past Mountains 13
iii
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Figure Caption Pa#e
A: 1 Scale ranges of significance for atmospheric boundary 22
layer phenomena and measuring devices
A: 2 Vertical section of heat island thermal circulation 24
and the temperature distribution producing it
A: 3 Layout of regions for topographic and thermal windfield 25
analyses
A: 4 Topography of Connecticut 26
A: 5 Streamlines on Connecticut grid from interpolation 26
between stream functions at 15 data stations
A: 6 Streamlines from topographic analysis of the same data 26
as in Figure 5
A: 7 Net topography relative to a highly smoothed "mean" 27
surface for Toronto region
A: 8 Potential of topographically induced wind disturbance 27
for Toronto region due to unit west wind
A: 9 Heat island temperature distribution for Toronto 28
region
A: 10 Heat island disturbance potential for the Toronto 28
region
A: 11 Lake-breeze disturbance potential for Toronto region 29
A: 12 West-wind component of net wind in Toronto region for 29
4m sec" mean wind from west with topographic and
thermal effects
C-l Isotherms (°F) x 10"^ in Los Angeles Basin 41
IV
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ABSTRACT
The rationale, derivation, and use of a mesoscale windfield
analysis is presented. In the program reported on herein, the analy-
sis was applied to a specific region - the Los Angeles Basin. This
application is in support of a multi-phased effort of modelling
ground level and/or three-dimensional air pollution distributions
in the region. Los Angeles air pollution modelling efforts supported
by the Environmental Protection Agency are using data collected during
an experimental program carried out during the fall of 1969. The meso-
scale windfield analysis described here was specifically applied to 13
hourly periods from 5:00 am to 5:00 pm on 29 September 1969, and one
period at 6:00 am on 30 September 1969.
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1. Introduction
A detailed description of an analytical technique for defining
two-dimensional (horizontal) wind patterns is presented in Reference 1.
A modified version of this analysis is herein presented and applied to
a specific site, the Los Angeles Basin.
The basic assumption of the analysis is that in many situations
atmospheric boundary layer flows are approximately two-dimensional. The
scale of vertical variability is so much smaller than the horizontal
scale that the flow may be considered as a horizontal flow perturbed by
vertical disturbances.
All two-dimensional flows may be decomposed into uniform flows,
source^sink flows, and vortices. That is, every real two-dimensional
flow is the superposition of a uniform flow and a distribution of sources,
sinks and vortices.
Vorticity can only be introduced into a flow by a transfer-of-
energy process, as, for example, by friction. In the atmospheric boundary
layer, friction against the ground surface introduces vorticity about
horizontal axes, but only vorticity about vertical axes can affect the
horizontal wind patterns. Vorticity in the horizontal patterns may be
introduced by variations in the surface friction. For example, the wind
is turned in toward rough regions. Thus, a "friction island" will be
produced by a rough city sitting on a smooth plain. This effect is
generally less than the "heat island" effect of the same urban area. The
weakness of the friction effect on horizontal wind patterns is fortunate,
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since it is very difficult to define, measure and/or describe the friction
patterns of a large urban-rural complex.
Source-sink effects (divergence-convergence) on horizontal flows
often dominate the horizontal wind patterns and at least some of these
effects are observable and may be related to measureable characteristics
of the atmosphere.
Since the mass of air is conserved in the atmospheric flows under
consideration only one mechanism exists for producing divergence Of) .
Air must move vertically from or to the two-dimensional layer under consi-
deration. Such vertical motions can occur in the near-ground layer because
of complex interactions with upper layers, but perhaps the dominant mecha-
nisms are thermal and mechanical interactions with the ground surface
itself.
Air flowing across a topographic surface must rise and fall to
follow the contours. Since this effect is forced by the surface, it dies
out with altitude. Thus, there must be a net rise or fall in the lowest
layer at each horizontal location.
Similarly, air heated over a relatively warm surface rises, and it
falls over relatively cool areas. The rise and fall depend on the rela-
tive surface temperatures. These major mechanisms that produce rising
and falling air are determined by surface characteristics, topography
and temperature, that may be measured with some precision. The resultant
wind patterns may be determined by assuming linear relationships between
the divergence and the surface property. The analysis then correlates
cause and effect, but falls short of solving the relevant momentum and
energy equations that express the full range of interactions. The present
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analysis is based solely on the mass continuity equation.
The relevant derivations are presented in Reference 1. The
results are given in terms of the velocity potential. The velocity
itself is the vector gradient of the potential
V = V$
The flow divergence is the Laplacian of the potential
V.V = V2$
In Reference 2 the potential was presented as being composed of
three superposeable components, the mean flow potential, the topographic
potential, and the thermal effect potential.
$ = $ 4- $ + $
mean topographic thermal
In the present analysis, the application to the Los Angeles Basin involved
such large perturbations to the mean flow that this linear combination was
no longer assumed. The topographic velocity potential is here assumed
to depend on the thermal potential patterns.
The divergence due to the thermal effect is found to be proportional
to the thermal updraft velocity which, in turn, is assumed proportional to
the relative temperature of the ground surface.
V2$ , ~ (T - ?)
thermal '
where. T is the local temperature
and T is some area mean
The divergence due to the topographic effect is found to be
proportional to the topographic slopes and to the wind vector approaching
those slopes
V2$ , . ~ (V$ + V$ , n) -V(AH)
topographic mean thermal
where AH is height of inversion above the
local topography
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The application of these equations to the determination of wind
patterns in the Los Angeles area (see Figure 1) is described below.
Figure 1 shows the square outline of the region of analysis and the
surrounding land and ocean area. San Nicholas Island, a data station for
this analysis, is shown in the lower left hand corner of Figure 1.
2. Atmospheric Model
Since the climate of Los Angeles shows considerable stability (i.e.,
the short-term variability is small) and the chosen experimental day is
typical of adverse air pollution conditions, the windfield model presented
is most applicable to the meteorological situation of that day and season.
However, that situation is of long duration and of significant concern.
Characteristics of the autumn Los Angeles meteorology were inferred
from examination of Northern Hemisphere Data Tabulations for several Cali-
fornia coastal stations (Point Mugu, Vandenberg, and San Diego) as well as
the offshore station on San Nicholas Island. This data was available in
CEM's library. In addition, Weather Bureau records for Los Angeles Inter-
national Airport were obtained from the National Weather Records Center,
Asheville, North Carolina.
The meteorological situation modeled on the basis of these records
is one of a Pacific High over a cool ocean surface producing a surface-based
inversion extending up to about 2000 ft. RAOB's from these stations indi-
cated a persistent inversion with a nearly constant temperature gradient and
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a nearly constant upper limit near 2000 ft. In this inversion layer, the
synoptic scale pressure field is driving a light onshore breeze. Land
surface temperatures become cooler than the ocean at night and may become
considerably higher than the ocean temperature during the day.
During periods of a relatively hot land surface, a mixing layer based
at the ground raises the bottom of the inversion to some altitude above the
ground. Sea breezes are concurrently developed. When land surface tempera-
tures fall below ocean temperature, land breezes are developed, but the in-
version remains ground-based.
The temporal stability of the upper portion of the inversion layer,
combined with a physical concept of thermal mixing over a hot land surface,
led to the use of a simple, but not novel, model of the thermal structure.
The altitude of and temperature at the top of the basic inversion are taken
to be defined by soundings at San Nicholas Island. San Nicholas Island is
taken to be representative of the meteorology of the region as it is undis-
turbed by the topographic and thermal effects of the Los Angeles area.
Since the height required is of the order of 2000 ft, it is assumed that
the island itself has little thermal effect on the upper portion of the
inversion.
It is further assumed that a gentle, synoptic scale breeze is
continuously advecting the air mass from the ocean to the land. This ad-
vective velocity is also defined by wind profiles reported at San Nicholas.
Wind soundings exhibit more variability at all stations than do the tempera-
ture soundings, This is true also at San Nicholas. It is particularly
true in light wind conditions such as prevailed on 29, 30 September 1969.
It is also true that for very light synoptic scale winds, the local
flow in the Los Angeles Basin is much more determined by the thermal
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driving forces. Thus, the determination of the "driving" wind is not as
critical for the present cases as it would be for cases with stronger
winds. The advected thermal profile is simplified to a constant poten-
tial temprerature gradient between sea surface temperature and the tempera-
ture at the top of the inversion.
The actual driving wind used in the analysis was a single constant
wind of 0.7 mps at 225°. This is a somewhat subjective choice representing
an averaging, turning, and reducing (to make appropriate to the mixing zone)
of twice daily soundings taken at 500 and 1000 meters.
Over hot land, it is assumed that a mixing layer of constant
potential temperature is adjacent to the surface. The layer is assumed to
extend to the altitude at which the inversion temperature equals the local
surface temperature. The resultant profile is shown in Figure 2.
T1constant
'above inversion
Z=H' I i | )t Inversion Top
T-TSea " T'-TSea
T"TSea ~ TLand " TSea
Figure 2. Model determination of inversion base.
7
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Thus, H, the height of the inversion base, is simply
|-T(X,Y) - T "]
H = »' T- - T
L SEA J
Inversion heights from this formula compare favorably with inversion
heights identified directly from temperature profiles. Comparisons are shown
in Figure 3 where profiles reprinted from Roth (Reference No. 1) are marked
with inversion base location determined by the present method along with
those presented in Reference No. 1.
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. Annupv
(KtT AflOVI
HCflN It A. LLVEL)
2400
2000
1500
1700
800
400
Temperature (°F)
74 6?
Tcriiperatiire (°f)
OBIS rST
0910 PST
1206 PST
-1257 PST
66
74 82
Temperature (T)
ALT IT UK
(ffCT ABOVE
MEAN SEA LEVEL)
2400
2000
1600
1200
800
100
74 ZZ 90
Temperature ('F)
Invrr.: i on Dnscs H.-srlcpd
>i: Cor-^ut»?d by prt- c nY mcchtd
C Vrora Roth ivporc
Figure 3. Vertical temperature profiles for 29 September 1969: a) Los Angeles
International Airport, b) Hawthorne, c) Commerce, d) El Monte.
Reprinted from Roth (Reference 1).
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Basic modifications to the windfield model described in Appendix A were
required to account for the typical presence of a strong inversion which
severely inhibits vertical motion and to account for the presence of the
very large scale topography present. The formulation of the thermal pertur-
bation to the windfield was actually eased because well distributed surface
temperature observations were available.
Equation A(8) of Appendix A is linear and eq. A(5) may be considered
linear if the windfield perturbations are small. In the Los Angeles case,
windfield variations typically exceed the synoptic scale wind. Thus, no
uniform "mean" wind can be reasonably defined for use in the forcing function
in eq. A(5). For the model used here, the thermal effect is computed first
from the ground surface temperature distribution. The resulting velocity
vector field is added to the synoptic scale (uniform on this scale) wind
vector. The net windfield is used in the forcing function on the right-hand
side of eq. A(5).
The presence of an elevated base of a strong inversion developed by
vertical thermal motions has a significant effect on the formulation of the
flow model. As discussed in Appendix A, the model basically equates the
average over a chosen depth of the horizontal divergence to the difference
in vertical velocity over that depth. Since the inversion itself has thermal
stability which inhibits vertical motion, its base is assumed to be a sur-
face of zero vertical velocity; that is, mass does not penetrate the inver-
>
sion base. These assumptions cannot be completely true since the inversion
base, itself rises and falls in a diurnal cycle. The velocity of the inver-
sion base is, however, generally small compared to the maximum vertical
velocity in the layer b«low the inversion base.
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Consistent with the above discussion, it is assumed that the mesoscale
i.
thermal circulations are contained within the mixing layer below the inver-
sion base shown in Figure 4. An exception to this concept is assumed when
the land is colder than the ocean. In this case, the inversion is ground
based, yet down slope thermal drainage is not inhibited. Another exception
is that where the computed H is near zero (as over the ocean), a minimum
value of H = 200 ft is assumed. This allows flow from the cold regions,
and is consistent with empirical estimates of turbulence scales for very
stable layers.
Inversion Base
200
Minimum [
00 ft. 1 (
inimum ) ^ .
Level of Zero
Divergence
Cool Surface
Warm Surface
Figure 4. Circulation pattern in vertical slice.
It is recognized that such a pattern will be partially hidden by ther-
mal and shear turbulence found in the mixing layer. The conceptual model
shown in the sketch suggests that at about one-half the height of the in-
version base, the thermal motion is purely vertical. H/2 then, is a con-
venient upper surface to define as the upper boundary of a near ground flow
regime. The space between H/2 and the inversion base would then be occu-
pied by a flow moving counter to the near ground flow. With AH defined
as the inversion altitude minus the local topographic altitude, the model
uses AH/2 as the layer depth over which the windfield is averaged.
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In regions where the topography penetrates the inversion base, the layer
thickness goes to zero, thus producing a very large flow perturbation. This
represents the turning of the wind as it becomes parallel to the topographic
contours because of the extreme thermal stability of the inversion layer.
Numerically, however, the accuracy is lost as the singularity of the inter-
section is approached. The correct analytic condition should be that the
component of the wind vector normal to the intersection should be zero; i.e.,
n
- ^.
where n is a unit normal vector and V$ = V.
The algorithm programmed for solution of the Poisson equation, however,
only allowed specification of $ as a boundary value. Therefore, the bound-
ary condition was approximated by specifying large arbitrary values of VH
(the topographic gradient) at the edges of topographic penetrations of the
inversion base. This was done by setting VH to a constant large value
wherever VH was negative (and the land surface temperature exceeded the
ocean's). Thus, topographic penetrations became "mesas" with topographic
gradients large at the rims, but zero at the interior of these "mesas."
Another view is that the vertical resistance of the inversion increases
the effective topographic slope (see Figure 5).
H
"Effective" h
Fig. 5. Effective topographic surface at an inversion.
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A separate trial of this scheme was carried out and Figure 6
shows the potential lines corresponding to flow about such topographic
islands (the shaded areas). It is seen that the condition of n'V = 0
is approximately met at the "shores" of the "islands" (Cliffs of the
mesas). The trajectories, which would be lines normal to the potential
lines, are thus turned to be tangent to the "shores".
Figure 6. Constant potential lines for flow past mountains.
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The program was written in ANAL70, a language available for use on a
UNIVAC 1108. The program is printed in Appendix D and the program specifi-
cations in Appendix B. Since ANAL70 programs are executed in fixed sequence,
flow charting is generally irrelevant and the type of specification used
s
seems most appropriate.
5. Empirical Constants
Although the model does not make use of the full set of relevant dynamic
equations, there is little empiricism in the solution of the equations used.
The only arbitrary constants defined are:
1) the altitude heating effect. The surface temperature in an other-
wise homogeneous thermal region is assumed' to lie one-third of the
way between the constant temperature value and the constant poten-
tial value. This allows computation of an altitude effect on tem-
perature that is reasonable in regions of significant topography
far from temperature data stations. The correction is not large,
so the accuracy of the one-third estimate is not critical.
2) the minimum AH . It is set at 200 ft (as discussed above).
3) the "mesa" walls at topographic.penetrations of the inversion. They
are assumed to be 600 ft high. Again, the exact value chosen here
is not critical.
4) the constant relating the ground temperature and the thermal updraft
velocity generated. It is assumed to be
W • = .001 .
T - T
SEA
This value was chosen as producing the most nearly correct wind
speed at the coast for sea breeze occasions, and is most subject
to "tuning" adjustments.
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6. Data
Ground surface temperatures were taken from data provided by Roth
from a 1969 Los Angeles experiment (Reference 1). Specifically, data was
used for thirteen (13) hourly periods from 5:00 am to 5:00 pm on 29 Septem-
ber 1969 and for 6:00 am on 30 September 1969. Temperatures were provided
for nine (9) stations for most periods, but a few reports were missing in
the early morning hours. Missing temperatures were assumed by inferring
consistency of patterns with the available data. Gridpoint temperatures
were interpolated by the method described in Appendix C.
Topographic height on a 50 x 50 mile grid with two mile grid
spacing x^ere taken from Roth (Reference 1). Additional topographic data
was obtained from Dr. James Angell of ARL/NOAA. This data was defined on
a 1/2 km grid of 116 points (N-S) by 137 points (E-W). An ANAL70 program
combined (by interpolation, where necessary) both sets of data on a 49 x 49
(1 mile) grid. Point (1, 1) was located at 118° 37' 13" W, 33° 34' 53" N.
The inversion height, surface and inversion top temperatures, and the surface
synoptic wind were taken from San Nicholas Island soundings.
7. Results
The model was run for thirteen (13) temperature sets from 5:00 am
to 5:00 pm, 29 September 1969, assuming the San Nicholas Island data to be
constant for the entire day. One run was made for data from 6:00 am,
30 September 1969.
Computer printouts were obtained for:
• the analyzed temperature field (T),
• the grid point values of the velocity potential (PHI),
• the grid point values of the south wind component (V),
• the grid point values of the west wind component (U).
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These printouts are reproduced in Appendix D. Each printout sheet is labeled
at the top with the dependent variable name and a power of ten scaling factor.
Each label also includes the SETS number (e.g., 5:00 am is labeled SETS = 1).
All fields were printed out on a 25 x 25 grid (i.e., every other point of the
49 x 49 grid) although the computations were done on a doubly dense net, as
noted above. In the printouts, north (Y) is to the right. Also zeroes are
printed on grid points of the PHI, U, and V fields where the topographic
surface rose above the local inversion.
In addition, graphic display was generated with an SC4020 film
writer. The fourteen (14) SC4020 frames are reproduced in Appendix D. They
show wind vectors at the output grid points (i.e., at every other point of
the analysis grid). The wind vectors are superimposed on topographic con-
tours, and regions warmer than the ocean that rise above the inversion base
are cross-hatched with grid lines. Wind vectors in cross-hatched regions
are suppressed. Winds in these regions are not computed by the present model,
Indeed, they are not needed since it is assumed that the extreme topographic
contours are coincident with wind trajectories in the cross-hatched regions.
The known general features of the Los Angeles winds are reproduced
with both land and sea breezes generated at the appropriate times. Inclu-
sion of the 6:00 am 30 September 1969 case was specifically to provide a
case for which significant portions of the ground surface were cooler than
the ocean. The analysis results in land breezes for this condition.
Although the wind speeds for the land breeze case are too low for the
vectors to be displayed at many points in Frame 14, the land breeze is dis-
played in the grid prints of PHI, U, and V. It will be noted in these dis-
plays that zeroes appear over much of the ground surface. This indicates
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that much of the ground surface was warmer than the ocean for even this
case. The warm ground region appears as the gridded area in Frame 14.
The land breezes computed for the fourteenth SET are, again, net
results. They include a mean driving wind of 0.7 raps from the SW. The
land breeze would be stronger in the absence of this synoptic component.
Winds this light are extremely difficult to define analytically and
observationally, but the use of observation to better define the mixing
depth (200 m used here) would increase the confidence in analytical results.
Gridprint output of PHI may be interpreted by noting that flow is from
low PHI values to high PHI values. The flow speed is proportional to the
differences between PHI values at adjacent grid points. For SETS = 14, the
output shows a minimum PHI at (x, y) = (37, 25); [i.e., (19, 13) on the
25 x 25 grid =37, 25 on the 49 x 49]. The location of a minimum PHI is a
center of divergence. Since flow is constrained by the inversion from
leaving the valley northward, flow spreads out as a land breeze southward,
flowing about both sides of the Palos Verdes elevation. West winds appear
near the major area of inversion at both the western and eastern borders
of the region. The west wind region at the west edge is much smaller
because the synoptic scale wind is blowing counter to the land breeze,
whereas in the east it is adding to the divergent flow. West winds at the
eastern border may be unrealistic but the analysis cannot make predictions
without data, and no data is available on ground temperatures at or beyond
the limits of the region.
In the rest of the region the land breeze is seen to be a maximum
near the coast and to be stronger and more uniform at sea than inland.
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Sharp vertical gradients of the wind often observed in extremely
stable slope wind, valley drainage, and land breeze cases also emphasize
problems in defining horizontal wind fields for regional pollution analyses.
The breeze blowing in the face of a man on the ground may be quite differ-
ent than that read by the anemometer (at, say, 20 ft) that he is tending
and could be in the opposite direction from the breeze which entrains
effluent from a nearby chimney stack.
Some boundary effects seem somewhat unrealistic. At the northern
edge of the region this is probably because the mountains and the boundary
condition prevent flow from crossing much of the north border, but this is
also the region of the most complex topography and most commonly lies above
the inversion base, so it is difficult to judge the flow features realisti-
cally for this region. The closed circulation cell that appears in the San
Fernando valley seems superficially like that observed. It is doubtful,
however, that the analysis is accurate enough in this region to trust.
The inversion does not rise to allow mixing layer flow into the
San Fernando valley until 10:00 am on the 29th (Frame 6). By 11:00 am it
has risen more and mixing layer flow is crossing much of the northern ridge
bordering the Los Angeles basin. The net flow across the northern border
of the analysis region is zero, however, because of boundary conditions
applied in the absence of data. It is unclear how realistic the solution
is near the borders of unknown temperature and/or flow.
