EPA-600/4-76-025
June 1976
Environmental Monitoring Series
CALCULATED ACTINIC FLUXES (290 • 700 nm)
FOR AIR POLLUTION
PHOTOCHEMISTRY APPLICATIONS
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into five series. These five broad
categories were established to facilitate further development and application of
environmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the ENVIRONMENTAL MONITORING series.
This series describes research conducted to develop new or improved methods
and instrumentation for the identification and quantification of environmental
pollutants at the lowest conceivably significant concentrations. It also includes
studies to determine the ambient concentrations of pollutants in the environment
and/or the variance of pollutants as a function of time or meteorological factors.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/4-76-025
June 1976
CALCULATED ACTINIC FLUXES (290-700 nm) FOR
AIR POLLUTION PHOTOCHEMISTRY APPLICATIONS
by
James T. Peterson
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
Research Triangle Park, NC 27711
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF RESEARCH AND DEVELOPMENT
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
RESEARCH TRIANGLE PARK, NC 27711
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DISCLAIMER
This report has been reviewed by the Environmental Sciences
Research Laboratory, U.S. Environmental Protection Agency, and approved
for publication. Mention of trade names or commercial products does
not constitute endorsement or recommendation for use.
AUTHOR'S AFFILIATION
The author is on assignment with the U.S. Environmental Protection
Agency from the National Oceanic and Atmospheric Administration,
U.S. Department of Commerce.
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ABSTRACT
Calculations are presented of the actinic (spherically integrated)
solar flux from 290 to 700 nm at solar zenith angles between 0 and
86°. The calculated values are obtained by using a radiative transfer
program developed by Dave that accounts for molecular scattering,
ozone absorption, and aerosol scattering and absorption. Input data
consists of aerosol size distribution, aerosol number and ozone concen-
trations as a function of height, aerosol index of refraction, and
the following as a function of wavelength: ozone absorption coefficient,
molecular scattering coefficient, solar constant, and surface reflectivity.
The calculated actinic flux values are evaluated for their dependence
on variations of surface reflectivity, aerosol amount, ozone amount
and station elevation. The variation of the actinic flux with altitude
above the surface is discussed with emphasis on the change through
the lowest kilometer of the atmosphere. Finally, the flux values
presented here are compared to those of Leighton (1961); the differences
in the methodology and input data between the two studies are illustrated.
These calculated actinic flux data are useful for estimating photo-
dissociation rate constants for application to photochemical air
pollution problems.
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CONTENTS
Abstract iii
List of Figures vi
List of Tables vii
Acknowledgements viii
I. Introduction 1
II. Description of Radiative Transfer Model 3
Actinic flux modifications 6
III. Input Data 9
Division of solar spectrum 9
Ozone 10
Aerosols 13
Rayleigh scattering 15
Surface albedo 15
Solar constant 16
Solar zenith angles 19
IV. Results 20
Sensitivity tests 26
Variation of actinic flux with altitude 30
Comparison to Leighton 38
Clouds 40
V. Discussion 45
References 47
Appendices
A. Listing of vertically dependent input data 50
B. Listing of wavelength dependent input data 51
C. Listing of solar zenith angles by time and month 53
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LIST OF FIGURES
Number Page
1 Variation with height (km) of aerosol number concentration
(cm~3) and ozone concentration (g m~3) used as input for the
actinic flux concentrations . . 11
2 Normal optical thickness as a function of wavelength (nm)
for aerosol scattering and extinction, Rayleigh scattering,
and ozone absorption used as input for the actinic flux
calculations 12
3 Calculated actinic flux (10 photons cm sec~ ) within five
nm wavelength intervals, centered on the indicated wave-
lengths, at the earth's surface using best estimate
albedos as a function of solar zenith angle (°) . 25
4 Calculated actinic flux (units relative to solar constant
of pi) at the earth's surface using best estimate albedos
for the upward-directed component (F+), downward-directed
component (F~), and their sum (F') as a function of height
at 332.5 nm wavelength for (a) solar zenith angle e0 of
20°, (b) 50°, and (c) 78° 32
5 Calculated actinic flux (units relative to solar constant
of pi) at the earth's surface using best estimate albedos
for the upward-directed component (F+), downward-directed
component (F~), and their sum (F^) as a function of height
at 412.5 nm wavelength for (a) solar zenith angle 60 of
20°, (b) 50°, and (c) 78° 33
6 Calculated actinic flux (units relative to solar constant
of pi) at the earth's surface using best estimate albedos
for the upward-directed component (F+), downward-directed
component (F~), and their sum (FT) as a function of height
at 575 nm wavelength for (a) solar zenith angle e0 of
20°, (b) 50°, and (c) 78° 34
7 Calculated actinic flux (10 photons cm" sec~ nm )
averaged over indicated wavelength intervals (nm) at
the earth's surface for solar zenith angle of 20° from this
study (using best estimate albedos) and from Leighton ... 41
8 Calculated actinic flux (10 photons cm sec" nm"1)
averaged over indicated wavelength intervals (nm) at
the earth's surface for solar zenith angle of 60° from this
study (using best estimate albedos) and from Leighton ... 42
VI
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LIST OF TABLES
Number Page
1 Extraterrestrial Solar Flux from Various Sources 17
2 Correction Factors fro Extraterrestrial Solar Flux .... 18
3 Optical Air Mass at Sea Level 19
4 Calculated Actinic Flux for Best Estimate Albedos .... 21
5 Calculated Actinic Flux for Zero Albedo 23
6 Actinic Flux Increase for Albedo Increase 27
7 Actinic Flux Change for Aerosol Change 28
8 Actinic Flux Decrease for Ozone Increase 29
9 Actinic Flux Increase for Surface Elevation Increase . . 30
10 Actinic Flux Increase for Altitude Increase 36
11 Comparison of Actinic Fluxes from this Study and Leighton . 39
12 Solar Radiation Transmission Through Clouds 43
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ACKNOWLEDGEMENTS
Dale Coventry adapted the Dave radiative routines to the EPA computer.
Craig Meisner was responsible for much of the execution of the many computer
runs and tabulations of the actinic flux data. Margaret Wilder typed the
drafts and final version of the manuscript. Their assistance is very
gratefully acknowledged.
vm
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SECTION I
INTRODUCTION
The sun is the driving force for atmospheric photochemical reactions.
In a polluted urban atmosphere constituents are produced and destroyed
by a complex process that involves tens of specific kinetic reactions.
The chemical products of this process strongly depend on the reactions
between incident solar radiation and N0? and the aldehyde group (Dodge
and Hecht, 1975).
This report is intended to update and amplify the pioneering work
of Leighton (1961) on the application of solar radiation to air pollution
photochemistry. In his book he used a simple, yet effective, radiative
transfer model to calculate the actinic flux at the earth's surface at
various zenith angles over the ultraviolet and visible solar spectrum.
Many of Leighton's computational results were first reported by Leighton
and Perkins (1956). Thus, most of the methodologies and input data that
were available to him are now 20 years old. In addition, his tabulations
apply only to the atmospheric level at the earth's surface. He also did
not attempt to describe the sensitivity of his calculated fluxes to input
data variability. Today, the radiative fluxes can be calculated in more
detail on high speed computers, and more accurate data are available for
the solar constant, surface reflectivity, total ozone amount, and atmospheric
aerosol optical properties.
Leighton's actinic flux values have previously been used to determine
photodissociation rate constants of several species, especially N0?, as
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a function of time of day (zenith angle). Such rate constants have been
used in mathematical diffusion modeling of photochemical pollution (Reynolds
et al., 1973) and in computer simulations of mixtures of reactive chemical
species to evaluate various mechanisms for photochemical smog formation
(Demerjian et al., 1974). Since actinic flux refers to the radiative
energy incident on a molecule, it is difficult to measure or estimate
from customary radiometric measurements with a flat sensor that is horizontal
or normal to the sun. Thus, many users of actinic flux data have relied
on Leighton's tabulations.
A table of theoretical values of the solar energy available for
photochemical reactions, as a function of wavelength and solar zenith
angle, has been prepared for general application. Also included are
descriptions of the computational techniques and various aspects of the
input data. The vertical variation of the actinic flux is discussed along
with an analysis of the dependence of the actinic flux on typical variations
of surface reflectivity, station elevation, total ozone amount and aerosol
concentrations.
The body of this report is comprised of three main sections. The
first describes the radiative transfer model used to calculate the actinic
fluxes. The second focuses on input data necessary for the computations:
atmospheric constituents, solar constant, surface reflectivity, etc.
The last section discusses the results of the calculations and includes
descriptions of the actinic flux values.
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SECTION II
DESCRIPTION OF THE RADIATIVE TRANSFER MODEL
The basic radiative transfer model used for all calculations described
in this report was developed for NASA by Dave (1972). It includes molecular
scattering, ozone absorption and aerosol scattering and absorption. Subse-
quently, absorption by water vapor, oxygen and carbon dioxide were included.
Readers interested in the computational details are referred to a description
of the complete model by Braslau and Dave (1973a, b). The model atmosphere
is assumed to be cloudless, plane-parallel, and non-homogeneous. A monochromatic
unidirectional solar flux is incident at the top with the bottom bounded
by an idealized Lambert ground. The atmosphere contains arbitrary vertical
distributions of ozone and aerosol number density and is divided into
a finite number of layers. At each level the attenuated direct solar
flux and upward and downward diffuse components are calculated. The
program can be used to compute radiative intensities, including the degree,
direction and ellipticity of polarization, but only flux values are reported
here.
Much of the program computer time is used to calculate the optical
properties of the model aerosols. First, coefficients are computed for
the Legendre series representing the normalized scattering phase function
for a unit volume containing an aerosol with a known size distribution.
The FORTRAN computer code is available from NASA Goddard Space
Flight Center, Greenbelt, MD as program RADTMO, # S00080.
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Next, the Legendre coefficients are used to calculate the Fourier coefficients
of a series representing the normalized aerosol scattering phase function.
The argument of this series is the difference between the azimuth angles
of incident and scattered radiation. The basic equation of radiative
transfer for a given atmospheric model is then divided into a set of
mutually independent integro-differential equations that represent the
transfer of the n-th Fourier component of the scattered radiative intensity.
Finally, each of these equations is individually solved by using an iterative
procedure through a finite number of atmospheric layers. Use of the Fourier
series to represent the normalized scattering phase function permits inte-
gration over azimuth to be carried out analytically. Integration over
zenith angle (e) is done numerically with A9=2°. The result is the computation
of the intensity of the radiation scattered in all directions emerging
at selected levels of a model atmosphere.
Atmospheric aerosols are assumed to be spherical, be homogeneous,
have a known refractive index, and have a given size distribution. Their
size distribution and refractive index are assumed to be independent
of height. The total number of particles per unit volume, however, can
be varied for each atmospheric layer. The ozone content of each layer
can also be specified as well as the ozone absorption coefficient for
the wavelength in question. Additional input includes the Rayleigh scattering
normal optical thickness; its value above any level is a linear function
of pressure. The model atmosphere can be divided into 16, 20, 32, 40,
80, or 160 layers of varying pressure thicknesses. Forty layers were
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selected for these computations as a compromise between greater computational
accuracy from more layers and less computer time from fewer layers.
The thinnest pressure layer (0.58 mb) is at the top of the atmosphere.
Layer pressure thickness increases downward to 53.3 mb (675 m) at about
4 km height and then decreases to 17.4 mb (150 m) for the lowest layer.
The lowest level ("the earth's surface") is not at the earth-atmosphere
interface, but rather is considered to be within the atmosphere a few
meters above the surface.
One of the strengths of this radiative model is its accuracy. Braslau
and Dave (1973a) stated that their calculations of spectrally integrated
flux values were accurate within about *0.5%. In this study, the computational
scheme, itself, will have a slightly greater error because the atmosphere
was divided into 40 layers, whereas Braslau and Dave used 160. Thus,
the uncertainty in the computed actinic flux values should be governed
by the uncertainties in the model input data, such as the solar constant
and aerosol characteristics, which can exceed several percent. A large
error, however, can be expected for results for the largest zenith angle
(86°) reported here. In this instance, the sun is very near the horizon
with an optical air mass of 12.4. The direct solar beam is almost entirely
attenuated before reaching the earth's surface so that the small actinic
fluxes are largely composed of multiply scattered radiation. Thus, the
86° values should be used cautiously since small percentage errors in
the atmospheric constituents lead to larger percentage errors in the calcu-
lated fluxes.
