EPA-600/4-77-015
Jtaeb 1977
Environmental Monitoring Series
CALCULATION OF SELECTED PHOTOLYTIC RATE
CONSTANTS OVER A DIURNAL RANGE:
A Computer Algorithm
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environ-
mental Protection Agency, have been grouped into five series. These five broad
categories were established to facilitate further development and application
of environmental technology. Elimination of traditional grouping was con-
sciously planned to foster technology transfer and a maximum interface in
related fields. The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the ENVIRONMENTAL HEALTH EFFECTS
RESEARCH series. This series describes projects and studies relating to the
tolerances of man for unhealthful substances or conditions. This work is gener-
ally assessed from a medical viewpoint, including physiological or psycho-
logical studies. In addition to toxicology and other medical specialities, study
areas include biomedical instrumentation and health research techniques uti-
lizing animals—but always with intended application to human health measures.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/4-77-015
March 1977
CALCULATION OF SELECTED PHOTOLYTIC RATE
CONSTANTS OVER A DIURNAL RANGE
A Computer Algorithm
by
Kenneth L. Schere and Kenneth L. Demerjian
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
Research Triangle Park, N.C. 27711
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, N.C. 27711
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DISCLAIMER
This report has been reviewed by the Environmental Sciences Research
Laboratory, U.S. Environmental Protection Agency, and approved for publica-
tion. Mention of trade names or commercial products does not constitute
endorsement or recommendation for use.
AUTHORS' AFFILIATION
The authors are on assignment with the U.S. Environmental Protection
Agency from the National Oceanic and Atmospheric Administration, U.S.
Department of Commerce.
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ABSTRACT
An increasing number of mathematical models are being developed which
theoretically simulate the chemical reactions that comprise the urban smog
formation mechanism. These models have necessitated the development of a
technique for the accurate and efficient calculation of photolytic rate
constants for certain smog-related chemical species. A computer program
has been created and is described herein which employs the theoretical for-
mulation of the photolytic rate constant to calculate these rate constants
for specific chemical species over a diurnal time period in clear-sky con-
ditions. A user of the program must specify the date, time and location for
which the rate constants are desired. With this information and specific
data on zenith angles, solar irradiance, and species characteristics of ab-
sorption cross-sections and primary quantum yields, which are provided in
the program package, the computer program generates a diurnal range of pho-
tolytic rate constants for each species. The species included are NCL, CL,
MONO, HON02, H2CO, CHgCHO, and H202- Provision is made for the addition or
deletion of species as the user desires. The appendices to this report con-
tain program and data listings as well as a User's Guide to program opera-
tion.
The program^generated photolytic rate constants for N02 are compared to
direct measurements of this quantity as taken at Research Triangle Park,
N.C. during April 1975. The two methods are generally in close agreement
after the theoretically computed rate constants are scaled by a simplistic
method for the compensation of solar radiation attention by clouds.
This report covers a period from 7/75 to 3/76 and work was completed
as of 3/76.
111
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CONTENTS
Abstract i i i
Fi gures vi
Tab! es vi i
Acknowl edgment vi i i
I. Introduction 1
11. Theoreti cal Formalati on 3
III. Photolytic Species Data 8
IV. Description of Computer Program 10
V. Sample Output and Interpretation 14
VI. Theoretical. Results and Experimental Observations 31
VII. Summary and Conclusions 36
References 37
Addendum ....'. 39
Appendices
A. Listing of computer program code , 41
B. Listing of sample data set 53
C. User's guide , 57
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FIGURES
Number Page
1 Flow diagram of logic controlling computer program to calculate
photolytic rate constants 11
2 Card deck set-up for data input of J(x,e) matrix invoked by pho-
tolyti c rate constant program 12
3 Diurnal variation of the photolytic rate constant for the forma-
tion of 0(3P) from N02 in Los Angeles (34.1°N, 118.3°W) for
three times of the year 26
4 Diurnal variation of the photolytic rate constant for the forma-
tion of O^D) from 03 in Los Angeles (34.1°N, 118.3 W) for
three times of the year 27
5 Diurnal variation of the photolytic rate constant for the forma-
tion of HCO or H from CH20 in Los Angeles (34.1°N, 118.3°W) for
three times of the year 28
o
6 Normal optical thickness for a zenith angle of 0 as a function
of wavelength (nm) for aerosol scattering and extinction, Ray-
o
leigh scattering, and ozone absorption (from Peterson ) 29
7 Comparison of the experimental (circles), theoretical (dashed
line), and U.V.-scaled theoretical (solid line) diurnal varia-
tion of the photolytic rate constant for the photolysis of
N0? near Raleigh, N.C. (35.8°N, 78.6°W) on April 27, 1975 33
8 Comparison of the experimental (circles), theoretical (dashed
line), and U.V.-scaled theoretical (solid line) diurnal varia-
tion of the photolytic rate constant for the photolysis of
N02 near Raleigh, N.C. (35.8°N, 78.6°W) on April 23, 1975 33
9 Comparison of the experimental (circles), theoretical (dashed
line), and U.V.-scaled theoretical (solid line) diurnal varia-
tion of the photolytic rate constant for the photolysis of the
photolytic rate constant for the photolysis of N02 near Raleigh,
N.C. (35.8°N, 78.6°W) on April 25, 1975, 34
vi
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10 Comparison of the experimental (circles), theoretical (dashed
line), and U.V.-scaled theoretical (solid line) diurnal varia-
tion of the photolytic rate constant for the photolysis of
N02 near Raleigh, N.C. (35.8°N, 78.6°W) on April 28, 1975 34
TABLES
Number Page
1 A Comparison of Calculated Photolytic Rate Constants for Reac-
tion Processes Using Actinic Fluxes Reported by Peterson and
(Leighton8) 7
Program Results for L.A., June 21, 1975 14
vii
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ACKNOWLEDGMENT
The assistance of Betty M. Ortman and Patricia Smith who typed the drafts
and final version of the manuscript is greatfully appreciated.
vm
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SECTION 1
INTRODUCTION
The driving force behind the chemical kinetic mechanism which is respon-
sible for smog formation in urban atmospheres is solar radiation. The rate at
which the mechanism proceeds is, in large part, controlled by the intensity of
this radiation. Key chemical species such as nitrogen dioxide, nitrous acid,
and certain oxygenated hydrocarbons absorb light in specific wavelength bands
and are consequently photodissociated. These reactive product species subse-
quently participate in chain reactions comprising the hydrocarbon-NO oxida-
A
tion process.
Controlled chamber studies have simulated the processes by which photo-
1 2
chemical smog is created. ' They have documented the direct proportionality
between light intensity, rates of hydrocarbon-NO photo-oxidation, and ozone
production. Further, an increasingly better understanding of the complex chem-
ical kinetic mechanism of smog formation has led to the development of models
which theoretically simulate the reactions in the mechanism. Several of these
chemical kinetic models have been incorporated into larger regional photochem-
ical air quality simulation models (PAQSM). The accuracy in the specification
of the photolytic rate constants within the chemical model is paramount in pro-
ducing a credible simulation of regional air quality in a PAQSM. A typical
simulation in such a model might extend from sunrise until late afternoon,
during which time the light intensity of solar radiation varies through a diur-
nal cycle of values. The predicted levels of ozone from the model run have
4 5
been shown to be highly sensitive to variations in solar light intensity. '
The photolytic rate constants which are input to the model must accurately re-
flect the diurnal changes in this radiation intensity.
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Increasing sophistication in the developing chemical kinetic models for
smog formation is allowing more photolytic species to be included. There ex-
ists a need, therefore, for the generation of photolytic rate constants for
these species over a diurnal range in an accurate and efficient manner so as
to produce compatible input to the present and future generations of chemical
kinetic models and PAQSM's. A computer program has been developed which helps
to fill this need. Presented with information concerning latitude, longitude,
and date for a specific location, the program will generate photolytic rate
constants for various species over a preselected diurnal time range at a speci-
fied time interval (1 min < At < 60 min). Currently, the photolytic species
included in the program are NCL, O, (three reactions), HONO, HON02 ,H2CO (two
reactions), CH3CHO (two reactions), and FLCL.
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SECTION II
THEORETICAL FORMULATION
The rate expression for a primary photochemical reaction, such as the
photolysis of N02,
is described by
N02 + hv -»• NO + 0 (1)
-d(NO?)
—af- - kN02 - (N02) (2)
whf* V*P k
*N02 is the photolytic rate constant for the reaction. The rate of
photolysis of NOp is dependent upon the efficiency with which the species ab-
sorbs light. This efficiency varies over the wavelength range of absorption.
For N0p> the absorptive range of wavelengths extends from 290 nm to approxi-
mately 440 nm. It is also possible, therefore, to describe the rate expres-
sion for N02 photolysis by
-d(N00) 440nm
—gf-= z i (x) . (x) is the primary quantum yield, or the
number of molecules of N02 dissociated per photon absorbed at a specific wave-
length X. The primary quantum yield, <|>(x), by definition, cannot exceed unity.
From equations (2) ;and (3) it follows that
. 44Qnm i;
KNO? . (NOJ = z I (x) ,..*(x) (4)
d L x = 290nm a
or,
-------
k..n 440nm
N02 = 1 i I (x) . +(x) (5)
TNOTJ" x = 290nm
The rate of photon absorption, IaU)> is estimated using the weak absorption
form of the Beer-Lambert Law, an appropriate approximation for the low concen-
g
tration of ambient pollutants considered in this application . As a result,
I (x), is proportional to the concentration of the species, its absorption
d
cross-section, a(x), and the actinic irradiance, J(x), or the radiation inten-
sity integrated over all angles as seen by a sample of absorbing species; or
L(x) = (NO,) . a(x) . J(x) (6)
a L,
The photolytic rate constant for the reaction described in (1) now takes the
form
. 440nm
KNO? = E J(A) . a(x) . (x) (7)
X = 290nm
where the variables on the right-hand side of the expression are either
measured or calculated. For clear sky conditions and an assumed surface-
albedo function, the actinic irradiance is functionally dependent upon the
solar zenith angle, , a spatially and temporally varying quantity, and alti-
tude h. Thus for a specific location and altitude, J(x,e,h), and hence, k,,
will strictly be a function of time.
More generally, the rate constant for the photodissociation of species i
in the lower atmosphere may be expressed as
SOOnm
k (e,h) = z J(x,e,h) . ^(x) . ^(x) (8)
X = 290nm
where k (e,h) = photolytic rate constant (sec~ ) for species i at solar
zenith angle 9 and altitude h,
r\ -I
J(x,e,h) = radiation intensity (photons cm~ sec"') averaged over wave-
length interval AX centered about x at solar zenith angle e
and altitude h,
4
-------
i 2
a (x) 5 absorption cross sections (cm ) for species i averaged over
wavelength interval AX centered about x,
loge
where n is the concentration of species i (molecules cm~ ),
Si is the path length (cm), and IQ and I are incident and trans
mitted radiation respectively,
primary quantum yield of spec
interval AX centered about X.
and <|>IJ;(A) « primary quantum yield of species i averaged over wavelength
The current version of the computer algorithm does not permit a variation
in altitude in J(x,e)v Rate constants are generated, therefore, for only one
altitude at a time, typically the level being some representative average for
approximately the first several tens of meters or so above ground. Typical
variations>of kNO with altitude have recently been discussed by Peterson .
J,(x,e) values used by the program were selected as follows. The original
Q
working version of the algorithm utilized J(x,e) data from Leighton . His
values are averaged over 10-nm wavelength intervals and are representative of
average solar irradiance at or near the earth's surface in a cloud-free atmos-
phere. In his treatment of the calculation of J(x,e), Leighton invoked several
simplifying assumptions in his approach to Rayleigh scattering, aerosol scat-
tering, and absorption of light within the atmosphere. These values may be con-
Q
trasted with the actinic irradiance data calculated recently by Peterson using
a sophisticated radiative transfer model (RTM) developed by Dave . This model
also treats the vertical variation in J(x,e,h). Several of the differences be-
tween Leigh ton's approach and that of Peterson are illuminating. First, Leighton
assumed the surface of the earth to be nonreflective, whereas Peterson used a
surface albedo of 5 to 15% as a function of wavelength. This difference mani-
fests itself in the fact that the newest values of the actinic flux are 5 to 11%
higher in the ultraviolet wavelengths and up to 30% higher at the longest wave-
lengths than those of Leighton. Second,, evidence suggests that the solar con-
stant data available to Leighton were about 9% too high. This effect has been
corrected in the latest model. Third, the climatological data available to
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Leighton on the total amount of atmospheric ozone, based on Dobson spectro-
photometer measurements, has been amended so that contemporary values are about
35% higher than the earlier values. The higher climatological values of total
ozone as currently used resulted in significantly lower actinic fluxes at wave-
lengths below about 325nm. Lastly, Leighton assumed that half the scattered
radiation from atmospheric aerosols was directed backward, whereas the RTM
handles the large majority of this radiation as directed forward. Leighton's
aerosols therefore caused more depletion of the actinic flux than did the aero-
Q
sols used by Peterson . The present version of the rate constant computer pro-
gram incorporates values of J(x,e) calculated by Peterson for his lowest model
level, which is representative of the atmosphere from the surface to around'50m.
