THE TREATMENT OF METEOROLOGICAL VARIABLES
Appendix C
of
Development of a Simulation Model
for Estimating Ground Level Concentrations
of Photochemical Pollutants
Prepared by
Systems Applications, Inc.
Beverly Hills, California 90212
for the
Air Pollution Control Office
of the Environmental Protection Agency
Durham, North Carolina 27701
-------
THE TREATMENT OF METEOROLOGICAL VARIABLES
Appendix C
of
Development of a Simulation Model
for Estimating Ground Level Concentrations
of Photochemical Pollutants
Philip M. Roth
Steven D. Reynolds
Philip J. W. ROberts
Report 7l-SAI-17
June 1971
Prepared by
Systems Applications, Inc.
Beverly Hills, California 90212
for the
Air Pollution Control Office
of the Environmental Protection Agency
Durham, North Carolina 27701
under Contract CPA 70-148
-------
ACKNOWLEDGMENTS
We are very grateful to Professor James G. Edinger of the.
Department of Meteorology at University of California at Los Angeles
for his many contributions to this work. In addition to his direct
participation in the preparation of' surface wind maps, Professor Edinger
gave readily of his time in a number of informative and helpful
discussions .
We also wish to aCknowledge the contributions of Clarence L.
Nelson, William Tiedemann, and Vikram BUdhraja to various aspects
of this effort. Mr. Nelson supervised and coordinated all computer-
related activities in the data preparation and digitization effort,
including those associated with the interactive computer graphics
system. William Tiedemann converted to digital form and entered onto
coding sheets virtually all surface wind field data. Mr. Budhraja
prepared and digitized all the maps of mixing depth. We wish to
extend our thanks to each of these participants.
Finally, we wish to express our appreciation to the Shell Development
Company, Emeryville, California, for permitting us to us.e their interactive
computer graphics system. Dr. Richard W. Watson and Mr. Leonard Barton
of their staff gave unstintingly of their time in rendering assistance
to us.
-------
CONTENTS
Pacre
-
INTRODUCrION . . . . . . . . . . . . . . . . . . . . . . . . C-l
I. THE INVERSION . . . . .. . . . . . . . . . . . . . . . . . . C-4
A. The Inversion Over Los Angeles . . . . . . . . . . . . . C-6
B. The Work of J. G. Edinger . . . . . . . . . . . . . . C-8
C. Vertical Temperature Profile Data . . . . . . C-9
D. preparation of Maps of Mixing Depth . . . . . . . C-17
E. An Evaluation . . . . . . . . . . . . . . . . . C-21
II. THE SURFACE WINDS . . . . . .. . . . . . . . . . . . C-30
A. The Data . . . . . . . . . . . . . . . . . . . . C-30
B. Preparation of Surface Wind Maps and Conversion to
Digi tal Form . . . . . . . . C-33
III. WINDS ALOFT . . . . . . . . . . . . . . . . . . . . . . . . . . C-39
IV. TREA'lMENT OF TURBULENT DIFFUSIVITY . . . . . . . .C-43
References . . . . . . . . . . . . . . . . . . . C-46
-------
INTRODUCTION
Atmospheric transport and dispersion processes find expression in
the overall airshed model in a number of ways, as can be seen from the
governing conservation equations, in which horizontal turbulent
diffusion is neglected:
aCi aCi aCi aCi a (, aCi)
'it" + u ax + v ay- + w a;- a az \Kz az- + Ri (cl' c2'"'' cp) + 5i
i . 1,2,...,p
(C-l)
for
~~x~~
Ys ~ Y ~ YN
h(x,y) ~ z ~ Hex,y,t)
t > t
- 0
where
x,y = horizontal coordinates
z ~ vertical coordinate
u,v,w ~ three components of average
wind velocity vector
ci = time-averaged concentration
K = turbulent eddy diffusivity
z
S1 = rate of emission of species
elevated sources
of species
i
i
from
Ri ~ rate of production of species
through chemical reaction
Yw' YE' yS' YN -= west, east, south, and north
h(x,y)= terrain elevation
H(x,y,t)-= elevation of the inversion base above sea level
i
The initial and boundary caridi tions are:
boundary
(1)
c1(x,y,z,to) D fi(x,y,z)
a.~i .
-Kzb" 2i (x,y ,t)
at z - h(x,y)
initial
C-l
\';' .
.-,
-------
boundary
(2)
if W ~ 0, then
aCi
-K - =0
z 3z
aCi
if W < 0, then W gi(x,y,z,t)= W ci - Kz a;-
at z = H(x,y,t)
where
3H 3H aH
W = w - u ax - v iY - at
(3)
cico9i (x,y,z,t)
at x = Xw (or ~)
y co yS (or YN)
where
x and yare at boundaries through which the
prevailing winds enter.
and where
Qi(x,y,t) e surface flux of species i
fi(x,y,z) = initial concentration distribution of
species i
gi(x,y,z,t) co function expressing the concentration of
species i on the boundary at points of
inflow.
Wind speed and rvind direction enter through the component variables u, v, and
w. The height of the invel'sion base H must be known in order to specify
the boundary conditions, while the tUI'buZent diffusivity K enters into
z
both the continuity equations and the boundary conditions. One must look
further, however, to appreciate the extent to which the incorporation of
these meteorological variables dominates data preparation and model input
requirements.
In order to integrate the equations of continuity using finite
difference techniques, it is necessary to cre~te a three-dimensional
network of cells having nodes at their centers. In our case, this array
is comprised of 625 nodes in each of ten horizontal layers up to the
inversion, a total of.6250 nodes. The three components of the wind
velocity vector must be specified at each node point for each time step.
This may be accomplished in part by constructing maps which represent
the surface wind field for hourly time intervals using data gathered at the
network of ground-based monitoring stations. Unfortunately, virtually
no measurements are made of the winds aloft. (Of particular interest is the
wind field up to about 3000 feet above the ground~) This wind field must
be specified, however, so as to satisfy the requirement of conservation
of mass at the surface and aloft for.both air and pollutant species. It
is thus necessary either to construct or to calculate wind fields at
regular time intervals for all horizontal layers between the ground and
the base of the inversion. Finally, spatial and temporal variations
in the height of the inversion base must also be entered as data--625 values
of H for each hourly interval.
C-2
-------
It is clear that a very large amount of meteorological information
must be collected, codified, stored, and retrieved in order to carry
out the necessary calculations. For example, thirteen hourly wind fields
at the ground and thirteen hourly inversion maps are required to simulate
a twelve-hour time period. This is' the equivalent of nearly twenty-five
thousand data entries (625 x 13 x 3) --and this despite the fact that the
wind field aloft is not entered as data, but is generated by the computer
program. We emphasize that these data constitute the input requirements
for the daylight hours of only one validation day.
It is apparent that methods of generating, manipulating, and trans-
ferring meteorological' data' are needed that are more sophisticated than manual
dX'afting and translation of hand-drawn maps to punched cards. ' "The. ..
, e~imination of the manual preparation of maps would also be most welcome.
Unfortunately, with the exception of two efforts that have yet to bear
fruit (and which will be described) .;.-the development of a model of
inversion behavior and the application of computer graphics in the
preparation and digitization of wind maps--we have not been able to give
adequate attention to the problem, largely due to limitations in time.
The development of methods and models for organizing, codifying, and
transferring meteorological data, in fact, constitutes a task of highest
priority in future work if the airshed model is to be of general applicability.
Having discussed the difficulties experie.nced in the treat-:nent of
meteorological variables, we turn now to achievements--the preparation and
conversion to digital form of contour maps of surface wind speed and
direction (isotachs and streamlines, respectively) and of the height
of the inversion base--in each case hourly representations. . We have
also explored several approaches to the calculation of the wind field
aloft, one of which ~pears to be a useful method for the automatic
generation of these wind fields. The four sections that follow are
concerned respectively with inversions, surface wind fields, winds aloft,
and turbulent diffusivities. In each section we describe, for the days
of validation,
1)
2)
3)
4)
the computational and data requirements,
the nature of the available data base,
our efforts in satisfying the stated requirements, and
the deficiencies in our approach and, thus, recommended future
efforts as they relate to the particular aspect of meteorology
under discussion. '.
C-3
-'V..
, ...
:1" .'" J
-------
I.
THE INVERSION
A crude measure that is often invoked to characterize air pollution
potential is the ventilation factor U (H-h), where U is the mean wind speed
and H-h is the mean depth through which mixing occurs. When an inversion
is present, H 'is the mean elevation of the inversion base. The ventilation
factor decreases, and the potential for "smogginessn increases, if either
U or JI-h assumes a low value for any length of time. A,S knowledge of these
variables is of major importance in the prediction of ground level
concentrations, we must have the capability of incorporating these
variables, and their variations in space and time, into our model. In
this first section, we focus on the nature of the inversion that persists
over the Los Angeles Basin during the summer and autumn months. In
~ubsequent sections, we direct our attention to the wind field.
The degree to which pollutants will mix and disperse vertically
is best characterized by considering the change in temperature of the
ambient atmosphere with height, the negative of which is termed the
lapse rate, r, where
aT
r 0:: --
dz
Typically, the lapse rate observed in the lowest levels of the atmosphere
is positive, Le., temperature decreases with height. To determine
the extent to which vertical mixing and dispersion will occur in an
atmosphere of known lapse rate, it is only necessary to compare that
lapse rate with the adiabatic rate of cooling, r. (See Figure C-l).
o
ro is the rate of cooling a rising parcel of air will undergo wh~n no
heat is exChanged between the parcel and its surroundings. Suppose,
for example, that a parcel of pOllutant-qearing air is displaced upward
in an atmosphere in which r > r o. The rising parcel will expand adiabatically
and its temperature will decrease, but at a less rapid rate than the decrease
in atmospheric temperature with height. Thus, the parcel will be at a
higher temperature than its surroundings, and being less dense than the
surrounding air, will continue to rise. Similarly, displacement downward
will result in continued sinking. Thus, an atmosphere in which r > ro
is unstable relative to vertical displacements. High dispersion rates
and low pollutant concentrations typify this atmospheric condition.
In contrast, th~ atmosphere i8 stable to vertical displacements
when r < roo A parcel displaced upward will be cooler, and thU$ more
dense, than .its surroundings. It will thus tend to sink to its original
vertical position. Downward displacements are also stable. Consider
now atmospheric conditions under which r is negative, e.q., temperature
increases with height. Such conditions, termed inversions, represent
an extreme in atmospheric stability, conditions under which vertical
displacements are almost entirely suppressed. Finally, we may wish to
characterize the stroength of an inversion, and thus, the degree to which
it will suppress vertical dispersion, by the magnitude of the quantity
r 0 - r. CJ!t is clear that the greater the slope of the vertical temperature
profile dZ ' the more stable is the inversion layer. .
C-4
Fiqure C-l follows.
-------
He1 ght (z)
n
,
U1
Adiabatic Rate
of Cooling
61 ]
[r = --
o 6z
,
,
,
,
,
,
~6r
Stable'
,
,
,
FIGURE C-1.