Similarly, flow in the eastern part of the region is strongly
influenced by assumed boundary conditions there. If the region to the
east of the analysis region is warmer than is assumed, there would be a
more westerly component to the wind vectors, and flow out through the
eastern border.
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Since the cool-land drainage patterns involve extremely thin layers,
they would be most sensitive to small-scale topography in the real world
and to assumed values of empirical constant in the computer. Thus, solu-
tions for cool-land regions and/or times should be more suspect than hot-
land regions and/or times.
A magnetic tape record of the numerical results for these fourteen
(14) cases was submitted to EPA to be compared, by their computer, with
observational data and with windfields defined by several objective inter-
polation techniques.
8. Recommendations
Since the guiding of the flow by the largest scale topographic
features seems to be such a major feature of the results, it would seem
important to use the more correct gradient type boundary condition. This
assures that the flow is parallel to the topographic contours. The
algorithm for this type of boundary condition has been written, but has
not yet been included in the program.
Formulation of the boundary conditions for the thermally driven
wind seem unduly arbitrary and seems to lead to unrealistic flow patterns
in a limited section along the northern border. This could probably be
improved.
Further calibration runs could improve the specification of the
constants of the problem.
A small amount of additional programming could produce output with
above-inversion windfields in the same display. It might be somewhat mis-
leading, however, since there should be little pollutant transfer at the
19
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field intersections. That is, pollutant leaving a zone in which the topo-
graphic surface lies above the inversion should override the mixing layer,
while pollutant reaching the edge of a ground-level mixing region should
be swept into the counter-current flow in the upper half of the mixing
layer.
9. References
1 Roth, P. M., S.D. Reynolds, and P.J.W. Roberts, 1971: The
treatment of meteorological variables. Appendix C,
Development of a Simulation Model for Estimating Ground
Level Concentrations of Photochemical Pollutants^
Report 71-SAI-17, June.
2 Anderson, G. E., 1971: Mesoscale Influences on Wind Fields.
J. Appl. Meteor., 10, 377-386.
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Appendix A: Mesoscale Influences on Wind Fields*
ABSTRACT
An analysis of meso^cale influences on protind level wind fields indicates that topocraphy and the thermal
cells associated with mc^o^cale ground temperature anomalies (urban heat Uhuids and !anj-\vuter con-
tiasts^ arc the major dctciminors of hori/ontal trajector>r perturbations on scales appropiiatc tor air pollu-
tion analyse.- Simple an.ilv-es ba-ed on the divergence equalion [u:mit calculations of uiml fields for aii
pollution trajectories that appear much more iralistic than conventional objective anaKsis of surface wind
observations The anaUsi- provide? a unique objictive procedure for ical-tinie inU-.uiMiion of the conserva-
tion of pollutant equation or for the development of regional air pollution climatolosy
1. Introduction
When atmospheric winds are measured, the icsulting
reported values are on physical micro- or macroseales
that are inappropriate for many theoretical 01 applied
needs. A particular need is for knowledge of mesoscale
wind fields to be used in calculations of the dispersion
of atmospheric pollutants. ]n spite of the power of
modern computers and programming languages, it is
not practical for wind-field analyses lo press the analvti-
cal state-of-the-art. Thus, in the following work, it is
intended that t!;<- i.iiahsis shuiilel provide an an Unite,
quantitative model of the most significant known
effects, should not violate important consliaints of
neglected effects, and should be simply and economi-
cally appropriate for real applications. The analysis
presented here was developed in its original form by
the author for use in the Connecticut air pollution
simulation model (Hilst, 19681. Kxtensions to 'hcnnal
perturbations \\ ere made for the Center for the Kn\ iion-
ment and .Man (C-CM) air pollution model for the
Toronto Metropolitan Region.
The difficulties encountered in trying to measure
mcsoseale wind fields are suggested by Fig. 1. The
relevant scales for atmospheric pollution are roughly
mapped out as the appropriately grey area in this
figure. The heavily outlined Male regime-, \\hich are
susceptible to direct measurement by wind measuring
devices such as anemometers, pib.il.- and tetioon-, over-
lap very little of the regime of interest for pollution
problems.
Alternative approaches to determining wind fields on
the scale of pollution cloud,' include incline I measure-
ment and the use- of theory. Pressure iiieasurxiiients
are used lo el. fine wind field-, on a svnoptic si.dc, but
the macros'/ale "wealher" pattern-- 5,0 defined aic also
seen (Fig. 1) to be o! an inelc vant scale. ''Theimal"
fields are sometimes of appropriate scale--, but diiect
measurements of these field-, .ue: not usuallv 'i\ ailahle,
and the theory of the'se- fields as a function o: --uif.ice,
moisture and i adiation < ejiulil ion-, is not fu in e iiou^li to
allo\\ us to obtain solutions for all such theimal motion
fields. In this paper, the only thermal fields treated
are tho-^e due to "heat island" and "lake breeze"
effects. The long time-scales of these phenomena make
them significant thermal influences on pollution wind
patterns.
Suiface faction elements and their effect on boundary
layer ilow may be significant, but technical work, to date
in meteorology has not disclosed suitably simple analy-
ses appropriate to our needs for mesose-alc influences
usable in the air pollution model. Comparative analysis
indicates thy I the generally greater roughness of the
built-up area of a city creates a "friction huirp,"
analogous to a heat island in urban areas, but the
magnitude of the friction effect on wind field..-, is con-
siderablv less than the heat island effect on wind fields.
In geneial, it is onlv the horizontal variation of rough-
ness (e.g., the urban-rural contrast) that affects hori-
zontal wind trajectories. Since, icni^hness cannot be
described with precision, inclusion of fiiclional eilects
in this analysis does not seem feasible at this time.
One more factor is depicted in Fig. 1—topography.
Topographic elements are measurable, their influence
on atmospheric flow is subject to objective analysis,
and their scales neatlv overlap the scales of interest
for pollution problems. \Ve ma}1 anticipate a correspond-
ence between the scale of the topoguiphic elements and
of tin- atmospheric motions they induce. Therefore, a
call.ulation of low-altitude flow over a given topography
should give at least a component of a real wind field
th:tt would be relevant to pollution and other mcsoseale
aiuth ses.
It would seem that thermal, topographic and fric-
tion.il eilects could, to a reasonable appio\imation at
le'asa, be decoupled. In the- following an.'.lysis, frictional
cllecis a;e ignored, and thermal and topographical
el'cMs are each treakd separately. The solutions are
added io obtain the' nel wind-field disturbance. The
disturbance he-Id added to the obseived or assumed
--\ iioplii uinel field \icld-, the net cal< ulaled wind.
* Manuscript by G.E. Anderson (GEM), reprinted from Journal of Applied
Meteorology, Vol. 10, No. 3, June 1971, pp. 377-386.
21
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JOL'KNAI. OK Al'I'f. IK. I) M M 'I K I) K () I. I) G V
Vol L'MK 10
2. Analysis
ii. Typographic i^iinl Jiclih
It was intended to develop u technique for defining
mesoscalc wind lields that would be feasible and eco-
nomically practical for use in routine operation of a
computerized pollution model. Therefore, it \vus »>M.-n-
tial to determine those analytic featuits of gieatesl
significance. The topographic anuKsis presented here
specifically considers conservation of ina^s only. Cu tain
aspects of dynamics .ire used but. the momentum
equation is not solved. The energetics of the problem
are not considered. This approach seems reasonable
in light of the remarks of the previous .section. If the
momentum (friction) and heat exchanges between the
atmosphere and the surface are not considered, the
impenetrability of the surface is its most significant
characteristic. \Ve write, then, the three-dimensional
continuity equation for an incompiessible atmosphere,
assuming a limited vertical motion, so that pressure
changes are small:
dll dv du
—+—+ —=0,
dx dy dz
(i)
where .r, y, z are the orthogonal mean wind-oriented
coordinates, and H, v, u are the corresponding velocity
perturbations.
ff we are concerned with the horizontal wind field
averaged over the depth of the pollutant cloud, we may
write (1) as
f
/
Jk
dw
(2)
where V i-, the gradient vector in the hoii/.ontal plane,
V the total pi rliirbrd velon'tv i'i the horizontal plane,
Si the local altitude of the smf.u •_, // the upper bound of
the disturbed ail, and the ovcibar indicates an average
o\ er 3.
K.\pre--ion (2) may be integi.tted and the result
-implilied b> noting that
(//—//,!--//, if the wind-field disturbance h thick]
compared to toponi.iphical variations
ic(H) ~0, i.e., the topographic effect is not felt
.•bo\e the height //
:.'(/;) ~ LT- V//, v\here II is the unperturbed mean
velocity
(3)
\\'e also define
V = V0', where ' is the potcntialjunctioii of the
perturbation.
Then (2) becomes
1
//
(4)
(5)
If, now, velocities are normalised by the mean wind
speed [', h is normalized by the layer depth //, and
the divergence by its suiface value V:(h), i.e.,
V =U'U,
h* =h'H,
we obtain
= v V/;*.
(6)
OOOOO O O
Pollutant clouds
10
Horizontal scale—meters
KlG. 1. Srale ranges of significance for aUnojihcrir boundary |a>'er
pluToincn.i ,ind me
22
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JUNE 1971
G K K A I. 0 K . A N D E R S () X
379
Eq. (ft) is an expression for Ihr mean disturbance to
the wind field over the layer which is disturbed. If we
are concerned with tracing the flow of pollutant, we
would wish to know the mass-'icciglitrd mam disturbance
to the wind field.
Classical Indrodvnamie calculations (see Lamb, 1932,
and Shapiro, 1953) show thai the potential disturbance
due to topogiaphic elements is felt with little diminu-
tion to heights that arc of the order of the dimensions
of the elements (i.e., a hill's uidins of curvutuie or the
spacing between ridges); thus, the topographic dis-
turbance should be substantially constant ovei depths
of significant pollution.
b. Mean isiitJs
To generalise the calculation, and to avoid the re-
quirement of solving (6) for every/ mean wind field, the
only input wind fields used were a unit west wind
(yz=\, Pj = 0) and, separately, a unit south wind
(i>,—Q, i'j, = l). If the mean wind fields are uniform,
Eq. (6) is linear, and perturbation fields can be ob-
tained by scaling and adding the fields due to each of
the unit component winds.
In some cases the synoptic-scale patterns may be
small enough to warrant the definition of a non-
uniform mean wind field. In these cases, it is a simple
matter to assign vx, vb mean wind components to each
calculation grid point.
c. Topography
Topographic heights h are icquired at a suitable
array of grid points.
For the Connecticut analysis, a single, low-pass
smoothing of the topographic data was used to remove
regional-scale topographic ''trends." The net topog-
raphy used in the model, then, is the local grid point
height above or below the topographic "trend."
Since Eq. (6) relates the hoiizonlal flow divergence
to the topographic gradient, the wind-field solutions
using unadjusted topography will include divergence
at all scales for which topographic gradients exist.
Modeling of the largest scale (i.e., scales comparable
to the dimensions of the region) perturbation-, of the
wind may be quite unrealistic. Topographic effects at
these scales depend heavily on lopograpln be\ond the
region's boundaries. Topographic wind-field perturba-
tions on the regional scale are not geneialK significant
for pollution modeling in an\ case since they would
superimpose a weak convergent or divergent wind field
over the entire region. This would merely affect the
overall space-averaged conuntration levels bv a vcrv
small amount. In Connecticut there is an overall
increase of mean height abo\c sea level from .south to
north. The hill.s and vallt\-, then, represent depai lures
from the local mean height.
iJat v conditions
To solve (6) the velocity perturbation potential y specification of a zero potential on the
boundary. This coi responds to the assumption that the
mean, synoptic wind pievails outside of and on the
boundary but is pertuibcd within the region.
c. 27. crmallv ilri: en ^ i'/;,;'j
The mass conservation equation (2} piovides a
faiih good model of the effect of nicsoscale thermal
cells on hoiixontal wind-field patterns. The relevant
growth or decay time scales are long with respect to
dispel sion integration time scales, and the vertical
extent of suih thermal cells is often large with respect
to the pollution Liver thickness of interest; thus, the
theimal effect is to produce a quasi-steady, quasi-
hoiisontal wind disturbance in the near-ground layer.
The thermal effect is assumed to be independent of
the lopogiaphic effect -note that Fqs. (o) and (7)
are both linear -and thus, the thermal effect is calcu-
lated for a flat surface. On a flat suiface the vertical
velocity at the surface is zero, but surface temperature
anomalies produce finite vertical velocities at the upper
limit of the polluted laves (Fig. 2). Fq. (2) then reduces
to
since
at the top of the layer; w* is assumed to
depend on Ts, the ground temperature (a function of
x and y) and f, the spatial mean value of Ta. Without
solving the dynamics of the thermal cell, a large mea-
sure of realism may be obtained by simpK setting
A(T,-T)
7/o
(8)
where .1 is a constant of proportion:ditv to be deter-
mined from observations.
The scale factor A in (8) represent* the sensitivity
of the wind field 10 the temperature potential. It must
be evaluated experimentally. Experimental measure-
ments of the Toionto heat island etlecl reported by
Findlay and Hirl (1969) were used to determine A.
Cia'tKs' theorem for souice-sink fields relates the flu\
acros/- a closed buundarv to the total divergence
(bouue strength) inclosed; thus,
f n.v,j7'= f
J i' J n
where /' is the perimeter, R the ana of the region and
n n unit vector normal to the perimeter.
23
-------
380
JO I" UN A I. 01- A IT I. I l-ll; M P. r F, O k O I.O G Y
t: 10
Since (8) relates V-V (and, hence,
7',, — T, we have
to .1 and
-i r if v" /f>\
-= / n.V,/P/ / (fa-T)tlR = --- _ ( -),
// y/. / ./* (T,-r)\R/
(in)
where {'„ is the outward normal component of wind
across the boundary, the caret represents an average
over A', or P, and the overbar is an average over some
area that is large with respect to R.
Thus, .1 may be determined from a single deteimina-
tion of the radius of ina.\iinum inilow associated with a
given temperature field. The case studied by Findlay
and llirt indicated a maximum inflow velocity of 1.7
m sec"1 associated with a temperature potential of
~2.5C. With the temperature field characteristics
postulated in the next section, these data give a value
of A/II =0.1. The precision of this result obviously
leaves something to be desired but Findlay and Ilirt's
comparison with Gold's (1956) theoretical results
should be valid for lhi< result also. The result should
be more effective than anemometer \\ind readings to
sort out thermal and topographic wind-field modes.
As a minimum, this linear relationship centers up-
drafts over "hot spots" and makes the intensitv of a
thermal cell proportional to the energy input. Advec-
tion of the thermal patterns has not been accounted
for, but could easily be included in multi-layered models.
f. Thermal patterns
When the wind generating routine was developed for
the Connecticut air pollution simulation model, the
scale of the entire state was large compared to urban
and coastline effects. For Metropolitan Toronto, the
uiban development and the lake front are both signi-
iicant to the scale size oi the region. This section
addresses the heat island and hind-water interface
patterns which were analyzed only for the Toronto
region.
In addition to linear superposition of thermal and
topographic wind fields, it is assumed that distinct
thermal effects can be separated from each other and
that these effects are also additive. By identifying in
lilt; Toronto region, for example, separate "city heat
island" and "lake brec/.c" ell'ects, suitably repiemula-
tive ground temperature patterns ma\ be established for
each by Using a minimum number of parameters.
If. Heat island
For a heat island, the temperature is assumed con-
stant over the heat source area and is assumed to have
different (lower) values at a suburban strip along the
lake shore and on a perimeter that is far enough away
to be unatfeclcd b\ these heat sources. These tempera-
tures are used as boundary conditions for the solution
of the La Place equation
V2rs = 0, (11)
to determine the temperature field between the heat
island and the remote perimeter.
The only free parameters are the center city tempera-
ture and the remote temperature (the suburban tem-
perature anomaly is assumed to be propoi tional to
that of the urban area). This pattern, combined with
the lake-land temperature field described in the next
section, reproduces the major characteristics of the
climatological temperature fields observed for the
Toronto region (Findlay and Hirt, 1969; Munn et al.,
196-1.) The actual wind-field computation assumes a
unit (city-remote) temperature. The perimeter is
assumed to be experiencing a pure inflow; thus, it
should be a line of non (horizontal) divergence. Ac-
cordingly, is zero on the perimeter as a boundary
condition for the solution of the wind potential equation
(
-------
JUNE 1971
G E R A 1. U E . A N O E R S O X
381
Ty at K ing Creek -^*
Heat island
Toronto International
Airport ~~*
I at Islington
Coarse grid lak*? breeze rvgiou-^
0 Ilef. U-mp. locations for
(Mi-aMU't«ri?ed thermal fit-Ms,
Toronto region v .^f
*"* "
•— ———»O —i
5 c
V f \
Fine topo. region^. *
FIG. 3. Layout of regions for topographic and thermal wind-field anah ses.
A. Lake breeze
The surface temperature is assumed to have a con-
stant value over the water and another constant value
over the land.
Since the thermal circulation cell analyzed is larger
than the dispersion model region, finite values of the
velocity disturbance potential should be expected on
the region's boundaries. Thus, boundary conditions
for the solution of (8) depend on the wind field outside
the region. Further, the scale of the external effect is
large compared to the dimensions of the analyzed
region; therefore, the effect of enors in the boundary
conditions might be expected to be observable well
inside the region. That is, the ''window frame" may be
quite wide for the case of Metropolitan Toronto.
To provide more realistic boundary conditions, the
thermal cell problem is solved on a much coarser grid
for a much larger region. As an example, the region
used in this study extended beyond the south shore of
Lake Ontario and comparable distances in the other
directions, as depicted in Fig. 3. Since the large region
ought to more nearly match the extent of the overall
thermal cell and since the Toronto region lav well in
the interior of the larger region, the coarse-grid solution
was deemed to provide realistic boundary conditions .
for the inner, fine-grid region. The ground temperature
distributions assumed for the coarse-grid problem
consisted of a constant tempeialure on the lake and a
different constant lempcratuie over the land. The lake
geometry used is superimposed on a. true outline of the
lake in Fig. 3. Data required for the Toronto region
consist of temperatures at the lake, and far inland.
3. Limitations and extensions
The analysis applies to problems that: 1) are sub-
stantially steady during many model time-steps, 2) ex-
hibit spatial variability of topography or ground tem-
perature at scales from regional-scale to grid-space-
scale, 3) exhibit absolute topographic slopes that arc
much less than unity, 4) consider vertical scales small
enough that pressure is substantially constant, and 5)
consider advective velocities that are much larger than
the relative velocities of diffusion across streamlines.
The major arbitrary assumptions are: 1) that the
advective transport of pollutant can be meaningfully
determined by a "bulk velocity" even though the
advective trajectories vary with altitude (for "thin"
pollution layers or "thick" velocity perturbation layers
this assumption is irrelevant); 2) that local vertical
thermal velocities are proportional to local ground
temperature anomaly; and 3) that the ground tempera-
ture distribution can be adequate!}' described by a
limited parameter (variable data) pattern derived from
climatology.
The constant pressure limitation suggests that this
analysis is inapplicable to mountainous regions. It is
suggested that replacing Kq; (1) with the compressible
form of the conservation of mass equation would permit
considi-ialion of (.uses for which the Houssinesq appro\i-
25
-------
382
JOCKX.U. or Ai'i'Liri) \i r.'i r.o i' 5.
26
-------
JUNE 1971
GERALD E. ANDERSON
383
FIG. 7. Net topography relative to a highly smoothed "mean" surface
for Toronto region.
dimensional arrays ma)' be controlled by single ANAL only a few hours, and the program requires only a few
70 statements. For example, solution of a Laplace or seconds of 1108 computer time per time step.
Poisson equation as required in this work is effected by The topographv of Connecticut is shown, for refer-
a single ANAL 70 statement. Programming (of a first- ence, in Fig. 4, while Figs. 5 and 6 show the comparison
cut without de-bugging) of the total analysis requires of the present scheme with a conventional analysis of
I'"jO. 8. 1'oU-htia] of topographically induced v.aid disturbance for Toionto
region due lo unit \\tst uiiui
27
-------
384
JOCKN.M. OF A I1 I' I. I 1C I) M K '1 K O 1«) I. O C. Y
VOI.L-MK. 10
FIG. 9. Heat island temperature distribution for Toronto region.
surface wind observations for the state of Connecticut. produces spurious closed circulation cells and much
Fig. 5 shows a conventional objective analysis which large-seile wave structure that is not consistent with
fit values of streanifunctions which weic determined observed wind rields above the surface layer. It shows
f or each of 15 data stations. Fig. 6 shows the topographi- no structure consistent with the topography. The
cally determined wind field. The ''objective" technique topographic analysis, on the other hand, shows effects
FIG. 10. Heat island di«turbaiice potcntbl for the Toronto region.