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ACTINIC FLUX MODIFICATIONS
Most radiative flux calculations used in atmospheric science are
referenced to a flat, horizontal surface. The computer program used
by Dave was so designed. In photochemical applications, however, the
flux on a spherical surface, i.e., the flux "seen" by an ensemble of atmos-
pheric molecules without fixed orientations, is more appropriate. This
spherical flux was termed the actinic flux by Leighton (1961) after the
p
flux that would be measured by a chemical actinometer with radiation
incident from all directions. The term actinic formally refers to radiant
energy capable of initiating photochemical reactions (usually synonomous
with ultraviolet frequencies) (Huschke, 1959). In any event, actinic
flux as defined by Leighton is now in general use by the photochemical
community and will be followed here.
The difference between the actinic and horizontal fluxes is further
described in the following example. Consider only the radiation from
one hemisphere, e.g., the downward-directed stream. Given the monochromatic,
directional ly-dependent radiative intensity L(e,cf>) at wavelength X, where
A
c|> is the azimuth angle, the horizontal flux (F ) is defined by
A
O
Leighton (1961, p.30) states that the actinic flux J^ "is the irrad-
iance which would be measured by a weakly absorbing chemical actinometer
with a flat horizontal surface exposed to sun and sky." Since the actinic
flux is the flux on a spherical surface, J^ actually refers to the irradiance
which would be measured by a spherical chemical actinometer exposed to
incident radiation from all directions. Such devices have recently been
constructed for N09 photodissociation by Jackson et al. (1975) and Sickles
and Jeffries (1975).
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/2ir /-ir/2
I Lcosesinededcj). (1)
j Jo x
The actinic flux, J , for one hemisphere is defined by
A
. 2lT r TT/2
(2)
These definitions for F and J differ only by the cos 0 weighting factor.
A A
If the intensity is isotropic,
•TT/2
/i.
cosesinede = -uL , (3)
A
and J, equals ZirL . Applying these definitions the Dave program was modified
A A
to compute the upward-directed and downward-directed components of the
actinic flux at each level of the model atmosphere. Henceforth, unless
otherwise noted, actinic flux will refer to the sum of its upward and
downward components, i.e., the spherical flux obtained by integrating
a form of (2) over both hemispheres.
Within the model the ground is assumed to be an idealized Lambert
surface whereby the incident radiation is reflected with isotropic intensity.
The reflectivity of the ground is defined as the ratio of the upward hori-
zontal flux to the total (direct plus diffuse components) downward horizontal
flux incident at the ground. Thus, for a given reflectivity, near the
surface the upward actinic flux will be twice the upward horizontal flux
since the upward stream is isotropic. If the downward intensity is isotropic,
the reflectivities calculated from the actinic and horizontal fluxes will
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be identical. At the other extreme, if the downward radiative stream
consists only of the direct solar beam with the sun at the zenith, the
actinic reflectivity will be twice the horizontal reflectivity, since
the downward actinic and horizontal fluxes will be equal.
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SECTION III
INPUT DATA
Several internal and boundary parameters must be specified to calculate
the actinic flux. Properties of the atmospheric constituents—aerosols
and ozone—were selected to represent general conditions in the continental
U.S., but with some emphasis on typical urban concentrations. Emphasis
was also given to the particular characteristics of the Los Angeles atmosphere
since much practical and theoretical research has been done on its photochemical
pollution. The number of spectral intervals and solar zenith angles chosen
directly affected the amount of computer time. The solar constant and
surface albedo values determined the upper and lower model boundary conditions.
DIVISION OF SOLAR SPECTRUM
The solution to the radiative transfer equation is strictly applicable
only to monochromatic radiation. If the absorption or scattering coefficients
of the atmospheric constituents change only gradually with wavelength
and by a small amount, a single computation can be applied to a wavelength
interval. Thus, to achieve the greatest computational accuracy the solar
spectrum should be divided into many small intervals. This objective,
however, was tempered because computer time had to be minimized by performing
the computations over as few intervals as possible. The spectrum was divided
arbitrarily into 48 intervals from 290 to 700 nm. Practically no solar
energy at wavelengths less than 290 nm reaches the ground. Essentially
all photochemical reactions applicable to urban air pollution problems
occur at wavelengths less than 700 nm. Moreover, at longer wavelengths
absorption of radiation by water vapor, a highly variable atmospheric consti-
-------
tuent, becomes important. The spectral intervals are 5 nm wide between
290 and 420 nm, 10 nm wide between 420 and 580 nm, and 20 nm wide between
580 and 700 nm. The greatest resolution is at the shortest wavelengths
where the ozone absorption changes rapidly and most photochemical reactions
of interest occur.
OZONE
The general shape of the vertical ozone concentration profile used
was that of McClatchey et al. (1972) for mid-latitude, summer conditions.
All of their concentration values were multiplied by 0.893 to yield 0.285 cm-
atm of total ozone in a vertical atmospheric column. Based on total ozone
climatology (Craig, 1965; Komyhr et al., 1973), this is a representative,
average value for the latitude of Los Angeles during summer and autumn.
To account for an urban atmosphere, the ozone concentrations at the surface
and 1 km levels of the model atmosphere were increased by a factor of 3.3
to 2 X 10 g m (0.1 ppm). With this low-level increase, the total ozone
in a vertical column was 0.295 cm-atm. The final ozone concentrations
as a function of height are shown in Figure 1 and Appendix A. Data on
ozone absorption coefficients were taken from Howard et al. (1960). The
individual coefficients were plotted on semi-log paper versus wavelength
and subjectively averaged over each spectral interval of the model. The
values thus determined for the absorption coefficients for each interval
are given in Appendix B. The wavelength-dependent total ozone normal
optical thicknesses are also shown in Appendix B and Figure 2.
The ozone absorption coefficients used here are similar to those
used by Leighton. The total ozone (0.295 cm-atm) used here, however, is
significantly greater than the 0.22 cm-atm assumed by Leighton. The difference
10
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OZONE CONCENTRATION, g m'3
10-2
100 1Q1
AEROSOL CONCENTRATION, particles cm-3
102
103
Figure 1. Variation with height (km) of aerosol number concentration (cm-3) and ozone concentration (g nv3) used as input for the
actinic flux concentrations.
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10.0
oo
CO
O
X
O
t-
o.
O
AEROSOL EXTINCTION
AEROSOL SCATTERING
RAYLEIGH
SCATTERING
200
300
400 500
WAVELENGTH, nm
600
700
800
Figure 2. Normal optical thickness as a function of wavelength (nm) for aerosol
scattering and extinction, Rayleigh scattering, and ozone absorption used as in-
put for the actinic flux calculations.
12
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in total ozone between the two works mainly results from the 1957 change
in analysis procedure for ozone measurements by Dobson spectrophotometers.
Craig (1961) suggests that-all ozone concentrations reported before 1957
be increased by 35%. The larger ozone concentrations used here tend to
reduce the calculated actinic fluxes relative to those calculated by Leighton.
AEROSOLS
An average representation of atmospheric aerosols is difficult to
establish because of the day-to-day and place-to-place variation of many
characteristics of aerosols. Thus, whenever the actinic flux data generated
here are applied to a specific atmospheric situation the aerosol properties
projected for the model will likely differ from those of that situation.
Nonetheless, the characteristics of the aerosol model were defined so that
they reasonably agree with various ambient measurements.
The Dave radiative model uses a single aerosol size distribution
for all heights in the atmosphere. Following Braslau and Dave (1973a),
the modified gamma distribution of Diermendjian (1969) for haze L conditions
was selected to represent the aerosol distribution. The number of particles
-3 -1
n (cm ynf ), of size r (ym), is given by
n(r) = ar2exp(-br°'5), (4)
where b = 15.12 and a determines the absolute number concentration. This
distribution is a maximum for particles of 0.07 ym radius. For purposes
of calculating the radiative characteristics of the aerosols, (4) was
integrated between radii of 0.01 and 2.0 ym in increments of the size para-
meter (2TrrA) of 0.2.
The vertical distribution of particle number density applied here
was similar to the "average" height distribution model of Braslau and
13
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Dave (1973a), except that concentrations at the surface and 1 km were
increased by factors of 4 and 2, respectively (Figure 1 and Appendix A).
This distribution, therefore, is more representative of urban conditions
than that of Braslau and Dave. Combining these aerosol size and height
7 2
distributions results in 4.99 X 10 total particles in a cm atmospheric
column.
The aerosols were assumed to be partly absorbing with an index of
refraction (m), independent of height and wavelength, of m = 1.5 - O.Oli.
Although this value is somewhat uncertain, especially in the imaginary
part, it is in accord with recently measured values (Yamamoto and Tanaka,
1972).
Using these aerosol characteristics, the radiative properties of
the aerosol ensemble were calculated as a function of height for the midpoint
of each wavelength interval of the model. The aerosol normal optical thicknesses
for scattering and scattering plus absorption (extinction) as a function
of wavelength are presented in Appendix B and Ftgure 2. At 500 nm wavelength
the extinction normal optical thickness has a value of 0.254, of which
91% is due to scattering. Its variation over the spectral region of interest
is less than 7%. This can be compared to the value of 0.1 adopted by Rasool
and Schneider (1971) for average global atmospheric dust content and the
value of 0.23 measured by Herman et al. (1971) for typical haze conditions
at the UCLA campus of Los Angeles, which is considerably west of the haziest
sections of the Los Angeles area. The aerosol normal optical thickness
of 0.254 from this study corresponds to a decadic turbidity of 0.11, which
is similar to the annual average non-urban conditions over the eastern
U.S., but slightly less than average annual values at U.S. urban stations
14
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(Flowers et al., 1969).
Leighton used a much simpler approach to atmospheric aerosols. His
aerosol extinction was assumed to be totally due to scattering. The scattered
energy was assumed to be isotropic, with half the radiation propagating
forward and half backward. His aerosol normal optical thickness showed
more dependence on wavelength, varying between 0.390 and 0.140 at wavelengths
of 300 and 700 nm, respectively. At 500 nm his value was 0.204, slightly
less than that used here. Thus, his normal optical thickness for aerosols
was greater over the ultraviolet region and less at longer wavelengths.
RAYLEIGH SCATTERING
Values of the molecular (Rayleigh) scattering normal optical thickness
for standard sea level pressure were determined for the midpoint of each
model wavelength interval from the data of Penndorf (1957). These values
are presented in Figure 2 and Appendix B, where the -4 power wavelength
dependence is evident. Values of atmospheric pressure with height are
listed in Appendix A.
SURFACE ALBEDO
Since the actinic flux is sensitive to radiation propagating in all
directions, the surface albedo (reflectivity) is a critical input parameter
(Luther and Gelinas, 1976). Most natural and man-made materials have low
albedos in the ultraviolet region with progressively larger values at longer
wavelengths. The best estimate numbers used here, determined primarily
from the experimental data of Coulson and Reynolds (1971), are: 290 to
400 nm (5%), 400 to 450 nm (6%), 450 to 500 nm (8%), 500 to 550 nm (10%),
550 to 600 nm (11%), 600 to 640 nm (12%), 640 to 660 nm (13.5%), and
15
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660 to 700 nm (15%). As is customary, their data were derived from measurements
of incident and reflected horizontal fluxes. As pointed out above, however,
for a given albedo, the near-surface upward directed actinic flux is twice
the horizontal flux because the reflected radiation is assumed isotropic.
The treatment of surface albedo in this report is different from that
of Leighton. His calculations did not include the upward component of
the actinic flux and thus, in effect, he assumed an albedo of zero. In
a later section the sensitivity of these calculations will be discussed
to show that a change of albedo from 0 to 10% results in increased actinic
fluxes at the surface of about 10 to 20%, depending on wavelength and
solar zenith angle.
SOLAR CONSTANT
Unfortunately, the wavelength dependent values of the solar constant,
especially over the ultraviolet wavelengths, are still uncertain today.