Very Stable
(i nversi on)
Tempera ture (T)
Representative Atmospheric Temperature Profiles
-------
Inversions form in one of two ways, through cooling from below or
heating from above. Inversions often form, particularly at night, due
to radiation cooling at the ground. Horizontal movement of an air mass
from abpve a warm surface (land) to above a cool surface (water) also
produces an inversion. (Note that at night the land surface may be cooler
than the water} '. Such inversions are termed ground-based or surface.
inversions. Inversions that are the result of heating from above involve
the spreading, sinking, and compression of an air mass as it moves
horizontally. As upper layers undergo the greatest elevation change,
they experience the greatest degree of compression and thus the greatest
increase in temperature. If the temperature increase is sufficient, .
an inversion will result. The sinking and compression process is termed
subsidence and is associated with the clockwise movement of air accompanying
anticyclones.
The two types of inversions described, surface and subsidence, are
over-simplified representations of the vertical temperature profiles
that commonly occur over urban areas. More typical are the profiles shown
in Fiqure C-2. Their most notable feature is that the lapse rate in the
lowest layer is nearly always neutral or unstable. The persistence of
this temperature profile during the night is due primarily to the release
to the atmosphere of heat absorbed by bui ldings, streets, and other city
surfaces during the day. The disturbance of flow and the promotion of
mixing by buildings and other city structures also aids in establishing a
mixing layer. Vertical mixing i,s suppressed, however, throughout the
elevated inversion, denoted by the dashed line in each profile. Thus,
though an inversion is present over a city, there is a region through
which mixing is vigorous and which can be characterized by a "mixing
height", the distance from the ground to the base of the inversion.
A.
The Inversion Over Los Angeles
During the summer months the North Pacific anticyclone, a major
high pressure area, maintains a virtually stationary position several
hundred miles off the coast of California. Air emanating from this
"high" moves in a southeasterly direction along the Pacific Coast.
Subsidence occurs during this horizontal movement, heating the upper
layers through adiabatic compression. The lower levels of this air
mass are also heated, but to a lesser extent, during the course of
the journey over water, moving from colder to warmer (near the coast)
regions of the ocean. Mixing induced due to this warming process
results in the entrainment of moisture and the establishment of the
"marine layer", a layer several hundred feet deep. Finally, the
air mass encounters cold subsurface waters that have welled-up at the
coast. The lowest layers are cooled and, depending on the amount of
water in the air, the air temperature, and the time of contact with
the area of upWelling, fog may form. In any case, the. cooling from
below tends to form an inversion or strengthen an existing inversion.
Thus, air arriving over the Los Angeles Basin during the summer
months undergoes a series of transport and energy transfer processes
that tend to create an elevated inversion lying over a well-mixed .
marine layer. These processes occur over a spatial scale of the order
of 1,000 miles. It is necessary to examine a much smaller scale, of the
C-6
Figure C-2 follows.
-------
Hei ght
n
I
....,J
,
,
,
,
,
,
,
Temperature
FIGURE C-2. Typica' Vertical Temoer~.tllrp. Profiles Move Cities.
. (from Panofskv (1969))
-------
order of 10 to 100 miles, to understand the behavior of the inversion
over Los Angeles. Such an examination is necessary, because, unlike
inversions of approximately constant depth that lie over urban areas
situated inland, the depth of the well-mixed layer over Los Angeles
varies substantially from place to place at any instant in time. For
example, during the early afternoon it is not unusual for the height
of the inversion base over terrain at the coast to be onehfourth
the height of the inversion base at a point twenty miles inland.'
If the air were stagnant and pollutants were injected into the
atmosphere at equal rates at both points, concentrations near the
coast may reach levels four times greater than those at the inland
location. It is thus necessary to have knowledge of both spatial and
temporal variations in mixing depth in order to develop an accurate
airshed model.
B.
The Work of J. G. Edinger
During the summer of 1957, Professor J.. G. Edinger of UCLA carried
out an extensive measurement program to investigate variations in depth
of the marine layer over the Los Angeles Basin. Edinger and another
pilot/meteorologist flew 116 flights over a 45-day period, measuring
vertical temperature profiles over seven sites during each flight--at
El Monte, Fullerton, Compton, Torrance, Santa Monica, Van Nuys, and
Glendale. * As a result of analyzing the data he collected, Edinger (1959)
was able to make the following generalizations: "The marine layer
over the Los Angeles coastal plain during the daylight hours (a) is
shallow at the coast and deep inland, (b) increases in depth early in
the day and then becomes progressively shallower during the afternoon,
and (c) reaches its .maximum depth first at the coastal stations and
later at the inland stations." '
Analysis of the data collected indicated that variations in the
depth of the mixing layer as a function both of location and time
could be exp1ainea in terms of three atmospheric phenomena: (a) convergence
or divergence of the horizontal wind within the layer, (b) dilution of
the marine layer from above by the mixing of air from within the elevated
inversion layer with the marine air, and (c) advection of deeper or
shallower layers of m~ine air into the area.* The convergence-divergence
effect, attributable to the sinking of air moving from the sea to the
land, manifests itself through a decrease in depth of the marine layer
during the morning hours. Mixing of air' within the inversion layer with
marine air is attributable to the warming of the earth's surface by solar
radiation, thus initiating convective mixing processes which penetrate
the elevated inversion. Advection (horizontal flow) determines the length
of time over which this convective process occurs, the time of residence
of the air mass over land. . By considering each of the three mechanisms
separately, then cOmbining them, Edinger was able to develop a semi-
quantitative model of changes in the depth of the marine layer. \<1e
refer the interested reader to Edinger (1959) for a full discussion of
his findings.
* See Edinger (1959) for details.
C-8
-------
In a subsequent study Edinger and Helvey (1961) examined the
structure of one of the two major zones of horizontal wind convergence
that occur on the boundaries of the Los Angeles Basin--the San Fernando
and Elsinore convergence zones (see Figure C-3). The region that he
examined and the one of interest to us, because it falls within the
bounds of our modeling area, is the San Fernando convergence. Using
observational data, Edinger was able to construct a vertical wind pattern
that results from the convergence of two air masses, explore the
variations in location of the zone with time of day, and gain some
'insight into the redistribution of ground-based pollutants by the
rising flow of air produced by the converging winds.
Edinger's work (the 1959 study, in particular) has provided the
basis for the development of maps of the depth of the well-mixed layer
as a function of horizontal spatial coordinates and time. In particular,
we prepared maps showing the estimated average depth of the well-mixed
layer over each of the 625 2 mile x2 mile grid squares for each of
the thirteen hours between 6 AM and 6 PM Pur for 29 and 30 September 1969.
To do this, however, we required measurements of mixing depth on the
two days of interest. In the two sections that follow we describe the
pertinent data available for the two validation days, the rationale
and procedures upon which the preparation of maps were based, and
examples of the completed maps.
C.
Vertical Temperature Profile Data
Generally speaking, the only vertical temperature soundings taken
over ~he Los Angeles Basin prior ~o May 1971 were the radiosonde measure-
ments made twice daily at Los Angeles International Airport (LAX)--
at 6 AM and 10 AM PST. (SincE! May 1971 measurements have been made
routinely ,at El Monte). During the summer of 1969, however; the Scott
Research Laboratories, as part of a comprehensive data gathering
program, flew 26 aircraft flights over the ~os Angeles Basin in order
to make measurements of chemical and meteorological variables in the
atmosphere. Two flights were made on both 29 and 30 September,
commencing at about 7 :30 AM and noon PST each day. These flights
originated and terminated at EI Monte Airport and had a duration of
approximately l~ hours~ The flight plan is illustrated in Figure C-4
and is described in detail in the Scott Research Laboratories report
(1970, Vol. I, p. 3-2).
Essential to the determination of inversion height is the
measurement of vertical temperature profiles during spiral ascents
and descents. Such profiles were measured at the points 1, 2, and 5
in Figure C-4--at El Monte, Commerce, and Hawthorne respectively.
The morning and mid-day profiles measured ,at these locations on 29
and 30 September 1969 are shown in Figures C-5 through C-7., (See
Scott Research Laboratories (1970, Vol. IV) for a complete listing
of the data.) The LAX radiosonde profiles for these days are given
in Figure C-8. Corresponding depths of the well-mixed layer, as recorded
"in Table C"'l, were determined from these profiles.
C-9
Figures C-3 to C-8
and Table C-I follow.
-------
n
I
....
o
~
...:.
'(J
~
...
o
I
SO
I
. .
.,.
.''''''11'.
_I~.S
FIGURE C-3.
Path of Pollutant Transport Over the
Los Angeles
Area During Typical Sea Breeze
(from Edinger and Helvey (1961))
-------
1 1 ~ ',- _~_6 7 _t -~-r!-D.-..1L !.!r'3,..I-~T''.i, '16_..!J"""!,!.L'9..2£.~-'-r!2 H,~~ Jts
2S T T" 'T- I I I I! I i 2S
- -r .. -Tiel. -;,i' i~rl---t-~-; j 24
, ! ' I .~ . i, I ~'-T-~t-l-"I-----TT- 2~
, i.~. i1l--n t r, I I'll; " 21
--'- . t . i! :. . I . i
: I " :! Ii!! -:-r-,', 'I' ", '"
.! f i I ~. ~ t I' J . . ~
,i , mi,'! j ! :!J I j; 120'
T 'I " i 1 i.. i' i' " i ! : G
,I , : 1- , i . I h
1-- ~-r- 'I - -1--' 'I I -..1---1-
" I I! ,'!! I ~ ! ! t8
! 0 ! : I T i I ~ -1-1-T---r i -r-'-r-'7
I ,,! I: i ~ . '2 1~ -+--1 i ; r i ;;
! '" ': r l' J I I : : I'
I~ ! 'j 0 !~ i :. i I i;/; :,: Ii; 1: I /~
I ,,:, ii' I i/;" - '. ! I I '
'It __-+_L~h-+-~,; -J -~J, kL-1- ~- I ; ! -+~ _j_~_LJ- If "
'3 I I :' ! i "'-: ./ , 'i I i I I I ! I ~
il,: ;:"1 1./ I I I: . I I I 1.01
. 11 1.: !! 1. ..1 lW ;, i I !;, I j!! - '1
I' - t--r .--;.- --t-,-- ---1\-J'--D- ---;--'1--1-'-- -T--I-, ---r- -- I--t---T---,
'e i !: ,T ,i ~I ~ I l-,t-1; -- I ,-J ! t-t ---J.--- ~--~,- 10
I I. . ~ I i I -r ill ., I"
-~- - f7 -+- : -~-+-+.- --~--+- -- -i- ___1__,
; 1-! I, V I ;! I I I! ; I 8
1-r--.tl j; 1\ 7/~r+-~ i ! j--' 1--7
'. I --~ : -- !' ~,-..J [Vr i ,1 "-J -r---'- ,- (.
i_+~++ ::' I' J_f-LL -r~+J- -4--1 :
-;---'--r :t- I -~+-+F~~,,~--t--.-~-~3
: I -t->- LIt l~ -r'-- -",~ ~ - 2
j: I --I I ! r- j--r -~ 1
'..l- 0 I' .i-.- ,...1.....- , '-
., 2. 3 Ip 5 E. ? 8 q 10 II 11 " 'It ,,.,, '7 Ii 1'1 ~o 2./ H 2.3 2... 2s
2.~
23
11
11
26
I
I.