28
-------
JUNE 1971
GERALD K . AN D KK S O \
385
FIG. 11. Lake-breeze disturbance potential for Toronto region.
only on the scale of the Berkshire (western) and eastern wind field, and the heat island and lake breeze tcmpera-
hills'and the Connecticut River Valley. All disturbances ture and potential fields for the Toronto region. Fig. 12
are small in the Long Island Sound and shore area, shows a net wind field for the specific case of U = 4i+0j
Figs. 7-11 show computer-generated net (filtered) (m sec~'), a \ve»t wind, 7'.u = 2C = 7\and — T,^c, Te
topography, the lopographicallv induced potential =\C — Tcny — T,Kmoie, and crz — 150 m.
FIG. 12. \Vest-win
-------
386
JOURNAL OF A PI'I. IK I) M I-. T K O K O I, O G Y
Yol I MI, 1(1
The net wind field is calculated according to
where
(14)
For the Toronto case the topographic effect is teen
to be minimal. There are few topographic features in
the region with slopes on the order of oV_\ (A is the
grid spacing). From (8) it may be seen that slopes
of this order are required to produce velocity changes
that are a significant percentage of the mean wind
velocity.
The bluffs along the lakeshore and some ravines
more or less transverse to the coast are quite steep and
represent significant height changes. Each is, however,
a linear feature with transverse dimensions less than one
grid spacing. As discussed in the previous section, sub-
grid-scale features are effectively filtered and thus con-
tributed little to the computed wind-field perturbation.
To more cleailv sre the- effect of the-e topogiaphu
features, a smaller region was defined encompassing
only the urban center and some of the coastal bluffs.
The dimensions of this area were one-third of those of
the previously defined region, and the topography was
read on a grid three times finer. The array unit dimen-
sions were thus the same as for the large region. Stronger
perturbations were noted with this calculation, but
they were, naturally, confined to the immediate vicinity
of the topographic disturbance. The effect on a trajec-
tory crossing the disturbance was minimal. It may be
noted that wind-field divergence is produced only by
topographic gradients parallel to the mean wind, and
therefore wind along a linear feature will produce no
effect. If wind crosses a ravine, it diverges on the
upwind bank and converges on the opposite slope.
Thus, the net effect is not strong unless inegularities
in the ravine topography meet the scale criteria dis-
cussed above. Wind crossing a bluff or cliff line experi-
ences a simple expansion or contraction, but the stream-
lines downwind continue on parallel to the upwind
direction.
Although the apparent changes in the «ind field aie
small, and change the local trajectories little, the effect
on long-distance trajectories can be significant. Since
small perturbations integrated over long path lengths
can produce large displacements, small changes in
divergence patterns have much \ote inlluence near
the beginning of a trajectory tl\ui thev do further on.
The thrrmalK induced wind held* are gc-nnallv ob-
served a^ coinponi nls of mole ( ompli \ wind in ld-> and,
as discussed in tin- Introduction, observations are not
generally valid in defining mi so.si ale wind Ik Ids. There-
fore, tin re is litllc physical evidence upon which the
present calculations may be judged The patterns stem
theoretically xiti -fucloiv and are consistent with such
observations as i \isi. Validation of the pollution dis-
persion model would be, perhaps, the best test, of the
wind-field analysis.
5. Conclusions
An objective analysis of mesoscale wind Helds has
been presented. The analysis makes use of precisely
known pin sit al characteristics (topography) and the
geographic distribution of homogeneous surface tem-
perature regions,' lo reduce a previous dependence
upon observational data of doubtful validitv or appli-
cability. Topically, as for Metropolitan Toronto, the
only temporal data requiicd are the mean, s\ noptic
scale surface \\ind, and surface temperatures at three
prescribed locations.
The wind Fields computed by this analysis appear
much more realistic than do wind fields produced by
other objective anahses. The analysis is computation-
al!} simple, and the parameterized .lesults can be linearly
combined as required for real-time, forecast or hypo-
thetical caac-s. .Regional eliinaiolog} would depend only
on synoptic-scale wind roses and thus pro\ides the
only known objective scheme for regional air pollution
climatology.
REl-F.KEXCES
Fmdla\ H. F and >f S. Hirl, 1U69. \i\ nrbnn-indnred rneso-
circulation. .\lmnsplicric Environment, Xcw York, Peigamon
Press, Vol. 3, 537-542.
Gold, K , 1956. Smox—The rate of influx of surrounding cleaner
air II cat/in, 11, 230-232.
Hiht. G R , 1968. An air pollution model of Connecticut Froc.
IBM Sci. Ci'inp. Sy»:j>.. \\~iiUr and Air Resource \[aiuge-
nicnt. 11!M Data Processing Division, White Plains, N. Y.,
251-J71.
Lamb, Sir Hoi ace, 1932. Uvdri'dyiiamics. Xeu York. Dover
Publ , p. 76.
Munn R F , K f.. Tilus and K J \\ ikon, 1964: A pri-limmary
c^imialc <>f th<- m\erMon climalolouv al'"»n^ the Toionto
laki-hori--. Mc'tcfirolo'.'ic.il lirarrh, Department of Transport,
Canada, CIR-U:.?. 1 FC 5o'>.
Sh;i[)iro. Archer H., 1933" The Pyn>irnics and T/ifrntt'dyHdniics of
Coinfic^ililc Fl.ii'J F/o;^, \"ol. 1. New Y"ork, Ronald Press
163 pp
30
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Appendix B: Los Anpeles Windfield ANAL70 Program Specifications
Definitions of required arrays
GRID is basic analysis grid of 49 by 49. Point (1, 1) is at
118° 37' 13" W, 33° 34' 53" N.
GRID' is a grid staggered with respect to GRID. Only interior
points are included.
GRID" is a grid staggered with respect to GRID'. It's inter-
sections are thus on GRID intersections, but since only
points interior to GRID' are included, the peripheral
points of GRID are excluded.
Input Data
Read the data that is the same for all sets -
X (PLACES - vector of nine (9) X grid locations of
temperature observing stations measured
east of western edge.
Y (PLACES) - ditto, nine (9) Y locations measured N of
southern edge.
H (X, Y) - 49 x 49 array of grid point topographic
heights.
• Repeat • steps for each set.
• Read data for the current set -
VARIABLES
T (PLACES) - vector of temperatures observed at 9 places.
NW (X, Y) - temperature at sea and at NW corner;
i.e., at (1, 31) and (1, 49).
SE (X, Y) - temperature at sea and at SE corner;
i.e., at (43, 1) and (49, 1).
CONSTANTS
SEA - sea surface temperature
H1 - height of top of inversion (over sea).
T1 - potential temperature at top of inversion (over sea)
Us - west wind component at sea.
V - south wind component at sea.
SL
31
-------
* * * * Compute Surface Temperature Distribution * * * *
• Subtract 1/3 of adiabatic lapse (i.e., from sea level to station
altitude) from observed temperatures, giving
estimated temperature for similar geographic
location and similar surface thermal properties
if the surface were at sea level.
• Define known data temperatures at proper grid points in GRID -
T(SEA) - temperature at X, Y's for which H = 0;
i.e., at all ocean gridpoints;
i.e., IF H(X, Y) = 0, T(X, Y) = SEA
T(SE) - linear increase in temperature from coast to SE
corner along southern row;
i.e., T(X, 1) 49 = SEA + 2—2- [T(49, 1) - SEA]
43 °
T(49, 1) = T (between SEA and Santa Anna)
T(NW) - linear increase in temperature from coast to NW corner
along western column;
i.e., T(l, Y) tt9 = SEA + ^|i [T(l, 49) - SEA]
31 1°
1(1, 49) = T(Burbank)
T(N) - constant temperature along northern row equal to
that at NW corner;
i.e., T(X, 49) = T(l, 49)
T(E) - linear decrease in temperature along eastern column
from NE corner to SE corner;
i.e., T(49, Y) = T(49, 1) + |jp [T(49, 49) - T(49, 1)]
T - modified observed temperature at the 9 data stations;
i.e., At PLACES; T(X, Y) = T[X(FLACES), Y(PLACES)]
NOTE: Temperature not yet defined at remaining points.
Temperature field initial fit
Keeping above defined temperatures as boundary values (internal
and peripheral), solve V2T = 0 at remaining points. Note that
keeping ocean points at T(SEA) effectively moves the boundary
to the shore.
32
-------
Compute V2T at the 9 observing stations; i.e., at X(PLACES), Y(PLACES).
(Note V T will be zero everywhere else except at shore; do not compute
V2T at shore).
Repeat • • steps 10 times to smooth V2T.
Smoothing by interpolation spreads V2T, the curvature
of the T field, so that the total curvature is conserved,
but is spread over an area around data points. The limits
of the spread field expand radially one grid point per
double interpolation. In each interpolation the function
at a point on one grid is the average of the function values
at the four (surrounding) nearest points of the other grid.
• • Interpolate V2T onto GRID.
• • Interpolate V2T back onto GRID; F (X, Y) = V2T smoothed.
• Re-solve temperature field from V2T = F (X, Y).
• Add 1/3 of adiabatic lapse (up to altitude of each X, Y gridpoint)
to each gridpoint temperature. Result is temperature field.
T(X, Y) = T(X, Y) + .002 H(X, Y)
) * * * * Compute Thermal Wind * * * *
Compute
(T-SEA)/(T,_SEA)
H1 - H I = AH (X, Y)
AH is the depth of the atmospheric mixing layer.
• Generate a mask array (GRID) with 1's where the mixing depth is
negative (i.e., the topography penetrates the inversion base)
and the temperature exceeds the sea temperature (i.e., if T - SEA
is positive, the base of the inversion must be above sea level).
MASK is zero elsewhere on GRID.
• Set AH <200 to 200: i.e., set a minimum AH.
• Compute thermal forcing function
where MASK is zero
FT(X, Y) = - <<(T-SEA)/jtAH/2)
33
-------
The constant empirically relates the updraft to the temperature;
a =
w
T - SEA '
Compute thermal boundary conditions.
1) At W and S boundaries, assume all divergence is along boundaries
Divergence across these boundaries is zero. These are boundaries
along which significant thermal gradients exist. Isotherms are
substantially normal to the boundaries. There is no observational
data for thermal gradients across these boundaries.
2) Assume divergence along N boundary is zero, since N boundary has
already been assumed to be isothermal (except for small altitude
effect).
3) Assume velocity (V) across N boundary at X = 25 is zero. Thus
N boundary is a pure updraft zone of maximum convergence. This
assumes that surface temperatures north of the region do not greatly
exceed those at the northern edge of the region. Observational data
is absent outside the region.
4) Assume the intersections of the coastline with the W and S bound-
aries are at equal potential. Solve (integrate V2$ = FrjO for
each boundary:
at W boundary:
9$
$(1,1) = 0 ; —- (1,49) = 0 ;
dy
49 y y
.'. $(1,1) = -(y-1) f FT(25,y)dy + J J FT(l,y)dydy ;
1 11
at N boundary:
$(x,49) = $(1,49) ,
i.e, constant value from NW corner is used along N;
34
-------
at S boundary:
$(1,1) = 0
$(43,1) = $(1,31) ,
i.e., $ is equal at coastal points,
49
.'. $(x,l) = X-^1 - 30 y* FT(l,y)dy +
1 '11
43 x xx
~ If FT(x»1)dxdx + Jj FT(x»Ddxdx ;
31 y '
i i
i i
at E boundary:
$(49,y) = $(49,1) + [$(49,49) - $(49,1)]
49
j
y y
•— (49,y)dydy
1 1
49
48
49 y
/ /
Solve Poisson equation V2 $ = F for thermal wind potential.
) * * * * Compute Topographic Wind * * * *
e Add synoptic (at sea) surface wind to thermal wind
U+U,_
s T
x
V -
Vy$ .
« At inversion mask, sec AH = -600 to represent extreme damping of
vertical motion.
® Compute gradient of topographic height, V(--AH/2).
o Compute local vertical component of surface wind due to topography.
V$ • V(-AH/2) -
35
-------
o Set minimum of AH/2 to 100.
« Compute topographic forcing function w /AH/2 = F
e Compute net flow boundary conditions
*_- U X + V Y + *_
BC s s T
« Solve Poisson equation V2 = F,rnp for resultant wind potential,
• Compute gradient of resultant wind potential to give resultant
wind vector.
V = V$
• Return to beginning of loop
End
36
-------
Appendix C: Poisson Surface Data Fitting Technique
It was desired to provide an interpolative (surface fitting) scheme
for defining two-dimensional fields consistent with data observed at a sparse
set of randomly located stations. The specific application for which an inter-
j
polaticn was desired was the surface temperature distribution in the Los Angeles
basin. The mesoscale windfield analysis described in the body of this report
requires a surface temperature distribution as a forcing function for the
thermal perturbation of the wind.
In the Los Angeles experiment, surface temperatures were taken at nine
(9) observing stations. Although the stations were not located on any regular
grid pattern, they were well spread over the 50 x 50 mile experiment region.
A significant portion of the experimental region is ocean surface. Although
sea surface temperature observations were not available, sea surface climatology
for the region shows the temperature is exceedingly steady in time and uniform
in space. The assumption was made that all ocean grid points were at 64°F
during the test period. Four general types of interpolative techniques were
noted that have been used widely for analyzing gridded fields from observed
data. They are -
e Statistical fits - e.g., "least squares" fits of the constants
of a chosen functional form (often plane surfaces).
e Influence factor fits - the value of the field at any grid, point
is the sum of "contributions" from each data point, where each
contribution is the value at the data point weighted by some functional
of the distance between the data point and the grid point in question.
37
-------
• Spectral fits - whereby a family of surfaces of a periodic
functional form (sine and cosine waves for Fourier analysis)
is spectrally weighted to provide a desired degree of
approximation to the data points. Spectral filtering is
often used to limit the family "membership" and/or to specify
/
the data fitting accuracy required.
» Boundary value fits - the value of the field at any grid
point is the solution of an equation given the data points
as boundary values.
Each of these approaches offers advantages for certain classes of
problems. Statistical fits are used where there are many more data points
than there are acceptable degrees of freedom in the fit surface. Influence
factor approaches seem appropriate when they represent a conceptual model;
that is, the field at one location is seen to actually depend on the field
shape at points beyond the nearest neighbor data point. Spectral fits are
generally used when there are not only many more data points than acceptable
degrees of freedom, but there are also many realizations of each degree of
freedom (i.e., many wave lengths) within the analyzed region.
Several facts and assurnptions about the surface temperature observations
in the Los Angeles region suggest that the last scheme, the boundary value fit,
would be more appropriate than the.other schemes described.
It is assumed here that "noise" in the data is not great, and need not
be filtered. Certainly the observational noise is very small - thermometers
are very accurate - while sub-grid scale variability of the temperature field
38
-------
does exist, subjective examination of the data suggests that for this appli-
cation the variability is much less than the temperature differences between
'observation stations. Thus, we want a surface that goes exactly through the
data points, introduces no degrees of freedom not required by the data, and
allows each data point to influence the field very strongly in its own
neighborhood.
The scheme developed fulfills these requirements. The equation
V2T = F(X,Y) is solved with T
held fixed at all known or assumed interior data points and at peripheral points,
Specification at data points allows a perfect fit of the data while the form of
the equation and the specification of F(X,Y) (given below) assure that only
enough degrees of freedom to fit the data are allowed. Specification of
peripheral values lends an arbitrariness to the scheme, but seems consistent
with the view that no analytic scheme can be known to be correct near a region
where data is not available. Therefore, boundary values which simply preserve
the essentials of the interior of the region do the least violence to our
sensibilities.
It is desired to define a forcing function, F(X,Y)9that reduces the
surface curvature, V2T as much as possible in the neighborhood of each data
point while allowing "smooth" transitions between neighborhoods. That is,
neighboring points should determine surface slopes in intervening regions,
but surface curvature should be small everywhere. To accomplish this, we
first solve the Laplace equation -
V2T =0 (T specified at data points and periphery)
and then compute the Laplacian at the data points (it is necessarily zero
39
-------
elsewhere). Repeated smoothing of the point values of V2T is carried out
by an operation which preserves total curvature. This then produces a
distribution of surface curvature which, in a region about any data point,
is proportional to the deviation of that data point from a mean surface.
The smoothing algorithm used first defines the value at the center of each
grid cell to be the average of the values at each corner of that cell. Next,
the value at each grid intersection is the average of the values at centers
of the four adjacent cells. Each pass through this smoothing operation
spreads the same total surface curvature to a region one grid square larger
all around. The smoothing is repeated for a number of times equal to the
average spacing between data points.
Trials of this technique on Los Angeles temperature data gave
temperature distributions qualitatively consistent with subjective analyses,
with somewhat more detail, i.e., smaller scale content, in the patterns.
A typical computed temperature field is shown in Figure C-l.
Several manually drawn isotherm maps from the same data all showed
much the same qualitative characteristics, but the variations between manually
contoured maps were comparable to the difference between each and the analyti-
cal map.
Required computer time for a 49 x 49 grid (2401 grid points) with
an ANAL70 program on an 1108 is about 10 sees.
40
-------
-2
Figure C-l. Isotherms (°F) * 10 in Los Angeles Basin
41
-------
Appendix D: Computer Output
Contained herein is a set of results of windfield analyses for thirteen
(13) consecutive hourly periods from 5:00 am to 5:00 pm on 29 September 1969,
and one for 6:00 am 30 September 1969. The first sheet is a listing of the
ANAL70 program. The next 56 sheets are reproductions of computer printout
of (x,y) gridpoint values of four variables for each time period. Each
sheet has a computer printed label containing:
1) the number of the case (SETS = 1 is 5:00 am, etc.);
2) the variable name -
T = temperature field (°F) fitted to the 9 data points,
PHI = computed velocity potential,
V = the south wind component in m/sec,
U = the west wind component in m/sec;
3) a power-of-ten scaling factor; and
4) the names of the independent variables, x and y, in each. case.
The format for all printouts is the same. The 25 x 25 array represents
the values of the variable on a grid consisting of every other computed point,
North is to the right. On the PHI, U, and V printouts, zeroes are printed
where the topographic surface lay above the inversion base, a.nd_ the ground
temperature, simultaneously, is above the sea surface temperature.
Finally, there are fourteen (14) computer-drawn maps, for the same cases
showing -
1) topographic contours at 500 ft intervals, the first being
the coastline;
2) grid lines where inversion restricts flow;
3) wind vectors at alternate grid points - scale may be
determined from grid-line interval (vector one interval
long represents a wind of one m/sec).