Values of the intensity of the extraterrestrial solar beam at the mean
earth-sun distance reported by five sources as well as that used by Leighton
are shown in Table 1. The earliest data by Johnson (Howard et al., 1960)
are 1% to 11% higher in the ultraviolet region than the more recent measurements
of Thekaekara (1974), DeLuisi (1975), and Arvesen et al., (1969). In contrast,
Labs and Neckel (1968) list values in the ultraviolet significantly lower
than the other sources. Even though the three most recent sources are
in general agreement when summed over the ultraviolet, they disagree by
up to 10% at specific wavelengths. For this report, the data of DeLuisi
were used from 300 to 400 nm and those of Thekaekara elsewhere. DeLuisi's
published monochromatic data were integrated trapezoidally to yield the
values in Table 1 over 5 nm intervals. Any user of the actinic fluxes
16
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TABLE 1. EXTRATERRESTRIAL SOLAR FLUX (W nf2) WITHIN SPECIFIED WAVELENGTH
INTERVALS (nm) USED BY LEIGHTON AND REPORTED BY FIVE SOURCES
(SEE TEXT). VALUES FOR LEIGHTON AND LABS AND NECKEL FROM 290
THROUGH 420 nm ARE FOR 10 nm INTERVALS.
WAVELENGTH LEIGHTON JOHNSON THEKAEKARA DELUISI ARVENSEN LABS &
(nm) ET AL. NECKEL
290-295
295-300
300-305
305-310
310-315
315-320
320-325
325-330
330-335
335-340
340-345
345-350
350-355
355-360
360-365
365-370
370-375
375-380
380-385
385-390
390-395
395-400
400-405
405-410
410-415
415-420
420-430
430-440
440-450
450-460
460-470
470-480
480-490
490-500
500-510
510-520
520-530
530-540
540-550
550-560
560-570
570-580
580-600
600-620
620-640
640-660
660-680
680-700
300-400
290-700
TOTAL
3.08
6.3 3.02
3.00
6.7 3.50
3.90
8.2 4.05
4.65
10.2 5.50
5.60
11.1 5.60
5.80
11.7 5.82
5.90
11.6 5.85
6.15
12.9 6.35
6.62
13.2 6.18
6.00
11.5 5.63
5.73
12.0 7.00
8.71
9.48
9.60
9.67
18.27
18.10
21.10
21.78
21.64
21.50
20.47
20.50
19.60
19.25
19.40
19.75
19.65
19.32
19.02
19.14
37.87
35.66
34.22
32.99
32.06
30.34
109.1 108.83
674.0
1396
2.67
2.75
2.79
3.23
3.63
3.99
4.51
5.09
5.35
5.39
5.36
5.41
5.44
5.38
5.50
5.78
5.85
5.69
5.55
5.49
5.72
6.55
7.68
8.49
8.81
8.80
16.93
16.94
19.15
21.47
20.49
20.49
19.94
19.54
19.16
18.45
18.45
18.15
17.54
17.15
17.04
17.16
33.92
32.67
31.43
30.26
29.13
28.00
101.68
613.3
1353
2.70
3.17
3.90
3.92
4.09
5.28
5.19
4.89
5.09
4.94
5.47
4.92
5.34
6.43
5.70
6.24
5.07
5.48
5.55
6.62
99.98
2.64
2.78
2.78
3.06
3.61
3.75
3.75
5.14
5.28
4.87
5.14
4.87
5.42
4.87
5.00
6.39
5.14
6.12
5.00
5.56
5.42
6.67
8.76
8.90
9.45
9.45
17.60
17.50
20.10
21.00
20.80
21.10
19.80
20.00
19.74
18.63
19.04
19.18
18.90
18.49
18.35
18.77
36.70
35.31
34.06
31.97
31.83
30.30
97.86
651.8
1390
5.14
5.47
6.70
8.33
9.16
9.10
9.65
10.69
10.57
9.60
11.51
16.56
17.25
16.83
16.95
19.54
20.33
20.12
20.14
19.12
19.80
19.25
18.53
18.80
19.39
18.77
18.61
18.48
18.53
36.08
34.80
33.27
31.34
30.71
29.39
90.78
628.5
1365
17
-------
presented in this report who prefers other solar constant data may make
a linear adjustment to the actinic fluxes for any spectral interval.
_o
The preferred values used here are listed in Appendix B in W m (column 2)
and 10 photons cm sec" (column 3) summed over the given wavelength
interval.
The values used by Leighton (based on Johnson's data) for the extraterres
trial solar flux averaged 9% higher over the ultraviolet region than those
used herein. This difference contributed directly to the difference between
the two studies in the calculated actinic fluxes.
The solar constant data discussed above are representative for the
mean earth-sun distance, which occurs in early April and October. During
other times of the year the extraterrestrial solar flux changes by as
much as 13.4% due to changes in the earth-sun distance (Table 2). Although
this correction is small, all actinic flux data presented here should
be multiplied by the values of Table 2 when they are applied to a specific
situation at a given time of year.
TABLE 2. CORRECTION FACTORS FOR EXTRATERRESTRIAL SOLAR FLUX VALUES
DEPENDING ON EARTH-SUN DISTANCE AT VARIOUS TIMES OF YEAR.
CORRECTION CORRECTION
DATE FACTOR DATE FACTOR
Jan 1 1.033 July 1 0.966
Jan 15 1.032 July 15 0.967
Feb 1 1.029 Aug 1 0.970
Feb 15 1.024 Aug 15 0.974
Mar 1 1.018 Sept 1 0.982
Mar 15 1.011 Sept 15 0.989
Apr 1 1.001 Oct 1 0.998
Apr 15 0.993 Oct 15 1.006
May 1 0.984 Nov 1 1.015
May 15 0.978 Nov 15 1.022
June 1 0.971 Dec 1 1.027
June 15 0.968 Dec 15 1.031
18
-------
SOLAR ZENITH ANGLES
Actinic fluxes were calculated for solar zenith angles of 0, 10,
20, 30, 40, 50, 60, 70, 78, and 86°. The optical air mass, uncorrected
and corrected for atmospheric refraction, for each zenith angle is given
in Table 3. The normal optical thicknesses shown in Figure 2 and Appendix B
should be multiplied by the corresponding air mass value to determine
the optical thickness for any zenith angle. When the sun is near the
horizon (zenith angle of 86°), the long path length through the atmosphere
almost depletes the entire direct solar beam. When the sun is within
20° of the zenith the atmospheric path length changes relatively little.
At 35° N latitude, for example, zenith angles of 86, 78, and 70° occur
about 20 minutes, 1 hour, and 1 hour 40 minutes, respectively, after sunrise
and before sunset during late summer and early autumn. A listing of solar
zenith angles as a function of true solar time and month is presented
in Appendix C for latitudes of 20, 30, 40, and 50°N.
TABLE 3. OPTICAL AIR MASS AT SEA LEVEL, UNCORRECTED AND CORRECTED FOR
ATMOSPHERIC REFRACTION, FOR VARIOUS SOLAR ZENITH ANGLES.
Zenith Angle (°) 0 10 20 30 40 50 60 70 78 86
Optical Air Mass
Uncorrected 1.00 1.02 1.06 1.15 1.31 1.56 2.00 2.92 4.81 14.3
Corrected 1.00 1.02 1.06 1.15 1.31 1.56 2.00 2.90 4.72 12.4
19
-------
SECTION IV
RESULTS
Input to the radiative transfer equations consisted of distributions
of aerosols and ozone for a cloud-free atmosphere, the extraterrestrial
solar flux, and the pressure-height relation. With this input the equations
were solved for each of the ten solar zenith angles, each of the 48 spectral
intervals from 290 to 700 nm wavelength, and for surface albedos of 0.0,
0.1, and the best estimate values. The resulting actinic fluxes at the
surface are shown in Tables 4 and 5 for best estimate and zero albedos,
-2 -1
respectively, in units of photons cm sec within the specified wavelength
interval. The second column gives the power of ten by which each value
should be multip!ied.
The data in both tables show a general increase of actinic flux
with increasing wavelength and decreasing solar zenith angle. The marked
increase from 290 to about 340 nm results from the strong inverse dependence
of ozone absorption on wavelength over that interval. The gradual actinic
flux increase with wavelength beyond 340 nm results from decreasing Rayleigh
scattering, increasing surface albedo and increasing solar constant photon
flux. The actinic flux values at any given wavelength show a strong non-
linear decrease with increasing solar zenith angle. This is shown in
Figure 3 where the actinic fluxes determined from best estimate albedos
are plotted as a function of zenith angle for several selected wavelengths.
The flux change with zenith angle is slight for small angles, but large
when the sun is near the horizon, similar to the change of optical air
mass with zenith angle. Thus, during the early morning and late afternoon
hours the solar energy available for photochemical reactions changes far
20
-------
TABLE 4.
CALCULATED ACTINIC FLUX (photons cm"2 sec"1) AT THE EARTH'S SURFACE, AS A FUNCTION OF WAVELENGTH
AND ZENITH ANGLE, WITHIN SPECIFIED WAVELENGTH INTERVALS FOR BEST ESTIMATE SURFACE ALBEDOS.
THE SECOND COLUMN (EXP) LISTS THE POWER OF TEN BY WHICH ALL ENTRIES SHOULD BE MULTIPLIED.
WAVELENGTH EXP
(nm)
10
20
ZENITH ANGLE (°)
30 40
50
60
70
78
86
290-295
295-300
300-305
305-310
310-315
315-320
320-325
325-330
330-335
335-340
340-345
345-350
350-355
355-360
360-365
365-370
370-375
375-380
380-385
385-390
390-395
395-400
400-405
405-410
410-415
415-420
420-430
430-440
440-450
450-460
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
0.001
0.041
0.398
1.41
3.14
4.35
5.48
7.89
8.35
8.24
8.89
8.87
10.05
9.26
10.25
1.26
1.14
1.27
1.05
1.15
1.19
1.44
1.73
1.94
2.05
2.08
4.08
4.20
4.87
5.55
0.001
0.038
0.381
1.37
3.10
4.31
5.41
7.79
8.25
8.16
8.80
8.79
9.96
9.18
10.16
1.25
1.13
1.26
1.04
1.15
1.18
1.43
1.72
1.93
2.04
2.07
4.06
4.18
4.85
5.51
_
0.030
0.331
1.25
2.91
4.10
5.19
7.51
7.98
7.91
8.54
8.54
9.70
8.94
9.91
1.22
1.10
1.23
1.02
1.12
1.16
1.40
1.69
1.90
2.00
2.03
3.99
4.11
4.77
5.43
_
0.019
0.255
1.05
2.58
3.74
4.80
7.01
7.50
7.46
8.09
8.11
9.22
8.52
9.46
1.17
1.06
1.18
0.980
1.08
1.11
1.35
1.63
1.83
1.93
1.96
3.87
3.99
4.64
5.27
_
0.009
0.167
0.800
2.13
3.21
4.23
6.27
6.76
6.78
7.38
7.43
8.48
7.86
8.76
1.08
0.983
1.10
0.917
1.01
1.05
1.28
1.53
1.73
1.83
1.86
3.67
3.80
4.43
5.03
-
0.003
0.084
0.513
1.56
2.52
3.43
5.21
5.72
5.79
6.36
6.44
7.39
6.88
7.71
0.958
0.873
0.983
0.820
0.909
0.943
1.15
1.39
1.57
1.66
1.70
3.36
3.49
4.09
4.64
-
-
0.027
0.244
0.922
1.67
2.43
3.83
4.30
4.43
4.93
5.04
5.83
5.47
6.17
0.772
0.708
0.802
0.673
0.750
0.783
0.962
1.16
1.32
1.41
1.44
2.87
3.01
3.54
4.02
-
-
0.004
0.064
0.357
0.793
1.29
2.17
2.54
2.69
3.04
3.15
3.69
3.50
3.99
0.505
0.467
0.535
0.453
0.510
0.537
0.666
0.809
0.926
0.993
1.03
2.07
2.19
2.61
2.99
-
-
0.001
0.011
0.090
0.264
0.502
0.928
1.15
1.25
1.44
1.51
1.77
1.69
1.94
0.247
0.230
0.265
0.226
0.257
0.273
0.341
0.418
0.482
0.522
0.543
1.11
1.20
1.45
1.67
-
-
-
0.002
0.009
0.030
0.073
0.167
0.241
00282
0.333
0.352
0.414
0.391
0.444
0.055
0.051
0.058
0.049
0.054
0.057
0.070
0.085
0.097
0.104
0.107
0.216
0.229
0.272
0.312
-------
TABLE 4. CONTINUED
WAVELENGTH EXP
(nm)
10
20
ZENITH ANGLE (°)
30 40
50
60
70
78
86
460-470
470-480
480-490
490-500
500-510
510-520
520-530
530-540
540-550
550-560
560-570
570-580
580-600
600-620
620-640
640-660
660-680
680-700
15
15
15
15
15
15
15
15
15
15
15
15
16
16
16
16
16
16
5.68
5.82
5.78
5.79
5.99
5.88
5.98
5.98
5.88
5.94
5.99
6.12
1.25
1.26
1.27
1.30
1.33
1.33
5.65
5.79
5.75
5.76
5.96
5.86
5.95
5.95
5.85
5.91
5.96
6.09
1.24
1.26
1.26
1.30
1.33
1.32
5.57
5.70
5.67
5.68
5.87
5.77
5.87
5.87
5.77
5.83
5.88
6.00
1.22
1.24
1.24
1.28
1.31
1.30
5.42
5.55
5.53
5.54
5.71
5.62
5.72
5.72
5.62
5.68
5.73
5.85
1.19
1.21
1.17
1.25
1.28
1.27
5.17
5.31
5.29
5.31
5.47
5.38
5.48
5.48
5.40
5.44
5.49
5.61
1.14
1.16
1.10
1.20
1.23
1.23
4.79
4.91
4.93
4.96
5.09
5.02
5.11
5.12
5.04
5.08
5.13
5.24
1.07
1.08
1.10
1.13
1.16
1.16
4.17
4.32
4.33
4.37
4.47
4.43
4.52
4.52
4.46
4.49
4.54
4.63
0.951
0.963
0.980
1.01
1.04
1.04
3.12
3.26
3.29
3.34
3.41
3.40
3.47
3.48
3.44
3.46
3.50
3.57
0.737
0.748
0.771
0.803
0.828
0.839
1.77
1.87
1.90
1.95
1.99
2.00
2.04
2.05
2.03
2.04
2.06
2.10
0.439
0.448
0.473
0.502
0.527
0.541
0,325
0.341
0.339
0.344
0.340
0.340
0.336
Oo326
0.317
0.312
0.306
0,301
0.064
0.065
0.074
0.086
0.096
0.104
-------
PO
co
TABLE 5. CALCULATED ACTINIC FLUX (photons cm"2 sec"1) AT THE EARTH'S SURFACE, AS A FUNCTION OF WAVELENGTH
AND ZENITH ANGLE, WITHIN SPECIFIED WAVELENGTH INTERVALS FOR SURFACE ALBEDO OF ZERO. THE
SECOND COLUMN (EXP) LISTS THE POWER OF TEN BY WHICH ALL ENTRIES SHOULD BE MULTIPLIED.
