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

-------
                 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  animalsbut 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.

-------
                                            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

-------
                                 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.

-------
                                 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

-------
                               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

-------
                                 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  (34.1N, 118.3W) 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  (34.1N, 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  (34.1N, 118.3W) 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. (35.8N, 78.6W) 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. (35.8N, 78.6W) 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. (35.8N, 78.6W) on April  25, 1975,	  34
                                    vi

-------
 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. (35.8N,  78.6W)  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

-------
                               ACKNOWLEDGMENT

    The assistance of Betty M. Ortman and Patricia Smith who typed the drafts
and final version of the manuscript is greatfully appreciated.
                                    vm

-------
                                   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.

-------
     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.

-------
                                 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

-------
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.

-------
              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)

 H22 + 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.

-------
                                 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.

-------
                                 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
                   145
                   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
                                               1o3 > 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                              ,757804
                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, 118.3W) 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, 118,3W) 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 (34.1N, 118.3W) 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. (35.8N, 78.6W) 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. (35.8N,  78.6W) 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.  (35.8N, 78.6W) 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. (35.8N, 78.6W) 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.
t
1.
.
2.
.
2.
.
2.
.
3.
f
3.
1.
4.
1.
4.
1.
4.
1.
5 .
1.
5 .
1.
5 .
1.
5 .
1.
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.

5 .

5 .

5.

5.

5.

5.

5 .

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

-------
                                 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 ,
ni 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
H0? 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

-------