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I
,q
, 18
on
i
---- -
I
!
!
"
If
e
s
I,
3
2.
, .
, ,
I
..' . . ~
1.
2.
3.
4.
5.
El Monte Airport
Conunerce
Intersection of Los
Hawthorne Airport
Alondra Park
Angeles and' Rio Hondo Rivers
Spiral ascents and/or descents to collect data were made over
El Monte, Commerce and Alondra Park.
"
Figure C-4.
Aircraft Flight Plan
.C-ll
-------
111 TITUrE
(FEET ABOVE
MEAN SEt. LEVEL)
\
\
\
,
,
0756 PST \
0924 PST)
'1156 PST'
I
\
/
"
""","'"
\-
\
"
,/
\
\
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......t
, -
,
,
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1
,
,
-,
,
,
0730 PST
0855 PST
1330 PST
2400
----
......--
- - - --
---
2000
1600
n
,
....
N
1200
I
,
I
,
,
I
,
I
,
,
\
\
\
\
\
"'...
...
800
400
66
74
82
Temperature (oF)
90
90
74 82
Temperature (OF).
66
. ... .
Seotember 30, 1969
September 29. 1969
I :11>',
,
Vertical Temperature Profiles Over El Monte
FIGURE C-5.
-------
"-\ AtTITUDE
(FEET ABOVE
".\ MEAN SEA lEVEL)
:,\
- 0815 PST \\ 2400 0750 PST
. . . . . 0910 PST :1 1235 PST
- - - - 1206 PST :~
1257 PST :.\
-- ',1 2000
:1
;' \
\
( I
I : 1 1600
I
, , \
, . ,
, \ ,
I
, \ '
, I
(') , . ' / '
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.... \ .", ,
W '.' ,/ 1200
.', \
\ I
"
" 1
- -,
,
\
MO \
"
,
,
400
66 74 82 90 66 74 82 90
Temperature (OF) Temperature (OF)
September 29, 1969 Septe~ber 30, 1969
FIGURE C-6. . Vert1 cal Temperature Profiles Over Commerce
-------
\ ALTITUDE
\ (FEET ABOVE
\ MEAN SEA lEVEL)
\
\
\ 2.1.00 0820 PST
\
\
\
'
\
\
\ 2000
\
\
\
\ \
\
0826 PST \ \
\ I
- ---- 1228 PST I I 16no
\
- - - 1248 PST I I
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(') I
I I , 1200
~
~ I I
I
I I
/
,, "
,
'"
,
,
...'" 800
-
400
66
74 82
Temperature (OF)
September 29, 1969
90
66
74 ~
. Temperature (~F)
September 30; 1969
FIGURE C-7. Vertical Temperature Profiles Over Hawthorne
90
-------
AL TITUDE
(FEET ABOVE
MEAN SE~. LEVEL)
. 0600 PST
- - - - 1000 PST
0600 PST
1000 PST
211 on
- - --
I
,
,
,
,
I
I
,
,
,
,
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,
,
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\
,
,
,
200n
I
I
I
,
I
I
I
,
I
I
I
,
~
"
,
"
,
,
"
"
"
,
,
,
,
,
,
I
,
,
, .
,
,
1600
n
I
....
U1
1200
800
-
. .40n
6 74
Temperature (OF)
September 30, 1969
SA
A2
82
66 7
Temperature ( oF)
September 29, 1969
58
FIGURE C-S. Vertical Temperature Profiles Over Los Angeles Ihternational Airport
-------
TABLE C-1. Height of The Inversion Base, As Taken From
Vertical ~emperature Soundings over Four
Locations in the Los Angeles Basin
29 September 1969 30 September 1969
Location
Time Heigh t of the Time Height of the
(PST) Inversion Base, H (PST) Inversion Base, 'H
(feet above mean (feet above mean
sea level) sea level)
0815 600
0910 950 0750 900
Commerce 1206 1300 1235 1700
1257 1000
0756 450 0730 500
0924 925 0955 900
E1 Monte 1156 1700 1330 2900
1312 a
Hawthorne 0826 650 0820 740
1228 700
LoS Angeles 0600 550 0600 500
International 1000 750 1000 540
Airport
a)
Inversion breaks up, a height of 2800 feet assigned.
C-16
-------
D.
Preparation of Maps of Mixing Depth
Measured vertical tempera~ure profiles, along with the quidelines based
on the findings of Edinger and other investigators, formed the strategic
basis for the preparation of maps of mixing" depth. We consider first
the procedures by which mixing depth contours for the Los Angeles Basin
were constructed. {Rules applicable to ocean and mountain regions
and the San Fernando Valley will then be discussed.) One of the
observations made by Edinger is that contours of the inversion base over
the Los Angeles Basin (that portion of the mOdeling region south of .
the Santa Monica Mountains) roughly parallel the curvature of the local
coastline. The three points at which aircraft soundings were made, 1, 2,
and 5 in Figure C-4, all lie within the Basin and are colinear, with sep-
arations of l2~ miles and 10 miles between points 5 and 2 and between
points 2 and 1, respective ly. Furthermore, the line connecting 5 and '1
is approximately perpendicular to the coastline. We thus adopted the
following strategyl
a}
Interpolate in time between the 8 AM and 1 PM soundings at each
of the three measurement sites to estimate average hourly
heights of the inversion base at these sites. {LAX and
Hawthorne are separated by only 2~ miles and are approximately
equidistant from the coast. They are thus considered as having about
the same mixing depth}. Extrapolate prior to 8 AM and after 1 PM.
Interpolation and extrapolation rules may be inferred from
observed variations in mean height of the inversion base and
observed variations of these ooight/time profiles with'
distance from the coast (see Edinger (1959) for details of
variational patterns). See Tables C-2 and C-3 for interpolated
and extrapolated values.
b}
In accordance wi th Edinger's findings, plot contours of
constant height of the inversion base on hourly maps
(6 AM - 6 PM PDT), the contours ~eing roughly parallel to
the coastline. Enter at the three colinear sites on each
of the thirteen maps the mean height of the inversion base,
as estimated in (a).
c)
For each map, interp::>late in space along the line connecting
Hawthorne (point 5) and El Monte (point .l) . As the line is
approximately perpendicular to the contours, average heights
of the inversion base assignable to each contour can be
estimated through this procedure. (As an exan\ple, see
Figure C-lO).
In this way, the height of the inversion base may be estimated
throughout the Los Angeles Basin during the daylight hours.
This procedure, unfortunately, may only be used for the Basin,
other rule.s are needed to estimate variations in the height of the
inversion base over the San Fernando Valley and over mountainous
areas.
Thus:
C-17
Tables C-2 and C-3
follow
-------
TABLE C-2. Height of The Inversion Base
Over Three Colinear Locations in the Los Angeles Basin
Interpolated and Extrapolated Values for September 29, 1969
Location
Time
(PST) Hawthorne Commerce El Monte
0600 . .500 360 375
0700 525 400 450
0800 550 460 500
0900 650 800 700
1000 750 950 950
1100 725 1100 1300
1200 700 1250 1650
1300 700 1000 2800
1400 700 950 Inversion
1500 675 900 breaks up
1600 650 800
1700 650 750
1800 650 750
C-l8
-------
~ABLE C-3. Height of the Inversion Base
Qver Three Colinear Locations in The Los Angeles Basin
tnterpolated and Extrapolated Values for September 30, 1969
Time Location
(PST) Hawthorne Commerce El Monte
0600 500 550 350
0700 550 600 400
0800 600 750 500
0900 700 800 800
1000 650 1150 1300
1100 600 1500 1900
1200 550 1700 2500
1300 550 1600 2900
1400 550 1500 2600
1500 550 1200 2300
1600 550 1000 1900
1700 450 900 1400
1800 450 700 1050
C-19
-------
d)
For the San Fernando Valley, the assigned mixing depth
(height of inversion base less terrain height) is equal
to that over El Monte at the same time. This rule was
adopted as the residence time over land of air over the
Valley, and thus the time available for convective heating
of the air, is about equal to that of air over EI Monte during
the daylight hours. As a result, the lapse rate profiles
are expected to be similar at both locations.
e)
The contour surface representing the height of the inversion
base will be allowed to intersect the terrain for mountain
areas adjacent to the ocean. (Actually, this rule was later
ignored so as to avoid zero mixing depths). Inland, however,
a mixing depth of 50 feet is assumed for the early morning
hours, increasing thereafter. In accordance with observations
made in other regions, the maximum allowable mixing depth
over mountains is 600 feet.
Finally, the following qenera1 rules were adopted:
f)
In the absence of specific data and at points removed from
regions where interpolation is reliable, it was assumed that
mixing depth increases curing the morning hours (after
sunrise) at a rate of about 200 feet per hour in the absence
of advection (an increase of about 300 feet per hour due
to surface heating and a decrease of 100 feet per hour due to ,
convergence-divergence effects. See Edinger (1959) for details).
In the presence of advection, the rate of rise was assumed to
be the sum of (a) a surface heating effect--a rise of 300
feet per hour times the time (in hours) of residence of the
air parcel over land and (b) a convergence-divergence effect--a
sinking of 100 feet per hour from 8 AM to noon, or a maximum
decrease in height of 400 feet.
g)
Subsequent to interpolation, certain checks were made:
1.
Time at which peak height occurs is checked with
Edinger's observations.
2.
Variations in height of the inversion base with time,
at any, location, should correspond with contours
reported by Edinger.
h)
Contour lines follow the coaSt line (approximately) during
the morning hours, but the pattern changes progressively
through the day due to the effect of the wind (see Edinger
(1959» .
i)
If the inversion breaks up during the afternoon, (as it does
for example, over El Monte, and probably over the San Fernando
Valley also, on 29 September) 'the only mechanism working to
restore it is refreshment of the sea breeze. A mixing height
of 3000 feet was assigned to those regions over which the
C-20
-------
inversion did break up, an exception being the high mountain
region north and east of El Monte, where a height of 5000 feet
was assigned.
j)
Linear interpolation was used to arrive at magnitudes of mixing
depths at locations between measurement points.
k)
Minor changes in terrain height were ignored in the preparation
of maps.
upon completion of maps constructed according to these rules, a final
step is necessary.
1,)
Smooth maps of mixing depth, H(x,y,t) - h(x,y), then reconstruct
H(x,y,t). (A map of average ground elevations is given in
Figure C-9). Nearly all previous steps in the procedure
are based only on the estimation of H(x,y,t), since both
Edinger's model and collected data are reported for this
variable (i.e., relative to sea level).
By fOllowing these rules, a map such as that shown in Figure C-10
can be extended to the entire modeling region and then converted to
digital form by assigning values of mixing depth to each of the 625
2 mile x 2 mile grid squares, as shown in Figure C-l3. The procedure
outlined above was used to construct thirteen hourly maps for each
of the two ,validation days. Figures C-lO to C-l2, along with Figures C-l3
to C-lS, illustrate the variations that occur throughout the morning and
mid-day hours of one of the validation days.