WAVELENGTH
(nm)
290-295
295-300
300-305
306-310
310-315
315-320
320-325
325-330
330-335
335-340
340-345
345-350
350-355
355-360
360-365
365-370
370-375
375-380
380-385
385-390
390-395
395-400
400-405
405-410
410-415
415-420
420-430
430-440
440-450
EXP
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
15
15
15
15
15
15
15
15
15
15
15
15
15
15
0
0.001
0.037
0.362
1.28
2.85
3.94
4.96
7.14
7.54
7.45
8.03
8.02
9.08
8.36
9.25
1.14
1.03
1.15
0.948
1.04
1.07
1.30
1.54
1.72
1.82
1.84
3.62
3.72
4.32
10
0.001
0.035
0.347
1.24
2.81
3.91
4.90
7.06
7.47
7.38
7.97
7.95
9.01
8.30
9.19
1.13
1.02
1.14
0.942
1.04
1.07
1.29
1.53
1.71
1.81
1.83
3.60
3.71
4.30
20
_
0.027
0.302
1.14
2.65
3.73
4.71
6.82
7.25
7.18
7.76
7.75
8.80
8.12
9.00
1.11
1.00
1.12
0.926
1.02
1.05
1.28
1.51
1.69
1.78
1.81
3.56
3.67
4.26
ZENITH
30
—
0.017
0.234
0.965
2.36
3.42
4.38
6.40
6.84
6.81
7.38
7.40
8.42
7.78
8.64
1.07
0.965
1.07
0.895
0.987
1.02
1.24
1.46
1.64
1.74
1.77
3.48
3.59
4.18
ANGLE (°
40
—
0.008
0.154
0.737
1.96
2.96
3.88
5.76
6.22
6.23
6.79
6.84
7.80
7.23
8.06
0.997
0.906
1.02
0.845
0.933
0.965
1.18
1.39
1.57
1.66
1.69
3.34
3.45
4.03
)
50
«.
0.003
0.078
0.476
1.44
2.33
3.18
4.83
5.30
5.37
5.90
5.98
6.86
6.39
7.16
0.890
0.811
0.914
0.763
0.846
0.878
1.07
1.28
1.44
1.53
1.56
3.09
3.22
3.77
60
_
-
0.025
0.227
0.858
1.56
2.26
3.57
4.01
4.14
4.60
4.71
5.45
5.12
5.78
0.724
0.664
0.753
0.633
0.705
0.737
0.905
1.08
1.23
1.31
1.34
2.68
2.80
3.31
70
_
-
0.004
0.060
0.332
0.739
1.20
2.02
2.38
2.52
2.85
2.97
3.47
3.30
3.77
0.477
0.442
0.506
0.429
0.484
0.510
0.632
0.761
0.872
0.937
0.968
1.95
2.07
2.47
78
_
-
0.001
0.010
0.083
0.245
0.466
0.864
1.07
1.17 -
K34
1.41
1.66
1.59
1.83
0.233
0.217
0.251
0.214
0.244
0.259
0.324
0.394
0.455
0.493
0.514
1.05
1.13
1.38
86
_
-
-
0.001
0.008
0.027
0.067
0.155
0.221
0.262
Oo310
0.327
Oo385
00364
0.413
0,052
0.048
0.054
0,045
0.051
0.053
0.066
0.079
0.090
0.097
0.100
0.201
0.214
0.255
-------
TABLE 5. CONTINUED
WAVELENGTH EXP
(nm)
10
20
ZENITH ANGLE (°)
30 40
50
60
70
78
86
450-460
460-470
470-480
480-490
490-500
500-510
510-520
520-530
530-540
540-550
550-560
560-570
570-580
580-600
600-620
620-640
640-660
660-680
680-700
15
15
15
15
15
15
15
15
15
15
15
15
15
16
16
16
16
16
16
4.73
4.85
4.96
4.93
4.94
4.93
4.85
4.93
4.92
4.84
4.81
4.86
4.96
1.01
1.01
1.01
1.01
1.01
1.01
4.72
4.84
4.95
4.93
4.93
4.92
4.83
4.92
4.92
4,83
4.80
4.85
4.95
1.01
1.00
1.01
1.01
1.01
1.01
4.67
4.80
4.91
4.88
4.89
4.88
4.80
4.88
4.89
4.80
4.78
4.82
4,92
1.00
1.00
1.00
1.01
1.01
1.01
4.59
4.71
4.83
4.81
4.82
4.82
4.74
4.82
4.83
4.75
4.72
4.76
4.87
0.992
0.990
0.995
1.00
1.00
1.00
4.43
4.56
4.69
4.68
4.69
4.69
4.62
4.71
4.71
4.64
4.61
4.66
4.76
0.971
0.970
0.978
0.986
0.990
0.988
4.16
4.30
4.43
4.43
4.46
4.46
4.41
4.49
4.49
4.43
4.41
4.45
4.55
0.931
0.931
0.943
0.954
0.960
0.961
3.68
3.82
3.96
3.97
4.01
4.02
3.98
4.06
4.07
4.02
4.00
4.04
4.13
0.848
0.852
0.867
0.883
0.893
0.897
2.78
2.91
3.04
3.07
3.12
3.14
3.13
3.20
3.21
3.17
3.17
3.20
3.27
0.676
0.682
0.703
0.724
0.740
0.749
1.57
1.66
1.76
1.79
1.84
1.85
1.86
1.91
1.92
1.90
1.90
1.92
1.96
0.409
0.417
0.439
0.463
0.482
0.496
0.287
0.299
0.314
0.341
Oo319
0.310
0.309
0.524
0.299
0.291
0.285
0.279
0.276
0.059
0.060
0.068
0.078
0.087
0.094
-------
10
30 50
SOLAR ZENITH ANGLE, degrees
70
90
Figure 3. Calculated actinic flux (1014 photons cm"2 sec'1) within five nm wavelength intervals,
centered on the indicated wavelengths, at the earth's surface using best estimate albedos as a
function of solar zenith angle(o).
25
-------
more rapidly with time than during mid-day.
SENSITIVITY TESTS
The calculated actinic fluxes were evaluated for their dependence
on variations of surface albedo, aerosol amount, ozone amount, and station
elevation. The actinic flux values in Table 4 calculated from best estimate
albedo data are intended for general use. However, the albedo of the
earth's surface depends on type and amount of vegetation, type and moisture
content of the soil, solar angle, urban or natural surface, snow cover,
etc. (Lenschow et al., 1964). The dependence of the calculated actinic
fluxes on surface albedo is shown in Table 6. The percentage increase
of actinic flux for the lowest model level is presented, as a function
of wavelength and solar zenith angle, corresponding to a change of surface
albedo from zero to 10%. The greatest increases, exceeding 20%, generally
occur at small zenith angles. A general trend is also evident toward
smaller increases at larger zenith angles and longer wavelengths. The
data in Table 6 can be used in conjunction with the actinic fluxes calculated
for albedos of zero (Table 5) to determine the fluxes for other surface
albedos when they are known to be different from the best estimate values.
For albedos less than about 20%, the actinic fluxes are approximately
linearly dependent on surface albedo.
The dependence of the actinic flux on atmospheric aerosol concentrations
was studied next. The radiative model was rerun for best estimate albedos
at four selected wavelengths (342.5, 402.5, 545, and 690 nm) for atmospheres
with no aerosols and with aerosol concentrations twice those of the original
values listed in Appendix A. The results for the lowest model level are
shown in Table 7 as percentage changes in the calculated actinic fluxes
26
-------
TABLE 6. PERCENTAGE INCREASE OF CALCULATED ACTINIC FLUX AT THE EARTH'S
SURFACE, AS A FUNCTION OF SOLAR ZENITH ANGLE AND SELECTED
WAVELENGTHS, RELATIVE TO THE VALUES IN TABLE 5 WHEN SURFACE
ALBEDO IS INCREASED FROM 0.0 TO 10%.
WAVELENGTH
(nm)
10
ZENITH ANGLE (°)
20 30 40 50 60 70 78 86
290-295
295-300
300-305
305-310
315-320
330-335
350-355
370-375
390-395
410-415
440-450
480-490
520-530
560-570
620-640
680-700
19
19
20
20
21
21
21
21
21
21
21
21
21
21
21
21
.0
.6
.0
.5
.2
.6
.7
.7
.7
.7
.6
.5
.4
.3
.2
.1
18.8
19.3
19.8
20.3
21.0
21.4
21.5
21.5
21.4
21.4
21.3
21.2
21.1
21.0
20.9
20.8
_
18.8
19.1
19.7
20.3
20.6
20.6
20.6
20.5
20.5
20.3
20.2
20.1
20.0
19.9
19.8
_
17.3
18.1
18.6
19.2
19.4
19.3
19.2
19.1
19.0
18.8
18.7
18.5
18.4
18.2
18.2
_
15.2
16.8
17.3
17.8
17.9
17.7
17.4
17.2
17.0
16.8
16.6
16.4
16.3
16.1
16.0
_
15.0
15.6
16.0
16.3
16.2
15.8
15.4
15.0
14.8
14.5
14.1
13.9
13.8
13.6
13.5
_
-
14.4
14.9
15.0
14.7
13.9
13.3
12.7
12.4
11.9
11.5
11.2
11.0
10.8
10.7
_
-
15.6
15.0
14.7
13.9
12.6
11.6
10.8
10.2
9.5
8.9
8.5
8.3
8.1
7.9
_
-
17.2
17.0
15.8
14.9
13.3
11.9
10.7
9.7
8.5
7.6
7.0
6.7
6.3
6.1
-
-
-
17.3
16.5
16.0
15.2
14.3
13.4
12.7
11.6
10.3
9.3
9.2
7.6
6.9
that would occur, relative to the values in Table 4, if the model aerosol conceir
trations were zero and double those used originally. The instance with
no aerosols obviously represents the limit for clean atmospheres whereas
the doubled concentrations occasionally could be exceeded over most large
U.S. cities. Thus, the actinic fluxes for the no aerosol case are indicative
of the maximum values that would occur at sea level for cloudless skies.