These actinic fluxes, based on typical atmospheric aerosol and ozone profiles,
were calculated to represent general conditions in the continental U.S. The
data have been averaged over 10-nm wavelength intervals from 290 to 700nm. It
has been necessary to extrapolate Peterson's J(x,e) data for wavelengths from
700 to SOOnm to satisfy at least one species which absorbs light at these longer
wavelengths. To calculate photolytic rate constants for an altitude other than
the surface level, the J(x,e,h.) va-lues may be obtained for the particular level
J
j from the RTM and be used in place of the J(x,e,h fc) values in the program,
leaving all other parameters the same.
In order to gain some insight into the effect of the newly calculated ac-
tinic fluxes on photolytic rate processes, a comparison is presented in Table 1
of the calculated photolytic rate constants at selected zenith angles using the
actinic flux data reported by Peterson and those reported by Leighton8. The
wavelength ranges of radiative absorption for each of the listed processes are
described in the next section.
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TABLE 1. A COMPARISON OF CALCULATED PHOTOLYTIC RATE CONSTANTS FOR REACTION PROCESSES USING
ACTINIC FLUXES REPORTED BY PETERSON AND (LEIGHTONB)*
PROCESS
o - <-« 40° 60°
N02+hv+0(P)+NO 9.64xlO"3(1.00xlO"2) 9.33xlO"3 (9.67 x 10"3) 8.25X10'3 (8.46 x 10"3) 5.94xlO"3 (5.93 x 10"3)
0( P) + 02 5.51X10"4 (5.16 x 10"4) 5.36xlO"4 (5.01 x 10'4) 4.82x10"4 (4.51 x 10"4) 3.79xlO"4 (3.44 x 10"4)
0(]D) + 02 7.02X10"5 (1.33 x 10"4) 6.22X10'5 (1.17 x 10"4) 4.04X10"5 (7.37 x 10"5) 1.42xlO"5 (1.99 x 10"5)
- 02(]A) + 0 1.21xlO"4 (1.93 x 10"4) l.lOxlO"4 (1.74 x 10"4) 7.92X10'5 (1.21 x 10"4) 3.66xlO"5 (4.86 x 10"5)
HONO + hv , HO + NO 5.4lx10"4 (5.83 x 10"4) 5.22xlO"4 (5.61 x 10"4) 4.56xlO"4 (4.86 x 10"4) 3.22xlO"4 (3.34 x 10"4)
HON02 + hv -> HO + NO, 5.28X10"7 (9.58 x 10"7) 4.71X10"7 (8.52 x 10"7) SJOxlO"7 (5.48 x 10"7) LUxlO"7 (1.51 x 10"7)
H2CO + hv + HCO + H 3.57X10"5 (4.51 x 10"5) 3.35xlO"5 (4.23 x 10"5) 2.68xlO"5 (3.37 x 10"5) 1.53X10"5 (1.86 x 10"5)
- CO + H2 9.33xlO"5 (1.08 x 10"4) 8.88xlO"5 (1.03 x 10"4) 7.43x10"5 (8.61 x 10"5) 4.74xlO"5 (5.39 x 10"5)
CH3CHO + hv . CH3 + HCO 7.08xlO"6 (1.01 x 10"5) 6.55xlO"6 (9.31 x 10"6) 4.90xlO"6 (6.91 x 10"6) 2.39xlO"6 (3.10 x 10'6)
- CH4 + CO l.SOxlO"7 (3.17 x 10"7) 1.31xlO"7 (2.75 x 10"7) 8.12xlO"8 (1.63 x 10"7) 2.63xlO"8 (4.17 x 10"8)
H2°2 + hv ^ 2HO 2.72X10"5 (3.24 x 10"5) 2.58xlO"5 (3.07 x 10"5) 2.14x10"5 (2.52 x 10'5) 1.34xlO"5 (1.53 x 10"5)
Calculated photolytic rate constants using Leighton's actinic fluxes from Demerjian and Schere6.
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SECTION III
PHOTOLYTIC SPECIES DATA
The method of computing photolytic rate constants for various chemical
species, as given by equation (8), demands certain pertinent information con-
cerning each species: the wavelength range over which it absorbs light must be
known, as well as the values of the absorption cross-section throughout this
range, and also the primary quantum yields for the same wavelength intervals
as the absorption cross-sections. For the purposes of the computer program,
the data were averaged over 10-nm wavelength intervals in all cases, centered
at \= 290m, SOOnm, ---- , SOOnm.
The specific photolytic reactions for which rate constants are automati-
cally generated and the sources of the required species information are listed
below.
N02 + hv (x < 440nm) -t NO + 0(3P) (9)
The values of absorption cross-section for N00 were taken from a National
11
Bureau of Standards review by Hampson , while the corresponding primary quan-
1 2
turn yield data are those given in another NBS review by Hampson and Garvin .
HONO + hv (SOOnm < x < 400nm) -> HO + NO (10)
HONO^ + hv(x < SOOnm) -> HO + N02 (11)
Absorption cross-sections for both HONO and HON00 are those reported in
13
Johnston and Graham . The primary quantum yield values for HONOp were taken
from the same source, while those for HONO were assumed equal to unity over
the full absorption range shown in reaction (10).
hv (SlOnm < x < 350nm; 450nm < x < 750nm) ^0(P) + 0 (12)
-------
03 + hv (A < 310nm) + 0(]D) + 02 (13)
03 + hv (A < 350nm) •* O^A) + 0 (14)
Ozone participates in three distinctphotolytic reactions: (12), (13),
and (14). Jhe absorption cross-sections are identical for corresponding wave-
length intervals in the above reactions. They were calculated from spectra
reported by Griggs . The primary quantum yields, as taken from Hampson ,
differ, however, according to the reaction far which they are applicable.
H2CO + hv (A < 370nm) -> H + HCO (15)
H2CO + hv (A < 370nm) -»• H2 + CO (16)
Formaldehyde undergoes two photolytic processes, one of which contains
free radical products (15) while the other results in molecular products (.16).
The absorption cross-sections and primary quantum yield data for both reactions
are those reported in Calvert et al.
H202 + hv (A < 370nm) -*• 2HO (17)
Absorption cross-sections for hydrogen peroxide are those reported in
Q
Leighton (p. 86), and primary quantum yields were assumed equal to unity over
the entire absorption range.
CH3CHO + hv (A < 350nm) -»• CH3 + HCO (18)
CH3CHO + hv (A < 320nm) + CH^ + CO (19)
The absorption cross-sections for acetaldehyde were taken from Calvert
and Pitts . The primary quantum yield data were based on the studies of
Blacet, Loeffer, and Heldman ' . The limited quantum yield information
suggests that the photolysis rate constants reported here represent a lower
limit estimation. An upper limit for the acetaldehyde photolysis rate con-
stant may be estimated by assuming a primary quantum yield of one over the
absorptive region of interest.
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SECTION IV
DESCRIPTION OF COMPUTER PROGRAM
The task of calculating the photolytic rate constants is performed by a
user-oriented computer program which operates with a given complement of seven
chemical species. There is adequate flexibility in the program to delete ex-
isting species or add new ones. The FORTRAN code is composed of a main program
segment, six subroutines, and one function. A listing is provided in Appendix
A, a sample data set in Appendix B, and the User's Guide in Appendix C of this
report.
Figure 1 portrays a flow chart of the logic invoked by the program. Sev-
eral blocks of input data are required to initiate program operation. First,
the user must specify the location (by latitude, longitude, and time zone),
the date (month, day,and year), and time (both time range and increment) for
which the photolytic rate constants are to be generated. The full range of
wavelength values over which there are corresponding inputs of actinic flux,
J(x,e), is specified next as well as the wavelength increment used to average
the quantities J(x,e), a(x), and (x). The current version of the program
employs a wavelength range of 290nm to 800nm with an increment of lOnm. Zenith
angle values, e, which have corresponding inputs of J(x,e) are next specified.
Presently ten values of e from 0° to 86° are used. Figure 2 shows the matrix
form of J(x,0) data which must be input at this point. Actual values used
9
from Peterson are included in the sample data set presented in Appendix B.
Upon completion of these data inputs, the program has been initialized.
As the flow of logic in Figure 1 shows, program control now passes into
the loop which is responsible for generating the photolytic rate constants
over the specified diurnal time range for each chemical species. For each
species being photolyzed, the wavelength range of absorption, absorption cross-
sections, a(x), and primary quantum yields, (x), must be specified. The pro-
gram subroutines are now called upon to perform their individual tasks in the
10
..- --I-
-------
SPECIES (i),
i/ABSORPTION^
\ RANGE '
a',0'
RATE_
CALCULATES
k< FOR EACH
0 INPUT
RETURN )
JNTERP
INTERPOLATES
DIURNAL RANGE
OF k>
INCREMENT
CLOCK
BY TIME
INCR.
/RANGE
VAN D INCR./,
LOCATION,
DATE,
TIME RANGE,
TIME INCR.
INPUTS
SOLAR_
"GIVEN t,
PROVIDE d(
; RETURN}
SPL.NA, SPLNB
" CUBIC'SPUNE
INTERPOLATION
OF ki's FOR
Mt)
-------
J(800,0) J(800,10) J(800,20) J(800,30) J(800,40) J(800,50) J(800,60) J(800,70) J(800,78) J(800,86)
J(790,0) J(790,10)...
...J(800,78) J(790,86)
J(X,0) MATRIX
J(320,0) J(320,10)...
... .1(320,78) J(320,86)
J(310,0)
....1(310,78) J(310,86)
J(300,0) J(300,TO)...
...J(300,78) J(300,86)
J(290,0) J(290,10) J(290,20) J(290,30) J(290,40) J(290,50) J(290,60) J(290,70) J(290,78) J(290,86)
CARD 52
CARD 51
CARD 4
CARD 3
CARD 2
CARD1
Figure 2. Card deck set-up for data input of J(X, 0) matrix invoked by photolytic rate constant
program.
remaining steps of the rate constant calculations. They are briefly described
here.
A. Subroutine RATE
This routine calculates rate constants for a given species, i, at
each of the zenith angles specified in the inputs. The general form
for the theoretical formulation of the photolytic rate constant is that
given in equation (8). This is the form utilized by RATE, with the
range of the summation corresponding to .the limits of the absorptive
wavelength range.
B. Subroutine INTERP
The logic control for the inner loop seen in the flow chart in
Figure 1 is presented in this subprogram. Provided with a tabulation
of e and k (0) at the input values of zenith angle as calculated by
12
-------
RATE, the inner loop generates interpolated k^ej's corresponding to
6 values over the specified diurnal time range of interest. INTERP
calls upon several of the remaining subroutines to do this.
C. Subroutine SOLAR
20
This subroutine was written by Busse , based on a paper by
21
Woolf . Given the information on location, date, and time, SOLAR
returns a value of solar elevation angle, from which the zenith angle,
9, is readily found. The basic working equation used by this subpro-
gram for the solar elevation angle is
sin « = cos (j> sin D + cos <|> cos D cos h (20)
where <= = solar elevation angle, <(> = latitude,
D = declination angle of the sun, and h = solar hour
angle, a measure of the longitudinal distance to
the sun from the point for which the calculation
is being made.
D. Subroutines SPLNA, SPLNB
In these subroutines a set of n points is exactly fit with an
interpolating function made up of n-1 cubics. Given three consecutive
points, the cubic between x.._i and x. must agree with the cubic between
points x.. and x^+1 at the point x.. in both the first and second deriva-
tives. The n points used by the cubic interpolation scheme consist of
those (e,k^(e)) pairs computed in RATE.
E. Subroutine OUT
Finally, the results of the photolytic rate constant calculations
are printed in tabular form in the temporal sequence as specified by
the diurnal time range and increment. An example of the printed out-
put for a run of the program for Los Angeles, California on June 21,
1975 follows in the next section.
Upon completion of the print cycle for species i , program control
again returns to the point at which species parameters of x range,
a(x), and (x) must be provided. The rate constant calculations are
then performed again for the new species.
13
-------
SECTION V
SAMPLE OUTPUT AND INTERPRETATION
The following table contains a complete listing of program results for 11
species photolyzed in Los Angeles, California on June 21, 1975.
TABLE 2. PROGRAM RESULTS FOR L.A., JUNE 21, 1975
PHOTOLYTIC RATE CONSTANTS, ,K, FOR VARIOUS SPECIES AS
A FUNCTION OF TIME AND Z KNIT II ANCLE
LOCATION: LOS ANGELES, CALIF.,
LATITUDE: 34.058
LONGITUDE: 118.250
DATE: 6 21 1975
TIME: 400 TO 2100 LOCAL STANDARD TIM]
(continued)
14
-------
TABLE 2. (continued)
INITIAL DATA 1'CIUTS llSr.ll I" SUgSLqUCMT CAI.CIM.AT HISS:
Ai:i;i.r.)