42
-------
T 4 f t 4X4^. , «/ 4. 4 . . * If ^4 | 4 . ^ . * -4 . < » 4
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.b40 .o40 .6,0-.ol;- .6,0—640 .640 -640 -640 .641 .643 .616 .651 -657 .664-673 .677 -.678 .684-.698 .705-.706 .740 .732
.640 .olO .640 ,o4p .C-lC .640 .640 .640 .639 .MO .642 .645 .649 .654 .660 .f.69 .675 .678 .6^3 .689 .696 .701 .712 .756
.04o ."40 .040 .640' .o4o .640 -6i9 .6^8 .637 .63?-.638 .640 .643 .647 .652 .657-.665 .669 .673 .680 .687 .696 .731 .755 .772
.64U .040 .o4g .640 .64f. .649 .6J8 ,6j6 .635 .6^5 .&J6 .638 .641 .645 .649 .654 .6f>l .663 .668 .676 .684 .706 .751 .767 .776
.t.4o-.040 ,o40 .040 ,e»4c .f'00 ,6j6 ,6j4 .633 .6^3 .634 .6J& .638 .642 -.648 .653 .6H6 .661- .666-.672 .683- ,738 .75=; .717 .772
.04t, .b'tO .u4u .6i« .63,. .6^b .6^4 .6ji .632 .63? .631 .633 .637 .642 .657 .667 .656".660 .664 .6'Q .683 .713 .739 .735 .772
-,t>4u .040 .040 .<>37 .o36 ,6j4 .632 .6jl .t>30 .6jO .629 .630 .t-33 .615 .6S8 .657 .656 .660- .665 .670 .681 .724 .713 .735 .772
.olu -o'lO .oJ7 .ti5 .1.3.; .6^2 .6jl .6,;9 ,u27 .6^8 .ft2o .635 .620 .645 .655 .653 .657 .662 .666 .673 .691 .743 .717 .727 .761
- ,o4(J ,030 ,o3b .6.13 .o3/ .kj,?_ ,&j) .6^8 .620 .6^9 .fjl .636 ,637 .657-.656 .656 .664 .665 .669 .675 ,6«9 ,715 ,736 ,7?6 ,756
.t>4J .616 .oil ,fc^9 ,03, .f-jj .&j3 ,6iE .632 .6i5 ,^3U .f43 .649 .666 .659 .663 .677 ,669 .674 .679 .703 .713 .73? .716 .740
.039 ,o22 .6^0 .6i>r- .6j4 .6J7 ,6^V .64l) .643 .645 .649- .657 .669 .670 .667 ,671 ,6f.l .679 .616 .704 ,725 .713 .716 .744
.646 .^i? .fi^ ,o3, .6^'! .fa,) ,6sb .&47 ,6i,l .c-,5., .656 .667 .671 .674 ,67i ,67'i .582 .C.C2 .6-17 ,7n9 ,724 .730 .7?! .752
.o4i> .1.41 .lo? .o'»1 .*"i;< ,t3,P ,d^l .t.56 .6ol .r'in .665 ,*77 .679 .681 .682 .6«1 .6^3 .6"8 ,6^b .716 .7?4 .732 .738 .770
58
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-7U9 ---L.A. SilNDFNy.O ANALYSIS - - — ANAL70 PAGE- ... _ 2—23-MAR 73 1B;((3:OE
OR10r>RINT OF PUi ( X. Y) IN UNITS 1.0000+01
. 062. ,j94 .Ii:6-.i5d -.19o -.222-.253. .234 .316 .347 .370 ,tlO-.'*'tl .173 .509 .000 .000 .000 .000 .000-.000 .000 .000 .000
.087 .ill .136 ,16o .Ia5 .210 «23b .263 .269 .316 .343 .369 .395 .1(20 .441 .000 .000 .000 .000 .000 .000 .000 .000 .000
• l)9t .111 «i2ti . I4b .16.? .Joe .1*9 .219 .2"*! .263 .28b .3o7- .326 .349 .370 .390 .000 .000 .000 .000 .000 .000 .000 .000-.000
• I2o .130 .l4o .Ib5 .164 .173 .1(35 ,2jo .216 .236 .254 .271 .287 .304 .321 .3tO .000 .000 .000 .000 .000 .000 .000 .000 .000
• l5d .161 ..±63 .104 .164 .Io4- .lu7 .179 .195 ,2'll .224 .236 -.?46 .258 .282 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
• l9,j ,lQ6'.j.Bl .175 .105 .ID? -1U .IbO -174 .Iu7 .]9j ,?03 .208 .000 .000 .000 -OnO -000 .000 .000 .000 .000 .000 .000 .000
• ^Zj. .212 .202-.lii& .16<; .H3 .0-iO .OoO-.iob-.163 .173 .000 .000- .000. . 000 -,-000 .000 .000 .000 .000 .000 -.000-,000 .000 .000
.^S^ .240 .<^b .?-ii° .iS.i ,!H£ .030 .0U0 ,U00 .01.0 .p03 .003 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
.c8i ,2b9 .^53 .?-33 ,io3 .C-OC -000 .O^O-.^OO .0U3 'POO -000 .000 -.000 .000 .000 .0^0 .000 .000 .OflO .000 .000 .000 .000 .000
.31j .300 .c:66 .20B .^42 .Don .QJO .OjO ,(,CO .00" -000 .000 .000 .000 .000 .000 .QfO .000 .000 .000 .000 .000 .000 .000 .000
• -51*,; .332-.J21 .3il..j,^ -ijn- .3^7 -.349-,^47-.3^3 ..(jOa .000 -OPO .000 .000-000 .0"0 .000 .000 .000 .000 .000-.000 .000 .000
.i7t .3u4 ,Jb6 ..15,0 O43 .Jo? .3^0 .351 .339 ,3^'J .cOJ .000 .000 .000 .000 -000 .000 .000 .000 .000 .000 .000 .000 .000 .000
."tOi .396 ,jfe9 .3»4-.o3t-.37^ .373 .3ua . .t2o .M5 .411 -''o7 -^JO .^c3 -'129 .441 .138 .00.1 .000 -000 .000 .000 -OnC .000 .000 .000 .000 .000 .000 .000 .000
--.46j. .456 ."+bl .446.--. 442 .Ion .4^7- .442 -. nbO - .4b5 .453 .POO .000-.000 .000 -.000 .000 .000 .000 .000 .000 .000 .000 .000 .000
• 49j. .4at> .-»B1 .476 ,>»7i .'l;,7 .4'i? .too .q69 .474 .481 .493 .000 -000 .000 .000 .0"0 .000 .000 .000 .000 .000 .000 .000 .000
02i .516 tJlu .;.u5--.^0r) •il'r> •"*'! - ,(»o«-.i»9l-.i»95 .502 .512 ,52b .000 .000 .000-.000-.000 .000 .000 .000 .000 .000 .000-.000
.55^ .540 ..,40 .J^4 ,b25 .5^? .5j.7 .514 .514 ,5i7 .523 .532 .^42 .000 .000 .000 .000 .000 .POO .000 .000 .000 .000 .000 .000
.bflj. .b7o ,o7o .bo4 .b57 .'•-». .&-»5 .540 ,'ji9 ,545-.54b .5r>A ,R63 .000 .000 .000 .000 .000 .000 .000 .000 .000-.000 .0"0 .000
.Oil .60o .ul,l .jV'., .^(!V .5o? .b.V1. ,S7j .j67 .5t>7 .£71 .579 .^92 .000 .000 .000 .000 .OCO .000 .000 .000 .000 .000 .OHO .000
-.o4i .637 ,334 .6jO .035 .(=,JP ,6^1 ,6u4 ,b99 ,5'j? ,60.j .605 .f-.SJ .OnO-.OOO .000 .OnO .000 .000 .000 .000 .000 .000 .OnO ,000
.o7j. .6oV ,u7,j ,f,71 .06': .6^1 .0^2 .6-11 . o3b .637 ,f.3fl .000 .-00 .000 .POO .000 .O"" .000 .000 .000 .000 .000 .000 .010 .000
.VOo .697 .71^ .7<;1 .72i ."'ifr .6^,4 .f.04 . j',0 .OuO .fOj ,00'> ."00 .000 ,000 .000 .nOo .000 .000 .000 .000 .000 .POO .000 .000
• i.oj .oeo •(>•>') .7^4 .r-j;, .70f> .c *j .ooi ."Oo .opo .000 .000 OOT .000 .or>o .000 .000 .000 .non ,ono .000
• oOo .Oi«0 ..lO'j .'--.,'J ."0.; .'u'1 .C--C .OjO ...Oil .OuO .fPj .Ooi> .«f'(j .000 .Ol'O .000 .010 .000 .000 .000 .0"0 .000 .100 .000 .000
59
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—7«cl L,l..-*i*,W-If.U< -*U«i.YS.IS . — ANAL70-PAGE 3—23 KAR- 73-18:US:02
bLTS^l
GRlDHKiNT OF VI X. Y) iN Uu!T3 1.0000+01
16<^ .l&O—loO—lt>f.-.JoO .i;fi .Ji.7-,156—.1!>7—)bu . 157-- 157--. 157—.156 .118—ortp -000 ..COO -.000 ,000-. 000—.000 -.000 — 000
.12-* .J.22 .1<;2 .i^i .1^:5 .l — 112--, 111 — ; 1 j -.507-,, 107 ,106 — 101—103 ,.000 .000 .noO—000 .000-.000 .000 .000—000
• lit* .051) .ut" .0<<5 .c,"4b .0;-2 -0<=f> .Oo!> .G?2 .090 .088 .082 .0^3 .OE5 .076 .1?2 .000 .000 .POO .000 .000 .000 .000 .000 ,000
--.iio-..-013 — oOa— Ow£!-.OfrJ—f_-G3— G-34—.CiiO—C33— 070 --.f,63-. 055 —01S—Ot7_-. 156 —000--.000--.000 .000-.000 -.000 . 000 .000 .000-.000
-.Olo-.C2C~.o2'l-.Osl-.u5.-l-.Cu9-.Gl'l .171* .CS1 .0<*B .028 .OtJ .070 .000 .000 .000 .000 .OPO .000 .000 .0"0 .000 .000 .000 .000
.01>2_.HO_.lolt .C-00 .OiW)-.ol7 -.Oil -,t-09 .OOO-.OOO-.-OOO-.OOO-.OOO- .000 -.000 .COO .000 -.-00a-.000-.000-.000_.000
-.li2-.i5«)-.?^7 .cOrj .CjO .c,00 -OoO .(jOj -POO .000 .000 .OPO .000 .000 .000 .COO .000 .COO .000 .000 .000 .000
,^6o_.072_.oS7_.1^2_.i63 .WC ,0i—t)2l-i<:0 -.0^3-.C-63-..l22^m5_.oOO —COO—00&—000—.000—000--.000 .000 -000 -.000 .000-.000 .000 .OnO_000
-.jtH-.Ofl-.u3o-.o21 ,00V ,0^9-.00'*-.C'»l-.c,7o-.Ol9 .COO .000 .000 .000 .000 -000 .010 .000 .000 .000 .000 .000 .000 .000 .000
- --.U3j-.032-.t)29--.o20--.ulli.0l5--.c-*'1=-li5 . uW-«CoO—.C-DO — 000 — 000-— 000 -.000—.000 — 0"0- .000 -.COO-.000-,000—.000 -.000 .000-. 000
-.i,2V-.02uOO-.000 -.COO .000 .000 .000 .flOO-.OOO ,<>no .000 -.900-.090 -.OOO-.flOO -.000 -.000- ,000
60
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ft6C tt—23 MAR -73.ia:U3:03
l
0^ J ( Xi Y) JIM lil'ilTb l.OOoO+OQ
•IbJ. -,1.21-_,os^ -.C^'J—.dl3--fl^3^--OJ5-.0^0--i05--J-41--l5't-,179-,20o~236-.2e3-.5?-l- .000 -.000-.000 -.000—000—.000-—000 .000 ,.000
«lf>0 -121* .08° -049 .jl2-.c-<:4-.o:i7-.e<»:i-.iC.9-.132-. 155-. l79-.20'i-.2?9-.255-.2?7 «000 .000 .000 .000 .000 ,OPO .000 .000 .000
.l6j ,.1£1 -.086 ^0/4B-.iO<.'^.0<;9-.o6:l-.r.;iy-%ill-.132-.l55--,l79-.2C3-.226-.247--.263. .000 .000 .000 -.000 .000 .000- .000 — 000... 000
• 161 .12.5 .^,65 . o-«6 .oO{i — i?.1* — oey -.c*B--v>G;.--.''b?--.ic'*-,i.<>i-. ii5--.i26--.i0_l5i .161 ,ii7_o.uo .G-00--.CaA--.tiOO-.OoC--. eOO-.OoO-.oOO--.000—.COO-.000-.000 -.000-^COO — 000 ^000—000 -.000 .000-.000
• i1*? .Ib7 .172 .2j5 .JOJ .CoC .OCO .CuO .jOO .OcO .r.Oo .POO .000 .000 .000 .000 ,pno .000 .000 .000 .000 .000 .000 .000 .000
.A-t/-.lS9-.i77 .2o9^«^-) , l0t-.ot7-!»C^^-.oi.3-=-.JloO-. 0*0—000-. 000-.000--. 000-. 000-.8flO-« 000-..000—000 ..000--000--.000 -.000—nOO
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.I1*/ ,lb9 .169 .179 ,173 .1^3 .0"S ,t>Zi-. 009 .079 .000 .000 .OCO .000 .000 .000 .OOp. .000 .000 .000 .000 .000 .001 .000 .000
.it*-.lb5 -.161 .10? .154-, 15^ .103 .QU1-.uCO -OoO .COO .000 -.000 -.OOO -000- ,000- .0"0 -.000-.000 — 000 .000 ,000-.nOO .000 -.000
• itV .153 ,i£o .Ib6 .153 .l->7 .239 ,?i»3 .id9 .Ot7 .lOo .POO .000 «OCO .000 -000 .000 .000 .000 .000 ,000 ^000 .000 .000 .000
...So .lbO — j.52 .152-,166-.l^o-.lao-.lii'* ,o9) -,0ba_ii6 .000-.OCO-.000 .000->000 -.QOO-iOOO —000-000 .000--.000— 000- .000 .000
• ib'j .149 ,i<+9 .1H7 .it3 ,!to .131 .H7 .^03 .lal .103 .309 .pOO .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
.l&O -.!"»» . 146 .1H1- . 1J3 .127 ,116-,iJl . 1C5~.101-.091*--. 115-.000 -.000 .000 -.000-. 000 — 000--. 000-,000 -.000--000 .OOO-.OOO
.150 .143 .115 .143 .Ji9 .133 .126 .118 .112 .10? .r98 .002 .000 .000 .000 .OOC .000 .000 .000 .000 .000 .000 .000 .000
• ASy -.U-1 -.152 -.152- .152-.lt>l-.l',7- .U9 .J32-.125 .|2i-.l?l .126 -.000 .OOO .000-,0»0 -.000-.OOO-.OOO .000-.000—000 .OOO-.OOO
.iU9 .lb .107 ,^d .t.ol .J07 ,?y? .20? ,24;> .(,00 .000 .{-Ou .OCO .000 .000 .OOa .000 -.0"0 .000 .000 .000 .000 .000 .000 .OOP .OOO
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• uPt> .000 .jOO .37S .{'Oo .f'L.,', .!"'• f-. bb u7 of, 6,1 t>] t.1 c.1 ) 6 AM
61
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-- L.A.-»lm>fJEI O-rtHAuYilS --ANAL70 PAGE S---23 .MAR-73 1B;<43:29
s=2 . • •
6KJDKFUNT OF T( Xi Y) IN UUITS l.OOCO+02
- .o4o.<>40 .o40-.640-.o4» .640 .6*e-.640--,6tO-.640 -.640 .640-.640 .6*0 .610 .640-.653 .081 .679 ,6B6-.6fll-.683 .688 .695 ,710 -
,64j .640 .o40 .tlO .o40 .f"*0 -6-tC .640 .6tO .640 .643 .640 .640 .640 .610 .640 .6r>3 .670 .683 .687 .681 .682 .687 ,694 .704
.o4j .040 .o'lO .640 .o4,l .640 .6-.0 .640-.O40 .640 .fclo .640-.6^0 .640-.640 .640 .646 .685 .702 .696 .686 .684 .686 .693 .704
,o4i) ,64C ,o40 .640 ,o4G .640 .640 .649 .oMO .643 .fi'j ,6'!0 .640 .610 .610 .640 .651 .670 ,6°3 .699 .683 .683 .685 ,6«$ §7o2
—.b4u- .640 .040 .640-.040 .6na .6-K> .640 .640-.&40 .f-4u .6UU-.640 .640 .640 .644 .652 .663 .680-.691 .680 .683 .686 .693 .699
.bio .640 .040 .f>40 .olc .6-*C .6'tO .640 .640 .640 .640 .640 .640 .6'12 .643 .647 .652 .662 .672 .685 .678 .683 .686 .6q3 .700
, --.o4j .640 .o4& .6^0 .040 .6tO- -6tB .6^0 -.640 -.640 -.f.40 .643 .643 .645 .645 .648 .655 .659 .677 .685-.678 -.683 .686 .693 .702 -
.64u ,640 .t.40 .640 «t,4n .640 .669 ,6t>9 .645 .643 .(,44 .642 .{.40 .645 .650 -657 .655 .658 .672 .6f7 .678 .683 .687 .6q4 .7fl2
-; .o4u .640 .o4C -DtO -o4i- .61,2 .667 ,6t,a .644 .644 .644 .643 .644 .650 .653 -657 .659 .663 .669 .685 .677 .682 .695 .700 .710
.64u .64U .040 .640 .o40 .6^6 .644 ,6^S .645 .645 .645 .646 .651 .654 .656 .660 .664 .667 .672 .694 ,68Q .686 .707 .707 ,7i2
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_ .640 .640 .o40 .640 .040—6.4^ .642 .645 .647^.647 .(,4d .650 .651 .655 .660-.666 .671 .675 .677- .678 .679_.7o5 .71? .'716 .744
.6,40 .640 .o40 .b40 .o4o .&40 .6>»1 .640 .651 .651 .651 .650 .652 .657 .663 ,67o .680 .681 .680 .682 .69fl .701 .702 .732 .752
-.040 .640 .&40 .640 .o40-»640--.6'40-.64o-.66o -653 .65.) .650 .652 .657 -.663—670 .67fl .6Bl_ .682-.6B7. .701 .707 .707 .740 .732
.b4u ,b40 .o40 .040 .o4Cl .6,0 .640 .64(3 .6bO .649 .f-4u .649 .651 .656 .662 .670 .676 .681 .684 .607 .693 .699 .709 .712 .756
.04^ .640 .o40-.640-.o40 .&-*0—.640 .64^ .643 .644 -.644 .646-.649 .653 .6&0 .666 .674 .677-.681 -.6S6_.691_ .700 .734 -.757 .772
.fa4o .640 .o4Q .640 .640 .640 .6J9 ,6jo .638 .639 .640 .611 .645 .650 .656 .662 .672 .674 .678 .684 ,69fl .710 .754 .769 .776
-.6-4^ -.640 .u40 .640 -,i>4t) - .6j7- .6J5 .6^4 .o34 .634 .635 .636 .640 .645 .653-.661-.667 .674 .677-.631-.689- .742 .758 .749 .772
.o4j .640 .u40 .biB .o37 .6i3 .6i2 .631 .630 .630 .630 .631 .635 ,&'»2 .660 .674 .669" .680 ,677 .680 .689 .717 .742 .737 .772
.otj ,640 .o40 .635 .o3i .6jQ -.6^8-.6^7 .o25 .6^5 .625 .625 .626 .642 .659 -.662 -.665 .672 .675 .678- .690 - .728 .745 .736 .772
,t.4u .640 ,o35 .Aol .029 .6^7 .6.'i5 .5^3 .o20 .f>ZS .(££ .628 .610 .640 .654 .655 .663 .669 .673 .679 .695 .747 .749 ,7?8 .764
,04t> ,t,3b ,o31 ,0£6 .024 .-6£4 .6£4 ,632 .636 ,63d -.643 .652 .664-. 667 .665 .677 .681 ,6f>0 .6% .70^ .725 .713 ,717 .744
.037 ,63J ,o26 .t'u9 .,,23 .f,^. ,6i1 .6^7 .640 .641 .6'i4 .651 .66i .-',67 .670 .66B .672 .680 .*>?! .686 .709 ,7?3 .730 ,7?1 .7S2
.636 .u3
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--7y9 .- --U.A. «I,,U'ia.O-WWLYiIi - - - . ANAL70 PAGF. — 6-23 MAR-73 lfi:H3!45
OF Phl( X. Y) IN UNITS 1.0000+02
«015 -.021 .026 .0-5?. .0-53 .Ct3-.(,H9 . .Os'l .0&0 .065 .071 .076 .082 .008 .000 .000 .000 .000-.000 .000 .000 ,000 .000
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.01? ,j2C .C<:4 .j27 .030 .C-5'.' .CJJ -jlB .OfG -r-Sj .05t2 .<}'*& ,0'l9 .Q53 .QE6 ,Qb9 ,0f>2 .010 .000 .000 .000 .000 .000 .000 .000 .000