At all wavelengths the changes increase as the solar zenith angle, and
thus relative aerosol optical thickness, increases. Aside from the largest
zenith angles, the percentage changes decrease with increasing wavelength
although the aerosol optical thickness has little dependence on wavelength.
At the longest wavelengths with the sun near the zenith, the actinic
flux actually increases as the atmospheric aerosol concentration increases.
27
-------
This results because the attenuation by Rayleigh scattering and ozone
absorption is relatively small at these wavelengths, and near the surface
multiple scattering by the aerosols causes some radiation to pass through
a level of the atmosphere several times.
TABLE 7. PERCENTAGE CHANGE OF CALCULATED ACTINIC FLUX AT THE EARTH'S
SURFACE USING BEST ESTIMATE ALBEDOS, AS A FUNCTION OF SOLAR
ZENITH ANGLE AND SELECTED WAVELENGTHS, RELATIVE TO THE VALUES
IN TABLE 4 WHEN MODEL AEROSOL CONCENTRATIONS ARE ZERO AND
DOUBLED.
WAVELENGTH ZENITH ANGLE (°)
0 10 20 30 40 50 60 70 78 86
340-345 nm
NO AEROSOL +8.2 +8.4 +8.8 +9.5 +10.7 +12.7 +16.1 +22.3 +26.5 +17.6
DOUBLE -6.1 -6.3 -6.6 -7.3 -8.3 -10.1 -12.8 -16.1 -16.4 -12.5
400-405 nm
NO AEROSOL +5.8 +6.0 +6.4 +7.1 +8.3 +10.7 +15.3 +26.2 +46.8 +35.7
DOUBLE -4.0 -4.1 -4.5 -5.3 -6.6 -8.8 -12.6 -19.4 -24.9 -15.9
540-550 nm
NO AEROSOL +0.9 +1.0 +1.2 +1.8 +2.9 +5.1 +10.4 +25.4 +67.1 +261.
DOUBLE -0.8 -0.9 -1.4 -2.2 -3.7 -6.4 -11.6 -21.4 -33.6 -27.4
680-700 nm
NO AEROSOL -2.4 -2.4 -2.2 -1.8 -0.9 +1.1 +6.2 +21.7 +67.0+447.
DOUBLE +0.7 +0o6 +0.2 -0.6 -2.1 -4.9 -10.4 -20.8 -34.9 -35.5
Variations in the amount of total ozone in the atmosphere, most of
which is in the stratosphere, can exceed 50% throughout the year from
pole to equator (Craig, 1961). Within a season or latitude belt changes
of total ozone of 10% are common. The effects of these changes on actinic
flux at the earth's surface are confined to a narrow wavelength interval.
At wavelengths greater than about 325 nm the ozone optical thickness is
less than 10% of that for aerosols and Rayleigh extinction combined (see
Figure 2). At wavelengths shorter than about 305 nm, the ozone optical
thickness is so large that the absolute amount of energy reaching the
28
-------
surface is small. Thus, outside of these limits only very large changes
in total ozone will significantly influence the actinic flux. To estimate
the effect of varying ozone levels, two additional model runs were undertaken
at 302.5 and 322.5 nm wavelength using best estimate albedos. In each
case the vertical ozone profiles were uniformly increased by 5%. The
percentage decrease of actinic flux at the surface is shown in Table 8
for both wavelength intervals as a function of zenith angle. At the longer
wavelength the change in ozone has a small effect, except when the sun
is near the horizon. At 302.5 nm the actinic flux is sensitive to ozone
variations; the change varied from near 10% to more than 21% for small
to large zenith angles, respectively.
TABLE 8. PERCENTAGE DECREASE OF CALCULATED ACTINIC FLUX AT THE EARTH'S
SURFACE USING BEST ESTIMATE ALBEDOS, AS A FUNCTION OF SOLAR
ZENITH ANGLE AND SELECTED WAVELENGTHS, RELATIVE TO THE VALUES
IN TABLE 4 WHEN MODEL OZONE CONCENTRATIONS ARE INCREASED BY
FIVE PERCENT.
WAVELENGTH ZENITH ANGLE (°)
0 10 20 30 40 50 60 70 78 86
300-305 nm 9.9 10.1 10.5 11.3 12.6 14.6 17.7 21.3 18.3 16.3
320-325 nm 1.7 1.7 1.8 1.9 2.2 2.5 3.1 4.3 6.3 10.5
All actinic flux calculations presented in this paper are based
on a surface elevation of sea level. To test the sensitivity of the compu-
tations to higher station elevations a new set of fluxes was determined
at four selected wavelengths for a surface elevation of 1500 m, or atmospheric
pressure of 852 mb. For this test, using best estimate albedos, the vertical
ozone and particle concentrations as a function of height above the surface
were not changed from the original computations. Thus, the optical thicknesses
for ozone absorption and Mie extinction were identical for both sets of
29
-------
calculations. However, the Rayleigh scattering optical thickness at all
wavelengths was reduced by a factor of 0.841 to account for the higher
elevation.
The results of these calculations are shown in Table 9. The percentage
increases of calculated actinic flux for the lowest model level for 1500 m
surface elevation as compared to sea level elevation (Table 4), are presented
as a function of wavelength and solar zenith angle. The tabulated values
generally increase for shorter wavelengths and larger zenith angles.
The effect of changing elevation on the calculated actinic fluxes generally
is not large; the percentage increases are less than 5% except for the
largest zenith angles.
TABLE 9. PERCENTAGE INCREASE OF CALCULATED ACTINIC FLUX AT THE EARTH'S
SURFACE USING BEST ESTIMATE ALBEDOS, AS A FUNCTION OF SOLAR
ZENITH ANGLE AND SELECTED WAVELENGTHS, RELATIVE TO THE VALUES
OF TABLE 4 WHEN SURFACE ELEVATION IS INCREASED TO 1500 m.
WAVELENGTH ZENITH ANGLE (°)
0 10 20 30 40 50 60 70 78 86
340-345 nm 2.1 2.3 2.6 3.2 4.2 5.7 8.1 11.4 12.4 7.5
400-405 nm 0.9 0.9 1.1 1.5 2.1 3.0 4.6 7.6 10.9 6.7
540-550 nm 0.2 0.2 0.2 0.4 0.5 0.9 1.4 2.4 4.3 4.7
680-700 nni 0.02 0.02 0.05 0.1 0.2 0.3 0.5 1.0 1.7 2.8
VARIATION OF ACTINIC FLUX WITH ALTITUDE
For application to urban photochemical problems, one of the most
important aspects of these calculations is the variation of actinic flux
with altitude above the surface, especially through the surface-based
mixing height of the atmosphere. The data available on this subject
to date have resulted mainly from occasional ultraviolet radiometric
measurements of the horizontal flux over Los Angeles (Nader, 1965; Peterson
30
-------
and Flowers, 1975). As will be shown below, the actinic flux typically
shows a marked increase through the lowest few kilometers of the atmosphere.
The more intense radiation aloft could partly explain the occurrence
of higher ozone concentrations at the base of, or within, the subsidence
temperature inversion over Los Angeles than at the surface as observed
by Edinger (1973) and Gloria et al., (1974).
For the computations of this paper, the atmosphere was divided
into 40 layers and the actinic fluxes were calculated by the radiative
transfer model at each atmospheric level. Examples of the variation
with height of the upward (F ) and downward (F~) components and total
(F ) actinic flux for solar zenith angles of 20°, 50°, and 78° are shown
in Figures 4, 5, and 6 for wavelengths 332.5, 412.5, and 575 nm, respectively.
The fluxes have all been normalized to a solar constant value of pi.
Although the model output extended above 45 km, the height scale of the
figures was abbreviated to 25 km, since only small changes occurred above
that height.
At the surface, the upward component of the actinic flux depends
on the direct and diffuse parts of the downward component and the surface
albedo. Generally, the upward component increases rapidly with height
near the earth's surface, but the rate of change with height decreases
at progressively higher levels. Above 10 km or so, the greatest relative
values of the upward flux occur at short wavelengths and small zenith
angles. The downward component generally increases slightly from the
top of the atmosphere down to about 10 to 15 km, except at the largest
zenith angles, as atmospheric scattering redirects some of the upward
stream back downwards. The greatest increases occur at short wavelengths
31
-------
CO
ro
25
20
15
10
332.5
332.5 nm
01234501234501234
ACTINIC FLUX, relative units
Figure 4. Calculated actinic flux (units relative to solar constant of pi) at the earth's surface using best estimate albedos for the upward-
directed component (F+), downward-directed component (F~), and their sum (FT) as a function of height at 332.5 nm wavelength for
(a) solar zenith angle 6O of 20°, (b) 50°, and (c) 78°.
-------
C3
UJ
X
to
CO
25
20
15
10
e0 = 20°
412.5nm
e0 = 50°
412.5nm
1234
ACTINIC FLUX, relative units
Figure 5. Calculated actinic flux (units relative to solar constant of pi) at the earth's surface using best estimate albedos for the upward-
directed component (F+), downward-directed component (F-), and their sum (FT) as a function of height at 412.5 nm wavelength for
(a) solar zenith angle 6O of 20°, (b) 50°, and (c) 78°.
-------
CO
-pi
25
20
15
10
575 nm
A
80 = 50°
575 nm
i J
F+
0 12340123401234
ACTINIC FLUX, relative units
Figure 6. Calculated actinic flux (units relative to solar constant of pi) at the earth's surface using best estimate albedos for the
upward-directed component (F+), downward-directed component (F~), and their sum (FT) as a function of height at 575 nm
wavelength for (a) solar zenith angle 6O of 20°, (b) 50° and (c) 78°.
-------
and with a high sun. The downward component then decreases at progressively
lower heights through the troposphere. The greatest rate of change
occurs near the surface where high aerosol and ozone concentrations
deplete the downward stream by absorption and back scattering.
Since both the upward and downward components change rapidly near
the earth's surface, the total actinic flux also exhibits this change
with height. In several cases shown in Figures 4 to 6, the total flux
more than doubles between the surface and 5 km. The dependence of the
vertical profiles of actinic flux on optical thickness is evident by
comparing Figures 4c and 6a. In the former case, the combined vertical
optical thickness for all atmospheric constituents is 1.066; the optical
air mass is 4.81. The large atmospheric attenuation causes a substantial
decrease of the downward stream. Since 74% of the optical thickness
is due to Rayleigh scattering, much of the decrease occurs above the
near-surface layer of high aerosol concentrations. At 10 km the actinic
flux is already reduced to about one-half of its extraterrestrial value.
In the latter case (575 nm, 20°), the vertical optical thickness is only
0.370 with an optical air mass of 1.06. With this relatively small atmos-
pheric attenuation the actinic flux shows little change with height.
Since atmospheric aerosols account for 69% of the optical thickness,
the components of the actinic flux change most noticeably in the layer
of high aerosol concentrations near the earth's surface.
The percent increase of the total actinic flux between the surface
and 980 m (the fourth model level above the surface) was determined
for each model run with best estimate albedos. These data are presented
in Table 10 for selected wavelengths and all zenith angles. A strong
35
-------
TABLE 10. PERCENTAGE INCREASE OF THE CALCULATED ACTINIC FLUX USING BEST
ESTIMATE ALBEDOS, AS A FUNCTION OF SOLAR ZENITH ANGLE AND
SELECTED WAVELENGTHS, AT 980 m ALTITUDE RELATIVE TO THE VALUES
FOR THE EARTH'S SURFACE IN TABLE 4.
WAVELENGTH
(nm)
10
20
ZENITH ANGLE (°)
30 40 50 60
70
78
86
290-295
295-300
300-305
305-310
315-320
325-330
335-340
345-350
355-360
365-370
375-380
385-390
395-400
405-410
415-420
430-440
450-460
470-480
490-500
510-520
530-540
550-560
570-580
600-620
640-660
680-700
63.
48.
41.
37
34.
30.
27.
25.
23.
21.
19.
18.
17.
15.
14.
12.
9.
8.
7.
5.
4.
3.
2.
1.
0.
-1.