E.
An Evaluation
The procedure for estimating mixing depths that we have outlined
, is based on a very 11mi ted amount of data (three or four soundings taken
twice a day) and On a semi-quantitative model derived from a comprehensive
measurement program. The accuracy of the procedure is probably quite
adequate for those regions for whiCh heights of the inversion base w~re
derived through interpolation. Inversion heights for the period before
8 AM and after 2 PM PI1l' and for the San Fernando Valley and mountain
and ocean regions are certainly less accurate. The accuracy of these
maps, however, probably compares quite favorably with the accuracy of
the estimated wind fields (see Sections II and III).
'rt1e major problem that is faced in the construction of the maps
is that a substantial amount of labor is involved in manual preparation
and conversion to digital form. Approximately twenty man-days were
required to carry out all steps in the process of converting original
temperature profile data to maps of mixing depths, and these mixing
depths to punched cards for input to the computer. If the airshed
model'is to be easily used, an automated procedure for the generation
of mixing depths is mandatory.
, Edinger's work offers a valid basis from which to develop an
automated procedure. His model can be expressed quantitatively as:
C-2l
Figures C-9 to C-15
follow
-------
Zb j---r-I -T i1200'120qjE~~~'=r~-..1 C:J-r--_Ll~~J" r--I -., - I~-J__l_J
I ..L1'~I-Lr "-~T7:r~'T-!~.. !.o ..lLr!J.Tg,..!..~.!.;[ .l6-;.!.'!-r!..~~_L9.-~,~E ~..!..T~'S:~'!7:-~~-"
2i 1..s~0_!~~0_~ ~~?~ 1-~:1-9_7 1-?2~'~~3,11..2_d. -~~O ~6_0.0 ~2?Oi ~~0~~6~~i.~80~~~60- 4.~~~6_~~L4fjO~14~~ ,4200 38:0!'.i3.00~l!!,OOr36?~~~? ZS'
2.~ 9501 925 90~ 9j~0 ~t~~- _9:.t~~5 16~,~ ~~-~~~~t~ooi~~~~~OO- ~~~/_600;~.~~OJ~-~~01~~O~ ~5_00.e~O~I~OOO~~~d_30.O I
23 845j 825 .,ed 7801_~~- ,80d .~~ -~~i..~~~O~~~ ~~~~1.~1~~_O~~~0~~~ ~0~O~~2~~_~~~~~~;3~O ~~~~1.~0.~~~~~.~~~.~~0 23
21 1'125! 790 7~ 73 720. 71 70~ 65j 730 1600: 120~1400; 1160' 128 1800' 2f100. 240ch600 :2900 2400:UOO; 1600:2600: 250 2.1
2.1 -9~~~~ 90t;~~~-:;; ~~~..;; -6-;f-;~~~;~ ~~01-;~;~2-;~;;;:-;; -84~18;:";-;--.;o;:i60; i4~~;i60o;-i90~200~-i20 2.,
2D 400 15~ ~_~~oi.~O~O 1°~t~~ol ~t.~1~~~ ~~l 560: ~~;-~~~~.?~ ~t..~40; _~t460 ~.:.2~. .~~l~5i-8~~~~~1 ~~~ J 0
.q 300 150011S+~1~0 9~~~~~1' ~~~- ~1-~ ,~~i~2,t_6~~+~~0~, 5,3. -~4°1i- 3j~~!-~~0 l~:~ ~~~_~~~_7~~;_~,~0~ ~0_2 I 00 ~SO. 5001 75~10ooillO ~-
-t-r- _..-r-:-+._.~_...-+-. -- --:--+-~, -=r:::-~-r-:- -t- --1--.,...--t-1
'41---.t ""11_.~-i- . 30 i _~2.5i -~~~ -~:l~~-~~~~~~~~~~L~15r! -~~. _~_4~,~==t-~_2~i:.0~.~.~0~- _7~ i,~~~~~~1~~. ~Or't.
13 r- . : I 11001 90 70 160 130 90' 90 i. 95, 10 115 i 13 511 1~~0! 300 350. 4O~ 550' 900 110~ 3
. +--,.J .. I I I I -::r -;:;r;,;+ I . ..J
Il_-rt~J . .'.~ . -;;;r~~." ~;-;f;'~.~I-~ ~_"I-"; l~i"'L'~' -;;1;"IJ1~~'''.I''
II I . I I .01 12 651 40 35 1001 551 55 6 60 55 60, 85 r 120 160 I 210: 250: 270 359"
~ ~. : #!-1-- _.+.~-;11'~ -::'~~~~:h:!":::f-~~:f~j: ::f:i~:<:i.:j: .
8~'- +- --,--- ';o{-;;~'ioo. 30;'''1o~-'4"-s5t-;i;-r..i-;;I-;;1-.;dJ-i~;;1'18
1 ~r: -..- +_LI .,-- -350 -800 ~hoo ---; -; -1~lii --1 -si-"ioj-;ST"icif'o '-00 lo~ni4~ i60r'30-]7
(,; T-:-' --t-, --r ~50'! -1- -- - -- ---;-- J-~~' -'3~ -~~ -;; ._-.I_~O - ~~ ~ .
s i L_'~-r! -- -_. --LJ- I
I . I
" Ii'
I '
3 -t-- ---i--- - -r:- --..
~. -t.. - -,-- -.-
&. ;
, I
".
"1
8
q
10
I I I
-- ---t--
-- -1-
I
----, ---t
--- .. -IT
,,." .f 7 '8
2,0 2"
1
~
5
(.
II
FIGURE C-9.
Average.Ground Elevations, h
(feet)
C-22
-------
L-~-,.J.-r-~- .~. ,-'~_,..7_..8. --:~...Jo...! ...~2'r-'_':'?'.'!~-r!~' .!.~...~7__!?T'-J..}~. ~~T:f-r!.l..'-~!.1~-'fl
25 : I I r ,! 1-1"'.".'-' _.....;..-......___._.L..~...l...i", ""'.'" .......:...._.. J.S
- . -7-- -r . .~ ..... - -......" ....,. ... T" . I..' I I t
2.4 ~I-! _L_- .._1- -~._.. -..-.+.-L--i.... :...- ~AN. .GA8J:IEL: " ..;.. .!. .... .~ . ..,24-
I .' !. t I I . I MO NTf'\INS . , 1 ~
23 .: t' +' ! .; Ir-- --I--.ir,'--"'r' ._'~-''''-':''._'''''''-'-f- ..._..~_....._;..'-
-- "--'j-'- -.--- ... r--- . - i" ." :
2l' i " (I .; ,,: 1'2.
-. - _..:J........!.._- ._.-.~..- _....~.--t._.--_.j.__....l._-+-_._~---.._.._;._._... .._~.. .. "-r-.-t-_..~--...~--
. I! : ',. .;! Ii: I':: 2.'
LI ." ' . ' . :
10 S j'..M~i ~. ;.. ::; ~ . i ;: i H)
"I' I ' '. I'. .
- . - -~._... .-. .L..... .... --1'----- :.--.-.--.- _.. .- +.....~ ............-. ._._..:......---....J...
'.' 'I . I
::~+ ,,-~UNT~T-+~-+ -+r;--; -1650'- L__!_:_:+.;;
t. .~.....L 1-'+--"--~---'-~"- :--+-- _....t..._~.._~. _...:-.-- '''-1-' ~-..: ... 1" ... h --;.---: '-r -j _17
11:_-~-_1 '! ~~ ~ ~ -l....~._:._~-_. .-..-,-.... .--~ _...~._. -.....:..-..1..-. ...~- I
--. "--r- : --,- -. . - - . - ~. ~ ':. ~ i ~
I" i I : I
FIGURE C-lO. Contours of the Height of the Inversion Base, H
OVer the Los Angeles Basin at 7 AM PST on 29 September 1969
(Feet Above l-Iean Sea Level)
C-23
-------
FIGURE C-ll. Contours of the Height of the Inversion Base, H
Over the Los Apge1es Basin at 10 AM PST on 29 September 1969
(Feet Above Mean Sea Level)
C-24
-------
, 2 ., '" S (;, 7 8 Ii '0 II 12 13 ,~ I;';' 16 '7 I.!\' 19 :, 21 1.2 1~ .14 ~ -
25r~-1 ~'T-T---' .'T'" '1,oor'-r'-- - .. 'r" -:--"1"-' .- .,;' . r".q: --':--"j"-r--lr-'"'7-T- 2S
2.1.~' ...~_.__. .. t "'1- .. .. "-r' ...! ""/'''1 ..... . . ",' !.. T':"- -, sAN' A.-A' B ~I'E" ':' .., ':-' . " --. -:." .t.,-- 2~
1 .-H-+-.-4--. ---t--t--.t-'f--""" "'-r-'j'" .-.... ..~ 1-=1""~ .., 'q .., .
23 '__L-!'.-1.---. ..,,-~_....~..:.~. -..1-". "_'1I,--I_u.~....~.-_.. .. :..... . ,:._l~O~~T.~~.N~...__...~.- 23
I I " I"; i" .
22 ...-L..t'__.L_-i-.- '-'~'-.'I._...l.-_L_.,.._.J_-~_..1.....~-- ......~_.-.. '" ...~- . ".:.....: ---~---~,.... 22
. 1 I, ' I: I" 1 ; I .
2.1. :' ':, ' i I I -:' ,:: 2.,
2~ SA T A: M N Ie; 'I ;; i'. ; :. ! j ~ ,)
Iq 1]' - '- MOUiNT' I'Ns;-'-'I-"~'--1 ,- ".+- ~--"i"-':""- .- t' 2800 _..~.,...- :..-i....:-...t-1,~
18 -; ,,. .--.n__. -- ''''', . r---;- -'!-----r---j"'--j .._~ - -. :"'" ~.- :" . q.,,;.-. ",'" ~...-~...I/1i'
17 r" +:...'. ; "---;1: "'" "'-r----( "-~-'''''I:' - -- - ~.._. >q.;. -. 'n-- . ~I-:" ; ... : . ---1-'" ." :.. . - ';' .. .~. "'l-..I'7
. . I . I. 'I J
Id=--:--T i'- 1-- -~---1---'-"f '-'f-"'~--T--I'- . .....~.''''. ....-.. i - 'I" ..... ..---..-. h
I' !! I 'I. .
'~i i: I 'I . 1 . ': : . . .:. i ':'-
l it r , l ' , ." . .
14' - '''T-;--r-- nT' ~--700: ..- ---: -'T--7T--r-.--' -~-""1400-""--' ---i'-'7'-~-; --- It
IJ! .. .. r' '-1' "':'-'~ - -'r-'.--; -: . . -~._. -:'-' :-- ... j --~- . ..-; .,:-.",.. --;'" ". ;---'i _..~- --1" . }13
. !.._-_.+-._.t-.~_.-1_- - 1___+_.' -~--- --~- --.~~--- ._-;.._..~-!---;_._... ...l...'-I---.-'" '.....