.no
10.00
20. 00
30. UO
40. OU
50. DO
60.00
70.00
711.00
lid. 00
K (KATI: CO;;.STA::T)
(/SIX)
.3640-02
.9560-02
.9325-02
.89115-02
.8250-02
.7278-02
iS937-02
.3349-02
.111-14-02
.4073-03
(LOCAL STANDAKD)
400
415
4'JO
445
500
515
53,0
545
600
615
630
645
7
-------
TABLE 2. (continued)
.54 13-03
. 3 3') 4-0
. 32I')-0
. 4'J6U-0
.ftir.a-o
. j')7 3-0
. 32iii-o
. rj'j J-:)
.y 5 5o-o
.2127-0
KATi: CUNSTAMT
. onoo
. uouo
. 0110 0
. U I) IJ 0
. Sft^'J-03
.JH'J-04
. 3(jf>o,-04
. B 4 7 2 - 0 4
. 1 1B2-C]')
. i 3-03
. I
-------
TABLE 2. (continued)
MMXll.S: ii'MJ
r (-IATI: CH:;STA::T)
.4710-J.i
. ill I J-'J('
. 1 1 'jJ-IK)
..!•!<> j-afi
.Ill 11-11 II
, Jill i-!)7
7H'I
71 >
'7 j.i
') « . 1 4 J
•I 3. ") 7 >
7 I. IJj
7-1. 14.'.
li 7 . 1 i 7
Ii4. I 'IK
ii.'Jl i
l I . :; I 'I
4 •> . 7 J •;
4J.611
J7. |-.'l
J 4 . 1 ... 'i
J 1 . J U
I.I. ))'l
I ).'I77
1 1.7(14
1 I . 'HIJ
I J . S J 3
1-I.I.7S
I 1. >l>7
I I . I J -i
I ) . J .i J
AII; CONS L'A;:T
(/set)
.1516-OS
. J405-J3
.(.'173-UH
.l'Ji-J-07
.UJ45-07
. J7 J6-U7
.)5'J)-:i7
.7706-117
. lOitl-Jfi
. 1 JV j-06
, 1 t!l(l-ij<>
. li'J'J-06
.2S31-UO
. JlliU-00
.Uill-06
.4701-06
. b 0 'J 7 -0 (>
.il i'J-Oli
.31 J7-u(i
. illl-llli
J;:. 4 .i 7 ,
J'l. l >
47.HJII
i4.111 7
l 7 . 1 "1-1
nil. 1 7J
. 1HU-06
. JiJ'J-06
. 3247-11 'i
. 1 J7'l-0li
. 1 a') 7 -II (i
01 JS-07
121 5-:l 7
:iii. 7')7
.:•! .4d'i
•/ 1 . I 7 !i
.42I4-U.1
. I'lMi-ilU
. IHHKI
. '.KliUl
.'.II1IIN
.'.Ml (1:1
(continued)
17
-------
TABLE 2. (continued)
4i)U
4 L 3
7'Ju
7) -I
730
745
bUU
943
IJIJD
.101 2-UJ
. 1312-03
. i
-------
TABLE 2. (continued)
\i. i>.\TA nu:;rs
.'10
111. jo
20. o
'10.
4ll.
JO.
60.
70.
la.
CAU:I:LATI.<::S:
UAH: cn::sr.\:;T)
(/sr.o
.7022-04
. 6!I4'3-!|4
.2lti;5-M4
. 1416-04
. I I .'11-0 5
.1121-01)
; 1:11:
(LUCAI. S I'MIJAKD)
ii ATI: CU;;STA::T
(/sue)
4'Kj
41 i
4 i,l
44 3
3lH!
)1 i
3 JO
(.11.)
1) 1 ')
643
7'JO
71 >
7 ill
745
KIIO
SI i
S10
;. 4 j
'11)0
•II 3
lulMI
1 Jl )
111 3 1)
11 )U
114']
120
121
12 I
12i
I JO
, 1 Jl
I J)
1 J«
14U
141
1 4 I
1 4'. >
1 ioo
I i ! )
I )):i
I 14 i
I'HI il
I ') I •>
I'iin
V . 2 (. 2
'• 'I. 273
7 2 . 2 'i J
7 ) . 2 2 '1
7S. T>2
SI .M4/.
.". I.S'):i
.'. ft . 7 'I 7
:; ') . r, tt 2 1-04
.1404-04
.2'llil-l)4
.2)61-114
.2152-04
. 17(U-04
. 1 J')6-U4
.-1-J65-04
.774')-()3
.511^-05
. J4(|5-'J 5
. 2002-05
. lU'O-Oi
.52611-06
.2447-06
.702 1-07
.')dOO
.1)00(1
.OO'lo
. OP'.IO
.0000
. MiMIII
.0000
.'.1000
.IMlOO
(continued)
19
-------
TABLE 2. (continued)
IMT1AI. DATA I'OINTS US!:i> I" S LIB S HQli KNT CALCULATIONS:
(KATi: CO:JST1NT)
(/SEC)
. 12H5-03
.1 IB2-03
. loyy-0 3
. y676-04
. 7y2o-o
. 5B4 3-0
. 365JJ-0
.1676-0
.5676-0
. 'J02G-0
400
413
430
445
500
315
5'JO
545
600
6 1 5
6 JO
645
700
715
7JU
745
BOO
8 I 5
» 30
B45
'JOO
'Jl 5
'} 30
'J45
1 0 0 0
101 5
10JO
1U45
1 100
1115
1 1 JO
1145
Uljl]
1215
12 JO
1245
1 JOU
1 J15
1330
1 J45
1 4011
1415
1 4 jo
1445
1 50!]
1315
15)0
1543
1600
1615
I JU
'J 8 . 142
1J 5 . 3 8 0
1J 2 . 9 3 0
') 0 . 2 5 'J
87. 51 I
X 4 . 7 1 7
SI. 876
7 8 . y 9 4
76.075
7 J. 124
70. 144
67. 1 J7
64. 108
61.058
5 7 . 'J 'J 2
5 4 . 1J 1 1
5 1 . 8 1 ')
48.719
45.614
42. 508
J <; . 4 0 5
J 6 . J 1 1
-1J. 232
30. 1 7 M
2 7 . 1 5 'J
24. 195
21.312
1 K . 550
5.977
3.704
1 . y 0 5
'I.82J
;i . 6 7 3
1 1. 507
13.124
1 5. 2B2
1 7 . 7 a 2
2 0 . 4 'J 7
23. 350
2 6 . 2 y '.
2 '1 . 2 y 'J
32.345
33.419
3 II . 5 0 II
4 1 . 6 0 'J
44.715
4 7 . B20
5 0 . y 2 2
017
57.101
60. 1 72
63.226
66. 262
6 y . 2 7 5
72.263
75. 223
73.132
H 1 . 0 4 4
H 3 . H y H
B 6 . 7 0 7
B y . 4 6 y
'J 2 . 176
'J 4 . 8 2 4
'J 7 . 4 0 7
') ') . y 1 7
1 '12. 341!
1 0 4 . 6 y 0
i y 6 . y 3 6
1 0 ') . 0 7 j
RATi: CONSTANT
(/SEC)
.0000
.0000
.0000
.0000
.2 5 4'J-06
. 144'J-05
.2832-05
.471)7-05
.7733-05
.1170-04
.1651-04
.2 ly8-04
.2795-04
.3432-04
. 4 0 (J 3 - 0 4
.4767-04
.5446-04
.6121-04
.6 7H2-04
.7422-04
.8035-04
.86 L 4-04
.y154-04
. y 6 4 y - o 4
. iooy-o3
. 1049-03
. 10B4-03
.1114-03
. 1 1 3'J-03
.115B-03
.1171-03
.1177-03
. 117B-0 3
.1173-03
.1163-03
. 1 145-0'3
.1122-03
.10'J3-03
. 1 060-03
. 1021-03
.'J783-04
. (J 3 0 2 - 0 4
.3775-04
.8207-04
.7603-04
.6970-04
.6314-^4
.564 3-04
.4'J64-04
. 42H 7-04
.3621-04
. 2 y 7 6 - 0 4
.2 166-04
.1803-04
.1301-04
.8733-05
.5533-05
.3324-05
. IS 13-05
.6024-06
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
(continued)
20
-------
TABLE 2. (continued)
SI'ECIKS: F011I
INITIAL DATA I'OIIiTS USED IN
Z (ZENITH ANCLE)
.00
10.00
20.OU
30.00
40.00
50.00
60.OU
70.00
7s.oo
86. 00
1' CALCULATIONS:
(RATE CONSTANT)
(/SEC)
.3565-04
.3517-04
.3354-04
.3078-04
.2681-04
.2158-04
.1531-04
.8213-05
.3354-05
.6446-06
Tim:
(LOCAL STANDARD)
400
415
430
445
500
515
530
545
600
615
630
645
7=00
715
730
745
80(1
315
830 '
845
900
'J15
931]
945
1000
1015
1030
1045
1100
1115
I 130
1145
1 JOO
1215
1230
1245
1)00
1315
1330
1345
140(1
1415
1430'
1445
liOO
1515
1530
1545
1600
1615
163')
1645
17011
1715
I 73(1
1745
1800
181}
I mil
1«45
I 'JOO
1915
mo
1145
21100
2015
20311
21)45
2 1 Oil
.ZENITH ANCLI
(DECREES)
98.142
95.580
'J2.95Q
2
69.275
72.203
75.223
78.152
1)1.044
83.898
86.7(17
.19.469
92.-176
94.824
97.407
99.917
102.148
104.690
106.936
109.1175
KATE CONSTANT
(/SEC)
.0000
.0000
.0000
.0000
.2252-06
.9994-06
.18484-05
.2914-05
.4335-05
.6106-05
.8113-05
.1024-04
.1242-04
.1458-04
.1666-04
.1864-04
.2052-04
.2231-04
.2402-04
.2561-04
.2709-04
.2843-04
.2964-04
.3072-04
.3168-04
.3252-04
.3324-04
.3385-04
.3435-04
.3471-04
.3496-04
.3508-04
.3510-04
.3501-04
.3480-04
.3446-04
.3401-04
.3343-04
.3274-04
.3193-04
.3101-04
. 2996-04
.2879-04
.2749-04
.2605-04
.2449-04
.2282-04
.2105-04
.1919-04
.1724-04
.1519-04
.1305-04
.1087-04
.8721-05
.6668-05
.4817-05
.3234-05
.2128-05
.1232-05
.4497-06
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
(continued)
21
-------
TABLE 2. (continued)
INITIAL HAT* POINTS Lbtl) IN S UB s EO.OEHT CALCULATIONS:
K (KATE CONSTANT)
(/SEC)
.9327-04
.9221-04
.8834-04
.8298-04
.7425-04
.6212-04
.4736-04
.2692-04
.1194-04
.2521-05
- RATE CONSTANT
(LOCAL STANDARD) (DECREES) (/SEC)
400 98.142 .0000
413 95.530 .0000
4"JU 92.950 .0000
44j 90.259 .0000
500 87.513 .9798-06
Jl3 84.717 .3826-05
?30 81.876 .6879-05
>'» 78.994 .1050-04
'"" 76.075 .1506-04
615 73.124 .2053-04
',? 70-144 .2661-04
"5 67.137 .3301-04
I"? 64.108 .3939-04
75 61.058 .4542-04
7J" 57.992 .5078-04
745 54.911 .5547-04
""',' 51.819 .5973-04
",l 48.719 .6379-04
"" 45.614 .6773-04
"„ "-508 .7147-04
,,," 39.405 .7487-04
,,.,., 36.311 .7788-04
..-' 33.232 .3053-04
1 00 J"'173 .8285-04
,.,,. 27.1^9 .8490-04
030 "•'!'3 .8668-04
,,,,.-, fU-J!2 .8821-04
1o•3 > 0 .8949-04
15-IJ77 .9051-04
U.704 .9127-04
U-905 .9178-04
10.823 .9204-04
10.673 .9207-04
" 11.507 .9188-04
2J" 13.124 .9144-04
1245 15-282 .9076-04
1300 17.782 .8981-04
1315 20.497 .8861-04
1JJU 2J.350 .8715-04
J, 3 26.294 .8544-04
400 29.299 .8347-04
4.3 32.J4S .D123-04
JJ" :J5-4'" .7868-04
._, Jo.3Uo ,7578—04
50" 41.609 .7249-04
\'. \l 44.715 .6884-04
..,- 47.820 .6495-04
'43 50.922 .6091-04
?J" 54-«l' .5674-04
(3,, 57.101 .5219-04
' '- 60.172 .4705-04
nun 63.226 .4119-04
!',' 66.262 .3487-04
.2845-04
.2224-04
. 1 656-04
. 1 171-04
. 7853-05
.4674-05
. 1803-05
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
(continued)
22
-------
TABLE 2. (continued)
species: 1120.!