7
9
4
5
5
2
6
3
3
5
8
4
1
3
2
5
8
4
3
4
5
4
7
4
0
0
64.7
49.6
41.9
37.9
34.2
30.6
28.0
25.7
23.7
21.9
20.2
18.8
17.4
15.6
14.5
12.9
10.1
8.8
7.6
5.7
4.8
3.6
3.0
1.6
0.3
-0.9
-
51.8
43.6
39.3
35.3
31.7
29.1
26.8
24.8
22.9
21.3
19.8
18.4
16.6
15.5
13.8
11.1
9.7
8.5
6.5
5.7
4.5
3.8
2.4
1.0
-0.1
-
55.6
46.4
41.7
37.3
33.6
31.0
28.7
26.6
24.7
23.1
21.6
20.2
18.3
17.2
15.5
12.7
11.3
10.1
8.1
7.2
6.0
5.2
3.9
2.4
1.2
-
61.3
50.8
45.4
40.5
36.6
33.9
31.6
29.5
27.7
26.0
24.4
23.0
21.1
20.0
18.3
15.4
13.9
12.7
10.7
9.8
8.5
7.8
6.4
4.9
3.6
-
68.9
56.8
50.6
45.1
41.0
38.3
36.0
34.1
32.1
30.5
29.0
27.5
25.7
24.5
22.7
19.9
18.5
17.2
15.2
14.2
13.0
12.2
10.7
9.2
7.9
-
-
63.9
57.5
51.6
47.5
45.0
43.0
41.3
39.6
38.1
36.7
35.4
33.6
32.5
30.8
28.1
26.7
25.5
23.6
22.6
21.4
20.7
19.2
17.7
16.3
-
-
63.0
61.9
58.9
56.2
55.1
54.4
53.7
52.9
52.3
51.6
50.9
49.6
48.9
47.9
45.7
44.8
44.1
42.4
41.8
40.7
40.2
39.0
37.3
35.9
-
-
51.4
52.8
56.6
57.5
59.7
62.3
65.1
68.0
70.6
73.1
75.4
76.4
78.1
80.5
81.3
83.0
84.3
84.0
84.8
84.6
85.0
84.5
83.1
81.6
-
-
-
47.5
46.9
45.7
45.1
44.8
45.2
46.2
48.2
51.1
55.4
60.0
67.1
82.4
102.
128.
154.
177.
201.
222.
242.
273.
300.
318.
36
-------
dependence can be seen between the vertical divergence of actinic flux
and both wavelength and zenith angle. At wavelengths less than 330 nin,
the change of actinic flux in the lowest kilometer of the atmosphere
exceeds 30% at all solar angles. The change exceeds 50% over much of
the spectrum for zenith angles of 70° and greater. In contrast, at
long wavelengths in combination with a high sun the flux increase is
less than 10%. Although the largest percentage changes of actinic flux
occur at the largest zenith angles, the greatest absolute changes typically
occur at smaller zenith angles. This results because at low sun angles
the downward stream is strongly attenuated before it gets to the 1 km
level.
An example of the practical importance of the vertical variation
of actinic flux is its relation to the N0? photodissociation rate constant,
a critical parameter in photochemical smog models. The NO,, rate constant
is computed by summing the product of the actinic flux, the N02 absorption
coefficient, and the quantum yield from 290 to about 420 nm. A rough
estimate of the difference in the rate constant through the lowest kilometer
of the model atmosphere can thus be obtained from Table 10. These data
suggest an N0? rate constant increase of about 25% for small zenith angles,
about 35% at 50°, to more than 60% at 78°. Rate constant changes throughout
(horizontally and vertically) the mixing layer of only 10% have been
shown, by a contemporary photochemical diffusion model, to have a measureable
change on surface ozone concentrations in the Los Angeles Basin (Peterson
and Demerjian, 1976). Therefore, the vertical rate constant changes
identified here likely will noticeably impact on calculated ozone concen-
trations. Actinic flux values, as a function of zenith angle and wavelength
37
-------
(290 to 440 nm), for each of the lowest 11 model levels (surface to
4.21 km) have been tabulated by the author and can be supplied upon request.
COMPARISON TO LEIGHTON
This study was undertaken to update and improve the actinic flux
calculations of Leighton. Besides the intracacies of the radiative
model calculations, differences in four specific areas led to discrepancies
between Leighton's results and those of this study. First and most
important, Leighton effectively assumed a surface albedo of zero, whereas
in this report the surface albedo varied between 5% and 15% as a function
of wavelength. Consequently, due to the albedo differences alone, the
actinic fluxes calculated here were some 5 to 11% higher in the UV and
up to about 30% higher at the longest wavelengths (see Table 6) than
those of Leighton. Second, recent measurements have indicated that the
solar constant data available to Leighton were too high. The values
herein were overall about 9% less than those used by Leighton. Third,
in 1957 the scheme used to deduce total ozone amounts from Dobson spectro-
photometer data was changed so that contemporary values are about 35%
higher than the pre-1957 values. In the preceeding discussion on sensitivity
tests, the actinic fluxes were shown to be dependent on changes of ozone
concentrations over a narrow spectral region in the ultraviolet. Thus,
the higher climatological values of total ozone used here caused significantly
lower actinic fluxes at wavelengths less than about 325 nm. Fourth,
the optical thickness for aerosols used by Leighton varied widely with
wavelength whereas for this report it was fairly constant. The values
for the two studies were similar at 420 nm with Leighton's data greater
(smaller) at shorter (longer) wavelengths. His extinction was totally
38
-------
due to scattering whereas for these computations some 8 to 15% of the
extinction was due to absorption. The most important difference, however,
was Leighton's assumption that half the scattered radiation was directed
backward whereas for the aerosol ensemble used herein the large majority
was directed forward. Thus, Leighton's aerosols, especially in the ultraviolet,
caused more depletion of the actinic flux than did the aerosols used
here.
Since Leighton's computations yielded actinic fluxes only at the
surface, a comparison between the two studies must be restricted to that
level. For the solar zenith angles common to both studies, the actinic
fluxes (using best estimate albedos from this report) were summed over
three spectral intervals: 295 to 395 nm, 395 to 450 nm, and 450 to 700 nm.
These divisions were selected since within each interval the differences
between the studies were similar. For each broad spectral interval and
zenith angle the percentage difference between the results presented here
in comparison to Leighton's data are shown in Table 11. Generally, the
actinic flux values computed here are lower over the ultraviolet region,
slightly higher within the middle interval, and considerably greater
than Leighton's numbers throughout the longer wavelength region. Much
TABLE 11. PERCENTAGE DIFFERENCE BETWEEN THE CALCULATED ACTINIC FLUX
VALUES AT THE EARTH'S SURFACE FROM THIS STUDY (USING BEST
ESTIMATE ALBEDOS) AND THOSE OF LEIGHTON SUMMED OVER SELECTED
WAVELENGTH INTERVALS FOR SELECTED SOLAR ZENITH ANGLES.
WAVELENGTH
(nm)
295-395
395-450
450-700
0
-6.1
+2.4
+18.8
ZENITH ANGLE (°)
20 40
-6.4 -5.5
+2.1 +3.4
+18.4 +17.0
60
-4.3
+5.9
+15.7
39
-------
of the dependence on wavelength of the differences between the two reports,
stems from the differences in the treatment of surface albedo.
The absolute actinic fluxes for the two studies are shown graphically
as a function of wavelength for zenith angles of 20° and 60° in Figures 7
and 8, respectively. The comparisons shown in Table 11 are again evident
in the figures. The actinic fluxes generally increase with wavelength
in response to changes of the solar constant photon flux, optical thickness,
and surface albedo. All values for 60° zenith angle are less than the
corresponding values at 20°, a result of the greater atmospheric attenuation
as the optical air mass increases.
CLOUDS
Because of the importance of solar radiation, high photochemical
pollutant concentrations usually occur when no, or few, clouds are present.
Results from a numerical diffusion model for Los Angeles, for example,
showed that when overcast stratus occurred oxidant concentrations were
generally reduced to 10 to 20% of their expected values for clear skies
(Peterson and Demerjian, 1976). However, the model results also suggested
that even high altitude cirrus clouds could cause a measureable decrease
in oxidant concentrations.
All actinic flux data presented in this report were calculated for
cloudless sky conditions. If these data are to be applied during cloudy
conditions, they can be modified by either of two approximate methods.
The first method, suggested by Leighton, is based on measurements of
total solar flux during clear and cloudy skies by Haurwitz (1948).
He determined cloud transmissivities as a function of zenith angle for
40
-------
E
c
u
OJ
CNI
U
c
O
I
Q.
LL
O
O
<
SOLAR ZENITH ANGLE = 20°
LEIGHTON
THIS STUDY
250
300
350
400
450
500
550
600
650
700
WAVELENGTH, nm
Figure 7. Calculated actinic flux (1014 photons cm-2 sec'1 nm-1) averaged over indicated wavelength intervals (nm) at the earth's
surface for solar zenith angle of 20° from this study (using best estimate albedos) and from Leighton.
-------
E
c
csj
'E
u
(/J
c
o
+->
o
.c
Q.
-pi
rv>
CJ
SOLAR ZENITH ANGLE = 60°
LEIGHTON
THIS STUDY
250
300
350
400
450
500
550
600
650
700
WAVELENGTH, nm
Figure 8. Calculated actinic flux (1014 photons cm-2 sec-1 nnrl) averaged over indicated wavelength intervals (nm) at the earth's
surface for solar zenith angle of 60° from this study (using best estimate albedos) and from Leighton.
-------
3
representative cloud types, thicknesses, and densities. Transmission
functions developed from these data by Atwater and Brown (1974) are given
in Table 12. They suggest that when clouds are present the clear sky
fluxes should be multiplied by
n
n [i - c.(i - T)]
i=l ^
(5)
where n is the number of cloud layers present, c. is the amount of cloud
in each layer, and T represents the transmission of solar radiation through
the specified cloud type (Table 12).
TABLE 12. TRANSMISSION (T) OF SOLAR RADIATION THROUGH VARIOUS CLOUD TYPES AS
A FUNCTION OF OPTICAL AIR MASS (M) (FROM ATWATER AND BROWN, 1974).
CLOUD TYPE EQUATION
Fog T = 0.1626 + 0.0054 M
Stratus T = 0.2684 - 0.0101 M
Stratocumulus T = 0.3658 - 0.0149 M
Cumulus T = 0.3658 - 0.0149 M
Cumulonimbus T = 0.2363 + 0.0145 M
Altostratus T = 0.4130 - 0.0014 M
Altocumulus T = 0.5456 - 0.0236 M
Cirrus T = 0.8717 - 0.0179 M
Cirrostratus T = 0.9055 - 0.0638 M
The expression (5) and accompanying cloud transmissivities should
only be considered as a rough approximation to the true effect of clouds
on actinic flux. Variations of the vertical thickness of cloud layers
are not taken into account. Moreover, Haurwitz1 data are based on horizontal,
not actinic, solar flux measurements. Our experience in making simultaneous
Due to a typographical error, the transmissivity for cirrus at m = 2.0
should read 0.84 in Table 10 (page 40) of Leighton (1961).
43
-------
measurements of the ultraviolet and all-wave solar flux has indicated
that clouds do not attenuate the ultraviolet wavelengths as much as the
longer wavelengths. Finally, these expressions should be used cautiously
during partly cloudy conditions since the actual actinic flux may show
large variability over short time periods as the sun is alternately behind
and free of clouds.
A second approximate method for estimating the effect of clouds
on actinic flux relies on continuous measurements of the incident radiation.
A variety of commercial instruments are available for horizontal flux
measurements. By comparing the measured flux to that expected for cloudless
conditions, the amount of solar depletion resulting from a specific cloud
situation can be estimated.
44
-------
SECTION V
DISCUSSION
The data and computational techniques available to Leighton for
his work on the application of solar radiation to photochemical pollution
problems some 20 years ago have become outdated. Thus, this report was
undertaken to redo, update, and expand upon his calculations of actinic
flux. His results and those computed herein generally agree within 10%
at wavelengths less than about 450 nm, which is a favorable reflection
on this area of Leighton's work. However, this similarity in computed
fluxes resulted partly because some of the errors in his data cancelled
each other. For example, his extraterrestrial flux data were too high
whereas his neglect of surface albedo led to reduced actinic fluxes.
At wavelengths greater than 450 nm the two studies diverge significantly.