12, :.. :, :',; OQ' .' i: l : ,,11
. I .. & J I ". I t I' J!.
: -': I' i' - .,... ... 1"'--','---i-------;" -:. '. '''r .-... "r--' ~.., "" .. ..!';" :... "'i"
II ~ : r . : \ . I : ~ : I I::. ;!; !
. " ... '., .' I -
It, i ! L 1 +' I ! I !; J j ,: ; " ~ 110
~f-r---':-;--i.-- ~- I ",' .j---'I--' ...---:' T"'-,""1'- --'~----'-""r-j ,''1'' ,":":- '1~
: '~.~FH~T~nrt~.1~=t~~ . ~_.:::.: M .~-1..:L .1-.[-. --l7]5: .0' ;-:",H~
'~~-"~""'I"'."~"--r-'- '-i~' '-i--' i -1--;--1- '~-'r I...~.. h " j_.. it.
'. ,I I! I It. f I ...
s' 1 i I. : i +. I I ; '", .. I 600 i I \ IS
4 ~_..~L..t~t~:..t~ ~-.~t~'11.~= =)=-:. :ul-1t:. :..Jt:J.} . ,',i ,~r,l.'-'.-"':4
: - i. -~++u. +.._,- J.. -. --;.- f- --I' on + +- j'-i-. fu--l- - -I:
I -'i-T-'''- -- - _L'ln .+.!-- u_--,U T--r + ~.n '"r: rut -"
L-1 ~ I: ~-~~ ---':"-"ii-'---L.. -_........_L,,-~_. -...1
" 2. '} ". S E. 7 8 q 10 " 11 IJ 14 ,,.,, " , 'I! 10 z., U 2.:'- l4- 25
FIGURE C-l2. Contours of the Height of the Inversion Base, H
Over the Los Angeles Basin at 1 PM PST on 29 September 1969
(Feet Above Mean Sea Level)
C-25
-------
I L .~- _£. ~- _.~. 7.ili.8-f:~'-'..'.o- .lL.r-!J.J!J-'~T~~: ..!J!._!...7_.!JL..!..~2.! 2.'-.1~2 !~T~~~-
25 .~~ 2001. .~~~_. ~~l"!~0 .2.~oI ~~.~ _2~~.~~~1200. 2~0- _2~~ 1-~~0~_2~~~ 2~~ - ~~~-1.-~~~.~2.~~_!?_0~4 ~o~ 2~0--' .~o_~ 2~.? ..~~.o.. 0. t2~.~.- 2 S
11 '" '" u~ uJ'" ~~~' T~ ~-'~eL~::.". -~'~c'~j'.".".". '~'J~,,:"'ooi'" 24
23 105' 100 10~0~ 100 100 i 100 1°1.:2SI1~. .2~0 I ~~O 1200~~~~~~0 2~.~_~~~~0 200 GOc:. ~~t~~ !2~~-~l:~~ 23
2! ''', '" ,,' .~'.". ~-"'-r''' .~~t,~- .q.~~-~~":'-"',:,' ~':~' :~l'''- ,~~r~~~~~ 21 .
11 150' 150 150 IS~ 150 150: 150 150: 150:150 12S! 12S! 125: IS0~IS0 IS0lrlS0'IS~SO ;150 150 1200:200 :200 ;200 1/
2D 200 200 20~,:,~0r.~~~ -~0_01-1~ ~~~j~~s _l~: ~~.L~: ~_5~l~~~~~S ~~S.L1!~:,~-~:_.~~.. ~~~.L1:~~I~~_~.2.~~,?~0 20
Iq 2S0! 250 2S~~Si~.~~ _2~~t' ~~Ol ~~OL~~~~~~ ~~~L~~~T~~L~~:~~- .~~~1".~~:~2:1~-i-1_2~. ~~~~~~~I~O_:~~o.f~O- I~
18 ~~~I'-~'~~' ~_5 _~~ol_~ -~~ ~.~t ~~. ~7sl~~0 ~~~r! 2.2.~..~~~-.~~t1~5_,I~~.:S.~-~:oj~~~_i~_~s. .~~J..~~;~~..~~~0.}~~_'8
11 450 I 450 4Sd. 4S~ 400 350 r 325 325: 300h7S 250 j 250: 225; 200j 200 1751175 i17S 117~S f 150 .150: 150 !200. 200 i200 17
.' ! , ~.f ,. '-4-- I ., I j J. :
, -;;-;50 ~ 3751350' 325',1300 2~t 2S0! 230i22;-2-;0~1' 200:;~;T;00 11;;- ~~Tll~I'2~~ ,2~~'~00'"
" ~O~ 'i 500 I. ; '. I! . I . '
IS 500: 5001 SOO! 50014 470: 415.; 375: 350i 325 300; 300 i 27S! 260: 150 215' 1251225 :225 '200 200 '175 :150 '150 ~0~'S"
'4 ~o~ '~~~~~~3~500 ~8~~-4.S~1~~~I~~~1.3~~ ~2~F~s.!.3~~!~~:;~~, ~~r~1~~~~~~~ -~.~~~~~~~70~~J/~
13 -~-' I_'::e"i '" 00' . '-:1~': '''~ '" :~~'! no i '" ~~':'" j'" : '" ~'j~~~~_2" ,," 3
11 S~~,5001S00i.5OO~SOO. 500 500.:,' .~~~t:_~~Ot:~~~ - ~7~. ~37-~f ~~O: .~~O ~2S. .3~0! ~.~0.!3~~.llm -{~~ 2?5 ~~~ ;2.~~-t~~~ .0.1
II SOO! 500 I 500: SOO! 500 500 t 4 0 j 4801 4501420 400.37S! 37S i 360 350 330 r 3251325 1320 .300 300 275 ~SO ,225 ;~'I"
: ~f:t-::L-:;~:~;t.~:t ::h '~~~::; ~1:?,~~;-t::: t;- :: 1~:~t-i:~::J;
, "J;;; t-;;.C;;;r ;" ;;~i,;-:r- ;~; ~-:.;;;+;;;, t: ,-I,;,!,,;! ,;;1::; ,-; r;;; i ;;t,~" I,
: ; :tl~:~~~!:;~Jt-:~1TI~ .~~t~~ E1~-:~:,~i:~. *~i:~ff~.. ~;t~f~l~ .~I:
1 '" '" ~ 00' '''- '''Fo '" -,A~, '~~~[~~IS'O~': :O~~~J ~~~ 500 SO~. 48~ ~t~o.. 'f~~~. ~~ 2
, 500 500 500: ~O 500 I 500 500 50~ 500 500 500: 500 I SOO 500 500 Isoo ~OO 500 .500 500 SO 70 t; SO 1
I I . I ~-
2: '3 ,.. 5 Eo ., ~ q 10 II 11 " ,,, ,,.,, 17 , I q 10 z., 2. 2 2.J H 2
FIGURE C-13.
Estimated Mixing Depths, H-h, Over the Los Angeles Basin
At 7 AM PST on 29 September 1969 (feet)
C-26
-------
15 750 7:0 ~~TI!~ ~~~, '~~l~~'j!i~0;'~'l?~~ ~~~~1~~';' f~F.f.~~ ~;~~T. :~r~-117;.: ;.i~~~2~~. ,,;~.:;~t:!- 2S
, 2.4 650 ! 650 650: 650 650 650! 650 650 I 670'i'00 700 ,700 700! 700 :700 700; 700 ' 700 J 700 700 700 i 700 700 700 ! 700 24
6~~40 640- 6~T;; ~;T~~17~~- ;;-j,00 i';;T;;i;;;;~~T7~ i;~~';~~ 7~~-' 7;~'!7~'~ ~O~ .;~o-f 70~ 23
640i6~1:~ ~~;; 640 '~T~~t~; ;;~lj,;~~-r;~~r;~~':;~-; ;;~';O~~';~I' 700170~" ;~;t;;o-r-;;;;;~;~o 21
I -I ' ~' ;, , I :.:J t
630:6;; ~30 ~;:'~~ ~;~:"650';~~' ;;0-!'690T7~0: 7~~:~;; ;~~t;~0~'7~1~50;65~ ~';~;;50 1~0;~;~TI650 2..1
, " '. I.. I 'I
I I .. I I: , '.. i
2D 620 6~0 ,~r20 f~:~~.!,~~- ~~~I-~~ 6~~, 6~~ r~~t7,~~.i-7~~~.. ~~~.!~_5~,:-~~~+.~~~~~~~_. ~~~.too i ~~~~O~r~~fO
Iq 6101615, 6~~~~~~~. ~~~j~~O_I.~~~~~. 690 - 7~~_; ~~~i-~.9.0 i6.8.~- ~_7~J.6.6~~.:5~L6~~:~ - 6~~~3~l~~~_;~~~-i.~.~01' ~
IS 650 1650 t 6i650 1650 660 i 671680: 6901690 700 r700 ! 690 i 690 :680 67~ 660 : 650: 650 :650 630: 650; 650 650 16501.. 8
17 ~;5-:'5~;' "~~51 ~;~;;- -6~~T~0 ;;'~~;01670 ;;0-:;;-1-;1~~-;~~~- ~o I ~;~'r;;t6-.;~t~~~.. ~;~'+6~~-:'~-~~~~~-i'6-jl'l7
. -- -+- -t-.J_-L-_--- ..-+--, . ---r --""--,--~-_L-,
" S50: 550 550' 5 ! 550 560: 600 650: 680.680 700 J 720 i 740 ~ 7701760 760 i 760 i 750 i 7S0 i700 670 1'50 I 650 ~650 ! 650 /(,
1:$ 550 550~5~ i5 570!625;650: 690'1'710 730 750_1770:790,780 800!780'760i 720;710 700 :670i650;650!650j';'
I_~-r- -~I --+'-~-"'-r -- f-- --t--t--l+-. t..-L-T~
1ft ~.5~'1! ~~ -~s.~.~~~~~5.~. _70_t-~~~..~ ~+6B~+,~~ ~t7~Ot~5_j.~'~r''!.~- ~~~~,~~~-! 76~j~2_0_~~0- 700.l~.01~~:~~.~-~~0 If
13 S50 550 I S50, 550 '550 55 ! 600 j 650' 675,700 730 i 750 I 750 I 770 760 770 I 760 : 750 I 7301700 700 1680 -r 670 :670 ' 670 13
- ...L--T-~-+-" -' ,-t---.L-:..- .----J--.L---~--1-- '-~-+- I -- -:i-L -,
12 S_~O! 5501 550; 550,j550 550 j 5~~L6601..~~~,i~~~. 73~,~~~0 ~ ~50 L~~~!7.~_~ 7~0 l7_50.l7~'~I; .7!.~_!?~~- 7~~_:~90! ~70;6~_0- ~7.~t"1
" S50! 550 I 550,550 ! 550 S50 I 5 0 1660 i 6601700 700: 710 : 730 ! 740 735 740 I 740 I 740 I 7401700 700 1690 r 680 ,670 660"
,~ ~O 5~~~js~~- ,~5~~.55~_1 61~~ ~~~~6~~.. 6~O,}67.5_~~~~+~~1~1~ 7~or.3~-j.~~~-7~~11~~~. 715 ~~~.0_;.~.0~6~~;~~~'O
, ~550 1 S5~550;~~~.L~~~ ~.~,' ~5~ 5~0 ~.~.~i60~. ~~0_~~5~! .~.8~t9~170.~. ~o~ 1~~0_i~4~ t-~~ ~2.~ 7~~.170~j'.~~~.~8~1 ~~~~
8'" ~1~1:~";~'.+:' ,,~~ ,-+,~~,~~", ~" '~1'~-'(~"1"'.'-.90-1 '" [~'r" '''- '~-f''' '~i"~f~~a
7 550 i 550 550i 550 i 550 550 i 00 1~00 I 5001500 5(f I ~ 620 630 650; 680 , 680 680 680 670 660 ;650 640t7
,! 5~~-r-~~~ -~5~~~;~ ~;r~;o, ~~';~0!500 .. 0 I' 5~0 I ~~O -~~t;o . ~--r~~:r62~- '62~ 6~0 - 6~;!~;5 '~~1'6~~' -~~~ l.
t I : I ) I I .