INITIAL II ATA PilJSTS USE]! I:; SUBSCqUCKT CALC
' (ZENiril AKCLE)
( DECREES)
.00,
1 0. 00
20.00
30.00
40.00
50.00
6.0.00
70.00
78.00
S6.00
K (RATE CIKJSTAKT)
(/SEC)
.2717-04
.2685-04
.2580-04
.2401-04
.2138-04
.1778-04
.1344-04
.7634-05
.3370-05
.707 6-0 6
TIME
(LOCAL STANDARD)
400
415
430
445
500
515
530
545
600
615
030
645
700
715
730
745
80.0
815
830
845
900
•115
930
'J45
1000
1015
10JO
I.J45
1100
1115
1 I 30
1145
1200
1215
12'JO
1245
1300
I JI5
I 130
1345
1400
1415
1430
1445
1>00
1H>
mo
1545
1600
1Mb
1110
Ki45
1700
1715
1730
1 745
la.oo
1815
ISJO
1845
1900
I'115
I 'J 3 0
I'M 5
20LIO
2015
2030
2045
2100
ZESmi AUCLi:
(DEGREES)
') 8 . 1 4 2
95.580
92.950
'JO. 259
87.513
84.717
31.876
78.994
76.075
73.124
70.144
67.137
64.108
61.058
57.992
54.911
51.819
48.719
45.614
42.508
39.405
36.311
33.232
30.17H
27.159
24.195
21.312
lit. 550
15.977
13.704
11.905
10.323
10.678
11.507
13.124
15.2H2
17.71)2
20.497
23.350
26.2'J4
29.299
32.345
35.418
38.508
41.60V
44.715
47.820
50.922
54.017
57.101
60. I 72
63.226
66.242
69.275
7 2.26 3
75.223
78.152
81.044
K3.89S
86,7g7
89.469
92.176
-94.S24
97.407
99.917
102.34B
104.6'JO
106.936
109.075
RATE CONSTANT
(/SEC)
.0000
.0000
.0000
.'0000
.2741-06
. 1075-05
.1935-05
.2961-05
.4257-05
.5817-05
.7549-05
.9360-05
.1116-04
.1288-04
.1443-04
.1580-04
.1707-04
.1827-04
.1944-04
.2055-04
.2156-04
.2247-04
.2326-04
.2307-04
. .2460-04
.2514-04
.2561-04
.2600-04
.2632-04
.2656-04
.2671-04
.267'J-04
.2680-04
.2674-04
.2661-04
.2640-04
.2610-04
.2573-04
.2529-04
.2476-04
.2416-04
.2348-04
.2271-04
.2183-04
.2085-04
.1977-04
.1K62-04
.1742-04
.1613-04
.1484-04
.1335-04
.1167-04
.9887-05
.8069-05
.6305-05
.4686-05
.3305-05
.2210-05
.1313-05
.5058-06
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
(continued)
23
-------
TABLE 2. (continued)
;; IT iAi. DAI \ i'01 NTS us i:n i :i SUBSICQUKNT CALCULATIONS :
t (KATE CONSTANT)
(/SLC)
.00 . 70JJ4-05
1 U. OU - (»'J66-05
2u. 00 - 654'J-05
JU.'JU . 5U57-05
40.00 . 4 'J 0 2 - 0 5
5U.00 .3717-03
60.OU . 2 3 37.101 .27M2-05
lri 30 Ml. 172 .2 371-05
l*'t -> *i3. 22(. . 1406-05
170U M,. 262 . 1578-03
1715 f>'J. 275 . 1213-05
1 7 JO 72. 263 .HBl 1-06
174^ 75.223 . 51J69-06
1 -"OD 7H. I 32 .3763-06
U 1 ) H 1 . u 4 /i .2257-06
a 3 . H . 707 .3976-07
«'J. 4 fi 'J .0000
'J 2 . 1 7 (> .0000
'J4.H24 .0000
y 7. 4 [j 7 .UOOO
'>1J . 'J 1 7 .0000
102. 34K .0000
i j 4. f, y u .ooou
. 0000
. (jOOO
(continued)
24
-------
TABLE 2. (continued)
INITIAL. DATA I'OIKTS USED IN SUB SEQUENT CAI.CIII.ATIOI.'S :
E (RATE COKSTAXT)
(/SEC)
. 1503-06
.1459-06
. 1 310-0 (•
. 1089-Ud
.8116-07
.3197-07
.2625-07
.B5S1-OB
.1921-08
.1951-09
/. (ZENITH AUCiLE)
(DEUKECS)
.00
10.00
20.00
30.00
40. 00
50.00
60.00
70.00
78.00
86.00
T 1:11-:
(U)CAL STANDARD)
400
415
4JO
445
500
515
5'JO
545
600
615
630
645
700
715
730
745
BOO
815
830
1345
900
'J15
930
945
1000
1015
1030
1045
1100
1115
1110
1145
1200
1215
1230-
1245
1300
1315
1330
1345
14UO
1415
1410
1445
1500
1515
1330
1545
1600
HI 5
1630
1645
1700
1715
17)1)
1745
1800
1815
1830
1845
191)0
1915
1930
1945
201)0
201:
2030
2045
2100
xtuirn ANCLI:
(DEGREES)
98. 142
95.580
92.950
90.259
87.513
84.717
81.876
78.994
76.075
73.124
70.144
67.137
64.108
61.05U
57.992
54.911
51.819
48.719
45.614
42.508
39.405
3 6. 3 1 1
33.232
JO.178
27.159
24.195
21.312
18.550
15.977
13.704
11.905
10.823
10.678
11.507
13.124
15.282
17.732
207497
23.350
26.294
29.299
32.345
3 5 . 4 1 H
3S.50I1
4 1.609
44.715
47.820
50.922
54.017
57.101
f.0.172
63.226
66.262
69.275
72.263
75.223
78.152
81.044
B3.U9U
86.707
89.469
92.176
94.824
97.407
'J9.917
102.348
1 0 4 . d 9 0
106.936
109.075
RATE CONSTANT
(/SEC)
.0000
.0000
.0000
.0000
.3889-10
.3261-09
.7316-09
.1516-08
.2950-08
.5210-08
.8402-08
.1261-07
.17S1-07
.2393-07
.3090-07
.3860-07
.4689-07
.5561-07
.6463-07 .
.7377-07
.8290-07
.9184-07
.1004-06
.1085-06
.1158-06
.1225-06
.1285-06
.1338-06
.1382-06
.1416-06
.1439-06
.1451-06
.1453-06
.1444-06
.1424-06
.1393-06
.1351-06
.1301-06
.1243-06
.1178-06
.1107-06
.1028-06
.9437-07
.8551-07
.7642-07
.6727-07
.5020-07
.'i938-07
.4094-07
.330'.-07
.2586-07
.1949-07
.1402-07
.9516-08
.6034-08
.3515-08
.1,153-08
.9073-09
.4203-09
.1244-09
.0000
.0000
.0000
.0000
.'JOOO
. 0000
.0000
.0000
.0000
25
-------
These data and those from similar program listings for March 21 and
December 21 have been incorporated into Figures 3, 4, and 5, which show the
seasonal variations in the diurnal rate constant curves for three photolytic
3
reactions. These include the formation of NO and 0( P) from the photolysis
of N02, O^D) and 02 formation from 03 photolysis, and HCO and H formation
from CHpO photolysis respectively.
The large seasonal variation in the rate constant for the given 0^ photo-
lysis reaction as compared to the other two reactions is immediately apparent.
This sensitivity is a consequence of the photolysis process occurring in the
g
wavelength region X < SlOnm. Figure 6, from Peterson , depicts the normal
10.0
0600
0800
1000
1200
TIME, LSI
1400
1600
1800
Figure 3. Diurnal variation of the photolytic rate constant for the formation of 0(3p) from N02
in Los Angeles (34.1 °N, 118.3°W) for three times of the year.
26
-------
0600
0800
1000
1200
TIME. LSI
1400
1600
1800
Figure 4. Diurnal variation of the photolytic rate constant for the formation of 0( 1D) from 03
in Los Angeles (34.1 °N, 118,3°W) for three times of the year.
27
-------
4.0
+
o
3.0
o
CM
o^
Uj"
2.0
1.0
0600
0800
1000
1200
TIME, LSI
1400
1600
1800
Figure 5. Diurnal variation of the photolytic rate constant for the formation of HCO or H from
,CH20 in Los Angeles (34.1°N, 118.3°W) for three times of the year.
optical thickness (NOT), a measure of the extinction of the direct solar beam
by the atmosphere, as a function of wavelength for a zenith angle of 0°. The
normal optical thickness is described by the equation
NOT = /
"top
dz
(21)
where k is a wavelength-dependent extinction coefficient, p is the density of
op
the absorbing medium, and z, represents the top of the atmosphere . In the
wavelength region from 290 to 310nm the optical thickness is completely domi-
nated by the effects of ozone absorption and Rayleigh scattering. From Beer's
Law, the intensity of the transmitted radiation, IT, is given by
-a(NOT)
(22)
28
-------
10.0
1.0
o
X
<
u
0.1
0,01
RAYLEIGH
SCATTERING
200
300
400 500 600
WAVELENGTH, nm
700
800
Figure 6. Normal optical thickness for a zenith angle of 0° as a function of wavelength (nm)
for aerosol scattering and extinction, Rayleigh scattering, and ozone absorption (from Peterson^},
29
-------
where I is the light intensity at the top of the atmosphere and a is the op-
tical air mass, the length of the path of light through the atmosphere as a
multiple of that from a source at a zenith angle of 0° (a=l). At larger zenith
angles the optical air mass increases by a factor ranging from 1.02 at 10°, 1.56
at 50°, 4.72 at 78°, to 12.4 at 86°
The transmitted radiation, therefore, shows greater sensitivity to vari-
ations in solar zenith angle at the shorter wavelengths. This is a result of
the exponential dependence of IT on optical air mass and total atmospheric ex-
I 1
tinction. Hence, the December curve in Figure 4 for 0( D) production from
ozone is proportionately more depressed than are the winter curves for other
reactions. This is due to the larger zenith angles occurring throughout the
day at this time of the year and also to ozone's absorption at wavelengths
less than 310nm.
30
-------
SECTION VI
THEORETICAL RESULTS AND EXPERIMENTAL OBSERVATIONS
To test the applicability of the computed photolytic rate constants to a
realistic ambient atmospheric situation, a comparison was made between the com-
puted results and observed rate constants. Until relatively recently direct
measurement of photolytic rate constants has been cumbersome, if not impossible.
Of late, however, a device has been designed and built which provides a con-
tinuous in situ measurment of the rate constant (kMn ) for the photolysis of
23 • INU2
N02 . The device consists of a 1-liter round bottom quartz flask through
which nitrogen dioxide is pumped. When the" flask is placed in sunlight the
N02 photolyzes into NO and 0. The concentrations of NO and'NOp are frequently
monitored, and from these measurements k^Q is readily calculated. The device
was operative at Research Triangle Park, N.C. over a period of several days in
late April 1975. Research Triangle Institute, under contract with the Environ-
mental Protection Agency, conducted the project. During this time a variety
of meteorological conditions prevailed over the area.
Since the photolytic rate constants generated by the program are applica-
ble only to clear-sky conditions a method of relating them to conditions when
• • '-,\ •..- -' ; vf" .-'• •'',," >, • : :.' ..'•",'. '' ." . '"•-!, . "
clouds were present was formulated. The experimental k^ data were primarily
dependent on light absorption in the ultraviolet wavelength range. Thus, it
was decided to. scale the program-generated values by the. simultaneous measure-
ments of ultraviolet (UV) radiation at Research Triangle Park. The percentage
departure of the UV, measurements, from their expected values during cloudless
sky conditions were used to scale the rate constants from their clear-sky val-
ues. In this manner the rate constants for N02 photolysis directly measured
at RTP were compared to those calculated by the program described here. Fig-
ures 7, 8, 9 and 10 present these comparisons.
31
-------
Only one day for which data were available contained a period of time in
which clear-sky conditions prevailed. This occurred from approximately sun-
rise until 1100 on April 27, 1975. Figure 7 presents the comparison for this
day. The clear-sky and UV-scaled plots of kNQ are coincident here until 1100
when a cloud cover began to obscure the sky. After this point the UV-scaled
portion of the plot deviates from the clear-sky case according to the UV at-
tenuation factor. Figures 8 and 9 depict the results from two days within the
experimental period during which time varying degrees of cloud cover prevailed
over the region. Finally, Figure 10 shows the comparison for a day with com-
pletely overcast skies and some rain during the morning hours.
In all cases the observations of kNQ were averaged over 10-minute inter-
vals. The UV scaling factors for the k^Q plot were computed over a com-
parable time period. Generally the observations and the UV-scaled plot of
k.,Q are in quite close agreement. There are, however, several exceptions
that should be noted. The measured kNO values for a large portion of the
day on April 27, 1975, shown in Figure 7, are lower than the UV-scaled val-
ues by as much as 27% at 1000. This difference may possibly be understood by
examining certain characteristics of the spherical-quartz flask measuring de-
vice. This type of system requires thorough mixing for maximum efficiency of
NO? conversion. Moreover, the kwn value measured from the spherical reactor
INU2 24
was found to be flow dependent, yielding higher values at higher flow rates
Thus, a mixing or flow problem, or both, may have held the measured kNO
values below expected levels here.
Figures 8, 9, and 10 show a less pronounced difference between measured
and UV-scaled k^Q values. However, there does seem to exist a small, yet
systematic, deviation in the morning hours as compared to the very close agree-
ment in the afternoon. It has been noted that aerosol present in the atmos-
phere in higher concentrations during the morning hours tended to reduce the
UV intensity, and hence the k^Q measured values^. The relative effects of
higher aerosol concentrations on the UV radiometer and the kNQ reactor device
may not be linear, causing a difference to exist between the observed and UV-
scaled KNC,2 values. Lower temperatures also tended to reduce the values of
32
-------
10.0
0600
0800
1400
1600
1800
1000 1200
TIME, LSI
Figure 7. Comparison of the experimental (circles), theoretical (dashed line), and U.V.-scaled
theoretical (solid line) diurnal variation of the phdtolytic rate constant for the photolysis of NO2
near Raleigh, N.C. (35.8°N, 78.6°W) on April 27, 1975.