The large albedo values used here at longer wavelengths caused the calculated
actinic fluxes to be substantially greater than Leightons.
In this report the actinic fluxes calculated as a function of solar
zenith angle and wavelength for "typical" atmospheric conditions are
intended for general application. However, in some instances these data
may be applied where the radiative characteristics of the atmospheric
constituents are known to differ considerably from those used here. Therefore,
a study of the dependence of the calculated fluxes on typical variations
of the model input parameters was also undertaken. Various tabulations
were presented here to give users information to adjust the actinic fluxes
to their particular circumstance, when they have specific information
on the input parameters. The actinic fluxes were generally shown to be
relatively insensitive to changes of surface elevation and ozone concentrations,
45
-------
and relatively sensitive to typical changes of atmospheric aerosols and
surface albedo. The fluxes are directly dependent on the extraterrestrial
solar flux.
An interesting aspect of these calculations was the description of
the variation of actinic flux with height above the surface. Previously,
only sketchy information was available on this topic, and most photochemical
atmospheric diffusion models neglected to account for it. To show the
importance of the vertical change of actinic flux, an estimate was made
of the consequent change of the N0? photodissociation rate constant in
the lowest kilometer of the atmosphere. The data indicated a rate constant
increase of about 25% at small zenith angles to more than 50% at zenith
angles of 70 and 78°.
46
-------
REFERENCES
Atwater, M.A., and P.S. Brown, 1974: Numerical computations of the
latitudinal variation of solar radiation for an atmosphere of varying
opacity. J. Appl. Meteor., 13, 289-297.
Arvesen, J.C. et al., 1969: Determination of extraterrestrial solar
spectral irradiance from a research aircraft. Appl. Optics, 11,
2215-2232. ~
Braslau, N., and J.V. Dave, 1973a: Effect of aerosols on the transfer
of solar energy through realistic model atmospheres. Part I: Non-
absorbing aerosols. J. Appl. Meteor., ^2_, 601-615.
Braslau, N., and J.V. Dave, 1973b: Effect of aerosols on the transfer
of solar energy through realistic model atmospheres. Part II: Partly
absorbing aerosols. J. Appl. Meteor., ]2_, 616-619.
Coulson, K.L., and D.W. Reynolds, 1971: The spectral reflectance of
natural surfaces. J. Appl. Meteor., 1_0_, 1285-1295.
Craig, R.A., 1965: The upper atmosphere. New York, Academic Press,
509 pp.
Dave, J.V., 1972: Development of programs for computing characteristics
of ultraviolet radiation. Final Rept. under Contr. NAS 5-21680.
NASA Rept. CR-139134. Nat. Aeronautics and Space Admin., Goddard
Space Flight Ctr., Greenbelt, MD, (NTIS No. N75-10746/6SL). 27 pp.
DeLuisi, J.J., 1975: Measurements of the extraterrestrial solar radiant
flux from 2981 to 4000 A and its transmission through the earth's
atmosphere as it is affected by dust and ozone. J. Geophys. Res.,
80, 345-354.
Demerjian, K.L., et al., 1974: The mechanism of photochemical smog formation.
In: Advances in Envr. Sc i. and Techno!., vol. 4, J. Pitts and R. Metcalf
eds. New York, Wiley & Sons, p. 1-262.
Diermendjian, D., 1969: Electromagnetic scattering on spherical poly-
dispersions. New York, Elsevier Publ. Co., 290 pp.
Dodge, M.C., and T.A. Hecht, 1975: Rate constant measurements needed to improve
a general kinetic mechanism for photochemical smog. Int. J. Chem.
Kinetics, 7_, 155-163.
Edinger, J.G., 1973: Vertical distribution of photochemical smog in
Los Angeles Basin. Environ. Sci. Techno!., 7_, 247-252.
Flowers, E.G., et al., 1969: Atmospheric turbidity over the United States,
1961-1966. J. Appl. Meteor., 8_, 955-962.
47
-------
Gloria, H.R. et al.s 1974: Airborne survey of major air basins in Cali-
fornia. J. Air Poll. Contr. Asso., 2_4, 645-652.
Haurwitz, B., 1948: Insolation in relation to cloud type. J. Meteor.,
5_, 110-113.
Herman, B.M., et al., 1971: The effect of atmospheric aerosols on scattered
sunlight. J. Atm. Sci., 28, 419-428.
Howard, J.N. et al., 1960: Thermal radiation. Handbook of geophysics
(Rev. Ed_.). New York, McMillan, Chapt. 16.
Huschke, R.E., 1959: Glossary of meteorology. Boston, Amer. Meteorol.
Soc., 638 pp.
Jackson, J.O. et al., 1975: Direct N09 photolysis rate monitor. Rev.
Sci. Inst., 46, 376-378. ^
Komyhr, W.D. et al., 1973: Total ozone increase over North America during
the 1960s. Pure and Appl. Geophys., 106-108,, 981-999.
Labs, D. and H.0Neckel, 1968: The radiation of the solar photosphere
from 2000 A to 100 p. Zeitschrift fur Astrophysik, 69_, 1-73.
Leighton, P.A., and W.A. Perkins, 1956: Solar radiation, absorption
rates, and photochemical primary processes in urban air. Rept.
No. 14, Air Poll. Found., Los Angeles, Calif. 129 pp.
Leighton, P.A., 1961: Photochemistry ojf air pollution. New York, Academic
Press, 300 pp.
Lenschow, D.H., et al., 1964: Study of a continental surface albedo
on the basis of flight measurements and structure of the earth's
surface cover over North America. Mon. Wea. Rev., 92^, 543-564.
Luther, P.M., and R.J. Gelinas, 1976: Effect of molecular multiple
scattering and surface albedo on atmospheric photodissociation
rates. J. Geophys. Res., 81_, 1125-1132.
McClatchey, R.A. et al., 1972: Optical properties of the atmosphere
(Third Ed.). Tech. Rept. AFCRL-72-0497, Air Force Cambridge Res.
Labs., Bedford, Mass. 108 pp.
Nader, J.S., 1967: Pilot study of ultraviolet radiation in Los Angeles
October 1965. Pub!. No. 999-AP-38, Public Health Service, Nat.
Ctr. for Air Poll. Control, Cincinnati, Ohio. 91 pp.
Penndorf, R., 1957: Tables of refractive index for standard air and the
Rayleigh scattering coefficient for the spectral region between
0.2 and 20.0 y and their application to atmospheric optics. J. Opt
Soc. Am., 47., 176-182.
48
-------
Peterson, J.T., and E.G. Flowers, 1976: Interactions between air pollution
and solar radiation. Int. Conf. on Environ. Sensing and Assessment,
Las Vegas, Nev., Vol. 2, Paper 32-4, Inst. of Electrical & Electronics
Eng., New York.
Peterson, J.T., and K.L. Demerjian, 1976: The sensitivity of computed
ozone concentrations to ultraviolet radiation in the Los Angeles
area. Atm. Environ, in press.
Rasool, S.I., and S.H. Schneider, 1971: Atmospheric carbon dioxide and
aerosols: Effects of large increases on global climate. Science,
173, 138-141.
Reynolds, S.D., et al., 1973: Mathematical modeling of photochemical
air pollution-I. Formulation of the model. Atm. Environ., _7,
1033-1061.
Sickles, J.E., and H.E. Jeffries, 1975: Development and operation of
a device for the continuous measurement of k for nitrogen dioxide.
Publ. No. 396, Dept. of Environ. Sci. and Engfn., Univ. No. Car.,
Chapel Hill, NC.
o
Thekaekara. M.P., 1974: Extraterrestrial solar spectrum, 3000-6100 A
at 1-A intervals. Appl. Optics, ]3_, 518-522.
Yamamoto, G., and M. Tanaka, 1972: Increase of global albedo due to
air pollution. J. Atm. Sci., 29_, 1405-1412.
49
-------
APPENDIX A.
APPENDICES
VARIATION OF ATMOSPHERIC PRESSURE (mb), NUMBER OF ATMOSPHERIC
AEROSOLS (cm'3), AND OZONE CONCENTRATION (g nT3) AS A FUNCTION OF
HEIGHT ABOVE THE SURFACE (km) USED AS INPUT TO THE RADIATIVE
TRANSFER MODEL.
HEIGHT
(km)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
30
35
40
45
50
55
60
65
70
PRESSURE
(mb)
1.013E+03
9.020E+02
8.020E+02
7.100E+02
6.280E+02
5.540E+02
4.870E+02
4.260E+02
3.720E+02
3.240E+02
2.810E+02
2.430E+02
2.090E+02
1.790E+02
1.530E+02
1.300E+02
1.110E+02
9.500E+01
8.120E+01
6.950E+01
5.950E+01
5.100E+01
4.370E+01
3.760E+01
3.220E+01
2.770E+01
1.320E+01
6.520E+00
3.330E+00
1.760E+00
9.510E-01
4.850E-01
2.500E-01
1.300E-01
6.710E-02
AEROSOLS
(cnr 3)
8.62E+02
1.43E+02
1.77E+01
7.41E+00
2.45E+00
7.98E-01
6.21E-01
4.79E-01
3.69E-01
3.71E-01
3.73E-01
3.76E-01
4.19E-01
4.56E-01
5.07E-01
5.47E-01
5.87E-01
6.67E-01
7.35E-01
7.98E-01
8.84E-01
7.92E-01
6.78E-01
3.31E-01
1.54E-01
7.01E-02
2.68E-02
9.69E-03
3.53E-03
1.03E-03
2.85E-04
8.27E-05
2.34E-05
6.56E-06
1.88E-06
OZONE
(g nT3)
2.00E-04
2.00E-04
5.34E-05
5.54E-05
5.72E-05
5.89E-05
6.16E-05
6.70E-05
7.05E-05
7.68E-05
8.04E-05
9.82E-05
1.07E-04
1.34E-04
1.61E-04
1.70E-04
1.88E-04
2.14E-04
2.50E-04
2.86E-04
3.04E-04
3.21E-04
3.21E-04
3.04E-04
2.86E-04
2.68E-04
1.79E-04
8.22E-05
3.66E-05
1.16E-05
3.84E-06
1.43E-06
5.34E-07
2.01E-07
7.68E-08
50
-------
APPENDIX B.
WAVELENGTH
VALUES OF MODEL INPUT DATA FOR EACH WAVELENGTH INTERVAL (nm):
EXTRATERRESTRIAL SOLAR FLUX (ETR) IN W nT2 AND 10^ 4 photons.,
cm'2 sec'1, OZONE ABSORPTION COEFFICIENT (03ABS) IN cm atm'1,
NORMAL OZONE OPTICAL THICKNESS (030PT), NORMAL RAYLEIGH SCATTERING
OPTICAL THICKNESS (R OPT), NORMAL AEROSOL SCATTERING OPTICAL THICK-
NESS (SCOPT), NORMAL AEROSOL EXTINCTION OPTICAL THICKNESS (EXOPT),
AND SURFACE ALBEDO (ALB) IN %.