.1,2-* .02a ,,,2b .026 .527 .027 .029 .032 -i,35 .039 .p$ .u'J1* -Cb3 .^bS .0-i3 .0^"3 .Oi& -C58 .Ob's .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
.06i .060 .Ji>9 -GliS .OM-.037 ,0'JS .Cj5 .U57 .00^ -000 .000 .000 -000 .000 .000 .000 -• 000 .000 .000 .000 .000 .000 .000 .000
. .000 .QOo .000 .&00 .000 .QOO .000 .000 .000 .000 .000 .000 .0"0 .000
.080 .079 .079 .0/fc .(,7« .07? .079 .060 .u8i .Otiri .087 .009-.o92 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
.08. .084 .y63 .noi . r,P3 .Co3 .Oo3 .Ou't .u06 ,0(,7 .c89 .090 .091 .000 .000 .000 .0"0 .000 .000 .000 .000 .000 .000 .000 .000
.08* ,06V .u«<> .Ou6 . c-e,0 -,0u8 .0-iS .Port-..j69 .090 .C^l . 092 .093- . 000 .000 .COO-.OOO .000 .000 .000 .010 .000 .000 .000 .000
.u9t .093 ,j93 ...yi .U93 .093 .0^3 .'-1v3 . Ci9>» .0911 .C'9'j .095 .096 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
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.*!«- .11!) .il7 >,i.:, ,i .121 .j.25 ,j«9 .^33 . l,',7 .0^0 .C,0 .uUO .t./1 .fpj .OQi' ."Ou .000 • 0(10 -COO .nOO .Of1 .OPO .000 .000 .000 .000 ,0"0 ,000
63
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JlUALTO-PJleE- ----- 3-23 KiR .73 18:«3:U6
Y) IN ijUITS l.OCOO-iOP
.-£7»--..i75 ,274 .?75—277-.?79—S?8 —000 — 000—000 -.000—000 --.000 -000 -.000 -000
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.16.U -loo—16<» ,lo?. -l6f. -.4J6 .190 —2u.i—210 -.?.l>9-.20<» .203 .19d .lB7-,lf)b . 1<*9 -.000 -. 000 .000—000 .000 .000 .000 - 000 — 000
..J.OJ .105 .j.OJ .u*9 .ICi .JiT .1(7 . iyy .166 .179 .171 .167 .166 .161 .126 ,?6t .000 .000 .000 .000 .000 .000 .000 .QUO .000
.t)5ti-.Ot7-j'U—3j3 —o£9—ft*l .0^9 . 1-u'J—l7t—li*3 —132 .1?3 -.1-33 —lia .1CS — 000 — 000 -.000 .000-000 .000 -. 000-000 .000 .000
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,-ull—.OV1 -o«9 -.000-. 000 -,900— 000--.OHO-.OOO—• 000 .000 .000 -.000—000 — 000 — 000-.000
.000 .OjO .U00 .000 -OOu .000 .000 -000 .000 .000 .0"0 .000 .000 .000 .000 .000 .000 .000 .000
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S .000 .000 .OuO .uOO .000 -COO .000 -DOO .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
.-(>7o-.0ii''-«ud3~.i>7& .il3—.136 .0^5 -C—U<)0-'.1*>3 -rjOO ~»OOJ—000 —000--000 -OOO — OOO -.000 -000 .000 —000—000 .000-.000-.000
. (,6o-.06o-.o61-.OH3 .00r) .Cbl .Qi2 .120 -007 .Ou7 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 ,000
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l'J-.Olb-.vO? -,Oo& .c-2o — 03l*".i)'»'« .OM -.05j-.0*l .006-,000—.000 -.000-— OOQ-.OOO .000 —000-,OOQ - .000-.000 .000 — 000 -
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.yl/ .017 .020 .03t> .Jt3 .C1 .059 .uSci .075 .yfll .047-.009-.(J3i>-,ol«-.Cl7-.c02 .flOO .000 -j600-.OOO .000-.OCO .000 .000 .OOO-.OOfl .000 .000-. 000 .000
.137 .122 .117 .120 .13] .r.B9-.l21 ,0ot .000 .OoO .000 .POO .100 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 ,000 .000
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«-L.A. *H,OF1ELO-AHA1.YSIS — ANAL70-PAGE 8 -23 MAR 73 18:143:16
faftlOr'KINT OF U( Xi Y) IN ONIT^ 1.0000+CO '
.175 .125 .070 -.olit-.C37-.0-it-.1.27-..l62-.19 121-. 3-.-J-. 220-. 108-. l-i^-. 2Q7-. 2C2-. ?Co .000 .166 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
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<_3i .237 .£45 ,2to .2 .1C2 ,0^0 -106 .000 .000 .000 .pOO .000 .000 .000 .OCO .000 ,0"0 .000 .000 .000 ,000
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_2i8 . . ----U.A.-«:lNUfICLD-ANAuY£.l!> ANAL70-PA6E 9 - 23 MAR 73 18:44: 13
S>ETi.-3
OF T( Xi Y) IK UNITS l.OOiiO+C? ,
.Liu .640-.040 '.&40 .o4o-.640 .6t3 .6l»a .6tO .640-.640 .&<»0 .640 .640 .610 .6tO-.662-.6BB .689 .699-.698 .703 .711 .721 .740
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.o'tu ."40 >o40 .640 -64j .6-tO -660 .661 .647 .646 .648 .649 .6Sc .655 .662 .67o .669 .676 .692 .710 .703 .710 -715 .723 .732
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.l>4j .b4C .o40 .64C .oto-.^'+O-.642 .fcbl-.656 .661 .664 .668 .f,73 .680 .688 .695-.70i .706 .709-.715 .721 .729 .763 .786 .802
.640 .640 .o40 .640 .o4o .fi'to .645 .6iQ .654 .658 .662 .666 .672 .679 .686 .693 .702 .704 .7o7 .713 .719 .740 .783 ,798 .806
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.64u .040 .040 .641 .o44 .645 .648 .651 .654 .657 .660 .663 .670 .677 .694 .707 .700 .710 .7fl7 .710 .719 .747 .77? .7*7 .002
.o4u .640 -.i>40 .643 .046-.6H7 .650 .6i>i-.655 .658 .659 .663 .668 .680- .695 -.696 .697 .703 »70& .70^ .720-.759- .776 .767 .802
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.o4D .64J .o47 .6bO ,o51 .633 .655 .6bd-.^60 ,6o2 .664 .669 .672 ,691-.689 .690 .6<« .700 .705 .710 .723 .748 .767 .756 .786
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-709 --- -~UA. tvl,,bFlEI 0 hNAuYilS - - ANAL70PAGE- -10 -23-KAR-73 1B:M4:33-
3
OF PHI( Xi Y) IN UNITS 1.0000+02
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RNA1.70 PAGE - 11 — 23. HAP. 73 19
OF V( X. Y) Ih U..ITS 1.0000+01
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_.uay_080_>;86 .Co6 ,l)9U—092 -.057—101 — 102 -.099 — 095 -.091-, 06t-.072-. 052 .039 .000 .000 .000 .000 —000 .000 .000 .000 .000
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-l..A.-*I:,ui-lfEL.O -«KALYSI5 . RNAL70-PAGE -12—23 -MAR -7
GKIDPK1IO OF U( Xi Y) IU Ui.ITS 1.0000401
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-709 —- --L.A. -wIl.OKlflO -ANM YSIS — ANAL70 PAGE . 18-23-MAR-73 18:i6!17
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SfUOi'RINT OF Pn'H X. Y) IN UNITS 1.0069+03
,liO2 .OIL .051 .Ob13 ,n61 .069 ,Q72 .075 .077 .076 .000 .000 .000 .000 .000 .000 .000 .000 .000
• 1,17 .022 ,!)26 ,/jjd .U3h .039 -C-»1 .fbl ,ob8 .063 .066 .073-.077 .079 .081 .0-11 .000 .000 .000 .000 ,000 .000 .000 .000 ,000
.g2i .021/' .02* .0.13 . o37 .nil .C'tb" .Cjl . C&3 . 06fl .073 .078 .062 .081 .086 .087 .088 .000 .000 .000 .000 .000 .POO .000 .000
.0£9 .0^3 .037 ,0i|0 .pi,2 ,oGG .£,,,0 -.<)71 .07*4 .073 -.000 .088 .090 .091 -,fl92 .Oq3 .0?5 .000 000 .000 .000 .000 .000 ,.000
-033 ,j37 .040 .o1*^ .C".S .000 .CU0 .oOO .064 .r9o .091 .o?1* .095 .095 .097 .oq7 .097 .000 .000 .000 .000 .000 .000 .000
• U3i .037 .^m ,i..i»5 .ui,0 ,&uC-.C30 ,f,9B .100 .100 -102 .102 .103 ,]02 .102 .103 .000 .000 .000 .000 .000 .000
--.L,"»l> .0"*b -050 -Cb6 .ufi^ .0-71- .Oa<* «f-iJl .U96 ,09C .ICu .102 .103 .10"» .10'* . ^0'* .10't .10"* .10& . 110-.112-.000 -000 .pOO .000
.LtJ -04^ .uDb .Lul ,ui,f, .077 .0°5 .C-'Ji .j97 .l(jO .102 .10* -JOb .106 -106 .106 .J06 .106 .107 ,i()9 ,QOO .000 .000 .000 .000
.1,47 .053 .Q59-.Col. .y?^ .079-.0^7 .t-9-* .o9fl .lol .103 .IflS ,106 .107 .108 .10? .107 .10S-.109 .000 .000 .000 .000 .000 .fino
• Lr5i ,0&7 .(,63 .Co'* .yVi. .0^2 .0^9 .C'Jb .Q99 .lo? .10t .106 .107 .108 .109 ,1fl9 .109 .110 .111 .000 .000 .000 .000 .000 ,000
.-1,5.) .060 .u66 .075 .U79 , OaE. ,c'51 .0"J7 .1^1 ,lo^ ,io5 .106-.1C8 .109 .llo .110 .HI .112 .113 .111 .000 .000 .001 .000 .000
. l)5o . Oi.'* .j7C .C76 .yfli ,ot:S .o'^'l -C^^ .102 .Jo'* -106 .107 .308 .109 .110 .112 .113 ,111 ,JJ5 .116 ,000 .OPO .000 .000 ,000
.1)6^ ,0t.t ,j73 .079 ,ottS-,090 .0^6 .1U0 ,103 .1 j=- .106 .107-,106 .109 .111 .113 .115 .116 .117 .117 .000 .000 .000 .OPO .000
,u6o .1)71 .u77 .Oo2 ,i;0(i ,ovJ ,C»n . Ul .101 ,10^ .106 .107 .30.1 .109 .110 .000 .1)7 .118 .118 .119 .000 .OPO .000 .OPO .000
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,u7-. .u7'j .^1 .f'o9 . U91 .C/7 .1 .r' ,lj3 .101 .lO1"' -106 .107 .101", .110 .000 .119 .1?) .121 .12? .122 .000 .OPO .000 .000 ,000
.1)7^ .0;;^ ,U87 .CSL.9? .r-j'-i ,j;r .li,.'. .105 .l^
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AI1AL70-PiGE 19_23-MAR-7-J-aa:«6il7
feKIOPfUNT OF Vt Xr Y) IN UNITS l.OOOC+Cl
,i59-.2ba.-.257--.2;>&-255 —2jU—251—256—25iJ-,261-.!?6b_.27i_.277-,.232-.0<>0—000 .000-.000 —000-.000 -.000 .000 -.000
,256 .^53 .252 .£53 .2a6 .259 .2ol .260 .255 .213 .?3S .225 ,201 .166 .057 .QOO .000 .000 .000 .000 .000 .000 .000 .000
_.i .266 .261 .237 .208 .166 . US-.037-. 101 .000 .000 .000 .000 .000 .000 .000 .000 .000
—.220—217 -JUS—/IT—.231 -239 _3i>U_.316_265-_2J6-^?o9— 156— 101—.C3B-- 050 -.000 -.000 — 000 .000-.000-.000 -000 .000 .000
.20^'.^03 .191 .181 .liio .237 ,5b& .319 .238 .222 .?S3 .111 .003 .fl62 .061 .o?5 .000 .000 .000 .000 .000 .000 .000 .000
—.iOu -.2o2_i93-^17b_ll*7 —Io9—000 -OoO-.-JSl—O60—213—COO —&&£—0£>7--Oil—071—068 .119 -.000-.000 -.000 ..000—000 -000 -.000
• 209 .2fl1 -l9l -1°1 -123 .096 .QOO «0U0 -uOO «02B ,?Ql .018-.002 .O'S .051 .083 .OU-.00& .000 .000 .000 .000 .000 .000 .000
.^02 -1-70 —111-,GOO — 000-00^—1?9--»000 -.o55-.000-.000 .000 -.000
.236 ,^3o .2iO .111 .C&O .000 -3''t) .151 .125 .(i85 .017 .n63 .051 .Ql6-.00l-.005 .Q12 .0^0 .000 .000 .000 .000 .000 .000
- .051 -.l39--.i83--.o25-.000--000-.pOO-.000
.«;8y .261 .«;96 .327 .389 .1-40 -107 .3j7 .151 .106 .101 .071 .051 .031 .010-.0l1-.007 .Q16 .o"5l .072 .000 .000 .000 .000 .000
*>a.l--.296-_.}o6-32i_.j5&—376 .3/5-.2d3 -.131-.125— C97-.078 -.e5a-,037--H.012--Ol8T.001 -.Q36—013 -OOO—OOO—.000 — 000 -.000--.000 -
.«;9o .299 .30<> -3lB .332 .340 .337 .267 .135 .112 .0^1 .077 .061 .Oil .019-.011 .Oil .017 .037 ,000 .000 .000 .000 .000 .000
296^—300 — 3^6—.^i3—Jl5^-»3l-l—.2S3—129—099—£.82 .,070 -.058—-016 _031 — 017—.flSo — 013 -.053 -103 .000—.OOO-.OOO -.000-.000
* .290 «<;92 .295 .^97 .297 .291 .2j1 .123 .088 .Q71 .060 .c5l .055 .0&0 .058 .o'o .010 .0*6 .071 .000 .000 .000 .000 .000
i-.263— £83-.2fa1—,«:«3-.2<»0-.25& -.16.9-. 108—077 .058- .050-.01* -.05& -,098-. 126—.065—.037— .038—050 -.000—000—000 -.000—000-'-
.£74 .271 .<;75 .273 ,£69 .?60 .203 .110 -093 .065 .013 .038 .Q16 .038 .173 .000 .026-.021 '021 .031 .000 .000 .000 .000 .000
—.£6a-.2a6-.^66 .262-,£51--.^ifi .-162-. 11?-.a79-,«S3-.{v26 .013 .O35-.O02-.000-.135 .010-.011—01S-.OW .000-.000 .000 .000 — 000-
.t5o .258 .tStJ .262 .«U3 .Io9 .1^1 .lul .066 .016 .019 .088 .013 .169 .COO .019 .039 .020 .012 .016 .000 .000 .000 .000 .000
,23o .21d -.£52 .216 .460 . l^-.115-.091.—.-058 ,049 .030 .093 .P50-.OOO-.166 .036 ,1?3 .018-.012 .001 .000-. OOO-.OOO .010-.000
..12* .215 .tip .lib .123 .110 .103 .067 .066 .056 .036 .066 .131 .000 .121-.013 .000-.OJ9 .037-.025 .000 .000 .000 .000 .000
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76
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fJAUfil;.- - AUAL70 PAGE — -20—23 MAft-73 -18:»6: 18
5
OF l/( X. Y) IN UNITS 1.0000 + 01
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.180 ,i70 ,i62 .155 .119 ,l-*6 .l-t9 .Ia5 .163 .166 ,]61 .115 .115 .065-.013-.C50 .010 .000 .000 .000 .000 .000 .000 .000 .000
-.l9l--.176-.l61 -.153 .. lls . 14C> .U3-.154—16B-.176 .174-.l63-.1tl.lOl -.019-, 030 -.000 -.000 -.000 .000-.000 .000-000 .000 .000
• l9i ,17ti .i&D .Ibl .137 .125 .1^7 .1 ol .161 .195 . ] 97 . ] 93 .102 .161 .132 .0^5 .000 .000 .COO .000 .000 .000 .000 .000 .000
l9l .179 .j.6o — If9 -,12? _( »a .0,13- .143-.212-.227 .£<23 ,?31-. ?3i>-.2?l4-.J-3G .373 — 000--.000 .000 - 000 .000—. 000 -000 .000 .000
>l9i . li>2 .171 . ibl .12!) .f/o7-.0"l .137 .307 .275 .T3j .281 .294 .270 .269 .?79 .291 .000 .000 .000 .000 .000 .000 .000 .000
, — Id* .186 '.±61-.170 .147 .Il5-.0o0-.0s/e-. 499 -.311-.407 -,000--.355 -.273-.234 -.240 - . ?33 -. flSO -.000 — 000 — 000 _000 -000 — 000 -.000
.ia/ .193 ,;93 .198 ,i90 .24" .QOO .OjO .uOO .551 .330 .J78 .205 .198 .209 .211 .156 .115 .000 .000 .000 .000 .000 ,000 .000
3-« .2ol ..^19 .iid..255 -.00" -.QUO . 0^,0 -• 1^0 --.275 -^ 201 .1'I2-. 1 9 .160 .159 .124 . ] 15 .159 .153 .117 .101 -O99 -107 ,156 .000 .000 .000 .000 .000 .000
.-iS^ — 250 .^3.6 .2>' .0^7- .022-.00°-.00l-.007 .f-lk -.031-.000 -.075 .of>1)-«-0R3 — 0*51 .0«0- .000 .OOC-,000 -. 000 .000
.J.8J .160 .i72 .lol .i2j .c/3 .C4?. ,?2o .015 .009 .011 -029 .027 .060 .000 .022 .(j72 .0^0 .OF3 .079 .000 .000 .000 .000 .000
.19u .173 ,lod .142 .UB? .Of". .Odr .CU4 ,u09 .014 .020 .C?l . 03b .000 -.055 .018 ,0)8-.0ei .075 .OR? .000 .000 .000 .000 .000
• iBl .130 .133 .o'Jl .052 .C'3o .01^ -013 .621 -029 .p35 .022 .nil .000 .00?-.015 .000 .032 .0^5 ,070 .000 .000 .000 .000 .000
--.i&4 .000 .113 .0^4 .JHC .033 .c?9 ,0^7 .U32 .<'45 .c52 .047 .cOu .000^.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
• uOj .000 .130 .r.j2 .^47 .039 .e-'4 .C31 .037 .046 .i;65 .OB4 .nCO .000 .000 .000 .OnO .000 .000 .000 .000 .000 .000 .000 .000
v-.uOj ,0'.'0-.i.i97 .034 .,.,53 .fjS .O"1* .''uO .ji« .00" .()65 .000 .000 .000 .000 -.000 .000 .000 .000 .000 .000 .000 .000 .000 .000
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77
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-20B -_L»A._tt lOlfliLD-^faLjrSlS -ANAL70 PAGE 2L_23 .MAR -73 -IflJ 16 :19 . _.