10.0
8.0
t "
6.0
4.0
2.0
0600
0.800
1000
1200
TIME, LST
1400
1600
1800
Figure 8. Comparison of the experimental (circles), theoretical (dashed line), and U.V.-scaled
theoretical (solid line) diurnal variation of the photolytic rate constant for the photolysis of N02
near Raleigh, N.C. (35.8°N, 78.6°W) on April 23, 1975.
33
-------
10.0
6.0
4.0
2.0
0600 0800 1000 1200 1400
TIME, LSI
1600
1800
Figure 9. Comparison of the experimental (circles), theoretical (dashed line), and U.V.-scaled
theoretical (solid line) diurnal variation of the photolytic rate constant for the photolysis of N02
near Raleigh, N.C. (35.8°N, 78.6°W) on April 25, 1975.
10.0
8.0
6.0
4.0
2.0
0600
0800 1000
1200
1400 1600
1800
TIME, 1ST
Figure 10. Comparison of the experimental (circles), theoretical (dashed line), and U.V.-scaled
theoretical (solid line) diurnal variation of the photolytic rate constant for the photolysis of NO?
near Raleigh, N.C. (35.8°N, 78.6°W) on April 28, 1975.
34
-------
23
kNO measured by the reactor mechanism. This may also help account for the
slight systematic difference seen in the morning.
The difference between theoretical clear-sky and observed (or scaled)
k^jQ values can be substantial, amounting to over 90% in the most overcast-
sky situation. However, even in this case the UV-scaled theoretical values
match the observations quite well as figure 10 shows. Implicitly, the program-
generated photo.lytic rate constants are accurate in themselves for use in a
photochemical kinetic mechanism as applied to clear-sky conditions. Should
they be utilized in such a.mechanism for other than clear-sky conditions it
is apparent that some method of scaling the values, such as the one used here,
is necessary. The full treatment of the attenuation of the solar radiation
by fluctuations in cloud cover is beyond the scope of this work.
35
-------
SECTION VII
SUMMARY AND CONCLUSIONS
The generation of the diurnal variation of photolytic rate constants by
a computer program based on their theoretical formulation has been shown.
These rate constants may be computed for a specific location and time given
inputs of latitude, longitude, date, and local standard time. At present, the
program generates rate constants applicable to the lower atmospheric photo-
dissociation of N02, 03, MONO, HON02, H2CO, CH3CHO, and H^.
Comparisons between observed and theoretical rate constant values for the
photolysis of NOp in the real atmosphere show good agreement in clear-sky con-
ditions and in cloudy-sky situations when the theoretical values are scaled by
a UV attenuation factor. The diurnal variation in the photolytic rate constants
produced by the program provides a tractable method for including this daily
cycle in a chemical kinetic mechanism that may run through many hours of the
day.
Integration of a relatively simple method of treating the solar radiation
attenuation by varying amounts of cloud cover into the routine would provide
greater flexibility in the application of the program. This constitutes the
major suggestion for further research on the topic.
36
-------
REFERENCES
1. Tuesday, C.S., 1961: The Atmospheric Photooxidation of Trans-Butene-2
and N.itrie. Oxide. Chemical Reactions in_ the Upper and Lower Atmosphere,
pp. 1-32. Interscience Publishers.
2. Bufalini, J.J., B.W. Gay, and K.L. Brubaker, 1972:. Hydrogen Peroxide
Formation from Formaldehyde Photooxidation and Its Presence in Urban-
Atmospheres. Environ. Sci. Techno!., 6_, pp. 816-821.
3. Demerjian, K.L.., J.A. Kerr, and J.G. Calvert, 1974: The Mfechanism of •
Photochemical Smog Formation.- Adv. in Environ. Sci. Technol., 4, -pp.>
1-262. John Wiley and Sons.
4. Peterson, J.T, and K.L. Demerjian, 1976: The Sensitivity of Computed
Ozone Concentrations to Ultraviolet Radiation in the Los Angeles Area"-.
Atmos. Environ., 10, pp. 459-468.
5. Liu, M.K., D.C. Whitney, and P.M. Roth, 1976: Effects of Atmospheric
Parameters on the Concentration, of Photochemical Air Pollutants. JvAppl.
Meteor., J5>, pp. 829-835.
6. Demerjian, K;L. and K.L. Schere, 1975: A Computer Program for'Generating
the Diurnal Variation of Photolytic Rate Constants for Atmospheric Pol-
lutants, Proceedings of the International Conference on Environmental
Sensing an:d Assessment* Vol,ume .II, 20-2, Las Vegas, Nevada.
7. Peterson, J.T., 1976: Dependence of the N0£ Photodissociation Rate Con-
stant with Altitude. Submitted to Atmos. Environ.
8. Leighton, P.A., 1961: Photochemistry of Air Pollution. 300.pages.
Academic Press.
9. Peterson, J.T.,1976: Calculated Actinic Fluxes"(290-700nm) for Air.Pol-
lution Photochemistry Applications. Report EPA-600/4-76-002, Environ.
Sci. Res. Lab., Environmental Protection Agency, Research Triangle Park,
N.C.~ 55 pages.
10. Dave, J.V.* 1972: Development of Programs for Computing Characteristics
of Ultraviolet Radiation. Final Rept. under Contr. NAS 5-21680. NASA
Rept. CR-139134. National Aeronautics and Space Admin., Goddard Space
Fit. Crt., Greenbelt, Md. (NTIS No. N75-16746/6SL).
37
-------
11. Hampson, R.F. (editor), 1973: Chemical Kinetics Data Survey VI. Photo-
chemical and Rate Data for Twelve Gas Phase Reactions of Interest for
Atmospheric Chemistry, NBSIR 73-207, 124 pages.
12. Hampson, R.F. and G. Garvin (editors), 1975: Chemical Kinetic and Photo-
chemical Data for Modeling Atmospheric Chemistry. NMS, Technical Note
866, 118 pages.
13. Johnston, H.S. and R. Graham, 1974: Photochemistry of NO and HNO Com-
pounds. Can. J_. Chem., _52_, pp. 1415-1423.
14. Griggs, M., 1968: Absorption Coefficients of Ozone in the Ultraviolet
and Visible Regions. J_. Chem. Phys., _49_, pp. 857-859.
15. Hampson, R.F. (editor), 1973: Survey of Photochemical and Rate Data for
Twenty-eight Reactions of Interest in Atmospheric Chemistry. J_. Phys.
Chem. Ref. Data, 2., pp. 267-312.
16. Calvert, J.G., J.A. Kerr, K.L. Demerjian, and R.D. McQuigg, 1972: Photol-
ysis of Formaldehyde as a Hydrogen Atom Source in the Lower Atmosphere.
Science. 175, pp. 751-752.
17. Calvert, J.G. and J.N. Pitts, 1966: Photochemistry. 368 pages. John
Wiley and Sons.
18. Blacet, F.E. and D.E. Loeffer, 1942: J_. Amer. Chem. Soc.. 64, p. 893.
19. Blacet, F.E. and J.D. Heldman, 1942: JL Amer. Chem. Soc., 64, p. 889.
20. Busse, A.D., 1971: Attributes of the Earth-Sun Relationship, Internal
Memorandum. Meteorology and Assessment Division, NOAA/EPA, RTP, N.C.
21. Woolf, H.M., 1967: On the Computation of Solar Elevation Angles and the
Determination of Sunrise and Sunset Times. NASA Technical Memorandum
1646. 12 pages.
22. Craig, R.A., 1965: The Upper Atmosphere. 509 pages. Academic Press.
23. Sickles, J.E. and H.E. Jeffries, 1975: Development and Operation of a
Device for the Continuous Measurement of ka for Nitrogen Dioxide. Depart-
ment of Environmental Sciences and Engineering. Publication No. 396,
School of Public Health, Univ. of North Carolina, Chapel Hill, N.C.
24. Zafonte, L., P.L. Rieger, and J.R. Holmes, 1976: Nitrogen Dioxide Photol-
ysis in the Los Angeles Atmosphere. Publication No. DTS-76-18, Atmos-
pheric Studies Section, California Air Resources Board. Submitted to
Environ. Sci. Techno!.
38
-------
ADDENDUM
During the final preparation of this report, new experimental data on
the absorption cross section for nitrogen dioxide were reported by Bass,
Ledford and Laufer at the National Bureau of Standards.
It is recommended that these cross section data be used in place of
those currently available in the computer algorithm, which are based on the
work of Hall am
are as follows:
2
work of Hall and Blacet . The recommended averaged N09 cross section data
nm
a cm2X 1020 nm a cm2X 1020
290 8.52 380 56.99
300 12.83 390 58.22
310 18.26 400 59.52
320 24.74 410 58.03
330 30.95 420 (54.52)
340 37.39 430 (51.46)
350 44.90 440 (48.48)
360 50.11 450 (45.51)
370 54.05
These new data represent approximately a thirteen percent reduction in the
nitrogen dioxide cross sections currently in use. The Bass et al. work did
not extend the measurements beyond 410 nm and therefore the values reported
in parenthesis are estimates based on extrapolating the averaged percentage
reduction between the Bass et al. and Hall and Blacet cross sections to the
Hall and Blacet averaged values at 420, 430, 440 and 450nm.
39
-------
The calculated photolytic rate constant for nitrogen dioxide dissocia-
tion using the Bass et al. cross section at ten zenith angles is given below.
degrees seconds"
0.0 8.548 X 10"3
10.0 8.478 X 10"3
20.0 8.271 X 10"3
30.0 7.900 X 10"3
40.0 7.325 X 10"3
50.0 6.468 X 10"3
60.0 5.281 X 10"3
70.0 3.431 X 10"3
78.0 1.691 X 10"3
86.0 3.635 X 10"4
1. Bass, A.M., A.E. Ledford, Jr. and A.M. Laufer, 1976: Extinction Coeffi-
cients of N02 and N_0 . Journal of Research of the National Bureau of
Standards - A. Physics and Chemistry Vol. 80A, (2), pp. 143-166.
2. Hall, T.C., Jr., and F.E. Blacet, 1952: Separation of the Absorption of
Spectra of N02 and N^ in the Range of 2400-5000 A. J_. Chem. Phys. 20^
pp. 1745-1749.
40
-------
APPENDIX A
LISTING OF COMPUTER PROGRAM CODE
On the following pages the FORTRAN code for the computer program is
listed. It is composed of a main segment, six subroutines, and one function.
Although the program was developed and originally run on the UNIVAC 1110 at
the National Computer Center in Research Triangle Park, N.C., the code is of
a general nature so as to be easily adapted to most computer installations.
The central processing time for an execution of the compiled program as listed
here and run on the UNIVAC 1110 is.approximately 5 seconds.
41
-------
ro 27
23
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
*RATECOMSTANT.MAIN
I
3
4
5
6
7
8
9
10
1 1
12
1 3
14
15
16
1 7
18
19
20
21
22
23
24
25
26
c
c
c
c
c
c
c
**** RATE CONSTANT CALCULATIONS FOR FIRST ORDER PHOTOCHEMICAL REACT
REAL* 8 K
COMMON XJ(52, 10) ,SICMA(52,20) .PHI (52, 20) ,
COMMON LAM1 , INC, SLA, SLO.TZ, IY, IM, I)), ISTRT
COMMON SPECIE, MAXZ , ITIME( 100) , XZ ( 100) , K ( 1
DIMENSION PLACE(6)
**** INPUT LOCATION LATIT U DE , LOHGI TU 1)E ,
Z( 10) .RTCON(lO)
, ISTOP, I INC
00) , JSTRT, JSTOP
TIME ZONE, DATE,
**** TIMES TO BECIN AND END CALCULATIONS, AND TIME INCREMENT
RDM) (5, 14) PLACE, SLA , SLO , 17. , I Y , Itl , 1 1) , JSTRT, JSTOP, I ISC
14 FORHAT(6A4, 5X,2F10.4,/,F5.l,4X,I4,4X,I2,4X,12,/,3(I4,4X))
C
C
C
c
c
c
c
c
c
c
c
c
**** INPUT NUMBER OF SPECIES, NUMBER OF
ZENITH ANGLES,
**** NUMBER OF U AV E LENCTII VALUES USED, INITIAL WAVELENGTH VALUE
***,* AMD WAVELENGTH INCREMENT.
READ(5,100) MAXL, MAXZ , MAXJ, LAM 1 , INC
100 FORMAT(5I4)
**** INPUT VALUES OF ZENITH ANGLES
REAI)(5,105) (Z( I) , 1 = 1 ,HAXX.)