ETR
ETR 03ABS 030PT R OPT SCOPT EXOPT ALB
290-295
295-300
300-305
305-310
310-315
315-320
320-325
325-330
330-335
335-340
340-345
345-350
350-355
355-360
360-365
365-370
370-375
375-380
380-385
385-390
390-395
395-400
400-405
405-410
410-415
415-420
420-430
430-440
440-450
450-460
460-470
470-480
480-490
490-500
500-510
510-520
520-530
530-540
540-550
550-560
2.67
2.75
2.70
3.17
3.90
3.92
4.09
5.28
5.19
4.89
5.09
4.94
5.47
4.92
5.34
6.43
5.70
6.24
5.07
5.48
5.55
6.62
7.68
8.49
8.81
8.80
16.93
16.94
19.15
20.47
20.49
20.49
19.94
19.54
19.16
18.45
18.45
18.15
17o54
17.15
3.93
4.11
4.11
4.91
6.14
6.26
6.64
8.70
8.69
8.31
8.78
8.65
9.70
8.86
9.74
11.91
10.69
11.85
9.77
10.69
10.96
13.25
15.57
17.41
18.30
18.15
36.23
37.10
42.91
46.89
47.97
49.00
48.70
48.69
48.72
47.85
48.76
48.90
48.13
47.93
26.0
14.0
6.80
3.50
1.75
.90
.48
.25
.12
.055
.025
.010
.0045
.0020
_
_
-
_
_
_
_
_
_
_
_
_
_
_
.0031
.0045
.0080
.0105
.019
.022
.038
.041
.054
.069
.078
.089
7.60
4.09
1.99
1.02
.511
.263
.140
.0730
.0351
.0161
.0073
.0029
.0013
.0006
_
-
-
_
-
-
_
-
-
-
-
-
-
-
.0009
.0013
.0023
.0031
.0054
.0063
.0110
.0118
.0158
.0202
.0228
.0260
1.361
1.265
1.178
1.098
1.025
.958
.896
.839
.788
.739
.694
.653
.617
.582
.548
.517
.489
.462
.438
.415
.393
.373
.354
.336
.320
.304
.283
.257
.233
.213
.195
.178
.163
.151
.139
.128
.119
.110
.102
.0946
.203
.204
.205
.206
.206
.207
.209
.210
.211
.211
.212
.213
.214
.215
.216
.217
.217
.218
.219
.219
.220
.221
.221
.222
.222
.223
.224
.225
.226
.227
.227
.228
.229
.229
.230
.230
.231
.231
.231
.231
.238
.238
.239
.240
.240
.241
.242
.242
.243
.243
.244
.244
.245
.245
.246
.247
.247
.248
.248
.248
.249
.249
.250
.250
.250
.251
.251
.252
.252
.252
.252
.253
.253
.253
.254
.254
.254
.254
.254
.254
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
6.
6.
6.
6.
6.
6.
6.
8.
8.
8.
8.
8.
10.
10.
10.
10.
10.
11.
51
-------
APPENDIX B. CONTINUED
WAVELENGTH ETR ETR 03ABS 030PT R OPT SCOPT EXOPT ALB
560-570 17.04 48.48 .103 .0301 .0880 .232 .253 11.
570-580 17.16 49.69 .118 .0345 .0819 .232 .253 11.
580-600 33.92 100.78 .113 .0330 .0737 .232 .253 11.
600-620 32.67 100.36 .117 .0342 .0643 .231 .252 12.
620-640 31.43 99.70 .091 .0266 .0564 .231 .251 12.
640-660 30.26 99,04 .063 .0184 .0497 .230 .250 13.5
660-680 29.13 98.26 .042 .0123 .0440 .229 .248 15.
680-700 28.00 97.28 .027 .0079 .0391 .228 .247 15.
52
-------
APPENDIX C.
TABULATION OF SOLAR ZENITH ANGLES AS A FUNCTION OF TRUE SOLAR TIME AND MONTH. FOR
DETERMINATION OF AFTERNOON VALUES, THE TABLE IS SYMMETRIC ABOUT NOON. FOUR TABLES
ARE PRESENTED FOR LATITUDES 20, 30, 40, AND 50°N.
TRUE SOLAR TIME
0400 0430 0500 0530 0600 0630 0700 0730 0800 0830 0900 0930 1000 1030 1100 1130 1200
Latitude 20°N
JANUARY 1
FEBRUARY 1
MARCH 1
APRIL 1
MAY 1
JUNE 1
JULY 1
AUGUST 1
SEPTEMBER 1
OCTOBER 1
en NOVEMBER 1
w DECEMBER 1
Latitude 30°N
JANUARY 1
FEBRUARY 1
MARCH 1
APRIL 1
MAY 1
JUNE 1
JULY 1
AUGUST 1
SEPTEMBER 1
OCTOBER 1
NOVEMBER 1
DECEMBER 1
89.2
88.8
88.9
85.3
84.7
87.2
88.5
85.0
82.7
82.3
83.8
87.2
87.2
82.7
79.2
78.7
81.0
85.9
88.9
85.7
81.5
78.2
76,0
75.7
77.1
80.2
84.1
87.8
87.5
81.4
76.3
73.1
72.5
74.7
79.4
85.1
84.9
82.5
78.8
74.4
71.2
69.3
69.1
70.2
73.2
77.1
81.3
84.3
89.4
86.2
81.1
74.9
69.9
66.8
66.3
68.3
72.9
78.7
84.6
88.7
78.7 72.7 66.1
75.8 69.6 63.3
72.0 65.2 58.6
67.4 60.3 53.4
64.3 57.2 50.2
62o5 55.7 48.8
62.3 55.5 48.7
63.3 56.4 49.4
66.1 59.1 52.1
70.2 63.3 56.5
74.5 68.3 61.8
78.0 71.8 66.1
83.7 78.3 73.2
80.3 74.6 69.1
74.9 68.8 62.9
68.5 62.1 55.8
63.4 56.9 50.4
60.4 54.0 47.5
60.0 53.5 47.1
61.9 55.4 48.9
66.4 60.0 53.6
72.4 66.2 60.1
78.4 72.8 67.1
82.8 77.3 72.2
61.5
57.7
52.3
46.5
43.2
41.9
41.8
42.4
45.1
49.9
56.0
60.5
68.4
64.1
57.4
49.6
44.0
41.0
40.6
42.4
47.3
54.4
62.0
67.3
56.5
52.2
46.2
39.7
36.1
35.0
35.0
35.4
38.1
43.5
50.2
55.6
64.1
59.4
52.2
43.8
37.6
34.5
34.1
36.0
41.2
48.8
57.0
63.0
52.1
47.4
40.5
33.2
29.1
28.1
28.1
28.3
31.3
37.5
45.3
50.9
60.4
55.3
47.5
38.2
31.4
28.1
27.7
29.7
35.5
43.8
53.0
59.2
48.3
43.1
35.5
26.9
26.1
21.1
21.2
21.3
24.7
32.0
40.7
47.2
57.3
51.9
43.5
33.3
25.6
21.7
21.2
23.6
30.2
39.5
49.3
56.0
45.5
40.0
31.4
21.3
15.2
14.2
14.3
14.3
18.6
27.4
37.4
44.2
55.0
49.3
40.3
29.3
20.4
15.7
15.1
18.1
25.8
36.1
46.7
53.7
43.6
37.8
28.6
17.2
8.8
7.3
7.7
7.3
13.7
24.3
35.1
42.4
53.5
47.7
38.4
26,5
16.5
10.5
9.6
13.7
22.8
33.9
44.9
52.2
43.0
37.2
27.7
15.5
5.0
2.0
3.1
1.9
11.6
23.1
34.4
41.8
53.0
47.2
37.7
25.5
15.0
8.0
6.9
11.9
21.6
33.1
44.4
51.8
-------
en
APPENDIX C. CONTINUED
TRUE SOLAR TIME
0400 0430 0500 0530 0600 0630 0700 0730 0800 0830 0900 0930 1000 1030 1100 1130 1200
Latitude 40°
JANUARY 1 89.0 84.2 79.8 75.7 72.1 69.0 66.4 64.6 63.4 63.0
FEBRUARY 1 84.8 79.8 75.2 70.7 67.0 63.5 60.9 58.8 57.6 57.2
MARCH 1 89.1 83.7 78.1 72.8 67.8 63.1 58.8 55.1 51.9 49.6 48.1 47.7
APRIL 1 87.1 81.4 75.6 70.0 64.4 59.0 53.8 49.0 44.6 40.9 38.0 36.2 35.5
MAY 1 85.9 80.5 74.7 68.9 63.2 57.5 51.8 46.3 41.0 36.1 31.7 28.2 25.8 25.0
JUNE 1 86.8 81.5 76.1 70.5 64.9 59.2 53.4 47.7 42.0 36.5 31.2 26.2 22.1 19.1 18.0
JULY 1 86.0 80.8 75.4 69.9 64.3 58.6 52.8 47.1 41.4 35.8 30.4 25.4 21.1 18.0 16.9
AUGUST 1 89.3 83.9 78.4 72.8 67.1 61.4 55.6 49.9 44.4 39.0 33.8 29.2 25.4 22.8 21.9
SEPTEMBER 1 84.6 78.9 73.2 67.5 61.8 56.3 51.0 46.0 41.4 37.5 34.4 32.3 31.6
OCTOBER 1 86.3 80.6 75.1 69.7 64.5 59.6 55.1 51.2 47.8 45.3 43.6 43.1
NOVEMBER 1 88.1 82.6 77.8 72.8 68.6 64.4 61.1 58.2 56.1 54.7 54.4
DECEMBER 1 88.1 83.3 78.8 74.7 71.0 67.8 65.3 63.3 62.2 61.8
Latitude 50°
JANUARY 1 86.5 83.2 80.2 77.7 75.7 74.2 73.3 73.0
FEBRUARY 1 89.5 85.3 81.5 78.0 74.9 72.2 70.0 68.5 67.5 67.2
MARCH 1 86.3 81.8 77.4 73.3 69.6 66.2 63.2 60.9 59.1 58.0 57.7
APRIL 1 86.6 81.8 76.9 72.2 67.6 63.2 59.1 55.4 52.0 49.3 47.2 45.9 45.5
MAY 1 87.8 83.2 78.5 73.7 68.9 64.1 59.4 54.7 50.3 46.2 42.5 39.4 37.0 35.5 35.0
JUNE 1 86.7 82.4 78.0 73.3 68.6 63.8 59.0 54.2 49.5 44.9 40.6 36.6 33.1 30.4 28.6 28.0
JULY 1 89.7 85.7 81.5 77.1 72.5 67.8 63.0 58.2 53.4 48.7 44.1 39.7 35.6 32.1 29.3 27.5 26.9
AUGUST 1 89.7 85.4 80.8 76.2 71.4 66.6 61.8 57.0 52.4 47.9 43.7 39.9 36.6 34.1 32.5 31.9
SEPTEMBER 1 88.3 83.6 78.8 74.0 69.2 64.6 60.1 55.9 52.0 48.5 45.7 43.5 42.1 41.6
OCTOBER 1 87.6 82.8 78.2 73.8 69.6 65.7 62.1 59.1 56.5 54.7 53.5 53.1
NOVEMBER 1 87.1 83.0 79.0 75.5 86.2 69,5 67.3 65.7 64.7 64.4
DECEMBER 1 89.2 85.5 82.1 79.1 76.5 74.5 73.0 72.1 71.8
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
REPORT NO.
EPA-600/4-76-025
2.
3. RECIPIENT'S ACCESSI OF* NO.
4. TITLE AND SUBTITLE
CALCULATED ACTINIC FLUXES (290 - 700 nm) FOR AIR
POLLUTION PHOTOCHEMISTRY APPLICATIONS
5. REPORT DATE
June 1976
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
James T. Peterson
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Environmental Sciences Research Laboratory
Office of Research and Development
U. S. Environmental Projection Agency
Research Triangle Park, NC 27711
10. PROGRAM ELEMENT NO.
1AA009
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory
Office of Research and Development
U. S. Environmental Protection Agency
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
In-House
14. SPONSORING AGENCY CODE
EPA - ORD
15. SUPPLEMENTARY NOTES
16. ABSTRACT • " ~T "
Calculations are presented of the actinic (spherically integrated) solar
flux from 290 to 700 nm at solar zenith angles between 0 and 86 . The calculated
values are obtained by using a radiative transfer program (developed by Dave)
that accounts for molecular scattering, ozone absorption, and aerosol scattering
and absorption. Input data consists of aerosol size distribution, aerosol
number and ozone concentrations as a function of height, aerosol index of
refraction, and the following as a function of wavelength: ozone absorption
coefficient, molecular scattering coefficient, solar constant, and surface
reflectivity. The calculated actinic flux values are evaluated for their
dependence on variations of surface reflectivity, aerosol amount, ozone
amount and station elevation. The variation of the actinic flux with altitude
above the surface is discussed with emphasis on the change through the lowest
kilometer of the atmosphere. Finally, the flux values presented here are
compared to those of Leighton (1961); the differences in the methodology and
input data between the two studies are illustrated. These calculated actinic
flux data are useful for estimating photodissociation rate constants for
application to photochemical air pollution problems.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. COS AT I Field/Group
*Air pollution
*Solar radiation
Radiant flux density
Computation
*Aerosols
*Photochemical reactions
*Reaction kinetics
rfrAtmospherii
i. DisTfmBDtToN s
c model's
13B
03B
20F
12A
07D
17E
14B
STATEMENl
RELEASE TO PUBLIC
19. SECURITY CLASS (This Report)
UNCLASSIFIED
21. NO. OF PAGES
63
20. SECURITY CLASS (Thispage)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
55
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