5 I S5~ _5~~' '~~~:_O"f~~- 550 t~~~~t~~~~O -~5~_:~~L=~+5~ ~~.l.~. '_~O :~~;~~-, ~~~ ~~O- ~O.O-t~ I~~~t 5
4' ~~.t:~o -~~~/~~-f5~ ~~ -~_5_0~.'-~~4-5~~~~~- ~~,~ 5~~5~~~0t.5_~. .~~t50 _..0: ~T~~. ~~1~~~ ~~~I~~~.5.8.r
3 550 i 550 550,550' S50 55~ 550E~: 550,550 550 5501S50 i 550'550 5501550.550 0550 565 575 S60 550 5303
1 550 I 550 ~t., ~~-;;-t~;o ;~O: ~5'~ _55_ol~_0_' r~~-. ;,.~.-.O- is5~ !_5_;_J_5~-~,', r5'5~., .~.;._~;.;-~~t_;_5~ ..;;~ 5~.-- ~~. I ~;. '5_-5~ 5~; '~;5i1
550iS50 1550, 550 550 55~t-;50r550 55~~ 550 t 550~ 550~;;1 550 550550 550 ~ 525 475 32~i,
. .J...-.i. ' -L
q 10 /I U. ., ," I~ I' '7 '8 ,q 10 z.,
23 640 : 640
22 6~~
1,1 630 i 630
1
'3
".
FIGURE C-14.
Estimated.Mixing Depths, H-h, Over the Los Angeles Basin
At 10 AM PST on 29 September 1969 (feet)
.'
~ ..,;---
C-27
-------
- '-rL .~_.~ ~- ..J>T7=r_t.~'J..~..!~- .!lJ:'~2 ,l~"..!'~T!€ '!~_.!.D~1T~- ~-~r~-~-~', J~f~~-
2~ 2:~,~;!_~~ 2.~0~5~~ E~~. 2~<:°t~~01° ~3~~ ~~~y.~~. ~0.0.t,8~_0160'~i~4~1. ~2?. ~~O ~12?0.t1'~0~f,~2~?P.2~0 1_2.0.~!20d12C.12.?t ~o- -7-~176°.1-7~.~!.~~~.~_3 ~4~~~.0~~00~~~~~.~~0 15~j:~0-1~~0~~6~1.8_0 It
IJ -~~i'~~~~~'~ ~.1 ~"1~,,-~~-,~. ~~.'" i '" I '" " ~~": "'~"i '''' ~~'j"'" 1~'E1'3
12 ~51550, 550; 550 ~ 550 550 j 58~ J ~~0i..~~~- 6.70 - ~~O: 7~5.; ~~O L~~~j_~~ 770 i 7~ ~ ~lO! _83~! . 8.60 10~~.~1.+~~~~U~ ~~~T1
II SS~ S50! S5~ 550 i S50 550 i 0 6001 620! 660 680. 690! 700; 710' 720 730 r 750 i 7701 7901 810 8301 8~1l00:120 120011
'0 J~~ 5501 ~~O~~L~~~ _~~~J~7~ I .5~0J.~lt_620 _~~OL~5~~ ~~~~ ~8~~~~ 7~Oj ~~~ L ~~r .7.6~ - ~8~ .80~1.~~ .~~~0~i1.~OJ~'D
, t~50f5~:~~~~. ~~~.~ ~~O -~~~~.~~l.~~_0 ..6.1~r'~~S: 6~~.~4~i.~. 670~.~~0~ ~~O -~~~ -~~O .~~~~._7i 8.10.:-~~1~~.~'1
8 ..!_~~_~~t~5:~~~;50 ~~~~: "*0 ~.'~.5~'~"';:'~' r ~"!".{~'!~+~'J..;~" .'." -'j-'j"d.~"~~B
1 ~_5.o:"I' .~~~ '~50~:.~~ ~~5~ 5~~. 5_0. ~~O'. 5~~l-!~0 .' ~~~, ..~~-; --. 0 60~ i ~~0.l ~5_01 ~~~t. ~?~ .~~Ot..?... ?~~t' _7... !.617
'. 5~ S50 SSO) 550 : 550 550! 55 I 5 550; 500 ~ ;50 i S50 I 550! 550 I 600! 620 I .650 660 6701 6~ 700 72 73~l.
: ; ':~::~'::0~i~:: ::H;~~~.g~;~:~~:~J~f~ .::;l~i~~~~~f~:~~~I.~. :;~. :
3 S5~ S50 t SSO. 550 ! S50 550 ~50 5501 550 550 5501550 ~ 550~550! 550 550 ! 55~~ 550 ~Ol 570 580! 60 610 l 63 6413
1 SS, 550 551, ;;O~ ~~~t 5;~ ';;0' -~;I~~ _--~501;~t~,;~t~;; ~;i-;;~; ;~~ ;';+;;1 ~;I:: :;;,
s5d 5~SO 550 550 S50 5~ 550 550550,550 S50r SSO 550 550 1550 550 550550 I 15501: 50 50~ I
. , --l.... .; . , .l-
Eo 7 8 q 10 II 11 '3 ,t, IS" 17' , 2.0 1.' 2.2 2.3 2... 25
2.
)
~
FIGURE C-1S.
Estimated Mixing Depths, H-h, Over the Los Angeles Basin
At 1 PM PST on 29 September 1969 (feet)
C-28
-------
o
H(x,y,t) =,H (x,y) - 100 (t-B) + 300r(x,y)
for 8 < t'< 12(noon)
o
= H (XiY) - 400 + 300r(x,y)
for 12 (noon) .::. t ~ 16
and H(x,y,t) > h(x,y) for all t
o
H (x,y)
= height of the inversion base (feet)
= elevation of terrain (feet)
c time (in hours PST)
= time that a parcel of air at (x,y) has
spent over land
= initial height of the inversion base
(1.e., at t = 8)
where
H(x,y,t)
h (x, y)
t
r(x,y)
We applied this model, in conjunction with the wind maps of Section II
(needed to cetermine r), in the prediction of inversion height at the
points at which vertical soundings were taken on the two validation
days (i.e., th~ data were not included as a part of the calculation,
but only as a standard of comparison). The computed values of H(x,y,t)
compared favorably with experimental values (~ 100 ft.) for each of
the three measurement sites for the morning hours. However, comparisons
were poor (with some exceptions) for the noon and early afternoon hours.
While we were able to identify some of the reasons for the afternoon
discrepancies, time did not permit the pursuance of this predictive
effort. We believe, however, that a model of this type can be
developed for the prediction of inversion heights over the Los Angeles
Basin, and that an attempt should be made to do so.
While this approach to the development of a prediction model
requires a relatively short time to develop, other, more theoretically
sound approaches might also be considered. The solution of the
boundary layer equations for coupled energy and momentum transport,
although potentially very difficult problem~, may prove to be a useful
approach. Or, more simply, the solution of the energy equations, in
conjunction with a constructed wind field (as described in the next
section) might be considered. However, regardless of the modeling
approach adopted, it would also be most useful if
1)
Measurements of inversion height were made during the
summer in portions of the modeling area and at times not
included in or covered by the Edinger study.
2)
Routine measurement of vertical temperature profiles were
made, not only at Los Angeles International Airport
and EI Monte, but at other sites in the modeling region
as well.
C-29
-------
II;. THE' SURFACE WINDS
As:indicated earlier, the North Pacific anticyclone exerts the
dominant influence over air moveme~ts along the Southern California
COast ,during the summer and autumn months. In general, daytime winds
over,LOs Angeles move from the ocean to the land in an easterly
direction with an average speed of about five to seven miles per hour
(see Figure C-3). At night, there is a reversal in the direction of
flow, and winds are typically light. The movement of air near the
ground 'is heavily influenced, however, by the hills and mountains that
surround the Basin--notably the Santa Monica, San Gabriel, and Santa Ana
Mountains, and the Palos Verdes and Puente Hills. The effects of these
terrain'features--in channeling and re-routing flows, in inducing flow
up,'inclined, heated surfaces during the day and down along these same,
cooled' surfaces during the night, and in creating regions of convergence
and'divergence--are paramount in determining the complex flow patterns
that. characterize air movements in the Basin. The heating (or cooling) .
that.an air mass undergoes in flowing from sea to land (or from land to
sea) also influences flow patterns, as do the unique roughness features
of.'the city. t-lhile many studies have been carried out in an attempt
to:better understand the movements of air masses in the Basin (see, for
examp~e, Neiburger and Edinger (1954), Neiburger, Renzetti, and Tice
(1956), and Bell (1959», it remains virtually impossible to predict
local'surface wind behavior. .
In:.the absence of a predictive capability,. we constructed manually
a:series of hourly surface wind maps describing the flow patterns in
the.Basin for the two validation days. These maps, convert~d to digital
form; were the surface wind inputs to the airshed model. In this section
we:describe the meteorological data upon which the maps were based, the
p~ep~ration of the maps, and their conversion to digital form. We also
discuss briefly the need for automating these processes.
A;. .
The Data
Surface wind speed and direction measurements were Obtained
from three agencies that routinely collect these data in the Basin--
the,LOs Angeles County Air Pollution Control District (LACAPCD), the
Orange.County Air Pollution Control District (OCAPCD), and the
Weatner Bureau (WB) (since October 1970, the National Weather Service).
In-.addition, Scott Research Laboratories made surface wind measurements
at '.El .Monte and Commerce during the validation period. The thirty-four
measuring sites are shown in Figure C-l6 and listed according to agency
in-Table C-4. Unfortunately, frequency of measurement and averaging
~riod vary. Wind speed and direction averages are reported for periods
of:one hour, ten minutes, and one minute, depending on the particular
measurement station. Averaging periods for each station are indicated
in:Table C-4.
.'The'soltition of the momentum (or Navier-Stokes) equations is, in itself,
more complex than the solution of the coupled Equations (C-l), and thus
was. not considered.