105 FORM AT ( 2 OF 4. 0)
**** PRINT OUT HEADING
WRITE (6, 1 1 2) PLACE, SLA, SLO, 111 , ID, IY, JSTRT
, JSTOP
112 KOKMAT( ' 1 ',////////// ,40X,' 1M10TOLYT 1C RATE CONSTANTS, K, FOK VA R 1 0
+US SPECIES AS',/,48X,'A FUNCTION OF TIME
+ 40X, ' LOCATION: ' , 6A4 , / / , 40X , ' LAT ITU DE : ',
AND ZENITH ANGLE ',11111,
FlO. 3, / / , 4 OX, ' LONG I I'UDE:
+ ' , F10. 3,//,40X,'DATE: ' , 5X, 3 ( I 4 , 3X) , / / , 40X, ' T III E : * , 5X, 14 , 5X , ' TO' ,
C
C
C
c
c
c
c
c
c
c
c
+3X, 14, 5X, 'LOCAL STANDARD TIME')
**** INPUT VALUES OF ACTINIC IRRADIANCE
**** ZENITH ANGLES
DO 5 1=1, MAXJ
REAIH5, 1 10) (XJ(I,J), J=1,MAXZ)
110 FORMAT(8F10. 7,/ ,2F10. 7)
5 CONTINUE
**** FOR EACH SPECIES INPUT THE SPECIES
**** WAVELENGTH AT WHICH TO BEGIN
**** WHICH TO STOP SUMMATION
10 READ(3,H5) L, SPECIE, M I N LAM , MAXI.AM
115 FORMAT( 12, 2X, A4, 2X, 14, 2X, 14)
ISTRT = (MINLAM-LAM1) /INC + 1
ISTOP = (MAXLAM-LAM1) /INC + 1
**** INPUT ABSORPTION COEFFICIENTS FOR
(J) FOR THE CORRESPONDING
NUMBER, THE SPECIES NAME,
SUMMATION, AND WAVELENGTH AT
EACH SPECIES
-------
56 C
57 RKAD(5,120) (SIGMA(I,L) , I = I.STRT, I STOP)
58 120 FOR!1AT(5 ( 10E8. 2,/) , 2E8. 2)
59 C
60 C *'*** INPUT QUANTUM YIELDS FOR EACH SPECIES
61 C
62 KEAI)(5, 125) (PUI(J.L), J = I STRT, I STOP)
63 125 FORMAT(5(10F8.4,/) ,2F8.4)
64 !JO 15 M = 1,MAXZ
65 C
66 C **** CALL SUBROUTINE TO CALCULATE KATE CONSTANTS
67 C
68 CALL RATE(L, M.MIN'LAM .MAXLAM, RTCON(M) )
69 15 CONTINUE
70 C
71 C ***ft CALL SUBROUTINE FOR SPLINE INTERPOLATION OF RATE CONSTANTS
72 C
7 J CALL INTERP
74
75 C
76 C **** CALL SUBROUTINE FOR PROGRAM OUTPUT
77 C
78 CALL OUT
79 C
80 C **** TEST FOR LAST SPECIES
:U C
82 IF(L.G E.MA X L) STOP
8 J CO TO 1 0
tt 4 EN I)
-------
*KATE
1
2
3
4
5
6
7
8
y
10
1 1
12
1 3
14
15
16
CONS')
C
C
C
C
TANT. RAT 1C
SUBROUTINE KATK( L , HZ , fl I NLAll, MAXLAM, SUM)
REAL*8 K
COMMON XJ(52, 10) ,SICMA(52,20) , t'll I(52,20) , Z( 10) ,RTCON(10)
COMMON LAM1 , INC, SLA, SLO.T2, I Y , IN , 11), I STRT , I STO I', I [ NC
COMMON Sl'ECIK, MAX2 , IT IM K ( 1 00) , XX. ( 1 00) , K( 1 00) , JSTKT, J STOI'
A ***
A A A*
THIS SUBROUTINE CALCULATES
THE GIVEN INI'UTS
A SINGLE RATE CONSTANT ACCORD I.NC TO
20
SUM =0.0
DO 20 I=MINLAM,MAXLA:I, INC
II = (I-LAMD/INC + 1
SUM = SUM + XJ(II.NX) * l.OK+15
CONTINUE
RETURN
1- N 1)
* SIGMAdl.L) * PHKI1.L)
-------
01 27 C
*RAIECONSTANT.INTERP
1 C
2 C **** THIS SUBROUTINE COMPUTES INTERPOLATED VALUES OF RATE CONSTANTS
3 C **** FOR PARTIGULA-R TIMES OF THE DAY AND ZENITH ANGLES
4 C
5 SUBROUTINE INTERP
6 REAL*8 K
7 COMMON XJ(52, 10) ,SIGMA(52,20),PH1(52,20),2(10) , KTCON(IO)
8 COMMON LAMI,INC,SLA,SLO.TZ,IY,in,ID,ISTRT,ISTOP,UNO
9 COMMON SPECIE,MAXZ,ITIME(100),XZ(100),K(100),JSTRT,JSTOP
1U DIMENSION D(2),C(27),W(27),V(5),ZZ(10),TK(10)
11 DATA D/0.0,0.0/
12 NN=MAXZ
13 DO 27 JP=1,NN
14 ZZ(JP)=Z(JP)
15 TK(JP)=R1'CON(JP)
16 27 CONTINUE
17 C
18 C **** CALL FIRST SUBROUTINE FOR SPLINE INTERPOLATION OF RATE CONSTANTS
19 C *
20 CALL SPLNA( N'N , ZZ.TK, 2, U , C , W)
21 II = 0 " ' ' -
22 TIME = JSTRT
23 5011-= II+l
24 ,XG=0.0
25 C
26 C **** CALL SUBROUTINE TO COMPUTE ZENITH ANGLES FROM TIME OF DAY
28 C-ALL SOLAR(SLA, SLO.TZ, IY, IM, ID.TIME, XC , 5)
29' X1) = 9Q.-XC
30 ITIME(II) = TIME
31 XZ(II) =XD
32 V(l) = XD
33 IF(XD.GT.90.0) GO TO 20
34 G '
35 C **** CALL SECOND SUBROUTINE IN SPLINE INTERPOLATION SCHEME
36 C
37 CALL SPLNB(NN,ZZ.TK,C,V)
38 K(I I) =' V(2)
3'J IF(K( I I) .LT.0.0) K(I1)^T).0
40 GO TO 25 - —
41 2 0 K(I I) = 0.0
42 25 Tl ='TIME
43 TIME = CLOCK(T1,IINC)
44 NTIME = TIME
45 IF(NTI:1E.GT. JSTOP) GO TO 60
46 GO TO 50
47 60 RETURN
48 END
-------
* RAT INCONSTANT. OUT
1 C
2 C **ft* THIS SUBROUTINE PRINTS OUT ALL RELEVANT PARAMETERS
3 C
4 SUBROUTINE OUT
5 HEAL*8 1C
6 COMMON XJ(52, 10) ,SI(;ilA( 32,20) ,PHI(52,20) , 2(10) , RTCO:i(10)
7 COMMON LAM1, INC, SLA, SLO.TZ, IV, IM, II), ISTRT, ISTOP, I INC
8 COMMON SPECIE.MAXX. , ITIMK(IOO) , XX. ( 1 00) , K( 1 00) , JSTRT , JSTOP
'J . URITE(6,100) SPECIE
10 100 KORMAT('1',57X,'SPECIES: ',AA,////)
11 WRITE(6,105)
12 105 FOtttlAT(AOX, ' INITIAL DATA POINTS USED IN SUBSEQUENT CALCULATIONS: '
13 + ,//.AOX,'X. (ZENITH ANCLE) ', 2()X ,' K (RATE CONSTANT) ',/, A 3X,
14 +'(DEGREES)',29X,'(/SEC)',/)
1 D 1)0 UO 1 = 1 , MAXX.
16 'JKITE(f), 1 10) 2(1), RTCON(I)
•17 110 FORtlAT(AAX, F8. 2, 25X, K10.4)
Id HO CONTINUE
19 WRITE(6,115)
20 115 1"OHMAT( '0' ,///, 2HX, 'TIME' , 23S, ' ZENITH ANCLE', 25X,' RATE CONSTANT',/
21 +, 23X, ' (LOCAL STANDARD) ' , 1 'JX , ' (1) ECREES) ' , 29X , ' (/SEC) ' ,/)
22 A = JSTOP - JSTRT
23 ii = FLOAT( (JSTOP-JSTRT)/I 00)
2k 1ENI) = (II + (A-B*100.) 760.) * FLOAT( 6 O/1 INC) + 1.
25 DO 'JO II=1,IEN!)
2f> URITE(6, 1 20) IT IME( I I) , XX. ( I I) , K( I I)
27 120 FORMAT(28X, IA, 27X, F8. "J, 28X, ElO. A)
2H 90 CONTINUE
29 RETURN
3D END
-------
*UATECONSTANT.
1
2
3
4
5-
6
7
8
9
10
1 1
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
3U
39
40
4 1
42
43
44
45
46
47
4b
49
50
51
52
33
54
55
C***
C***
C***
C***
c***
C***
c***
c***
c***
c***
c***
C***
c***
c***
c***
c***
c***
c***
c***
c***
C*ft*
1
2
SOLAR
SUBROUTINE SOLAR ( S LA , SLO, TZ , IY , IM , ID, TIME, D, NV)
SLA... LATITUDE (DEC) SOUTH = MINUS
SLO... LONGITUDE (DEC) EAST = MINUS
TZ. . . TIME ZONE
ALSO INCLUDES FRACTION IF LOCAL TIME IS NOT-
STANDARD MERIDIAN TIME. E.G. I'OOHA, INDIA
IY. . YEAR
111.. MONTH
ID...- DAY
TIME.. LOCAL STANDARD TIME IN HOURS AND MINUTES.
1:30 PM = 1330 ** STANDARD TIME **
D. . -RETURNED VALUE
NV.. VALUE TO BE RETURNED, SELECTED AS FOLLOWS...
1 ... DECLINATION (DEC.)
2.... EQUATION OF TIME ADJUSTMENT (HRS.)
3... TRUE SOLAR TIME (HRS.)
£.". . HOUR ANGLE (DEG.)
5... SOLAR ELEVATION (DEC.)
6. . .• OPTICAL AIRMASS
0 < NV < 7. OTHERWISE, D = 9999.
DIMENSION MD( 1 1)
DATA "MO/ 31 , 29, 3 f , 30, 31,'30, 2*31, 30, 31, 30 /
DATA A, B,C, SIGA/0. 15, 3. 885, 1.253, 27 9. 9 3 48/
RA!) = 572957. 75913K-4
SDCC=39784.988432E-5
RE=1 .
IF(SLO.LT.O.) RE=-1.
KZ=TZ
TC=(TZ-KZ) *RE
TZZ=KZ*RE
SLB=SLA/ RAD
K=ID
TIMH=TIME/ 100.
I=TIMI1
TIMLOC=(TIMH-I) /O. 6+I+TC
IMC=IM-1
IF ( IMC. LT. 1) GOTO 2
D01I=1 , IMC
K=K+M»( 1)
LEA1>=1-'
NL = M'OD( I Y, 4)
IF(ML.LT.l) LEA1' = 2
SMER=TZZ*1 5.
TK=( (SMER-SLO) *4.) /60.
KR = 1
IF( K. GE. 6 1 . AtJD. LEA]'. LT. 2) KR = 2
DAD=(TIMLOC+TZZ) /24.
DAD=DAD+K-KR
DF=DAD*360./365. 242
DE=DF/ RAD
D E S I N = S I » ( D E )
DECOS = COS(1)E)
DESIN2 = SIN(Di:*2.)
5. 5
-------
56 DECOS2 = GOS(U-E*2.)
57 SIG~SIGA+UF+1 . 9 1 482 7* I) ES IN-0 . 0 79 52 5*UECOS+0 . 0 1
60 UEGSIN = SI)EC*SIN(SIG)
61 EFFOEG=ASIN(DKCSIN)
62 IF(NV.ME.1) GOTOIO
63 D=EFFUEG*RAU
64 RETURN
65 10 EQT=0. 12357*DES1N-0. 004289* I)ECOS+0. 1 5 3809*1) E SI N 2+0 . 060 783*0 EGOS 2
66 IF(NV.tJE.2) COT011
67 I) = EQT
68 RETURN
69 11 TST = TK+TIMU)C-EQT
70 IF(KV.NE.3) GOT012
71 D=TST
72 IF(D.LT.O.) l)"l) + 24.
73 IF(U.GE.24.) D=D-24.
74 RETURN
75 12 11RANGL = A11S(TST-12.) *15.
76 IF(NV.ME.4) GOTO 13
77 0 = IIRANGL
78 RETURN
79 13 HRANGL-HRANGL/RAI)
80 SOLS IN-0!iGSIN*S IN ( SLIi) +GOS(EFFOEC) *GOS( SLB) *GOS(HRA?1GL)
Bl SOLEL= ASIN(SOLSIN)*RAU
82 1F(NV.NE.5) GOTO 14
83 0=30LEL
84 RETURN
85 14 IF(NV.NE.ft) GOT08
86 IF(SOLEL.LE.O.) GOT08
87 TK=SOLEL+B
88 E=1./TK**G
89 !)=!./( A* E + SOLS IN)
'JO RETURN
91 8 U = 999'J.
'J2 RETURN
93 • ENO
-------
*RATECONSTANT. Sl'LNA
1 SUBROUTINE Sl'LNA ( N , X, Y , J , D , C , W)
2 DIMENSION X(10) ,Y(10) ,U(2) , C(30) ,W(30)
3 c
4 C OVER THE INTERVAL X(I) TO X(I+1), THE INTERPOLATING
5 C POLYNOMIAL
6 C ' Y = Y(I)+A(I)*Z+B<1)*2**2 + E(I)*Z**3
7 C ' WHEKE Z=(X-X(I))/(X(I+1)-X(I))
8 C IS USED. THE COEFFICIENTS A(I),B(I) AND E(I) ARE COMPUTED
9 C BY SL'LNA AND STORED IN LOCATIONS C(3*1-2) ,C(3*1-1) AND
10 C C(3*I) RESPECTIVELY.
11 C WHILE WORKING IN THE ITH INTERVAL,THE VARIABLE Q HILL
12 C REPRESENT Q=X(I+1) - X(I), AND Y(I) WILL REPRESENT
13 C , Y(I+1)-Y(I)
14 c
15 C -,
16 Q=X(2) - X(l)
17 Yl =Y(2) - Y(l)
18 IF .( J . EQ. 2) GO TO 100
iy c ' . .