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iiKlWRlNT OK T( X. Y) IN IMITS 1.0000+C2
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-,o4u-640—o40 .640 -640 .61,0—6^0 -.640 -.640 -640-.640 .6tO -640—640—640—640 -666-,737 .779 .796 — 807 -.825 .847 .873 .904
-.b4u .640 .040 .640 .o4j -Sufi -6^0 .6^0 .O40 .&40 .6'IJ .643 .640 .640 .640 .640 .685 .732 .778 .806 .810 .630 .850 .876 .902
..64j-.6nOi-.o40 — 6*0—. s>t*f>--.ti»n—SAG—640 —b"*!) —640—640 -,6UO— f>«0— 640 -.640 -&71 .703 — 737 — 776. .80? -815 — 835 .854 .877 -.899
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—-.o4u-.640-.o4G--C40--.oiH-".640—•f>^1—.^Si —040-.640-.6ta .667— 689_»7oi _7o8 -.722--.743 -763 .796-823-831 -.849 _.R65 -.8B3 —9o3
-b4u .640 -u40 -640 -aHf, .&-*0 -6o7 .67S .667 .672 .605 .7o"4 .740 -732 .738 .750 .758 .776 .8c6 .837 .842 .859 .871 .8«6 .9fl2
&40-. 040—640— 64p—6i,fc- .efij—630—604 — 697—710 -3PA-.743-. 752 — 757 -.765-776 . 792-.8j4_.8u8 —855-.867-.P85 -.8°5 .9lo
"640 -o40 -640 .o^r "6^2 -6°6 .6U7 .70b -720 .732 .74"* -758 .766 -.771 .778 ,79fl .805 >B26 .867 .880 .880 .901 .904 .912
-o40 .MO—64rt—6^0—6oS_7H>O^J731—746.—755 —763—77<)_.777—785-^792-801—aifi .8^5-.853-.86a_.89a_?07-.913 .944
-.o4u .640 -o40 -6tO .64c "&40 -657 .7i7 .766 .777 .77d .777 .783 ,79j .800 -.806 .800 .828 .843 .857 .875 .892 .896 «9/>9 .952
.-.64u ..&40-.040— JM40—o4o-— 6^0— 64Q—.7^3 — 6»Q -.B(,9—79o —789—794—804 —8J5—825-.831—flu 1-—851-.B65-.BBS—.B97_.9oi-.93T—932
-.64U .640 .o4C .t)40 .640 .fc-tO .640 .7^0 .777 .791 .792 .795 .802 .813 .828 .850 .846 .853 .859 .868 .878 ."<89 .90? .909 .956
— u40-.640~— o4Q -64A— 669 -7l J_754 — 777— 783 ,796—806 — 818 -.832— 844 — 853—.8S6--.862-.87J)_»879_.890- .928 ..95U .9.72
.640 .640 »o40 .640 .o4o .640 -6So .7J.5 .746 .769 .784 .796 .808 .820 .832 .843 .855 .851 .863 .871 .879 .902 •''t* .966 .976
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.640 .u4Q .6i,b .67o -&J9 .712 .7ob .755 .773 .787 .800 .814 .825 .645 .861 .857 .870 .867 .870 .881 .910 -937 .934 .972
-_.l>4^..,640 .o40 .671 ,o9l .7&9- ,7i9-.7-4» .767-.761 .794 .8Q6-.-818—833 ~.648-,850-,fl54—8&2-,86k .869- .sai —922-.941 -.93H-.972
.64u .640 ,U70 .693 .712 ,78 .763 .7o4 .770 .7111 .792 .798 .80i .812 .S22 .»M3 .836 .841 .858 .652 .860 .867 .B<>4 .906 .927 .913 ."40
-.6&U-.712 ,7bl .8£0 .78o .772 .774 ,7dl . 788 V795 .600 -.80*- -820 .835-. 839- ."39 .853 .859-. 861 -.870 .891-. 915 .907 .913 .944
.70J .73^ .751 ,7ofl .76;, ,7u7 .7/0 .777 .784 .792 .796 .BO& ,*!21 .829 .035 .837 .843 .855 .859 .867 ,8°4 .912 .923 .917 .952
.741 ./40 ./'.a . Mh .?b6 .7o6 .TW .7ii .79? .794 .605 .822 .829 .835 .P1*! ."»45 .651 .860 .872- ,3«7- .910 -.923 .933 .970
78
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-709 - L,A. nI|..rJFitl O .ANALYSIS . -- - .- - - - - - - -- -- JIMAL70 PAGE . 22 . 23 f'AR 73 1B:U7!10
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GK1DHRINT OF PHI ( Xi Yl ill U'UTb 1.0000 + 03
• U0«: .006 .ylt .019 .Cxi!. .0.10 .0-55 .Chi .o46 .OJ2 -Ob7 .062 .068 .07H .079 .036 .000 .000 .000 .000 .000 .115 .120 .121 .127
• UOo .012 .017 .023 .02''. .Oi". .C^O .O'tb .Q'jl .OaO .C&2 .067 ,p72 .077 .002 .0^5 .000 .000 .000 .000 .000 .125 .126 ,1?6 .127
• ulo .010 ,j21 .1^7 .fl.X .nJC .0''2 .(.VJ .u3b -Ool .,',67 .072 .;77 .&Sl .085 •0'?7 ,o«9 .000 .000 .000 .000 .132 . 13<) .1?R .126
• ul*i .CliC .Jib .C30 . o3o .0-41 .Ct7 .CjH .060 .Ou7 ,(./2 .078 .oC2 .0'"6 .0?0 .091 .OOP .000 .000 .000 .000 .135 .132 .129 .127
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• Ui«: .027 n,32 .037 .ct? .O'f7 .0-'? .C->1 .o72 .079 .;,85 .09j -C95 .009 .102 .105 .108 .112 .000 .000 .136 .135 .13? ,13n .127
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-C^b .yll .CHS ,c."»Si .C-b? .000 .&U3 -oOO .097 .103 .10& .500 .110 .112 .115 .117 .110 . ] ?Q .000 .133 .132 .131 .iSfl .128
U1*5 -CSO .flb<. .OoC -000 «"UJ .102 . IjS .10U .110-.112 .113 .115 .118 .119 .120 .1?! .000 .131 .130 .130 .130 .129
jbj .cab ,06,i .CuO .Oi-n .Iji .107 .1L,9 .111 .113 .114 .116 .110 .119 ,j?o .121 .1?3 .000 .12P .l?fi .000 .000 .000
• U.T .OJb" .! j't .109 .lj.1 . , 1 j .115-.117 .113 .119 .120 .1?! .122 ,12t ,1?6 .126 .000 .000 .'000 .000
• o^u .05.'. .uj .125 .000 .001 .000 .000
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• uB-J .0'.-' -j9i .10? .1C. ,Jy7 .159 ,U1 .113 .li't .)lo .117 .119 ,OCO -126 .126 .127 .12^ ,1?9 .1^9 .000 .000 .nOO .000 .000
.u9u ,o3'i .'j9'J .I^T . ic«i .U*- -li'' • !i'.' -il2 .ll1* -lib .116 .110 .000 .12t .125 ,1?6 .12B .]?« .128 ,QOO .000 .000 .000 .000
• LOj .J.'O .101 .Ijt. .10J .)„'•> .!-•' ,1i,» .111 .11? .Ill ,11ft .Ho .120 .122 .1214 ,]?b .126 .1?7 ,1'8 .QOO .000 .000 .000 .000
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79
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.-7,U - t.A..»I*lDfIEt&-*NAUi>IS -ANAU70-PAGC- - 23-25-MAR 73 Ifltll7:ll
S,£TS=6
GRIDPRINT OF Vt Xi Y) IN UNITS 1.0000+01
.334- .278 .273 .272 .;;71 .270- .2u9-.£o3 -.363 .2o9 .271 .274 .27-7-.202 .267 .237-.000 ,QOO .000 .000 .000--.278 .223 .172 .113
,29b .280 .274 .273 .275 .278 .201 .2t>3 .282 .278 .?7i .263 .252 .235 .199 .085 .QOO .000 .000 .000 .000 .063 .034 .023 .025
.277 .271 .*72 .272 .276 .235 .295 .3!,2 .299 .2d8 .?7i .255 .232 .200 .150 .077-.202 .000 .000 .000 .000-.098-.09B-.OR2-.07t
,26U ,2fa7 .^66 .268 .274 .20" ,3i3 .3jl .324 .3fl2 .277 .251 .2^0 .1" .130 .033 .000 .000 .000 .000 .000-.063-.143-.135-.148
.«:6i._.2&0-' .259 .258-.263-.2JU-.3J1 .393 .365 .316 .283 .?52 .214-. 189 .Otb .L-7'i .''i/Ti .076 ,C?o .u7» .079 ,f!»u .Ofi3 .000 .000 .074 .0^3 ,072 .074 .079 .068 .000 .000 .000 ,0"0 .000
80
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L,A. *ll*ritlO-AlJALYjJS . ANA1.7C PAGE ft -23 MftR -73 1B;U7:U
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JT OF b( Xr Y) lii UNITS l.OCCC+Ol
—.i7-j--lJl-.iBJ.-.it,-t -i£o -iJl- .2UM —2l7_'230 —2<40--?tt»4- .237- .Hi?-.175 -.n76-.391 -000--000 .000-. Of)0 — 000 _57B -332 ,120-.037
• l9o .166 .j8'j .Ib5 .ifV, .192 ,2l,2 .?17 .232 .?-H<* .219 .211 .227 .191 .139 .]15 .000 .000 .000 .000 .000 .153 .?59 .109-.0)6
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•iOl .191 .i37 .lc3 .174 .171 .1»1 .211 .213 .27? .282 .2M .?79 .270 .266 .281 .000 .000 .000 .000 .000 .O^l .P7ft .OlP .010
iOl .19& -i&a ..177 -162 ..11,14 ,l,l.-,lSQ-_.276-3(,1_-J1U .3l7-.?.]1 .310—321-351 . 389- ,000 -POO - 000 - 0^8 -.008 — 021 .022-017
tOl .197. .191 .179 ,15i .Jjf> -Oj2 .ll,a . 3b6 .355 .:2d . ?67 .75c .312 .3?6 .320 .301 ,113 .000 .000-. OU-.036-.019 .003 ,0?t
.20" .^17 .iZl .tin .2dC .OJC .lji,J .L00 .5o? .;;83 .?61 .?P9 .IBS .181 .198 .110 .106 ,n51 .000-. 115-. 108-.07?-. 016 .033
l9'» ..iji—.^37 .tol -.ZBi--.OjO-.0-Jfr--.OoO —230 --.££>9 .203 .151- . l"t5-.16S-. 1&0 —087 _oS9-. fl86 -.062 . 000-. 0^7--^ 123-..076-. On6 .-026
l9«. .221 .-5:> .."-jl .41.S .OjS -Ci'C .1^5 .i3<> -13*> .111 .Job .535 .125 .09o -C&6 .059 .057 .p76 .000-. 09°-. 111 .nOO .OnO .000
2«:0-.<:S3 .Jo^—i^'J -. J j7-.o27 —CWh- .^ft-.Oo?- — {.S1;! -, 007 _. n£2_07-0 -0&1 -OS1--. Q16-.015 ,012-.017-.[|90 -000--000- .000 ..000
.210 .^3i .iZy .241 .Iu3 .O'JJ .O^ . ;,.18 .011 -C.S3 .052 .0E3 .053 .Q5? .016 .Q13 .0?6 .011-. 005-. 0?1 .000 .OOn .000 .000
/ -.20" .«il2 •ili'-,l9i .H*) -0'-r' -.051--.021 -035 .(,33 . 03&-.r>3<* —OlO -.(}39 -.. 036^.fl2& -,037_.flS9 -. 010 ^000 -.000—000 .000 -000
J .200 •J.'5y .1^1 .173 .1-*'! .Iu7 ,OVi> .ju3 .0-<9 .f3a .032 .n26 .026 .025 .028 .0-39 .051 .o36'.01g .037 .006 .000 .000 .000
-<-Oo .197 .l9£-.Jo2-.1G7-.l-»b .119 .QO7 -.o1-8 - .o1*" -o3S . C2b- .01 6- .016 -.C,l9_o30 -. 050 —036--. 02s -022 .00?-. Oil-.000 .000-000
.<:0u .19b .169 .IbO .ICft ,l-*9 .117 ,?o6 ,U33 .031 .c2J .D12 .p05 .003 .010 .030 .03H -026 .02? .015-.00? ,000 .000 .000 .000
-iOu--l'i" -i9c .iu£-.169 -loO -0=3-.Oia-.L,22 . 015 -006-. 001-. 0-11-. 016--pl2 -.027—035 _.0?3 . 021--011--006--000-000 .000-000
.^Ou .197 ..93 .)b6 .i72 .li^- .O'JO .0^0 . J&6-. dc^-. f 11-. 019-. Q17-. 018 .QOC .096 .051 .026 .019 .012 .001 ,000 .000 .000 .000
.i9> ,19d .iS9 ,iyH .it,, ,»'.j5 .0<:3 ,<>ul-. ^lo-' Ol7~. (-2*-. f'23-. OlO- .012 .101 -.OG6 .0*-'' ,016 .015 ,013 .013 -.000 ,POn .000 .000
• l^J .IJh ,X9J .Jj .^^2 .j3i-.Ci )--L'''-.1-0-. jlu-.O^l-.r 3e-.n31-.'.Ju-.090-.I25-.0''9-.o76-.09l-.C65-,036 .000 .000 .000 .000 .000
uGu .0?0-»«3l ."I"'. ,,,,l^-.< v!-.C'.'—..'>;y-. jt-2-.Ou!-. .163-.n?6 .000 .300". 1 i*'t-.210-. 1 56-, 121-. 1 ] 6-. 01 3 .000 .000 -.000 .0"0 .000
71 T jf 'J rc.ACL^:-;' lj r'l -'1 J7 ~i! 1'" fl tl? )11 6M
-Vi.- -l,'B-<_tr ' t -r.-v-~*J- 1---t9^t-t ^j.'f." "r ? - >.- -'V'-t- >,:-i-T-. 4,Q :-tyi—7*~ Ml *"•
81
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-218 --L.A. (.luOFItLO-ANALYSIS —- ANAL70 PAGE 25- 23-MAR 73 lBt(t7:il3
oRIOHRINT OF Tt Xt Yl IN ONUS 1.0000+03
.Ok* .064-,(,64 .Oo4-,u6i» .Oo4 .flUI* -.064 .064 -.064.-, 064 .064 .064 .064 -0&4 .064-.fl69 .074 .076 .080 .082 .085 .O^P ,092 .096
.061* .064 ,u64 .064 ,06<1 .Dot .Do1! .fl&4 .064 .Dot .06"* .061 .064 .064 .064 .064 ,0&fl .073 .077 .flSO .083 .085 .08ft .092 .095
,U&4 .064 ,o64 .064 .064 .Oo4 .064- .064 ,c64 .064 .064 .064 .064-.064 -.0&4 .064 ,0&7 .075 .080 .082 .084 ,086 .089 ,0P2 .095
.u6*t .064 .064 .Co4 .ubit ,0u4 ,0i4 .064 .364 ,0o4 .064 .064 .064 .064 ,0£4 .064 .069 .075 .080 .083 .0«4 .087 .089 . 0P2 .095
-.064 .064-|.0&4-.C&4 -. 0°4 .Oo4 .0=>4-.0o-l .4- .Ou5 .066 ,o&4 .064 .fl64 .068 .Q71-.073 .074 .075 ,077 .flSO .083 .086 .087 .089-,09l .0^3 .095
.064 .0&4 .Cu4 .064 .Oo4 .0&7 ,06d .^67 .QoB ,o7o .074 .080 .078 .078 .079 .QflO .0«1 .084 .068 .QB8 ,o9o .092 ,0q3 .095
.064 .0&4 .064^.^64 .065 .0"9 .Ob9-.o7o .072 .074 .076-.079 .080 .oBfl "081 .0B2 .084 .086 ,0«9 ,Q9o .091 .093 . Oq4 .096 --
.064 .o64 .oo4 . fl6!( .065 .0*7 .070 .^72 .074 .()76 .078 .£180 .081 .082 -083 .fl84 .Q85 -0B7 .091 .Q92 .fl92 .095 .Oq5 .096
.064 .u&<* .064 .064—<;o4 .fl6.Z-.071 —fl75 .o77-.fl79 .n80 .Oal .083 .o&t -.095-.Q86 . QS7- .Q89. .090 .091 .094 .095 .0^6 .099
.Q64 .j64 .064 .gbn .0^4 .0"6 .073 .u79 .061 -o8l .082 .063 .OE4 .066 .087 ,fl87 .089 .090 .091 .092 .094 .09"5 .098 .100
-.U6<* .064 .064 .064_.()64~-.<.o4-.o°4_0?4 -.o87-.083-.p83 .083 .084 .065 .087-.089--.o9fl . 090-.091 .092 . .094. .095 .095 .0^9 ,098._.
.06-* .U64 .064 .0614 .Oi>4 .0^4 .073 .080 .082 .083 .084 .385 .086 .088 .091 .Q91 .091 .092 .092 .093 .094 .095 .096 .101
.064 .064 .^64 -.064,.o&4 -C<-4 .066-.073 .fl78- .081 -.082 .084..085 .0^7 .Ofl9 .090 .091 .092-.092 .093 .093-.094 .098 .100 .102 -
.064 .064 ,uu4 .064 .064 .Co<* .069 .073 .j77 .ObO .082 .084 .Q8B .087 .088 .090 .091 -092 .092 .Oq3 .093 .096 .100 .102 .103
.o6n-.064-.0&4 .064-.664-.067 .071-.074 .077-.060 -082 .084 .Q85- .087 -088 .090 -.Q9! .092-.092 .093 - .093-.099 .100 .100 .102
• 06-* ,064 ,06'l ,066 ,U68 .070 .073 .076 .0?8 .061 .0^2 .084 .Q86 .087 .O^O .091 .fl9] -.093 .092 .093 .094 .096 .099 . Oq9 .102
--.t,6'» ,064 .004 .OoS-.ti?! ,073-.0'5-,078 ,o2 ,0u3 .u»4 .064 .085 .086 .087 .089 .069 .089 ,oql ,091 .091-.092 .Q94-.097 .096 .096 .099
.o74 .07U .U80 .Oo2 .082 .Oa2 .03? .''-iJ .084 .064 .cn5 .0.16 ,c07 .OflO .069 ,0fl9 .Q9Q .091 .091 ,092 .095 .096 .097 .097 ,100
.060 .u"0 .OhO .Cl?l ,"u] ,082 iOo4 .yU4 ,0t]5 .C8S .006 .086 .06U .QB9 .089 ,o°0 .090 .0°! ,0°2 .095-.096 .097 .09B .102
82
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_ --_L,A. --tiOirjei C- AMALYS1S-- - — —ANAL70 PAGE 2G-,-23 .MA* 73 18:i|B!05
=7
OF Plli( X. Y) IN Or.ITS 1.0000+03
-OiA .j21 .030—V3:, ^C«, ^tu>5--tuj—G71-.C79-oBa .096-.1 05-.113-. 1^2—1 32-.000 ^000 .000 .000—166—177-.185 .193 .199
.Old .027 .035 .o't'l .052 .Col .070 . 079 .067 ."9o .lot .112 .120 .126 .131 .000 .000 .COO .000 .1B7 .1Q1 .194 .1«6 .199
—024 .U33 .041 .050 -C59 -.oo£..677—066 — 096 .104 .112 -l?u .127 . 13P -. 136 . 139 -000 .000-000-.000 .202 — 200 .199 .198
.030 . j39 .o-«7 ,[,bj .r.oS .071 .Od't . L!95 .1L,'I .113 .121 .126 .135 .l»»o -I113 .000 .000 .000 .000 .206 .206 .203 .200 .198
U2o -03o'—04i .0^3 -.,.61 -.(WO -.C-S& .091—.1-03-.11«—123 . I J 1 — 1 3J-. I'.1*- . 149 — 153 - 157—000 -. POO—000 .20B-.207—204 .201 .198
.<
• i)3-» "042 .oSfl .Obfl .0G6 .P/t .0=3 .097 .113 .1^5 .13H .142 .1Mb . I5'l .J59 .162 .1^6 .l7l .]80 .000 .2n6 .205 .203 .201 .199
.U5u -.U>"»-.J7^ -.«73 .GOO— OuO-.l£a -.13£_. jito-,153- .lS9-.ie3-.lU6-. J69..172 . 175 .. 179. .000 .203 _203 -.202 .201 ,200
.U63 .1,71 .(,70 .flj3 .000 .3,,J -uOO -153 .l^d .It3 .16t> .lf-b .17(j .17H ,]7f- .179 .162 .0(10 .199 .200 .200 .200 .200
ljSt-.Ool .u7o .C73- .U6b -Cj" -OOP -.OjO-.lW> -lu? • 1"6 - 1(.S—17& .172 -.175 .177 .179 ,l3l .Ifil . 190 -. 195-. 196 .197 .200 .?01
U5o .066 ,,,77 .Oo7 .^9^ .twC .139 .lao .163 .167 .[7o .172 .173 .175 .]77 .179 .iPl .162 . ] 8t ,1B8 .192 .192 .OOn .Iq9 .?02
_-^u6t —071 .jS5 .c*£>-. iC^ —l^S — lH5-.lao ^165 _.1(,9-^ J72 — 1 V»— I7o — 178 ^j79-.lBJ_. jBg _.l83 . l£5 ^ 137 -,.189 — QOO -.OOn .0"0 ,2n2
• 07u .uSi .u«<; -ij1* -ilc. ,1J? .l-»n .loo .!67 ,17C -573 .376 .178 .179 .jBl .182 .lf*3 .lP .J.,6 .lS5-_lo7- .171-.171* -.]7o -.178 .180 . 162 - 183 -. 1^1-.!«'»—166 - Ifld .JS7 , IBS — l9j ... 000 .201 .203
.l&t .^17 .1^9 .11; .1 = 1 .162 .lotJ .172 .175 .177 .)79 .180 .18? .183 .184 .185 .166 .187 .117 .1«8 .000 .19P .201 .201
.lOo .112 -i?i .lit .;".'.• .Iaft-.lu5 -.17j .173-.175 .177-.179-.ISO-.182 -.183-.185-,!h6-.J87- .187_188 ^188-^000-.J9B .2P1 ,2n4
.lOu .lib .i^9 .liO . iD] .lo'-i .165 .170 .173 .175 .177 .176 ,i6u .181 .163 .186 .1 «7 .1"0 .IBB .1B8 .181 .000 .000 .010 .?(|4
.lie .IcH .^3-) . 1<*7 . i5t- .1^? . 1«7 ,171 .i73 .175 .177 .173 -.179 . Jfil-.iat -,1«7 .^BB-.1P8-, 1F.8 , 1B6 --. 169- ,000 -. In7 .000 .?04
•llo .liC .i42 .1^1 .i5j .to3 .Id7 ,17u .173 .175 .]7o .178 .179 .1*1 .165 .117 ,]BB .1P9 .119 ,1«9 .IB" .193 .191 ,0"0 ,?05
.i3<. .157 .i".7 .!:,<. . Ib'J . loi . Io7 .12 .186 .137 .IBB .189 .190 .190 .190-.000 .000 .OPO. .205