C-30
Figure C-l6 and
Table C-4 follow
-------
- 15 './~~_( ~~f~ ~if ~f-;r~~-~r~'{~8~~T:' ~'-j:~:(~-'t:.-;:
1\" ,~ - -1- --1-' ;;t--i---r--!-+-r---f-+TT 23
23 I'. ;--, , -r-!.-_+-- ----f.--~'-i-r- -i-.,-.:--1I----:-- ---~-+'-T-T"-
21 so 1 , I &URK . t ~ ;;.! i' I 2~
, -: --r- " -~.- .-, -,--r---j'--" --'t--t-'-t--i. - '_._~, -t-r-~--
,1.1 ;' 'Ene ;, ! I !: t I I ,!! '.1
20 'I t t' I; I :. i ; i 1 .! ~ ; 1 '0
Iq Ii 1- '-.. - -.. - - -- --'--". '-'t --~,' '- -'1,' -:-,' --+(i,co-t't!, -- --r--I,--,,!" I,', av /.<:1
Ie> !,' ._- --- '. -", g, r-r, -I, --r---' -_.J .- -f, ~~,~;i, -"----;, --tl --;--1,-"" ,;
\I .--., "-' ...- ---4-. --.. PI t- -bP-~---~--' --1---+-1"-'1-'"'' --'~'--I.-+--t-- 'B01A
17 i t WEST. I ,. l' : . . i ' I i I' ! I : I 17
, ,- - I --r- -:- I --r--r--1~-~--+- --1.----;-:-1-'
'" !: ; I ,I I! ;!! I ! I ; ; ,I,
I~ I I ~ I : I t ! y{~ j (;cott I : :: : 'W!fTT I I I>'
-r _.+-rt~-_....- -_L-~ --~---L.-!-_+-- _..J... ...r::~-1
.:4] ---1-- .~,+-+-- .. '~I;-~-1-+- --- '-~--'!"-+RiA~ ~~~~ --.L-R,i-+lAn -- L.+-T---i-I,/~
I .-:.-1.' --L I I .. ~~ ,. I . 1 . '"
12 --'-1-1 ! .-+-- I! i t~--r---;- I i r-t- ,-l-T.- -i'~
" -':' '~""JI"-- tOo. .-... ---'1-"""""1--[--- '--'~-.--r--.'t. -.--. ""1'-"-r-(~1-"-!"""- "--r--r-- -""II
, .I I I I .! f
i I ; . I I 'I I
~-t+-+- -- -- - -t-fj-L~'-~'~-' --1 u~!'--I--i-- --j~
, j:::T~C::-f=- -=t-- -_:J::r::-'=:L j:Trt:: :::tI:t:: -)
: t-' +-+- -- - I. - 1-- - -_J-I----+_ul-t---I~
,1 -r- -t--\- - -_.~.- . -- --, ---. --- ----I .- -- ..,.,...-' -.. _._- 2
I r - -- -- -t l.. -- --. --- ~ I
L-.L - '
~I 8 qlo II 11 I' ,~ .,. I' '7 '8 ,q Z-O z., 2.2 2.3 U 2$
. ,
2. ~
t,.
FIGURE C-16.
Locations of Wind Measurement Stations Operative in the
Los Angeles Basin in September 1969
C-31
-------
TABLE C-4.
Wind Measurement Status--Operating Agencies
and Methods of Reporting Data
Los Angeles County
Air Pollution Control District
L
Orange County
Air Pollution Control District
RB (1)
VEN (1)
RLA (2)
PIC (2)
HOL (2)
VER (2)
CPK (1)
CAP (3)
RVA (1)
ENC (1)
BKT (1)
AZU (1)
BURl< (1)
LONB (1)
WEST (1)
WNTT. (1)
RESD (1)
LACA (1)
POMA (1)
. ELM (1)
COMA (1)
MISH (1)
WHTR (1)
PASA (1)
KFI (1)
ANA (3)
SNA (3 )
LAH (3)
3
Weather Bureau
LAX (2)
LGB (2)
BUR (2)
VNY (2)
4
Scott
Conunerce (4)
EIM (4)
2
25
/'
(1 )
(2)
(3)
(4)
Averaged over 1 hour between 1/2 hours, e.g. 6:00 = 5:30 - 6:30
Instantaneous - averaged over 1 minute
Averaged over 1 hour between hours, e.g. 6:00 = 6:00 - 7:00
Ten-minute averages.
C-J2
-------
In general, the measurement apparatus for both wind speed and
direction have thresholds of approximately three miles per hour.
Thus, these quantities are poorly determined during periods of low
winds,. which occur primarily during the night and early morning hours.
B.
Preparation of Surface Wind Maps and Conversion to Digital Form
Initially, we considered two possibilities--manual preparation
of surface wind maps and development of an interpolation scheme with
which wind speed and direction would be computed automatically, given
an array of measurements for the day in question. The Obvious advantages
of an interpolation scheme, when compared with manual procedures, were
ease of use and savings in time. However, as we were concerned with
only two validation days in this phase of development, we felt that
it would be beneficial to prepare hourly representations of the wind
fields--to get a "feel" for the data. The magnitudes of pollutant
concentrations predicted using the airshed model were expected to be
quite sensitive to the magnitude and direction of the wind vector, and
we wished, not only to minimize inaccuracies, but also to be aware of the
sources of inaccuracies. Thus, While realizing the need for an automated
computational procedure, we postponed its development.
At the outset, we realized that the assistance of a person having
an intimate knowledge of Los Angeles' unique meteorology was mandatory.
We approached Professor Edinger and asked if he would aid in the
preparation of the maps. He consented, and, in fact, prepared the full
set of maps for both validation days. We supplied Professor Edinger
with thirteen hourly maps for each day (6 AM to 6 PM PDT)., ~ith ~ind
speed and direction indicated on each map at each of the thirty-four
measurement sites. He then drew streamlines and isotachs (contours of
constant wind speed) for the twenty~six maps, checking maps individually
and from hour to hour to insure consistency. We have subsequently
reconstructed these maps, placing streamlines and isotachs for each
hour on separate sheets to facilitate their use. Examples of these
maps, for 7 AM, 10 AM, and 1 PM PST on 29 September 1969 (these times
corresponding with those of the inversion maps shown in Figures C-lO
to C-1S) are presented in Figures C-l7 to C-19 respectively.*
It was necessary, once the maps were prepared, to convert them
to digital form, so that values of wind speed and direction might be
stored in the computer for each of the 625 surface grid squares for
each of the 26 hourly maps. As digitization is a substantial undertaking
if carried out manually, we explored alternative possibilities. The
one that appeared to have the greatest potential was the use of an
interactive computer graphics system. Our hope was that it would
be possible, through the use of a cathode ray tube (and light pen) ,
tablet, or other input device, to enter the maps into 'computer memory.
Appropriate computer software to be developed especially for this
application would be required to convert the maps into the desired
digital form. Retrieval of the data from memory would complete the
conversion process.
JLI
*The maps presented in the Figures have been simplified for clarity of
presentation and thus display a less dense array of isotachs and streamlines
than appear in the actual maps.
C-33
Figures C-l7 to C-l9
follow.
-------
".
11 "
118 L
Streamlines
Isotachs (wind speeds given in
miles per hour)
-------
, FIGURE C-17.
Surface Wind Map for the' Los Angeles Basin
29 September 1969 .
Averaging Period: 6:30 - 7:30 AM PST
C-34
-------
2. 3
. Streamlines
- - - - - - - Isotachs (wind speeds given in
miles per hour)
FIGURE C-18..
Surface Wind Map for the Los Angeles Basin
29 September 1969
Averaging Period: 9:30 - 10:30 AM PST
C-35
-------
. ~ . . . . . , Streamlines
- - - - - - - - Isotac.~s (...~!n(l spep.t'lg qbl~!'. !r\
miles per hour)
FIGURE C-l9.
Surface Wind Map for the Los Angeles Basin
29 September 1969
Averaging Period: 12:30 - 1:30 PM PST
C-36
-------
~\
Unfortunately, the time required for input of an individual
map was quite a bit longer than expected--approximately an hour
per map, and thus this mode of input proved to be unacceptably
expensive. Input time could have been reduced substantially, but
only through the mounting of a sizable software development program.
Such an effort could have been justifieC1 only if a large number of maps
were to be converted to digital form. Manual digitization of maps
is much less expensive for the relatively small number we needed
to convert, and was thus the procedure adopted. However, computer
graphics'remains an attractive future alternative. It is substantially
less expensive per map if a large number of maps are to be converted
to digital form on a routine basis. Furthermpre, if a competent
meteorologist operates the system, manual preparation of the maps can
be carried out at the computer console, and thus the production of
hard copy and the conversion to digital form can be accomplished
simul taneous-ly . ' " , ;:'-
5 -~
Manual digitization of the 26 maps invO!1ved several steps. Wind
direction was measured at each square with Iprotractor; wind speed
was read directly or interpolated by eye. The values were enter~d onto
coding sheets, which were then used to prepare punched cards for
actual input. Finally, these cards were checked for accuracy. It
is apparent that this mode of data preparation is tedious and time
consuming and requires several verification steps to minimize errors.
While the manual procedure was justifiable both in terms of cost and
time for. the limited number of maps that were converted, automated
methods of conversion will eventually be needed.
As we noted earlier, a computer graphics system is useful, both
for the conversion ~f wind data to digital form and for the simultaneous
preparation and digitization of maps. An alternative method for calculating
wind speed and direction at each surface node point is the development
and use of a computer-based interpolation procedure. A computer program
for the computation of wind trajectories has been developed at
Jet Propulsion Laboratory for the LACAPCD and, we are told, can be
easily modified to compute streamlines and isotachs. Additional work
is required, however, to take into account the effects of the Los Angeles
Basin's complex topography.
In summary, we believe that automated methods for the preparation
and digitization of surface wind are badly needed. Both the use of .
interactive computer graphics and the development of computer-based
interpolation techniques should be explored as possible means for
satisfying this need.
It is useful to close this section with a few comments pertaining
to the wind data itself. Our experience thus far indicates that hourly
representation of wind fields is probably satisfactory from overall
considerations of accuracy. Furthermore, the existing measurement
network of thirty-two stations scattered throughout the modeling region
seems sufficiently dense to permit adequate representation of the wind
field. However, the variation among stations in the mode of reporting
data--in length of the averaging periods, in duration of measurement,
C-37
-------
and in initial time of averaging period--creates an obvious problem
in dealing with the data, a problem that could easily be eliminated
by the adoption of a standard format (or formats). Finally, as we
alluded to earlier, the relative. inaccuracy of wind data collected
during periods of low wind speed, largely due to the high thresholds
characteristic of the monitorinq equipment, can create serious difficulties
in modeling. Monitoring equipment that is responsive to low speed air
movements is badly needed.