20 C IF THE FIRST DERIVATIVE AT THE END POINTS IS GIVEN,
21 C A(l) IS KNOWN, AMD THE SECOND EQUATION BECOMES
22 C MERELY 11 ( 1)+E(1)=YI - Q*D(1).
23 G r — '-'
24 C(1)=Q*D(1)
25 C ( 2)=1.0
26 W(2) =YI-.C(.l)
27 GO TO 200
28 C
2'J C - IF THE SECOND DERIVATIVE AT THE END PpI.NTS IS GIVEN
30 C B(l) IS KNOWN, THE SECOND EQUATION BECOMES
31 G A(1)+E(1)=YI-0.5*Q*Q*D(1). DURING THE SOLUTION OF
32 C . THE '3II-4 EQUATIONS,A 1 \I1LL_BE KEPT. IN CELL G.(2)
33 G INSTEAD OF C(l) TO RETAIN THE TRIDIAGONAL FORM OF THE
34 c 'COEFFICIENT MATRIX.
35 C . .
36 100 C(2)= 0.0 '
37 W(2)=0.5*Q*Q*D(1),
3U 200 M=N-2
3 CJ I F ( M . L E . 0) G 0 T 0 3 5 0
40 G .
41 C UPPER TRIANGULARIX/ATION OF T.HE TRIDIAGONAL SYSTEM OF
42 C EQUATIONS FOR THE COEFFICIENT MATRIX FOLLOWS—
43 G •
44 DO 300 1=1,M
45 AI=Q
46 Q=X(I+2)- X(I+1)
47 H=A1/Q
4» C(3*I)=-H/(2.0-G(3*I-1))
4y W(3*I)=(-YI-W(3*I-1))/(2.0 - C(3*I-1))
50 G(3*1+1)=-H*U/(H-C(3*I))
51 U(3*1+1)=(YI-W(3*1))/(H-C(3*1))
52 YI=Y(I+2)- Y(I+1)
53 C(3*I + 2) = 1.0/(1.0-C(3*I + D)
54 30U W(3*I+2)=(YI-U(3*1+1))/(1.0-C(3*I+D)
55 C
-------
56 C E(N-l) IS DETERMINED DIRECTLY FROM THE LAST EQUATION
57 C OBTAINED ABOVE, AND THE FIRST OR SECOND DERIVATIVE
58 C VALUE GIVEN AT THE END POINT.
59 C
60 350 IF(J.EQ.l) GO TO 400
61 C(3*N-3)=(Q*Q*D(2)/2.0-W(3*N-4))/(3.0- C(3*N-4))
62 GO TO 500
63 400 C(3*N-3)=(Q*D(2)-YI-U(3*N-4))/(2.0-C(3*N-4))
64 500 M = 3 * N - 6
65 IF(M.LE.O) GO TO 700
{,(, C
67 C BACK SOLUTION FOR ALL COEFFICIENTS EXCEPT
68 G A(l) AND B(l) FOLLOWS—
6y c '
70 DO 600 11=1,M
tn 71 I=U-Il+3
O 72 600 C(I)=W(I)-C(1)*C(I+1)
73 700 IF(J.Kg.l) CO TO 800
74 C
75 G IF THE SECOND DERIVATIVE IS GIVEN AT THE END POINTS,
76 C A(l) CAN NOW BE COMPUTED FROM THE KNOWN VALUES OF
77 C B(l) AND E(l). THEN A(l) AMD B(l) ARE PUT INTO THEIR
78 G PROPER PLACES IN THE C ARRAY.
79 C '
80 C(1)=Y(2) - Y(1)-U(2)-CO)
81 G(2)=U(2)
82 RETURN
83 800 C(2)=W(2)-C(3)
84 KETURN
85 END
-------
* It AT EGO MS T ANT . S1' 1MB
1 SUBROUTINE Sl'LNU (N.X.Y.C.V)
2 DIMENSION X(10),Y(10),C(3U),V(5)
3 V(5)=2.0
3 G .
(> G DKTKRMINE IN WHICH INTERVAL T Hi; I NUT. 1'r.NIM'.NT
7 G VAKIABLK, V( I ) ,,LIi:S.
a c
'} DO 10 1 = 2,L1M
10 10 IF(V( 1) .LT.X(I)) GO TO 20
11 I =!!
12 IF ( V ( 1) . G T . X (!!) ) V ( 5 ) = 3 . 0
13 GO TO 30
14 20 IF(V(1).LT.X(l)) V(5) =1.0
13 c .
16 G g is Tin; si/i; or Tin; INTI:IIVM, GO.NTMMJU; v(i).
17 c , _
id G z is A LIHI:AU TRANSFORMATION or THK INTT.KVAL
iy G ONTO (o,i) A;:D is Tin; VARIAISLI: I-OK uincii
20 G Tin; cuiiF i" IG II;NTS WKRK COMJ'UTHI) HY SPLNA.
21 G
22 30 IJ=X( I)-X( I-l)
24 V(2) = ( U*C(3*I-3)+C( 3*1 -4) )*X+C( 3*1-5) ) */.+Y( I-l )
25 V ( 3) = ( ( 3 . * •/.* G ( 3 * 1 - 3 ) +2 . 0 * G ( 3 * I - 4 ) ) * ;:+G ( 3 * I - 5) ) / Q
2f> V(4) = (fi.*X*C(3*I-3)+2.0*C(3*I-4))/(H*Q)
27 IU-;TUH;J
2H I:N!)
-------
*RATi;CO:iSTANT. CLOCK
1 REAL FUNCTION C 1,OC K ( T 1 , I I iJC)
2 C
3 C **** ADD A Tlili: IN MINUTCS TO A 2400 HOUR TIMi; AND KKTURN A 2400
4 C ***ft HOUR TIM i;
5 C
6 T 2 = I I S C
cn 1 I100=Tl/100
I"0 H T 3 = T 1 - 1 0 0 . 0 * I 1 0 0 + T 2
y 1100 = 1100 + i;;i(T3/6o)
10 CLOCK=l100*100.0 + T3 -60.0 * INT(T3/60)
11 RI;TUR;<'
i 2 t: N D
-------
APPENDIX B
LISTING OF SAMPLE DATA SET
An example of a data set for the photolytic rate constant program is
listed below. Information is contained therein for the computation of photo-
lytic rate constants for eleven species at Los Angeles, California, on June
21, 1975, from 0400 to 2100 hours. Each line of the following data set repre-
sents a single data card. The exact format for all input data to the program
is specified in Appendix C, the User's Guide. However, a brief explanation of
the sample data set is included here.
Line No. Comments
1 Location for which photolytic rate constants are to be
computed: name of location, latitude, and longitude.
2 Time zone and date (year, month, day).
3 Time range and increment for which rate constants are
to be computed.
4 No. of species, no. of zenith angles, no. of wavelength
intervals, center point of initial wavelength interval,
and wavelength increment.
5 Zenith angles used in initial calculation of rate con-
stants (Subroutine: RATE).
6-109 Values of actinic irradiance, J(x,e), for all wave-
length intervals A, and zenith angles e.
110-154 Species information including wavelength band of ab-
sorption, absorption cross sections (x) for each photolytic species.
53
-------
1
3
4
5
6
7
8
9
10
1 1
1 2
1 3
14
15
16
17
18
19
20
2 1
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
LOS A;;GI:I.I:S, CAI.IF.
8.0 1975 6
0400 2100 15
11 10 522900 100
0
.
t
.
.
,
.
.
t
1 .
.
1 .
m
1.
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3.
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3.
1.
4.
1.
4.
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4.
1.
5 .
1.
5 .
1.
5 .
1.
5 .
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5.
1 .
5 .
1 .
5.
I.
5 .
2.
5.
2.
. 10. 20. 30. 40.
0001 500
0000000
0398350
0000000
4394000
0092690
9551000
0637200
6132000
2029100
7134000
2689000
8924000
3276000
9508000
3626000
3974000
4767000
3177000
4913000
3415000
5291000
1737000
7580000
9935000
0035000
1 188000
0973000
2224500
1513500
61 72000
3207000
2089000
5589500
6146000
7205500
7505000
8205500
7988000
8874500
7835500
9265000
8866000
9704500
9349500
9941500
9323000
0198000
9797000
0455000
. 0001500
.0000000
.0380150
. 0000000
. 4U13000
.0009416
.9438000
.0088930
1 . 5944000
.03K9400
1.6964000
.0614900
1 . 8748000
.0765300
1.9335000
. 0834100
2. 3782000
. 1065300
2 . 3008000
. 1065000
2.3254000
. 1 1 13600
3. 1530000
. 1555700
3. 9685000
. 2017300
'4.0949000
. 21 53800
4. 1 180000
. 2226250
4. 5 120000
. 2506650
5. 1817000
.2921350
5. 5851500
.3188350
5.721 1000
. 3330000
5. 7708000
. 3398000
5. 7564500
. 3416000
5.8571500
. 3420500
5.9050500
. 3394000
5.9032000
. 3376000
5.9503500
.3312500
50
.
.
.
.
1 .
1 .
1 .
1 .
2 B
2.
2.
3.
3.
4.
4.
4.
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•5 .
5.
5.
5.
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5.
5.
21
34.058
118. 250
. 60. 70. 78. 86.
0000000
0325460
4012000
9006000
5384000
6450000
8237000
8849000
3233000
2508000
2789000
0929000
8957000
0250000
0509500
4421000
1007500
4983500
6363000
6876500
6759000
7735000
8182500
8178500
8656000
.0000000
.0246470
. 3505500
.8261000
1 . 4402000
1.5547000
1 . 7327000
1. 7982000
2. 2238000
2. 1609000
2. 1947000
2. 9841000
3. 7652000
3.8985000
3.9301500
4. 3168499
4.9576500
5. 3444500
5.4851000
5. 5407500
5. 5333000
5. 6254000
5. 6660000
5. 6686000
5.7171000
.
.
.
.
1.
1 .
1 .
1 .
2.
2
2.
2 .
3.
3.
3.
4.
4.
5 .
5.
5.
5.
5.
5.
5.
5.
0000000
0155188
2 H 1 4 0 0 0
7174000
2922000
4 160000
5915000
6621000
0668000
0189000
0594000
8100000
5559000
6956000
7348000
1135000
7279500
0991000
2420000
3036000
3046500
3897000
4247000
4327000
4816500
. 0000000
.0074586
.1978000
. 5706000
1 .0832000
I . 2153000
1 . 3834000
1.4590000
1 . 8310000
1.8026000
1 . 8520000
2. 5412000
3. 2319000
3. 3780000
3.4279500
3. 7932000
4. 3661000
4. 7 150000
4.8484500
4.9180000
4.9435500
5.0215500
5.0527000
5.0667000
5. 1156000
.
.
.
.
.
.
1 .
I .
1.
1 .
1 .
2.
2
2
2.
3.
3.
4.
4.
4.
4.
4.
4.
4.
4.