• l3i .142 . ibO .ljf» .!•'),- .loT -lof- .lo'J .i7l .173 .175 .177 .179 .!«? .166 .117 . JflO .190 .190 .191 .000 .000 .000 .OHO .Ono
.14S> .ib2 .IjO .iS1" .!L2 .luc . 1 u-i .1/0 .173 .l7b .177 .179 .1S2 .135 .1*7 . 1"B .1?! .191 ,1°2 .000-. 000 .000 .0"0 ,?06
.11,^ .i5J .ID.. .;:..• .Jo; . IMi .Jj/ .j69 .17"- . • 7-» .176 .179 .1?2 .185 ,!°7 .l«f .191 .1«2 .193 .000 ,000 .OOP .0"0 .206
ib'l .1-)".' .;-•'- .Jo! .1-1 . lj-i ,j69 .171 ,;7i, .170 .'.74 .I"! .lt>3 . ! •' & . 1W. .190 .193 .196 ,0no ,000 .OOr .0^0 .206
83
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—7£1 -- - J--L.A.-*IU;FILLO «NAi_YiIi — - - — ANAL70 PAGE -- 27- -23 MAR 73 18:18:05
SRIDr'RINT OF v( X. Y) IN UNITS l.OOoO + CZ
-,013-.UU2-.OH2 .ol? .0*2-0*1- .041-.G:'l .042 .012 .012 .0"*3 .013 .oil .037 .000 .000 .000 .000 .026-. Oil .038 .031-.030
.011 .013 .012 .013 .013 .0*1 .011 .oil .043 .(-U2 .OH .039 .037 ,o31 ,C12 .000 .000 .000 .000 .031 .011 .011 .012 .015
--.oil .013 .1)13 .013 .(jl3 .015 .0-.6 .017^016 .015 .f.12 .039 .036 .032 .025 .016 .006 .000 .000 .000 .000-.008-.OOB-. 001-.000
.013 .01-2 -u12 .013 .31114 .016 .0-19 .OD2 .051 .017 ,c12 .038 .031 .029 .022 .011 .000 .000 .000 .000 .027-.012-. 015-. OH-.011
--.fc12 .012-.042 .utl .0'12 .015 ,0'->3 >C°2 ,c57 .019 .t12 .037 ,c3i .028-.023 .018 ,o?l .000 .000 .000 .000-.010~.0l5-.0l3-.015
.b1 -o73 .010 -c-37 .033 .021 .020-. Oil .017 .017 .016 .027 .000 .003-.001-.006-. 006-.007
• OU .013 .oil .037 .331 ,ca6 .03'} .OjJ .000 .023 .C^O .019 .COU .013 .Qll .019 .oil .011 .0?B .000 .007 .003 .002 .001 .000
---.l>1o .01,5 .043 .Oj9 .032 .060 .000 .5^0 .aZl .£).<) .015 .CjO .10? ,0l2 .013 .012 ,0<>e .OlO .018 ,0u5 .006 .003 .015 .008 .007
.019 .o-)9 .013 .016 ,o3"4 .000 -065 .0/2 .Q25 .016 .ell .008 .OlO -010 -009 .OO8 .008 .OOB .010 .028 .QO? .005 .000 .008 .020
.^5^ .053-.U51 .06fi .,>71-.li,l .o'/5 ,052 .()26-.Oir> .{il2-.CH .OlO .008 "007-.006 .006-.009 .010 .Oil .002 .000 .000 .000 .022
.U5» .056 ,j53 .063 .072 .07" -075 .015 ,&22 .015 -ell .011 .009 .007 .006 .001 .005 .007 .007 .005 .009 .031 .007 .000 .001
—,j5/ ,05d .059 .«o2 .u66 — Co9 .0^9-.Oi8-.£,l7 - .Ol& .013 .011 .009 .007--.005-.003-.001 .005-.006 .001 .016-.000 .OlO .000 .000
.l)5o .O5t) .j59 .QUJ .jo? .oo3 .0"! .033 .Ul7 .Oil -C12 .011 .009 .007 .005 .002 .flOl .005 .005 .005 .012 .016 .POO .018 .013
-.()Sd-.058 .ySa-.05? .oS9-.C58.oa7.0^9 ,015 .012-.£,11 -.010-.008 .007-.005 .OQ3-.005-.001 .003 .005 .007- .011 ..000 .016 .008
•fl5o .058 ,jb7 .057 .057 .Ci5 .0'*7 .021 .Ql5 .Oil .010 -008 -006 .007 .006 .005 ,fl06 .OO3 -002 .003 .005 .000 .022 .015 .012
• 1)57 ,o57-*,)57-.J56 ,O55-.060 .0-53 .020--.013 .010 .OOft-.OO7 .007 .007-.009 .OO'-.flOS—.002 .002-.002 ,00"-.000 .017 ,016 ,012
.l)5u ,057 .j56 .055 .oS2 .037 .0^5 .017 .012 .Ofl9 .007 .007 .C07 .006 .013 .013 .003 .001 .001 .Ofll .001 .000 .000 .000-,002
.u54 ,05
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--L.A.--.I,.!*IUO-hHAl.YCIS- . - -AHAL70 PAGC 28_23 .MAR. 73 .ie:«ia:06 -
SETS=V
JT OF 01 X, Y) ill UNITS 1.0000*02
.4,2V-..02&-.ijaa—C29 .G30-W?—033--0,>u-. G3fl-. OHO .01G-..039 ^ o3o-.030 — 015--. PES—. 0"0 .000 -OOO -000 .,145. ,.086 ..OMB .019-..005
.i)3u .029 ,u29 .029 .030 .031 ,032 .OJ6 .(,30 .010 .CHI .OHO .03fa .033 .025 .021 .000 .000 .000 .000 .070 .061 .03R .016-.003
-.«3.i .030 .j29._o£9 .024 -CuO—032—C36 .,,039 ^012 ..r.H3--.p12 - . OH —037 —033-.027 -012-.000 ..000-..000-. 000-.036—023 .011-.001
.03.1 .030 .J29 .029 . c,2B .UO .0-C .03b .OH .01^ .0*6 .OH6 ,'i'l5 .OH3 .012 .ClHH .o"0 .000 .000 .000 .0?! .00q .010 .006 .001
.G31--.030 .029 ,(.;&-. i,26-.021--. 025 .1.31-.046-Ofal—652—051 .OH9-.-Oia-.W9 . 052 -.0S6 — 000 -000— 000-.003-. 003—001-.002 .002
.H3l .030..030 .Ofc9 ,j25 .ClB -Oil • 031 -031 .023-0^3 .00o--.00tt — 0a6—073 -.0-63 -060 -.(T4-6—. 03H -.025 — 0?8 -. 026 -.017 _. 005 ^ OOO-.-Ol^-^OlS-.OOg-. 003. . 004
,U3(1 .OJi: .033 .035 .oJ1* .011 -000 .CuO -000 -Oo^ . p55 .036 .021 .021 .021 .022 .017 .0)1 .012 .OnO-.0?0-.017-.01?-.OP1 .001
,03-1 -.i>36.-C^O -.o11--«CoO -000 .000—031-»C33 ^p2fa -020 —f>la-.019_01fl -010 . OlO -. 009 .005-. 013^. 016-. 019-.012-.DD2 ,P01
.031 .Q33 .c.i.7 .066 .000 .OJ'1 -Oo9 .flU -OlS .nil .013 ,pl6 -.015 .Oil -008 .On6 '005 .005 .001-. Q11-. 017 .000-.002-.P01
-U3J-.033 ..j3ti .015 .OEH .Cl6 .(,16 -.013— 0»a — Oo7 .rOa—.010 —OlO — 009-. 006 — 006 .-.001 -.003 .OM-.006-.012--.000 -.000 -.000 .006
• 03u .032 .U35 .037 .U3b ,c<;1 .016 .Ol2 .007 .Qc"1 -006 -OO6 .CO" .006 .006 .005 .003 .Q02-.OP1-. On3-.003-.001~.00^ .000 .002
.tl3o -031 .j3 -.023. .019 . 010— 007 .Oc6— POH .003 -. 002—fl02-.002 — 003-.005.-.OOH .002 -.OOl-.OOl-. 000 -.000 - . 001 .001
.030 .030 .CtB .Q27 ,C.£t .OiS .Cu" .005 .Co1* -C03 .002 .001 .000 .001 .003 .001 .003 .C02 .OOl-.Ofl .000 .003 .001 .002
• G3l .030 ^O3o .0<;9 . -j?.t> .0^1 -C^l ,Gj5--,c03-,0fl2 —e01-.000-.'C!l-.005--.o01 .003~.o01--.003 .003 _ OOl-.OOO--.000--000 -.001 ,002
.L'3U .031 .C'31 .039 .Oi'l .015 .[C6 .ru2 .U01-.000-.p01-.00 .003 .000-.001 .000 ,001 .001 .001 ,007 ,000 .000 .OOP-.000
.1,3., .0£0 oil -CO-*-. jCl-.fu3-.CC1*-. Cob-. ;01-.0c?-.002-. 002-.fOi-. 001-.001-. 000 .000 .003 .001 .005 .000 .000 .000 .000 .000
.017 .a07-.t Jl-.1/C2-.','u3-.C"-'''-.Cu'*-.uUl-.00^-.('02-.Oo2 .001-. 901-.003-. 000 .OnO-.001 .001-.005 .000 .000 .000 .000 .001
.OJU .U0d .OC2-.030-.rc?-.0'c''-.C|^b-.L'0'<-.Ol,"'!-.f.02-.OOl-.rOO-.D03-.005-.no3-.oni-.000 .P01 .010 .000 .000 .000 .000 .003
• liio .Ol."- .{/O^ .OjJ .LGl-.rCl~.',")".Ci,l-.u'33-.r._'!'-.r03 .002 . "0 J-. B06--.010- .PP9-.()01-.001 .003 .013 .000 .000 .000 .000-.005
71 1 UF S< tu.'Lii:.:^) 7-1 (. c, J1 93 96 91 VlJ ol )12 M
,(,-.. --nn, OK- ^ t ft-^; 'i—(f- j,y;f,i, o,,;^" OF- 2-7 -r^n;',-«jTO-uo:^/i—So ->ia-—"4 •
85
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218 --4-,A,-»lN;iFICLD-AtMLVSJS HNAL7.O PAGE -29—23 MAR 73 18JH8:M
SE1S=8
GIUDPRilJT OF 1 < X. Y) IN UNITb 1.00CO+C3
.4—064 ..o64~.t;64-—G&4 -064— Ol>» ..064-.0&U —06»—G&4 ,064-,o64—.064—064.-.;»64 —064 — <-64 -P&<; -0°4 ,0i>4-..o64—064 ^064 ,.064- ,p64 ..06»l — 06^_064 -.068 -.076 _.o82 . 095—087 —0^0 -093 .,096—100
.1)64 .Dot .U&4 ,0ot .064 .Co4 .001 .Out . 0&4 ,064 .C&H .06"» .p6»6t — r.6'l-.<'6'* -.06^— 064_^o6l»-.06fl-»o73--.o7T .062-. 036_ 088-^091 — 09i(_ 097 _100
U6l« .Ool .0&1* .Col -064 .0611 .061 .Dot .064 .Ool .064 .064 .064 .067 .069 .tflZ .075 .079 .083 .087 .0«9 .-092 .095 .097 ,100
__ .0&H--.06U-. I)64_fro*-.v6* .Del— .O6b-.&o&-.0o4-^064-.oi4— 067-. 0^9—071—. 073—0-75 ~.o7B-^081_ 086 . OS9_.o9l— .093--095_09B_.100
..&64 .ot,i» .yOl .Ool -u61 .Oo'4 .0&7 .OoB .067 .Oo8 -0&9 ^071 ,c74 .075 .077 .079 .08! .083 .fl87 .091 .092 .095 .096 .OqB ,100
..064- ,U64-,064 _j6l, -.065 .0&9 -,0->9— 07t-.O71 -,c,73-,l>74_.|;76 — 07B_^7-9—.<|8l-.o83-.0B6--.oB9 ^093 -.094—.096-.098-.099--.101
.064 ,ofa-» -Ot)4 -.o6i( .Ot>5 «0o7 .070 .073 .075 .C76 .077 .Q79 .081 .of>2 .083 .0B5 .O"8 ,091 .095 .098 ,Q98 .100 .100 .101
-.083—.QB1—.366 ..Qfl7 -»o90-*092--.09-*_096—»100—.101-. 101-.101
-.064 .064 .0&4 ,0o4 .1,64 .Ool .0°6 .074 .jBl .063 .fB3 .083-084 .085 .fl87 .088 .0^8 .091 .093 .095 ,097 ,Q99 ,()99 ,103 .105
.^6H_064_.o64^.0o4_-.o64-^4-.85-r687—,e89-,090—.092—.093-.091*—.095—096 -.096 -.098—.103^-. 105--, 104—,107
.064 .064 .066 .069 .071 .075 .079 ,oB2 .084 .086 .088 .o9fl .091 .093 .095 ,fl95 .096 .096 .096 .098 .101 .103 .103 .107
.U6-* .064 .064 ,069 .07S- .9l .093-.o93 .093 ,o95--t095--.o96-.097 .099-.101 .100-.101 ,10<»
,07o .07« ,j62 .Cd4 .084 .Obf ,025 .Oo6 ,u87 .088 .089 .090 .091 .092 .093 .093 .094 .095 .095 .096 .099 .101 .102 .102 .105
.089-.fl9l-,09g ,053 ,093 .o9* ,0°5 -.096 -.097 -.099 ,lol ,102 .lnV.107
86
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.031' .043 .051 .flSn .Ot>5 .0"'3 .Dili -u" -lO9 .117 .121 .13o .137 .113 .It7 ,1M .156 .162 .000 .1«0 .177 .171 .171 .168
-034 .041 ,049 .056 .062 . OoO .OCQ. .CiO -.112 -121 .123 .134 .140 .145-.l5Q .154 .157-.160 .164 .176 .178 .176 .174 ,l7l .168
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.•.0'tt-.052 .jfco -06B .07!> .000 .000 .Ojfl .139-. 143 .147 .150 .153 .156 -.159 .162 .16M ,166 .168 .173 _. 175-. 174 .173 .171 .169
.(,49 .05U .j67 .076 ,(,Kt, .OSO .1^? .1J7 .144 .148 .]5l .153 .156 .159 .161 .164 ,lftf, .167 .169 .172 .174 .173 .173 .17] .169
.flu1* 4U74 .064 .o9i, .Ii3-.li8 .140 .l46~.15r, .J53 .156.. 158-. 161 - .163 .165 .166 .168..170 .171 .172.,173 .173 .172 .170
.069 tu6o .091 .103 .117 .131 .m2 .148 .151 .154 .157 .!&o .162 .164 .165 .1*7 .168 .l^o .171 .172 .173 .173 .17? ,17o
.fl7t) .0Bi .0*7 ,10'J .]<;! .134 ,n,l» .149 .152 .ibb .150 .]6o .163 .164 .166 .167 .168 .170 .171 .172 .J.73 .173 .172 .171
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.079 .090 .101 .112 .123 .U3 .143 ,ln9 .152 .155 .157 .159 .]6l .163 .164 .166 .167 .169 .170 .171 .172 .173 .175 .173 .172
,j8, .09% .XC& .117 .127 .107 .145 .IbO .153 .155 .157 .159 .160 .162 .164-.166 .167 .169 .170 .170 .172 .173 .17.1 .173 .172
.089 .ICO .ill .122 .132 .1'tO .l'»6 ,]:>u .152 .15* .156 .158 .159 .161 .163 .166 .1*7 .168 .169 .170 .171 .173 .173 .173 .173
,(j<3-j .106 .^17 .1^7 .iis .!,] .i;t-.l,y .^52 ,JS4 . ] bS .157 .159-. 16o .163 .166 . ] 67 .1^8 .lf-9 .170 .171 ,172 .173 .173 .173
.100 -111 .j.22 .1JO .137 .14? , 1-.5 .1,6 .151 .lj' ,1?H .156 .158 .159 .163 .165 ,]fi6 .168 ,lf,9 .170 .171 .172 .173 ,17J ,]73
.lOj .Ho .l^o .1^^ ,ii7 ,1-tl .l«tfc ,1^7 .149 .Ibl .l')3 .154 .156 .159 .162 .164 , 1*Sb .167 ,lf.« .169 .171 .172 .173 .171) .171,
.Ho .liJ •i2'i -1.53 ..3'' . Inr .1^3 ,1'tb -147 .149 ,]5i .]53 ,5S5 .150 .161 .162 .]64 .166 .167 .169 .170 .172 .173 . 174 .174
• lie, .1*3 ,1?'J .1J3 .j.it, .JJQ .1-,] .]-.-, .146 .14"? .ibj ^152 .154 ,ir.7 .159 .161 .163 ,165 .166 .168 .17Q .171 .173 .174 ,)74
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87
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AUA1.70.-PAGE 31—23JMR
OF Vt Xi Y) IN UNITS 1.0000+01
3i»6-.3U7-_>349 -.351 .351-, J57 -.362^366 -.304^,000—.000 -000 .000—27S-.35I1 -.321 -291--262
_ _ ^ ____.- _J __ __ __ '_ _
— 39J .370 ..J63 .3f>l .363 .3o7 .371 .373 .372 .3t>6 .359 .350 .339 .321 .279 .121 .000 .000 .000 .000 .217 .071 .095 .101 .110
-.370^.371-.J68 ,I09 -;7 -.296 — 246-- 180 -009-.000 -OOO-.OOO-.148-.o96-.072-.043-.029
.372 .371 .J69 .371 .374 .390 .127 ,4bO .440 .4()9 .376 .348 .321 .290 .215 .174 .007 .000 .000 .OCO-.040-.149-. 1 So-. 126-.130
,~.-}66—36Z—,573 .399—«&3_5u7-.500—«32-3flo ~315—3-19—297-_262-.229 -217.-356 _000 .000-^085^. 119-.170-.J63-.18fl
.372 ,J66 .357 .349 .3^B .<*98 .BoO .b79 .132 .367 .33t .313 .308 ,2U3 .213 .201 .281 .359 .000-.o92-.12M-.16o-.1&7-.IflS
624—350 -32b_311- .279-^260 —155—lB9_,i7l» _. 158^305- .3H1-.016--093--13S-- 150-.17Q
-397 .392 .378 .3tB .;9b .255 ,000 .OoO .QOO «193 .263 .233 .177 .179 .It3 .189 .116 .118 .2*6 .2'55-.o?t-.07o-.Ot»<'-. I2t-. 155
309 ,000 .OOt-.CjO-.E31-.lfl3 .17! .151— .13fr- .15g ..lie .430 .091 ^.099 ,lt7 ,235_.ol7-.057-.0'»lt_.108-. 13&
.tSo .454 .450 ."t33 .329 .000 -731 .tb2 ,31*7 .167 .137 .126 .117 .139 .11U .0^7 .flSS -086 -091 .207-.0l7-.0m-.038-.o"8-.llilo_.b47_a5o-.55i*—&57-,5b3--520--2^'*~.l;'*5-.12l(_ji7 -.1JO — 100--087-—o74 —058 —o72-.o59-.p51 —OS3-.o56_.013-.017-.Otl-.067
.5tS .5"m .5^3 .b38 .528 .tfl6 .213 .138 .112 .102 .096 .Q9o .085 .oao .072 -077 .o5"» .C»8 .052 .fl57 .02H-.006-.o32-.058
-.t>»0- .533-.S2fr-.463-.293--.104-, 121-^ 1<)2- -.e^o -^086-. |>83--. 082--.O'1* -.095-»o70—o53-.OtS--.0»7-.06&--028 —003--023-. 049
,b4t> .b4H ,b38 .522 .486 .335 .232 .162 .117 .09U .p8o .078 .081 .078 .125 .126 .flSBioSO .0*7 .018 .068 .039 .012-.011-.OUO
.t^->-.i>51 -.&43- .479-.J60-.a*e-^.l4i»-.144-Tioa-.OB8 .072 -.081-. 078- . 107-.159-.o95-.o53-.o51 .0^9 -. 0«9 ,o««t .0«» - .019-.006-.031
,b64 .b60 .505 .365 .<;7:> .212 .168 .131 .100 .04>6 .072 .102 .071 .126 .127 .074 .0&6 .057 .053 .053 .110 .0*6 .025 .012-.022
.011-.54& ,397 .230-.215-.177- .1<>8 .121 ,»94 .OS9-.001 .105-.085-.203 .108 .071 .088 .062 -.058- .059 .119 -,018 .031 .011-.Oil
.bO<* .444 .J13 .213 .172 .151 .133 .116 .fl99 .095 .088 .099 .105 .224 .099 .073 .124 .061 .063 .061 .161 .050 .040 ,0?4 .004
.jflo .347 .^32 .158-.147 .Ii4-.l24 .113 ,103 ,lc2 .c92^.093-. 117- . 155 . lll-.O™-. 110 -.077-.065 -.071 ,166 .060 .055 ,0«2 .024
.24a .232 .145 .1^3 .,.24 .118 .112 .111 .106 .Ic8 .r94 .097 .123 .126 .112 .088 . o°6 .101 .P'4 .082 .100 .080 .076 .0^8 .053
.i2? .077 .085 .C9B- .10c .Iu2-.lt)3 .lut> ,1-Ofr .lcA .107 .lo* .105 .097 .101-. IC'6-. 101 .Ie3—1{)6-. 107 ~.09O~.1CO . 100 .099-.095-
88
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-. L.A.-nlUUrTCI a -AUALYSli - -- - - -ANAL70-PAGE —32—23-KAR 73-
6R10PR1NT OF U( X. Y) IN wIlTS l.OOJO-lOZ
—02A -.fe2!>- .0.1D--J2V.—OtO —031—.033 — S36 ~,<)3S-_ 039--.039 — 03B_.03 ,c^i> .u^1* .0^3 ..<)2«_0il-. 0*2 -,0".7-.0*7- .017 .<.«& .O'i7-,nlt9 ,052 .Q5G..03& -. COO —000 ^C01-.00'*-.00';_.0n3 .001
.02"' .U2o .Oi6 .023 . OiB .012 ,C<:S ,j53 . Ob5 . 0&2 .OTiO .fib ,0'»7 .Q1*6 .039 .0^6 ,0?7 .018 .000-.00?—. 003-. OOP .0"! .002
,027 .027 -.0^7 .i)£t>-. fi^? ,00»-.0»,0 , o77 -. Oo5 . cS5 .051 -."18-.039 -•• 02<> -020 . o?5--. 019 — 011--. 005-.01I'-.005--.00?--1 000 -.003
.027 .o2'J .OJ1 .U31 .a1*! .0^0 -OuO -O0u -ObO -C52 . plO -n29 .023 .£,2? .022 .Ql7 .0)3 .009-. 0! 3-. Q08-. OH6-.003 .OHO .003
-.^^! . Oi5 -.G39 .0^,0 .o<.-0--.CuO-,o2'1-.Oi?-.n2a^022_.nl9-,Ol9-017 -.010 .OlO--003 , OOS-.OflS--, 006-.006-.n01 .001 .002
.U3J .cm .(jb? .OoO .0^6 .C1H .Ol& -01& .CIS . Ol1* -nl5 .013 .009 .007 .005 .001 -OO1* . OQl-.005-.003-.001 .000 .002
--.,,23 -.Oil -.(,3i . C,J9--. uHc— 015— Oi5 -.C13 —<,!»-. OO9 -C-09 -.010 -• 009 -.007--006 -OO1*-—0"3-.002 -.002-. 00"*-. 006--001r.OOO .001- .002
tu2.> ,O^S .uio .032 ,j3n .Oil .0*5 .012 .{,07 ,0o5 .fdo .C05 .r05 .001 -CO1* .003 .50? .001-.C01-.OQ2-.00? .002 .00? .001 ,002