C-38
-------
III. WINDS ALOFT
One of the assumptions upon which the governing Equations. (C-l)
are based is that turbulent atmospheric flow is incompressible, i.e.,
~... av +'~ = 0
ax ay a z
(C-2)
Unfortunately, the surface wind field, in general, does not satisfy this
equation with w = o. (Note that the vertical component of the wind, w, was
not considered in Section II). In fact, if it is assumed that w = 0
everywhere and that the wind field aloft is identical to that at the
surface (i.e., at each of the nine strata above the surface), the
divergence of the surface wind field* produces an artificial inflation
(or depression) of concentrations in the solution of Equations (C-l),
.an effect which is hiqhly significant due to its cumulative nature. It
is thus necessary that the entire wind field, however constructed, obey
Equation (C-2).
Virtually no measurements are made of winds aloft. The only upper
wind field data available for the validation period are those based on a
tetroon program carried out by Pack, et ale (1970). One tetroon flight
was made on 29 September and four on 30 September. Of these only three
fall within the 6 AM - 6 PM PST modeling period. These data are obviously
insufficient to serve as a basis for developing a description of winds
above the surface.
In the absence of data, it was necessary to devise a means for
constructing an elevated wind field. The following principles were
observed in establishing a basis for the calculations:
1.
Continuity must be satisfied for each cell in the
25 x 25 x 10 grid--i.e., inflow and outflow must be equal.
Thus, for example, all w at the ground stratum should be
chosen so that Equation (C-2) is, satisfied for each cell
in the layer.
2.
The winds aloft, up to the base of the inversion, do not vary
greatly in speed from winds at the surface. Wind directions
do not vary significantly between the surface and the inversion
base. (The latter assumption is undoubtedly violated, but in
the absence of data, it is the safest assumption to make.)
3.
Flow is smoothe"r and less tortuous aloft than at the surface.
4.
Flow through the inversion base is negligible. (Regions of wind
convergence, such as the central San Fernando Valley, are an . .
exception in that a continuous rising flow of air disrupts the
inversion layer.) However, air from within the inversion layer
* If a mass balance is made over a portion of the surface wind field in
x and y, there will typically be a net accumulation or depletion of material.
Such a wind field is termed divergent.
C-39
. .
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mixes with marine air as the inversion base rises.
5.
Lateral winds more or less follow the contours of the surface
of the inversion base. (This effect is accounted for through
the transformed Equations D-4.)
FOllowing these guidelines, we considered two highly simplified approaches
to establishing an upper wind field.
au av
The first method is based on the assumption that az = az = 0,
i.e., that the wind field aloft is identical to that at the ground. However,
air is brought down through the inversion base, or released upward through
it, as needed to satisfy continuity. Thus a vertical component of wind
is calculated for each surface cell through a simple mass balance. If this
component has magnitude p(x,y), and if there are n horizontal strata of
cells, the magnitude of this component for each column of cells is
np(x,y) at the inversion base and ip at the i~~ stratum, counting from
the ground (See Figure C-20c). This approach was applied in initial
calculations and in the validation runs carried out early in the project.
While this treatment is highly simplified and its shortcomings
are apparent, it is nevertheless a convenient method for insuring
that continuity is satisfied.
The second method that we have considered for constructing the wind
field aloft combines the first method with a means for allowing flow
variations in elevated strata. This approach represents an effort to
satisfy continuity through the redistribution of air in the marine layer
when divergence occurs at the surface. In this approach, it is assumed
that a vertical wind component exists, and has the distribution shown
in Figure C-20a. This is the equivalent of assuming that the horizontal
wind vector has the distribution shown 'in Figure C-20b--in effect, two
separate wind fields with a discontinuity. The surface wind field applies
to the five lower strata, the wind field to be constructed applies to the
five upper strata. Note the contrast between the vertical distribution
of w assumed in this method and the distribution of w in the first method
discussed, shown in Figure C-20c.
To calculate wind velocities in the elevated wind field for each
column of cells, we seek a horizontal wind vector that does not vary more
o
than 22~ from the ground vector and that has a magnitude between one and
two times that of the ground vector. (We wish to avoid unduly high wind
speeds aloft, and at the same time ~ we expect that surface winds, hindered
by resistance to flow at the ground, will be slower than those aloft).
If this constraint cannot be satisfied through the redistribution of air
from below the inversion base (at the same time, of course, satisfying
continuity), we allow the entry of air from ab~ve (or flow upward) to
an extent that the upper level horizontal wind speed and direction satisfy
th~ following constraints:
1)
Speed - within a factor of two of the surface wind speed in the
same column of cells
Direction - within 221:10 of the surface wind direction in the
same column,
2)
C-40
Figure C-20 follows.
-------
z
H
H-h
2
h
t,(x.y)
a. Assumed Vertical Distribution 6f'iI--
Second t1ethod (no air through
inversion)
z
H
h
w(x.y)
c. Assumed Vertical Distribution of w--
First Nethod
H-h
T
H-h
T
z
J
H -
h '
-
-
u(x.y) or v(x.y)
b. Vertical Distribution of u (or v)--
Second Hethod
z
H
Due to flo\'l
through inversion
h
w ( x.y)
d. Assump.d Vertical Distribution
of w--Second Method (air
permitted through inversion)
FIGURE C-2n. Vertical Wind Velocity Profiles
C-41
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at the same time minimizing the contribution of air through the inversion
base. It should be noted that, in the event air.is brollght in from above
~the inversion base (or passed upward through it), the distribution of w is
modified from that shown in Figure C-20a, becoming the sum of the
distributions in Figure C-20d. .
The actual calculation proceeds column by column, beginning at the
southwest corner of the Basin, moving easterly until the southernmost
rCM is completed, then continuing at the westernmost column of the second
most southerly row. The calculation is dependent on the order in which.
it is carried out, as the calculated rate and direction of efflux from
a column are the input variables to the next column. Comparisons were
made of upper wind fields calculated beginning at the southwest and north-
~ast corners of the modeling region.* In general, the two calculated wind
fields were virtually the same in areas of smooth flow (over the ocean and
the central and southern Basin), but tended to differ markedly over the
San Gabriel Mountains, the San Fernando Valley, and a small portion of the
Puente Hills. The wind'field calculated beginning in the southwest
corresponded to the surface wind field in a satisfying way, and this
starting point was adopted.
In many ways this. approach is rather appealing, based on physical
considerations. Unfortunately, its development and incorporation into
the main computer program did not take place until nearly the end of the
work effort, and thus it has been the subject of only limited tests. We
believe that its evaluation should be a part of future efforts.
I
!
. I
* These comparisons were made using an earlier method of calculation, in which
the opportunity to utilize air from above was much more restricted than in
the approach desc:dbed here. Thus, much poorer comparison was achieved
in this test than would be expected in a test of the method actually described.
C-42
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IV.
TREATMENT OF TURBULENT DIFFUSIVITY
As horizontal turbulent diffusion has been neglected in the governing
equations of continuity (C-1) ,.it is necessary to consider only the
vertical turbulent diffusivity, K ,. and its variation with elevation (z),
. z.
with location (x,y), and with time (t). However, turbulent diffusivity
is one of the more elusive quantities that must.be estimated. It is not
established through a direct measurement, it must be calculated from
observed data. Furthermore, there is relatively little guidance available
in the literature that is useful in estimating K. '!bus, the accurate. .
estimation of this parameter is currently virtuai1y impossible.
Some useful quaZitative observations can be made, however, regarding
the turbulent diffusivity. K is a function of local velocity, shear
. z
field, and lapse rate, unfortunately, the functional relationship between
K and these variables is largely unknown. In general, K increases
a~proximate1y linearly with z near the ground. In the pr~sence of an
elevated inversion, however, we expect K to decrease with increasing z
z
in the upper portions of the surface layer due to suppression of vertical
buoyant fluctuations near the inversion base. Finally, values of
K vary from about 300 ft.2/minute. under stable conditions to about
60,000 ft. 2/minute under unstable conditions.
Eschenroeder and Martinez (1969) reviewed the literature pertaining
to the turbulent structure of the atmosphere and, based on thi.s effort,
adopted the following formulation for Kz (reported for 180 meter inversion
base and 1 meter/second wind): 30 m2/minute at the ground, increasing
. linearly to a height of 80 meters, at which height Kz = SO(u+5) m2/minute
(u is the horizon~a1 wind speed). Kz is held constant from 80 to 135 meters
elevation, whereupon it decreases linearly to 30 m2/minute at the inversion
base. Based on this work, we have adopted a similar relationship:
5
+ 2 p(x,y,z,t)q(x,y,t)
K (x,y,z,t) ..
z
I l66.5[2-Se(x,y,z,t)]
q(x,y,t)
333(Sp(x,y,z,t) - 4) + S[l-P(x;y,z,t)]q(x,y,t)
p(x,y,z,t).. z - h(x,y)
H(x,y,t) - h(x,y)
. 500 ruz l;~vZ + s).
o
-------
1.0
0.8
p
0.4
o
333
q
Kz(ft2/min)
FIGURE C-2l. Assumed Vertical Distribution of Turbulent Diffusi.vity. Kz
(For definitions of p and q. see EquatiQn (C-3».
C-44
-------
This relationship has been applied in our validation runs to date.
Calculations carried out thus far appear to be!nsensitive to modest
variations in the form of the distribution. Much work is required,
however, to properly include the effects of independent variables not
considered here, and thus to better. establish the functionality expressing
turbulent diffusivity and its variations.
C-45
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References
Bell, Gordon B., "A Study of Pollutant Transport Due to Surface Winds in
Los Angeles, Orange, Riverside and San Bernardi~o Counti~s," State
of California, Dept. of Public Health, Bureau of Air Sanitation
(December 1969).
Edinger, James G., "Changes in the Depth of the l-2arine Layer OVer the
LoS Angeles Basin," Journal of l-leteorolo;JY, Vol. 16, No.3
(June 1959), pp. 219-226.
Edinger, James G., and Roger A. Helvey, "The San Fernando Convergence
Zone," Bulletin of the American Meteorological Society, Vol. 42, No.9
(September 1961), pp. 626-627. .
Eschenroeder, A. Q., and J. R. Martinez, "Mathematical Modeling of Photochemical
Smog," General Research Corp., Santa Barbara, Calif., IMR 1210
(December 1969).
Neiburgcr, Morris, and James Edinger, "Meteorology of the Los Angeles Basin,"
Air Pollution Foundation, Los Angeles, California, Vol. 1, No.1
(Apri 1 1954). .
Neiburger, Morris, Nicholas A. Renzetti, and Rita Tice, "Wind Trajectory Studies
of the Movement of Polluted Air in the Los Angeles Basin," Air Pollution
Foundation, Los Angeles, California, Vol. 2, No.1 (April 1956).
Pack, D. H., J. K. Angell, M. Hodges, W. Hoecker, and C. R. Dickson, "Tetroon
Flights in Los Angeles, California - 1969," ESSA Technical Memorandum
ERLTM-ARI, 19, Air Resources Laboratories; Silver Spring, Md. (.June 1970).
Panofsky, Hans A., "Air Pollution Meteorology," American Scientist, ~,
2, pp. 269-285 (1969).
Scott Research Laboratories, Inc., "Program Design and ~~thodology
D~ta Summary and Discussion," 1969 Atmospheric Reaction Studies
in the Los .Ange1es Basin, Final Report, Vol. 1
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