0000000
0022850
1 104300
3890000
8031000
9357000
2429000
1638000
4799000
4751000
5336000
1246000
7246000
8754000
9379000
2742000
7832500
0991000
2483000
3271000
3521500
4222500
4501500
4724000
5209500
. 0000000
. 0003046
.0392490
.1937200
.4628000
. 5726000
. 684 1000
. 7493000
. 9722000
.9879000
1 . 0468000
1 . 4744000
1 .9188000
2. 0589000
2. 1285500
2.4022500
2.7996500
3.0552500
3. 1934500
3.2775000
3. 3168000
3. 3773000
3.4050000
3.4337500
3.4756000
54
-------
56 5.9271500 5.8988000 5.8161500 5.6701500 5.4392500 5.0801500 4.4947500 3.4615500
57 2.0399500 .3217000
58 5.9095>00 5.8814500 5.7972500 5.6504500 5.4197000 5.0612000 4.4787000 3.4521000
59 2.0371500 .3147000
60 5.9687500 5.9396500 5.8528500 5.7025500 5.4671000 5.1035000 4.5142000 3.4785500
61 2,0515500 .3088500
62 6.0576000 6.0280000 5.9412000 5.7889500 5.5507000 5.1827500 4.5850500 3.5335500
63 2.0813000 .3034500
64 6.1739000 6.1445000 6.0576000 5.9047000 5.6665000 5.2964000 4.7142000 3.6287000
65 2.1482000 .3108000
66 6.2265000 6.1975000 6.1110000 5.9585000 5.7225000 5.3540000 4.7538500 3.6857000
67 2.1941000 .3201000
68 6.2692500 '6.2397500 6.1517500 5.9972500 5.7577500 5.3875000 4.7846750 3.7140000
69- 2.2183000 .3236750
70 '- 6.3120000 6.2820000 6.1925000 6.0360000 5.7930000 5.4210000 4.8155000 3.7423000
71 2.2425000 .3272500
72 6.3210000 6.2917500 6.2047500 5.9370000 5.6377500 5.4517500 4.B578000 3.7983500
73 2.3026500 .3494500
74 6.3300000 6.3015000 6.2170000 5.8380000 5.4825000 5.4825000 4.90010003.8544000
75 2.3628000.3716500
76 6.4215000 6.3922500 6.3060000 6.0392500 5.7432500 5.5620000 4.97905>00 3.9345500
•77 2.4376250 .4003750
7b 6.5130000 6.4830000 6.3950000 6.2405000 6.0040000 5.6415000 5.0580000 4.0147000
79 2.5124500 .4291000
HO 6.5937500 6.5630000 6.4720000 6.3142500 6.0740000 5.7082500 5.1225000 4.0785750
81 2.57370.00 .4548250
82 6.6745000 6.6430000 6.5490000 6.3880000 6.1440000 5.7750000 5.1870000 4.1424500
83 2.6349500 .4805500
84 6.6590000 6.6265000 6.5367500 6.3787500 6.1392500 5.7772500 5.1992500 4.1676250
85 2.6706250 .4994500
86 6.6435000 6.6100000 6.5245000 6.3695000 6.1345000 5.7795000 5.2115000 4.1*128000
87 2.7063000 .5184000
88 6.46 6/45 6.35 6.20 5.98 5.71 5.15 4.09
89 2.74 0.53
90 6.40 6.38 6.29 6.14 5.91 5.65 5.11 4.07
91 2.75 0.54
92 6.34 6.32 6.22 6.08 5.87 5.60 5.05 4.05
93 2.76 0.56
94 6.27 6.25 6.16 6.02 5.80 5.55 5.02 4.04
95 2.77 0.56
96 6.21 6.19 6.10 5.96 5*75 5.49 4.97 4.02
97 2.78 0.58
98 6.14 6.12 6.03 5.90 5.68 5.43 4.92 4.00
99 2.79 0.59
100 6.08 6.06 5.97 5.84 5.64 5.40 4.90 3.99
101 2.79 0.59
102 6.02 6.00 5.91 5.78 5.58 5.34 4.86 3.97
103 2.79 0.59
104 5.95 5.94 5.85 5.72 5.53 5,31 4.8,4 3.96
105 2.79 0.60
106 5.89 5.88 5.79 5.66 5.47 5.25 4.80 3.94
107 2.78 0.60
108 5.82 5.81 5.73 5.59 5.42 5.22 4.78 3.93
109 2.78 0.60
110 1 N02 2900 4500
HI 0.99E-191.41E-192.18E-192.98E-193.74E-194.54E-195.2.0E-195.69E-196.04E-196.23E-19
112 6.38E-196.53E-196.38E-196.23E-195T88E-195.54E-195.20E-19
55
-------
1.0
0. 0
1.0
1 .0
1.0
1. 0
0. 0
1.0
1. 0
1. 0
1. 0
0. 0
1.0
1. 0
1 . 0
1. 0
1. 0
1.0
1. 0
1. 0
0. 0
1 . 0
1.0
1.0
0. 0
1.0
1.0
1. 0
0. 0
1.0
1.0
1 . 0
113 0.988 0.980 0.972 0.964 0.956 0.948 0.940 0.932 0.924 0.916
114 0.908 0.699 0.175 0.025 0.006 0.001 0.000
115 2 HOtJO 3000 3900
116 0.79E-201.14E-201.75E-202.86E-204.23E-205.29E-203.98E-206.08E-203.33E~201,78E-20
117 00000000
118 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.00
119 00000000
120 3 UN03 2900 3200
121 6.34E-212.76E-219.50E-221.80E-22
122 1.00 1.00 1.00 0.00
123 4 0331' 2900 7500
124 1.62i;-184.44E-191.19i:-193.36E-208.79E-211.94E-213.86E-22
125 1.99E-223.60E-225.38E-227.48E-22
•126 9.58E-221.31E-211.74E-212.20E-212.76E-213.3lE-213.78ii-214.54E-215,09E-214.93E-21
127 5.15E-215.52E-214.98E-214.17E-213.61E-213.18E-212.69E-212.17E-211.79E-211.52E-21
128 1.26E-219.77E-228.06E-226.76E-225.56E-224.84E-224.07E-22
129 0.0 0.0 I . 0
130 0.0 0.0 0.0
131 1.0 1.0 1.0
132 1.0 1.0 1.0
133 1.0 1.0 1.0
134 5 0311) 2900 3100
135 1.62E-184.44E-191.19E-193.36E-208.791-;-211.94r.-213.86E-22
.136 1.0 1.0 1.0
137 6 03SU 2900 3500
138 1. 62E-184.44E-191. 19E-193.36E-208.79E-211.94E-213.86E-22
139 1.0 1.0 1.0 1.0 1.0 1.0 1.0
140 7 FOkl 2900 3600
141 3.18E-203.25E-203.15i:-202.34E-202.37E-201.98i:-208.37E-211.76E-21
142 U.31 0.66 0.52 0.40 0.29 0.18 0.09 0.01
143 8 FOH2 2900 3600
144 3. 18E-203.25E-203. 15K-202.34E-202.37E-201.98E-208.37E-211.76E-21
145 0.19 0.34 0.48 0.60 0.71 0.82 0.91 0.99
146 9 11202 2900 3700
147 1.49E-209.94E-216.88E-214.97E-213.82E-213.01K-211.91E-211.15E-210.76E-21
148 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
149 10 ACM 2900 3400
150 4.66E-204.09E-202.96E-20L.69E-206.92E-211.34E-21
151 0.329 0.274 0.221 0.158 0.100 0.041
152 11 ACA2 2900 3100
153 4.66E-204.09E-202.96i;-201.69E-206.92l-:-2H.34E-21
154 0.087 0.036 0.007
56
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APPENDIX C
USER'S GUIDE
The photolytic rate constant program may easily be run with the sample
data set provided. Should the user wish to change the location, date or time
for which the program is run, these inputs are contained on the first three
data cards and may easily be amended to fit the needs of the user. The follow-
ing User's Guide describes the format of these first three data cards, as well
as the rest of the cards should more extensive changes be desired.
Further, a listing of all photolytic reactions currently handled by the
rate constant program is provided. The alphameric representation of each
species as used in the program is listed.
57
-------
SPECIES INFORMATION INCLUDED ON CARDS PROVIDED FOR USER
o o
A A
SPECIES NO. ALPHAMERIC MINLAM _< X _< MAXLAM
ortUlLo INHrlt KtrKLoLIN 1 M 1 lulx KLMb I J.UIN ^H T nv - • • u
1
NITROGEN DIOXIDE
2
NITROUS ACID
3
NITRIC ACID
4
OZONE
5
OZONE
6
OZONE
7
FORMALDEHYDE
8
FORMALDEHYDE
9
HYDROGEN PEROXIDE
10
ACETALDEHYDE
11
ACETALDEHYDE
2900 < X < 4500 ~
Mfio MA | UM • "> NO + D( P)
INU£ INU^J i nv x iiu ^ u v ' /
3000 <_ X _< 3900
i inMn iinwn i h-n > HD + ND
MUINU IIUINU i nv f nu ~ i\iu
2900 _< A £ 3200
nNm i-inwn 4- hn . . ^ HO + MO
I iiiU j iiuinUo nv / nu T ixup
2900 < X < 7500 .
m?p n + h^.1 . . . . *> o^ P^ + n
UNJJI L/O ~ nv x u i i / ~ uo
o ^
2900 < A < 3100 ,
n°i n n + h-i > n^ n^ + n
2900 ^X ^ 3500 ,
m^n n+h^i ., \r\fh\4-c\
2900 < X < 3600
rnrn H rn + h\) ^ H + urn
2900 _< X < 3600
FDR? H ffl + h\i ...... \ u \ cc\
2900 < X < 3700
H°0? H n + h-o .' ^ °nn
C. L>
2900 < x < 3400
ACA1 TH CHO + h-o ~~ \ ni i urn
/\wvi unoL-nu T nv • •• -^ ^||_ l IIL.U
O O
2900 < x < 3100
ACA? TH THO + h-o • ~~ -^ m i m
58
-------
DATA INPUT TO RATE CONSTANT PROGRAM
Card No.
Column No.
Variable
Format
Units
Comments
1-24
PLACE
6A4
This is the alphameric name of the location
for which the rate constant computations are
to be made.
30-39
SLA
F10. 4
DEGREES
+=North Lat.
-=South Lat.
Latitude of PLACE
40-49
SLO
F10.4
DEGREES
+=West Long.
-=East Long.
Longitude of PLACE
1-5
TZ
F5.1
Number of time zones distant from Greenwich
Mean Time (G.H.T,), i.e.
L.A. DEN. CHI. N.Y. LONDON PARIS ATHENS
....(G.M.T.)
8. 7. 6. 5. 0. 1. 2. etc.
also includes fraction if local time is not
standard meridian time: eg. Poona, India = 5.5
2 10-13
2 18-19
2 24-25
IY
IM
ID
14
12
12
Year for which
Month
Day
computations are to be made
3 1-4
JSTRT
14 Time
(24-Hr Clock)
Time of dav to
rate constants
begin listing of photolytic
(Local Standard Time)
-------
Card No. Column No.
3 9-12
3 19-20
Variable Format
JSTOP
IINC
NOTE; The previous three cards must be
subsequent data input cards have
the user wish to make changes of
4 1-4
4 5-8
4 9-12
4 13-16
MAXL
MAXZ
MAXJ
LAM1
14
12
supplied by the user
been supplied for the
his own, these cards
14
14
14
14
Units Comments
Time (24-Hr Time of day to end listing of photolvtic rate
Clock) constants (Local Standard Time)
Minutes Time increment to use in listing of rate con-
stants (IINC >_ 1 minute).
for proper execution of the program. All
user, along with the nrogram deck. Should
are described below.
Number of soecies for which rate constants are to
be comouted.
Number of zenith angles used for base values
with inputs of J, the actinic irradiance.
The number of wavelength values for which cor-
responding values of J are input.
A Initial wavelength value for which values of
J are incut.
17-20
INC
14
Constant increment value for updating wavelength.
(This is also the size of the wavelength interval
over which the values of J have been averaged.)
-------
Card No.
Column No.
Variable
Format
Units
Comments
1-80
20F4.0
Degrees
Values of zenith angles used with inputs of J.
The number of angles must equal MAXZ.
6-109 1-80 J 8F10.7,/, Photons x 1015
2F10'7 cm2-sec-A
interval
Each card lists MAXZ values of J, the actinic
irradiance, corresponding to the values of Z
inout on card no. 5. There are MAXZ cards of
this form; the first of which corresponds to
the J values at LAM1 , next at LAM1 + INC,
LAM1 + 2 -INC, etc.
NOTE: A complete set of the following three types of cards is needed for each species included in the rate constant computations.
110 1-2 L 12
Species number (1 < L < MAXL)
110 5-8 SPECIE A4
Alphameric
designation of species
L.
no
11-14
MINLAM
14
Starting wavelength in rate constant computations
for species L.
no
17-20
MAXLAM
14
Ending wavelength in rate constant computations for
species L.
-------
Card No.
Column No.
Variable
Format
Units
Comments
111-112
1-80
SIGMA
(10E8.2,/)
err
Values of absorption cross-sections for species
L, at wavelengths from MINLAM to MAXLAM in incre-
ments of INC.
113-114
1-80
PHI
(10F8.4,/)
Values of primary quantum yields for species L,
at wavelengths from MINLAM to MAXLAM in incre-
ments of INC.
01
ro
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/4-77-015
3. RECIPIENT'S ACCESSIOf+NO.
4 TITLE AND SUBTITLE
CALCULATION OF SELECTED PHOTOLYTIC RATE CONSTANTS
OVER A DIURNAL RANGE
A Computer Algorithm
5. REPORT DATE
March 1977
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
8. PERFORMING ORGANIZATION REPORT NO.
Kenneth L. Schere and Kenneth L. Demerjian
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, N.C. 27711
10. PROGRAM ELEMENT NO.
1AA603
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory - RTP, NC
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, N.C. 27711
13. TYPE OF REPORT AND PERIOD COVERED
Tn-Hnnsp
14. SPONSORING AGENCY CODE
EPA 7600/09
15. SUPPLEMENTARY NOTES
^.ABSTRACT /\ computer program has been created and is described herein which employs
the theoretical formulation of the photolytic rate constant to calculate these rate
constants for specific chemical species over a diurnal time period in clear-sky con-
ditions. A user of the program must specify the date, time and location for which
the rate constants are desired. With this information and specific data on zenith
angles, solar irradiance, and species characteristics of absorption cross-sections
and primary quantum yields, which are provided in the program package, the computer
program generates a diurnal range of photolytic rate constants for each species. The
species included are NOp, 03, MONO, HON02, H2CO, CH3CHO, and H?0?. The aopendices to
this report contain program and data listings as well as a User's Guide to program
operation.
The program-generated photolytic rate constants for N0? are compared to direct
measurements of this quantity as taken at Research Triangle'Park, N.C. during April
1975. The two methods are generally in close agreement after the theoretically com-
puted rate constants are scaled by a simplistic method for the compensation of solar
radiation attention by clouds.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
*Air Pollution
*Photochemical Reactions
*Reaction Kinetics
*Atmospheric Modeling
Computerized Simulation
*Computer Programs
*Algorithms
13B
07E
07D
14A
14B
09B
12A
8. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (ThisReport)
UNCLASSIFIED
21. NO. OF PAGES
71
20. SECURITY CLASS (This page)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
63
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