.U2i-.027 ,02r) -u27-.o2S-.OiO .Ci"1 -.OjJ -uC't .OtA .801 .003-.003~.002 .002 -.001 ,o"0-.001—OOO-.OOO .002- -001-~nOO .001 -.002
,02o .026 ,j2o .C2b .023 .0 .o2!i .021* .023 .;.<:! ,0i3 ,GU5 -(.o2 .00? .P01-.?0l-.f102-.002-.o02-.000 .010-. 000-.000-. 000-. 001-. 001 .000 .001 .002
-.U2o-.o;'o .j2£> .Ci5-.o24 .C19 .Q07 .0^2 . OCO-. 001--002-. ?03-. 003-. 001-. 003-. 001-.0f>0-.001-.001-. Onl--,OOC-,0-.Occ>-.--06-.'iC16-.r05-.003 .O00-.003--.nn3-. 002-. 002-.001-. 001-^000 -.000 .001 .002
.U2u .Or.7 .^j23 .«.-12 . JdU-.^oJ-.o J"-.fijo-.r,07-.Oj7-.' a7-.005-.rC5-.OOt-. 0&2-.005-.omi-. TP3-.002-.002-.001-.000 .000 .001 .002
-.u27 .Uib ,i.lb .Gj6 .00!-.i.u'i-. Jv7-.0jd-.i0a-.0u"-. ",J7-.C'07-.f-Cy-.CCM|-.c06-.006-,006-,00't-.OC3-.Cn3-.00?-.001-.OOn ,011 .002
.o20 .Ulfa .,'07 .Cjl-.a04-.''.jf,-.O^P,-.0^9-. ,Ofl-.Oo-l-.-,07-.007-.:07-.006-.007-.007-.Of'6-.OOJ,-.OOl-.001-.002-.002-.001 .OHO .002
-.o£7 .013 .00-»-.0'j3-. OOh-.3-j7-.fiOS-.C jd-.-j09-.036-.o06-, 007-.o06-.007-. 009-. 008-.oOB-.006-.006-.OOt>-.on1— .091-. 00?-.001 .002
.u2o ,01b , uO1*-. 002-, ;U.i-.; „•"'-. C''a-,- „«-. U09-.0j9-. f)0;i-. 1fl7-. ^07-. 0?9-. oil-. 010-. onq-. 0'0-. 000-.006-.006-.006-.00il-. 00? .002
-.jiu .OO-i-.-O J-.'JJ.^-. ,0"-."l.f-.:ii7-.0j7-... 19-. 0:; °-. •< ri»-, f-nb-. c Ob-. 012-.clh-.nl 5-. <)t?-. 01 1-. 01 1-. 006-. 013-. 00«-. OOf,-. On3 .001
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89
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_ _ == : -ANAL70 PAGE 33-23-MAR 73 1B;U9!37--
toRIDHRiNT OF T( X. Y) IN UNITS 1.0000+03
.Oo* .^ .Ob*-.u6* -.OoU-.O"* «06* .U&U-.06* .(16* .06* .O61-.0ht-.o6* '0&* • 0&9 ,075 .078..032-.085-.089 .093 .097 .102
.06* . u6» .ub* . C'6l .Cot .0&* *0o* . 06* .06* .06* .06* . 06* .06* '0»* .06* . Ofi9 >fl7* .079 . QH3 .086 . OB9 .093 .097 .101
.Out-1)6* .06* .(16* .Oo* -0Q* .Ob*-.06* .061 .«6j6'*-.l,6* -c-6* -Gt*-—0"5 .Oo6-.o6* .06* -06* .067 .1)69 .O7l-.fl72.o75 .078 .081 .086 .089-.Q91 .09* .096-.0°9 .101
Ofa* «o&* -Co* .06* .06* .067 ,po6 .067 .06« -0&9 .071 ,o73 .07* .o?6 .078 .ofio .0R3 '0*1 »091 .fl93 .095 .097 ,0"9 .101
-.4,64 ^ 06*—06* -.00* .u6i( .Ou5-.069 .Ot>9-.Q69 .071-072 .07* .075 .077 .079 .flSO .083 .085 .089 .093 .Q95-.097 .099 .100 .102
• fl6n .fl6* «U6* .Oo* .0&U .Oo5 .0<=7 .070 -u72 -07* -o75 .076 .Q76 .Oflfl -O8! .0S2 .0s* '0B7 .090 .096 ,Q99 .Q98 .101 .101 .102
-.I)<»*-.U6* .06* Vtf6*—0<>*—.0D7-.C.72-.075-^077-.o7d-.079-.(180 .082 .Q83-.08* .08& .O89 .092 .09*. .097-. 100 .101 .102 .105
.Out .06* .06* .06* .Oo* .0°6 «C7U .4,80 .081 -cB2 .082 .083 .O8* .065 .086 ,086 .090 .09? .095 .097 .099 .100 .10* .106
,06* «06*--0-.oa9—085-.08* -08* .Q8S .086-.088 - .089 .o9o .Q92-.09* .096. .o98_ .100-.101 - .10* .10*
,06* .06* .Oo* .06* .06'! .OoM .07* .0^2 .08* .085 .085 .n86 .088 .Q9o .092 .Oq2 .09* .095 .096 .Q9B .099 .101 .102 .107
«i)6««-.0&* .«&* .Oo*-.t)6* -.0t>*-.0°7 •O7*--.flao-.083 .085 .086 .987 .069-.o91-.o92 .O9*-.095 .095 .09-7 .098 .099 .103-106 .108
,i&4 .06t .06* .OLt .06* .Oo* .070 .075 .079 .083 .C85 .087 .083 .090 -092 .093 .095 .095 .096 .097 .Q98 .101 .105 .107 .109
.06*- .06*-.Oo* .o6*_eoft -073 .077-»o80-«083 .o8fr .088-^089 .091—.Q92 - .09*-.o95-.o96--.o97- .097 -.098- ,lo*-.106 . 105 . 10B -
.Ob* .06* .Ol>6 .069 .072 .075 .079 .(j82 .085 .087 .089 .091 .092 .09* .096 .Q96. .098 .097 .098 .099 .102 .10* .10* .108
-.fe6"»-.Ou*- ,u6*-.069-.G72 ,075—.0*6 .Oofc-.tffiS—-067 .089 .091 ,Q9i: .09* .095-.096 .096-.097 .097 .098. .099 .103-. 105 .10* .108
• U&-, .Out .1)68 .072 .u7b .078 .0 .080 .iititt .cBb .Oo5 .flof' -087 .Q69-.090 .c9fl .091 .092 .09*-.o9* .09* .096-.096 .0«7 ,o<>8 ,100 .102 .101 .102 .105
.(,7o .079 .(j(J£ .Co* .j»5 ,0s5 .03f> ."'>"' . J68 ,0o9 .089 .090 .09.2 .093 .Q9* ,09* .o°1 .096 .096 .097 .100 .102 .103 .103 .106
- «t,(U .OS2 ,o82-.0tl3 .uu3-.C»*-tO'>3 .Ob7 ,067 .Ob« .C>i9-.090 -09£ .092-.093 .09* .f)9* ,095 .096 ,0q8 .100 .102 .103 .10* .108
90
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-709 - - - --L,,ft,-«JwW ICI.B-ANAL^SIS -— ANAL70PAGE - .31—23-V»R 73 .18:50: 00
OHJDr'RIf.T Of fnl ( X. Y) IN UNITS 1.0000+03
...oO.i-010 . U17—C.;J-.,j3o—036 -{M3--.CJO—.OS6 _ Ct.3 —c&9-.n76 ..032 -.089. .096 — 104 — 000 .OCO-.COO .000-.132...140 _«146 -.152 -158
-.00' ,01b .(J21 .028 ,'j35 .042 .OH9 .PiO .0"3 •07'.' .r.76 .Cf-3 .P9o .096 .102 .106 .000 .000 .000 .000 .150 .152 .153 .1*5 .157
-.01^ -019 -,>2o -033 .QIC .047 ,oS4 .Ou2 ,&7fl - .077 —( 84 .- 191 -,f97 . 103 .100 . ] 12 - 115 -.000 .000 -.000 -.161 .160 -.159 -. 158 ..157
.017 ,0e4 . o31 .036 .ulb ,l'b? -0°0 .CoJ .J7t .Cot -C92 .C99 .105 .111 .116 ,1?0 .1?2 .000 .000 .000 .167 .165 .162 .1^9 .157
— U2.i -029 ..C3o --043-.oS£i-.CJ7 -fruS—O?1* — 0<>1 -033-.10u-.107 — 11* -120— 125-. 130 .1^1 -.111 -000 .000 -.169 —167—163 .160 .157
.U2/ -Oi4 .ull .r. 47 .L,='t .COT .flCift .079 ..j93 .1^,2 .109 .117 .123 .129 .135 .179 .113 .I'lS .153 .000 .16,1 .167 .16* .16] . ] S7
.039 .j^o ,,;o£ .ut>f>-.f-o«- .000~.00>>.10i)-.li3-.119 .l?7-.]32 -. 137-^. JU2-. 1H5-. 1«9-. 152 .155 -. 166^. 168 ^166-^.1614 .161-.158
. OH-* .o&l -Ubo . ub-» .009 .floO .CuO .yCO .1?6 -13Q .136 .mo .113 .117 .151 .153 .155 .158 .165 .166 .165 .163 .1M .158
•<)L>'i .vs"/--0ft -u7o -.£-oO -.000—0j»—131 .135^133 . 1 ^i _ 115 -. l^S ^ 151 -. l5t. . l56_.l57_J. 160--.163 . 165 „, 164-.163 .l6l_.159
-Obi .joi .071 .U76 .0^0 .115 .129 .136 .Ii9 .1H2 .115 .IKS .151 .J53 .155 .157 .159 .160 .163 .16'! .161 ,163 .1*1 .159
.Oi-0-.o6y -079 .o9c -luf. .1^0 .ijl -13« .In?— )1b -1 .135 .141 .145 .147 .119 .151 .153 .155 .156 .158 .159 .1&0 .161 .162 .163 .163 .163 .163 .161
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.jO"* .O^b ,i05 -lib .125 .1J3 .130 .142 .mb .147 .110 .150 .152 .153 .155 ,157 .159 .160 .160 .161 .162 ,163 .163 .163 .162
- .u8-j .0"J9 .110 .1^0 .l--t- .1^1 .130 .1^1 ,111 ,iMft ,j47 .119 .150 .152 .J55-.1S7 .158-. 159 .160 .161 .162 .163 .163 .163 — 163
.j9-« .10-* .115 .l4;3 .!?--; .iy» .lif .1^0 .113 .141 .146 .I'lS .119 .151 .Ibl ,156 .157 .156 .159 .160 .16? ,163 .163 .163 .163
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.lO-i .113 ,iij .1J5 .12S' .IjT .l->b ,lj7 .139 .mj .]43 .J15 .116 .119 .152 ,153 .lb5 .157 .158 .159 .161 .162 .163 .163 .164
,iO^ .116 -i.il. .l--b >l2^ .Ul .1-5? .!-5J .137 .139 .ill .143 .145 .118 ,lfto .152 .1">3 .155 . 157 .158 .160 .161 .16? .163 . ] 61
.i!4 .lid ,i22 .]_-( .127 . 1.;° .)jl .U-i .130 .130 . ] 39 .111 . t'li .116 .jlf, ,l5o .15? .153 .lr>5 .157 .159 .1&0 .162 .163 ,161
.!„; .1^^ .131 .13', .)lo .1"j . )",£• .111 .lib .147 .119 .151 .153 .155-. 157 .159 -,161 .163 .165
91
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-7.il -^L.A. jiluUFIeiO-rttlAuYilS ANAL70-PAGE- — 35-23.MAR 73 1«:50:01
bETS=9
GR10HRJNT OF V( X( Y) IN UNITS l.OOCO+01
- .HOQ .337 .331 .330-.329 ,37 .085
^351-.317 ..541 .345 .35o .3oO .372-,3UO-.377 .36"* .346 .330 .310 -282 -?37 .174 .010 .000 .000 .000 .135-.092-.06B-.01J-.OWO
.317 .316 ,j15 .346 .351 .37? ,1go .1^^ .113 .366 ,358 .33 .240 .030 -OjO -.592 .318-215 .231-.26{,-.258-. 155 .. 185 .167 .117 .279-.309-.051-.099-.13H-. 153-.159
.370 .365 .JSl .3^1 .272 .230 -OuO .OuO .000 .164 .277 .226 .175 .176 .Ho .181 .110 .ID? .225 .227-.031-.o78-. 100-. l3o-. 149
_..^9l_,3a9-.476-.34i .281 .coo -000-.OuO-.226 .161 .179 .157 .136 .157 .145 ,126..o89 ,o?2 .132 .2o5-.02S-.o65-.fl7?-. 111-. 131
.42t» ,1a4 .420 .1o3 .30? .OJO .723 .6^1 .221 .162 -I3a .128 .116 .138 .112 .095 ,o"5 .QS1 .QflO .178-.Q??-.036-.06l-.fl93-.118
—.450 -.462 -.473 .bu5 '"35 .8^7 .648- ,4bo-.235 .15?-.140 .137-. 133 .110 .095-.0B0 .07I» «081 «075 .079 .003-.013-.05o-. OflO-. 10&
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_ja9 .-_,UA,-»U,QHEl D-A'JALYSIS ANU.70-P-ASE-- -38—23 KAR 73.18:50:56-
toKiOr>RiNT OF PHI ( X. Y) IN UllITS 1.0000+03
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-39_23 -MftR J73-18J50J57
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_7Hl --UA. WJIUFICIO ANAUT5IS ANAL70 PAGE- -.-•»»_ 23 MAR 73 16:51:53 _
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_JZV9 J-_U,A.-.-J,twtF.IEU>-HMAUr.SI-S> AIUL70 PAGE 16 -23-MAR 73 46:52!51 _
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>6fUDrtUNT OF V( X. Y) IN UNITS 1.0000+02 • .
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• 012 -.Ol1* .uli, .-tn4 «0i't .015 .tH& <0l5 «rl5 .&15 .oJ4 .013 .014 .015 .Olt -.015~.015 ,{)15 .000 -.000 -.Ol'i -.Olt -.Olt
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7i,» --L.A. ,,]NliFIELa^4ALTSIS — ANAL70 .PAGE -_. 48 -23- MAR. 73 1B:52!53-.
feFUCVKINT OF U( Xi Y) IN UNITS 1.0000+02
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• u6t .06H .061 .061 .O6t .061 .061 .Ool ,o61 .061 .cf'1 .061 .1361 .066 .067 .070 .073 .076 ,079 .083 ,Q81 .086 .088 .091 .093
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• U61 .061 .Q61 .Uol >o6it .061 .0&5 .069 .g73 .071 .fl71 .075 .Q76 .077 .078 .080 «082 .081 .086 .088 .Q9o .092 .092 .096 .098
»<»64 .061 .061 :-061- .064-.O61 .0°ll-.07S-,o77 ,075- .075 .076 ,{t77 .078 .079-. .080 -,0fi3 -.085 -.086 -.088 .091- .092 -.093 .097 . 096 ._
• u(>t .061 .0&1 .uol .36u .Obi .Q°1 .070 .p71 .075 -076 .077 .078 .079 .fl8o .0"0 .083 .085 .087 .088 .Q9o .091 .093 «fl9l .099
.061 .(,61 .Ool .O6n-.0o4-.0o6-.070 .073-.075-.076 »077-.o7B .080 .0^1 .082 - .081-.OS6 ,087-.089 .fl90-.091 .&95 .098 .100
• U&1* .061 .061 >0o1 .Q61 .Col .Ob8 .071 .o73 .075 .C77 .078 ,fl79 .080 .082 .083 .085 .086 .088 ,089 ,o9fl .093 .097 ,099 ,101
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• 064 .061 .061 .065 .067 .Ou9 ,oV2 .074 -o76 .078 .079 .080 .C8l .082 .085 .087 .flST .090 .089 .089 .Q9o .091 .096 .096 ,ln6
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.073 .i>73 .074 ,U75 .075 .0"/7 ,078 ,Q79 . Oi30 -*060--tBl .083 .081 .065 .086 .086-.087 ,088 .089 .Q9? ,093 .095 .096 .100
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107
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-6R1DPRINT OF V( Xt Y) -IN UNITS -1.0000+01
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110—.0
.267 .^52 .223 .177 .119 .000 ..000 -000 .086 .297 .140 .117 .146 .125 .190 .Q85 .flB2 .200 .000-.0?0-.056-.B6'(-.o79-.o97
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.366 .370 .385 .419 ,49i .5o3 .525 .390 .217 ,lt,3 .162 .131 .111 .091 .074 .tlSl .040 .055 .041 .009 .016 .178 .003 .000 .000
-. 124_105— .087— .068-^O4~.e92-^SO-.<)69—.050-.959_^1—.019-.023-^831-.O25— 000 — 000-.051
.394 .395 .397 .399 ,4oo .397 .373 .235 .153 .119 .101 .091 .085 .oBl .077 .063 ,fl6l .021 .009 .Oil .012 .000 .000 .fl4o-.0l4
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.380 .387 .388 .385 .382 .310 .223 .Ib9 .114 .089 .072 .070 .076 .073 .141 .131 .028- .OCB-.001-.010-.004 .000 .000 .000 .058
-.a8i_.333-,3fi4 .37fr-.328-.2j6-.181-.145-.697—.076 -.058-.072 -.067-. MS-.190 .078 -.0-15-,005-.0«3~.OW-^003-.«00-.OOn .000 .066
.37-4 .370 .301 .123 ,i:47 .192 .Ii3 .117 .082 .069 .054 .102 .053 .116 .122 .040 .026 .011-.00l-.011 .016 .000 .000 .000 .070
— .357 .3b5 .J46 .i45 .188 .l!>6 .131-.-1U4 .071 .073-.O65 .106 .076-, 269 ^86 ,032 -.051-.015-.O04-.OOi- .031 -.000 -.000 .000 .000
.k93 .339 .277 .162 .146 .129 .114 .096 .078 .078 .072 .095 .llfl .000 .0?! .031 .093 .015 .010-. 002 .000 .000 .000 .000 .000
.1,56 .339 .208 .13O-.122 ~.ii2--.103- .093 2 . 0=*3-,0dl>- «T)H5-.OS6 -, fB7 .CB9 -«10e .071 .i»79 .086 .0"0-«081 -,p87—,035-^DOO .000 -.500 -.000 .076
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108
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7l»<4 - L.A.-»lMJI=-IElO-ANAl.riIS ANAL70 £AGE -52 -23 MAR 73 Ifl:53:i5
bE.TS=13
GH10PKINT OF Ut Xi Yl IM UNITS 1.0000401
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4 ---UA._*rWJM£U>-AUAL^SIS ANAL74-PACE 56—21 MAR .73-.18:51:31
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113
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-650/4-73-001
2.
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
A Mesoscale Windfield Analysis of The Los Angeles
Basin
5. REPORT DATE
June 1973
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
G. E. Anderson
8. PERFORMING ORGANIZATION REPORT NO.
CEM 4121-01-490C
9. PERFORMING ORGANIZATION NAME AND ADDRESS
The Center for the Environment & Man, Inc.
275 Windsor Street
Hartford, Connecticut 06120
10. PROGRAM ELEMENT NO.
1A1009
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
13. TYPE OF REPORT AND PERIOD COVERED
Environmental Protection Agency
National Environmental Research Center
Meteorology Laboratory
Research Triangle Park, North Carolina 27711
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
The rationale, derivation, and use of a mesoscale windfield analysis is
presented. In the program reported on herein, the analysis was applied to a
specific region - the Los Angeles Basin. This application is in support of
a multi-phased effort of modelling ground level and/or three dimenstnal air
pollution distributions in the region. Los Angeles air pollution modelling
efforts supported by the Environmental Protection Agency are using data
collected during an experimental program carried out during the fall of 1969.
The mesoscale windfield analysis described here was specifically applied to
13 hourly periods from 5:00 am to 5:00 pm on 29 September 1969, and one
period at 6:00 am on 30 September 1969.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COS AT I Field/Group
Thesaurus Descriptors
99 Meteorology and Climatology
ATmospheric Motion
Sea Breeze
Temperature
Wind
144 Sanitary Engineering
Atmospheric Pol 1ution
Atmosphere Models
Los Angeles Windfield
Analysis
Topographic Effects
Divergence Analysis
04 (Atmos. Sci)/
01 (Atmos. Pfosics
STATEMENT
19. SECURITY CLASS {ThisReport)
Unclassified
21. NO. OF PAGES
120
Unlimited
20. SECURITY CLASS (Thispage)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
114
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